Finite Group Databasebeta

← C₄×C₂₆₈₉ #24924441

Subgroups — C₄×C₂₆₈₉ #24924441

Order 10756.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₆₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂₆₈₉	C₄	1	1	yes	characteristic, direct product factor, Sylow
3	C₄	C₂₆₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂	C₂×C₂₆₈₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₂₆₈₉
socle, prime radical	C₂×C₂₆₈₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₆₈₉	C₄	direct (N × H)
3. C₄	C₂₆₈₉	direct (N × H)