Moving a large table to another filegroup I have a 30 million row table, which is causing performance issues. I thought of moving it to a new filegroup for better performance. 

My questions are: 

This table has many foreign key references. If I just move the clustered index to another filegroup, will it still work right? Or do I also need to move the references to the new filegroup? 

How about leaving the nonclustered indexes on the old filegroup? 

Please suggest on my approach and my question.
Yes your Foreign Key constraints (References) will work once you move the clustered index to a different filegroup.
You can leave the non-clustered indexes in the old file group (in my personal opinion it has some advantage to have clustered and non clustered index  in different file group especially if the underlying disks are different and write heavy workload)
Remember when you create a non-clustered index by default it goes to the same file group where your clustered index is. If you want non-clustered indexes in a separate file group you need to explicitly mention that. Here is a good example of this.