Finite Group Databasebeta

← C₅×C₈×C₃₁₁ #72190800

Subgroups — C₅×C₈×C₃₁₁ #72190800

Order 12440.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₃₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₃₁₁	C₄	1	1	yes	characteristic
3	C₈×C₃₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₃₁₁	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₃₁₁	C₂×C₅	1	1	yes	characteristic
6	C₂×C₃₁₁	C₄×C₅	1	1	yes	characteristic
7	C₃₁₁	C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
8	C₅×C₈	C₃₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₅	C₂×C₃₁₁	1	1	yes	characteristic
10	C₂×C₅	C₄×C₃₁₁	1	1	yes	characteristic
11	C₈	C₅×C₃₁₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₅	C₈×C₃₁₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₄	C₂×C₅×C₃₁₁	1	1	yes	characteristic
14	C₂	C₄×C₅×C₃₁₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₅×C₃₁₁
socle, prime radical	C₂×C₅×C₃₁₁	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×C₃₁₁	C₅	direct (N × H)
4. C₅×C₃₁₁	C₈	direct (N × H)
7. C₃₁₁	C₅×C₈	direct (N × H)
8. C₅×C₈	C₃₁₁	direct (N × H)
11. C₈	C₅×C₃₁₁	direct (N × H)
12. C₅	C₈×C₃₁₁	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×C₃₁₁	2
C₈×C₃₁₁	5
C₅×C₈	311