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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 524 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
81000.bb.1.a1.a1 $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ ✓ ✓ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_1$ $1$ ✓
81000.bb.2.a1.a1 $C_{15}^3.A_4$ $2^{2} \cdot 3^{4} \cdot 5^{3}$ ✓ ✓ ✓ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_2$ $2$ ✓
81000.bb.3.a1.a1 $C_{15}^3.D_4$ $2^{3} \cdot 3^{3} \cdot 5^{3}$ ✓ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3$ $-$
81000.bb.4.a1.a1 $C_{15}\wr S_3$ $2 \cdot 3^{4} \cdot 5^{3}$ ✓ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2}$ $-$
81000.bb.6.a1.a1 $C_{15}^3.C_2^2$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $S_3$ $2 \cdot 3$
81000.bb.6.b1.a1 $C_{15}\times C_5^2:S_3^2$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3$ $-$
81000.bb.6.c1.a1 $C_{15}^3.C_4$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3$ $-$
81000.bb.8.a1.a1 $C_{15}\wr C_3$ $3^{4} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{3}$ $-$
81000.bb.9.a1.a1 $C_5^3.S_3\wr C_2$ $2^{3} \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3^{2}$ $-$
81000.bb.12.a1.a1 $C_{15}\times C_{15}\times D_{15}$ $2 \cdot 3^{3} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3$ $-$
81000.bb.12.b1.a1 $C_5\times C_{15}^2:S_3$ $2 \cdot 3^{3} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3$ $-$
81000.bb.12.c1.a1 $C_{15}\times C_{15}:D_{15}$ $2 \cdot 3^{3} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3$ $-$
81000.bb.15.a1.a1 $C_{15}^2.C_3:D_4$ $2^{3} \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3 \cdot 5$ $-$
81000.bb.18.a1.a1 $C_{15}\times D_5\times D_{15}$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.bb.18.b1.a1 $C_5\times C_5^2:S_3^2$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.bb.18.c1.a1 $C_5^3:(C_3:S_3.C_2)$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.bb.18.d1.a1 $C_5^3:S_3^2$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.bb.20.a1.a1 $(C_3\times C_{15}^2):S_3$ $2 \cdot 3^{4} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 5$ $-$
81000.bb.24.a1.a1 $C_{15}^3$ $3^{3} \cdot 5^{3}$ ✓ ✓ ✓ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $S_4$ $2^{3} \cdot 3$
81000.bb.24.b1.a1 $C_{15}^2:C_{15}$ $3^{3} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{3} \cdot 3$ $-$
81000.bb.24.c1.a1 $C_{15}^2.C_{15}$ $3^{3} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{3} \cdot 3$ $-$
81000.bb.27.a1.a1 $C_5^3:(C_3:D_4)$ $2^{3} \cdot 3 \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3^{3}$ $-$
81000.bb.27.b1.a1 $C_5^3:S_4$ $2^{3} \cdot 3 \cdot 5^{3}$ ✓ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3^{3}$ $-$
81000.bb.30.a1.a1 $C_{15}\times S_3\times D_{15}$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
81000.bb.30.b1.a1 $C_3\times C_5^2:S_3^2$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
81000.bb.30.c1.a1 $C_5^2:(C_3^2:(C_3:C_4))$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
81000.bb.30.d1.a1 $C_5^2:(C_3^2:(C_3:C_4))$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
81000.bb.30.e1.a1 $C_5^2:(C_3^3:C_2^2)$ $2^{2} \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3 \cdot 5$ $-$
81000.bb.36.a1.a1 $C_3\times C_{15}\times C_5\times D_5$ $2 \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2}$ $-$
81000.bb.36.b1.a1 $C_5\times C_{15}\times D_{15}$ $2 \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2}$ $-$
81000.bb.36.c1.a1 $C_3\times C_5\wr S_3$ $2 \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2}$ $-$
81000.bb.36.d1.a1 $C_{15}\times C_5\times D_{15}$ $2 \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2}$ $-$
81000.bb.36.e1.a1 $C_5\times C_{15}\times D_{15}$ $2 \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2}$ $-$
81000.bb.36.f1.a1 $C_{15}\times C_5:D_{15}$ $2 \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2}$ $-$
81000.bb.36.g1.a1 $C_{15}\times C_5:D_{15}$ $2 \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2}$ $-$
81000.bb.36.h1.a1 $C_5\times C_{15}:D_{15}$ $2 \cdot 3^{2} \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2}$ $-$
81000.bb.40.a1.a1 $C_{15}^2.C_3^2$ $3^{4} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{3} \cdot 5$ $-$
81000.bb.45.a1.a1 $D_{15}\wr C_2$ $2^{3} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
81000.bb.54.a1.a1 $C_{15}\times D_5^2$ $2^{2} \cdot 3 \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{3}$ $-$
81000.bb.54.b1.a1 $C_5^2:D_{30}$ $2^{2} \cdot 3 \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{3}$ $-$
81000.bb.54.c1.a1 $(C_5\times C_{15}):F_5$ $2^{2} \cdot 3 \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{3}$ $-$
81000.bb.54.d1.a1 $C_5^3:A_4$ $2^{2} \cdot 3 \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{3}$ $-$
81000.bb.54.e1.a1 $C_5^2:D_{30}$ $2^{2} \cdot 3 \cdot 5^{3}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{3}$ $-$
81000.bb.60.a1.a1 $S_3\times C_{15}^2$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
81000.bb.60.b1.a1 $C_{15}^2:C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
81000.bb.60.c1.a1 $C_{15}^2:C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
81000.bb.60.d1.a1 $C_{15}^2:C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
81000.bb.60.e1.a1 $C_{15}^2:C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
81000.bb.60.f1.a1 $C_{15}^2:S_3$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
81000.bb.60.g1.a1 $C_{15}^2:C_6$ $2 \cdot 3^{3} \cdot 5^{2}$ $C_{15}^3.S_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
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