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Extensions 1→N→G→Q→1 with N=C2×C4⋊C4 and Q=D5

Direct product G=N×Q with N=C2×C4⋊C4 and Q=D5
dρLabelID
C2×D5×C4⋊C4160C2xD5xC4:C4320,1173

Semidirect products G=N:Q with N=C2×C4⋊C4 and Q=D5
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4)⋊1D5 = C2×D20⋊6C4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):1D5320,592
(C2×C4⋊C4)⋊2D5 = C4○D20⋊9C4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):2D5320,593
(C2×C4⋊C4)⋊3D5 = (C2×C10).40D8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):3D5320,594
(C2×C4⋊C4)⋊4D5 = C4⋊C4.228D10φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):4D5320,595
(C2×C4⋊C4)⋊5D5 = D10⋊4(C4⋊C4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):5D5320,614
(C2×C4⋊C4)⋊6D5 = (C2×D20)⋊22C4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):6D5320,615
(C2×C4⋊C4)⋊7D5 = D10⋊5(C4⋊C4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):7D5320,616
(C2×C4⋊C4)⋊8D5 = C10.90(C4×D4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):8D5320,617
(C2×C4⋊C4)⋊9D5 = (C2×C4)⋊3D20φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):9D5320,618
(C2×C4⋊C4)⋊10D5 = (C2×C20).289D4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):10D5320,619
(C2×C4⋊C4)⋊11D5 = (C2×C20).290D4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):11D5320,620
(C2×C4⋊C4)⋊12D5 = (C2×C20).56D4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):12D5320,621
(C2×C4⋊C4)⋊13D5 = C10.82+ 1+4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):13D5320,1176
(C2×C4⋊C4)⋊14D5 = C2×D10.13D4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):14D5320,1177
(C2×C4⋊C4)⋊15D5 = C2×C4⋊D20φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):15D5320,1178
(C2×C4⋊C4)⋊16D5 = C10.2- 1+4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):16D5320,1179
(C2×C4⋊C4)⋊17D5 = C2×D10⋊Q8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):17D5320,1180
(C2×C4⋊C4)⋊18D5 = C2×D10⋊2Q8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):18D5320,1181
(C2×C4⋊C4)⋊19D5 = C10.2+ 1+4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):19D5320,1182
(C2×C4⋊C4)⋊20D5 = C10.102+ 1+4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):20D5320,1183
(C2×C4⋊C4)⋊21D5 = C2×C4⋊C4⋊D5φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):21D5320,1184
(C2×C4⋊C4)⋊22D5 = C10.52- 1+4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):22D5320,1185
(C2×C4⋊C4)⋊23D5 = C10.112+ 1+4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):23D5320,1186
(C2×C4⋊C4)⋊24D5 = C10.62- 1+4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4):24D5320,1187
(C2×C4⋊C4)⋊25D5 = C2×C4⋊C4⋊7D5φ: trivial image160(C2xC4:C4):25D5320,1174
(C2×C4⋊C4)⋊26D5 = C2×D20⋊8C4φ: trivial image160(C2xC4:C4):26D5320,1175

Non-split extensions G=N.Q with N=C2×C4⋊C4 and Q=D5
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4).1D5 = (C2×C20)⋊C8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).1D5320,86
(C2×C4⋊C4).2D5 = C20.31C42φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).2D5320,87
(C2×C4⋊C4).3D5 = (C2×C20).Q8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).3D5320,88
(C2×C4⋊C4).4D5 = C2×C10.D8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).4D5320,589
(C2×C4⋊C4).5D5 = C2×C20.Q8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).5D5320,590
(C2×C4⋊C4).6D5 = C20.47(C4⋊C4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).6D5320,591
(C2×C4⋊C4).7D5 = C2×C10.Q16φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).7D5320,596
(C2×C4⋊C4).8D5 = C4⋊C4.230D10φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).8D5320,597
(C2×C4⋊C4).9D5 = C4⋊C4.231D10φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).9D5320,598
(C2×C4⋊C4).10D5 = C10.96(C4×D4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).10D5320,599
(C2×C4⋊C4).11D5 = C20⋊4(C4⋊C4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).11D5320,600
(C2×C4⋊C4).12D5 = (C2×Dic5)⋊6Q8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).12D5320,601
(C2×C4⋊C4).13D5 = C20⋊5(C4⋊C4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).13D5320,603
(C2×C4⋊C4).14D5 = C20.48(C4⋊C4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).14D5320,604
(C2×C4⋊C4).15D5 = C10.97(C4×D4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).15D5320,605
(C2×C4⋊C4).16D5 = (C2×C4)⋊Dic10φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).16D5320,606
(C2×C4⋊C4).17D5 = (C2×C20).287D4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).17D5320,607
(C2×C4⋊C4).18D5 = C4⋊C4⋊5Dic5φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).18D5320,608
(C2×C4⋊C4).19D5 = (C2×C20).288D4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).19D5320,609
(C2×C4⋊C4).20D5 = (C2×C20).53D4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).20D5320,610
(C2×C4⋊C4).21D5 = (C2×C20).54D4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).21D5320,611
(C2×C4⋊C4).22D5 = C20⋊6(C4⋊C4)φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).22D5320,612
(C2×C4⋊C4).23D5 = (C2×C20).55D4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).23D5320,613
(C2×C4⋊C4).24D5 = C2×C20⋊Q8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).24D5320,1169
(C2×C4⋊C4).25D5 = C2×Dic5.Q8φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).25D5320,1170
(C2×C4⋊C4).26D5 = C2×C4.Dic10φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4320(C2xC4:C4).26D5320,1171
(C2×C4⋊C4).27D5 = C10.12- 1+4φ: D5/C5 → C2 ⊆ Out C2×C4⋊C4160(C2xC4:C4).27D5320,1172
(C2×C4⋊C4).28D5 = C4⋊C4×Dic5φ: trivial image320(C2xC4:C4).28D5320,602
(C2×C4⋊C4).29D5 = C2×Dic5⋊3Q8φ: trivial image320(C2xC4:C4).29D5320,1168

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