These words are easily confused. Subsequent means "succeeding," "following in order or time": "Subsequent to his release from prison, he got back his old job." Each of the following constructions indicates "later": "subsequent events," "a talk held subsequent to the party," "a talk held subsequently." Consequent means "following as a natural result, effect, or conclusion": "Reckless driving was the charge, and consequent investigation caused him to lose his license." A consequent occurrence is always a subsequent happening, but a subsequent event is not necessarily consequent.
Dictionary of problem words and expressions. Harry Shaw. 1975.