Subgroups — C₅×D₃×C₁₁×C₃₇⋊C₃ #49143753

Order 36630.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₁₁×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₁×C₃₇⋊C₃	—	3	1	no	maximal
4	D₃×C₁₁×C₃₇⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₁×C₃₇⋊C₃	—	2	1	no	—
6	C₅×C₁₁×C₃₇⋊C₃	D₃	1	1	yes	characteristic, direct product factor
7	C₃×C₅×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅×C₁₁×C₃₇	—	3	1	no	Hall
9	C₃×C₁₁×C₃₇⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×D₃×C₃₇⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₃×C₁₁×C₃₇	C₃×C₅	1	1	yes	characteristic, complemented
12	C₂×C₁₁×C₃₇⋊C₃	—	3	1	no	—
13	C₅×C₁₁×C₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₃₇⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁×C₃₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	C₁₁×C₃₇⋊C₃	—	2	1	no	—
17	C₁₁×C₃₇⋊C₃	C₅×D₃	1	1	yes	characteristic, direct product factor
18	C₅×D₃×C₃₇	C₃×C₁₁	1	1	yes	characteristic, complemented
19	C₂×C₅×C₃₇⋊C₃	—	3	1	no	—
20	C₃×C₅×D₃×C₁₁	—	37	1	no	maximal, Hall
21	C₂×C₁₁×C₃₇	—	3	1	no	Hall
22	D₃×C₃₇⋊C₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₃₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
24	C₅×C₃₇⋊C₃	—	2	1	no	—
25	C₅×C₃₇⋊C₃	D₃×C₁₁	1	1	yes	characteristic, direct product factor
26	C₃²×C₅×C₁₁	—	37	1	no	Hall
27	C₁₁×C₃₇	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×C₃₇	—	3	1	no	Hall
29	C₃×C₃₇⋊C₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅×C₁₁	—	111	1	no	—
31	C₅×D₃×C₁₁	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
32	D₃×C₃₇	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
33	C₂×C₃₇⋊C₃	—	3	1	no	—
34	C₃×D₃×C₁₁	—	37	1	no	Hall
35	C₅×C₃₇	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
36	C₃×C₅×C₁₁	—	37	1	no	—
37	C₃×C₅×C₁₁	—	74	1	no	—
38	C₃×C₅×C₁₁	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
39	C₃×C₃₇	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
40	C₃₇⋊C₃	—	2	1	no	—
41	C₃₇⋊C₃	C₅×D₃×C₁₁	1	1	yes	characteristic, direct product factor
42	C₂×C₅×C₁₁	—	3	1	no	Hall
43	C₃²×C₁₁	—	37	1	no	Hall
44	C₃×C₅×D₃	—	37	1	no	Hall
45	C₂×C₃₇	—	3	1	no	Hall
46	C₂×C₃×C₁₁	—	111	1	no	—
47	D₃×C₁₁	C₅×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
48	C₅×C₁₁	D₃×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
49	C₃²×C₅	—	37	1	no	Hall
50	C₃₇	C₃×C₅×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
51	C₃×C₁₁	—	37	1	no	—
52	C₃×C₁₁	—	74	1	no	—
53	C₃×C₁₁	C₂×C₅×C₃₇⋊C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅	—	111	1	no	—
55	C₅×D₃	C₁₁×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
56	C₂×C₁₁	—	3	1	no	Hall
57	C₃×D₃	—	37	1	no	Hall
58	C₃×C₅	—	37	1	no	—
59	C₃×C₅	—	74	1	no	—
60	C₃×C₅	C₂×C₁₁×C₃₇⋊C₃	1	1	yes	characteristic, complemented
61	C₁₁	C₅×D₃×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₅	—	3	1	no	Hall
63	C₃²	—	37	1	no	Sylow
64	C₂×C₃	—	111	1	no	—
65	D₃	C₅×C₁₁×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
66	C₅	D₃×C₁₁×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
67	C₃	—	37	1	no	—
68	C₃	—	74	1	no	—
69	C₃	C₂×C₅×C₁₁×C₃₇⋊C₃	1	1	yes	characteristic, complemented
70	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₃×C₃₇⋊C₃
commutator, cosocle, hypocenter	C₃×C₃₇	C₂×C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₃₇	C₂×C₃
LCS	G ▷ C₃×C₃₇
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₃₇⋊C₃	C₂	semidirect
2. C₅×D₃×C₁₁×C₃₇	C₃	semidirect
4. D₃×C₁₁×C₃₇⋊C₃	C₅	direct (N × H)
6. C₅×C₁₁×C₃₇⋊C₃	D₃	direct (N × H)
7. C₃×C₅×C₁₁×C₃₇	C₂×C₃	semidirect
9. C₃×C₁₁×C₃₇⋊C₃	C₂×C₅	semidirect
10. C₅×D₃×C₃₇⋊C₃	C₁₁	direct (N × H)
11. D₃×C₁₁×C₃₇	C₃×C₅	semidirect
13. C₅×C₁₁×C₃₇	C₃×D₃	semidirect
14. C₃×C₅×C₃₇⋊C₃	C₂×C₁₁	semidirect
15. C₃×C₁₁×C₃₇	C₂×C₃×C₅	semidirect
17. C₁₁×C₃₇⋊C₃	C₅×D₃	direct (N × H)
18. C₅×D₃×C₃₇	C₃×C₁₁	semidirect
22. D₃×C₃₇⋊C₃	C₅×C₁₁	direct (N × H)
23. C₃×C₅×C₃₇	C₂×C₃×C₁₁	semidirect
25. C₅×C₃₇⋊C₃	D₃×C₁₁	direct (N × H)
27. C₁₁×C₃₇	C₃×C₅×D₃	semidirect
29. C₃×C₃₇⋊C₃	C₂×C₅×C₁₁	semidirect
31. C₅×D₃×C₁₁	C₃₇⋊C₃	direct (N × H)
32. D₃×C₃₇	C₃×C₅×C₁₁	semidirect
35. C₅×C₃₇	C₃×D₃×C₁₁	semidirect
38. C₃×C₅×C₁₁	C₂×C₃₇⋊C₃	semidirect
39. C₃×C₃₇	C₂×C₃×C₅×C₁₁	semidirect
41. C₃₇⋊C₃	C₅×D₃×C₁₁	direct (N × H)
47. D₃×C₁₁	C₅×C₃₇⋊C₃	direct (N × H)
48. C₅×C₁₁	D₃×C₃₇⋊C₃	direct (N × H)
50. C₃₇	C₃×C₅×D₃×C₁₁	semidirect
53. C₃×C₁₁	C₂×C₅×C₃₇⋊C₃	semidirect
55. C₅×D₃	C₁₁×C₃₇⋊C₃	direct (N × H)
60. C₃×C₅	C₂×C₁₁×C₃₇⋊C₃	semidirect
61. C₁₁	C₅×D₃×C₃₇⋊C₃	direct (N × H)
65. D₃	C₅×C₁₁×C₃₇⋊C₃	direct (N × H)
66. C₅	D₃×C₁₁×C₃₇⋊C₃	direct (N × H)
69. C₃	C₂×C₅×C₁₁×C₃₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₁×C₃₇⋊C₃	2
C₅×D₃×C₁₁×C₃₇	3
C₂×C₅×C₁₁×C₃₇⋊C₃	3
D₃×C₁₁×C₃₇⋊C₃	5
C₅×D₃×C₃₇⋊C₃	11
C₃×C₅×D₃×C₁₁	37

Subgroups — C5×D3×C11×C37⋊C3 #49143753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₁₁×C₃₇⋊C₃ #49143753