Subgroups — #13183232

Order 1760.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊D₅₅	C₂	1	4	yes	maximal, complemented
3	C₂×D₂₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×Dic₅₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₅×C₁₁	C₂²	1	2	yes	—
6	C₂²×D₅₅	C₂²	1	2	yes	—
7	C₅×D₄×C₁₁	—	2	2	no	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂²⋊D₅₅	—	2	8	no	—
10	C₂×Dic₅₅	C₂²	1	2	yes	—
11	D₂₂₀	—	2	2	no	—
12	#66993	—	5	1	no	maximal, Hall
13	C₂²×C₅×C₁₁	—	2	4	no	—
14	C₂²×C₅×C₁₁	—	2	2	no	—
15	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
16	C₂×D₅₅	—	2	2	no	—
17	C₂×D₅₅	—	2	4	no	—
18	C₄×C₅×C₁₁	D₄	1	2	yes	complemented
19	Dic₅₅	D₄	1	4	yes	complemented
20	C₂×D₄×C₁₁	D₅	1	1	yes	characteristic, complemented
21	C₂×C₂²⋊D₁₁	—	5	4	no	—
22	C₂×D₄₄	—	5	1	no	—
23	C₄×Dic₁₁	—	5	1	no	—
24	#4086	—	11	1	no	maximal, Hall
25	C₂×C₅×C₁₁	—	4	2	no	—
26	C₂×C₅×C₁₁	C₂×D₄	1	2	yes	—
27	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
28	D₅₅	—	4	2	no	—
29	C₂³×C₁₁	C₂×D₅	1	2	yes	—
30	C₂²×D₁₁	—	5	2	no	—
31	D₄×C₁₁	—	2	2	no	—
32	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
33	C₂²⋊D₁₁	—	10	8	no	—
34	C₂×Dic₁₁	—	5	2	no	—
35	D₄₄	—	10	2	no	—
36	C₂×C₅×D₄	D₁₁	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊D₅	—	11	4	no	—
38	C₂×D₂₀	—	11	1	no	—
39	C₄×Dic₅	—	11	1	no	—
40	C₅×C₁₁	#127	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	2	4	no	—
42	C₂²×C₁₁	—	2	2	no	—
43	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
44	C₂×D₁₁	—	10	4	no	—
45	C₂×D₁₁	—	10	2	no	—
46	C₄×C₁₁	C₂²⋊D₅	1	2	yes	complemented
47	Dic₁₁	—	5	4	no	—
48	C₂³×C₅	C₂×D₁₁	1	2	yes	—
49	C₂²×D₅	—	11	2	no	—
50	C₅×D₄	—	2	2	no	—
51	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
52	C₂²⋊D₅	—	22	8	no	—
53	C₂×Dic₅	—	11	2	no	—
54	D₂₀	—	22	2	no	—
55	#127	—	55	1	no	Sylow
56	C₂×C₁₁	—	4	2	no	—
57	C₂×C₁₁	D₄×D₅	1	2	yes	—
58	C₂×C₁₁	C₂×C₂²⋊D₅	1	1	yes	characteristic
59	D₁₁	—	20	2	no	—
60	C₂²×C₅	—	2	4	no	—
61	C₂²×C₅	—	2	2	no	—
62	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
63	C₂×D₅	—	22	4	no	—
64	C₂×D₅	—	22	2	no	—
65	C₄×C₅	C₂²⋊D₁₁	1	2	yes	complemented
66	Dic₅	—	11	4	no	—
67	C₂×D₄	—	55	4	no	—
68	C₂×D₄	—	55	1	no	—
69	C₂×D₄	D₅₅	1	1	yes	characteristic, complemented
70	C₄²	—	55	1	no	—
71	C₁₁	#4086	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₅	—	4	2	no	—
73	C₂×C₅	D₄×D₁₁	1	2	yes	—
74	C₂×C₅	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
75	D₅	—	44	2	no	—
76	C₂³	—	55	2	no	—
77	C₂³	C₂×D₅₅	1	2	yes	—
78	D₄	—	2	2	no	—
79	D₄	—	110	8	no	—
80	D₄	—	110	2	no	—
81	C₂×C₄	—	55	2	no	—
82	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
83	C₅	#66993	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	2	4	no	—
85	C₂²	—	2	2	no	—
86	C₂²	—	110	4	no	—
87	C₂²	—	110	2	no	—
88	C₂²	C₂²×D₅₅	1	1	yes	characteristic
89	C₄	—	55	4	no	—
90	C₄	C₂²⋊D₅₅	1	2	yes	complemented
91	C₂	—	4	2	no	—
92	C₂	—	220	2	no	—
93	C₂	D₄×D₅₅	1	2	yes	—
94	C₂	C₂×C₂²⋊D₅₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅₅
commutator, socle, cosocle	C₂²×C₅×C₁₁	C₂³
Fitting	C₂×C₅×D₄×C₁₁	C₂
hypercenter	C₂×D₄	D₅₅
hypocenter	C₅×C₁₁	#127
LCS	G ▷ C₂²×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₄×C₁₁	C₂	semidirect
2. C₂×C₂²⋊D₅₅	C₂	semidirect
3. C₂×D₂₂₀	C₂	semidirect
4. C₄×Dic₅₅	C₂	semidirect
18. C₄×C₅×C₁₁	D₄	semidirect
19. Dic₅₅	D₄	semidirect
20. C₂×D₄×C₁₁	D₅	semidirect
36. C₂×C₅×D₄	D₁₁	semidirect
40. C₅×C₁₁	#127	semidirect
46. C₄×C₁₁	C₂²⋊D₅	semidirect
65. C₄×C₅	C₂²⋊D₁₁	semidirect
69. C₂×D₄	D₅₅	semidirect
71. C₁₁	#4086	semidirect
83. C₅	#66993	semidirect
90. C₄	C₂²⋊D₅₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₄×C₁₁	2
C₂×C₂²⋊D₅₅	2
C₂×D₂₂₀	2
C₄×Dic₅₅	2
#66993	5
#4086	11