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The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)

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Results (displaying both matches)

  displayed columns for results
Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
20T6 $C_4\times D_5$ $40$ $-1$ $4$ $C_2$, $C_4$, $D_{5}$, $D_{10}$ 20T6, 40T9
40T9 $C_4\times D_5$ $40$ $1$ $40$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{5}$, $C_4\times C_2$, $D_5$, $D_{10}$ x 2, $D_{10}$, $C_4\times D_5$ x 2 20T6 x 2
  displayed columns for results