Subgroups — C₁₉×C₁₃₁⋊C₁₃ #44568998

Order 32357.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₁₃₁	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃₁⋊C₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₁₉	—	131	1	no	maximal, Hall
4	C₁₃₁	C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
5	C₁₉	C₁₃₁⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₁₃	—	131	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₁₃₁⋊C₁₃
commutator, cosocle, hypocenter	C₁₃₁	C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₁₃₁	C₁₃
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₁₉

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.