Finite Group Databasebeta

← C₂₅×C₄₃₁ #24924679

Subgroups — C₂₅×C₄₃₁ #24924679

Order 10775.

6 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
2	C₄₃₁	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
3	C₂₅	C₄₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₅	C₅×C₄₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₅×C₄₃₁
socle, prime radical	C₅×C₄₃₁	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃₁	C₂₅	direct (N × H)
3. C₂₅	C₄₃₁	direct (N × H)