# Extensions 1→N→G→Q→1 with N=D5×C10 and Q=C22

Direct product G=N×Q with N=D5×C10 and Q=C22
dρLabelID
D5×C22×C1080D5xC2^2xC10400,219

Semidirect products G=N:Q with N=D5×C10 and Q=C22
extensionφ:Q→Out NdρLabelID
(D5×C10)⋊1C22 = D5×D20φ: C22/C1C22 ⊆ Out D5×C10404+(D5xC10):1C2^2400,170
(D5×C10)⋊2C22 = C20⋊D10φ: C22/C1C22 ⊆ Out D5×C10404(D5xC10):2C2^2400,171
(D5×C10)⋊3C22 = D5×C5⋊D4φ: C22/C1C22 ⊆ Out D5×C10404(D5xC10):3C2^2400,179
(D5×C10)⋊4C22 = D10⋊D10φ: C22/C1C22 ⊆ Out D5×C10204+(D5xC10):4C2^2400,180
(D5×C10)⋊5C22 = C2×C522D4φ: C22/C2C2 ⊆ Out D5×C1080(D5xC10):5C2^2400,176
(D5×C10)⋊6C22 = C2×C5⋊D20φ: C22/C2C2 ⊆ Out D5×C1040(D5xC10):6C2^2400,177
(D5×C10)⋊7C22 = C10×D20φ: C22/C2C2 ⊆ Out D5×C1080(D5xC10):7C2^2400,183
(D5×C10)⋊8C22 = C5×D4×D5φ: C22/C2C2 ⊆ Out D5×C10404(D5xC10):8C2^2400,185
(D5×C10)⋊9C22 = C10×C5⋊D4φ: C22/C2C2 ⊆ Out D5×C1040(D5xC10):9C2^2400,190
(D5×C10)⋊10C22 = C22×D52φ: C22/C2C2 ⊆ Out D5×C1040(D5xC10):10C2^2400,218

Non-split extensions G=N.Q with N=D5×C10 and Q=C22
extensionφ:Q→Out NdρLabelID
(D5×C10).1C22 = D205D5φ: C22/C1C22 ⊆ Out D5×C10804-(D5xC10).1C2^2400,164
(D5×C10).2C22 = D20⋊D5φ: C22/C1C22 ⊆ Out D5×C10404(D5xC10).2C2^2400,165
(D5×C10).3C22 = Dic5.D10φ: C22/C1C22 ⊆ Out D5×C10404(D5xC10).3C2^2400,173
(D5×C10).4C22 = D10.4D10φ: C22/C1C22 ⊆ Out D5×C10404-(D5xC10).4C2^2400,174
(D5×C10).5C22 = Dic5×F5φ: C22/C1C22 ⊆ Out D5×C10808-(D5xC10).5C2^2400,117
(D5×C10).6C22 = D5.D20φ: C22/C1C22 ⊆ Out D5×C10408+(D5xC10).6C2^2400,118
(D5×C10).7C22 = D5.Dic10φ: C22/C1C22 ⊆ Out D5×C10808-(D5xC10).7C2^2400,119
(D5×C10).8C22 = C2×D5×F5φ: C22/C1C22 ⊆ Out D5×C10408+(D5xC10).8C2^2400,209
(D5×C10).9C22 = D5×Dic10φ: C22/C2C2 ⊆ Out D5×C10804-(D5xC10).9C2^2400,163
(D5×C10).10C22 = D10.9D10φ: C22/C2C2 ⊆ Out D5×C10404(D5xC10).10C2^2400,167
(D5×C10).11C22 = Dic105D5φ: C22/C2C2 ⊆ Out D5×C10404+(D5xC10).11C2^2400,168
(D5×C10).12C22 = C4×D52φ: C22/C2C2 ⊆ Out D5×C10404(D5xC10).12C2^2400,169
(D5×C10).13C22 = C2×D5×Dic5φ: C22/C2C2 ⊆ Out D5×C1080(D5xC10).13C2^2400,172
(D5×C10).14C22 = C5×C4○D20φ: C22/C2C2 ⊆ Out D5×C10402(D5xC10).14C2^2400,184
(D5×C10).15C22 = C5×D42D5φ: C22/C2C2 ⊆ Out D5×C10404(D5xC10).15C2^2400,186
(D5×C10).16C22 = C5×Q82D5φ: C22/C2C2 ⊆ Out D5×C10804(D5xC10).16C2^2400,188
(D5×C10).17C22 = C20×F5φ: C22/C2C2 ⊆ Out D5×C10804(D5xC10).17C2^2400,137
(D5×C10).18C22 = C5×C4⋊F5φ: C22/C2C2 ⊆ Out D5×C10804(D5xC10).18C2^2400,138
(D5×C10).19C22 = C5×C22⋊F5φ: C22/C2C2 ⊆ Out D5×C10404(D5xC10).19C2^2400,141
(D5×C10).20C22 = C4×D5.D5φ: C22/C2C2 ⊆ Out D5×C10804(D5xC10).20C2^2400,144
(D5×C10).21C22 = C205F5φ: C22/C2C2 ⊆ Out D5×C10804(D5xC10).21C2^2400,145
(D5×C10).22C22 = D10.D10φ: C22/C2C2 ⊆ Out D5×C10404(D5xC10).22C2^2400,148
(D5×C10).23C22 = F5×C2×C10φ: C22/C2C2 ⊆ Out D5×C1080(D5xC10).23C2^2400,214
(D5×C10).24C22 = C22×D5.D5φ: C22/C2C2 ⊆ Out D5×C1080(D5xC10).24C2^2400,215
(D5×C10).25C22 = D5×C2×C20φ: trivial image80(D5xC10).25C2^2400,182
(D5×C10).26C22 = C5×Q8×D5φ: trivial image804(D5xC10).26C2^2400,187

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