Subgroups — C₅×C₁₉×D₁₉⋊C₃ #24925317

Order 10830.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×C₁₉⋊C₃	C₂	semidirect
2. C₅×C₁₉×D₁₉	C₃	semidirect
3. C₁₉×D₁₉⋊C₃	C₅	direct (N × H)
4. C₅×C₁₉²	C₂×C₃	semidirect
5. C₁₉×C₁₉⋊C₃	C₂×C₅	semidirect
6. C₁₉×D₁₉	C₃×C₅	semidirect
8. C₅×D₁₉⋊C₃	C₁₉	direct (N × H)
9. C₁₉²	C₂×C₃×C₅	semidirect
11. C₅×C₁₉⋊C₃	C₂×C₁₉	semidirect
13. C₅×D₁₉	C₃×C₁₉	semidirect
15. D₁₉⋊C₃	C₅×C₁₉	direct (N × H)
17. C₅×C₁₉	D₁₉⋊C₃	direct (N × H)
18. C₅×C₁₉	C₂×C₃×C₁₉	semidirect
20. C₁₉⋊C₃	C₂×C₅×C₁₉	semidirect
22. D₁₉	C₃×C₅×C₁₉	semidirect
25. C₁₉	C₅×D₁₉⋊C₃	direct (N × H)
26. C₁₉	C₂×C₃×C₅×C₁₉	semidirect
30. 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
C₅×C₁₉×C₁₉⋊C₃	2
C₅×C₁₉×D₁₉	3
C₁₉×D₁₉⋊C₃	5
C₂×C₃×C₅×C₁₉	19
C₅×D₁₉⋊C₃	19

Subgroups — C5×C19×D19⋊C3 #24925317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉×D₁₉⋊C₃ #24925317