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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (1-50 of 746 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
100.10.100.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_5:F_5$ $2^{2} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
200.19.100.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_5^2:C_8$ $2^{3} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
200.46.100.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{10}:F_5$ $2^{3} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
300.29.100.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_{15}:F_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
300.33.100.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{15}:F_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
400.57.100.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_5^2:C_{16}$ $2^{4} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
400.142.100.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{20}.F_5$ $2^{4} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
400.143.100.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}.F_5$ $2^{4} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
400.144.100.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
400.145.100.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
400.146.100.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{10}^2.C_4$ $2^{4} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
400.147.100.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_5^2:\OD_{16}$ $2^{4} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
400.148.100.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{10}^2:C_4$ $2^{4} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
400.215.100.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{10}^2:C_4$ $2^{4} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
500.19.100.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_{25}:F_5$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.20.100.b1.a1 $C_5$ $5$ ✓ ✓ ✓ $D_{25}.D_5$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.21.100.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_5^2:F_5$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.42.100.a1.a1 $C_5$ $5$ ✓ ✓ ✓ ✓ $C_5^2:C_{20}$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.45.100.a1.a1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.45.100.a1.b1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.45.100.a1.c1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.45.100.a1.d1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.45.100.a1.e1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.45.100.a1.f1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.46.100.b1.a1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.46.100.b1.b1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.47.100.b1.a1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.47.100.b1.b1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.47.100.b1.c1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.47.100.b1.d1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.47.100.b1.e1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
500.47.100.b1.f1 $C_5$ $5$ ✓ ✓ $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
600.73.100.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_5^2:C_{24}$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
600.77.100.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{30}.F_5$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
600.168.100.a1.a1 $S_3$ $2 \cdot 3$ ✓ ✓ $S_3\times C_5:F_5$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
600.187.100.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{30}:F_5$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
600.191.100.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{30}:F_5$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
700.24.100.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_5^2:C_{28}$ $2^{2} \cdot 5^{2} \cdot 7$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
700.25.100.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{35}:F_5$ $2^{2} \cdot 5^{2} \cdot 7$ $C_5:F_5$ $2^{2} \cdot 5^{2}$ ✓
800.238.100.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ $C_5^2:C_{32}$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.491.100.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ $C_{40}.F_5$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.492.100.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ $C_5^2:\OD_{32}$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.493.100.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ $C_{40}:F_5$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.494.100.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ $C_{40}:F_5$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.495.100.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ $C_{40}:F_5$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.496.100.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ $C_{40}:F_5$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.497.100.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ $C_{40}.F_5$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.498.100.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ $C_{40}.F_5$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.499.100.a1.a1 $C_2\times C_4$ $2^{3}$ ✓ ✓ ✓ ✓ $C_{10}^2.C_8$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
800.500.100.a1.a1 $C_2\times C_4$ $2^{3}$ ✓ ✓ ✓ $C_5^2:\OD_{32}$ $2^{5} \cdot 5^{2}$ $C_5:F_5$ $2^{2} \cdot 5^{2}$
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