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/20130426/TotalCloudCover/?show_all"

Name
TotalCloudCover_2013-04-26-12-00.png
TotalCloudCover_2013-04-26-13-00.png
msevi-20130426T1200Z-airmass-rss-de.jpg
msevi-20130426T1200Z-daynat-rss-de.jpg
msevi-20130426T1300Z-airmass-rss-de.jpg
msevi-20130426T1300Z-daynat-rss-de.jpg