  We study a subclass of Horndeski gravity which has both global conformal and
shift symmetries. Global symmetries are characterised by the presence of a
conserved current which has been shown to be of particular importance for the
integrability features of the theory at hand yielding numerous compact object
solutions. We find the general conserved current associated to global conformal
symmetry of Horndeski theories. We discuss some of its properties, how it can
be conveniently broken by physically relevant terms and, show how it is related
to that of shift symmetry when shift symmetry is present. Given our results, we
consider a particular theory and demonstrate how the presence of symmetries
provides integrability for the given black hole solution. We then find the
charged extension of the solution thanks to the conformal invariance of the
Maxwell action.
