  The paper considers the plane one-dimensional flows for magnetohydrodynamics
in the mass Lagrangian coordinates. The inviscid, thermally non-conducting
medium is modeled by a polytropic gas. The equations are examined for
symmetries and conservation laws. For the case of the finite electric
conductivity we establish Lie group classification, i.e. we describe all cases
of the conductivity $ \sigma ( \rho , p)$ for which there are symmetry
extensions. The conservation laws are derived by the direct computation. For
the case of the infinite electrical conductivity the equations can be brought
into a variational form in the Lagrangian coordinates. Lie group classification
is performed for the entropy function as an arbitrary element. Using the
variational structure, we employ the Noether theorem for obtaining conservation
laws. The conservation laws are also given in the physical variables.
