To download all objects using wget:

wget -r -H -N --cut-dirs=5 --include-directories="/v1/" "https://swiftbrowser.dkrz.de/public/dkrz_1e33ba3a-9ecb-452f-93b9-583cf4a66e57/ICON-HDCP2-DE/20160526-default-cont_month/RADOLAN/?show_all"

Name
20160525
20160526
20160527
20160528
20160529
20160530
20160531
20160601
20160602
20160603
20160604
20160605
20160606
20160607
20160608
20160609
20160610
complete.nc
complete_rr.nc
complete_rr_daily.nc