Subgroups — D₅₃×#2335 #27542978

Order 13568.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#123×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20277512	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277511	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277510	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277509	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277508	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277507	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277506	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277505	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277504	C₂	1	1	yes	maximal, characteristic, complemented
11	#20277503	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277502	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277501	C₂	1	1	yes	maximal, characteristic, complemented
14	#20277500	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277499	C₂	1	1	yes	maximal, characteristic, complemented
16	#20277498	C₂	1	1	yes	maximal, characteristic, complemented
17	#390×D₅₃	C₂	1	1	yes	maximal, characteristic
18	#389×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#388×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#388×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#388×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#388×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	#386×D₅₃	C₂	1	1	yes	maximal, characteristic
26	#385×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
27	#380×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
34	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
35	C₂×#13133202	C₂²	1	1	yes	characteristic
36	C₂×#13133202	C₂²	1	1	yes	characteristic
37	C₂×#13133201	C₂²	1	1	yes	characteristic
38	C₂×#13133200	C₂²	1	1	yes	characteristic
39	C₂×#13133199	C₂²	1	1	yes	characteristic
40	C₂×#13133199	C₂²	1	1	yes	characteristic
41	C₂×#13133198	C₂²	1	1	yes	characteristic
42	#123×D₅₃	C₄	1	16	yes	complemented
43	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
60	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
61	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
62	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
65	#16810526	C₂²	1	1	yes	characteristic
66	#16810525	C₂²	1	1	yes	characteristic
67	#16810524	C₂²	1	1	yes	characteristic
68	#16810523	C₂²	1	1	yes	characteristic
69	#16810523	C₂²	1	1	yes	characteristic
70	#16810523	C₂²	1	1	yes	characteristic
71	#16810523	C₂²	1	1	yes	characteristic
72	#16810522	C₂²	1	1	yes	characteristic, complemented
73	#16810521	C₂²	1	1	yes	characteristic, complemented
74	#16810520	C₂²	1	1	yes	characteristic, complemented
75	#16810520	C₂²	1	1	yes	characteristic, complemented
76	#16810519	C₂²	1	1	yes	characteristic, complemented
77	#16810518	C₂²	1	1	yes	characteristic, complemented
78	#16810518	C₂²	1	1	yes	characteristic, complemented
79	#16810517	C₂²	1	1	yes	characteristic, complemented
80	#16810517	C₂²	1	1	yes	characteristic, complemented
81	#16810517	C₂²	1	1	yes	characteristic, complemented
82	#16810517	C₂²	1	1	yes	characteristic, complemented
83	#16810516	C₂²	1	1	yes	characteristic, complemented
84	#16810516	C₂²	1	1	yes	characteristic, complemented
85	#16810516	C₂²	1	1	yes	characteristic, complemented
86	#16810516	C₂²	1	1	yes	characteristic, complemented
87	#16810515	C₂²	1	1	yes	characteristic, complemented
88	#16810515	C₂²	1	1	yes	characteristic, complemented
89	#16810515	C₂²	1	1	yes	characteristic, complemented
90	#16810515	C₂²	1	1	yes	characteristic, complemented
91	#16810514	C₂²	1	1	yes	characteristic, complemented
92	#16810514	C₂²	1	1	yes	characteristic, complemented
93	#16810514	C₂²	1	1	yes	characteristic, complemented
94	#16810514	C₂²	1	1	yes	characteristic, complemented
95	#16810513	C₂²	1	1	yes	characteristic, complemented
96	#16810513	C₂²	1	1	yes	characteristic, complemented
97	#16810513	C₂²	1	1	yes	characteristic, complemented
98	#16810513	C₂²	1	1	yes	characteristic, complemented
99	#16810512	C₂²	1	1	yes	characteristic, complemented
100	#16810512	C₂²	1	1	yes	characteristic, complemented
101	#16810512	C₂²	1	1	yes	characteristic, complemented
102	#16810512	C₂²	1	1	yes	characteristic, complemented
103	#16810511	C₂²	1	1	yes	characteristic, complemented
104	#16810511	C₂²	1	1	yes	characteristic, complemented
105	#16810511	C₂²	1	1	yes	characteristic, complemented
106	#16810511	C₂²	1	1	yes	characteristic, complemented
107	#16810510	C₂²	1	1	yes	characteristic, complemented
108	#16810510	C₂²	1	1	yes	characteristic, complemented
109	#16810509	C₂²	1	1	yes	characteristic, complemented
110	#16810509	C₂²	1	1	yes	characteristic, complemented
111	#16810508	C₂²	1	1	yes	characteristic, complemented
112	#16810508	C₂²	1	1	yes	characteristic, complemented
113	#16810507	C₂²	1	1	yes	characteristic, complemented
114	#16810507	C₂²	1	1	yes	characteristic, complemented
115	#16810506	C₂²	1	1	yes	characteristic, complemented
116	#16810506	C₂²	1	1	yes	characteristic, complemented
117	#16810505	C₂²	1	1	yes	characteristic, complemented
118	#16810505	C₂²	1	1	yes	characteristic, complemented
119	#16810504	C₂²	1	1	yes	characteristic, complemented
120	#16810504	C₂²	1	1	yes	characteristic, complemented
121	#16810503	C₂²	1	1	yes	characteristic
122	#16810502	C₂²	1	1	yes	characteristic
123	#16810501	C₂²	1	1	yes	characteristic
124	#16810501	C₂²	1	1	yes	characteristic
125	#16810500	C₂²	1	1	yes	characteristic
126	#16810499	C₂²	1	1	yes	characteristic
127	#16810499	C₂²	1	1	yes	characteristic
128	#16810498	C₂²	1	1	yes	characteristic, complemented
129	#16810497	C₂²	1	1	yes	characteristic, complemented
130	#16810497	C₂²	1	1	yes	characteristic, complemented
131	#16810496	C₂²	1	1	yes	characteristic, complemented
132	#16810495	C₂²	1	1	yes	characteristic, complemented
133	#16810494	C₂²	1	1	yes	characteristic, complemented
134	#16810494	C₂²	1	1	yes	characteristic, complemented
135	#16810483	C₂²	1	1	yes	characteristic, complemented
136	#16810482	C₂²	1	1	yes	characteristic, complemented
137	#16810482	C₂²	1	1	yes	characteristic, complemented
138	#16810481	C₂²	1	1	yes	characteristic, complemented
139	#16810481	C₂²	1	1	yes	characteristic, complemented
140	#16810480	C₂²	1	1	yes	characteristic, complemented
141	#16810480	C₂²	1	1	yes	characteristic, complemented
142	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
143	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
144	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
145	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
146	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
147	#16810474	C₂²	1	1	yes	characteristic, complemented
148	#16810474	C₂²	1	1	yes	characteristic, complemented
149	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
150	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
151	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
152	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
153	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
154	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
155	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
156	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
157	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
158	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
159	#16810470	C₂²	1	1	yes	characteristic, complemented
160	#16810470	C₂²	1	1	yes	characteristic, complemented
161	#16810470	C₂²	1	1	yes	characteristic, complemented
162	#16810470	C₂²	1	1	yes	characteristic, complemented
163	#95×D₅₃	C₂²	1	1	yes	characteristic
164	#95×D₅₃	C₂²	1	1	yes	characteristic
165	#95×D₅₃	C₂²	1	1	yes	characteristic
166	#95×D₅₃	C₂²	1	1	yes	characteristic
167	#95×D₅₃	C₂²	1	1	yes	characteristic
168	#95×D₅₃	C₂²	1	1	yes	characteristic
169	#95×D₅₃	C₂²	1	1	yes	characteristic
170	#95×D₅₃	C₂²	1	1	yes	characteristic
171	#95×D₅₃	C₂²	1	1	yes	characteristic
172	#95×D₅₃	C₂²	1	1	yes	characteristic
173	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
174	C₅₃×#390	C₂²	1	1	yes	characteristic
175	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#386	C₂²	1	1	yes	characteristic
183	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
189	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
190	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
191	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
193	C₂×D₄×D₅₃	—	4	2	no	—
194	C₂×D₄×D₅₃	—	4	2	no	—
195	C₂×D₄×D₅₃	C₂×C₄	1	8	yes	—
196	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅₃	—	2	4	no	—
199	C₂²×C₄×D₅₃	—	4	2	no	—
200	C₂²×C₄×D₅₃	—	4	2	no	—
201	C₂²×C₄×D₅₃	—	4	2	no	—
202	C₂²×C₄×D₅₃	—	4	2	no	—
203	C₂²×C₄×D₅₃	C₂×C₄	1	8	yes	complemented
204	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
211	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
214	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
215	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
216	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
217	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
218	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
219	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
220	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
221	#13133202	C₂×C₄	1	8	yes	complemented
222	#13133202	C₂×C₄	1	8	yes	complemented
223	#13133201	C₂×C₄	1	8	yes	complemented
224	#13133200	C₂×C₄	1	8	yes	complemented
225	#13133199	C₂×C₄	1	8	yes	complemented
226	#13133199	C₂×C₄	1	8	yes	complemented
227	#13133198	C₂×C₄	1	8	yes	complemented
228	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	C₂³	1	1	yes	characteristic
243	C₂×#11719919	C₂³	1	1	yes	characteristic
244	C₂×#11719919	C₂³	1	1	yes	characteristic
245	C₂×#11719919	C₂³	1	1	yes	characteristic
246	C₂×#11719919	C₂³	1	1	yes	characteristic
247	C₂×#11719919	C₂³	1	1	yes	characteristic
248	C₂×#11719919	C₂³	1	1	yes	characteristic
249	C₄⋊C₄×D₅₃	—	2	4	no	—
250	C₄⋊C₄×D₅₃	—	4	2	no	—
251	C₄⋊C₄×D₅₃	—	4	2	no	—
252	C₄⋊C₄×D₅₃	—	4	2	no	—
253	C₄⋊C₄×D₅₃	—	4	2	no	—
254	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
255	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
256	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
266	C₂×#11719921	C₂³	1	1	yes	characteristic
267	C₂×#11719921	C₂³	1	1	yes	characteristic
268	C₂×#11719921	C₂³	1	1	yes	characteristic
269	C₂×#11719921	C₂³	1	1	yes	characteristic
270	C₂×#11719921	C₂³	1	1	yes	characteristic
271	C₂×#11719921	C₂³	1	1	yes	characteristic
272	C₂×#11719921	C₂³	1	1	yes	characteristic
273	C₂×#11719921	C₂³	1	1	yes	characteristic
274	C₂×#11719921	C₂³	1	1	yes	characteristic
275	C₂×#11719921	C₂³	1	1	yes	characteristic
276	C₂×#11719921	C₂³	1	1	yes	characteristic
277	C₂×#11719921	C₂³	1	1	yes	characteristic
278	C₂×#11719921	C₂³	1	1	yes	characteristic
279	C₂×#11719921	C₂³	1	1	yes	characteristic
280	C₂×#11719921	C₂³	1	1	yes	characteristic
281	C₂×#11719921	C₂³	1	1	yes	characteristic
282	C₂×#11719921	C₂³	1	1	yes	characteristic
283	C₂×#11719921	C₂³	1	1	yes	characteristic
284	C₂×#11719921	C₂³	1	1	yes	characteristic
285	C₂×#11719921	C₂³	1	1	yes	characteristic
286	C₂²⋊C₄×D₅₃	—	2	4	no	—
287	C₂²⋊C₄×D₅₃	—	2	4	no	—
288	C₂²⋊C₄×D₅₃	—	2	4	no	—
289	C₂²⋊C₄×D₅₃	—	4	2	no	—
290	C₂²⋊C₄×D₅₃	—	4	2	no	—
291	C₂²⋊C₄×D₅₃	—	4	2	no	—
292	C₂²⋊C₄×D₅₃	—	4	2	no	—
293	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
294	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
295	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
296	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
311	C₄²×D₅₃	—	2	4	no	—
312	C₄²×D₅₃	—	4	2	no	—
313	C₄²×D₅₃	—	4	2	no	—
314	C₄²×D₅₃	—	4	2	no	—
315	C₄²×D₅₃	—	4	2	no	—
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	#13133124	C₂³	1	1	yes	characteristic
327	#13133124	C₂³	1	1	yes	characteristic
328	#13133124	C₂³	1	1	yes	characteristic
329	#13133124	C₂³	1	1	yes	characteristic
330	#13133124	C₂³	1	1	yes	characteristic
331	#13133124	C₂³	1	1	yes	characteristic
332	#13133124	C₂³	1	1	yes	characteristic
333	#13133124	C₂³	1	1	yes	characteristic
334	#13133124	C₂³	1	1	yes	characteristic
335	#13133124	C₂³	1	1	yes	characteristic
336	#13133124	C₂³	1	1	yes	characteristic
337	#13133124	C₂³	1	1	yes	characteristic
338	#13133124	C₂³	1	1	yes	characteristic
339	#13133124	C₂³	1	1	yes	characteristic
340	#13133124	C₂³	1	1	yes	characteristic
341	#13133124	C₂³	1	1	yes	characteristic
342	#13133124	C₂³	1	1	yes	characteristic
343	#13133124	C₂³	1	1	yes	characteristic
344	#13133124	C₂³	1	1	yes	characteristic
345	#13133124	C₂³	1	1	yes	characteristic
346	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
349	#123×C₅₃	C₂×C₄	1	8	yes	complemented
350	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
368	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
369	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
370	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
371	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
372	#95×C₅₃	C₂³	1	1	yes	characteristic
373	#95×C₅₃	C₂³	1	1	yes	characteristic
374	#95×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	#95×C₅₃	C₂³	1	1	yes	characteristic
377	#95×C₅₃	C₂³	1	1	yes	characteristic
378	#95×C₅₃	C₂³	1	1	yes	characteristic
379	#95×C₅₃	C₂³	1	1	yes	characteristic
380	#95×C₅₃	C₂³	1	1	yes	characteristic
381	#95×C₅₃	C₂³	1	1	yes	characteristic
382	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂³×D₅₃	—	2	2	no	—
385	C₂³×D₅₃	—	2	2	no	—
386	C₂³×D₅₃	—	2	2	no	—
387	C₂³×D₅₃	—	2	2	no	—
388	C₂³×D₅₃	—	2	2	no	—
389	C₂³×D₅₃	—	2	2	no	—
390	C₂³×D₅₃	—	2	2	no	—
391	C₂³×D₅₃	—	2	2	no	—
392	C₂³×D₅₃	—	2	2	no	—
393	C₂³×D₅₃	—	2	2	no	—
394	C₂³×D₅₃	—	2	2	no	—
395	C₂³×D₅₃	—	2	2	no	—
396	C₂³×D₅₃	C₂²×C₄	1	4	yes	—
397	C₂³×D₅₃	C₂²×C₄	1	4	yes	—
398	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
399	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
400	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×D₄×C₅₃	—	4	1	no	—
402	C₂×D₄×C₅₃	—	4	1	no	—
403	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
404	C₂²×C₄×C₅₃	—	2	2	no	—
405	C₂²×C₄×C₅₃	—	4	1	no	—
406	C₂²×C₄×C₅₃	—	4	1	no	—
407	C₂²×C₄×C₅₃	—	4	1	no	—
408	C₂²×C₄×C₅₃	—	4	1	no	—
409	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
410	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂×C₂²⋊D₅₃	—	4	1	no	—
424	C₂×C₂²⋊D₅₃	—	4	1	no	—
425	C₂×C₂²⋊D₅₃	—	4	1	no	—
426	C₂×C₂²⋊D₅₃	—	4	1	no	—
427	C₂×C₂²⋊D₅₃	C₂²×C₄	1	4	yes	—
428	C₂×C₂²⋊D₅₃	C₂²×C₄	1	4	yes	—
429	C₂²×Dic₅₃	—	2	2	no	—
430	C₂²×Dic₅₃	—	4	1	no	—
431	C₂²×Dic₅₃	—	4	1	no	—
432	C₂²×Dic₅₃	—	4	1	no	—
433	C₂²×Dic₅₃	—	4	1	no	—
434	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	complemented
435	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
436	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
438	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
439	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
440	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
446	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
447	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
448	D₄×D₅₃	—	4	16	no	—
449	C₂×D₂₁₂	—	4	1	no	—
450	C₂×D₂₁₂	—	4	1	no	—
451	C₂×D₂₁₂	C₂²×C₄	1	4	yes	—
452	C₂×C₄×D₅₃	—	2	2	no	—
453	C₂×C₄×D₅₃	—	2	2	no	—
454	C₂×C₄×D₅₃	—	2	2	no	—
455	C₂×C₄×D₅₃	—	2	2	no	—
456	C₂×C₄×D₅₃	—	2	2	no	—
457	C₂×C₄×D₅₃	—	2	2	no	—
458	C₂×C₄×D₅₃	—	2	2	no	—
459	C₂×C₄×D₅₃	—	2	2	no	—
460	C₂×C₄×D₅₃	—	2	2	no	—
461	C₂×C₄×D₅₃	—	2	2	no	—
462	C₂×C₄×D₅₃	—	2	2	no	—
463	C₂×C₄×D₅₃	—	2	2	no	—
464	C₂×C₄×D₅₃	—	2	2	no	—
465	C₂×C₄×D₅₃	—	2	2	no	—
466	C₂×C₄×D₅₃	—	2	2	no	—
467	C₂×C₄×D₅₃	—	2	2	no	—
468	C₂×C₄×D₅₃	—	2	2	no	—
469	C₂×C₄×D₅₃	—	2	2	no	—
470	C₂×C₄×D₅₃	—	2	2	no	—
471	C₂×C₄×D₅₃	—	2	2	no	—
472	C₂×C₄×D₅₃	—	2	2	no	—
473	C₂×C₄×D₅₃	—	2	2	no	—
474	C₂×C₄×D₅₃	—	2	2	no	—
475	C₂×C₄×D₅₃	—	2	2	no	—
476	C₂×C₄×D₅₃	—	2	2	no	—
477	C₂×C₄×D₅₃	—	2	2	no	—
478	C₂×C₄×D₅₃	—	2	2	no	—
479	C₂×C₄×D₅₃	—	2	2	no	—
480	C₂×C₄×D₅₃	—	2	2	no	—
481	C₂×C₄×D₅₃	—	2	2	no	—
482	C₂×C₄×D₅₃	—	2	2	no	—
483	C₂×C₄×D₅₃	—	2	2	no	—
484	C₂×C₄×D₅₃	—	2	2	no	—
485	C₂×C₄×D₅₃	—	2	2	no	—
486	C₂×C₄×D₅₃	—	4	16	no	—
487	C₂×C₄×D₅₃	—	4	16	no	—
488	C₂×C₄×D₅₃	—	4	1	no	—
489	C₂×C₄×D₅₃	—	4	1	no	—
490	C₂×C₄×D₅₃	—	4	1	no	—
491	C₂×C₄×D₅₃	—	4	1	no	—
492	C₂×C₄×D₅₃	—	4	1	no	—
493	C₂×C₄×D₅₃	—	4	1	no	—
494	C₂×C₄×D₅₃	—	4	1	no	—
495	C₂×C₄×D₅₃	—	4	1	no	—
496	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
497	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
498	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
499	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
500	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
501	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	complemented
502	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	complemented
503	C₂×C₄×D₅₃	#41	1	4	yes	—
504	C₂×C₄×D₅₃	#41	1	4	yes	—
505	C₄⋊C₄×C₅₃	—	2	2	no	—
506	C₄⋊C₄×C₅₃	—	4	1	no	—
507	C₄⋊C₄×C₅₃	—	4	1	no	—
508	C₄⋊C₄×C₅₃	—	4	1	no	—
509	C₄⋊C₄×C₅₃	—	4	1	no	—
510	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
511	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
512	C₂²⋊C₄×C₅₃	—	2	2	no	—
513	C₂²⋊C₄×C₅₃	—	2	2	no	—
514	C₂²⋊C₄×C₅₃	—	2	2	no	—
515	C₂²⋊C₄×C₅₃	—	4	1	no	—
516	C₂²⋊C₄×C₅₃	—	4	1	no	—
517	C₂²⋊C₄×C₅₃	—	4	1	no	—
518	C₂²⋊C₄×C₅₃	—	4	1	no	—
519	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
520	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
521	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
522	C₄²×C₅₃	—	2	2	no	—
523	C₄²×C₅₃	—	4	1	no	—
524	C₄²×C₅₃	—	4	1	no	—
525	C₄²×C₅₃	—	4	1	no	—
526	C₄²×C₅₃	—	4	1	no	—
527	C₂²⋊Dic₅₃	—	2	2	no	—
528	C₂²⋊Dic₅₃	—	2	2	no	—
529	C₂²⋊Dic₅₃	—	2	2	no	—
530	C₂²⋊Dic₅₃	—	4	1	no	—
531	C₂²⋊Dic₅₃	—	4	1	no	—
532	C₂²⋊Dic₅₃	—	4	1	no	—
533	C₂²⋊Dic₅₃	—	4	1	no	—
534	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
535	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
536	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	complemented
537	#11719921	—	2	2	no	—
538	#11719921	—	2	2	no	—
539	#11719921	—	2	2	no	—
540	#11719921	—	2	2	no	—
541	#11719921	—	2	2	no	—
542	#11719921	—	2	2	no	—
543	#11719921	—	4	1	no	—
544	#11719921	—	4	1	no	—
545	#11719921	—	4	1	no	—
546	#11719921	—	4	1	no	—
547	#11719921	—	4	1	no	—
548	#11719921	—	4	1	no	—
549	#11719921	—	4	1	no	—
550	#11719921	—	4	1	no	—
551	#11719921	C₂²×C₄	1	4	yes	—
552	#11719921	C₂²×C₄	1	4	yes	—
553	#11719921	C₂²×C₄	1	4	yes	—
554	#11719921	C₂²×C₄	1	4	yes	—
555	#11719921	C₂²×C₄	1	4	yes	complemented
556	#11719921	C₂²×C₄	1	4	yes	complemented
557	C₄⋊Dic₅₃	—	2	2	no	—
558	C₄⋊Dic₅₃	—	4	1	no	—
559	C₄⋊Dic₅₃	—	4	1	no	—
560	C₄⋊Dic₅₃	—	4	1	no	—
561	C₄⋊Dic₅₃	—	4	1	no	—
562	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	complemented
563	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	complemented
564	#11719919	—	2	2	no	—
565	#11719919	—	2	2	no	—
566	#11719919	—	4	1	no	—
567	#11719919	—	4	1	no	—
568	#11719919	—	4	1	no	—
569	#11719919	—	4	1	no	—
570	#11719919	—	4	1	no	—
571	#11719919	—	4	1	no	—
572	#11719919	—	4	1	no	—
573	#11719919	—	4	1	no	—
574	#11719919	C₂²×C₄	1	4	yes	complemented
575	#11719919	C₂²×C₄	1	4	yes	complemented
576	#11719919	C₂²×C₄	1	4	yes	complemented
577	#11719919	C₂²×C₄	1	4	yes	complemented
578	C₄×Dic₅₃	—	2	2	no	—
579	C₄×Dic₅₃	—	2	2	no	—
580	C₄×Dic₅₃	—	2	2	no	—
581	C₄×Dic₅₃	—	4	1	no	—
582	C₄×Dic₅₃	—	4	1	no	—
583	C₄×Dic₅₃	—	4	1	no	—
584	C₄×Dic₅₃	—	4	1	no	—
585	C₄×Dic₅₃	—	4	1	no	—
586	C₄×Dic₅₃	—	4	1	no	—
587	C₄×Dic₅₃	—	4	1	no	—
588	C₄×Dic₅₃	—	4	1	no	—
589	C₄×Dic₅₃	—	4	1	no	—
590	C₄×Dic₅₃	—	4	1	no	—
591	C₄×Dic₅₃	—	4	1	no	—
592	C₄×Dic₅₃	—	4	1	no	—
593	C₂³×C₅₃	—	2	1	no	—
594	C₂³×C₅₃	—	2	1	no	—
595	C₂³×C₅₃	—	2	1	no	—
596	C₂³×C₅₃	—	2	1	no	—
597	C₂³×C₅₃	—	2	1	no	—
598	C₂³×C₅₃	—	2	1	no	—
599	C₂³×C₅₃	—	2	1	no	—
600	C₂³×C₅₃	—	2	1	no	—
601	C₂³×C₅₃	—	2	1	no	—
602	C₂³×C₅₃	—	2	1	no	—
603	C₂³×C₅₃	—	2	1	no	—
604	C₂³×C₅₃	—	2	1	no	—
605	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
606	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
607	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
608	C₂²×D₅₃	—	2	1	no	—
609	C₂²×D₅₃	—	2	1	no	—
610	C₂²×D₅₃	—	2	1	no	—
611	C₂²×D₅₃	—	2	1	no	—
612	C₂²×D₅₃	—	2	1	no	—
613	C₂²×D₅₃	—	2	1	no	—
614	C₂²×D₅₃	—	2	1	no	—
615	C₂²×D₅₃	—	2	1	no	—
616	C₂²×D₅₃	—	2	1	no	—
617	C₂²×D₅₃	—	2	1	no	—
618	C₂²×D₅₃	—	2	1	no	—
619	C₂²×D₅₃	—	2	1	no	—
620	C₂²×D₅₃	—	2	8	no	—
621	C₂²×D₅₃	—	2	8	no	—
622	C₂²×D₅₃	—	2	8	no	—
623	C₂²×D₅₃	—	2	8	no	—
624	C₂²×D₅₃	—	2	8	no	—
625	C₂²×D₅₃	—	2	8	no	—
626	C₂²×D₅₃	—	4	4	no	—
627	C₂²×D₅₃	—	4	4	no	—
628	C₂²×D₅₃	—	4	4	no	—
629	C₂²×D₅₃	—	4	4	no	—
630	C₂²×D₅₃	—	4	4	no	—
631	C₂²×D₅₃	—	4	4	no	—
632	C₂²×D₅₃	—	4	4	no	—
633	C₂²×D₅₃	—	4	4	no	—
634	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
635	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
636	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
637	C₂²×D₅₃	C₂×#41	1	2	yes	—
638	C₂²×D₅₃	C₂×#41	1	2	yes	—
639	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
640	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
641	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
642	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
643	D₄×C₅₃	—	4	4	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	2	1	no	—
646	C₂×C₄×C₅₃	—	2	1	no	—
647	C₂×C₄×C₅₃	—	2	1	no	—
648	C₂×C₄×C₅₃	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	2	1	no	—
652	C₂×C₄×C₅₃	—	2	1	no	—
653	C₂×C₄×C₅₃	—	2	1	no	—
654	C₂×C₄×C₅₃	—	2	1	no	—
655	C₂×C₄×C₅₃	—	2	1	no	—
656	C₂×C₄×C₅₃	—	2	1	no	—
657	C₂×C₄×C₅₃	—	2	1	no	—
658	C₂×C₄×C₅₃	—	2	1	no	—
659	C₂×C₄×C₅₃	—	2	1	no	—
660	C₂×C₄×C₅₃	—	2	1	no	—
661	C₂×C₄×C₅₃	—	2	1	no	—
662	C₂×C₄×C₅₃	—	2	1	no	—
663	C₂×C₄×C₅₃	—	2	1	no	—
664	C₂×C₄×C₅₃	—	2	1	no	—
665	C₂×C₄×C₅₃	—	2	1	no	—
666	C₂×C₄×C₅₃	—	2	1	no	—
667	C₂×C₄×C₅₃	—	2	1	no	—
668	C₂×C₄×C₅₃	—	2	1	no	—
669	C₂×C₄×C₅₃	—	2	1	no	—
670	C₂×C₄×C₅₃	—	2	1	no	—
671	C₂×C₄×C₅₃	—	2	1	no	—
672	C₂×C₄×C₅₃	—	2	1	no	—
673	C₂×C₄×C₅₃	—	2	1	no	—
674	C₂×C₄×C₅₃	—	2	1	no	—
675	C₂×C₄×C₅₃	—	2	1	no	—
676	C₂×C₄×C₅₃	—	4	4	no	—
677	C₂×C₄×C₅₃	—	4	4	no	—
678	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
679	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
680	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
681	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
682	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
683	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
684	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
685	C₂²⋊D₅₃	—	4	4	no	—
686	C₂²⋊D₅₃	—	4	4	no	—
687	C₂×Dic₅₃	—	2	1	no	—
688	C₂×Dic₅₃	—	2	1	no	—
689	C₂×Dic₅₃	—	2	1	no	—
690	C₂×Dic₅₃	—	2	1	no	—
691	C₂×Dic₅₃	—	2	1	no	—
692	C₂×Dic₅₃	—	2	1	no	—
693	C₂×Dic₅₃	—	2	1	no	—
694	C₂×Dic₅₃	—	2	1	no	—
695	C₂×Dic₅₃	—	2	1	no	—
696	C₂×Dic₅₃	—	2	1	no	—
697	C₂×Dic₅₃	—	2	1	no	—
698	C₂×Dic₅₃	—	2	1	no	—
699	C₂×Dic₅₃	—	2	1	no	—
700	C₂×Dic₅₃	—	2	1	no	—
701	C₂×Dic₅₃	—	2	1	no	—
702	C₂×Dic₅₃	—	2	1	no	—
703	C₂×Dic₅₃	—	2	1	no	—
704	C₂×Dic₅₃	—	2	1	no	—
705	C₂×Dic₅₃	—	2	1	no	—
706	C₂×Dic₅₃	—	2	1	no	—
707	C₂×Dic₅₃	—	2	1	no	—
708	C₂×Dic₅₃	—	2	1	no	—
709	C₂×Dic₅₃	—	2	1	no	—
710	C₂×Dic₅₃	—	2	1	no	—
711	C₂×Dic₅₃	—	2	1	no	—
712	C₂×Dic₅₃	—	2	1	no	—
713	C₂×Dic₅₃	—	2	1	no	—
714	C₂×Dic₅₃	—	2	1	no	—
715	C₂×Dic₅₃	—	2	1	no	—
716	C₂×Dic₅₃	—	2	1	no	—
717	C₂×Dic₅₃	—	2	1	no	—
718	C₂×Dic₅₃	—	2	1	no	—
719	C₂×Dic₅₃	—	4	4	no	—
720	C₂×Dic₅₃	—	4	4	no	—
721	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
722	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
723	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
724	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
725	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
726	C₂×Dic₅₃	C₂×#41	1	2	yes	—
727	C₂×Dic₅₃	C₂×#41	1	2	yes	—
728	D₂₁₂	—	4	4	no	—
729	C₄×D₅₃	—	2	8	no	—
730	C₄×D₅₃	—	2	8	no	—
731	C₄×D₅₃	—	2	8	no	—
732	C₄×D₅₃	—	2	8	no	—
733	C₄×D₅₃	—	2	8	no	—
734	C₄×D₅₃	—	2	8	no	—
735	C₄×D₅₃	—	2	8	no	—
736	C₄×D₅₃	—	4	4	no	—
737	C₄×D₅₃	—	4	4	no	—
738	C₄×D₅₃	—	4	4	no	—
739	C₄×D₅₃	—	4	4	no	—
740	C₄×D₅₃	—	4	4	no	—
741	C₄×D₅₃	—	4	4	no	—
742	C₄×D₅₃	—	4	4	no	—
743	C₄×D₅₃	—	4	4	no	—
744	C₄×D₅₃	—	4	4	no	—
745	C₄×D₅₃	—	4	4	no	—
746	C₂×#2335	—	53	1	no	maximal, Sylow
747	C₂²×C₅₃	—	2	2	no	—
748	C₂²×C₅₃	—	2	2	no	—
749	C₂²×C₅₃	—	2	2	no	—
750	C₂²×C₅₃	—	2	2	no	—
751	C₂²×C₅₃	—	2	2	no	—
752	C₂²×C₅₃	—	2	2	no	—
753	C₂²×C₅₃	—	4	1	no	—
754	C₂²×C₅₃	—	4	1	no	—
755	C₂²×C₅₃	—	4	1	no	—
756	C₂²×C₅₃	—	4	1	no	—
757	C₂²×C₅₃	—	4	1	no	—
758	C₂²×C₅₃	—	4	1	no	—
759	C₂²×C₅₃	—	4	1	no	—
760	C₂²×C₅₃	—	4	1	no	—
761	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
762	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
763	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
764	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
765	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
766	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
767	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
768	C₂×D₅₃	—	2	2	no	—
769	C₂×D₅₃	—	2	2	no	—
770	C₂×D₅₃	—	2	2	no	—
771	C₂×D₅₃	—	2	2	no	—
772	C₂×D₅₃	—	2	2	no	—
773	C₂×D₅₃	—	2	2	no	—
774	C₂×D₅₃	—	4	1	no	—
775	C₂×D₅₃	—	4	1	no	—
776	C₂×D₅₃	—	4	1	no	—
777	C₂×D₅₃	—	4	1	no	—
778	C₂×D₅₃	—	4	1	no	—
779	C₂×D₅₃	—	4	1	no	—
780	C₂×D₅₃	—	4	1	no	—
781	C₂×D₅₃	—	4	1	no	—
782	C₂×D₅₃	—	4	16	no	—
783	C₂×D₅₃	—	4	16	no	—
784	C₂×D₅₃	C₄×#41	1	4	yes	—
785	C₂×D₅₃	#518	1	4	yes	—
786	C₂×D₅₃	#520	1	4	yes	—
787	C₂×D₅₃	#538	1	4	yes	—
788	C₂×D₅₃	#539	1	4	yes	—
789	C₂×D₅₃	#540	1	4	yes	—
790	C₂×D₅₃	#542	1	4	yes	—
791	C₄×C₅₃	—	2	2	no	—
792	C₄×C₅₃	—	2	2	no	—
793	C₄×C₅₃	—	2	2	no	—
794	C₄×C₅₃	—	2	2	no	—
795	C₄×C₅₃	—	2	2	no	—
796	C₄×C₅₃	—	2	2	no	—
797	C₄×C₅₃	—	2	2	no	—
798	C₄×C₅₃	—	4	1	no	—
799	C₄×C₅₃	—	4	1	no	—
800	C₄×C₅₃	—	4	1	no	—
801	C₄×C₅₃	—	4	1	no	—
802	C₄×C₅₃	—	4	1	no	—
803	C₄×C₅₃	—	4	1	no	—
804	Dic₅₃	—	2	2	no	—
805	Dic₅₃	—	2	2	no	—
806	Dic₅₃	—	2	2	no	—
807	Dic₅₃	—	2	2	no	—
808	Dic₅₃	—	2	2	no	—
809	Dic₅₃	—	2	2	no	—
810	Dic₅₃	—	2	2	no	—
811	Dic₅₃	—	4	1	no	—
812	Dic₅₃	—	4	1	no	—
813	Dic₅₃	—	4	1	no	—
814	Dic₅₃	—	4	1	no	—
815	Dic₅₃	—	4	1	no	—
816	Dic₅₃	—	4	1	no	—
817	C₂²×#123	—	53	1	no	—
818	#2335	—	53	1	no	—
819	#2335	—	53	1	no	—
820	#2335	—	53	1	no	—
821	#2335	—	53	1	no	—
822	#2335	—	53	1	no	—
823	#2335	—	53	1	no	—
824	#2335	—	53	1	no	—
825	#2335	—	53	1	no	—
826	#2335	—	53	1	no	—
827	#2335	—	53	1	no	—
828	#2335	—	53	1	no	—
829	#2335	—	53	1	no	—
830	#2335	—	53	1	no	—
831	#2335	—	53	1	no	—
832	#2335	—	53	1	no	—
833	#2335	D₅₃	1	1	yes	characteristic, direct product factor
834	C₂×#390	—	53	1	no	—
835	C₂×#389	—	53	1	no	—
836	C₂×#388	—	53	1	no	—
837	C₂×#388	—	53	1	no	—
838	C₂×#388	—	53	1	no	—
839	C₂×#388	—	53	1	no	—
840	C₂×#387	—	53	1	no	—
841	C₂×#387	—	53	1	no	—
842	C₂×#386	—	53	1	no	—
843	C₂×#385	—	53	1	no	—
844	C₂×#380	—	53	1	no	—
845	C₂×C₄×C₄⋊C₄	—	53	1	no	—
846	C₂×C₄×C₂²⋊C₄	—	53	1	no	—
847	C₂×C₄×C₂²⋊C₄	—	53	1	no	—
848	C₂×C₅₃	—	4	2	no	—
849	C₂×C₅₃	—	4	2	no	—
850	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
851	C₂×C₅₃	C₂×#518	1	1	yes	characteristic
852	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
853	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
854	C₂×C₅₃	C₂×#539	1	1	yes	characteristic
855	C₂×C₅₃	C₂×#540	1	1	yes	characteristic
856	C₂×C₅₃	C₂×#542	1	1	yes	characteristic
857	D₅₃	—	4	2	no	—
858	D₅₃	—	4	2	no	—
859	D₅₃	#2335	1	8	yes	direct product factor
860	C₂³×D₄	—	53	1	no	—
861	C₂⁴×C₄	—	53	1	no	—
862	C₂⁴×C₄	—	53	1	no	—
863	C₂×#123	—	53	1	no	—
864	C₂×#123	—	53	1	no	—
865	C₂×#123	—	53	16	no	—
866	C₂×#123	—	53	1	no	—
867	C₂×#123	—	53	1	no	—
868	C₂×#123	—	53	1	no	—
869	C₂×#123	—	53	1	no	—
870	C₂×#123	—	53	1	no	—
871	C₂×#123	C₂×D₅₃	1	1	yes	characteristic
872	C₂²×C₄⋊C₄	—	53	1	no	—
873	C₂²×C₄⋊C₄	—	53	1	no	—
874	C₂²×C₄⋊C₄	—	53	1	no	—
875	C₂²×C₄⋊C₄	—	53	1	no	—
876	C₂²×C₄⋊C₄	—	53	1	no	—
877	C₂²×C₄⋊C₄	—	53	1	no	—
878	C₂²×C₄⋊C₄	—	53	1	no	—
879	C₂²×C₂²⋊C₄	—	53	1	no	—
880	C₂²×C₂²⋊C₄	—	53	1	no	—
881	C₂²×C₂²⋊C₄	—	53	1	no	—
882	C₂²×C₂²⋊C₄	—	53	1	no	—
883	C₂²×C₂²⋊C₄	—	53	1	no	—
884	C₂²×C₂²⋊C₄	—	53	1	no	—
885	C₂²×C₂²⋊C₄	—	53	1	no	—
886	C₂²×C₂²⋊C₄	—	53	1	no	—
887	C₂²×C₂²⋊C₄	—	53	1	no	—
888	C₂²×C₂²⋊C₄	—	53	1	no	—
889	C₂²×C₄²	—	53	1	no	—
890	C₂²×C₄²	—	53	1	no	—
891	C₂²×C₄²	—	53	1	no	—
892	C₂²×C₄²	—	53	1	no	—
893	C₂²×C₄²	—	53	1	no	—
894	#390	—	53	1	no	—
895	#390	—	53	1	no	—
896	#390	—	53	1	no	—
897	#390	—	53	1	no	—
898	#390	—	53	1	no	—
899	#390	—	53	1	no	—
900	#390	—	53	1	no	—
901	#390	C₂×D₅₃	1	1	yes	characteristic
902	#389	—	53	1	no	—
903	#389	—	53	1	no	—
904	#389	—	53	1	no	—
905	#389	—	53	1	no	—
906	#389	—	53	1	no	—
907	#389	—	53	1	no	—
908	#389	—	53	1	no	—
909	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
910	#388	—	53	1	no	—
911	#388	—	53	1	no	—
912	#388	—	53	1	no	—
913	#388	—	53	1	no	—
914	#388	—	53	1	no	—
915	#388	—	53	1	no	—
916	#388	—	53	1	no	—
917	#388	—	53	1	no	—
918	#388	—	53	1	no	—
919	#388	—	53	1	no	—
920	#388	—	53	1	no	—
921	#388	—	53	1	no	—
922	#388	—	53	1	no	—
923	#388	—	53	1	no	—
924	#388	—	53	1	no	—
925	#388	—	53	1	no	—
926	#388	—	53	1	no	—
927	#388	—	53	1	no	—
928	#388	—	53	1	no	—
929	#388	—	53	1	no	—
930	#388	—	53	1	no	—
931	#388	—	53	1	no	—
932	#388	—	53	1	no	—
933	#388	—	53	1	no	—
934	#388	—	53	1	no	—
935	#388	—	53	1	no	—
936	#388	—	53	1	no	—
937	#388	—	53	1	no	—
938	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
939	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
940	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
941	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
942	#387	—	53	1	no	—
943	#387	—	53	1	no	—
944	#387	—	53	1	no	—
945	#387	—	53	1	no	—
946	#387	—	53	1	no	—
947	#387	—	53	1	no	—
948	#387	—	53	1	no	—
949	#387	—	53	1	no	—
950	#387	—	53	1	no	—
951	#387	—	53	1	no	—
952	#387	—	53	1	no	—
953	#387	—	53	1	no	—
954	#387	—	53	1	no	—
955	#387	—	53	1	no	—
956	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
957	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
958	#386	—	53	1	no	—
959	#386	—	53	1	no	—
960	#386	—	53	1	no	—
961	#386	—	53	1	no	—
962	#386	—	53	1	no	—
963	#386	—	53	1	no	—
964	#386	—	53	1	no	—
965	#386	C₂×D₅₃	1	1	yes	characteristic
966	#385	—	53	1	no	—
967	#385	—	53	1	no	—
968	#385	—	53	1	no	—
969	#385	—	53	1	no	—
970	#385	—	53	1	no	—
971	#385	—	53	1	no	—
972	#385	—	53	1	no	—
973	#385	C₂×D₅₃	1	1	yes	characteristic, complemented
974	#380	—	53	1	no	—
975	#380	—	53	1	no	—
976	#380	—	53	1	no	—
977	#380	—	53	1	no	—
978	#380	—	53	1	no	—
979	#380	—	53	1	no	—
980	#380	—	53	1	no	—
981	#380	C₂×D₅₃	1	1	yes	characteristic, complemented
982	C₄×C₄⋊C₄	—	53	1	no	—
983	C₄×C₄⋊C₄	—	53	1	no	—
984	C₄×C₄⋊C₄	—	53	1	no	—
985	C₄×C₄⋊C₄	—	53	1	no	—
986	C₄×C₄⋊C₄	—	53	1	no	—
987	C₄×C₄⋊C₄	—	53	1	no	—
988	C₄×C₄⋊C₄	—	53	1	no	—
989	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
990	C₄×C₂²⋊C₄	—	53	1	no	—
991	C₄×C₂²⋊C₄	—	53	1	no	—
992	C₄×C₂²⋊C₄	—	53	1	no	—
993	C₄×C₂²⋊C₄	—	53	1	no	—
994	C₄×C₂²⋊C₄	—	53	1	no	—
995	C₄×C₂²⋊C₄	—	53	1	no	—
996	C₄×C₂²⋊C₄	—	53	1	no	—
997	C₄×C₂²⋊C₄	—	53	1	no	—
998	C₄×C₂²⋊C₄	—	53	1	no	—
999	C₄×C₂²⋊C₄	—	53	1	no	—
1000	C₄×C₂²⋊C₄	—	53	1	no	—
1001	C₄×C₂²⋊C₄	—	53	1	no	—
1002	C₄×C₂²⋊C₄	—	53	1	no	—
1003	C₄×C₂²⋊C₄	—	53	1	no	—
1004	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
1005	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
1006	C₂×#95	—	53	1	no	—
1007	C₂×#95	—	53	1	no	—
1008	C₂×#95	—	53	1	no	—
1009	C₂×#95	—	53	1	no	—
1010	C₂×#95	—	53	1	no	—
1011	C₂×#95	—	53	1	no	—
1012	C₂×#95	—	53	1	no	—
1013	C₂×#95	—	53	1	no	—
1014	C₂×#95	—	53	1	no	—
1015	C₂×#95	—	53	1	no	—
1016	C₅₃	C₂×#2335	1	1	yes	characteristic, complemented, Sylow
1017	C₂⁵	—	53	1	no	—
1018	C₂⁵	—	53	1	no	—
1019	C₂²×D₄	—	53	1	no	—
1020	C₂²×D₄	—	53	1	no	—
1021	C₂²×D₄	—	53	8	no	—
1022	C₂²×D₄	—	53	1	no	—
1023	C₂²×D₄	—	212	2	no	—
1024	C₂²×D₄	—	212	2	no	—
1025	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1026	C₂³×C₄	—	53	1	no	—
1027	C₂³×C₄	—	53	1	no	—
1028	C₂³×C₄	—	53	1	no	—
1029	C₂³×C₄	—	53	1	no	—
1030	C₂³×C₄	—	53	1	no	—
1031	C₂³×C₄	—	53	1	no	—
1032	C₂³×C₄	—	53	1	no	—
1033	C₂³×C₄	—	53	1	no	—
1034	C₂³×C₄	—	53	8	no	—
1035	C₂³×C₄	—	53	1	no	—
1036	C₂³×C₄	—	53	1	no	—
1037	C₂³×C₄	—	53	1	no	—
1038	C₂³×C₄	—	53	1	no	—
1039	C₂³×C₄	—	53	1	no	—
1040	C₂³×C₄	—	53	1	no	—
1041	C₂³×C₄	—	53	1	no	—
1042	C₂³×C₄	—	53	1	no	—
1043	C₂³×C₄	—	53	1	no	—
1044	C₂³×C₄	—	53	1	no	—
1045	C₂³×C₄	—	53	1	no	—
1046	C₂³×C₄	—	106	4	no	—
1047	C₂³×C₄	—	212	2	no	—
1048	C₂³×C₄	—	212	2	no	—
1049	C₂³×C₄	—	212	2	no	—
1050	C₂³×C₄	—	212	2	no	—
1051	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1052	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1053	#123	—	53	8	no	—
1054	#123	—	53	8	no	—
1055	#123	—	53	8	no	—
1056	#123	—	53	8	no	—
1057	#123	—	53	8	no	—
1058	#123	—	53	8	no	—
1059	#123	—	53	8	no	—
1060	#123	C₄×D₅₃	1	8	yes	complemented
1061	C₂×C₄⋊C₄	—	53	1	no	—
1062	C₂×C₄⋊C₄	—	53	1	no	—
1063	C₂×C₄⋊C₄	—	53	1	no	—
1064	C₂×C₄⋊C₄	—	53	1	no	—
1065	C₂×C₄⋊C₄	—	53	1	no	—
1066	C₂×C₄⋊C₄	—	53	1	no	—
1067	C₂×C₄⋊C₄	—	53	8	no	—
1068	C₂×C₄⋊C₄	—	53	8	no	—
1069	C₂×C₄⋊C₄	—	53	1	no	—
1070	C₂×C₄⋊C₄	—	53	1	no	—
1071	C₂×C₄⋊C₄	—	53	1	no	—
1072	C₂×C₄⋊C₄	—	53	1	no	—
1073	C₂×C₄⋊C₄	—	53	1	no	—
1074	C₂×C₄⋊C₄	—	53	1	no	—
1075	C₂×C₄⋊C₄	—	53	1	no	—
1076	C₂×C₄⋊C₄	—	53	1	no	—
1077	C₂×C₄⋊C₄	—	53	1	no	—
1078	C₂×C₄⋊C₄	—	53	1	no	—
1079	C₂×C₄⋊C₄	—	53	1	no	—
1080	C₂×C₄⋊C₄	—	53	1	no	—
1081	C₂×C₄⋊C₄	—	53	1	no	—
1082	C₂×C₄⋊C₄	—	53	1	no	—
1083	C₂×C₄⋊C₄	—	53	1	no	—
1084	C₂×C₄⋊C₄	—	106	4	no	—
1085	C₂×C₄⋊C₄	—	212	2	no	—
1086	C₂×C₄⋊C₄	—	212	2	no	—
1087	C₂×C₄⋊C₄	—	212	2	no	—
1088	C₂×C₄⋊C₄	—	212	2	no	—
1089	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1090	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1091	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1092	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1093	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1094	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1095	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1096	C₂×C₂²⋊C₄	—	53	1	no	—
1097	C₂×C₂²⋊C₄	—	53	1	no	—
1098	C₂×C₂²⋊C₄	—	53	1	no	—
1099	C₂×C₂²⋊C₄	—	53	1	no	—
1100	C₂×C₂²⋊C₄	—	53	1	no	—
1101	C₂×C₂²⋊C₄	—	53	1	no	—
1102	C₂×C₂²⋊C₄	—	53	1	no	—
1103	C₂×C₂²⋊C₄	—	53	1	no	—
1104	C₂×C₂²⋊C₄	—	53	1	no	—
1105	C₂×C₂²⋊C₄	—	53	8	no	—
1106	C₂×C₂²⋊C₄	—	53	8	no	—
1107	C₂×C₂²⋊C₄	—	53	8	no	—
1108	C₂×C₂²⋊C₄	—	53	1	no	—
1109	C₂×C₂²⋊C₄	—	53	1	no	—
1110	C₂×C₂²⋊C₄	—	53	1	no	—
1111	C₂×C₂²⋊C₄	—	53	1	no	—
1112	C₂×C₂²⋊C₄	—	53	1	no	—
1113	C₂×C₂²⋊C₄	—	53	1	no	—
1114	C₂×C₂²⋊C₄	—	53	1	no	—
1115	C₂×C₂²⋊C₄	—	53	1	no	—
1116	C₂×C₂²⋊C₄	—	53	1	no	—
1117	C₂×C₂²⋊C₄	—	53	1	no	—
1118	C₂×C₂²⋊C₄	—	53	1	no	—
1119	C₂×C₂²⋊C₄	—	53	1	no	—
1120	C₂×C₂²⋊C₄	—	53	1	no	—
1121	C₂×C₂²⋊C₄	—	53	1	no	—
1122	C₂×C₂²⋊C₄	—	53	1	no	—
1123	C₂×C₂²⋊C₄	—	53	1	no	—
1124	C₂×C₂²⋊C₄	—	53	1	no	—
1125	C₂×C₂²⋊C₄	—	53	1	no	—
1126	C₂×C₂²⋊C₄	—	53	1	no	—
1127	C₂×C₂²⋊C₄	—	53	1	no	—
1128	C₂×C₂²⋊C₄	—	53	1	no	—
1129	C₂×C₂²⋊C₄	—	106	4	no	—
1130	C₂×C₂²⋊C₄	—	106	4	no	—
1131	C₂×C₂²⋊C₄	—	106	4	no	—
1132	C₂×C₂²⋊C₄	—	212	2	no	—
1133	C₂×C₂²⋊C₄	—	212	2	no	—
1134	C₂×C₂²⋊C₄	—	212	2	no	—
1135	C₂×C₂²⋊C₄	—	212	2	no	—
1136	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1137	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1138	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1139	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1140	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1141	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1142	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1143	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1144	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1145	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1146	C₂×C₄²	—	53	1	no	—
1147	C₂×C₄²	—	53	1	no	—
1148	C₂×C₄²	—	53	1	no	—
1149	C₂×C₄²	—	53	1	no	—
1150	C₂×C₄²	—	53	1	no	—
1151	C₂×C₄²	—	53	1	no	—
1152	C₂×C₄²	—	53	1	no	—
1153	C₂×C₄²	—	53	1	no	—
1154	C₂×C₄²	—	53	1	no	—
1155	C₂×C₄²	—	53	1	no	—
1156	C₂×C₄²	—	53	1	no	—
1157	C₂×C₄²	—	53	1	no	—
1158	C₂×C₄²	—	53	1	no	—
1159	C₂×C₄²	—	53	1	no	—
1160	C₂×C₄²	—	53	1	no	—
1161	C₂×C₄²	—	106	4	no	—
1162	C₂×C₄²	—	212	2	no	—
1163	C₂×C₄²	—	212	2	no	—
1164	C₂×C₄²	—	212	2	no	—
1165	C₂×C₄²	—	212	2	no	—
1166	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1167	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1168	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1169	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1170	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1171	#95	—	53	1	no	—
1172	#95	—	53	1	no	—
1173	#95	—	53	1	no	—
1174	#95	—	53	1	no	—
1175	#95	—	53	1	no	—
1176	#95	—	53	1	no	—
1177	#95	—	53	1	no	—
1178	#95	—	53	1	no	—
1179	#95	—	53	1	no	—
1180	#95	—	53	1	no	—
1181	#95	—	53	1	no	—
1182	#95	—	53	1	no	—
1183	#95	—	53	1	no	—
1184	#95	—	53	1	no	—
1185	#95	—	53	1	no	—
1186	#95	—	53	1	no	—
1187	#95	—	53	1	no	—
1188	#95	—	53	1	no	—
1189	#95	—	53	1	no	—
1190	#95	—	53	1	no	—
1191	#95	—	53	1	no	—
1192	#95	—	53	1	no	—
1193	#95	—	53	1	no	—
1194	#95	—	53	1	no	—
1195	#95	—	53	1	no	—
1196	#95	—	53	1	no	—
1197	#95	—	53	1	no	—
1198	#95	—	53	1	no	—
1199	#95	—	53	1	no	—
1200	#95	—	53	1	no	—
1201	#95	C₂²×D₅₃	1	1	yes	characteristic
1202	#95	C₂²×D₅₃	1	1	yes	characteristic
1203	#95	C₂²×D₅₃	1	1	yes	characteristic
1204	#95	C₂²×D₅₃	1	1	yes	characteristic
1205	#95	C₂²×D₅₃	1	1	yes	characteristic
1206	#95	C₂²×D₅₃	1	1	yes	characteristic
1207	#95	C₂²×D₅₃	1	1	yes	characteristic
1208	#95	C₂²×D₅₃	1	1	yes	characteristic
1209	#95	C₂²×D₅₃	1	1	yes	characteristic
1210	#95	C₂²×D₅₃	1	1	yes	characteristic
1211	C₂⁴	—	53	1	no	—
1212	C₂⁴	—	53	4	no	—
1213	C₂⁴	—	53	4	no	—
1214	C₂⁴	—	53	1	no	—
1215	C₂⁴	—	53	1	no	—
1216	C₂⁴	—	106	2	no	—
1217	C₂⁴	—	106	2	no	—
1218	C₂⁴	—	106	2	no	—
1219	C₂⁴	—	106	2	no	—
1220	C₂⁴	—	106	2	no	—
1221	C₂⁴	—	106	2	no	—
1222	C₂⁴	—	106	2	no	—
1223	C₂⁴	—	106	2	no	—
1224	C₂⁴	—	106	2	no	—
1225	C₂⁴	—	106	2	no	—
1226	C₂⁴	—	106	2	no	—
1227	C₂⁴	—	106	2	no	—
1228	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1229	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1230	C₂×D₄	—	4	1	no	—
1231	C₂×D₄	—	4	1	no	—
1232	C₂×D₄	—	53	4	no	—
1233	C₂×D₄	—	53	4	no	—
1234	C₂×D₄	—	53	4	no	—
1235	C₂×D₄	—	212	1	no	—
1236	C₂×D₄	—	212	1	no	—
1237	C₂×D₄	—	212	16	no	—
1238	C₂×D₄	—	212	1	no	—
1239	C₂×D₄	—	212	1	no	—
1240	C₂×D₄	—	212	1	no	—
1241	C₂×D₄	—	212	1	no	—
1242	C₂×D₄	C₂×C₄×D₅₃	1	4	yes	—
1243	C₂²×C₄	—	2	2	no	—
1244	C₂²×C₄	—	4	1	no	—
1245	C₂²×C₄	—	4	1	no	—
1246	C₂²×C₄	—	4	1	no	—
1247	C₂²×C₄	—	4	1	no	—
1248	C₂²×C₄	—	53	1	no	—
1249	C₂²×C₄	—	53	1	no	—
1250	C₂²×C₄	—	53	1	no	—
1251	C₂²×C₄	—	53	1	no	—
1252	C₂²×C₄	—	53	1	no	—
1253	C₂²×C₄	—	53	1	no	—
1254	C₂²×C₄	—	53	1	no	—
1255	C₂²×C₄	—	53	4	no	—
1256	C₂²×C₄	—	53	4	no	—
1257	C₂²×C₄	—	53	4	no	—
1258	C₂²×C₄	—	53	4	no	—
1259	C₂²×C₄	—	53	4	no	—
1260	C₂²×C₄	—	53	4	no	—
1261	C₂²×C₄	—	53	4	no	—
1262	C₂²×C₄	—	53	4	no	—
1263	C₂²×C₄	—	53	4	no	—
1264	C₂²×C₄	—	53	4	no	—
1265	C₂²×C₄	—	53	1	no	—
1266	C₂²×C₄	—	53	1	no	—
1267	C₂²×C₄	—	53	1	no	—
1268	C₂²×C₄	—	53	1	no	—
1269	C₂²×C₄	—	53	1	no	—
1270	C₂²×C₄	—	53	1	no	—
1271	C₂²×C₄	—	106	2	no	—
1272	C₂²×C₄	—	106	2	no	—
1273	C₂²×C₄	—	106	2	no	—
1274	C₂²×C₄	—	106	2	no	—
1275	C₂²×C₄	—	106	2	no	—
1276	C₂²×C₄	—	106	2	no	—
1277	C₂²×C₄	—	106	2	no	—
1278	C₂²×C₄	—	106	2	no	—
1279	C₂²×C₄	—	106	2	no	—
1280	C₂²×C₄	—	106	2	no	—
1281	C₂²×C₄	—	106	2	no	—
1282	C₂²×C₄	—	106	2	no	—
1283	C₂²×C₄	—	106	2	no	—
1284	C₂²×C₄	—	106	2	no	—
1285	C₂²×C₄	—	106	2	no	—
1286	C₂²×C₄	—	106	2	no	—
1287	C₂²×C₄	—	106	2	no	—
1288	C₂²×C₄	—	106	2	no	—
1289	C₂²×C₄	—	106	2	no	—
1290	C₂²×C₄	—	106	2	no	—
1291	C₂²×C₄	—	106	2	no	—
1292	C₂²×C₄	—	106	2	no	—
1293	C₂²×C₄	—	106	2	no	—
1294	C₂²×C₄	—	106	2	no	—
1295	C₂²×C₄	—	106	2	no	—
1296	C₂²×C₄	—	106	2	no	—
1297	C₂²×C₄	—	106	2	no	—
1298	C₂²×C₄	—	106	2	no	—
1299	C₂²×C₄	—	106	2	no	—
1300	C₂²×C₄	—	106	2	no	—
1301	C₂²×C₄	—	106	2	no	—
1302	C₂²×C₄	—	106	2	no	—
1303	C₂²×C₄	—	106	2	no	—
1304	C₂²×C₄	—	106	2	no	—
1305	C₂²×C₄	—	106	2	no	—
1306	C₂²×C₄	—	212	1	no	—
1307	C₂²×C₄	—	212	1	no	—
1308	C₂²×C₄	—	212	1	no	—
1309	C₂²×C₄	—	212	1	no	—
1310	C₂²×C₄	—	212	1	no	—
1311	C₂²×C₄	—	212	1	no	—
1312	C₂²×C₄	—	212	1	no	—
1313	C₂²×C₄	—	212	1	no	—
1314	C₂²×C₄	—	212	16	no	—
1315	C₂²×C₄	—	212	16	no	—
1316	C₂²×C₄	—	212	1	no	—
1317	C₂²×C₄	—	212	1	no	—
1318	C₂²×C₄	—	212	1	no	—
1319	C₂²×C₄	—	212	1	no	—
1320	C₂²×C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1321	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1322	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1323	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1324	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1325	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1326	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1327	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1328	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1329	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1330	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1331	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1332	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1333	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1334	C₄⋊C₄	—	2	2	no	—
1335	C₄⋊C₄	—	4	1	no	—
1336	C₄⋊C₄	—	4	1	no	—
1337	C₄⋊C₄	—	4	1	no	—
1338	C₄⋊C₄	—	4	1	no	—
1339	C₄⋊C₄	—	53	4	no	—
1340	C₄⋊C₄	—	53	4	no	—
1341	C₄⋊C₄	—	53	4	no	—
1342	C₄⋊C₄	—	53	4	no	—
1343	C₄⋊C₄	—	53	4	no	—
1344	C₄⋊C₄	—	53	4	no	—
1345	C₄⋊C₄	—	106	2	no	—
1346	C₄⋊C₄	—	106	2	no	—
1347	C₄⋊C₄	—	106	2	no	—
1348	C₄⋊C₄	—	212	1	no	—
1349	C₄⋊C₄	—	212	1	no	—
1350	C₄⋊C₄	—	212	1	no	—
1351	C₄⋊C₄	—	212	1	no	—
1352	C₄⋊C₄	—	212	1	no	—
1353	C₄⋊C₄	—	212	1	no	—
1354	C₄⋊C₄	—	212	1	no	—
1355	C₄⋊C₄	—	212	1	no	—
1356	C₄⋊C₄	—	212	1	no	—
1357	C₄⋊C₄	—	212	1	no	—
1358	C₄⋊C₄	—	212	1	no	—
1359	C₄⋊C₄	—	212	1	no	—
1360	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1361	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1362	C₂²⋊C₄	—	2	2	no	—
1363	C₂²⋊C₄	—	2	2	no	—
1364	C₂²⋊C₄	—	2	2	no	—
1365	C₂²⋊C₄	—	4	1	no	—
1366	C₂²⋊C₄	—	4	1	no	—
1367	C₂²⋊C₄	—	4	1	no	—
1368	C₂²⋊C₄	—	4	1	no	—
1369	C₂²⋊C₄	—	53	4	no	—
1370	C₂²⋊C₄	—	53	4	no	—
1371	C₂²⋊C₄	—	53	4	no	—
1372	C₂²⋊C₄	—	53	4	no	—
1373	C₂²⋊C₄	—	53	4	no	—
1374	C₂²⋊C₄	—	53	4	no	—
1375	C₂²⋊C₄	—	53	4	no	—
1376	C₂²⋊C₄	—	53	4	no	—
1377	C₂²⋊C₄	—	53	4	no	—
1378	C₂²⋊C₄	—	106	2	no	—
1379	C₂²⋊C₄	—	106	2	no	—
1380	C₂²⋊C₄	—	106	2	no	—
1381	C₂²⋊C₄	—	106	2	no	—
1382	C₂²⋊C₄	—	106	2	no	—
1383	C₂²⋊C₄	—	106	2	no	—
1384	C₂²⋊C₄	—	106	2	no	—
1385	C₂²⋊C₄	—	106	2	no	—
1386	C₂²⋊C₄	—	106	2	no	—
1387	C₂²⋊C₄	—	212	1	no	—
1388	C₂²⋊C₄	—	212	1	no	—
1389	C₂²⋊C₄	—	212	1	no	—
1390	C₂²⋊C₄	—	212	1	no	—
1391	C₂²⋊C₄	—	212	1	no	—
1392	C₂²⋊C₄	—	212	1	no	—
1393	C₂²⋊C₄	—	212	1	no	—
1394	C₂²⋊C₄	—	212	1	no	—
1395	C₂²⋊C₄	—	212	1	no	—
1396	C₂²⋊C₄	—	212	1	no	—
1397	C₂²⋊C₄	—	212	1	no	—
1398	C₂²⋊C₄	—	212	1	no	—
1399	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1400	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1401	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1402	C₄²	—	2	2	no	—
1403	C₄²	—	4	1	no	—
1404	C₄²	—	4	1	no	—
1405	C₄²	—	4	1	no	—
1406	C₄²	—	4	1	no	—
1407	C₄²	—	106	2	no	—
1408	C₄²	—	106	2	no	—
1409	C₄²	—	106	2	no	—
1410	C₄²	—	212	1	no	—
1411	C₄²	—	212	1	no	—
1412	C₄²	—	212	1	no	—
1413	C₄²	—	212	1	no	—
1414	C₄²	—	212	1	no	—
1415	C₄²	—	212	1	no	—
1416	C₄²	—	212	1	no	—
1417	C₄²	—	212	1	no	—
1418	C₄²	—	212	1	no	—
1419	C₄²	—	212	1	no	—
1420	C₄²	—	212	1	no	—
1421	C₄²	—	212	1	no	—
1422	C₂³	—	2	1	no	—
1423	C₂³	—	2	1	no	—
1424	C₂³	—	2	1	no	—
1425	C₂³	—	2	1	no	—
1426	C₂³	—	2	1	no	—
1427	C₂³	—	2	1	no	—
1428	C₂³	—	2	1	no	—
1429	C₂³	—	2	1	no	—
1430	C₂³	—	2	1	no	—
1431	C₂³	—	2	1	no	—
1432	C₂³	—	2	1	no	—
1433	C₂³	—	2	1	no	—
1434	C₂³	—	53	2	no	—
1435	C₂³	—	53	2	no	—
1436	C₂³	—	53	2	no	—
1437	C₂³	—	53	2	no	—
1438	C₂³	—	53	2	no	—
1439	C₂³	—	53	2	no	—
1440	C₂³	—	53	2	no	—
1441	C₂³	—	53	2	no	—
1442	C₂³	—	53	2	no	—
1443	C₂³	—	106	8	no	—
1444	C₂³	—	106	8	no	—
1445	C₂³	—	106	8	no	—
1446	C₂³	—	106	8	no	—
1447	C₂³	—	106	8	no	—
1448	C₂³	—	106	8	no	—
1449	C₂³	—	106	1	no	—
1450	C₂³	—	106	1	no	—
1451	C₂³	—	106	1	no	—
1452	C₂³	—	106	1	no	—
1453	C₂³	—	106	1	no	—
1454	C₂³	—	106	1	no	—
1455	C₂³	—	106	1	no	—
1456	C₂³	—	106	1	no	—
1457	C₂³	—	106	1	no	—
1458	C₂³	—	106	1	no	—
1459	C₂³	—	106	1	no	—
1460	C₂³	—	106	1	no	—
1461	C₂³	—	212	4	no	—
1462	C₂³	—	212	4	no	—
1463	C₂³	—	212	4	no	—
1464	C₂³	—	212	4	no	—
1465	C₂³	—	212	4	no	—
1466	C₂³	—	212	4	no	—
1467	C₂³	—	212	4	no	—
1468	C₂³	—	212	4	no	—
1469	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1470	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1471	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1472	D₄	—	4	4	no	—
1473	D₄	—	212	4	no	—
1474	D₄	—	212	4	no	—
1475	D₄	—	212	4	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	1	no	—
1478	C₂×C₄	—	2	1	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	2	1	no	—
1482	C₂×C₄	—	2	1	no	—
1483	C₂×C₄	—	2	1	no	—
1484	C₂×C₄	—	2	1	no	—
1485	C₂×C₄	—	2	1	no	—
1486	C₂×C₄	—	2	1	no	—
1487	C₂×C₄	—	2	1	no	—
1488	C₂×C₄	—	2	1	no	—
1489	C₂×C₄	—	2	1	no	—
1490	C₂×C₄	—	2	1	no	—
1491	C₂×C₄	—	2	1	no	—
1492	C₂×C₄	—	2	1	no	—
1493	C₂×C₄	—	2	1	no	—
1494	C₂×C₄	—	2	1	no	—
1495	C₂×C₄	—	2	1	no	—
1496	C₂×C₄	—	2	1	no	—
1497	C₂×C₄	—	2	1	no	—
1498	C₂×C₄	—	2	1	no	—
1499	C₂×C₄	—	2	1	no	—
1500	C₂×C₄	—	2	1	no	—
1501	C₂×C₄	—	2	1	no	—
1502	C₂×C₄	—	2	1	no	—
1503	C₂×C₄	—	2	1	no	—
1504	C₂×C₄	—	2	1	no	—
1505	C₂×C₄	—	2	1	no	—
1506	C₂×C₄	—	2	1	no	—
1507	C₂×C₄	—	2	1	no	—
1508	C₂×C₄	—	4	4	no	—
1509	C₂×C₄	—	4	4	no	—
1510	C₂×C₄	—	53	2	no	—
1511	C₂×C₄	—	53	2	no	—
1512	C₂×C₄	—	53	2	no	—
1513	C₂×C₄	—	53	2	no	—
1514	C₂×C₄	—	53	2	no	—
1515	C₂×C₄	—	53	2	no	—
1516	C₂×C₄	—	53	2	no	—
1517	C₂×C₄	—	106	8	no	—
1518	C₂×C₄	—	106	8	no	—
1519	C₂×C₄	—	106	8	no	—
1520	C₂×C₄	—	106	8	no	—
1521	C₂×C₄	—	106	8	no	—
1522	C₂×C₄	—	106	8	no	—
1523	C₂×C₄	—	106	8	no	—
1524	C₂×C₄	—	106	1	no	—
1525	C₂×C₄	—	106	1	no	—
1526	C₂×C₄	—	106	1	no	—
1527	C₂×C₄	—	106	1	no	—
1528	C₂×C₄	—	106	1	no	—
1529	C₂×C₄	—	106	1	no	—
1530	C₂×C₄	—	106	1	no	—
1531	C₂×C₄	—	106	1	no	—
1532	C₂×C₄	—	106	1	no	—
1533	C₂×C₄	—	106	1	no	—
1534	C₂×C₄	—	106	1	no	—
1535	C₂×C₄	—	106	1	no	—
1536	C₂×C₄	—	106	1	no	—
1537	C₂×C₄	—	106	1	no	—
1538	C₂×C₄	—	106	1	no	—
1539	C₂×C₄	—	106	1	no	—
1540	C₂×C₄	—	106	1	no	—
1541	C₂×C₄	—	106	1	no	—
1542	C₂×C₄	—	106	1	no	—
1543	C₂×C₄	—	106	1	no	—
1544	C₂×C₄	—	106	1	no	—
1545	C₂×C₄	—	106	1	no	—
1546	C₂×C₄	—	106	1	no	—
1547	C₂×C₄	—	106	1	no	—
1548	C₂×C₄	—	106	1	no	—
1549	C₂×C₄	—	106	1	no	—
1550	C₂×C₄	—	106	1	no	—
1551	C₂×C₄	—	106	1	no	—
1552	C₂×C₄	—	106	1	no	—
1553	C₂×C₄	—	106	1	no	—
1554	C₂×C₄	—	106	1	no	—
1555	C₂×C₄	—	106	1	no	—
1556	C₂×C₄	—	212	4	no	—
1557	C₂×C₄	—	212	4	no	—
1558	C₂×C₄	—	212	4	no	—
1559	C₂×C₄	—	212	4	no	—
1560	C₂×C₄	—	212	4	no	—
1561	C₂×C₄	—	212	4	no	—
1562	C₂×C₄	—	212	4	no	—
1563	C₂×C₄	—	212	4	no	—
1564	C₂×C₄	—	212	4	no	—
1565	C₂×C₄	—	212	4	no	—
1566	C₂×C₄	—	212	4	no	—
1567	C₂×C₄	—	212	4	no	—
1568	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1569	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1570	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1571	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1572	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1573	C₂×C₄	#41×D₅₃	1	2	yes	—
1574	C₂×C₄	#41×D₅₃	1	2	yes	—
1575	C₂²	—	2	2	no	—
1576	C₂²	—	2	2	no	—
1577	C₂²	—	2	2	no	—
1578	C₂²	—	2	2	no	—
1579	C₂²	—	2	2	no	—
1580	C₂²	—	2	2	no	—
1581	C₂²	—	4	1	no	—
1582	C₂²	—	4	1	no	—
1583	C₂²	—	4	1	no	—
1584	C₂²	—	4	1	no	—
1585	C₂²	—	4	1	no	—
1586	C₂²	—	4	1	no	—
1587	C₂²	—	4	1	no	—
1588	C₂²	—	4	1	no	—
1589	C₂²	—	53	4	no	—
1590	C₂²	—	53	4	no	—
1591	C₂²	—	53	4	no	—
1592	C₂²	—	53	4	no	—
1593	C₂²	—	53	4	no	—
1594	C₂²	—	53	4	no	—
1595	C₂²	—	53	4	no	—
1596	C₂²	—	106	2	no	—
1597	C₂²	—	106	2	no	—
1598	C₂²	—	106	2	no	—
1599	C₂²	—	106	2	no	—
1600	C₂²	—	106	2	no	—
1601	C₂²	—	106	2	no	—
1602	C₂²	—	212	16	no	—
1603	C₂²	—	212	16	no	—
1604	C₂²	—	212	1	no	—
1605	C₂²	—	212	1	no	—
1606	C₂²	—	212	1	no	—
1607	C₂²	—	212	1	no	—
1608	C₂²	—	212	1	no	—
1609	C₂²	—	212	1	no	—
1610	C₂²	—	212	1	no	—
1611	C₂²	—	212	1	no	—
1612	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1613	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1614	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1615	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1616	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1617	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1618	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1619	C₄	—	2	2	no	—
1620	C₄	—	2	2	no	—
1621	C₄	—	2	2	no	—
1622	C₄	—	2	2	no	—
1623	C₄	—	2	2	no	—
1624	C₄	—	2	2	no	—
1625	C₄	—	2	2	no	—
1626	C₄	—	4	1	no	—
1627	C₄	—	4	1	no	—
1628	C₄	—	4	1	no	—
1629	C₄	—	4	1	no	—
1630	C₄	—	4	1	no	—
1631	C₄	—	4	1	no	—
1632	C₄	—	106	2	no	—
1633	C₄	—	106	2	no	—
1634	C₄	—	106	2	no	—
1635	C₄	—	106	2	no	—
1636	C₄	—	106	2	no	—
1637	C₄	—	106	2	no	—
1638	C₄	—	106	2	no	—
1639	C₄	—	212	1	no	—
1640	C₄	—	212	1	no	—
1641	C₄	—	212	1	no	—
1642	C₄	—	212	1	no	—
1643	C₄	—	212	1	no	—
1644	C₄	—	212	1	no	—
1645	C₂	—	4	2	no	—
1646	C₂	—	4	2	no	—
1647	C₂	—	53	8	no	—
1648	C₂	—	212	2	no	—
1649	C₂	—	212	2	no	—
1650	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1651	C₂	#518×D₅₃	1	1	yes	characteristic
1652	C₂	#520×D₅₃	1	1	yes	characteristic
1653	C₂	#538×D₅₃	1	1	yes	characteristic
1654	C₂	#539×D₅₃	1	1	yes	characteristic
1655	C₂	#540×D₅₃	1	1	yes	characteristic
1656	C₂	#542×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2335	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×D₄×D₅₃	C₂²
hypercenter	#2335	D₅₃
hypocenter	C₅₃	C₂×#2335
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2335

Complements

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

N	H ≅ G/N	type
2. #20277512	C₂	semidirect
3. #20277511	C₂	semidirect
4. #20277510	C₂	semidirect
5. #20277509	C₂	semidirect
6. #20277508	C₂	semidirect
7. #20277507	C₂	semidirect
8. #20277506	C₂	semidirect
9. #20277505	C₂	semidirect
10. #20277504	C₂	semidirect
11. #20277503	C₂	semidirect
12. #20277502	C₂	semidirect
13. #20277501	C₂	semidirect
14. #20277500	C₂	semidirect
15. #20277499	C₂	semidirect
16. #20277498	C₂	semidirect
18. #389×D₅₃	C₂	semidirect
19. #388×D₅₃	C₂	semidirect
20. #388×D₅₃	C₂	semidirect
21. #388×D₅₃	C₂	semidirect
22. #388×D₅₃	C₂	semidirect
23. #387×D₅₃	C₂	semidirect
24. #387×D₅₃	C₂	semidirect
26. #385×D₅₃	C₂	semidirect
27. #380×D₅₃	C₂	semidirect
28. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
29. C₄×C₂²⋊C₄×D₅₃	C₂	semidirect
30. C₄×C₂²⋊C₄×D₅₃	C₂	semidirect
31. C₅₃×#2335	C₂	semidirect
42. #123×D₅₃	C₄	semidirect
72. #16810522	C₂²	semidirect
73. #16810521	C₂²	semidirect
74. #16810520	C₂²	semidirect
75. #16810520	C₂²	semidirect
76. #16810519	C₂²	semidirect
77. #16810518	C₂²	semidirect
78. #16810518	C₂²	semidirect
79. #16810517	C₂²	semidirect
80. #16810517	C₂²	semidirect
81. #16810517	C₂²	semidirect
82. #16810517	C₂²	semidirect
83. #16810516	C₂²	semidirect
84. #16810516	C₂²	semidirect
85. #16810516	C₂²	semidirect
86. #16810516	C₂²	semidirect
87. #16810515	C₂²	semidirect
88. #16810515	C₂²	semidirect
89. #16810515	C₂²	semidirect
90. #16810515	C₂²	semidirect
91. #16810514	C₂²	semidirect
92. #16810514	C₂²	semidirect
93. #16810514	C₂²	semidirect
94. #16810514	C₂²	semidirect
95. #16810513	C₂²	semidirect
96. #16810513	C₂²	semidirect
97. #16810513	C₂²	semidirect
98. #16810513	C₂²	semidirect
99. #16810512	C₂²	semidirect
100. #16810512	C₂²	semidirect
101. #16810512	C₂²	semidirect
102. #16810512	C₂²	semidirect
103. #16810511	C₂²	semidirect
104. #16810511	C₂²	semidirect
105. #16810511	C₂²	semidirect
106. #16810511	C₂²	semidirect
107. #16810510	C₂²	semidirect
108. #16810510	C₂²	semidirect
109. #16810509	C₂²	semidirect
110. #16810509	C₂²	semidirect
111. #16810508	C₂²	semidirect
112. #16810508	C₂²	semidirect
113. #16810507	C₂²	semidirect
114. #16810507	C₂²	semidirect
115. #16810506	C₂²	semidirect
116. #16810506	C₂²	semidirect
117. #16810505	C₂²	semidirect
118. #16810505	C₂²	semidirect
119. #16810504	C₂²	semidirect
120. #16810504	C₂²	semidirect
128. #16810498	C₂²	semidirect
129. #16810497	C₂²	semidirect
130. #16810497	C₂²	semidirect
131. #16810496	C₂²	semidirect
132. #16810495	C₂²	semidirect
133. #16810494	C₂²	semidirect
134. #16810494	C₂²	semidirect
135. #16810483	C₂²	semidirect
136. #16810482	C₂²	semidirect
137. #16810482	C₂²	semidirect
138. #16810481	C₂²	semidirect
139. #16810481	C₂²	semidirect
140. #16810480	C₂²	semidirect
141. #16810480	C₂²	semidirect
142. C₄⋊C₄×Dic₅₃	C₂²	semidirect
143. C₄⋊C₄×Dic₅₃	C₂²	semidirect
144. C₄×#11719919	C₂²	semidirect
145. C₄×#11719919	C₂²	semidirect
146. C₄×C₄⋊Dic₅₃	C₂²	semidirect
147. #16810474	C₂²	semidirect
148. #16810474	C₂²	semidirect
149. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
150. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
151. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
152. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
153. C₄×#11719921	C₂²	semidirect
154. C₄×#11719921	C₂²	semidirect
155. C₄×#11719921	C₂²	semidirect
156. C₄×#11719921	C₂²	semidirect
157. C₄×C₂²⋊Dic₅₃	C₂²	semidirect
158. C₄×C₂²⋊Dic₅₃	C₂²	semidirect
159. #16810470	C₂²	semidirect
160. #16810470	C₂²	semidirect
161. #16810470	C₂²	semidirect
162. #16810470	C₂²	semidirect
175. C₅₃×#389	C₂²	semidirect
176. C₅₃×#388	C₂²	semidirect
177. C₅₃×#388	C₂²	semidirect
178. C₅₃×#388	C₂²	semidirect
179. C₅₃×#388	C₂²	semidirect
180. C₅₃×#387	C₂²	semidirect
181. C₅₃×#387	C₂²	semidirect
183. C₅₃×#385	C₂²	semidirect
184. C₅₃×#380	C₂²	semidirect
185. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
186. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
187. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
203. C₂²×C₄×D₅₃	C₂×C₄	semidirect
221. #13133202	C₂×C₄	semidirect
222. #13133202	C₂×C₄	semidirect
223. #13133201	C₂×C₄	semidirect
224. #13133200	C₂×C₄	semidirect
225. #13133199	C₂×C₄	semidirect
226. #13133199	C₂×C₄	semidirect
227. #13133198	C₂×C₄	semidirect
254. C₄⋊C₄×D₅₃	C₂×C₄	semidirect
255. C₄⋊C₄×D₅₃	C₂×C₄	semidirect
295. C₂²⋊C₄×D₅₃	C₂×C₄	semidirect
349. #123×C₅₃	C₂×C₄	semidirect
409. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
434. C₂²×Dic₅₃	C₂²×C₄	semidirect
501. C₂×C₄×D₅₃	C₂²×C₄	semidirect
502. C₂×C₄×D₅₃	C₂²×C₄	semidirect
510. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
511. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
521. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
536. C₂²⋊Dic₅₃	C₂²×C₄	semidirect
555. #11719921	C₂²×C₄	semidirect
556. #11719921	C₂²×C₄	semidirect
562. C₄⋊Dic₅₃	C₂²×C₄	semidirect
563. C₄⋊Dic₅₃	C₂²×C₄	semidirect
574. #11719919	C₂²×C₄	semidirect
575. #11719919	C₂²×C₄	semidirect
576. #11719919	C₂²×C₄	semidirect
577. #11719919	C₂²×C₄	semidirect
833. #2335	D₅₃	direct (N × H)
859. D₅₃	#2335	direct (N × H)
909. #389	C₂×D₅₃	semidirect
938. #388	C₂×D₅₃	semidirect
939. #388	C₂×D₅₃	semidirect
940. #388	C₂×D₅₃	semidirect
941. #388	C₂×D₅₃	semidirect
956. #387	C₂×D₅₃	semidirect
957. #387	C₂×D₅₃	semidirect
973. #385	C₂×D₅₃	semidirect
981. #380	C₂×D₅₃	semidirect
989. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
1004. C₄×C₂²⋊C₄	C₂×D₅₃	semidirect
1005. C₄×C₂²⋊C₄	C₂×D₅₃	semidirect
1016. C₅₃	C₂×#2335	semidirect
1060. #123	C₄×D₅₃	semidirect
1320. C₂²×C₄	C₂×C₄×D₅₃	semidirect
1360. C₄⋊C₄	C₂×C₄×D₅₃	semidirect
1361. C₄⋊C₄	C₂×C₄×D₅₃	semidirect
1401. C₂²⋊C₄	C₂×C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#123×D₅₃	2
#20277512	2
#20277511	2
#20277510	2
#20277509	2
#20277508	2
#20277507	2
#20277506	2
#20277505	2
#20277504	2
#20277503	2
#20277502	2
#20277501	2
#20277500	2
#20277499	2
#20277498	2
#390×D₅₃	2
#389×D₅₃	2
#388×D₅₃	2
#387×D₅₃	2
#386×D₅₃	2
#385×D₅₃	2
#380×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
C₄×C₂²⋊C₄×D₅₃	2
C₅₃×#2335	2
C₂×#2335	53

Subgroups — D53×#2335 #27542978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2335 #27542978