Subgroups — D₈×D₅₅ #13183209

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₅₅	C₂	1	2	yes	maximal, complemented
2	C₅×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11724933	C₂	1	2	yes	maximal, complemented
4	D₄₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₅₅	—	2	2	no	—
7	C₅×D₄×C₁₁	C₂²	1	2	yes	complemented
8	C₂²⋊D₅₅	—	2	2	no	—
9	D₂₂₀	C₂²	1	2	yes	complemented
10	C₄×D₅₅	C₂²	1	1	yes	characteristic
11	C₅×C₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
12	C₁₁⋊#168	C₂²	1	1	yes	characteristic, complemented
13	D₈×D₁₁	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	—	2	2	no	—
15	C₂×D₅₅	—	2	2	no	—
16	C₂×D₅₅	—	4	4	no	—
17	C₂×D₅₅	D₄	1	1	yes	characteristic
18	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
19	Dic₅₅	D₄	1	1	yes	characteristic
20	D₄×D₁₁	—	5	2	no	—
21	C₁₁×D₈	D₅	1	1	yes	characteristic, complemented
22	#4323	—	5	2	no	—
23	D₈₈	—	5	1	no	—
24	C₈×D₁₁	—	5	1	no	—
25	D₅×D₈	—	11	1	no	maximal, Hall
26	C₂×C₅×C₁₁	—	4	2	no	—
27	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
28	D₅₅	—	4	2	no	—
29	D₅₅	D₈	1	2	yes	direct product factor
30	C₂²×D₁₁	—	10	2	no	—
31	D₄×C₁₁	C₂×D₅	1	2	yes	complemented
32	C₂²⋊D₁₁	—	10	2	no	—
33	D₄₄	—	5	2	no	—
34	C₄×D₁₁	—	5	1	no	—
35	C₈×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented
36	C₁₁⋊C₈	—	5	1	no	—
37	D₄×D₅	—	11	2	no	—
38	C₅×D₈	D₁₁	1	1	yes	characteristic, complemented
39	#686	—	11	2	no	—
40	D₄₀	—	11	1	no	—
41	C₈×D₅	—	11	1	no	—
42	C₅×C₁₁	C₂×D₈	1	1	yes	characteristic, complemented, Hall
43	C₂²×C₁₁	—	2	2	no	—
44	C₂×D₁₁	—	5	1	no	—
45	C₂×D₁₁	—	10	2	no	—
46	C₂×D₁₁	—	20	4	no	—
47	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
48	Dic₁₁	—	5	1	no	—
49	C₂²×D₅	—	22	2	no	—
50	C₅×D₄	C₂×D₁₁	1	2	yes	complemented
51	C₂²⋊D₅	—	22	2	no	—
52	D₂₀	—	11	2	no	—
53	C₄×D₅	—	11	1	no	—
54	C₅×C₈	C₂×D₁₁	1	1	yes	characteristic, complemented
55	#168	—	11	1	no	—
56	C₂×D₈	—	55	1	no	Sylow
57	C₂×C₁₁	—	4	2	no	—
58	C₂×C₁₁	D₄×D₅	1	1	yes	characteristic
59	D₁₁	—	5	2	no	—
60	D₁₁	—	20	2	no	—
61	C₂²×C₅	—	2	2	no	—
62	C₂×D₅	—	11	1	no	—
63	C₂×D₅	—	22	2	no	—
64	C₂×D₅	—	44	4	no	—
65	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
66	Dic₅	—	11	1	no	—
67	C₂×D₄	—	55	2	no	—
68	D₈	—	55	2	no	—
69	D₈	—	55	1	no	—
70	D₈	D₅₅	1	1	yes	characteristic, direct product factor
71	C₂×C₈	—	55	1	no	—
72	C₁₁	D₅×D₈	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	4	2	no	—
74	C₂×C₅	D₄×D₁₁	1	1	yes	characteristic
75	D₅	—	11	2	no	—
76	D₅	—	44	2	no	—
77	C₂³	—	110	2	no	—
78	D₄	—	55	2	no	—
79	D₄	—	110	2	no	—
80	D₄	C₂×D₅₅	1	2	yes	complemented
81	C₂×C₄	—	55	1	no	—
82	C₈	—	55	1	no	—
83	C₈	C₂×D₅₅	1	1	yes	characteristic, complemented
84	C₅	D₈×D₁₁	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	2	2	no	—
86	C₂²	—	55	1	no	—
87	C₂²	—	110	2	no	—
88	C₂²	—	220	4	no	—
89	C₄	—	55	1	no	—
90	C₄	C₂²×D₅₅	1	1	yes	characteristic
91	C₂	—	4	2	no	—
92	C₂	—	55	2	no	—
93	C₂	—	220	2	no	—
94	C₂	D₄×D₅₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. D₄×D₅₅	C₂	semidirect
2. C₅×C₁₁×D₈	C₂	semidirect
3. #11724933	C₂	semidirect
4. D₄₄₀	C₂	semidirect
5. C₈×D₅₅	C₂	semidirect
7. C₅×D₄×C₁₁	C₂²	semidirect
9. D₂₂₀	C₂²	semidirect
11. C₅×C₈×C₁₁	C₂²	semidirect
12. C₁₁⋊#168	C₂²	semidirect
21. C₁₁×D₈	D₅	semidirect
29. D₅₅	D₈	direct (N × H)
31. D₄×C₁₁	C₂×D₅	semidirect
35. C₈×C₁₁	C₂×D₅	semidirect
38. C₅×D₈	D₁₁	semidirect
42. C₅×C₁₁	C₂×D₈	semidirect
50. C₅×D₄	C₂×D₁₁	semidirect
54. C₅×C₈	C₂×D₁₁	semidirect
70. D₈	D₅₅	direct (N × H)
72. C₁₁	D₅×D₈	semidirect
80. D₄	C₂×D₅₅	semidirect
83. C₈	C₂×D₅₅	semidirect
84. C₅	D₈×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
D₄×D₅₅	2
C₅×C₁₁×D₈	2
#11724933	2
D₄₄₀	2
C₈×D₅₅	2
D₈×D₁₁	5
D₅×D₈	11

Subgroups — D8×D55 #13183209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×D₅₅ #13183209