PUZZLE 119 A Friend for Y

Here are several letters divided into three groups.
The group on the left contains 'M' and 'U', the group in the middle contains 'H' and 'O', and the group on the right contains 'C' and 'E'.
The middle group has the special features of both the left and right groups.
Now 'Y' has come along, but which group should it join?

Hint 1

See if you can find the common characteristics of the letters in each group.
As a hint, 'D' would go in the right-hand group.

Hint 2

The letters are divided according to their shape.

Hint 3

Here is a hint: vertical and horizontal.

Super Hint

The letters on the left have a vertical line of symmetry.
The letters on the right have a horizontal line of symmetry.

Answer for 'A Friend for Y'

The answer is '1'.