In this work, we investigate the structural properties, distribution and abundance of ΛCDM dark matter subhaloes using the Phi-4096 and Uchuu suite of N-body cosmological simulations. Thanks to the combination of their large volume, high mass resolution and superb statistics, we are able to quantify -for the first time consistently over more than seven decades in ratio of subhalo-to-host-halo mass -dependencies of subhalo properties with mass, maximum circular velocity, 𝑉 max , host halo mass and distance to host halo centre. We also dissect the evolution of these dependencies over cosmic time. We provide accurate fits for the subhalo mass and velocity functions, both exhibiting decreasing power-law slopes in the expected range of values and with no significant dependence on redshift. We also find subhalo abundance to depend weakly on host halo mass. More precisely, we find a factor ∼ 2 − 3 more subhaloes in clustersize haloes compared to dwarf-size haloes at the present time, and more subhaloes at higher redshift for the same host halo mass, as expected from a less evolved population of subhaloes. We explore the distribution of subhaloes within their hosts and its evolution over cosmic time for subhaloes located as deep as ∼ 0.1 per cent of the host virial radius. Subhalo structural properties are codified via a concentration parameter, 𝑐 V , that does not depend on any specific, pre-defined density profile and relies only on 𝑉 max . We derive the 𝑐 V − 𝑉 max relation in the range 7 − 1500 km s −1 and find an important dependence on distance of the subhalo to the host halo centre, as already described in Moliné et al. (2017) for subhaloes in Milky-Way-like hosts. The innermost, less massive subhaloes exhibit 𝑐 v values a factor ∼ 3 higher than those located in the outskirts. This difference decreases to a factor ∼ 1.5 for the most massive subhaloes. Interestingly, we also find subhaloes of the same mass to be significantly more concentrated when they reside inside more massive hosts. Finally, we investigate the redshift evolution of 𝑐 v , and provide accurate fits that take into account all mentioned dependencies. Our results offer an unprecedented detailed characterization of the subhalo population, consistent over a wide range of subhalo and host halo masses, as well as cosmic times. Our work enables precision work in any future research involving dark matter halo substructure.