Subgroups — C₁₇×C₂₈₁⋊C₅ #37560576

Order 23885.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₂₈₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₈₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₈₁	C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
4	C₅×C₁₇	—	281	1	no	maximal, Hall
5	C₁₇	C₂₈₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	—	281	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	C₂₈₁⋊C₅
commutator, cosocle, hypocenter	C₂₈₁	C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₂₈₁	C₅
LCS	G ▷ C₂₈₁
UCS	C₁ ◁ C₁₇

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.