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

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

Semidirect products G=N:Q with N=C10 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
C10⋊(C2×C20) = F5×C2×C10φ: C2×C20/C10C4 ⊆ Aut C1080C10:(C2xC20)400,214
C102(C2×C20) = D5×C2×C20φ: C2×C20/C20C2 ⊆ Aut C1080C10:2(C2xC20)400,182
C103(C2×C20) = Dic5×C2×C10φ: C2×C20/C2×C10C2 ⊆ Aut C1080C10:3(C2xC20)400,189

Non-split extensions G=N.Q with N=C10 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
C10.1(C2×C20) = C5×D5⋊C8φ: C2×C20/C10C4 ⊆ Aut C10804C10.1(C2xC20)400,135
C10.2(C2×C20) = C5×C4.F5φ: C2×C20/C10C4 ⊆ Aut C10804C10.2(C2xC20)400,136
C10.3(C2×C20) = C20×F5φ: C2×C20/C10C4 ⊆ Aut C10804C10.3(C2xC20)400,137
C10.4(C2×C20) = C5×C4⋊F5φ: C2×C20/C10C4 ⊆ Aut C10804C10.4(C2xC20)400,138
C10.5(C2×C20) = C10×C5⋊C8φ: C2×C20/C10C4 ⊆ Aut C1080C10.5(C2xC20)400,139
C10.6(C2×C20) = C5×C22.F5φ: C2×C20/C10C4 ⊆ Aut C10404C10.6(C2xC20)400,140
C10.7(C2×C20) = C5×C22⋊F5φ: C2×C20/C10C4 ⊆ Aut C10404C10.7(C2xC20)400,141
C10.8(C2×C20) = D5×C40φ: C2×C20/C20C2 ⊆ Aut C10802C10.8(C2xC20)400,76
C10.9(C2×C20) = C5×C8⋊D5φ: C2×C20/C20C2 ⊆ Aut C10802C10.9(C2xC20)400,77
C10.10(C2×C20) = C5×C10.D4φ: C2×C20/C20C2 ⊆ Aut C1080C10.10(C2xC20)400,84
C10.11(C2×C20) = C5×D10⋊C4φ: C2×C20/C20C2 ⊆ Aut C1080C10.11(C2xC20)400,86
C10.12(C2×C20) = C10×C52C8φ: C2×C20/C2×C10C2 ⊆ Aut C1080C10.12(C2xC20)400,81
C10.13(C2×C20) = C5×C4.Dic5φ: C2×C20/C2×C10C2 ⊆ Aut C10402C10.13(C2xC20)400,82
C10.14(C2×C20) = Dic5×C20φ: C2×C20/C2×C10C2 ⊆ Aut C1080C10.14(C2xC20)400,83
C10.15(C2×C20) = C5×C4⋊Dic5φ: C2×C20/C2×C10C2 ⊆ Aut C1080C10.15(C2xC20)400,85
C10.16(C2×C20) = C5×C23.D5φ: C2×C20/C2×C10C2 ⊆ Aut C1040C10.16(C2xC20)400,91
C10.17(C2×C20) = C22⋊C4×C25central extension (φ=1)200C10.17(C2xC20)400,21
C10.18(C2×C20) = C4⋊C4×C25central extension (φ=1)400C10.18(C2xC20)400,22
C10.19(C2×C20) = M4(2)×C25central extension (φ=1)2002C10.19(C2xC20)400,24
C10.20(C2×C20) = C22⋊C4×C52central extension (φ=1)200C10.20(C2xC20)400,109
C10.21(C2×C20) = C4⋊C4×C52central extension (φ=1)400C10.21(C2xC20)400,110
C10.22(C2×C20) = M4(2)×C52central extension (φ=1)200C10.22(C2xC20)400,112

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