Virus particles and other protein-based supramolecular complexes have a vast nanotechnological potential. However, protein nanostructures are "soft" materials prone to disruption by force. Whereas some non-biological nanoparticles (NPs) may be stronger, for certain applications protein- and virus-based NPs have potential advantages related to their structure, self-assembly, production, engineering, and/or inbuilt functions. Thus, it may be desirable to acquire the knowledge needed to engineer protein-based nanomaterials with a higher strength against mechanical breakage. Here we have used the capsid of the minute virus of mice to experimentally identify individual chemical groups that determine breakage-related properties of a virus particle. Individual amino acid side chains that establish interactions between building blocks in the viral particle were truncated using protein engineering. Indentation experiments using atomic force microscopy were carried out to investigate the role of each targeted side chain in determining capsid strength and brittleness, by comparing the maximum force and deformation each modified capsid withstood before breaking apart. Side chains with major roles in determining capsid strength against breakage included polar groups located in solvent-exposed positions, and did not generally correspond with those previously identified as determinants of mechanical stiffness. In contrast, apolar side chains buried along the intersubunit interfaces that generally determined capsid stiffness had, at most, a minor influence on strength against disruption. Whereas no correlated variations between strength and either stiffness or brittleness were found, brittleness and stiffness were quantitatively correlated. Implications for developing robust protein-based NPs and for acquiring a deeper physics-based perspective of viruses are discussed.