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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 139 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
135.4.135.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_9:C_{15}$ $3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
270.22.135.a1.a1 $C_2$ $2$ $2$ ✓ ✓ ✓ ✓ $C_9:C_{30}$ $2 \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
405.3.135.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2:C_{45}$ $3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
405.3.135.b1.b1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2:C_{45}$ $3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
405.4.135.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_9:C_{45}$ $3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
405.4.135.b1.b1 $C_3$ $3$ ✓ ✓ ✓ $C_9:C_{45}$ $3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
405.4.135.b1.c1 $C_3$ $3$ ✓ ✓ ✓ $C_9:C_{45}$ $3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
405.13.135.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{45}:C_3^2$ $3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
405.13.135.a1.b1 $C_3$ $3$ ✓ ✓ ✓ $C_{45}:C_3^2$ $3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
405.13.135.a1.c1 $C_3$ $3$ ✓ ✓ ✓ $C_{45}:C_3^2$ $3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
540.30.135.a1.a1 $C_4$ $2^{2}$ $2$ ✓ ✓ ✓ ✓ $C_9:C_{60}$ $2^{2} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
540.58.135.a1.a1 $C_2^2$ $2^{2}$ $2$ ✓ ✓ ✓ $C_{45}:A_4$ $2^{2} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
540.60.135.a1.a1 $C_2^2$ $2^{2}$ $2$ ✓ ✓ ✓ $C_6^2.C_{15}$ $2^{2} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
540.79.135.a1.a1 $C_2^2$ $2^{2}$ $2$ ✓ ✓ ✓ ✓ $C_{18}:C_{30}$ $2^{2} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
675.4.135.a1.a1 $C_5$ $5$ ✓ ✓ ✓ ✓ $C_9:C_{75}$ $3^{3} \cdot 5^{2}$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
675.15.135.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_{45}:C_{15}$ $3^{3} \cdot 5^{2}$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
675.15.135.a1.b1 $C_5$ $5$ ✓ ✓ ✓ $C_{45}:C_{15}$ $3^{3} \cdot 5^{2}$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
675.15.135.a1.c1 $C_5$ $5$ ✓ ✓ ✓ $C_{45}:C_{15}$ $3^{3} \cdot 5^{2}$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
675.15.135.a1.d1 $C_5$ $5$ ✓ ✓ ✓ $C_{45}:C_{15}$ $3^{3} \cdot 5^{2}$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
675.15.135.a1.e1 $C_5$ $5$ ✓ ✓ ✓ $C_{45}:C_{15}$ $3^{3} \cdot 5^{2}$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
675.15.135.a1.f1 $C_5$ $5$ ✓ ✓ ✓ $C_{45}:C_{15}$ $3^{3} \cdot 5^{2}$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
810.55.135.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_3^2:C_{90}$ $2 \cdot 3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
810.55.135.b1.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_3^2:C_{90}$ $2 \cdot 3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
810.56.135.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_9:C_{90}$ $2 \cdot 3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
810.56.135.b1.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_9:C_{90}$ $2 \cdot 3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
810.56.135.b1.c1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_9:C_{90}$ $2 \cdot 3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
810.72.135.a1.a1 $S_3$ $2 \cdot 3$ ✓ ✓ $C_3^3.C_{30}$ $2 \cdot 3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
810.99.135.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{90}:C_3^2$ $2 \cdot 3^{4} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
945.4.135.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{315}:C_3$ $3^{3} \cdot 5 \cdot 7$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
945.5.135.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{315}:C_3$ $3^{3} \cdot 5 \cdot 7$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
945.7.135.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{105}.C_3^2$ $3^{3} \cdot 5 \cdot 7$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
945.11.135.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_9:C_{105}$ $3^{3} \cdot 5 \cdot 7$ $C_9:C_{15}$ $3^{3} \cdot 5$ ✓
1080.50.135.a1.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ $C_9:C_{120}$ $2^{3} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1080.164.135.a1.a1 $Q_8$ $2^{3}$ $2$ ✓ ✓ $C_{45}:\SL(2,3)$ $2^{3} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1080.166.135.a1.a1 $Q_8$ $2^{3}$ $2$ ✓ ✓ $C_5\times C_3^2.\SL(2,3)$ $2^{3} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1080.245.135.a1.a1 $C_2\times C_4$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ $C_{18}:C_{60}$ $2^{3} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1080.248.135.a1.a1 $D_4$ $2^{3}$ $2$ ✓ ✓ $C_{180}:C_6$ $2^{3} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1080.251.135.a1.a1 $Q_8$ $2^{3}$ $2$ ✓ ✓ $C_{180}.C_6$ $2^{3} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1080.341.135.a1.a1 $C_2^3$ $2^{3}$ $2$ ✓ ✓ ✓ $C_{90}:A_4$ $2^{3} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1080.343.135.a1.a1 $C_2^3$ $2^{3}$ $2$ ✓ ✓ ✓ $C_6^2.C_{30}$ $2^{3} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1080.362.135.a1 $C_2^3$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ $C_{30}.C_6^2$ $2^{3} \cdot 3^{3} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1215.2.135.b1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_{15}.C_9^2$ $3^{5} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1215.12.135.c1.a1 $C_9$ $3^{2}$ ✓ ✓ ✓ $C_3^2:C_{135}$ $3^{5} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1215.12.135.c1.b1 $C_9$ $3^{2}$ ✓ ✓ ✓ $C_3^2:C_{135}$ $3^{5} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1215.13.135.c1 $C_3^2$ $3^{2}$ ✓ ✓ $C_3^3:C_{45}$ $3^{5} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1215.14.135.c1.a1 $C_3^2$ $3^{2}$ ✓ ✓ $(C_3\times C_9):C_{45}$ $3^{5} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1215.14.135.c1.b1 $C_3^2$ $3^{2}$ ✓ ✓ $(C_3\times C_9):C_{45}$ $3^{5} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1215.15.135.c1.a1 $C_3^2$ $3^{2}$ ✓ ✓ $(C_3\times C_9):C_{45}$ $3^{5} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1215.15.135.c1.b1 $C_3^2$ $3^{2}$ ✓ ✓ $(C_3\times C_9):C_{45}$ $3^{5} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
1215.16.135.c1.a1 $C_9$ $3^{2}$ ✓ ✓ $C_3^3.C_{45}$ $3^{5} \cdot 5$ $C_9:C_{15}$ $3^{3} \cdot 5$
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