Subgroups — D₉×C₃₇×D₁₉ #38760913

Order 25308.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×D₁₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₉×C₁₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₃₇×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₃₇×D₁₉	—	3	1	no	maximal
5	C₉×C₁₉×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃₇×D₅₇	—	3	1	no	—
7	D₃×C₁₉×C₃₇	—	3	1	no	—
8	C₃×C₃₇×D₁₉	D₃	1	1	yes	characteristic
9	C₂×C₃₇×D₁₉	—	9	1	no	Hall
10	C₃×C₁₉×C₃₇	C₂×D₃	1	1	yes	characteristic
11	C₂×C₁₉×C₃₇	—	9	1	no	—
12	C₃₇×D₁₉	—	9	1	no	—
13	C₃₇×D₁₉	D₉	1	1	yes	characteristic, direct product factor
14	C₂×D₉×C₃₇	—	19	1	no	maximal, Hall
15	C₁₉×C₃₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	D₉×D₁₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₉×C₃₇	—	19	1	no	—
18	D₉×C₃₇	—	19	1	no	—
19	D₉×C₃₇	D₁₉	1	1	yes	characteristic, direct product factor
20	C₂×D₃×C₃₇	—	57	1	no	—
21	D₁₇₁	C₂×C₃₇	1	1	yes	characteristic, complemented
22	C₉×D₁₉	C₂×C₃₇	1	1	yes	characteristic, complemented
23	D₉×C₁₉	C₂×C₃₇	1	1	yes	characteristic, complemented
24	C₉×C₃₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
25	D₃×D₁₉	—	3	1	no	—
26	C₂×C₃×C₃₇	—	19	1	no	—
27	D₃×C₃₇	—	3	1	no	—
28	D₃×C₃₇	—	57	1	no	—
29	C₉×C₁₉	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃₇	—	171	1	no	Hall
31	D₅₇	—	3	1	no	—
32	C₃×D₁₉	D₃×C₃₇	1	1	yes	characteristic
33	D₃×C₁₉	—	3	1	no	—
34	C₃×C₃₇	D₃×D₁₉	1	1	yes	characteristic
35	C₂×D₁₉	—	9	1	no	Hall
36	C₂×C₃₇	—	9	1	no	—
37	C₂×C₃₇	—	19	1	no	—
38	C₂×C₃₇	—	171	1	no	—
39	C₃×C₁₉	C₂×D₃×C₃₇	1	1	yes	characteristic
40	C₂×C₁₉	—	9	1	no	—
41	D₁₉	—	9	1	no	—
42	D₁₉	D₉×C₃₇	1	1	yes	characteristic, direct product factor
43	C₃₇	D₉×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×D₉	—	19	1	no	Hall
45	C₁₉	C₂×D₉×C₃₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₉	—	19	1	no	—
47	D₉	—	19	1	no	—
48	D₉	C₃₇×D₁₉	1	1	yes	characteristic, direct product factor
49	C₂×D₃	—	57	1	no	—
50	C₉	C₂×C₃₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	19	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	57	1	no	—
54	C₂²	—	171	1	no	Sylow
55	C₃	D₃×C₃₇×D₁₉	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	19	1	no	—
58	C₂	—	171	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	D₉×D₁₉
commutator, hypocenter	C₉×C₁₉	C₂²×C₃₇
Frattini	C₃	D₃×C₃₇×D₁₉
Fitting	C₉×C₁₉×C₃₇	C₂²
socle	C₃×C₁₉×C₃₇	C₂×D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃₇×D₁₇₁	C₂	semidirect
2. D₉×C₁₉×C₃₇	C₂	semidirect
3. C₉×C₃₇×D₁₉	C₂	semidirect
5. C₉×C₁₉×C₃₇	C₂²	semidirect
13. C₃₇×D₁₉	D₉	direct (N × H)
15. C₁₉×C₃₇	C₂×D₉	semidirect
16. D₉×D₁₉	C₃₇	direct (N × H)
19. D₉×C₃₇	D₁₉	direct (N × H)
21. D₁₇₁	C₂×C₃₇	semidirect
22. C₉×D₁₉	C₂×C₃₇	semidirect
23. D₉×C₁₉	C₂×C₃₇	semidirect
24. C₉×C₃₇	C₂×D₁₉	semidirect
29. C₉×C₁₉	C₂²×C₃₇	semidirect
42. D₁₉	D₉×C₃₇	direct (N × H)
43. C₃₇	D₉×D₁₉	direct (N × H)
45. C₁₉	C₂×D₉×C₃₇	semidirect
48. D₉	C₃₇×D₁₉	direct (N × H)
50. C₉	C₂×C₃₇×D₁₉	semidirect

Subgroups — D9×C37×D19 #38760913

Conjugacy classes of subgroups

Complements

Subgroups — D₉×C₃₇×D₁₉ #38760913