hasNormalSubgroup

URI: https://gptkb.org/prop/hasNormalSubgroup

114 triples

GPTKB property

has normal subgroup • is a normal subgroup of • isNormalSubgroupOf • minimalNormalSubgroup

Subject	Object
gptkb:symmetric_group_on_5_elements	alternating group on 5 elements
gptkb:GL(n,q)	gptkb:SL(n,q)
gptkb:octahedral_group	cyclic group of order 4
gptkb:symmetric_group_S_8	trivial group
gptkb:Principal_congruence_subgroup	gptkb:SL(2,ℤ)
gptkb:tetrahedral_group	gptkb:Klein_four-group
gptkb:D_4	gptkb:Klein_four-group
gptkb:dihedral_group_D3	order 1 subgroup
gptkb:alternating_group_A4	gptkb:symmetric_group_S4
gptkb:general_linear_group_GL(2n,q)	gptkb:special_linear_group_SL(2n,q)
gptkb:Projective_General_Linear_Group_of_3x3_matrices_over_GF(2)	itself
gptkb:alternating_group_A_7	symmetric group S_7
gptkb:alternating_group_A24	gptkb:symmetric_group_S24
gptkb:symmetric_group_S8	gptkb:alternating_group_A8
gptkb:alternating_group_A4	gptkb:Klein_four-group
gptkb:Dih_6	gptkb:C_6
gptkb:symmetric_group_S4	gptkb:alternating_group_A4
gptkb:octahedral_group	gptkb:Klein_four-group
gptkb:Dihedral_group_of_order_8	gptkb:Klein_four-group
gptkb:dihedral_group_of_order_2^{n+1}	\langle r \rangle