Transforming the Letters

In Miss Chan's class, a group were working with a box of large wooden capital letters. They were exploring what happened when they rotated them one half turn, or flipped them sideways and from top to bottom.
They started with "F". They found four Fs in the box.
"Billy, you just push yours into the middle of the table," said Katie who was rather bossy, "then we can see how the others change."
Here is Billy's F:

"I'll turn my F upside-down," continued Katie, "that's half a turn."
"A $180^o$ turn about its centre," remarked Ali.
This is what Katie's looked like:

George said, "I'll flip mine over sideways."
Here is George's F:

"That leaves me to flip my F from top to bottom," said Ali.
So then Ali's looked like this:

"Look, they are all different. I wonder if all the letters are like that. Which ones shall we try?"
Katie had spelt out Miss Chan's name with four of the letters:

"Let's try with those," suggested George. So they did.

What did they find out?

"What happens if you do a half turn followed by a sideways flip?" wondered Ali. "Do you think any of the letters in the box get back to the same as they were to begin with?"

They did find some which did just that. Which letters are they?

Do these letters also go back to the same if you do a half turn followed by a flip from top to bottom?