Finite Group Databasebeta

Subgroups — #22552002

Order 8271.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₉₁₉	C₉	1	1	yes	characteristic, complemented, Sylow
3	C₉	—	919	1	no	maximal, Sylow
4	C₃	—	919	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₉₁₉	C₉
LCS	G ▷ C₉₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₉₁₉	C₉	semidirect