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/20130425/SpecialTime-MODIS/?show_all"

Name
Map-20130425-clwvi-R002500m-Dom01-Time_1030.png
Map-20130425-clwvi-R002500m-Dom01-Time_1215.png
Map-20130425-clwvi-R002500m-Dom02-Time_1030.png
Map-20130425-clwvi-R002500m-Dom02-Time_1215.png
Map-20130425-clwvi-R002500m-Dom03-Time_1030.png
Map-20130425-clwvi-R002500m-Dom03-Time_1215.png