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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 56 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
750.30.1.a1.a1 $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ ✓ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $C_1$ $1$ ✓
750.30.2.a1.a1 $C_5\wr C_3$ $3 \cdot 5^{3}$ ✓ ✓ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $C_2$ $2$ ✓
750.30.3.a1.a1 $C_5^3:C_2$ $2 \cdot 5^{3}$ ✓ ✓ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $C_3$ $3$ ✓
750.30.5.a1.a1 $C_5^2:C_6$ $2 \cdot 3 \cdot 5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $5$ $-$
750.30.6.a1.a1 $C_5^3$ $5^{3}$ $5$ ✓ ✓ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $C_6$ $2 \cdot 3$ ✓
750.30.10.a1.a1 $C_5^2:C_3$ $3 \cdot 5^{2}$ ✓ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $D_5$ $2 \cdot 5$
750.30.15.a1.a1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.a1.b1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.b1.a1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.b1.b1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.b1.c1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.b1.d1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.b1.e1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.b1.f1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.b1.g1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.b1.h1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.15.c1.a1 $C_5:D_5$ $2 \cdot 5^{2}$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5$ $-$
750.30.25.a1.a1 $C_3\times D_5$ $2 \cdot 3 \cdot 5$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $5^{2}$ $-$
750.30.30.a1.a1 $C_5^2$ $5^{2}$ ✓ ✓ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $C_3\times D_5$ $2 \cdot 3 \cdot 5$ ✓
750.30.30.b1.a1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.30.b1.b1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.30.c1.a1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.30.c1.b1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.30.c1.c1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.30.c1.d1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.30.c1.e1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.30.c1.f1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.30.c1.g1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.30.c1.h1 $C_5^2$ $5^{2}$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
750.30.50.a1.a1 $C_{15}$ $3 \cdot 5$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 5^{2}$ $-$
750.30.75.a1.a1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.b1.a1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.b1.b1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.c1.a1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.c1.b1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.c1.c1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.c1.d1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.c1.e1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.c1.f1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.c1.g1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.75.c1.h1 $D_5$ $2 \cdot 5$ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $3 \cdot 5^{2}$ $-$
750.30.125.a1.a1 $C_6$ $2 \cdot 3$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $5^{3}$ $-$
750.30.150.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $C_5^2:C_6$ $2 \cdot 3 \cdot 5^{2}$ ✓
750.30.150.b1.a1 $C_5$ $5$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5^{2}$ $-$
750.30.150.b1.b1 $C_5$ $5$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5^{2}$ $-$
750.30.150.c1.a1 $C_5$ $5$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5^{2}$ $-$
750.30.150.c1.b1 $C_5$ $5$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5^{2}$ $-$
750.30.150.c1.c1 $C_5$ $5$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5^{2}$ $-$
750.30.150.c1.d1 $C_5$ $5$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5^{2}$ $-$
750.30.150.c1.e1 $C_5$ $5$ ✓ $C_5^3:C_6$ $2 \cdot 3 \cdot 5^{3}$ $2 \cdot 3 \cdot 5^{2}$ $-$
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