The attempt to study magnetism in (n,m) chiral space of single-walled carbon nanotubes (SWNTs) with embedded metal cluster is presented. Co13 metallic cluster inside zigzag and chiral single-walled nanotubes was investigated using density functional theory (DFT). Magnetic properties of the endohedral nanotubes with the various chiral index (n,m) were characterized by calculation of the total spin magnetic moment (S). The dependence of S on the chiral symmetry of nanotubes, as well as the orientation of Co13 cluster within nanotubes was found. Longitudinal orientation of icosahedral Co13 cluster was preferable for magnetization in general. However, it was shown that the magnetic landscape M = f(n,m) of endohedral nanotubes is very complex and sharp.