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In MAGMA, if you are dealing with an element $x\in H$ for some group $H$, and you know that $H

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    I think holding someone over magma is probably a good method of coercion. (Apologies for the nonconstructive comment, but I couldn't resist.)2012-11-02
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    Why didn't I think of that!2012-11-02
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    Sorry that is my mistake for using the worng MAGMA tag! Many apologese.2012-11-02
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    No need to apologize; after all, the correct tag didn't even exist when you asked this question.2012-11-02

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G!CycleDecomposition(g);

will work

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    Thanks for the quick and helpful responses.2012-11-02
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One way would be to define the inclusion homomorphism $H \hookrightarrow G$ and apply it to your element $x$. See http://magma.maths.usyd.edu.au/magma/handbook/text/547#5783 for how to define homomorphisms.