A Way to Construct Ten-Order Subgroup of A₅

The maximum order of A5's element is 5. By using Lagrange theorem, the could-be order of the element of A5's subgroup are 2 and 5, but in general the inverse of the Lagrange theorem is not hold, whether the ten-order subgroup of A5 exist is still a problem to discuss. Based on the researching and calculation on the power of 5-cyclic permutation, the forming law of the 10 order subgroup of A5 is fined and therefore 6 10-order subgroup of A5 are obtained by using the law.