Too many joins can make a query perform poorly and it can help to break down an extremely large query, especially if some of them are filtering logic joins and...

It's difficult to tell from this small a sample of data, but here's a couple of options, depending on how many rows per GROUPID you have in your history table...

The 2 are not necessarily correlated.  You can get a quick summary of file latency and a view of how much log space is used like this:
SELECT...

I'd say my favorite would have banana peppers, sausage, and black olives on it.  I'm not much a fan of Pizza Hut's crust though, there's some local chains I prefer...

Have you looked at the execution plan of the stored proc to see if the index is actually used?
Also, what other queries are executed against this table UO_MList?  If...

It's actually a 20% threshold for autoupdate of stats, although there's a trace flag that can somewhat improve that behavior.  Here's an article that has many subtopics about database statistics:

you can get some information about growths by looking at the default trace:
--history
DECLARE @path NVARCHAR(260);
SELECT @path = REVERSE(SUBSTRING(REVERSE([path]), CHARINDEX('\', REVERSE([path])), 260)) + N'log.trc'
...

the other easy option that comes to mind then is a SQL Server Agent job that has a step of type:
Operating System (CmdExec)