Groups of order 120

Factorization and useful forms
The number 120 has prime factors 2,3,and 5, and factorization:

$$120 = 2^3 \cdot 3^1 \cdot 5^1 = 8 \cdot 3 \cdot 5$$.

Other expressions for this number are:

$$120 = 5! = 5^3 - 5 = 2(4^3 - 4) = \frac{4}{\frac{1}{2} + \frac{1}{3} + \frac{1}{5} - 1}$$

Classification of non-solvable groups
The classification proceeds in steps, which are presented in sequence for clarity:

Divisors of the order
More in-depth information can be found under subgroup structure of groups of order 120.

Multiples of the order
Related in-depth information can be found under supergroups of groups of order 120.

GAP implementation
gap> SmallGroupsInformation(120);

There are 47 groups of order 120. They are sorted by their Frattini factors. 1 has Frattini factor [ 30, 1 ]. 2 has Frattini factor [ 30, 2 ]. 3 has Frattini factor [ 30, 3 ]. 4 has Frattini factor [ 30, 4 ]. 5 has Frattini factor [ 60, 5 ]. 6 has Frattini factor [ 60, 6 ]. 7 has Frattini factor [ 60, 7 ]. 8 - 14 have Frattini factor [ 60, 8 ]. 15 has Frattini factor [ 60, 9 ]. 16 - 20 have Frattini factor [ 60, 10 ]. 21 - 25 have Frattini factor [ 60, 11 ]. 26 - 30 have Frattini factor [ 60, 12 ]. 31 - 33 have Frattini factor [ 60, 13 ]. 34 - 47 have trivial Frattini subgroup.

For the selection functions the values of the following attributes are precomputed and stored: IsAbelian, IsNilpotentGroup, IsSupersolvableGroup, IsSolvableGroup, LGLength, FrattinifactorSize and FrattinifactorId.

This size belongs to layer 2 of the SmallGroups library. IdSmallGroup is available for this size.