Subgroups — C₃×C₁₃×C₁₉×D₁₅ #36372728

Order 22230.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₁₉×D₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₅×C₁₃×C₁₉	—	3	1	no	maximal
4	C₃×D₃×C₁₃×C₁₉	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₃×C₁₉	—	2	1	no	—
6	C₃×C₅×C₁₃×C₁₉	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₁₃×C₁₉	—	3	1	no	Hall
9	C₃²×C₁₃×C₁₉	D₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₉×D₁₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₁₃×C₁₉	—	15	1	no	—
12	D₃×C₁₃×C₁₉	—	5	1	no	—
13	C₅×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₃×D₁₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃²×C₅×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₃×C₁₉	—	2	1	no	—
17	C₃×C₁₃×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
18	C₃×C₁₃×C₁₉	D₁₅	1	1	yes	characteristic, direct product factor
19	C₃²×C₅×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
20	C₁₉×D₁₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor
21	C₃×D₅×C₁₉	—	3	1	no	—
22	C₂×C₁₃×C₁₉	—	15	1	no	Hall
23	C₁₃×D₁₅	C₃×C₁₉	1	1	yes	characteristic, direct product factor
24	C₃×D₅×C₁₃	—	3	1	no	—
25	C₃×D₃×C₁₉	—	5	1	no	Hall
26	C₃×C₅×C₁₉	—	2	1	no	—
27	C₃×C₅×C₁₉	D₃×C₁₃	1	1	yes	characteristic, complemented
28	C₃×C₅×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
29	C₁₃×C₁₉	C₃×D₁₅	1	1	yes	characteristic, direct product factor, Hall
30	C₃×D₃×C₁₃	—	5	1	no	Hall
31	C₃×C₅×C₁₃	—	2	1	no	—
32	C₃×C₅×C₁₃	D₃×C₁₉	1	1	yes	characteristic, complemented
33	C₃×C₅×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
34	D₅×C₁₉	—	3	1	no	Hall
35	C₃²×C₁₉	D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
36	D₅×C₁₃	—	3	1	no	Hall
37	C₃²×C₁₃	D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
38	C₂×C₃×C₁₉	—	15	1	no	—
39	D₃×C₁₉	—	5	1	no	—
40	C₅×C₁₉	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
41	C₃×D₁₅	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₃×C₁₃	—	15	1	no	—
43	D₃×C₁₃	—	5	1	no	—
44	C₅×C₁₃	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
45	C₃×C₁₉	—	2	1	no	—
46	C₃×C₁₉	C₃×D₅×C₁₃	1	1	yes	characteristic, complemented
47	C₃×C₁₉	C₁₃×D₁₅	1	1	yes	characteristic, direct product factor
48	C₃²×C₅	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Hall
49	C₃×C₁₃	—	2	1	no	—
50	C₃×C₁₃	C₃×D₅×C₁₉	1	1	yes	characteristic, complemented
51	C₃×C₁₃	C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
52	C₂×C₁₉	—	15	1	no	Hall
53	D₁₅	C₃×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor
54	C₃×D₅	—	3	1	no	—
55	C₂×C₁₃	—	15	1	no	Hall
56	C₁₉	C₃×C₁₃×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
57	C₃×D₃	—	5	1	no	Hall
58	C₃×C₅	—	2	1	no	—
59	C₃×C₅	D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented
60	C₃×C₅	C₂×C₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented
61	C₁₃	C₃×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
62	D₅	—	3	1	no	Hall
63	C₃²	D₅×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	15	1	no	—
65	D₃	—	5	1	no	—
66	C₅	C₃×D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×D₅×C₁₃×C₁₉	1	1	yes	characteristic, complemented
69	C₃	C₁₃×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
70	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₉	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₃×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₃×C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃×C₁₉	C₂	semidirect
2. C₁₃×C₁₉×D₁₅	C₃	direct (N × H)
6. C₃×C₅×C₁₃×C₁₉	D₃	semidirect
7. C₃×C₅×C₁₃×C₁₉	C₂×C₃	semidirect
9. C₃²×C₁₃×C₁₉	D₅	semidirect
10. C₃×C₁₉×D₁₅	C₁₃	direct (N × H)
13. C₅×C₁₃×C₁₉	C₃×D₃	semidirect
14. C₃×C₁₃×D₁₅	C₁₉	direct (N × H)
15. C₃²×C₅×C₁₉	C₂×C₁₃	semidirect
17. C₃×C₁₃×C₁₉	C₃×D₅	semidirect
18. C₃×C₁₃×C₁₉	D₁₅	direct (N × H)
19. C₃²×C₅×C₁₃	C₂×C₁₉	semidirect
20. C₁₉×D₁₅	C₃×C₁₃	direct (N × H)
23. C₁₃×D₁₅	C₃×C₁₉	direct (N × H)
27. C₃×C₅×C₁₉	D₃×C₁₃	semidirect
28. C₃×C₅×C₁₉	C₂×C₃×C₁₃	semidirect
29. C₁₃×C₁₉	C₃×D₁₅	direct (N × H)
32. C₃×C₅×C₁₃	D₃×C₁₉	semidirect
33. C₃×C₅×C₁₃	C₂×C₃×C₁₉	semidirect
35. C₃²×C₁₉	D₅×C₁₃	semidirect
37. C₃²×C₁₃	D₅×C₁₉	semidirect
40. C₅×C₁₉	C₃×D₃×C₁₃	semidirect
41. C₃×D₁₅	C₁₃×C₁₉	direct (N × H)
44. C₅×C₁₃	C₃×D₃×C₁₉	semidirect
46. C₃×C₁₉	C₃×D₅×C₁₃	semidirect
47. C₃×C₁₉	C₁₃×D₁₅	direct (N × H)
48. C₃²×C₅	C₂×C₁₃×C₁₉	semidirect
50. C₃×C₁₃	C₃×D₅×C₁₉	semidirect
51. C₃×C₁₃	C₁₉×D₁₅	direct (N × H)
53. D₁₅	C₃×C₁₃×C₁₉	direct (N × H)
56. C₁₉	C₃×C₁₃×D₁₅	direct (N × H)
59. C₃×C₅	D₃×C₁₃×C₁₉	semidirect
60. C₃×C₅	C₂×C₃×C₁₃×C₁₉	semidirect
61. C₁₃	C₃×C₁₉×D₁₅	direct (N × H)
63. C₃²	D₅×C₁₃×C₁₉	semidirect
66. C₅	C₃×D₃×C₁₃×C₁₉	semidirect
68. C₃	C₃×D₅×C₁₃×C₁₉	semidirect
69. C₃	C₁₃×C₁₉×D₁₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₅×C₁₃×C₁₉	2
C₁₃×C₁₉×D₁₅	3
C₃×D₅×C₁₃×C₁₉	3
C₃×D₃×C₁₃×C₁₉	5
C₃×C₁₉×D₁₅	13
C₃×C₁₃×D₁₅	19

Subgroups — C3×C13×C19×D15 #36372728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×C₁₉×D₁₅ #36372728