Theorems with an extraordinary exception or a small number of sporadic exceptions

The Whitney graph isomorphism theorem gives an example of an extraordinary exception: a very general statement holds except for one very specific case.

Another example is the classification theorem for finite simple groups: a very general statement holds except for very few (26) sporadic cases.

I am looking for more of this kind of theorems-with-not-so-many-sporadic-exceptions

(added:) where the exceptions don’t come in a row and/or
in the beginning – but are scattered truly sporadically.

(A late thanks to Asaf!)

Every automorphism of $S_n$ is inner if $n \neq 6$.
P.S. That $S_6$ has an `essentially’ unique outer automorphism is quite a non-obvious fact.