Subgroups — C₇×#63306 #14519965

Order 1960.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×C₇×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₇²	C₂²	1	1	yes	characteristic
5	C₇×D₃₅	—	2	1	no	—
6	C₅×C₇×D₇	—	2	1	no	—
7	C₇×D₂₈	—	5	1	no	maximal, Hall
8	C₇×C₂²⋊D₅	—	7	1	no	maximal
9	#63306	C₇	1	1	yes	maximal, characteristic, direct product factor
10	C₅×C₇²	D₄	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×D₇	—	5	1	no	—
12	C₂×C₇×D₇	D₅	1	1	yes	characteristic, complemented
13	C₄×C₇²	—	5	1	no	—
14	C₂²×C₅×C₇	—	7	1	no	—
15	C₂×D₃₅	C₂×C₇	1	1	yes	characteristic, complemented
16	C₂×C₇×D₅	—	7	1	no	—
17	C₂×C₅×D₇	C₂×C₇	1	1	yes	characteristic, complemented
18	C₇×Dic₅	—	2	3	no	—
19	C₇×Dic₅	D₇	1	1	yes	characteristic, complemented
20	C₇×Dic₅	C₂×C₇	1	1	yes	characteristic, complemented
21	C₂×C₇²	C₂×D₅	1	1	yes	characteristic
22	C₇×D₇	—	2	1	no	—
23	C₇×D₇	—	10	1	no	—
24	C₂×C₅×C₇	—	2	3	no	—
25	C₂×C₅×C₇	—	14	1	no	—
26	C₂×C₅×C₇	C₂×D₇	1	1	yes	characteristic
27	C₂×C₅×C₇	C₂²×C₇	1	1	yes	characteristic
28	D₃₅	—	2	1	no	—
29	C₅×D₇	—	2	1	no	—
30	C₇×D₅	—	14	1	no	—
31	C₇×D₄	—	35	1	no	—
32	D₂₈	—	5	1	no	—
33	C₇²	C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
34	C₂²⋊D₅	—	7	1	no	Hall
35	C₅×C₇	—	2	3	no	—
36	C₅×C₇	D₂₈	1	1	yes	characteristic, complemented
37	C₅×C₇	C₇×D₄	1	1	yes	characteristic, complemented
38	C₂²×C₇	—	7	1	no	—
39	C₂²×C₇	—	35	1	no	—
40	C₂×D₇	—	5	1	no	—
41	C₂×D₇	C₇×D₅	1	1	yes	characteristic, complemented
42	C₄×C₇	—	5	1	no	—
43	C₄×C₇	—	5	1	no	—
44	C₄×C₇	—	10	3	no	—
45	C₂²×C₅	—	7	1	no	—
46	C₂×D₅	—	7	1	no	—
47	Dic₅	C₇×D₇	1	1	yes	characteristic, complemented
48	C₂×C₇	—	2	3	no	—
49	C₂×C₇	—	14	1	no	—
50	C₂×C₇	—	70	1	no	—
51	C₂×C₇	D₅×D₇	1	1	yes	characteristic
52	C₂×C₇	C₂×C₇×D₅	1	1	yes	characteristic
53	D₇	—	2	1	no	—
54	D₇	—	10	1	no	—
55	C₂×C₅	—	14	1	no	—
56	C₂×C₅	C₂×C₇×D₇	1	1	yes	characteristic
57	D₅	—	14	1	no	—
58	D₄	—	35	1	no	Sylow
59	C₇	—	2	3	no	—
60	C₇	#63306	1	1	yes	characteristic, direct product factor
61	C₇	C₇×C₂²⋊D₅	1	1	yes	characteristic, complemented
62	C₅	C₇×D₂₈	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	7	1	no	—
64	C₂²	—	35	1	no	—
65	C₄	—	5	1	no	—
66	C₂	—	14	1	no	—
67	C₂	—	70	1	no	—
68	C₂	C₇×D₅×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇	D₅×D₇
commutator, cosocle	C₂×C₅×C₇	C₂²×C₇
Frattini	C₂	C₇×D₅×D₇
Fitting, socle	C₂×C₅×C₇²	C₂²
hypocenter	C₅×C₇	C₇×D₄
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×D₃₅	C₂	semidirect
2. C₂×C₅×C₇×D₇	C₂	semidirect
3. C₇²×Dic₅	C₂	semidirect
9. #63306	C₇	direct (N × H)
10. C₅×C₇²	D₄	semidirect
12. C₂×C₇×D₇	D₅	semidirect
15. C₂×D₃₅	C₂×C₇	semidirect
17. C₂×C₅×D₇	C₂×C₇	semidirect
19. C₇×Dic₅	D₇	semidirect
20. C₇×Dic₅	C₂×C₇	semidirect
33. C₇²	C₂²⋊D₅	semidirect
36. C₅×C₇	D₂₈	semidirect
37. C₅×C₇	C₇×D₄	semidirect
41. C₂×D₇	C₇×D₅	semidirect
47. Dic₅	C₇×D₇	semidirect
60. C₇	#63306	direct (N × H)
61. C₇	C₇×C₂²⋊D₅	semidirect
62. C₅	C₇×D₂₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×D₃₅	2
C₂×C₅×C₇×D₇	2
C₇²×Dic₅	2
C₇×D₂₈	5
C₇×C₂²⋊D₅	7
#63306	7

Subgroups — C7×#63306 #14519965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#63306 #14519965