Subgroups — D₃₇×C₃⋊D₁₅ #20269146

Order 6660.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₅₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₅×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅×D₃₇	—	3	4	no	maximal
5	C₃²×C₅×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₃×D₃₇	—	5	1	no	maximal, Hall
7	D₅₅₅	—	3	4	no	—
8	D₁₅×C₃₇	—	3	4	no	—
9	C₃×C₅×D₃₇	D₃	1	4	yes	complemented
10	D₅×D₃₇	—	9	1	no	Hall
11	C₃⋊D₁₁₁	—	5	1	no	—
12	C₃⋊D₃×C₃₇	—	5	1	no	—
13	C₃²×D₃₇	D₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₃₇	C₂×D₃	1	4	yes	complemented
15	D₃×D₃₇	—	15	4	no	—
16	D₁₈₅	—	9	1	no	—
17	C₅×D₃₇	C₃⋊D₃	1	1	yes	characteristic, complemented
18	D₅×C₃₇	—	9	1	no	—
19	C₃²×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₁₁₁	—	15	4	no	—
21	C₃×D₃₇	D₁₅	1	4	yes	complemented
22	D₃×C₃₇	—	15	4	no	—
23	C₅×C₃₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃⋊D₁₅	—	37	1	no	maximal, Hall
25	C₂×D₃₇	—	45	1	no	Hall
26	C₃×C₃₇	C₂×D₁₅	1	4	yes	complemented
27	C₂×C₃²×C₅	—	37	1	no	—
28	C₃⋊D₁₅	—	37	1	no	—
29	C₃⋊D₁₅	D₃₇	1	1	yes	characteristic, direct product factor
30	C₂×C₃₇	—	45	1	no	—
31	D₃₇	—	45	1	no	—
32	D₃₇	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
33	C₂×D₁₅	—	111	4	no	—
34	C₃²×C₅	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
35	C₃₇	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃⋊D₃	—	185	1	no	Hall
37	C₂×C₃×C₅	—	37	4	no	—
38	D₁₅	—	3	4	no	—
39	D₁₅	—	111	4	no	—
40	C₂×D₅	—	333	1	no	Hall
41	C₂×C₃²	—	37	1	no	—
42	C₃⋊D₃	—	5	1	no	—
43	C₃⋊D₃	—	185	1	no	—
44	C₃×C₅	D₃×D₃₇	1	4	yes	complemented
45	C₂×D₃	—	555	4	no	—
46	C₂×C₅	—	37	1	no	—
47	D₅	—	9	1	no	—
48	D₅	—	333	1	no	—
49	C₃²	D₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	37	4	no	—
51	D₃	—	15	4	no	—
52	D₃	—	555	4	no	—
53	C₅	C₃⋊D₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	1665	1	no	Sylow
55	C₃	D₁₅×D₃₇	1	4	yes	complemented
56	C₂	—	37	1	no	—
57	C₂	—	45	1	no	—
58	C₂	—	1665	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₅₅₅	C₂	semidirect
2. C₃₇×C₃⋊D₁₅	C₂	semidirect
3. C₃²×C₅×D₃₇	C₂	semidirect
5. C₃²×C₅×C₃₇	C₂²	semidirect
9. C₃×C₅×D₃₇	D₃	semidirect
13. C₃²×D₃₇	D₅	semidirect
14. C₃×C₅×C₃₇	C₂×D₃	semidirect
17. C₅×D₃₇	C₃⋊D₃	semidirect
19. C₃²×C₃₇	C₂×D₅	semidirect
21. C₃×D₃₇	D₁₅	semidirect
23. C₅×C₃₇	C₂×C₃⋊D₃	semidirect
26. C₃×C₃₇	C₂×D₁₅	semidirect
29. C₃⋊D₁₅	D₃₇	direct (N × H)
32. D₃₇	C₃⋊D₁₅	direct (N × H)
34. C₃²×C₅	C₂×D₃₇	semidirect
35. C₃₇	C₂×C₃⋊D₁₅	semidirect
44. C₃×C₅	D₃×D₃₇	semidirect
49. C₃²	D₅×D₃₇	semidirect
53. C₅	C₃⋊D₃×D₃₇	semidirect
55. C₃	D₁₅×D₃₇	semidirect

Subgroups — D37×C3⋊D15 #20269146

Conjugacy classes of subgroups

Complements

Subgroups — D₃₇×C₃⋊D₁₅ #20269146