# Extensions 1→N→G→Q→1 with N=C10 and Q=C23×C4

Direct product G=N×Q with N=C10 and Q=C23×C4
dρLabelID
C24×C20320C2^4xC20320,1628

Semidirect products G=N:Q with N=C10 and Q=C23×C4
extensionφ:Q→Aut NdρLabelID
C10⋊(C23×C4) = C24×F5φ: C23×C4/C23C4 ⊆ Aut C1080C10:(C2^3xC4)320,1638
C102(C23×C4) = D5×C23×C4φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10:2(C2^3xC4)320,1609
C103(C23×C4) = C24×Dic5φ: C23×C4/C24C2 ⊆ Aut C10320C10:3(C2^3xC4)320,1626

Non-split extensions G=N.Q with N=C10 and Q=C23×C4
extensionφ:Q→Aut NdρLabelID
C10.1(C23×C4) = C22×D5⋊C8φ: C23×C4/C23C4 ⊆ Aut C10160C10.1(C2^3xC4)320,1587
C10.2(C23×C4) = C22×C4.F5φ: C23×C4/C23C4 ⊆ Aut C10160C10.2(C2^3xC4)320,1588
C10.3(C23×C4) = C2×D5⋊M4(2)φ: C23×C4/C23C4 ⊆ Aut C1080C10.3(C2^3xC4)320,1589
C10.4(C23×C4) = C22×C4×F5φ: C23×C4/C23C4 ⊆ Aut C1080C10.4(C2^3xC4)320,1590
C10.5(C23×C4) = C22×C4⋊F5φ: C23×C4/C23C4 ⊆ Aut C1080C10.5(C2^3xC4)320,1591
C10.6(C23×C4) = C2×D10.C23φ: C23×C4/C23C4 ⊆ Aut C1080C10.6(C2^3xC4)320,1592
C10.7(C23×C4) = C2×D4.F5φ: C23×C4/C23C4 ⊆ Aut C10160C10.7(C2^3xC4)320,1593
C10.8(C23×C4) = Dic5.C24φ: C23×C4/C23C4 ⊆ Aut C10808-C10.8(C2^3xC4)320,1594
C10.9(C23×C4) = C2×D4×F5φ: C23×C4/C23C4 ⊆ Aut C1040C10.9(C2^3xC4)320,1595
C10.10(C23×C4) = D10.C24φ: C23×C4/C23C4 ⊆ Aut C10408+C10.10(C2^3xC4)320,1596
C10.11(C23×C4) = C2×Q8.F5φ: C23×C4/C23C4 ⊆ Aut C10160C10.11(C2^3xC4)320,1597
C10.12(C23×C4) = Dic5.20C24φ: C23×C4/C23C4 ⊆ Aut C10808+C10.12(C2^3xC4)320,1598
C10.13(C23×C4) = C2×Q8×F5φ: C23×C4/C23C4 ⊆ Aut C1080C10.13(C2^3xC4)320,1599
C10.14(C23×C4) = D5.2- 1+4φ: C23×C4/C23C4 ⊆ Aut C10808-C10.14(C2^3xC4)320,1600
C10.15(C23×C4) = Dic5.21C24φ: C23×C4/C23C4 ⊆ Aut C10808C10.15(C2^3xC4)320,1601
C10.16(C23×C4) = Dic5.22C24φ: C23×C4/C23C4 ⊆ Aut C10808C10.16(C2^3xC4)320,1602
C10.17(C23×C4) = C4○D4×F5φ: C23×C4/C23C4 ⊆ Aut C10408C10.17(C2^3xC4)320,1603
C10.18(C23×C4) = D5.2+ 1+4φ: C23×C4/C23C4 ⊆ Aut C10408C10.18(C2^3xC4)320,1604
C10.19(C23×C4) = C23×C5⋊C8φ: C23×C4/C23C4 ⊆ Aut C10320C10.19(C2^3xC4)320,1605
C10.20(C23×C4) = C22×C22.F5φ: C23×C4/C23C4 ⊆ Aut C10160C10.20(C2^3xC4)320,1606
C10.21(C23×C4) = C22×C22⋊F5φ: C23×C4/C23C4 ⊆ Aut C1080C10.21(C2^3xC4)320,1607
C10.22(C23×C4) = C2×C4×Dic10φ: C23×C4/C22×C4C2 ⊆ Aut C10320C10.22(C2^3xC4)320,1139
C10.23(C23×C4) = D5×C2×C42φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.23(C2^3xC4)320,1143
C10.24(C23×C4) = C2×C42⋊D5φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.24(C2^3xC4)320,1144
C10.25(C23×C4) = C2×C4×D20φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.25(C2^3xC4)320,1145
C10.26(C23×C4) = C4×C4○D20φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.26(C2^3xC4)320,1146
C10.27(C23×C4) = C2×C23.11D10φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.27(C2^3xC4)320,1152
C10.28(C23×C4) = C2×D5×C22⋊C4φ: C23×C4/C22×C4C2 ⊆ Aut C1080C10.28(C2^3xC4)320,1156
C10.29(C23×C4) = C2×Dic54D4φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.29(C2^3xC4)320,1157
C10.30(C23×C4) = C24.24D10φ: C23×C4/C22×C4C2 ⊆ Aut C1080C10.30(C2^3xC4)320,1158
C10.31(C23×C4) = C2×Dic53Q8φ: C23×C4/C22×C4C2 ⊆ Aut C10320C10.31(C2^3xC4)320,1168
C10.32(C23×C4) = C2×D5×C4⋊C4φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.32(C2^3xC4)320,1173
C10.33(C23×C4) = C2×C4⋊C47D5φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.33(C2^3xC4)320,1174
C10.34(C23×C4) = C2×D208C4φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.34(C2^3xC4)320,1175
C10.35(C23×C4) = C10.82+ 1+4φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.35(C2^3xC4)320,1176
C10.36(C23×C4) = C42.87D10φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.36(C2^3xC4)320,1188
C10.37(C23×C4) = D5×C42⋊C2φ: C23×C4/C22×C4C2 ⊆ Aut C1080C10.37(C2^3xC4)320,1192
C10.38(C23×C4) = C427D10φ: C23×C4/C22×C4C2 ⊆ Aut C1080C10.38(C2^3xC4)320,1193
C10.39(C23×C4) = C42.188D10φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.39(C2^3xC4)320,1194
C10.40(C23×C4) = C42.91D10φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.40(C2^3xC4)320,1195
C10.41(C23×C4) = C4×D42D5φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.41(C2^3xC4)320,1208
C10.42(C23×C4) = C4×D4×D5φ: C23×C4/C22×C4C2 ⊆ Aut C1080C10.42(C2^3xC4)320,1216
C10.43(C23×C4) = C4211D10φ: C23×C4/C22×C4C2 ⊆ Aut C1080C10.43(C2^3xC4)320,1217
C10.44(C23×C4) = C42.108D10φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.44(C2^3xC4)320,1218
C10.45(C23×C4) = C4×Q8×D5φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.45(C2^3xC4)320,1243
C10.46(C23×C4) = C42.125D10φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.46(C2^3xC4)320,1244
C10.47(C23×C4) = C4×Q82D5φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.47(C2^3xC4)320,1245
C10.48(C23×C4) = C42.126D10φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.48(C2^3xC4)320,1246
C10.49(C23×C4) = D5×C22×C8φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.49(C2^3xC4)320,1408
C10.50(C23×C4) = C22×C8⋊D5φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.50(C2^3xC4)320,1409
C10.51(C23×C4) = C2×D20.3C4φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.51(C2^3xC4)320,1410
C10.52(C23×C4) = C2×D5×M4(2)φ: C23×C4/C22×C4C2 ⊆ Aut C1080C10.52(C2^3xC4)320,1415
C10.53(C23×C4) = C2×D20.2C4φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.53(C2^3xC4)320,1416
C10.54(C23×C4) = C40.47C23φ: C23×C4/C22×C4C2 ⊆ Aut C10804C10.54(C2^3xC4)320,1417
C10.55(C23×C4) = D5×C8○D4φ: C23×C4/C22×C4C2 ⊆ Aut C10804C10.55(C2^3xC4)320,1421
C10.56(C23×C4) = C20.72C24φ: C23×C4/C22×C4C2 ⊆ Aut C10804C10.56(C2^3xC4)320,1422
C10.57(C23×C4) = C22×C4×Dic5φ: C23×C4/C22×C4C2 ⊆ Aut C10320C10.57(C2^3xC4)320,1454
C10.58(C23×C4) = C22×C10.D4φ: C23×C4/C22×C4C2 ⊆ Aut C10320C10.58(C2^3xC4)320,1455
C10.59(C23×C4) = C22×D10⋊C4φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.59(C2^3xC4)320,1459
C10.60(C23×C4) = C2×C4×C5⋊D4φ: C23×C4/C22×C4C2 ⊆ Aut C10160C10.60(C2^3xC4)320,1460
C10.61(C23×C4) = C23×C52C8φ: C23×C4/C24C2 ⊆ Aut C10320C10.61(C2^3xC4)320,1452
C10.62(C23×C4) = C22×C4.Dic5φ: C23×C4/C24C2 ⊆ Aut C10160C10.62(C2^3xC4)320,1453
C10.63(C23×C4) = C22×C4⋊Dic5φ: C23×C4/C24C2 ⊆ Aut C10320C10.63(C2^3xC4)320,1457
C10.64(C23×C4) = C2×C23.21D10φ: C23×C4/C24C2 ⊆ Aut C10160C10.64(C2^3xC4)320,1458
C10.65(C23×C4) = C2×D4×Dic5φ: C23×C4/C24C2 ⊆ Aut C10160C10.65(C2^3xC4)320,1467
C10.66(C23×C4) = C24.38D10φ: C23×C4/C24C2 ⊆ Aut C1080C10.66(C2^3xC4)320,1470
C10.67(C23×C4) = C2×Q8×Dic5φ: C23×C4/C24C2 ⊆ Aut C10320C10.67(C2^3xC4)320,1483
C10.68(C23×C4) = C10.422- 1+4φ: C23×C4/C24C2 ⊆ Aut C10160C10.68(C2^3xC4)320,1484
C10.69(C23×C4) = C2×D4.Dic5φ: C23×C4/C24C2 ⊆ Aut C10160C10.69(C2^3xC4)320,1490
C10.70(C23×C4) = C20.76C24φ: C23×C4/C24C2 ⊆ Aut C10804C10.70(C2^3xC4)320,1491
C10.71(C23×C4) = C4○D4×Dic5φ: C23×C4/C24C2 ⊆ Aut C10160C10.71(C2^3xC4)320,1498
C10.72(C23×C4) = C10.1062- 1+4φ: C23×C4/C24C2 ⊆ Aut C10160C10.72(C2^3xC4)320,1499
C10.73(C23×C4) = C22×C23.D5φ: C23×C4/C24C2 ⊆ Aut C10160C10.73(C2^3xC4)320,1511
C10.74(C23×C4) = C22⋊C4×C2×C10central extension (φ=1)160C10.74(C2^3xC4)320,1514
C10.75(C23×C4) = C4⋊C4×C2×C10central extension (φ=1)320C10.75(C2^3xC4)320,1515
C10.76(C23×C4) = C10×C42⋊C2central extension (φ=1)160C10.76(C2^3xC4)320,1516
C10.77(C23×C4) = D4×C2×C20central extension (φ=1)160C10.77(C2^3xC4)320,1517
C10.78(C23×C4) = Q8×C2×C20central extension (φ=1)320C10.78(C2^3xC4)320,1518
C10.79(C23×C4) = C4○D4×C20central extension (φ=1)160C10.79(C2^3xC4)320,1519
C10.80(C23×C4) = C5×C22.11C24central extension (φ=1)80C10.80(C2^3xC4)320,1520
C10.81(C23×C4) = C5×C23.32C23central extension (φ=1)160C10.81(C2^3xC4)320,1521
C10.82(C23×C4) = C5×C23.33C23central extension (φ=1)160C10.82(C2^3xC4)320,1522
C10.83(C23×C4) = M4(2)×C2×C10central extension (φ=1)160C10.83(C2^3xC4)320,1568
C10.84(C23×C4) = C10×C8○D4central extension (φ=1)160C10.84(C2^3xC4)320,1569
C10.85(C23×C4) = C5×Q8○M4(2)central extension (φ=1)804C10.85(C2^3xC4)320,1570

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