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

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

Semidirect products G=N:Q with N=C4×D5 and Q=C23
extensionφ:Q→Out NdρLabelID
(C4×D5)⋊1C23 = C2×D46D10φ: C23/C2C22 ⊆ Out C4×D580(C4xD5):1C2^3320,1614
(C4×D5)⋊2C23 = C2×D48D10φ: C23/C2C22 ⊆ Out C4×D580(C4xD5):2C2^3320,1619
(C4×D5)⋊3C23 = D5×2+ 1+4φ: C23/C2C22 ⊆ Out C4×D5408+(C4xD5):3C2^3320,1622
(C4×D5)⋊4C23 = C22×D4×D5φ: C23/C22C2 ⊆ Out C4×D580(C4xD5):4C2^3320,1612
(C4×D5)⋊5C23 = C22×D42D5φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5):5C2^3320,1613
(C4×D5)⋊6C23 = C22×Q82D5φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5):6C2^3320,1616
(C4×D5)⋊7C23 = C2×D5×C4○D4φ: C23/C22C2 ⊆ Out C4×D580(C4xD5):7C2^3320,1618
(C4×D5)⋊8C23 = C22×C4○D20φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5):8C2^3320,1611

Non-split extensions G=N.Q with N=C4×D5 and Q=C23
extensionφ:Q→Out NdρLabelID
(C4×D5).1C23 = C2×D8⋊D5φ: C23/C2C22 ⊆ Out C4×D580(C4xD5).1C2^3320,1427
(C4×D5).2C23 = D813D10φ: C23/C2C22 ⊆ Out C4×D5804(C4xD5).2C2^3320,1429
(C4×D5).3C23 = C2×D40⋊C2φ: C23/C2C22 ⊆ Out C4×D580(C4xD5).3C2^3320,1431
(C4×D5).4C23 = C2×SD16⋊D5φ: C23/C2C22 ⊆ Out C4×D5160(C4xD5).4C2^3320,1432
(C4×D5).5C23 = D20.29D4φ: C23/C2C22 ⊆ Out C4×D5804(C4xD5).5C2^3320,1434
(C4×D5).6C23 = C2×Q16⋊D5φ: C23/C2C22 ⊆ Out C4×D5160(C4xD5).6C2^3320,1436
(C4×D5).7C23 = D20.30D4φ: C23/C2C22 ⊆ Out C4×D51604(C4xD5).7C2^3320,1438
(C4×D5).8C23 = Q16⋊D10φ: C23/C2C22 ⊆ Out C4×D5804(C4xD5).8C2^3320,1440
(C4×D5).9C23 = D815D10φ: C23/C2C22 ⊆ Out C4×D5804+(C4xD5).9C2^3320,1441
(C4×D5).10C23 = D811D10φ: C23/C2C22 ⊆ Out C4×D5804(C4xD5).10C2^3320,1442
(C4×D5).11C23 = D20.47D4φ: C23/C2C22 ⊆ Out C4×D51604-(C4xD5).11C2^3320,1443
(C4×D5).12C23 = D5×C8⋊C22φ: C23/C2C22 ⊆ Out C4×D5408+(C4xD5).12C2^3320,1444
(C4×D5).13C23 = D85D10φ: C23/C2C22 ⊆ Out C4×D5808+(C4xD5).13C2^3320,1446
(C4×D5).14C23 = D86D10φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).14C2^3320,1447
(C4×D5).15C23 = D5×C8.C22φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).15C2^3320,1448
(C4×D5).16C23 = C40.C23φ: C23/C2C22 ⊆ Out C4×D5808+(C4xD5).16C2^3320,1450
(C4×D5).17C23 = D20.44D4φ: C23/C2C22 ⊆ Out C4×D51608-(C4xD5).17C2^3320,1451
(C4×D5).18C23 = C2×Q8.10D10φ: C23/C2C22 ⊆ Out C4×D5160(C4xD5).18C2^3320,1617
(C4×D5).19C23 = C2×D4.10D10φ: C23/C2C22 ⊆ Out C4×D5160(C4xD5).19C2^3320,1620
(C4×D5).20C23 = D20.37C23φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).20C2^3320,1623
(C4×D5).21C23 = D5×2- 1+4φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).21C2^3320,1624
(C4×D5).22C23 = D20.39C23φ: C23/C2C22 ⊆ Out C4×D5808+(C4xD5).22C2^3320,1625
(C4×D5).23C23 = D8×F5φ: C23/C2C22 ⊆ Out C4×D5408+(C4xD5).23C2^3320,1068
(C4×D5).24C23 = D40⋊C4φ: C23/C2C22 ⊆ Out C4×D5408+(C4xD5).24C2^3320,1069
(C4×D5).25C23 = D85F5φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).25C2^3320,1070
(C4×D5).26C23 = D8⋊F5φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).26C2^3320,1071
(C4×D5).27C23 = SD16×F5φ: C23/C2C22 ⊆ Out C4×D5408(C4xD5).27C2^3320,1072
(C4×D5).28C23 = SD16⋊F5φ: C23/C2C22 ⊆ Out C4×D5408(C4xD5).28C2^3320,1073
(C4×D5).29C23 = SD163F5φ: C23/C2C22 ⊆ Out C4×D5808(C4xD5).29C2^3320,1074
(C4×D5).30C23 = SD162F5φ: C23/C2C22 ⊆ Out C4×D5808(C4xD5).30C2^3320,1075
(C4×D5).31C23 = Q16×F5φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).31C2^3320,1076
(C4×D5).32C23 = Dic20⋊C4φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).32C2^3320,1077
(C4×D5).33C23 = Q165F5φ: C23/C2C22 ⊆ Out C4×D5808+(C4xD5).33C2^3320,1078
(C4×D5).34C23 = Q16⋊F5φ: C23/C2C22 ⊆ Out C4×D5808+(C4xD5).34C2^3320,1079
(C4×D5).35C23 = C2×D20⋊C4φ: C23/C2C22 ⊆ Out C4×D580(C4xD5).35C2^3320,1104
(C4×D5).36C23 = (D4×C10)⋊C4φ: C23/C2C22 ⊆ Out C4×D5408+(C4xD5).36C2^3320,1105
(C4×D5).37C23 = C2×D4⋊F5φ: C23/C2C22 ⊆ Out C4×D580(C4xD5).37C2^3320,1106
(C4×D5).38C23 = (C2×D4)⋊6F5φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).38C2^3320,1107
(C4×D5).39C23 = C2×Q8⋊F5φ: C23/C2C22 ⊆ Out C4×D580(C4xD5).39C2^3320,1119
(C4×D5).40C23 = (C2×Q8)⋊4F5φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).40C2^3320,1120
(C4×D5).41C23 = C2×Q82F5φ: C23/C2C22 ⊆ Out C4×D580(C4xD5).41C2^3320,1121
(C4×D5).42C23 = (C2×Q8)⋊6F5φ: C23/C2C22 ⊆ Out C4×D5808+(C4xD5).42C2^3320,1122
(C4×D5).43C23 = D5⋊C4≀C2φ: C23/C2C22 ⊆ Out C4×D5408(C4xD5).43C2^3320,1130
(C4×D5).44C23 = C4○D4⋊F5φ: C23/C2C22 ⊆ Out C4×D5408(C4xD5).44C2^3320,1131
(C4×D5).45C23 = C4○D20⋊C4φ: C23/C2C22 ⊆ Out C4×D5808(C4xD5).45C2^3320,1132
(C4×D5).46C23 = D4⋊F5⋊C2φ: C23/C2C22 ⊆ Out C4×D5808(C4xD5).46C2^3320,1133
(C4×D5).47C23 = C2×D4.F5φ: C23/C2C22 ⊆ Out C4×D5160(C4xD5).47C2^3320,1593
(C4×D5).48C23 = Dic5.C24φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).48C2^3320,1594
(C4×D5).49C23 = C2×D4×F5φ: C23/C2C22 ⊆ Out C4×D540(C4xD5).49C2^3320,1595
(C4×D5).50C23 = D10.C24φ: C23/C2C22 ⊆ Out C4×D5408+(C4xD5).50C2^3320,1596
(C4×D5).51C23 = C2×Q8.F5φ: C23/C2C22 ⊆ Out C4×D5160(C4xD5).51C2^3320,1597
(C4×D5).52C23 = Dic5.20C24φ: C23/C2C22 ⊆ Out C4×D5808+(C4xD5).52C2^3320,1598
(C4×D5).53C23 = C2×Q8×F5φ: C23/C2C22 ⊆ Out C4×D580(C4xD5).53C2^3320,1599
(C4×D5).54C23 = D5.2- 1+4φ: C23/C2C22 ⊆ Out C4×D5808-(C4xD5).54C2^3320,1600
(C4×D5).55C23 = Dic5.21C24φ: C23/C2C22 ⊆ Out C4×D5808(C4xD5).55C2^3320,1601
(C4×D5).56C23 = Dic5.22C24φ: C23/C2C22 ⊆ Out C4×D5808(C4xD5).56C2^3320,1602
(C4×D5).57C23 = C4○D4×F5φ: C23/C2C22 ⊆ Out C4×D5408(C4xD5).57C2^3320,1603
(C4×D5).58C23 = D5.2+ 1+4φ: C23/C2C22 ⊆ Out C4×D5408(C4xD5).58C2^3320,1604
(C4×D5).59C23 = C2×D5×D8φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).59C2^3320,1426
(C4×D5).60C23 = C2×D83D5φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).60C2^3320,1428
(C4×D5).61C23 = C2×D5×SD16φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).61C2^3320,1430
(C4×D5).62C23 = C2×SD163D5φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).62C2^3320,1433
(C4×D5).63C23 = C2×D5×Q16φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).63C2^3320,1435
(C4×D5).64C23 = C2×Q8.D10φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).64C2^3320,1437
(C4×D5).65C23 = D5×C4○D8φ: C23/C22C2 ⊆ Out C4×D5804(C4xD5).65C2^3320,1439
(C4×D5).66C23 = SD16⋊D10φ: C23/C22C2 ⊆ Out C4×D5808-(C4xD5).66C2^3320,1445
(C4×D5).67C23 = D40⋊C22φ: C23/C22C2 ⊆ Out C4×D5808+(C4xD5).67C2^3320,1449
(C4×D5).68C23 = C22×Q8×D5φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).68C2^3320,1615
(C4×D5).69C23 = C22×C8⋊D5φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).69C2^3320,1409
(C4×D5).70C23 = C2×D20.3C4φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).70C2^3320,1410
(C4×D5).71C23 = C2×D20.2C4φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).71C2^3320,1416
(C4×D5).72C23 = C40.47C23φ: C23/C22C2 ⊆ Out C4×D5804(C4xD5).72C2^3320,1417
(C4×D5).73C23 = C20.72C24φ: C23/C22C2 ⊆ Out C4×D5804(C4xD5).73C2^3320,1422
(C4×D5).74C23 = C10.C25φ: C23/C22C2 ⊆ Out C4×D5804(C4xD5).74C2^3320,1621
(C4×D5).75C23 = C2×C40⋊C4φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).75C2^3320,1057
(C4×D5).76C23 = C2×D5.D8φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).76C2^3320,1058
(C4×D5).77C23 = (C2×C8)⋊6F5φ: C23/C22C2 ⊆ Out C4×D5804(C4xD5).77C2^3320,1059
(C4×D5).78C23 = C2×C40.C4φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).78C2^3320,1060
(C4×D5).79C23 = C2×D10.Q8φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).79C2^3320,1061
(C4×D5).80C23 = (C8×D5).C4φ: C23/C22C2 ⊆ Out C4×D5804(C4xD5).80C2^3320,1062
(C4×D5).81C23 = M4(2)⋊1F5φ: C23/C22C2 ⊆ Out C4×D5408(C4xD5).81C2^3320,1065
(C4×D5).82C23 = M4(2).1F5φ: C23/C22C2 ⊆ Out C4×D5808(C4xD5).82C2^3320,1067
(C4×D5).83C23 = C22×C4.F5φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).83C2^3320,1588
(C4×D5).84C23 = C22×C4⋊F5φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).84C2^3320,1591
(C4×D5).85C23 = C2×C8×F5φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).85C2^3320,1054
(C4×D5).86C23 = C2×C8⋊F5φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).86C2^3320,1055
(C4×D5).87C23 = C20.12C42φ: C23/C22C2 ⊆ Out C4×D5804(C4xD5).87C2^3320,1056
(C4×D5).88C23 = M4(2)×F5φ: C23/C22C2 ⊆ Out C4×D5408(C4xD5).88C2^3320,1064
(C4×D5).89C23 = M4(2)⋊5F5φ: C23/C22C2 ⊆ Out C4×D5808(C4xD5).89C2^3320,1066
(C4×D5).90C23 = C22×D5⋊C8φ: C23/C22C2 ⊆ Out C4×D5160(C4xD5).90C2^3320,1587
(C4×D5).91C23 = C2×D5⋊M4(2)φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).91C2^3320,1589
(C4×D5).92C23 = C22×C4×F5φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).92C2^3320,1590
(C4×D5).93C23 = C2×D10.C23φ: C23/C22C2 ⊆ Out C4×D580(C4xD5).93C2^3320,1592
(C4×D5).94C23 = D5×C22×C8φ: trivial image160(C4xD5).94C2^3320,1408
(C4×D5).95C23 = C2×D5×M4(2)φ: trivial image80(C4xD5).95C2^3320,1415
(C4×D5).96C23 = D5×C8○D4φ: trivial image804(C4xD5).96C2^3320,1421

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