Subgroups — C₁₀₁×C₁₀₃⋊C₃ #44530113

Order 31209.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₀₃⋊C₃	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₀₁	—	103	1	no	maximal, Hall
4	C₁₀₃	C₃×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
5	C₁₀₁	C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	103	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₀₁	C₁₀₃⋊C₃
commutator, cosocle, hypocenter	C₁₀₃	C₃×C₁₀₁
Frattini	C₁	G
Fitting, socle	C₁₀₁×C₁₀₃	C₃
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₁₀₁

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.