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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 154 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2700.q.1.a1.a1 $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ ✓ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_1$ $1$ ✓
2700.q.2.a1.a1 $C_{15}^2:C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ ✓ ✓ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_2$ $2$ ✓
2700.q.2.b1.a1 $C_{15}^2:S_3$ $2 \cdot 3^{3} \cdot 5^{2}$ ✓ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_2$ $2$ ✓
2700.q.2.b1.b1 $C_{15}^2:S_3$ $2 \cdot 3^{3} \cdot 5^{2}$ ✓ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_2$ $2$ ✓
2700.q.3.a1.a1 $C_{15}^2:C_2^2$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3$ $-$
2700.q.3.b1.a1 $C_3\times C_5^2:D_6$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3$ $-$
2700.q.3.b1.b1 $C_3\times C_5^2:D_6$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3$ $-$
2700.q.3.b1.c1 $C_3\times C_5^2:D_6$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3$ $-$
2700.q.4.a1.a1 $C_{15}^2:C_3$ $3^{3} \cdot 5^{2}$ ✓ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_2^2$ $2^{2}$ ✓
2700.q.6.a1.a1 $C_{15}^2:C_2$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $S_3$ $2 \cdot 3$
2700.q.6.b1.a1 $C_3\times C_5^2:C_6$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $S_3$ $2 \cdot 3$
2700.q.6.b1.b1 $C_3\times C_5^2:C_6$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $S_3$ $2 \cdot 3$
2700.q.6.b1.c1 $C_3\times C_5^2:C_6$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $S_3$ $2 \cdot 3$
2700.q.6.c1.a1 $C_{15}\times D_{15}$ $2 \cdot 3^{2} \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3$ $-$
2700.q.6.c1.b1 $C_{15}\times D_{15}$ $2 \cdot 3^{2} \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3$ $-$
2700.q.6.d1.a1 $C_3\times C_5^2:S_3$ $2 \cdot 3^{2} \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3$ $-$
2700.q.6.d1.b1 $C_3\times C_5^2:S_3$ $2 \cdot 3^{2} \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3$ $-$
2700.q.6.d1.c1 $C_3\times C_5^2:S_3$ $2 \cdot 3^{2} \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3$ $-$
2700.q.6.d1.d1 $C_3\times C_5^2:S_3$ $2 \cdot 3^{2} \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3$ $-$
2700.q.6.d1.e1 $C_3\times C_5^2:S_3$ $2 \cdot 3^{2} \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3$ $-$
2700.q.6.d1.f1 $C_3\times C_5^2:S_3$ $2 \cdot 3^{2} \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3$ $-$
2700.q.9.a1.a1 $C_3\times D_5^2$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3^{2}$ $-$
2700.q.9.b1.a1 $C_{15}:D_{10}$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3^{2}$ $-$
2700.q.9.c1.a1 $C_5^2:D_6$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3^{2}$ $-$
2700.q.9.c1.b1 $C_5^2:D_6$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3^{2}$ $-$
2700.q.9.c1.c1 $C_5^2:D_6$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3^{2}$ $-$
2700.q.12.a1.a1 $C_{15}^2$ $3^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $D_6$ $2^{2} \cdot 3$
2700.q.12.b1.a1 $C_5^2:C_3^2$ $3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $D_6$ $2^{2} \cdot 3$
2700.q.12.b1.b1 $C_5^2:C_3^2$ $3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $D_6$ $2^{2} \cdot 3$
2700.q.12.b1.c1 $C_5^2:C_3^2$ $3^{2} \cdot 5^{2}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $D_6$ $2^{2} \cdot 3$
2700.q.15.a1.a1 $C_{15}:D_6$ $2^{2} \cdot 3^{2} \cdot 5$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3 \cdot 5$ $-$
2700.q.15.a1.b1 $C_{15}:D_6$ $2^{2} \cdot 3^{2} \cdot 5$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3 \cdot 5$ $-$
2700.q.18.a1.a1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ ✓ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_3:S_3$ $2 \cdot 3^{2}$
2700.q.18.b1.a1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.c1.a1 $C_5^2:C_6$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.c1.b1 $C_5^2:C_6$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.c1.c1 $C_5^2:C_6$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.d1.a1 $D_5\times C_{15}$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.d1.b1 $D_5\times C_{15}$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.e1.a1 $C_5\times D_{15}$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.e1.b1 $C_5\times D_{15}$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.f1.a1 $C_5^2:S_3$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.f1.b1 $C_5^2:S_3$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.f1.c1 $C_5^2:S_3$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.f1.d1 $C_5^2:S_3$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.f1.e1 $C_5^2:S_3$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.18.f1.f1 $C_5^2:S_3$ $2 \cdot 3 \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3^{2}$ $-$
2700.q.25.a1.a1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $5^{2}$ $-$
2700.q.27.a1.a1 $D_5^2$ $2^{2} \cdot 5^{2}$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $3^{3}$ $-$
2700.q.30.a1.a1 $C_3^2\times D_5$ $2 \cdot 3^{2} \cdot 5$ $C_{15}^2:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
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