Sort objects in List by properties on the object

You could use linq extensions (leaving the original list unsorted):

var sorted = theList.OrderBy(o => o.code1).ThenBy(o => o.code2);

To replace the original list with a sorted one, make a slight amendment (not very efficient, it creates a new list):

theList = theList.OrderBy(o => o.code1).ThenBy(o => o.code2).ToList();

This assumes that your list is of the correct type, something like:

List<MyClass> theList = new List<MyClass>();

And not a list of objects, in which case you would need to make use of .Cast<>() or .OfType<>().

Note that Adam Houldsworth's answer with the .ToList() call needlessly creates a new list. If your list is large, this may create unacceptable memory pressure. It would most likely be better to sort the list in place by providing a custom comparison function:

theList.Sort((a, b) =>
    {
        var firstCompare = a.code1.CompareTo(b.code1);
        return firstCompare != 0 ? firstCompare : a.code2.CompareTo(b.code2);
    });

Alternatively, if this ordering is an intrinsic property of your type, you could implement IComparable<T> on your type, and just call

theList.Sort();

... which will use the IComparable<T>.CompareTo() implementation.