# Extensions 1→N→G→Q→1 with N=S3×C10 and Q=C2×C4

Direct product G=N×Q with N=S3×C10 and Q=C2×C4
dρLabelID
S3×C22×C20240S3xC2^2xC20480,1151

Semidirect products G=N:Q with N=S3×C10 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(S3×C10)⋊1(C2×C4) = F5×D12φ: C2×C4/C1C2×C4 ⊆ Out S3×C10608+(S3xC10):1(C2xC4)480,995
(S3×C10)⋊2(C2×C4) = D603C4φ: C2×C4/C1C2×C4 ⊆ Out S3×C10608+(S3xC10):2(C2xC4)480,997
(S3×C10)⋊3(C2×C4) = F5×C3⋊D4φ: C2×C4/C1C2×C4 ⊆ Out S3×C10608(S3xC10):3(C2xC4)480,1010
(S3×C10)⋊4(C2×C4) = C3⋊D4⋊F5φ: C2×C4/C1C2×C4 ⊆ Out S3×C10608(S3xC10):4(C2xC4)480,1012
(S3×C10)⋊5(C2×C4) = C2×D6⋊F5φ: C2×C4/C2C4 ⊆ Out S3×C10120(S3xC10):5(C2xC4)480,1000
(S3×C10)⋊6(C2×C4) = S3×C22⋊F5φ: C2×C4/C2C4 ⊆ Out S3×C10608+(S3xC10):6(C2xC4)480,1011
(S3×C10)⋊7(C2×C4) = C22×S3×F5φ: C2×C4/C2C4 ⊆ Out S3×C1060(S3xC10):7(C2xC4)480,1197
(S3×C10)⋊8(C2×C4) = Dic54D12φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10):8(C2xC4)480,481
(S3×C10)⋊9(C2×C4) = Dic1514D4φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10):9(C2xC4)480,482
(S3×C10)⋊10(C2×C4) = Dic5×D12φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10):10(C2xC4)480,491
(S3×C10)⋊11(C2×C4) = Dic158D4φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10):11(C2xC4)480,511
(S3×C10)⋊12(C2×C4) = D6⋊(C4×D5)φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10):12(C2xC4)480,516
(S3×C10)⋊13(C2×C4) = Dic159D4φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10):13(C2xC4)480,518
(S3×C10)⋊14(C2×C4) = D5×D6⋊C4φ: C2×C4/C2C22 ⊆ Out S3×C10120(S3xC10):14(C2xC4)480,547
(S3×C10)⋊15(C2×C4) = D30.27D4φ: C2×C4/C2C22 ⊆ Out S3×C10120(S3xC10):15(C2xC4)480,549
(S3×C10)⋊16(C2×C4) = Dic5×C3⋊D4φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10):16(C2xC4)480,627
(S3×C10)⋊17(C2×C4) = Dic1517D4φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10):17(C2xC4)480,636
(S3×C10)⋊18(C2×C4) = C4×C15⋊D4φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10):18(C2xC4)480,515
(S3×C10)⋊19(C2×C4) = C1517(C4×D4)φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10):19(C2xC4)480,517
(S3×C10)⋊20(C2×C4) = C4×C5⋊D12φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10):20(C2xC4)480,521
(S3×C10)⋊21(C2×C4) = C1522(C4×D4)φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10):21(C2xC4)480,522
(S3×C10)⋊22(C2×C4) = S3×C2×C4×D5φ: C2×C4/C4C2 ⊆ Out S3×C10120(S3xC10):22(C2xC4)480,1086
(S3×C10)⋊23(C2×C4) = C20×D12φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10):23(C2xC4)480,752
(S3×C10)⋊24(C2×C4) = C5×Dic34D4φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10):24(C2xC4)480,760
(S3×C10)⋊25(C2×C4) = C5×Dic35D4φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10):25(C2xC4)480,772
(S3×C10)⋊26(C2×C4) = C20×C3⋊D4φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10):26(C2xC4)480,807
(S3×C10)⋊27(C2×C4) = C2×D6⋊Dic5φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10):27(C2xC4)480,614
(S3×C10)⋊28(C2×C4) = S3×C23.D5φ: C2×C4/C22C2 ⊆ Out S3×C10120(S3xC10):28(C2xC4)480,630
(S3×C10)⋊29(C2×C4) = C22×S3×Dic5φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10):29(C2xC4)480,1115
(S3×C10)⋊30(C2×C4) = C5×S3×C22⋊C4φ: C2×C4/C22C2 ⊆ Out S3×C10120(S3xC10):30(C2xC4)480,759
(S3×C10)⋊31(C2×C4) = C10×D6⋊C4φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10):31(C2xC4)480,806

Non-split extensions G=N.Q with N=S3×C10 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(S3×C10).1(C2×C4) = D12.2F5φ: C2×C4/C1C2×C4 ⊆ Out S3×C102408-(S3xC10).1(C2xC4)480,987
(S3×C10).2(C2×C4) = D12.F5φ: C2×C4/C1C2×C4 ⊆ Out S3×C102408-(S3xC10).2(C2xC4)480,989
(S3×C10).3(C2×C4) = C5⋊C8.D6φ: C2×C4/C1C2×C4 ⊆ Out S3×C102408(S3xC10).3(C2xC4)480,1003
(S3×C10).4(C2×C4) = D15⋊C8⋊C2φ: C2×C4/C1C2×C4 ⊆ Out S3×C102408(S3xC10).4(C2xC4)480,1005
(S3×C10).5(C2×C4) = C4⋊F53S3φ: C2×C4/C2C4 ⊆ Out S3×C101208(S3xC10).5(C2xC4)480,983
(S3×C10).6(C2×C4) = (C4×S3)⋊F5φ: C2×C4/C2C4 ⊆ Out S3×C101208(S3xC10).6(C2xC4)480,985
(S3×C10).7(C2×C4) = S3×D5⋊C8φ: C2×C4/C2C4 ⊆ Out S3×C101208(S3xC10).7(C2xC4)480,986
(S3×C10).8(C2×C4) = S3×C4.F5φ: C2×C4/C2C4 ⊆ Out S3×C101208(S3xC10).8(C2xC4)480,988
(S3×C10).9(C2×C4) = D15⋊M4(2)φ: C2×C4/C2C4 ⊆ Out S3×C101208(S3xC10).9(C2xC4)480,991
(S3×C10).10(C2×C4) = C5⋊C8⋊D6φ: C2×C4/C2C4 ⊆ Out S3×C101208(S3xC10).10(C2xC4)480,993
(S3×C10).11(C2×C4) = C4×S3×F5φ: C2×C4/C2C4 ⊆ Out S3×C10608(S3xC10).11(C2xC4)480,994
(S3×C10).12(C2×C4) = S3×C4⋊F5φ: C2×C4/C2C4 ⊆ Out S3×C10608(S3xC10).12(C2xC4)480,996
(S3×C10).13(C2×C4) = C2×S3×C5⋊C8φ: C2×C4/C2C4 ⊆ Out S3×C10240(S3xC10).13(C2xC4)480,1002
(S3×C10).14(C2×C4) = S3×C22.F5φ: C2×C4/C2C4 ⊆ Out S3×C101208-(S3xC10).14(C2xC4)480,1004
(S3×C10).15(C2×C4) = C2×D6.F5φ: C2×C4/C2C4 ⊆ Out S3×C10240(S3xC10).15(C2xC4)480,1008
(S3×C10).16(C2×C4) = D5×C8⋊S3φ: C2×C4/C2C22 ⊆ Out S3×C101204(S3xC10).16(C2xC4)480,320
(S3×C10).17(C2×C4) = C40⋊D6φ: C2×C4/C2C22 ⊆ Out S3×C101204(S3xC10).17(C2xC4)480,322
(S3×C10).18(C2×C4) = C40.34D6φ: C2×C4/C2C22 ⊆ Out S3×C102404(S3xC10).18(C2xC4)480,342
(S3×C10).19(C2×C4) = C40.35D6φ: C2×C4/C2C22 ⊆ Out S3×C102404(S3xC10).19(C2xC4)480,344
(S3×C10).20(C2×C4) = D12.2Dic5φ: C2×C4/C2C22 ⊆ Out S3×C102404(S3xC10).20(C2xC4)480,362
(S3×C10).21(C2×C4) = D12.Dic5φ: C2×C4/C2C22 ⊆ Out S3×C102404(S3xC10).21(C2xC4)480,364
(S3×C10).22(C2×C4) = D6.(C4×D5)φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10).22(C2xC4)480,474
(S3×C10).23(C2×C4) = (S3×Dic5)⋊C4φ: C2×C4/C2C22 ⊆ Out S3×C10240(S3xC10).23(C2xC4)480,476
(S3×C10).24(C2×C4) = S3×C8×D5φ: C2×C4/C4C2 ⊆ Out S3×C101204(S3xC10).24(C2xC4)480,319
(S3×C10).25(C2×C4) = S3×C8⋊D5φ: C2×C4/C4C2 ⊆ Out S3×C101204(S3xC10).25(C2xC4)480,321
(S3×C10).26(C2×C4) = C40.54D6φ: C2×C4/C4C2 ⊆ Out S3×C102404(S3xC10).26(C2xC4)480,341
(S3×C10).27(C2×C4) = C40.55D6φ: C2×C4/C4C2 ⊆ Out S3×C102404(S3xC10).27(C2xC4)480,343
(S3×C10).28(C2×C4) = C4×S3×Dic5φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10).28(C2xC4)480,473
(S3×C10).29(C2×C4) = S3×C10.D4φ: C2×C4/C4C2 ⊆ Out S3×C10240(S3xC10).29(C2xC4)480,475
(S3×C10).30(C2×C4) = S3×D10⋊C4φ: C2×C4/C4C2 ⊆ Out S3×C10120(S3xC10).30(C2xC4)480,548
(S3×C10).31(C2×C4) = C5×C8○D12φ: C2×C4/C4C2 ⊆ Out S3×C102402(S3xC10).31(C2xC4)480,780
(S3×C10).32(C2×C4) = C5×D12.C4φ: C2×C4/C4C2 ⊆ Out S3×C102404(S3xC10).32(C2xC4)480,786
(S3×C10).33(C2×C4) = C2×S3×C52C8φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10).33(C2xC4)480,361
(S3×C10).34(C2×C4) = S3×C4.Dic5φ: C2×C4/C22C2 ⊆ Out S3×C101204(S3xC10).34(C2xC4)480,363
(S3×C10).35(C2×C4) = C2×D6.Dic5φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10).35(C2xC4)480,370
(S3×C10).36(C2×C4) = (S3×C20)⋊5C4φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10).36(C2xC4)480,414
(S3×C10).37(C2×C4) = (S3×C20)⋊7C4φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10).37(C2xC4)480,447
(S3×C10).38(C2×C4) = S3×C4⋊Dic5φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10).38(C2xC4)480,502
(S3×C10).39(C2×C4) = C5×C422S3φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10).39(C2xC4)480,751
(S3×C10).40(C2×C4) = C5×C4⋊C47S3φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10).40(C2xC4)480,771
(S3×C10).41(C2×C4) = C10×C8⋊S3φ: C2×C4/C22C2 ⊆ Out S3×C10240(S3xC10).41(C2xC4)480,779
(S3×C10).42(C2×C4) = S3×C4×C20φ: trivial image240(S3xC10).42(C2xC4)480,750
(S3×C10).43(C2×C4) = C5×S3×C4⋊C4φ: trivial image240(S3xC10).43(C2xC4)480,770
(S3×C10).44(C2×C4) = S3×C2×C40φ: trivial image240(S3xC10).44(C2xC4)480,778
(S3×C10).45(C2×C4) = C5×S3×M4(2)φ: trivial image1204(S3xC10).45(C2xC4)480,785

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