Subgroups — C₂×C₅×C₃₇×D₃₃ #37567642

Order 24420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×D₃₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₁₁×C₃₇	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₇×D₃₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₁₁×C₃₇	—	3	2	no	—
7	C₂×C₅×C₁₁×C₃₇	D₃	1	1	yes	characteristic, complemented
8	C₃₇×D₃₃	C₂×C₅	1	2	yes	direct product factor
9	C₂×C₃×C₁₁×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
10	C₂×C₅×D₃×C₃₇	—	11	1	no	maximal, Hall
11	C₅×C₁₁×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×D₁₁×C₃₇	—	3	1	no	Hall
13	C₃×C₁₁×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×C₃₇	D₁₁	1	1	yes	characteristic, complemented
15	C₅×D₃×C₃₇	—	11	2	no	—
16	C₂×C₁₁×C₃₇	C₅×D₃	1	1	yes	characteristic, complemented
17	D₁₁×C₃₇	—	3	2	no	—
18	C₂²×C₅×C₃₇	—	33	1	no	Hall
19	C₂×C₅×D₃₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₃×C₅×C₃₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃×C₃₇	—	11	1	no	Hall
22	C₁₁×C₃₇	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₃₇	—	33	2	no	—
24	C₂×C₅×C₃₇	D₃₃	1	1	yes	characteristic, direct product factor
25	C₂×C₃×C₅×C₁₁	C₂×C₃₇	1	1	yes	characteristic, complemented
26	C₅×D₃₃	C₂×C₃₇	1	2	yes	direct product factor
27	C₂×C₃×C₃₇	C₅×D₁₁	1	1	yes	characteristic, complemented
28	D₃×C₃₇	—	11	2	no	—
29	C₂×C₅×D₁₁	—	3	1	no	Hall
30	C₅×C₃₇	C₂×D₃₃	1	1	yes	characteristic, direct product factor, Hall
31	C₃×C₅×C₁₁	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₃₇	—	33	1	no	Hall
33	C₂×D₃₃	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
34	C₃×C₃₇	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₅×C₁₁	D₃×C₃₇	1	1	yes	characteristic, complemented
36	C₅×D₁₁	—	3	2	no	—
37	C₂×C₃₇	—	33	2	no	—
38	C₂×C₃₇	C₅×D₃₃	1	1	yes	characteristic, direct product factor
39	C₂×C₃×C₁₁	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented
40	D₃₃	C₂×C₅×C₃₇	1	2	yes	direct product factor
41	C₂×C₅×D₃	—	11	1	no	Hall
42	C₅×C₁₁	C₂×D₃×C₃₇	1	1	yes	characteristic, complemented, Hall
43	C₂×D₁₁	—	3	1	no	Hall
44	C₃₇	C₂×C₅×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃×C₁₁	C₂²×C₅×C₃₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₅	D₁₁×C₃₇	1	1	yes	characteristic, complemented
47	C₅×D₃	—	11	2	no	—
48	C₂×C₁₁	C₅×D₃×C₃₇	1	1	yes	characteristic, complemented
49	D₁₁	—	3	2	no	—
50	C₂²×C₅	—	33	1	no	Hall
51	C₃×C₅	C₂×D₁₁×C₃₇	1	1	yes	characteristic, complemented, Hall
52	C₂×D₃	—	11	1	no	Hall
53	C₁₁	C₂×C₅×D₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₅	—	33	2	no	—
55	C₂×C₅	C₃₇×D₃₃	1	1	yes	characteristic, direct product factor
56	C₂×C₃	C₅×D₁₁×C₃₇	1	1	yes	characteristic, complemented
57	D₃	—	11	2	no	—
58	C₅	C₂×C₃₇×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	33	1	no	Sylow
60	C₃	C₂×C₅×D₁₁×C₃₇	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	33	2	no	—
62	C₂	C₅×C₃₇×D₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₃₇	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂²×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₃₇	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₂×C₅×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₇×D₃₃	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₃₇	C₂	semidirect
4. C₃×C₅×C₁₁×C₃₇	C₂²	semidirect
5. C₂×C₃₇×D₃₃	C₅	direct (N × H)
7. C₂×C₅×C₁₁×C₃₇	D₃	semidirect
8. C₃₇×D₃₃	C₂×C₅	direct (N × H)
9. C₂×C₃×C₁₁×C₃₇	C₂×C₅	semidirect
11. C₅×C₁₁×C₃₇	C₂×D₃	semidirect
13. C₃×C₁₁×C₃₇	C₂²×C₅	semidirect
14. C₂×C₃×C₅×C₃₇	D₁₁	semidirect
16. C₂×C₁₁×C₃₇	C₅×D₃	semidirect
19. C₂×C₅×D₃₃	C₃₇	direct (N × H)
20. C₃×C₅×C₃₇	C₂×D₁₁	semidirect
22. C₁₁×C₃₇	C₂×C₅×D₃	semidirect
24. C₂×C₅×C₃₇	D₃₃	direct (N × H)
25. C₂×C₃×C₅×C₁₁	C₂×C₃₇	semidirect
26. C₅×D₃₃	C₂×C₃₇	direct (N × H)
27. C₂×C₃×C₃₇	C₅×D₁₁	semidirect
30. C₅×C₃₇	C₂×D₃₃	direct (N × H)
31. C₃×C₅×C₁₁	C₂²×C₃₇	semidirect
33. C₂×D₃₃	C₅×C₃₇	direct (N × H)
34. C₃×C₃₇	C₂×C₅×D₁₁	semidirect
35. C₂×C₅×C₁₁	D₃×C₃₇	semidirect
38. C₂×C₃₇	C₅×D₃₃	direct (N × H)
39. C₂×C₃×C₁₁	C₂×C₅×C₃₇	semidirect
40. D₃₃	C₂×C₅×C₃₇	direct (N × H)
42. C₅×C₁₁	C₂×D₃×C₃₇	semidirect
44. C₃₇	C₂×C₅×D₃₃	direct (N × H)
45. C₃×C₁₁	C₂²×C₅×C₃₇	semidirect
46. C₂×C₃×C₅	D₁₁×C₃₇	semidirect
48. C₂×C₁₁	C₅×D₃×C₃₇	semidirect
51. C₃×C₅	C₂×D₁₁×C₃₇	semidirect
53. C₁₁	C₂×C₅×D₃×C₃₇	semidirect
55. C₂×C₅	C₃₇×D₃₃	direct (N × H)
56. C₂×C₃	C₅×D₁₁×C₃₇	semidirect
58. C₅	C₂×C₃₇×D₃₃	direct (N × H)
60. C₃	C₂×C₅×D₁₁×C₃₇	semidirect
62. C₂	C₅×C₃₇×D₃₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₃₇×D₃₃	2
C₂×C₃×C₅×C₁₁×C₃₇	2
C₂×C₅×D₁₁×C₃₇	3
C₂×C₃₇×D₃₃	5
C₂×C₅×D₃×C₃₇	11
C₂×C₅×D₃₃	37

Subgroups — C2×C5×C37×D33 #37567642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₃₇×D₃₃ #37567642