# Extensions 1→N→G→Q→1 with N=C2×C30 and Q=C22

Direct product G=N×Q with N=C2×C30 and Q=C22
dρLabelID
C23×C30240C2^3xC30240,208

Semidirect products G=N:Q with N=C2×C30 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C2×C30)⋊1C22 = D4×D15φ: C22/C1C22 ⊆ Aut C2×C30604+(C2xC30):1C2^2240,179
(C2×C30)⋊2C22 = D5×C3⋊D4φ: C22/C1C22 ⊆ Aut C2×C30604(C2xC30):2C2^2240,149
(C2×C30)⋊3C22 = S3×C5⋊D4φ: C22/C1C22 ⊆ Aut C2×C30604(C2xC30):3C2^2240,150
(C2×C30)⋊4C22 = D10⋊D6φ: C22/C1C22 ⊆ Aut C2×C30604+(C2xC30):4C2^2240,151
(C2×C30)⋊5C22 = C22×S3×D5φ: C22/C1C22 ⊆ Aut C2×C3060(C2xC30):5C2^2240,202
(C2×C30)⋊6C22 = C3×D4×D5φ: C22/C1C22 ⊆ Aut C2×C30604(C2xC30):6C2^2240,159
(C2×C30)⋊7C22 = C5×S3×D4φ: C22/C1C22 ⊆ Aut C2×C30604(C2xC30):7C2^2240,169
(C2×C30)⋊8C22 = D4×C30φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30):8C2^2240,186
(C2×C30)⋊9C22 = C2×C157D4φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30):9C2^2240,184
(C2×C30)⋊10C22 = C23×D15φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30):10C2^2240,207
(C2×C30)⋊11C22 = C6×C5⋊D4φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30):11C2^2240,164
(C2×C30)⋊12C22 = D5×C22×C6φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30):12C2^2240,205
(C2×C30)⋊13C22 = C10×C3⋊D4φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30):13C2^2240,174
(C2×C30)⋊14C22 = S3×C22×C10φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30):14C2^2240,206

Non-split extensions G=N.Q with N=C2×C30 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C2×C30).1C22 = D42D15φ: C22/C1C22 ⊆ Aut C2×C301204-(C2xC30).1C2^2240,180
(C2×C30).2C22 = Dic3×Dic5φ: C22/C1C22 ⊆ Aut C2×C30240(C2xC30).2C2^2240,25
(C2×C30).3C22 = D10⋊Dic3φ: C22/C1C22 ⊆ Aut C2×C30120(C2xC30).3C2^2240,26
(C2×C30).4C22 = D6⋊Dic5φ: C22/C1C22 ⊆ Aut C2×C30120(C2xC30).4C2^2240,27
(C2×C30).5C22 = D304C4φ: C22/C1C22 ⊆ Aut C2×C30120(C2xC30).5C2^2240,28
(C2×C30).6C22 = C30.Q8φ: C22/C1C22 ⊆ Aut C2×C30240(C2xC30).6C2^2240,29
(C2×C30).7C22 = Dic155C4φ: C22/C1C22 ⊆ Aut C2×C30240(C2xC30).7C2^2240,30
(C2×C30).8C22 = C6.Dic10φ: C22/C1C22 ⊆ Aut C2×C30240(C2xC30).8C2^2240,31
(C2×C30).9C22 = C2×D5×Dic3φ: C22/C1C22 ⊆ Aut C2×C30120(C2xC30).9C2^2240,139
(C2×C30).10C22 = Dic5.D6φ: C22/C1C22 ⊆ Aut C2×C301204(C2xC30).10C2^2240,140
(C2×C30).11C22 = C30.C23φ: C22/C1C22 ⊆ Aut C2×C301204-(C2xC30).11C2^2240,141
(C2×C30).12C22 = C2×S3×Dic5φ: C22/C1C22 ⊆ Aut C2×C30120(C2xC30).12C2^2240,142
(C2×C30).13C22 = Dic3.D10φ: C22/C1C22 ⊆ Aut C2×C301204(C2xC30).13C2^2240,143
(C2×C30).14C22 = C2×D30.C2φ: C22/C1C22 ⊆ Aut C2×C30120(C2xC30).14C2^2240,144
(C2×C30).15C22 = C2×C15⋊D4φ: C22/C1C22 ⊆ Aut C2×C30120(C2xC30).15C2^2240,145
(C2×C30).16C22 = C2×C3⋊D20φ: C22/C1C22 ⊆ Aut C2×C30120(C2xC30).16C2^2240,146
(C2×C30).17C22 = C2×C5⋊D12φ: C22/C1C22 ⊆ Aut C2×C30120(C2xC30).17C2^2240,147
(C2×C30).18C22 = C2×C15⋊Q8φ: C22/C1C22 ⊆ Aut C2×C30240(C2xC30).18C2^2240,148
(C2×C30).19C22 = C3×D42D5φ: C22/C1C22 ⊆ Aut C2×C301204(C2xC30).19C2^2240,160
(C2×C30).20C22 = C5×D42S3φ: C22/C1C22 ⊆ Aut C2×C301204(C2xC30).20C2^2240,170
(C2×C30).21C22 = C15×C4○D4φ: C22/C2C2 ⊆ Aut C2×C301202(C2xC30).21C2^2240,188
(C2×C30).22C22 = C4×Dic15φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).22C2^2240,72
(C2×C30).23C22 = C30.4Q8φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).23C2^2240,73
(C2×C30).24C22 = C605C4φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).24C2^2240,74
(C2×C30).25C22 = D303C4φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).25C2^2240,75
(C2×C30).26C22 = C30.38D4φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).26C2^2240,80
(C2×C30).27C22 = C2×Dic30φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).27C2^2240,175
(C2×C30).28C22 = C2×C4×D15φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).28C2^2240,176
(C2×C30).29C22 = C2×D60φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).29C2^2240,177
(C2×C30).30C22 = D6011C2φ: C22/C2C2 ⊆ Aut C2×C301202(C2xC30).30C2^2240,178
(C2×C30).31C22 = C22×Dic15φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).31C2^2240,183
(C2×C30).32C22 = C12×Dic5φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).32C2^2240,40
(C2×C30).33C22 = C3×C10.D4φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).33C2^2240,41
(C2×C30).34C22 = C3×C4⋊Dic5φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).34C2^2240,42
(C2×C30).35C22 = C3×D10⋊C4φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).35C2^2240,43
(C2×C30).36C22 = C3×C23.D5φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).36C2^2240,48
(C2×C30).37C22 = C6×Dic10φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).37C2^2240,155
(C2×C30).38C22 = D5×C2×C12φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).38C2^2240,156
(C2×C30).39C22 = C6×D20φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).39C2^2240,157
(C2×C30).40C22 = C3×C4○D20φ: C22/C2C2 ⊆ Aut C2×C301202(C2xC30).40C2^2240,158
(C2×C30).41C22 = C2×C6×Dic5φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).41C2^2240,163
(C2×C30).42C22 = Dic3×C20φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).42C2^2240,56
(C2×C30).43C22 = C5×Dic3⋊C4φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).43C2^2240,57
(C2×C30).44C22 = C5×C4⋊Dic3φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).44C2^2240,58
(C2×C30).45C22 = C5×D6⋊C4φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).45C2^2240,59
(C2×C30).46C22 = C5×C6.D4φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).46C2^2240,64
(C2×C30).47C22 = C10×Dic6φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).47C2^2240,165
(C2×C30).48C22 = S3×C2×C20φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).48C2^2240,166
(C2×C30).49C22 = C10×D12φ: C22/C2C2 ⊆ Aut C2×C30120(C2xC30).49C2^2240,167
(C2×C30).50C22 = C5×C4○D12φ: C22/C2C2 ⊆ Aut C2×C301202(C2xC30).50C2^2240,168
(C2×C30).51C22 = Dic3×C2×C10φ: C22/C2C2 ⊆ Aut C2×C30240(C2xC30).51C2^2240,173
(C2×C30).52C22 = C15×C22⋊C4central extension (φ=1)120(C2xC30).52C2^2240,82
(C2×C30).53C22 = C15×C4⋊C4central extension (φ=1)240(C2xC30).53C2^2240,83
(C2×C30).54C22 = Q8×C30central extension (φ=1)240(C2xC30).54C2^2240,187

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