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Topological insulators (TIs), exhibiting the quantum spin Hall (QSH) effect, are promising for developing dissipationless transport devices that can be realized under a wide range of temperatures. The search for new two-dimensional (2D) TIs is essential for TIs to be utilized at room-temperature, with applications in optoelectronics, spintronics, and magnetic sensors. In this work, we used first-principles calculations to investigate the geometric, electronic, and topological properties of GeX and GeMX (M = C, N, P, As; X = H, F, Cl, Br, I, O, S, Se, Te). In 26 of these materials, the QSH effect is demonstrated by a spin–orbit coupling (SOC) induced large band gap and a band inversion at the Γ point, similar to the case of an HgTe quantum well. In addition, engineering the intra-layer strain of certain GeMX species can transform them from a regular insulator into a 2D TI. This work demonstrates that asymmetrical chemical functionalization is a promising method to induce the QSH effect in 2D hexagonal materials, paving the way for practical application of TIs in electronics.