Subgroups — C₂×ΓL(1,𝔽₃₂) #64579

Order 310.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₅	—	31	1	no	maximal, Hall
5	C₅	—	31	1	no	Sylow
6	C₂	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂

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.