There are only 230 "official" space groups, but you can write them differently depending on the ordering of the a/b/c/α/β/γ cell parameters.
All space groups in the same row on this page refer to the same class of symmetry.

1P1A1B1C1I1F1
2P1A1B1C1I1F1
3P2
4P21
5A2A21B2B21C2C21
6Pm
7PaPbPc
8AmAbAcBmBaBcCmCaCb
9AaAnBbBnCcCn
10P2/m
11P21/m
12A2/mA21/bA21/cB2/mB21/aB21/cC2/mC21/aC21/b
13P2/aP2/bP2/c
14P21/aP21/bP21/cP21/n
15A2/aA21/nB2/bB21/nC2/cC21/n
16P222
17P2221P2212P2122
18P21212P21221P22121
19P212121
20A2122B2212C2221A212121B212121C212121
21A222B222C222A22121B21221C21212
22F222F212121
23I222
24I212121
25P2mmPm2mPmm2
26Pmc21P21maPb21mPm21bPcm21P21am
27Pcc2P2aaPb2b
28Pma2P2mbPc2mPm2aPbm2P2cm
29Pca21P21abPc21bPb21aPbc21P21ca
30Pnc2P2naPb2nPn2bPcn2P2an
31Pmn21P21mnPn21mPm21nPnm21P21nm
32Pba2P2cbPc2a
33Pna21P21nbPc21nPn21aPbn21P21cn
34Pnn2P2nnPn2n
35Cmm2A2mmBm2mCba2A2cbBc2a
36A21amA21maA21cnA21nbBb21mBm21bBn21aBc21nCcm21Cmc21Cbn21Cna21
37A2aaA2nnBb2bBn2nCcc2Cnn2;
38Amm2Am2mAnc21An21bB2mmBmm2B21naBcn21C2mmCm2mCb21nC21an
39Abm2Ac2mAcc21Ab21bB2cmBma2B21aaBcc21Cm2aC2mbCb21bC21aa
40Ama2Am2aAnn21An21nB2mbBbm2B21nnBnn21Cc2mC2cmCn21nC21nn
41Aba2Ac2aAcn21Ab21nB2cbBba2B21anBnc21Cc2aC2cbCn21bC21na
42Fmm2Fbc21Fca21Fnn2Fm2mFb21aFc21bFn2n
43Fdd2Fdd21F2ddF21ddFd2dFd21d
44Imm2Inn21I2mmI21nnIm2mIn21n
45Iba2Icc21I2cbI21aaIc2aIb21b
46Ima2Inc21I2mbI21naIc2mIb21nIm2aIn21bIbm2Icn21I2cmI21an
47Pmmm
48Pnnn
49PccmPmaaPbmb
50PbanPncbPcna
51PmmaPbmmPmcmPmamPmmbPcmm
52PnnaPbnnPncnPnanPnnbPcnn
53PmnaPbmnPncmPmanPnmbPcnm
54PccaPbaaPbcbPbabPccbPcaa
55PbamPmcbPcma
56PccnPnaaPbnb
57PbcmPmcaPbmaPcmbPcamPmab
58PnnmPmnnPnmn
59PmmnPnmmPmnm
60PbcnPncaPbnaPcnbPcanPnab
61PbcaPcab
62PnmaPbnmPmcnPnamPmnbPcmn
63CmcmCbnnAmmaAncnBbmmBnnaBmmbBcnnCcmmCnanAmamAnnb
64CmcaCbnbAbmaAccnBbcmBnaaBmabBccnCcmbCnaaAcamAbnbBbamBmcb
65CmmmCbanAmmmAncbBmmmBcna
66CccmCnnnAmaaAnnnBbmbBnnn
67CmmaCbabAbmmAccbBmcmBcaaBmamBccaCmmbCbaaAcmmAbcb
68CccaCnnbAbaaAcnnBbcbAnanBbabBncnCccbCnnaAcaaAbnn
69FmmmFbcaFcabFnnn
70Fddd
71ImmmInnn
72IbamIccnImcbInaaIcmaIbnb
73IbcaIcab
74ImmaInnbIbmmIcnnImcmInanImamIncnImmbInnaIcmmIbnn
75P4C4
76P41C41
77P42C42
78P43C43
79I4F4
80I41F41
81P4C4
82I4F4
83P4/mC4/m
84P42/mC42/m
85P4/nC4/n
86P42/nC42/n
87I4/mF4/m
88I41/aF41/a
89P422C422
90P4212C4221
91P4122C4122
92P41212C41221
93P4222C4222
94P42212C42221
95P4322C4322
96P43212C43221
97I422F422
98I4122F4122
99P4mmC4mm
100P4bmC4mb
101P42cmC42mc
102P42nmC42mn
103P4ccC4cc
104P4ncC4cn
105P42mcC42cm
106P42bcC42cb
107I4mmF4mm
108I4cmF4mc
109I41mdF41dm
110I41cdF41dc
111P42mC4m2
112P42cC4c2
113P421mC4m21
114P421cC4c21
115P4m2C42m
116P4c2C42c
117P4bcC42b
118P4n2C42n
119I4m2F42m
120I4c2F42c
121I42mF4m2
122I42dF4d2
123P4/mmmC4/mmmP4/m2/m2/mC4/m2/m2/m
124P4/mccC4/mccP4/m2/c2/cC4/m2/c2/c
125P4/nbmC4/nmbP4/n2/b2/mC4/n2/m2/b
126P4/nncC4/ncnP4/n2/n2/cC4/n2/c2/n
127P4/mbmC4/mmbP4/m21/b2/mC4/m2/m21/b
128P4/mncC4/mcnP4/m21/n2/cC4/m2/c21/n
129P4/nmmC4/nmmP4/n21/m2/mC4/n2/m21/m
130P4/nccC4/nccP4/n21/c2/cC4/n2/c21/c
131P42/mmcC42/mcmP42/m2/m2/cC42/m2/c2/m
132P42/mcmC42/mmcP42/m2/c2/mC42/m2/m2/c
133P42/nbcC42/ncbP42/n2/b2/cC42/n2/c2/b
134P42/nnmC42/nmnP42/n2/n2/mC42/n2/m2/n
135P42/mbcC42/mcbP42/m21/b2/cC42/m2/c21/b
136P42/mnmC42/mmnP42/m21/n2/mC42/m2/m21/n
137P42/nmcC42/ncmP42/n21/m2/cC42/n2/c21/m
138P42/ncmC42/nmcP42/n21/c2/mC42/n2/m21/c
139I4/mmmF4/mmmI4/m2/m2/mF4/m2/m2/m
140I4/mcmF4/mmcI4/m2/c2/mF4/m2/m2/c
141I41/amdF41/admI41/a2/m2/dF41/a2/d2/m
142I41/acdF41/adcI41/a2/c2/dF41/a2/d2/c
143P3
144P31
145P32
146R3
147P3
148R3
149P312
150P321
151P3112
152P3121
153P3212
154P3221
155R32
156P3m1
157P31m
158P3c1
159P31c
160R3m
161R3c
162P31mP312/m
163P31cP312/c
164P3m1P32/m1
165P3c1P32/c1
166R3mR32/m
167R3cR32/c
168P6
169P61
170P65
171P62
172P64
173P63
174P6
175P6/m
176P63/m
177P622
178P6122
179P6522
180P6222
181P6422
182P6322
183P6mm
184P6cc
185P63cm
186P63mc
187P6m2
188P6c2
189P62m
190P62c
191P6/mmmP6/m2/m2/m
192P6/mccP6/m2/c2/c
193P63/mcmP63/m2/c2/m
194P63/mmcP63/m2/m2/c
195P23
196F23
197I23
198P213
199I213
200Pm3P2/m3
201Pn3P2/n3
202Fm3F2/m3
203Fd3F2/d3
204Im3I2/m3
205Pa3P21/a3
206Ia3I21/a3
207P432
208P4232
209F432
210F4132
211I432
212P4332
213P4132
214I4132
215P43m
216F43m
217I43m
218P43n
219F43c
220I43d
221Pm3mP4/m32/m
222Pn3nP4/n32/n
223Pm3nP41/m32/n
224Pn3mP41/n32/m
225Fm3mF4/m32/m
226Fm3cF4/m32/c
227Fd3mF41/d32/m
228Fd3cF41/d32/c
229Im3mI4/m32/m
230Ia3dI41/a32/dIa3d

Space Groups in AMCSD but not in RRUFF
I2/mB21/dC2/aB21/mFm3mF2/dI2/cP2/nI2/aFd3m
PnF2/mF2mmImabPm3mF2I2FdIm3m
A2/nIbIaImC21/dP4b2I2/bB2/n


Download Space Group List