Millimeter wave spectroscopy has been used to record high-resolution spectra of high-n (n=51-64), low-l (l=1-3) Rydberg states of ortho H-2 located below the N+=1 rotational level of the X (2)Sigma (+)(g)(upsilon (+)=0) ground vibronic state of H-2(+). The spectral resolution of better than 1 MHz enables the observation of the hyperfine structure in these spectra. A simple procedure, based on the determination of combination differences, is used to reconstruct the energy level structure in np, nd, and nf Rydberg states of H-2. The Stark effect is used to distinguish experimentally between p and f Rydberg states. In the weakly penetrating nf series, the hyperfine interaction dominates and the observed hyperfine components are of mixed singlet (S=0) and triplet (S=1) character. In the penetrating np series, the dominant interactions are between the electron orbital and spin angular momenta and the molecular rotation and the observed hyperfine components are characterized by a well-defined total electron spin. The nd Rydberg states show a behavior intermediate between these two limiting cases. The observed levels are of mixed singlet (S=0) and triplet (S=1) character but the main energy separation departs from the energy separation between the G(c)=1/2 and G(c)=3/2 levels of the H-2(+) ion.