We investigate the subhalo populations of dark matter haloes in the concordance Λ cold dark matter (ΛCDM) cosmology. We use a large cosmological simulation and a variety of high-resolution resimulations of individual cluster and galaxy haloes to study the systematics of subhalo populations over ranges of 1000 in halo mass and 1000 in the ratio of subhalo to parent halo mass. The subhalo populations of different haloes are not scaled copies of each other, but vary systematically with halo properties. On average, the amount of substructure increases with halo mass. At fixed mass, it decreases with halo concentration and with halo formation redshift. These trends are comparable in size to the scatter in subhalo abundance between similar haloes. Averaged over all haloes of given mass, the abundance of low-mass subhaloes per unit parent halo mass is independent of parent mass. It is very similar to the abundance per unit mass of low-mass haloes in the Universe as a whole, once differing boundary definitions for subhaloes and haloes are accounted for. The radial distribution of subhaloes within their parent haloes is substantially less centrally concentrated than that of the dark matter. It varies at most weakly with the mass (or concentration) of the parent halo and not at all with subhalo mass. It does depend on the criteria used to define the subhalo population considered. About 90 per cent of present-day subhaloes were accreted after z= 1 and about 70 per cent after z= 0.5. Only about 8 per cent of the total mass of all haloes accreted at z= 1 survives as bound subhaloes at z= 0. For haloes accreted at z= 2, the survival mass fraction is just 2 per cent. Subhaloes seen near the centre of their parent typically were accreted earlier and retain less of their original mass than those seen near the edge. These strong systematics mean that comparison with galaxies in real clusters is only possible if the formation of the luminous component is modelled appropriately.