Sort by content types in a view
Tried several things, but the one bulletproof solution that I could come up with is to use Views Attachments


add a page display, filter by node type 1.
add an attachment display, filter by node type 4, attach to the page display, after its content.


Repeat 2 for each of the remaining node types in the desired order.

It will be a big view, but should do the trick.

Edit: that is the best solution I came up with, without an extra module.