Subgroups — #13183211

Order 1760.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11725033	C₂	1	2	yes	maximal, complemented
2	C₅×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11724934	C₂	1	2	yes	maximal, complemented
4	Dic₂₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₄×C₁₁	C₂²	1	2	yes	—
7	C₂²⋊D₅₅	—	2	2	no	—
8	C₂×Dic₅₅	—	2	2	no	—
9	C₄×D₅₅	C₂²	1	1	yes	characteristic
10	Dic₁₁₀	C₂²	1	2	yes	—
11	C₅×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁⋊#168	C₂²	1	1	yes	characteristic
13	#66965	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	—	2	2	no	—
15	C₂×D₅₅	D₄	1	1	yes	characteristic
16	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
17	Dic₅₅	—	2	2	no	—
18	Dic₅₅	D₄	1	1	yes	characteristic
19	#4341	—	5	2	no	—
20	C₁₁×D₈	D₅	1	1	yes	characteristic, complemented
21	#4324	—	5	2	no	—
22	Dic₄₄	—	5	1	no	—
23	C₈×D₁₁	—	5	1	no	—
24	#4058	—	11	1	no	maximal, Hall
25	C₂×C₅×C₁₁	—	4	2	no	—
26	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
27	D₅₅	—	2	1	no	—
28	D₄×C₁₁	C₂×D₅	1	2	yes	—
29	C₂²⋊D₁₁	—	10	2	no	—
30	C₂×Dic₁₁	—	10	2	no	—
31	C₄×D₁₁	—	5	1	no	—
32	Dic₂₂	—	5	2	no	—
33	C₈×C₁₁	C₂×D₅	1	1	yes	characteristic
34	C₁₁⋊C₈	—	5	1	no	—
35	#711	—	11	2	no	—
36	C₅×D₈	D₁₁	1	1	yes	characteristic, complemented
37	#687	—	11	2	no	—
38	Dic₂₀	—	11	1	no	—
39	C₈×D₅	—	11	1	no	—
40	C₅×C₁₁	#135	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	2	2	no	—
42	C₂×D₁₁	—	5	1	no	—
43	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
44	Dic₁₁	—	5	1	no	—
45	Dic₁₁	—	10	2	no	—
46	C₅×D₄	C₂×D₁₁	1	2	yes	—
47	C₂²⋊D₅	—	22	2	no	—
48	C₂×Dic₅	—	22	2	no	—
49	C₄×D₅	—	11	1	no	—
50	Dic₁₀	—	11	2	no	—
51	C₅×C₈	C₂×D₁₁	1	1	yes	characteristic
52	#168	—	11	1	no	—
53	#135	—	55	1	no	Sylow
54	C₂×C₁₁	—	4	2	no	—
55	C₂×C₁₁	D₄×D₅	1	1	yes	characteristic
56	D₁₁	—	10	1	no	—
57	C₂²×C₅	—	2	2	no	—
58	C₂×D₅	—	11	1	no	—
59	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
60	Dic₅	—	11	1	no	—
61	Dic₅	—	22	2	no	—
62	#41	—	55	2	no	—
63	Q₁₆	—	55	1	no	—
64	SD₁₆	—	55	2	no	—
65	D₈	D₅₅	1	1	yes	characteristic, complemented
66	C₂×C₈	—	55	1	no	—
67	C₁₁	#4058	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₅	—	4	2	no	—
69	C₂×C₅	D₄×D₁₁	1	1	yes	characteristic
70	D₅	—	22	1	no	—
71	Q₈	—	55	2	no	—
72	D₄	—	110	2	no	—
73	D₄	C₂×D₅₅	1	2	yes	—
74	C₂×C₄	—	55	1	no	—
75	C₂×C₄	—	110	2	no	—
76	C₈	—	55	1	no	—
77	C₈	C₂×D₅₅	1	1	yes	characteristic
78	C₅	#66965	1	1	yes	characteristic, complemented, Sylow
79	C₂²	—	2	2	no	—
80	C₂²	—	55	1	no	—
81	C₄	—	55	1	no	—
82	C₄	—	110	2	no	—
83	C₄	C₂²×D₅₅	1	1	yes	characteristic
84	C₂	—	4	2	no	—
85	C₂	—	110	1	no	—
86	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	#135
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. #11725033	C₂	semidirect
2. C₅×C₁₁×D₈	C₂	semidirect
3. #11724934	C₂	semidirect
4. Dic₂₂₀	C₂	semidirect
5. C₈×D₅₅	C₂	semidirect
20. C₁₁×D₈	D₅	semidirect
36. C₅×D₈	D₁₁	semidirect
40. C₅×C₁₁	#135	semidirect
65. D₈	D₅₅	semidirect
67. C₁₁	#4058	semidirect
78. C₅	#66965	semidirect

Maximal subgroups

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

subgroup	index
#11725033	2
C₅×C₁₁×D₈	2
#11724934	2
Dic₂₂₀	2
C₈×D₅₅	2
#66965	5
#4058	11