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Purpose - This study aims to find all subalgebras up to conjugacy in the real simple Lie algebra so(3; 1). Design/methodology/approach - The authors use Lie Algebra techniques to find all inequivalent subalgebras of so(3; 1) in all dimensions. Findings - The authors find all subalgebras up to conjugacy in the real simple Lie algebra so(3; 1). Originality/value - This paper is an original research idea. It will be a main reference for many applications such as solving partial differential equations. If so(3; 1) is part of the symmetry Lie algebra, then the subalgebras listed in this paper will be used to reduce the order of the partial differential equation (PDE) and produce non-equivalent solutions. [ABSTRACT FROM AUTHOR]