Subgroups — C₅×#1159 #10587969

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	C₅×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×Dic₇	C₂	1	2	yes	maximal, complemented
4	C₄×C₅×D₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×C₇	C₂²	1	2	yes	—
7	C₂×C₅×D₇	C₂²	1	1	yes	characteristic
8	C₄×C₅×C₇	C₂²	1	1	yes	characteristic
9	C₅×Dic₇	C₂²	1	2	yes	—
10	C₅×Dic₇	C₂²	1	1	yes	characteristic
11	#1159	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×#41	—	7	1	no	maximal, Hall
13	C₂×C₅×C₇	—	2	2	no	—
14	C₂×C₅×C₇	C₂³	1	1	yes	characteristic
15	C₅×D₇	—	2	1	no	—
16	C₇×D₄	C₂×C₅	1	1	yes	characteristic, complemented
17	C₂²⋊D₇	C₂×C₅	1	2	yes	complemented
18	C₂×Dic₇	C₂×C₅	1	2	yes	complemented
19	C₄×D₇	C₂×C₅	1	1	yes	characteristic, complemented
20	Dic₁₄	C₂×C₅	1	1	yes	characteristic, complemented
21	C₅×Q₈	—	7	1	no	—
22	C₅×D₄	—	7	2	no	—
23	C₅×D₄	D₇	1	1	yes	characteristic, complemented
24	C₂×C₄×C₅	—	7	2	no	—
25	C₂×C₄×C₅	—	7	1	no	—
26	C₅×C₇	#41	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₇	C₂²×C₅	1	2	yes	—
28	C₂×D₇	C₂²×C₅	1	1	yes	characteristic
29	C₄×C₇	C₂²×C₅	1	1	yes	characteristic
30	Dic₇	C₂²×C₅	1	2	yes	—
31	Dic₇	C₂²×C₅	1	1	yes	characteristic
32	C₂²×C₅	—	7	1	no	—
33	C₂²×C₅	C₂×D₇	1	2	yes	—
34	C₄×C₅	—	7	1	no	—
35	C₄×C₅	—	7	2	no	—
36	C₄×C₅	C₂×D₇	1	1	yes	characteristic
37	#41	—	7	1	no	Sylow
38	C₂×C₇	—	2	2	no	—
39	C₂×C₇	C₂³×C₅	1	1	yes	characteristic
40	D₇	—	2	1	no	—
41	C₂×C₅	—	2	2	no	—
42	C₂×C₅	—	14	1	no	—
43	C₂×C₅	C₂²×D₇	1	1	yes	characteristic
44	Q₈	—	7	1	no	—
45	D₄	—	7	2	no	—
46	D₄	C₅×D₇	1	1	yes	characteristic, complemented
47	C₂×C₄	—	7	2	no	—
48	C₂×C₄	—	7	1	no	—
49	C₇	C₅×#41	1	1	yes	characteristic, complemented, Sylow
50	C₅	#1159	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²	—	7	1	no	—
52	C₂²	C₂×C₅×D₇	1	2	yes	—
53	C₄	—	7	1	no	—
54	C₄	—	7	2	no	—
55	C₄	C₂×C₅×D₇	1	1	yes	characteristic
56	C₂	—	2	2	no	—
57	C₂	—	14	1	no	—
58	C₂	C₂²×C₅×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²×D₇
commutator, cosocle	C₂×C₇	C₂³×C₅
Frattini	C₂	C₂²×C₅×D₇
Fitting	C₅×C₇×D₄	C₂
socle	C₂×C₅×C₇	C₂³
hypercenter	C₅×D₄	D₇
hypocenter	C₇	C₅×#41
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₅ ◁ C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₄	C₂	semidirect
2. C₅×C₂²⋊D₇	C₂	semidirect
3. C₂×C₅×Dic₇	C₂	semidirect
4. C₄×C₅×D₇	C₂	semidirect
5. C₅×Dic₁₄	C₂	semidirect
11. #1159	C₅	direct (N × H)
16. C₇×D₄	C₂×C₅	semidirect
17. C₂²⋊D₇	C₂×C₅	semidirect
18. C₂×Dic₇	C₂×C₅	semidirect
19. C₄×D₇	C₂×C₅	semidirect
20. Dic₁₄	C₂×C₅	semidirect
23. C₅×D₄	D₇	semidirect
26. C₅×C₇	#41	semidirect
46. D₄	C₅×D₇	semidirect
49. C₇	C₅×#41	semidirect
50. C₅	#1159	direct (N × H)

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
C₅×C₂²⋊D₇	2
C₂×C₅×Dic₇	2
C₄×C₅×D₇	2
C₅×Dic₁₄	2
#1159	5
C₅×#41	7

Subgroups — C5×#1159 #10587969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#1159 #10587969