We report six new inflated hot Jupiters (HATS-25b through HATS-30b) discovered using the HATSouth global network of automated telescopes. The planets orbit stars with $V$ magnitudes in the range $sim 12-14$ and have masses in the largely populated $0.5M_J-0.7M_J$ region of parameter space but span a wide variety of radii, from $1.17R_J$ to $1.75 R_J$. HATS-25b, HATS-28b, HATS-29b and HATS-30b are typical inflated hot Jupiters ($R_p = 1.17-1.26R_J$) orbiting G-type stars in short period ($P=3.2-4.6$ days) orbits. However, HATS-26b ($R_p = 1.75R_J$, $P = 3.3024$ days) and HATS-27b ($R_p=1.50R_J$, $P=4.6370$ days) stand out as highly inflated planets orbiting slightly evolved F stars just after and in the turn-off points, respectively, which are among the least dense hot Jupiters, with densities of $0.153$ g cm$^{-3}$ and $0.180$ g cm$^{-3}$, respectively. All the presented exoplanets but HATS-27b are good targets for future atmospheric characterization studies, while HATS-27b is a prime target for Rossiter-McLaughlin monitoring in order to determine its spin-orbit alignment given the brightness ($V = 12.8$) and stellar rotational velocity ($v sin i approx 9.3$ km/s) of the host star. These discoveries significantly increase the number of inflated hot Jupiters known, contributing to our understanding of the mechanism(s) responsible for hot Jupiter inflation.
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