# Extensions 1→N→G→Q→1 with N=C5×C20 and Q=C22

Direct product G=N×Q with N=C5×C20 and Q=C22
dρLabelID
C2×C10×C20400C2xC10xC20400,201

Semidirect products G=N:Q with N=C5×C20 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C5×C20)⋊1C22 = D5×D20φ: C22/C1C22 ⊆ Aut C5×C20404+(C5xC20):1C2^2400,170
(C5×C20)⋊2C22 = C20⋊D10φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20):2C2^2400,171
(C5×C20)⋊3C22 = C5×D4×D5φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20):3C2^2400,185
(C5×C20)⋊4C22 = D4×C5⋊D5φ: C22/C1C22 ⊆ Aut C5×C20100(C5xC20):4C2^2400,195
(C5×C20)⋊5C22 = C4×D52φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20):5C2^2400,169
(C5×C20)⋊6C22 = C2×C20⋊D5φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20):6C2^2400,193
(C5×C20)⋊7C22 = C10×D20φ: C22/C2C2 ⊆ Aut C5×C2080(C5xC20):7C2^2400,183
(C5×C20)⋊8C22 = D5×C2×C20φ: C22/C2C2 ⊆ Aut C5×C2080(C5xC20):8C2^2400,182
(C5×C20)⋊9C22 = C2×C4×C5⋊D5φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20):9C2^2400,192
(C5×C20)⋊10C22 = D4×C5×C10φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20):10C2^2400,202

Non-split extensions G=N.Q with N=C5×C20 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C5×C20).1C22 = C522D8φ: C22/C1C22 ⊆ Aut C5×C20804(C5xC20).1C2^2400,64
(C5×C20).2C22 = C5⋊D40φ: C22/C1C22 ⊆ Aut C5×C20404+(C5xC20).2C2^2400,65
(C5×C20).3C22 = D20.D5φ: C22/C1C22 ⊆ Aut C5×C20804(C5xC20).3C2^2400,66
(C5×C20).4C22 = C523SD16φ: C22/C1C22 ⊆ Aut C5×C20804-(C5xC20).4C2^2400,67
(C5×C20).5C22 = C524SD16φ: C22/C1C22 ⊆ Aut C5×C20404+(C5xC20).5C2^2400,68
(C5×C20).6C22 = C522Q16φ: C22/C1C22 ⊆ Aut C5×C20804(C5xC20).6C2^2400,69
(C5×C20).7C22 = C523Q16φ: C22/C1C22 ⊆ Aut C5×C20804-(C5xC20).7C2^2400,70
(C5×C20).8C22 = C5×D4⋊D5φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20).8C2^2400,87
(C5×C20).9C22 = C5×D4.D5φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20).9C2^2400,88
(C5×C20).10C22 = C5×Q8⋊D5φ: C22/C1C22 ⊆ Aut C5×C20804(C5xC20).10C2^2400,89
(C5×C20).11C22 = C5×C5⋊Q16φ: C22/C1C22 ⊆ Aut C5×C20804(C5xC20).11C2^2400,90
(C5×C20).12C22 = C527D8φ: C22/C1C22 ⊆ Aut C5×C20200(C5xC20).12C2^2400,103
(C5×C20).13C22 = C528SD16φ: C22/C1C22 ⊆ Aut C5×C20200(C5xC20).13C2^2400,104
(C5×C20).14C22 = C5210SD16φ: C22/C1C22 ⊆ Aut C5×C20200(C5xC20).14C2^2400,105
(C5×C20).15C22 = C527Q16φ: C22/C1C22 ⊆ Aut C5×C20400(C5xC20).15C2^2400,106
(C5×C20).16C22 = D5×Dic10φ: C22/C1C22 ⊆ Aut C5×C20804-(C5xC20).16C2^2400,163
(C5×C20).17C22 = D205D5φ: C22/C1C22 ⊆ Aut C5×C20804-(C5xC20).17C2^2400,164
(C5×C20).18C22 = D20⋊D5φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20).18C2^2400,165
(C5×C20).19C22 = Dic10⋊D5φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20).19C2^2400,166
(C5×C20).20C22 = Dic105D5φ: C22/C1C22 ⊆ Aut C5×C20404+(C5xC20).20C2^2400,168
(C5×C20).21C22 = C5×D42D5φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20).21C2^2400,186
(C5×C20).22C22 = C5×Q8×D5φ: C22/C1C22 ⊆ Aut C5×C20804(C5xC20).22C2^2400,187
(C5×C20).23C22 = C5×Q82D5φ: C22/C1C22 ⊆ Aut C5×C20804(C5xC20).23C2^2400,188
(C5×C20).24C22 = C20.D10φ: C22/C1C22 ⊆ Aut C5×C20200(C5xC20).24C2^2400,196
(C5×C20).25C22 = Q8×C5⋊D5φ: C22/C1C22 ⊆ Aut C5×C20200(C5xC20).25C2^2400,197
(C5×C20).26C22 = C20.26D10φ: C22/C1C22 ⊆ Aut C5×C20200(C5xC20).26C2^2400,198
(C5×C20).27C22 = D5×C52C8φ: C22/C1C22 ⊆ Aut C5×C20804(C5xC20).27C2^2400,60
(C5×C20).28C22 = C20.29D10φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20).28C2^2400,61
(C5×C20).29C22 = C20.30D10φ: C22/C1C22 ⊆ Aut C5×C20804(C5xC20).29C2^2400,62
(C5×C20).30C22 = C20.31D10φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20).30C2^2400,63
(C5×C20).31C22 = D10.9D10φ: C22/C1C22 ⊆ Aut C5×C20404(C5xC20).31C2^2400,167
(C5×C20).32C22 = C402D5φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20).32C2^2400,94
(C5×C20).33C22 = C525D8φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20).33C2^2400,95
(C5×C20).34C22 = C40.D5φ: C22/C2C2 ⊆ Aut C5×C20400(C5xC20).34C2^2400,96
(C5×C20).35C22 = C2×C524Q8φ: C22/C2C2 ⊆ Aut C5×C20400(C5xC20).35C2^2400,191
(C5×C20).36C22 = C20.50D10φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20).36C2^2400,194
(C5×C20).37C22 = C5×C40⋊C2φ: C22/C2C2 ⊆ Aut C5×C20802(C5xC20).37C2^2400,78
(C5×C20).38C22 = C5×D40φ: C22/C2C2 ⊆ Aut C5×C20802(C5xC20).38C2^2400,79
(C5×C20).39C22 = C5×Dic20φ: C22/C2C2 ⊆ Aut C5×C20802(C5xC20).39C2^2400,80
(C5×C20).40C22 = C10×Dic10φ: C22/C2C2 ⊆ Aut C5×C2080(C5xC20).40C2^2400,181
(C5×C20).41C22 = C5×C4○D20φ: C22/C2C2 ⊆ Aut C5×C20402(C5xC20).41C2^2400,184
(C5×C20).42C22 = D5×C40φ: C22/C2C2 ⊆ Aut C5×C20802(C5xC20).42C2^2400,76
(C5×C20).43C22 = C5×C8⋊D5φ: C22/C2C2 ⊆ Aut C5×C20802(C5xC20).43C2^2400,77
(C5×C20).44C22 = C10×C52C8φ: C22/C2C2 ⊆ Aut C5×C2080(C5xC20).44C2^2400,81
(C5×C20).45C22 = C5×C4.Dic5φ: C22/C2C2 ⊆ Aut C5×C20402(C5xC20).45C2^2400,82
(C5×C20).46C22 = C8×C5⋊D5φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20).46C2^2400,92
(C5×C20).47C22 = C40⋊D5φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20).47C2^2400,93
(C5×C20).48C22 = C2×C527C8φ: C22/C2C2 ⊆ Aut C5×C20400(C5xC20).48C2^2400,97
(C5×C20).49C22 = C20.59D10φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20).49C2^2400,98
(C5×C20).50C22 = D8×C52φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20).50C2^2400,113
(C5×C20).51C22 = SD16×C52φ: C22/C2C2 ⊆ Aut C5×C20200(C5xC20).51C2^2400,114
(C5×C20).52C22 = Q16×C52φ: C22/C2C2 ⊆ Aut C5×C20400(C5xC20).52C2^2400,115
(C5×C20).53C22 = Q8×C5×C10φ: C22/C2C2 ⊆ Aut C5×C20400(C5xC20).53C2^2400,203
(C5×C20).54C22 = M4(2)×C52central extension (φ=1)200(C5xC20).54C2^2400,112
(C5×C20).55C22 = C4○D4×C52central extension (φ=1)200(C5xC20).55C2^2400,204

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