Subgroups — #44540985

Order 31775.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₁×C₄₁	C₅	1	1	yes	maximal, characteristic
2	C₃₁×C₄₁	C₂₅	1	1	yes	characteristic, complemented, Hall
3	C₄₁⋊C₂₅	—	31	1	no	maximal, Hall
4	C₃₁⋊C₂₅	—	41	1	no	maximal, Hall
5	C₅×C₄₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic
6	C₅×C₃₁	C₄₁⋊C₅	1	1	yes	characteristic
7	C₄₁	C₃₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
8	C₃₁	C₄₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
9	C₂₅	—	1271	1	no	Sylow
10	C₅	#20263757	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₅	#20263757
commutator, hypocenter	C₃₁×C₄₁	C₂₅
Fitting, socle, prime radical, cosocle	C₅×C₃₁×C₄₁	C₅
LCS	G ▷ C₃₁×C₄₁
UCS	C₁ ◁ C₅

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.