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Are there any software packages out there that can do equations like:

$$ \frac{SU(5)}{SU(3)}=SU(2)\times U(1)$$

or...

$$\frac{E_8}{E_6} = SU(3)$$

or...

$$ \frac{O(32)}{O(10)\times O(4)} = \text{?}$$

Probably you wouldn't need software to do this as you would just need a table of maximal subgroups. But it might be nice. I remember first learning about Lie Groups and working out subgroups is a bit tricky.

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