# Extensions 1→N→G→Q→1 with N=C10 and Q=C4.10D4

Direct product G=N×Q with N=C10 and Q=C4.10D4
dρLabelID
C10×C4.10D4160C10xC4.10D4320,913

Semidirect products G=N:Q with N=C10 and Q=C4.10D4
extensionφ:Q→Aut NdρLabelID
C10⋊(C4.10D4) = C2×Dic5.D4φ: C4.10D4/C2×C4C4 ⊆ Aut C10160C10:(C4.10D4)320,1098
C102(C4.10D4) = C2×C4.12D20φ: C4.10D4/M4(2)C2 ⊆ Aut C10160C10:2(C4.10D4)320,763
C103(C4.10D4) = C2×C20.10D4φ: C4.10D4/C2×Q8C2 ⊆ Aut C10160C10:3(C4.10D4)320,853

Non-split extensions G=N.Q with N=C10 and Q=C4.10D4
extensionφ:Q→Aut NdρLabelID
C10.1(C4.10D4) = C10.C4≀C2φ: C4.10D4/C2×C4C4 ⊆ Aut C10320C10.1(C4.10D4)320,208
C10.2(C4.10D4) = Dic5.D8φ: C4.10D4/C2×C4C4 ⊆ Aut C10320C10.2(C4.10D4)320,211
C10.3(C4.10D4) = (C2×C20)⋊1C8φ: C4.10D4/C2×C4C4 ⊆ Aut C10160C10.3(C4.10D4)320,251
C10.4(C4.10D4) = (C22×C4).F5φ: C4.10D4/C2×C4C4 ⊆ Aut C10160C10.4(C4.10D4)320,252
C10.5(C4.10D4) = C22.F5⋊C4φ: C4.10D4/C2×C4C4 ⊆ Aut C10160C10.5(C4.10D4)320,257
C10.6(C4.10D4) = C42.2D10φ: C4.10D4/M4(2)C2 ⊆ Aut C10320C10.6(C4.10D4)320,23
C10.7(C4.10D4) = (C2×Dic5)⋊C8φ: C4.10D4/M4(2)C2 ⊆ Aut C10160C10.7(C4.10D4)320,27
C10.8(C4.10D4) = C20.47D8φ: C4.10D4/M4(2)C2 ⊆ Aut C10320C10.8(C4.10D4)320,40
C10.9(C4.10D4) = C20.2D8φ: C4.10D4/M4(2)C2 ⊆ Aut C10320C10.9(C4.10D4)320,44
C10.10(C4.10D4) = M4(2)⋊Dic5φ: C4.10D4/M4(2)C2 ⊆ Aut C10160C10.10(C4.10D4)320,112
C10.11(C4.10D4) = (C2×C20)⋊C8φ: C4.10D4/C2×Q8C2 ⊆ Aut C10160C10.11(C4.10D4)320,86
C10.12(C4.10D4) = (C2×C20).Q8φ: C4.10D4/C2×Q8C2 ⊆ Aut C10160C10.12(C4.10D4)320,88
C10.13(C4.10D4) = C42.8D10φ: C4.10D4/C2×Q8C2 ⊆ Aut C10320C10.13(C4.10D4)320,101
C10.14(C4.10D4) = C20.10D8φ: C4.10D4/C2×Q8C2 ⊆ Aut C10320C10.14(C4.10D4)320,105
C10.15(C4.10D4) = C5×C22.M4(2)central extension (φ=1)160C10.15(C4.10D4)320,129
C10.16(C4.10D4) = C5×C42.2C22central extension (φ=1)320C10.16(C4.10D4)320,135
C10.17(C4.10D4) = C5×C4.10D8central extension (φ=1)320C10.17(C4.10D4)320,137
C10.18(C4.10D4) = C5×C22.C42central extension (φ=1)160C10.18(C4.10D4)320,148

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