Extensions 1→N→G→Q→1 with N=C4xD5 and Q=S3

Direct product G=NxQ with N=C4xD5 and Q=S3
dρLabelID
C4xS3xD5604C4xS3xD5240,135

Semidirect products G=N:Q with N=C4xD5 and Q=S3
extensionφ:Q→Out NdρLabelID
(C4xD5):1S3 = D12:5D5φ: S3/C3C2 ⊆ Out C4xD51204-(C4xD5):1S3240,133
(C4xD5):2S3 = C12.28D10φ: S3/C3C2 ⊆ Out C4xD51204+(C4xD5):2S3240,134
(C4xD5):3S3 = D5xD12φ: S3/C3C2 ⊆ Out C4xD5604+(C4xD5):3S3240,136
(C4xD5):4S3 = D6.D10φ: S3/C3C2 ⊆ Out C4xD51204(C4xD5):4S3240,132

Non-split extensions G=N.Q with N=C4xD5 and Q=S3
extensionφ:Q→Out NdρLabelID
(C4xD5).1S3 = D5xDic6φ: S3/C3C2 ⊆ Out C4xD51204-(C4xD5).1S3240,125
(C4xD5).2S3 = C20.32D6φ: S3/C3C2 ⊆ Out C4xD51204(C4xD5).2S3240,10
(C4xD5).3S3 = C12.F5φ: S3/C3C2 ⊆ Out C4xD51204(C4xD5).3S3240,119
(C4xD5).4S3 = C60:C4φ: S3/C3C2 ⊆ Out C4xD5604(C4xD5).4S3240,121
(C4xD5).5S3 = C60.C4φ: S3/C3C2 ⊆ Out C4xD51204(C4xD5).5S3240,118
(C4xD5).6S3 = C4xC3:F5φ: S3/C3C2 ⊆ Out C4xD5604(C4xD5).6S3240,120
(C4xD5).7S3 = D5xC3:C8φ: trivial image1204(C4xD5).7S3240,7

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