Subgroups — C₃×D₂₃×D₈₅ #37553305

Order 23460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₉₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂₃×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₇×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₃×D₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₁₇×D₂₃	—	5	1	no	maximal, Hall
7	D₁₉₅₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂₃×D₈₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₇×D₂₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₃₉₁	—	5	1	no	—
11	C₃×C₂₃×D₁₇	—	5	1	no	—
12	C₃×C₁₇×D₂₃	D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₇×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₁₇×D₂₃	—	5	1	no	Hall
15	C₃×D₅×D₂₃	—	17	1	no	maximal, Hall
16	C₃×C₁₇×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×D₈₅	—	23	1	no	maximal, Hall
18	D₃₉₁	—	5	1	no	—
19	C₁₇×D₂₃	C₃×D₅	1	1	yes	characteristic, complemented
20	C₂₃×D₁₇	—	5	1	no	—
21	C₃×D₁₁₅	—	17	1	no	—
22	C₃×D₅×C₂₃	—	17	1	no	—
23	C₃×C₅×D₂₃	D₁₇	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×C₁₇	—	23	1	no	—
25	C₃×D₈₅	—	23	1	no	—
26	C₃×D₈₅	D₂₃	1	1	yes	characteristic, direct product factor
27	D₅×D₂₃	—	17	1	no	Hall
28	C₁₇×C₂₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×C₂₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×D₈₅	—	23	1	no	Hall
31	C₂×C₃×D₂₃	—	85	1	no	Hall
32	C₃×C₅×C₁₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
33	D₁₁₅	—	17	1	no	—
34	C₅×D₂₃	C₃×D₁₇	1	1	yes	characteristic, complemented
35	D₅×C₂₃	—	17	1	no	—
36	C₂×C₃×D₁₇	—	115	1	no	Hall
37	C₂×C₅×C₁₇	—	23	1	no	—
38	D₈₅	—	23	1	no	—
39	D₈₅	C₃×D₂₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₂₃	—	85	1	no	—
41	C₃×D₂₃	—	85	1	no	—
42	C₃×D₂₃	D₈₅	1	1	yes	characteristic, direct product factor
43	C₅×C₂₃	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₁₇	—	23	1	no	—
45	C₃×D₁₇	—	5	1	no	—
46	C₃×D₁₇	—	115	1	no	—
47	C₂×D₂₃	—	85	1	no	Hall
48	C₅×C₁₇	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
49	C₃×C₂₃	C₂×D₈₅	1	1	yes	characteristic, complemented, Hall
50	C₂×D₁₇	—	115	1	no	Hall
51	C₂×C₃×D₅	—	391	1	no	Hall
52	C₃×C₁₇	D₅×D₂₃	1	1	yes	characteristic, complemented, Hall
53	C₂×C₂₃	—	85	1	no	—
54	D₂₃	—	85	1	no	—
55	D₂₃	C₃×D₈₅	1	1	yes	characteristic, direct product factor
56	C₂×C₁₇	—	23	1	no	—
57	D₁₇	—	5	1	no	—
58	D₁₇	—	115	1	no	—
59	C₂×C₃×C₅	—	23	1	no	—
60	C₃×D₅	—	17	1	no	—
61	C₃×D₅	—	391	1	no	—
62	C₂₃	C₂×C₃×D₈₅	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	391	1	no	Hall
64	C₁₇	C₃×D₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	D₁₇×D₂₃	1	1	yes	characteristic, complemented, Hall
66	C₂²×C₃	—	1955	1	no	Hall
67	C₂×C₅	—	23	1	no	—
68	D₅	—	17	1	no	—
69	D₅	—	391	1	no	—
70	C₂×C₃	—	23	1	no	—
71	C₂×C₃	—	85	1	no	—
72	C₂×C₃	—	1955	1	no	—
73	C₅	C₃×D₁₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	1955	1	no	Sylow
75	C₃	D₂₃×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	23	1	no	—
77	C₂	—	85	1	no	—
78	C₂	—	1955	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₂₃×D₈₅
commutator, cosocle, hypocenter	C₅×C₁₇×C₂₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₂₃	C₂²
LCS	G ▷ C₅×C₁₇×C₂₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₉₅₅	C₂	semidirect
2. C₃×C₂₃×D₈₅	C₂	semidirect
3. C₃×C₅×C₁₇×D₂₃	C₂	semidirect
4. D₂₃×D₈₅	C₃	direct (N × H)
5. C₃×C₅×C₁₇×C₂₃	C₂²	semidirect
7. D₁₉₅₅	C₂×C₃	semidirect
8. C₂₃×D₈₅	C₂×C₃	semidirect
9. C₅×C₁₇×D₂₃	C₂×C₃	semidirect
12. C₃×C₁₇×D₂₃	D₅	semidirect
13. C₅×C₁₇×C₂₃	C₂²×C₃	semidirect
16. C₃×C₁₇×C₂₃	C₂×D₅	semidirect
19. C₁₇×D₂₃	C₃×D₅	semidirect
23. C₃×C₅×D₂₃	D₁₇	semidirect
26. C₃×D₈₅	D₂₃	direct (N × H)
28. C₁₇×C₂₃	C₂×C₃×D₅	semidirect
29. C₃×C₅×C₂₃	C₂×D₁₇	semidirect
32. C₃×C₅×C₁₇	C₂×D₂₃	semidirect
34. C₅×D₂₃	C₃×D₁₇	semidirect
39. D₈₅	C₃×D₂₃	direct (N × H)
42. C₃×D₂₃	D₈₅	direct (N × H)
43. C₅×C₂₃	C₂×C₃×D₁₇	semidirect
48. C₅×C₁₇	C₂×C₃×D₂₃	semidirect
49. C₃×C₂₃	C₂×D₈₅	semidirect
52. C₃×C₁₇	D₅×D₂₃	semidirect
55. D₂₃	C₃×D₈₅	direct (N × H)
62. C₂₃	C₂×C₃×D₈₅	semidirect
64. C₁₇	C₃×D₅×D₂₃	semidirect
65. C₃×C₅	D₁₇×D₂₃	semidirect
73. C₅	C₃×D₁₇×D₂₃	semidirect
75. C₃	D₂₃×D₈₅	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×D₁₉₅₅	2
C₃×C₂₃×D₈₅	2
C₃×C₅×C₁₇×D₂₃	2
D₂₃×D₈₅	3
C₃×D₁₇×D₂₃	5
C₃×D₅×D₂₃	17
C₂×C₃×D₈₅	23

Subgroups — C3×D23×D85 #37553305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₂₃×D₈₅ #37553305