One of the reasons mathematicians and physicists are interested in Lie groups is that these groups are very good at describing the symmetries which occur in nature. For instance, rotations in three dimensions can be described either with the Lie group SO(3,R) or the Lie group SU(2,C). Rather than studying the groups themselves, it is often useful to study "infinitesimal versions" of the group transformations. These infinitesimal transformations form a Lie algebra corresponding to the group, and all of the information contained in a Lie algebra, including its multiplication table, can be encoded into a highly symmetric diagram called a "Root" diagram. In this talk, I will demonstrate two methods that use root diagrams to visually identify the subalgebras of a Lie algebra. In particular, these two methods will be applied to algebras (F_4, A_5, and E_6) whose root diagrams are of dimension 4, 5, and 6.