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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 88 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
600.178.1.a1.a1 $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_1$ $1$ ✓
600.178.2.a1.a1 $A_4\times C_5^2$ $2^{2} \cdot 3 \cdot 5^{2}$ ✓ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_2$ $2$ ✓
600.178.3.a1.a1 $C_{10}^2:C_2$ $2^{3} \cdot 5^{2}$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $3$ $-$
600.178.4.a1.a1 $C_5:D_{15}$ $2 \cdot 3 \cdot 5^{2}$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{2}$ $-$
600.178.5.a1.a1 $C_5:S_4$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $5$ $-$
600.178.5.a1.b1 $C_5:S_4$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $5$ $-$
600.178.5.a1.c1 $C_5:S_4$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $5$ $-$
600.178.5.a1.d1 $C_5:S_4$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $5$ $-$
600.178.5.a1.e1 $C_5:S_4$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $5$ $-$
600.178.5.a1.f1 $C_5:S_4$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $5$ $-$
600.178.6.a1.a1 $C_{10}^2$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $S_3$ $2 \cdot 3$
600.178.6.b1.a1 $C_5:D_{10}$ $2^{2} \cdot 5^{2}$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3$ $-$
600.178.6.c1.a1 $C_5^2:C_4$ $2^{2} \cdot 5^{2}$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3$ $-$
600.178.8.a1.a1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{3}$ $-$
600.178.10.a1.a1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_5$ $2 \cdot 5$
600.178.10.a1.b1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_5$ $2 \cdot 5$
600.178.10.a1.c1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_5$ $2 \cdot 5$
600.178.10.a1.d1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_5$ $2 \cdot 5$
600.178.10.a1.e1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_5$ $2 \cdot 5$
600.178.10.a1.f1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_5$ $2 \cdot 5$
600.178.12.a1.a1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{2} \cdot 3$ $-$
600.178.12.b1.a1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{2} \cdot 3$ $-$
600.178.15.a1.a1 $C_5:D_4$ $2^{3} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $3 \cdot 5$ $-$
600.178.15.a1.b1 $C_5:D_4$ $2^{3} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $3 \cdot 5$ $-$
600.178.15.a1.c1 $C_5:D_4$ $2^{3} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $3 \cdot 5$ $-$
600.178.15.a1.d1 $C_5:D_4$ $2^{3} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $3 \cdot 5$ $-$
600.178.15.a1.e1 $C_5:D_4$ $2^{3} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $3 \cdot 5$ $-$
600.178.15.a1.f1 $C_5:D_4$ $2^{3} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $3 \cdot 5$ $-$
600.178.20.a1.a1 $D_{15}$ $2 \cdot 3 \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{2} \cdot 5$ $-$
600.178.20.a1.b1 $D_{15}$ $2 \cdot 3 \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{2} \cdot 5$ $-$
600.178.20.a1.c1 $D_{15}$ $2 \cdot 3 \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{2} \cdot 5$ $-$
600.178.20.a1.d1 $D_{15}$ $2 \cdot 3 \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{2} \cdot 5$ $-$
600.178.20.a1.e1 $D_{15}$ $2 \cdot 3 \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{2} \cdot 5$ $-$
600.178.20.a1.f1 $D_{15}$ $2 \cdot 3 \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2^{2} \cdot 5$ $-$
600.178.24.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $S_4$ $2^{3} \cdot 3$
600.178.25.a1.a1 $S_4$ $2^{3} \cdot 3$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $5^{2}$ $-$
600.178.30.a1.a1 $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_{15}$ $2 \cdot 3 \cdot 5$
600.178.30.a1.b1 $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_{15}$ $2 \cdot 3 \cdot 5$
600.178.30.a1.c1 $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_{15}$ $2 \cdot 3 \cdot 5$
600.178.30.a1.d1 $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_{15}$ $2 \cdot 3 \cdot 5$
600.178.30.a1.e1 $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_{15}$ $2 \cdot 3 \cdot 5$
600.178.30.a1.f1 $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $D_{15}$ $2 \cdot 3 \cdot 5$
600.178.30.b1.a1 $D_{10}$ $2^{2} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
600.178.30.b1.b1 $D_{10}$ $2^{2} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
600.178.30.b1.c1 $D_{10}$ $2^{2} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
600.178.30.b1.d1 $D_{10}$ $2^{2} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
600.178.30.b1.e1 $D_{10}$ $2^{2} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
600.178.30.b1.f1 $D_{10}$ $2^{2} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
600.178.30.c1.a1 $C_5:C_4$ $2^{2} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
600.178.30.c1.b1 $C_5:C_4$ $2^{2} \cdot 5$ $C_5^2:S_4$ $2^{3} \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
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