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Extensions 1→N→G→Q→1 with N=C23 and Q=C22×C10

Direct product G=N×Q with N=C23 and Q=C22×C10
dρLabelID
C25×C10320C2^5xC10320,1640

Semidirect products G=N:Q with N=C23 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C23⋊1(C22×C10) = C10×C22≀C2φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3:1(C2^2xC10)320,1523
C23⋊2(C22×C10) = C10×2+ 1+4φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3:2(C2^2xC10)320,1632
C23⋊3(C22×C10) = D4×C22×C10φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3:3(C2^2xC10)320,1629

Non-split extensions G=N.Q with N=C23 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C23.1(C22×C10) = C10×C23⋊C4φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3.1(C2^2xC10)320,910
C23.2(C22×C10) = C5×C23.C23φ: C22×C10/C10 → C22 ⊆ Aut C23804C2^3.2(C2^2xC10)320,911
C23.3(C22×C10) = C5×C2≀C22φ: C22×C10/C10 → C22 ⊆ Aut C23404C2^3.3(C2^2xC10)320,958
C23.4(C22×C10) = C5×C23.7D4φ: C22×C10/C10 → C22 ⊆ Aut C23804C2^3.4(C2^2xC10)320,959
C23.5(C22×C10) = C10×C22.D4φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.5(C2^2xC10)320,1526
C23.6(C22×C10) = C10×C4.4D4φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.6(C2^2xC10)320,1528
C23.7(C22×C10) = C5×C23.36C23φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.7(C2^2xC10)320,1531
C23.8(C22×C10) = C10×C4⋊1D4φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.8(C2^2xC10)320,1532
C23.9(C22×C10) = C5×C22.29C24φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3.9(C2^2xC10)320,1537
C23.10(C22×C10) = C5×C23.38C23φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.10(C2^2xC10)320,1538
C23.11(C22×C10) = C5×C22.32C24φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3.11(C2^2xC10)320,1540
C23.12(C22×C10) = C5×C22.34C24φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.12(C2^2xC10)320,1542
C23.13(C22×C10) = C5×C22.35C24φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.13(C2^2xC10)320,1543
C23.14(C22×C10) = C5×C22.36C24φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.14(C2^2xC10)320,1544
C23.15(C22×C10) = C5×D42φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3.15(C2^2xC10)320,1547
C23.16(C22×C10) = C5×D4⋊5D4φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3.16(C2^2xC10)320,1548
C23.17(C22×C10) = C5×Q8⋊6D4φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.17(C2^2xC10)320,1552
C23.18(C22×C10) = C5×C22.45C24φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3.18(C2^2xC10)320,1553
C23.19(C22×C10) = C5×C22.47C24φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.19(C2^2xC10)320,1555
C23.20(C22×C10) = C5×C22.49C24φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.20(C2^2xC10)320,1557
C23.21(C22×C10) = C5×C22.50C24φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.21(C2^2xC10)320,1558
C23.22(C22×C10) = C5×C22.53C24φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.22(C2^2xC10)320,1561
C23.23(C22×C10) = C5×C22.54C24φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3.23(C2^2xC10)320,1562
C23.24(C22×C10) = C5×C24⋊C22φ: C22×C10/C10 → C22 ⊆ Aut C2380C2^3.24(C2^2xC10)320,1563
C23.25(C22×C10) = C5×C22.56C24φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.25(C2^2xC10)320,1564
C23.26(C22×C10) = C5×C22.57C24φ: C22×C10/C10 → C22 ⊆ Aut C23160C2^3.26(C2^2xC10)320,1565
C23.27(C22×C10) = C5×C2.C25φ: C22×C10/C10 → C22 ⊆ Aut C23804C2^3.27(C2^2xC10)320,1634
C23.28(C22×C10) = D4×C2×C20φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.28(C2^2xC10)320,1517
C23.29(C22×C10) = C4○D4×C20φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.29(C2^2xC10)320,1519
C23.30(C22×C10) = C5×C22.11C24φ: C22×C10/C2×C10 → C2 ⊆ Aut C2380C2^3.30(C2^2xC10)320,1520
C23.31(C22×C10) = C5×C23.32C23φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.31(C2^2xC10)320,1521
C23.32(C22×C10) = C5×C23.33C23φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.32(C2^2xC10)320,1522
C23.33(C22×C10) = C5×C22.19C24φ: C22×C10/C2×C10 → C2 ⊆ Aut C2380C2^3.33(C2^2xC10)320,1527
C23.34(C22×C10) = C5×C22.26C24φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.34(C2^2xC10)320,1534
C23.35(C22×C10) = C5×C23.37C23φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.35(C2^2xC10)320,1535
C23.36(C22×C10) = C5×C23⋊3D4φ: C22×C10/C2×C10 → C2 ⊆ Aut C2380C2^3.36(C2^2xC10)320,1536
C23.37(C22×C10) = C5×C22.31C24φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.37(C2^2xC10)320,1539
C23.38(C22×C10) = C5×C22.33C24φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.38(C2^2xC10)320,1541
C23.39(C22×C10) = C5×C23⋊2Q8φ: C22×C10/C2×C10 → C2 ⊆ Aut C2380C2^3.39(C2^2xC10)320,1545
C23.40(C22×C10) = C5×C23.41C23φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.40(C2^2xC10)320,1546
C23.41(C22×C10) = C5×D4⋊6D4φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.41(C2^2xC10)320,1549
C23.42(C22×C10) = C5×Q8⋊5D4φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.42(C2^2xC10)320,1550
C23.43(C22×C10) = C5×D4×Q8φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.43(C2^2xC10)320,1551
C23.44(C22×C10) = C5×C22.46C24φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.44(C2^2xC10)320,1554
C23.45(C22×C10) = C5×D4⋊3Q8φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.45(C2^2xC10)320,1556
C23.46(C22×C10) = C4○D4×C2×C10φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.46(C2^2xC10)320,1631
C23.47(C22×C10) = C10×2- 1+4φ: C22×C10/C2×C10 → C2 ⊆ Aut C23160C2^3.47(C2^2xC10)320,1633
C23.48(C22×C10) = C10×C2.C42central extension (φ=1)320C2^3.48(C2^2xC10)320,876
C23.49(C22×C10) = C5×C42⋊4C4central extension (φ=1)320C2^3.49(C2^2xC10)320,877
C23.50(C22×C10) = C22⋊C4×C20central extension (φ=1)160C2^3.50(C2^2xC10)320,878
C23.51(C22×C10) = C4⋊C4×C20central extension (φ=1)320C2^3.51(C2^2xC10)320,879
C23.52(C22×C10) = C5×C24⋊3C4central extension (φ=1)80C2^3.52(C2^2xC10)320,880
C23.53(C22×C10) = C5×C23.7Q8central extension (φ=1)160C2^3.53(C2^2xC10)320,881
C23.54(C22×C10) = C5×C23.34D4central extension (φ=1)160C2^3.54(C2^2xC10)320,882
C23.55(C22×C10) = C5×C42⋊8C4central extension (φ=1)320C2^3.55(C2^2xC10)320,883
C23.56(C22×C10) = C5×C42⋊5C4central extension (φ=1)320C2^3.56(C2^2xC10)320,884
C23.57(C22×C10) = C5×C42⋊9C4central extension (φ=1)320C2^3.57(C2^2xC10)320,885
C23.58(C22×C10) = C5×C23.8Q8central extension (φ=1)160C2^3.58(C2^2xC10)320,886
C23.59(C22×C10) = C5×C23.23D4central extension (φ=1)160C2^3.59(C2^2xC10)320,887
C23.60(C22×C10) = C5×C23.63C23central extension (φ=1)320C2^3.60(C2^2xC10)320,888
C23.61(C22×C10) = C5×C24.C22central extension (φ=1)160C2^3.61(C2^2xC10)320,889
C23.62(C22×C10) = C5×C23.65C23central extension (φ=1)320C2^3.62(C2^2xC10)320,890
C23.63(C22×C10) = C5×C24.3C22central extension (φ=1)160C2^3.63(C2^2xC10)320,891
C23.64(C22×C10) = C5×C23.67C23central extension (φ=1)320C2^3.64(C2^2xC10)320,892
C23.65(C22×C10) = C22⋊C4×C2×C10central extension (φ=1)160C2^3.65(C2^2xC10)320,1514
C23.66(C22×C10) = C4⋊C4×C2×C10central extension (φ=1)320C2^3.66(C2^2xC10)320,1515
C23.67(C22×C10) = C10×C42⋊C2central extension (φ=1)160C2^3.67(C2^2xC10)320,1516
C23.68(C22×C10) = Q8×C2×C20central extension (φ=1)320C2^3.68(C2^2xC10)320,1518
C23.69(C22×C10) = C10×C4⋊D4central extension (φ=1)160C2^3.69(C2^2xC10)320,1524
C23.70(C22×C10) = C10×C22⋊Q8central extension (φ=1)160C2^3.70(C2^2xC10)320,1525
C23.71(C22×C10) = C10×C42.C2central extension (φ=1)320C2^3.71(C2^2xC10)320,1529
C23.72(C22×C10) = C10×C42⋊2C2central extension (φ=1)160C2^3.72(C2^2xC10)320,1530
C23.73(C22×C10) = C10×C4⋊Q8central extension (φ=1)320C2^3.73(C2^2xC10)320,1533
C23.74(C22×C10) = Q8×C22×C10central extension (φ=1)320C2^3.74(C2^2xC10)320,1630
C23.75(C22×C10) = C5×C23⋊2D4central stem extension (φ=1)160C2^3.75(C2^2xC10)320,893
C23.76(C22×C10) = C5×C23⋊Q8central stem extension (φ=1)160C2^3.76(C2^2xC10)320,894
C23.77(C22×C10) = C5×C23.10D4central stem extension (φ=1)160C2^3.77(C2^2xC10)320,895
C23.78(C22×C10) = C5×C23.78C23central stem extension (φ=1)320C2^3.78(C2^2xC10)320,896
C23.79(C22×C10) = C5×C23.Q8central stem extension (φ=1)160C2^3.79(C2^2xC10)320,897
C23.80(C22×C10) = C5×C23.11D4central stem extension (φ=1)160C2^3.80(C2^2xC10)320,898
C23.81(C22×C10) = C5×C23.81C23central stem extension (φ=1)320C2^3.81(C2^2xC10)320,899
C23.82(C22×C10) = C5×C23.4Q8central stem extension (φ=1)160C2^3.82(C2^2xC10)320,900
C23.83(C22×C10) = C5×C23.83C23central stem extension (φ=1)320C2^3.83(C2^2xC10)320,901
C23.84(C22×C10) = C5×C23.84C23central stem extension (φ=1)320C2^3.84(C2^2xC10)320,902

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