Subgroups — C₃²×C₅×C₁₉⋊D₁₉ #44570622

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×C₅×C₁₉⋊D₁₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₉⋊D₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₉²	C₂×C₃	1	4	yes	complemented
5	C₅×C₁₉⋊D₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₁₉²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₉⋊D₁₉	C₃×C₅	1	4	yes	direct product factor
8	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₅×D₁₉	—	19	20	no	maximal
10	C₃×C₁₉²	C₂×C₃×C₅	1	4	yes	complemented
11	C₃²×C₅×C₁₉	D₁₉	1	20	yes	complemented
12	C₁₉⋊D₁₉	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×D₁₉	—	19	80	no	—
14	C₁₉²	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
15	C₃²×D₁₉	—	19	20	no	—
16	C₃×C₅×C₁₉	C₃×D₁₉	1	80	yes	complemented
17	C₅×D₁₉	—	19	20	no	—
18	C₃²×C₁₉	C₅×D₁₉	1	20	yes	complemented
19	C₃×D₁₉	—	19	80	no	—
20	C₅×C₁₉	C₃²×D₁₉	1	20	yes	complemented
21	C₂×C₃²×C₅	—	361	1	no	Hall
22	C₃×C₁₉	C₃×C₅×D₁₉	1	80	yes	complemented
23	C₃²×C₅	C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Hall
24	D₁₉	—	19	20	no	—
25	C₂×C₃×C₅	—	361	4	no	—
26	C₁₉	C₃²×C₅×D₁₉	1	20	yes	complemented
27	C₂×C₃²	—	361	1	no	Hall
28	C₃×C₅	C₃×C₁₉⋊D₁₉	1	4	yes	direct product factor
29	C₂×C₅	—	361	1	no	Hall
30	C₃²	C₅×C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	361	4	no	—
32	C₅	C₃²×C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₅×C₁₉⋊D₁₉	1	4	yes	direct product factor
34	C₂	—	361	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₉²	C₂	semidirect
2. C₃×C₅×C₁₉⋊D₁₉	C₃	direct (N × H)
3. C₃²×C₁₉⋊D₁₉	C₅	direct (N × H)
4. C₃×C₅×C₁₉²	C₂×C₃	semidirect
5. C₅×C₁₉⋊D₁₉	C₃²	direct (N × H)
6. C₃²×C₁₉²	C₂×C₅	semidirect
7. C₃×C₁₉⋊D₁₉	C₃×C₅	direct (N × H)
8. C₅×C₁₉²	C₂×C₃²	semidirect
10. C₃×C₁₉²	C₂×C₃×C₅	semidirect
11. C₃²×C₅×C₁₉	D₁₉	semidirect
12. C₁₉⋊D₁₉	C₃²×C₅	direct (N × H)
14. C₁₉²	C₂×C₃²×C₅	semidirect
16. C₃×C₅×C₁₉	C₃×D₁₉	semidirect
18. C₃²×C₁₉	C₅×D₁₉	semidirect
20. C₅×C₁₉	C₃²×D₁₉	semidirect
22. C₃×C₁₉	C₃×C₅×D₁₉	semidirect
23. C₃²×C₅	C₁₉⋊D₁₉	direct (N × H)
26. C₁₉	C₃²×C₅×D₁₉	semidirect
28. C₃×C₅	C₃×C₁₉⋊D₁₉	direct (N × H)
30. C₃²	C₅×C₁₉⋊D₁₉	direct (N × H)
32. C₅	C₃²×C₁₉⋊D₁₉	direct (N × H)
33. C₃	C₃×C₅×C₁₉⋊D₁₉	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×C₅×C₁₉⋊D₁₉	3
C₃²×C₁₉⋊D₁₉	5
C₃²×C₅×D₁₉	19

Subgroups — C32×C5×C19⋊D19 #44570622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×C₁₉⋊D₁₉ #44570622