  In this paper we give a classification of symplectic birational involutions
of manifolds of $OG10$-type. We approach this classification with three
techniques - via involutions of the Leech lattice, via involutions of cubic
fourfolds and finally lattice enumeration via a modified Kneser's neighbour
algorithm. In particular, the classification consists of three involutions with
an explicit geometric realisation via cubic fourfolds, and three exceptional
involutions which cannot be obtained by any known construction.
