# Extensions 1→N→G→Q→1 with N=C22×C4 and Q=C5×S3

Direct product G=N×Q with N=C22×C4 and Q=C5×S3
dρLabelID
S3×C22×C20240S3xC2^2xC20480,1151

Semidirect products G=N:Q with N=C22×C4 and Q=C5×S3
extensionφ:Q→Aut NdρLabelID
(C22×C4)⋊1(C5×S3) = C20×S4φ: C5×S3/C5S3 ⊆ Aut C22×C4603(C2^2xC4):1(C5xS3)480,1014
(C22×C4)⋊2(C5×S3) = C5×C4⋊S4φ: C5×S3/C5S3 ⊆ Aut C22×C4606(C2^2xC4):2(C5xS3)480,1015
(C22×C4)⋊3(C5×S3) = C10×D6⋊C4φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4):3(C5xS3)480,806
(C22×C4)⋊4(C5×S3) = C20×C3⋊D4φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4):4(C5xS3)480,807
(C22×C4)⋊5(C5×S3) = C5×C23.28D6φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4):5(C5xS3)480,808
(C22×C4)⋊6(C5×S3) = C5×C127D4φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4):6(C5xS3)480,809
(C22×C4)⋊7(C5×S3) = C2×C10×D12φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4):7(C5xS3)480,1152
(C22×C4)⋊8(C5×S3) = C10×C4○D12φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4):8(C5xS3)480,1153

Non-split extensions G=N.Q with N=C22×C4 and Q=C5×S3
extensionφ:Q→Aut NdρLabelID
(C22×C4).1(C5×S3) = C5×A4⋊C8φ: C5×S3/C5S3 ⊆ Aut C22×C41203(C2^2xC4).1(C5xS3)480,255
(C22×C4).2(C5×S3) = C5×A4⋊Q8φ: C5×S3/C5S3 ⊆ Aut C22×C41206(C2^2xC4).2(C5xS3)480,1013
(C22×C4).3(C5×S3) = C5×C12.55D4φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4).3(C5xS3)480,149
(C22×C4).4(C5×S3) = C5×C6.C42φ: C5×S3/C15C2 ⊆ Aut C22×C4480(C2^2xC4).4(C5xS3)480,150
(C22×C4).5(C5×S3) = C10×Dic3⋊C4φ: C5×S3/C15C2 ⊆ Aut C22×C4480(C2^2xC4).5(C5xS3)480,802
(C22×C4).6(C5×S3) = C10×C4.Dic3φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4).6(C5xS3)480,800
(C22×C4).7(C5×S3) = C5×C12.48D4φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4).7(C5xS3)480,803
(C22×C4).8(C5×S3) = C10×C4⋊Dic3φ: C5×S3/C15C2 ⊆ Aut C22×C4480(C2^2xC4).8(C5xS3)480,804
(C22×C4).9(C5×S3) = C5×C23.26D6φ: C5×S3/C15C2 ⊆ Aut C22×C4240(C2^2xC4).9(C5xS3)480,805
(C22×C4).10(C5×S3) = C2×C10×Dic6φ: C5×S3/C15C2 ⊆ Aut C22×C4480(C2^2xC4).10(C5xS3)480,1150
(C22×C4).11(C5×S3) = C2×C10×C3⋊C8central extension (φ=1)480(C2^2xC4).11(C5xS3)480,799
(C22×C4).12(C5×S3) = Dic3×C2×C20central extension (φ=1)480(C2^2xC4).12(C5xS3)480,801

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