Finite Group Databasebeta

← C₅⋊(D₂₁₁⋊C₅) #24902166

Subgroups — C₅⋊(D₂₁₁⋊C₅) #24902166

Order 10550.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₅₅	C₅	1	1	yes	maximal, characteristic, complemented
3	D₂₁₁⋊C₅	—	5	1	no	maximal
4	C₅×C₂₁₁	C₂×C₅	1	1	yes	characteristic, complemented
5	C₂₁₁⋊C₅	—	2	2	no	—
6	C₂₁₁⋊C₅	D₅	1	1	yes	characteristic, complemented
7	D₂₁₁	—	5	1	no	Hall
8	C₂₁₁	C₅×D₅	1	1	yes	characteristic, complemented, Sylow
9	C₅×D₅	—	211	1	no	maximal, Hall
10	C₅²	—	211	1	no	Sylow
11	C₂×C₅	—	1055	1	no	—
12	D₅	—	211	1	no	—
13	C₅	—	422	2	no	—
14	C₅	—	211	1	no	—
15	C₅	D₂₁₁⋊C₅	1	1	yes	characteristic, complemented
16	C₂	—	1055	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₂₁₁	C₂×C₅
LCS	G ▷ C₅×C₂₁₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₁₁⋊C₅	C₂	semidirect
2. D₁₀₅₅	C₅	semidirect
4. C₅×C₂₁₁	C₂×C₅	semidirect
6. C₂₁₁⋊C₅	D₅	semidirect
8. C₂₁₁	C₅×D₅	semidirect
15. C₅	D₂₁₁⋊C₅	semidirect