Cyclic groups are those that are generated by a single permutation. When a permutation is represented in cycle notation, the order of the cyclic subgroup that it generates is the least common multiple of the lengths of its cycles. For example, in S 5, one cyclic subgroup of order 5 is generated by (13254), whereas the largest cyclic subgroups of S 5 are generated by elements like (123)(45) that have one cycle of length 3 and another cycle of length 2. This rules out many groups as possible subgroups of symmetric groups of a given size. For example, S 5 has no subgroup of order 15 (a divisor of the order of S 5), because the only group of order 15 is the cyclic group. The largest possible order of a cyclic subgroup (equivalently, the largest possible order of an element in S n) is given by Landau's function.