Finite Group Databasebeta

← C₁₉⋊(D₁₈₁⋊C₅) #46806102

Subgroups — C₁₉⋊(D₁₈₁⋊C₅) #46806102

Order 34390.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₁₈₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₄₃₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×C₁₈₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	D₁₈₁⋊C₅	—	19	1	no	maximal, Hall
5	C₁₈₁⋊C₅	D₁₉	1	1	yes	characteristic, complemented, Hall
6	D₁₈₁	—	19	1	no	Hall
7	C₅×D₁₉	—	181	1	no	maximal, Hall
8	C₁₈₁	C₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₉	—	181	1	no	Hall
10	D₁₉	—	181	1	no	Hall
11	C₁₉	D₁₈₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	3439	1	no	Hall
13	C₅	—	181	1	no	Sylow
14	C₂	—	3439	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉×C₁₈₁	C₂×C₅
LCS	G ▷ C₁₉×C₁₈₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₁₈₁⋊C₅	C₂	semidirect
2. D₃₄₃₉	C₅	semidirect
3. C₁₉×C₁₈₁	C₂×C₅	semidirect
5. C₁₈₁⋊C₅	D₁₉	semidirect
8. C₁₈₁	C₅×D₁₉	semidirect
11. C₁₉	D₁₈₁⋊C₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×C₁₈₁⋊C₅	2
D₃₄₃₉	5
D₁₈₁⋊C₅	19
C₅×D₁₉	181