Subgroups — C₄×#89166 #13182799

Order 1760.

216 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	C₂×#89166	C₂	1	2	yes	maximal
3	C₄×C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₅×Dic₁₁	C₂	1	2	yes	maximal, complemented
6	C₂²×D₅₅	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₅₅	C₂²	1	1	yes	characteristic
9	C₄×D₅₅	C₄	1	4	yes	complemented
10	C₂×C₁₁×Dic₅	C₂²	1	2	yes	—
11	C₂×C₅×Dic₁₁	C₂²	1	2	yes	—
12	#89166	C₄	1	8	yes	direct product factor
13	C₄²×D₁₁	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×D₅₅	C₂×C₄	1	4	yes	—
16	C₂×D₅₅	C₂×C₄	1	2	yes	—
17	C₄×C₅×C₁₁	C₂×C₄	1	2	yes	complemented
18	Dic₅₅	C₂×C₄	1	2	yes	complemented
19	C₅×Dic₁₁	C₂×C₄	1	4	yes	complemented
20	C₁₁×Dic₅	C₂×C₄	1	4	yes	complemented
21	C₂×C₄×D₁₁	—	5	2	no	—
22	C₂×C₄×D₁₁	—	5	1	no	—
23	C₄²×C₁₁	—	5	1	no	—
24	C₄×Dic₁₁	—	5	2	no	—
25	C₄×Dic₁₁	D₅	1	1	yes	characteristic, complemented
26	C₄²×D₅	—	11	1	no	maximal, Hall
27	C₂×C₅×C₁₁	C₂²×C₄	1	2	yes	—
28	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
29	D₅₅	C₄²	1	4	yes	complemented
30	C₂²×D₁₁	—	5	1	no	—
31	C₂×C₄×C₁₁	—	5	2	no	—
32	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
33	C₂×Dic₁₁	—	5	1	no	—
34	C₂×Dic₁₁	C₂×D₅	1	2	yes	—
35	C₄×D₁₁	—	5	4	no	—
36	C₄×D₁₁	—	5	8	no	—
37	C₂×C₄×D₅	—	11	1	no	—
38	C₂×C₄×D₅	—	11	2	no	—
39	C₄²×C₅	—	11	1	no	—
40	C₄×Dic₅	—	11	2	no	—
41	C₄×Dic₅	D₁₁	1	1	yes	characteristic, complemented
42	C₅×C₁₁	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
43	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
44	C₂×D₁₁	—	5	4	no	—
45	C₂×D₁₁	—	5	2	no	—
46	C₄×C₁₁	—	5	4	no	—
47	C₄×C₁₁	C₄×D₅	1	2	yes	complemented
48	Dic₁₁	—	5	2	no	—
49	Dic₁₁	C₄×D₅	1	4	yes	complemented
50	C₂²×D₅	—	11	1	no	—
51	C₂×C₄×C₅	—	11	2	no	—
52	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
53	C₂×Dic₅	—	11	1	no	—
54	C₂×Dic₅	C₂×D₁₁	1	2	yes	—
55	C₄×D₅	—	11	4	no	—
56	C₄×D₅	—	11	8	no	—
57	C₂×C₄²	—	55	1	no	Sylow
58	C₂×C₁₁	C₂×C₄×D₅	1	2	yes	—
59	C₂×C₁₁	C₂×C₄×D₅	1	1	yes	characteristic
60	D₁₁	—	5	4	no	—
61	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
62	C₂×D₅	—	11	4	no	—
63	C₂×D₅	—	11	2	no	—
64	C₄×C₅	—	11	4	no	—
65	C₄×C₅	C₄×D₁₁	1	2	yes	complemented
66	Dic₅	—	11	2	no	—
67	Dic₅	C₄×D₁₁	1	4	yes	complemented
68	C₂²×C₄	—	55	2	no	—
69	C₂²×C₄	—	55	1	no	—
70	C₄²	—	5	1	no	—
71	C₄²	—	11	1	no	—
72	C₄²	—	55	2	no	—
73	C₁₁	C₄²×D₅	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₅	C₂×C₄×D₁₁	1	2	yes	—
75	C₂×C₅	C₂×C₄×D₁₁	1	1	yes	characteristic
76	D₅	—	11	4	no	—
77	C₂³	—	55	1	no	—
78	C₂×C₄	—	5	2	no	—
79	C₂×C₄	—	11	2	no	—
80	C₂×C₄	—	55	8	no	—
81	C₂×C₄	—	55	1	no	—
82	C₂×C₄	—	55	4	no	—
83	C₂×C₄	D₅×D₁₁	1	1	yes	characteristic
84	C₅	C₄²×D₁₁	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	55	4	no	—
86	C₂²	—	55	2	no	—
87	C₂²	C₂×D₅×D₁₁	1	1	yes	characteristic
88	C₄	—	5	4	no	—
89	C₄	—	11	4	no	—
90	C₄	—	55	2	no	—
91	C₄	#89166	1	2	yes	direct product factor
92	C₂	—	55	4	no	—
93	C₂	C₄×D₅×D₁₁	1	2	yes	—
94	C₂	C₂×#89166	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₅×D₁₁
commutator, hypocenter	C₅×C₁₁	C₂×C₄²
Frattini	C₂²	C₂×D₅×D₁₁
Fitting	C₂×C₄×C₅×C₁₁	C₂²
socle, cosocle	C₂²×C₅×C₁₁	C₂³
prime radical	C₂²×D₅₅	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×C₁₁×Dic₅	C₂	semidirect
4. C₄×C₅×Dic₁₁	C₂	semidirect
5. Dic₅×Dic₁₁	C₂	semidirect
9. C₄×D₅₅	C₄	semidirect
12. #89166	C₄	direct (N × H)
17. C₄×C₅×C₁₁	C₂×C₄	semidirect
18. Dic₅₅	C₂×C₄	semidirect
19. C₅×Dic₁₁	C₂×C₄	semidirect
20. C₁₁×Dic₅	C₂×C₄	semidirect
25. C₄×Dic₁₁	D₅	semidirect
29. D₅₅	C₄²	semidirect
41. C₄×Dic₅	D₁₁	semidirect
42. C₅×C₁₁	C₂×C₄²	semidirect
47. C₄×C₁₁	C₄×D₅	semidirect
49. Dic₁₁	C₄×D₅	semidirect
65. C₄×C₅	C₄×D₁₁	semidirect
67. Dic₅	C₄×D₁₁	semidirect
73. C₁₁	C₄²×D₅	semidirect
84. C₅	C₄²×D₁₁	semidirect
91. C₄	#89166	direct (N × H)

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
C₂×#89166	2
C₄×C₁₁×Dic₅	2
C₄×C₅×Dic₁₁	2
Dic₅×Dic₁₁	2
C₄²×D₁₁	5
C₄²×D₅	11

Subgroups — C4×#89166 #13182799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#89166 #13182799