From this, and using the fact that G has odd order, sufficient information is available to obtain estimates for |G| and arrive at a contradiction to the assumption that G is simple. This part of the argument works similarly in the CN-group case. In the proof of the Feit–Thompson theorem, however, this step is (as usual) vastly more complicated. The character theory only eliminates some of the possible configurations left after step 1. First they show that the maximal subgroups of type I are all Frobenius groups. If all maximal subgroups are type I then an argument similar to the CN case shows that the group G cannot be an odd-order minimal simple group, so there are exactly two classes of maximal subgroups of types II, III, IV or V. Most of the rest of the proof now focuses on these two types of maximal subgroup S and T and the relation between them. More character-theoretic arguments show that they cannot be of types IV or V. The two subgroups have a precise structure: the subgroup S is of order pq×q×(pq–1)/(p–1) and consists of all automorphisms of the underlying set of the finite field of order pq of the form x→axσ+b where a has norm 1 and σ is an automorphism of the finite field, where p and q are distinct primes. The maximal subgroup T has a similar structure with p and q reversed. The subgroups S and T are closely linked. Taking p>q, one can show that the cyclic subgroup of S of order (pq–1)/(p–1) is conjugate to a subgroup of the cyclic subgroup of T of order (qp–1)/(q–1). (In particular, the first number divides the second, so if the Feit–Thompson conjecture is true, it would assert that this cannot happen, and this could be used to finish the proof at this point. The conjecture is still unproven, however.) The conclusion from applying character theory to the group G is that G has the following structure: there are primes p>q such that (pq–1)/(p–1) is coprime to p–1 and G has a subgroup given by the semidirect product PU where P is the additive group of a finite field of order pq and U its elements of norm 1. Moreover G has an abelian subgroup Q of order prime to p containing an element y such that P0 normalizes Q and (P0)y normalizes U, where P0 is the additive