We determine the phase diagram of a quasi-one-dimensional conductor (w
eakly coupled chains system with an open Fermi surface) in a magnetic
field. The superconducting state evolves from an Abrikosov vortex latt
ice in weak field to a Josephson vortex lattice in very strong field,
with a reentrance of the superconducting phase. Between these two limi
ts, there is a cascade of first order transitions between different su
perconducting phases due to commensurability effects between the cryst
alline lattice and the order parameter. In these phases, the order par
ameter has a laminar structure.