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Klein four-group

374 bytes removed, 16:32, 21 December 2014
{{further|[[subgroup structure of Klein four-group]]}}
{{normal subgroups}}[[File:V4latticeofsubgroups.png|400px]]
All subgroups are normal, since the group is abelian. There is a total of five subgroups{{#lst: the whole group, the trivial subgroup, and twostructure of Klein four-element subgroups (viz., copies of [[cyclic group:Z2|the cyclic group of order 2]]). {{characteristic subgroupssummary}} The Klein-four group is a [[characteristically simple group]], since it is a direct power of a simple group. Hence, the only characteristic subgroups are the trivial subgroup and the whole group.
==Bigger groups==
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