We have used the quasiclassical trajectory (QCT) method to determine state-to-state rate coefficients for all transitions among the 348 (upsilon, j) states of the ground electronic state (Sigma(g)(+)) of the hydrogen molecule caused by collision with a hydrogen atom. Direct and indirect results were combined to give best possible rate coefficients within the quasiclassical approximation. Because energy transfer behavior differs for reactive and nonreactive channels and these channels are distinguishable classically, it is appropriate to consider separately the rate coefficients for each channel. Where available, quantum cross sections were incorporated into our calculation. The temperature dependence of the rate coefficients is parametrized over the temperature range 600 to 10 000 K. We use this complete set of state-to-state rate coefficients to test several scaling laws.