Subgroups — C₁₃⋊C₃×C₆₅₃ #38764301

Order 25467.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₆₅₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₆₅₃	—	13	1	no	maximal, Hall
3	C₆₅₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
4	C₁₃⋊C₃	C₆₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃	C₃×C₆₅₃	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₅₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₆₅₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₆₅₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₆₅₃

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.