Subgroups — C₂×C₃×C₇×D₅×C₂₃ #23751655

Order 9660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₅×C₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₅×C₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₃×C₇×C₂₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₅×C₂₃	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×D₅×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₂₃	—	5	2	no	—
10	C₂×C₃×C₇×C₂₃	D₅	1	1	yes	characteristic, 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×D₅×C₂₃	C₂×C₇	1	2	yes	direct product factor
14	C₂²×C₇×C₂₃	—	5	1	no	Hall
15	C₃×C₇×C₂₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×D₅×C₂₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₇×D₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₃×C₅×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₂₃	—	5	2	no	—
20	C₂×C₇×C₂₃	C₃×D₅	1	1	yes	characteristic, direct product factor
21	C₂²×C₃×C₂₃	—	5	1	no	Hall
22	C₂×C₅×C₂₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	D₅×C₂₃	C₂×C₃×C₇	1	2	yes	direct product factor
24	C₂×C₃×C₅×C₇	C₂×C₂₃	1	1	yes	characteristic, complemented
25	C₃×C₇×D₅	C₂×C₂₃	1	2	yes	direct product factor
26	C₇×C₂₃	C₂×C₃×D₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₇×D₅	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₂₃	—	5	2	no	—
29	C₂×C₃×C₂₃	C₇×D₅	1	1	yes	characteristic, direct product factor
30	C₅×C₂₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×C₇	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₂₃	—	5	1	no	Hall
33	C₂²×C₃×C₇	—	5	1	no	Hall
34	C₂×C₅×C₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
35	C₇×D₅	C₂×C₃×C₂₃	1	2	yes	direct product factor
36	C₃×C₂₃	C₂×C₇×D₅	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₃×D₅	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₂₃	—	5	2	no	—
39	C₂×C₂₃	C₃×C₇×D₅	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₇	—	5	2	no	—
41	C₂×C₃×C₇	D₅×C₂₃	1	1	yes	characteristic, direct product factor
42	C₅×C₇	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₅	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
44	C₃×D₅	C₂×C₇×C₂₃	1	2	yes	direct product factor
45	C₂²×C₇	—	5	1	no	Hall
46	C₂₃	C₂×C₃×C₇×D₅	1	1	yes	characteristic, direct product factor, Sylow
47	C₃×C₇	C₂×D₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
48	C₂×D₅	C₃×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
49	C₃×C₅	C₂²×C₇×C₂₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	—	5	2	no	—
51	C₂×C₇	C₃×D₅×C₂₃	1	1	yes	characteristic, direct product factor
52	C₂²×C₃	—	5	1	no	Hall
53	C₂×C₅	C₂×C₃×C₇×C₂₃	1	1	yes	characteristic, complemented
54	D₅	C₂×C₃×C₇×C₂₃	1	2	yes	direct product factor
55	C₇	C₂×C₃×D₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃	—	5	2	no	—
57	C₂×C₃	C₇×D₅×C₂₃	1	1	yes	characteristic, direct product factor
58	C₅	C₂²×C₃×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	5	1	no	Sylow
60	C₃	C₂×C₇×D₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	5	2	no	—
62	C₂	C₃×C₇×D₅×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₂₃	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₂₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₇×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₅×C₂₃	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₂₃	C₂	semidirect
3. C₂×C₇×D₅×C₂₃	C₃	direct (N × H)
4. C₃×C₅×C₇×C₂₃	C₂²	semidirect
6. C₂×C₅×C₇×C₂₃	C₂×C₃	semidirect
7. C₇×D₅×C₂₃	C₂×C₃	direct (N × H)
8. C₂×C₃×D₅×C₂₃	C₇	direct (N × H)
10. C₂×C₃×C₇×C₂₃	D₅	direct (N × H)
11. C₅×C₇×C₂₃	C₂²×C₃	semidirect
12. C₂×C₃×C₅×C₂₃	C₂×C₇	semidirect
13. C₃×D₅×C₂₃	C₂×C₇	direct (N × H)
15. C₃×C₇×C₂₃	C₂×D₅	direct (N × H)
16. C₂×D₅×C₂₃	C₃×C₇	direct (N × H)
17. C₂×C₃×C₇×D₅	C₂₃	direct (N × H)
18. C₃×C₅×C₂₃	C₂²×C₇	semidirect
20. C₂×C₇×C₂₃	C₃×D₅	direct (N × H)
22. C₂×C₅×C₂₃	C₂×C₃×C₇	semidirect
23. D₅×C₂₃	C₂×C₃×C₇	direct (N × H)
24. C₂×C₃×C₅×C₇	C₂×C₂₃	semidirect
25. C₃×C₇×D₅	C₂×C₂₃	direct (N × H)
26. C₇×C₂₃	C₂×C₃×D₅	direct (N × H)
27. C₂×C₇×D₅	C₃×C₂₃	direct (N × H)
29. C₂×C₃×C₂₃	C₇×D₅	direct (N × H)
30. C₅×C₂₃	C₂²×C₃×C₇	semidirect
31. C₃×C₅×C₇	C₂²×C₂₃	semidirect
34. C₂×C₅×C₇	C₂×C₃×C₂₃	semidirect
35. C₇×D₅	C₂×C₃×C₂₃	direct (N × H)
36. C₃×C₂₃	C₂×C₇×D₅	direct (N × H)
37. C₂×C₃×D₅	C₇×C₂₃	direct (N × H)
39. C₂×C₂₃	C₃×C₇×D₅	direct (N × H)
41. C₂×C₃×C₇	D₅×C₂₃	direct (N × H)
42. C₅×C₇	C₂²×C₃×C₂₃	semidirect
43. C₂×C₃×C₅	C₂×C₇×C₂₃	semidirect
44. C₃×D₅	C₂×C₇×C₂₃	direct (N × H)
46. C₂₃	C₂×C₃×C₇×D₅	direct (N × H)
47. C₃×C₇	C₂×D₅×C₂₃	direct (N × H)
48. C₂×D₅	C₃×C₇×C₂₃	direct (N × H)
49. C₃×C₅	C₂²×C₇×C₂₃	semidirect
51. C₂×C₇	C₃×D₅×C₂₃	direct (N × H)
53. C₂×C₅	C₂×C₃×C₇×C₂₃	semidirect
54. D₅	C₂×C₃×C₇×C₂₃	direct (N × H)
55. C₇	C₂×C₃×D₅×C₂₃	direct (N × H)
57. C₂×C₃	C₇×D₅×C₂₃	direct (N × H)
58. C₅	C₂²×C₃×C₇×C₂₃	semidirect
60. C₃	C₂×C₇×D₅×C₂₃	direct (N × H)
62. C₂	C₃×C₇×D₅×C₂₃	direct (N × H)

Subgroups — C2×C3×C7×D5×C23 #23751655

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₇×D₅×C₂₃ #23751655