Final answer:
The subject of the given sentence is 'Five groups' as they are the ones performing the action. The sentence has a grammatical error with the verb agreement and should use 'fly' to match the plural subject.
Step-by-step explanation:
In the sentence "Five groups of marathon runners flies past Mr. Lancaster on the way to the park," the subject is "Five groups." This is because the subject of a sentence is who or what the sentence is about, and in this case, it's the groups that are performing the action of flying past Mr. Lancaster. Note that the verb should actually agree with the plural subject, and thus it should be "fly" instead of "flies."