Subgroups — #14519970

Order 1960.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic
2	C₇²×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₇²	C₂²	1	1	yes	characteristic
5	C₅⋊(C₇⋊D₇)	C₄	1	2	yes	complemented
6	C₄×C₇⋊D₇	—	5	1	no	maximal, Hall
7	#63304	—	7	8	no	maximal
8	C₅×C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇⋊D₇	—	5	1	no	—
10	C₄×C₇²	—	5	1	no	—
11	C₇⋊Dic₇	D₅	1	1	yes	characteristic, complemented
12	C₂×D₃₅	—	7	8	no	—
13	C₅×Dic₇	—	7	8	no	—
14	C₇×Dic₅	D₇	1	8	yes	complemented
15	C₂×C₇²	C₂×D₅	1	1	yes	characteristic
16	C₇⋊D₇	—	5	2	no	—
17	C₂×C₅×C₇	C₂×D₇	1	8	yes	—
18	D₃₅	—	7	16	no	—
19	C₄×D₇	—	35	8	no	—
20	C₇²	C₄×D₅	1	1	yes	characteristic, complemented, Sylow
21	C₄×D₅	—	49	1	no	Hall
22	C₅×C₇	C₄×D₇	1	8	yes	complemented
23	C₂×D₇	—	35	8	no	—
24	C₄×C₇	—	5	8	no	—
25	Dic₇	—	7	8	no	—
26	C₂×D₅	—	49	1	no	—
27	C₄×C₅	—	49	1	no	—
28	Dic₅	C₇⋊D₇	1	1	yes	characteristic, complemented
29	C₂×C₇	D₅×D₇	1	8	yes	—
30	D₇	—	35	16	no	—
31	C₂×C₅	C₂×C₇⋊D₇	1	1	yes	characteristic
32	D₅	—	49	2	no	—
33	C₂×C₄	—	245	1	no	Sylow
34	C₇	#63304	1	8	yes	complemented
35	C₅	C₄×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
36	C₂²	—	245	1	no	—
37	C₄	—	5	1	no	—
38	C₄	—	49	1	no	—
39	C₂	—	245	2	no	—
40	C₂	D₅×C₇⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×C₇⋊D₇
commutator, hypocenter	C₅×C₇²	C₂×C₄
Fitting, socle, cosocle	C₂×C₅×C₇²	C₂²
prime radical	C₂×C₅⋊(C₇⋊D₇)	C₂
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.