# Extensions 1→N→G→Q→1 with N=C4○D4 and Q=C5×S3

Direct product G=N×Q with N=C4○D4 and Q=C5×S3
dρLabelID
C5×S3×C4○D41204C5xS3xC4oD4480,1160

Semidirect products G=N:Q with N=C4○D4 and Q=C5×S3
extensionφ:Q→Out NdρLabelID
C4○D41(C5×S3) = C5×C4.6S4φ: C5×S3/C5S3 ⊆ Out C4○D4802C4oD4:1(C5xS3)480,1020
C4○D42(C5×S3) = C5×C4.3S4φ: C5×S3/C5S3 ⊆ Out C4○D4804C4oD4:2(C5xS3)480,1021
C4○D43(C5×S3) = C5×D4⋊D6φ: C5×S3/C15C2 ⊆ Out C4○D41204C4oD4:3(C5xS3)480,828
C4○D44(C5×S3) = C5×Q8.13D6φ: C5×S3/C15C2 ⊆ Out C4○D42404C4oD4:4(C5xS3)480,829
C4○D45(C5×S3) = C5×D4○D12φ: C5×S3/C15C2 ⊆ Out C4○D41204C4oD4:5(C5xS3)480,1161
C4○D46(C5×S3) = C5×Q8○D12φ: C5×S3/C15C2 ⊆ Out C4○D42404C4oD4:6(C5xS3)480,1162

Non-split extensions G=N.Q with N=C4○D4 and Q=C5×S3
extensionφ:Q→Out NdρLabelID
C4○D4.1(C5×S3) = C5×U2(𝔽3)φ: C5×S3/C5S3 ⊆ Out C4○D41202C4oD4.1(C5xS3)480,257
C4○D4.2(C5×S3) = C5×C4.S4φ: C5×S3/C5S3 ⊆ Out C4○D41604C4oD4.2(C5xS3)480,1019
C4○D4.3(C5×S3) = C5×Q83Dic3φ: C5×S3/C15C2 ⊆ Out C4○D41204C4oD4.3(C5xS3)480,156
C4○D4.4(C5×S3) = C5×Q8.14D6φ: C5×S3/C15C2 ⊆ Out C4○D42404C4oD4.4(C5xS3)480,830
C4○D4.5(C5×S3) = C5×D4.Dic3φ: trivial image2404C4oD4.5(C5xS3)480,827

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