Login to your D* user account and go to products.
You will find the following info and a picture of the specified remote.
I bought one and it is identical in appearance and function to the one that came with my H10.
Note the "Universal" in the first sentence below.
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Replace a lost or damaged remote control with a DIRECTV® Universal Remote Control for your receiver for only $15.
This remote works with all DIRECTV® Receivers except the Samsung 360 HD Receiver. If you need to replace a remote for a Samsung 360 HD Receiver, please contact your local retailer.
If you rent your DIRECTV® System or if it is covered under the DIRECTV Protection Plan, you may be eligible to get your first remote control replacement for free. Please call for details. All additional remotes are $15.
Your new DIRECTV® Universal Remote is under a 90-day warranty -- just call 1-800-DIRECTV if it fails in that time frame.
Your new remote should arrive via FedEx in 3-4 business days.