Subgroups — C₂×C₂₃×D₃₈₅ #47978490

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₃₈₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₁	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₁×C₂₃	C₂
LCS	G ▷ C₅×C₇×C₁₁
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₃₈₅	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₁×C₂₃	C₂	semidirect
3. C₅×C₇×C₁₁×C₂₃	C₂²	semidirect
7. C₂×C₇×C₁₁×C₂₃	D₅	semidirect
10. C₂×C₅×C₁₁×C₂₃	D₇	semidirect
11. C₇×C₁₁×C₂₃	C₂×D₅	semidirect
12. C₂×C₅×C₇×C₂₃	D₁₁	semidirect
14. C₂×D₃₈₅	C₂₃	direct (N × H)
15. C₅×C₁₁×C₂₃	C₂×D₇	semidirect
17. C₅×C₇×C₂₃	C₂×D₁₁	semidirect
18. C₂×C₅×C₇×C₁₁	C₂×C₂₃	semidirect
19. D₃₈₅	C₂×C₂₃	direct (N × H)
21. C₂×C₁₁×C₂₃	D₃₅	semidirect
24. C₅×C₇×C₁₁	C₂²×C₂₃	semidirect
25. C₂×C₇×C₂₃	D₅₅	semidirect
28. C₁₁×C₂₃	C₂×D₃₅	semidirect
29. C₂×C₅×C₂₃	D₇₇	semidirect
32. C₇×C₂₃	C₂×D₅₅	semidirect
33. C₂×C₇×C₁₁	D₅×C₂₃	semidirect
36. C₅×C₂₃	C₂×D₇₇	semidirect
37. C₂×C₅×C₁₁	D₇×C₂₃	semidirect
40. C₇×C₁₁	C₂×D₅×C₂₃	semidirect
41. C₂×C₅×C₇	D₁₁×C₂₃	semidirect
43. C₅×C₁₁	C₂×D₇×C₂₃	semidirect
45. C₂×C₂₃	D₃₈₅	direct (N × H)
47. C₅×C₇	C₂×D₁₁×C₂₃	semidirect
49. C₂₃	C₂×D₃₈₅	direct (N × H)
50. C₂×C₁₁	C₂₃×D₃₅	semidirect
53. C₂×C₇	C₂₃×D₅₅	semidirect
55. C₁₁	C₂×C₂₃×D₃₅	semidirect
56. C₂×C₅	C₂₃×D₇₇	semidirect
58. C₇	C₂×C₂₃×D₅₅	semidirect
59. C₅	C₂×C₂₃×D₇₇	semidirect
62. C₂	C₂₃×D₃₈₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×D₃₈₅	2
C₂×C₅×C₇×C₁₁×C₂₃	2
C₂×C₂₃×D₇₇	5
C₂×C₂₃×D₅₅	7
C₂×C₂₃×D₃₅	11
C₂×D₃₈₅	23

Subgroups — C2×C23×D385 #47978490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×D₃₈₅ #47978490