Subgroups — C₅×C₁₃×C₁₉×D₁₅ #49150331

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×D₅×C₁₃×C₁₉	—	3	1	no	maximal, Hall
3	C₁₃×C₁₉×D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×D₃×C₁₃×C₁₉	—	5	1	no	maximal
5	C₅²×C₁₃×C₁₉	D₃	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	C₅×C₁₉×D₁₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	D₅×C₁₃×C₁₉	—	3	1	no	—
11	C₂×C₅×C₁₃×C₁₉	—	15	1	no	—
12	C₅×C₁₃×D₁₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	D₃×C₁₃×C₁₉	—	5	1	no	Hall
14	C₃×C₅²×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₃×C₁₉	—	2	2	no	—
16	C₅×C₁₃×C₁₉	C₅×D₃	1	1	yes	characteristic, complemented
17	C₅×C₁₃×C₁₉	D₁₅	1	1	yes	characteristic, direct product factor
18	C₃×C₅²×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₅×D₅×C₁₉	—	3	1	no	Hall
20	C₃×C₁₃×C₁₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
21	C₅×D₅×C₁₃	—	3	1	no	Hall
22	C₁₉×D₁₅	C₅×C₁₃	1	1	yes	characteristic, direct product factor
23	C₅×D₃×C₁₉	—	5	1	no	—
24	C₂×C₁₃×C₁₉	—	15	1	no	Hall
25	C₅²×C₁₉	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₁₃×D₁₅	C₅×C₁₉	1	1	yes	characteristic, direct product factor
27	C₅×D₃×C₁₃	—	5	1	no	—
28	C₅²×C₁₃	D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×C₁₉	—	2	2	no	—
30	C₃×C₅×C₁₉	D₅×C₁₃	1	1	yes	characteristic, complemented
31	C₃×C₅×C₁₉	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
32	C₁₃×C₁₉	C₅×D₁₅	1	1	yes	characteristic, direct product factor, 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	—	15	1	no	—
37	D₅×C₁₉	—	3	1	no	—
38	C₅×D₁₅	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₅×C₁₃	—	15	1	no	—
40	D₅×C₁₃	—	3	1	no	—
41	D₃×C₁₉	—	5	1	no	Hall
42	C₅×C₁₉	—	2	2	no	—
43	C₅×C₁₉	C₅×D₃×C₁₃	1	1	yes	characteristic, complemented
44	C₅×C₁₉	C₁₃×D₁₅	1	1	yes	characteristic, direct product factor
45	D₃×C₁₃	—	5	1	no	Hall
46	C₃×C₅²	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Hall
47	C₅×C₁₃	—	2	2	no	—
48	C₅×C₁₃	C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
49	C₅×C₁₃	C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
50	C₃×C₁₉	C₅×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
51	C₅×D₅	—	3	1	no	Hall
52	C₃×C₁₃	C₅×D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
53	C₂×C₁₉	—	15	1	no	Hall
54	D₁₅	C₅×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor
55	C₅×D₃	—	5	1	no	—
56	C₂×C₁₃	—	15	1	no	Hall
57	C₅²	D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
58	C₁₉	C₅×C₁₃×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
59	C₃×C₅	—	2	2	no	—
60	C₃×C₅	C₂×C₅×C₁₃×C₁₉	1	1	yes	characteristic, complemented
61	C₃×C₅	D₅×C₁₃×C₁₉	1	1	yes	characteristic, complemented
62	C₁₃	C₅×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₅	—	15	1	no	—
64	D₅	—	3	1	no	—
65	D₃	—	5	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₅×D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented
68	C₅	C₁₃×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
69	C₃	C₅×D₅×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
70	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃×C₁₉	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₅×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₅×C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₃×C₁₉	C₂	semidirect
3. C₁₃×C₁₉×D₁₅	C₅	direct (N × H)
5. C₅²×C₁₃×C₁₉	D₃	semidirect
7. C₃×C₅×C₁₃×C₁₉	D₅	semidirect
8. C₃×C₅×C₁₃×C₁₉	C₂×C₅	semidirect
9. C₅×C₁₉×D₁₅	C₁₃	direct (N × H)
12. C₅×C₁₃×D₁₅	C₁₉	direct (N × H)
14. C₃×C₅²×C₁₉	C₂×C₁₃	semidirect
16. C₅×C₁₃×C₁₉	C₅×D₃	semidirect
17. C₅×C₁₃×C₁₉	D₁₅	direct (N × H)
18. C₃×C₅²×C₁₃	C₂×C₁₉	semidirect
20. C₃×C₁₃×C₁₉	C₅×D₅	semidirect
22. C₁₉×D₁₅	C₅×C₁₃	direct (N × H)
25. C₅²×C₁₉	D₃×C₁₃	semidirect
26. C₁₃×D₁₅	C₅×C₁₉	direct (N × H)
28. C₅²×C₁₃	D₃×C₁₉	semidirect
30. C₃×C₅×C₁₉	D₅×C₁₃	semidirect
31. C₃×C₅×C₁₉	C₂×C₅×C₁₃	semidirect
32. C₁₃×C₁₉	C₅×D₁₅	direct (N × H)
34. C₃×C₅×C₁₃	D₅×C₁₉	semidirect
35. C₃×C₅×C₁₃	C₂×C₅×C₁₉	semidirect
38. C₅×D₁₅	C₁₃×C₁₉	direct (N × H)
43. C₅×C₁₉	C₅×D₃×C₁₃	semidirect
44. C₅×C₁₉	C₁₃×D₁₅	direct (N × H)
46. C₃×C₅²	C₂×C₁₃×C₁₉	semidirect
48. C₅×C₁₃	C₅×D₃×C₁₉	semidirect
49. C₅×C₁₃	C₁₉×D₁₅	direct (N × H)
50. C₃×C₁₉	C₅×D₅×C₁₃	semidirect
52. C₃×C₁₃	C₅×D₅×C₁₉	semidirect
54. D₁₅	C₅×C₁₃×C₁₉	direct (N × H)
57. C₅²	D₃×C₁₃×C₁₉	semidirect
58. C₁₉	C₅×C₁₃×D₁₅	direct (N × H)
60. C₃×C₅	C₂×C₅×C₁₃×C₁₉	semidirect
61. C₃×C₅	D₅×C₁₃×C₁₉	semidirect
62. C₁₃	C₅×C₁₉×D₁₅	direct (N × H)
67. C₅	C₅×D₃×C₁₃×C₁₉	semidirect
68. C₅	C₁₃×C₁₉×D₁₅	direct (N × H)
69. C₃	C₅×D₅×C₁₃×C₁₉	semidirect

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×D₅×C₁₃×C₁₉	3
C₁₃×C₁₉×D₁₅	5
C₅×D₃×C₁₃×C₁₉	5
C₅×C₁₉×D₁₅	13
C₅×C₁₃×D₁₅	19

Subgroups — C5×C13×C19×D15 #49150331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃×C₁₉×D₁₅ #49150331