Subgroups — C₅×C₉×C₁₉⋊D₁₉ #44570494

Order 32490.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₉⋊D₁₉	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₉⋊D₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₉⋊D₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₉²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₉⋊D₁₉	C₃×C₅	1	1	yes	characteristic
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅×C₉×D₁₉	—	19	20	no	maximal
10	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic
11	C₅×C₉×C₁₉	D₁₉	1	20	yes	complemented
12	C₁₉⋊D₁₉	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×D₁₉	—	19	20	no	—
14	C₁₉²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
15	C₉×D₁₉	—	19	20	no	—
16	C₃×C₅×C₁₉	C₃×D₁₉	1	20	yes	—
17	C₅×D₁₉	—	19	20	no	—
18	C₉×C₁₉	C₅×D₁₉	1	20	yes	complemented
19	C₃×D₁₉	—	19	20	no	—
20	C₅×C₁₉	C₉×D₁₉	1	20	yes	complemented
21	C₂×C₅×C₉	—	361	1	no	Hall
22	C₃×C₁₉	C₃×C₅×D₁₉	1	20	yes	—
23	C₅×C₉	C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Hall
24	D₁₉	—	19	20	no	—
25	C₂×C₃×C₅	—	361	1	no	—
26	C₁₉	C₅×C₉×D₁₉	1	20	yes	complemented
27	C₂×C₉	—	361	1	no	Hall
28	C₃×C₅	C₃×C₁₉⋊D₁₉	1	1	yes	characteristic
29	C₂×C₅	—	361	1	no	Hall
30	C₉	C₅×C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	361	1	no	—
32	C₅	C₉×C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₅×C₁₉⋊D₁₉	1	1	yes	characteristic
34	C₂	—	361	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₉	C₁₉⋊D₁₉
commutator, hypocenter	C₁₉²	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×C₁₉⋊D₁₉
Fitting	C₅×C₉×C₁₉²	C₂
socle	C₃×C₅×C₁₉²	C₂×C₃
prime radical	C₃×C₅×C₁₉⋊D₁₉	C₃
cosocle	C₃×C₁₉²	C₂×C₃×C₅
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₅×C₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₉²	C₂	semidirect
3. C₉×C₁₉⋊D₁₉	C₅	direct (N × H)
5. C₅×C₁₉⋊D₁₉	C₉	direct (N × H)
6. C₉×C₁₉²	C₂×C₅	semidirect
8. C₅×C₁₉²	C₂×C₉	semidirect
11. C₅×C₉×C₁₉	D₁₉	semidirect
12. C₁₉⋊D₁₉	C₅×C₉	direct (N × H)
14. C₁₉²	C₂×C₅×C₉	semidirect
18. C₉×C₁₉	C₅×D₁₉	semidirect
20. C₅×C₁₉	C₉×D₁₉	semidirect
23. C₅×C₉	C₁₉⋊D₁₉	direct (N × H)
26. C₁₉	C₅×C₉×D₁₉	semidirect
30. C₉	C₅×C₁₉⋊D₁₉	direct (N × H)
32. C₅	C₉×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
C₅×C₉×C₁₉²	2
C₃×C₅×C₁₉⋊D₁₉	3
C₉×C₁₉⋊D₁₉	5
C₅×C₉×D₁₉	19

Subgroups — C5×C9×C19⋊D19 #44570494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×C₁₉⋊D₁₉ #44570494