The Mendeleev periodic table is over 140 years old but is not the only periodic table in existence and new representations regularly appear.
The so-called left step table (Charles Janet 1929) demonstrates more clearly than the Mendeleev table how blocks form from the first two quantum numbers n and l.
Another classic is Timmothy Stowe's physicists periodic table. This is a three-dimensional representation with three axes for each of the first three quantum numbers.
In both tables helium is placed with elements in period 2 (the one with sodium, magnesium etc) with which it has very little in common chemically and this presents a problem.
In a new (2008) periodic table modification (Link), Eric Scerri is repositioning some of the elements in the left-step table based on the re-examination of so-called periodic table triads, a phenomenon already studied by the early chemistry pioneers.
In these triads the atomic weight of an element is the average of that of the element above and the one below. This relationship is exact for atomic numbers. For example the atomic number for arsenic is 33 which is the mean of 15 (phosphorus) and 51 (antimony). The reason is the long periodicity of 18 in the periodic table.
This relationship also holds for atomic weights, an observation first made by chemist Döbereiner in 1829 with the chlorine (35.47) , bromine (80.97 = ( Cl + I ) / 2) and iodine (126.47) triad. In fact the study of triads gave chemists the first clue about periodicity in the first place. This relationship is not obvious as the exact atomic weight depends on isotopic distribution and geological history.
Helium is also part of a triad, together with neon and argon and for this reason Scerri favors placement of helium with the noble gases. To restore order, he also positions hydrogen with the halogens which also makes sense chemically. For instance hydrogen like the halogens can form negatively charged ions.
Update: 31 May Tom emails that there are in fact four quantum numbers, so noted!