Finite Group Databasebeta

← C₃×C₇₀₁⋊C₅ #24901929

Subgroups — C₃×C₇₀₁⋊C₅ #24901929

Order 10515.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₀₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₇₀₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₀₁	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₅	—	701	1	no	maximal, Hall
5	C₅	—	701	1	no	Sylow
6	C₃	C₇₀₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₃	C₇₀₁⋊C₅
commutator, cosocle, hypocenter	C₇₀₁	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₇₀₁	C₅
LCS	G ▷ C₇₀₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₇₀₁⋊C₅	C₃	direct (N × H)
2. C₃×C₇₀₁	C₅	semidirect
3. C₇₀₁	C₃×C₅	semidirect
6. C₃	C₇₀₁⋊C₅	direct (N × H)