Subgroups — C₃×C₁₉×C₅⋊(D₁₉⋊C₃) #44570586

Order 32490.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×D₉₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×C₅⋊(D₁₉⋊C₃)	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₁₉×D₁₉⋊C₃	—	5	1	no	maximal, Hall
5	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×D₉₅	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉×C₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₉×D₁₉	—	5	1	no	—
10	C₁₉×D₁₉⋊C₃	—	5	3	no	—
11	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃²×D₅×C₁₉	—	19	1	no	maximal
13	C₃×C₅⋊(D₁₉⋊C₃)	C₁₉	1	1	yes	maximal, characteristic, direct product factor
14	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented
15	C₁₉×C₁₉⋊C₃	C₃×D₅	1	3	yes	complemented
16	C₃²×C₅×C₁₉	—	19	1	no	—
17	C₃×C₅×C₁₉⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented
18	C₁₉×D₁₉	—	5	1	no	Hall
19	C₃×D₉₅	C₃×C₁₉	1	1	yes	characteristic, complemented
20	C₃×D₅×C₁₉	—	19	3	no	—
21	C₃×D₅×C₁₉	—	19	1	no	—
22	C₅⋊(D₁₉⋊C₃)	C₃×C₁₉	1	3	yes	direct product factor
23	C₁₉²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃²×C₁₉	—	95	1	no	—
25	C₃×D₁₉⋊C₃	—	5	1	no	—
26	C₃×C₅×C₁₉	—	6	3	no	—
27	C₃×C₅×C₁₉	—	19	3	no	—
28	C₃×C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
29	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
30	C₅×C₁₉⋊C₃	C₂×C₃×C₁₉	1	3	yes	complemented
31	D₉₅	C₃²×C₁₉	1	1	yes	characteristic, complemented
32	D₅×C₁₉	—	19	1	no	—
33	C₃²×C₁₉	—	19	1	no	—
34	C₃×C₁₉⋊C₃	D₅×C₁₉	1	1	yes	characteristic, complemented
35	C₂×C₃×C₁₉	—	95	3	no	—
36	C₂×C₃×C₁₉	—	95	1	no	—
37	C₃×D₁₉	—	5	1	no	—
38	D₁₉⋊C₃	—	5	3	no	—
39	C₅×C₁₉	—	6	3	no	—
40	C₅×C₁₉	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
41	C₅×C₁₉	C₂×C₃²×C₁₉	1	1	yes	characteristic, complemented
42	C₃²×D₅	—	19	1	no	Hall
43	C₃×C₁₉	—	6	3	no	—
44	C₃×C₁₉	—	19	3	no	—
45	C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
46	C₃×C₁₉	C₃×D₅×C₁₉	1	1	yes	characteristic, complemented
47	C₁₉⋊C₃	C₃×D₅×C₁₉	1	3	yes	complemented
48	C₃²×C₅	—	19	1	no	Hall
49	C₂×C₁₉	—	95	1	no	—
50	D₁₉	—	5	1	no	—
51	C₃×D₅	—	19	3	no	—
52	C₃×D₅	—	19	1	no	—
53	C₁₉	—	6	3	no	—
54	C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
55	C₁₉	C₃²×D₅×C₁₉	1	1	yes	characteristic, complemented
56	C₂×C₃²	—	95	1	no	Hall
57	C₃×C₅	—	19	3	no	—
58	C₃×C₅	C₁₉×D₁₉⋊C₃	1	1	yes	characteristic, complemented
59	D₅	—	19	1	no	Hall
60	C₃²	—	19	1	no	Sylow
61	C₂×C₃	—	95	3	no	—
62	C₂×C₃	—	95	1	no	—
63	C₅	C₃×C₁₉×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
64	C₃	—	19	3	no	—
65	C₃	C₁₉×C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
66	C₂	—	95	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₅⋊(D₁₉⋊C₃)
commutator, cosocle, hypocenter	C₅×C₁₉	C₂×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₉×C₁₉⋊C₃	C₂	semidirect
2. C₃×C₁₉×D₉₅	C₃	semidirect
3. C₁₉×C₅⋊(D₁₉⋊C₃)	C₃	direct (N × H)
5. C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	semidirect
6. C₃×C₅×C₁₉²	C₂×C₃	semidirect
7. C₁₉×D₉₅	C₃²	semidirect
8. C₃×C₁₉×C₁₉⋊C₃	D₅	semidirect
11. C₅×C₁₉²	C₂×C₃²	semidirect
13. C₃×C₅⋊(D₁₉⋊C₃)	C₁₉	direct (N × H)
14. C₃×C₁₉²	C₃×D₅	semidirect
15. C₁₉×C₁₉⋊C₃	C₃×D₅	semidirect
17. C₃×C₅×C₁₉⋊C₃	C₂×C₁₉	semidirect
19. C₃×D₉₅	C₃×C₁₉	semidirect
22. C₅⋊(D₁₉⋊C₃)	C₃×C₁₉	direct (N × H)
23. C₁₉²	C₃²×D₅	semidirect
28. C₃×C₅×C₁₉	D₁₉⋊C₃	semidirect
29. C₃×C₅×C₁₉	C₂×C₃×C₁₉	semidirect
30. C₅×C₁₉⋊C₃	C₂×C₃×C₁₉	semidirect
31. D₉₅	C₃²×C₁₉	semidirect
34. C₃×C₁₉⋊C₃	D₅×C₁₉	semidirect
40. C₅×C₁₉	C₃×D₁₉⋊C₃	semidirect
41. C₅×C₁₉	C₂×C₃²×C₁₉	semidirect
45. C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	direct (N × H)
46. C₃×C₁₉	C₃×D₅×C₁₉	semidirect
47. C₁₉⋊C₃	C₃×D₅×C₁₉	semidirect
54. C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	direct (N × H)
55. C₁₉	C₃²×D₅×C₁₉	semidirect
58. C₃×C₅	C₁₉×D₁₉⋊C₃	semidirect
63. C₅	C₃×C₁₉×D₁₉⋊C₃	semidirect
65. C₃	C₁₉×C₅⋊(D₁₉⋊C₃)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×C₁₉×C₁₉⋊C₃	2
C₃×C₁₉×D₉₅	3
C₁₉×C₅⋊(D₁₉⋊C₃)	3
C₃×C₁₉×D₁₉⋊C₃	5
C₃²×D₅×C₁₉	19
C₃×C₅⋊(D₁₉⋊C₃)	19

Subgroups — C3×C19×C5⋊(D19⋊C3) #44570586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×C₅⋊(D₁₉⋊C₃) #44570586