Subgroups — D₅₉×C₂₅₁ #44444152

Order 29618.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₅₁	—	59	1	no	maximal, Hall
3	C₂₅₁	D₅₉	1	1	yes	characteristic, direct product factor, Sylow
4	D₅₉	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅₉	C₂×C₂₅₁	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	59	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₅₁	D₅₉
commutator, cosocle, hypocenter	C₅₉	C₂×C₂₅₁
Frattini	C₁	G
Fitting, socle	C₅₉×C₂₅₁	C₂
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₂₅₁

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.