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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 65 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
160.68.80.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{40}:C_4$ $2^{5} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
160.69.80.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{40}:C_4$ $2^{5} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
160.70.80.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{40}.C_4$ $2^{5} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
160.71.80.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{40}.C_4$ $2^{5} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
160.76.80.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{20}:C_8$ $2^{5} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
160.79.80.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{10}.\OD_{16}$ $2^{5} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
160.81.80.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{10}.C_4^2$ $2^{5} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
160.204.80.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $D_{10}.D_4$ $2^{5} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
160.204.80.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $D_{10}.D_4$ $2^{5} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
240.97.80.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $D_{10}.D_6$ $2^{4} \cdot 3 \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
240.114.80.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_{20}:C_{12}$ $2^{4} \cdot 3 \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
240.121.80.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{60}:C_4$ $2^{4} \cdot 3 \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.31.80.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_{100}:C_4$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.119.80.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $D_{10}.D_{10}$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.126.80.a1.a1 $C_5$ $5$ ✓ ✓ $C_{10}.(C_2\times F_5)$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.126.80.a1.b1 $C_5$ $5$ ✓ ✓ $C_{10}.(C_2\times F_5)$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.138.80.a1.a1 $C_5$ $5$ ✓ ✓ ✓ ✓ $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.145.80.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.152.80.a1.a1 $C_5$ $5$ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.152.80.a1.b1 $C_5$ $5$ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.152.80.a1.c1 $C_5$ $5$ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.152.80.a1.d1 $C_5$ $5$ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.152.80.a1.e1 $C_5$ $5$ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.152.80.a1.f1 $C_5$ $5$ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.159.80.a1.a1 $C_5$ $5$ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
400.159.80.a1.b1 $C_5$ $5$ ✓ ✓ $C_{20}:F_5$ $2^{4} \cdot 5^{2}$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
560.90.80.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $D_{10}.D_{14}$ $2^{4} \cdot 5 \cdot 7$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
560.98.80.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_{20}:C_{28}$ $2^{4} \cdot 5 \cdot 7$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
560.105.80.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{140}:C_4$ $2^{4} \cdot 5 \cdot 7$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
720.462.80.a1.a1 $C_3^2$ $3^{2}$ $3$ ✓ ✓ ✓ $C_{15}:C_{12}:C_4$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
720.585.80.a1.a1 $C_3^2$ $3^{2}$ $3$ ✓ ✓ ✓ $(C_3\times C_{60}):C_4$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
720.775.80.a1.a1 $C_3^2$ $3^{2}$ $3$ ✓ ✓ ✓ $D_5.\SOPlus(4,2)$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
720.776.80.a1.a1 $C_3^2$ $3^{2}$ $3$ ✓ ✓ ✓ $D_5.\PSU(3,2)$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
880.126.80.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $D_{10}.D_{22}$ $2^{4} \cdot 5 \cdot 11$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
880.138.80.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $C_{20}:C_{44}$ $2^{4} \cdot 5 \cdot 11$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
880.145.80.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{220}:C_4$ $2^{4} \cdot 5 \cdot 11$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1040.94.80.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $D_{65}.D_4$ $2^{4} \cdot 5 \cdot 13$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1040.101.80.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $D_{10}.D_{26}$ $2^{4} \cdot 5 \cdot 13$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1040.123.80.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $C_{20}:C_{52}$ $2^{4} \cdot 5 \cdot 13$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1040.130.80.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{260}:C_4$ $2^{4} \cdot 5 \cdot 13$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1040.137.80.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{260}:C_4$ $2^{4} \cdot 5 \cdot 13$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1040.144.80.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{260}:C_4$ $2^{4} \cdot 5 \cdot 13$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1280.1116374.80.a1.a1 $C_2^4$ $2^{4}$ ✓ ✓ ✓ $(C_2^4\times C_4):F_5$ $2^{8} \cdot 5$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1360.98.80.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $D_{85}.D_4$ $2^{4} \cdot 5 \cdot 17$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1360.105.80.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $D_{10}.D_{34}$ $2^{4} \cdot 5 \cdot 17$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1360.127.80.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $C_{20}:C_{68}$ $2^{4} \cdot 5 \cdot 17$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1360.134.80.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_{340}:C_4$ $2^{4} \cdot 5 \cdot 17$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1360.141.80.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_{340}:C_4$ $2^{4} \cdot 5 \cdot 17$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1360.148.80.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_{340}:C_4$ $2^{4} \cdot 5 \cdot 17$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
1520.90.80.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $D_{10}.D_{38}$ $2^{4} \cdot 5 \cdot 19$ $C_{20}:C_4$ $2^{4} \cdot 5$ ✓
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