Subgroups — C₃×C₃₁×D₁₆₅ #44501880

Order 30690.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₁₆₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₃₁×D₅₅	—	3	1	no	maximal
4	C₃×C₃₁×D₃₃	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₁×C₃₁	—	2	1	no	—
6	C₃×C₅×C₁₁×C₃₁	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₁×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃₁×D₅₅	—	3	1	no	Hall
9	C₃²×C₁₁×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₅×C₃₁	—	11	1	no	maximal, Hall
11	C₃₁×D₃₃	—	5	1	no	—
12	C₃×D₁₁×C₃₁	—	15	1	no	—
13	C₅×C₁₁×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	C₃²×C₅×C₃₁	D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁×C₃₁	—	2	1	no	—
16	C₃×C₁₁×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
17	C₃×C₁₁×C₃₁	D₁₅	1	1	yes	characteristic, complemented
18	C₃×D₁₆₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	D₁₅×C₃₁	—	11	1	no	—
20	C₃×D₅×C₃₁	—	33	1	no	—
21	D₁₁×C₃₁	—	15	1	no	Hall
22	C₃×D₃×C₃₁	—	55	1	no	Hall
23	C₃²×C₅×C₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₃₁	—	2	1	no	—
25	C₃×C₅×C₃₁	C₃×D₁₁	1	1	yes	characteristic, complemented
26	C₃×C₅×C₃₁	D₃₃	1	1	yes	characteristic, complemented
27	C₁₁×C₃₁	C₃×D₁₅	1	1	yes	characteristic, complemented, Hall
28	D₁₆₅	C₃×C₃₁	1	1	yes	characteristic, direct product factor
29	C₃×D₅₅	—	3	1	no	—
30	D₅×C₃₁	—	33	1	no	Hall
31	C₃²×C₃₁	D₅₅	1	1	yes	characteristic, complemented, Hall
32	C₃×D₃₃	—	5	1	no	Hall
33	C₂×C₃×C₃₁	—	165	1	no	—
34	D₃×C₃₁	—	55	1	no	—
35	C₃×C₅×C₁₁	—	2	1	no	—
36	C₃×C₅×C₁₁	D₃×C₃₁	1	1	yes	characteristic, complemented
37	C₃×C₅×C₁₁	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
38	C₅×C₃₁	C₃×D₃₃	1	1	yes	characteristic, complemented, Hall
39	D₅₅	—	3	1	no	Hall
40	C₃²×C₁₁	D₅×C₃₁	1	1	yes	characteristic, complemented, Hall
41	C₃×C₃₁	—	2	1	no	—
42	C₃×C₃₁	C₃×D₅₅	1	1	yes	characteristic, complemented
43	C₃×C₃₁	D₁₆₅	1	1	yes	characteristic, direct product factor
44	C₃×D₁₅	—	11	1	no	Hall
45	D₃₃	—	5	1	no	—
46	C₃×D₁₁	—	15	1	no	—
47	C₂×C₃₁	—	165	1	no	Hall
48	C₅×C₁₁	C₃×D₃×C₃₁	1	1	yes	characteristic, complemented, Hall
49	C₃²×C₅	D₁₁×C₃₁	1	1	yes	characteristic, complemented, Hall
50	C₃×C₁₁	—	2	1	no	—
51	C₃×C₁₁	C₃×D₅×C₃₁	1	1	yes	characteristic, complemented
52	C₃×C₁₁	D₁₅×C₃₁	1	1	yes	characteristic, complemented
53	C₃₁	C₃×D₁₆₅	1	1	yes	characteristic, direct product factor, Sylow
54	D₁₅	—	11	1	no	—
55	C₃×D₅	—	33	1	no	—
56	D₁₁	—	15	1	no	Hall
57	C₃×D₃	—	55	1	no	Hall
58	C₃×C₅	—	2	1	no	—
59	C₃×C₅	C₃×D₁₁×C₃₁	1	1	yes	characteristic, complemented
60	C₃×C₅	C₃₁×D₃₃	1	1	yes	characteristic, complemented
61	C₁₁	C₃×D₁₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
62	D₅	—	33	1	no	Hall
63	C₃²	C₃₁×D₅₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	165	1	no	—
65	D₃	—	55	1	no	—
66	C₅	C₃×C₃₁×D₃₃	1	1	yes	characteristic, complemented, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×C₃₁×D₅₅	1	1	yes	characteristic, complemented
69	C₃	C₃₁×D₁₆₅	1	1	yes	characteristic, direct product factor
70	C₂	—	165	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₁	D₁₆₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₁	C₂×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₃₁	C₂
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₁×C₃₁	C₂	semidirect
2. C₃₁×D₁₆₅	C₃	direct (N × H)
6. C₃×C₅×C₁₁×C₃₁	D₃	semidirect
7. C₃×C₅×C₁₁×C₃₁	C₂×C₃	semidirect
9. C₃²×C₁₁×C₃₁	D₅	semidirect
13. C₅×C₁₁×C₃₁	C₃×D₃	semidirect
14. C₃²×C₅×C₃₁	D₁₁	semidirect
16. C₃×C₁₁×C₃₁	C₃×D₅	semidirect
17. C₃×C₁₁×C₃₁	D₁₅	semidirect
18. C₃×D₁₆₅	C₃₁	direct (N × H)
23. C₃²×C₅×C₁₁	C₂×C₃₁	semidirect
25. C₃×C₅×C₃₁	C₃×D₁₁	semidirect
26. C₃×C₅×C₃₁	D₃₃	semidirect
27. C₁₁×C₃₁	C₃×D₁₅	semidirect
28. D₁₆₅	C₃×C₃₁	direct (N × H)
31. C₃²×C₃₁	D₅₅	semidirect
36. C₃×C₅×C₁₁	D₃×C₃₁	semidirect
37. C₃×C₅×C₁₁	C₂×C₃×C₃₁	semidirect
38. C₅×C₃₁	C₃×D₃₃	semidirect
40. C₃²×C₁₁	D₅×C₃₁	semidirect
42. C₃×C₃₁	C₃×D₅₅	semidirect
43. C₃×C₃₁	D₁₆₅	direct (N × H)
48. C₅×C₁₁	C₃×D₃×C₃₁	semidirect
49. C₃²×C₅	D₁₁×C₃₁	semidirect
51. C₃×C₁₁	C₃×D₅×C₃₁	semidirect
52. C₃×C₁₁	D₁₅×C₃₁	semidirect
53. C₃₁	C₃×D₁₆₅	direct (N × H)
59. C₃×C₅	C₃×D₁₁×C₃₁	semidirect
60. C₃×C₅	C₃₁×D₃₃	semidirect
61. C₁₁	C₃×D₁₅×C₃₁	semidirect
63. C₃²	C₃₁×D₅₅	semidirect
66. C₅	C₃×C₃₁×D₃₃	semidirect
68. C₃	C₃×C₃₁×D₅₅	semidirect
69. C₃	C₃₁×D₁₆₅	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×C₁₁×C₃₁	2
C₃₁×D₁₆₅	3
C₃×C₃₁×D₅₅	3
C₃×C₃₁×D₃₃	5
C₃×D₁₅×C₃₁	11
C₃×D₁₆₅	31

Subgroups — C3×C31×D165 #44501880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₁×D₁₆₅ #44501880