Groups of order 120
This article gives information about, and links to more details on, groups of order 120
See pages on algebraic structures of order 120 | See pages on groups of a particular order
Statistics at a glance
| Quantity | Value | List/comment |
|---|---|---|
| Total number of groups | 47 | |
| Number of abelian groups | 3 | ((Number of abelian groups of order 8) = 3) times ((number of abelian groups of order 3) = 1) times ((number of abelian groups of order 5) = 1). See also classification of finite abelian groups and structure theorem for finitely generated abelian groups |
| Number of nilpotent groups | 5 | ((Number of groups of order 8) = 5) times ((number of groups of order 3) = 1) times ((number of groups of order 5) = 1). See also equivalence of definitions of finite nilpotent group |
| Number of solvable groups | 44 | The three non-solvable groups are special linear group:SL(2,5), direct product of A5 and Z2, and symmetric group:S5 |
| Number of simple groups | 0 | |
| Number of almost simple groups | 1 | symmetric group:S5 (isomorphic to ) |
| Number of quasisimple groups | 1 | special linear group:SL(2,5) (also the binary icosahedral group) |