Subgroups — C₃×C₁₃×D₂₃₁ #31825086

Order 18018.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₃×D₇₇	—	3	1	no	maximal
4	C₃×C₇×C₁₁×C₁₃	—	2	1	no	—
5	C₃×C₇×C₁₁×C₁₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×C₁₃×D₃₃	—	7	1	no	maximal, Hall
8	C₁₃×D₇₇	—	3	1	no	Hall
9	C₃×C₁₃×D₂₁	—	11	1	no	maximal, Hall
10	C₃×D₂₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₁₁×C₁₃	D₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₁×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₁₃×D₃₃	—	7	1	no	—
14	C₃×C₁₃×D₁₁	—	21	1	no	—
15	C₃²×C₇×C₁₃	D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₁₃×D₂₁	—	11	1	no	—
18	C₃×C₁₃×D₇	—	33	1	no	—
19	D₂₃₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor
20	C₃×D₇₇	—	3	1	no	—
21	C₃×C₁₁×C₁₃	—	2	1	no	—
22	C₃×C₁₁×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
23	C₃×C₁₁×C₁₃	D₂₁	1	1	yes	characteristic, complemented
24	C₁₃×D₁₁	—	21	1	no	Hall
25	C₃×C₇×C₁₃	—	2	1	no	—
26	C₃×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented
27	C₃×C₇×C₁₃	D₃₃	1	1	yes	characteristic, complemented
28	C₃×D₃×C₁₃	—	77	1	no	Hall
29	C₃×C₇×C₁₁	—	2	1	no	—
30	C₃×C₇×C₁₁	D₃×C₁₃	1	1	yes	characteristic, complemented
31	C₃×C₇×C₁₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
32	C₃×D₃₃	—	7	1	no	Hall
33	C₁₃×D₇	—	33	1	no	Hall
34	D₇₇	—	3	1	no	Hall
35	C₁₁×C₁₃	C₃×D₂₁	1	1	yes	characteristic, complemented, Hall
36	C₃×D₂₁	—	11	1	no	Hall
37	C₃²×C₁₃	D₇₇	1	1	yes	characteristic, complemented, Hall
38	C₃²×C₁₁	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
39	C₇×C₁₃	C₃×D₃₃	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×C₁₃	—	231	1	no	—
41	D₃×C₁₃	—	77	1	no	—
42	C₇×C₁₁	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
43	D₃₃	—	7	1	no	—
44	C₃×D₁₁	—	21	1	no	—
45	C₃²×C₇	C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
46	D₂₁	—	11	1	no	—
47	C₃×D₇	—	33	1	no	—
48	C₃×C₁₃	—	2	1	no	—
49	C₃×C₁₃	C₃×D₇₇	1	1	yes	characteristic, complemented
50	C₃×C₁₃	D₂₃₁	1	1	yes	characteristic, direct product factor
51	C₃×C₁₁	—	2	1	no	—
52	C₃×C₁₁	C₃×C₁₃×D₇	1	1	yes	characteristic, complemented
53	C₃×C₁₁	C₁₃×D₂₁	1	1	yes	characteristic, complemented
54	C₂×C₁₃	—	231	1	no	Hall
55	D₁₁	—	21	1	no	Hall
56	C₃×C₇	—	2	1	no	—
57	C₃×C₇	C₃×C₁₃×D₁₁	1	1	yes	characteristic, complemented
58	C₃×C₇	C₁₃×D₃₃	1	1	yes	characteristic, complemented
59	C₃×D₃	—	77	1	no	Hall
60	D₇	—	33	1	no	Hall
61	C₁₃	C₃×D₂₃₁	1	1	yes	characteristic, direct product factor, Sylow
62	C₁₁	C₃×C₁₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
63	C₃²	C₁₃×D₇₇	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₃×C₁₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	231	1	no	—
66	D₃	—	77	1	no	—
67	C₃	—	2	1	no	—
68	C₃	C₃×C₁₃×D₇₇	1	1	yes	characteristic, complemented
69	C₃	C₁₃×D₂₃₁	1	1	yes	characteristic, direct product factor
70	C₂	—	231	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₂₃₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₁	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₃	C₂	semidirect
2. C₁₃×D₂₃₁	C₃	direct (N × H)
5. C₃×C₇×C₁₁×C₁₃	D₃	semidirect
6. C₃×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
10. C₃×D₂₃₁	C₁₃	direct (N × H)
11. C₃²×C₁₁×C₁₃	D₇	semidirect
12. C₇×C₁₁×C₁₃	C₃×D₃	semidirect
15. C₃²×C₇×C₁₃	D₁₁	semidirect
16. C₃²×C₇×C₁₁	C₂×C₁₃	semidirect
19. D₂₃₁	C₃×C₁₃	direct (N × H)
22. C₃×C₁₁×C₁₃	C₃×D₇	semidirect
23. C₃×C₁₁×C₁₃	D₂₁	semidirect
26. C₃×C₇×C₁₃	C₃×D₁₁	semidirect
27. C₃×C₇×C₁₃	D₃₃	semidirect
30. C₃×C₇×C₁₁	D₃×C₁₃	semidirect
31. C₃×C₇×C₁₁	C₂×C₃×C₁₃	semidirect
35. C₁₁×C₁₃	C₃×D₂₁	semidirect
37. C₃²×C₁₃	D₇₇	semidirect
38. C₃²×C₁₁	C₁₃×D₇	semidirect
39. C₇×C₁₃	C₃×D₃₃	semidirect
42. C₇×C₁₁	C₃×D₃×C₁₃	semidirect
45. C₃²×C₇	C₁₃×D₁₁	semidirect
49. C₃×C₁₃	C₃×D₇₇	semidirect
50. C₃×C₁₃	D₂₃₁	direct (N × H)
52. C₃×C₁₁	C₃×C₁₃×D₇	semidirect
53. C₃×C₁₁	C₁₃×D₂₁	semidirect
57. C₃×C₇	C₃×C₁₃×D₁₁	semidirect
58. C₃×C₇	C₁₃×D₃₃	semidirect
61. C₁₃	C₃×D₂₃₁	direct (N × H)
62. C₁₁	C₃×C₁₃×D₂₁	semidirect
63. C₃²	C₁₃×D₇₇	semidirect
64. C₇	C₃×C₁₃×D₃₃	semidirect
68. C₃	C₃×C₁₃×D₇₇	semidirect
69. C₃	C₁₃×D₂₃₁	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×C₇×C₁₁×C₁₃	2
C₁₃×D₂₃₁	3
C₃×C₁₃×D₇₇	3
C₃×C₁₃×D₃₃	7
C₃×C₁₃×D₂₁	11
C₃×D₂₃₁	13

Subgroups — C3×C13×D231 #31825086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×D₂₃₁ #31825086