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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 82 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
480.26.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.C_4^2$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.27.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.C_4^2$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.29.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.C_4^2$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.30.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.C_4^2$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.32.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.33.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{30}:C_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.43.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{10}.D_{24}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.45.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{60}:C_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.49.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.51.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.59.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.60.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.61.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.64.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{10}.D_{24}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.67.2.a1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.80.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{20}:C_{24}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.80.2.b1.b1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{20}:C_{24}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.81.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.C_4^2$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.81.2.b1.b1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.C_4^2$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.82.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{20}:C_{24}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.82.2.b1.b1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{20}:C_{24}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.85.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.D_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.86.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.87.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{20}:C_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.88.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.91.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{120}:C_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.92.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.93.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{120}:C_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.98.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{10}:C_{24}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.100.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.108.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.108.2.b1.b1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.110.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.D_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.113.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.277.2.a1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{10}:C_{48}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.278.2.a1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{15}:\OD_{32}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.302.2.a1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:C_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.303.2.a1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{15}:\OD_{32}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.361.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.C_2^3$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.362.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.C_2^3$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.365.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{30}:C_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.366.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{60}.C_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.370.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:\OD_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.371.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:\OD_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.378.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{10}:D_{24}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.379.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.392.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:\SD_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.393.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:\SD_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.396.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:Q_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.692.2.c1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{10}\times C_{24}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
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