Subgroups — C₂×C₃×D₃×C₁₉×C₂₃ #30628656

Order 15732.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₁₉×C₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₉×C₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂²×C₃×C₁₉×C₂₃	—	3	1	no	maximal
5	C₃²×C₁₉×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₉×C₂₃	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₃×C₁₉×C₂₃	—	2	1	no	—
8	C₂×C₃×C₁₉×C₂₃	—	3	2	no	—
9	C₂×C₃×C₁₉×C₂₃	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₁₉×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×C₁₉×C₂₃	—	3	1	no	Hall
12	C₃×C₁₉×C₂₃	—	2	1	no	—
13	C₃×C₁₉×C₂₃	C₂×D₃	1	1	yes	characteristic, direct product factor
14	C₃×C₁₉×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₁₉×C₂₃	—	3	2	no	—
16	C₂×C₁₉×C₂₃	C₃×D₃	1	1	yes	characteristic, direct product factor
17	C₂×C₃×D₃×C₂₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₃×D₃×C₁₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₁₉×C₂₃	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃²×C₂₃	C₂×C₁₉	1	1	yes	characteristic, complemented
21	C₃×D₃×C₂₃	C₂×C₁₉	1	2	yes	direct product factor
22	C₂×C₃²×C₁₉	C₂×C₂₃	1	1	yes	characteristic, complemented
23	C₃×D₃×C₁₉	C₂×C₂₃	1	2	yes	direct product factor
24	C₂²×C₃×C₂₃	—	3	1	no	—
25	C₂×D₃×C₂₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor
26	C₂²×C₃×C₁₉	—	3	1	no	—
27	C₂×D₃×C₁₉	C₃×C₂₃	1	1	yes	characteristic, direct product factor
28	C₃²×C₂₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
29	C₃²×C₁₉	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₂₃	—	2	1	no	—
31	C₂×C₃×C₂₃	—	3	2	no	—
32	C₂×C₃×C₂₃	D₃×C₁₉	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₂₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
34	D₃×C₂₃	C₂×C₃×C₁₉	1	2	yes	direct product factor
35	C₂×C₃×C₁₉	—	2	1	no	—
36	C₂×C₃×C₁₉	—	3	2	no	—
37	C₂×C₃×C₁₉	D₃×C₂₃	1	1	yes	characteristic, direct product factor
38	C₂×C₃×C₁₉	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
39	D₃×C₁₉	C₂×C₃×C₂₃	1	2	yes	direct product factor
40	C₂²×C₂₃	—	3	1	no	Hall
41	C₂²×C₁₉	—	3	1	no	Hall
42	C₃×C₂₃	—	2	1	no	—
43	C₃×C₂₃	C₂×D₃×C₁₉	1	1	yes	characteristic, direct product factor
44	C₃×C₂₃	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented
45	C₃×C₁₉	—	2	1	no	—
46	C₃×C₁₉	C₂×D₃×C₂₃	1	1	yes	characteristic, direct product factor
47	C₃×C₁₉	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented
48	C₂×C₂₃	—	3	2	no	—
49	C₂×C₂₃	C₃×D₃×C₁₉	1	1	yes	characteristic, direct product factor
50	C₂×C₁₉	—	3	2	no	—
51	C₂×C₁₉	C₃×D₃×C₂₃	1	1	yes	characteristic, direct product factor
52	C₂×C₃×D₃	C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
53	C₂₃	C₂×C₃×D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
54	C₁₉	C₂×C₃×D₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×C₃²	C₂×C₁₉×C₂₃	1	1	yes	characteristic, complemented
56	C₃×D₃	C₂×C₁₉×C₂₃	1	2	yes	direct product factor
57	C₂²×C₃	—	3	1	no	—
58	C₂×D₃	C₃×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor
59	C₃²	C₂²×C₁₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	3	2	no	—
62	C₂×C₃	C₂×C₃×C₁₉×C₂₃	1	1	yes	characteristic, complemented
63	C₂×C₃	D₃×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor
64	D₃	C₂×C₃×C₁₉×C₂₃	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂²×C₃×C₁₉×C₂₃	1	1	yes	characteristic, complemented
68	C₃	C₂×D₃×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor
69	C₂	—	3	2	no	—
70	C₂	C₃×D₃×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉×C₂₃	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₁₉×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₂₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₁₉×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₁₉×C₂₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₉×C₂₃	C₂	semidirect
3. C₂×D₃×C₁₉×C₂₃	C₃	direct (N × H)
5. C₃²×C₁₉×C₂₃	C₂²	semidirect
6. D₃×C₁₉×C₂₃	C₂×C₃	direct (N × H)
9. C₂×C₃×C₁₉×C₂₃	D₃	direct (N × H)
10. C₂×C₃×C₁₉×C₂₃	C₂×C₃	semidirect
13. C₃×C₁₉×C₂₃	C₂×D₃	direct (N × H)
14. C₃×C₁₉×C₂₃	C₂²×C₃	semidirect
16. C₂×C₁₉×C₂₃	C₃×D₃	direct (N × H)
17. C₂×C₃×D₃×C₂₃	C₁₉	direct (N × H)
18. C₂×C₃×D₃×C₁₉	C₂₃	direct (N × H)
19. C₁₉×C₂₃	C₂×C₃×D₃	direct (N × H)
20. C₂×C₃²×C₂₃	C₂×C₁₉	semidirect
21. C₃×D₃×C₂₃	C₂×C₁₉	direct (N × H)
22. C₂×C₃²×C₁₉	C₂×C₂₃	semidirect
23. C₃×D₃×C₁₉	C₂×C₂₃	direct (N × H)
25. C₂×D₃×C₂₃	C₃×C₁₉	direct (N × H)
27. C₂×D₃×C₁₉	C₃×C₂₃	direct (N × H)
28. C₃²×C₂₃	C₂²×C₁₉	semidirect
29. C₃²×C₁₉	C₂²×C₂₃	semidirect
32. C₂×C₃×C₂₃	D₃×C₁₉	direct (N × H)
33. C₂×C₃×C₂₃	C₂×C₃×C₁₉	semidirect
34. D₃×C₂₃	C₂×C₃×C₁₉	direct (N × H)
37. C₂×C₃×C₁₉	D₃×C₂₃	direct (N × H)
38. C₂×C₃×C₁₉	C₂×C₃×C₂₃	semidirect
39. D₃×C₁₉	C₂×C₃×C₂₃	direct (N × H)
43. C₃×C₂₃	C₂×D₃×C₁₉	direct (N × H)
44. C₃×C₂₃	C₂²×C₃×C₁₉	semidirect
46. C₃×C₁₉	C₂×D₃×C₂₃	direct (N × H)
47. C₃×C₁₉	C₂²×C₃×C₂₃	semidirect
49. C₂×C₂₃	C₃×D₃×C₁₉	direct (N × H)
51. C₂×C₁₉	C₃×D₃×C₂₃	direct (N × H)
52. C₂×C₃×D₃	C₁₉×C₂₃	direct (N × H)
53. C₂₃	C₂×C₃×D₃×C₁₉	direct (N × H)
54. C₁₉	C₂×C₃×D₃×C₂₃	direct (N × H)
55. C₂×C₃²	C₂×C₁₉×C₂₃	semidirect
56. C₃×D₃	C₂×C₁₉×C₂₃	direct (N × H)
58. C₂×D₃	C₃×C₁₉×C₂₃	direct (N × H)
59. C₃²	C₂²×C₁₉×C₂₃	semidirect
62. C₂×C₃	C₂×C₃×C₁₉×C₂₃	semidirect
63. C₂×C₃	D₃×C₁₉×C₂₃	direct (N × H)
64. D₃	C₂×C₃×C₁₉×C₂₃	direct (N × H)
67. C₃	C₂²×C₃×C₁₉×C₂₃	semidirect
68. C₃	C₂×D₃×C₁₉×C₂₃	direct (N × H)
70. C₂	C₃×D₃×C₁₉×C₂₃	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×D₃×C₁₉×C₂₃	2
C₂×C₃²×C₁₉×C₂₃	2
C₂×D₃×C₁₉×C₂₃	3
C₂²×C₃×C₁₉×C₂₃	3
C₂×C₃×D₃×C₂₃	19
C₂×C₃×D₃×C₁₉	23

Subgroups — C2×C3×D3×C19×C23 #30628656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃×C₁₉×C₂₃ #30628656