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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 184 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1944.3966.1.a1 $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $C_1$ $1$ ✓
1944.3966.2.a1 $C_3^3:C_6^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3966.2.b1 $C_3^4:D_6$ $2^{2} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3966.2.c1 $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3966.3.a1 $C_3^4:C_2^3$ $2^{3} \cdot 3^{4}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $3$ $-$
1944.3966.3.b1 $C_3^4:C_2^3$ $2^{3} \cdot 3^{4}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $3$ $-$
1944.3966.4.a1 $C_3^4\times C_6$ $2 \cdot 3^{5}$ ✓ ✓ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3966.4.b1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3966.4.c1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3966.6.a1 $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
1944.3966.6.b1 $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
1944.3966.6.c1 $C_3^2:C_6^2$ $2^{2} \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3966.6.d1 $C_3^2:C_6^2$ $2^{2} \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3966.6.e1 $C_3^2:C_6^2$ $2^{2} \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3966.6.f1 $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3966.6.g1 $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3966.6.h1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3966.6.i1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3966.8.a1 $C_3^5$ $3^{5}$ $3$ ✓ ✓ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $C_2^3$ $2^{3}$ ✓
1944.3966.9.a1 $C_6:S_3^2$ $2^{3} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $3^{2}$ $-$
1944.3966.9.b1 $C_6:S_3^2$ $2^{3} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $3^{2}$ $-$
1944.3966.9.c1 $C_6:S_3^2$ $2^{3} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $3^{2}$ $-$
1944.3966.12.a1 $C_3^3\times C_6$ $2 \cdot 3^{4}$ ✓ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $D_6$ $2^{2} \cdot 3$
1944.3966.12.b1 $C_3^3\times C_6$ $2 \cdot 3^{4}$ ✓ ✓ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $D_6$ $2^{2} \cdot 3$
1944.3966.12.c1 $C_3^3:C_6$ $2 \cdot 3^{4}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $D_6$ $2^{2} \cdot 3$
1944.3966.12.d1 $C_3^3:S_3$ $2 \cdot 3^{4}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $D_6$ $2^{2} \cdot 3$
1944.3966.12.e1 $C_3^3\times C_6$ $2 \cdot 3^{4}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3966.12.f1 $C_3^3\times C_6$ $2 \cdot 3^{4}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3966.12.g1 $C_3^3\times C_6$ $2 \cdot 3^{4}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3966.12.h1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3966.12.i1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3966.12.j1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3966.12.k1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3966.12.l1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3966.18.a1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $C_3:S_3$ $2 \cdot 3^{2}$
1944.3966.18.b1 $C_3^2\times D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.c1 $C_3^2\times D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.d1 $C_3^2\times D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.e1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.f1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.g1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.h1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.i1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.j1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.k1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.l1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.m1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.n1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.o1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3966.18.p1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^5:C_2^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
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