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Extensions 1→N→G→Q→1 with N=C6 and Q=C5×C4⋊C4

Direct product G=N×Q with N=C6 and Q=C5×C4⋊C4
dρLabelID
C4⋊C4×C30480C4:C4xC30480,921

Semidirect products G=N:Q with N=C6 and Q=C5×C4⋊C4
extensionφ:Q→Aut NdρLabelID
C6⋊1(C5×C4⋊C4) = C10×Dic3⋊C4φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C6480C6:1(C5xC4:C4)480,802
C6⋊2(C5×C4⋊C4) = C10×C4⋊Dic3φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C6480C6:2(C5xC4:C4)480,804

Non-split extensions G=N.Q with N=C6 and Q=C5×C4⋊C4
extensionφ:Q→Aut NdρLabelID
C6.1(C5×C4⋊C4) = C5×C12⋊C8φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.1(C5xC4:C4)480,123
C6.2(C5×C4⋊C4) = C5×C6.Q16φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.2(C5xC4:C4)480,126
C6.3(C5×C4⋊C4) = C5×C12.Q8φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.3(C5xC4:C4)480,127
C6.4(C5×C4⋊C4) = C5×Dic3⋊C8φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.4(C5xC4:C4)480,133
C6.5(C5×C4⋊C4) = C5×C8⋊Dic3φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.5(C5xC4:C4)480,136
C6.6(C5×C4⋊C4) = C5×C24⋊1C4φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.6(C5xC4:C4)480,137
C6.7(C5×C4⋊C4) = C5×C24.C4φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C62402C6.7(C5xC4:C4)480,138
C6.8(C5×C4⋊C4) = C5×C12.53D4φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C62404C6.8(C5xC4:C4)480,141
C6.9(C5×C4⋊C4) = C5×C6.C42φ: C5×C4⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.9(C5xC4:C4)480,150
C6.10(C5×C4⋊C4) = C15×C2.C42central extension (φ=1)480C6.10(C5xC4:C4)480,198
C6.11(C5×C4⋊C4) = C15×C4⋊C8central extension (φ=1)480C6.11(C5xC4:C4)480,208
C6.12(C5×C4⋊C4) = C15×C4.Q8central extension (φ=1)480C6.12(C5xC4:C4)480,209
C6.13(C5×C4⋊C4) = C15×C2.D8central extension (φ=1)480C6.13(C5xC4:C4)480,210
C6.14(C5×C4⋊C4) = C15×C8.C4central extension (φ=1)2402C6.14(C5xC4:C4)480,211

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