Subgroups — C₁₃×C₄₃₉⋊C₃ #30686124

Order 17121.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₄₃₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₃₉	C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₁₃	—	439	1	no	maximal, Hall
5	C₁₃	C₄₃₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	439	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	C₄₃₉⋊C₃
commutator, cosocle, hypocenter	C₄₃₉	C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₄₃₉	C₃
LCS	G ▷ C₄₃₉
UCS	C₁ ◁ C₁₃

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.