# Extensions 1→N→G→Q→1 with N=C6 and Q=C5×C22⋊C4

Direct product G=N×Q with N=C6 and Q=C5×C22⋊C4
dρLabelID
C22⋊C4×C30240C2^2:C4xC30480,920

Semidirect products G=N:Q with N=C6 and Q=C5×C22⋊C4
extensionφ:Q→Aut NdρLabelID
C61(C5×C22⋊C4) = C10×D6⋊C4φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C6240C6:1(C5xC2^2:C4)480,806
C62(C5×C22⋊C4) = C10×C6.D4φ: C5×C22⋊C4/C22×C10C2 ⊆ Aut C6240C6:2(C5xC2^2:C4)480,831

Non-split extensions G=N.Q with N=C6 and Q=C5×C22⋊C4
extensionφ:Q→Aut NdρLabelID
C6.1(C5×C22⋊C4) = C5×C424S3φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C61202C6.1(C5xC2^2:C4)480,124
C6.2(C5×C22⋊C4) = C5×C23.6D6φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C61204C6.2(C5xC2^2:C4)480,125
C6.3(C5×C22⋊C4) = C5×C6.D8φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C6240C6.3(C5xC2^2:C4)480,128
C6.4(C5×C22⋊C4) = C5×C6.SD16φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C6480C6.4(C5xC2^2:C4)480,129
C6.5(C5×C22⋊C4) = C5×C2.Dic12φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C6480C6.5(C5xC2^2:C4)480,135
C6.6(C5×C22⋊C4) = C5×D6⋊C8φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C6240C6.6(C5xC2^2:C4)480,139
C6.7(C5×C22⋊C4) = C5×C2.D24φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C6240C6.7(C5xC2^2:C4)480,140
C6.8(C5×C22⋊C4) = C5×C12.46D4φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C61204C6.8(C5xC2^2:C4)480,142
C6.9(C5×C22⋊C4) = C5×C12.47D4φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C62404C6.9(C5xC2^2:C4)480,143
C6.10(C5×C22⋊C4) = C5×D12⋊C4φ: C5×C22⋊C4/C2×C20C2 ⊆ Aut C61204C6.10(C5xC2^2:C4)480,144
C6.11(C5×C22⋊C4) = C5×C12.55D4φ: C5×C22⋊C4/C22×C10C2 ⊆ Aut C6240C6.11(C5xC2^2:C4)480,149
C6.12(C5×C22⋊C4) = C5×C6.C42φ: C5×C22⋊C4/C22×C10C2 ⊆ Aut C6480C6.12(C5xC2^2:C4)480,150
C6.13(C5×C22⋊C4) = C5×D4⋊Dic3φ: C5×C22⋊C4/C22×C10C2 ⊆ Aut C6240C6.13(C5xC2^2:C4)480,151
C6.14(C5×C22⋊C4) = C5×C12.D4φ: C5×C22⋊C4/C22×C10C2 ⊆ Aut C61204C6.14(C5xC2^2:C4)480,152
C6.15(C5×C22⋊C4) = C5×C23.7D6φ: C5×C22⋊C4/C22×C10C2 ⊆ Aut C61204C6.15(C5xC2^2:C4)480,153
C6.16(C5×C22⋊C4) = C5×Q82Dic3φ: C5×C22⋊C4/C22×C10C2 ⊆ Aut C6480C6.16(C5xC2^2:C4)480,154
C6.17(C5×C22⋊C4) = C5×C12.10D4φ: C5×C22⋊C4/C22×C10C2 ⊆ Aut C62404C6.17(C5xC2^2:C4)480,155
C6.18(C5×C22⋊C4) = C5×Q83Dic3φ: C5×C22⋊C4/C22×C10C2 ⊆ Aut C61204C6.18(C5xC2^2:C4)480,156
C6.19(C5×C22⋊C4) = C15×C2.C42central extension (φ=1)480C6.19(C5xC2^2:C4)480,198
C6.20(C5×C22⋊C4) = C15×C22⋊C8central extension (φ=1)240C6.20(C5xC2^2:C4)480,201
C6.21(C5×C22⋊C4) = C15×C23⋊C4central extension (φ=1)1204C6.21(C5xC2^2:C4)480,202
C6.22(C5×C22⋊C4) = C15×C4.D4central extension (φ=1)1204C6.22(C5xC2^2:C4)480,203
C6.23(C5×C22⋊C4) = C15×C4.10D4central extension (φ=1)2404C6.23(C5xC2^2:C4)480,204
C6.24(C5×C22⋊C4) = C15×D4⋊C4central extension (φ=1)240C6.24(C5xC2^2:C4)480,205
C6.25(C5×C22⋊C4) = C15×Q8⋊C4central extension (φ=1)480C6.25(C5xC2^2:C4)480,206
C6.26(C5×C22⋊C4) = C15×C4≀C2central extension (φ=1)1202C6.26(C5xC2^2:C4)480,207

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