We report extensive calculations of energy positions and autoionization widths for the doubly excited states of H-2 between the first and the second ionization thresholds. We present results for 60 doubly excited states of the (1,3)Sigma(g,u)(+), (1,3)Pi(g,u), and (1,3)Delta(g,u) symmetries in the range of internuclear distances 0 less than or equal to R less than or equal to 5 a.u. The resonance parameters have been obtained using the Feshbach theory and an L-2 representation of the non resonant continuum with B-spline functions, We discuss the main features of the energy correlation diagrams and the corresponding widths. We point out the existence of avoided crossings in the Franck-Condon region that significantly affect the autoionization properties of the doubly excited states, Our data are compared with previous results reported in the literature.