Subgroups — C₂×C₇×D₄₀ #11765147

Order 1120.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₂₀	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₄₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₇×D₅	—	2	2	no	—
5	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₇×D₂₀	—	2	2	no	—
7	C₇×D₂₀	C₂²	1	4	yes	complemented
8	C₅×C₇×C₈	C₂²	1	2	yes	complemented
9	C₂×C₇×D₈	—	5	1	no	maximal, Hall
10	C₂×D₄₀	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₅×C₇	D₄	1	1	yes	characteristic
12	C₂×C₇×D₅	—	2	4	no	—
13	C₂×C₇×D₅	—	4	4	no	—
14	C₄×C₅×C₇	D₄	1	1	yes	characteristic
15	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
16	C₂×C₇×D₄	—	5	2	no	—
17	C₇×D₈	—	5	4	no	—
18	C₂×C₇×C₈	D₅	1	1	yes	characteristic, complemented
19	C₂×D₂₀	C₂×C₇	1	2	yes	complemented
20	C₂×C₅×C₈	C₂×C₇	1	1	yes	characteristic, complemented
21	D₄₀	C₂×C₇	1	4	yes	direct product factor
22	C₂×C₅×C₇	D₈	1	2	yes	complemented
23	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
24	C₇×D₅	—	4	4	no	—
25	C₂³×C₇	—	10	2	no	—
26	C₇×D₄	—	5	4	no	—
27	C₇×D₄	—	10	2	no	—
28	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
29	C₇×C₈	C₂×D₅	1	2	yes	complemented
30	C₂²×D₅	—	2	2	no	—
31	C₂×C₄×C₅	C₂²×C₇	1	1	yes	characteristic
32	D₂₀	—	2	2	no	—
33	D₂₀	C₂²×C₇	1	4	yes	complemented
34	C₅×C₈	C₂²×C₇	1	2	yes	complemented
35	C₅×C₇	C₂×D₈	1	1	yes	characteristic, complemented, Hall
36	C₂×D₈	—	5	1	no	Sylow
37	C₂²×C₇	—	10	4	no	—
38	C₂²×C₇	—	20	4	no	—
39	C₂²×C₇	D₂₀	1	1	yes	characteristic
40	C₄×C₇	D₂₀	1	1	yes	characteristic
41	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
42	C₂²×C₅	C₇×D₄	1	1	yes	characteristic
43	C₂×D₅	—	2	4	no	—
44	C₂×D₅	—	4	4	no	—
45	C₄×C₅	C₇×D₄	1	1	yes	characteristic
46	C₄×C₅	C₂³×C₇	1	1	yes	characteristic
47	C₂×D₄	—	5	2	no	—
48	D₈	—	5	4	no	—
49	C₂×C₈	C₇×D₅	1	1	yes	characteristic, complemented
50	C₂×C₇	—	20	4	no	—
51	C₂×C₇	D₄₀	1	2	yes	direct product factor
52	C₂×C₇	C₂×D₂₀	1	1	yes	characteristic
53	C₂×C₅	C₇×D₈	1	2	yes	complemented
54	C₂×C₅	C₂×C₇×D₄	1	1	yes	characteristic
55	D₅	—	4	4	no	—
56	C₂³	—	10	2	no	—
57	D₄	—	5	4	no	—
58	D₄	—	10	2	no	—
59	C₂×C₄	C₂×C₇×D₅	1	1	yes	characteristic
60	C₈	C₂×C₇×D₅	1	2	yes	complemented
61	C₇	C₂×D₄₀	1	1	yes	characteristic, direct product factor, Sylow
62	C₅	C₂×C₇×D₈	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	10	4	no	—
64	C₂²	—	20	4	no	—
65	C₂²	C₇×D₂₀	1	1	yes	characteristic
66	C₄	C₇×D₂₀	1	1	yes	characteristic
67	C₄	C₂²×C₇×D₅	1	1	yes	characteristic
68	C₂	—	20	4	no	—
69	C₂	C₇×D₄₀	1	2	yes	direct product factor
70	C₂	C₂×C₇×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₇	D₂₀
commutator, cosocle	C₄×C₅	C₂³×C₇
Frattini	C₄	C₂²×C₇×D₅
Fitting	C₂×C₅×C₇×C₈	C₂
socle	C₂²×C₅×C₇	D₄
hypercenter	C₂×C₇×C₈	D₅
hypocenter	C₅	C₂×C₇×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×D₂₀	C₂	semidirect
2. C₂×C₅×C₇×C₈	C₂	semidirect
3. C₇×D₄₀	C₂	direct (N × H)
7. C₇×D₂₀	C₂²	semidirect
8. C₅×C₇×C₈	C₂²	semidirect
10. C₂×D₄₀	C₇	direct (N × H)
18. C₂×C₇×C₈	D₅	semidirect
19. C₂×D₂₀	C₂×C₇	semidirect
20. C₂×C₅×C₈	C₂×C₇	semidirect
21. D₄₀	C₂×C₇	direct (N × H)
22. C₂×C₅×C₇	D₈	semidirect
29. C₇×C₈	C₂×D₅	semidirect
33. D₂₀	C₂²×C₇	semidirect
34. C₅×C₈	C₂²×C₇	semidirect
35. C₅×C₇	C₂×D₈	semidirect
49. C₂×C₈	C₇×D₅	semidirect
51. C₂×C₇	D₄₀	direct (N × H)
53. C₂×C₅	C₇×D₈	semidirect
60. C₈	C₂×C₇×D₅	semidirect
61. C₇	C₂×D₄₀	direct (N × H)
62. C₅	C₂×C₇×D₈	semidirect
69. C₂	C₇×D₄₀	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×C₇×D₂₀	2
C₂×C₅×C₇×C₈	2
C₇×D₄₀	2
C₂×C₇×D₈	5
C₂×D₄₀	7

Subgroups — C2×C7×D40 #11765147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₄₀ #11765147