To quote from Remy Landau's website:
The 19 year cycle does not cause the Hebrew calendar to repeat itself every 19 Hebrew years. The 19 year cycle only refers to the positions of the 13-month years in those cycles. These years are the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of the cycle. Any of those years can be either 383, 384, or 385 days long.
Moreover all periods of 19 Hebrew years can be either 6938, 6939, 6940, 6941, or 6942 days each. Since none of these values are exact multiples of 7 it follows that no two consecutive periods of 19 years can begin on the same day of the week. Hence, the Hebrew calendar clearly does not repeat itself after every 19 years.
At one time some authorities suggested that the calendar would repeat itself after every 13 cycles of 19 years, that is, once every 247 years. However, simple arithmetic shows that the 247 year cycle is short by 905 halaqim (about 50 minutes) and therefore cannot be a full repetition cycle.
Periods of 247 Hebrew years can be either 90214d, 90215d, or 90216d. The period of 90,216d is a complete number of weeks and occurs 98% of the time over the full Hebrew calendar repetition cycle.
The true calendar repetition cycle is 689,472 Hebrew years long, requiring 36,288 cycles of 19 years.
I'm not aware of any online resources that list years together with their length, but I happen to have created a helpful calendar in Excel, and have made the first 6000 years available as a Google Sheet here.
For your purposes, you would want to look up the relevant year number in column B and then move across to column G to see whether the year is shleimah, kesidrah or chaseirah.