This paper aims to treat a study on the order of every element in the higher even, odd and prime order of group for composition. Infact, express order of a group and order of an element of a group in real numbers. Here we discuss the higher order of groups indifferent types of order, which will give us practical knowledge to see the applications of the composition. In order to find out theorder of an elementam2Gin whichan=e= identity element, then find the least common multiple (i.e.(LCM))=𝜆) ofmandn. The leastcommon multiple of two numbers is the "smallest non-zero common number," which is a multiple of both the numbers. SoO(am)=𝜆/m. Also, ifGis a finite group,nis a positive integer, anda2Gthen the order of the productsna. WhenGis a finite group, everyelement must have finite order, but the converse is false. There are infinite groups where each element has finite order. Finally, findout the order of every element of a group in different types of the higher even, odd and prime order of group for composition.