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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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
240.25.2.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{15}:C_4^2$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.26.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_6.D_{20}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.28.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{30}:C_4$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.29.2.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{10}.D_{12}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.30.2.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.D_4$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.31.2.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_6.D_{20}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.56.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{12}:C_{20}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.56.2.b1.b1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{12}:C_{20}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.57.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.D_4$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.57.2.c1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.D_4$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.58.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{12}:C_{20}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.58.2.b1.b1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{12}:C_{20}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.59.2.c1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_6:C_{20}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.64.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.D_4$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.64.2.b1.b1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.D_4$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.139.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{10}.D_6$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.140.2.c1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{10}.D_6$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.144.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{30}:C_4$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.146.2.c1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_6:D_{20}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.148.2.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.165.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.165.2.b1.b1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.166.2.c1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_6\times C_{20}$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.170.2.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{20}.D_6$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.170.2.b1.b1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{20}.D_6$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.173.2.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.C_2^3$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.173.2.a1.b1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.C_2^3$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.173.2.a1.c1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.C_2^3$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.173.2.a1.d1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.C_2^3$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.173.2.a1.e1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.C_2^3$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.173.2.a1.f1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}.C_2^3$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
240.174.2.c1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:D_4$ $2^{4} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
360.23.3.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{18}:C_{20}$ $2^{3} \cdot 3^{2} \cdot 5$ $3$ $-$
360.72.3.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $3$ $-$
360.98.3.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_6:C_{60}$ $2^{3} \cdot 3^{2} \cdot 5$ $C_3$ $3$ ✓
360.108.3.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $3$ $-$
360.108.3.a1.b1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $3$ $-$
360.108.3.a1.c1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $3$ $-$
360.108.3.a1.d1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $3$ $-$
480.256.4.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $\SL(2,3):C_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2}$ $-$
480.1016.4.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_2\times C_{10}.S_4$ $2^{5} \cdot 3 \cdot 5$ $2^{2}$ $-$
480.1022.4.c1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_2\times A_4:C_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2}$ $-$
600.23.5.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_6:C_{100}$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_5$ $5$ ✓
600.85.5.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{30}.D_{10}$ $2^{3} \cdot 3 \cdot 5^{2}$ $5$ $-$
600.129.5.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}:C_{20}$ $2^{3} \cdot 3 \cdot 5^{2}$ $C_5$ $5$ ✓
600.134.5.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{30}:C_{20}$ $2^{3} \cdot 3 \cdot 5^{2}$ $5$ $-$
600.188.5.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{30}:C_{20}$ $2^{3} \cdot 3 \cdot 5^{2}$ $5$ $-$
840.49.7.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{30}.D_{14}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ $7$ $-$
840.114.7.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_6:C_{140}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ $C_7$ $7$ ✓
840.119.7.a1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{210}:C_4$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ $7$ $-$
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