We investigate the class of Banach spaces that can be subspaces of indecomposable Banach spaces of densities up to continuum showing that it includes all Banach spaces of such densities which do not admit $\ell_\infty$ as quotients. It remains open if every Banach space that does not contain a copy of $\ell_\infty$ is a subspace of an indecomposable Banach space. The constructed indecomposable Banach space including an appropriate Banach space $X$ is a subalgebra of the algebra $C(K)$, where $K$ is the Cech-Stone remainder of the cartesian product of the dual ball of $X$ and the euclidean plane. The results were obtainen together with Zdenek Silber.