Subgroups — C₁₃⋊C₃×D₂₃₁ #31825072

Order 18018.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃×D₇₇	—	3	1	no	maximal
3	C₁₃×D₂₃₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₁×C₁₃⋊C₃	—	2	1	no	—
5	C₇×C₁₁×C₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃⋊C₃×D₃₃	—	7	1	no	maximal, Hall
8	C₁₃×D₇₇	—	3	1	no	Hall
9	C₁₃⋊C₃×D₂₁	—	11	1	no	maximal, Hall
10	C₃×D₂₃₁	—	13	1	no	maximal, Hall
11	C₃×C₁₁×C₁₃⋊C₃	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	D₁₁×C₁₃⋊C₃	—	21	1	no	—
15	C₃×C₇×C₁₃⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇×C₁₁	—	13	1	no	Hall
17	C₁₃×D₂₁	—	11	1	no	—
18	D₇×C₁₃⋊C₃	—	33	1	no	—
19	D₂₃₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
20	C₃×D₇₇	—	39	1	no	—
21	C₃×C₁₁×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
22	C₁₁×C₁₃⋊C₃	—	2	1	no	—
23	C₁₁×C₁₃⋊C₃	D₂₁	1	1	yes	characteristic, complemented
24	C₁₃×D₁₁	—	21	1	no	Hall
25	C₃×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented
26	C₇×C₁₃⋊C₃	—	2	1	no	—
27	C₇×C₁₃⋊C₃	D₃₃	1	1	yes	characteristic, complemented
28	D₃×C₁₃⋊C₃	—	77	1	no	Hall
29	C₃×C₇×C₁₁	—	13	1	no	—
30	C₃×C₇×C₁₁	—	26	1	no	—
31	C₃×C₇×C₁₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₃×D₃₃	—	91	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	—	143	1	no	Hall
37	C₃×C₁₃⋊C₃	D₇₇	1	1	yes	characteristic, complemented, Hall
38	C₃²×C₁₁	—	13	1	no	Hall
39	C₇×C₁₃	C₃×D₃₃	1	1	yes	characteristic, complemented, Hall
40	D₃×C₁₃	—	77	1	no	—
41	C₂×C₁₃⋊C₃	—	231	1	no	—
42	C₇×C₁₁	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
43	D₃₃	—	7	1	no	—
44	C₃×D₁₁	—	273	1	no	—
45	C₃²×C₇	—	13	1	no	Hall
46	D₂₁	—	11	1	no	—
47	C₃×D₇	—	429	1	no	—
48	C₃×C₁₃	C₃×D₇₇	1	1	yes	characteristic, complemented
49	C₁₃⋊C₃	—	2	1	no	—
50	C₁₃⋊C₃	D₂₃₁	1	1	yes	characteristic, direct product factor
51	C₃×C₁₁	—	13	1	no	—
52	C₃×C₁₁	—	26	1	no	—
53	C₃×C₁₁	D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
54	C₂×C₁₃	—	231	1	no	Hall
55	D₁₁	—	21	1	no	Hall
56	C₃×C₇	—	13	1	no	—
57	C₃×C₇	—	26	1	no	—
58	C₃×C₇	D₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
59	C₃×D₃	—	1001	1	no	Hall
60	D₇	—	33	1	no	Hall
61	C₁₃	C₃×D₂₃₁	1	1	yes	characteristic, complemented, Sylow
62	C₁₁	C₁₃⋊C₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
63	C₃²	—	13	1	no	Sylow
64	C₇	C₁₃⋊C₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	3003	1	no	—
66	D₃	—	77	1	no	—
67	C₃	—	13	1	no	—
68	C₃	—	26	1	no	—
69	C₃	C₁₃⋊C₃×D₇₇	1	1	yes	characteristic, complemented
70	C₂	—	231	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₁₃⋊C₃	C₂	semidirect
3. C₁₃×D₂₃₁	C₃	semidirect
5. C₇×C₁₁×C₁₃⋊C₃	D₃	semidirect
6. C₃×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
11. C₃×C₁₁×C₁₃⋊C₃	D₇	semidirect
12. C₇×C₁₁×C₁₃	C₃×D₃	semidirect
15. C₃×C₇×C₁₃⋊C₃	D₁₁	semidirect
19. D₂₃₁	C₁₃⋊C₃	direct (N × H)
21. C₃×C₁₁×C₁₃	C₃×D₇	semidirect
23. C₁₁×C₁₃⋊C₃	D₂₁	semidirect
25. C₃×C₇×C₁₃	C₃×D₁₁	semidirect
27. C₇×C₁₃⋊C₃	D₃₃	semidirect
31. C₃×C₇×C₁₁	C₂×C₁₃⋊C₃	semidirect
35. C₁₁×C₁₃	C₃×D₂₁	semidirect
37. C₃×C₁₃⋊C₃	D₇₇	semidirect
39. C₇×C₁₃	C₃×D₃₃	semidirect
42. C₇×C₁₁	D₃×C₁₃⋊C₃	semidirect
48. C₃×C₁₃	C₃×D₇₇	semidirect
50. C₁₃⋊C₃	D₂₃₁	direct (N × H)
53. C₃×C₁₁	D₇×C₁₃⋊C₃	semidirect
58. C₃×C₇	D₁₁×C₁₃⋊C₃	semidirect
61. C₁₃	C₃×D₂₃₁	semidirect
62. C₁₁	C₁₃⋊C₃×D₂₁	semidirect
64. C₇	C₁₃⋊C₃×D₃₃	semidirect
69. C₃	C₁₃⋊C₃×D₇₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₇×C₁₁×C₁₃⋊C₃	2
C₁₃⋊C₃×D₇₇	3
C₁₃×D₂₃₁	3
C₁₃⋊C₃×D₃₃	7
C₁₃⋊C₃×D₂₁	11
C₃×D₂₃₁	13

Subgroups — C13⋊C3×D231 #31825072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×D₂₃₁ #31825072