Finite Group Databasebeta

← C₅×C₄₃₁⋊C₅ #24924680

Subgroups — C₅×C₄₃₁⋊C₅ #24924680

Order 10775.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₃₁	C₅	1	1	yes	maximal, characteristic, complemented
2	C₄₃₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
3	C₄₃₁	C₅²	1	1	yes	characteristic, complemented, Sylow
4	C₅²	—	431	1	no	maximal, Sylow
5	C₅	—	431	5	no	—
6	C₅	C₄₃₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₅	C₄₃₁⋊C₅
commutator, cosocle, hypocenter	C₄₃₁	C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₄₃₁	C₅
LCS	G ▷ C₄₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₄₃₁	C₅	semidirect
2. C₄₃₁⋊C₅	C₅	direct (N × H)
3. C₄₃₁	C₅²	semidirect
6. C₅	C₄₃₁⋊C₅	direct (N × H)