# Extensions 1→N→G→Q→1 with N=C10 and Q=C42.C2

Direct product G=N×Q with N=C10 and Q=C42.C2
dρLabelID
C10×C42.C2320C10xC4^2.C2320,1529

Semidirect products G=N:Q with N=C10 and Q=C42.C2
extensionφ:Q→Aut NdρLabelID
C101(C42.C2) = C2×C20.6Q8φ: C42.C2/C42C2 ⊆ Aut C10320C10:1(C4^2.C2)320,1141
C102(C42.C2) = C2×Dic5.Q8φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10:2(C4^2.C2)320,1170
C103(C42.C2) = C2×C4.Dic10φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10:3(C4^2.C2)320,1171

Non-split extensions G=N.Q with N=C10 and Q=C42.C2
extensionφ:Q→Aut NdρLabelID
C10.1(C42.C2) = (C2×C4).Dic10φ: C42.C2/C42C2 ⊆ Aut C10320C10.1(C4^2.C2)320,287
C10.2(C42.C2) = C207(C4⋊C4)φ: C42.C2/C42C2 ⊆ Aut C10320C10.2(C4^2.C2)320,555
C10.3(C42.C2) = C10.92(C4×D4)φ: C42.C2/C42C2 ⊆ Aut C10320C10.3(C4^2.C2)320,560
C10.4(C42.C2) = C429Dic5φ: C42.C2/C42C2 ⊆ Aut C10320C10.4(C4^2.C2)320,563
C10.5(C42.C2) = C10.49(C4×D4)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.5(C4^2.C2)320,274
C10.6(C42.C2) = C52(C428C4)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.6(C4^2.C2)320,277
C10.7(C42.C2) = C10.51(C4×D4)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.7(C4^2.C2)320,279
C10.8(C42.C2) = C2.(C4×D20)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.8(C4^2.C2)320,280
C10.9(C42.C2) = C4⋊Dic515C4φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.9(C4^2.C2)320,281
C10.10(C42.C2) = C10.52(C4×D4)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.10(C4^2.C2)320,282
C10.11(C42.C2) = C2.(C20⋊Q8)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.11(C4^2.C2)320,284
C10.12(C42.C2) = (C2×Dic5).Q8φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.12(C4^2.C2)320,285
C10.13(C42.C2) = (C2×C20).28D4φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.13(C4^2.C2)320,286
C10.14(C42.C2) = C10.(C4⋊Q8)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.14(C4^2.C2)320,288
C10.15(C42.C2) = C10.96(C4×D4)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.15(C4^2.C2)320,599
C10.16(C42.C2) = C204(C4⋊C4)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.16(C4^2.C2)320,600
C10.17(C42.C2) = C20.48(C4⋊C4)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.17(C4^2.C2)320,604
C10.18(C42.C2) = C10.97(C4×D4)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.18(C4^2.C2)320,605
C10.19(C42.C2) = (C2×C20).287D4φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.19(C4^2.C2)320,607
C10.20(C42.C2) = C4⋊C45Dic5φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.20(C4^2.C2)320,608
C10.21(C42.C2) = (C2×C20).288D4φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.21(C4^2.C2)320,609
C10.22(C42.C2) = (C2×C20).53D4φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.22(C4^2.C2)320,610
C10.23(C42.C2) = (C2×C20).54D4φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.23(C4^2.C2)320,611
C10.24(C42.C2) = C206(C4⋊C4)φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.24(C4^2.C2)320,612
C10.25(C42.C2) = (C2×C20).55D4φ: C42.C2/C4⋊C4C2 ⊆ Aut C10320C10.25(C4^2.C2)320,613
C10.26(C42.C2) = C5×C428C4central extension (φ=1)320C10.26(C4^2.C2)320,883
C10.27(C42.C2) = C5×C23.63C23central extension (φ=1)320C10.27(C4^2.C2)320,888
C10.28(C42.C2) = C5×C23.65C23central extension (φ=1)320C10.28(C4^2.C2)320,890
C10.29(C42.C2) = C5×C23.81C23central extension (φ=1)320C10.29(C4^2.C2)320,899
C10.30(C42.C2) = C5×C23.83C23central extension (φ=1)320C10.30(C4^2.C2)320,901

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