The manifestations of topological effects in finite antiferromagnetic Heisenberg chains are examined by density-matrix renormalization-group techniques. We find that the difference between integer and half-integer spin chains shows up in ground-state energy per site when the length of the spin chain is longer than \ensuremath{\sim}\ensuremath{\xi}, where $\ensuremath{\xi}\ensuremath{\sim}\mathrm{exp}(\ensuremath{\pi}S)$ is a spin-spin correlation length, for spin magnitudes S up to
5/2. For open chains with spin magnitudes
S=5/2 to
S=5, we verify that end states with fractional spin quantum numbers ${S}^{\ensuremath{'}}$ exist and are visible in the structure of the low-energy excitation spectrum even when the chain length is much smaller than the correlation length \ensuremath{\xi}. The robustness of end states points to the possibility of the existence of general hidden topological order in quantum spin chains with spin magnitudes
S> 1.We propose a set of maximized string order parameters to describe the hidden topological order in the valence bond solid states of quantum integer spin- S chains. These optimized string order parameters involve spin-twist angles corresponding to Z S +1 rotations around z or x -axes, suggesting a hidden Z S +1 × Z S +1 symmetry. Our results also suggest that a local triplet excitation in the valence bond solid states carries a Z S +1 topological charge measured by these maximized string order parameters.