Subgroups — C₅×#6432 #11765027

Order 1120.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₁₄	C₂	1	2	yes	maximal
2	C₄²×C₅×C₇	C₂	1	1	yes	maximal, characteristic
3	C₅×C₄⋊Dic₇	C₂	1	4	yes	maximal
4	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₇	C₂²	1	2	yes	—
6	C₂×C₅×Dic₇	C₂²	1	4	yes	—
7	C₅×Dic₁₄	—	2	4	no	—
8	#6432	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₄⋊Q₈	—	7	1	no	maximal, Hall
10	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
11	C₄×C₅×C₇	D₄	1	2	yes	—
12	C₄×C₅×C₇	Q₈	1	4	yes	complemented
13	C₅×Dic₇	—	2	4	no	—
14	C₂×Dic₁₄	C₂×C₅	1	2	yes	—
15	C₄²×C₇	C₂×C₅	1	1	yes	characteristic
16	C₄⋊Dic₇	C₂×C₅	1	4	yes	—
17	C₂×C₅×Q₈	—	7	2	no	—
18	C₅×C₄⋊C₄	—	7	4	no	—
19	C₄²×C₅	D₇	1	1	yes	characteristic
20	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
21	C₂×C₅×C₇	C₂×Q₈	1	2	yes	—
22	C₂×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
23	C₂×C₄×C₇	C₂²×C₅	1	2	yes	—
24	C₂×Dic₇	C₂²×C₅	1	4	yes	—
25	Dic₁₄	—	2	4	no	—
26	C₅×Q₈	—	14	4	no	—
27	C₂×C₄×C₅	—	7	4	no	—
28	C₂×C₄×C₅	C₂×D₇	1	2	yes	—
29	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
30	C₅×C₇	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
31	C₄⋊Q₈	—	7	1	no	Sylow
32	C₂²×C₇	C₂³×C₅	1	1	yes	characteristic
33	C₄×C₇	C₅×D₄	1	2	yes	—
34	C₄×C₇	C₅×Q₈	1	4	yes	complemented
35	Dic₇	—	2	4	no	—
36	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
37	C₄×C₅	—	14	4	no	—
38	C₄×C₅	Dic₁₄	1	4	yes	complemented
39	C₄×C₅	D₂₈	1	2	yes	—
40	C₂×Q₈	—	7	2	no	—
41	C₄⋊C₄	—	7	4	no	—
42	C₄²	C₅×D₇	1	1	yes	characteristic
43	C₂×C₇	C₂×C₅×D₄	1	1	yes	characteristic
44	C₂×C₇	C₂×C₅×Q₈	1	2	yes	—
45	C₂×C₅	C₂×Dic₁₄	1	2	yes	—
46	C₂×C₅	C₂×D₂₈	1	1	yes	characteristic
47	Q₈	—	14	4	no	—
48	C₂×C₄	—	7	4	no	—
49	C₂×C₄	C₂×C₅×D₇	1	2	yes	—
50	C₂×C₄	C₂×C₅×D₇	1	1	yes	characteristic
51	C₇	C₅×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
52	C₅	#6432	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²	C₂²×C₅×D₇	1	1	yes	characteristic
54	C₄	—	14	4	no	—
55	C₄	C₅×Dic₁₄	1	4	yes	complemented
56	C₄	C₅×D₂₈	1	2	yes	—
57	C₂	C₂×C₅×Dic₁₄	1	2	yes	—
58	C₂	C₂×C₅×D₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₇
commutator, cosocle	C₂²×C₇	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₇
Fitting	C₄²×C₅×C₇	C₂
socle, prime radical	C₂²×C₅×C₇	C₂³
hypercenter	C₄²×C₅	D₇
hypocenter	C₇	C₅×C₄⋊Q₈
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
8. #6432	C₅	direct (N × H)
12. C₄×C₅×C₇	Q₈	semidirect
30. C₅×C₇	C₄⋊Q₈	semidirect
34. C₄×C₇	C₅×Q₈	semidirect
38. C₄×C₅	Dic₁₄	semidirect
51. C₇	C₅×C₄⋊Q₈	semidirect
52. C₅	#6432	direct (N × H)
55. C₄	C₅×Dic₁₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Dic₁₄	2
C₄²×C₅×C₇	2
C₅×C₄⋊Dic₇	2
#6432	5
C₅×C₄⋊Q₈	7

Subgroups — C5×#6432 #11765027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6432 #11765027