Subgroups — C₃×C₁₀₅₁⋊C₅ #30628813

Order 15765.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₅₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₀₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₀₅₁	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₅	—	1051	1	no	maximal, Hall
5	C₅	—	1051	1	no	Sylow
6	C₃	C₁₀₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₀₅₁⋊C₅
commutator, cosocle, hypocenter	C₁₀₅₁	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₁₀₅₁	C₅
LCS	G ▷ C₁₀₅₁
UCS	C₁ ◁ C₃

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.