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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
240.60.240.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
480.126.240.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{30}.D_8$ $2^{5} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
480.128.240.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{12}:C_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
480.145.240.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{15}:D_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
480.146.240.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{15}:\SD_{32}$ $2^{5} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
480.147.240.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{15}:\SD_{32}$ $2^{5} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
480.148.240.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{15}:Q_{32}$ $2^{5} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
480.151.240.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{30}.D_8$ $2^{5} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
480.810.240.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{30}:D_8$ $2^{5} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
480.810.240.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_{30}:D_8$ $2^{5} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
720.61.240.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{45}:D_8$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
720.249.240.a1.a1 $C_3$ $3$ ✓ ✓ $C_{60}.D_6$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
720.249.240.a1.b1 $C_3$ $3$ ✓ ✓ $C_{60}.D_6$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
720.250.240.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{15}:D_{24}$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
720.330.240.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $D_{12}:C_{30}$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
720.362.240.a1 $C_3$ $3$ ✓ ✓ $C_{60}.D_6$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ ✓
960.345.240.c1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2\times D_{12}):C_{20}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.373.240.d1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.376.240.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.377.240.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $D_{12}:C_{40}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.379.240.e1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}.D_{24}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.382.240.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $D_{24}:C_{20}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.383.240.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{30}.D_{16}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.384.240.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{120}.Q_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.385.240.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $D_{24}:C_{20}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.386.240.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{30}.Q_{32}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.387.240.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.389.240.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{120}.D_4$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.390.240.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{120}.D_4$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.391.240.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{120}.D_4$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.413.240.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{15}:D_{32}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.414.240.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{15}:\SD_{64}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.415.240.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{15}:\SD_{64}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.416.240.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{15}:Q_{64}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.423.240.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{60}.C_4^2$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.428.240.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.431.240.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_6\times D_4):C_{20}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.438.240.a1.a1 $C_4$ $2^{2}$ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.438.240.a1.b1 $C_4$ $2^{2}$ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.441.240.d1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.456.240.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{30}.D_{16}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.457.240.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{120}.D_4$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.458.240.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{30}.Q_{32}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.459.240.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{120}.D_4$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.460.240.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{120}.D_4$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.461.240.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{120}.D_4$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.4656.240.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2\times C_{30}.D_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.4656.240.a1.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2\times C_{30}.D_8$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.4659.240.c1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2\times D_{12}:C_{20}$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
960.4661.240.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ $C_6.(C_{10}\times D_8)$ $2^{6} \cdot 3 \cdot 5$ $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$
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