Subgroups — C₂×C₁₁×D₄₀ #13183116

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×D₂₀	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₄₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×D₅×C₁₁	—	2	2	no	—
5	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×D₂₀	—	2	2	no	—
7	C₁₁×D₂₀	C₂²	1	4	yes	complemented
8	C₅×C₈×C₁₁	C₂²	1	2	yes	complemented
9	C₂×C₁₁×D₈	—	5	1	no	maximal, Hall
10	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
11	C₂×D₅×C₁₁	—	2	4	no	—
12	C₂×D₅×C₁₁	—	4	4	no	—
13	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
14	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×D₄×C₁₁	—	5	2	no	—
16	C₁₁×D₈	—	5	4	no	—
17	C₂×C₈×C₁₁	D₅	1	1	yes	characteristic, complemented
18	C₂×D₄₀	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×C₁₁	D₈	1	2	yes	complemented
20	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
21	D₅×C₁₁	—	4	4	no	—
22	C₂³×C₁₁	—	10	2	no	—
23	D₄×C₁₁	—	5	4	no	—
24	D₄×C₁₁	—	10	2	no	—
25	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
26	C₈×C₁₁	C₂×D₅	1	2	yes	complemented
27	C₂×D₂₀	C₂×C₁₁	1	2	yes	complemented
28	C₂×C₅×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
29	D₄₀	C₂×C₁₁	1	4	yes	direct product factor
30	C₅×C₁₁	C₂×D₈	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₁₁	—	10	4	no	—
32	C₂²×C₁₁	—	20	4	no	—
33	C₂²×C₁₁	D₂₀	1	1	yes	characteristic
34	C₄×C₁₁	D₂₀	1	1	yes	characteristic
35	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
36	C₂²×D₅	—	2	2	no	—
37	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
38	D₂₀	—	2	2	no	—
39	D₂₀	C₂²×C₁₁	1	4	yes	complemented
40	C₅×C₈	C₂²×C₁₁	1	2	yes	complemented
41	C₂×D₈	—	5	1	no	Sylow
42	C₂×C₁₁	—	20	4	no	—
43	C₂×C₁₁	D₄₀	1	2	yes	direct product factor
44	C₂×C₁₁	C₂×D₂₀	1	1	yes	characteristic
45	C₂²×C₅	D₄×C₁₁	1	1	yes	characteristic
46	C₂×D₅	—	2	4	no	—
47	C₂×D₅	—	4	4	no	—
48	C₄×C₅	D₄×C₁₁	1	1	yes	characteristic
49	C₄×C₅	C₂³×C₁₁	1	1	yes	characteristic
50	C₂×D₄	—	5	2	no	—
51	D₈	—	5	4	no	—
52	C₂×C₈	D₅×C₁₁	1	1	yes	characteristic, complemented
53	C₁₁	C₂×D₄₀	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₅	C₁₁×D₈	1	2	yes	complemented
55	C₂×C₅	C₂×D₄×C₁₁	1	1	yes	characteristic
56	D₅	—	4	4	no	—
57	C₂³	—	10	2	no	—
58	D₄	—	5	4	no	—
59	D₄	—	10	2	no	—
60	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
61	C₈	C₂×D₅×C₁₁	1	2	yes	complemented
62	C₅	C₂×C₁₁×D₈	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	10	4	no	—
64	C₂²	—	20	4	no	—
65	C₂²	C₁₁×D₂₀	1	1	yes	characteristic
66	C₄	C₁₁×D₂₀	1	1	yes	characteristic
67	C₄	C₂²×D₅×C₁₁	1	1	yes	characteristic
68	C₂	—	20	4	no	—
69	C₂	C₁₁×D₄₀	1	2	yes	direct product factor
70	C₂	C₂×C₁₁×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₁	D₂₀
commutator, cosocle	C₄×C₅	C₂³×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₂×C₅×C₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	D₄
hypercenter	C₂×C₈×C₁₁	D₅
hypocenter	C₅	C₂×C₁₁×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₈×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×D₂₀	C₂	semidirect
2. C₂×C₅×C₈×C₁₁	C₂	semidirect
3. C₁₁×D₄₀	C₂	direct (N × H)
7. C₁₁×D₂₀	C₂²	semidirect
8. C₅×C₈×C₁₁	C₂²	semidirect
17. C₂×C₈×C₁₁	D₅	semidirect
18. C₂×D₄₀	C₁₁	direct (N × H)
19. C₂×C₅×C₁₁	D₈	semidirect
26. C₈×C₁₁	C₂×D₅	semidirect
27. C₂×D₂₀	C₂×C₁₁	semidirect
28. C₂×C₅×C₈	C₂×C₁₁	semidirect
29. D₄₀	C₂×C₁₁	direct (N × H)
30. C₅×C₁₁	C₂×D₈	semidirect
39. D₂₀	C₂²×C₁₁	semidirect
40. C₅×C₈	C₂²×C₁₁	semidirect
43. C₂×C₁₁	D₄₀	direct (N × H)
52. C₂×C₈	D₅×C₁₁	semidirect
53. C₁₁	C₂×D₄₀	direct (N × H)
54. C₂×C₅	C₁₁×D₈	semidirect
61. C₈	C₂×D₅×C₁₁	semidirect
62. C₅	C₂×C₁₁×D₈	semidirect
69. C₂	C₁₁×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×C₁₁×D₂₀	2
C₂×C₅×C₈×C₁₁	2
C₁₁×D₄₀	2
C₂×C₁₁×D₈	5
C₂×D₄₀	11

Subgroups — C2×C11×D40 #13183116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₄₀ #13183116