Finite Group Databasebeta

← C₅×C₄₃×ΓL(1,𝔽₃₂) #45686708

Subgroups — C₅×C₄₃×ΓL(1,𝔽₃₂) #45686708

Order 33325.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₁×C₄₃	C₅	1	1	yes	maximal, characteristic, complemented
2	C₄₃×ΓL(1,𝔽₃₂)	C₅	1	5	yes	maximal, direct product factor
3	C₃₁×C₄₃	C₅²	1	1	yes	characteristic, complemented, Hall
4	C₅²×C₄₃	—	31	1	no	maximal, Hall
5	C₅×ΓL(1,𝔽₃₂)	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₄₃	—	31	5	no	—
7	C₅×C₄₃	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
8	C₅×C₃₁	C₅×C₄₃	1	1	yes	characteristic, complemented
9	ΓL(1,𝔽₃₂)	C₅×C₄₃	1	5	yes	direct product factor
10	C₄₃	C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₁	C₅²×C₄₃	1	1	yes	characteristic, complemented, Sylow
12	C₅²	—	31	1	no	Sylow
13	C₅	—	31	5	no	—
14	C₅	C₄₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₅×C₄₃	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₅²×C₄₃
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₄₃	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₁×C₄₃	C₅	semidirect
2. C₄₃×ΓL(1,𝔽₃₂)	C₅	direct (N × H)
3. C₃₁×C₄₃	C₅²	semidirect
5. C₅×ΓL(1,𝔽₃₂)	C₄₃	direct (N × H)
7. C₅×C₄₃	ΓL(1,𝔽₃₂)	direct (N × H)
8. C₅×C₃₁	C₅×C₄₃	semidirect
9. ΓL(1,𝔽₃₂)	C₅×C₄₃	direct (N × H)
10. C₄₃	C₅×ΓL(1,𝔽₃₂)	direct (N × H)
11. C₃₁	C₅²×C₄₃	semidirect
14. C₅	C₄₃×ΓL(1,𝔽₃₂)	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×C₄₃	5
C₄₃×ΓL(1,𝔽₃₂)	5
C₅²×C₄₃	31
C₅×ΓL(1,𝔽₃₂)	43