Sorting on a Composite Collection throws a NotSupportedException

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;
using System.Collections.ObjectModel;
using System.ComponentModel;

namespace TestCompositeCollection
{
public class A
{
string test;
public string Test { get { return test; } set { test = value; } }

public A(string a)
{
test = a;
}
}

/// <summary>
/// Interaction logic for Window1.xaml
/// </summary>
public partial class Window1 : Window
{
ObservableCollection<A> list1;
public Window1()
{
InitializeComponent();

list1 = new ObservableCollection<A>();
for (int i = 0; i < 9; i++)
{
list1.Add(new A(i.ToString()));
}

ObservableCollection<A> list2 = new ObservableCollection<A>();
for (int i = 10; i < 19; i++)
{
list2.Add(new A(i.ToString()));
}

CompositeCollection col = new CompositeCollection();
CollectionContainer c = new CollectionContainer();
c.Collection = list1;
col.Add(c);

c = new CollectionContainer();
c.Collection = list2;
col.Add(c);

CompositeCollection list = new CompositeCollection();
c = new CollectionContainer();
c.Collection = col;
list.Add(c);

testList.ItemsSource = list;

AddHandler(GridViewColumnHeader.ClickEvent, new RoutedEventHandler(test1));

}

public void test1(object sender, RoutedEventArgs e)
{
ICollectionView view = CollectionViewSource.GetDefaultView(testList.ItemsSource);
view.SortDescriptions.Add(new SortDescription("Test", ListSortDirection.Ascending));
}

public void test(object sender, RoutedEventArgs e)
{
list1.Add(new A("s"));
}
}
}