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Extensions 1→N→G→Q→1 with N=C23 and Q=C4×D5

Direct product G=N×Q with N=C23 and Q=C4×D5
dρLabelID
D5×C23×C4160D5xC2^3xC4320,1609

Semidirect products G=N:Q with N=C23 and Q=C4×D5
extensionφ:Q→Aut NdρLabelID
C23⋊1(C4×D5) = D5×C23⋊C4φ: C4×D5/D5 → C4 ⊆ Aut C23408+C2^3:1(C4xD5)320,370
C23⋊2(C4×D5) = C24.12D10φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3:2(C4xD5)320,583
C23⋊3(C4×D5) = C24.24D10φ: C4×D5/C10 → C22 ⊆ Aut C2380C2^3:3(C4xD5)320,1158
C23⋊4(C4×D5) = C2×Dic5⋊4D4φ: C4×D5/Dic5 → C2 ⊆ Aut C23160C2^3:4(C4xD5)320,1157
C23⋊5(C4×D5) = C2×C4×C5⋊D4φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3:5(C4xD5)320,1460
C23⋊6(C4×D5) = C2×D5×C22⋊C4φ: C4×D5/D10 → C2 ⊆ Aut C2380C2^3:6(C4xD5)320,1156

Non-split extensions G=N.Q with N=C23 and Q=C4×D5
extensionφ:Q→Aut NdρLabelID
C23.1(C4×D5) = C5⋊3C2≀C4φ: C4×D5/D5 → C4 ⊆ Aut C23408+C2^3.1(C4xD5)320,29
C23.2(C4×D5) = (C2×C20).D4φ: C4×D5/D5 → C4 ⊆ Aut C23808-C2^3.2(C4xD5)320,30
C23.3(C4×D5) = C23.3D20φ: C4×D5/D5 → C4 ⊆ Aut C23408+C2^3.3(C4xD5)320,33
C23.4(C4×D5) = C23.4D20φ: C4×D5/D5 → C4 ⊆ Aut C23808-C2^3.4(C4xD5)320,34
C23.5(C4×D5) = C23⋊C4⋊5D5φ: C4×D5/D5 → C4 ⊆ Aut C23808-C2^3.5(C4xD5)320,367
C23.6(C4×D5) = D5×C4.D4φ: C4×D5/D5 → C4 ⊆ Aut C23408+C2^3.6(C4xD5)320,371
C23.7(C4×D5) = M4(2).19D10φ: C4×D5/D5 → C4 ⊆ Aut C23808-C2^3.7(C4xD5)320,372
C23.8(C4×D5) = C24.D10φ: C4×D5/C10 → C22 ⊆ Aut C2380C2^3.8(C4xD5)320,84
C23.9(C4×D5) = (C2×C40)⋊C4φ: C4×D5/C10 → C22 ⊆ Aut C23804C2^3.9(C4xD5)320,114
C23.10(C4×D5) = M4(2)⋊4Dic5φ: C4×D5/C10 → C22 ⊆ Aut C23804C2^3.10(C4xD5)320,117
C23.11(C4×D5) = C40⋊8C4⋊C2φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3.11(C4xD5)320,347
C23.12(C4×D5) = C22⋊C8⋊D5φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3.12(C4xD5)320,354
C23.13(C4×D5) = D10⋊4M4(2)φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3.13(C4xD5)320,355
C23.14(C4×D5) = Dic5⋊2M4(2)φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3.14(C4xD5)320,356
C23.15(C4×D5) = C24.3D10φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3.15(C4xD5)320,571
C23.16(C4×D5) = C24.4D10φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3.16(C4xD5)320,572
C23.17(C4×D5) = C2×C23.1D10φ: C4×D5/C10 → C22 ⊆ Aut C2380C2^3.17(C4xD5)320,581
C23.18(C4×D5) = C24.13D10φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3.18(C4xD5)320,584
C23.19(C4×D5) = C40⋊D4φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3.19(C4xD5)320,754
C23.20(C4×D5) = C40⋊18D4φ: C4×D5/C10 → C22 ⊆ Aut C23160C2^3.20(C4xD5)320,755
C23.21(C4×D5) = M4(2).31D10φ: C4×D5/C10 → C22 ⊆ Aut C23804C2^3.21(C4xD5)320,759
C23.22(C4×D5) = C40.47C23φ: C4×D5/C10 → C22 ⊆ Aut C23804C2^3.22(C4xD5)320,1417
C23.23(C4×D5) = C5⋊5(C8×D4)φ: C4×D5/Dic5 → C2 ⊆ Aut C23160C2^3.23(C4xD5)320,352
C23.24(C4×D5) = C5⋊2C8⋊26D4φ: C4×D5/Dic5 → C2 ⊆ Aut C23160C2^3.24(C4xD5)320,357
C23.25(C4×D5) = C24.46D10φ: C4×D5/Dic5 → C2 ⊆ Aut C23160C2^3.25(C4xD5)320,573
C23.26(C4×D5) = C23.45D20φ: C4×D5/Dic5 → C2 ⊆ Aut C23160C2^3.26(C4xD5)320,585
C23.27(C4×D5) = C20.51(C4⋊C4)φ: C4×D5/Dic5 → C2 ⊆ Aut C23160C2^3.27(C4xD5)320,746
C23.28(C4×D5) = C20.37C42φ: C4×D5/Dic5 → C2 ⊆ Aut C23160C2^3.28(C4xD5)320,749
C23.29(C4×D5) = C4.89(C2×D20)φ: C4×D5/Dic5 → C2 ⊆ Aut C23160C2^3.29(C4xD5)320,756
C23.30(C4×D5) = C2×D20.2C4φ: C4×D5/Dic5 → C2 ⊆ Aut C23160C2^3.30(C4xD5)320,1416
C23.31(C4×D5) = C20.42C42φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3.31(C4xD5)320,728
C23.32(C4×D5) = C20.65(C4⋊C4)φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3.32(C4xD5)320,729
C23.33(C4×D5) = C8×C5⋊D4φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3.33(C4xD5)320,736
C23.34(C4×D5) = (C22×C8)⋊D5φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3.34(C4xD5)320,737
C23.35(C4×D5) = C40⋊32D4φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3.35(C4xD5)320,738
C23.36(C4×D5) = C4×C23.D5φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3.36(C4xD5)320,836
C23.37(C4×D5) = C24.62D10φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3.37(C4xD5)320,837
C23.38(C4×D5) = C24.65D10φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3.38(C4xD5)320,840
C23.39(C4×D5) = C2×D20.3C4φ: C4×D5/C20 → C2 ⊆ Aut C23160C2^3.39(C4xD5)320,1410
C23.40(C4×D5) = C5⋊3(C23⋊C8)φ: C4×D5/D10 → C2 ⊆ Aut C2380C2^3.40(C4xD5)320,26
C23.41(C4×D5) = (C2×Dic5)⋊C8φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.41(C4xD5)320,27
C23.42(C4×D5) = C24.2D10φ: C4×D5/D10 → C2 ⊆ Aut C2380C2^3.42(C4xD5)320,85
C23.43(C4×D5) = M4(2)⋊Dic5φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.43(C4xD5)320,112
C23.44(C4×D5) = Dic5.14M4(2)φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.44(C4xD5)320,345
C23.45(C4×D5) = Dic5.9M4(2)φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.45(C4xD5)320,346
C23.46(C4×D5) = D5×C22⋊C8φ: C4×D5/D10 → C2 ⊆ Aut C2380C2^3.46(C4xD5)320,351
C23.47(C4×D5) = D10⋊7M4(2)φ: C4×D5/D10 → C2 ⊆ Aut C2380C2^3.47(C4xD5)320,353
C23.48(C4×D5) = C22⋊C4×Dic5φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.48(C4xD5)320,568
C23.49(C4×D5) = C24.44D10φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.49(C4xD5)320,569
C23.50(C4×D5) = C23.42D20φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.50(C4xD5)320,570
C23.51(C4×D5) = C24.48D10φ: C4×D5/D10 → C2 ⊆ Aut C2380C2^3.51(C4xD5)320,582
C23.52(C4×D5) = M4(2)×Dic5φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.52(C4xD5)320,744
C23.53(C4×D5) = Dic5⋊5M4(2)φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.53(C4xD5)320,745
C23.54(C4×D5) = D10⋊8M4(2)φ: C4×D5/D10 → C2 ⊆ Aut C2380C2^3.54(C4xD5)320,753
C23.55(C4×D5) = C2×C20.46D4φ: C4×D5/D10 → C2 ⊆ Aut C2380C2^3.55(C4xD5)320,757
C23.56(C4×D5) = C2×C4.12D20φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.56(C4xD5)320,763
C23.57(C4×D5) = C2×C23.11D10φ: C4×D5/D10 → C2 ⊆ Aut C23160C2^3.57(C4xD5)320,1152
C23.58(C4×D5) = C2×D5×M4(2)φ: C4×D5/D10 → C2 ⊆ Aut C2380C2^3.58(C4xD5)320,1415
C23.59(C4×D5) = (C2×C40)⋊15C4central extension (φ=1)320C2^3.59(C4xD5)320,108
C23.60(C4×D5) = C2×C8×Dic5central extension (φ=1)320C2^3.60(C4xD5)320,725
C23.61(C4×D5) = C2×C20.8Q8central extension (φ=1)320C2^3.61(C4xD5)320,726
C23.62(C4×D5) = C2×C40⋊8C4central extension (φ=1)320C2^3.62(C4xD5)320,727
C23.63(C4×D5) = C2×D10⋊1C8central extension (φ=1)160C2^3.63(C4xD5)320,735
C23.64(C4×D5) = C2×C10.10C42central extension (φ=1)320C2^3.64(C4xD5)320,835
C23.65(C4×D5) = D5×C22×C8central extension (φ=1)160C2^3.65(C4xD5)320,1408
C23.66(C4×D5) = C22×C8⋊D5central extension (φ=1)160C2^3.66(C4xD5)320,1409
C23.67(C4×D5) = C22×C4×Dic5central extension (φ=1)320C2^3.67(C4xD5)320,1454
C23.68(C4×D5) = C22×C10.D4central extension (φ=1)320C2^3.68(C4xD5)320,1455
C23.69(C4×D5) = C22×D10⋊C4central extension (φ=1)160C2^3.69(C4xD5)320,1459

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