SubGen generates Monte-Carlo samples of dark matter subhaloes. It fully describes the joint distribution of subhaloes in final mass, infall mass, and radius; it can be used to predict derived distributions involving combinations of these quantities, including the universal subhalo mass function, the subhalo spatial distribution, the gravitational lensing profile, the dark matter annihilation radiation profile and boost factor. SubGen works only for CDM subhaloes; for an extension of the code to also work with WDM subhaloes, see SubGen2 (ascl:2312.036).