Subgroups — C₃×C₅×C₂₃×D₃₅ #37563404

Order 24150.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₂₃×D₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₃×D₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₅×D₇×C₂₃	—	5	1	no	maximal
5	C₅²×C₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×D₅×C₂₃	—	7	1	no	maximal, Hall
7	C₃×C₅×C₇×C₂₃	—	2	2	no	—
8	C₃×C₅×C₇×C₂₃	D₅	1	1	yes	characteristic, complemented
9	C₃×C₅×C₇×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×C₅²×C₂₃	D₇	1	1	yes	characteristic, complemented, Hall
11	C₂₃×D₃₅	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₅×D₇×C₂₃	—	5	1	no	—
13	C₅×D₅×C₂₃	—	7	1	no	Hall
14	C₃×C₅×D₃₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×D₇×C₂₃	—	5	1	no	Hall
16	C₅×C₇×C₂₃	—	2	2	no	—
17	C₅×C₇×C₂₃	C₃×D₅	1	1	yes	characteristic, complemented
18	C₅×C₇×C₂₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
19	C₂×C₃×C₅×C₂₃	—	35	1	no	—
20	C₃×D₅×C₂₃	—	7	1	no	—
21	C₅²×C₂₃	C₃×D₇	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅²×C₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₂₃	C₅×D₅	1	1	yes	characteristic, complemented, Hall
24	C₅×D₃₅	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₅×C₂₃	—	2	2	no	—
26	C₃×C₅×C₂₃	C₅×D₇	1	1	yes	characteristic, complemented
27	C₃×C₅×C₂₃	D₃₅	1	1	yes	characteristic, direct product factor
28	D₇×C₂₃	—	5	1	no	Hall
29	C₂×C₅×C₂₃	—	35	1	no	—
30	D₅×C₂₃	—	7	1	no	—
31	C₃×D₃₅	C₅×C₂₃	1	1	yes	characteristic, direct product factor
32	C₃×C₅×D₇	—	5	1	no	—
33	C₅²×C₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
34	C₇×C₂₃	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Hall
35	C₃×C₅×D₅	—	7	1	no	Hall
36	C₂×C₃×C₂₃	—	35	1	no	Hall
37	C₅×C₂₃	—	2	2	no	—
38	C₅×C₂₃	C₃×C₅×D₇	1	1	yes	characteristic, complemented
39	C₅×C₂₃	C₃×D₃₅	1	1	yes	characteristic, direct product factor
40	C₃×C₅×C₇	—	2	2	no	—
41	C₃×C₅×C₇	D₅×C₂₃	1	1	yes	characteristic, complemented
42	C₃×C₅×C₇	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented
43	C₃×C₅²	D₇×C₂₃	1	1	yes	characteristic, complemented, Hall
44	D₃₅	C₃×C₅×C₂₃	1	1	yes	characteristic, direct product factor
45	C₅×D₇	—	5	1	no	—
46	C₃×C₂₃	C₅×D₃₅	1	1	yes	characteristic, direct product factor, Hall
47	C₅×D₅	—	7	1	no	Hall
48	C₂×C₂₃	—	35	1	no	Hall
49	C₃×D₇	—	5	1	no	Hall
50	C₅×C₇	—	2	2	no	—
51	C₅×C₇	C₃×D₅×C₂₃	1	1	yes	characteristic, complemented
52	C₅×C₇	C₂×C₃×C₅×C₂₃	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅	—	35	1	no	—
54	C₃×D₅	—	7	1	no	—
55	C₅²	C₃×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
56	C₂₃	C₃×C₅×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
57	C₃×C₇	C₅×D₅×C₂₃	1	1	yes	characteristic, complemented, Hall
58	C₃×C₅	—	2	2	no	—
59	C₃×C₅	C₅×D₇×C₂₃	1	1	yes	characteristic, complemented
60	C₃×C₅	C₂₃×D₃₅	1	1	yes	characteristic, direct product factor
61	D₇	—	5	1	no	Hall
62	C₂×C₅	—	35	1	no	—
63	D₅	—	7	1	no	—
64	C₇	C₃×C₅×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	35	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₃×C₅×D₇×C₂₃	1	1	yes	characteristic, complemented
68	C₅	C₃×C₂₃×D₃₅	1	1	yes	characteristic, direct product factor
69	C₃	C₅×C₂₃×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	—	35	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₂₃	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₃×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₂₃	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₃×C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇×C₂₃	C₂	semidirect
2. C₅×C₂₃×D₃₅	C₃	direct (N × H)
3. C₃×C₂₃×D₃₅	C₅	direct (N × H)
5. C₅²×C₇×C₂₃	C₂×C₃	semidirect
8. C₃×C₅×C₇×C₂₃	D₅	semidirect
9. C₃×C₅×C₇×C₂₃	C₂×C₅	semidirect
10. C₃×C₅²×C₂₃	D₇	semidirect
11. C₂₃×D₃₅	C₃×C₅	direct (N × H)
14. C₃×C₅×D₃₅	C₂₃	direct (N × H)
17. C₅×C₇×C₂₃	C₃×D₅	semidirect
18. C₅×C₇×C₂₃	C₂×C₃×C₅	semidirect
21. C₅²×C₂₃	C₃×D₇	semidirect
22. C₃×C₅²×C₇	C₂×C₂₃	semidirect
23. C₃×C₇×C₂₃	C₅×D₅	semidirect
24. C₅×D₃₅	C₃×C₂₃	direct (N × H)
26. C₃×C₅×C₂₃	C₅×D₇	semidirect
27. C₃×C₅×C₂₃	D₃₅	direct (N × H)
31. C₃×D₃₅	C₅×C₂₃	direct (N × H)
33. C₅²×C₇	C₂×C₃×C₂₃	semidirect
34. C₇×C₂₃	C₃×C₅×D₅	semidirect
38. C₅×C₂₃	C₃×C₅×D₇	semidirect
39. C₅×C₂₃	C₃×D₃₅	direct (N × H)
41. C₃×C₅×C₇	D₅×C₂₃	semidirect
42. C₃×C₅×C₇	C₂×C₅×C₂₃	semidirect
43. C₃×C₅²	D₇×C₂₃	semidirect
44. D₃₅	C₃×C₅×C₂₃	direct (N × H)
46. C₃×C₂₃	C₅×D₃₅	direct (N × H)
51. C₅×C₇	C₃×D₅×C₂₃	semidirect
52. C₅×C₇	C₂×C₃×C₅×C₂₃	semidirect
55. C₅²	C₃×D₇×C₂₃	semidirect
56. C₂₃	C₃×C₅×D₃₅	direct (N × H)
57. C₃×C₇	C₅×D₅×C₂₃	semidirect
59. C₃×C₅	C₅×D₇×C₂₃	semidirect
60. C₃×C₅	C₂₃×D₃₅	direct (N × H)
64. C₇	C₃×C₅×D₅×C₂₃	semidirect
67. C₅	C₃×C₅×D₇×C₂₃	semidirect
68. C₅	C₃×C₂₃×D₃₅	direct (N × H)
69. C₃	C₅×C₂₃×D₃₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₇×C₂₃	2
C₅×C₂₃×D₃₅	3
C₃×C₂₃×D₃₅	5
C₃×C₅×D₇×C₂₃	5
C₃×C₅×D₅×C₂₃	7
C₃×C₅×D₃₅	23

Subgroups — C3×C5×C23×D35 #37563404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₂₃×D₃₅ #37563404