Subgroups — C₂×C₇×D₅⋊C₈ #11765342

Order 1120.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#170	C₂	1	2	yes	maximal, complemented
3	C₇×D₅⋊C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₇×D₅	C₄	1	1	yes	characteristic
5	C₂×C₄×C₅×C₇	C₄	1	1	yes	characteristic
6	C₂×C₇×Dic₅	C₂²	1	1	yes	characteristic
7	C₄×C₇×D₅	C₄	1	2	yes	—
8	C₄×C₇×D₅	C₂²	1	2	yes	—
9	C₇×#170	C₂²	1	4	yes	complemented
10	C₂²×C₇×C₈	—	5	1	no	maximal, Hall
11	C₂×D₅⋊C₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₅×C₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₇×D₅	C₈	1	4	yes	complemented
14	C₂×C₇×D₅	C₂×C₄	1	2	yes	—
15	C₄×C₅×C₇	C₂×C₄	1	2	yes	—
16	C₇×Dic₅	C₂×C₄	1	1	yes	characteristic
17	C₇×Dic₅	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₇	—	5	1	no	—
19	C₂×C₇×C₈	—	5	4	no	—
20	C₂×C₇×C₈	—	5	2	no	—
21	C₂×C₄×D₅	C₂×C₇	1	1	yes	characteristic
22	C₂×#170	C₂×C₇	1	2	yes	complemented
23	D₅⋊C₈	C₂×C₇	1	4	yes	direct product factor
24	C₂×C₅×C₇	C₂×C₈	1	2	yes	complemented
25	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
26	C₇×D₅	C₂×C₈	1	4	yes	complemented
27	C₂³×C₇	—	5	1	no	—
28	C₂×C₄×C₇	—	5	1	no	—
29	C₂×C₄×C₇	—	5	2	no	—
30	C₂×C₄×C₇	—	5	2	no	—
31	C₂×C₄×C₇	AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₇×C₈	—	5	4	no	—
33	C₂²×D₅	C₄×C₇	1	1	yes	characteristic
34	C₂×C₄×C₅	C₄×C₇	1	1	yes	characteristic
35	C₂×Dic₅	C₂²×C₇	1	1	yes	characteristic
36	C₄×D₅	C₄×C₇	1	2	yes	—
37	C₄×D₅	C₂²×C₇	1	2	yes	—
38	#170	C₂²×C₇	1	4	yes	complemented
39	C₅×C₇	C₂²×C₈	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₈	—	5	1	no	Sylow
41	C₂²×C₇	—	5	4	no	—
42	C₂²×C₇	—	5	2	no	—
43	C₂²×C₇	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
44	C₄×C₇	—	5	1	no	—
45	C₄×C₇	—	5	1	no	—
46	C₄×C₇	C₂×AGL(1,𝔽₅)	1	2	yes	—
47	C₂²×C₅	C₂×C₄×C₇	1	1	yes	characteristic
48	C₂×D₅	C₇×C₈	1	4	yes	complemented
49	C₂×D₅	C₂×C₄×C₇	1	2	yes	—
50	C₄×C₅	C₂×C₄×C₇	1	2	yes	—
51	Dic₅	C₂×C₄×C₇	1	1	yes	characteristic
52	Dic₅	C₂³×C₇	1	1	yes	characteristic
53	C₂²×C₄	—	5	1	no	—
54	C₂×C₈	—	5	4	no	—
55	C₂×C₈	—	5	2	no	—
56	C₂×C₇	—	5	4	no	—
57	C₂×C₇	D₅⋊C₈	1	2	yes	direct product factor
58	C₂×C₇	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
59	C₂×C₅	C₂×C₇×C₈	1	2	yes	complemented
60	C₂×C₅	C₂²×C₄×C₇	1	1	yes	characteristic
61	D₅	C₂×C₇×C₈	1	4	yes	complemented
62	C₂³	—	5	1	no	—
63	C₂×C₄	—	5	1	no	—
64	C₂×C₄	—	5	2	no	—
65	C₂×C₄	—	5	2	no	—
66	C₂×C₄	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic
67	C₈	—	5	4	no	—
68	C₇	C₂×D₅⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
69	C₅	C₂²×C₇×C₈	1	1	yes	characteristic, complemented, Sylow
70	C₂²	—	5	4	no	—
71	C₂²	—	5	2	no	—
72	C₂²	C₂×C₇×AGL(1,𝔽₅)	1	1	yes	characteristic
73	C₄	—	5	1	no	—
74	C₄	—	5	1	no	—
75	C₄	C₂×C₇×AGL(1,𝔽₅)	1	2	yes	—
76	C₂	—	5	4	no	—
77	C₂	C₇×D₅⋊C₈	1	2	yes	direct product factor
78	C₂	C₂²×C₇×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₇	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₂²×C₇×C₈
Frattini	C₂	C₂²×C₇×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅×C₇	C₄
socle	C₂²×C₅×C₇	C₂×C₄
prime radical	C₂²×C₇×D₅	C₄
cosocle	Dic₅	C₂³×C₇
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₇

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#170	C₂	semidirect
3. C₇×D₅⋊C₈	C₂	direct (N × H)
9. C₇×#170	C₂²	semidirect
11. C₂×D₅⋊C₈	C₇	direct (N × H)
13. C₂×C₇×D₅	C₈	semidirect
22. C₂×#170	C₂×C₇	semidirect
23. D₅⋊C₈	C₂×C₇	direct (N × H)
24. C₂×C₅×C₇	C₂×C₈	semidirect
26. C₇×D₅	C₂×C₈	semidirect
38. #170	C₂²×C₇	semidirect
39. C₅×C₇	C₂²×C₈	semidirect
48. C₂×D₅	C₇×C₈	semidirect
57. C₂×C₇	D₅⋊C₈	direct (N × H)
59. C₂×C₅	C₂×C₇×C₈	semidirect
61. D₅	C₂×C₇×C₈	semidirect
68. C₇	C₂×D₅⋊C₈	direct (N × H)
69. C₅	C₂²×C₇×C₈	semidirect
77. C₂	C₇×D₅⋊C₈	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×C₄×C₇×D₅	2
C₂×C₇×#170	2
C₇×D₅⋊C₈	2
C₂²×C₇×C₈	5
C₂×D₅⋊C₈	7

Subgroups — C2×C7×D5⋊C8 #11765342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₅⋊C₈ #11765342