# Extensions 1→N→G→Q→1 with N=C10 and Q=C8.C4

Direct product G=N×Q with N=C10 and Q=C8.C4
dρLabelID
C10×C8.C4160C10xC8.C4320,930

Semidirect products G=N:Q with N=C10 and Q=C8.C4
extensionφ:Q→Aut NdρLabelID
C101(C8.C4) = C2×C40.C4φ: C8.C4/C8C4 ⊆ Aut C10160C10:1(C8.C4)320,1060
C102(C8.C4) = C2×D10.Q8φ: C8.C4/C8C4 ⊆ Aut C10160C10:2(C8.C4)320,1061
C103(C8.C4) = C2×C40.6C4φ: C8.C4/C2×C8C2 ⊆ Aut C10160C10:3(C8.C4)320,734
C104(C8.C4) = C2×C20.53D4φ: C8.C4/M4(2)C2 ⊆ Aut C10160C10:4(C8.C4)320,750

Non-split extensions G=N.Q with N=C10 and Q=C8.C4
extensionφ:Q→Aut NdρLabelID
C10.1(C8.C4) = C402C8φ: C8.C4/C8C4 ⊆ Aut C10320C10.1(C8.C4)320,219
C10.2(C8.C4) = C401C8φ: C8.C4/C8C4 ⊆ Aut C10320C10.2(C8.C4)320,220
C10.3(C8.C4) = C20.26M4(2)φ: C8.C4/C8C4 ⊆ Aut C10320C10.3(C8.C4)320,221
C10.4(C8.C4) = Dic5.13D8φ: C8.C4/C8C4 ⊆ Aut C10320C10.4(C8.C4)320,222
C10.5(C8.C4) = C20.10C42φ: C8.C4/C8C4 ⊆ Aut C10160C10.5(C8.C4)320,234
C10.6(C8.C4) = C406C8φ: C8.C4/C2×C8C2 ⊆ Aut C10320C10.6(C8.C4)320,15
C10.7(C8.C4) = C405C8φ: C8.C4/C2×C8C2 ⊆ Aut C10320C10.7(C8.C4)320,16
C10.8(C8.C4) = C20.40C42φ: C8.C4/C2×C8C2 ⊆ Aut C10160C10.8(C8.C4)320,110
C10.9(C8.C4) = C20.53D8φ: C8.C4/M4(2)C2 ⊆ Aut C10320C10.9(C8.C4)320,37
C10.10(C8.C4) = C20.39SD16φ: C8.C4/M4(2)C2 ⊆ Aut C10320C10.10(C8.C4)320,38
C10.11(C8.C4) = C20.34C42φ: C8.C4/M4(2)C2 ⊆ Aut C10160C10.11(C8.C4)320,116
C10.12(C8.C4) = C5×C82C8central extension (φ=1)320C10.12(C8.C4)320,139
C10.13(C8.C4) = C5×C81C8central extension (φ=1)320C10.13(C8.C4)320,140
C10.14(C8.C4) = C5×C4.C42central extension (φ=1)160C10.14(C8.C4)320,146

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