Subgroups — C₅×C₁₀₆₃⋊C₃ #30630010

Order 15945.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₀₆₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₀₆₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₀₆₃	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₅	—	1063	1	no	maximal, Hall
5	C₅	C₁₀₆₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	1063	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₀₆₃⋊C₃
commutator, cosocle, hypocenter	C₁₀₆₃	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₀₆₃	C₃
LCS	G ▷ C₁₀₆₃
UCS	C₁ ◁ C₅

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.