  In this work we will show that if $F$ is a positive integer, then
${\mathrm{Sat}}(F)=\{S\mid S \mbox{ is a saturated numerical semigroup with
Frobenius number } F\}$ is a covariety. As a consequence, we present two
algorithms: one that computes ${\mathrm{Sat}}(F),$ and the other which computes
all the elements of ${\mathrm{Sat}}(F)$ with a fixed genus.
  If $X\subseteq S\backslash \Delta(F)$ for some $S\in {\mathrm{Sat}}(F),$ then
we will see that there is the least element of ${\mathrm{Sat}}(F)$ containing a
$X$. This element will denote by ${\mathrm{Sat}}(F)[X].$
  If $S\in{\mathrm{Sat}}(F),$ then we define the ${\mathrm{Sat}}(F)$-rank of
$S$ as the minimum of $\{\mbox{cardinality}(X)\mid S={\mathrm{Sat}}(F)[X]\}.$
In this paper, also we present an algorithm to compute all the element of
${\mathrm{Sat}}(F)$ with a given
  ${\mathrm{Sat}}(F)$-rank.
