  A scalar field with an exponential potential in FLRW universe admits the
exact solution. We uncover the hidden symmetries behind the system by utilising
the Eisenhart lift of field theories. We find that a conformal Killing vector
field in the field space exists only for a particular combination of
exponential functions which includes a single exponential potential. This
implies the existence of additional conserved quantity and explains the
integrability of the system.
