Predicting crystal symmetry simply from chemical composition has remained challenging. Several machine-learning approaches can be employed, but the predictive value of popular crystallographic databases is relatively modest due to the paucity of data and uneven distribution across the 230 space groups. In this work, virtually all crystallographic information available to science has been compiled and used to train and test multiple machine-learning models. Composition-driven random-forest classification relying on a large set of descriptors showed the best performance. The predictive models for crystal system, Bravais lattice, point group and space group of inorganic compounds are made publicly available as easy-to-use software downloadable from https://gitlab.com/vishsoft/cosy.