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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 (41 matches)

  displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
120.15.60.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_5\times \SL(2,3)$ $2^{3} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
120.43.60.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{10}\times A_4$ $2^{3} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
180.8.60.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_2^2:C_{45}$ $2^{2} \cdot 3^{2} \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
180.31.60.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $A_4\times C_{15}$ $2^{2} \cdot 3^{2} \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
240.32.60.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_4^2:C_{15}$ $2^{4} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
240.204.60.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ $C_2^4:C_{15}$ $2^{4} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
240.204.60.a1.b1 $C_2^2$ $2^{2}$ ✓ ✓ $C_2^4:C_{15}$ $2^{4} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
240.204.60.a1.c1 $C_2^2$ $2^{2}$ ✓ ✓ $C_2^4:C_{15}$ $2^{4} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
240.204.60.a1.d1 $C_2^2$ $2^{2}$ ✓ ✓ $C_2^4:C_{15}$ $2^{4} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
240.204.60.a1.e1 $C_2^2$ $2^{2}$ ✓ ✓ $C_2^4:C_{15}$ $2^{4} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
300.8.60.a1.a1 $C_5$ $5$ ✓ ✓ ✓ ✓ $A_4\times C_{25}$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
300.42.60.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $A_4\times C_5^2$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
300.42.60.a1.b1 $C_5$ $5$ ✓ ✓ ✓ $A_4\times C_5^2$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
300.42.60.a1.c1 $C_5$ $5$ ✓ ✓ ✓ $A_4\times C_5^2$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
300.42.60.a1.d1 $C_5$ $5$ ✓ ✓ ✓ $A_4\times C_5^2$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
300.42.60.a1.e1 $C_5$ $5$ ✓ ✓ ✓ $A_4\times C_5^2$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
300.42.60.a1.f1 $C_5$ $5$ ✓ ✓ ✓ $A_4\times C_5^2$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
420.32.60.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $A_4\times C_{35}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
420.33.60.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{35}:A_4$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
660.16.60.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $A_4\times C_{11}:C_5$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
660.32.60.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $A_4\times C_{55}$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
780.44.60.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $A_4\times C_{65}$ $2^{2} \cdot 3 \cdot 5 \cdot 13$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
780.45.60.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{65}:A_4$ $2^{2} \cdot 3 \cdot 5 \cdot 13$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
960.11366.60.a1 $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_2^6:C_{15}$ $2^{6} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
960.11367.60.a1 $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_2^2:F_{16}$ $2^{6} \cdot 3 \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1020.29.60.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $A_4\times C_{85}$ $2^{2} \cdot 3 \cdot 5 \cdot 17$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1140.32.60.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ ✓ $A_4\times C_{95}$ $2^{2} \cdot 3 \cdot 5 \cdot 19$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1140.33.60.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{95}:A_4$ $2^{2} \cdot 3 \cdot 5 \cdot 19$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1380.21.60.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ ✓ $A_4\times C_{115}$ $2^{2} \cdot 3 \cdot 5 \cdot 23$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1500.166.60.a1.a1 $C_5^2$ $5^{2}$ ✓ ✓ ✓ $C_{10}^2:C_{15}$ $2^{2} \cdot 3 \cdot 5^{3}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1620.423.60.a1.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_5\times C_3^3:A_4$ $2^{2} \cdot 3^{4} \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1740.29.60.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ ✓ $A_4\times C_{145}$ $2^{2} \cdot 3 \cdot 5 \cdot 29$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1860.23.60.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $A_4\times C_{31}:C_5$ $2^{2} \cdot 3 \cdot 5 \cdot 31$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1860.24.60.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $(C_2\times C_{62}):C_{15}$ $2^{2} \cdot 3 \cdot 5 \cdot 31$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1860.47.60.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ ✓ $A_4\times C_{155}$ $2^{2} \cdot 3 \cdot 5 \cdot 31$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
1860.48.60.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{155}:A_4$ $2^{2} \cdot 3 \cdot 5 \cdot 31$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
3600.dm.60.b1.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $C_5\times A_4\times A_5$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
7500.o.60.a1.a1 $C_5^3$ $5^{3}$ ✓ ✓ ✓ $C_5\wr A_4$ $2^{2} \cdot 3 \cdot 5^{4}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
21600.bg.60.a1.a1 $A_6$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_5\times A_4\times A_6$ $2^{5} \cdot 3^{3} \cdot 5^{2}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
79860.ba.60.a1.a1 $C_{11}^3$ $11^{3}$ $11$ ✓ ✓ ✓ $C_{11}^3:(C_5\times A_4)$ $2^{2} \cdot 3 \cdot 5 \cdot 11^{3}$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
31886460.b.60._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.(C_5\times A_4)$ $2^{2} \cdot 3^{13} \cdot 5$ $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓
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