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Go to the highest subdivision level and clone the subtool you wish to mirror. Append the clone as a new subtool.
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Switch to the clone subtool and delete the lower subdivision levels by pressing Tool:Geometry: Del Lower.
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Press Tool: Deformation: Mirror after selecting the axis you want.
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Press Tool:Texture:Enable UVs if they are not enabled.
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Press Tool:Geometry:Reconstruct Subdiv repeatedly until all the previous levels are restored.

That would be the hardest way.
The easy way is to go to level 1 and mask the half of the model that has the details you want to copy. Then use Tool>Deformation>Smart ReSym with the appropriate axis selected. Now just go up one level at a time and apply Smart ReSym again at each level.
That’s it!