Subgroups — C₅×#6386 #11764483

Order 1120.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₅×C₇	C₄	1	1	yes	characteristic
4	C₅×C₇×C₈	C₄	1	1	yes	characteristic
5	C₅×C₇×C₈	C₂²	1	1	yes	characteristic
6	#6386	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×M₃₂	—	7	1	no	maximal, Hall
8	C₂²×C₅×C₇	C₈	1	1	yes	characteristic
9	C₄×C₅×C₇	C₈	1	1	yes	characteristic
10	C₄×C₅×C₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₇×C₈	C₂×C₅	1	1	yes	characteristic
12	C₇⋊C₁₆	C₂×C₅	1	2	yes	complemented
13	C₂×C₅×C₈	D₇	1	1	yes	characteristic
14	C₅×C₁₆	—	7	2	no	—
15	C₂×C₅×C₇	—	2	1	no	—
16	C₂×C₅×C₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₄×C₇	C₄×C₅	1	1	yes	characteristic
18	C₇×C₈	C₄×C₅	1	1	yes	characteristic
19	C₇×C₈	C₂²×C₅	1	1	yes	characteristic
20	C₂×C₄×C₅	Dic₇	1	1	yes	characteristic
21	C₅×C₈	Dic₇	1	1	yes	characteristic
22	C₅×C₈	C₂×D₇	1	1	yes	characteristic
23	C₅×C₇	M₃₂	1	1	yes	characteristic, complemented, Hall
24	M₃₂	—	7	1	no	Sylow
25	C₂²×C₇	C₅×C₈	1	1	yes	characteristic
26	C₄×C₇	C₅×C₈	1	1	yes	characteristic
27	C₄×C₇	C₂×C₄×C₅	1	1	yes	characteristic
28	C₂²×C₅	C₇⋊C₈	1	1	yes	characteristic
29	C₄×C₅	C₇⋊C₈	1	1	yes	characteristic
30	C₄×C₅	C₂×Dic₇	1	1	yes	characteristic
31	C₂×C₈	C₅×D₇	1	1	yes	characteristic
32	C₁₆	—	7	2	no	—
33	C₂×C₇	—	2	1	no	—
34	C₂×C₇	C₂×C₅×C₈	1	1	yes	characteristic
35	C₂×C₅	—	2	1	no	—
36	C₂×C₅	C₂×C₇⋊C₈	1	1	yes	characteristic
37	C₂×C₄	C₅×Dic₇	1	1	yes	characteristic
38	C₈	C₅×Dic₇	1	1	yes	characteristic
39	C₈	C₂×C₅×D₇	1	1	yes	characteristic
40	C₇	C₅×M₃₂	1	1	yes	characteristic, complemented, Sylow
41	C₅	#6386	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²	C₅×C₇⋊C₈	1	1	yes	characteristic
43	C₄	C₅×C₇⋊C₈	1	1	yes	characteristic
44	C₄	C₂×C₅×Dic₇	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	C₂×C₅×C₇⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₅×C₈	C₂×D₇
commutator	C₂×C₇	C₂×C₅×C₈
Frattini	C₈	C₂×C₅×D₇
Fitting	C₂×C₅×C₇×C₈	C₂
socle	C₂×C₅×C₇	C₂×C₈
prime radical	C₂²×C₅×C₇	C₈
cosocle	C₇×C₈	C₂²×C₅
hypercenter	C₂×C₅×C₈	D₇
hypocenter	C₇	C₅×M₃₂
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₅×C₈ ◁ C₂×C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₅×C₇⋊C₁₆	C₂	semidirect
6. #6386	C₅	direct (N × H)
12. C₇⋊C₁₆	C₂×C₅	semidirect
23. C₅×C₇	M₃₂	semidirect
40. C₇	C₅×M₃₂	semidirect
41. C₅	#6386	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇×C₈	2
C₅×C₇⋊C₁₆	2
#6386	5
C₅×M₃₂	7

Subgroups — C5×#6386 #11764483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6386 #11764483