Triclinic

a ≠ b ≠ c
α ≠ β ≠ γ

Point group
$\overline{1}= S_2 = C_i$

Triclinic (aP)
Space group: 2
Primitive = Conventional

Monoclinic

a ≠ b ≠ c
α ≠ 90°
β = γ= 90°

Point group
$2/m = C_{2h}$

Monoclinic simple (mP)
Space group: 10
Primitive = Conventional

Monoclinic Base centered (mS)
Space group: 12
2 × Primitive = Conventional

Orthorhombic

a ≠ b ≠ c
α = β = γ = 90°

Point group
$mmm = V_h = D_{2h}$

Orthorhombic simple (oP)
Space group: 47
Primitive = Conventional

Base centered (oS)
Space group: 65
2 × Primitive = Conventional

Face centered (oF)
Space group: 69
4 × Primitive = Conventional

Body centered (oI)
Space group: 71
2 × Primitive = Conventional

Tetragonal

a = b ≠ c
α = β = γ = 90°

Point group
$\frac{4}{m}mm = D_{4h}$

Simple (tP)
Space group: 123
Primitive = Conventional

Body centered (tI)
Space group: 139
2 × Primitive = Conventional

Trigonal

a = b = c
α = β = γ ≠ 90°

Point group
$\overline{3}m = D_{3d}$

Trigonal (hR)
Space group: 166
Primitive = Conventional

Hexagonal

a = b ≠ c
α = 120°, β = γ = 90°

Point group
$\frac{6}{m}mm = D_{6h}$

Hexagonal (hP)
Space group: 191
Primitive = Conventional

Cubic

a = b = c
α = β = γ = 90°

Point group
$m3m = O_h$

Simple (cP)
Space group: 221
Primitive = Conventional

Face centered (cF)
Space group: 225
4 × Primitive = Conventional

Body centered (cI)
Space group: 229
2 × Primitive = Conventional