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Extensions 1→N→G→Q→1 with N=D4 and Q=C5⋊D4

Direct product G=N×Q with N=D4 and Q=C5⋊D4
dρLabelID
D4×C5⋊D480D4xC5:D4320,1473

Semidirect products G=N:Q with N=D4 and Q=C5⋊D4
extensionφ:Q→Out NdρLabelID
D4⋊1(C5⋊D4) = Dic5⋊D8φ: C5⋊D4/Dic5 → C2 ⊆ Out D4160D4:1(C5:D4)320,777
D4⋊2(C5⋊D4) = D20⋊D4φ: C5⋊D4/D10 → C2 ⊆ Out D480D4:2(C5:D4)320,783
D4⋊3(C5⋊D4) = Dic10⋊D4φ: C5⋊D4/D10 → C2 ⊆ Out D4160D4:3(C5:D4)320,785
D4⋊4(C5⋊D4) = D20⋊18D4φ: C5⋊D4/D10 → C2 ⊆ Out D4408+D4:4(C5:D4)320,825
D4⋊5(C5⋊D4) = (C2×C10)⋊8D8φ: C5⋊D4/C2×C10 → C2 ⊆ Out D480D4:5(C5:D4)320,844
D4⋊6(C5⋊D4) = (C5×D4)⋊14D4φ: C5⋊D4/C2×C10 → C2 ⊆ Out D4160D4:6(C5:D4)320,865
D4⋊7(C5⋊D4) = 2+ 1+4⋊D5φ: C5⋊D4/C2×C10 → C2 ⊆ Out D4408+D4:7(C5:D4)320,868
D4⋊8(C5⋊D4) = C24.42D10φ: trivial image80D4:8(C5:D4)320,1478
D4⋊9(C5⋊D4) = C10.1042- 1+4φ: trivial image160D4:9(C5:D4)320,1496
D4⋊10(C5⋊D4) = C10.1452+ 1+4φ: trivial image80D4:10(C5:D4)320,1501

Non-split extensions G=N.Q with N=D4 and Q=C5⋊D4
extensionφ:Q→Out NdρLabelID
D4.1(C5⋊D4) = (C2×D8).D5φ: C5⋊D4/Dic5 → C2 ⊆ Out D4160D4.1(C5:D4)320,780
D4.2(C5⋊D4) = Dic5⋊3SD16φ: C5⋊D4/Dic5 → C2 ⊆ Out D4160D4.2(C5:D4)320,789
D4.3(C5⋊D4) = (C5×D4).D4φ: C5⋊D4/Dic5 → C2 ⊆ Out D4160D4.3(C5:D4)320,792
D4.4(C5⋊D4) = M4(2).D10φ: C5⋊D4/Dic5 → C2 ⊆ Out D4808+D4.4(C5:D4)320,826
D4.5(C5⋊D4) = M4(2).13D10φ: C5⋊D4/Dic5 → C2 ⊆ Out D4808-D4.5(C5:D4)320,827
D4.6(C5⋊D4) = M4(2).15D10φ: C5⋊D4/Dic5 → C2 ⊆ Out D4808+D4.6(C5:D4)320,830
D4.7(C5⋊D4) = M4(2).16D10φ: C5⋊D4/Dic5 → C2 ⊆ Out D41608-D4.7(C5:D4)320,831
D4.8(C5⋊D4) = D10⋊6SD16φ: C5⋊D4/D10 → C2 ⊆ Out D480D4.8(C5:D4)320,796
D4.9(C5⋊D4) = Dic10.16D4φ: C5⋊D4/D10 → C2 ⊆ Out D4160D4.9(C5:D4)320,800
D4.10(C5⋊D4) = D20.38D4φ: C5⋊D4/D10 → C2 ⊆ Out D4808-D4.10(C5:D4)320,828
D4.11(C5⋊D4) = D20.39D4φ: C5⋊D4/D10 → C2 ⊆ Out D4808+D4.11(C5:D4)320,829
D4.12(C5⋊D4) = D20.40D4φ: C5⋊D4/D10 → C2 ⊆ Out D4808-D4.12(C5:D4)320,832
D4.13(C5⋊D4) = (C5×D4).31D4φ: C5⋊D4/C2×C10 → C2 ⊆ Out D480D4.13(C5:D4)320,845
D4.14(C5⋊D4) = (C5×D4).32D4φ: C5⋊D4/C2×C10 → C2 ⊆ Out D4160D4.14(C5:D4)320,866
D4.15(C5⋊D4) = 2+ 1+4.D5φ: C5⋊D4/C2×C10 → C2 ⊆ Out D4808-D4.15(C5:D4)320,869
D4.16(C5⋊D4) = 2- 1+4⋊2D5φ: C5⋊D4/C2×C10 → C2 ⊆ Out D4808+D4.16(C5:D4)320,872
D4.17(C5⋊D4) = 2- 1+4.2D5φ: C5⋊D4/C2×C10 → C2 ⊆ Out D4808-D4.17(C5:D4)320,873
D4.18(C5⋊D4) = D20.32C23φ: trivial image808+D4.18(C5:D4)320,1507
D4.19(C5⋊D4) = D20.33C23φ: trivial image808-D4.19(C5:D4)320,1508
D4.20(C5⋊D4) = D20.34C23φ: trivial image808+D4.20(C5:D4)320,1509
D4.21(C5⋊D4) = D20.35C23φ: trivial image1608-D4.21(C5:D4)320,1510

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