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In this paper, charged asymptotically flat black hole solutions are numerically constructed in the Einstein-Maxwell-Weyl gravity. These solutions can be interpreted as generalizations of two different groups of non-charged asymptotically flat spacetimes: Schwarzschild black hole (SBH) and non-Schwarzschild black hole (NSBH) solutions. In addition, we discuss the thermodynamic properties of two groups of charged black holes in detail, and show that these obey the first law of thermodynamics of black hole.