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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 (50 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1400.100.1.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ ✓ $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_1$ $1$ ✓
2800.c.2.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ ✓ $D_{140}:C_{10}$ $2^{4} \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
2800.c.2.a1.b1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ ✓ $D_{140}:C_{10}$ $2^{4} \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
4200.b.3.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $D_{210}:C_{10}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $3$ $-$
4200.c.3.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $D_{70}:C_{30}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_3$ $3$ ✓
5600.a.4.d1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{140}:C_{20}$ $2^{5} \cdot 5^{2} \cdot 7$ $2^{2}$ $-$
5600.b.4.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $C_{40}.D_{70}$ $2^{5} \cdot 5^{2} \cdot 7$ $C_4$ $2^{2}$ ✓
5600.b.4.a1.b1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $C_{40}.D_{70}$ $2^{5} \cdot 5^{2} \cdot 7$ $C_4$ $2^{2}$ ✓
5600.f.4.f1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{280}:C_{10}$ $2^{5} \cdot 5^{2} \cdot 7$ $2^{2}$ $-$
5600.f.4.f1.b1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{280}:C_{10}$ $2^{5} \cdot 5^{2} \cdot 7$ $2^{2}$ $-$
8400.i.6.b1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 3$ $-$
8400.i.6.b1.b1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{420}:C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $2 \cdot 3$ $-$
8400.j.6.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $D_{140}:C_{30}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_6$ $2 \cdot 3$ ✓
8400.j.6.a1.b1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $D_{140}:C_{30}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ $C_6$ $2 \cdot 3$ ✓
9800.a.7.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $C_{70}\wr C_2$ $2^{3} \cdot 5^{2} \cdot 7^{2}$ $C_7$ $7$ ✓
9800.i.7.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $D_{490}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7^{2}$ $7$ $-$
11200.a.8._.K $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{40}.D_{140}$ $2^{6} \cdot 5^{2} \cdot 7$ $2^{3}$ $-$
11200.a.8._.O $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{40}.D_{140}$ $2^{6} \cdot 5^{2} \cdot 7$ $2^{3}$ $-$
12600.a.9.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{30}.D_{210}$ $2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7$ $3^{2}$ $-$
16800.d.12._.F $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{20}.D_{420}$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 7$ $2^{2} \cdot 3$ $-$
16800.e.12._.F $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{60}.D_{140}$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 7$ $2^{2} \cdot 3$ $-$
19600.a.14._.D $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $C_{140}.D_{70}$ $2^{4} \cdot 5^{2} \cdot 7^{2}$ $C_{14}$ $2 \cdot 7$ ✓
19600.a.14._.F $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $C_{140}.D_{70}$ $2^{4} \cdot 5^{2} \cdot 7^{2}$ $C_{14}$ $2 \cdot 7$ ✓
22400.a.16._.M $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{40}.D_{280}$ $2^{7} \cdot 5^{2} \cdot 7$ $2^{4}$ $-$
25200.d.18._.C $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{60}.D_{210}$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7$ $2 \cdot 3^{2}$ $-$
25200.d.18._.E $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{60}.D_{210}$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7$ $2 \cdot 3^{2}$ $-$
29400.a.21._.A $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{70}.D_{210}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ $3 \cdot 7$ $-$
29400.b.21._.A $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $D_{70}.C_{210}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ $C_{21}$ $3 \cdot 7$ ✓
39200.a.28._.Q $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{140}\wr C_2$ $2^{5} \cdot 5^{2} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
39200.b.28._.K $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $C_{280}.D_{70}$ $2^{5} \cdot 5^{2} \cdot 7^{2}$ $C_{28}$ $2^{2} \cdot 7$ ✓
39200.b.28._.M $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $C_{280}.D_{70}$ $2^{5} \cdot 5^{2} \cdot 7^{2}$ $C_{28}$ $2^{2} \cdot 7$ ✓
39200.c.28._.U $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{140}.D_{140}$ $2^{5} \cdot 5^{2} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
39200.c.28._.W $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{140}.D_{140}$ $2^{5} \cdot 5^{2} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
50400.a.36._.F $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{60}.D_{420}$ $2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7$ $2^{2} \cdot 3^{2}$ $-$
58800.c.42._.G $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{140}.D_{210}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ $2 \cdot 3 \cdot 7$ $-$
58800.c.42._.I $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{140}.D_{210}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ $2 \cdot 3 \cdot 7$ $-$
58800.e.42._.D $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $C_{420}.D_{70}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ $C_{42}$ $2 \cdot 3 \cdot 7$ ✓
58800.e.42._.F $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $C_{420}.D_{70}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ $C_{42}$ $2 \cdot 3 \cdot 7$ ✓
68600.a.49._.A $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{70}.D_{490}$ $2^{3} \cdot 5^{2} \cdot 7^{3}$ $7^{2}$ $-$
68600.b.49._.A $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $D_{70}.C_{490}$ $2^{3} \cdot 5^{2} \cdot 7^{3}$ $C_{49}$ $7^{2}$ ✓
78400.a.56._.BL $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{280}.D_{140}$ $2^{6} \cdot 5^{2} \cdot 7^{2}$ $2^{3} \cdot 7$ $-$
78400.a.56._.BP $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{280}.D_{140}$ $2^{6} \cdot 5^{2} \cdot 7^{2}$ $2^{3} \cdot 7$ $-$
88200.a.63.B $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{105}^2:D_4$ $2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2}$ $3^{2} \cdot 7$ $-$
117600.e.84.D $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{140}.D_{420}$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ $2^{2} \cdot 3 \cdot 7$ $-$
117600.f.84.F $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $D_{140}.C_{420}$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ $2^{2} \cdot 3 \cdot 7$ $-$
156800.a.112.L $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{280}.D_{280}$ $2^{7} \cdot 5^{2} \cdot 7^{2}$ $2^{4} \cdot 7$ $-$
176400.a.126._.G $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{420}.D_{210}$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2}$ $2 \cdot 3^{2} \cdot 7$ $-$
176400.a.126._.I $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{420}.D_{210}$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2}$ $2 \cdot 3^{2} \cdot 7$ $-$
480200.a.343._.A $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ $C_{245}^2:D_4$ $2^{3} \cdot 5^{2} \cdot 7^{4}$ $7^{3}$ $-$
3578400.a.2556.a1.a1 $D_{70}:C_{10}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ $C_{10}.\PGL(2,71)$ $2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 71$ $2^{2} \cdot 3^{2} \cdot 71$ $-$
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