# Extensions 1→N→G→Q→1 with N=C20 and Q=C2×C10

Direct product G=N×Q with N=C20 and Q=C2×C10
dρLabelID
C2×C10×C20400C2xC10xC20400,201

Semidirect products G=N:Q with N=C20 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C20⋊(C2×C10) = C5×D4×D5φ: C2×C10/C5C22 ⊆ Aut C20404C20:(C2xC10)400,185
C202(C2×C10) = C10×D20φ: C2×C10/C10C2 ⊆ Aut C2080C20:2(C2xC10)400,183
C203(C2×C10) = D5×C2×C20φ: C2×C10/C10C2 ⊆ Aut C2080C20:3(C2xC10)400,182
C204(C2×C10) = D4×C5×C10φ: C2×C10/C10C2 ⊆ Aut C20200C20:4(C2xC10)400,202

Non-split extensions G=N.Q with N=C20 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C20.1(C2×C10) = C5×D4⋊D5φ: C2×C10/C5C22 ⊆ Aut C20404C20.1(C2xC10)400,87
C20.2(C2×C10) = C5×D4.D5φ: C2×C10/C5C22 ⊆ Aut C20404C20.2(C2xC10)400,88
C20.3(C2×C10) = C5×Q8⋊D5φ: C2×C10/C5C22 ⊆ Aut C20804C20.3(C2xC10)400,89
C20.4(C2×C10) = C5×C5⋊Q16φ: C2×C10/C5C22 ⊆ Aut C20804C20.4(C2xC10)400,90
C20.5(C2×C10) = C5×D42D5φ: C2×C10/C5C22 ⊆ Aut C20404C20.5(C2xC10)400,186
C20.6(C2×C10) = C5×Q8×D5φ: C2×C10/C5C22 ⊆ Aut C20804C20.6(C2xC10)400,187
C20.7(C2×C10) = C5×Q82D5φ: C2×C10/C5C22 ⊆ Aut C20804C20.7(C2xC10)400,188
C20.8(C2×C10) = C5×C40⋊C2φ: C2×C10/C10C2 ⊆ Aut C20802C20.8(C2xC10)400,78
C20.9(C2×C10) = C5×D40φ: C2×C10/C10C2 ⊆ Aut C20802C20.9(C2xC10)400,79
C20.10(C2×C10) = C5×Dic20φ: C2×C10/C10C2 ⊆ Aut C20802C20.10(C2xC10)400,80
C20.11(C2×C10) = C10×Dic10φ: C2×C10/C10C2 ⊆ Aut C2080C20.11(C2xC10)400,181
C20.12(C2×C10) = C5×C4○D20φ: C2×C10/C10C2 ⊆ Aut C20402C20.12(C2xC10)400,184
C20.13(C2×C10) = D5×C40φ: C2×C10/C10C2 ⊆ Aut C20802C20.13(C2xC10)400,76
C20.14(C2×C10) = C5×C8⋊D5φ: C2×C10/C10C2 ⊆ Aut C20802C20.14(C2xC10)400,77
C20.15(C2×C10) = C10×C52C8φ: C2×C10/C10C2 ⊆ Aut C2080C20.15(C2xC10)400,81
C20.16(C2×C10) = C5×C4.Dic5φ: C2×C10/C10C2 ⊆ Aut C20402C20.16(C2xC10)400,82
C20.17(C2×C10) = D8×C25φ: C2×C10/C10C2 ⊆ Aut C202002C20.17(C2xC10)400,25
C20.18(C2×C10) = SD16×C25φ: C2×C10/C10C2 ⊆ Aut C202002C20.18(C2xC10)400,26
C20.19(C2×C10) = Q16×C25φ: C2×C10/C10C2 ⊆ Aut C204002C20.19(C2xC10)400,27
C20.20(C2×C10) = D4×C50φ: C2×C10/C10C2 ⊆ Aut C20200C20.20(C2xC10)400,46
C20.21(C2×C10) = Q8×C50φ: C2×C10/C10C2 ⊆ Aut C20400C20.21(C2xC10)400,47
C20.22(C2×C10) = C4○D4×C25φ: C2×C10/C10C2 ⊆ Aut C202002C20.22(C2xC10)400,48
C20.23(C2×C10) = D8×C52φ: C2×C10/C10C2 ⊆ Aut C20200C20.23(C2xC10)400,113
C20.24(C2×C10) = SD16×C52φ: C2×C10/C10C2 ⊆ Aut C20200C20.24(C2xC10)400,114
C20.25(C2×C10) = Q16×C52φ: C2×C10/C10C2 ⊆ Aut C20400C20.25(C2xC10)400,115
C20.26(C2×C10) = Q8×C5×C10φ: C2×C10/C10C2 ⊆ Aut C20400C20.26(C2xC10)400,203
C20.27(C2×C10) = C4○D4×C52φ: C2×C10/C10C2 ⊆ Aut C20200C20.27(C2xC10)400,204
C20.28(C2×C10) = M4(2)×C25central extension (φ=1)2002C20.28(C2xC10)400,24
C20.29(C2×C10) = M4(2)×C52central extension (φ=1)200C20.29(C2xC10)400,112

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