The subquery is being run for each row because it is a correlated query. One can make a correlated query into a non-correlated query by selecting everything from the subquery, like so:
SELECT * FROM
(
SELECT relevant_field
FROM some_table
GROUP BY relevant_field
HAVING COUNT(*) > 1
) AS subquery
The final query would look like this:
SELECT *
FROM some_table
WHERE relevant_field IN
(
SELECT * FROM
(
SELECT relevant_field
FROM some_table
GROUP BY relevant_field
HAVING COUNT(*) > 1
) AS subquery
)