# Extensions 1→N→G→Q→1 with N=C23 and Q=C5×Q8

Direct product G=N×Q with N=C23 and Q=C5×Q8
dρLabelID
Q8×C22×C10320Q8xC2^2xC10320,1630

Semidirect products G=N:Q with N=C23 and Q=C5×Q8
extensionφ:Q→Aut NdρLabelID
C231(C5×Q8) = C5×C23⋊Q8φ: C5×Q8/C10C22 ⊆ Aut C23160C2^3:1(C5xQ8)320,894
C232(C5×Q8) = C5×C232Q8φ: C5×Q8/C10C22 ⊆ Aut C2380C2^3:2(C5xQ8)320,1545
C233(C5×Q8) = C10×C22⋊Q8φ: C5×Q8/C20C2 ⊆ Aut C23160C2^3:3(C5xQ8)320,1525

Non-split extensions G=N.Q with N=C23 and Q=C5×Q8
extensionφ:Q→Aut NdρLabelID
C23.1(C5×Q8) = C5×C4.10C42φ: C5×Q8/C10C22 ⊆ Aut C23804C2^3.1(C5xQ8)320,143
C23.2(C5×Q8) = C5×C23.9D4φ: C5×Q8/C10C22 ⊆ Aut C2380C2^3.2(C5xQ8)320,147
C23.3(C5×Q8) = C5×C23.Q8φ: C5×Q8/C10C22 ⊆ Aut C23160C2^3.3(C5xQ8)320,897
C23.4(C5×Q8) = C5×C23.4Q8φ: C5×Q8/C10C22 ⊆ Aut C23160C2^3.4(C5xQ8)320,900
C23.5(C5×Q8) = C5×M4(2).C4φ: C5×Q8/C10C22 ⊆ Aut C23804C2^3.5(C5xQ8)320,931
C23.6(C5×Q8) = C5×C4.C42φ: C5×Q8/C20C2 ⊆ Aut C23160C2^3.6(C5xQ8)320,146
C23.7(C5×Q8) = C5×C23.7Q8φ: C5×Q8/C20C2 ⊆ Aut C23160C2^3.7(C5xQ8)320,881
C23.8(C5×Q8) = C5×C23.8Q8φ: C5×Q8/C20C2 ⊆ Aut C23160C2^3.8(C5xQ8)320,886
C23.9(C5×Q8) = C10×C8.C4φ: C5×Q8/C20C2 ⊆ Aut C23160C2^3.9(C5xQ8)320,930
C23.10(C5×Q8) = C10×C2.C42central extension (φ=1)320C2^3.10(C5xQ8)320,876
C23.11(C5×Q8) = C4⋊C4×C2×C10central extension (φ=1)320C2^3.11(C5xQ8)320,1515

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