I recently stumbled upon the Mathieu groupoid and I found them fascinating.

It appears as a subset of $S_{13}$ which is not closed under multiplication, but it turns out to be a groupoid with 13 objects. The "first" sporadic finite simple group $M_{12}$ appear as the Automorphism of a point. One can further find $M_{11}$ from this.

Now that people classified finite simple groups with decades of effort, I'm wondering if there has been any attempt to classify finite groupoids.

(Maybe some results like this is already implied by the classification of finite simple groups, but the groupoid $M_{13}$ seems so amazing, so I got curious.)