  We report on the discovery and characterization of the transiting planet
K2-39b (EPIC 206247743b). With an orbital period of 4.6 days, it is the
shortest-period planet orbiting a subgiant star known to date. Such planets are
rare, with only a handful of known cases. The reason for this is poorly
understood, but may reflect differences in planet occurrence around the
relatively high-mass stars that have been surveyed, or may be the result of
tidal destruction of such planets. K2-39 is an evolved star with a
spectroscopically derived stellar radius and mass of
$3.88^{+0.48}_{-0.42}~\mathrm{R_\odot}$ and
$1.53^{+0.13}_{-0.12}~\mathrm{M_\odot}$, respectively, and a very close-in
transiting planet, with $a/R_\star = 3.4$. Radial velocity (RV) follow-up using
the HARPS, FIES and PFS instruments leads to a planetary mass of
$50.3^{+9.7}_{-9.4}~\mathrm{M_\oplus}$. In combination with a radius
measurement of $8.3 \pm 1.1~\mathrm{R_\oplus}$, this results in a mean
planetary density of $0.50^{+0.29}_{-0.17}$ g~cm$^{-3}$. We furthermore
discover a long-term RV trend, which may be caused by a long-period planet or
stellar companion. Because K2-39b has a short orbital period, its existence
makes it seem unlikely that tidal destruction is wholly responsible for the
differences in planet populations around subgiant and main-sequence stars.
Future monitoring of the transits of this system may enable the detection of
period decay and constrain the tidal dissipation rates of subgiant stars.
