Subgroups — C₃×C₅×C₁₃×D₅₁ #34091071

Order 19890.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₃×D₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×C₁₃×D₁₇	—	3	1	no	maximal
4	C₃×C₁₃×D₅₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₃×C₁₇	—	2	1	no	—
6	C₃×C₅×C₁₃×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×C₁₃×D₁₇	—	3	1	no	Hall
9	C₃²×C₁₃×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×D₅₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₃×D₅₁	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₃×C₁₃×D₁₇	—	3	1	no	—
13	C₃×C₅×D₃×C₁₃	—	17	1	no	maximal, Hall
14	C₅×C₁₃×C₁₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
15	C₃²×C₅×C₁₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₃×C₁₇	—	2	1	no	—
17	C₃×C₁₃×C₁₇	C₅×D₃	1	1	yes	characteristic, complemented
18	C₃×C₁₃×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
19	C₃²×C₅×C₁₃	D₁₇	1	1	yes	characteristic, complemented, Hall
20	C₅×D₅₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor
21	C₃×C₅×D₁₇	—	3	1	no	—
22	C₁₃×D₁₇	—	3	1	no	Hall
23	C₂×C₃×C₅×C₁₃	—	51	1	no	—
24	C₅×D₃×C₁₃	—	17	1	no	—
25	C₃×D₅₁	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅×C₁₇	—	2	1	no	—
27	C₃×C₅×C₁₇	D₃×C₁₃	1	1	yes	characteristic, complemented
28	C₃×C₅×C₁₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
29	C₃×D₃×C₁₃	—	17	1	no	Hall
30	C₁₃×C₁₇	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×C₁₃	—	2	1	no	—
32	C₃×C₅×C₁₃	C₃×D₁₇	1	1	yes	characteristic, complemented
33	C₃×C₅×C₁₃	D₅₁	1	1	yes	characteristic, direct product factor
34	C₅×D₁₇	—	3	1	no	Hall
35	C₃²×C₁₇	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₃	—	51	1	no	Hall
37	C₃²×C₁₃	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
38	D₅₁	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor
39	C₃×D₁₇	—	3	1	no	—
40	C₃×C₅×D₃	—	17	1	no	Hall
41	C₅×C₁₇	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₁₃	—	51	1	no	—
43	D₃×C₁₃	—	17	1	no	—
44	C₅×C₁₃	C₃×D₅₁	1	1	yes	characteristic, direct product factor, Hall
45	C₃×C₁₇	—	2	1	no	—
46	C₃×C₁₇	C₅×D₃×C₁₃	1	1	yes	characteristic, complemented
47	C₃×C₁₇	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
48	C₃²×C₅	C₁₃×D₁₇	1	1	yes	characteristic, complemented, Hall
49	C₃×C₁₃	—	2	1	no	—
50	C₃×C₁₃	C₃×C₅×D₁₇	1	1	yes	characteristic, complemented
51	C₃×C₁₃	C₅×D₅₁	1	1	yes	characteristic, direct product factor
52	D₁₇	—	3	1	no	Hall
53	C₂×C₃×C₅	—	51	1	no	—
54	C₅×D₃	—	17	1	no	—
55	C₂×C₁₃	—	51	1	no	Hall
56	C₃×D₃	—	17	1	no	Hall
57	C₁₇	C₃×C₅×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₃×C₅	—	2	1	no	—
59	C₃×C₅	C₃×C₁₃×D₁₇	1	1	yes	characteristic, complemented
60	C₃×C₅	C₁₃×D₅₁	1	1	yes	characteristic, direct product factor
61	C₁₃	C₃×C₅×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₅	—	51	1	no	Hall
63	C₃²	C₅×C₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	51	1	no	—
65	D₃	—	17	1	no	—
66	C₅	C₃×C₁₃×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×C₅×C₁₃×D₁₇	1	1	yes	characteristic, complemented
69	C₃	C₅×C₁₃×D₅₁	1	1	yes	characteristic, direct product factor
70	C₂	—	51	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₃	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₃×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃×C₁₇	C₂	semidirect
2. C₅×C₁₃×D₅₁	C₃	direct (N × H)
4. C₃×C₁₃×D₅₁	C₅	direct (N × H)
6. C₃×C₅×C₁₃×C₁₇	D₃	semidirect
7. C₃×C₅×C₁₃×C₁₇	C₂×C₃	semidirect
9. C₃²×C₁₃×C₁₇	C₂×C₅	semidirect
10. C₃×C₅×D₅₁	C₁₃	direct (N × H)
11. C₁₃×D₅₁	C₃×C₅	direct (N × H)
14. C₅×C₁₃×C₁₇	C₃×D₃	semidirect
15. C₃²×C₅×C₁₇	C₂×C₁₃	semidirect
17. C₃×C₁₃×C₁₇	C₅×D₃	semidirect
18. C₃×C₁₃×C₁₇	C₂×C₃×C₅	semidirect
19. C₃²×C₅×C₁₃	D₁₇	semidirect
20. C₅×D₅₁	C₃×C₁₃	direct (N × H)
25. C₃×D₅₁	C₅×C₁₃	direct (N × H)
27. C₃×C₅×C₁₇	D₃×C₁₃	semidirect
28. C₃×C₅×C₁₇	C₂×C₃×C₁₃	semidirect
30. C₁₃×C₁₇	C₃×C₅×D₃	semidirect
32. C₃×C₅×C₁₃	C₃×D₁₇	semidirect
33. C₃×C₅×C₁₃	D₅₁	direct (N × H)
35. C₃²×C₁₇	C₂×C₅×C₁₃	semidirect
37. C₃²×C₁₃	C₅×D₁₇	semidirect
38. D₅₁	C₃×C₅×C₁₃	direct (N × H)
41. C₅×C₁₇	C₃×D₃×C₁₃	semidirect
44. C₅×C₁₃	C₃×D₅₁	direct (N × H)
46. C₃×C₁₇	C₅×D₃×C₁₃	semidirect
47. C₃×C₁₇	C₂×C₃×C₅×C₁₃	semidirect
48. C₃²×C₅	C₁₃×D₁₇	semidirect
50. C₃×C₁₃	C₃×C₅×D₁₇	semidirect
51. C₃×C₁₃	C₅×D₅₁	direct (N × H)
57. C₁₇	C₃×C₅×D₃×C₁₃	semidirect
59. C₃×C₅	C₃×C₁₃×D₁₇	semidirect
60. C₃×C₅	C₁₃×D₅₁	direct (N × H)
61. C₁₃	C₃×C₅×D₅₁	direct (N × H)
63. C₃²	C₅×C₁₃×D₁₇	semidirect
66. C₅	C₃×C₁₃×D₅₁	direct (N × H)
68. C₃	C₃×C₅×C₁₃×D₁₇	semidirect
69. C₃	C₅×C₁₃×D₅₁	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×C₁₇	2
C₅×C₁₃×D₅₁	3
C₃×C₅×C₁₃×D₁₇	3
C₃×C₁₃×D₅₁	5
C₃×C₅×D₅₁	13
C₃×C₅×D₃×C₁₃	17

Subgroups — C3×C5×C13×D51 #34091071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₃×D₅₁ #34091071