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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 54 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
900.79.2.a1.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}:C_{60}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.80.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}^2:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.81.2.a1.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}:C_{60}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.82.2.a1.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}:C_{60}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.83.2.a1.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}^2:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.84.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}^2:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.85.2.a1.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}^2:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.86.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}^2:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.87.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ ✓ $C_{15}\times C_{60}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.142.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{30}:C_{30}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.143.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_5^2:C_6^2$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.144.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{30}:C_{30}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.145.2.a1.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}\times D_{30}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.146.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}:D_{30}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.147.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_3^2:C_{10}^2$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.148.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}:D_{30}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.149.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}:D_{30}$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
900.150.2.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{30}^2$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
1350.62.3.a1.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}^2.C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_3$ $3$ ✓
1350.63.3.a1.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}^2.C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_3$ $3$ ✓
1350.64.3.a1.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}^2:C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_3$ $3$ ✓
1350.89.3.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ ✓ $C_{15}\times C_{90}$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_3$ $3$ ✓
1350.90.3.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{15}^2:C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_3$ $3$ ✓
1350.91.3.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{45}:C_{30}$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_3$ $3$ ✓
1350.100.3.b1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_{15}^2:C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_3$ $3$ ✓
1350.103.3.b1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $S_3\times C_{15}^2$ $2 \cdot 3^{3} \cdot 5^{2}$ $3$ $-$
1350.112.3.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ $C_3\times C_{15}\times C_{30}$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_3$ $3$ ✓
1800.510.4.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $Q_8:C_{15}^2$ $2^{3} \cdot 3^{2} \cdot 5^{2}$ $2^{2}$ $-$
1800.739.4.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_2^3:C_{15}^2$ $2^{3} \cdot 3^{2} \cdot 5^{2}$ $2^{2}$ $-$
2250.a.5.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ ✓ $C_{15}\times C_{150}$ $2 \cdot 3^{2} \cdot 5^{3}$ $C_5$ $5$ ✓
3150.a.7.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ ✓ $C_{15}\times C_{210}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 7$ $C_7$ $7$ ✓
4950.d.11.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ ✓ ✓ $C_{15}\times C_{330}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 11$ $C_{11}$ $11$ ✓
13950.a.31.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{15}\times F_{31}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 31$ $31$ $-$
13950.b.31.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{465}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 31$ $31$ $-$
27450.a.61.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{915}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 61$ $61$ $-$
27450.b.61.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{1830}:C_{15}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 61$ $61$ $-$
54450.a.121.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{15}\times C_{11}^2:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 11^{2}$ $11^{2}$ $-$
54450.b.121.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{11}^2:C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 11^{2}$ $11^{2}$ $-$
67950.g.151.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{2265}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 151$ $151$ $-$
67950.h.151.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{2265}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 151$ $151$ $-$
81450.c.181.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{2715}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 181$ $181$ $-$
81450.h.181.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{2715}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 181$ $181$ $-$
94950.a.211.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{3165}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 211$ $211$ $-$
94950.b.211.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{3165}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 211$ $211$ $-$
108450.a.241.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{3615}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 241$ $241$ $-$
108450.b.241.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{3615}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 241$ $241$ $-$
121950.a.271.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{4065}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 271$ $271$ $-$
121950.c.271.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{4065}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 271$ $271$ $-$
148950.a.331.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{4965}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 331$ $331$ $-$
148950.b.331.a1 $C_{15}\times C_{30}$ $2 \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $C_{4965}:C_{30}$ $2 \cdot 3^{2} \cdot 5^{2} \cdot 331$ $331$ $-$
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