Subgroups — C₂×C₅²×C₃⋊D₃×C₃₇ #45686520

Order 33300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₃×C₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×D₃×C₃₇	—	3	4	no	maximal
4	C₃²×C₅²×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×C₃⋊D₃×C₃₇	C₅	1	6	yes	maximal, direct product factor
6	C₅²×D₃×C₃₇	—	3	8	no	—
7	C₂×C₃×C₅²×C₃₇	D₃	1	4	yes	complemented
8	C₂²×C₅²×C₃₇	—	9	1	no	Hall
9	C₅×C₃⋊D₃×C₃₇	C₂×C₅	1	12	yes	direct product factor
10	C₂×C₃²×C₅×C₃₇	C₂×C₅	1	6	yes	complemented
11	C₃×C₅²×C₃₇	C₂×D₃	1	4	yes	complemented
12	C₂×C₅×D₃×C₃₇	—	3	24	no	—
13	C₂×C₅²×C₃₇	—	9	2	no	—
14	C₂×C₅²×C₃₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₃²×C₅×C₃₇	C₂²×C₅	1	6	yes	complemented
16	C₂×C₃⋊D₃×C₃₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₅×C₃₇	C₅×D₃	1	24	yes	complemented
18	C₅×D₃×C₃₇	—	3	48	no	—
19	C₅²×C₃₇	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅²×C₃⋊D₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×C₃₇	—	9	6	no	—
22	C₂×C₃²×C₃₇	C₂×C₅²	1	1	yes	characteristic, complemented
23	C₃⋊D₃×C₃₇	C₂×C₅²	1	2	yes	direct product factor
24	C₃×C₅×C₃₇	C₂×C₅×D₃	1	24	yes	complemented
25	C₂×C₃²×C₅²	C₂×C₃₇	1	1	yes	characteristic, complemented
26	C₅²×C₃⋊D₃	C₂×C₃₇	1	2	yes	direct product factor
27	C₂×D₃×C₃₇	—	3	4	no	—
28	C₂×C₅×C₃₇	—	9	12	no	—
29	C₂×C₅×C₃₇	C₅×C₃⋊D₃	1	6	yes	direct product factor
30	C₃²×C₃₇	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅²×D₃	—	3	4	no	—
32	C₃²×C₅²	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₃₇	C₅²×D₃	1	4	yes	complemented
34	D₃×C₃₇	—	3	8	no	—
35	C₅×C₃₇	C₂×C₅×C₃⋊D₃	1	6	yes	direct product factor
36	C₂×C₅×C₃⋊D₃	C₅×C₃₇	1	6	yes	direct product factor
37	C₂×C₃×C₅²	D₃×C₃₇	1	4	yes	complemented
38	C₅²×D₃	—	3	8	no	—
39	C₂²×C₃₇	—	9	1	no	Hall
40	C₃×C₃₇	C₂×C₅²×D₃	1	4	yes	complemented
41	C₂²×C₅²	—	9	1	no	Hall
42	C₂×C₃²×C₅	C₂×C₅×C₃₇	1	6	yes	complemented
43	C₅×C₃⋊D₃	C₂×C₅×C₃₇	1	12	yes	direct product factor
44	C₃×C₅²	C₂×D₃×C₃₇	1	4	yes	complemented
45	C₂×C₃₇	—	9	2	no	—
46	C₂×C₃₇	C₅²×C₃⋊D₃	1	1	yes	characteristic, direct product factor
47	C₂×C₅×D₃	—	3	24	no	—
48	C₂×C₅²	—	9	2	no	—
49	C₂×C₅²	C₃⋊D₃×C₃₇	1	1	yes	characteristic, direct product factor
50	C₃²×C₅	C₂²×C₅×C₃₇	1	6	yes	complemented
51	C₃₇	C₂×C₅²×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₃⋊D₃	C₅²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₃×C₅	C₅×D₃×C₃₇	1	24	yes	complemented
54	C₅×D₃	—	3	48	no	—
55	C₅²	C₂×C₃⋊D₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²×C₅	—	9	6	no	—
57	C₂×C₃²	C₂×C₅²×C₃₇	1	1	yes	characteristic, complemented
58	C₃⋊D₃	C₂×C₅²×C₃₇	1	2	yes	direct product factor
59	C₃×C₅	C₂×C₅×D₃×C₃₇	1	24	yes	complemented
60	C₂×D₃	—	3	4	no	—
61	C₂×C₅	—	9	12	no	—
62	C₂×C₅	C₅×C₃⋊D₃×C₃₇	1	6	yes	direct product factor
63	C₃²	C₂²×C₅²×C₃₇	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₅²×D₃×C₃₇	1	4	yes	complemented
65	D₃	—	3	8	no	—
66	C₅	C₂×C₅×C₃⋊D₃×C₃₇	1	6	yes	direct product factor
67	C₂²	—	9	1	no	Sylow
68	C₃	C₂×C₅²×D₃×C₃₇	1	4	yes	complemented
69	C₂	—	9	2	no	—
70	C₂	C₅²×C₃⋊D₃×C₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₃₇	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅²×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₃₇	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅²×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅²×C₃⋊D₃×C₃₇	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₃₇	C₂	semidirect
4. C₃²×C₅²×C₃₇	C₂²	semidirect
5. C₂×C₅×C₃⋊D₃×C₃₇	C₅	direct (N × H)
7. C₂×C₃×C₅²×C₃₇	D₃	semidirect
9. C₅×C₃⋊D₃×C₃₇	C₂×C₅	direct (N × H)
10. C₂×C₃²×C₅×C₃₇	C₂×C₅	semidirect
11. C₃×C₅²×C₃₇	C₂×D₃	semidirect
14. C₂×C₅²×C₃₇	C₃⋊D₃	direct (N × H)
15. C₃²×C₅×C₃₇	C₂²×C₅	semidirect
16. C₂×C₃⋊D₃×C₃₇	C₅²	direct (N × H)
17. C₂×C₃×C₅×C₃₇	C₅×D₃	semidirect
19. C₅²×C₃₇	C₂×C₃⋊D₃	direct (N × H)
20. C₂×C₅²×C₃⋊D₃	C₃₇	direct (N × H)
22. C₂×C₃²×C₃₇	C₂×C₅²	semidirect
23. C₃⋊D₃×C₃₇	C₂×C₅²	direct (N × H)
24. C₃×C₅×C₃₇	C₂×C₅×D₃	semidirect
25. C₂×C₃²×C₅²	C₂×C₃₇	semidirect
26. C₅²×C₃⋊D₃	C₂×C₃₇	direct (N × H)
29. C₂×C₅×C₃₇	C₅×C₃⋊D₃	direct (N × H)
30. C₃²×C₃₇	C₂²×C₅²	semidirect
32. C₃²×C₅²	C₂²×C₃₇	semidirect
33. C₂×C₃×C₃₇	C₅²×D₃	semidirect
35. C₅×C₃₇	C₂×C₅×C₃⋊D₃	direct (N × H)
36. C₂×C₅×C₃⋊D₃	C₅×C₃₇	direct (N × H)
37. C₂×C₃×C₅²	D₃×C₃₇	semidirect
40. C₃×C₃₇	C₂×C₅²×D₃	semidirect
42. C₂×C₃²×C₅	C₂×C₅×C₃₇	semidirect
43. C₅×C₃⋊D₃	C₂×C₅×C₃₇	direct (N × H)
44. C₃×C₅²	C₂×D₃×C₃₇	semidirect
46. C₂×C₃₇	C₅²×C₃⋊D₃	direct (N × H)
49. C₂×C₅²	C₃⋊D₃×C₃₇	direct (N × H)
50. C₃²×C₅	C₂²×C₅×C₃₇	semidirect
51. C₃₇	C₂×C₅²×C₃⋊D₃	direct (N × H)
52. C₂×C₃⋊D₃	C₅²×C₃₇	direct (N × H)
53. C₂×C₃×C₅	C₅×D₃×C₃₇	semidirect
55. C₅²	C₂×C₃⋊D₃×C₃₇	direct (N × H)
57. C₂×C₃²	C₂×C₅²×C₃₇	semidirect
58. C₃⋊D₃	C₂×C₅²×C₃₇	direct (N × H)
59. C₃×C₅	C₂×C₅×D₃×C₃₇	semidirect
62. C₂×C₅	C₅×C₃⋊D₃×C₃₇	direct (N × H)
63. C₃²	C₂²×C₅²×C₃₇	semidirect
64. C₂×C₃	C₅²×D₃×C₃₇	semidirect
66. C₅	C₂×C₅×C₃⋊D₃×C₃₇	direct (N × H)
68. C₃	C₂×C₅²×D₃×C₃₇	semidirect
70. C₂	C₅²×C₃⋊D₃×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₃⋊D₃×C₃₇	2
C₂×C₃²×C₅²×C₃₇	2
C₂×C₅²×D₃×C₃₇	3
C₂×C₅×C₃⋊D₃×C₃₇	5
C₂×C₅²×C₃⋊D₃	37

Subgroups — C2×C52×C3⋊D3×C37 #45686520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×C₃⋊D₃×C₃₇ #45686520