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Extensions 1→N→G→Q→1 with N=C5×Q8 and Q=D6

Direct product G=N×Q with N=C5×Q8 and Q=D6
dρLabelID
S3×Q8×C10240S3xQ8xC10480,1157

Semidirect products G=N:Q with N=C5×Q8 and Q=D6
extensionφ:Q→Out NdρLabelID
(C5×Q8)⋊D6 = D5×GL2(𝔽3)φ: D6/C1 → D6 ⊆ Out C5×Q8404(C5xQ8):D6480,974
(C5×Q8)⋊2D6 = C2×Q8⋊D15φ: D6/C2 → S3 ⊆ Out C5×Q880(C5xQ8):2D6480,1028
(C5×Q8)⋊3D6 = C10×GL2(𝔽3)φ: D6/C2 → S3 ⊆ Out C5×Q880(C5xQ8):3D6480,1017
(C5×Q8)⋊4D6 = D5×Q8⋊2S3φ: D6/C3 → C22 ⊆ Out C5×Q81208+(C5xQ8):4D6480,577
(C5×Q8)⋊5D6 = D20⋊D6φ: D6/C3 → C22 ⊆ Out C5×Q81208+(C5xQ8):5D6480,578
(C5×Q8)⋊6D6 = D15⋊SD16φ: D6/C3 → C22 ⊆ Out C5×Q81208-(C5xQ8):6D6480,581
(C5×Q8)⋊7D6 = D60⋊C22φ: D6/C3 → C22 ⊆ Out C5×Q81208+(C5xQ8):7D6480,582
(C5×Q8)⋊8D6 = SD16×D15φ: D6/C3 → C22 ⊆ Out C5×Q81204(C5xQ8):8D6480,878
(C5×Q8)⋊9D6 = Q8⋊3D30φ: D6/C3 → C22 ⊆ Out C5×Q81204+(C5xQ8):9D6480,879
(C5×Q8)⋊10D6 = S3×Q8⋊D5φ: D6/S3 → C2 ⊆ Out C5×Q81208+(C5xQ8):10D6480,579
(C5×Q8)⋊11D6 = D12⋊D10φ: D6/S3 → C2 ⊆ Out C5×Q81208+(C5xQ8):11D6480,580
(C5×Q8)⋊12D6 = S3×Q8×D5φ: D6/S3 → C2 ⊆ Out C5×Q81208-(C5xQ8):12D6480,1107
(C5×Q8)⋊13D6 = D5×Q8⋊3S3φ: D6/S3 → C2 ⊆ Out C5×Q81208+(C5xQ8):13D6480,1108
(C5×Q8)⋊14D6 = S3×Q8⋊2D5φ: D6/S3 → C2 ⊆ Out C5×Q81208+(C5xQ8):14D6480,1109
(C5×Q8)⋊15D6 = D20⋊16D6φ: D6/S3 → C2 ⊆ Out C5×Q81208-(C5xQ8):15D6480,1110
(C5×Q8)⋊16D6 = D20⋊17D6φ: D6/S3 → C2 ⊆ Out C5×Q81208+(C5xQ8):16D6480,1111
(C5×Q8)⋊17D6 = C5×S3×SD16φ: D6/S3 → C2 ⊆ Out C5×Q81204(C5xQ8):17D6480,792
(C5×Q8)⋊18D6 = C5×Q8⋊3D6φ: D6/S3 → C2 ⊆ Out C5×Q81204(C5xQ8):18D6480,793
(C5×Q8)⋊19D6 = C2×Q8⋊2D15φ: D6/C6 → C2 ⊆ Out C5×Q8240(C5xQ8):19D6480,906
(C5×Q8)⋊20D6 = D4⋊D30φ: D6/C6 → C2 ⊆ Out C5×Q81204+(C5xQ8):20D6480,914
(C5×Q8)⋊21D6 = C2×Q8×D15φ: D6/C6 → C2 ⊆ Out C5×Q8240(C5xQ8):21D6480,1172
(C5×Q8)⋊22D6 = C2×Q8⋊3D15φ: D6/C6 → C2 ⊆ Out C5×Q8240(C5xQ8):22D6480,1173
(C5×Q8)⋊23D6 = C4○D4×D15φ: D6/C6 → C2 ⊆ Out C5×Q81204(C5xQ8):23D6480,1175
(C5×Q8)⋊24D6 = D4⋊8D30φ: D6/C6 → C2 ⊆ Out C5×Q81204+(C5xQ8):24D6480,1176
(C5×Q8)⋊25D6 = C10×Q8⋊2S3φ: D6/C6 → C2 ⊆ Out C5×Q8240(C5xQ8):25D6480,820
(C5×Q8)⋊26D6 = C5×D4⋊D6φ: D6/C6 → C2 ⊆ Out C5×Q81204(C5xQ8):26D6480,828
(C5×Q8)⋊27D6 = C10×Q8⋊3S3φ: trivial image240(C5xQ8):27D6480,1158
(C5×Q8)⋊28D6 = C5×S3×C4○D4φ: trivial image1204(C5xQ8):28D6480,1160
(C5×Q8)⋊29D6 = C5×D4○D12φ: trivial image1204(C5xQ8):29D6480,1161

Non-split extensions G=N.Q with N=C5×Q8 and Q=D6
extensionφ:Q→Out NdρLabelID
(C5×Q8).1D6 = CSU2(𝔽3)⋊D5φ: D6/C1 → D6 ⊆ Out C5×Q81604(C5xQ8).1D6480,967
(C5×Q8).2D6 = Dic5.6S4φ: D6/C1 → D6 ⊆ Out C5×Q8804(C5xQ8).2D6480,968
(C5×Q8).3D6 = Dic5.7S4φ: D6/C1 → D6 ⊆ Out C5×Q8804+(C5xQ8).3D6480,969
(C5×Q8).4D6 = GL2(𝔽3)⋊D5φ: D6/C1 → D6 ⊆ Out C5×Q8804+(C5xQ8).4D6480,970
(C5×Q8).5D6 = D5×CSU2(𝔽3)φ: D6/C1 → D6 ⊆ Out C5×Q8804-(C5xQ8).5D6480,971
(C5×Q8).6D6 = D10.1S4φ: D6/C1 → D6 ⊆ Out C5×Q8804-(C5xQ8).6D6480,972
(C5×Q8).7D6 = D10.2S4φ: D6/C1 → D6 ⊆ Out C5×Q8804(C5xQ8).7D6480,973
(C5×Q8).8D6 = C2×Q8.D15φ: D6/C2 → S3 ⊆ Out C5×Q8160(C5xQ8).8D6480,1027
(C5×Q8).9D6 = Q8.D30φ: D6/C2 → S3 ⊆ Out C5×Q8804(C5xQ8).9D6480,1029
(C5×Q8).10D6 = C20.2S4φ: D6/C2 → S3 ⊆ Out C5×Q81604-(C5xQ8).10D6480,1030
(C5×Q8).11D6 = C20.6S4φ: D6/C2 → S3 ⊆ Out C5×Q8804(C5xQ8).11D6480,1031
(C5×Q8).12D6 = C20.3S4φ: D6/C2 → S3 ⊆ Out C5×Q8804+(C5xQ8).12D6480,1032
(C5×Q8).13D6 = C10×CSU2(𝔽3)φ: D6/C2 → S3 ⊆ Out C5×Q8160(C5xQ8).13D6480,1016
(C5×Q8).14D6 = C5×Q8.D6φ: D6/C2 → S3 ⊆ Out C5×Q8804(C5xQ8).14D6480,1018
(C5×Q8).15D6 = C5×C4.S4φ: D6/C2 → S3 ⊆ Out C5×Q81604(C5xQ8).15D6480,1019
(C5×Q8).16D6 = C5×C4.6S4φ: D6/C2 → S3 ⊆ Out C5×Q8802(C5xQ8).16D6480,1020
(C5×Q8).17D6 = C5×C4.3S4φ: D6/C2 → S3 ⊆ Out C5×Q8804(C5xQ8).17D6480,1021
(C5×Q8).18D6 = D5×C3⋊Q16φ: D6/C3 → C22 ⊆ Out C5×Q82408-(C5xQ8).18D6480,583
(C5×Q8).19D6 = D20.13D6φ: D6/C3 → C22 ⊆ Out C5×Q82408-(C5xQ8).19D6480,584
(C5×Q8).20D6 = D15⋊Q16φ: D6/C3 → C22 ⊆ Out C5×Q82408-(C5xQ8).20D6480,587
(C5×Q8).21D6 = C60.C23φ: D6/C3 → C22 ⊆ Out C5×Q82408+(C5xQ8).21D6480,588
(C5×Q8).22D6 = D12.27D10φ: D6/C3 → C22 ⊆ Out C5×Q82408-(C5xQ8).22D6480,589
(C5×Q8).23D6 = D20.14D6φ: D6/C3 → C22 ⊆ Out C5×Q82408-(C5xQ8).23D6480,590
(C5×Q8).24D6 = C60.39C23φ: D6/C3 → C22 ⊆ Out C5×Q82408+(C5xQ8).24D6480,591
(C5×Q8).25D6 = D20.D6φ: D6/C3 → C22 ⊆ Out C5×Q82408+(C5xQ8).25D6480,592
(C5×Q8).26D6 = D20.16D6φ: D6/C3 → C22 ⊆ Out C5×Q82408+(C5xQ8).26D6480,597
(C5×Q8).27D6 = D20.17D6φ: D6/C3 → C22 ⊆ Out C5×Q82408-(C5xQ8).27D6480,598
(C5×Q8).28D6 = D12.D10φ: D6/C3 → C22 ⊆ Out C5×Q82408+(C5xQ8).28D6480,599
(C5×Q8).29D6 = D30.44D4φ: D6/C3 → C22 ⊆ Out C5×Q82408-(C5xQ8).29D6480,600
(C5×Q8).30D6 = SD16⋊D15φ: D6/C3 → C22 ⊆ Out C5×Q82404-(C5xQ8).30D6480,880
(C5×Q8).31D6 = D4.5D30φ: D6/C3 → C22 ⊆ Out C5×Q82404(C5xQ8).31D6480,881
(C5×Q8).32D6 = Q16×D15φ: D6/C3 → C22 ⊆ Out C5×Q82404-(C5xQ8).32D6480,882
(C5×Q8).33D6 = Q16⋊D15φ: D6/C3 → C22 ⊆ Out C5×Q82404(C5xQ8).33D6480,883
(C5×Q8).34D6 = D120⋊8C2φ: D6/C3 → C22 ⊆ Out C5×Q82404+(C5xQ8).34D6480,884
(C5×Q8).35D6 = S3×C5⋊Q16φ: D6/S3 → C2 ⊆ Out C5×Q82408-(C5xQ8).35D6480,585
(C5×Q8).36D6 = Dic10.26D6φ: D6/S3 → C2 ⊆ Out C5×Q82408-(C5xQ8).36D6480,586
(C5×Q8).37D6 = D20.27D6φ: D6/S3 → C2 ⊆ Out C5×Q82408-(C5xQ8).37D6480,593
(C5×Q8).38D6 = D20.28D6φ: D6/S3 → C2 ⊆ Out C5×Q82408-(C5xQ8).38D6480,594
(C5×Q8).39D6 = Dic10.27D6φ: D6/S3 → C2 ⊆ Out C5×Q82408+(C5xQ8).39D6480,595
(C5×Q8).40D6 = C60.44C23φ: D6/S3 → C2 ⊆ Out C5×Q82408+(C5xQ8).40D6480,596
(C5×Q8).41D6 = D20.29D6φ: D6/S3 → C2 ⊆ Out C5×Q82408-(C5xQ8).41D6480,1104
(C5×Q8).42D6 = C30.33C24φ: D6/S3 → C2 ⊆ Out C5×Q82408+(C5xQ8).42D6480,1105
(C5×Q8).43D6 = D12.29D10φ: D6/S3 → C2 ⊆ Out C5×Q82408-(C5xQ8).43D6480,1106
(C5×Q8).44D6 = C5×D4.D6φ: D6/S3 → C2 ⊆ Out C5×Q82404(C5xQ8).44D6480,794
(C5×Q8).45D6 = C5×Q8.7D6φ: D6/S3 → C2 ⊆ Out C5×Q82404(C5xQ8).45D6480,795
(C5×Q8).46D6 = C5×S3×Q16φ: D6/S3 → C2 ⊆ Out C5×Q82404(C5xQ8).46D6480,796
(C5×Q8).47D6 = C5×Q16⋊S3φ: D6/S3 → C2 ⊆ Out C5×Q82404(C5xQ8).47D6480,797
(C5×Q8).48D6 = C5×D24⋊C2φ: D6/S3 → C2 ⊆ Out C5×Q82404(C5xQ8).48D6480,798
(C5×Q8).49D6 = Q8.11D30φ: D6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).49D6480,907
(C5×Q8).50D6 = C2×C15⋊7Q16φ: D6/C6 → C2 ⊆ Out C5×Q8480(C5xQ8).50D6480,908
(C5×Q8).51D6 = D4.8D30φ: D6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).51D6480,915
(C5×Q8).52D6 = D4.9D30φ: D6/C6 → C2 ⊆ Out C5×Q82404-(C5xQ8).52D6480,916
(C5×Q8).53D6 = Q8.15D30φ: D6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).53D6480,1174
(C5×Q8).54D6 = D4.10D30φ: D6/C6 → C2 ⊆ Out C5×Q82404-(C5xQ8).54D6480,1177
(C5×Q8).55D6 = C5×Q8.11D6φ: D6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).55D6480,821
(C5×Q8).56D6 = C10×C3⋊Q16φ: D6/C6 → C2 ⊆ Out C5×Q8480(C5xQ8).56D6480,822
(C5×Q8).57D6 = C5×Q8.13D6φ: D6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).57D6480,829
(C5×Q8).58D6 = C5×Q8.14D6φ: D6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).58D6480,830
(C5×Q8).59D6 = C5×Q8.15D6φ: trivial image2404(C5xQ8).59D6480,1159
(C5×Q8).60D6 = C5×Q8○D12φ: trivial image2404(C5xQ8).60D6480,1162

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