# Extensions 1→N→G→Q→1 with N=C24 and Q=C2×C10

Direct product G=N×Q with N=C24 and Q=C2×C10
dρLabelID
C25×C10320C2^5xC10320,1640

Semidirect products G=N:Q with N=C24 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C24⋊(C2×C10) = C22×C24⋊C5φ: C2×C10/C22C5 ⊆ Aut C2420C2^4:(C2xC10)320,1637
C242(C2×C10) = C5×C2≀C22φ: C2×C10/C5C22 ⊆ Aut C24404C2^4:2(C2xC10)320,958
C243(C2×C10) = C5×C233D4φ: C2×C10/C5C22 ⊆ Aut C2480C2^4:3(C2xC10)320,1536
C244(C2×C10) = C5×D42φ: C2×C10/C5C22 ⊆ Aut C2480C2^4:4(C2xC10)320,1547
C245(C2×C10) = C5×C24⋊C22φ: C2×C10/C5C22 ⊆ Aut C2480C2^4:5(C2xC10)320,1563
C246(C2×C10) = C10×2+ 1+4φ: C2×C10/C5C22 ⊆ Aut C2480C2^4:6(C2xC10)320,1632
C247(C2×C10) = C10×C22≀C2φ: C2×C10/C10C2 ⊆ Aut C2480C2^4:7(C2xC10)320,1523
C248(C2×C10) = D4×C22×C10φ: C2×C10/C10C2 ⊆ Aut C24160C2^4:8(C2xC10)320,1629

Non-split extensions G=N.Q with N=C24 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C24.1(C2×C10) = C5×C23.9D4φ: C2×C10/C5C22 ⊆ Aut C2480C2^4.1(C2xC10)320,147
C24.2(C2×C10) = C5×C24.C22φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.2(C2xC10)320,889
C24.3(C2×C10) = C5×C24.3C22φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.3(C2xC10)320,891
C24.4(C2×C10) = C5×C232D4φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.4(C2xC10)320,893
C24.5(C2×C10) = C5×C23⋊Q8φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.5(C2xC10)320,894
C24.6(C2×C10) = C5×C23.10D4φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.6(C2xC10)320,895
C24.7(C2×C10) = C5×C23.Q8φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.7(C2xC10)320,897
C24.8(C2×C10) = C5×C23.11D4φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.8(C2xC10)320,898
C24.9(C2×C10) = C5×C23.4Q8φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.9(C2xC10)320,900
C24.10(C2×C10) = C10×C23⋊C4φ: C2×C10/C5C22 ⊆ Aut C2480C2^4.10(C2xC10)320,910
C24.11(C2×C10) = C5×C22.11C24φ: C2×C10/C5C22 ⊆ Aut C2480C2^4.11(C2xC10)320,1520
C24.12(C2×C10) = C10×C4⋊D4φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.12(C2xC10)320,1524
C24.13(C2×C10) = C10×C4.4D4φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.13(C2xC10)320,1528
C24.14(C2×C10) = C10×C422C2φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.14(C2xC10)320,1530
C24.15(C2×C10) = C10×C41D4φ: C2×C10/C5C22 ⊆ Aut C24160C2^4.15(C2xC10)320,1532
C24.16(C2×C10) = C5×C22.29C24φ: C2×C10/C5C22 ⊆ Aut C2480C2^4.16(C2xC10)320,1537
C24.17(C2×C10) = C5×C22.32C24φ: C2×C10/C5C22 ⊆ Aut C2480C2^4.17(C2xC10)320,1540
C24.18(C2×C10) = C5×C232Q8φ: C2×C10/C5C22 ⊆ Aut C2480C2^4.18(C2xC10)320,1545
C24.19(C2×C10) = C5×D45D4φ: C2×C10/C5C22 ⊆ Aut C2480C2^4.19(C2xC10)320,1548
C24.20(C2×C10) = C5×C22.45C24φ: C2×C10/C5C22 ⊆ Aut C2480C2^4.20(C2xC10)320,1553
C24.21(C2×C10) = C5×C22.54C24φ: C2×C10/C5C22 ⊆ Aut C2480C2^4.21(C2xC10)320,1562
C24.22(C2×C10) = C22⋊C4×C20φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.22(C2xC10)320,878
C24.23(C2×C10) = C5×C243C4φ: C2×C10/C10C2 ⊆ Aut C2480C2^4.23(C2xC10)320,880
C24.24(C2×C10) = C5×C23.7Q8φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.24(C2xC10)320,881
C24.25(C2×C10) = C5×C23.34D4φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.25(C2xC10)320,882
C24.26(C2×C10) = C5×C23.8Q8φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.26(C2xC10)320,886
C24.27(C2×C10) = C5×C23.23D4φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.27(C2xC10)320,887
C24.28(C2×C10) = C22⋊C4×C2×C10φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.28(C2xC10)320,1514
C24.29(C2×C10) = C10×C42⋊C2φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.29(C2xC10)320,1516
C24.30(C2×C10) = D4×C2×C20φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.30(C2xC10)320,1517
C24.31(C2×C10) = C10×C22⋊Q8φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.31(C2xC10)320,1525
C24.32(C2×C10) = C10×C22.D4φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.32(C2xC10)320,1526
C24.33(C2×C10) = C5×C22.19C24φ: C2×C10/C10C2 ⊆ Aut C2480C2^4.33(C2xC10)320,1527
C24.34(C2×C10) = C4○D4×C2×C10φ: C2×C10/C10C2 ⊆ Aut C24160C2^4.34(C2xC10)320,1631
C24.35(C2×C10) = C10×C2.C42central extension (φ=1)320C2^4.35(C2xC10)320,876
C24.36(C2×C10) = C4⋊C4×C2×C10central extension (φ=1)320C2^4.36(C2xC10)320,1515
C24.37(C2×C10) = Q8×C22×C10central extension (φ=1)320C2^4.37(C2xC10)320,1630

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