In this question:
The answer indicates that the order of all points on the curve over the finite field
2^255 - 19 is 8 times the size of the subgroup formed by G.
i.e. the subgroup size is
2^252+27742317777372353535851937790883648493 whereas the number of points in the curve itself is 8(𝑝1).
The answer then states: "This means that there are a few remaining points that have small order."
However, as stated in the answer the
few remaining points are in fact 8 times the number of points in the cyclic subgroup G.
So how can one conclude that the remaining points form small order groups?
Isn't there scope for a group within the set of remaining points to be bigger than 𝑝1?
How do we know the other points not inside 𝑝1, form a variety of small order groups?