  The generalized Kawahara equation $u_t=a(t) u_{xxxxx} +b(t)u_{xxx} +c(t)f(u)
u_x$ appears in many physical applications. A complete classification of
low-order conservation laws and point symmetries is obtained for this equation,
which includes as a special case the usual Kawahara equation $u_t = \alpha u
u_x+\beta u^2u_x +\gamma u_{xxx}+\mu u_{xxxxx}$. A general connection between
conservation laws and symmetries for the generalized Kawahara equation is
derived through the Hamiltonian structure of this equation and its relationship
to Noether's theorem using a potential formulation.
