In this paper non abstract finite semigroups which satisfy classical Lagrange’s Theorem is analysed. It is found that finite
semigroups in general does not satisfy Lagrange’s theorem. So to overcome this problem two new properties satisfied by finite semigroups in terms of subsemigroups are defined. The two new notions are anti Lagrange’s property and weak Lagrange’s property. Finite semigroups in general satisfy both these properties barring the semigroup S={Zp, ×, p a prime} which does not satisfy weak Lagrange’s property.