Lots of inaccurate info here...
VLF is 3-30kHz, wavelengths from 10-100km. Under ideal conditions, a groundwave could theoretically penetrate to a depth equal to it's wavelength. Practically speaking, reception is reliable down to 40-50m, but because of the "noise" problem, it is only useful for slow data transmission. However, not used in WWII, despite experimentation in the '30s and during the 40's. Came into use by the USN and others during the Cold War.
WWII long distance communications were HF; 3-30mHz (short wave radio, encrypted Morse Code...think "Enigma"), wavelengths 10-100m.
HF reception is very workable at keel depths of 10-30m/30-100ft, using horizontal wire antennas, which you can see installed forward and aft of the conning tower on both U-Boats and US Fleet Boats. Neither used "trailing wire" antennas...impractical for the day. You cannot transmit effectively, or at all for that matter, on a "trailing wire" antenna...it's in the water...grounded. WWII boats could only transmit when surfaced; using either the aforementioned wire antennas or whip antennas, either retractable or mounted fore-aft horizontally (to avoid vibration when submerged). Late in the war, Fleet Boats could transmit at periscope depth with periscope-mounted or mast-mounted antennas, but those were VHF/UHF for "line of sight" tactical voice RT (radio telephone) communications with nearby friendly units.
ELF is used today; 3-30Hz, wavelengths from 10,000-100,000km. Very slow data transmission rate, but very reliable reception at deep depths; let's say that's "in excess of 100m". ELF reception depends on use of long trailing wire antennas. Think amplitude modulation on a radio wave at least 10,000km long! Frequency modulation (single sideband or dual sideband) is just slightly more workable.
Satellite data links use UHF/EHF with buoy-mounted and mast-mounted antennas. But the philosophy is still that submarines are the "Silent Service"...listen but don't transmit unless absolutely necessary.
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