Subgroups — C₃×C₅×C₁₉×D₁₉⋊C₃ #44570577

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×C₅×C₁₉×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉×D₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₁₉×D₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₁₉×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₉×D₁₉	C₃×C₅	1	1	yes	characteristic, complemented
10	C₁₉×D₁₉⋊C₃	C₃×C₅	1	3	yes	direct product factor
11	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃²×C₅×C₁₉	—	19	1	no	maximal
13	C₃×C₅×D₁₉⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor
14	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
15	C₁₉×C₁₉⋊C₃	C₂×C₃×C₅	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	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₅×C₁₉	—	19	3	no	—
20	C₂×C₃×C₅×C₁₉	—	19	1	no	—
21	C₃×C₅×D₁₉	C₃×C₁₉	1	1	yes	characteristic, complemented
22	C₅×D₁₉⋊C₃	C₃×C₁₉	1	3	yes	direct product factor
23	C₁₉²	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃²×C₁₉	—	19	1	no	—
25	C₃×D₁₉⋊C₃	C₅×C₁₉	1	1	yes	characteristic, direct product factor
26	C₃×C₅×C₁₉	—	6	3	no	—
27	C₃×C₅×C₁₉	—	19	3	no	—
28	C₃×C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
29	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
30	C₅×C₁₉⋊C₃	C₂×C₃×C₁₉	1	3	yes	complemented
31	C₂×C₅×C₁₉	—	19	1	no	—
32	C₅×D₁₉	C₃²×C₁₉	1	1	yes	characteristic, complemented
33	C₃²×C₁₉	—	19	1	no	—
34	C₃×C₁₉⋊C₃	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
35	C₂×C₃×C₁₉	—	19	3	no	—
36	C₂×C₃×C₁₉	—	19	1	no	—
37	C₃×D₁₉	C₃×C₅×C₁₉	1	1	yes	characteristic, complemented
38	D₁₉⋊C₃	C₃×C₅×C₁₉	1	3	yes	direct product factor
39	C₅×C₁₉	—	6	3	no	—
40	C₅×C₁₉	C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
41	C₅×C₁₉	C₂×C₃²×C₁₉	1	1	yes	characteristic, complemented
42	C₂×C₃²×C₅	—	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	C₂×C₃×C₅×C₁₉	1	1	yes	characteristic, complemented
47	C₁₉⋊C₃	C₂×C₃×C₅×C₁₉	1	3	yes	complemented
48	C₃²×C₅	—	19	1	no	Hall
49	C₂×C₁₉	—	19	1	no	—
50	D₁₉	C₃²×C₅×C₁₉	1	1	yes	characteristic, complemented
51	C₂×C₃×C₅	—	19	3	no	—
52	C₂×C₃×C₅	—	19	1	no	—
53	C₁₉	—	6	3	no	—
54	C₁₉	C₃×C₅×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
55	C₁₉	C₂×C₃²×C₅×C₁₉	1	1	yes	characteristic, complemented
56	C₂×C₃²	—	19	1	no	Hall
57	C₃×C₅	—	19	3	no	—
58	C₃×C₅	C₁₉×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
59	C₂×C₅	—	19	1	no	Hall
60	C₃²	—	19	1	no	Sylow
61	C₂×C₃	—	19	3	no	—
62	C₂×C₃	—	19	1	no	—
63	C₅	C₃×C₁₉×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
64	C₃	—	19	3	no	—
65	C₃	C₅×C₁₉×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
66	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₉	D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₅×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×C₅×C₁₉×D₁₉	C₃	semidirect
3. C₅×C₁₉×D₁₉⋊C₃	C₃	direct (N × H)
4. C₃×C₁₉×D₁₉⋊C₃	C₅	direct (N × H)
5. C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	semidirect
6. C₃×C₅×C₁₉²	C₂×C₃	semidirect
7. C₅×C₁₉×D₁₉	C₃²	semidirect
8. C₃×C₁₉×C₁₉⋊C₃	C₂×C₅	semidirect
9. C₃×C₁₉×D₁₉	C₃×C₅	semidirect
10. C₁₉×D₁₉⋊C₃	C₃×C₅	direct (N × H)
11. C₅×C₁₉²	C₂×C₃²	semidirect
13. C₃×C₅×D₁₉⋊C₃	C₁₉	direct (N × H)
14. C₃×C₁₉²	C₂×C₃×C₅	semidirect
15. C₁₉×C₁₉⋊C₃	C₂×C₃×C₅	semidirect
17. C₃×C₅×C₁₉⋊C₃	C₂×C₁₉	semidirect
18. C₁₉×D₁₉	C₃²×C₅	semidirect
21. C₃×C₅×D₁₉	C₃×C₁₉	semidirect
22. C₅×D₁₉⋊C₃	C₃×C₁₉	direct (N × H)
23. C₁₉²	C₂×C₃²×C₅	semidirect
25. C₃×D₁₉⋊C₃	C₅×C₁₉	direct (N × H)
28. C₃×C₅×C₁₉	D₁₉⋊C₃	direct (N × H)
29. C₃×C₅×C₁₉	C₂×C₃×C₁₉	semidirect
30. C₅×C₁₉⋊C₃	C₂×C₃×C₁₉	semidirect
32. C₅×D₁₉	C₃²×C₁₉	semidirect
34. C₃×C₁₉⋊C₃	C₂×C₅×C₁₉	semidirect
37. C₃×D₁₉	C₃×C₅×C₁₉	semidirect
38. D₁₉⋊C₃	C₃×C₅×C₁₉	direct (N × H)
40. C₅×C₁₉	C₃×D₁₉⋊C₃	direct (N × H)
41. C₅×C₁₉	C₂×C₃²×C₁₉	semidirect
45. C₃×C₁₉	C₅×D₁₉⋊C₃	direct (N × H)
46. C₃×C₁₉	C₂×C₃×C₅×C₁₉	semidirect
47. C₁₉⋊C₃	C₂×C₃×C₅×C₁₉	semidirect
50. D₁₉	C₃²×C₅×C₁₉	semidirect
54. C₁₉	C₃×C₅×D₁₉⋊C₃	direct (N × H)
55. C₁₉	C₂×C₃²×C₅×C₁₉	semidirect
58. C₃×C₅	C₁₉×D₁₉⋊C₃	direct (N × H)
63. C₅	C₃×C₁₉×D₁₉⋊C₃	direct (N × H)
65. C₃	C₅×C₁₉×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×C₅×C₁₉×D₁₉	3
C₅×C₁₉×D₁₉⋊C₃	3
C₃×C₁₉×D₁₉⋊C₃	5
C₂×C₃²×C₅×C₁₉	19
C₃×C₅×D₁₉⋊C₃	19

Subgroups — C3×C5×C19×D19⋊C3 #44570577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₉×D₁₉⋊C₃ #44570577