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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 Subfields Low Degree Siblings
13T2 $D_{13}$ $26$ $1$ 26T2
26T2 $D_{13}$ $26$ $-1$ $C_2$, $D_{13}$ 13T2
  displayed columns for results

Results are complete for degrees $\leq 23$.