Subgroups — C₈₉×D₆₁ #24925780

Order 10858.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₈₉	—	61	1	no	maximal, Hall
3	D₆₁	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₈₉	D₆₁	1	1	yes	characteristic, direct product factor, Sylow
5	C₆₁	C₂×C₈₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	61	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₈₉	D₆₁
commutator, cosocle, hypocenter	C₆₁	C₂×C₈₉
Frattini	C₁	G
Fitting, socle	C₆₁×C₈₉	C₂
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₈₉

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.