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Extensions 1→N→G→Q→1 with N=C2×C4⋊C4 and Q=C10

Direct product G=N×Q with N=C2×C4⋊C4 and Q=C10
dρLabelID
C4⋊C4×C2×C10320C4:C4xC2xC10320,1515

Semidirect products G=N:Q with N=C2×C4⋊C4 and Q=C10
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4)⋊1C10 = C5×C23.7Q8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):1C10320,881
(C2×C4⋊C4)⋊2C10 = C5×C23.8Q8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):2C10320,886
(C2×C4⋊C4)⋊3C10 = C5×C24.C22φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):3C10320,889
(C2×C4⋊C4)⋊4C10 = C5×C24.3C22φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):4C10320,891
(C2×C4⋊C4)⋊5C10 = C5×C23.10D4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):5C10320,895
(C2×C4⋊C4)⋊6C10 = C5×C23.Q8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):6C10320,897
(C2×C4⋊C4)⋊7C10 = C5×C23.11D4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):7C10320,898
(C2×C4⋊C4)⋊8C10 = C5×C23.4Q8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):8C10320,900
(C2×C4⋊C4)⋊9C10 = C10×D4⋊C4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):9C10320,915
(C2×C4⋊C4)⋊10C10 = C5×C23.36D4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):10C10320,918
(C2×C4⋊C4)⋊11C10 = C5×C22.D8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):11C10320,981
(C2×C4⋊C4)⋊12C10 = C5×C23.46D4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):12C10320,982
(C2×C4⋊C4)⋊13C10 = C5×C23.33C23φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):13C10320,1522
(C2×C4⋊C4)⋊14C10 = C10×C4⋊D4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):14C10320,1524
(C2×C4⋊C4)⋊15C10 = C10×C22⋊Q8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):15C10320,1525
(C2×C4⋊C4)⋊16C10 = C10×C22.D4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):16C10320,1526
(C2×C4⋊C4)⋊17C10 = C10×C42⋊2C2φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):17C10320,1530
(C2×C4⋊C4)⋊18C10 = C5×C22.31C24φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):18C10320,1539
(C2×C4⋊C4)⋊19C10 = C5×C22.33C24φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):19C10320,1541
(C2×C4⋊C4)⋊20C10 = C5×D4⋊6D4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):20C10320,1549
(C2×C4⋊C4)⋊21C10 = C5×C22.46C24φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):21C10320,1554
(C2×C4⋊C4)⋊22C10 = C5×C22.47C24φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):22C10320,1555
(C2×C4⋊C4)⋊23C10 = C5×D4⋊3Q8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):23C10320,1556
(C2×C4⋊C4)⋊24C10 = C10×C42⋊C2φ: trivial image160(C2xC4:C4):24C10320,1516
(C2×C4⋊C4)⋊25C10 = D4×C2×C20φ: trivial image160(C2xC4:C4):25C10320,1517

Non-split extensions G=N.Q with N=C2×C4⋊C4 and Q=C10
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4).1C10 = C5×C22.M4(2)φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).1C10320,129
(C2×C4⋊C4).2C10 = C5×C22.4Q16φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).2C10320,145
(C2×C4⋊C4).3C10 = C5×C22.C42φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).3C10320,148
(C2×C4⋊C4).4C10 = C5×C42⋊8C4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).4C10320,883
(C2×C4⋊C4).5C10 = C5×C42⋊9C4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).5C10320,885
(C2×C4⋊C4).6C10 = C5×C23.63C23φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).6C10320,888
(C2×C4⋊C4).7C10 = C5×C23.65C23φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).7C10320,890
(C2×C4⋊C4).8C10 = C5×C23.67C23φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).8C10320,892
(C2×C4⋊C4).9C10 = C5×C23.78C23φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).9C10320,896
(C2×C4⋊C4).10C10 = C5×C23.81C23φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).10C10320,899
(C2×C4⋊C4).11C10 = C5×C23.83C23φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).11C10320,901
(C2×C4⋊C4).12C10 = C10×Q8⋊C4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).12C10320,916
(C2×C4⋊C4).13C10 = C10×C4.Q8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).13C10320,926
(C2×C4⋊C4).14C10 = C10×C2.D8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).14C10320,927
(C2×C4⋊C4).15C10 = C5×M4(2)⋊C4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).15C10320,929
(C2×C4⋊C4).16C10 = C5×C23.47D4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).16C10320,984
(C2×C4⋊C4).17C10 = C5×C23.48D4φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).17C10320,985
(C2×C4⋊C4).18C10 = C10×C42.C2φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).18C10320,1529
(C2×C4⋊C4).19C10 = C10×C4⋊Q8φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).19C10320,1533
(C2×C4⋊C4).20C10 = C5×C23.41C23φ: C10/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).20C10320,1546
(C2×C4⋊C4).21C10 = C4⋊C4×C20φ: trivial image320(C2xC4:C4).21C10320,879
(C2×C4⋊C4).22C10 = Q8×C2×C20φ: trivial image320(C2xC4:C4).22C10320,1518

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