Subgroups — #13182731

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#11724886	C₂	1	4	yes	maximal, complemented
5	C₂²×D₅₅	C₂²	1	2	yes	—
6	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
7	D₂₂₀	—	2	2	no	—
8	C₂×C₁₁×Dic₅	C₂²	1	2	yes	—
9	C₂×C₅×Dic₁₁	C₂²	1	2	yes	—
10	C₅×Dic₂₂	—	2	2	no	—
11	#66928	—	5	1	no	maximal, Hall
12	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×D₅₅	—	2	2	no	—
14	C₂×D₅₅	—	2	4	no	—
15	C₄×C₅×C₁₁	D₄	1	2	yes	—
16	C₅×Dic₁₁	—	2	2	no	—
17	C₁₁×Dic₅	—	2	2	no	—
18	C₂×D₄₄	—	5	1	no	—
19	C₂×Dic₂₂	D₅	1	1	yes	characteristic, complemented
20	C₄²×C₁₁	—	5	1	no	—
21	(C₂×D₁₁)⋊C₄	—	5	4	no	—
22	#4093	—	11	1	no	maximal, Hall
23	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
24	C₂×C₅×C₁₁	#41	1	2	yes	—
25	D₅₅	—	4	2	no	—
26	C₂²×D₁₁	—	5	2	no	—
27	C₂×C₄×C₁₁	—	5	2	no	—
28	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
29	C₂×Dic₁₁	C₂×D₅	1	2	yes	—
30	D₄₄	—	10	2	no	—
31	Dic₂₂	—	2	2	no	—
32	C₂×C₅×Q₈	—	11	1	no	—
33	C₂×D₂₀	—	11	1	no	—
34	#685	—	11	4	no	—
35	C₄×Dic₅	D₁₁	1	1	yes	characteristic, complemented
36	C₅×C₁₁	#124	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
38	C₂×D₁₁	—	10	4	no	—
39	C₂×D₁₁	—	10	2	no	—
40	C₄×C₁₁	—	10	2	no	—
41	C₄×C₁₁	C₂²⋊D₅	1	2	yes	—
42	Dic₁₁	—	2	2	no	—
43	C₂²×D₅	—	11	2	no	—
44	C₅×Q₈	—	22	2	no	—
45	C₂×C₄×C₅	—	11	2	no	—
46	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
47	C₂×Dic₅	C₂×D₁₁	1	2	yes	—
48	D₂₀	—	22	2	no	—
49	#124	—	55	1	no	Sylow
50	C₂×C₁₁	#713	1	2	yes	—
51	C₂×C₁₁	C₂×C₂²⋊D₅	1	1	yes	characteristic
52	D₁₁	—	20	2	no	—
53	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
54	C₂×D₅	—	22	2	no	—
55	C₂×D₅	—	22	4	no	—
56	C₄×C₅	—	22	2	no	—
57	C₄×C₅	D₄₄	1	2	yes	—
58	Dic₅	—	2	2	no	—
59	C₂×Q₈	—	11	1	no	—
60	C₂×D₄	—	55	1	no	—
61	C₂²⋊C₄	—	55	4	no	—
62	C₄²	—	5	1	no	—
63	C₁₁	#4093	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	C₂×D₄₄	1	1	yes	characteristic
65	C₂×C₅	#4339	1	2	yes	—
66	D₅	—	44	2	no	—
67	C₂³	—	55	2	no	—
68	Q₈	—	22	2	no	—
69	D₄	—	110	2	no	—
70	C₂×C₄	—	5	2	no	—
71	C₂×C₄	—	11	2	no	—
72	C₂×C₄	D₅×D₁₁	1	1	yes	characteristic
73	C₅	#66928	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	110	4	no	—
75	C₂²	—	110	2	no	—
76	C₂²	C₂×D₅×D₁₁	1	1	yes	characteristic
77	C₄	—	10	2	no	—
78	C₄	—	22	2	no	—
79	C₄	#89168	1	2	yes	—
80	C₂	—	220	2	no	—
81	C₂	#11724986	1	2	yes	—
82	C₂	C₂×#89168	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×D₅×D₁₁
commutator, socle, cosocle	C₂²×C₅×C₁₁	C₂³
Fitting	C₂×C₄×C₅×C₁₁	C₂²
prime radical	C₂×D₂₂₀	C₂
hypercenter	C₂×C₄	D₅×D₁₁
hypocenter	C₅×C₁₁	#124
LCS	G ▷ C₂²×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Dic₂₂	C₂	semidirect
3. C₄×C₁₁×Dic₅	C₂	semidirect
4. #11724886	C₂	semidirect
19. C₂×Dic₂₂	D₅	semidirect
35. C₄×Dic₅	D₁₁	semidirect
36. C₅×C₁₁	#124	semidirect
63. C₁₁	#4093	semidirect
73. C₅	#66928	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₂₀	2
C₂×C₅×Dic₂₂	2
C₄×C₁₁×Dic₅	2
#11724886	2
#66928	5
#4093	11