If you don't need to give special permissions to each subject, you could have the subjects as Taxonomies with this extension https://discuss.flarum.org/d/30499-flamarkt-taxonomies
Then the same taxonomy will be usable under any primary tag, and you can filter the homepage by subject with the Taxonomy filter (option "show on homepage")
You could also do the opposite and have classes be taxonomies, or both.
Using Tags is necessary if you want to scope permissions, as Taxonomies don't have that feature.
If you don't want to use another extension, you could have the subjects are secondary tags. But if you have other secondary tags they will all be mixed together in the selection modal.