Subgroups — C₂×C₃²×D₅×C₃₇ #20269183

Order 6660.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅×C₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅×C₃₇	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₃²×C₃₇	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅×C₃₇	C₂×C₃	1	4	yes	complemented
7	C₃×D₅×C₃₇	C₂×C₃	1	8	yes	direct product factor
8	C₂×D₅×C₃₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₃₇	—	5	2	no	—
10	C₂×C₃²×C₃₇	D₅	1	1	yes	characteristic, direct product factor
11	C₃×C₅×C₃₇	C₂²×C₃	1	4	yes	complemented
12	C₂²×C₃×C₃₇	—	5	4	no	—
13	C₂×C₅×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented
14	D₅×C₃₇	C₂×C₃²	1	2	yes	direct product factor
15	C₃²×C₃₇	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₃₇	—	5	8	no	—
17	C₂×C₃×C₃₇	C₃×D₅	1	4	yes	direct product factor
18	C₅×C₃₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃²×D₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₃₇	—	5	1	no	Hall
21	C₃×C₃₇	C₂×C₃×D₅	1	4	yes	direct product factor
22	C₂×C₃²×C₅	C₂×C₃₇	1	1	yes	characteristic, complemented
23	C₃²×D₅	C₂×C₃₇	1	2	yes	direct product factor
24	C₂×C₃₇	—	5	2	no	—
25	C₂×C₃₇	C₃²×D₅	1	1	yes	characteristic, direct product factor
26	C₂×C₃×D₅	C₃×C₃₇	1	4	yes	direct product factor
27	C₃²×C₅	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
28	C₃₇	C₂×C₃²×D₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₃²	—	5	1	no	Hall
30	C₂×C₃×C₅	C₂×C₃×C₃₇	1	4	yes	complemented
31	C₃×D₅	C₂×C₃×C₃₇	1	8	yes	direct product factor
32	C₂×D₅	C₃²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃²	—	5	2	no	—
34	C₂×C₃²	D₅×C₃₇	1	1	yes	characteristic, direct product factor
35	C₃×C₅	C₂²×C₃×C₃₇	1	4	yes	complemented
36	C₂²×C₃	—	5	4	no	—
37	C₂×C₅	C₂×C₃²×C₃₇	1	1	yes	characteristic, complemented
38	D₅	C₂×C₃²×C₃₇	1	2	yes	direct product factor
39	C₃²	C₂×D₅×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	5	8	no	—
41	C₂×C₃	C₃×D₅×C₃₇	1	4	yes	direct product factor
42	C₅	C₂²×C₃²×C₃₇	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	5	1	no	Sylow
44	C₃	C₂×C₃×D₅×C₃₇	1	4	yes	direct product factor
45	C₂	—	5	2	no	—
46	C₂	C₃²×D₅×C₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₃₇	D₅
commutator, hypocenter	C₅	C₂²×C₃²×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₃₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃²×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃²×D₅×C₃₇	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₃₇	C₂	semidirect
3. C₂×C₃×D₅×C₃₇	C₃	direct (N × H)
4. C₃²×C₅×C₃₇	C₂²	semidirect
6. C₂×C₃×C₅×C₃₇	C₂×C₃	semidirect
7. C₃×D₅×C₃₇	C₂×C₃	direct (N × H)
8. C₂×D₅×C₃₇	C₃²	direct (N × H)
10. C₂×C₃²×C₃₇	D₅	direct (N × H)
11. C₃×C₅×C₃₇	C₂²×C₃	semidirect
13. C₂×C₅×C₃₇	C₂×C₃²	semidirect
14. D₅×C₃₇	C₂×C₃²	direct (N × H)
15. C₃²×C₃₇	C₂×D₅	direct (N × H)
17. C₂×C₃×C₃₇	C₃×D₅	direct (N × H)
18. C₅×C₃₇	C₂²×C₃²	semidirect
19. C₂×C₃²×D₅	C₃₇	direct (N × H)
21. C₃×C₃₇	C₂×C₃×D₅	direct (N × H)
22. C₂×C₃²×C₅	C₂×C₃₇	semidirect
23. C₃²×D₅	C₂×C₃₇	direct (N × H)
25. C₂×C₃₇	C₃²×D₅	direct (N × H)
26. C₂×C₃×D₅	C₃×C₃₇	direct (N × H)
27. C₃²×C₅	C₂²×C₃₇	semidirect
28. C₃₇	C₂×C₃²×D₅	direct (N × H)
30. C₂×C₃×C₅	C₂×C₃×C₃₇	semidirect
31. C₃×D₅	C₂×C₃×C₃₇	direct (N × H)
32. C₂×D₅	C₃²×C₃₇	direct (N × H)
34. C₂×C₃²	D₅×C₃₇	direct (N × H)
35. C₃×C₅	C₂²×C₃×C₃₇	semidirect
37. C₂×C₅	C₂×C₃²×C₃₇	semidirect
38. D₅	C₂×C₃²×C₃₇	direct (N × H)
39. C₃²	C₂×D₅×C₃₇	direct (N × H)
41. C₂×C₃	C₃×D₅×C₃₇	direct (N × H)
42. C₅	C₂²×C₃²×C₃₇	semidirect
44. C₃	C₂×C₃×D₅×C₃₇	direct (N × H)
46. C₂	C₃²×D₅×C₃₇	direct (N × H)

Subgroups — C2×C32×D5×C37 #20269183

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×D₅×C₃₇ #20269183