Finite Group Databasebeta

← C₃×C₉₁₉⋊C₃ #22552003

Subgroups — C₃×C₉₁₉⋊C₃ #22552003

Order 8271.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉₁₉	C₃	1	1	yes	maximal, characteristic, complemented
2	C₉₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₉₁₉	C₃²	1	1	yes	characteristic, complemented, Sylow
4	C₃²	—	919	1	no	maximal, Sylow
5	C₃	—	919	3	no	—
6	C₃	C₉₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃	C₉₁₉⋊C₃
commutator, hypocenter	C₉₁₉	C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₉₁₉	C₃
LCS	G ▷ C₉₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₉₁₉	C₃	semidirect
2. C₉₁₉⋊C₃	C₃	direct (N × H)
3. C₉₁₉	C₃²	semidirect
6. C₃	C₉₁₉⋊C₃	direct (N × H)