The motherboard model is Supermicro X11SAE-O. Supermicro offers Intel drivers for download on their website, but I don't think they're all the latest ones:
Description: Intel (Skylake) HD graphic (64bit)
Post Date: 09/08/2015
Description: Intel INF C236
Post Date: 10/21/2015
Description: Intel SATA
Post Date: 09/24/2015
Description: Intel USB 3.0 Driver
Post Date: 09/05/2014
So I visited the Intel download center thinking I could easily check for the latest ones, but alas! it's impossible to find any of the above there.
Aha, today the search field shows possible results while you type. That didn't work the last time. Was my browser malfunctioning or did the website not work correctly yesterday?
So I found the magic keywords now:
Intel HD Graphics -> 220.127.116.11.4300 (still no results which say they are for the non-mobile Xeon E3 v5 processors - maybe Intel considers them "Core"s with unlocked functions?)
Chipset Driver for Windows -> 18.104.22.168.10
Intel SATA -> 22.214.171.1243 (these don't mention the C230 chipset, but neither do those from the Supermicro website)
Intel USB -> 126.96.36.199 (this one even mentions "Intel C230 series chipset family")
So all the drivers from Supermicro were outdated...