Finite Group Databasebeta

← C₅×C₈×C₂₈₁ #72189727

Subgroups — C₅×C₈×C₂₈₁ #72189727

Order 11240.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₂₈₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₂₈₁	C₄	1	1	yes	characteristic
3	C₈×C₂₈₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₂₈₁	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₂₈₁	C₂×C₅	1	1	yes	characteristic
6	C₂×C₂₈₁	C₄×C₅	1	1	yes	characteristic
7	C₂₈₁	C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
8	C₅×C₈	C₂₈₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₅	C₂×C₂₈₁	1	1	yes	characteristic
10	C₂×C₅	C₄×C₂₈₁	1	1	yes	characteristic
11	C₈	C₅×C₂₈₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₅	C₈×C₂₈₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₄	C₂×C₅×C₂₈₁	1	1	yes	characteristic
14	C₂	C₄×C₅×C₂₈₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₅×C₂₈₁
socle, prime radical	C₂×C₅×C₂₈₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈×C₂₈₁	C₅	direct (N × H)
4. C₅×C₂₈₁	C₈	direct (N × H)
7. C₂₈₁	C₅×C₈	direct (N × H)
8. C₅×C₈	C₂₈₁	direct (N × H)
11. C₈	C₅×C₂₈₁	direct (N × H)
12. C₅	C₈×C₂₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₂₈₁	2
C₈×C₂₈₁	5
C₅×C₈	281