Finite Group Databasebeta

← C₃×C₈×C₁₀₁₃ #72201601

Subgroups — C₃×C₈×C₁₀₁₃ #72201601

Order 24312.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₁₀₁₃	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₀₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₁₀₁₃	C₄	1	1	yes	characteristic
4	C₄×C₁₀₁₃	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₀₁₃	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₀₁₃	C₃×C₄	1	1	yes	characteristic
7	C₁₀₁₃	C₃×C₈	1	1	yes	characteristic, direct product factor, Sylow
8	C₃×C₈	C₁₀₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₄	C₂×C₁₀₁₃	1	1	yes	characteristic
10	C₈	C₃×C₁₀₁₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₃	C₄×C₁₀₁₃	1	1	yes	characteristic
12	C₄	C₂×C₃×C₁₀₁₃	1	1	yes	characteristic
13	C₃	C₈×C₁₀₁₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₃×C₄×C₁₀₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₀₁₃
socle, prime radical	C₂×C₃×C₁₀₁₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₁₀₁₃	C₃	direct (N × H)
5. C₃×C₁₀₁₃	C₈	direct (N × H)
7. C₁₀₁₃	C₃×C₈	direct (N × H)
8. C₃×C₈	C₁₀₁₃	direct (N × H)
10. C₈	C₃×C₁₀₁₃	direct (N × H)
13. C₃	C₈×C₁₀₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₁₀₁₃	2
C₈×C₁₀₁₃	3
C₃×C₈	1013