Question: The [Whitney graph isomorphism theorem](https://en.wikipedia.org/wiki/Line_graph#Whitney_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](http://en.wikipedia.org/wiki/Classification_of_finite_simple_groups#Statement_of_the_classification_theorem): 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](https://en.wiktionary.org/wiki/sporadically).
> 
> 
> 

(A late thanks to Asaf!)

Answer: 
Here's a beautiful theorem of Peter J Cameron from the theory of designs: 

**Theorem.** 
If symmetric $2-(v,k,\lambda)$ design $\mathscr{D}$ extends, then it is one of the following :

1. $2-(4\lambda+3,\;\; 2\lambda+1,\;\; \lambda )$1
2. $2-((\lambda+2)(\lambda^2+4\lambda+2), \;\;\lambda^2+3\lambda+1, \;\;\lambda)$
3. $2-(495,39,3)$

This appeared in the 1973 paper of Prof. P J Cameron [Cam]. When it was stated, the existence of the design of parameters $2-(111, 11, 1)$2 was yet undecided. It has been now proved with an extensive computer search $[10]$ that this design does not exist.

**Some (perhaps) Useful References.** 

[Cam] **Cameron P. J.,** 
 Extending Symmetric Designs,
 *Journal of Combinatorial Theory, Series A*
 Vol. 14, Issue 2 (Mar., 1973), pp. 215-220. 

$[10]$ **Lam C. W. H., Thiel L. H., Swiercz S.,**
 The Non-existence of Finite Projective Plane of Order 10
 *Can. J. Math.,*
**XLI** (1989), pp. 1117-1123.

 1 Note that these are the parameters of a Hadamard $2$-design.  

2Some readers will recognise that this is a projective plane of order 10.
The number of partitions of $n\geq 0$ into parts congruent to $\pm 1,
\pm 4, \pm 5, \pm 6, \pm 7, \pm 9, \pm 11, \pm 13, \pm 16, \pm 21, \pm
23, \pm 28$ (mod 66) is equal to the number of partitions of $n\geq 0$
into parts congruent to $\pm 1, \pm 4, \pm 5, \pm 6, \pm 7, \pm 9, \pm
11, \pm 14, \pm 16, \pm 17, \pm 27, \pm 29$ (mod 66) except for
$n=13$. See [here](https://qseries.org/fgarvan/papers/shifted.pdf) and [here](https://arxiv.org/pdf/math/0605317.pdf) for this and
many similar results.