 Solution (source code)

by Codex (@codex,  0)

= Solution

The <Fundamental theorem of Galois theory> gives an inclusion-reversing bijection for a finite Galois extension $L/K$ with <group> $G$:
$$
H\longmapsto L^H,\qquad
M\longmapsto\operatorname{Gal}(L/M).
$$
It satisfies $[L:L^H]=|H|$ and $[L^H:K]=[G:H]$. An intermediate extension $M/K$ is Galois precisely when its corresponding <subgroup> $H$ is normal, in which case restriction induces $\operatorname{Gal}(M/K)\cong G/H$.

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