Finite Group Databasebeta

← C₅²×C₃₁×C₄₁ #44540988

Subgroups — C₅²×C₃₁×C₄₁ #44540988

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	6	yes	maximal, direct product factor
2	C₃₁×C₄₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
3	C₅²×C₄₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅²×C₃₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₄₁	C₅×C₃₁	1	6	yes	direct product factor
6	C₅×C₃₁	C₅×C₄₁	1	6	yes	direct product factor
7	C₄₁	C₅²×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
8	C₃₁	C₅²×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
9	C₅²	C₃₁×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₅	C₅×C₃₁×C₄₁	1	6	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₁×C₄₁	C₅	direct (N × H)
2. C₃₁×C₄₁	C₅²	direct (N × H)
3. C₅²×C₄₁	C₃₁	direct (N × H)
4. C₅²×C₃₁	C₄₁	direct (N × H)
5. C₅×C₄₁	C₅×C₃₁	direct (N × H)
6. C₅×C₃₁	C₅×C₄₁	direct (N × H)
7. C₄₁	C₅²×C₃₁	direct (N × H)
8. C₃₁	C₅²×C₄₁	direct (N × H)
9. C₅²	C₃₁×C₄₁	direct (N × H)
10. C₅	C₅×C₃₁×C₄₁	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
C₅²×C₄₁	31
C₅²×C₃₁	41