Finite Group Databasebeta

← C₅×D₆₈₃ #20292001

Subgroups — C₅×D₆₈₃ #20292001

Order 6830.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₆₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₈₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₆₈₃	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₅	—	683	1	no	maximal, Hall
5	C₅	D₆₈₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	683	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₆₈₃
commutator, hypocenter	C₆₈₃	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₆₈₃	C₂
LCS	G ▷ C₆₈₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₆₈₃	C₂	semidirect
2. D₆₈₃	C₅	direct (N × H)
3. C₆₈₃	C₂×C₅	semidirect
5. C₅	D₆₈₃	direct (N × H)