Subgroups — C₂×D₄₄₀ #13183202

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₂₀	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₄₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×D₅₅	—	2	2	no	—
5	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	D₂₂₀	—	2	2	no	—
7	D₂₂₀	C₂²	1	4	yes	complemented
8	C₅×C₈×C₁₁	C₂²	1	2	yes	complemented
9	C₂×D₈₈	—	5	1	no	maximal, Hall
10	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
11	C₂×D₅₅	—	2	4	no	—
12	C₂×D₅₅	—	4	4	no	—
13	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
14	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×D₄₄	—	5	2	no	—
16	C₂×C₈×C₁₁	D₅	1	1	yes	characteristic, complemented
17	D₈₈	—	5	4	no	—
18	C₂×D₄₀	—	11	1	no	maximal, Hall
19	C₂×C₅×C₁₁	D₈	1	2	yes	complemented
20	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
21	D₅₅	—	4	4	no	—
22	C₂²×D₁₁	—	10	2	no	—
23	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
24	D₄₄	—	5	4	no	—
25	D₄₄	—	10	2	no	—
26	C₈×C₁₁	C₂×D₅	1	2	yes	complemented
27	C₂×D₂₀	—	11	2	no	—
28	C₂×C₅×C₈	D₁₁	1	1	yes	characteristic, complemented
29	D₄₀	—	11	4	no	—
30	C₅×C₁₁	C₂×D₈	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₁₁	D₂₀	1	1	yes	characteristic
32	C₂×D₁₁	—	10	4	no	—
33	C₂×D₁₁	—	20	4	no	—
34	C₄×C₁₁	D₂₀	1	1	yes	characteristic
35	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
36	C₂²×D₅	—	22	2	no	—
37	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
38	D₂₀	—	11	4	no	—
39	D₂₀	—	22	2	no	—
40	C₅×C₈	C₂×D₁₁	1	2	yes	complemented
41	C₂×D₈	—	55	1	no	Sylow
42	C₂×C₁₁	D₄₀	1	2	yes	complemented
43	C₂×C₁₁	C₂×D₂₀	1	1	yes	characteristic
44	D₁₁	—	20	4	no	—
45	C₂²×C₅	D₄₄	1	1	yes	characteristic
46	C₂×D₅	—	22	4	no	—
47	C₂×D₅	—	44	4	no	—
48	C₄×C₅	D₄₄	1	1	yes	characteristic
49	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
50	C₂×D₄	—	55	2	no	—
51	D₈	—	55	4	no	—
52	C₂×C₈	D₅₅	1	1	yes	characteristic, complemented
53	C₁₁	C₂×D₄₀	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₅	D₈₈	1	2	yes	complemented
55	C₂×C₅	C₂×D₄₄	1	1	yes	characteristic
56	D₅	—	44	4	no	—
57	C₂³	—	110	2	no	—
58	D₄	—	55	4	no	—
59	D₄	—	110	2	no	—
60	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
61	C₈	C₂×D₅₅	1	2	yes	complemented
62	C₅	C₂×D₈₈	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	110	4	no	—
64	C₂²	—	220	4	no	—
65	C₂²	D₂₂₀	1	1	yes	characteristic
66	C₄	D₂₂₀	1	1	yes	characteristic
67	C₄	C₂²×D₅₅	1	1	yes	characteristic
68	C₂	—	220	4	no	—
69	C₂	D₄₄₀	1	2	yes	direct product factor
70	C₂	C₂×D₂₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₂₀
commutator, cosocle	C₄×C₅×C₁₁	C₂³
Frattini	C₄	C₂²×D₅₅
Fitting	C₂×C₅×C₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	D₄
hypercenter	C₂×C₈	D₅₅
hypocenter	C₅×C₁₁	C₂×D₈
LCS	G ▷ C₄×C₅×C₁₁ ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₂₀	C₂	semidirect
2. C₂×C₅×C₈×C₁₁	C₂	semidirect
3. D₄₄₀	C₂	direct (N × H)
7. D₂₂₀	C₂²	semidirect
8. C₅×C₈×C₁₁	C₂²	semidirect
16. C₂×C₈×C₁₁	D₅	semidirect
19. C₂×C₅×C₁₁	D₈	semidirect
26. C₈×C₁₁	C₂×D₅	semidirect
28. C₂×C₅×C₈	D₁₁	semidirect
30. C₅×C₁₁	C₂×D₈	semidirect
40. C₅×C₈	C₂×D₁₁	semidirect
42. C₂×C₁₁	D₄₀	semidirect
52. C₂×C₈	D₅₅	semidirect
53. C₁₁	C₂×D₄₀	semidirect
54. C₂×C₅	D₈₈	semidirect
61. C₈	C₂×D₅₅	semidirect
62. C₅	C₂×D₈₈	semidirect
69. C₂	D₄₄₀	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×D₂₂₀	2
C₂×C₅×C₈×C₁₁	2
D₄₄₀	2
C₂×D₈₈	5
C₂×D₄₀	11

Subgroups — C2×D440 #13183202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₄₀ #13183202