Subgroups — C₅×D₃²×C₃₇ #20269151

Order 6660.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₃×C₃₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₃×C₃₇	—	3	2	no	maximal
4	C₃²×C₅×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃²×C₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×C₃₇	—	3	2	no	—
7	C₅×D₃×C₃₇	—	3	2	no	—
8	C₅×D₃×C₃₇	—	6	1	no	—
9	C₅×D₃×C₃₇	D₃	1	2	yes	direct product factor
10	C₂²×C₅×C₃₇	—	9	1	no	Hall
11	C₃⋊D₃×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₃×C₃₇	C₂×C₅	1	2	yes	complemented
13	C₃×C₅×C₃₇	—	2	1	no	—
14	C₃×C₅×C₃₇	C₂×D₃	1	2	yes	complemented
15	C₂×D₃×C₃₇	—	3	2	no	—
16	C₂×C₅×C₃₇	—	3	2	no	—
17	C₂×C₅×C₃₇	—	9	1	no	—
18	C₃²×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₃₇	—	3	2	no	—
20	D₃×C₃₇	—	3	2	no	—
21	D₃×C₃₇	—	6	1	no	—
22	D₃×C₃₇	C₅×D₃	1	2	yes	direct product factor
23	C₅×C₃₇	D₃²	1	1	yes	characteristic, direct product factor, Hall
24	C₅×D₃²	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₃₇	—	9	1	no	Hall
26	C₃×C₃₇	—	2	1	no	—
27	C₃×C₃₇	C₂×C₅×D₃	1	2	yes	complemented
28	C₅×C₃⋊D₃	C₂×C₃₇	1	1	yes	characteristic, complemented
29	C₃×C₅×D₃	C₂×C₃₇	1	2	yes	complemented
30	C₂×C₃₇	—	3	2	no	—
31	C₂×C₃₇	—	9	1	no	—
32	C₂×C₅×D₃	—	3	2	no	—
33	C₃²×C₅	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
34	C₃₇	C₅×D₃²	1	1	yes	characteristic, direct product factor, Sylow
35	D₃²	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₃×C₅	—	3	2	no	—
37	C₅×D₃	—	3	2	no	—
38	C₅×D₃	—	6	1	no	—
39	C₅×D₃	D₃×C₃₇	1	2	yes	direct product factor
40	C₂²×C₅	—	9	1	no	Hall
41	C₃⋊D₃	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented
42	C₃×D₃	C₂×C₅×C₃₇	1	2	yes	complemented
43	C₃×C₅	—	2	1	no	—
44	C₃×C₅	C₂×D₃×C₃₇	1	2	yes	complemented
45	C₂×D₃	—	3	2	no	—
46	C₂×C₅	—	3	2	no	—
47	C₂×C₅	—	9	1	no	—
48	C₃²	C₂²×C₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃	—	3	2	no	—
50	D₃	—	3	2	no	—
51	D₃	—	6	1	no	—
52	D₃	C₅×D₃×C₃₇	1	2	yes	direct product factor
53	C₅	D₃²×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	—	9	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	C₂×C₅×D₃×C₃₇	1	2	yes	complemented
57	C₂	—	3	2	no	—
58	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₃₇	D₃²
commutator, hypocenter	C₃²	C₂²×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₇	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₃⋊D₃×C₃₇	C₂	semidirect
2. C₃×C₅×D₃×C₃₇	C₂	semidirect
4. C₃²×C₅×C₃₇	C₂²	semidirect
5. D₃²×C₃₇	C₅	direct (N × H)
9. C₅×D₃×C₃₇	D₃	direct (N × H)
11. C₃⋊D₃×C₃₇	C₂×C₅	semidirect
12. C₃×D₃×C₃₇	C₂×C₅	semidirect
14. C₃×C₅×C₃₇	C₂×D₃	semidirect
18. C₃²×C₃₇	C₂²×C₅	semidirect
22. D₃×C₃₇	C₅×D₃	direct (N × H)
23. C₅×C₃₇	D₃²	direct (N × H)
24. C₅×D₃²	C₃₇	direct (N × H)
27. C₃×C₃₇	C₂×C₅×D₃	semidirect
28. C₅×C₃⋊D₃	C₂×C₃₇	semidirect
29. C₃×C₅×D₃	C₂×C₃₇	semidirect
33. C₃²×C₅	C₂²×C₃₇	semidirect
34. C₃₇	C₅×D₃²	direct (N × H)
35. D₃²	C₅×C₃₇	direct (N × H)
39. C₅×D₃	D₃×C₃₇	direct (N × H)
41. C₃⋊D₃	C₂×C₅×C₃₇	semidirect
42. C₃×D₃	C₂×C₅×C₃₇	semidirect
44. C₃×C₅	C₂×D₃×C₃₇	semidirect
48. C₃²	C₂²×C₅×C₃₇	semidirect
52. D₃	C₅×D₃×C₃₇	direct (N × H)
53. C₅	D₃²×C₃₇	direct (N × H)
56. C₃	C₂×C₅×D₃×C₃₇	semidirect

Subgroups — C5×D32×C37 #20269151

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₃²×C₃₇ #20269151