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Subgroup structure of dihedral group:D8

31 bytes added, 16:21, 29 June 2011
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In the "List of subgroups" columns below, a row break within the cell indicates that ''each row represents one conjugacy class of subgroups''.
{| class="sortable" border="1"
! Automorphism class of subgroups !! List of subgroups !! Isomorphism class !! [[Order of a group|Order]] of subgroups !! [[Index of a subgroup|Index]] of subgroups !! Number of conjugacy classes (=1 iff [[automorph-conjugate subgroup]]) !! Size of each conjugacy class (=1 iff [[normal subgroup]]) !! Total number of subgroups (=1 iff [[characteristic subgroup]]) !! Isomorphism class of [[quotient group|quotient]] (if existssubgroup is normal) !! [[Subnormal depth]] (if proper and normal, this equals 1) !! [[Nilpotency class]]
|-
| trivial subgroup || <math>\{ e \}</math> || [[trivial group]] || 1 || 8 || 1 || 1 || 1 || [[dihedral group:D8]] || 1 || 0
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