Classification of simple groups upto order 200

Abstract

In this paper the focus is on simple groups up to order 200. After explaining the basic notions of a group, abelian groups, subgroup, p-subgroup, sylow p-subgroup various result/theorems that can be used to test that a group is simple or not are given. While we are talking about the simple groups a the main thing which is to be kept in mind that group of prime order is always simple. So as we discuss about the classification of simple groups it should be clear that we will discuss only groups of Composite order as a group of prime order is always simple. All the results which are to be used are proved mainly using sylow’s theorems. So after proving sylow theorem and using them to derive all the results that are to be used. we arrive at the conclusion that the only simple groups up to order 200 are only of order 60,168. Rest of the groups of Composite order are not simple by one way or another.