Subgroups — C₂₉×C₁₅₁⋊C₅ #36346352

Order 21895.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₁₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₅₁⋊C₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₅₁	C₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
4	C₅×C₂₉	—	151	1	no	maximal, Hall
5	C₂₉	C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	—	151	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	C₁₅₁⋊C₅
commutator, cosocle, hypocenter	C₁₅₁	C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₉×C₁₅₁	C₅
LCS	G ▷ C₁₅₁
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.