Subgroups — C₃×C₅×C₁₉×D₆₅ #49150321

Order 37050.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₉×D₆₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₉×D₆₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₅×C₁₉×D₁₃	—	5	1	no	maximal
5	C₅²×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₃×C₁₉	—	2	2	no	—
7	C₃×C₅×C₁₃×C₁₉	D₅	1	1	yes	characteristic, complemented
8	C₃×C₅×C₁₃×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃×C₅×D₅×C₁₉	—	13	1	no	maximal, Hall
10	C₁₉×D₆₅	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₅×C₁₉×D₁₃	—	5	1	no	—
12	C₃×C₅×D₆₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₁₉×D₁₃	—	5	1	no	Hall
14	C₃×C₅²×C₁₉	D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₃×C₁₉	—	2	2	no	—
16	C₅×C₁₃×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
17	C₅×C₁₃×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	C₃×C₅²×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₅×D₅×C₁₉	—	13	1	no	Hall
20	C₃×C₁₃×C₁₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
21	C₅×D₆₅	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅×C₁₉	—	65	1	no	—
23	C₃×D₅×C₁₉	—	13	1	no	—
24	C₁₉×D₁₃	—	5	1	no	Hall
25	C₅²×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₃×D₆₅	C₅×C₁₉	1	1	yes	characteristic, direct product factor
27	C₃×C₅×D₁₃	—	5	1	no	—
28	C₅²×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×C₁₉	—	2	2	no	—
30	C₃×C₅×C₁₉	C₅×D₁₃	1	1	yes	characteristic, complemented
31	C₃×C₅×C₁₉	D₆₅	1	1	yes	characteristic, direct product factor
32	C₁₃×C₁₉	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅×C₁₃	—	2	2	no	—
34	C₃×C₅×C₁₃	D₅×C₁₉	1	1	yes	characteristic, complemented
35	C₃×C₅×C₁₃	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
36	C₂×C₅×C₁₉	—	65	1	no	—
37	D₅×C₁₉	—	13	1	no	—
38	C₃×C₅×D₅	—	13	1	no	Hall
39	D₆₅	C₃×C₅×C₁₉	1	1	yes	characteristic, direct product factor
40	C₅×D₁₃	—	5	1	no	—
41	C₂×C₃×C₁₉	—	65	1	no	Hall
42	C₅×C₁₉	—	2	2	no	—
43	C₅×C₁₉	C₃×C₅×D₁₃	1	1	yes	characteristic, complemented
44	C₅×C₁₉	C₃×D₆₅	1	1	yes	characteristic, direct product factor
45	C₃×D₁₃	—	5	1	no	Hall
46	C₃×C₅²	C₁₉×D₁₃	1	1	yes	characteristic, complemented, Hall
47	C₅×C₁₃	—	2	2	no	—
48	C₅×C₁₃	C₃×D₅×C₁₉	1	1	yes	characteristic, complemented
49	C₅×C₁₃	C₂×C₃×C₅×C₁₉	1	1	yes	characteristic, complemented
50	C₃×C₁₉	C₅×D₆₅	1	1	yes	characteristic, direct product factor, Hall
51	C₅×D₅	—	13	1	no	Hall
52	C₃×C₁₃	C₅×D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
53	C₂×C₁₉	—	65	1	no	Hall
54	C₂×C₃×C₅	—	65	1	no	—
55	C₃×D₅	—	13	1	no	—
56	D₁₃	—	5	1	no	Hall
57	C₅²	C₃×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₁₉	C₃×C₅×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
59	C₃×C₅	—	2	2	no	—
60	C₃×C₅	C₅×C₁₉×D₁₃	1	1	yes	characteristic, complemented
61	C₃×C₅	C₁₉×D₆₅	1	1	yes	characteristic, direct product factor
62	C₁₃	C₃×C₅×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₅	—	65	1	no	—
64	D₅	—	13	1	no	—
65	C₂×C₃	—	65	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₃×C₅×C₁₉×D₁₃	1	1	yes	characteristic, complemented
68	C₅	C₃×C₁₉×D₆₅	1	1	yes	characteristic, direct product factor
69	C₃	C₅×C₁₉×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	—	65	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₉	D₆₅
commutator, cosocle, hypocenter	C₅×C₁₃	C₂×C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₃×C₁₉	C₂	semidirect
2. C₅×C₁₉×D₆₅	C₃	direct (N × H)
3. C₃×C₁₉×D₆₅	C₅	direct (N × H)
5. C₅²×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₃×C₅×C₁₃×C₁₉	D₅	semidirect
8. C₃×C₅×C₁₃×C₁₉	C₂×C₅	semidirect
10. C₁₉×D₆₅	C₃×C₅	direct (N × H)
12. C₃×C₅×D₆₅	C₁₉	direct (N × H)
14. C₃×C₅²×C₁₉	D₁₃	semidirect
16. C₅×C₁₃×C₁₉	C₃×D₅	semidirect
17. C₅×C₁₃×C₁₉	C₂×C₃×C₅	semidirect
18. C₃×C₅²×C₁₃	C₂×C₁₉	semidirect
20. C₃×C₁₃×C₁₉	C₅×D₅	semidirect
21. C₅×D₆₅	C₃×C₁₉	direct (N × H)
25. C₅²×C₁₉	C₃×D₁₃	semidirect
26. C₃×D₆₅	C₅×C₁₉	direct (N × H)
28. C₅²×C₁₃	C₂×C₃×C₁₉	semidirect
30. C₃×C₅×C₁₉	C₅×D₁₃	semidirect
31. C₃×C₅×C₁₉	D₆₅	direct (N × H)
32. C₁₃×C₁₉	C₃×C₅×D₅	semidirect
34. C₃×C₅×C₁₃	D₅×C₁₉	semidirect
35. C₃×C₅×C₁₃	C₂×C₅×C₁₉	semidirect
39. D₆₅	C₃×C₅×C₁₉	direct (N × H)
43. C₅×C₁₉	C₃×C₅×D₁₃	semidirect
44. C₅×C₁₉	C₃×D₆₅	direct (N × H)
46. C₃×C₅²	C₁₉×D₁₃	semidirect
48. C₅×C₁₃	C₃×D₅×C₁₉	semidirect
49. C₅×C₁₃	C₂×C₃×C₅×C₁₉	semidirect
50. C₃×C₁₉	C₅×D₆₅	direct (N × H)
52. C₃×C₁₃	C₅×D₅×C₁₉	semidirect
57. C₅²	C₃×C₁₉×D₁₃	semidirect
58. C₁₉	C₃×C₅×D₆₅	direct (N × H)
60. C₃×C₅	C₅×C₁₉×D₁₃	semidirect
61. C₃×C₅	C₁₉×D₆₅	direct (N × H)
62. C₁₃	C₃×C₅×D₅×C₁₉	semidirect
67. C₅	C₃×C₅×C₁₉×D₁₃	semidirect
68. C₅	C₃×C₁₉×D₆₅	direct (N × H)
69. C₃	C₅×C₁₉×D₆₅	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×C₅²×C₁₃×C₁₉	2
C₅×C₁₉×D₆₅	3
C₃×C₁₉×D₆₅	5
C₃×C₅×C₁₉×D₁₃	5
C₃×C₅×D₅×C₁₉	13
C₃×C₅×D₆₅	19

Subgroups — C3×C5×C19×D65 #49150321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₉×D₆₅ #49150321