Hi Sgroup,
The creative cloud Photography plan only includes Lightroom and Photoshop. It donot include Illustrator. You can download and install Illustrator using Creative cloud Desktop application but that will be a trial for 30 days.
You will find Creative Cloud Desktop under Applications in Macintosh and under All Programs in Windows.
If you wanted to use licensed version of Illustrator and other adobe applications then you have to subscribe for whole Creative cloud.
Thanks,
Nikhil Gupta.