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Based on high throughput density functional theory calculations, we evaluated systematically the stability of 580 M₂AX compounds. The thermodynamic, mechanical, and dynamical stability and the magnetic structure are calculated. We found 20 compounds fulfilling all three stability criteria, confirming Cr₂AlC, Cr₂GeC, Cr₂GaC, Cr₂GaN, and Mn₂GaC, which have been synthesized. The stability trends with respect to the M- and A-elements are discussed by analyzing the formation energies, indicating that Cr and Mn containing M₂AX compounds are more stable than Fe, Co, or Ni containing compounds. Further insights on the stability are obtained by detailed analysis of the crystal orbital Hamilton population (COHP).