Finite Group Databasebeta

← C₂×C₇₅₁⋊C₅ #21418913

Subgroups — C₂×C₇₅₁⋊C₅ #21418913

Order 7510.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₅₁	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₅	—	751	1	no	maximal, Hall
5	C₅	—	751	1	no	Sylow
6	C₂	C₇₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₇₅₁⋊C₅
commutator, hypocenter	C₇₅₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₇₅₁	C₅
LCS	G ▷ C₇₅₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₇₅₁⋊C₅	C₂	direct (N × H)
2. C₂×C₇₅₁	C₅	semidirect
3. C₇₅₁	C₂×C₅	semidirect
6. C₂	C₇₅₁⋊C₅	direct (N × H)