Subgroups — #10587989

Order 560.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₃₅	C₂	1	2	yes	maximal, complemented
3	C₂×Dic₃₅	C₂	1	2	yes	maximal, complemented
4	C₄×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₇₀	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×C₇	C₂²	1	2	yes	—
7	C₂×D₃₅	C₂²	1	1	yes	characteristic
8	C₄×C₅×C₇	C₂²	1	1	yes	characteristic
9	Dic₃₅	C₂²	1	2	yes	—
10	Dic₃₅	C₂²	1	1	yes	characteristic
11	#1159	—	5	1	no	maximal, Hall
12	#711	—	7	1	no	maximal, Hall
13	C₂×C₅×C₇	—	2	2	no	—
14	C₂×C₅×C₇	C₂³	1	1	yes	characteristic
15	D₃₅	—	2	1	no	—
16	C₇×D₄	D₅	1	1	yes	characteristic, complemented
17	C₂²⋊D₇	—	5	2	no	—
18	C₂×Dic₇	—	5	2	no	—
19	C₄×D₇	—	5	1	no	—
20	Dic₁₄	—	5	1	no	—
21	C₅×D₄	D₇	1	1	yes	characteristic, complemented
22	C₂²⋊D₅	—	7	2	no	—
23	C₂×Dic₅	—	7	2	no	—
24	C₄×D₅	—	7	1	no	—
25	Dic₁₀	—	7	1	no	—
26	C₅×C₇	#41	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₇	C₂×D₅	1	2	yes	—
28	C₂×D₇	—	5	1	no	—
29	C₄×C₇	C₂×D₅	1	1	yes	characteristic
30	Dic₇	—	5	2	no	—
31	Dic₇	—	5	1	no	—
32	C₂²×C₅	C₂×D₇	1	2	yes	—
33	C₂×D₅	—	7	1	no	—
34	C₄×C₅	C₂×D₇	1	1	yes	characteristic
35	Dic₅	—	7	2	no	—
36	Dic₅	—	7	1	no	—
37	#41	—	35	1	no	Sylow
38	C₂×C₇	—	2	2	no	—
39	C₂×C₇	C₂²×D₅	1	1	yes	characteristic
40	D₇	—	10	1	no	—
41	C₂×C₅	—	2	2	no	—
42	C₂×C₅	C₂²×D₇	1	1	yes	characteristic
43	D₅	—	14	1	no	—
44	Q₈	—	35	1	no	—
45	D₄	—	35	2	no	—
46	D₄	D₃₅	1	1	yes	characteristic, complemented
47	C₂×C₄	—	35	2	no	—
48	C₂×C₄	—	35	1	no	—
49	C₇	#711	1	1	yes	characteristic, complemented, Sylow
50	C₅	#1159	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	35	1	no	—
52	C₂²	C₂×D₃₅	1	2	yes	—
53	C₄	—	35	1	no	—
54	C₄	—	35	2	no	—
55	C₄	C₂×D₃₅	1	1	yes	characteristic
56	C₂	—	2	2	no	—
57	C₂	—	70	1	no	—
58	C₂	C₂²×D₃₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×D₃₅
commutator, socle, cosocle	C₂×C₅×C₇	C₂³
Fitting	C₅×C₇×D₄	C₂
hypercenter	D₄	D₃₅
hypocenter	C₅×C₇	#41
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₄	C₂	semidirect
2. C₂²⋊D₃₅	C₂	semidirect
3. C₂×Dic₃₅	C₂	semidirect
4. C₄×D₃₅	C₂	semidirect
5. Dic₇₀	C₂	semidirect
16. C₇×D₄	D₅	semidirect
21. C₅×D₄	D₇	semidirect
26. C₅×C₇	#41	semidirect
46. D₄	D₃₅	semidirect
49. C₇	#711	semidirect
50. C₅	#1159	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×D₄	2
C₂²⋊D₃₅	2
C₂×Dic₃₅	2
C₄×D₃₅	2
Dic₇₀	2
#1159	5
#711	7