# Extensions 1→N→G→Q→1 with N=C5×C10 and Q=D4

Direct product G=N×Q with N=C5×C10 and Q=D4
dρLabelID
D4×C5×C10200D4xC5xC10400,202

Semidirect products G=N:Q with N=C5×C10 and Q=D4
extensionφ:Q→Aut NdρLabelID
(C5×C10)⋊D4 = C2×D5≀C2φ: D4/C1D4 ⊆ Aut C5×C10204+(C5xC10):D4400,211
(C5×C10)⋊2D4 = C2×C522D4φ: D4/C2C22 ⊆ Aut C5×C1080(C5xC10):2D4400,176
(C5×C10)⋊3D4 = C2×C5⋊D20φ: D4/C2C22 ⊆ Aut C5×C1040(C5xC10):3D4400,177
(C5×C10)⋊4D4 = C10×D20φ: D4/C4C2 ⊆ Aut C5×C1080(C5xC10):4D4400,183
(C5×C10)⋊5D4 = C2×C20⋊D5φ: D4/C4C2 ⊆ Aut C5×C10200(C5xC10):5D4400,193
(C5×C10)⋊6D4 = C10×C5⋊D4φ: D4/C22C2 ⊆ Aut C5×C1040(C5xC10):6D4400,190
(C5×C10)⋊7D4 = C2×C527D4φ: D4/C22C2 ⊆ Aut C5×C10200(C5xC10):7D4400,200

Non-split extensions G=N.Q with N=C5×C10 and Q=D4
extensionφ:Q→Aut NdρLabelID
(C5×C10).1D4 = D52⋊C4φ: D4/C1D4 ⊆ Aut C5×C10204+(C5xC10).1D4400,129
(C5×C10).2D4 = C2.D5≀C2φ: D4/C1D4 ⊆ Aut C5×C10204(C5xC10).2D4400,130
(C5×C10).3D4 = C52⋊D8φ: D4/C1D4 ⊆ Aut C5×C10404(C5xC10).3D4400,131
(C5×C10).4D4 = C52⋊SD16φ: D4/C1D4 ⊆ Aut C5×C10404-(C5xC10).4D4400,132
(C5×C10).5D4 = C52⋊Q16φ: D4/C1D4 ⊆ Aut C5×C10804-(C5xC10).5D4400,133
(C5×C10).6D4 = C522D8φ: D4/C2C22 ⊆ Aut C5×C10804(C5xC10).6D4400,64
(C5×C10).7D4 = C5⋊D40φ: D4/C2C22 ⊆ Aut C5×C10404+(C5xC10).7D4400,65
(C5×C10).8D4 = D20.D5φ: D4/C2C22 ⊆ Aut C5×C10804(C5xC10).8D4400,66
(C5×C10).9D4 = C523SD16φ: D4/C2C22 ⊆ Aut C5×C10804-(C5xC10).9D4400,67
(C5×C10).10D4 = C524SD16φ: D4/C2C22 ⊆ Aut C5×C10404+(C5xC10).10D4400,68
(C5×C10).11D4 = C522Q16φ: D4/C2C22 ⊆ Aut C5×C10804(C5xC10).11D4400,69
(C5×C10).12D4 = C523Q16φ: D4/C2C22 ⊆ Aut C5×C10804-(C5xC10).12D4400,70
(C5×C10).13D4 = D10⋊Dic5φ: D4/C2C22 ⊆ Aut C5×C1080(C5xC10).13D4400,72
(C5×C10).14D4 = C10.D20φ: D4/C2C22 ⊆ Aut C5×C1040(C5xC10).14D4400,73
(C5×C10).15D4 = Dic5⋊Dic5φ: D4/C2C22 ⊆ Aut C5×C1080(C5xC10).15D4400,74
(C5×C10).16D4 = C10.Dic10φ: D4/C2C22 ⊆ Aut C5×C1080(C5xC10).16D4400,75
(C5×C10).17D4 = C5×C40⋊C2φ: D4/C4C2 ⊆ Aut C5×C10802(C5xC10).17D4400,78
(C5×C10).18D4 = C5×D40φ: D4/C4C2 ⊆ Aut C5×C10802(C5xC10).18D4400,79
(C5×C10).19D4 = C5×Dic20φ: D4/C4C2 ⊆ Aut C5×C10802(C5xC10).19D4400,80
(C5×C10).20D4 = C5×C4⋊Dic5φ: D4/C4C2 ⊆ Aut C5×C1080(C5xC10).20D4400,85
(C5×C10).21D4 = C5×D10⋊C4φ: D4/C4C2 ⊆ Aut C5×C1080(C5xC10).21D4400,86
(C5×C10).22D4 = C402D5φ: D4/C4C2 ⊆ Aut C5×C10200(C5xC10).22D4400,94
(C5×C10).23D4 = C525D8φ: D4/C4C2 ⊆ Aut C5×C10200(C5xC10).23D4400,95
(C5×C10).24D4 = C40.D5φ: D4/C4C2 ⊆ Aut C5×C10400(C5xC10).24D4400,96
(C5×C10).25D4 = C203Dic5φ: D4/C4C2 ⊆ Aut C5×C10400(C5xC10).25D4400,101
(C5×C10).26D4 = C10.11D20φ: D4/C4C2 ⊆ Aut C5×C10200(C5xC10).26D4400,102
(C5×C10).27D4 = C5×C10.D4φ: D4/C22C2 ⊆ Aut C5×C1080(C5xC10).27D4400,84
(C5×C10).28D4 = C5×D4⋊D5φ: D4/C22C2 ⊆ Aut C5×C10404(C5xC10).28D4400,87
(C5×C10).29D4 = C5×D4.D5φ: D4/C22C2 ⊆ Aut C5×C10404(C5xC10).29D4400,88
(C5×C10).30D4 = C5×Q8⋊D5φ: D4/C22C2 ⊆ Aut C5×C10804(C5xC10).30D4400,89
(C5×C10).31D4 = C5×C5⋊Q16φ: D4/C22C2 ⊆ Aut C5×C10804(C5xC10).31D4400,90
(C5×C10).32D4 = C5×C23.D5φ: D4/C22C2 ⊆ Aut C5×C1040(C5xC10).32D4400,91
(C5×C10).33D4 = C102.22C22φ: D4/C22C2 ⊆ Aut C5×C10400(C5xC10).33D4400,100
(C5×C10).34D4 = C527D8φ: D4/C22C2 ⊆ Aut C5×C10200(C5xC10).34D4400,103
(C5×C10).35D4 = C528SD16φ: D4/C22C2 ⊆ Aut C5×C10200(C5xC10).35D4400,104
(C5×C10).36D4 = C5210SD16φ: D4/C22C2 ⊆ Aut C5×C10200(C5xC10).36D4400,105
(C5×C10).37D4 = C527Q16φ: D4/C22C2 ⊆ Aut C5×C10400(C5xC10).37D4400,106
(C5×C10).38D4 = C10211C4φ: D4/C22C2 ⊆ Aut C5×C10200(C5xC10).38D4400,107
(C5×C10).39D4 = C22⋊C4×C52central extension (φ=1)200(C5xC10).39D4400,109
(C5×C10).40D4 = C4⋊C4×C52central extension (φ=1)400(C5xC10).40D4400,110
(C5×C10).41D4 = D8×C52central extension (φ=1)200(C5xC10).41D4400,113
(C5×C10).42D4 = SD16×C52central extension (φ=1)200(C5xC10).42D4400,114
(C5×C10).43D4 = Q16×C52central extension (φ=1)400(C5xC10).43D4400,115

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