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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 124 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
4500.n.1.a1.a1 $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ ✓ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_1$ $1$ ✓
4500.n.2.a1.a1 $C_5^3:C_{18}$ $2 \cdot 3^{2} \cdot 5^{3}$ ✓ ✓ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_2$ $2$ ✓
4500.n.3.a1.a1 $(C_5\times C_{15}):F_5$ $2^{2} \cdot 3 \cdot 5^{3}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3$ $-$
4500.n.4.a1.a1 $C_5^2:C_{45}$ $3^{2} \cdot 5^{3}$ ✓ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_4$ $2^{2}$ ✓
4500.n.5.a1.a1 $C_5^2:C_9:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{2}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $5$ $-$
4500.n.6.a1.a1 $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ ✓ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $S_3$ $2 \cdot 3$
4500.n.9.a1.a1 $C_5^3:C_4$ $2^{2} \cdot 5^{3}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3^{2}$ $-$
4500.n.10.a1.a1 $C_5^2:C_{18}$ $2 \cdot 3^{2} \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 5$ $-$
4500.n.12.a1.a1 $C_5^2\times C_{15}$ $3 \cdot 5^{3}$ ✓ ✓ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_3:C_4$ $2^{2} \cdot 3$
4500.n.15.a1.a1 $C_{15}:F_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5$ $-$
4500.n.15.b1.a1 $C_{15}:F_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5$ $-$
4500.n.15.c1.a1 $C_{15}:F_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5$ $-$
4500.n.15.c1.b1 $C_{15}:F_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5$ $-$
4500.n.15.c1.c1 $C_{15}:F_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5$ $-$
4500.n.15.c1.d1 $C_{15}:F_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5$ $-$
4500.n.15.d1.a1 $C_{15}:F_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5$ $-$
4500.n.18.a1.a1 $C_5^3:C_2$ $2 \cdot 5^{3}$ ✓ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $D_9$ $2 \cdot 3^{2}$
4500.n.20.a1.a1 $C_5^2:C_9$ $3^{2} \cdot 5^{2}$ ✓ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $F_5$ $2^{2} \cdot 5$
4500.n.25.a1.a1 $C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $5^{2}$ $-$
4500.n.30.a1.a1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
4500.n.30.b1.a1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
4500.n.30.c1.a1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
4500.n.30.c1.b1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
4500.n.30.d1.a1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
4500.n.30.d1.b1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
4500.n.30.d1.c1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
4500.n.30.d1.d1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
4500.n.30.e1.a1 $C_{15}:D_5$ $2 \cdot 3 \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
4500.n.36.a1.a1 $C_5^3$ $5^{3}$ $5$ ✓ ✓ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_9:C_4$ $2^{2} \cdot 3^{2}$
4500.n.45.a1.a1 $C_5:F_5$ $2^{2} \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
4500.n.45.b1.a1 $C_5:F_5$ $2^{2} \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
4500.n.45.c1.a1 $C_5:F_5$ $2^{2} \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
4500.n.45.c1.b1 $C_5:F_5$ $2^{2} \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
4500.n.45.c1.c1 $C_5:F_5$ $2^{2} \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
4500.n.45.c1.d1 $C_5:F_5$ $2^{2} \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
4500.n.45.d1.a1 $C_5:F_5$ $2^{2} \cdot 5^{2}$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
4500.n.50.a1.a1 $C_9\times D_5$ $2 \cdot 3^{2} \cdot 5$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2 \cdot 5^{2}$ $-$
4500.n.60.a1.a1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ ✓ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}:C_4$ $2^{2} \cdot 3 \cdot 5$
4500.n.60.b1.a1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
4500.n.60.c1.a1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
4500.n.60.d1.a1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
4500.n.60.d1.b1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
4500.n.60.e1.a1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
4500.n.60.e1.b1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
4500.n.60.e1.c1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
4500.n.60.e1.d1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
4500.n.75.a1.a1 $C_{15}:C_4$ $2^{2} \cdot 3 \cdot 5$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
4500.n.75.b1.a1 $C_{15}:C_4$ $2^{2} \cdot 3 \cdot 5$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
4500.n.75.b1.b1 $C_{15}:C_4$ $2^{2} \cdot 3 \cdot 5$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
4500.n.75.b1.c1 $C_{15}:C_4$ $2^{2} \cdot 3 \cdot 5$ $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
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