Extensions 1→N→G→Q→1 with N=C5xC10 and Q=C23

Direct product G=NxQ with N=C5xC10 and Q=C23
dρLabelID
C22xC102400C2^2xC10^2400,221

Semidirect products G=N:Q with N=C5xC10 and Q=C23
extensionφ:Q→Aut NdρLabelID
(C5xC10):C23 = C22xD52φ: C23/C2C22 ⊆ Aut C5xC1040(C5xC10):C2^3400,218
(C5xC10):2C23 = D5xC22xC10φ: C23/C22C2 ⊆ Aut C5xC1080(C5xC10):2C2^3400,219
(C5xC10):3C23 = C23xC5:D5φ: C23/C22C2 ⊆ Aut C5xC10200(C5xC10):3C2^3400,220

Non-split extensions G=N.Q with N=C5xC10 and Q=C23
extensionφ:Q→Aut NdρLabelID
(C5xC10).1C23 = D5xDic10φ: C23/C2C22 ⊆ Aut C5xC10804-(C5xC10).1C2^3400,163
(C5xC10).2C23 = D20:5D5φ: C23/C2C22 ⊆ Aut C5xC10804-(C5xC10).2C2^3400,164
(C5xC10).3C23 = D20:D5φ: C23/C2C22 ⊆ Aut C5xC10404(C5xC10).3C2^3400,165
(C5xC10).4C23 = Dic10:D5φ: C23/C2C22 ⊆ Aut C5xC10404(C5xC10).4C2^3400,166
(C5xC10).5C23 = D10.9D10φ: C23/C2C22 ⊆ Aut C5xC10404(C5xC10).5C2^3400,167
(C5xC10).6C23 = Dic10:5D5φ: C23/C2C22 ⊆ Aut C5xC10404+(C5xC10).6C2^3400,168
(C5xC10).7C23 = C4xD52φ: C23/C2C22 ⊆ Aut C5xC10404(C5xC10).7C2^3400,169
(C5xC10).8C23 = D5xD20φ: C23/C2C22 ⊆ Aut C5xC10404+(C5xC10).8C2^3400,170
(C5xC10).9C23 = C20:D10φ: C23/C2C22 ⊆ Aut C5xC10404(C5xC10).9C2^3400,171
(C5xC10).10C23 = C2xD5xDic5φ: C23/C2C22 ⊆ Aut C5xC1080(C5xC10).10C2^3400,172
(C5xC10).11C23 = Dic5.D10φ: C23/C2C22 ⊆ Aut C5xC10404(C5xC10).11C2^3400,173
(C5xC10).12C23 = D10.4D10φ: C23/C2C22 ⊆ Aut C5xC10404-(C5xC10).12C2^3400,174
(C5xC10).13C23 = C2xDic5:2D5φ: C23/C2C22 ⊆ Aut C5xC1040(C5xC10).13C2^3400,175
(C5xC10).14C23 = C2xC52:2D4φ: C23/C2C22 ⊆ Aut C5xC1080(C5xC10).14C2^3400,176
(C5xC10).15C23 = C2xC5:D20φ: C23/C2C22 ⊆ Aut C5xC1040(C5xC10).15C2^3400,177
(C5xC10).16C23 = C2xC52:2Q8φ: C23/C2C22 ⊆ Aut C5xC1080(C5xC10).16C2^3400,178
(C5xC10).17C23 = D5xC5:D4φ: C23/C2C22 ⊆ Aut C5xC10404(C5xC10).17C2^3400,179
(C5xC10).18C23 = D10:D10φ: C23/C2C22 ⊆ Aut C5xC10204+(C5xC10).18C2^3400,180
(C5xC10).19C23 = C10xDic10φ: C23/C22C2 ⊆ Aut C5xC1080(C5xC10).19C2^3400,181
(C5xC10).20C23 = D5xC2xC20φ: C23/C22C2 ⊆ Aut C5xC1080(C5xC10).20C2^3400,182
(C5xC10).21C23 = C10xD20φ: C23/C22C2 ⊆ Aut C5xC1080(C5xC10).21C2^3400,183
(C5xC10).22C23 = C5xC4oD20φ: C23/C22C2 ⊆ Aut C5xC10402(C5xC10).22C2^3400,184
(C5xC10).23C23 = C5xD4xD5φ: C23/C22C2 ⊆ Aut C5xC10404(C5xC10).23C2^3400,185
(C5xC10).24C23 = C5xD4:2D5φ: C23/C22C2 ⊆ Aut C5xC10404(C5xC10).24C2^3400,186
(C5xC10).25C23 = C5xQ8xD5φ: C23/C22C2 ⊆ Aut C5xC10804(C5xC10).25C2^3400,187
(C5xC10).26C23 = C5xQ8:2D5φ: C23/C22C2 ⊆ Aut C5xC10804(C5xC10).26C2^3400,188
(C5xC10).27C23 = Dic5xC2xC10φ: C23/C22C2 ⊆ Aut C5xC1080(C5xC10).27C2^3400,189
(C5xC10).28C23 = C10xC5:D4φ: C23/C22C2 ⊆ Aut C5xC1040(C5xC10).28C2^3400,190
(C5xC10).29C23 = C2xC52:4Q8φ: C23/C22C2 ⊆ Aut C5xC10400(C5xC10).29C2^3400,191
(C5xC10).30C23 = C2xC4xC5:D5φ: C23/C22C2 ⊆ Aut C5xC10200(C5xC10).30C2^3400,192
(C5xC10).31C23 = C2xC20:D5φ: C23/C22C2 ⊆ Aut C5xC10200(C5xC10).31C2^3400,193
(C5xC10).32C23 = C20.50D10φ: C23/C22C2 ⊆ Aut C5xC10200(C5xC10).32C2^3400,194
(C5xC10).33C23 = D4xC5:D5φ: C23/C22C2 ⊆ Aut C5xC10100(C5xC10).33C2^3400,195
(C5xC10).34C23 = C20.D10φ: C23/C22C2 ⊆ Aut C5xC10200(C5xC10).34C2^3400,196
(C5xC10).35C23 = Q8xC5:D5φ: C23/C22C2 ⊆ Aut C5xC10200(C5xC10).35C2^3400,197
(C5xC10).36C23 = C20.26D10φ: C23/C22C2 ⊆ Aut C5xC10200(C5xC10).36C2^3400,198
(C5xC10).37C23 = C22xC52:6C4φ: C23/C22C2 ⊆ Aut C5xC10400(C5xC10).37C2^3400,199
(C5xC10).38C23 = C2xC52:7D4φ: C23/C22C2 ⊆ Aut C5xC10200(C5xC10).38C2^3400,200
(C5xC10).39C23 = D4xC5xC10central extension (φ=1)200(C5xC10).39C2^3400,202
(C5xC10).40C23 = Q8xC5xC10central extension (φ=1)400(C5xC10).40C2^3400,203
(C5xC10).41C23 = C4oD4xC52central extension (φ=1)200(C5xC10).41C2^3400,204

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