Subgroups — C₂×C₃×C₅×C₇×D₂₃ #23751658

Order 9660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×D₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₇×D₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×D₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₇×D₂₃	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅×D₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×C₇×D₂₃	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₇×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented
13	C₃×C₅×D₂₃	C₂×C₇	1	2	yes	direct product factor
14	C₂×C₇×D₂₃	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₇×C₂₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₂₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×C₇	—	23	1	no	maximal, Hall
18	C₃×C₅×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₂₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
20	C₇×D₂₃	C₂×C₃×C₅	1	2	yes	direct product factor
21	C₂×C₃×D₂₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₅×C₂₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	C₅×D₂₃	C₂×C₃×C₇	1	2	yes	direct product factor
24	C₂×C₃×C₅×C₇	—	23	2	no	—
25	C₂×C₃×C₅×C₇	D₂₃	1	1	yes	characteristic, direct product factor
26	C₇×C₂₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₅×C₇	—	23	1	no	Hall
28	C₂×C₃×C₂₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
29	C₃×D₂₃	C₂×C₅×C₇	1	2	yes	direct product factor
30	C₅×C₂₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×C₇	C₂×D₂₃	1	1	yes	characteristic, direct product factor, Hall
32	C₂×D₂₃	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
33	C₂²×C₃×C₇	—	23	1	no	Hall
34	C₂×C₅×C₇	—	23	2	no	—
35	C₂×C₅×C₇	C₃×D₂₃	1	1	yes	characteristic, direct product factor
36	C₃×C₂₃	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₃×C₅	—	23	1	no	Hall
38	C₂×C₂₃	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented
39	D₂₃	C₂×C₃×C₅×C₇	1	2	yes	direct product factor
40	C₂×C₃×C₇	—	23	2	no	—
41	C₂×C₃×C₇	C₅×D₂₃	1	1	yes	characteristic, direct product factor
42	C₅×C₇	C₂×C₃×D₂₃	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×C₅	—	23	2	no	—
44	C₂×C₃×C₅	C₇×D₂₃	1	1	yes	characteristic, direct product factor
45	C₂²×C₇	—	23	1	no	Hall
46	C₂₃	C₂²×C₃×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
47	C₃×C₇	C₂×C₅×D₂₃	1	1	yes	characteristic, direct product factor, Hall
48	C₂²×C₅	—	23	1	no	Hall
49	C₃×C₅	C₂×C₇×D₂₃	1	1	yes	characteristic, direct product factor, Hall
50	C₂×C₇	—	23	2	no	—
51	C₂×C₇	C₃×C₅×D₂₃	1	1	yes	characteristic, direct product factor
52	C₂²×C₃	—	23	1	no	Hall
53	C₂×C₅	—	23	2	no	—
54	C₂×C₅	C₃×C₇×D₂₃	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₃×C₅×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃	—	23	2	no	—
57	C₂×C₃	C₅×C₇×D₂₃	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×C₇×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	23	1	no	Sylow
60	C₃	C₂×C₅×C₇×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	23	2	no	—
62	C₂	C₃×C₅×C₇×D₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₇	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂²×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₃×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×D₂₃	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₂₃	C₂	semidirect
3. C₂×C₅×C₇×D₂₃	C₃	direct (N × H)
4. C₃×C₅×C₇×C₂₃	C₂²	semidirect
5. C₂×C₃×C₇×D₂₃	C₅	direct (N × H)
6. C₂×C₅×C₇×C₂₃	C₂×C₃	semidirect
7. C₅×C₇×D₂₃	C₂×C₃	direct (N × H)
8. C₂×C₃×C₅×D₂₃	C₇	direct (N × H)
9. C₂×C₃×C₇×C₂₃	C₂×C₅	semidirect
10. C₃×C₇×D₂₃	C₂×C₅	direct (N × H)
11. C₅×C₇×C₂₃	C₂²×C₃	semidirect
12. C₂×C₃×C₅×C₂₃	C₂×C₇	semidirect
13. C₃×C₅×D₂₃	C₂×C₇	direct (N × H)
14. C₂×C₇×D₂₃	C₃×C₅	direct (N × H)
15. C₃×C₇×C₂₃	C₂²×C₅	semidirect
16. C₂×C₅×D₂₃	C₃×C₇	direct (N × H)
18. C₃×C₅×C₂₃	C₂²×C₇	semidirect
19. C₂×C₇×C₂₃	C₂×C₃×C₅	semidirect
20. C₇×D₂₃	C₂×C₃×C₅	direct (N × H)
21. C₂×C₃×D₂₃	C₅×C₇	direct (N × H)
22. C₂×C₅×C₂₃	C₂×C₃×C₇	semidirect
23. C₅×D₂₃	C₂×C₃×C₇	direct (N × H)
25. C₂×C₃×C₅×C₇	D₂₃	direct (N × H)
26. C₇×C₂₃	C₂²×C₃×C₅	semidirect
28. C₂×C₃×C₂₃	C₂×C₅×C₇	semidirect
29. C₃×D₂₃	C₂×C₅×C₇	direct (N × H)
30. C₅×C₂₃	C₂²×C₃×C₇	semidirect
31. C₃×C₅×C₇	C₂×D₂₃	direct (N × H)
32. C₂×D₂₃	C₃×C₅×C₇	direct (N × H)
35. C₂×C₅×C₇	C₃×D₂₃	direct (N × H)
36. C₃×C₂₃	C₂²×C₅×C₇	semidirect
38. C₂×C₂₃	C₂×C₃×C₅×C₇	semidirect
39. D₂₃	C₂×C₃×C₅×C₇	direct (N × H)
41. C₂×C₃×C₇	C₅×D₂₃	direct (N × H)
42. C₅×C₇	C₂×C₃×D₂₃	direct (N × H)
44. C₂×C₃×C₅	C₇×D₂₃	direct (N × H)
46. C₂₃	C₂²×C₃×C₅×C₇	semidirect
47. C₃×C₇	C₂×C₅×D₂₃	direct (N × H)
49. C₃×C₅	C₂×C₇×D₂₃	direct (N × H)
51. C₂×C₇	C₃×C₅×D₂₃	direct (N × H)
54. C₂×C₅	C₃×C₇×D₂₃	direct (N × H)
55. C₇	C₂×C₃×C₅×D₂₃	direct (N × H)
57. C₂×C₃	C₅×C₇×D₂₃	direct (N × H)
58. C₅	C₂×C₃×C₇×D₂₃	direct (N × H)
60. C₃	C₂×C₅×C₇×D₂₃	direct (N × H)
62. C₂	C₃×C₅×C₇×D₂₃	direct (N × H)

Subgroups — C2×C3×C5×C7×D23 #23751658

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅×C₇×D₂₃ #23751658