To download all objects using wget:

wget -r -H -N --cut-dirs=4 --include-directories="/v1/" "https://swiftbrowser.dkrz.de/public/dkrz_1e33ba3a-9ecb-452f-93b9-583cf4a66e57/ICON-HDCP2-DE/20160526-default-cont_month/?show_all"

Name
RADOLAN
20160526-default-cont_month_overview_rain_clouds_winds_perturbations_20160526-20160630.wmv
ICON_RADOLAN_5min_precip_Jun2016_HD720.mp4
ICON_RADOLAN_5min_precip_Jun2016_HD720_Speed.mp4
combined_bt108_map_DOM_20160526-27.ogv
combined_bt108_map_DOM_20160601-10.ogv
hist_bt108_ave_20160601.jpg
hist_bt108_ave_20160602.jpg
hist_bt108_ave_20160603.jpg
hist_bt108_ave_20160604.jpg
hist_bt108_ave_20160605.jpg
hist_bt108_ave_20160607.jpg
hist_bt108_ave_20160608.jpg
hist_bt108_ave_20160609.jpg
hist_bt108_ave_20160610.jpg
hist_bt108_tseries_20160601.jpg
hist_bt108_tseries_20160602.jpg
hist_bt108_tseries_20160603.jpg
hist_bt108_tseries_20160604.jpg
hist_bt108_tseries_20160605.jpg
hist_bt108_tseries_20160607.jpg
hist_bt108_tseries_20160608.jpg
hist_bt108_tseries_20160609.jpg
hist_bt108_tseries_20160610.jpg
timeseries_35day_cape_ml.png
timeseries_35day_cin_ml.png
timeseries_35day_clwvi.png
timeseries_35day_hurs.png
timeseries_35day_lhfl_s.png
timeseries_35day_prw.png
timeseries_35day_qv_s.png
timeseries_35day_rain_gsp_rate.png
timeseries_35day_shfl_s.png
timeseries_35day_t_s.png
timeseries_35day_tas.png
timeseries_35day_windspeed.png
timeseries_35day_z_pbl.png