In [28] S.J.Pride defined the concept of a large property of groups in order to give precision to vague notions of "largeness" and "smallness" in infinite group theory, and showed that any group G generates a large property t(G). He defined a quasi-ordering ≤ on the class of groups by letting H ≤ G if G has t(H), and by symmetrisation defined an equivalence relation = (that is, H = G if and only if H ≤ G and G ≤ H). This gives a partial ordering - the largeness ordering, also denoted ≤ - on the collection L of = -equivalence classes [G]. In this thesis we study these concepts and investigate the largeness of certain types of groups.