# Extensions 1→N→G→Q→1 with N=C6 and Q=C2×C20

Direct product G=N×Q with N=C6 and Q=C2×C20
dρLabelID
C22×C60240C2^2xC60240,185

Semidirect products G=N:Q with N=C6 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
C61(C2×C20) = S3×C2×C20φ: C2×C20/C20C2 ⊆ Aut C6120C6:1(C2xC20)240,166
C62(C2×C20) = Dic3×C2×C10φ: C2×C20/C2×C10C2 ⊆ Aut C6240C6:2(C2xC20)240,173

Non-split extensions G=N.Q with N=C6 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
C6.1(C2×C20) = S3×C40φ: C2×C20/C20C2 ⊆ Aut C61202C6.1(C2xC20)240,49
C6.2(C2×C20) = C5×C8⋊S3φ: C2×C20/C20C2 ⊆ Aut C61202C6.2(C2xC20)240,50
C6.3(C2×C20) = C5×Dic3⋊C4φ: C2×C20/C20C2 ⊆ Aut C6240C6.3(C2xC20)240,57
C6.4(C2×C20) = C5×D6⋊C4φ: C2×C20/C20C2 ⊆ Aut C6120C6.4(C2xC20)240,59
C6.5(C2×C20) = C10×C3⋊C8φ: C2×C20/C2×C10C2 ⊆ Aut C6240C6.5(C2xC20)240,54
C6.6(C2×C20) = C5×C4.Dic3φ: C2×C20/C2×C10C2 ⊆ Aut C61202C6.6(C2xC20)240,55
C6.7(C2×C20) = Dic3×C20φ: C2×C20/C2×C10C2 ⊆ Aut C6240C6.7(C2xC20)240,56
C6.8(C2×C20) = C5×C4⋊Dic3φ: C2×C20/C2×C10C2 ⊆ Aut C6240C6.8(C2xC20)240,58
C6.9(C2×C20) = C5×C6.D4φ: C2×C20/C2×C10C2 ⊆ Aut C6120C6.9(C2xC20)240,64
C6.10(C2×C20) = C15×C22⋊C4central extension (φ=1)120C6.10(C2xC20)240,82
C6.11(C2×C20) = C15×C4⋊C4central extension (φ=1)240C6.11(C2xC20)240,83
C6.12(C2×C20) = C15×M4(2)central extension (φ=1)1202C6.12(C2xC20)240,85

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