Subgroups — C₃×C₅×D₃×C₁₉² #44570626

Order 32490.

396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₁₉²	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₃×C₅×C₁₉²	—	3	1	no	maximal
4	C₃×D₃×C₁₉²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₉²	—	2	1	no	—
6	C₃×C₅×C₁₉²	D₃	1	1	yes	characteristic, direct product factor
7	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅×C₁₉²	—	3	1	no	Hall
9	C₃²×C₁₉²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₉²	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₁₉²	—	3	1	no	—
12	C₅×C₁₉²	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×D₃×C₁₉	C₁₉	1	20	yes	maximal, direct product factor
14	C₃×C₁₉²	—	2	1	no	—
15	C₃×C₁₉²	C₅×D₃	1	1	yes	characteristic, direct product factor
16	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
17	C₃²×C₅×C₁₉	C₂×C₁₉	1	20	yes	complemented
18	C₂×C₁₉²	—	3	1	no	Hall
19	C₂×C₃×C₅×C₁₉	—	3	20	no	—
20	C₅×D₃×C₁₉	C₃×C₁₉	1	20	yes	direct product factor
21	C₁₉²	C₃×C₅×D₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×D₃×C₁₉	C₅×C₁₉	1	20	yes	direct product factor
23	C₃×C₅×C₁₉	—	2	20	no	—
24	C₃×C₅×C₁₉	D₃×C₁₉	1	20	yes	direct product factor
25	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	20	yes	complemented
26	C₂×C₅×C₁₉	—	3	20	no	—
27	C₃²×C₁₉	C₂×C₅×C₁₉	1	20	yes	complemented
28	C₂×C₃×C₁₉	—	3	20	no	—
29	D₃×C₁₉	C₃×C₅×C₁₉	1	20	yes	direct product factor
30	C₅×C₁₉	C₃×D₃×C₁₉	1	20	yes	direct product factor
31	C₃×C₅×D₃	C₁₉²	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₉	—	2	20	no	—
33	C₃×C₁₉	C₅×D₃×C₁₉	1	20	yes	direct product factor
34	C₃×C₁₉	C₂×C₃×C₅×C₁₉	1	20	yes	complemented
35	C₃²×C₅	C₂×C₁₉²	1	1	yes	characteristic, complemented, Hall
36	C₂×C₁₉	—	3	20	no	—
37	C₂×C₃×C₅	—	3	1	no	—
38	C₅×D₃	C₃×C₁₉²	1	1	yes	characteristic, direct product factor
39	C₁₉	C₃×C₅×D₃×C₁₉	1	20	yes	direct product factor
40	C₃×D₃	C₅×C₁₉²	1	1	yes	characteristic, direct product factor, Hall
41	C₃×C₅	—	2	1	no	—
42	C₃×C₅	C₂×C₃×C₁₉²	1	1	yes	characteristic, complemented
43	C₃×C₅	D₃×C₁₉²	1	1	yes	characteristic, direct product factor
44	C₂×C₅	—	3	1	no	Hall
45	C₃²	C₂×C₅×C₁₉²	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	3	1	no	—
47	D₃	C₃×C₅×C₁₉²	1	1	yes	characteristic, direct product factor
48	C₅	C₃×D₃×C₁₉²	1	1	yes	characteristic, direct product factor, Sylow
49	C₃	—	2	1	no	—
50	C₃	C₂×C₃×C₅×C₁₉²	1	1	yes	characteristic, complemented
51	C₃	C₅×D₃×C₁₉²	1	1	yes	characteristic, direct product factor
52	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₉²	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₅×C₁₉²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₉²	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₅×C₁₉²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₉²	C₂	semidirect
2. C₅×D₃×C₁₉²	C₃	direct (N × H)
4. C₃×D₃×C₁₉²	C₅	direct (N × H)
6. C₃×C₅×C₁₉²	D₃	direct (N × H)
7. C₃×C₅×C₁₉²	C₂×C₃	semidirect
9. C₃²×C₁₉²	C₂×C₅	semidirect
10. D₃×C₁₉²	C₃×C₅	direct (N × H)
12. C₅×C₁₉²	C₃×D₃	direct (N × H)
13. C₃×C₅×D₃×C₁₉	C₁₉	direct (N × H)
15. C₃×C₁₉²	C₅×D₃	direct (N × H)
16. C₃×C₁₉²	C₂×C₃×C₅	semidirect
17. C₃²×C₅×C₁₉	C₂×C₁₉	semidirect
20. C₅×D₃×C₁₉	C₃×C₁₉	direct (N × H)
21. C₁₉²	C₃×C₅×D₃	direct (N × H)
22. C₃×D₃×C₁₉	C₅×C₁₉	direct (N × H)
24. C₃×C₅×C₁₉	D₃×C₁₉	direct (N × H)
25. C₃×C₅×C₁₉	C₂×C₃×C₁₉	semidirect
27. C₃²×C₁₉	C₂×C₅×C₁₉	semidirect
29. D₃×C₁₉	C₃×C₅×C₁₉	direct (N × H)
30. C₅×C₁₉	C₃×D₃×C₁₉	direct (N × H)
31. C₃×C₅×D₃	C₁₉²	direct (N × H)
33. C₃×C₁₉	C₅×D₃×C₁₉	direct (N × H)
34. C₃×C₁₉	C₂×C₃×C₅×C₁₉	semidirect
35. C₃²×C₅	C₂×C₁₉²	semidirect
38. C₅×D₃	C₃×C₁₉²	direct (N × H)
39. C₁₉	C₃×C₅×D₃×C₁₉	direct (N × H)
40. C₃×D₃	C₅×C₁₉²	direct (N × H)
42. C₃×C₅	C₂×C₃×C₁₉²	semidirect
43. C₃×C₅	D₃×C₁₉²	direct (N × H)
45. C₃²	C₂×C₅×C₁₉²	semidirect
47. D₃	C₃×C₅×C₁₉²	direct (N × H)
48. C₅	C₃×D₃×C₁₉²	direct (N × H)
50. C₃	C₂×C₃×C₅×C₁₉²	semidirect
51. C₃	C₅×D₃×C₁₉²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₉²	2
C₅×D₃×C₁₉²	3
C₂×C₃×C₅×C₁₉²	3
C₃×D₃×C₁₉²	5
C₃×C₅×D₃×C₁₉	19

Subgroups — C3×C5×D3×C192 #44570626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₃×C₁₉² #44570626