Subgroups — C₃²×D₅×C₁₉² #44570623

Order 32490.

528 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	C₃×D₅×C₁₉²	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₁₉²	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₉²	C₂×C₃	1	4	yes	complemented
5	D₅×C₁₉²	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₁₉²	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₁₉²	—	5	4	no	—
8	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×D₅×C₁₉	C₁₉	1	20	yes	maximal, direct product factor
10	C₃×C₁₉²	C₃×D₅	1	4	yes	direct product factor
11	C₃²×C₅×C₁₉	C₂×C₁₉	1	20	yes	complemented
12	C₂×C₁₉²	—	5	1	no	Hall
13	C₃×D₅×C₁₉	C₃×C₁₉	1	80	yes	direct product factor
14	C₁₉²	C₃²×D₅	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₃²×C₁₉	—	5	20	no	—
16	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	80	yes	complemented
17	D₅×C₁₉	C₃²×C₁₉	1	20	yes	direct product factor
18	C₃²×C₁₉	D₅×C₁₉	1	20	yes	direct product factor
19	C₂×C₃×C₁₉	—	5	80	no	—
20	C₅×C₁₉	C₂×C₃²×C₁₉	1	20	yes	complemented
21	C₃²×D₅	C₁₉²	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₉	C₃×D₅×C₁₉	1	80	yes	direct product factor
23	C₃²×C₅	C₂×C₁₉²	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₉	—	5	20	no	—
25	C₃×D₅	C₃×C₁₉²	1	4	yes	direct product factor
26	C₁₉	C₃²×D₅×C₁₉	1	20	yes	direct product factor
27	C₂×C₃²	—	5	1	no	Hall
28	C₃×C₅	C₂×C₃×C₁₉²	1	4	yes	complemented
29	D₅	C₃²×C₁₉²	1	1	yes	characteristic, direct product factor, Hall
30	C₃²	D₅×C₁₉²	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	5	4	no	—
32	C₅	C₂×C₃²×C₁₉²	1	1	yes	characteristic, complemented, Sylow
33	C₃	C₃×D₅×C₁₉²	1	4	yes	direct product factor
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₁₉²	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃²×C₁₉²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₉²	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃²×C₁₉²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₉²	C₂	semidirect
2. C₃×D₅×C₁₉²	C₃	direct (N × H)
4. C₃×C₅×C₁₉²	C₂×C₃	semidirect
5. D₅×C₁₉²	C₃²	direct (N × H)
6. C₃²×C₁₉²	D₅	direct (N × H)
8. C₅×C₁₉²	C₂×C₃²	semidirect
9. C₃²×D₅×C₁₉	C₁₉	direct (N × H)
10. C₃×C₁₉²	C₃×D₅	direct (N × H)
11. C₃²×C₅×C₁₉	C₂×C₁₉	semidirect
13. C₃×D₅×C₁₉	C₃×C₁₉	direct (N × H)
14. C₁₉²	C₃²×D₅	direct (N × H)
16. C₃×C₅×C₁₉	C₂×C₃×C₁₉	semidirect
17. D₅×C₁₉	C₃²×C₁₉	direct (N × H)
18. C₃²×C₁₉	D₅×C₁₉	direct (N × H)
20. C₅×C₁₉	C₂×C₃²×C₁₉	semidirect
21. C₃²×D₅	C₁₉²	direct (N × H)
22. C₃×C₁₉	C₃×D₅×C₁₉	direct (N × H)
23. C₃²×C₅	C₂×C₁₉²	semidirect
25. C₃×D₅	C₃×C₁₉²	direct (N × H)
26. C₁₉	C₃²×D₅×C₁₉	direct (N × H)
28. C₃×C₅	C₂×C₃×C₁₉²	semidirect
29. D₅	C₃²×C₁₉²	direct (N × H)
30. C₃²	D₅×C₁₉²	direct (N × H)
32. C₅	C₂×C₃²×C₁₉²	semidirect
33. C₃	C₃×D₅×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
C₃×D₅×C₁₉²	3
C₂×C₃²×C₁₉²	5
C₃²×D₅×C₁₉	19

Subgroups — C32×D5×C192 #44570623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₅×C₁₉² #44570623