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To manage progress toward the Sustainable Development Goals (SDGs), sustainability indicators and indices are useful analytical tools. Indices proposed in the literature rarely comprise all three contentual domains of sustainable development (environment, society, and economy), fail to enable comparisons of agents at multiple levels, and exhibit methodological shortcomings. Comparability of micro, meso, and macro agents is crucial because the macro SDGs can only be achieved if micro and meso agents contribute. Contributions must be measured in a methodologically sound manner to avoid misled decision making. To overcome these deficiencies, we develop the comprehensive and comparable Multilevel Sustainable Development Index (MLSDI). A novel information-theoretic algorithm is shown to outperform established multivariate statistical weighting methods such as the principal component analysis (PCA). The application of the MLSDI to 62 industries in the German economy reveals that the chemical industry requires urgent action with regard to environmental performances, and the agricultural industry demands assistance and action in all three domains. [ABSTRACT FROM AUTHOR]