  Generalised parallelisable spaces permit to uplift many maximal gauged
supergravities to ten or eleven dimensions. While some of the former are
explicitly known, the literature is still lacking a systematic construction and
a complete classification. We resolve this issue and present an explicit
construction, and with it a full classification, of generalised parallelisable
spaces for maximal gauged supergravities in four or more dimensions. All
embedding tensors that can be realised without breaking the section condition
of exceptional field theory are identified and the corresponding generalised
frame fields are constructed. This finally resolved the old question: "Which
maximal gauged supergravities have uplifts to 10/11d?". Furthermore, it
provides the basis to explore solution generating techniques based on
generalised dualities.
