Subgroups — C₅₉×C₁₃₉⋊C₃ #37589736

Order 24603.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃₉⋊C₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅₉	—	139	1	no	maximal, Hall
4	C₁₃₉	C₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
5	C₅₉	C₁₃₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	139	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₉	C₁₃₉⋊C₃
commutator, cosocle, hypocenter	C₁₃₉	C₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₅₉×C₁₃₉	C₃
LCS	G ▷ C₁₃₉
UCS	C₁ ◁ C₅₉

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.