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Elements of the group are displayed as permutations of degree 13.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | ||||||
| $A_5^2:C_6$ | 1A | $1$ | $1$ | $A_5^2:C_6$ | 1A | 1A | 1A | $()$ |
| $A_5^2:C_6$ | 2A | $2$ | $30$ | $C_2^2\times \GL(2,4)$ | 1A | 2A | 2A | $(1,7)(3,5)$ |
| $A_5^2:C_6$ | 2B | $2$ | $60$ | $C_6\times A_5$ | 1A | 2B | 2B | $(1,6)(2,10)(3,9)(4,7)(5,8)$ |
| $A_5^2:C_6$ | 2C | $2$ | $225$ | $C_2^4:C_6$ | 1A | 2C | 2C | $(1,5)(2,3)(4,8)(6,9)$ |
| $A_5^2:C_6$ | 3A1 | $3$ | $1$ | $A_5^2:C_6$ | 3A-1 | 1A | 3A-1 | $(11,13,12)$ |
| $A_5^2:C_6$ | 3A-1 | $3$ | $1$ | $A_5^2:C_6$ | 3A1 | 1A | 3A1 | $(11,12,13)$ |
| $A_5^2:C_6$ | 3B | $3$ | $40$ | $C_3\times \GL(2,4)$ | 3B | 1A | 3B | $(2,5,7)$ |
| $A_5^2:C_6$ | 3C1 | $3$ | $40$ | $C_3\times \GL(2,4)$ | 3C-1 | 1A | 3C-1 | $(4,10,6)(11,13,12)$ |
| $A_5^2:C_6$ | 3C-1 | $3$ | $40$ | $C_3\times \GL(2,4)$ | 3C1 | 1A | 3C1 | $(4,6,10)(11,12,13)$ |
| $A_5^2:C_6$ | 3D | $3$ | $400$ | $S_3\times C_3^2$ | 3D | 1A | 3D | $(2,3,5)(4,10,9)$ |
| $A_5^2:C_6$ | 3E1 | $3$ | $400$ | $S_3\times C_3^2$ | 3E-1 | 1A | 3E-1 | $(2,7,3)(4,10,8)(11,13,12)$ |
| $A_5^2:C_6$ | 3E-1 | $3$ | $400$ | $S_3\times C_3^2$ | 3E1 | 1A | 3E1 | $(2,3,7)(4,8,10)(11,12,13)$ |
| $A_5^2:C_6$ | 4A | $4$ | $900$ | $C_2\times C_{12}$ | 2C | 4A | 4A | $(1,9,5,6)(2,8,3,4)(7,10)$ |
| $A_5^2:C_6$ | 5A1 | $5$ | $24$ | $C_{15}\times A_5$ | 5A2 | 5A2 | 1A | $(1,7,2,3,5)$ |
| $A_5^2:C_6$ | 5A2 | $5$ | $24$ | $C_{15}\times A_5$ | 5A1 | 5A1 | 1A | $(1,2,5,7,3)$ |
| $A_5^2:C_6$ | 5B1 | $5$ | $144$ | $D_5\times C_{15}$ | 5B2 | 5B2 | 1A | $(1,7,5,2,3)(4,8,10,9,6)$ |
| $A_5^2:C_6$ | 5B2 | $5$ | $144$ | $D_5\times C_{15}$ | 5B1 | 5B1 | 1A | $(1,5,3,7,2)(4,10,6,8,9)$ |
| $A_5^2:C_6$ | 5C | $5$ | $288$ | $C_5\times C_{15}$ | 5C | 5C | 1A | $(1,3,5,2,7)(4,10,8,6,9)$ |
| $A_5^2:C_6$ | 6A1 | $6$ | $30$ | $C_2^2\times \GL(2,4)$ | 3A1 | 2A | 6A-1 | $(1,7)(2,5)(11,12,13)$ |
| $A_5^2:C_6$ | 6A-1 | $6$ | $30$ | $C_2^2\times \GL(2,4)$ | 3A-1 | 2A | 6A1 | $(1,7)(2,5)(11,13,12)$ |
| $A_5^2:C_6$ | 6B1 | $6$ | $60$ | $C_6\times A_5$ | 3A1 | 2B | 6B-1 | $(1,6)(2,10)(3,9)(4,7)(5,8)(11,12,13)$ |
| $A_5^2:C_6$ | 6B-1 | $6$ | $60$ | $C_6\times A_5$ | 3A-1 | 2B | 6B1 | $(1,6)(2,10)(3,9)(4,7)(5,8)(11,13,12)$ |
| $A_5^2:C_6$ | 6C1 | $6$ | $225$ | $C_2^4:C_6$ | 3A-1 | 2C | 6C-1 | $(1,5)(2,3)(4,8)(6,9)(11,13,12)$ |
| $A_5^2:C_6$ | 6C-1 | $6$ | $225$ | $C_2^4:C_6$ | 3A1 | 2C | 6C1 | $(1,5)(2,3)(4,8)(6,9)(11,12,13)$ |
| $A_5^2:C_6$ | 6D | $6$ | $600$ | $C_6^2$ | 3B | 2A | 6D | $(1,2)(4,6,8)(5,7)$ |
| $A_5^2:C_6$ | 6E1 | $6$ | $600$ | $C_6^2$ | 3C1 | 2A | 6E-1 | $(1,7)(3,5)(4,8,9)(11,12,13)$ |
| $A_5^2:C_6$ | 6E-1 | $6$ | $600$ | $C_6^2$ | 3C-1 | 2A | 6E1 | $(1,7)(3,5)(4,9,8)(11,13,12)$ |
| $A_5^2:C_6$ | 6F | $6$ | $1200$ | $C_3\times C_6$ | 3D | 2B | 6F | $(1,8)(2,10,3,9,5,4)(6,7)$ |
| $A_5^2:C_6$ | 6G1 | $6$ | $1200$ | $C_3\times C_6$ | 3E1 | 2B | 6G-1 | $(1,6)(2,4,7,10,3,8)(5,9)(11,12,13)$ |
| $A_5^2:C_6$ | 6G-1 | $6$ | $1200$ | $C_3\times C_6$ | 3E-1 | 2B | 6G1 | $(1,6)(2,8,3,10,7,4)(5,9)(11,13,12)$ |
| $A_5^2:C_6$ | 10A1 | $10$ | $360$ | $C_2\times C_{30}$ | 5A1 | 10A3 | 2A | $(1,7)(2,5)(4,10,9,6,8)$ |
| $A_5^2:C_6$ | 10A3 | $10$ | $360$ | $C_2\times C_{30}$ | 5A2 | 10A1 | 2A | $(1,7)(2,5)(4,6,10,8,9)$ |
| $A_5^2:C_6$ | 10B1 | $10$ | $720$ | $C_{30}$ | 5B1 | 10B3 | 2B | $(1,10,7,9,5,6,2,4,3,8)$ |
| $A_5^2:C_6$ | 10B3 | $10$ | $720$ | $C_{30}$ | 5B2 | 10B1 | 2B | $(1,9,2,8,7,6,3,10,5,4)$ |
| $A_5^2:C_6$ | 12A1 | $12$ | $900$ | $C_2\times C_{12}$ | 6C1 | 4A | 12A-1 | $(1,6,5,9)(2,4,3,8)(7,10)(11,12,13)$ |
| $A_5^2:C_6$ | 12A-1 | $12$ | $900$ | $C_2\times C_{12}$ | 6C-1 | 4A | 12A1 | $(1,9,5,6)(2,8,3,4)(7,10)(11,13,12)$ |
| $A_5^2:C_6$ | 15A1 | $15$ | $24$ | $C_{15}\times A_5$ | 15A2 | 5A1 | 3A1 | $(4,8,6,9,10)(11,12,13)$ |
| $A_5^2:C_6$ | 15A-1 | $15$ | $24$ | $C_{15}\times A_5$ | 15A-2 | 5A1 | 3A-1 | $(4,10,9,6,8)(11,13,12)$ |
| $A_5^2:C_6$ | 15A2 | $15$ | $24$ | $C_{15}\times A_5$ | 15A1 | 5A2 | 3A-1 | $(4,6,10,8,9)(11,13,12)$ |
| $A_5^2:C_6$ | 15A-2 | $15$ | $24$ | $C_{15}\times A_5$ | 15A-1 | 5A2 | 3A1 | $(4,9,8,10,6)(11,12,13)$ |
| $A_5^2:C_6$ | 15B1 | $15$ | $144$ | $D_5\times C_{15}$ | 15B2 | 5B1 | 3A1 | $(1,5,3,7,2)(4,10,6,8,9)(11,12,13)$ |
| $A_5^2:C_6$ | 15B-1 | $15$ | $144$ | $D_5\times C_{15}$ | 15B-2 | 5B1 | 3A-1 | $(1,2,7,3,5)(4,9,8,6,10)(11,13,12)$ |
| $A_5^2:C_6$ | 15B2 | $15$ | $144$ | $D_5\times C_{15}$ | 15B1 | 5B2 | 3A-1 | $(1,3,2,5,7)(4,6,9,10,8)(11,13,12)$ |
| $A_5^2:C_6$ | 15B-2 | $15$ | $144$ | $D_5\times C_{15}$ | 15B-1 | 5B2 | 3A1 | $(1,7,5,2,3)(4,8,10,9,6)(11,12,13)$ |
| $A_5^2:C_6$ | 15C1 | $15$ | $288$ | $C_5\times C_{15}$ | 15C-1 | 5C | 3A1 | $(1,5,7,3,2)(4,8,9,10,6)(11,12,13)$ |
| $A_5^2:C_6$ | 15C-1 | $15$ | $288$ | $C_5\times C_{15}$ | 15C1 | 5C | 3A-1 | $(1,2,3,7,5)(4,6,10,9,8)(11,13,12)$ |
| $A_5^2:C_6$ | 15D1 | $15$ | $480$ | $C_3\times C_{15}$ | 15D2 | 5A1 | 3B | $(2,7,5)(4,10,8,9,6)$ |
| $A_5^2:C_6$ | 15D2 | $15$ | $480$ | $C_3\times C_{15}$ | 15D1 | 5A2 | 3B | $(2,5,7)(4,8,6,10,9)$ |
| $A_5^2:C_6$ | 15E1 | $15$ | $480$ | $C_3\times C_{15}$ | 15E2 | 5A1 | 3C1 | $(1,2,5,7,3)(4,6,10)(11,12,13)$ |
| $A_5^2:C_6$ | 15E-1 | $15$ | $480$ | $C_3\times C_{15}$ | 15E-2 | 5A1 | 3C-1 | $(1,3,7,5,2)(4,10,6)(11,13,12)$ |