My laptop is pretty capable of running Skyrim on my 1080p display with all settings maxed out except for antialiasing and anisotropic filtering (which are both set to low levels) at around 60 frames per second, according to the Razer Game Booster. I also have a borderless window mod installed to help achieve that good framerate.
I decided to take my laptop upstairs, as I so rarely do, and it of course requires that I disconnect my external display from my laptop. As I stated earlier, the game runs fine at 1080p, on my 1080p display, but now that I've got my laptop running on its built-in display (which has a resolution of 1366x768), I only have two screen resolution options: 800x450 and 1280x720. I don't know why, either. I have had this problem in the past, but I don't remember how I fixed it. I brought my laptop out camping with me a few weeks back and all I did was play Skyrim, and I know for a fact that I had the game running at 1366x768.
The game has no problems running at 1080p when my laptop is attached to the external display, and as such I don't feel it necessary to mention my system's hardware specifications. Does anyone have any ideas?