Subgroups — C₅×D₁₂₈₉ #27166285

Order 12890.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₂₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₂₈₉	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₅	—	1289	1	no	maximal, Hall
5	C₅	D₁₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	1289	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₁₂₈₉
commutator, cosocle, hypocenter	C₁₂₈₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₂₈₉	C₂
LCS	G ▷ C₁₂₈₉
UCS	C₁ ◁ C₅

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.