Subgroups — C₂×C₃×D₃×C₁₃×C₂₃ #24924590

Order 10764.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₁₃×C₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₃×C₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂²×C₃×C₁₃×C₂₃	—	3	1	no	maximal
5	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₃×C₂₃	—	2	1	no	—
7	C₂×C₃×C₁₃×C₂₃	—	3	2	no	—
8	C₂×C₃×C₁₃×C₂₃	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
10	D₃×C₁₃×C₂₃	C₂×C₃	1	2	yes	direct product factor
11	C₂²×C₁₃×C₂₃	—	3	1	no	Hall
12	C₃×C₁₃×C₂₃	—	2	1	no	—
13	C₃×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, direct product factor
14	C₃×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃×D₃×C₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₁₃×C₂₃	—	3	2	no	—
17	C₂×C₁₃×C₂₃	C₃×D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₃×D₃×C₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃²×C₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₃×D₃×C₂₃	C₂×C₁₃	1	2	yes	direct product factor
21	C₁₃×C₂₃	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₃×C₂₃	—	3	1	no	—
23	C₂×D₃×C₂₃	C₃×C₁₃	1	1	yes	characteristic, direct product factor
24	C₂×C₃²×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
25	C₃×D₃×C₁₃	C₂×C₂₃	1	2	yes	direct product factor
26	C₃²×C₂₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₁₃	—	3	1	no	—
28	C₂×D₃×C₁₃	C₃×C₂₃	1	1	yes	characteristic, direct product factor
29	C₂×C₃×C₂₃	—	2	1	no	—
30	C₂×C₃×C₂₃	—	3	2	no	—
31	C₂×C₃×C₂₃	D₃×C₁₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃×C₂₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
33	D₃×C₂₃	C₂×C₃×C₁₃	1	2	yes	direct product factor
34	C₃²×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₂₃	—	3	1	no	Hall
36	C₂×C₃×C₁₃	—	2	1	no	—
37	C₂×C₃×C₁₃	—	3	2	no	—
38	C₂×C₃×C₁₃	D₃×C₂₃	1	1	yes	characteristic, direct product factor
39	C₂×C₃×C₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
40	D₃×C₁₃	C₂×C₃×C₂₃	1	2	yes	direct product factor
41	C₃×C₂₃	—	2	1	no	—
42	C₃×C₂₃	C₂×D₃×C₁₃	1	1	yes	characteristic, direct product factor
43	C₃×C₂₃	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
44	C₂²×C₁₃	—	3	1	no	Hall
45	C₂×C₂₃	—	3	2	no	—
46	C₂×C₂₃	C₃×D₃×C₁₃	1	1	yes	characteristic, direct product factor
47	C₃×C₁₃	—	2	1	no	—
48	C₃×C₁₃	C₂×D₃×C₂₃	1	1	yes	characteristic, direct product factor
49	C₃×C₁₃	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented
50	C₂×C₃×D₃	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₁₃	—	3	2	no	—
52	C₂×C₁₃	C₃×D₃×C₂₃	1	1	yes	characteristic, direct product factor
53	C₂₃	C₂×C₃×D₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₃²	C₂×C₁₃×C₂₃	1	1	yes	characteristic, complemented
55	C₃×D₃	C₂×C₁₃×C₂₃	1	2	yes	direct product factor
56	C₁₃	C₂×C₃×D₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₃	—	3	1	no	—
58	C₂×D₃	C₃×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor
59	C₃²	C₂²×C₁₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	3	2	no	—
62	C₂×C₃	D₃×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor
63	C₂×C₃	C₂×C₃×C₁₃×C₂₃	1	1	yes	characteristic, complemented
64	D₃	C₂×C₃×C₁₃×C₂₃	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂²×C₃×C₁₃×C₂₃	1	1	yes	characteristic, complemented
68	C₃	C₂×D₃×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor
69	C₂	—	3	2	no	—
70	C₂	C₃×D₃×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃×C₂₃	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₁₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₂₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₁₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₁₃×C₂₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₂₃	C₂	semidirect
3. C₂×D₃×C₁₃×C₂₃	C₃	direct (N × H)
5. C₃²×C₁₃×C₂₃	C₂²	semidirect
8. C₂×C₃×C₁₃×C₂₃	D₃	direct (N × H)
9. C₂×C₃×C₁₃×C₂₃	C₂×C₃	semidirect
10. D₃×C₁₃×C₂₃	C₂×C₃	direct (N × H)
13. C₃×C₁₃×C₂₃	C₂×D₃	direct (N × H)
14. C₃×C₁₃×C₂₃	C₂²×C₃	semidirect
15. C₂×C₃×D₃×C₂₃	C₁₃	direct (N × H)
17. C₂×C₁₃×C₂₃	C₃×D₃	direct (N × H)
18. C₂×C₃×D₃×C₁₃	C₂₃	direct (N × H)
19. C₂×C₃²×C₂₃	C₂×C₁₃	semidirect
20. C₃×D₃×C₂₃	C₂×C₁₃	direct (N × H)
21. C₁₃×C₂₃	C₂×C₃×D₃	direct (N × H)
23. C₂×D₃×C₂₃	C₃×C₁₃	direct (N × H)
24. C₂×C₃²×C₁₃	C₂×C₂₃	semidirect
25. C₃×D₃×C₁₃	C₂×C₂₃	direct (N × H)
26. C₃²×C₂₃	C₂²×C₁₃	semidirect
28. C₂×D₃×C₁₃	C₃×C₂₃	direct (N × H)
31. C₂×C₃×C₂₃	D₃×C₁₃	direct (N × H)
32. C₂×C₃×C₂₃	C₂×C₃×C₁₃	semidirect
33. D₃×C₂₃	C₂×C₃×C₁₃	direct (N × H)
34. C₃²×C₁₃	C₂²×C₂₃	semidirect
38. C₂×C₃×C₁₃	D₃×C₂₃	direct (N × H)
39. C₂×C₃×C₁₃	C₂×C₃×C₂₃	semidirect
40. D₃×C₁₃	C₂×C₃×C₂₃	direct (N × H)
42. C₃×C₂₃	C₂×D₃×C₁₃	direct (N × H)
43. C₃×C₂₃	C₂²×C₃×C₁₃	semidirect
46. C₂×C₂₃	C₃×D₃×C₁₃	direct (N × H)
48. C₃×C₁₃	C₂×D₃×C₂₃	direct (N × H)
49. C₃×C₁₃	C₂²×C₃×C₂₃	semidirect
50. C₂×C₃×D₃	C₁₃×C₂₃	direct (N × H)
52. C₂×C₁₃	C₃×D₃×C₂₃	direct (N × H)
53. C₂₃	C₂×C₃×D₃×C₁₃	direct (N × H)
54. C₂×C₃²	C₂×C₁₃×C₂₃	semidirect
55. C₃×D₃	C₂×C₁₃×C₂₃	direct (N × H)
56. C₁₃	C₂×C₃×D₃×C₂₃	direct (N × H)
58. C₂×D₃	C₃×C₁₃×C₂₃	direct (N × H)
59. C₃²	C₂²×C₁₃×C₂₃	semidirect
62. C₂×C₃	D₃×C₁₃×C₂₃	direct (N × H)
63. C₂×C₃	C₂×C₃×C₁₃×C₂₃	semidirect
64. D₃	C₂×C₃×C₁₃×C₂₃	direct (N × H)
67. C₃	C₂²×C₃×C₁₃×C₂₃	semidirect
68. C₃	C₂×D₃×C₁₃×C₂₃	direct (N × H)
70. C₂	C₃×D₃×C₁₃×C₂₃	direct (N × H)

Subgroups — C2×C3×D3×C13×C23 #24924590

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₃×C₁₃×C₂₃ #24924590