File:A4latticeofsubgroups.png

This file describes the subgroup structure of alternating group:A4. It was created using Graphviz using the following code:

digraph G{       rankdir = "BT"; Wholegroup[peripheries=3]; Trivialsubgroup[peripheries=3]; Doubletransposition12; Doubletransposition13; Doubletransposition14; Kleinfour[peripheries=2]; Threecyclesubgroup123; Threecyclesubgroup134; Threecyclesubgroup124; Threecyclesubgroup234; Trivialsubgroup -> Doubletransposition12 -> Kleinfour -> Wholegroup; Trivialsubgroup -> Doubletransposition13 -> Kleinfour; Trivialsubgroup -> Doubletransposition14 -> Kleinfour; Trivialsubgroup -> Threecyclesubgroup123 -> Wholegroup; Trivialsubgroup -> Threecyclesubgroup134 -> Wholegroup; Trivialsubgroup -> Threecyclesubgroup124 -> Wholegroup; Trivialsubgroup -> Threecyclesubgroup234 -> Wholegroup; Trivialsubgroup[label="Trivial subgroup {}"]; Doubletransposition12[label="{, (1,2)(3,4)}"]; Doubletransposition13[label="{, (1,3)(2,4)}"]; Doubletransposition14[label="{, (1,4)(2,3)}"]; Kleinfour[label="{,(1,2)(3,4), (1,3)(2,4), (1,4)(2,3)}, characteristic"]; Threecyclesubgroup123[label="{, (1,2,3), (1,3,2)}"]; Threecyclesubgroup134[label="{, (1,3,4), (1,4,3)}"]; Threecyclesubgroup124[label="{, (1,2,4), (1,4,2)}"]; Threecyclesubgroup234[label="{, (2,3,4), (2,4,3)}"]; Wholegroup[label="Whole group"]; }