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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 85 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
800.252.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_5^2:(C_4\times C_8)$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.254.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}.(C_4\times D_5)$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.269.2.b1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.270.2.b1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.271.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.298.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{40}:C_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.299.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_5\times C_{20}.D_4$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.300.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{40}:C_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.310.2.b1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $D_{20}:C_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.322.2.b1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.D_4$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.477.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}:C_{40}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.478.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}:C_{40}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.479.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_5\times C_{10}.C_4^2$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.481.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_5\times C_{10}.\OD_{16}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.502.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_4\times C_5^2:C_8$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.503.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $(C_5\times C_{20}):C_8$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.504.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $(C_{10}\times C_{20}).C_4$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.506.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $(C_{10}\times C_{20}).C_4$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.613.2.d1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.614.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.619.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.621.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.629.2.f1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.632.2.c1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.637.2.d1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.638.2.c1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.641.2.c1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.642.2.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.645.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.646.2.d1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.647.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.651.2.c1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.652.2.c1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.654.2.d1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.657.2.f1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.659.2.c1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.671.2.d1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.672.2.d1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.680.2.f1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}:D_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.688.2.d1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}:D_{20}$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.694.2.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.695.2.a1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.761.2.b1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ $C_{20}^2.C_2$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.761.2.b1.b1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ $C_{20}^2.C_2$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.764.2.b1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ $C_{20}^2:C_2$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.765.2.d1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2:C_2$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.770.2.d1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.770.2.d1.b1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.772.2.d1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
800.774.2.g1.a1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{10}^2.C_2^3$ $2^{5} \cdot 5^{2}$ $C_2$ $2$ ✓
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