  We realise the first and second Grushin distributions as symmetry reductions
of the 3-dimensional Heisenberg distribution and 4-dimensional Engel
distribution respectively. Similarly, we realise the Martinet distribution as
an alternative symmetry reduction of the Engel distribution. These reductions
allow us to derive the integrability conditions for the Grushin and Martinet
distributions and build certain complexes of differential operators. These
complexes are well-behaved despite the distributions they resolve being
non-regular.
