Subgroups — D₅₅⋊D₁₆₁ #47978475

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₈₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₂₃×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₇₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₁×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₁₆₁	—	5	1	no	maximal, Hall
6	D₅₅⋊D₂₃	—	7	1	no	maximal, Hall
7	D₁₇₇₁	D₅	1	1	yes	characteristic, complemented
8	C₁₁×D₁₆₁	—	5	1	no	—
9	C₇×D₁₁×C₂₃	—	5	1	no	—
10	D₅×D₁₆₁	—	11	1	no	maximal, Hall
11	C₂₃×D₅₅	D₇	1	1	yes	characteristic, complemented
12	C₁₁×D₁₁₅	—	7	1	no	—
13	C₅×D₂₅₃	—	7	1	no	—
14	C₇×C₁₁×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	D₈₀₅	D₁₁	1	1	yes	characteristic, complemented
16	C₇×D₅×C₂₃	—	11	1	no	—
17	C₅×D₁₆₁	—	11	1	no	—
18	D₃₅⋊D₁₁	—	23	1	no	maximal, Hall
19	C₅×C₁₁×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₁₁×D₂₃	—	35	1	no	Hall
21	C₅×C₇×C₂₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
22	C₁₁×D₃₅	—	23	1	no	—
23	C₇×D₅₅	D₂₃	1	1	yes	characteristic, complemented
24	C₅×D₇₇	—	23	1	no	—
25	C₂×D₁₆₁	—	55	1	no	Hall
26	D₂₅₃	—	7	1	no	—
27	C₁₁×D₂₃	—	35	1	no	—
28	D₁₁×C₂₃	—	5	1	no	—
29	D₅×D₂₃	—	77	1	no	Hall
30	C₅×C₇×C₁₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇×C₂₃	—	55	1	no	—
32	D₁₆₁	—	5	1	no	—
33	D₁₆₁	—	11	1	no	—
34	D₇×D₁₁	—	115	1	no	Hall
35	C₁₁×C₂₃	D₅×D₇	1	1	yes	characteristic, complemented, Hall
36	D₁₁₅	—	7	1	no	—
37	C₅×D₂₃	—	77	1	no	—
38	D₅×C₂₃	—	11	1	no	—
39	D₅×D₁₁	—	161	1	no	Hall
40	C₇×C₂₃	D₅×D₁₁	1	1	yes	characteristic, complemented, Hall
41	D₇₇	—	23	1	no	—
42	C₇×D₁₁	—	5	1	no	—
43	C₁₁×D₇	—	115	1	no	—
44	D₅×D₇	—	253	1	no	Hall
45	C₅×C₂₃	D₇×D₁₁	1	1	yes	characteristic, complemented, Hall
46	D₅₅	D₁₆₁	1	1	yes	characteristic, complemented
47	C₅×D₁₁	—	161	1	no	—
48	D₅×C₁₁	—	161	1	no	—
49	C₂×D₂₃	—	385	1	no	Hall
50	C₇×C₁₁	D₅×D₂₃	1	1	yes	characteristic, complemented, Hall
51	D₃₅	—	23	1	no	—
52	C₅×D₇	—	253	1	no	—
53	C₇×D₅	—	11	1	no	—
54	C₅×C₁₁	C₂×D₁₆₁	1	1	yes	characteristic, complemented, Hall
55	C₂×C₂₃	—	55	1	no	—
56	D₂₃	—	35	1	no	—
57	D₂₃	—	77	1	no	—
58	C₂×D₁₁	—	805	1	no	Hall
59	C₅×C₇	D₁₁×D₂₃	1	1	yes	characteristic, complemented, Hall
60	C₂×D₇	—	1265	1	no	Hall
61	C₂₃	D₃₅⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₁₁	—	805	1	no	—
63	D₁₁	—	5	1	no	—
64	D₁₁	—	161	1	no	—
65	C₂×D₅	—	1771	1	no	Hall
66	C₂×C₇	—	55	1	no	—
67	D₇	—	115	1	no	—
68	D₇	—	253	1	no	—
69	C₁₁	D₅×D₁₆₁	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₅	—	1771	1	no	—
71	D₅	—	11	1	no	—
72	D₅	—	161	1	no	—
73	C₇	D₅₅⋊D₂₃	1	1	yes	characteristic, complemented, Sylow
74	C₅	D₁₁×D₁₆₁	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	8855	1	no	Sylow
76	C₂	—	805	1	no	—
77	C₂	—	55	1	no	—
78	C₂	—	1771	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₁₁×C₂₃	C₂²
LCS	G ▷ C₅×C₇×C₁₁×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₈₀₅	C₂	semidirect
2. C₇×C₂₃×D₅₅	C₂	semidirect
3. C₅×D₁₇₇₁	C₂	semidirect
4. C₅×C₇×C₁₁×C₂₃	C₂²	semidirect
7. D₁₇₇₁	D₅	semidirect
11. C₂₃×D₅₅	D₇	semidirect
14. C₇×C₁₁×C₂₃	C₂×D₅	semidirect
15. D₈₀₅	D₁₁	semidirect
19. C₅×C₁₁×C₂₃	C₂×D₇	semidirect
21. C₅×C₇×C₂₃	C₂×D₁₁	semidirect
23. C₇×D₅₅	D₂₃	semidirect
30. C₅×C₇×C₁₁	C₂×D₂₃	semidirect
35. C₁₁×C₂₃	D₅×D₇	semidirect
40. C₇×C₂₃	D₅×D₁₁	semidirect
45. C₅×C₂₃	D₇×D₁₁	semidirect
46. D₅₅	D₁₆₁	semidirect
50. C₇×C₁₁	D₅×D₂₃	semidirect
54. C₅×C₁₁	C₂×D₁₆₁	semidirect
59. C₅×C₇	D₁₁×D₂₃	semidirect
61. C₂₃	D₃₅⋊D₁₁	semidirect
69. C₁₁	D₅×D₁₆₁	semidirect
73. C₇	D₅₅⋊D₂₃	semidirect
74. C₅	D₁₁×D₁₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×D₈₀₅	2
C₇×C₂₃×D₅₅	2
C₅×D₁₇₇₁	2
D₁₁×D₁₆₁	5
D₅₅⋊D₂₃	7
D₅×D₁₆₁	11
D₃₅⋊D₁₁	23

Subgroups — D55⋊D161 #47978475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₅⋊D₁₆₁ #47978475