Subgroups — D₄×D₅₅ #11725032

Order 880.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅₅	C₂	1	2	yes	maximal, complemented
2	C₅×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊D₅₅	C₂	1	2	yes	maximal, complemented
4	D₂₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×C₁₁	C₂²	1	2	yes	complemented
7	C₂×D₅₅	—	2	4	no	—
8	C₂×D₅₅	C₂²	1	1	yes	characteristic
9	C₂×D₅₅	C₂²	1	2	yes	complemented
10	C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic, complemented
11	Dic₅₅	C₂²	1	1	yes	characteristic, complemented
12	D₄×D₁₁	—	5	1	no	maximal, Hall
13	C₂×C₅×C₁₁	—	2	2	no	—
14	C₂×C₅×C₁₁	C₂³	1	1	yes	characteristic
15	D₅₅	—	2	2	no	—
16	D₅₅	D₄	1	2	yes	direct product factor
17	C₂²×D₁₁	—	5	2	no	—
18	D₄×C₁₁	D₅	1	1	yes	characteristic, complemented
19	C₂²⋊D₁₁	—	5	2	no	—
20	D₄₄	—	5	1	no	—
21	C₄×D₁₁	—	5	1	no	—
22	D₄×D₅	—	11	1	no	maximal, Hall
23	C₅×C₁₁	C₂×D₄	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₁₁	C₂×D₅	1	2	yes	complemented
25	C₂×D₁₁	—	5	1	no	—
26	C₂×D₁₁	—	5	2	no	—
27	C₂×D₁₁	—	10	4	no	—
28	C₄×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented
29	Dic₁₁	—	5	1	no	—
30	C₂²×D₅	—	11	2	no	—
31	C₅×D₄	D₁₁	1	1	yes	characteristic, complemented
32	C₂²⋊D₅	—	11	2	no	—
33	D₂₀	—	11	1	no	—
34	C₄×D₅	—	11	1	no	—
35	C₂×C₁₁	—	2	2	no	—
36	C₂×C₁₁	C₂²×D₅	1	1	yes	characteristic
37	D₁₁	—	5	2	no	—
38	D₁₁	—	10	2	no	—
39	C₂²×C₅	C₂×D₁₁	1	2	yes	complemented
40	C₂×D₅	—	11	1	no	—
41	C₂×D₅	—	11	2	no	—
42	C₂×D₅	—	22	4	no	—
43	C₄×C₅	C₂×D₁₁	1	1	yes	characteristic, complemented
44	Dic₅	—	11	1	no	—
45	C₂×D₄	—	55	1	no	Sylow
46	C₁₁	D₄×D₅	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅	—	2	2	no	—
48	C₂×C₅	C₂²×D₁₁	1	1	yes	characteristic
49	D₅	—	11	2	no	—
50	D₅	—	22	2	no	—
51	C₂³	—	55	2	no	—
52	D₄	—	55	2	no	—
53	D₄	—	55	1	no	—
54	D₄	D₅₅	1	1	yes	characteristic, direct product factor
55	C₂×C₄	—	55	1	no	—
56	C₅	D₄×D₁₁	1	1	yes	characteristic, complemented, Sylow
57	C₂²	—	55	1	no	—
58	C₂²	—	55	2	no	—
59	C₂²	—	110	4	no	—
60	C₂²	C₂×D₅₅	1	2	yes	complemented
61	C₄	—	55	1	no	—
62	C₄	C₂×D₅₅	1	1	yes	characteristic, complemented
63	C₂	—	2	2	no	—
64	C₂	—	55	2	no	—
65	C₂	—	110	2	no	—
66	C₂	C₂²×D₅₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×D₅₅	C₂	semidirect
2. C₅×D₄×C₁₁	C₂	semidirect
3. C₂²⋊D₅₅	C₂	semidirect
4. D₂₂₀	C₂	semidirect
5. C₄×D₅₅	C₂	semidirect
6. C₂²×C₅×C₁₁	C₂²	semidirect
9. C₂×D₅₅	C₂²	semidirect
10. C₄×C₅×C₁₁	C₂²	semidirect
11. Dic₅₅	C₂²	semidirect
16. D₅₅	D₄	direct (N × H)
18. D₄×C₁₁	D₅	semidirect
23. C₅×C₁₁	C₂×D₄	semidirect
24. C₂²×C₁₁	C₂×D₅	semidirect
28. C₄×C₁₁	C₂×D₅	semidirect
31. C₅×D₄	D₁₁	semidirect
39. C₂²×C₅	C₂×D₁₁	semidirect
43. C₄×C₅	C₂×D₁₁	semidirect
46. C₁₁	D₄×D₅	semidirect
54. D₄	D₅₅	direct (N × H)
56. C₅	D₄×D₁₁	semidirect
60. C₂²	C₂×D₅₅	semidirect
62. C₄	C₂×D₅₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₅₅	2
C₅×D₄×C₁₁	2
C₂²⋊D₅₅	2
D₂₂₀	2
C₄×D₅₅	2
D₄×D₁₁	5
D₄×D₅	11

Subgroups — D4×D55 #11725032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×D₅₅ #11725032