Subgroups — C₁₁×C₁₃⋊C₃ #88347

Order 429.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁	—	13	1	no	maximal, Hall
4	C₁₃	C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
5	C₁₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₁

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.