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This variant of Zuppos is currently undocumented, but used internally by LatticeByCyclicExtension. This change speeds it as follows: 1. If Zuppos(G) is already known, it is faster to simply filter that list. 2. It replaces Group(c) by Subgroup(G,[c]), which makes things faster if G is a IsHandledByNiceMonomorphism group (such as an automorphism group). 3. In addition, it only creates this subgroup once (not twice as before), which can lead to further improvements.
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