flag rows in groups with multiple conditions

I looked here and elsewhere, but I cannot find something that does exactly what I'm looking to accomplish using R.

I have data similar to below, where col1 is a unique ID, col2 is a group ID variable, col3 is a status code. I need to flag all rows with the same group ID, and where any of those rows have a specific status code, X in this case, as == 1, otherwise 0.

ID   GroupID    Status   Flag
 1    100        A        1
 2    100        X        1
 3    102        A        0
 4    102        B        0
 5    103        B        1 
 6    103        X        1
 7    104        X        1
 8    104        X        1
 9    105        A        0
 10   105        C        0

I have tried writing some ifelse where groupID == groupID and status == X then 1 else 0, but that doesn't work. The pattern of Status is random. In this example, the GroupID is exclusively pairs, but I don't want to assume that in the code, b/c I have other instance where there are 3 or more rows in a GroupID.

It would be helpful if this were open ended IE I could add other conditions if necessary, like, for each matching group ID, where Status == X, and other or other, etc.

Thank you !