Subgroups — C₂×C₃×D₃×C₇×C₂₃ #19154018

Order 5796.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₇×C₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₇×C₂₃	—	3	1	no	maximal
4	C₂×D₃×C₇×C₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₇×C₂₃	—	2	1	no	—
7	C₂×C₃×C₇×C₂₃	—	3	2	no	—
8	C₂×C₃×C₇×C₂₃	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₃×C₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
10	D₃×C₇×C₂₃	C₂×C₃	1	2	yes	direct product factor
11	C₂×C₃×D₃×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₇×C₂₃	—	3	1	no	Hall
13	C₃×C₇×C₂₃	—	2	1	no	—
14	C₃×C₇×C₂₃	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₃×C₇×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃²×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×D₃×C₂₃	C₂×C₇	1	2	yes	direct product factor
18	C₂×C₇×C₂₃	—	3	2	no	—
19	C₂×C₇×C₂₃	C₃×D₃	1	1	yes	characteristic, direct product factor
20	C₂²×C₃×C₂₃	—	3	1	no	—
21	C₂×D₃×C₂₃	C₃×C₇	1	1	yes	characteristic, direct product factor
22	C₂×C₃×D₃×C₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₃²×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
24	C₇×C₂₃	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₂₃	—	2	1	no	—
26	C₂×C₃×C₂₃	—	3	2	no	—
27	C₂×C₃×C₂₃	D₃×C₇	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₂₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
29	D₃×C₂₃	C₂×C₃×C₇	1	2	yes	direct product factor
30	C₂×C₃²×C₇	C₂×C₂₃	1	1	yes	characteristic, complemented
31	C₃×D₃×C₇	C₂×C₂₃	1	2	yes	direct product factor
32	C₂²×C₂₃	—	3	1	no	Hall
33	C₂²×C₃×C₇	—	3	1	no	—
34	C₂×D₃×C₇	C₃×C₂₃	1	1	yes	characteristic, direct product factor
35	C₃×C₂₃	—	2	1	no	—
36	C₃×C₂₃	C₂×D₃×C₇	1	1	yes	characteristic, direct product factor
37	C₃×C₂₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
38	C₃²×C₇	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₂₃	—	3	2	no	—
40	C₂×C₂₃	C₃×D₃×C₇	1	1	yes	characteristic, direct product factor
41	C₂×C₃×C₇	—	2	1	no	—
42	C₂×C₃×C₇	—	3	2	no	—
43	C₂×C₃×C₇	D₃×C₂₃	1	1	yes	characteristic, direct product factor
44	C₂×C₃×C₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
45	D₃×C₇	C₂×C₃×C₂₃	1	2	yes	direct product factor
46	C₂×C₃×D₃	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
47	C₂²×C₇	—	3	1	no	Hall
48	C₂₃	C₂×C₃×D₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
49	C₃×C₇	—	2	1	no	—
50	C₃×C₇	C₂×D₃×C₂₃	1	1	yes	characteristic, direct product factor
51	C₃×C₇	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented
52	C₂×C₃²	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
53	C₃×D₃	C₂×C₇×C₂₃	1	2	yes	direct product factor
54	C₂×C₇	—	3	2	no	—
55	C₂×C₇	C₃×D₃×C₂₃	1	1	yes	characteristic, direct product factor
56	C₂²×C₃	—	3	1	no	—
57	C₂×D₃	C₃×C₇×C₂₃	1	1	yes	characteristic, direct product factor
58	C₃²	C₂²×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
59	C₇	C₂×C₃×D₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	3	2	no	—
62	C₂×C₃	D₃×C₇×C₂₃	1	1	yes	characteristic, direct product factor
63	C₂×C₃	C₂×C₃×C₇×C₂₃	1	1	yes	characteristic, complemented
64	D₃	C₂×C₃×C₇×C₂₃	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×D₃×C₇×C₂₃	1	1	yes	characteristic, direct product factor
68	C₃	C₂²×C₃×C₇×C₂₃	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	C₃×D₃×C₇×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₂₃	D₃
commutator, hypocenter	C₃	C₂²×C₃×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₂₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₇×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₇×C₂₃	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₂₃	C₂	semidirect
4. C₂×D₃×C₇×C₂₃	C₃	direct (N × H)
5. C₃²×C₇×C₂₃	C₂²	semidirect
8. C₂×C₃×C₇×C₂₃	D₃	direct (N × H)
9. C₂×C₃×C₇×C₂₃	C₂×C₃	semidirect
10. D₃×C₇×C₂₃	C₂×C₃	direct (N × H)
11. C₂×C₃×D₃×C₂₃	C₇	direct (N × H)
14. C₃×C₇×C₂₃	C₂×D₃	direct (N × H)
15. C₃×C₇×C₂₃	C₂²×C₃	semidirect
16. C₂×C₃²×C₂₃	C₂×C₇	semidirect
17. C₃×D₃×C₂₃	C₂×C₇	direct (N × H)
19. C₂×C₇×C₂₃	C₃×D₃	direct (N × H)
21. C₂×D₃×C₂₃	C₃×C₇	direct (N × H)
22. C₂×C₃×D₃×C₇	C₂₃	direct (N × H)
23. C₃²×C₂₃	C₂²×C₇	semidirect
24. C₇×C₂₃	C₂×C₃×D₃	direct (N × H)
27. C₂×C₃×C₂₃	D₃×C₇	direct (N × H)
28. C₂×C₃×C₂₃	C₂×C₃×C₇	semidirect
29. D₃×C₂₃	C₂×C₃×C₇	direct (N × H)
30. C₂×C₃²×C₇	C₂×C₂₃	semidirect
31. C₃×D₃×C₇	C₂×C₂₃	direct (N × H)
34. C₂×D₃×C₇	C₃×C₂₃	direct (N × H)
36. C₃×C₂₃	C₂×D₃×C₇	direct (N × H)
37. C₃×C₂₃	C₂²×C₃×C₇	semidirect
38. C₃²×C₇	C₂²×C₂₃	semidirect
40. C₂×C₂₃	C₃×D₃×C₇	direct (N × H)
43. C₂×C₃×C₇	D₃×C₂₃	direct (N × H)
44. C₂×C₃×C₇	C₂×C₃×C₂₃	semidirect
45. D₃×C₇	C₂×C₃×C₂₃	direct (N × H)
46. C₂×C₃×D₃	C₇×C₂₃	direct (N × H)
48. C₂₃	C₂×C₃×D₃×C₇	direct (N × H)
50. C₃×C₇	C₂×D₃×C₂₃	direct (N × H)
51. C₃×C₇	C₂²×C₃×C₂₃	semidirect
52. C₂×C₃²	C₂×C₇×C₂₃	semidirect
53. C₃×D₃	C₂×C₇×C₂₃	direct (N × H)
55. C₂×C₇	C₃×D₃×C₂₃	direct (N × H)
57. C₂×D₃	C₃×C₇×C₂₃	direct (N × H)
58. C₃²	C₂²×C₇×C₂₃	semidirect
59. C₇	C₂×C₃×D₃×C₂₃	direct (N × H)
62. C₂×C₃	D₃×C₇×C₂₃	direct (N × H)
63. C₂×C₃	C₂×C₃×C₇×C₂₃	semidirect
64. D₃	C₂×C₃×C₇×C₂₃	direct (N × H)
67. C₃	C₂×D₃×C₇×C₂₃	direct (N × H)
68. C₃	C₂²×C₃×C₇×C₂₃	semidirect
70. C₂	C₃×D₃×C₇×C₂₃	direct (N × H)

Subgroups — C2×C3×D3×C7×C23 #19154018

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₃×C₇×C₂₃ #19154018