We investigate the magnetotransport properties of strained 80 nm thick HgTe layers featuring a high mobility of mu similar to 4 x 10(5) cm(2/)V . s. By means of a top gate, the Fermi energy is tuned from the valence band through the Dirac-type surface states into the conduction band. Magnetotransport measurements allow us to disentangle the different contributions of conduction band electrons, holes, and Dirac electrons to the conductivity. The results are in line with previous claims that strained HgTe is a topological insulator with a bulk gap of approximate to 15 meV and gapless surface states.