Finite Group Databasebeta

← C₅×#20263756 #44540993

Subgroups — C₅×#20263756 #44540993

Order 31775.

32 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, complemented
2	#20263756	C₅	1	5	yes	maximal, direct product factor
3	C₃₁×C₄₁	C₅²	1	1	yes	characteristic, complemented, Hall
4	C₅×C₄₁⋊C₅	—	31	1	no	maximal, Hall
5	C₅×ΓL(1,𝔽₃₂)	—	41	1	no	maximal, Hall
6	C₅×C₄₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
7	C₄₁⋊C₅	—	31	5	no	—
8	C₅×C₃₁	C₄₁⋊C₅	1	1	yes	characteristic, complemented
9	ΓL(1,𝔽₃₂)	—	41	5	no	—
10	C₄₁	C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
11	C₃₁	C₅×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
12	C₅²	—	1271	1	no	Sylow
13	C₅	—	1271	5	no	—
14	C₅	#20263756	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₅	#20263756
commutator, cosocle, hypocenter	C₃₁×C₄₁	C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₄₁	C₅
LCS	G ▷ C₃₁×C₄₁
UCS	C₁ ◁ C₅

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×C₃₁×C₄₁	C₅	semidirect
2. #20263756	C₅	direct (N × H)
3. C₃₁×C₄₁	C₅²	semidirect
6. C₅×C₄₁	ΓL(1,𝔽₃₂)	semidirect
8. C₅×C₃₁	C₄₁⋊C₅	semidirect
10. C₄₁	C₅×ΓL(1,𝔽₃₂)	semidirect
11. C₃₁	C₅×C₄₁⋊C₅	semidirect
14. C₅	#20263756	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₃₁×C₄₁	5
#20263756	5
C₅×C₄₁⋊C₅	31
C₅×ΓL(1,𝔽₃₂)	41