Subgroups — #13183203

Order 1760.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11725031	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₂₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	#11724924	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²⋊D₅₅	—	2	2	no	—
8	D₂₂₀	C₂²	1	2	yes	—
9	C₄×D₅₅	—	2	2	no	—
10	Dic₁₁₀	C₂²	1	2	yes	—
11	C₅×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₅×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	#66957	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
15	C₂×D₅₅	—	2	2	no	—
16	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
17	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
18	Dic₅₅	—	2	2	no	—
19	#4339	—	5	2	no	—
20	C₂×C₈×C₁₁	D₅	1	1	yes	characteristic, complemented
21	Dic₄₄	—	5	1	no	—
22	D₈₈	—	5	1	no	—
23	#4314	—	5	2	no	—
24	#4050	—	11	1	no	maximal, Hall
25	C₂×C₅×C₁₁	—	2	1	no	—
26	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
27	D₅₅	—	4	2	no	—
28	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
29	C₂²⋊D₁₁	—	10	2	no	—
30	D₄₄	—	5	2	no	—
31	C₄×D₁₁	—	10	2	no	—
32	Dic₂₂	—	5	2	no	—
33	C₈×C₁₁	C₂×D₅	1	1	yes	characteristic
34	C₈×C₁₁	C₂×D₅	1	1	yes	characteristic
35	#709	—	11	2	no	—
36	C₂×C₅×C₈	D₁₁	1	1	yes	characteristic, complemented
37	Dic₂₀	—	11	1	no	—
38	D₄₀	—	11	1	no	—
39	#677	—	11	2	no	—
40	C₅×C₁₁	#135	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	D₂₀	1	1	yes	characteristic
42	C₂×D₁₁	—	10	2	no	—
43	C₄×C₁₁	D₂₀	1	1	yes	characteristic
44	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
45	Dic₁₁	—	10	2	no	—
46	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
47	C₂²⋊D₅	—	22	2	no	—
48	D₂₀	—	11	2	no	—
49	C₄×D₅	—	22	2	no	—
50	Dic₁₀	—	11	2	no	—
51	C₅×C₈	C₂×D₁₁	1	1	yes	characteristic
52	C₅×C₈	C₂×D₁₁	1	1	yes	characteristic
53	#135	—	55	1	no	Sylow
54	C₂×C₁₁	—	2	1	no	—
55	C₂×C₁₁	C₂×D₂₀	1	1	yes	characteristic
56	D₁₁	—	20	2	no	—
57	C₂²×C₅	D₄₄	1	1	yes	characteristic
58	C₂×D₅	—	22	2	no	—
59	C₄×C₅	D₄₄	1	1	yes	characteristic
60	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
61	Dic₅	—	22	2	no	—
62	#41	—	55	2	no	—
63	Q₁₆	—	55	1	no	—
64	SD₁₆	—	55	2	no	—
65	D₈	—	55	1	no	—
66	C₂×C₈	D₅₅	1	1	yes	characteristic, complemented
67	C₁₁	#4050	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₅	—	2	1	no	—
69	C₂×C₅	C₂×D₄₄	1	1	yes	characteristic
70	D₅	—	44	2	no	—
71	Q₈	—	55	2	no	—
72	D₄	—	55	2	no	—
73	D₄	—	110	2	no	—
74	C₂×C₄	—	110	2	no	—
75	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
76	C₈	C₂×D₅₅	1	1	yes	characteristic
77	C₈	C₂×D₅₅	1	1	yes	characteristic
78	C₅	#66957	1	1	yes	characteristic, complemented, Sylow
79	C₂²	—	110	2	no	—
80	C₂²	D₂₂₀	1	1	yes	characteristic
81	C₄	—	110	2	no	—
82	C₄	D₂₂₀	1	1	yes	characteristic
83	C₄	C₂²×D₅₅	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	220	2	no	—
86	C₂	C₂×D₂₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₂₂₀
commutator, cosocle	C₄×C₅×C₁₁	C₂³
Frattini	C₄	C₂²×D₅₅
Fitting	C₂×C₅×C₈×C₁₁	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
hypercenter	C₂×C₈	D₅₅
hypocenter	C₅×C₁₁	#135
LCS	G ▷ C₄×C₅×C₁₁ ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #11725031	C₂	semidirect
2. C₂×C₅×C₈×C₁₁	C₂	semidirect
3. Dic₂₂₀	C₂	semidirect
4. D₄₄₀	C₂	semidirect
5. #11724924	C₂	semidirect
20. C₂×C₈×C₁₁	D₅	semidirect
36. C₂×C₅×C₈	D₁₁	semidirect
40. C₅×C₁₁	#135	semidirect
66. C₂×C₈	D₅₅	semidirect
67. C₁₁	#4050	semidirect
78. C₅	#66957	semidirect

Maximal subgroups

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

subgroup	index
#11725031	2
C₂×C₅×C₈×C₁₁	2
Dic₂₂₀	2
D₄₄₀	2
#11724924	2
#66957	5
#4050	11