Subgroups — #13183452

Order 1760.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₅₅	C₂	1	2	yes	maximal, complemented
3	#11725033	C₂	1	6	yes	maximal, complemented
4	#11725031	C₂	1	3	yes	maximal, complemented
5	C₂×Dic₁₁₀	C₂	1	3	yes	maximal, complemented
6	C₅×Q₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₅×D₄×C₁₁	C₂²	1	3	yes	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
9	C₂²⋊D₅₅	C₂²	1	6	yes	—
10	C₂×Dic₅₅	C₂²	1	6	yes	—
11	D₂₂₀	C₂²	1	1	yes	characteristic
12	C₄×D₅₅	C₂²	1	6	yes	—
13	Dic₁₁₀	C₂²	1	3	yes	—
14	Dic₁₁₀	C₂²	1	6	yes	—
15	#67043	—	5	1	no	maximal, Hall
16	C₂²×C₅×C₁₁	C₂³	1	3	yes	—
17	C₂×D₅₅	C₂³	1	2	yes	—
18	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
19	C₄×C₅×C₁₁	C₂³	1	3	yes	—
20	Dic₅₅	C₂³	1	6	yes	—
21	C₁₁×#41	D₅	1	1	yes	characteristic, complemented
22	Q₈×D₁₁	—	5	2	no	—
23	#4341	—	5	6	no	—
24	#4339	—	5	3	no	—
25	C₂×Dic₂₂	—	5	3	no	—
26	#4150	—	11	1	no	maximal, Hall
27	C₂×C₅×C₁₁	—	2	3	no	—
28	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
29	D₅₅	—	2	2	no	—
30	Q₈×C₁₁	C₂×D₅	1	1	yes	characteristic
31	D₄×C₁₁	C₂×D₅	1	3	yes	—
32	C₂×C₄×C₁₁	C₂×D₅	1	3	yes	—
33	C₂²⋊D₁₁	—	5	6	no	—
34	C₂×Dic₁₁	—	5	6	no	—
35	D₄₄	—	5	1	no	—
36	C₄×D₁₁	—	5	6	no	—
37	Dic₂₂	—	5	3	no	—
38	Dic₂₂	—	5	6	no	—
39	C₅×#41	D₁₁	1	1	yes	characteristic, complemented
40	Q₈×D₅	—	11	2	no	—
41	#711	—	11	6	no	—
42	#709	—	11	3	no	—
43	C₂×Dic₁₀	—	11	3	no	—
44	C₅×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₁₁	C₂²×D₅	1	3	yes	—
46	C₂×D₁₁	—	5	2	no	—
47	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
48	C₄×C₁₁	C₂²×D₅	1	3	yes	—
49	Dic₁₁	—	5	6	no	—
50	C₅×Q₈	C₂×D₁₁	1	1	yes	characteristic
51	C₅×D₄	C₂×D₁₁	1	3	yes	—
52	C₂×C₄×C₅	C₂×D₁₁	1	3	yes	—
53	C₂²⋊D₅	—	11	6	no	—
54	C₂×Dic₅	—	11	6	no	—
55	D₂₀	—	11	1	no	—
56	C₄×D₅	—	11	6	no	—
57	Dic₁₀	—	11	3	no	—
58	Dic₁₀	—	11	6	no	—
59	2₋¹⁺⁴	—	55	1	no	Sylow
60	C₂×C₁₁	—	2	3	no	—
61	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
62	D₁₁	—	10	2	no	—
63	C₂²×C₅	C₂²×D₁₁	1	3	yes	—
64	C₂×D₅	—	11	2	no	—
65	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
66	C₄×C₅	C₂²×D₁₁	1	3	yes	—
67	Dic₅	—	11	6	no	—
68	#41	—	55	6	no	—
69	#41	—	55	3	no	—
70	#41	D₅₅	1	1	yes	characteristic, complemented
71	C₂×Q₈	—	55	2	no	—
72	C₂×Q₈	—	55	3	no	—
73	C₁₁	#4150	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₅	—	2	3	no	—
75	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
76	D₅	—	22	2	no	—
77	Q₈	—	55	6	no	—
78	Q₈	—	55	3	no	—
79	Q₈	C₂×D₅₅	1	1	yes	characteristic
80	D₄	—	55	6	no	—
81	D₄	—	55	1	no	—
82	D₄	C₂×D₅₅	1	3	yes	—
83	C₂×C₄	—	55	6	no	—
84	C₂×C₄	—	55	6	no	—
85	C₂×C₄	C₂×D₅₅	1	3	yes	—
86	C₅	#67043	1	1	yes	characteristic, complemented, Sylow
87	C₂²	—	55	2	no	—
88	C₂²	C₂²×D₅₅	1	3	yes	—
89	C₄	—	55	6	no	—
90	C₄	C₂²×D₅₅	1	3	yes	—
91	C₄	C₂²×D₅₅	1	1	yes	characteristic
92	C₂	—	2	3	no	—
93	C₂	—	110	2	no	—
94	C₂	C₂³×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×D₅₅
commutator, socle, cosocle	C₂×C₅×C₁₁	C₂⁴
Fitting	C₅×C₁₁×#41	C₂
hypercenter	#41	D₅₅
hypocenter	C₅×C₁₁	2₋¹⁺⁴
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×#41	C₂	semidirect
2. Q₈×D₅₅	C₂	semidirect
3. #11725033	C₂	semidirect
4. #11725031	C₂	semidirect
5. C₂×Dic₁₁₀	C₂	semidirect
21. C₁₁×#41	D₅	semidirect
39. C₅×#41	D₁₁	semidirect
44. C₅×C₁₁	2₋¹⁺⁴	semidirect
70. #41	D₅₅	semidirect
73. C₁₁	#4150	semidirect
86. C₅	#67043	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×#41	2
Q₈×D₅₅	2
#11725033	2
#11725031	2
C₂×Dic₁₁₀	2
#67043	5
#4150	11