Subgroups — D₅×C₂₃×D₇₇ #47978469

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₃₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₅×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₃×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₁×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₃×D₇₇	—	5	1	no	maximal, Hall
6	D₅×D₁₁×C₂₃	—	7	1	no	maximal, Hall
7	C₂₃×D₇₇	—	5	1	no	—
8	C₂₃×D₇₇	D₅	1	1	yes	characteristic, direct product factor
9	C₂×C₇×C₁₁×C₂₃	—	5	1	no	—
10	D₅×D₇×C₂₃	—	11	1	no	maximal, Hall
11	C₂₃×D₅₅	—	7	1	no	—
12	D₅×C₁₁×C₂₃	D₇	1	1	yes	characteristic, complemented
13	C₅×D₁₁×C₂₃	—	7	1	no	—
14	C₇×C₁₁×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂₃×D₃₅	—	11	1	no	—
16	C₇×D₅×C₂₃	D₁₁	1	1	yes	characteristic, complemented
17	C₅×D₇×C₂₃	—	11	1	no	—
18	D₅×D₇₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₅×C₁₁×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₁×C₂₃	—	35	1	no	Hall
21	C₅×C₇×C₂₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
22	D₃₈₅	C₂×C₂₃	1	1	yes	characteristic, complemented
23	C₇×D₅×C₁₁	C₂×C₂₃	1	1	yes	characteristic, complemented
24	C₅×D₇₇	C₂×C₂₃	1	1	yes	characteristic, complemented
25	C₂×D₇×C₂₃	—	55	1	no	Hall
26	C₂×C₁₁×C₂₃	—	5	1	no	—
27	D₁₁×C₂₃	—	7	1	no	—
28	D₁₁×C₂₃	—	35	1	no	—
29	C₂×D₅×C₂₃	—	77	1	no	Hall
30	C₅×C₇×C₁₁	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇×C₂₃	—	5	1	no	—
32	D₇×C₂₃	—	11	1	no	—
33	D₇×C₂₃	—	55	1	no	—
34	C₂×D₇₇	—	5	1	no	Hall
35	C₁₁×C₂₃	D₅×D₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₂₃	—	77	1	no	—
37	D₅×C₂₃	—	77	1	no	—
38	D₅×C₂₃	D₇₇	1	1	yes	characteristic, direct product factor
39	D₅×D₁₁	—	7	1	no	Hall
40	C₇×C₂₃	D₅×D₁₁	1	1	yes	characteristic, complemented, Hall
41	C₂×C₇×C₁₁	—	5	1	no	—
42	D₇₇	—	5	1	no	—
43	D₇₇	D₅×C₂₃	1	1	yes	characteristic, direct product factor
44	D₅×D₇	—	11	1	no	Hall
45	C₅×C₂₃	C₂×D₇₇	1	1	yes	characteristic, complemented, Hall
46	D₅₅	—	7	1	no	—
47	C₅×D₁₁	—	7	1	no	—
48	D₅×C₁₁	D₇×C₂₃	1	1	yes	characteristic, complemented
49	C₂²×C₂₃	—	385	1	no	Hall
50	C₇×C₁₁	C₂×D₅×C₂₃	1	1	yes	characteristic, complemented, Hall
51	D₃₅	—	11	1	no	—
52	C₅×D₇	—	11	1	no	—
53	C₇×D₅	D₁₁×C₂₃	1	1	yes	characteristic, complemented
54	C₅×C₁₁	C₂×D₇×C₂₃	1	1	yes	characteristic, complemented, Hall
55	C₂×C₂₃	—	5	1	no	—
56	C₂×C₂₃	—	77	1	no	—
57	C₂×C₂₃	—	385	1	no	—
58	C₂×D₁₁	—	35	1	no	Hall
59	C₅×C₇	C₂×D₁₁×C₂₃	1	1	yes	characteristic, complemented, Hall
60	C₂×D₇	—	55	1	no	Hall
61	C₂₃	D₅×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₁₁	—	5	1	no	—
63	D₁₁	—	7	1	no	—
64	D₁₁	—	35	1	no	—
65	C₂×D₅	—	77	1	no	Hall
66	C₂×C₇	—	5	1	no	—
67	D₇	—	11	1	no	—
68	D₇	—	55	1	no	—
69	C₁₁	D₅×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₅	—	77	1	no	—
71	D₅	—	77	1	no	—
72	D₅	C₂₃×D₇₇	1	1	yes	characteristic, direct product factor
73	C₇	D₅×D₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
74	C₅	C₂×C₂₃×D₇₇	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	385	1	no	Sylow
76	C₂	—	5	1	no	—
77	C₂	—	77	1	no	—
78	C₂	—	385	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	D₅×D₇₇
commutator, cosocle, hypocenter	C₅×C₇×C₁₁	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₂₃	C₂²
LCS	G ▷ C₅×C₇×C₁₁
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₃₈₅	C₂	semidirect
2. C₇×D₅×C₁₁×C₂₃	C₂	semidirect
3. C₅×C₂₃×D₇₇	C₂	semidirect
4. C₅×C₇×C₁₁×C₂₃	C₂²	semidirect
8. C₂₃×D₇₇	D₅	direct (N × H)
12. D₅×C₁₁×C₂₃	D₇	semidirect
14. C₇×C₁₁×C₂₃	C₂×D₅	semidirect
16. C₇×D₅×C₂₃	D₁₁	semidirect
18. D₅×D₇₇	C₂₃	direct (N × H)
19. C₅×C₁₁×C₂₃	C₂×D₇	semidirect
21. C₅×C₇×C₂₃	C₂×D₁₁	semidirect
22. D₃₈₅	C₂×C₂₃	semidirect
23. C₇×D₅×C₁₁	C₂×C₂₃	semidirect
24. C₅×D₇₇	C₂×C₂₃	semidirect
30. C₅×C₇×C₁₁	C₂²×C₂₃	semidirect
35. C₁₁×C₂₃	D₅×D₇	semidirect
38. D₅×C₂₃	D₇₇	direct (N × H)
40. C₇×C₂₃	D₅×D₁₁	semidirect
43. D₇₇	D₅×C₂₃	direct (N × H)
45. C₅×C₂₃	C₂×D₇₇	semidirect
48. D₅×C₁₁	D₇×C₂₃	semidirect
50. C₇×C₁₁	C₂×D₅×C₂₃	semidirect
53. C₇×D₅	D₁₁×C₂₃	semidirect
54. C₅×C₁₁	C₂×D₇×C₂₃	semidirect
59. C₅×C₇	C₂×D₁₁×C₂₃	semidirect
61. C₂₃	D₅×D₇₇	direct (N × H)
69. C₁₁	D₅×D₇×C₂₃	semidirect
72. D₅	C₂₃×D₇₇	direct (N × H)
73. C₇	D₅×D₁₁×C₂₃	semidirect
74. C₅	C₂×C₂₃×D₇₇	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×D₃₈₅	2
C₇×D₅×C₁₁×C₂₃	2
C₅×C₂₃×D₇₇	2
C₂×C₂₃×D₇₇	5
D₅×D₁₁×C₂₃	7
D₅×D₇×C₂₃	11
D₅×D₇₇	23

Subgroups — D5×C23×D77 #47978469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₂₃×D₇₇ #47978469