Formats: - HTML - YAML - JSON - 2026-03-15T14:05:51.697454 - next page
Query: /api/gps_small/?_offset=0
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  1. label: 1.1
    {'abelian': True, 'abelian_quotient': '1.1', 'center': '1.1', 'clases': [[1, 1, 1]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 1, 'label': '1.1', 'maximal_subgroups': [], 'name': 'C1', 'normal_subgroups': [], 'order': 1, 'perfect': True, 'pretty': 'C_1', 'simple': False, 'solvable': True}
  2. label: 2.1
    {'abelian': True, 'abelian_quotient': '2.1', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 2, 'label': '2.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C2', 'normal_subgroups': [], 'order': 2, 'perfect': False, 'pretty': 'C_2', 'simple': True, 'solvable': True}
  3. label: 3.1
    {'abelian': True, 'abelian_quotient': '3.1', 'center': '3.1', 'clases': [[1, 1, 1], [3, 1, 2]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 3, 'label': '3.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C3', 'normal_subgroups': [], 'order': 3, 'perfect': False, 'pretty': 'C_3', 'simple': True, 'solvable': True}
  4. label: 4.1
    {'abelian': True, 'abelian_quotient': '4.1', 'center': '4.1', 'clases': [[1, 1, 1], [2, 1, 1], [4, 1, 2]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 4, 'label': '4.1', 'maximal_subgroups': [['2.1', 1]], 'name': 'C4', 'normal_subgroups': [['2.1', 1]], 'order': 4, 'perfect': False, 'pretty': 'C_4', 'simple': False, 'solvable': True}
  5. label: 4.2
    {'abelian': True, 'abelian_quotient': '4.2', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 2, 'label': '4.2', 'maximal_subgroups': [['2.1', 3]], 'name': 'C2^2', 'normal_subgroups': [['2.1', 3]], 'order': 4, 'perfect': False, 'pretty': 'C_2^2', 'simple': False, 'solvable': True}
  6. label: 5.1
    {'abelian': True, 'abelian_quotient': '5.1', 'center': '5.1', 'clases': [[1, 1, 1], [5, 1, 4]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 5, 'label': '5.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C5', 'normal_subgroups': [], 'order': 5, 'perfect': False, 'pretty': 'C_5', 'simple': True, 'solvable': True}
  7. label: 6.1
    {'abelian': False, 'abelian_quotient': '2.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 3, 1], [3, 2, 1]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 6, 'label': '6.1', 'maximal_subgroups': [['2.1', 1], ['3.1', 1]], 'name': 'S3', 'normal_subgroups': [['3.1', 1]], 'order': 6, 'perfect': False, 'pretty': 'S_3', 'simple': False, 'solvable': True}
  8. label: 6.2
    {'abelian': True, 'abelian_quotient': '6.2', 'center': '6.2', 'clases': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [6, 1, 2]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 6, 'label': '6.2', 'maximal_subgroups': [['2.1', 1], ['3.1', 1]], 'name': 'C6', 'normal_subgroups': [['2.1', 1], ['3.1', 1]], 'order': 6, 'perfect': False, 'pretty': 'C_6', 'simple': False, 'solvable': True}
  9. label: 7.1
    {'abelian': True, 'abelian_quotient': '7.1', 'center': '7.1', 'clases': [[1, 1, 1], [7, 1, 6]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 7, 'label': '7.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C7', 'normal_subgroups': [], 'order': 7, 'perfect': False, 'pretty': 'C_7', 'simple': True, 'solvable': True}
  10. label: 8.1
    {'abelian': True, 'abelian_quotient': '8.1', 'center': '8.1', 'clases': [[1, 1, 1], [2, 1, 1], [4, 1, 2], [8, 1, 4]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 8, 'label': '8.1', 'maximal_subgroups': [['4.1', 1]], 'name': 'C8', 'normal_subgroups': [['2.1', 1], ['4.1', 1]], 'order': 8, 'perfect': False, 'pretty': 'C_8', 'simple': False, 'solvable': True}
  11. label: 8.2
    {'abelian': True, 'abelian_quotient': '8.2', 'center': '8.2', 'clases': [[1, 1, 1], [2, 1, 3], [4, 1, 4]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 4, 'label': '8.2', 'maximal_subgroups': [['4.1', 2], ['4.2', 1]], 'name': 'C2*C4', 'normal_subgroups': [['2.1', 3], ['4.1', 2], ['4.2', 1]], 'order': 8, 'perfect': False, 'pretty': 'C_2\\times C_4', 'simple': False, 'solvable': True}
  12. label: 8.3
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [4, 2, 1]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 4, 'label': '8.3', 'maximal_subgroups': [['4.1', 1], ['4.2', 2]], 'name': 'D4', 'normal_subgroups': [['2.1', 1], ['4.1', 1], ['4.2', 2]], 'order': 8, 'perfect': False, 'pretty': 'D_4', 'simple': False, 'solvable': True}
  13. label: 8.4
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [4, 2, 3]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 4, 'label': '8.4', 'maximal_subgroups': [['4.1', 3]], 'name': 'Q8', 'normal_subgroups': [['2.1', 1], ['4.1', 3]], 'order': 8, 'perfect': False, 'pretty': 'Q_8', 'simple': False, 'solvable': True}
  14. label: 8.5
    {'abelian': True, 'abelian_quotient': '8.5', 'center': '8.5', 'clases': [[1, 1, 1], [2, 1, 7]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 2, 'label': '8.5', 'maximal_subgroups': [['4.2', 7]], 'name': 'C2^3', 'normal_subgroups': [['2.1', 7], ['4.2', 7]], 'order': 8, 'perfect': False, 'pretty': 'C_2^3', 'simple': False, 'solvable': True}
  15. label: 9.1
    {'abelian': True, 'abelian_quotient': '9.1', 'center': '9.1', 'clases': [[1, 1, 1], [3, 1, 2], [9, 1, 6]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 9, 'label': '9.1', 'maximal_subgroups': [['3.1', 1]], 'name': 'C9', 'normal_subgroups': [['3.1', 1]], 'order': 9, 'perfect': False, 'pretty': 'C_9', 'simple': False, 'solvable': True}
  16. label: 9.2
    {'abelian': True, 'abelian_quotient': '9.2', 'center': '9.2', 'clases': [[1, 1, 1], [3, 1, 8]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 3, 'label': '9.2', 'maximal_subgroups': [['3.1', 4]], 'name': 'C3^2', 'normal_subgroups': [['3.1', 4]], 'order': 9, 'perfect': False, 'pretty': 'C_3^2', 'simple': False, 'solvable': True}
  17. label: 10.1
    {'abelian': False, 'abelian_quotient': '2.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 5, 1], [5, 2, 2]], 'cyclic': False, 'derived_group': '5.1', 'exponent': 10, 'label': '10.1', 'maximal_subgroups': [['2.1', 1], ['5.1', 1]], 'name': 'D5', 'normal_subgroups': [['5.1', 1]], 'order': 10, 'perfect': False, 'pretty': 'D_5', 'simple': False, 'solvable': True}
  18. label: 10.2
    {'abelian': True, 'abelian_quotient': '10.2', 'center': '10.2', 'clases': [[1, 1, 1], [2, 1, 1], [5, 1, 4], [10, 1, 4]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 10, 'label': '10.2', 'maximal_subgroups': [['2.1', 1], ['5.1', 1]], 'name': 'C10', 'normal_subgroups': [['2.1', 1], ['5.1', 1]], 'order': 10, 'perfect': False, 'pretty': 'C_{10}', 'simple': False, 'solvable': True}
  19. label: 11.1
    {'abelian': True, 'abelian_quotient': '11.1', 'center': '11.1', 'clases': [[1, 1, 1], [11, 1, 10]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 11, 'label': '11.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C11', 'normal_subgroups': [], 'order': 11, 'perfect': False, 'pretty': 'C_{11}', 'simple': True, 'solvable': True}
  20. label: 12.1
    {'abelian': False, 'abelian_quotient': '4.1', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [3, 2, 1], [4, 3, 2], [6, 2, 1]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 12, 'label': '12.1', 'maximal_subgroups': [['4.1', 1], ['6.2', 1]], 'name': 'C3:C4', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['6.2', 1]], 'order': 12, 'perfect': False, 'pretty': 'C_3:C_4', 'simple': False, 'solvable': True}
  21. label: 12.2
    {'abelian': True, 'abelian_quotient': '12.2', 'center': '12.2', 'clases': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [4, 1, 2], [6, 1, 2], [12, 1, 4]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 12, 'label': '12.2', 'maximal_subgroups': [['4.1', 1], ['6.2', 1]], 'name': 'C12', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['4.1', 1], ['6.2', 1]], 'order': 12, 'perfect': False, 'pretty': 'C_{12}', 'simple': False, 'solvable': True}
  22. label: 12.3
    {'abelian': False, 'abelian_quotient': '3.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 3, 1], [3, 4, 2]], 'cyclic': False, 'derived_group': '4.2', 'exponent': 6, 'label': '12.3', 'maximal_subgroups': [['3.1', 1], ['4.2', 1]], 'name': 'A4', 'normal_subgroups': [['4.2', 1]], 'order': 12, 'perfect': False, 'pretty': 'A_4', 'simple': False, 'solvable': True}
  23. label: 12.4
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [6, 2, 1]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 6, 'label': '12.4', 'maximal_subgroups': [['4.2', 1], ['6.1', 2], ['6.2', 1]], 'name': 'D6', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['6.1', 2], ['6.2', 1]], 'order': 12, 'perfect': False, 'pretty': 'D_6', 'simple': False, 'solvable': True}
  24. label: 12.5
    {'abelian': True, 'abelian_quotient': '12.5', 'center': '12.5', 'clases': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [6, 1, 6]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 6, 'label': '12.5', 'maximal_subgroups': [['4.2', 1], ['6.2', 3]], 'name': 'C2*C6', 'normal_subgroups': [['2.1', 3], ['3.1', 1], ['4.2', 1], ['6.2', 3]], 'order': 12, 'perfect': False, 'pretty': 'C_2\\times C_6', 'simple': False, 'solvable': True}
  25. label: 13.1
    {'abelian': True, 'abelian_quotient': '13.1', 'center': '13.1', 'clases': [[1, 1, 1], [13, 1, 12]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 13, 'label': '13.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C13', 'normal_subgroups': [], 'order': 13, 'perfect': False, 'pretty': 'C_{13}', 'simple': True, 'solvable': True}
  26. label: 14.1
    {'abelian': False, 'abelian_quotient': '2.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 7, 1], [7, 2, 3]], 'cyclic': False, 'derived_group': '7.1', 'exponent': 14, 'label': '14.1', 'maximal_subgroups': [['2.1', 1], ['7.1', 1]], 'name': 'D7', 'normal_subgroups': [['7.1', 1]], 'order': 14, 'perfect': False, 'pretty': 'D_7', 'simple': False, 'solvable': True}
  27. label: 14.2
    {'abelian': True, 'abelian_quotient': '14.2', 'center': '14.2', 'clases': [[1, 1, 1], [2, 1, 1], [7, 1, 6], [14, 1, 6]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 14, 'label': '14.2', 'maximal_subgroups': [['2.1', 1], ['7.1', 1]], 'name': 'C14', 'normal_subgroups': [['2.1', 1], ['7.1', 1]], 'order': 14, 'perfect': False, 'pretty': 'C_{14}', 'simple': False, 'solvable': True}
  28. label: 15.1
    {'abelian': True, 'abelian_quotient': '15.1', 'center': '15.1', 'clases': [[1, 1, 1], [3, 1, 2], [5, 1, 4], [15, 1, 8]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 15, 'label': '15.1', 'maximal_subgroups': [['3.1', 1], ['5.1', 1]], 'name': 'C15', 'normal_subgroups': [['3.1', 1], ['5.1', 1]], 'order': 15, 'perfect': False, 'pretty': 'C_{15}', 'simple': False, 'solvable': True}
  29. label: 16.1
    {'abelian': True, 'abelian_quotient': '16.1', 'center': '16.1', 'clases': [[1, 1, 1], [2, 1, 1], [4, 1, 2], [8, 1, 4], [16, 1, 8]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 16, 'label': '16.1', 'maximal_subgroups': [['8.1', 1]], 'name': 'C16', 'normal_subgroups': [['2.1', 1], ['4.1', 1], ['8.1', 1]], 'order': 16, 'perfect': False, 'pretty': 'C_{16}', 'simple': False, 'solvable': True}
  30. label: 16.10
    {'abelian': True, 'abelian_quotient': '16.10', 'center': '16.10', 'clases': [[1, 1, 1], [2, 1, 7], [4, 1, 8]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 4, 'label': '16.10', 'maximal_subgroups': [['8.2', 6], ['8.5', 1]], 'name': 'C2^2*C4', 'normal_subgroups': [['2.1', 7], ['4.1', 4], ['4.2', 7], ['8.2', 6], ['8.5', 1]], 'order': 16, 'perfect': False, 'pretty': 'C_2^2\\times C_4', 'simple': False, 'solvable': True}
  31. label: 16.11
    {'abelian': False, 'abelian_quotient': '8.5', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3], [2, 2, 4], [4, 2, 2]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 4, 'label': '16.11', 'maximal_subgroups': [['8.2', 1], ['8.3', 4], ['8.5', 2]], 'name': 'C2*D4', 'normal_subgroups': [['2.1', 3], ['4.1', 2], ['4.2', 5], ['8.2', 1], ['8.3', 4], ['8.5', 2]], 'order': 16, 'perfect': False, 'pretty': 'C_2\\times D_4', 'simple': False, 'solvable': True}
  32. label: 16.12
    {'abelian': False, 'abelian_quotient': '8.5', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3], [4, 2, 6]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 4, 'label': '16.12', 'maximal_subgroups': [['8.2', 3], ['8.4', 4]], 'name': 'C2*Q8', 'normal_subgroups': [['2.1', 3], ['4.1', 6], ['4.2', 1], ['8.2', 3], ['8.4', 4]], 'order': 16, 'perfect': False, 'pretty': 'C_2\\times Q_8', 'simple': False, 'solvable': True}
  33. label: 16.13
    {'abelian': False, 'abelian_quotient': '8.5', 'center': '4.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [4, 1, 2], [4, 2, 3]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 4, 'label': '16.13', 'maximal_subgroups': [['8.2', 3], ['8.3', 3], ['8.4', 1]], 'name': 'D4:C2', 'normal_subgroups': [['2.1', 1], ['4.1', 4], ['4.2', 3], ['8.2', 3], ['8.3', 3], ['8.4', 1]], 'order': 16, 'perfect': False, 'pretty': 'D_4:C_2', 'simple': False, 'solvable': True}
  34. label: 16.14
    {'abelian': True, 'abelian_quotient': '16.14', 'center': '16.14', 'clases': [[1, 1, 1], [2, 1, 15]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 2, 'label': '16.14', 'maximal_subgroups': [['8.5', 15]], 'name': 'C2^4', 'normal_subgroups': [['2.1', 15], ['4.2', 35], ['8.5', 15]], 'order': 16, 'perfect': False, 'pretty': 'C_2^4', 'simple': False, 'solvable': True}
  35. label: 16.2
    {'abelian': True, 'abelian_quotient': '16.2', 'center': '16.2', 'clases': [[1, 1, 1], [2, 1, 3], [4, 1, 12]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 4, 'label': '16.2', 'maximal_subgroups': [['8.2', 3]], 'name': 'C4^2', 'normal_subgroups': [['2.1', 3], ['4.1', 6], ['4.2', 1], ['8.2', 3]], 'order': 16, 'perfect': False, 'pretty': 'C_4^2', 'simple': False, 'solvable': True}
  36. label: 16.3
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [4, 2, 4]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 4, 'label': '16.3', 'maximal_subgroups': [['8.2', 2], ['8.5', 1]], 'name': 'C2^2:C4', 'normal_subgroups': [['2.1', 3], ['4.2', 3], ['8.2', 2], ['8.5', 1]], 'order': 16, 'perfect': False, 'pretty': 'C_2^2:C_4', 'simple': False, 'solvable': True}
  37. label: 16.4
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3], [4, 2, 6]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 4, 'label': '16.4', 'maximal_subgroups': [['8.2', 3]], 'name': 'C4:C4', 'normal_subgroups': [['2.1', 3], ['4.1', 2], ['4.2', 1], ['8.2', 3]], 'order': 16, 'perfect': False, 'pretty': 'C_4:C_4', 'simple': False, 'solvable': True}
  38. label: 16.5
    {'abelian': True, 'abelian_quotient': '16.5', 'center': '16.5', 'clases': [[1, 1, 1], [2, 1, 3], [4, 1, 4], [8, 1, 8]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 8, 'label': '16.5', 'maximal_subgroups': [['8.1', 2], ['8.2', 1]], 'name': 'C2*C8', 'normal_subgroups': [['2.1', 3], ['4.1', 2], ['4.2', 1], ['8.1', 2], ['8.2', 1]], 'order': 16, 'perfect': False, 'pretty': 'C_2\\times C_8', 'simple': False, 'solvable': True}
  39. label: 16.6
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 2, 1], [8, 2, 4]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 8, 'label': '16.6', 'maximal_subgroups': [['8.1', 2], ['8.2', 1]], 'name': 'OD16', 'normal_subgroups': [['2.1', 1], ['4.1', 2], ['4.2', 1], ['8.1', 2], ['8.2', 1]], 'order': 16, 'perfect': False, 'pretty': 'OD_{16}', 'simple': False, 'solvable': True}
  40. label: 16.7
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 4, 2], [4, 2, 1], [8, 2, 2]], 'cyclic': False, 'derived_group': '4.1', 'exponent': 8, 'label': '16.7', 'maximal_subgroups': [['8.1', 1], ['8.3', 2]], 'name': 'D8', 'normal_subgroups': [['2.1', 1], ['4.1', 1], ['8.1', 1], ['8.3', 2]], 'order': 16, 'perfect': False, 'pretty': 'D_8', 'simple': False, 'solvable': True}
  41. label: 16.8
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 4, 1], [4, 2, 1], [4, 4, 1], [8, 2, 2]], 'cyclic': False, 'derived_group': '4.1', 'exponent': 8, 'label': '16.8', 'maximal_subgroups': [['8.1', 1], ['8.3', 1], ['8.4', 1]], 'name': 'SD16', 'normal_subgroups': [['2.1', 1], ['4.1', 1], ['8.1', 1], ['8.3', 1], ['8.4', 1]], 'order': 16, 'perfect': False, 'pretty': 'SD_{16}', 'simple': False, 'solvable': True}
  42. label: 16.9
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [4, 2, 1], [4, 4, 2], [8, 2, 2]], 'cyclic': False, 'derived_group': '4.1', 'exponent': 8, 'label': '16.9', 'maximal_subgroups': [['8.1', 1], ['8.4', 2]], 'name': 'Q16', 'normal_subgroups': [['2.1', 1], ['4.1', 1], ['8.1', 1], ['8.4', 2]], 'order': 16, 'perfect': False, 'pretty': 'Q_{16}', 'simple': False, 'solvable': True}
  43. label: 17.1
    {'abelian': True, 'abelian_quotient': '17.1', 'center': '17.1', 'clases': [[1, 1, 1], [17, 1, 16]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 17, 'label': '17.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C17', 'normal_subgroups': [], 'order': 17, 'perfect': False, 'pretty': 'C_{17}', 'simple': True, 'solvable': True}
  44. label: 18.1
    {'abelian': False, 'abelian_quotient': '2.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 9, 1], [3, 2, 1], [9, 2, 3]], 'cyclic': False, 'derived_group': '9.1', 'exponent': 18, 'label': '18.1', 'maximal_subgroups': [['6.1', 1], ['9.1', 1]], 'name': 'D9', 'normal_subgroups': [['3.1', 1], ['9.1', 1]], 'order': 18, 'perfect': False, 'pretty': 'D_9', 'simple': False, 'solvable': True}
  45. label: 18.2
    {'abelian': True, 'abelian_quotient': '18.2', 'center': '18.2', 'clases': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [6, 1, 2], [9, 1, 6], [18, 1, 6]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 18, 'label': '18.2', 'maximal_subgroups': [['6.2', 1], ['9.1', 1]], 'name': 'C18', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['6.2', 1], ['9.1', 1]], 'order': 18, 'perfect': False, 'pretty': 'C_{18}', 'simple': False, 'solvable': True}
  46. label: 18.3
    {'abelian': False, 'abelian_quotient': '6.2', 'center': '3.1', 'clases': [[1, 1, 1], [2, 3, 1], [3, 1, 2], [3, 2, 3], [6, 3, 2]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 6, 'label': '18.3', 'maximal_subgroups': [['6.1', 1], ['6.2', 1], ['9.2', 1]], 'name': 'C3*S3', 'normal_subgroups': [['3.1', 2], ['6.1', 1], ['9.2', 1]], 'order': 18, 'perfect': False, 'pretty': 'C_3\\times S_3', 'simple': False, 'solvable': True}
  47. label: 18.4
    {'abelian': False, 'abelian_quotient': '2.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 9, 1], [3, 2, 4]], 'cyclic': False, 'derived_group': '9.2', 'exponent': 6, 'label': '18.4', 'maximal_subgroups': [['6.1', 4], ['9.2', 1]], 'name': 'C3:S3', 'normal_subgroups': [['3.1', 4], ['9.2', 1]], 'order': 18, 'perfect': False, 'pretty': 'C_3:S_3', 'simple': False, 'solvable': True}
  48. label: 18.5
    {'abelian': True, 'abelian_quotient': '18.5', 'center': '18.5', 'clases': [[1, 1, 1], [2, 1, 1], [3, 1, 8], [6, 1, 8]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 6, 'label': '18.5', 'maximal_subgroups': [['6.2', 4], ['9.2', 1]], 'name': 'C3*C6', 'normal_subgroups': [['2.1', 1], ['3.1', 4], ['6.2', 4], ['9.2', 1]], 'order': 18, 'perfect': False, 'pretty': 'C_3\\times C_6', 'simple': False, 'solvable': True}
  49. label: 19.1
    {'abelian': True, 'abelian_quotient': '19.1', 'center': '19.1', 'clases': [[1, 1, 1], [19, 1, 18]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 19, 'label': '19.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C19', 'normal_subgroups': [], 'order': 19, 'perfect': False, 'pretty': 'C_{19}', 'simple': True, 'solvable': True}
  50. label: 20.1
    {'abelian': False, 'abelian_quotient': '4.1', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [4, 5, 2], [5, 2, 2], [10, 2, 2]], 'cyclic': False, 'derived_group': '5.1', 'exponent': 20, 'label': '20.1', 'maximal_subgroups': [['4.1', 1], ['10.2', 1]], 'name': 'C5:C4', 'normal_subgroups': [['2.1', 1], ['5.1', 1], ['10.2', 1]], 'order': 20, 'perfect': False, 'pretty': 'C_5:C_4', 'simple': False, 'solvable': True}
  51. label: 20.2
    {'abelian': True, 'abelian_quotient': '20.2', 'center': '20.2', 'clases': [[1, 1, 1], [2, 1, 1], [4, 1, 2], [5, 1, 4], [10, 1, 4], [20, 1, 8]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 20, 'label': '20.2', 'maximal_subgroups': [['4.1', 1], ['10.2', 1]], 'name': 'C20', 'normal_subgroups': [['2.1', 1], ['4.1', 1], ['5.1', 1], ['10.2', 1]], 'order': 20, 'perfect': False, 'pretty': 'C_{20}', 'simple': False, 'solvable': True}
  52. label: 20.3
    {'abelian': False, 'abelian_quotient': '4.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 5, 1], [4, 5, 2], [5, 4, 1]], 'cyclic': False, 'derived_group': '5.1', 'exponent': 20, 'label': '20.3', 'maximal_subgroups': [['4.1', 1], ['10.1', 1]], 'name': 'F5', 'normal_subgroups': [['5.1', 1], ['10.1', 1]], 'order': 20, 'perfect': False, 'pretty': 'F_5', 'simple': False, 'solvable': True}
  53. label: 20.4
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 5, 2], [5, 2, 2], [10, 2, 2]], 'cyclic': False, 'derived_group': '5.1', 'exponent': 10, 'label': '20.4', 'maximal_subgroups': [['4.2', 1], ['10.1', 2], ['10.2', 1]], 'name': 'D10', 'normal_subgroups': [['2.1', 1], ['5.1', 1], ['10.1', 2], ['10.2', 1]], 'order': 20, 'perfect': False, 'pretty': 'D_{10}', 'simple': False, 'solvable': True}
  54. label: 20.5
    {'abelian': True, 'abelian_quotient': '20.5', 'center': '20.5', 'clases': [[1, 1, 1], [2, 1, 3], [5, 1, 4], [10, 1, 12]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 10, 'label': '20.5', 'maximal_subgroups': [['4.2', 1], ['10.2', 3]], 'name': 'C2*C10', 'normal_subgroups': [['2.1', 3], ['4.2', 1], ['5.1', 1], ['10.2', 3]], 'order': 20, 'perfect': False, 'pretty': 'C_2\\times C_{10}', 'simple': False, 'solvable': True}
  55. label: 21.1
    {'abelian': False, 'abelian_quotient': '3.1', 'center': '1.1', 'clases': [[1, 1, 1], [3, 7, 2], [7, 3, 2]], 'cyclic': False, 'derived_group': '7.1', 'exponent': 21, 'label': '21.1', 'maximal_subgroups': [['3.1', 1], ['7.1', 1]], 'name': 'C7:C3', 'normal_subgroups': [['7.1', 1]], 'order': 21, 'perfect': False, 'pretty': 'C_7:C_3', 'simple': False, 'solvable': True}
  56. label: 21.2
    {'abelian': True, 'abelian_quotient': '21.2', 'center': '21.2', 'clases': [[1, 1, 1], [3, 1, 2], [7, 1, 6], [21, 1, 12]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 21, 'label': '21.2', 'maximal_subgroups': [['3.1', 1], ['7.1', 1]], 'name': 'C21', 'normal_subgroups': [['3.1', 1], ['7.1', 1]], 'order': 21, 'perfect': False, 'pretty': 'C_{21}', 'simple': False, 'solvable': True}
  57. label: 22.1
    {'abelian': False, 'abelian_quotient': '2.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 11, 1], [11, 2, 5]], 'cyclic': False, 'derived_group': '11.1', 'exponent': 22, 'label': '22.1', 'maximal_subgroups': [['2.1', 1], ['11.1', 1]], 'name': 'D11', 'normal_subgroups': [['11.1', 1]], 'order': 22, 'perfect': False, 'pretty': 'D_{11}', 'simple': False, 'solvable': True}
  58. label: 22.2
    {'abelian': True, 'abelian_quotient': '22.2', 'center': '22.2', 'clases': [[1, 1, 1], [2, 1, 1], [11, 1, 10], [22, 1, 10]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 22, 'label': '22.2', 'maximal_subgroups': [['2.1', 1], ['11.1', 1]], 'name': 'C22', 'normal_subgroups': [['2.1', 1], ['11.1', 1]], 'order': 22, 'perfect': False, 'pretty': 'C_{22}', 'simple': False, 'solvable': True}
  59. label: 23.1
    {'abelian': True, 'abelian_quotient': '23.1', 'center': '23.1', 'clases': [[1, 1, 1], [23, 1, 22]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 23, 'label': '23.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C23', 'normal_subgroups': [], 'order': 23, 'perfect': False, 'pretty': 'C_{23}', 'simple': True, 'solvable': True}
  60. label: 24.1
    {'abelian': False, 'abelian_quotient': '8.1', 'center': '4.1', 'clases': [[1, 1, 1], [2, 1, 1], [3, 2, 1], [4, 1, 2], [6, 2, 1], [8, 3, 4], [12, 2, 2]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 24, 'label': '24.1', 'maximal_subgroups': [['8.1', 1], ['12.2', 1]], 'name': 'C3:C8', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['4.1', 1], ['6.2', 1], ['12.2', 1]], 'order': 24, 'perfect': False, 'pretty': 'C_3:C_8', 'simple': False, 'solvable': True}
  61. label: 24.10
    {'abelian': False, 'abelian_quotient': '12.5', 'center': '6.2', 'clases': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [3, 1, 2], [4, 2, 1], [6, 1, 2], [6, 2, 4], [12, 2, 2]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 12, 'label': '24.10', 'maximal_subgroups': [['8.3', 1], ['12.2', 1], ['12.5', 2]], 'name': 'C3*D4', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['4.1', 1], ['4.2', 2], ['6.2', 1], ['8.3', 1], ['12.2', 1], ['12.5', 2]], 'order': 24, 'perfect': False, 'pretty': 'C_3\\times D_4', 'simple': False, 'solvable': True}
  62. label: 24.11
    {'abelian': False, 'abelian_quotient': '12.5', 'center': '6.2', 'clases': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [4, 2, 3], [6, 1, 2], [12, 2, 6]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 12, 'label': '24.11', 'maximal_subgroups': [['8.4', 1], ['12.2', 3]], 'name': 'C3*Q8', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['4.1', 3], ['6.2', 1], ['8.4', 1], ['12.2', 3]], 'order': 24, 'perfect': False, 'pretty': 'C_3\\times Q_8', 'simple': False, 'solvable': True}
  63. label: 24.12
    {'abelian': False, 'abelian_quotient': '2.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 3, 1], [2, 6, 1], [3, 8, 1], [4, 6, 1]], 'cyclic': False, 'derived_group': '12.3', 'exponent': 12, 'label': '24.12', 'maximal_subgroups': [['6.1', 1], ['8.3', 1], ['12.3', 1]], 'name': 'S4', 'normal_subgroups': [['4.2', 1], ['12.3', 1]], 'order': 24, 'perfect': False, 'pretty': 'S_4', 'simple': False, 'solvable': True}
  64. label: 24.13
    {'abelian': False, 'abelian_quotient': '6.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 4, 2], [6, 4, 2]], 'cyclic': False, 'derived_group': '4.2', 'exponent': 6, 'label': '24.13', 'maximal_subgroups': [['6.2', 1], ['8.5', 1], ['12.3', 1]], 'name': 'C2*A4', 'normal_subgroups': [['2.1', 1], ['4.2', 1], ['8.5', 1], ['12.3', 1]], 'order': 24, 'perfect': False, 'pretty': 'C_2\\times A_4', 'simple': False, 'solvable': True}
  65. label: 24.14
    {'abelian': False, 'abelian_quotient': '8.5', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [3, 2, 1], [6, 2, 3]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 6, 'label': '24.14', 'maximal_subgroups': [['8.5', 1], ['12.4', 6], ['12.5', 1]], 'name': 'C2^2*S3', 'normal_subgroups': [['2.1', 3], ['3.1', 1], ['4.2', 1], ['6.1', 4], ['6.2', 3], ['12.4', 6], ['12.5', 1]], 'order': 24, 'perfect': False, 'pretty': 'C_2^2\\times S_3', 'simple': False, 'solvable': True}
  66. label: 24.15
    {'abelian': True, 'abelian_quotient': '24.15', 'center': '24.15', 'clases': [[1, 1, 1], [2, 1, 7], [3, 1, 2], [6, 1, 14]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 6, 'label': '24.15', 'maximal_subgroups': [['8.5', 1], ['12.5', 7]], 'name': 'C2^2*C6', 'normal_subgroups': [['2.1', 7], ['3.1', 1], ['4.2', 7], ['6.2', 7], ['8.5', 1], ['12.5', 7]], 'order': 24, 'perfect': False, 'pretty': 'C_2^2\\times C_6', 'simple': False, 'solvable': True}
  67. label: 24.2
    {'abelian': True, 'abelian_quotient': '24.2', 'center': '24.2', 'clases': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [4, 1, 2], [6, 1, 2], [8, 1, 4], [12, 1, 4], [24, 1, 8]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 24, 'label': '24.2', 'maximal_subgroups': [['8.1', 1], ['12.2', 1]], 'name': 'C24', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['4.1', 1], ['6.2', 1], ['8.1', 1], ['12.2', 1]], 'order': 24, 'perfect': False, 'pretty': 'C_{24}', 'simple': False, 'solvable': True}
  68. label: 24.3
    {'abelian': False, 'abelian_quotient': '3.1', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [3, 4, 2], [4, 6, 1], [6, 4, 2]], 'cyclic': False, 'derived_group': '8.4', 'exponent': 12, 'label': '24.3', 'maximal_subgroups': [['6.2', 1], ['8.4', 1]], 'name': 'SL(2,3)', 'normal_subgroups': [['2.1', 1], ['8.4', 1]], 'order': 24, 'perfect': False, 'pretty': '\\SL(2,3)', 'simple': False, 'solvable': True}
  69. label: 24.4
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [3, 2, 1], [4, 2, 1], [4, 6, 2], [6, 2, 1], [12, 2, 2]], 'cyclic': False, 'derived_group': '6.2', 'exponent': 12, 'label': '24.4', 'maximal_subgroups': [['8.4', 1], ['12.1', 2], ['12.2', 1]], 'name': 'C3:Q8', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['4.1', 1], ['6.2', 1], ['12.1', 2], ['12.2', 1]], 'order': 24, 'perfect': False, 'pretty': 'C_3:Q_8', 'simple': False, 'solvable': True}
  70. label: 24.5
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [4, 1, 2], [4, 3, 2], [6, 2, 1], [12, 2, 2]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 12, 'label': '24.5', 'maximal_subgroups': [['8.2', 1], ['12.1', 1], ['12.2', 1], ['12.4', 1]], 'name': 'C4*S3', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['4.1', 1], ['6.1', 2], ['6.2', 1], ['12.1', 1], ['12.2', 1], ['12.4', 1]], 'order': 24, 'perfect': False, 'pretty': 'C_4\\times S_3', 'simple': False, 'solvable': True}
  71. label: 24.6
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 6, 2], [3, 2, 1], [4, 2, 1], [6, 2, 1], [12, 2, 2]], 'cyclic': False, 'derived_group': '6.2', 'exponent': 12, 'label': '24.6', 'maximal_subgroups': [['8.3', 1], ['12.2', 1], ['12.4', 2]], 'name': 'D12', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['4.1', 1], ['6.2', 1], ['12.2', 1], ['12.4', 2]], 'order': 24, 'perfect': False, 'pretty': 'D_{12}', 'simple': False, 'solvable': True}
  72. label: 24.7
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 3, 4], [6, 2, 3]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 12, 'label': '24.7', 'maximal_subgroups': [['8.2', 1], ['12.1', 2], ['12.5', 1]], 'name': 'C2*C3:C4', 'normal_subgroups': [['2.1', 3], ['3.1', 1], ['4.2', 1], ['6.2', 3], ['12.1', 2], ['12.5', 1]], 'order': 24, 'perfect': False, 'pretty': 'C_2\\times C_3:C_4', 'simple': False, 'solvable': True}
  73. label: 24.8
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 6, 1], [3, 2, 1], [4, 6, 1], [6, 2, 3]], 'cyclic': False, 'derived_group': '6.2', 'exponent': 12, 'label': '24.8', 'maximal_subgroups': [['8.3', 1], ['12.1', 1], ['12.4', 1], ['12.5', 1]], 'name': 'C3:D4', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['4.2', 1], ['6.2', 1], ['12.1', 1], ['12.4', 1], ['12.5', 1]], 'order': 24, 'perfect': False, 'pretty': 'C_3:D_4', 'simple': False, 'solvable': True}
  74. label: 24.9
    {'abelian': True, 'abelian_quotient': '24.9', 'center': '24.9', 'clases': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [4, 1, 4], [6, 1, 6], [12, 1, 8]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 12, 'label': '24.9', 'maximal_subgroups': [['8.2', 1], ['12.2', 2], ['12.5', 1]], 'name': 'C2*C12', 'normal_subgroups': [['2.1', 3], ['3.1', 1], ['4.1', 2], ['4.2', 1], ['6.2', 3], ['8.2', 1], ['12.2', 2], ['12.5', 1]], 'order': 24, 'perfect': False, 'pretty': 'C_2\\times C_{12}', 'simple': False, 'solvable': True}
  75. label: 25.1
    {'abelian': True, 'abelian_quotient': '25.1', 'center': '25.1', 'clases': [[1, 1, 1], [5, 1, 4], [25, 1, 20]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 25, 'label': '25.1', 'maximal_subgroups': [['5.1', 1]], 'name': 'C25', 'normal_subgroups': [['5.1', 1]], 'order': 25, 'perfect': False, 'pretty': 'C_{25}', 'simple': False, 'solvable': True}
  76. label: 25.2
    {'abelian': True, 'abelian_quotient': '25.2', 'center': '25.2', 'clases': [[1, 1, 1], [5, 1, 24]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 5, 'label': '25.2', 'maximal_subgroups': [['5.1', 6]], 'name': 'C5^2', 'normal_subgroups': [['5.1', 6]], 'order': 25, 'perfect': False, 'pretty': 'C_5^2', 'simple': False, 'solvable': True}
  77. label: 26.1
    {'abelian': False, 'abelian_quotient': '2.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 13, 1], [13, 2, 6]], 'cyclic': False, 'derived_group': '13.1', 'exponent': 26, 'label': '26.1', 'maximal_subgroups': [['2.1', 1], ['13.1', 1]], 'name': 'D13', 'normal_subgroups': [['13.1', 1]], 'order': 26, 'perfect': False, 'pretty': 'D_{13}', 'simple': False, 'solvable': True}
  78. label: 26.2
    {'abelian': True, 'abelian_quotient': '26.2', 'center': '26.2', 'clases': [[1, 1, 1], [2, 1, 1], [13, 1, 12], [26, 1, 12]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 26, 'label': '26.2', 'maximal_subgroups': [['2.1', 1], ['13.1', 1]], 'name': 'C26', 'normal_subgroups': [['2.1', 1], ['13.1', 1]], 'order': 26, 'perfect': False, 'pretty': 'C_{26}', 'simple': False, 'solvable': True}
  79. label: 27.1
    {'abelian': True, 'abelian_quotient': '27.1', 'center': '27.1', 'clases': [[1, 1, 1], [3, 1, 2], [9, 1, 6], [27, 1, 18]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 27, 'label': '27.1', 'maximal_subgroups': [['9.1', 1]], 'name': 'C27', 'normal_subgroups': [['3.1', 1], ['9.1', 1]], 'order': 27, 'perfect': False, 'pretty': 'C_{27}', 'simple': False, 'solvable': True}
  80. label: 27.2
    {'abelian': True, 'abelian_quotient': '27.2', 'center': '27.2', 'clases': [[1, 1, 1], [3, 1, 8], [9, 1, 18]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 9, 'label': '27.2', 'maximal_subgroups': [['9.1', 3], ['9.2', 1]], 'name': 'C3*C9', 'normal_subgroups': [['3.1', 4], ['9.1', 3], ['9.2', 1]], 'order': 27, 'perfect': False, 'pretty': 'C_3\\times C_9', 'simple': False, 'solvable': True}
  81. label: 27.3
    {'abelian': False, 'abelian_quotient': '9.2', 'center': '3.1', 'clases': [[1, 1, 1], [3, 1, 2], [3, 3, 8]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 3, 'label': '27.3', 'maximal_subgroups': [['9.2', 4]], 'name': 'He3', 'normal_subgroups': [['3.1', 1], ['9.2', 4]], 'order': 27, 'perfect': False, 'pretty': 'He_3', 'simple': False, 'solvable': True}
  82. label: 27.4
    {'abelian': False, 'abelian_quotient': '9.2', 'center': '3.1', 'clases': [[1, 1, 1], [3, 1, 2], [3, 3, 2], [9, 3, 6]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 9, 'label': '27.4', 'maximal_subgroups': [['9.1', 3], ['9.2', 1]], 'name': 'C9:C3', 'normal_subgroups': [['3.1', 1], ['9.1', 3], ['9.2', 1]], 'order': 27, 'perfect': False, 'pretty': 'C_9:C_3', 'simple': False, 'solvable': True}
  83. label: 27.5
    {'abelian': True, 'abelian_quotient': '27.5', 'center': '27.5', 'clases': [[1, 1, 1], [3, 1, 26]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 3, 'label': '27.5', 'maximal_subgroups': [['9.2', 13]], 'name': 'C3^3', 'normal_subgroups': [['3.1', 13], ['9.2', 13]], 'order': 27, 'perfect': False, 'pretty': 'C_3^3', 'simple': False, 'solvable': True}
  84. label: 28.1
    {'abelian': False, 'abelian_quotient': '4.1', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [4, 7, 2], [7, 2, 3], [14, 2, 3]], 'cyclic': False, 'derived_group': '7.1', 'exponent': 28, 'label': '28.1', 'maximal_subgroups': [['4.1', 1], ['14.2', 1]], 'name': 'C7:C4', 'normal_subgroups': [['2.1', 1], ['7.1', 1], ['14.2', 1]], 'order': 28, 'perfect': False, 'pretty': 'C_7:C_4', 'simple': False, 'solvable': True}
  85. label: 28.2
    {'abelian': True, 'abelian_quotient': '28.2', 'center': '28.2', 'clases': [[1, 1, 1], [2, 1, 1], [4, 1, 2], [7, 1, 6], [14, 1, 6], [28, 1, 12]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 28, 'label': '28.2', 'maximal_subgroups': [['4.1', 1], ['14.2', 1]], 'name': 'C28', 'normal_subgroups': [['2.1', 1], ['4.1', 1], ['7.1', 1], ['14.2', 1]], 'order': 28, 'perfect': False, 'pretty': 'C_{28}', 'simple': False, 'solvable': True}
  86. label: 28.3
    {'abelian': False, 'abelian_quotient': '4.2', 'center': '2.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 7, 2], [7, 2, 3], [14, 2, 3]], 'cyclic': False, 'derived_group': '7.1', 'exponent': 14, 'label': '28.3', 'maximal_subgroups': [['4.2', 1], ['14.1', 2], ['14.2', 1]], 'name': 'D14', 'normal_subgroups': [['2.1', 1], ['7.1', 1], ['14.1', 2], ['14.2', 1]], 'order': 28, 'perfect': False, 'pretty': 'D_{14}', 'simple': False, 'solvable': True}
  87. label: 28.4
    {'abelian': True, 'abelian_quotient': '28.4', 'center': '28.4', 'clases': [[1, 1, 1], [2, 1, 3], [7, 1, 6], [14, 1, 18]], 'cyclic': False, 'derived_group': '1.1', 'exponent': 14, 'label': '28.4', 'maximal_subgroups': [['4.2', 1], ['14.2', 3]], 'name': 'C2*C14', 'normal_subgroups': [['2.1', 3], ['4.2', 1], ['7.1', 1], ['14.2', 3]], 'order': 28, 'perfect': False, 'pretty': 'C_2\\times C_{14}', 'simple': False, 'solvable': True}
  88. label: 29.1
    {'abelian': True, 'abelian_quotient': '29.1', 'center': '29.1', 'clases': [[1, 1, 1], [29, 1, 28]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 29, 'label': '29.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C29', 'normal_subgroups': [], 'order': 29, 'perfect': False, 'pretty': 'C_{29}', 'simple': True, 'solvable': True}
  89. label: 30.1
    {'abelian': False, 'abelian_quotient': '10.2', 'center': '5.1', 'clases': [[1, 1, 1], [2, 3, 1], [3, 2, 1], [5, 1, 4], [10, 3, 4], [15, 2, 4]], 'cyclic': False, 'derived_group': '3.1', 'exponent': 30, 'label': '30.1', 'maximal_subgroups': [['6.1', 1], ['10.2', 1], ['15.1', 1]], 'name': 'C5*S3', 'normal_subgroups': [['3.1', 1], ['5.1', 1], ['6.1', 1], ['15.1', 1]], 'order': 30, 'perfect': False, 'pretty': 'C_5\\times S_3', 'simple': False, 'solvable': True}
  90. label: 30.2
    {'abelian': False, 'abelian_quotient': '6.2', 'center': '3.1', 'clases': [[1, 1, 1], [2, 5, 1], [3, 1, 2], [5, 2, 2], [6, 5, 2], [15, 2, 4]], 'cyclic': False, 'derived_group': '5.1', 'exponent': 30, 'label': '30.2', 'maximal_subgroups': [['6.2', 1], ['10.1', 1], ['15.1', 1]], 'name': 'C3*D5', 'normal_subgroups': [['3.1', 1], ['5.1', 1], ['10.1', 1], ['15.1', 1]], 'order': 30, 'perfect': False, 'pretty': 'C_3\\times D_5', 'simple': False, 'solvable': True}
  91. label: 30.3
    {'abelian': False, 'abelian_quotient': '2.1', 'center': '1.1', 'clases': [[1, 1, 1], [2, 15, 1], [3, 2, 1], [5, 2, 2], [15, 2, 4]], 'cyclic': False, 'derived_group': '15.1', 'exponent': 30, 'label': '30.3', 'maximal_subgroups': [['6.1', 1], ['10.1', 1], ['15.1', 1]], 'name': 'D15', 'normal_subgroups': [['3.1', 1], ['5.1', 1], ['15.1', 1]], 'order': 30, 'perfect': False, 'pretty': 'D_{15}', 'simple': False, 'solvable': True}
  92. label: 30.4
    {'abelian': True, 'abelian_quotient': '30.4', 'center': '30.4', 'clases': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [5, 1, 4], [6, 1, 2], [10, 1, 4], [15, 1, 8], [30, 1, 8]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 30, 'label': '30.4', 'maximal_subgroups': [['6.2', 1], ['10.2', 1], ['15.1', 1]], 'name': 'C30', 'normal_subgroups': [['2.1', 1], ['3.1', 1], ['5.1', 1], ['6.2', 1], ['10.2', 1], ['15.1', 1]], 'order': 30, 'perfect': False, 'pretty': 'C_{30}', 'simple': False, 'solvable': True}
  93. label: 31.1
    {'abelian': True, 'abelian_quotient': '31.1', 'center': '31.1', 'clases': [[1, 1, 1], [31, 1, 30]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 31, 'label': '31.1', 'maximal_subgroups': [['1.1', 1]], 'name': 'C31', 'normal_subgroups': [], 'order': 31, 'perfect': False, 'pretty': 'C_{31}', 'simple': True, 'solvable': True}
  94. label: 32.1
    {'abelian': True, 'abelian_quotient': '32.1', 'center': '32.1', 'clases': [[1, 1, 1], [2, 1, 1], [4, 1, 2], [8, 1, 4], [16, 1, 8], [32, 1, 16]], 'cyclic': True, 'derived_group': '1.1', 'exponent': 32, 'label': '32.1', 'maximal_subgroups': [['16.1', 1]], 'name': 'C32', 'normal_subgroups': [['2.1', 1], ['4.1', 1], ['8.1', 1], ['16.1', 1]], 'order': 32, 'perfect': False, 'pretty': 'C_{32}', 'simple': False, 'solvable': True}
  95. label: 32.10
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3], [4, 2, 2], [4, 4, 4], [8, 2, 4]], 'cyclic': False, 'derived_group': '4.1', 'exponent': 8, 'label': '32.10', 'maximal_subgroups': [['16.4', 1], ['16.5', 1], ['16.12', 1]], 'name': 'Q8:C4', 'normal_subgroups': [['2.1', 3], ['4.1', 2], ['4.2', 1], ['8.2', 1], ['8.4', 2], ['16.4', 1], ['16.5', 1], ['16.12', 1]], 'order': 32, 'perfect': False, 'pretty': 'Q_8:C_4', 'simple': False, 'solvable': True}
  96. label: 32.11
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [4, 1, 2], [4, 2, 5], [4, 4, 1], [8, 4, 2]], 'cyclic': False, 'derived_group': '4.1', 'exponent': 8, 'label': '32.11', 'maximal_subgroups': [['16.2', 1], ['16.6', 1], ['16.13', 1]], 'name': 'C4wrC2', 'normal_subgroups': [['2.1', 1], ['4.1', 2], ['4.2', 1], ['8.2', 1], ['8.3', 1], ['8.4', 1], ['16.2', 1], ['16.6', 1], ['16.13', 1]], 'order': 32, 'perfect': False, 'pretty': 'C_4\\wr C_2', 'simple': False, 'solvable': True}
  97. label: 32.12
    {'abelian': False, 'abelian_quotient': '16.5', 'center': '8.2', 'clases': [[1, 1, 1], [2, 1, 3], [4, 1, 4], [4, 2, 4], [8, 2, 8]], 'cyclic': False, 'derived_group': '2.1', 'exponent': 8, 'label': '32.12', 'maximal_subgroups': [['16.2', 1], ['16.5', 2]], 'name': 'C4:C8', 'normal_subgroups': [['2.1', 3], ['4.1', 4], ['4.2', 1], ['8.2', 3], ['16.2', 1], ['16.5', 2]], 'order': 32, 'perfect': False, 'pretty': 'C_4:C_8', 'simple': False, 'solvable': True}
  98. label: 32.13
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3], [4, 2, 2], [4, 4, 4], [8, 2, 4]], 'cyclic': False, 'derived_group': '4.1', 'exponent': 8, 'label': '32.13', 'maximal_subgroups': [['16.4', 2], ['16.5', 1]], 'name': 'C8:C4', 'normal_subgroups': [['2.1', 3], ['4.1', 2], ['4.2', 1], ['8.1', 2], ['8.2', 1], ['16.4', 2], ['16.5', 1]], 'order': 32, 'perfect': False, 'pretty': 'C_8:C_4', 'simple': False, 'solvable': True}
  99. label: 32.14
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.2', 'clases': [[1, 1, 1], [2, 1, 3], [4, 2, 2], [4, 4, 4], [8, 2, 4]], 'cyclic': False, 'derived_group': '4.1', 'exponent': 8, 'label': '32.14', 'maximal_subgroups': [['16.4', 2], ['16.5', 1]], 'name': 'C2.D8', 'normal_subgroups': [['2.1', 3], ['4.1', 2], ['4.2', 1], ['8.1', 2], ['8.2', 1], ['16.4', 2], ['16.5', 1]], 'order': 32, 'perfect': False, 'pretty': 'C_2.D_8', 'simple': False, 'solvable': True}
  100. label: 32.15
    {'abelian': False, 'abelian_quotient': '8.2', 'center': '4.1', 'clases': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 2, 1], [8, 2, 4], [8, 4, 4]], 'cyclic': False, 'derived_group': '4.1', 'exponent': 8, 'label': '32.15', 'maximal_subgroups': [['16.5', 1], ['16.6', 2]], 'name': 'C8.C4', 'normal_subgroups': [['2.1', 1], ['4.1', 2], ['4.2', 1], ['8.1', 2], ['8.2', 1], ['16.5', 1], ['16.6', 2]], 'order': 32, 'perfect': False, 'pretty': 'C_8.C_4', 'simple': False, 'solvable': True}