Extensions 1→N→G→Q→1 with N=C6 and Q=C5×M4(2)

Direct product G=N×Q with N=C6 and Q=C5×M4(2)

Semidirect products G=N:Q with N=C6 and Q=C5×M4(2)
extensionφ:Q→Aut NdρLabelID
C61(C5×M4(2)) = C10×C8⋊S3φ: C5×M4(2)/C40C2 ⊆ Aut C6240C6:1(C5xM4(2))480,779
C62(C5×M4(2)) = C10×C4.Dic3φ: C5×M4(2)/C2×C20C2 ⊆ Aut C6240C6:2(C5xM4(2))480,800

Non-split extensions G=N.Q with N=C6 and Q=C5×M4(2)
extensionφ:Q→Aut NdρLabelID
C6.1(C5×M4(2)) = C5×Dic3⋊C8φ: C5×M4(2)/C40C2 ⊆ Aut C6480C6.1(C5xM4(2))480,133
C6.2(C5×M4(2)) = C5×C24⋊C4φ: C5×M4(2)/C40C2 ⊆ Aut C6480C6.2(C5xM4(2))480,134
C6.3(C5×M4(2)) = C5×D6⋊C8φ: C5×M4(2)/C40C2 ⊆ Aut C6240C6.3(C5xM4(2))480,139
C6.4(C5×M4(2)) = C5×C42.S3φ: C5×M4(2)/C2×C20C2 ⊆ Aut C6480C6.4(C5xM4(2))480,122
C6.5(C5×M4(2)) = C5×C12⋊C8φ: C5×M4(2)/C2×C20C2 ⊆ Aut C6480C6.5(C5xM4(2))480,123
C6.6(C5×M4(2)) = C5×C12.55D4φ: C5×M4(2)/C2×C20C2 ⊆ Aut C6240C6.6(C5xM4(2))480,149
C6.7(C5×M4(2)) = C15×C8⋊C4central extension (φ=1)480C6.7(C5xM4(2))480,200
C6.8(C5×M4(2)) = C15×C22⋊C8central extension (φ=1)240C6.8(C5xM4(2))480,201
C6.9(C5×M4(2)) = C15×C4⋊C8central extension (φ=1)480C6.9(C5xM4(2))480,208