Subgroups — C₂²×C₁₁×D₂₀ #13183427

Order 1760.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₅×C₁₁	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×D₂₀	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic
5	C₂²×D₅×C₁₁	—	2	8	no	—
6	C₂²×D₅×C₁₁	C₂²	1	12	yes	complemented
7	C₂×C₄×C₅×C₁₁	C₂²	1	6	yes	complemented
8	C₁₁×D₂₀	C₂²	1	16	yes	direct product factor
9	C₂²×D₄×C₁₁	—	5	1	no	maximal, Hall
10	C₂²×C₅×C₁₁	D₄	1	4	yes	complemented
11	C₂²×C₅×C₁₁	C₂³	1	3	yes	—
12	C₂×D₅×C₁₁	—	2	24	no	—
13	C₂×D₅×C₁₁	C₂³	1	8	yes	complemented
14	C₄×C₅×C₁₁	C₂³	1	4	yes	complemented
15	C₂⁴×C₁₁	—	5	2	no	—
16	C₂×D₄×C₁₁	—	5	12	no	—
17	C₂²×C₄×C₁₁	D₅	1	1	yes	characteristic, complemented
18	C₂²×D₂₀	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×C₁₁	C₂×D₄	1	6	yes	complemented
20	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
21	D₅×C₁₁	—	2	8	no	—
22	C₂³×C₁₁	—	5	12	no	—
23	C₂³×C₁₁	—	10	8	no	—
24	C₂³×C₁₁	C₂×D₅	1	1	yes	characteristic
25	D₄×C₁₁	—	5	16	no	—
26	C₂×C₄×C₁₁	C₂×D₅	1	6	yes	complemented
27	C₂³×D₅	C₂×C₁₁	1	2	yes	complemented
28	C₂²×C₄×C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
29	C₂×D₂₀	C₂×C₁₁	1	12	yes	direct product factor
30	C₅×C₁₁	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₁₁	—	5	8	no	—
32	C₂²×C₁₁	—	10	24	no	—
33	C₂²×C₁₁	D₂₀	1	4	yes	direct product factor
34	C₂²×C₁₁	C₂²×D₅	1	3	yes	—
35	C₄×C₁₁	C₂²×D₅	1	4	yes	complemented
36	C₂³×C₅	C₂²×C₁₁	1	1	yes	characteristic
37	C₂²×D₅	—	2	8	no	—
38	C₂²×D₅	C₂²×C₁₁	1	12	yes	complemented
39	C₂×C₄×C₅	C₂²×C₁₁	1	6	yes	complemented
40	D₂₀	C₂²×C₁₁	1	16	yes	direct product factor
41	C₂²×D₄	—	5	1	no	Sylow
42	C₂×C₁₁	—	10	8	no	—
43	C₂×C₁₁	C₂×D₂₀	1	6	yes	direct product factor
44	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
45	C₂²×C₅	D₄×C₁₁	1	4	yes	complemented
46	C₂²×C₅	C₂³×C₁₁	1	3	yes	—
47	C₂×D₅	—	2	24	no	—
48	C₂×D₅	C₂³×C₁₁	1	8	yes	complemented
49	C₄×C₅	C₂³×C₁₁	1	4	yes	complemented
50	C₂⁴	—	5	2	no	—
51	C₂×D₄	—	5	12	no	—
52	C₂²×C₄	D₅×C₁₁	1	1	yes	characteristic, complemented
53	C₁₁	C₂²×D₂₀	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₅	C₂×D₄×C₁₁	1	6	yes	complemented
55	C₂×C₅	C₂⁴×C₁₁	1	1	yes	characteristic
56	D₅	—	2	8	no	—
57	C₂³	—	5	12	no	—
58	C₂³	—	10	8	no	—
59	C₂³	C₂×D₅×C₁₁	1	1	yes	characteristic
60	D₄	—	5	16	no	—
61	C₂×C₄	C₂×D₅×C₁₁	1	6	yes	complemented
62	C₅	C₂²×D₄×C₁₁	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	5	8	no	—
64	C₂²	—	10	24	no	—
65	C₂²	C₁₁×D₂₀	1	4	yes	direct product factor
66	C₂²	C₂²×D₅×C₁₁	1	3	yes	—
67	C₄	C₂²×D₅×C₁₁	1	4	yes	complemented
68	C₂	—	10	8	no	—
69	C₂	C₂×C₁₁×D₂₀	1	6	yes	direct product factor
70	C₂	C₂³×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₁₁	C₂×D₅
commutator, cosocle	C₂×C₅	C₂⁴×C₁₁
Frattini	C₂	C₂³×D₅×C₁₁
Fitting	C₂²×C₄×C₅×C₁₁	C₂
socle	C₂³×C₅×C₁₁	C₂²
hypercenter	C₂²×C₄×C₁₁	D₅
hypocenter	C₅	C₂²×D₄×C₁₁
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂³×D₅×C₁₁	C₂	semidirect
2. C₂²×C₄×C₅×C₁₁	C₂	semidirect
3. C₂×C₁₁×D₂₀	C₂	direct (N × H)
6. C₂²×D₅×C₁₁	C₂²	semidirect
7. C₂×C₄×C₅×C₁₁	C₂²	semidirect
8. C₁₁×D₂₀	C₂²	direct (N × H)
10. C₂²×C₅×C₁₁	D₄	semidirect
13. C₂×D₅×C₁₁	C₂³	semidirect
14. C₄×C₅×C₁₁	C₂³	semidirect
17. C₂²×C₄×C₁₁	D₅	semidirect
18. C₂²×D₂₀	C₁₁	direct (N × H)
19. C₂×C₅×C₁₁	C₂×D₄	semidirect
26. C₂×C₄×C₁₁	C₂×D₅	semidirect
27. C₂³×D₅	C₂×C₁₁	semidirect
28. C₂²×C₄×C₅	C₂×C₁₁	semidirect
29. C₂×D₂₀	C₂×C₁₁	direct (N × H)
30. C₅×C₁₁	C₂²×D₄	semidirect
33. C₂²×C₁₁	D₂₀	direct (N × H)
35. C₄×C₁₁	C₂²×D₅	semidirect
38. C₂²×D₅	C₂²×C₁₁	semidirect
39. C₂×C₄×C₅	C₂²×C₁₁	semidirect
40. D₂₀	C₂²×C₁₁	direct (N × H)
43. C₂×C₁₁	C₂×D₂₀	direct (N × H)
45. C₂²×C₅	D₄×C₁₁	semidirect
48. C₂×D₅	C₂³×C₁₁	semidirect
49. C₄×C₅	C₂³×C₁₁	semidirect
52. C₂²×C₄	D₅×C₁₁	semidirect
53. C₁₁	C₂²×D₂₀	direct (N × H)
54. C₂×C₅	C₂×D₄×C₁₁	semidirect
61. C₂×C₄	C₂×D₅×C₁₁	semidirect
62. C₅	C₂²×D₄×C₁₁	semidirect
65. C₂²	C₁₁×D₂₀	direct (N × H)
67. C₄	C₂²×D₅×C₁₁	semidirect
69. C₂	C₂×C₁₁×D₂₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₅×C₁₁	2
C₂²×C₄×C₅×C₁₁	2
C₂×C₁₁×D₂₀	2
C₂²×D₄×C₁₁	5
C₂²×D₂₀	11

Subgroups — C22×C11×D20 #13183427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×D₂₀ #13183427