Fagi is difficult to differentiate from its close cousin, the Rock Grayling (H. alcyone). A more detailed appraisal of the differences (at least as they appear to me) is given on the alcyone page.

These are a selection of undersides showing the variation in the shape of the discal line and hence the difficulty in making an educated ID guess.

Many of the ID rationales are based on the size of the butterfly when seen at the time, plus the clear area (or not) around the ocellus (when visible).

observations

a clear bite out of the discal line, with a deep angled indent at v6, otherwise a reasonably straight discal line, with a clear white largely unmarked band, and the unf line only slightly angled at v4: all of these factors suggest alcyone, but my notes made at the time presumably suggested fagi on the grounds of size.

a strange underside, compared to the norm, with a very grey post-discal band, where it is normally white or pale, and well-contrasted to the grey areas. Maybe this indicates female. The discal line is quite smooth, without the usual sharp angles, and the bite is the roundest I have ever seen.

less clear, but I feel on balance this is still fagi. Records made at the time indicated it was rather large. Maybe a female on the basis of the heavy-ish irrorations and the lateness of the flight period.

a fagi from the central département of Côte-d'Or, toward the northern end of the range for fagi, and showing and unusually white and broad post-discal band. It was very large, so no doubt that it was fagi.

a female upperside seen during courtship.