  The aim of this paper is to study sub-algebras of the
$\mathbb{Z}/2$-equivariant Steenrod algebra (for cohomology with coefficients
in the constant Mackey functor $\mathbb{F}_2$) which come from quotient Hopf
algebroids of the $\mathbb{Z}/2$-equivariant dual Steenrod algebra. In
particular, we study the equivariant counterpart of profile functions, exhibit
the equivariant analogues of the classical $\mathcal{A}(n)$ and
$\mathcal{E}(n)$ and show that the Steenrod algebra is free as a module over
these.
