## Subgroups of $E_8$ by using extended Dynkin diagrams

I need to show that the following are subgroups of $$E_8$$ using extended Dynkin diagrams.

$$SU\left(5\right)\times SU\left(5\right)$$ $$SU\left(3\right)\times E_6$$ $$SU\left(4\right)\times SO\left(10\right)$$ and $$SO\left(16\right)$$ $$SU\left(2\right)\times E_7$$ $$SU\left(9\right)$$

Is it enough to find the Dynkin diagrams for the subgroups by deleting edges in the Dynkin diagram for $$E_8$$? If so, I can only seem to do this for the first ones listed.

Is the use of extended Dynkin diagrams important?