Finite Group Databasebeta

← C₂³×C₁₃₀₁ #23780968

Subgroups — C₂³×C₁₃₀₁ #23780968

Order 10408.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃₀₁	C₂	1	7	yes	maximal, direct product factor
2	C₂×C₁₃₀₁	C₂²	1	7	yes	direct product factor
3	C₁₃₀₁	C₂³	1	1	yes	characteristic, direct product factor, Sylow
4	C₂³	C₁₃₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²	C₂×C₁₃₀₁	1	7	yes	direct product factor
6	C₂	C₂²×C₁₃₀₁	1	7	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. C₂²×C₁₃₀₁	C₂	direct (N × H)
2. C₂×C₁₃₀₁	C₂²	direct (N × H)
3. C₁₃₀₁	C₂³	direct (N × H)
4. C₂³	C₁₃₀₁	direct (N × H)
5. C₂²	C₂×C₁₃₀₁	direct (N × H)
6. C₂	C₂²×C₁₃₀₁	direct (N × H)