Subgroups — C₂₉×C₂₇₁⋊C₃ #37556021

Order 23577.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₂₇₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₇₁⋊C₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₇₁	C₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₂₉	—	271	1	no	maximal, Hall
5	C₂₉	C₂₇₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	271	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	C₂₇₁⋊C₃
commutator, cosocle, hypocenter	C₂₇₁	C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₉×C₂₇₁	C₃
LCS	G ▷ C₂₇₁
UCS	C₁ ◁ C₂₉

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.