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Extensions 1→N→G→Q→1 with N=C4 and Q=C5⋊D4

Direct product G=N×Q with N=C4 and Q=C5⋊D4
dρLabelID
C4×C5⋊D480C4xC5:D4160,149

Semidirect products G=N:Q with N=C4 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C5⋊D4) = C20⋊D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C480C4:1(C5:D4)160,161
C4⋊2(C5⋊D4) = C20⋊2D4φ: C5⋊D4/D10 → C2 ⊆ Aut C480C4:2(C5:D4)160,159
C4⋊3(C5⋊D4) = C20⋊7D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C480C4:3(C5:D4)160,151

Non-split extensions G=N.Q with N=C4 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C4.1(C5⋊D4) = C5⋊D16φ: C5⋊D4/Dic5 → C2 ⊆ Aut C4804+C4.1(C5:D4)160,33
C4.2(C5⋊D4) = D8.D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C4804-C4.2(C5:D4)160,34
C4.3(C5⋊D4) = C5⋊SD32φ: C5⋊D4/Dic5 → C2 ⊆ Aut C4804+C4.3(C5:D4)160,35
C4.4(C5⋊D4) = C5⋊Q32φ: C5⋊D4/Dic5 → C2 ⊆ Aut C41604-C4.4(C5:D4)160,36
C4.5(C5⋊D4) = C2×D4⋊D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C480C4.5(C5:D4)160,152
C4.6(C5⋊D4) = C2×D4.D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C480C4.6(C5:D4)160,154
C4.7(C5⋊D4) = C20.17D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C480C4.7(C5:D4)160,157
C4.8(C5⋊D4) = C2×Q8⋊D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C480C4.8(C5:D4)160,162
C4.9(C5⋊D4) = C2×C5⋊Q16φ: C5⋊D4/Dic5 → C2 ⊆ Aut C4160C4.9(C5:D4)160,164
C4.10(C5⋊D4) = Dic5⋊Q8φ: C5⋊D4/Dic5 → C2 ⊆ Aut C4160C4.10(C5:D4)160,165
C4.11(C5⋊D4) = C20.23D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C480C4.11(C5:D4)160,168
C4.12(C5⋊D4) = D4⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C480C4.12(C5:D4)160,39
C4.13(C5⋊D4) = C20.D4φ: C5⋊D4/D10 → C2 ⊆ Aut C4404C4.13(C5:D4)160,40
C4.14(C5⋊D4) = Q8⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C4160C4.14(C5:D4)160,42
C4.15(C5⋊D4) = C20.10D4φ: C5⋊D4/D10 → C2 ⊆ Aut C4804C4.15(C5:D4)160,43
C4.16(C5⋊D4) = D4.D10φ: C5⋊D4/D10 → C2 ⊆ Aut C4404C4.16(C5:D4)160,153
C4.17(C5⋊D4) = C20.C23φ: C5⋊D4/D10 → C2 ⊆ Aut C4804C4.17(C5:D4)160,163
C4.18(C5⋊D4) = D10⋊3Q8φ: C5⋊D4/D10 → C2 ⊆ Aut C480C4.18(C5:D4)160,167
C4.19(C5⋊D4) = C20.44D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C4160C4.19(C5:D4)160,23
C4.20(C5⋊D4) = D20⋊5C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C480C4.20(C5:D4)160,28
C4.21(C5⋊D4) = C20.46D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C4404+C4.21(C5:D4)160,30
C4.22(C5⋊D4) = C4.12D20φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C4804-C4.22(C5:D4)160,31
C4.23(C5⋊D4) = C20.48D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C480C4.23(C5:D4)160,145
C4.24(C5⋊D4) = D4⋊D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C4404+C4.24(C5:D4)160,170
C4.25(C5⋊D4) = D4.9D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C4804-C4.25(C5:D4)160,172
C4.26(C5⋊D4) = C20.8Q8central extension (φ=1)160C4.26(C5:D4)160,21
C4.27(C5⋊D4) = D10⋊1C8central extension (φ=1)80C4.27(C5:D4)160,27
C4.28(C5⋊D4) = C20.53D4central extension (φ=1)804C4.28(C5:D4)160,29
C4.29(C5⋊D4) = D20⋊7C4central extension (φ=1)404C4.29(C5:D4)160,32
C4.30(C5⋊D4) = C20.55D4central extension (φ=1)80C4.30(C5:D4)160,37
C4.31(C5⋊D4) = D4⋊2Dic5central extension (φ=1)404C4.31(C5:D4)160,44
C4.32(C5⋊D4) = D4.8D10central extension (φ=1)804C4.32(C5:D4)160,171

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