Subgroups — C₅²⋊(C₃₁₃⋊C₃) #37553404

Order 23475.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₃₁₃	—	3	2	no	—
3	C₃₁₃⋊C₃	—	25	1	no	maximal, Hall
4	C₃₁₃	C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
5	C₅²⋊C₃	—	313	1	no	maximal, Hall
6	C₅²	C₃₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
7	C₅	—	3	2	no	—
8	C₃	—	7825	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₃₁₃	C₃
LCS	G ▷ C₅²×C₃₁₃
UCS	C₁

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.