Subgroups — C₂²×C₃×C₅×C₃₇⋊C₃ #20269173

Order 6660.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₅	C₃₇⋊C₃
commutator, hypocenter	C₃₇	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅×C₃₇	C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂²×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₃₇⋊C₃	C₂	direct (N × H)
2. C₂²×C₅×C₃₇⋊C₃	C₃	direct (N × H)
3. C₂²×C₃×C₅×C₃₇	C₃	semidirect
4. C₃×C₅×C₃₇⋊C₃	C₂²	direct (N × H)
5. C₂²×C₃×C₃₇⋊C₃	C₅	direct (N × H)
6. C₂×C₃×C₅×C₃₇	C₂×C₃	semidirect
7. C₂×C₅×C₃₇⋊C₃	C₂×C₃	direct (N × H)
8. C₂²×C₅×C₃₇	C₃²	semidirect
9. C₂×C₃×C₃₇⋊C₃	C₂×C₅	direct (N × H)
10. C₃×C₅×C₃₇	C₂²×C₃	semidirect
11. C₅×C₃₇⋊C₃	C₂²×C₃	direct (N × H)
12. C₂²×C₃×C₃₇	C₃×C₅	semidirect
13. C₂²×C₃₇⋊C₃	C₃×C₅	direct (N × H)
14. C₂×C₅×C₃₇	C₂×C₃²	semidirect
15. C₃×C₃₇⋊C₃	C₂²×C₅	direct (N × H)
16. C₂×C₃×C₃₇	C₂×C₃×C₅	semidirect
17. C₂×C₃₇⋊C₃	C₂×C₃×C₅	direct (N × H)
18. C₅×C₃₇	C₂²×C₃²	semidirect
20. C₂²×C₃₇	C₃²×C₅	semidirect
21. C₃×C₃₇	C₂²×C₃×C₅	semidirect
22. C₃₇⋊C₃	C₂²×C₃×C₅	direct (N × H)
24. C₂×C₃₇	C₂×C₃²×C₅	semidirect
26. C₂²×C₃×C₅	C₃₇⋊C₃	direct (N × H)
28. C₃₇	C₂²×C₃²×C₅	semidirect
31. C₂×C₃×C₅	C₂×C₃₇⋊C₃	direct (N × H)
32. C₂²×C₅	C₃×C₃₇⋊C₃	direct (N × H)
35. C₃×C₅	C₂²×C₃₇⋊C₃	direct (N × H)
37. C₂²×C₃	C₅×C₃₇⋊C₃	direct (N × H)
38. C₂×C₅	C₂×C₃×C₃₇⋊C₃	direct (N × H)
41. C₂×C₃	C₂×C₅×C₃₇⋊C₃	direct (N × H)
42. C₅	C₂²×C₃×C₃₇⋊C₃	direct (N × H)
43. C₂²	C₃×C₅×C₃₇⋊C₃	direct (N × H)
45. C₃	C₂²×C₅×C₃₇⋊C₃	direct (N × H)
46. C₂	C₂×C₃×C₅×C₃₇⋊C₃	direct (N × H)

Subgroups — C22×C3×C5×C37⋊C3 #20269173

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₃×C₅×C₃₇⋊C₃ #20269173