# Extensions 1→N→G→Q→1 with N=C6 and Q=C5×D4

Direct product G=N×Q with N=C6 and Q=C5×D4
dρLabelID
D4×C30120D4xC30240,186

Semidirect products G=N:Q with N=C6 and Q=C5×D4
extensionφ:Q→Aut NdρLabelID
C61(C5×D4) = C10×D12φ: C5×D4/C20C2 ⊆ Aut C6120C6:1(C5xD4)240,167
C62(C5×D4) = C10×C3⋊D4φ: C5×D4/C2×C10C2 ⊆ Aut C6120C6:2(C5xD4)240,174

Non-split extensions G=N.Q with N=C6 and Q=C5×D4
extensionφ:Q→Aut NdρLabelID
C6.1(C5×D4) = C5×C24⋊C2φ: C5×D4/C20C2 ⊆ Aut C61202C6.1(C5xD4)240,51
C6.2(C5×D4) = C5×D24φ: C5×D4/C20C2 ⊆ Aut C61202C6.2(C5xD4)240,52
C6.3(C5×D4) = C5×Dic12φ: C5×D4/C20C2 ⊆ Aut C62402C6.3(C5xD4)240,53
C6.4(C5×D4) = C5×C4⋊Dic3φ: C5×D4/C20C2 ⊆ Aut C6240C6.4(C5xD4)240,58
C6.5(C5×D4) = C5×Dic3⋊C4φ: C5×D4/C2×C10C2 ⊆ Aut C6240C6.5(C5xD4)240,57
C6.6(C5×D4) = C5×D6⋊C4φ: C5×D4/C2×C10C2 ⊆ Aut C6120C6.6(C5xD4)240,59
C6.7(C5×D4) = C5×D4⋊S3φ: C5×D4/C2×C10C2 ⊆ Aut C61204C6.7(C5xD4)240,60
C6.8(C5×D4) = C5×D4.S3φ: C5×D4/C2×C10C2 ⊆ Aut C61204C6.8(C5xD4)240,61
C6.9(C5×D4) = C5×Q82S3φ: C5×D4/C2×C10C2 ⊆ Aut C61204C6.9(C5xD4)240,62
C6.10(C5×D4) = C5×C3⋊Q16φ: C5×D4/C2×C10C2 ⊆ Aut C62404C6.10(C5xD4)240,63
C6.11(C5×D4) = C5×C6.D4φ: C5×D4/C2×C10C2 ⊆ Aut C6120C6.11(C5xD4)240,64
C6.12(C5×D4) = C15×C22⋊C4central extension (φ=1)120C6.12(C5xD4)240,82
C6.13(C5×D4) = C15×C4⋊C4central extension (φ=1)240C6.13(C5xD4)240,83
C6.14(C5×D4) = C15×D8central extension (φ=1)1202C6.14(C5xD4)240,86
C6.15(C5×D4) = C15×SD16central extension (φ=1)1202C6.15(C5xD4)240,87
C6.16(C5×D4) = C15×Q16central extension (φ=1)2402C6.16(C5xD4)240,88

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