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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 205 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1458.1107.1.a1 $C_3^5:C_6$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_1$ $1$ ✓
1458.1107.2.a1 $C_3^5:C_3$ $3^{6}$ $3$ ✓ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_2$ $2$ ✓
1458.1107.3.a1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3$ $3$ ✓
1458.1107.3.b1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3$ $3$ ✓
1458.1107.3.c1 $C_3^4.C_6$ $2 \cdot 3^{5}$ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3$ $3$ ✓
1458.1107.3.d1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3$ $-$
1458.1107.6.a1 $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_6$ $2 \cdot 3$ ✓
1458.1107.6.b1 $C_3^4:C_3$ $3^{5}$ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $S_3$ $2 \cdot 3$
1458.1107.6.c1 $C_3^4:C_3$ $3^{5}$ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_6$ $2 \cdot 3$ ✓
1458.1107.6.d1 $C_3^4.C_3$ $3^{5}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_6$ $2 \cdot 3$ ✓
1458.1107.6.e1 $C_3^4:C_3$ $3^{5}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3$ $-$
1458.1107.6.f1 $C_3^4:C_3$ $3^{5}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3$ $-$
1458.1107.6.g1 $C_3^4:C_3$ $3^{5}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3$ $-$
1458.1107.9.a1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3^2$ $3^{2}$ ✓
1458.1107.9.b1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{2}$ $-$
1458.1107.9.c1 $S_3\times C_3^3$ $2 \cdot 3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{2}$ $-$
1458.1107.9.d1 $S_3\times \He_3$ $2 \cdot 3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{2}$ $-$
1458.1107.9.e1 $C_3^3.C_6$ $2 \cdot 3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{2}$ $-$
1458.1107.9.f1 $S_3\times C_3^3$ $2 \cdot 3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{2}$ $-$
1458.1107.9.g1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{2}$ $-$
1458.1107.9.h1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{2}$ $-$
1458.1107.9.i1 $C_3^2:C_{18}$ $2 \cdot 3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{2}$ $-$
1458.1107.9.j1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{2}$ $-$
1458.1107.18.a1 $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3\times S_3$ $2 \cdot 3^{2}$
1458.1107.18.b1 $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3\times C_6$ $2 \cdot 3^{2}$ ✓
1458.1107.18.c1 $C_3\times \He_3$ $3^{4}$ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3\times S_3$ $2 \cdot 3^{2}$
1458.1107.18.d1 $C_9:C_3^2$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $C_3\times S_3$ $2 \cdot 3^{2}$
1458.1107.18.e1 $C_3^4$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.f1 $C_3\times \He_3$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.g1 $C_9:C_3^2$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.h1 $C_3^4$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.i1 $C_3^4$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.j1 $C_3\times \He_3$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.k1 $C_3^2:C_9$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.l1 $C_3\times \He_3$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.m1 $C_3^2:C_9$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.n1 $C_3^4$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.o1 $C_3\wr C_3$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.p1 $C_3\wr C_3$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.q1 $C_3^4$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.r1 $C_3\wr C_3$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.s1 $C_3\wr C_3$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.t1 $C_3^4$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.u1 $C_3\wr C_3$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.v1 $C_3\wr C_3$ $3^{4}$ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.w1 $C_3^4$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.x1 $C_3^4$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.18.y1 $C_3^4$ $3^{4}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1458.1107.27.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $\He_3$ $3^{3}$
1458.1107.27.b1 $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ $C_3^5:C_6$ $2 \cdot 3^{6}$ $3^{3}$ $-$
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