Subgroups — #13183171

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅₅	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#11724932	C₂	1	2	yes	maximal
4	#11724930	C₂	1	2	yes	maximal, complemented
5	C₄×Dic₅₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₅₅	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₁₁	C₂²	1	2	yes	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₅	C₂²	1	2	yes	—
10	C₂×Dic₅₅	C₂²	1	1	yes	characteristic
11	C₄×D₅₅	C₄	1	4	yes	complemented
12	#66925	—	5	1	no	maximal, Hall
13	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
14	C₂×D₅₅	—	2	2	no	—
15	C₂×D₅₅	C₂×C₄	1	2	yes	—
16	C₄×C₅×C₁₁	—	2	2	no	—
17	C₄×C₅×C₁₁	C₂×C₄	1	2	yes	—
18	Dic₅₅	—	2	2	no	—
19	Dic₅₅	C₂×C₄	1	2	yes	—
20	C₂×C₄×D₁₁	—	5	1	no	—
21	C₄²×C₁₁	D₅	1	1	yes	characteristic, complemented
22	(C₂×D₁₁)⋊C₄	—	5	2	no	—
23	Dic₁₁⋊C₄	—	5	2	no	—
24	C₄×Dic₁₁	—	5	1	no	—
25	#4018	—	11	1	no	maximal, Hall
26	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₅×C₁₁	#41	1	2	yes	—
28	D₅₅	—	2	2	no	—
29	C₂²×D₁₁	—	5	1	no	—
30	C₂×C₄×C₁₁	C₂×D₅	1	2	yes	—
31	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
32	C₂×Dic₁₁	—	5	1	no	—
33	C₂×Dic₁₁	—	5	2	no	—
34	C₄×D₁₁	—	5	4	no	—
35	C₂×C₄×D₅	—	11	1	no	—
36	C₄²×C₅	D₁₁	1	1	yes	characteristic, complemented
37	#685	—	11	2	no	—
38	#683	—	11	2	no	—
39	C₄×Dic₅	—	11	1	no	—
40	C₅×C₁₁	#117	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
42	C₂×D₁₁	—	5	2	no	—
43	C₂×D₁₁	—	10	2	no	—
44	C₄×C₁₁	—	2	2	no	—
45	C₄×C₁₁	C₄×D₅	1	2	yes	—
46	Dic₁₁	—	5	2	no	—
47	Dic₁₁	—	10	2	no	—
48	C₂²×D₅	—	11	1	no	—
49	C₂×C₄×C₅	C₂×D₁₁	1	2	yes	—
50	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
51	C₂×Dic₅	—	11	1	no	—
52	C₂×Dic₅	—	11	2	no	—
53	C₄×D₅	—	11	4	no	—
54	#117	—	55	1	no	Sylow
55	C₂×C₁₁	C₂×C₄×D₅	1	1	yes	characteristic
56	C₂×C₁₁	#709	1	2	yes	—
57	D₁₁	—	10	2	no	—
58	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
59	C₂×D₅	—	11	2	no	—
60	C₂×D₅	—	22	2	no	—
61	C₄×C₅	—	2	2	no	—
62	C₄×C₅	C₄×D₁₁	1	2	yes	—
63	Dic₅	—	11	2	no	—
64	Dic₅	—	22	2	no	—
65	C₂²×C₄	—	55	1	no	—
66	C₄⋊C₄	—	55	2	no	—
67	C₂²⋊C₄	—	55	2	no	—
68	C₄²	—	55	1	no	—
69	C₄²	D₅₅	1	1	yes	characteristic, complemented
70	C₁₁	#4018	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₅	C₂×C₄×D₁₁	1	1	yes	characteristic
72	C₂×C₅	#4339	1	2	yes	—
73	D₅	—	22	2	no	—
74	C₂³	—	55	1	no	—
75	C₂×C₄	—	55	1	no	—
76	C₂×C₄	—	55	4	no	—
77	C₂×C₄	—	55	2	no	—
78	C₂×C₄	C₂×D₅₅	1	2	yes	—
79	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
80	C₅	#66925	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	55	2	no	—
82	C₂²	—	110	2	no	—
83	C₂²	C₂²×D₅₅	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	—	55	2	no	—
86	C₄	—	110	2	no	—
87	C₄	C₄×D₅₅	1	2	yes	—
88	C₂	—	110	2	no	—
89	C₂	C₂×C₄×D₅₅	1	1	yes	characteristic
90	C₂	#11725031	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₅₅
commutator	C₂×C₅×C₁₁	C₂²×C₄
Frattini	C₂²	C₂²×D₅₅
Fitting	C₄²×C₅×C₁₁	C₂
socle, cosocle	C₂²×C₅×C₁₁	C₂³
prime radical	C₂²×D₅₅	C₂²
hypercenter	C₄²	D₅₅
hypocenter	C₅×C₁₁	#117
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄²×C₅×C₁₁	C₂	semidirect
4. #11724930	C₂	semidirect
5. C₄×Dic₅₅	C₂	semidirect
11. C₄×D₅₅	C₄	semidirect
21. C₄²×C₁₁	D₅	semidirect
36. C₄²×C₅	D₁₁	semidirect
40. C₅×C₁₁	#117	semidirect
69. C₄²	D₅₅	semidirect
70. C₁₁	#4018	semidirect
80. C₅	#66925	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₅₅	2
C₄²×C₅×C₁₁	2
#11724932	2
#11724930	2
C₄×Dic₅₅	2
#66925	5
#4018	11