# Extensions 1→N→G→Q→1 with N=C2×C4×D5 and Q=C6

Direct product G=N×Q with N=C2×C4×D5 and Q=C6
dρLabelID
D5×C22×C12240D5xC2^2xC12480,1136

Semidirect products G=N:Q with N=C2×C4×D5 and Q=C6
extensionφ:Q→Out NdρLabelID
(C2×C4×D5)⋊1C6 = C3×C4⋊D20φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):1C6480,688
(C2×C4×D5)⋊2C6 = C3×C202D4φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):2C6480,731
(C2×C4×D5)⋊3C6 = C6×D4×D5φ: C6/C3C2 ⊆ Out C2×C4×D5120(C2xC4xD5):3C6480,1139
(C2×C4×D5)⋊4C6 = C6×D42D5φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):4C6480,1140
(C2×C4×D5)⋊5C6 = C6×Q82D5φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):5C6480,1143
(C2×C4×D5)⋊6C6 = C3×D5×C4○D4φ: C6/C3C2 ⊆ Out C2×C4×D51204(C2xC4xD5):6C6480,1145
(C2×C4×D5)⋊7C6 = C12×D20φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):7C6480,666
(C2×C4×D5)⋊8C6 = C3×D5×C22⋊C4φ: C6/C3C2 ⊆ Out C2×C4×D5120(C2xC4xD5):8C6480,673
(C2×C4×D5)⋊9C6 = C3×Dic54D4φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):9C6480,674
(C2×C4×D5)⋊10C6 = C3×D10.12D4φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):10C6480,676
(C2×C4×D5)⋊11C6 = C3×D10⋊D4φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):11C6480,677
(C2×C4×D5)⋊12C6 = C3×D208C4φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):12C6480,686
(C2×C4×D5)⋊13C6 = C3×D10.13D4φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):13C6480,687
(C2×C4×D5)⋊14C6 = C12×C5⋊D4φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):14C6480,721
(C2×C4×D5)⋊15C6 = C6×C4○D20φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5):15C6480,1138

Non-split extensions G=N.Q with N=C2×C4×D5 and Q=C6
extensionφ:Q→Out NdρLabelID
(C2×C4×D5).1C6 = C3×C4⋊C47D5φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).1C6480,685
(C2×C4×D5).2C6 = C3×D102Q8φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).2C6480,690
(C2×C4×D5).3C6 = C3×D5×M4(2)φ: C6/C3C2 ⊆ Out C2×C4×D51204(C2xC4xD5).3C6480,699
(C2×C4×D5).4C6 = C3×D103Q8φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).4C6480,739
(C2×C4×D5).5C6 = C6×Q8×D5φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).5C6480,1142
(C2×C4×D5).6C6 = C3×D101C8φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).6C6480,98
(C2×C4×D5).7C6 = C3×D10⋊C8φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).7C6480,283
(C2×C4×D5).8C6 = C3×D10.3Q8φ: C6/C3C2 ⊆ Out C2×C4×D5120(C2xC4xD5).8C6480,286
(C2×C4×D5).9C6 = C3×C42⋊D5φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).9C6480,665
(C2×C4×D5).10C6 = C3×D5×C4⋊C4φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).10C6480,684
(C2×C4×D5).11C6 = C3×D10⋊Q8φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).11C6480,689
(C2×C4×D5).12C6 = C6×C8⋊D5φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).12C6480,693
(C2×C4×D5).13C6 = C6×C4.F5φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).13C6480,1048
(C2×C4×D5).14C6 = C6×C4⋊F5φ: C6/C3C2 ⊆ Out C2×C4×D5120(C2xC4xD5).14C6480,1051
(C2×C4×D5).15C6 = C3×D5⋊M4(2)φ: C6/C3C2 ⊆ Out C2×C4×D51204(C2xC4xD5).15C6480,1049
(C2×C4×D5).16C6 = C3×D10.C23φ: C6/C3C2 ⊆ Out C2×C4×D51204(C2xC4xD5).16C6480,1052
(C2×C4×D5).17C6 = C6×D5⋊C8φ: C6/C3C2 ⊆ Out C2×C4×D5240(C2xC4xD5).17C6480,1047
(C2×C4×D5).18C6 = F5×C2×C12φ: C6/C3C2 ⊆ Out C2×C4×D5120(C2xC4xD5).18C6480,1050
(C2×C4×D5).19C6 = D5×C4×C12φ: trivial image240(C2xC4xD5).19C6480,664
(C2×C4×D5).20C6 = D5×C2×C24φ: trivial image240(C2xC4xD5).20C6480,692

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