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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 186 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
160.16.160.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $D_{20}:C_4$ $2^{5} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
320.9.160.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times D_{20}):C_4$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.40.160.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{20}.D_8$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.41.160.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{20}:C_8$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.43.160.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4.D_{40}$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.46.160.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{40}:C_4$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.49.160.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{40}:C_4$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.50.160.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_8.D_{20}$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.53.160.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_8.D_{20}$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.54.160.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_8.D_{20}$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.55.160.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_8.D_{20}$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.87.160.d1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{20}.C_4^2$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
320.592.160.c1 $C_2$ $2$ ✓ ✓ ✓ $C_2\times D_{20}:C_4$ $2^{6} \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
480.40.160.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
480.45.160.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $D_{60}:C_4$ $2^{5} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
480.87.160.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $D_{20}:C_{12}$ $2^{5} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
480.169.160.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $D_{60}:C_4$ $2^{5} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
800.17.160.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $D_{100}:C_4$ $2^{5} \cdot 5^{2}$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
800.262.160.b1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
800.264.160.b1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_{10}.D_{40}$ $2^{5} \cdot 5^{2}$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
800.294.160.a1.a1 $C_5$ $5$ ✓ ✓ ✓ ✓ $D_{20}:C_{20}$ $2^{5} \cdot 5^{2}$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
800.335.160.a1 $C_5$ $5$ ✓ ✓ $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
800.393.160.b1.a1 $C_5$ $5$ ✓ ✓ ✓ $D_{20}:F_5$ $2^{5} \cdot 5^{2}$ $D_{20}:C_4$ $2^{5} \cdot 5$ ✓
960.29.160.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.34.160.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $D_{60}:C_8$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.47.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{12}.D_{40}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.49.160.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{12}.D_{40}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.51.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.54.160.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{20}.D_{24}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.86.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{24}.D_{20}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.91.160.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $D_{120}:C_4$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.92.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{24}.D_{20}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.97.160.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{24}.D_{20}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.98.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{24}.D_{20}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.103.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{20}.D_{24}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.104.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{24}.D_{20}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.109.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $D_{120}:C_4$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.110.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{24}.D_{20}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.115.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{20}.D_{24}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.116.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{24}.D_{20}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.121.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{20}.D_{24}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.149.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_6\times D_{20}):C_4$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.154.160.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_2\times D_{60}):C_4$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.174.160.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{60}.C_4^2$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.176.160.g1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{60}.C_4^2$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.223.160.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $(C_2\times D_{20}):C_{12}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.254.160.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{60}.D_8$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.255.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $D_{20}:C_{24}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.257.160.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{12}.D_{40}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
960.260.160.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $D_{40}:C_{12}$ $2^{6} \cdot 3 \cdot 5$ $D_{20}:C_4$ $2^{5} \cdot 5$
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