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Gardner Louden is listed in the book, _Minnesota in the Civil and Indian Wars, 1861-1865_, by the Minnesota Board of Commissioners on Publication of History of Minnesota in Civil and Indian Wars, 2nd edition (1891), page 233, as serving in Company F, 4th Minnesota Infantry regiment, mustered in 12 August 1864, mustered out 12 June 1865. This work is available online at Google Books.
It would be worthwhile to see if he or his surviving family members ever applied for a pension. Where they exist, Civil War pension files are frequently useful information sources. Copies of pension files are not free, unfortunately.