(International Tables) Maximal subgroups of space group 85

P4/n	No. 85	P4/n	C_4h³

ORIGIN CHOICE 1, Origin at -4 on n, at -1/4, 1/4, 0 from -1

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)

General position

Multiplicity, Wyckoff letter,
Site symmetry

Coordinates

(1) x, y, z	(2) -x, -y, z	(3) -y + 1/2, x + 1/2, z	(4) y + 1/2, -x + 1/2, z
(5) -x + 1/2, -y + 1/2, -z	(6) x + 1/2, y + 1/2, -z	(7) y, -x, -z	(8) -y, x, -z

I Maximal translationengleiche subgroups

[2] P-4 (81)	1; 2; 7; 8
[2] P4 (75)	1; 2; 3; 4		1/2, 0, 0
[2] P2/n (13, P112/a)	1; 2; 5; 6	-a - b, a, c	1/4, 1/4, 0

II Maximal klassengleiche subgroups

Enlarged unit cell

[2] c' = 2c

P4₂/n (86)	<2; 5; 3 + (0, 0, 1)>	a, b, 2c	0, 0, 1/2
P4₂/n (86)	<2; (3; 5) + (0, 0, 1)>	a, b, 2c
P4/n (85)	<2; 3; 5>	a, b, 2c
P4/n (85)	<2; 3; 5 + (0, 0, 1)>	a, b, 2c	0, 0, 1/2

[3] c' = 3c

P4/n (85)	<2; 3; 5>	a, b, 3c
P4/n (85)	<2; 3; 5 + (0, 0, 2)>	a, b, 3c	0, 0, 1
P4/n (85)	<2; 3; 5 + (0, 0, 4)>	a, b, 3c	0, 0, 2

Series of maximal isomorphic subgroups

[p] c' = pc

P4/n (85)	<2; 3; 5 + (0, 0, 2u)>	a, b, pc	0, 0, u
	p > 2; 0 ≤ u < p p conjugate subgroups for the prime p

[p²] a' = pa, b' = pb

P4/n (85)	<2 + (2u, 2v, 0); 3 + (p/2 - 1/2 + u + v, p/2 - 1/2 - u + v, 0); 5 + (p/2 - 1/2 + 2u, p/2 - 1/2 + 2v, 0)>	pa, pb, c	u, v, 0
	p > 2; 0 ≤ u < p; 0 ≤ v < p p² conjugate subgroups for prime p ≡ 3 (mod 4)

[p = q² + r²] a' = qa - rb, b' = ra + qb

P4/n (85)	<2 + (2u, 0, 0); 3 + (q/2 + r/2 - 1/2 + u, q/2 - r/2 - 1/2 - u, 0); 5 + (q/2 + r/2 - 1/2 + 2u, q/2 - r/2 - 1/2, 0)>	qa - rb, ra + qb, c	u, 0, 0
	q > 0; r > 0; p > 4; 0 ≤ u < p p conjugate subgroups for prime p ≡ 1 (mod 4)

I Minimal translationengleiche supergroups

[2] P4/nbm (125); [2] P4/nnc (126); [2] P4/nmm (129); [2] P4/ncc (130)

II Minimal non-isomorphic klassengleiche supergroups

Additional centring translations

[2] C4/m (83, P4/m); [2] I4/m (87)

Decreased unit cell

none

P4/n	No. 85	P4/n	C_4h³

ORIGIN CHOICE 2, Origin at -1 on n, at 1/4, -1/4, 0 from -4