Subgroups — C₅×C₃⋊D₃×D₃₇ #20269140

Order 6660.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₁₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃⋊D₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₅×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×D₃₇	—	3	4	no	maximal
5	C₃²×C₅×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₃×D₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₁₁₁	—	3	4	no	—
8	C₅×D₃×C₃₇	—	3	4	no	—
9	C₃×C₅×D₃₇	D₃	1	4	yes	complemented
10	C₂×C₅×D₃₇	—	9	1	no	Hall
11	C₃⋊D₁₁₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃⋊D₃×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃²×D₃₇	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₃₇	C₂×D₃	1	4	yes	complemented
15	D₃×D₃₇	—	3	4	no	—
16	C₂×C₅×C₃₇	—	9	1	no	—
17	C₅×D₃₇	—	9	1	no	—
18	C₅×D₃₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	C₃²×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	D₁₁₁	—	3	4	no	—
21	C₃×D₃₇	C₅×D₃	1	4	yes	complemented
22	D₃×C₃₇	—	3	4	no	—
23	C₅×C₃₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₃⋊D₃	—	37	1	no	maximal, Hall
25	C₂×D₃₇	—	9	1	no	Hall
26	C₃×C₃₇	C₂×C₅×D₃	1	4	yes	complemented
27	C₂×C₃²×C₅	—	37	1	no	—
28	C₅×C₃⋊D₃	—	37	1	no	—
29	C₅×C₃⋊D₃	D₃₇	1	1	yes	characteristic, direct product factor
30	C₂×C₃₇	—	9	1	no	—
31	D₃₇	—	9	1	no	—
32	D₃₇	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
33	C₂×C₅×D₃	—	111	4	no	—
34	C₃²×C₅	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
35	C₃₇	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃⋊D₃	—	37	1	no	Hall
37	C₂×C₃×C₅	—	37	4	no	—
38	C₅×D₃	—	3	4	no	—
39	C₅×D₃	—	111	4	no	—
40	C₂²×C₅	—	333	1	no	Hall
41	C₂×C₃²	—	37	1	no	—
42	C₃⋊D₃	—	37	1	no	—
43	C₃⋊D₃	C₅×D₃₇	1	1	yes	characteristic, direct product factor
44	C₃×C₅	D₃×D₃₇	1	4	yes	complemented
45	C₂×D₃	—	111	4	no	—
46	C₂×C₅	—	9	1	no	—
47	C₂×C₅	—	37	1	no	—
48	C₂×C₅	—	333	1	no	—
49	C₃²	C₂×C₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	37	4	no	—
51	D₃	—	3	4	no	—
52	D₃	—	111	4	no	—
53	C₅	C₃⋊D₃×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	—	333	1	no	Sylow
55	C₃	C₅×D₃×D₃₇	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	37	1	no	—
58	C₂	—	333	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₃×D₃₇
commutator, hypocenter	C₃²×C₃₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₇	C₂²
LCS	G ▷ C₃²×C₃₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₃⋊D₁₁₁	C₂	semidirect
2. C₅×C₃⋊D₃×C₃₇	C₂	semidirect
3. C₃²×C₅×D₃₇	C₂	semidirect
5. C₃²×C₅×C₃₇	C₂²	semidirect
6. C₃⋊D₃×D₃₇	C₅	direct (N × H)
9. C₃×C₅×D₃₇	D₃	semidirect
11. C₃⋊D₁₁₁	C₂×C₅	semidirect
12. C₃⋊D₃×C₃₇	C₂×C₅	semidirect
13. C₃²×D₃₇	C₂×C₅	semidirect
14. C₃×C₅×C₃₇	C₂×D₃	semidirect
18. C₅×D₃₇	C₃⋊D₃	direct (N × H)
19. C₃²×C₃₇	C₂²×C₅	semidirect
21. C₃×D₃₇	C₅×D₃	semidirect
23. C₅×C₃₇	C₂×C₃⋊D₃	semidirect
26. C₃×C₃₇	C₂×C₅×D₃	semidirect
29. C₅×C₃⋊D₃	D₃₇	direct (N × H)
32. D₃₇	C₅×C₃⋊D₃	direct (N × H)
34. C₃²×C₅	C₂×D₃₇	semidirect
35. C₃₇	C₂×C₅×C₃⋊D₃	semidirect
43. C₃⋊D₃	C₅×D₃₇	direct (N × H)
44. C₃×C₅	D₃×D₃₇	semidirect
49. C₃²	C₂×C₅×D₃₇	semidirect
53. C₅	C₃⋊D₃×D₃₇	direct (N × H)
55. C₃	C₅×D₃×D₃₇	semidirect

Subgroups — C5×C3⋊D3×D37 #20269140

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₃⋊D₃×D₃₇ #20269140