Subgroups — C₂×#20289279 #28291435

Order 13568.

7258 conjugacy classes of subgroups.

The subgroup lattice has 1964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289279	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811372	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16811340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16811303	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16811302	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16811297	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16811288	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16811286	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16811282	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16811281	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16811265	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16811262	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16811248	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16811248	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16811245	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16811243	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16811239	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#16811237	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16811237	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂×#16811209	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#16811207	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂×#16811196	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂×#16811195	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#16811177	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16811156	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#124×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
33	C₂²×#11719945	C₂²	1	1	yes	characteristic
34	C₂²×#11719947	C₂²	1	1	yes	characteristic
35	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
36	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
37	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
39	#16811376	C₂²	1	16	yes	complemented
40	#16811372	C₂²	1	16	yes	complemented
41	#16811369	C₂²	1	16	yes	complemented
42	#16811368	C₂²	1	16	yes	complemented
43	#16811341	C₂²	1	16	yes	complemented
44	#16811340	C₂²	1	16	yes	complemented
45	#16811303	C₂²	1	16	yes	complemented
46	#16811302	C₂²	1	16	yes	complemented
47	#16811298	C₂²	1	16	yes	complemented
48	#16811297	C₂²	1	16	yes	complemented
49	#16811288	C₂²	1	16	yes	complemented
50	#16811286	C₂²	1	16	yes	complemented
51	#16811282	C₂²	1	16	yes	complemented
52	#16811281	C₂²	1	16	yes	complemented
53	#16811265	C₂²	1	16	yes	complemented
54	#16811262	C₂²	1	16	yes	complemented
55	#16811248	C₂²	1	16	yes	complemented
56	#16811248	C₂²	1	16	yes	complemented
57	#16811245	C₂²	1	16	yes	complemented
58	#16811243	C₂²	1	16	yes	complemented
59	#16811239	C₂²	1	16	yes	complemented
60	#16811237	C₂²	1	16	yes	complemented
61	#16811237	C₂²	1	16	yes	complemented
62	#16811209	C₂²	1	16	yes	complemented
63	#16811207	C₂²	1	16	yes	complemented
64	#16811196	C₂²	1	16	yes	complemented
65	#16811195	C₂²	1	16	yes	complemented
66	#16811177	C₂²	1	16	yes	complemented
67	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
68	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
69	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
70	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
71	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
72	C₂×#13133215	C₂²	1	1	yes	characteristic, complemented
73	C₂×#13133215	C₂²	1	1	yes	characteristic, complemented
74	#16811156	C₂²	1	16	yes	complemented
75	C₂×#13133212	C₂²	1	1	yes	characteristic, complemented
76	C₂×#13133212	C₂²	1	1	yes	characteristic, complemented
77	C₂×#13133212	C₂²	1	1	yes	characteristic, complemented
78	C₂×#13133211	C₂²	1	1	yes	characteristic, complemented
79	C₂×#13133211	C₂²	1	1	yes	characteristic, complemented
80	C₂×#13133211	C₂²	1	1	yes	characteristic, complemented
81	C₂×#13133211	C₂²	1	1	yes	characteristic, complemented
82	C₂×#13133210	C₂²	1	1	yes	characteristic, complemented
83	C₂×#13133210	C₂²	1	1	yes	characteristic, complemented
84	C₂×#13133210	C₂²	1	1	yes	characteristic, complemented
85	C₂×#13133210	C₂²	1	1	yes	characteristic, complemented
86	C₂×#13133210	C₂²	1	1	yes	characteristic, complemented
87	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
88	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
89	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
90	C₂×#13133206	C₂²	1	1	yes	characteristic
91	C₂×#13133206	C₂²	1	1	yes	characteristic, complemented
92	C₂×#13133205	C₂²	1	1	yes	characteristic
93	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
94	C₂×#13133204	C₂²	1	1	yes	characteristic
95	C₂×#13133203	C₂²	1	1	yes	characteristic
96	C₂×#13133203	C₂²	1	1	yes	characteristic
97	C₂×#13133203	C₂²	1	1	yes	characteristic
98	C₂×#13133203	C₂²	1	1	yes	characteristic
99	C₂×#13133203	C₂²	1	1	yes	characteristic
100	C₂×#13133203	C₂²	1	1	yes	characteristic
101	C₂×#13133203	C₂²	1	1	yes	characteristic, complemented
102	C₂×#13133203	C₂²	1	1	yes	characteristic, complemented
103	C₂×#13133203	C₂²	1	1	yes	characteristic, complemented
104	C₂×#13133203	C₂²	1	1	yes	characteristic, complemented
105	C₂×#13133203	C₂²	1	1	yes	characteristic, complemented
106	#124×D₅₃	C₂²	1	16	yes	complemented
107	C₂×#13133202	C₂²	1	1	yes	characteristic
108	C₂×#13133202	C₂²	1	1	yes	characteristic
109	C₂×#13133202	C₂²	1	1	yes	characteristic
110	C₂×#13133202	C₂²	1	1	yes	characteristic, complemented
111	C₂×#13133202	C₂²	1	1	yes	characteristic, complemented
112	C₂×#13133202	C₂²	1	1	yes	characteristic, complemented
113	C₂×#13133201	C₂²	1	1	yes	characteristic, complemented
114	C₂×#13133200	C₂²	1	1	yes	characteristic, complemented
115	C₂×#13133200	C₂²	1	1	yes	characteristic, complemented
116	C₂×#13133199	C₂²	1	1	yes	characteristic
117	C₂×#13133199	C₂²	1	1	yes	characteristic, complemented
118	C₂×#13133199	C₂²	1	1	yes	characteristic, complemented
119	C₂×#13133199	C₂²	1	1	yes	characteristic, complemented
120	C₂×#13133198	C₂²	1	1	yes	characteristic
121	C₂×#13133198	C₂²	1	1	yes	characteristic, complemented
122	C₂×#13133198	C₂²	1	1	yes	characteristic, complemented
123	C₂×#13133197	C₂²	1	1	yes	characteristic
124	C₂×#13133197	C₂²	1	1	yes	characteristic
125	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
126	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
127	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
128	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
129	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
130	C₂×#13133195	C₂²	1	1	yes	characteristic
131	C₂×#13133195	C₂²	1	1	yes	characteristic
132	C₂×#13133195	C₂²	1	1	yes	characteristic
133	C₂×#13133195	C₂²	1	1	yes	characteristic
134	C₂×#13133195	C₂²	1	1	yes	characteristic
135	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
136	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
137	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
138	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
139	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
140	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
141	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
142	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
143	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
144	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
145	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
146	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
147	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
148	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
149	C₂×#13133193	C₂²	1	1	yes	characteristic
150	C₂×#13133193	C₂²	1	1	yes	characteristic
151	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
152	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
153	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
154	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
155	C₂×#13133192	C₂²	1	1	yes	characteristic
156	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
157	C₂×#13133190	C₂²	1	1	yes	characteristic
158	C₂×#13133190	C₂²	1	1	yes	characteristic
159	C₂×#13133190	C₂²	1	1	yes	characteristic
160	C₂×#13133190	C₂²	1	1	yes	characteristic, complemented
161	C₂×#13133189	C₂²	1	1	yes	characteristic
162	C₂×#13133189	C₂²	1	1	yes	characteristic
163	C₂×#13133189	C₂²	1	1	yes	characteristic, complemented
164	C₂×#13133188	C₂²	1	1	yes	characteristic, complemented
165	C₂×#13133187	C₂²	1	1	yes	characteristic
166	C₂×#13133187	C₂²	1	1	yes	characteristic
167	C₂×#13133185	C₂²	1	1	yes	characteristic
168	C₂×#13133185	C₂²	1	1	yes	characteristic
169	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
170	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
171	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
172	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
173	C₂×#13133182	C₂²	1	1	yes	characteristic, complemented
174	C₂×#13133182	C₂²	1	1	yes	characteristic, complemented
175	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
176	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
177	C₂×#13133179	C₂²	1	1	yes	characteristic
178	C₂×#13133179	C₂²	1	1	yes	characteristic
179	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
180	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
181	C₂×#13133177	C₂²	1	1	yes	characteristic
182	C₂×#13133177	C₂²	1	1	yes	characteristic
183	C₂×#13133177	C₂²	1	1	yes	characteristic
184	C₂×#13133177	C₂²	1	1	yes	characteristic, complemented
185	C₂×#13133177	C₂²	1	1	yes	characteristic, complemented
186	C₂×#13133177	C₂²	1	1	yes	characteristic, complemented
187	C₂×#13133175	C₂²	1	1	yes	characteristic, complemented
188	C₂×#13133175	C₂²	1	1	yes	characteristic, complemented
189	C₂×#13133174	C₂²	1	1	yes	characteristic
190	C₂×#13133174	C₂²	1	1	yes	characteristic
191	C₂×#13133174	C₂²	1	1	yes	characteristic, complemented
192	C₂×#13133173	C₂²	1	1	yes	characteristic, complemented
193	C₂×#13133173	C₂²	1	1	yes	characteristic, complemented
194	C₂²×#11719921	C₂²	1	1	yes	characteristic
195	C₂²×#11719921	C₂²	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
202	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
203	C₅₃×#542	C₂²	1	16	yes	complemented
204	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
205	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
206	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
207	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
208	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
209	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
210	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
211	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
212	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
213	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
214	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
215	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
216	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
217	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
218	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
219	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
220	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
221	C₂×#11719945	—	4	4	no	—
222	C₂×#11719945	C₂³	1	8	yes	—
223	C₂×#11719947	—	4	4	no	—
224	C₂×#11719947	C₂³	1	8	yes	—
225	C₂²×Dic₁₀₆	—	4	4	no	—
226	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
227	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
228	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
229	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
230	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
231	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
232	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
233	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
234	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
235	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
236	C₂²×Dic₁₀₆	C₂³	1	8	yes	complemented
237	C₂×Q₈×D₅₃	—	4	4	no	—
238	C₂×Q₈×D₅₃	—	4	4	no	—
239	C₂×Q₈×D₅₃	C₂³	1	8	yes	—
240	C₂×Q₈×D₅₃	C₂³	1	8	yes	complemented
241	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
242	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
243	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
244	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
245	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
246	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
247	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
248	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
249	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
250	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
251	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
252	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
253	C₂×D₄×D₅₃	—	4	4	no	—
254	C₂×D₄×D₅₃	C₂³	1	8	yes	—
255	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
258	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
260	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
261	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
262	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
263	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
264	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
265	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
266	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
267	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
268	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
269	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
270	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
271	#13133216	C₂³	1	8	yes	complemented
272	#13133216	C₂³	1	8	yes	complemented
273	#13133216	C₂³	1	8	yes	complemented
274	#13133216	C₂³	1	8	yes	complemented
275	#13133216	C₂³	1	8	yes	complemented
276	#13133215	C₂³	1	8	yes	complemented
277	#13133215	C₂³	1	8	yes	complemented
278	#13133212	C₂³	1	8	yes	complemented
279	#13133212	C₂³	1	8	yes	complemented
280	#13133212	C₂³	1	8	yes	complemented
281	#13133211	C₂³	1	8	yes	complemented
282	#13133211	C₂³	1	8	yes	complemented
283	#13133211	C₂³	1	8	yes	complemented
284	#13133211	C₂³	1	8	yes	complemented
285	#13133210	C₂³	1	8	yes	complemented
286	#13133210	C₂³	1	8	yes	complemented
287	#13133210	C₂³	1	8	yes	complemented
288	#13133210	C₂³	1	8	yes	complemented
289	#13133210	C₂³	1	8	yes	complemented
290	#13133207	C₂³	1	8	yes	complemented
291	#13133207	C₂³	1	8	yes	complemented
292	#13133207	C₂³	1	8	yes	complemented
293	#13133206	C₂³	1	8	yes	—
294	#13133206	C₂³	1	8	yes	complemented
295	#13133205	C₂³	1	8	yes	—
296	#13133205	C₂³	1	8	yes	complemented
297	#13133204	C₂³	1	8	yes	—
298	#13133203	C₂³	1	8	yes	—
299	#13133203	C₂³	1	8	yes	—
300	#13133203	C₂³	1	8	yes	—
301	#13133203	C₂³	1	8	yes	—
302	#13133203	C₂³	1	8	yes	—
303	#13133203	C₂³	1	8	yes	—
304	#13133203	C₂³	1	8	yes	complemented
305	#13133203	C₂³	1	8	yes	complemented
306	#13133203	C₂³	1	8	yes	complemented
307	#13133203	C₂³	1	8	yes	complemented
308	#13133203	C₂³	1	8	yes	complemented
309	#13133202	C₂³	1	8	yes	—
310	#13133202	C₂³	1	8	yes	—
311	#13133202	C₂³	1	8	yes	—
312	#13133202	C₂³	1	8	yes	complemented
313	#13133202	C₂³	1	8	yes	complemented
314	#13133202	C₂³	1	8	yes	complemented
315	#13133201	C₂³	1	8	yes	complemented
316	#13133200	C₂³	1	8	yes	complemented
317	#13133200	C₂³	1	8	yes	complemented
318	#13133199	C₂³	1	8	yes	—
319	#13133199	C₂³	1	8	yes	complemented
320	#13133199	C₂³	1	8	yes	complemented
321	#13133199	C₂³	1	8	yes	complemented
322	#13133198	C₂³	1	8	yes	—
323	#13133198	C₂³	1	8	yes	complemented
324	#13133198	C₂³	1	8	yes	complemented
325	#13133197	C₂³	1	8	yes	—
326	#13133197	C₂³	1	8	yes	—
327	#13133197	C₂³	1	8	yes	complemented
328	#13133197	C₂³	1	8	yes	complemented
329	#13133196	C₂³	1	8	yes	complemented
330	#13133196	C₂³	1	8	yes	complemented
331	#13133196	C₂³	1	8	yes	complemented
332	#13133195	C₂³	1	8	yes	—
333	#13133195	C₂³	1	8	yes	—
334	#13133195	C₂³	1	8	yes	—
335	#13133195	C₂³	1	8	yes	—
336	#13133195	C₂³	1	8	yes	—
337	#13133195	C₂³	1	8	yes	complemented
338	#13133195	C₂³	1	8	yes	complemented
339	#13133195	C₂³	1	8	yes	complemented
340	#13133195	C₂³	1	8	yes	complemented
341	#13133195	C₂³	1	8	yes	complemented
342	#13133195	C₂³	1	8	yes	complemented
343	#13133195	C₂³	1	8	yes	complemented
344	#13133194	C₂³	1	8	yes	complemented
345	#13133194	C₂³	1	8	yes	complemented
346	#13133194	C₂³	1	8	yes	complemented
347	#13133194	C₂³	1	8	yes	complemented
348	#13133194	C₂³	1	8	yes	complemented
349	#13133194	C₂³	1	8	yes	complemented
350	#13133194	C₂³	1	8	yes	complemented
351	#13133193	C₂³	1	8	yes	—
352	#13133193	C₂³	1	8	yes	—
353	#13133193	C₂³	1	8	yes	complemented
354	#13133193	C₂³	1	8	yes	complemented
355	#13133193	C₂³	1	8	yes	complemented
356	#13133193	C₂³	1	8	yes	complemented
357	#13133192	C₂³	1	8	yes	—
358	#13133191	C₂³	1	8	yes	complemented
359	#13133190	C₂³	1	8	yes	—
360	#13133190	C₂³	1	8	yes	—
361	#13133190	C₂³	1	8	yes	—
362	#13133190	C₂³	1	8	yes	complemented
363	#13133189	C₂³	1	8	yes	—
364	#13133189	C₂³	1	8	yes	—
365	#13133189	C₂³	1	8	yes	complemented
366	#13133188	C₂³	1	8	yes	complemented
367	#13133187	C₂³	1	8	yes	—
368	#13133187	C₂³	1	8	yes	—
369	#13133185	C₂³	1	8	yes	—
370	#13133185	C₂³	1	8	yes	—
371	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
372	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
373	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
374	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
375	#13133182	C₂³	1	8	yes	complemented
376	#13133182	C₂³	1	8	yes	complemented
377	C₄×D₂₁₂	C₂³	1	8	yes	—
378	C₄×D₂₁₂	C₂³	1	8	yes	complemented
379	#13133179	C₂³	1	8	yes	—
380	#13133179	C₂³	1	8	yes	—
381	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
382	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
383	#13133177	C₂³	1	8	yes	—
384	#13133177	C₂³	1	8	yes	—
385	#13133177	C₂³	1	8	yes	—
386	#13133177	C₂³	1	8	yes	complemented
387	#13133177	C₂³	1	8	yes	complemented
388	#13133177	C₂³	1	8	yes	complemented
389	#13133175	C₂³	1	8	yes	complemented
390	#13133175	C₂³	1	8	yes	complemented
391	#13133174	C₂³	1	8	yes	—
392	#13133174	C₂³	1	8	yes	—
393	#13133174	C₂³	1	8	yes	complemented
394	#13133173	C₂³	1	8	yes	complemented
395	#13133173	C₂³	1	8	yes	complemented
396	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
397	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
398	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
399	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
400	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
401	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
402	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
403	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
404	C₂×#11719919	C₂³	1	1	yes	characteristic
405	C₂×#11719919	C₂³	1	1	yes	characteristic
406	C₂×#11719919	C₂³	1	1	yes	characteristic
407	C₂×#11719919	C₂³	1	1	yes	characteristic
408	C₂×#11719919	C₂³	1	1	yes	characteristic
409	C₂×#11719919	C₂³	1	1	yes	characteristic
410	C₂×#11719919	C₂³	1	1	yes	characteristic
411	C₂×#11719919	C₂³	1	1	yes	characteristic
412	C₂×#11719919	C₂³	1	1	yes	characteristic
413	C₂×#11719919	C₂³	1	1	yes	characteristic
414	C₂×#11719919	C₂³	1	1	yes	characteristic
415	C₂×#11719919	C₂³	1	1	yes	characteristic
416	C₂×#11719919	C₂³	1	1	yes	characteristic
417	C₂×#11719919	C₂³	1	1	yes	characteristic
418	C₂×#11719919	C₂³	1	1	yes	characteristic
419	C₂×#11719919	C₂³	1	1	yes	characteristic
420	C₂×#11719919	C₂³	1	1	yes	characteristic
421	C₂×#11719919	C₂³	1	1	yes	characteristic
422	C₂×#11719919	C₂³	1	1	yes	characteristic
423	C₂×#11719919	C₂³	1	1	yes	characteristic
424	C₂×#11719919	C₂³	1	1	yes	characteristic
425	C₂×#11719919	C₂³	1	1	yes	characteristic
426	C₂×#11719919	C₂³	1	1	yes	characteristic
427	C₂×#11719919	C₂³	1	1	yes	characteristic
428	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
429	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
430	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
431	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
432	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
433	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
434	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
435	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
436	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
437	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
438	C₂×#11719921	C₂³	1	8	yes	—
439	C₂×#11719921	C₂³	1	8	yes	—
440	C₂×#11719921	C₂³	1	1	yes	characteristic
441	C₂×#11719921	C₂³	1	1	yes	characteristic
442	C₂×#11719921	C₂³	1	1	yes	characteristic
443	C₂×#11719921	C₂³	1	1	yes	characteristic
444	C₂×#11719921	C₂³	1	1	yes	characteristic
445	C₂×#11719921	C₂³	1	1	yes	characteristic
446	C₂×#11719921	C₂³	1	1	yes	characteristic
447	C₂×#11719921	C₂³	1	1	yes	characteristic
448	C₂×#11719921	C₂³	1	1	yes	characteristic
449	C₂×#11719921	C₂³	1	1	yes	characteristic
450	C₂×#11719921	C₂³	1	1	yes	characteristic
451	C₂×#11719921	C₂³	1	1	yes	characteristic
452	C₂×#11719921	C₂³	1	1	yes	characteristic
453	C₂×#11719921	C₂³	1	1	yes	characteristic
454	C₂×#11719921	C₂³	1	1	yes	characteristic
455	C₂×#11719921	C₂³	1	1	yes	characteristic
456	C₂×#11719921	C₂³	1	1	yes	characteristic
457	C₂×#11719921	C₂³	1	1	yes	characteristic
458	C₂×#11719921	C₂³	1	1	yes	characteristic
459	C₂×#11719921	C₂³	1	1	yes	characteristic
460	C₂×#11719921	C₂³	1	1	yes	characteristic
461	C₂×#11719921	C₂³	1	1	yes	characteristic
462	C₂×#11719921	C₂³	1	1	yes	characteristic
463	C₂×#11719921	C₂³	1	1	yes	characteristic
464	C₂×#11719921	C₂³	1	1	yes	characteristic
465	C₂×#11719921	C₂³	1	1	yes	characteristic
466	C₂×#11719921	C₂³	1	1	yes	characteristic
467	C₂×#11719921	C₂³	1	1	yes	characteristic
468	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
469	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
470	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
471	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
472	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
473	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
474	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
475	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
476	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
477	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
478	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
479	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
480	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
481	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
482	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
483	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
484	C₄²×D₅₃	C₂³	1	8	yes	—
485	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
486	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
487	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
488	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
489	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
490	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
491	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
492	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
493	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
494	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
495	#126×C₅₃	C₂³	1	8	yes	complemented
496	#126×C₅₃	C₂³	1	8	yes	complemented
497	#124×C₅₃	C₂³	1	8	yes	—
498	#124×C₅₃	C₂³	1	8	yes	complemented
499	#124×C₅₃	C₂³	1	8	yes	complemented
500	#123×C₅₃	C₂³	1	8	yes	—
501	#123×C₅₃	C₂³	1	8	yes	complemented
502	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
503	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
504	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
505	#121×C₅₃	C₂³	1	8	yes	—
506	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
507	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
508	#117×C₅₃	C₂³	1	8	yes	complemented
509	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
510	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
511	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
512	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
513	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
514	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
515	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
516	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
517	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
518	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
519	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
520	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
521	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
522	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
523	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
524	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
525	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
526	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
527	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
528	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
529	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
530	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
531	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
532	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
533	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
534	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
535	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
536	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂³×D₅₃	—	2	4	no	—
539	C₂³×D₅₃	—	2	4	no	—
540	C₂³×D₅₃	—	4	2	no	—
541	C₂³×D₅₃	—	4	2	no	—
542	C₂³×D₅₃	—	4	2	no	—
543	C₂³×D₅₃	—	4	2	no	—
544	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
545	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
546	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
547	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
548	C₂³×D₅₃	C₂⁴	1	4	yes	—
549	C₂³×D₅₃	C₂⁴	1	4	yes	—
550	C₂×Q₈×C₅₃	—	4	2	no	—
551	C₂×Q₈×C₅₃	—	4	2	no	—
552	C₂×Q₈×C₅₃	—	4	2	no	—
553	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
554	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
555	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
556	C₂×D₄×C₅₃	—	4	2	no	—
557	C₂×D₄×C₅₃	—	4	2	no	—
558	C₂×D₄×C₅₃	—	4	2	no	—
559	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
560	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
561	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
562	C₂²×C₄×C₅₃	—	4	2	no	—
563	C₂²×C₄×C₅₃	—	4	2	no	—
564	C₂²×C₄×C₅₃	—	4	2	no	—
565	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
566	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
567	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
568	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
569	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
570	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
571	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
572	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
573	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
574	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
575	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
576	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
577	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
578	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
579	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
580	C₂×C₂²⋊D₅₃	—	2	4	no	—
581	C₂×C₂²⋊D₅₃	—	2	4	no	—
582	C₂×C₂²⋊D₅₃	—	2	4	no	—
583	C₂×C₂²⋊D₅₃	—	4	2	no	—
584	C₂×C₂²⋊D₅₃	—	4	2	no	—
585	C₂×C₂²⋊D₅₃	—	4	2	no	—
586	C₂×C₂²⋊D₅₃	—	4	2	no	—
587	C₂×C₂²⋊D₅₃	—	4	2	no	—
588	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
589	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
590	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
591	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
592	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
593	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
594	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
595	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
596	C₂²×Dic₅₃	—	2	4	no	—
597	C₂²×Dic₅₃	—	4	2	no	—
598	C₂²×Dic₅₃	—	4	2	no	—
599	C₂²×Dic₅₃	—	4	2	no	—
600	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
601	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
602	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
603	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
604	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
605	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
606	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
607	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
608	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
609	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
610	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
611	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
612	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
613	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
614	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
615	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
616	Q₈×D₅₃	—	4	16	no	—
617	Q₈×D₅₃	—	4	16	no	—
618	#11719947	—	4	16	no	—
619	D₄×D₅₃	—	4	16	no	—
620	#11719945	—	4	16	no	—
621	C₂×D₂₁₂	—	2	4	no	—
622	C₂×D₂₁₂	—	4	2	no	—
623	C₂×D₂₁₂	—	4	2	no	—
624	C₂×D₂₁₂	—	4	2	no	—
625	C₂×D₂₁₂	C₂⁴	1	4	yes	—
626	C₂×D₂₁₂	C₂⁴	1	4	yes	—
627	C₂×D₂₁₂	C₂⁴	1	4	yes	—
628	C₂×D₂₁₂	C₂⁴	1	4	yes	—
629	C₂×C₄×D₅₃	—	2	4	no	—
630	C₂×C₄×D₅₃	—	2	4	no	—
631	C₂×C₄×D₅₃	—	2	4	no	—
632	C₂×C₄×D₅₃	—	4	2	no	—
633	C₂×C₄×D₅₃	—	4	2	no	—
634	C₂×C₄×D₅₃	—	4	2	no	—
635	C₂×C₄×D₅₃	—	4	2	no	—
636	C₂×C₄×D₅₃	—	4	2	no	—
637	C₂×C₄×D₅₃	—	4	2	no	—
638	C₂×C₄×D₅₃	—	4	2	no	—
639	C₂×C₄×D₅₃	—	4	2	no	—
640	C₂×C₄×D₅₃	—	4	2	no	—
641	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
642	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
643	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
644	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
645	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
646	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
647	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
648	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
649	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
650	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
651	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
652	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
653	C₂×Dic₁₀₆	—	2	4	no	—
654	C₂×Dic₁₀₆	—	2	4	no	—
655	C₂×Dic₁₀₆	—	2	4	no	—
656	C₂×Dic₁₀₆	—	2	4	no	—
657	C₂×Dic₁₀₆	—	4	16	no	—
658	C₂×Dic₁₀₆	—	4	2	no	—
659	C₂×Dic₁₀₆	—	4	2	no	—
660	C₂×Dic₁₀₆	—	4	2	no	—
661	C₂×Dic₁₀₆	—	4	2	no	—
662	C₂×Dic₁₀₆	—	4	2	no	—
663	C₂×Dic₁₀₆	—	4	2	no	—
664	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
665	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
666	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
667	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
668	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
669	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
670	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
671	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
672	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
673	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
674	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
675	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
676	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
677	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
678	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
679	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
680	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
681	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
682	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
683	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
684	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
685	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
686	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
687	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
688	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
689	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
690	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
691	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
692	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
693	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
694	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
695	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
696	C₄²×C₅₃	C₂⁴	1	4	yes	—
697	C₄²×C₅₃	C₂⁴	1	4	yes	—
698	C₄²×C₅₃	C₂⁴	1	4	yes	—
699	C₄²×C₅₃	C₂⁴	1	4	yes	—
700	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
701	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
702	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
703	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
704	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
705	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
706	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
707	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
708	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
709	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
710	#11719921	C₂⁴	1	4	yes	—
711	#11719921	C₂⁴	1	4	yes	—
712	#11719921	C₂⁴	1	4	yes	—
713	#11719921	C₂⁴	1	4	yes	—
714	#11719921	C₂⁴	1	4	yes	—
715	#11719921	C₂⁴	1	4	yes	—
716	#11719921	C₂⁴	1	4	yes	—
717	#11719921	C₂⁴	1	4	yes	—
718	#11719921	C₂⁴	1	4	yes	—
719	#11719921	C₂⁴	1	4	yes	—
720	#11719921	C₂⁴	1	4	yes	—
721	#11719921	C₂⁴	1	4	yes	—
722	#11719921	C₂⁴	1	4	yes	—
723	#11719921	C₂⁴	1	4	yes	—
724	#11719921	C₂⁴	1	4	yes	—
725	#11719921	C₂⁴	1	4	yes	—
726	#11719921	C₂⁴	1	4	yes	—
727	#11719921	C₂⁴	1	4	yes	—
728	#11719921	C₂⁴	1	4	yes	—
729	#11719921	C₂⁴	1	4	yes	—
730	#11719921	C₂⁴	1	4	yes	—
731	#11719921	C₂⁴	1	4	yes	—
732	#11719921	C₂⁴	1	4	yes	—
733	#11719921	C₂⁴	1	4	yes	—
734	#11719921	C₂⁴	1	4	yes	—
735	#11719921	C₂⁴	1	4	yes	—
736	#11719921	C₂⁴	1	4	yes	—
737	#11719921	C₂⁴	1	4	yes	—
738	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
739	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
740	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
741	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
742	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
743	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
744	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
745	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
746	#11719919	C₂⁴	1	4	yes	—
747	#11719919	C₂⁴	1	4	yes	—
748	#11719919	C₂⁴	1	4	yes	—
749	#11719919	C₂⁴	1	4	yes	—
750	#11719919	C₂⁴	1	4	yes	—
751	#11719919	C₂⁴	1	4	yes	—
752	#11719919	C₂⁴	1	4	yes	—
753	#11719919	C₂⁴	1	4	yes	—
754	#11719919	C₂⁴	1	4	yes	—
755	#11719919	C₂⁴	1	4	yes	—
756	#11719919	C₂⁴	1	4	yes	—
757	#11719919	C₂⁴	1	4	yes	—
758	#11719919	C₂⁴	1	4	yes	—
759	#11719919	C₂⁴	1	4	yes	—
760	#11719919	C₂⁴	1	4	yes	—
761	#11719919	C₂⁴	1	4	yes	—
762	#11719919	C₂⁴	1	4	yes	—
763	#11719919	C₂⁴	1	4	yes	—
764	#11719919	C₂⁴	1	4	yes	—
765	#11719919	C₂⁴	1	4	yes	—
766	#11719919	C₂⁴	1	4	yes	—
767	#11719919	C₂⁴	1	4	yes	—
768	#11719919	C₂⁴	1	4	yes	—
769	#11719919	C₂⁴	1	4	yes	—
770	C₄×Dic₅₃	C₂⁴	1	4	yes	—
771	C₄×Dic₅₃	C₂⁴	1	4	yes	—
772	C₄×Dic₅₃	C₂⁴	1	4	yes	—
773	C₄×Dic₅₃	C₂⁴	1	4	yes	—
774	C₄×Dic₅₃	C₂⁴	1	4	yes	—
775	C₄×Dic₅₃	C₂⁴	1	4	yes	—
776	C₄×Dic₅₃	C₂⁴	1	4	yes	—
777	C₄×Dic₅₃	C₂⁴	1	4	yes	—
778	C₄×Dic₅₃	C₂⁴	1	4	yes	—
779	C₄×Dic₅₃	C₂⁴	1	4	yes	—
780	C₂³×C₅₃	—	2	2	no	—
781	C₂³×C₅₃	—	2	2	no	—
782	C₂³×C₅₃	—	2	2	no	—
783	C₂³×C₅₃	—	2	2	no	—
784	C₂³×C₅₃	—	2	2	no	—
785	C₂³×C₅₃	—	2	2	no	—
786	C₂³×C₅₃	—	2	2	no	—
787	C₂³×C₅₃	—	2	2	no	—
788	C₂³×C₅₃	—	2	2	no	—
789	C₂³×C₅₃	C₂⁵	1	2	yes	—
790	C₂³×C₅₃	C₂⁵	1	2	yes	—
791	C₂³×C₅₃	C₂⁵	1	2	yes	—
792	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
793	C₂²×D₅₃	—	2	2	no	—
794	C₂²×D₅₃	—	2	2	no	—
795	C₂²×D₅₃	—	2	2	no	—
796	C₂²×D₅₃	—	2	2	no	—
797	C₂²×D₅₃	—	2	2	no	—
798	C₂²×D₅₃	—	2	2	no	—
799	C₂²×D₅₃	—	2	2	no	—
800	C₂²×D₅₃	—	2	2	no	—
801	C₂²×D₅₃	—	2	2	no	—
802	C₂²×D₅₃	—	2	2	no	—
803	C₂²×D₅₃	—	2	2	no	—
804	C₂²×D₅₃	—	2	8	no	—
805	C₂²×D₅₃	—	2	8	no	—
806	C₂²×D₅₃	—	4	4	no	—
807	C₂²×D₅₃	—	4	4	no	—
808	C₂²×D₅₃	—	4	4	no	—
809	C₂²×D₅₃	—	4	4	no	—
810	C₂²×D₅₃	—	8	8	no	—
811	C₂²×D₅₃	—	8	8	no	—
812	C₂²×D₅₃	2₋¹⁺⁴	1	4	yes	—
813	C₂²×D₅₃	C₂⁵	1	2	yes	—
814	C₂²×D₅₃	C₂⁵	1	2	yes	—
815	C₂²×D₅₃	C₂⁵	1	2	yes	—
816	C₂²×D₅₃	C₂⁵	1	2	yes	—
817	Q₈×C₅₃	—	4	4	no	—
818	Q₈×C₅₃	—	4	4	no	—
819	Q₈×C₅₃	—	4	4	no	—
820	D₄×C₅₃	—	4	4	no	—
821	D₄×C₅₃	—	4	4	no	—
822	D₄×C₅₃	—	4	4	no	—
823	C₂×C₄×C₅₃	—	2	2	no	—
824	C₂×C₄×C₅₃	—	2	2	no	—
825	C₂×C₄×C₅₃	—	2	2	no	—
826	C₂×C₄×C₅₃	—	2	2	no	—
827	C₂×C₄×C₅₃	—	2	2	no	—
828	C₂×C₄×C₅₃	—	2	2	no	—
829	C₂×C₄×C₅₃	—	2	2	no	—
830	C₂×C₄×C₅₃	—	2	2	no	—
831	C₂×C₄×C₅₃	—	2	2	no	—
832	C₂×C₄×C₅₃	—	2	2	no	—
833	C₂×C₄×C₅₃	—	2	2	no	—
834	C₂×C₄×C₅₃	—	2	2	no	—
835	C₂×C₄×C₅₃	—	4	4	no	—
836	C₂×C₄×C₅₃	—	4	4	no	—
837	C₂×C₄×C₅₃	—	4	4	no	—
838	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
839	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
840	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
841	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
842	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
843	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
844	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
845	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
846	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
847	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
848	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
849	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
850	C₂²⋊D₅₃	—	2	8	no	—
851	C₂²⋊D₅₃	—	2	8	no	—
852	C₂²⋊D₅₃	—	2	8	no	—
853	C₂²⋊D₅₃	—	4	4	no	—
854	C₂²⋊D₅₃	—	4	4	no	—
855	C₂²⋊D₅₃	—	4	4	no	—
856	C₂²⋊D₅₃	—	4	4	no	—
857	C₂²⋊D₅₃	—	4	4	no	—
858	C₂×Dic₅₃	—	2	2	no	—
859	C₂×Dic₅₃	—	2	2	no	—
860	C₂×Dic₅₃	—	2	2	no	—
861	C₂×Dic₅₃	—	2	2	no	—
862	C₂×Dic₅₃	—	2	2	no	—
863	C₂×Dic₅₃	—	2	2	no	—
864	C₂×Dic₅₃	—	2	2	no	—
865	C₂×Dic₅₃	—	2	2	no	—
866	C₂×Dic₅₃	—	2	2	no	—
867	C₂×Dic₅₃	—	2	2	no	—
868	C₂×Dic₅₃	—	2	2	no	—
869	C₂×Dic₅₃	—	2	8	no	—
870	C₂×Dic₅₃	—	4	4	no	—
871	C₂×Dic₅₃	—	4	4	no	—
872	C₂×Dic₅₃	—	4	4	no	—
873	C₂×Dic₅₃	H(5,𝔽₂)	1	4	yes	—
874	C₂×Dic₅₃	C₂⁵	1	2	yes	—
875	C₂×Dic₅₃	C₂⁵	1	2	yes	—
876	C₂×Dic₅₃	C₂⁵	1	2	yes	—
877	C₂×Dic₅₃	C₂⁵	1	2	yes	—
878	C₂×Dic₅₃	C₂⁵	1	2	yes	—
879	C₂×Dic₅₃	C₂⁵	1	2	yes	—
880	C₂×Dic₅₃	C₂⁵	1	2	yes	—
881	C₂×Dic₅₃	C₂⁵	1	2	yes	—
882	C₂×Dic₅₃	C₂⁵	1	2	yes	—
883	C₂×Dic₅₃	C₂⁵	1	2	yes	—
884	C₂×Dic₅₃	C₂⁵	1	2	yes	—
885	C₂×Dic₅₃	C₂⁵	1	2	yes	—
886	D₂₁₂	—	2	8	no	—
887	D₂₁₂	—	4	4	no	—
888	D₂₁₂	—	4	4	no	—
889	D₂₁₂	—	4	4	no	—
890	C₄×D₅₃	—	2	8	no	—
891	C₄×D₅₃	—	2	8	no	—
892	C₄×D₅₃	—	2	8	no	—
893	C₄×D₅₃	—	4	4	no	—
894	C₄×D₅₃	—	4	4	no	—
895	C₄×D₅₃	—	4	4	no	—
896	C₄×D₅₃	—	4	4	no	—
897	C₄×D₅₃	—	4	4	no	—
898	C₄×D₅₃	—	4	4	no	—
899	C₄×D₅₃	—	4	4	no	—
900	C₄×D₅₃	—	4	4	no	—
901	C₄×D₅₃	—	4	4	no	—
902	Dic₁₀₆	—	2	8	no	—
903	Dic₁₀₆	—	2	8	no	—
904	Dic₁₀₆	—	2	8	no	—
905	Dic₁₀₆	—	2	8	no	—
906	Dic₁₀₆	—	4	4	no	—
907	Dic₁₀₆	—	4	4	no	—
908	Dic₁₀₆	—	4	4	no	—
909	Dic₁₀₆	—	4	4	no	—
910	Dic₁₀₆	—	4	4	no	—
911	Dic₁₀₆	—	4	4	no	—
912	C₂×#3561	—	53	1	no	maximal, Sylow
913	C₂²×C₅₃	—	2	2	no	—
914	C₂²×C₅₃	—	2	2	no	—
915	C₂²×C₅₃	—	2	2	no	—
916	C₂²×C₅₃	—	2	2	no	—
917	C₂²×C₅₃	—	2	2	no	—
918	C₂²×C₅₃	—	2	2	no	—
919	C₂²×C₅₃	—	2	2	no	—
920	C₂²×C₅₃	—	2	2	no	—
921	C₂²×C₅₃	—	2	2	no	—
922	C₂²×C₅₃	—	4	4	no	—
923	C₂²×C₅₃	—	4	4	no	—
924	C₂²×C₅₃	—	4	4	no	—
925	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
926	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
927	C₂²×C₅₃	#585	1	2	yes	—
928	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
929	C₂×D₅₃	—	2	2	no	—
930	C₂×D₅₃	—	2	2	no	—
931	C₂×D₅₃	—	2	8	no	—
932	C₂×D₅₃	—	2	2	no	—
933	C₂×D₅₃	—	2	2	no	—
934	C₂×D₅₃	—	2	2	no	—
935	C₂×D₅₃	—	2	2	no	—
936	C₂×D₅₃	—	2	2	no	—
937	C₂×D₅₃	—	2	2	no	—
938	C₂×D₅₃	—	2	2	no	—
939	C₂×D₅₃	—	2	2	no	—
940	C₂×D₅₃	—	2	2	no	—
941	C₂×D₅₃	—	4	4	no	—
942	C₂×D₅₃	—	4	4	no	—
943	C₂×D₅₃	—	4	4	no	—
944	C₂×D₅₃	—	8	8	no	—
945	C₂×D₅₃	—	8	8	no	—
946	C₂×D₅₃	C₂×2₋¹⁺⁴	1	4	yes	—
947	C₄×C₅₃	—	2	2	no	—
948	C₄×C₅₃	—	2	2	no	—
949	C₄×C₅₃	—	2	2	no	—
950	C₄×C₅₃	—	2	2	no	—
951	C₄×C₅₃	—	2	2	no	—
952	C₄×C₅₃	—	2	2	no	—
953	C₄×C₅₃	—	2	2	no	—
954	C₄×C₅₃	—	2	2	no	—
955	C₄×C₅₃	—	2	2	no	—
956	C₄×C₅₃	—	2	2	no	—
957	C₄×C₅₃	—	2	2	no	—
958	C₄×C₅₃	—	2	2	no	—
959	Dic₅₃	—	2	2	no	—
960	Dic₅₃	—	2	2	no	—
961	Dic₅₃	—	2	2	no	—
962	Dic₅₃	—	2	2	no	—
963	Dic₅₃	—	2	2	no	—
964	Dic₅₃	—	2	2	no	—
965	Dic₅₃	—	2	2	no	—
966	Dic₅₃	—	2	2	no	—
967	Dic₅₃	—	2	2	no	—
968	Dic₅₃	—	2	2	no	—
969	Dic₅₃	—	2	2	no	—
970	Dic₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
971	#3561	—	53	32	no	—
972	C₂×#563	—	53	1	no	—
973	C₂×#563	—	53	1	no	—
974	C₂×#562	—	53	1	no	—
975	C₂×#562	—	53	1	no	—
976	C₂×#556	—	53	1	no	—
977	C₂×#556	—	53	1	no	—
978	C₂×#551	—	53	1	no	—
979	C₂×#551	—	53	1	no	—
980	C₂×#551	—	53	1	no	—
981	C₂×#551	—	53	1	no	—
982	C₂×D₄×Q₈	—	53	1	no	—
983	C₂×D₄×Q₈	—	53	1	no	—
984	C₂×#548	—	53	1	no	—
985	C₂×#548	—	53	1	no	—
986	C₂×#546	—	53	1	no	—
987	C₂×#546	—	53	1	no	—
988	C₂×#543	—	53	1	no	—
989	C₂×#543	—	53	1	no	—
990	C₂×#542	—	53	1	no	—
991	C₂×#542	—	53	1	no	—
992	C₂×#542	—	53	1	no	—
993	C₂×#542	—	53	1	no	—
994	C₂×#542	—	53	1	no	—
995	C₂×#542	D₅₃	1	1	yes	characteristic, complemented
996	C₂×#538	—	53	1	no	—
997	C₂×#538	—	53	1	no	—
998	C₂×#536	—	53	1	no	—
999	C₂×#536	—	53	1	no	—
1000	C₂×#533	—	53	1	no	—
1001	C₂×#529	—	53	1	no	—
1002	C₂²×#124	—	53	1	no	—
1003	C₂×C₅₃	—	4	2	no	—
1004	C₂×C₅₃	—	4	2	no	—
1005	C₂×C₅₃	—	4	2	no	—
1006	C₂×C₅₃	#3561	1	4	yes	complemented
1007	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1008	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
1009	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
1010	D₅₃	—	2	4	no	—
1011	D₅₃	—	4	2	no	—
1012	D₅₃	—	4	2	no	—
1013	D₅₃	—	4	2	no	—
1014	C₂²×#41	—	53	1	no	—
1015	C₂²×#41	—	53	1	no	—
1016	C₂³×Q₈	—	53	1	no	—
1017	C₂³×Q₈	—	53	1	no	—
1018	C₂³×Q₈	—	53	1	no	—
1019	C₂³×D₄	—	53	1	no	—
1020	#563	—	53	16	no	—
1021	#563	—	53	16	no	—
1022	#562	—	53	16	no	—
1023	#562	—	53	16	no	—
1024	#556	—	53	16	no	—
1025	#556	—	53	16	no	—
1026	#551	—	53	16	no	—
1027	#551	—	53	16	no	—
1028	#551	—	53	16	no	—
1029	#551	—	53	16	no	—
1030	D₄×Q₈	—	53	16	no	—
1031	D₄×Q₈	—	53	16	no	—
1032	#548	—	53	16	no	—
1033	#548	—	53	16	no	—
1034	#546	—	53	16	no	—
1035	#546	—	53	16	no	—
1036	#543	—	53	16	no	—
1037	#543	—	53	16	no	—
1038	#542	—	53	16	no	—
1039	#542	—	53	16	no	—
1040	#542	—	53	16	no	—
1041	#542	—	53	16	no	—
1042	#542	—	53	16	no	—
1043	#542	C₂×D₅₃	1	16	yes	complemented
1044	#538	—	53	16	no	—
1045	#538	—	53	16	no	—
1046	#536	—	53	16	no	—
1047	#536	—	53	16	no	—
1048	#533	—	53	16	no	—
1049	C₂×C₄⋊Q₈	—	53	1	no	—
1050	C₂×C₄⋊Q₈	—	53	1	no	—
1051	C₂×C₄⋊Q₈	—	53	1	no	—
1052	C₂×C₄⋊Q₈	—	53	1	no	—
1053	C₂×C₄⋊Q₈	—	53	1	no	—
1054	C₂×C₄⋊Q₈	—	53	1	no	—
1055	C₂×C₄⋊Q₈	—	53	1	no	—
1056	C₂×C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1057	#529	—	53	16	no	—
1058	C₂×#126	—	53	1	no	—
1059	C₂×#126	—	53	1	no	—
1060	C₂×#126	—	53	1	no	—
1061	C₂×#126	—	53	1	no	—
1062	C₂×#126	—	53	1	no	—
1063	C₂×#126	—	53	1	no	—
1064	C₂×#126	—	53	1	no	—
1065	C₂×#126	—	53	1	no	—
1066	C₂×#126	—	53	1	no	—
1067	C₂×#126	—	53	1	no	—
1068	C₂×#126	—	53	1	no	—
1069	C₂×#126	—	53	1	no	—
1070	C₂×#126	C₂×D₅₃	1	1	yes	characteristic, complemented
1071	C₂×#126	C₂×D₅₃	1	1	yes	characteristic, complemented
1072	C₂×#125	—	53	1	no	—
1073	C₂×#125	—	53	1	no	—
1074	C₂×#125	—	53	1	no	—
1075	C₂×#124	—	53	1	no	—
1076	C₂×#124	—	53	1	no	—
1077	C₂×#124	—	53	1	no	—
1078	C₂×#124	—	53	16	no	—
1079	C₂×#124	—	53	1	no	—
1080	C₂×#124	—	53	1	no	—
1081	C₂×#124	—	53	1	no	—
1082	C₂×#124	—	53	1	no	—
1083	C₂×#124	—	53	1	no	—
1084	C₂×#124	—	53	1	no	—
1085	C₂×#124	—	53	1	no	—
1086	C₂×#124	—	53	1	no	—
1087	C₂×#124	—	53	1	no	—
1088	C₂×#124	—	53	1	no	—
1089	C₂×#124	—	53	1	no	—
1090	C₂×#124	—	53	1	no	—
1091	C₂×#124	—	53	1	no	—
1092	C₂×#124	C₂×D₅₃	1	1	yes	characteristic
1093	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
1094	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
1095	C₂×#123	—	53	1	no	—
1096	C₂×#123	—	53	1	no	—
1097	C₂×#123	—	53	1	no	—
1098	C₂×#123	—	53	1	no	—
1099	C₂×#123	—	53	1	no	—
1100	C₂×#123	—	53	1	no	—
1101	C₂×#123	—	53	1	no	—
1102	C₂×#123	—	53	1	no	—
1103	C₂×#123	—	53	1	no	—
1104	C₂×#123	—	53	1	no	—
1105	C₂×#123	—	53	1	no	—
1106	C₂×#123	—	53	1	no	—
1107	C₂×#123	—	53	1	no	—
1108	C₂×#123	—	53	1	no	—
1109	C₂×#123	—	53	1	no	—
1110	C₂×#123	—	53	1	no	—
1111	C₂×#123	C₂×D₅₃	1	1	yes	characteristic
1112	C₂×#123	C₂×D₅₃	1	1	yes	characteristic, complemented
1113	C₂×C₂²⋊Q₈	—	53	1	no	—
1114	C₂×C₂²⋊Q₈	—	53	1	no	—
1115	C₂×C₂²⋊Q₈	—	53	1	no	—
1116	C₂×C₂²⋊Q₈	—	53	1	no	—
1117	C₂×C₂²⋊Q₈	—	53	1	no	—
1118	C₂×C₂²⋊Q₈	—	53	1	no	—
1119	C₂×C₂²⋊Q₈	—	53	1	no	—
1120	C₂×C₂²⋊Q₈	—	53	1	no	—
1121	C₂×C₂²⋊Q₈	—	53	1	no	—
1122	C₂×C₂²⋊Q₈	—	53	1	no	—
1123	C₂×C₂²⋊Q₈	—	53	1	no	—
1124	C₂×C₂²⋊Q₈	—	53	1	no	—
1125	C₂×C₂²⋊Q₈	—	53	1	no	—
1126	C₂×C₂²⋊Q₈	—	53	1	no	—
1127	C₂×C₂²⋊Q₈	—	53	1	no	—
1128	C₂×C₂²⋊Q₈	—	53	1	no	—
1129	C₂×C₂²⋊Q₈	—	53	1	no	—
1130	C₂×C₂²⋊Q₈	—	53	1	no	—
1131	C₂×C₂²⋊Q₈	—	53	1	no	—
1132	C₂×C₂²⋊Q₈	—	53	1	no	—
1133	C₂×C₂²⋊Q₈	—	53	1	no	—
1134	C₂×C₂²⋊Q₈	—	53	1	no	—
1135	C₂×C₂²⋊Q₈	—	53	1	no	—
1136	C₂×C₂²⋊Q₈	—	53	1	no	—
1137	C₂×C₂²⋊Q₈	—	53	1	no	—
1138	C₂×C₂²⋊Q₈	—	53	1	no	—
1139	C₂×C₂²⋊Q₈	—	53	1	no	—
1140	C₂×C₂²⋊Q₈	—	53	1	no	—
1141	C₂×C₂²⋊Q₈	—	53	1	no	—
1142	C₂×C₂²⋊Q₈	—	53	1	no	—
1143	C₂×C₂²⋊Q₈	—	53	1	no	—
1144	C₂×C₂²⋊Q₈	—	53	1	no	—
1145	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1146	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1147	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1148	C₂×#121	—	53	1	no	—
1149	C₂×#121	—	53	1	no	—
1150	C₂×#121	—	53	1	no	—
1151	C₂×#121	—	53	1	no	—
1152	C₂×#121	—	53	1	no	—
1153	C₂×#121	—	53	1	no	—
1154	C₂×#121	—	53	1	no	—
1155	C₂×#121	—	53	1	no	—
1156	C₂×#121	—	53	1	no	—
1157	C₂×#121	—	53	1	no	—
1158	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
1159	C₂×#120	—	53	1	no	—
1160	C₂×#120	—	53	1	no	—
1161	C₂×#120	—	53	1	no	—
1162	C₂×#120	—	53	1	no	—
1163	C₂×C₄×Q₈	—	53	1	no	—
1164	C₂×C₄×Q₈	—	53	1	no	—
1165	C₂×C₄×Q₈	—	53	1	no	—
1166	C₂×C₄×Q₈	—	53	1	no	—
1167	C₂×C₄×Q₈	—	53	1	no	—
1168	C₂×C₄×Q₈	—	53	1	no	—
1169	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1170	C₂×C₄×D₄	—	53	1	no	—
1171	C₂×C₄×D₄	—	53	1	no	—
1172	C₂×C₄×D₄	—	53	1	no	—
1173	C₂×C₄×D₄	—	53	1	no	—
1174	C₂×C₄×D₄	—	53	1	no	—
1175	C₂×C₄×D₄	—	53	1	no	—
1176	C₂×C₄×D₄	—	53	1	no	—
1177	C₂×C₄×D₄	—	53	1	no	—
1178	C₂×C₄×D₄	—	53	1	no	—
1179	C₂×C₄×D₄	—	53	1	no	—
1180	C₂×C₄×D₄	—	53	1	no	—
1181	C₂×C₄×D₄	—	53	1	no	—
1182	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
1183	C₂×#117	—	53	1	no	—
1184	C₂×#117	—	53	1	no	—
1185	C₂×#117	—	53	1	no	—
1186	C₂×#117	—	53	1	no	—
1187	C₂×#117	—	53	1	no	—
1188	C₂×#117	—	53	1	no	—
1189	C₂×#117	—	53	1	no	—
1190	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
1191	C₂²×C₂²⋊C₄	—	53	1	no	—
1192	C₂²×C₂²⋊C₄	—	53	1	no	—
1193	C₂²×C₂²⋊C₄	—	53	1	no	—
1194	C₂²×C₂²⋊C₄	—	53	1	no	—
1195	C₂²×C₂²⋊C₄	—	53	1	no	—
1196	C₂²×C₂²⋊C₄	—	53	1	no	—
1197	C₂²×C₂²⋊C₄	—	53	1	no	—
1198	C₂²×C₂²⋊C₄	—	53	1	no	—
1199	C₂²×C₄²	—	53	1	no	—
1200	C₅₃	C₂×#3561	1	1	yes	characteristic, complemented, Sylow
1201	C₂⁵	—	53	1	no	—
1202	C₂⁵	—	53	1	no	—
1203	C₂×#41	—	53	8	no	—
1204	C₂×#41	—	53	8	no	—
1205	C₂×#41	—	212	4	no	—
1206	C₂×#41	—	212	4	no	—
1207	C₂²×Q₈	—	53	8	no	—
1208	C₂²×Q₈	—	53	8	no	—
1209	C₂²×Q₈	—	53	1	no	—
1210	C₂²×Q₈	—	53	1	no	—
1211	C₂²×Q₈	—	53	1	no	—
1212	C₂²×Q₈	—	53	1	no	—
1213	C₂²×Q₈	—	53	1	no	—
1214	C₂²×Q₈	—	53	1	no	—
1215	C₂²×Q₈	—	53	1	no	—
1216	C₂²×Q₈	—	53	1	no	—
1217	C₂²×Q₈	—	53	1	no	—
1218	C₂²×Q₈	—	53	1	no	—
1219	C₂²×Q₈	—	53	8	no	—
1220	C₂²×Q₈	—	212	4	no	—
1221	C₂²×Q₈	—	212	4	no	—
1222	C₂²×Q₈	—	212	4	no	—
1223	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1224	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1225	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1226	C₂²×D₄	—	53	1	no	—
1227	C₂²×D₄	—	53	1	no	—
1228	C₂²×D₄	—	53	1	no	—
1229	C₂²×D₄	—	53	1	no	—
1230	C₂²×D₄	—	53	1	no	—
1231	C₂²×D₄	—	53	1	no	—
1232	C₂²×D₄	—	53	1	no	—
1233	C₂²×D₄	—	53	1	no	—
1234	C₂²×D₄	—	53	8	no	—
1235	C₂²×D₄	—	53	1	no	—
1236	C₂²×D₄	—	53	1	no	—
1237	C₂²×D₄	—	53	1	no	—
1238	C₂²×D₄	—	53	1	no	—
1239	C₂²×D₄	—	212	4	no	—
1240	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1241	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1242	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1243	C₂³×C₄	—	53	1	no	—
1244	C₂³×C₄	—	53	1	no	—
1245	C₂³×C₄	—	53	1	no	—
1246	C₂³×C₄	—	53	1	no	—
1247	C₂³×C₄	—	53	1	no	—
1248	C₂³×C₄	—	53	1	no	—
1249	C₂³×C₄	—	53	1	no	—
1250	C₂³×C₄	—	53	1	no	—
1251	C₂³×C₄	—	53	1	no	—
1252	C₂³×C₄	—	53	1	no	—
1253	C₂³×C₄	—	53	1	no	—
1254	C₂³×C₄	—	53	1	no	—
1255	C₂³×C₄	—	53	1	no	—
1256	C₂³×C₄	—	53	1	no	—
1257	C₂³×C₄	—	53	1	no	—
1258	C₂³×C₄	—	53	1	no	—
1259	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1260	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1261	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1262	C₄⋊Q₈	—	53	8	no	—
1263	C₄⋊Q₈	—	53	8	no	—
1264	C₄⋊Q₈	—	53	8	no	—
1265	C₄⋊Q₈	—	53	8	no	—
1266	C₄⋊Q₈	—	53	8	no	—
1267	C₄⋊Q₈	—	53	8	no	—
1268	C₄⋊Q₈	—	53	8	no	—
1269	C₄⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
1270	#126	—	53	8	no	—
1271	#126	—	53	8	no	—
1272	#126	—	53	8	no	—
1273	#126	—	53	8	no	—
1274	#126	—	53	8	no	—
1275	#126	—	53	8	no	—
1276	#126	—	53	8	no	—
1277	#126	—	53	8	no	—
1278	#126	—	53	8	no	—
1279	#126	—	53	8	no	—
1280	#126	—	53	8	no	—
1281	#126	—	53	8	no	—
1282	#126	C₂²×D₅₃	1	8	yes	complemented
1283	#126	C₂²×D₅₃	1	8	yes	complemented
1284	#125	—	53	8	no	—
1285	#125	—	53	8	no	—
1286	#125	—	53	8	no	—
1287	#124	—	53	8	no	—
1288	#124	—	53	8	no	—
1289	#124	—	53	8	no	—
1290	#124	—	53	8	no	—
1291	#124	—	53	8	no	—
1292	#124	—	53	8	no	—
1293	#124	—	53	8	no	—
1294	#124	—	53	8	no	—
1295	#124	—	53	8	no	—
1296	#124	—	53	8	no	—
1297	#124	—	53	8	no	—
1298	#124	—	53	8	no	—
1299	#124	—	53	8	no	—
1300	#124	—	53	8	no	—
1301	#124	—	53	8	no	—
1302	#124	—	53	8	no	—
1303	#124	C₂²×D₅₃	1	8	yes	—
1304	#124	C₂²×D₅₃	1	8	yes	complemented
1305	#124	C₂²×D₅₃	1	8	yes	complemented
1306	#123	—	53	8	no	—
1307	#123	—	53	8	no	—
1308	#123	—	53	8	no	—
1309	#123	—	53	8	no	—
1310	#123	—	53	8	no	—
1311	#123	—	53	8	no	—
1312	#123	—	53	8	no	—
1313	#123	—	53	8	no	—
1314	#123	—	53	8	no	—
1315	#123	—	53	8	no	—
1316	#123	—	53	8	no	—
1317	#123	—	53	8	no	—
1318	#123	—	53	8	no	—
1319	#123	—	53	8	no	—
1320	#123	—	53	8	no	—
1321	#123	—	53	8	no	—
1322	#123	C₂²×D₅₃	1	8	yes	—
1323	#123	C₂²×D₅₃	1	8	yes	complemented
1324	C₂²⋊Q₈	—	53	8	no	—
1325	C₂²⋊Q₈	—	53	8	no	—
1326	C₂²⋊Q₈	—	53	8	no	—
1327	C₂²⋊Q₈	—	53	8	no	—
1328	C₂²⋊Q₈	—	53	8	no	—
1329	C₂²⋊Q₈	—	53	8	no	—
1330	C₂²⋊Q₈	—	53	8	no	—
1331	C₂²⋊Q₈	—	53	8	no	—
1332	C₂²⋊Q₈	—	53	8	no	—
1333	C₂²⋊Q₈	—	53	8	no	—
1334	C₂²⋊Q₈	—	53	8	no	—
1335	C₂²⋊Q₈	—	53	8	no	—
1336	C₂²⋊Q₈	—	53	8	no	—
1337	C₂²⋊Q₈	—	53	8	no	—
1338	C₂²⋊Q₈	—	53	8	no	—
1339	C₂²⋊Q₈	—	53	8	no	—
1340	C₂²⋊Q₈	—	53	8	no	—
1341	C₂²⋊Q₈	—	53	8	no	—
1342	C₂²⋊Q₈	—	53	8	no	—
1343	C₂²⋊Q₈	—	53	8	no	—
1344	C₂²⋊Q₈	—	53	8	no	—
1345	C₂²⋊Q₈	—	53	8	no	—
1346	C₂²⋊Q₈	—	53	8	no	—
1347	C₂²⋊Q₈	—	53	8	no	—
1348	C₂²⋊Q₈	—	53	8	no	—
1349	C₂²⋊Q₈	—	53	8	no	—
1350	C₂²⋊Q₈	—	53	8	no	—
1351	C₂²⋊Q₈	—	53	8	no	—
1352	C₂²⋊Q₈	—	53	8	no	—
1353	C₂²⋊Q₈	—	53	8	no	—
1354	C₂²⋊Q₈	—	53	8	no	—
1355	C₂²⋊Q₈	—	53	8	no	—
1356	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
1357	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
1358	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
1359	#121	—	53	8	no	—
1360	#121	—	53	8	no	—
1361	#121	—	53	8	no	—
1362	#121	—	53	8	no	—
1363	#121	—	53	8	no	—
1364	#121	—	53	8	no	—
1365	#121	—	53	8	no	—
1366	#121	—	53	8	no	—
1367	#121	—	53	8	no	—
1368	#121	—	53	8	no	—
1369	#121	C₂²×D₅₃	1	8	yes	—
1370	#120	—	53	8	no	—
1371	#120	—	53	8	no	—
1372	#120	—	53	8	no	—
1373	#120	—	53	8	no	—
1374	C₄×Q₈	—	53	8	no	—
1375	C₄×Q₈	—	53	8	no	—
1376	C₄×Q₈	—	53	8	no	—
1377	C₄×Q₈	—	53	8	no	—
1378	C₄×Q₈	—	53	8	no	—
1379	C₄×Q₈	—	53	8	no	—
1380	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
1381	C₄×D₄	—	53	8	no	—
1382	C₄×D₄	—	53	8	no	—
1383	C₄×D₄	—	53	8	no	—
1384	C₄×D₄	—	53	8	no	—
1385	C₄×D₄	—	53	8	no	—
1386	C₄×D₄	—	53	8	no	—
1387	C₄×D₄	—	53	8	no	—
1388	C₄×D₄	—	53	8	no	—
1389	C₄×D₄	—	53	8	no	—
1390	C₄×D₄	—	53	8	no	—
1391	C₄×D₄	—	53	8	no	—
1392	C₄×D₄	—	53	8	no	—
1393	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1394	#117	—	53	8	no	—
1395	#117	—	53	8	no	—
1396	#117	—	53	8	no	—
1397	#117	—	53	8	no	—
1398	#117	—	53	8	no	—
1399	#117	—	53	8	no	—
1400	#117	—	53	8	no	—
1401	#117	C₂²×D₅₃	1	8	yes	complemented
1402	C₂×C₄⋊C₄	—	53	1	no	—
1403	C₂×C₄⋊C₄	—	53	1	no	—
1404	C₂×C₄⋊C₄	—	53	1	no	—
1405	C₂×C₄⋊C₄	—	53	1	no	—
1406	C₂×C₄⋊C₄	—	53	1	no	—
1407	C₂×C₄⋊C₄	—	53	1	no	—
1408	C₂×C₄⋊C₄	—	53	1	no	—
1409	C₂×C₄⋊C₄	—	53	1	no	—
1410	C₂×C₄⋊C₄	—	53	1	no	—
1411	C₂×C₄⋊C₄	—	53	1	no	—
1412	C₂×C₄⋊C₄	—	53	1	no	—
1413	C₂×C₄⋊C₄	—	53	1	no	—
1414	C₂×C₄⋊C₄	—	53	1	no	—
1415	C₂×C₄⋊C₄	—	53	1	no	—
1416	C₂×C₄⋊C₄	—	53	1	no	—
1417	C₂×C₄⋊C₄	—	53	1	no	—
1418	C₂×C₄⋊C₄	—	53	1	no	—
1419	C₂×C₄⋊C₄	—	53	1	no	—
1420	C₂×C₄⋊C₄	—	53	1	no	—
1421	C₂×C₄⋊C₄	—	53	1	no	—
1422	C₂×C₄⋊C₄	—	53	1	no	—
1423	C₂×C₄⋊C₄	—	53	1	no	—
1424	C₂×C₄⋊C₄	—	53	1	no	—
1425	C₂×C₄⋊C₄	—	53	1	no	—
1426	C₂×C₄⋊C₄	—	53	1	no	—
1427	C₂×C₄⋊C₄	—	53	1	no	—
1428	C₂×C₄⋊C₄	—	53	1	no	—
1429	C₂×C₄⋊C₄	—	53	1	no	—
1430	C₂×C₄⋊C₄	—	53	1	no	—
1431	C₂×C₄⋊C₄	—	53	1	no	—
1432	C₂×C₄⋊C₄	—	53	1	no	—
1433	C₂×C₄⋊C₄	—	53	1	no	—
1434	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1435	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1436	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1437	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1438	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1439	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1440	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1441	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1442	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1443	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1444	C₂×C₂²⋊C₄	—	53	1	no	—
1445	C₂×C₂²⋊C₄	—	53	1	no	—
1446	C₂×C₂²⋊C₄	—	53	1	no	—
1447	C₂×C₂²⋊C₄	—	53	1	no	—
1448	C₂×C₂²⋊C₄	—	53	1	no	—
1449	C₂×C₂²⋊C₄	—	53	1	no	—
1450	C₂×C₂²⋊C₄	—	53	1	no	—
1451	C₂×C₂²⋊C₄	—	53	1	no	—
1452	C₂×C₂²⋊C₄	—	53	1	no	—
1453	C₂×C₂²⋊C₄	—	53	1	no	—
1454	C₂×C₂²⋊C₄	—	53	1	no	—
1455	C₂×C₂²⋊C₄	—	53	1	no	—
1456	C₂×C₂²⋊C₄	—	53	1	no	—
1457	C₂×C₂²⋊C₄	—	53	1	no	—
1458	C₂×C₂²⋊C₄	—	53	1	no	—
1459	C₂×C₂²⋊C₄	—	53	1	no	—
1460	C₂×C₂²⋊C₄	—	53	1	no	—
1461	C₂×C₂²⋊C₄	—	53	1	no	—
1462	C₂×C₂²⋊C₄	—	53	1	no	—
1463	C₂×C₂²⋊C₄	—	53	1	no	—
1464	C₂×C₂²⋊C₄	—	53	1	no	—
1465	C₂×C₂²⋊C₄	—	53	1	no	—
1466	C₂×C₂²⋊C₄	—	53	1	no	—
1467	C₂×C₂²⋊C₄	—	53	1	no	—
1468	C₂×C₂²⋊C₄	—	53	1	no	—
1469	C₂×C₂²⋊C₄	—	53	1	no	—
1470	C₂×C₂²⋊C₄	—	53	1	no	—
1471	C₂×C₂²⋊C₄	—	53	1	no	—
1472	C₂×C₂²⋊C₄	—	53	8	no	—
1473	C₂×C₂²⋊C₄	—	53	8	no	—
1474	C₂×C₂²⋊C₄	—	53	1	no	—
1475	C₂×C₂²⋊C₄	—	53	1	no	—
1476	C₂×C₂²⋊C₄	—	53	1	no	—
1477	C₂×C₂²⋊C₄	—	53	1	no	—
1478	C₂×C₂²⋊C₄	—	53	1	no	—
1479	C₂×C₂²⋊C₄	—	53	1	no	—
1480	C₂×C₂²⋊C₄	—	53	1	no	—
1481	C₂×C₂²⋊C₄	—	53	1	no	—
1482	C₂×C₂²⋊C₄	—	53	1	no	—
1483	C₂×C₂²⋊C₄	—	53	1	no	—
1484	C₂×C₂²⋊C₄	—	53	8	no	—
1485	C₂×C₂²⋊C₄	—	53	8	no	—
1486	C₂×C₂²⋊C₄	—	53	8	no	—
1487	C₂×C₂²⋊C₄	—	53	8	no	—
1488	C₂×C₂²⋊C₄	—	53	8	no	—
1489	C₂×C₂²⋊C₄	—	53	8	no	—
1490	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1491	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1492	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1493	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1494	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1495	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1496	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1497	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1498	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1499	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1500	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1501	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1502	C₂×C₄²	—	53	1	no	—
1503	C₂×C₄²	—	53	1	no	—
1504	C₂×C₄²	—	53	1	no	—
1505	C₂×C₄²	—	53	1	no	—
1506	C₂×C₄²	—	53	1	no	—
1507	C₂×C₄²	—	53	1	no	—
1508	C₂×C₄²	—	53	1	no	—
1509	C₂×C₄²	—	53	1	no	—
1510	C₂×C₄²	—	53	1	no	—
1511	C₂×C₄²	—	53	1	no	—
1512	C₂×C₄²	—	53	8	no	—
1513	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1514	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1515	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1516	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1517	C₂⁴	—	53	1	no	—
1518	C₂⁴	—	53	1	no	—
1519	C₂⁴	—	53	1	no	—
1520	C₂⁴	—	53	1	no	—
1521	C₂⁴	—	53	4	no	—
1522	C₂⁴	—	53	4	no	—
1523	C₂⁴	—	106	4	no	—
1524	C₂⁴	—	106	4	no	—
1525	C₂⁴	—	212	2	no	—
1526	C₂⁴	—	212	2	no	—
1527	C₂⁴	—	212	2	no	—
1528	C₂⁴	—	212	2	no	—
1529	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1530	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1531	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1532	#41	—	212	16	no	—
1533	#41	—	212	16	no	—
1534	C₂×Q₈	—	4	2	no	—
1535	C₂×Q₈	—	4	2	no	—
1536	C₂×Q₈	—	4	2	no	—
1537	C₂×Q₈	—	53	4	no	—
1538	C₂×Q₈	—	53	4	no	—
1539	C₂×Q₈	—	53	4	no	—
1540	C₂×Q₈	—	53	4	no	—
1541	C₂×Q₈	—	53	4	no	—
1542	C₂×Q₈	—	53	4	no	—
1543	C₂×Q₈	—	53	4	no	—
1544	C₂×Q₈	—	53	4	no	—
1545	C₂×Q₈	—	53	4	no	—
1546	C₂×Q₈	—	53	4	no	—
1547	C₂×Q₈	—	106	4	no	—
1548	C₂×Q₈	—	106	4	no	—
1549	C₂×Q₈	—	106	4	no	—
1550	C₂×Q₈	—	106	4	no	—
1551	C₂×Q₈	—	212	2	no	—
1552	C₂×Q₈	—	212	2	no	—
1553	C₂×Q₈	—	212	2	no	—
1554	C₂×Q₈	—	212	2	no	—
1555	C₂×Q₈	—	212	2	no	—
1556	C₂×Q₈	—	212	2	no	—
1557	C₂×Q₈	—	212	16	no	—
1558	C₂×Q₈	—	212	16	no	—
1559	C₂×Q₈	—	212	16	no	—
1560	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1561	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1562	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1563	C₂×D₄	—	4	2	no	—
1564	C₂×D₄	—	4	2	no	—
1565	C₂×D₄	—	4	2	no	—
1566	C₂×D₄	—	53	4	no	—
1567	C₂×D₄	—	53	4	no	—
1568	C₂×D₄	—	53	4	no	—
1569	C₂×D₄	—	53	4	no	—
1570	C₂×D₄	—	53	4	no	—
1571	C₂×D₄	—	53	4	no	—
1572	C₂×D₄	—	53	4	no	—
1573	C₂×D₄	—	53	4	no	—
1574	C₂×D₄	—	53	4	no	—
1575	C₂×D₄	—	53	4	no	—
1576	C₂×D₄	—	53	4	no	—
1577	C₂×D₄	—	53	4	no	—
1578	C₂×D₄	—	106	4	no	—
1579	C₂×D₄	—	106	4	no	—
1580	C₂×D₄	—	106	4	no	—
1581	C₂×D₄	—	106	4	no	—
1582	C₂×D₄	—	212	2	no	—
1583	C₂×D₄	—	212	2	no	—
1584	C₂×D₄	—	212	2	no	—
1585	C₂×D₄	—	212	16	no	—
1586	C₂×D₄	—	212	2	no	—
1587	C₂×D₄	—	212	2	no	—
1588	C₂×D₄	—	212	2	no	—
1589	C₂×D₄	—	212	2	no	—
1590	C₂×D₄	—	212	2	no	—
1591	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1592	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1593	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1594	C₂²×C₄	—	4	2	no	—
1595	C₂²×C₄	—	4	2	no	—
1596	C₂²×C₄	—	4	2	no	—
1597	C₂²×C₄	—	53	1	no	—
1598	C₂²×C₄	—	53	4	no	—
1599	C₂²×C₄	—	53	1	no	—
1600	C₂²×C₄	—	53	1	no	—
1601	C₂²×C₄	—	53	1	no	—
1602	C₂²×C₄	—	53	1	no	—
1603	C₂²×C₄	—	53	1	no	—
1604	C₂²×C₄	—	53	1	no	—
1605	C₂²×C₄	—	53	1	no	—
1606	C₂²×C₄	—	53	1	no	—
1607	C₂²×C₄	—	53	1	no	—
1608	C₂²×C₄	—	53	1	no	—
1609	C₂²×C₄	—	53	1	no	—
1610	C₂²×C₄	—	53	4	no	—
1611	C₂²×C₄	—	53	4	no	—
1612	C₂²×C₄	—	53	4	no	—
1613	C₂²×C₄	—	53	4	no	—
1614	C₂²×C₄	—	53	4	no	—
1615	C₂²×C₄	—	53	4	no	—
1616	C₂²×C₄	—	53	4	no	—
1617	C₂²×C₄	—	53	4	no	—
1618	C₂²×C₄	—	53	4	no	—
1619	C₂²×C₄	—	53	4	no	—
1620	C₂²×C₄	—	53	4	no	—
1621	C₂²×C₄	—	53	4	no	—
1622	C₂²×C₄	—	53	4	no	—
1623	C₂²×C₄	—	53	4	no	—
1624	C₂²×C₄	—	53	4	no	—
1625	C₂²×C₄	—	106	4	no	—
1626	C₂²×C₄	—	106	4	no	—
1627	C₂²×C₄	—	106	4	no	—
1628	C₂²×C₄	—	106	4	no	—
1629	C₂²×C₄	—	212	2	no	—
1630	C₂²×C₄	—	212	2	no	—
1631	C₂²×C₄	—	212	2	no	—
1632	C₂²×C₄	—	212	2	no	—
1633	C₂²×C₄	—	212	2	no	—
1634	C₂²×C₄	—	212	2	no	—
1635	C₂²×C₄	—	212	2	no	—
1636	C₂²×C₄	—	212	2	no	—
1637	C₂²×C₄	—	212	2	no	—
1638	C₂²×C₄	—	212	2	no	—
1639	C₂²×C₄	—	212	2	no	—
1640	C₂²×C₄	—	212	2	no	—
1641	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1642	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1643	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1644	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1645	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1646	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1647	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1648	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1649	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1650	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1651	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1652	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1653	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1654	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1655	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1656	C₄⋊C₄	—	53	4	no	—
1657	C₄⋊C₄	—	53	4	no	—
1658	C₄⋊C₄	—	53	4	no	—
1659	C₄⋊C₄	—	53	4	no	—
1660	C₄⋊C₄	—	53	4	no	—
1661	C₄⋊C₄	—	53	4	no	—
1662	C₄⋊C₄	—	53	4	no	—
1663	C₄⋊C₄	—	53	4	no	—
1664	C₄⋊C₄	—	53	4	no	—
1665	C₄⋊C₄	—	53	4	no	—
1666	C₄⋊C₄	—	53	4	no	—
1667	C₄⋊C₄	—	53	4	no	—
1668	C₄⋊C₄	—	53	4	no	—
1669	C₄⋊C₄	—	53	4	no	—
1670	C₄⋊C₄	—	53	4	no	—
1671	C₄⋊C₄	—	53	4	no	—
1672	C₄⋊C₄	—	53	4	no	—
1673	C₄⋊C₄	—	53	4	no	—
1674	C₄⋊C₄	—	53	4	no	—
1675	C₄⋊C₄	—	53	4	no	—
1676	C₄⋊C₄	—	53	4	no	—
1677	C₄⋊C₄	—	53	4	no	—
1678	C₄⋊C₄	—	53	4	no	—
1679	C₄⋊C₄	—	53	4	no	—
1680	C₄⋊C₄	—	53	4	no	—
1681	C₄⋊C₄	—	53	4	no	—
1682	C₄⋊C₄	—	53	4	no	—
1683	C₄⋊C₄	—	53	4	no	—
1684	C₄⋊C₄	—	53	4	no	—
1685	C₄⋊C₄	—	53	4	no	—
1686	C₄⋊C₄	—	53	4	no	—
1687	C₄⋊C₄	—	53	4	no	—
1688	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1689	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1690	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1691	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1692	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1693	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1694	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1695	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1696	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1697	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1698	C₂²⋊C₄	—	53	4	no	—
1699	C₂²⋊C₄	—	53	4	no	—
1700	C₂²⋊C₄	—	53	4	no	—
1701	C₂²⋊C₄	—	53	4	no	—
1702	C₂²⋊C₄	—	53	4	no	—
1703	C₂²⋊C₄	—	53	4	no	—
1704	C₂²⋊C₄	—	53	4	no	—
1705	C₂²⋊C₄	—	53	4	no	—
1706	C₂²⋊C₄	—	53	4	no	—
1707	C₂²⋊C₄	—	53	4	no	—
1708	C₂²⋊C₄	—	53	4	no	—
1709	C₂²⋊C₄	—	53	4	no	—
1710	C₂²⋊C₄	—	53	4	no	—
1711	C₂²⋊C₄	—	53	4	no	—
1712	C₂²⋊C₄	—	53	4	no	—
1713	C₂²⋊C₄	—	53	4	no	—
1714	C₂²⋊C₄	—	53	4	no	—
1715	C₂²⋊C₄	—	53	4	no	—
1716	C₂²⋊C₄	—	53	4	no	—
1717	C₂²⋊C₄	—	53	4	no	—
1718	C₂²⋊C₄	—	53	4	no	—
1719	C₂²⋊C₄	—	53	4	no	—
1720	C₂²⋊C₄	—	53	4	no	—
1721	C₂²⋊C₄	—	53	4	no	—
1722	C₂²⋊C₄	—	53	4	no	—
1723	C₂²⋊C₄	—	53	4	no	—
1724	C₂²⋊C₄	—	53	4	no	—
1725	C₂²⋊C₄	—	53	4	no	—
1726	C₂²⋊C₄	—	53	4	no	—
1727	C₂²⋊C₄	—	53	4	no	—
1728	C₂²⋊C₄	—	53	4	no	—
1729	C₂²⋊C₄	—	53	4	no	—
1730	C₂²⋊C₄	—	53	4	no	—
1731	C₂²⋊C₄	—	53	4	no	—
1732	C₂²⋊C₄	—	53	4	no	—
1733	C₂²⋊C₄	—	53	4	no	—
1734	C₂²⋊C₄	—	53	4	no	—
1735	C₂²⋊C₄	—	53	4	no	—
1736	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1737	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1738	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1739	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1740	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1741	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1742	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1743	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1744	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1745	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1746	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1747	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1748	C₄²	—	53	4	no	—
1749	C₄²	—	53	4	no	—
1750	C₄²	—	53	4	no	—
1751	C₄²	—	53	4	no	—
1752	C₄²	—	53	4	no	—
1753	C₄²	—	53	4	no	—
1754	C₄²	—	53	4	no	—
1755	C₄²	—	53	4	no	—
1756	C₄²	—	53	4	no	—
1757	C₄²	—	53	4	no	—
1758	C₄²	C₂³×D₅₃	1	4	yes	—
1759	C₄²	C₂³×D₅₃	1	4	yes	—
1760	C₄²	C₂³×D₅₃	1	4	yes	—
1761	C₄²	C₂³×D₅₃	1	4	yes	—
1762	C₂³	—	2	2	no	—
1763	C₂³	—	2	2	no	—
1764	C₂³	—	2	2	no	—
1765	C₂³	—	2	2	no	—
1766	C₂³	—	2	2	no	—
1767	C₂³	—	2	2	no	—
1768	C₂³	—	2	2	no	—
1769	C₂³	—	2	2	no	—
1770	C₂³	—	2	2	no	—
1771	C₂³	—	53	4	no	—
1772	C₂³	—	53	2	no	—
1773	C₂³	—	53	2	no	—
1774	C₂³	—	53	2	no	—
1775	C₂³	—	53	2	no	—
1776	C₂³	—	106	8	no	—
1777	C₂³	—	106	8	no	—
1778	C₂³	—	106	2	no	—
1779	C₂³	—	106	2	no	—
1780	C₂³	—	106	2	no	—
1781	C₂³	—	106	2	no	—
1782	C₂³	—	106	2	no	—
1783	C₂³	—	106	2	no	—
1784	C₂³	—	106	2	no	—
1785	C₂³	—	106	2	no	—
1786	C₂³	—	106	2	no	—
1787	C₂³	—	106	2	no	—
1788	C₂³	—	106	2	no	—
1789	C₂³	—	424	8	no	—
1790	C₂³	—	424	8	no	—
1791	C₂³	—	212	4	no	—
1792	C₂³	—	212	4	no	—
1793	C₂³	—	212	4	no	—
1794	C₂³	—	212	4	no	—
1795	C₂³	C₂⁴×D₅₃	1	2	yes	—
1796	C₂³	C₂⁴×D₅₃	1	2	yes	—
1797	C₂³	C₂⁴×D₅₃	1	2	yes	—
1798	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1799	Q₈	—	4	4	no	—
1800	Q₈	—	4	4	no	—
1801	Q₈	—	4	4	no	—
1802	Q₈	—	106	8	no	—
1803	Q₈	—	106	8	no	—
1804	Q₈	—	106	8	no	—
1805	Q₈	—	106	8	no	—
1806	Q₈	—	212	4	no	—
1807	Q₈	—	212	4	no	—
1808	Q₈	—	212	4	no	—
1809	Q₈	—	212	4	no	—
1810	Q₈	—	212	4	no	—
1811	Q₈	—	212	4	no	—
1812	D₄	—	4	4	no	—
1813	D₄	—	4	4	no	—
1814	D₄	—	4	4	no	—
1815	D₄	—	106	8	no	—
1816	D₄	—	106	8	no	—
1817	D₄	—	106	8	no	—
1818	D₄	—	106	8	no	—
1819	D₄	—	212	4	no	—
1820	D₄	—	212	4	no	—
1821	D₄	—	212	4	no	—
1822	D₄	—	212	4	no	—
1823	D₄	—	212	4	no	—
1824	D₄	—	212	4	no	—
1825	D₄	—	212	4	no	—
1826	D₄	—	212	4	no	—
1827	C₂×C₄	—	2	2	no	—
1828	C₂×C₄	—	2	2	no	—
1829	C₂×C₄	—	2	2	no	—
1830	C₂×C₄	—	2	2	no	—
1831	C₂×C₄	—	2	2	no	—
1832	C₂×C₄	—	2	2	no	—
1833	C₂×C₄	—	2	2	no	—
1834	C₂×C₄	—	2	2	no	—
1835	C₂×C₄	—	2	2	no	—
1836	C₂×C₄	—	2	2	no	—
1837	C₂×C₄	—	2	2	no	—
1838	C₂×C₄	—	2	2	no	—
1839	C₂×C₄	—	4	4	no	—
1840	C₂×C₄	—	4	4	no	—
1841	C₂×C₄	—	4	4	no	—
1842	C₂×C₄	—	53	4	no	—
1843	C₂×C₄	—	53	2	no	—
1844	C₂×C₄	—	53	2	no	—
1845	C₂×C₄	—	53	2	no	—
1846	C₂×C₄	—	53	2	no	—
1847	C₂×C₄	—	53	2	no	—
1848	C₂×C₄	—	53	2	no	—
1849	C₂×C₄	—	53	2	no	—
1850	C₂×C₄	—	53	2	no	—
1851	C₂×C₄	—	53	2	no	—
1852	C₂×C₄	—	53	2	no	—
1853	C₂×C₄	—	53	2	no	—
1854	C₂×C₄	—	53	2	no	—
1855	C₂×C₄	—	106	8	no	—
1856	C₂×C₄	—	106	8	no	—
1857	C₂×C₄	—	106	8	no	—
1858	C₂×C₄	—	106	8	no	—
1859	C₂×C₄	—	106	2	no	—
1860	C₂×C₄	—	106	2	no	—
1861	C₂×C₄	—	106	2	no	—
1862	C₂×C₄	—	106	2	no	—
1863	C₂×C₄	—	106	2	no	—
1864	C₂×C₄	—	106	2	no	—
1865	C₂×C₄	—	106	2	no	—
1866	C₂×C₄	—	106	2	no	—
1867	C₂×C₄	—	106	2	no	—
1868	C₂×C₄	—	106	2	no	—
1869	C₂×C₄	—	106	2	no	—
1870	C₂×C₄	—	212	4	no	—
1871	C₂×C₄	—	212	4	no	—
1872	C₂×C₄	—	212	4	no	—
1873	C₂×C₄	—	212	4	no	—
1874	C₂×C₄	—	212	4	no	—
1875	C₂×C₄	—	212	4	no	—
1876	C₂×C₄	—	212	4	no	—
1877	C₂×C₄	—	212	4	no	—
1878	C₂×C₄	—	212	4	no	—
1879	C₂×C₄	—	212	4	no	—
1880	C₂×C₄	—	212	4	no	—
1881	C₂×C₄	—	212	4	no	—
1882	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1883	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1884	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1885	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1886	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1887	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1888	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1889	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1890	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1891	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1892	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1893	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1894	C₂²	—	2	2	no	—
1895	C₂²	—	2	2	no	—
1896	C₂²	—	2	2	no	—
1897	C₂²	—	2	2	no	—
1898	C₂²	—	2	2	no	—
1899	C₂²	—	2	2	no	—
1900	C₂²	—	2	2	no	—
1901	C₂²	—	2	2	no	—
1902	C₂²	—	2	2	no	—
1903	C₂²	—	4	4	no	—
1904	C₂²	—	4	4	no	—
1905	C₂²	—	4	4	no	—
1906	C₂²	—	53	4	no	—
1907	C₂²	—	106	2	no	—
1908	C₂²	—	106	2	no	—
1909	C₂²	—	106	8	no	—
1910	C₂²	—	106	2	no	—
1911	C₂²	—	106	2	no	—
1912	C₂²	—	106	2	no	—
1913	C₂²	—	106	2	no	—
1914	C₂²	—	106	2	no	—
1915	C₂²	—	106	2	no	—
1916	C₂²	—	106	2	no	—
1917	C₂²	—	106	2	no	—
1918	C₂²	—	106	2	no	—
1919	C₂²	—	424	8	no	—
1920	C₂²	—	424	8	no	—
1921	C₂²	—	212	4	no	—
1922	C₂²	—	212	4	no	—
1923	C₂²	—	212	4	no	—
1924	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	—
1925	C₂²	2₋¹⁺⁴×D₅₃	1	2	yes	—
1926	C₂²	#16811459	1	2	yes	—
1927	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1928	C₄	—	2	2	no	—
1929	C₄	—	2	2	no	—
1930	C₄	—	2	2	no	—
1931	C₄	—	2	2	no	—
1932	C₄	—	2	2	no	—
1933	C₄	—	2	2	no	—
1934	C₄	—	2	2	no	—
1935	C₄	—	2	2	no	—
1936	C₄	—	2	2	no	—
1937	C₄	—	2	2	no	—
1938	C₄	—	2	2	no	—
1939	C₄	—	2	2	no	—
1940	C₄	—	53	4	no	—
1941	C₄	—	106	2	no	—
1942	C₄	—	106	2	no	—
1943	C₄	—	106	2	no	—
1944	C₄	—	106	2	no	—
1945	C₄	—	106	2	no	—
1946	C₄	—	106	2	no	—
1947	C₄	—	106	2	no	—
1948	C₄	—	106	2	no	—
1949	C₄	—	106	2	no	—
1950	C₄	—	106	2	no	—
1951	C₄	—	106	2	no	—
1952	C₂	—	4	2	no	—
1953	C₂	—	4	2	no	—
1954	C₂	—	4	2	no	—
1955	C₂	—	106	4	no	—
1956	C₂	—	212	2	no	—
1957	C₂	—	212	2	no	—
1958	C₂	—	212	2	no	—
1959	C₂	#20289279	1	4	yes	direct product factor
1960	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1961	C₂	C₂×2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1962	C₂	C₂×#16811459	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#542	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#542	D₅₃
hypocenter	C₅₃	C₂×#3561
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20289279	C₂	direct (N × H)
2. C₂×#16811376	C₂	semidirect
3. C₂×#16811372	C₂	semidirect
4. C₂×#16811369	C₂	semidirect
5. C₂×#16811368	C₂	semidirect
6. C₂×#16811341	C₂	semidirect
7. C₂×#16811340	C₂	semidirect
8. C₂×#16811303	C₂	semidirect
9. C₂×#16811302	C₂	semidirect
10. C₂×#16811298	C₂	semidirect
11. C₂×#16811297	C₂	semidirect
12. C₂×#16811288	C₂	semidirect
13. C₂×#16811286	C₂	semidirect
14. C₂×#16811282	C₂	semidirect
15. C₂×#16811281	C₂	semidirect
16. C₂×#16811265	C₂	semidirect
17. C₂×#16811262	C₂	semidirect
18. C₂×#16811248	C₂	semidirect
19. C₂×#16811248	C₂	semidirect
20. C₂×#16811245	C₂	semidirect
21. C₂×#16811243	C₂	semidirect
22. C₂×#16811239	C₂	semidirect
23. C₂×#16811237	C₂	semidirect
24. C₂×#16811237	C₂	semidirect
25. C₂×#16811209	C₂	semidirect
26. C₂×#16811207	C₂	semidirect
27. C₂×#16811196	C₂	semidirect
28. C₂×#16811195	C₂	semidirect
29. C₂×#16811177	C₂	semidirect
30. C₂×#16811156	C₂	semidirect
31. C₂×#124×D₅₃	C₂	semidirect
32. C₂×C₅₃×#542	C₂	semidirect
35. C₂³×Dic₁₀₆	C₂²	semidirect
37. C₂²×Q₈×D₅₃	C₂²	semidirect
39. #16811376	C₂²	semidirect
40. #16811372	C₂²	semidirect
41. #16811369	C₂²	semidirect
42. #16811368	C₂²	semidirect
43. #16811341	C₂²	semidirect
44. #16811340	C₂²	semidirect
45. #16811303	C₂²	semidirect
46. #16811302	C₂²	semidirect
47. #16811298	C₂²	semidirect
48. #16811297	C₂²	semidirect
49. #16811288	C₂²	semidirect
50. #16811286	C₂²	semidirect
51. #16811282	C₂²	semidirect
52. #16811281	C₂²	semidirect
53. #16811265	C₂²	semidirect
54. #16811262	C₂²	semidirect
55. #16811248	C₂²	semidirect
56. #16811248	C₂²	semidirect
57. #16811245	C₂²	semidirect
58. #16811243	C₂²	semidirect
59. #16811239	C₂²	semidirect
60. #16811237	C₂²	semidirect
61. #16811237	C₂²	semidirect
62. #16811209	C₂²	semidirect
63. #16811207	C₂²	semidirect
64. #16811196	C₂²	semidirect
65. #16811195	C₂²	semidirect
66. #16811177	C₂²	semidirect
67. C₂×#13133216	C₂²	semidirect
68. C₂×#13133216	C₂²	semidirect
69. C₂×#13133216	C₂²	semidirect
70. C₂×#13133216	C₂²	semidirect
71. C₂×#13133216	C₂²	semidirect
72. C₂×#13133215	C₂²	semidirect
73. C₂×#13133215	C₂²	semidirect
74. #16811156	C₂²	semidirect
75. C₂×#13133212	C₂²	semidirect
76. C₂×#13133212	C₂²	semidirect
77. C₂×#13133212	C₂²	semidirect
78. C₂×#13133211	C₂²	semidirect
79. C₂×#13133211	C₂²	semidirect
80. C₂×#13133211	C₂²	semidirect
81. C₂×#13133211	C₂²	semidirect
82. C₂×#13133210	C₂²	semidirect
83. C₂×#13133210	C₂²	semidirect
84. C₂×#13133210	C₂²	semidirect
85. C₂×#13133210	C₂²	semidirect
86. C₂×#13133210	C₂²	semidirect
87. C₂×#13133207	C₂²	semidirect
88. C₂×#13133207	C₂²	semidirect
89. C₂×#13133207	C₂²	semidirect
91. C₂×#13133206	C₂²	semidirect
93. C₂×#13133205	C₂²	semidirect
101. C₂×#13133203	C₂²	semidirect
102. C₂×#13133203	C₂²	semidirect
103. C₂×#13133203	C₂²	semidirect
104. C₂×#13133203	C₂²	semidirect
105. C₂×#13133203	C₂²	semidirect
106. #124×D₅₃	C₂²	semidirect
110. C₂×#13133202	C₂²	semidirect
111. C₂×#13133202	C₂²	semidirect
112. C₂×#13133202	C₂²	semidirect
113. C₂×#13133201	C₂²	semidirect
114. C₂×#13133200	C₂²	semidirect
115. C₂×#13133200	C₂²	semidirect
117. C₂×#13133199	C₂²	semidirect
118. C₂×#13133199	C₂²	semidirect
119. C₂×#13133199	C₂²	semidirect
121. C₂×#13133198	C₂²	semidirect
122. C₂×#13133198	C₂²	semidirect
125. C₂×#13133197	C₂²	semidirect
126. C₂×#13133197	C₂²	semidirect
127. C₂×#13133196	C₂²	semidirect
128. C₂×#13133196	C₂²	semidirect
129. C₂×#13133196	C₂²	semidirect
135. C₂×#13133195	C₂²	semidirect
136. C₂×#13133195	C₂²	semidirect
137. C₂×#13133195	C₂²	semidirect
138. C₂×#13133195	C₂²	semidirect
139. C₂×#13133195	C₂²	semidirect
140. C₂×#13133195	C₂²	semidirect
141. C₂×#13133195	C₂²	semidirect
142. C₂×#13133194	C₂²	semidirect
143. C₂×#13133194	C₂²	semidirect
144. C₂×#13133194	C₂²	semidirect
145. C₂×#13133194	C₂²	semidirect
146. C₂×#13133194	C₂²	semidirect
147. C₂×#13133194	C₂²	semidirect
148. C₂×#13133194	C₂²	semidirect
151. C₂×#13133193	C₂²	semidirect
152. C₂×#13133193	C₂²	semidirect
153. C₂×#13133193	C₂²	semidirect
154. C₂×#13133193	C₂²	semidirect
156. C₂×#13133191	C₂²	semidirect
160. C₂×#13133190	C₂²	semidirect
163. C₂×#13133189	C₂²	semidirect
164. C₂×#13133188	C₂²	semidirect
169. C₂×C₄×Dic₁₀₆	C₂²	semidirect
170. C₂×C₄×Dic₁₀₆	C₂²	semidirect
171. C₂×C₄×Dic₁₀₆	C₂²	semidirect
172. C₂×C₄×Dic₁₀₆	C₂²	semidirect
173. C₂×#13133182	C₂²	semidirect
174. C₂×#13133182	C₂²	semidirect
176. C₂×C₄×D₂₁₂	C₂²	semidirect
184. C₂×#13133177	C₂²	semidirect
185. C₂×#13133177	C₂²	semidirect
186. C₂×#13133177	C₂²	semidirect
187. C₂×#13133175	C₂²	semidirect
188. C₂×#13133175	C₂²	semidirect
191. C₂×#13133174	C₂²	semidirect
192. C₂×#13133173	C₂²	semidirect
193. C₂×#13133173	C₂²	semidirect
203. C₅₃×#542	C₂²	semidirect
204. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
205. C₂×#126×C₅₃	C₂²	semidirect
206. C₂×#126×C₅₃	C₂²	semidirect
208. C₂×#124×C₅₃	C₂²	semidirect
209. C₂×#124×C₅₃	C₂²	semidirect
211. C₂×#123×C₅₃	C₂²	semidirect
212. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
213. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
214. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
216. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
217. C₂×C₄×D₄×C₅₃	C₂²	semidirect
218. C₂×#117×C₅₃	C₂²	semidirect
236. C₂²×Dic₁₀₆	C₂³	semidirect
240. C₂×Q₈×D₅₃	C₂³	semidirect
271. #13133216	C₂³	semidirect
272. #13133216	C₂³	semidirect
273. #13133216	C₂³	semidirect
274. #13133216	C₂³	semidirect
275. #13133216	C₂³	semidirect
276. #13133215	C₂³	semidirect
277. #13133215	C₂³	semidirect
278. #13133212	C₂³	semidirect
279. #13133212	C₂³	semidirect
280. #13133212	C₂³	semidirect
281. #13133211	C₂³	semidirect
282. #13133211	C₂³	semidirect
283. #13133211	C₂³	semidirect
284. #13133211	C₂³	semidirect
285. #13133210	C₂³	semidirect
286. #13133210	C₂³	semidirect
287. #13133210	C₂³	semidirect
288. #13133210	C₂³	semidirect
289. #13133210	C₂³	semidirect
290. #13133207	C₂³	semidirect
291. #13133207	C₂³	semidirect
292. #13133207	C₂³	semidirect
294. #13133206	C₂³	semidirect
296. #13133205	C₂³	semidirect
304. #13133203	C₂³	semidirect
305. #13133203	C₂³	semidirect
306. #13133203	C₂³	semidirect
307. #13133203	C₂³	semidirect
308. #13133203	C₂³	semidirect
312. #13133202	C₂³	semidirect
313. #13133202	C₂³	semidirect
314. #13133202	C₂³	semidirect
315. #13133201	C₂³	semidirect
316. #13133200	C₂³	semidirect
317. #13133200	C₂³	semidirect
319. #13133199	C₂³	semidirect
320. #13133199	C₂³	semidirect
321. #13133199	C₂³	semidirect
323. #13133198	C₂³	semidirect
324. #13133198	C₂³	semidirect
327. #13133197	C₂³	semidirect
328. #13133197	C₂³	semidirect
329. #13133196	C₂³	semidirect
330. #13133196	C₂³	semidirect
331. #13133196	C₂³	semidirect
337. #13133195	C₂³	semidirect
338. #13133195	C₂³	semidirect
339. #13133195	C₂³	semidirect
340. #13133195	C₂³	semidirect
341. #13133195	C₂³	semidirect
342. #13133195	C₂³	semidirect
343. #13133195	C₂³	semidirect
344. #13133194	C₂³	semidirect
345. #13133194	C₂³	semidirect
346. #13133194	C₂³	semidirect
347. #13133194	C₂³	semidirect
348. #13133194	C₂³	semidirect
349. #13133194	C₂³	semidirect
350. #13133194	C₂³	semidirect
353. #13133193	C₂³	semidirect
354. #13133193	C₂³	semidirect
355. #13133193	C₂³	semidirect
356. #13133193	C₂³	semidirect
358. #13133191	C₂³	semidirect
362. #13133190	C₂³	semidirect
365. #13133189	C₂³	semidirect
366. #13133188	C₂³	semidirect
371. C₄×Dic₁₀₆	C₂³	semidirect
372. C₄×Dic₁₀₆	C₂³	semidirect
373. C₄×Dic₁₀₆	C₂³	semidirect
374. C₄×Dic₁₀₆	C₂³	semidirect
375. #13133182	C₂³	semidirect
376. #13133182	C₂³	semidirect
378. C₄×D₂₁₂	C₂³	semidirect
386. #13133177	C₂³	semidirect
387. #13133177	C₂³	semidirect
388. #13133177	C₂³	semidirect
389. #13133175	C₂³	semidirect
390. #13133175	C₂³	semidirect
393. #13133174	C₂³	semidirect
394. #13133173	C₂³	semidirect
395. #13133173	C₂³	semidirect
494. C₄⋊Q₈×C₅₃	C₂³	semidirect
495. #126×C₅₃	C₂³	semidirect
496. #126×C₅₃	C₂³	semidirect
498. #124×C₅₃	C₂³	semidirect
499. #124×C₅₃	C₂³	semidirect
501. #123×C₅₃	C₂³	semidirect
502. C₂²⋊Q₈×C₅₃	C₂³	semidirect
503. C₂²⋊Q₈×C₅₃	C₂³	semidirect
504. C₂²⋊Q₈×C₅₃	C₂³	semidirect
506. C₄×Q₈×C₅₃	C₂³	semidirect
507. C₄×D₄×C₅₃	C₂³	semidirect
508. #117×C₅₃	C₂³	semidirect
995. C₂×#542	D₅₃	semidirect
1006. C₂×C₅₃	#3561	semidirect
1043. #542	C₂×D₅₃	semidirect
1056. C₂×C₄⋊Q₈	C₂×D₅₃	semidirect
1070. C₂×#126	C₂×D₅₃	semidirect
1071. C₂×#126	C₂×D₅₃	semidirect
1093. C₂×#124	C₂×D₅₃	semidirect
1094. C₂×#124	C₂×D₅₃	semidirect
1112. C₂×#123	C₂×D₅₃	semidirect
1145. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
1146. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
1147. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
1169. C₂×C₄×Q₈	C₂×D₅₃	semidirect
1182. C₂×C₄×D₄	C₂×D₅₃	semidirect
1190. C₂×#117	C₂×D₅₃	semidirect
1200. C₅₃	C₂×#3561	semidirect
1269. C₄⋊Q₈	C₂²×D₅₃	semidirect
1282. #126	C₂²×D₅₃	semidirect
1283. #126	C₂²×D₅₃	semidirect
1304. #124	C₂²×D₅₃	semidirect
1305. #124	C₂²×D₅₃	semidirect
1323. #123	C₂²×D₅₃	semidirect
1356. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1357. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1358. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1380. C₄×Q₈	C₂²×D₅₃	semidirect
1393. C₄×D₄	C₂²×D₅₃	semidirect
1401. #117	C₂²×D₅₃	semidirect
1959. C₂	#20289279	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20289279	2
C₂×#16811376	2
C₂×#16811372	2
C₂×#16811369	2
C₂×#16811368	2
C₂×#16811341	2
C₂×#16811340	2
C₂×#16811303	2
C₂×#16811302	2
C₂×#16811298	2
C₂×#16811297	2
C₂×#16811288	2
C₂×#16811286	2
C₂×#16811282	2
C₂×#16811281	2
C₂×#16811265	2
C₂×#16811262	2
C₂×#16811248	2
C₂×#16811245	2
C₂×#16811243	2
C₂×#16811239	2
C₂×#16811237	2
C₂×#16811209	2
C₂×#16811207	2
C₂×#16811196	2
C₂×#16811195	2
C₂×#16811177	2
C₂×#16811156	2
C₂×#124×D₅₃	2
C₂×C₅₃×#542	2
C₂×#3561	53

Subgroups — C2×#20289279 #28291435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20289279 #28291435