Abstarct: To solve differential equations is of particular importance in all sciences because the analysis of the problems can be done by using responses. However , achieving all responses may not be always easy. Therefore ,we use supporting devices . Of these devices , one is symmetry group . Through having one response and putting it in symmetry groups we can achieves lots of responses . Yet there is a variety of ways to achieve symmetry groups . In this thesis , two more practical ways are tried to be done . At first , for achieving symmetry groups , the vector fields method has been considered and the differential forms method is stated along side . Harrison method is also pointed.