Topological defects are ubiquitously found in physical systems and therefore have been an important research subject of not only condensed matter physics but also cosmology. However, their fine structures remain elusive because of the microscopic scales involved. In the case of a liquid crystal, optical microscopy, although routinely used for the identification of liquid crystal phases and associated defects, does not have resolution high enough to distinguish fine structures of topological defects. Here we show that polarised and fluorescence microscopy, with the aid of numerical calculations on the orientational order and resulting image distortions, can uncover the structural states of topological defects with strength m = +/- 1 in a thin cell of a nematic liquid crystal. Particularly, defects with m = +1 exhibit four different states arising from chiral symmetry breaking and up-down symmetry breaking. Our results demonstrate that optical microscopy is still a powerful tool to identify fine states of liquid crystalline defects.