Finite Group Databasebeta

← C₅×D₁₉×C₁₉₁ #49136804

Subgroups — C₅×D₁₉×C₁₉₁ #49136804

Order 36290.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉×C₁₉₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₉₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₉₁	—	19	1	no	maximal, Hall
5	C₅×C₁₉₁	D₁₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₉₁	—	19	1	no	Hall
7	C₁₉₁	C₅×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
8	C₅×D₁₉	C₁₉₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₉	C₂×C₁₉₁	1	1	yes	characteristic, complemented, Hall
10	D₁₉	C₅×C₁₉₁	1	1	yes	characteristic, direct product factor, Hall
11	C₁₉	C₂×C₅×C₁₉₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	19	1	no	Hall
13	C₅	D₁₉×C₁₉₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₉₁	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₅×C₁₉₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₁₉₁	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅×C₁₉₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×C₁₉₁	C₂	semidirect
2. D₁₉×C₁₉₁	C₅	direct (N × H)
3. C₁₉×C₁₉₁	C₂×C₅	semidirect
5. C₅×C₁₉₁	D₁₉	direct (N × H)
7. C₁₉₁	C₅×D₁₉	direct (N × H)
8. C₅×D₁₉	C₁₉₁	direct (N × H)
9. C₅×C₁₉	C₂×C₁₉₁	semidirect
10. D₁₉	C₅×C₁₉₁	direct (N × H)
11. C₁₉	C₂×C₅×C₁₉₁	semidirect
13. C₅	D₁₉×C₁₉₁	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×C₁₉₁	2
D₁₉×C₁₉₁	5
C₂×C₅×C₁₉₁	19
C₅×D₁₉	191