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Extensions 1→N→G→Q→1 with N=C22 and Q=C22×C20

Direct product G=N×Q with N=C22 and Q=C22×C20
dρLabelID
C24×C20320C2^4xC20320,1628

Semidirect products G=N:Q with N=C22 and Q=C22×C20
extensionφ:Q→Aut NdρLabelID
C22⋊1(C22×C20) = D4×C2×C20φ: C22×C20/C2×C20 → C2 ⊆ Aut C22160C2^2:1(C2^2xC20)320,1517
C22⋊2(C22×C20) = C22⋊C4×C2×C10φ: C22×C20/C22×C10 → C2 ⊆ Aut C22160C2^2:2(C2^2xC20)320,1514

Non-split extensions G=N.Q with N=C22 and Q=C22×C20
extensionφ:Q→Aut NdρLabelID
C22.1(C22×C20) = C4○D4×C20φ: C22×C20/C2×C20 → C2 ⊆ Aut C22160C2^2.1(C2^2xC20)320,1519
C22.2(C22×C20) = C5×C22.11C24φ: C22×C20/C2×C20 → C2 ⊆ Aut C2280C2^2.2(C2^2xC20)320,1520
C22.3(C22×C20) = C5×C23.33C23φ: C22×C20/C2×C20 → C2 ⊆ Aut C22160C2^2.3(C2^2xC20)320,1522
C22.4(C22×C20) = C10×C8○D4φ: C22×C20/C2×C20 → C2 ⊆ Aut C22160C2^2.4(C2^2xC20)320,1569
C22.5(C22×C20) = C5×Q8○M4(2)φ: C22×C20/C2×C20 → C2 ⊆ Aut C22804C2^2.5(C2^2xC20)320,1570
C22.6(C22×C20) = C10×C23⋊C4φ: C22×C20/C22×C10 → C2 ⊆ Aut C2280C2^2.6(C2^2xC20)320,910
C22.7(C22×C20) = C5×C23.C23φ: C22×C20/C22×C10 → C2 ⊆ Aut C22804C2^2.7(C2^2xC20)320,911
C22.8(C22×C20) = C10×C4.D4φ: C22×C20/C22×C10 → C2 ⊆ Aut C2280C2^2.8(C2^2xC20)320,912
C22.9(C22×C20) = C10×C4.10D4φ: C22×C20/C22×C10 → C2 ⊆ Aut C22160C2^2.9(C2^2xC20)320,913
C22.10(C22×C20) = C5×M4(2).8C22φ: C22×C20/C22×C10 → C2 ⊆ Aut C22804C2^2.10(C2^2xC20)320,914
C22.11(C22×C20) = C5×C23.32C23φ: C22×C20/C22×C10 → C2 ⊆ Aut C22160C2^2.11(C2^2xC20)320,1521
C22.12(C22×C20) = C10×C2.C42central extension (φ=1)320C2^2.12(C2^2xC20)320,876
C22.13(C22×C20) = C5×C42⋊4C4central extension (φ=1)320C2^2.13(C2^2xC20)320,877
C22.14(C22×C20) = C22⋊C4×C20central extension (φ=1)160C2^2.14(C2^2xC20)320,878
C22.15(C22×C20) = C4⋊C4×C20central extension (φ=1)320C2^2.15(C2^2xC20)320,879
C22.16(C22×C20) = C10×C8⋊C4central extension (φ=1)320C2^2.16(C2^2xC20)320,904
C22.17(C22×C20) = M4(2)×C20central extension (φ=1)160C2^2.17(C2^2xC20)320,905
C22.18(C22×C20) = C5×C8○2M4(2)central extension (φ=1)160C2^2.18(C2^2xC20)320,906
C22.19(C22×C20) = C10×C22⋊C8central extension (φ=1)160C2^2.19(C2^2xC20)320,907
C22.20(C22×C20) = C10×C4⋊C8central extension (φ=1)320C2^2.20(C2^2xC20)320,923
C22.21(C22×C20) = C5×C42.12C4central extension (φ=1)160C2^2.21(C2^2xC20)320,932
C22.22(C22×C20) = D4×C40central extension (φ=1)160C2^2.22(C2^2xC20)320,935
C22.23(C22×C20) = Q8×C40central extension (φ=1)320C2^2.23(C2^2xC20)320,946
C22.24(C22×C20) = C4⋊C4×C2×C10central extension (φ=1)320C2^2.24(C2^2xC20)320,1515
C22.25(C22×C20) = C10×C42⋊C2central extension (φ=1)160C2^2.25(C2^2xC20)320,1516
C22.26(C22×C20) = Q8×C2×C20central extension (φ=1)320C2^2.26(C2^2xC20)320,1518
C22.27(C22×C20) = M4(2)×C2×C10central extension (φ=1)160C2^2.27(C2^2xC20)320,1568
C22.28(C22×C20) = C5×C24⋊3C4central stem extension (φ=1)80C2^2.28(C2^2xC20)320,880
C22.29(C22×C20) = C5×C23.7Q8central stem extension (φ=1)160C2^2.29(C2^2xC20)320,881
C22.30(C22×C20) = C5×C23.34D4central stem extension (φ=1)160C2^2.30(C2^2xC20)320,882
C22.31(C22×C20) = C5×C42⋊8C4central stem extension (φ=1)320C2^2.31(C2^2xC20)320,883
C22.32(C22×C20) = C5×C42⋊5C4central stem extension (φ=1)320C2^2.32(C2^2xC20)320,884
C22.33(C22×C20) = C5×C42⋊9C4central stem extension (φ=1)320C2^2.33(C2^2xC20)320,885
C22.34(C22×C20) = C5×C23.8Q8central stem extension (φ=1)160C2^2.34(C2^2xC20)320,886
C22.35(C22×C20) = C5×C23.23D4central stem extension (φ=1)160C2^2.35(C2^2xC20)320,887
C22.36(C22×C20) = C5×C23.63C23central stem extension (φ=1)320C2^2.36(C2^2xC20)320,888
C22.37(C22×C20) = C5×C24.C22central stem extension (φ=1)160C2^2.37(C2^2xC20)320,889
C22.38(C22×C20) = C5×C23.65C23central stem extension (φ=1)320C2^2.38(C2^2xC20)320,890
C22.39(C22×C20) = C5×C24.3C22central stem extension (φ=1)160C2^2.39(C2^2xC20)320,891
C22.40(C22×C20) = C5×C23.67C23central stem extension (φ=1)320C2^2.40(C2^2xC20)320,892
C22.41(C22×C20) = C5×C24.4C4central stem extension (φ=1)80C2^2.41(C2^2xC20)320,908
C22.42(C22×C20) = C5×(C22×C8)⋊C2central stem extension (φ=1)160C2^2.42(C2^2xC20)320,909
C22.43(C22×C20) = C5×C4⋊M4(2)central stem extension (φ=1)160C2^2.43(C2^2xC20)320,924
C22.44(C22×C20) = C5×C42.6C22central stem extension (φ=1)160C2^2.44(C2^2xC20)320,925
C22.45(C22×C20) = C5×C42.6C4central stem extension (φ=1)160C2^2.45(C2^2xC20)320,933
C22.46(C22×C20) = C5×C42.7C22central stem extension (φ=1)160C2^2.46(C2^2xC20)320,934
C22.47(C22×C20) = C5×C8⋊9D4central stem extension (φ=1)160C2^2.47(C2^2xC20)320,936
C22.48(C22×C20) = C5×C8⋊6D4central stem extension (φ=1)160C2^2.48(C2^2xC20)320,937
C22.49(C22×C20) = C5×C8⋊4Q8central stem extension (φ=1)320C2^2.49(C2^2xC20)320,947

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