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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 936 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
81000.t.1.a1 $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_1$ $1$ ✓
81000.t.2.a1 $C_{15}\wr S_3:C_2$ $2^{2} \cdot 3^{4} \cdot 5^{3}$ ✓ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_2$ $2$ ✓
81000.t.2.b1 $C_{15}^3.C_{12}$ $2^{2} \cdot 3^{4} \cdot 5^{3}$ ✓ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_2$ $2$ ✓
81000.t.2.c1 $C_{15}\wr C_3:C_4$ $2^{2} \cdot 3^{4} \cdot 5^{3}$ ✓ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_2$ $2$ ✓
81000.t.3.a1 $C_{15}^3.C_2^2.C_2$ $2^{3} \cdot 3^{3} \cdot 5^{3}$ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3$ $-$
81000.t.3.b1 $C_{15}^2:(S_3\times F_5)$ $2^{3} \cdot 3^{3} \cdot 5^{3}$ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3$ $-$
81000.t.4.a1 $C_{15}\wr S_3$ $2 \cdot 3^{4} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_4$ $2^{2}$ ✓
81000.t.4.b1 $C_{15}\wr C_3:C_2$ $2 \cdot 3^{4} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_2^2$ $2^{2}$ ✓
81000.t.4.c1 $(C_3\times C_{15}^2):D_{15}$ $2 \cdot 3^{4} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_4$ $2^{2}$ ✓
81000.t.5.a1 $C_{15}^2:C_6.D_6$ $2^{3} \cdot 3^{4} \cdot 5^{2}$ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $5$ $-$
81000.t.6.a1 $(C_5\times C_{15}^2):D_6$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $S_3$ $2 \cdot 3$
81000.t.6.b1 $C_{15}^3.C_4$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $S_3$ $2 \cdot 3$
81000.t.6.c1 $C_3^2\times C_5^3:D_6$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3$ $-$
81000.t.6.d1 $(C_5\times C_{15}^2).C_{12}$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3$ $-$
81000.t.6.e1 $(C_5\times C_{15}^2):C_{12}$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3$ $-$
81000.t.6.f1 $C_{15}^2:C_{15}:C_4$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3$ $-$
81000.t.6.g1 $C_5^2:C_{45}:C_{12}$ $2^{2} \cdot 3^{3} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3$ $-$
81000.t.8.a1 $C_{15}\wr C_3$ $3^{4} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_2\times C_4$ $2^{3}$ ✓
81000.t.9.a1 $C_5^3.C_6^2.C_2$ $2^{3} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3^{2}$ $-$
81000.t.9.b1 $C_5^3.(C_6\times S_3).C_2$ $2^{3} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3^{2}$ $-$
81000.t.9.c1 $C_5^3:C_6.D_6$ $2^{3} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3^{2}$ $-$
81000.t.9.d1 $C_5^3.(C_6\times S_3).C_2$ $2^{3} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3^{2}$ $-$
81000.t.10.a1 $(C_3\times C_{15}^2):D_6$ $2^{2} \cdot 3^{4} \cdot 5^{2}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 5$ $-$
81000.t.10.b1 $(C_3\times C_{15}^2):C_{12}$ $2^{2} \cdot 3^{4} \cdot 5^{2}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 5$ $-$
81000.t.10.c1 $C_{15}^2:C_6.S_3$ $2^{2} \cdot 3^{4} \cdot 5^{2}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 5$ $-$
81000.t.12.a1 $C_5\times C_{15}^2:S_3$ $2 \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_3:C_4$ $2^{2} \cdot 3$
81000.t.12.b1 $C_3^3\times C_5^2:D_5$ $2 \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $D_6$ $2^{2} \cdot 3$
81000.t.12.c1 $(C_5\times C_{15}^2):C_6$ $2 \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $D_6$ $2^{2} \cdot 3$
81000.t.12.d1 $C_{15}^2:D_{15}$ $2 \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $C_3:C_4$ $2^{2} \cdot 3$
81000.t.12.e1 $C_{15}^2\times D_{15}$ $2 \cdot 3^{3} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3$ $-$
81000.t.12.f1 $(C_5\times C_{15}^2).C_6$ $2 \cdot 3^{3} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3$ $-$
81000.t.12.g1 $C_3^2\times C_5^3:S_3$ $2 \cdot 3^{3} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3$ $-$
81000.t.15.a1 $C_{15}^2.C_6.C_2^2$ $2^{3} \cdot 3^{3} \cdot 5^{2}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3 \cdot 5$ $-$
81000.t.15.b1 $C_{15}^2.C_6.C_2^2$ $2^{3} \cdot 3^{3} \cdot 5^{2}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3 \cdot 5$ $-$
81000.t.15.c1 $C_{15}^2.C_6.C_2^2$ $2^{3} \cdot 3^{3} \cdot 5^{2}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3 \cdot 5$ $-$
81000.t.15.d1 $C_{15}^2.C_6.C_2^2$ $2^{3} \cdot 3^{3} \cdot 5^{2}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3 \cdot 5$ $-$
81000.t.15.e1 $C_{15}^2:(C_4\times S_3)$ $2^{3} \cdot 3^{3} \cdot 5^{2}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $3 \cdot 5$ $-$
81000.t.18.a1 $C_3^2\times D_5\times C_5:D_5$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.b1 $C_3\times C_5^3:D_6$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.c1 $C_3\times C_5^3:D_6$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.d1 $C_3\times C_5^3:D_6$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.e1 $C_5^3:(C_3^2:C_4)$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.f1 $C_5^3:(C_3\times C_3:C_4)$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.g1 $C_5^3:(C_3^2:C_4)$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.h1 $C_5^3:(C_3^2:C_4)$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.i1 $(C_5^2\times C_{15}):C_{12}$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.j1 $C_5^3:C_3^2:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.k1 $C_5^2:C_{45}:C_4$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.l1 $C_5^3:(C_3^2:C_4)$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
81000.t.18.m1 $C_3\times C_5^3:(C_3:C_4)$ $2^{2} \cdot 3^{2} \cdot 5^{3}$ $C_{15}\wr S_3:C_4$ $2^{3} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2}$ $-$
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