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Extensions 1→N→G→Q→1 with N=C2×C10 and Q=D6

Direct product G=N×Q with N=C2×C10 and Q=D6
dρLabelID
S3×C22×C10120S3xC2^2xC10240,206

Semidirect products G=N:Q with N=C2×C10 and Q=D6
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊D6 = D5×S4φ: D6/C1 → D6 ⊆ Aut C2×C10206+(C2xC10):D6240,194
(C2×C10)⋊2D6 = C10×S4φ: D6/C2 → S3 ⊆ Aut C2×C10303(C2xC10):2D6240,196
(C2×C10)⋊3D6 = C2×C5⋊S4φ: D6/C2 → S3 ⊆ Aut C2×C10306+(C2xC10):3D6240,197
(C2×C10)⋊4D6 = D5×C3⋊D4φ: D6/C3 → C22 ⊆ Aut C2×C10604(C2xC10):4D6240,149
(C2×C10)⋊5D6 = D10⋊D6φ: D6/C3 → C22 ⊆ Aut C2×C10604+(C2xC10):5D6240,151
(C2×C10)⋊6D6 = D4×D15φ: D6/C3 → C22 ⊆ Aut C2×C10604+(C2xC10):6D6240,179
(C2×C10)⋊7D6 = C5×S3×D4φ: D6/S3 → C2 ⊆ Aut C2×C10604(C2xC10):7D6240,169
(C2×C10)⋊8D6 = S3×C5⋊D4φ: D6/S3 → C2 ⊆ Aut C2×C10604(C2xC10):8D6240,150
(C2×C10)⋊9D6 = C22×S3×D5φ: D6/S3 → C2 ⊆ Aut C2×C1060(C2xC10):9D6240,202
(C2×C10)⋊10D6 = C10×C3⋊D4φ: D6/C6 → C2 ⊆ Aut C2×C10120(C2xC10):10D6240,174
(C2×C10)⋊11D6 = C2×C15⋊7D4φ: D6/C6 → C2 ⊆ Aut C2×C10120(C2xC10):11D6240,184
(C2×C10)⋊12D6 = C23×D15φ: D6/C6 → C2 ⊆ Aut C2×C10120(C2xC10):12D6240,207

Non-split extensions G=N.Q with N=C2×C10 and Q=D6
extensionφ:Q→Aut NdρLabelID
(C2×C10).1D6 = C30.C23φ: D6/C3 → C22 ⊆ Aut C2×C101204-(C2xC10).1D6240,141
(C2×C10).2D6 = Dic3.D10φ: D6/C3 → C22 ⊆ Aut C2×C101204(C2xC10).2D6240,143
(C2×C10).3D6 = D4⋊2D15φ: D6/C3 → C22 ⊆ Aut C2×C101204-(C2xC10).3D6240,180
(C2×C10).4D6 = C5×D4⋊2S3φ: D6/S3 → C2 ⊆ Aut C2×C101204(C2xC10).4D6240,170
(C2×C10).5D6 = Dic3×Dic5φ: D6/S3 → C2 ⊆ Aut C2×C10240(C2xC10).5D6240,25
(C2×C10).6D6 = D10⋊Dic3φ: D6/S3 → C2 ⊆ Aut C2×C10120(C2xC10).6D6240,26
(C2×C10).7D6 = D6⋊Dic5φ: D6/S3 → C2 ⊆ Aut C2×C10120(C2xC10).7D6240,27
(C2×C10).8D6 = D30⋊4C4φ: D6/S3 → C2 ⊆ Aut C2×C10120(C2xC10).8D6240,28
(C2×C10).9D6 = C30.Q8φ: D6/S3 → C2 ⊆ Aut C2×C10240(C2xC10).9D6240,29
(C2×C10).10D6 = Dic15⋊5C4φ: D6/S3 → C2 ⊆ Aut C2×C10240(C2xC10).10D6240,30
(C2×C10).11D6 = C6.Dic10φ: D6/S3 → C2 ⊆ Aut C2×C10240(C2xC10).11D6240,31
(C2×C10).12D6 = C2×D5×Dic3φ: D6/S3 → C2 ⊆ Aut C2×C10120(C2xC10).12D6240,139
(C2×C10).13D6 = Dic5.D6φ: D6/S3 → C2 ⊆ Aut C2×C101204(C2xC10).13D6240,140
(C2×C10).14D6 = C2×S3×Dic5φ: D6/S3 → C2 ⊆ Aut C2×C10120(C2xC10).14D6240,142
(C2×C10).15D6 = C2×D30.C2φ: D6/S3 → C2 ⊆ Aut C2×C10120(C2xC10).15D6240,144
(C2×C10).16D6 = C2×C15⋊D4φ: D6/S3 → C2 ⊆ Aut C2×C10120(C2xC10).16D6240,145
(C2×C10).17D6 = C2×C3⋊D20φ: D6/S3 → C2 ⊆ Aut C2×C10120(C2xC10).17D6240,146
(C2×C10).18D6 = C2×C5⋊D12φ: D6/S3 → C2 ⊆ Aut C2×C10120(C2xC10).18D6240,147
(C2×C10).19D6 = C2×C15⋊Q8φ: D6/S3 → C2 ⊆ Aut C2×C10240(C2xC10).19D6240,148
(C2×C10).20D6 = C5×C4○D12φ: D6/C6 → C2 ⊆ Aut C2×C101202(C2xC10).20D6240,168
(C2×C10).21D6 = C4×Dic15φ: D6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).21D6240,72
(C2×C10).22D6 = C30.4Q8φ: D6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).22D6240,73
(C2×C10).23D6 = C60⋊5C4φ: D6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).23D6240,74
(C2×C10).24D6 = D30⋊3C4φ: D6/C6 → C2 ⊆ Aut C2×C10120(C2xC10).24D6240,75
(C2×C10).25D6 = C30.38D4φ: D6/C6 → C2 ⊆ Aut C2×C10120(C2xC10).25D6240,80
(C2×C10).26D6 = C2×Dic30φ: D6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).26D6240,175
(C2×C10).27D6 = C2×C4×D15φ: D6/C6 → C2 ⊆ Aut C2×C10120(C2xC10).27D6240,176
(C2×C10).28D6 = C2×D60φ: D6/C6 → C2 ⊆ Aut C2×C10120(C2xC10).28D6240,177
(C2×C10).29D6 = D60⋊11C2φ: D6/C6 → C2 ⊆ Aut C2×C101202(C2xC10).29D6240,178
(C2×C10).30D6 = C22×Dic15φ: D6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).30D6240,183
(C2×C10).31D6 = Dic3×C20central extension (φ=1)240(C2xC10).31D6240,56
(C2×C10).32D6 = C5×Dic3⋊C4central extension (φ=1)240(C2xC10).32D6240,57
(C2×C10).33D6 = C5×C4⋊Dic3central extension (φ=1)240(C2xC10).33D6240,58
(C2×C10).34D6 = C5×D6⋊C4central extension (φ=1)120(C2xC10).34D6240,59
(C2×C10).35D6 = C5×C6.D4central extension (φ=1)120(C2xC10).35D6240,64
(C2×C10).36D6 = C10×Dic6central extension (φ=1)240(C2xC10).36D6240,165
(C2×C10).37D6 = S3×C2×C20central extension (φ=1)120(C2xC10).37D6240,166
(C2×C10).38D6 = C10×D12central extension (φ=1)120(C2xC10).38D6240,167
(C2×C10).39D6 = Dic3×C2×C10central extension (φ=1)240(C2xC10).39D6240,173

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