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Extensions 1→N→G→Q→1 with N=C23 and Q=C2×C20

Direct product G=N×Q with N=C23 and Q=C2×C20
dρLabelID
C24×C20320C2^4xC20320,1628

Semidirect products G=N:Q with N=C23 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
C23⋊1(C2×C20) = C10×C23⋊C4φ: C2×C20/C10 → C4 ⊆ Aut C2380C2^3:1(C2xC20)320,910
C23⋊2(C2×C20) = C5×C23.23D4φ: C2×C20/C10 → C22 ⊆ Aut C23160C2^3:2(C2xC20)320,887
C23⋊3(C2×C20) = C5×C22.11C24φ: C2×C20/C10 → C22 ⊆ Aut C2380C2^3:3(C2xC20)320,1520
C23⋊4(C2×C20) = D4×C2×C20φ: C2×C20/C20 → C2 ⊆ Aut C23160C2^3:4(C2xC20)320,1517
C23⋊5(C2×C20) = C22⋊C4×C2×C10φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3:5(C2xC20)320,1514

Non-split extensions G=N.Q with N=C23 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
C23.1(C2×C20) = C5×C2≀C4φ: C2×C20/C10 → C4 ⊆ Aut C23404C2^3.1(C2xC20)320,156
C23.2(C2×C20) = C5×C23.D4φ: C2×C20/C10 → C4 ⊆ Aut C23804C2^3.2(C2xC20)320,157
C23.3(C2×C20) = C5×C23.C23φ: C2×C20/C10 → C4 ⊆ Aut C23804C2^3.3(C2xC20)320,911
C23.4(C2×C20) = C10×C4.D4φ: C2×C20/C10 → C4 ⊆ Aut C2380C2^3.4(C2xC20)320,912
C23.5(C2×C20) = C5×M4(2).8C22φ: C2×C20/C10 → C4 ⊆ Aut C23804C2^3.5(C2xC20)320,914
C23.6(C2×C20) = C5×C23.9D4φ: C2×C20/C10 → C22 ⊆ Aut C2380C2^3.6(C2xC20)320,147
C23.7(C2×C20) = C5×M4(2)⋊4C4φ: C2×C20/C10 → C22 ⊆ Aut C23804C2^3.7(C2xC20)320,149
C23.8(C2×C20) = C5×C24.C22φ: C2×C20/C10 → C22 ⊆ Aut C23160C2^3.8(C2xC20)320,889
C23.9(C2×C20) = C5×C24.3C22φ: C2×C20/C10 → C22 ⊆ Aut C23160C2^3.9(C2xC20)320,891
C23.10(C2×C20) = C5×(C22×C8)⋊C2φ: C2×C20/C10 → C22 ⊆ Aut C23160C2^3.10(C2xC20)320,909
C23.11(C2×C20) = C5×C42.7C22φ: C2×C20/C10 → C22 ⊆ Aut C23160C2^3.11(C2xC20)320,934
C23.12(C2×C20) = C5×C8⋊6D4φ: C2×C20/C10 → C22 ⊆ Aut C23160C2^3.12(C2xC20)320,937
C23.13(C2×C20) = C5×Q8○M4(2)φ: C2×C20/C10 → C22 ⊆ Aut C23804C2^3.13(C2xC20)320,1570
C23.14(C2×C20) = C22⋊C4×C20φ: C2×C20/C20 → C2 ⊆ Aut C23160C2^3.14(C2xC20)320,878
C23.15(C2×C20) = C5×C23.8Q8φ: C2×C20/C20 → C2 ⊆ Aut C23160C2^3.15(C2xC20)320,886
C23.16(C2×C20) = C5×C8○2M4(2)φ: C2×C20/C20 → C2 ⊆ Aut C23160C2^3.16(C2xC20)320,906
C23.17(C2×C20) = C5×C42.6C22φ: C2×C20/C20 → C2 ⊆ Aut C23160C2^3.17(C2xC20)320,925
C23.18(C2×C20) = D4×C40φ: C2×C20/C20 → C2 ⊆ Aut C23160C2^3.18(C2xC20)320,935
C23.19(C2×C20) = C5×C8⋊9D4φ: C2×C20/C20 → C2 ⊆ Aut C23160C2^3.19(C2xC20)320,936
C23.20(C2×C20) = C10×C8○D4φ: C2×C20/C20 → C2 ⊆ Aut C23160C2^3.20(C2xC20)320,1569
C23.21(C2×C20) = C5×C23⋊C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2380C2^3.21(C2xC20)320,128
C23.22(C2×C20) = C5×C22.M4(2)φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.22(C2xC20)320,129
C23.23(C2×C20) = C5×C22.C42φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.23(C2xC20)320,148
C23.24(C2×C20) = C5×C24⋊3C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2380C2^3.24(C2xC20)320,880
C23.25(C2×C20) = C5×C23.7Q8φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.25(C2xC20)320,881
C23.26(C2×C20) = C5×C23.34D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.26(C2xC20)320,882
C23.27(C2×C20) = M4(2)×C20φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.27(C2xC20)320,905
C23.28(C2×C20) = C10×C22⋊C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.28(C2xC20)320,907
C23.29(C2×C20) = C5×C24.4C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2380C2^3.29(C2xC20)320,908
C23.30(C2×C20) = C10×C4.10D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.30(C2xC20)320,913
C23.31(C2×C20) = C5×C4⋊M4(2)φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.31(C2xC20)320,924
C23.32(C2×C20) = C5×C42.12C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.32(C2xC20)320,932
C23.33(C2×C20) = C5×C42.6C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.33(C2xC20)320,933
C23.34(C2×C20) = C10×C42⋊C2φ: C2×C20/C2×C10 → C2 ⊆ Aut C23160C2^3.34(C2xC20)320,1516
C23.35(C2×C20) = C5×C22.7C42central extension (φ=1)320C2^3.35(C2xC20)320,141
C23.36(C2×C20) = C10×C2.C42central extension (φ=1)320C2^3.36(C2xC20)320,876
C23.37(C2×C20) = C10×C8⋊C4central extension (φ=1)320C2^3.37(C2xC20)320,904
C23.38(C2×C20) = C10×C4⋊C8central extension (φ=1)320C2^3.38(C2xC20)320,923
C23.39(C2×C20) = C4⋊C4×C2×C10central extension (φ=1)320C2^3.39(C2xC20)320,1515
C23.40(C2×C20) = M4(2)×C2×C10central extension (φ=1)160C2^3.40(C2xC20)320,1568

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