How to Create List from If/Then

I'm not even sure if if/then will be of use in this case but I am looking to create a separate list of data (preferably on a new worksheet) that is pulled from one particular column based on the cell data.

For example, I have a list of students in A, a list of ID numbers in B and the names of classes in C. If any class is listed in C, I want a formula to make a list of the corresponding data (A,B,C).

John Smith - #123456 - Class 101

Deb Green - #456789 - <blank>

Jane Doe - #321654 - Class 201

Should result in a new worksheet with:

John Smith - #123456 - Class 101

Jane Doe - #321654 - Class 201

Is this even doable? If not, suggestions on how to parse it on so I can reach this end result.