Subgroups — #27547638

Order 13568.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20277907	C₂	1	1	yes	maximal, characteristic, complemented
2	#20277889	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277872	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277863	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277839	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277800	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277790	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277767	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277735	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277735	C₂	1	1	yes	maximal, characteristic, complemented
11	#20277724	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277711	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277655	C₂	1	1	yes	maximal, characteristic, complemented
14	#20277644	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277625	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₄⋊Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#20277530	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277509	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277494	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277494	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277428	C₂	1	1	yes	maximal, characteristic, complemented
22	#20277420	C₂	1	1	yes	maximal, characteristic, complemented
23	#20277410	C₂	1	1	yes	maximal, characteristic, complemented
24	#20277387	C₂	1	1	yes	maximal, characteristic, complemented
25	#20277376	C₂	1	1	yes	maximal, characteristic, complemented
26	#20277376	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277313	C₂	1	1	yes	maximal, characteristic, complemented
28	#120×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
29	#120×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16810498	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic
32	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic
33	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
35	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
36	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
37	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
38	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
39	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
40	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
41	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
42	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
48	#16810530	C₂²	1	1	yes	characteristic, complemented
49	#16810530	C₂²	1	1	yes	characteristic, complemented
50	#16810530	C₂²	1	1	yes	characteristic, complemented
51	#16810526	C₂²	1	1	yes	characteristic
52	#16810526	C₂²	1	1	yes	characteristic
53	#16810526	C₂²	1	1	yes	characteristic
54	#16810526	C₂²	1	1	yes	characteristic
55	#16810526	C₂²	1	1	yes	characteristic, complemented
56	#16810522	C₂²	1	1	yes	characteristic, complemented
57	#16810522	C₂²	1	1	yes	characteristic, complemented
58	#16810522	C₂²	1	1	yes	characteristic, complemented
59	#16810522	C₂²	1	1	yes	characteristic, complemented
60	#16810522	C₂²	1	1	yes	characteristic, complemented
61	#16810522	C₂²	1	1	yes	characteristic, complemented
62	#16810522	C₂²	1	1	yes	characteristic, complemented
63	#16810522	C₂²	1	1	yes	characteristic, complemented
64	#16810516	C₂²	1	1	yes	characteristic
65	#16810516	C₂²	1	1	yes	characteristic
66	#16810516	C₂²	1	1	yes	characteristic
67	#16810516	C₂²	1	1	yes	characteristic
68	#16810516	C₂²	1	1	yes	characteristic
69	#16810516	C₂²	1	1	yes	characteristic
70	#16810516	C₂²	1	1	yes	characteristic
71	#16810516	C₂²	1	1	yes	characteristic
72	#16810516	C₂²	1	1	yes	characteristic
73	#16810516	C₂²	1	1	yes	characteristic
74	#16810516	C₂²	1	1	yes	characteristic
75	#16810516	C₂²	1	1	yes	characteristic
76	#16810516	C₂²	1	1	yes	characteristic
77	#16810516	C₂²	1	1	yes	characteristic
78	#16810516	C₂²	1	1	yes	characteristic
79	#16810516	C₂²	1	1	yes	characteristic
80	#16810516	C₂²	1	1	yes	characteristic, complemented
81	#16810516	C₂²	1	1	yes	characteristic, complemented
82	#16810516	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	#16810516	C₂²	1	1	yes	characteristic, complemented
88	#16810509	C₂²	1	1	yes	characteristic, complemented
89	#16810509	C₂²	1	1	yes	characteristic, complemented
90	#16810509	C₂²	1	1	yes	characteristic, complemented
91	#16810509	C₂²	1	1	yes	characteristic, complemented
92	#16810509	C₂²	1	1	yes	characteristic, complemented
93	#16810509	C₂²	1	1	yes	characteristic, complemented
94	#16810509	C₂²	1	1	yes	characteristic, complemented
95	#16810509	C₂²	1	1	yes	characteristic, complemented
96	#16810509	C₂²	1	1	yes	characteristic, complemented
97	#16810509	C₂²	1	1	yes	characteristic, complemented
98	#16810509	C₂²	1	1	yes	characteristic, complemented
99	#16810509	C₂²	1	1	yes	characteristic, complemented
100	#16810503	C₂²	1	1	yes	characteristic
101	#16810503	C₂²	1	1	yes	characteristic
102	#16810503	C₂²	1	1	yes	characteristic
103	#16810503	C₂²	1	1	yes	characteristic
104	#16810503	C₂²	1	1	yes	characteristic
105	#16810503	C₂²	1	1	yes	characteristic
106	#16810503	C₂²	1	1	yes	characteristic
107	#16810503	C₂²	1	1	yes	characteristic
108	#16810503	C₂²	1	1	yes	characteristic
109	#16810503	C₂²	1	1	yes	characteristic
110	#16810503	C₂²	1	1	yes	characteristic
111	#16810503	C₂²	1	1	yes	characteristic
112	#16810503	C₂²	1	1	yes	characteristic, complemented
113	#16810503	C₂²	1	1	yes	characteristic, complemented
114	#16810498	C₂²	1	1	yes	characteristic
115	#16810498	C₂²	1	1	yes	characteristic
116	#16810498	C₂²	1	1	yes	characteristic
117	#16810498	C₂²	1	1	yes	characteristic
118	#16810498	C₂²	1	1	yes	characteristic
119	#16810498	C₂²	1	1	yes	characteristic
120	#16810498	C₂²	1	1	yes	characteristic
121	#16810498	C₂²	1	1	yes	characteristic
122	#16810498	C₂²	1	1	yes	characteristic
123	#16810498	C₂²	1	1	yes	characteristic
124	#16810498	C₂²	1	1	yes	characteristic
125	#16810498	C₂²	1	1	yes	characteristic
126	#16810498	C₂²	1	1	yes	characteristic
127	#16810498	C₂²	1	1	yes	characteristic
128	#16810498	C₂²	1	1	yes	characteristic
129	#16810498	C₂²	1	1	yes	characteristic
130	#16810498	C₂²	1	1	yes	characteristic, complemented
131	#16810498	C₂²	1	1	yes	characteristic, complemented
132	#16810498	C₂²	1	1	yes	characteristic, complemented
133	#16810498	C₂²	1	1	yes	characteristic, complemented
134	#16810498	C₂²	1	1	yes	characteristic, complemented
135	#16810498	C₂²	1	1	yes	characteristic, complemented
136	#16810493	C₂²	1	1	yes	characteristic, complemented
137	#16810491	C₂²	1	1	yes	characteristic, complemented
138	#16810489	C₂²	1	1	yes	characteristic, complemented
139	#16810489	C₂²	1	1	yes	characteristic, complemented
140	#16810486	C₂²	1	1	yes	characteristic, complemented
141	#16810483	C₂²	1	1	yes	characteristic
142	#16810483	C₂²	1	1	yes	characteristic
143	#16810483	C₂²	1	1	yes	characteristic, complemented
144	#16810483	C₂²	1	1	yes	characteristic, complemented
145	#16810483	C₂²	1	1	yes	characteristic, complemented
146	#16810479	C₂²	1	1	yes	characteristic
147	#16810479	C₂²	1	1	yes	characteristic
148	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
149	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
150	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
151	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
152	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
153	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
154	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
155	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
156	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
157	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
158	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
159	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
160	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
161	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
164	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
165	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
166	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
167	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
168	#16810469	C₂²	1	1	yes	characteristic, complemented
169	C₂×#13133124	C₂²	1	1	yes	characteristic
170	C₂×#13133124	C₂²	1	1	yes	characteristic
171	C₂×#13133124	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#538	C₄	1	16	yes	complemented
173	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
174	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
175	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
176	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
177	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
178	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
179	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
180	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
181	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
182	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
183	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
184	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
185	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
188	C₂³×Dic₅₃	—	4	2	no	—
189	C₂³×Dic₅₃	—	4	2	no	—
190	C₂³×Dic₅₃	—	4	2	no	—
191	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
192	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
193	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
194	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
195	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
196	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
199	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
202	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
203	Q₈×Dic₅₃	—	4	2	no	—
204	D₄×Dic₅₃	—	4	2	no	—
205	D₄×Dic₅₃	—	4	2	no	—
206	D₄×Dic₅₃	—	4	2	no	—
207	D₄×Dic₅₃	—	4	2	no	—
208	D₄×Dic₅₃	—	4	2	no	—
209	D₄×Dic₅₃	—	4	2	no	—
210	D₄×Dic₅₃	—	4	2	no	—
211	D₄×Dic₅₃	—	4	2	no	—
212	D₄×Dic₅₃	—	4	2	no	—
213	#13133176	—	4	2	no	—
214	C₂×C₄⋊Dic₅₃	—	4	2	no	—
215	C₂×C₄⋊Dic₅₃	—	4	2	no	—
216	C₂×C₄⋊Dic₅₃	—	4	2	no	—
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
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×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₅₃	—	4	2	no	—
242	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	#13133124	C₂³	1	1	yes	characteristic
287	#13133124	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
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	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
327	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
328	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
339	#126×C₅₃	C₂×C₄	1	8	yes	complemented
340	#126×C₅₃	C₂×C₄	1	8	yes	complemented
341	#124×C₅₃	C₂×C₄	1	8	yes	complemented
342	#124×C₅₃	C₂×C₄	1	8	yes	complemented
343	#123×C₅₃	C₂×C₄	1	8	yes	complemented
344	#123×C₅₃	C₂×C₄	1	8	yes	complemented
345	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
346	#121×C₅₃	C₂×C₄	1	8	yes	complemented
347	#121×C₅₃	C₂×C₄	1	8	yes	complemented
348	#121×C₅₃	C₂×C₄	1	8	yes	complemented
349	#120×C₅₃	C₂×C₄	1	8	yes	complemented
350	#120×C₅₃	C₂×C₄	1	8	yes	complemented
351	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
352	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
371	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
373	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
374	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
375	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
376	C₂⁴×C₅₃	—	2	2	no	—
377	C₂⁴×C₅₃	—	2	2	no	—
378	C₂⁴×C₅₃	—	4	1	no	—
379	C₂⁴×C₅₃	—	4	1	no	—
380	C₂⁴×C₅₃	—	4	1	no	—
381	C₂⁴×C₅₃	—	4	1	no	—
382	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
383	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×Q₈×C₅₃	—	4	1	no	—
389	C₂×Q₈×C₅₃	—	4	1	no	—
390	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	complemented
391	C₂×D₄×C₅₃	—	2	2	no	—
392	C₂×D₄×C₅₃	—	2	2	no	—
393	C₂×D₄×C₅₃	—	2	2	no	—
394	C₂×D₄×C₅₃	—	2	2	no	—
395	C₂×D₄×C₅₃	—	4	1	no	—
396	C₂×D₄×C₅₃	—	4	1	no	—
397	C₂×D₄×C₅₃	—	4	1	no	—
398	C₂×D₄×C₅₃	—	4	1	no	—
399	C₂×D₄×C₅₃	—	4	1	no	—
400	C₂×D₄×C₅₃	—	4	1	no	—
401	C₂×D₄×C₅₃	—	4	1	no	—
402	C₂×D₄×C₅₃	—	4	1	no	—
403	C₂×D₄×C₅₃	—	4	1	no	—
404	C₂×D₄×C₅₃	—	4	1	no	—
405	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
406	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
407	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
408	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
409	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
410	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
411	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	complemented
412	C₂²×C₄×C₅₃	—	4	1	no	—
413	C₂²×C₄×C₅₃	—	4	1	no	—
414	C₂²×C₄×C₅₃	—	4	1	no	—
415	C₂²×C₄×C₅₃	—	4	1	no	—
416	C₂²×C₄×C₅₃	—	4	1	no	—
417	C₂²×C₄×C₅₃	—	4	1	no	—
418	C₂²×C₄×C₅₃	—	4	1	no	—
419	C₂²×C₄×C₅₃	—	4	1	no	—
420	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
421	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
422	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
423	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
424	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
434	C₂²×Dic₅₃	—	2	2	no	—
435	C₂²×Dic₅₃	—	2	2	no	—
436	C₂²×Dic₅₃	—	2	2	no	—
437	C₂²×Dic₅₃	—	2	2	no	—
438	C₂²×Dic₅₃	—	2	2	no	—
439	C₂²×Dic₅₃	—	2	2	no	—
440	C₂²×Dic₅₃	—	2	2	no	—
441	C₂²×Dic₅₃	—	2	2	no	—
442	C₂²×Dic₅₃	—	2	2	no	—
443	C₂²×Dic₅₃	—	2	2	no	—
444	C₂²×Dic₅₃	—	2	2	no	—
445	C₂²×Dic₅₃	—	2	2	no	—
446	C₂²×Dic₅₃	—	4	1	no	—
447	C₂²×Dic₅₃	—	4	1	no	—
448	C₂²×Dic₅₃	—	4	1	no	—
449	C₂²×Dic₅₃	—	4	1	no	—
450	C₂²×Dic₅₃	—	4	1	no	—
451	C₂²×Dic₅₃	—	4	1	no	—
452	C₂²×Dic₅₃	—	4	1	no	—
453	C₂²×Dic₅₃	—	4	1	no	—
454	C₂²×Dic₅₃	—	4	1	no	—
455	C₂²×Dic₅₃	—	4	1	no	—
456	C₂²×Dic₅₃	—	4	1	no	—
457	C₂²×Dic₅₃	—	4	1	no	—
458	C₂²×Dic₅₃	—	4	1	no	—
459	C₂²×Dic₅₃	—	4	1	no	—
460	C₂²×Dic₅₃	—	4	1	no	—
461	C₂²×Dic₅₃	—	4	1	no	—
462	C₂²×Dic₅₃	—	4	1	no	—
463	C₂²×Dic₅₃	—	4	1	no	—
464	C₂²×Dic₅₃	—	4	1	no	—
465	C₂²×Dic₅₃	—	4	1	no	—
466	C₂²×Dic₅₃	—	4	1	no	—
467	C₂²×Dic₅₃	—	4	1	no	—
468	C₂²×Dic₅₃	—	4	1	no	—
469	C₂²×Dic₅₃	—	4	1	no	—
470	C₂²×Dic₅₃	—	4	16	no	—
471	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
472	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
473	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
474	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
475	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
476	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
477	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
478	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
479	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
480	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
481	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
482	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
483	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
484	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
485	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
486	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
487	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
488	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
489	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
490	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
491	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
492	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
493	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
494	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
495	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
496	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
497	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
498	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
499	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
500	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
501	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
502	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
503	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
504	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
505	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
506	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
507	C₄²×C₅₃	C₂²×C₄	1	4	yes	complemented
508	C₄²×C₅₃	C₂²×C₄	1	4	yes	complemented
509	C₂²⋊Dic₅₃	—	2	2	no	—
510	C₂²⋊Dic₅₃	—	2	2	no	—
511	C₂²⋊Dic₅₃	—	2	2	no	—
512	C₂²⋊Dic₅₃	—	2	2	no	—
513	C₂²⋊Dic₅₃	—	2	2	no	—
514	C₂²⋊Dic₅₃	—	2	2	no	—
515	C₂²⋊Dic₅₃	—	4	1	no	—
516	C₂²⋊Dic₅₃	—	4	1	no	—
517	C₂²⋊Dic₅₃	—	4	1	no	—
518	C₂²⋊Dic₅₃	—	4	1	no	—
519	C₂²⋊Dic₅₃	—	4	1	no	—
520	C₂²⋊Dic₅₃	—	4	1	no	—
521	C₂²⋊Dic₅₃	—	4	1	no	—
522	C₂²⋊Dic₅₃	—	4	1	no	—
523	C₂²⋊Dic₅₃	—	4	1	no	—
524	C₂²⋊Dic₅₃	—	4	1	no	—
525	C₂²⋊Dic₅₃	—	4	1	no	—
526	C₂²⋊Dic₅₃	—	4	1	no	—
527	C₂²⋊Dic₅₃	—	4	1	no	—
528	C₂²⋊Dic₅₃	—	4	1	no	—
529	C₂²⋊Dic₅₃	—	4	1	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	—	4	1	no	—
535	C₂²⋊Dic₅₃	—	4	1	no	—
536	C₂²⋊Dic₅₃	—	4	1	no	—
537	C₄⋊Dic₅₃	—	2	2	no	—
538	C₄⋊Dic₅₃	—	2	2	no	—
539	C₄⋊Dic₅₃	—	2	2	no	—
540	C₄⋊Dic₅₃	—	2	2	no	—
541	C₄⋊Dic₅₃	—	2	2	no	—
542	C₄⋊Dic₅₃	—	2	2	no	—
543	C₄⋊Dic₅₃	—	4	1	no	—
544	C₄⋊Dic₅₃	—	4	1	no	—
545	C₄⋊Dic₅₃	—	4	1	no	—
546	C₄⋊Dic₅₃	—	4	1	no	—
547	C₄⋊Dic₅₃	—	4	1	no	—
548	C₄⋊Dic₅₃	—	4	1	no	—
549	C₄⋊Dic₅₃	—	4	1	no	—
550	C₄⋊Dic₅₃	—	4	1	no	—
551	C₄⋊Dic₅₃	—	4	1	no	—
552	C₄⋊Dic₅₃	—	4	1	no	—
553	C₄⋊Dic₅₃	—	4	1	no	—
554	C₄⋊Dic₅₃	—	4	1	no	—
555	C₄⋊Dic₅₃	—	4	1	no	—
556	C₄⋊Dic₅₃	—	4	1	no	—
557	C₄⋊Dic₅₃	—	4	1	no	—
558	C₄⋊Dic₅₃	—	4	1	no	—
559	C₄⋊Dic₅₃	—	4	1	no	—
560	C₄⋊Dic₅₃	—	4	1	no	—
561	C₄×Dic₅₃	—	2	2	no	—
562	C₄×Dic₅₃	—	2	2	no	—
563	C₄×Dic₅₃	—	4	1	no	—
564	C₄×Dic₅₃	—	4	1	no	—
565	C₄×Dic₅₃	—	4	1	no	—
566	C₄×Dic₅₃	—	4	1	no	—
567	C₄×Dic₅₃	—	4	1	no	—
568	C₄×Dic₅₃	—	4	1	no	—
569	C₄×Dic₅₃	—	4	1	no	—
570	C₄×Dic₅₃	—	4	1	no	—
571	C₄×Dic₅₃	—	4	1	no	—
572	C₄×Dic₅₃	—	4	1	no	—
573	C₄×Dic₅₃	—	4	1	no	—
574	C₄×Dic₅₃	—	4	1	no	—
575	C₄×Dic₅₃	—	4	1	no	—
576	C₄×Dic₅₃	—	4	1	no	—
577	C₂³×C₅₃	—	2	1	no	—
578	C₂³×C₅₃	—	2	1	no	—
579	C₂³×C₅₃	—	2	1	no	—
580	C₂³×C₅₃	—	2	1	no	—
581	C₂³×C₅₃	—	2	8	no	—
582	C₂³×C₅₃	—	2	1	no	—
583	C₂³×C₅₃	—	2	1	no	—
584	C₂³×C₅₃	—	2	1	no	—
585	C₂³×C₅₃	—	2	1	no	—
586	C₂³×C₅₃	—	2	1	no	—
587	C₂³×C₅₃	—	2	1	no	—
588	C₂³×C₅₃	—	2	1	no	—
589	C₂³×C₅₃	—	2	1	no	—
590	C₂³×C₅₃	—	2	1	no	—
591	C₂³×C₅₃	—	2	1	no	—
592	C₂³×C₅₃	—	2	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	—	2	1	no	—
606	C₂³×C₅₃	—	4	4	no	—
607	C₂³×C₅₃	—	4	4	no	—
608	C₂³×C₅₃	—	4	4	no	—
609	C₂³×C₅₃	—	4	4	no	—
610	C₂³×C₅₃	—	4	4	no	—
611	C₂³×C₅₃	—	4	4	no	—
612	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
613	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
614	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
615	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
616	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
617	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
618	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
619	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
620	Q₈×C₅₃	—	4	4	no	—
621	D₄×C₅₃	—	2	8	no	—
622	D₄×C₅₃	—	2	8	no	—
623	D₄×C₅₃	—	4	4	no	—
624	D₄×C₅₃	—	4	4	no	—
625	D₄×C₅₃	—	4	4	no	—
626	D₄×C₅₃	—	4	4	no	—
627	D₄×C₅₃	—	4	4	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	2	1	no	—
639	C₂×C₄×C₅₃	—	2	1	no	—
640	C₂×C₄×C₅₃	—	2	1	no	—
641	C₂×C₄×C₅₃	—	2	1	no	—
642	C₂×C₄×C₅₃	—	2	1	no	—
643	C₂×C₄×C₅₃	—	2	1	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	—	4	4	no	—
649	C₂×C₄×C₅₃	—	4	4	no	—
650	C₂×C₄×C₅₃	—	4	4	no	—
651	C₂×C₄×C₅₃	—	4	4	no	—
652	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
653	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
654	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
655	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
656	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
657	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
658	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
659	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
660	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
661	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
662	C₂×Dic₅₃	—	2	1	no	—
663	C₂×Dic₅₃	—	2	1	no	—
664	C₂×Dic₅₃	—	2	1	no	—
665	C₂×Dic₅₃	—	2	1	no	—
666	C₂×Dic₅₃	—	2	1	no	—
667	C₂×Dic₅₃	—	2	1	no	—
668	C₂×Dic₅₃	—	2	1	no	—
669	C₂×Dic₅₃	—	2	1	no	—
670	C₂×Dic₅₃	—	2	1	no	—
671	C₂×Dic₅₃	—	2	1	no	—
672	C₂×Dic₅₃	—	2	1	no	—
673	C₂×Dic₅₃	—	2	1	no	—
674	C₂×Dic₅₃	—	2	1	no	—
675	C₂×Dic₅₃	—	2	1	no	—
676	C₂×Dic₅₃	—	2	1	no	—
677	C₂×Dic₅₃	—	2	1	no	—
678	C₂×Dic₅₃	—	2	1	no	—
679	C₂×Dic₅₃	—	2	1	no	—
680	C₂×Dic₅₃	—	2	1	no	—
681	C₂×Dic₅₃	—	2	1	no	—
682	C₂×Dic₅₃	—	2	1	no	—
683	C₂×Dic₅₃	—	2	1	no	—
684	C₂×Dic₅₃	—	2	1	no	—
685	C₂×Dic₅₃	—	2	1	no	—
686	C₂×Dic₅₃	—	2	1	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	—	4	4	no	—
709	C₂×Dic₅₃	—	4	4	no	—
710	C₂×Dic₅₃	—	4	4	no	—
711	C₂×Dic₅₃	—	4	4	no	—
712	C₂×Dic₅₃	—	4	4	no	—
713	C₂×Dic₅₃	—	4	4	no	—
714	C₂×Dic₅₃	—	8	2	no	—
715	C₂×Dic₅₃	—	8	2	no	—
716	C₂×Dic₅₃	—	8	2	no	—
717	C₂×Dic₅₃	—	8	2	no	—
718	C₂×Dic₅₃	—	8	2	no	—
719	C₂×Dic₅₃	—	8	2	no	—
720	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
721	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
722	#34416	—	53	1	no	maximal, Sylow
723	C₂²×C₅₃	—	2	2	no	—
724	C₂²×C₅₃	—	2	2	no	—
725	C₂²×C₅₃	—	2	2	no	—
726	C₂²×C₅₃	—	2	2	no	—
727	C₂²×C₅₃	—	2	2	no	—
728	C₂²×C₅₃	—	2	2	no	—
729	C₂²×C₅₃	—	2	2	no	—
730	C₂²×C₅₃	—	2	2	no	—
731	C₂²×C₅₃	—	2	2	no	—
732	C₂²×C₅₃	—	2	2	no	—
733	C₂²×C₅₃	—	2	2	no	—
734	C₂²×C₅₃	—	2	2	no	—
735	C₂²×C₅₃	—	2	2	no	—
736	C₂²×C₅₃	—	2	2	no	—
737	C₂²×C₅₃	—	2	2	no	—
738	C₂²×C₅₃	—	2	2	no	—
739	C₂²×C₅₃	—	2	2	no	—
740	C₂²×C₅₃	—	2	2	no	—
741	C₂²×C₅₃	—	4	16	no	—
742	C₂²×C₅₃	—	4	1	no	—
743	C₂²×C₅₃	—	4	1	no	—
744	C₂²×C₅₃	—	4	1	no	—
745	C₂²×C₅₃	—	4	1	no	—
746	C₂²×C₅₃	—	4	1	no	—
747	C₂²×C₅₃	—	4	1	no	—
748	C₂²×C₅₃	—	4	1	no	—
749	C₂²×C₅₃	—	4	1	no	—
750	C₂²×C₅₃	—	4	1	no	—
751	C₂²×C₅₃	—	4	1	no	—
752	C₂²×C₅₃	—	4	1	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	#520	1	4	yes	—
759	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
760	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
762	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
763	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
764	C₂²×C₅₃	#585	1	1	yes	characteristic
765	C₂²×C₅₃	#585	1	1	yes	characteristic
766	C₄×C₅₃	—	2	2	no	—
767	C₄×C₅₃	—	2	2	no	—
768	C₄×C₅₃	—	2	2	no	—
769	C₄×C₅₃	—	2	2	no	—
770	C₄×C₅₃	—	2	2	no	—
771	C₄×C₅₃	—	2	2	no	—
772	C₄×C₅₃	—	2	2	no	—
773	C₄×C₅₃	—	2	2	no	—
774	C₄×C₅₃	—	2	2	no	—
775	C₄×C₅₃	—	2	2	no	—
776	Dic₅₃	—	2	2	no	—
777	Dic₅₃	—	2	2	no	—
778	Dic₅₃	—	4	1	no	—
779	Dic₅₃	—	4	1	no	—
780	Dic₅₃	—	4	1	no	—
781	Dic₅₃	—	4	1	no	—
782	Dic₅₃	—	4	1	no	—
783	Dic₅₃	—	4	1	no	—
784	Dic₅₃	—	4	1	no	—
785	Dic₅₃	—	4	1	no	—
786	Dic₅₃	—	4	1	no	—
787	Dic₅₃	—	4	1	no	—
788	Dic₅₃	—	4	1	no	—
789	Dic₅₃	—	4	1	no	—
790	Dic₅₃	—	4	1	no	—
791	Dic₅₃	—	4	1	no	—
792	C₂×#538	D₅₃	1	1	yes	characteristic
793	#2383	—	53	1	no	—
794	#2379	—	53	1	no	—
795	#2377	—	53	1	no	—
796	#2376	—	53	1	no	—
797	#2373	—	53	1	no	—
798	#2368	—	53	1	no	—
799	#2367	—	53	1	no	—
800	#2364	—	53	1	no	—
801	#2361	—	53	1	no	—
802	#2361	—	53	1	no	—
803	#2360	—	53	1	no	—
804	#2359	—	53	1	no	—
805	#2353	—	53	1	no	—
806	#2352	—	53	1	no	—
807	#2349	—	53	1	no	—
808	D₄×C₄⋊C₄	—	53	1	no	—
809	#2337	—	53	1	no	—
810	#2335	—	53	1	no	—
811	#2334	—	53	1	no	—
812	#2334	—	53	1	no	—
813	#2326	—	53	1	no	—
814	#2325	—	53	1	no	—
815	#2324	—	53	1	no	—
816	#2322	—	53	1	no	—
817	#2321	—	53	1	no	—
818	#2321	—	53	1	no	—
819	#2312	—	53	1	no	—
820	C₄×#120	—	53	1	no	—
821	C₄×#120	—	53	1	no	—
822	C₂×#385	—	53	1	no	—
823	C₂×C₅₃	—	2	4	no	—
824	C₂×C₅₃	—	4	2	no	—
825	C₂×C₅₃	—	4	2	no	—
826	C₂×C₅₃	—	4	2	no	—
827	C₂×C₅₃	—	4	2	no	—
828	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
829	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂×C₅₃	#3532	1	1	yes	characteristic
832	C₂×C₅₃	#3533	1	1	yes	characteristic
833	C₂×C₅₃	#3541	1	1	yes	characteristic
834	C₂×C₅₃	#3541	1	1	yes	characteristic
835	C₂⁴×C₄	—	53	1	no	—
836	#538	Dic₅₃	1	16	yes	complemented
837	C₂×#126	C₂×D₅₃	1	1	yes	characteristic
838	C₂×#126	C₂×D₅₃	1	1	yes	characteristic
839	C₂×#124	C₂×D₅₃	1	1	yes	characteristic
840	C₂×#124	C₂×D₅₃	1	1	yes	characteristic
841	C₂×#123	C₂×D₅₃	1	1	yes	characteristic
842	C₂×#123	C₂×D₅₃	1	1	yes	characteristic
843	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
844	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
845	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
846	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
847	C₂×#120	C₂×D₅₃	1	1	yes	characteristic
848	C₂×#120	C₂×D₅₃	1	1	yes	characteristic
849	C₂×C₄×Q₈	—	53	1	no	—
850	C₂×C₄×D₄	—	53	1	no	—
851	C₂×C₄×D₄	—	53	1	no	—
852	C₂×C₄×D₄	—	53	1	no	—
853	C₂×C₄×D₄	—	53	1	no	—
854	C₂×C₄×D₄	—	53	1	no	—
855	C₂×C₄×D₄	—	53	1	no	—
856	C₂×C₄×D₄	—	53	1	no	—
857	C₂×C₄×D₄	—	53	1	no	—
858	C₂×C₄×D₄	—	53	1	no	—
859	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
860	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
861	C₂×#117	—	53	1	no	—
862	C₂²×C₄⋊C₄	—	53	1	no	—
863	C₂²×C₄⋊C₄	—	53	1	no	—
864	C₂²×C₄⋊C₄	—	53	1	no	—
865	C₂²×C₂²⋊C₄	—	53	1	no	—
866	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
867	#391	—	53	1	no	—
868	#391	—	53	1	no	—
869	#391	—	53	1	no	—
870	#390	—	53	1	no	—
871	#390	—	53	1	no	—
872	#390	—	53	1	no	—
873	#390	—	53	1	no	—
874	#390	—	53	1	no	—
875	#389	—	53	1	no	—
876	#389	—	53	1	no	—
877	#389	—	53	1	no	—
878	#389	—	53	1	no	—
879	#389	—	53	1	no	—
880	#389	—	53	1	no	—
881	#389	—	53	1	no	—
882	#389	—	53	1	no	—
883	#388	—	53	1	no	—
884	#388	—	53	1	no	—
885	#388	—	53	1	no	—
886	#388	—	53	1	no	—
887	#388	—	53	1	no	—
888	#388	—	53	1	no	—
889	#388	—	53	1	no	—
890	#388	—	53	1	no	—
891	#388	—	53	1	no	—
892	#388	—	53	1	no	—
893	#388	—	53	1	no	—
894	#388	—	53	1	no	—
895	#388	—	53	1	no	—
896	#388	—	53	1	no	—
897	#388	—	53	1	no	—
898	#388	—	53	1	no	—
899	#388	—	53	1	no	—
900	#388	—	53	1	no	—
901	#388	—	53	1	no	—
902	#388	—	53	1	no	—
903	#388	—	53	1	no	—
904	#388	—	53	1	no	—
905	#388	—	53	1	no	—
906	#388	—	53	1	no	—
907	#387	—	53	1	no	—
908	#387	—	53	1	no	—
909	#387	—	53	1	no	—
910	#387	—	53	1	no	—
911	#387	—	53	1	no	—
912	#387	—	53	1	no	—
913	#387	—	53	1	no	—
914	#387	—	53	1	no	—
915	#387	—	53	1	no	—
916	#387	—	53	1	no	—
917	#387	—	53	1	no	—
918	#387	—	53	1	no	—
919	#386	—	53	1	no	—
920	#386	—	53	1	no	—
921	#386	—	53	1	no	—
922	#386	—	53	1	no	—
923	#386	—	53	1	no	—
924	#386	—	53	1	no	—
925	#386	—	53	1	no	—
926	#386	—	53	1	no	—
927	#386	—	53	1	no	—
928	#386	—	53	1	no	—
929	#386	—	53	1	no	—
930	#386	—	53	1	no	—
931	#386	—	53	1	no	—
932	#386	—	53	1	no	—
933	#385	—	53	1	no	—
934	#385	—	53	1	no	—
935	#385	—	53	1	no	—
936	#385	—	53	1	no	—
937	#385	—	53	1	no	—
938	#385	—	53	1	no	—
939	#385	—	53	1	no	—
940	#385	—	53	1	no	—
941	#385	—	53	1	no	—
942	#385	—	53	1	no	—
943	#385	—	53	1	no	—
944	#385	—	53	1	no	—
945	#385	—	53	1	no	—
946	#385	—	53	1	no	—
947	#385	—	53	1	no	—
948	#385	—	53	1	no	—
949	#385	—	53	1	no	—
950	#385	—	53	1	no	—
951	#385	—	53	1	no	—
952	#385	—	53	1	no	—
953	#385	—	53	1	no	—
954	#385	—	53	1	no	—
955	#384	—	53	1	no	—
956	#383	—	53	1	no	—
957	#382	—	53	1	no	—
958	#382	—	53	1	no	—
959	#381	—	53	1	no	—
960	#380	—	53	1	no	—
961	#380	—	53	1	no	—
962	#380	—	53	1	no	—
963	#380	—	53	1	no	—
964	#380	—	53	1	no	—
965	#379	—	53	1	no	—
966	#379	—	53	1	no	—
967	C₄×C₄⋊C₄	—	53	1	no	—
968	C₄×C₄⋊C₄	—	53	1	no	—
969	C₄×C₄⋊C₄	—	53	1	no	—
970	C₄×C₄⋊C₄	—	53	1	no	—
971	C₄×C₄⋊C₄	—	53	1	no	—
972	C₄×C₄⋊C₄	—	53	1	no	—
973	C₄×C₄⋊C₄	—	53	1	no	—
974	C₄×C₂²⋊C₄	—	53	1	no	—
975	C₄×C₂²⋊C₄	—	53	1	no	—
976	C₄×C₂²⋊C₄	—	53	1	no	—
977	C₄×C₂²⋊C₄	—	53	1	no	—
978	C₄×C₂²⋊C₄	—	53	1	no	—
979	C₄×C₂²⋊C₄	—	53	1	no	—
980	C₄×C₂²⋊C₄	—	53	1	no	—
981	C₄×C₂²⋊C₄	—	53	1	no	—
982	C₄×C₂²⋊C₄	—	53	1	no	—
983	C₄×C₂²⋊C₄	—	53	1	no	—
984	C₄×C₂²⋊C₄	—	53	1	no	—
985	C₄×C₂²⋊C₄	—	53	1	no	—
986	C₄×C₂²⋊C₄	—	53	1	no	—
987	#376	—	53	1	no	—
988	C₂×#95	—	53	1	no	—
989	C₂×#95	—	53	1	no	—
990	C₂×#95	—	53	1	no	—
991	C₅₃	#34416	1	1	yes	characteristic, complemented, Sylow
992	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
993	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
994	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
995	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
996	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
997	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
998	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
999	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1000	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1001	C₂³×C₄	—	53	1	no	—
1002	C₂³×C₄	—	53	1	no	—
1003	C₂³×C₄	—	53	1	no	—
1004	C₂³×C₄	—	53	1	no	—
1005	C₂³×C₄	—	53	1	no	—
1006	C₂³×C₄	—	53	1	no	—
1007	C₂³×C₄	—	53	1	no	—
1008	C₂³×C₄	—	53	1	no	—
1009	C₂³×C₄	—	53	1	no	—
1010	C₂³×C₄	—	53	1	no	—
1011	C₂³×C₄	—	53	1	no	—
1012	C₂³×C₄	—	53	1	no	—
1013	C₂³×C₄	—	212	2	no	—
1014	C₂³×C₄	—	212	2	no	—
1015	C₂³×C₄	—	212	2	no	—
1016	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1017	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1018	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1019	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1020	#126	C₂×Dic₅₃	1	8	yes	complemented
1021	#126	C₂×Dic₅₃	1	8	yes	complemented
1022	#124	C₂×Dic₅₃	1	8	yes	complemented
1023	#124	C₂×Dic₅₃	1	8	yes	complemented
1024	#123	C₂×Dic₅₃	1	8	yes	complemented
1025	#123	C₂×Dic₅₃	1	8	yes	complemented
1026	C₂²⋊Q₈	C₂×Dic₅₃	1	8	yes	complemented
1027	#121	C₂×Dic₅₃	1	8	yes	complemented
1028	#121	C₂×Dic₅₃	1	8	yes	complemented
1029	#121	C₂×Dic₅₃	1	8	yes	complemented
1030	#120	C₂×Dic₅₃	1	8	yes	complemented
1031	#120	C₂×Dic₅₃	1	8	yes	complemented
1032	C₄×Q₈	—	212	2	no	—
1033	C₄×D₄	—	212	2	no	—
1034	C₄×D₄	—	212	2	no	—
1035	C₄×D₄	—	212	2	no	—
1036	C₄×D₄	—	212	2	no	—
1037	C₄×D₄	—	212	2	no	—
1038	C₄×D₄	—	212	2	no	—
1039	C₄×D₄	—	212	2	no	—
1040	C₄×D₄	—	212	2	no	—
1041	C₄×D₄	—	212	2	no	—
1042	C₄×D₄	C₂×Dic₅₃	1	8	yes	complemented
1043	C₄×D₄	C₂×Dic₅₃	1	8	yes	complemented
1044	#117	—	212	2	no	—
1045	C₂×C₄⋊C₄	—	53	1	no	—
1046	C₂×C₄⋊C₄	—	53	1	no	—
1047	C₂×C₄⋊C₄	—	53	1	no	—
1048	C₂×C₄⋊C₄	—	53	1	no	—
1049	C₂×C₄⋊C₄	—	53	1	no	—
1050	C₂×C₄⋊C₄	—	53	1	no	—
1051	C₂×C₄⋊C₄	—	53	1	no	—
1052	C₂×C₄⋊C₄	—	53	1	no	—
1053	C₂×C₄⋊C₄	—	53	1	no	—
1054	C₂×C₄⋊C₄	—	53	1	no	—
1055	C₂×C₄⋊C₄	—	53	1	no	—
1056	C₂×C₄⋊C₄	—	53	1	no	—
1057	C₂×C₄⋊C₄	—	53	1	no	—
1058	C₂×C₄⋊C₄	—	53	1	no	—
1059	C₂×C₄⋊C₄	—	53	1	no	—
1060	C₂×C₄⋊C₄	—	53	1	no	—
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	1	no	—
1068	C₂×C₄⋊C₄	—	53	1	no	—
1069	C₂×C₄⋊C₄	—	212	2	no	—
1070	C₂×C₄⋊C₄	—	212	2	no	—
1071	C₂×C₄⋊C₄	—	212	2	no	—
1072	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1073	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1074	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1075	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1076	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1077	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1078	C₂×C₂²⋊C₄	—	53	1	no	—
1079	C₂×C₂²⋊C₄	—	53	1	no	—
1080	C₂×C₂²⋊C₄	—	53	1	no	—
1081	C₂×C₂²⋊C₄	—	53	1	no	—
1082	C₂×C₂²⋊C₄	—	53	1	no	—
1083	C₂×C₂²⋊C₄	—	53	1	no	—
1084	C₂×C₂²⋊C₄	—	53	1	no	—
1085	C₂×C₂²⋊C₄	—	53	1	no	—
1086	C₂×C₂²⋊C₄	—	53	1	no	—
1087	C₂×C₂²⋊C₄	—	53	1	no	—
1088	C₂×C₂²⋊C₄	—	53	1	no	—
1089	C₂×C₂²⋊C₄	—	53	1	no	—
1090	C₂×C₂²⋊C₄	—	53	1	no	—
1091	C₂×C₂²⋊C₄	—	53	1	no	—
1092	C₂×C₂²⋊C₄	—	53	1	no	—
1093	C₂×C₂²⋊C₄	—	53	1	no	—
1094	C₂×C₂²⋊C₄	—	53	1	no	—
1095	C₂×C₂²⋊C₄	—	53	1	no	—
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	1	no	—
1106	C₂×C₂²⋊C₄	—	212	2	no	—
1107	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	8	yes	complemented
1108	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1109	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1110	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1111	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1112	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1113	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1114	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1115	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1116	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1117	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1118	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1119	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1120	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1121	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1122	C₂×C₄²	—	53	1	no	—
1123	C₂×C₄²	—	53	1	no	—
1124	C₂×C₄²	—	53	1	no	—
1125	C₂×C₄²	—	53	1	no	—
1126	C₂×C₄²	—	53	1	no	—
1127	C₂×C₄²	—	53	1	no	—
1128	C₂×C₄²	—	53	1	no	—
1129	C₂×C₄²	—	53	1	no	—
1130	C₂×C₄²	—	53	1	no	—
1131	C₂×C₄²	—	53	1	no	—
1132	C₂×C₄²	—	53	1	no	—
1133	C₂×C₄²	—	53	1	no	—
1134	C₂×C₄²	—	53	1	no	—
1135	C₂×C₄²	—	53	1	no	—
1136	C₂×C₄²	—	53	1	no	—
1137	C₂×C₄²	—	53	1	no	—
1138	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1139	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1140	#95	—	53	1	no	—
1141	#95	—	53	1	no	—
1142	#95	—	53	1	no	—
1143	#95	—	53	1	no	—
1144	#95	—	53	1	no	—
1145	#95	—	53	1	no	—
1146	#95	—	53	1	no	—
1147	#95	—	53	1	no	—
1148	#95	—	53	1	no	—
1149	#95	—	53	1	no	—
1150	#95	—	53	1	no	—
1151	#95	—	53	1	no	—
1152	#95	—	53	1	no	—
1153	#95	—	53	1	no	—
1154	#95	—	53	1	no	—
1155	#95	—	53	1	no	—
1156	#95	—	53	1	no	—
1157	#95	—	53	1	no	—
1158	#95	—	53	1	no	—
1159	#95	—	53	1	no	—
1160	#95	—	53	1	no	—
1161	#95	—	53	1	no	—
1162	#95	—	53	1	no	—
1163	#95	—	53	1	no	—
1164	#95	—	53	1	no	—
1165	#95	—	53	1	no	—
1166	#95	—	53	1	no	—
1167	#95	—	53	1	no	—
1168	#95	—	53	1	no	—
1169	#95	—	53	1	no	—
1170	#95	—	53	1	no	—
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	C₂⁴	—	2	2	no	—
1181	C₂⁴	—	2	2	no	—
1182	C₂⁴	—	4	1	no	—
1183	C₂⁴	—	4	1	no	—
1184	C₂⁴	—	4	1	no	—
1185	C₂⁴	—	4	1	no	—
1186	C₂⁴	C₂²×Dic₅₃	1	4	yes	—
1187	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1188	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1189	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1190	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1191	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1192	C₂×Q₈	—	4	1	no	—
1193	C₂×Q₈	—	4	1	no	—
1194	C₂×Q₈	C₂²×Dic₅₃	1	4	yes	complemented
1195	C₂×D₄	—	2	2	no	—
1196	C₂×D₄	—	2	2	no	—
1197	C₂×D₄	—	2	2	no	—
1198	C₂×D₄	—	2	2	no	—
1199	C₂×D₄	—	4	1	no	—
1200	C₂×D₄	—	4	1	no	—
1201	C₂×D₄	—	4	1	no	—
1202	C₂×D₄	—	4	1	no	—
1203	C₂×D₄	—	4	1	no	—
1204	C₂×D₄	—	4	1	no	—
1205	C₂×D₄	—	4	1	no	—
1206	C₂×D₄	—	4	1	no	—
1207	C₂×D₄	—	4	1	no	—
1208	C₂×D₄	—	4	1	no	—
1209	C₂×D₄	C₂²×Dic₅₃	1	4	yes	—
1210	C₂×D₄	C₂²×Dic₅₃	1	4	yes	—
1211	C₂×D₄	C₂²×Dic₅₃	1	4	yes	—
1212	C₂×D₄	C₂²×Dic₅₃	1	4	yes	—
1213	C₂×D₄	C₂²×Dic₅₃	1	4	yes	—
1214	C₂×D₄	C₂²×Dic₅₃	1	4	yes	—
1215	C₂×D₄	C₂²×Dic₅₃	1	4	yes	complemented
1216	C₂²×C₄	—	4	1	no	—
1217	C₂²×C₄	—	4	1	no	—
1218	C₂²×C₄	—	4	1	no	—
1219	C₂²×C₄	—	4	1	no	—
1220	C₂²×C₄	—	4	1	no	—
1221	C₂²×C₄	—	4	1	no	—
1222	C₂²×C₄	—	4	1	no	—
1223	C₂²×C₄	—	4	1	no	—
1224	C₂²×C₄	—	53	1	no	—
1225	C₂²×C₄	—	53	1	no	—
1226	C₂²×C₄	—	53	1	no	—
1227	C₂²×C₄	—	53	1	no	—
1228	C₂²×C₄	—	53	1	no	—
1229	C₂²×C₄	—	53	1	no	—
1230	C₂²×C₄	—	53	1	no	—
1231	C₂²×C₄	—	53	1	no	—
1232	C₂²×C₄	—	53	1	no	—
1233	C₂²×C₄	—	53	1	no	—
1234	C₂²×C₄	—	53	1	no	—
1235	C₂²×C₄	—	53	1	no	—
1236	C₂²×C₄	—	53	1	no	—
1237	C₂²×C₄	—	53	1	no	—
1238	C₂²×C₄	—	53	1	no	—
1239	C₂²×C₄	—	53	1	no	—
1240	C₂²×C₄	—	106	2	no	—
1241	C₂²×C₄	—	106	2	no	—
1242	C₂²×C₄	—	106	2	no	—
1243	C₂²×C₄	—	106	2	no	—
1244	C₂²×C₄	—	106	2	no	—
1245	C₂²×C₄	—	106	2	no	—
1246	C₂²×C₄	—	106	2	no	—
1247	C₂²×C₄	—	106	2	no	—
1248	C₂²×C₄	—	106	2	no	—
1249	C₂²×C₄	—	106	2	no	—
1250	C₂²×C₄	—	106	2	no	—
1251	C₂²×C₄	—	106	2	no	—
1252	C₂²×C₄	—	212	1	no	—
1253	C₂²×C₄	—	212	1	no	—
1254	C₂²×C₄	—	212	1	no	—
1255	C₂²×C₄	—	212	1	no	—
1256	C₂²×C₄	—	212	1	no	—
1257	C₂²×C₄	—	212	1	no	—
1258	C₂²×C₄	—	212	1	no	—
1259	C₂²×C₄	—	212	1	no	—
1260	C₂²×C₄	—	212	1	no	—
1261	C₂²×C₄	—	212	1	no	—
1262	C₂²×C₄	—	212	1	no	—
1263	C₂²×C₄	—	212	1	no	—
1264	C₂²×C₄	—	212	1	no	—
1265	C₂²×C₄	—	212	1	no	—
1266	C₂²×C₄	—	212	1	no	—
1267	C₂²×C₄	—	212	1	no	—
1268	C₂²×C₄	—	212	1	no	—
1269	C₂²×C₄	—	212	1	no	—
1270	C₂²×C₄	—	212	1	no	—
1271	C₂²×C₄	—	212	1	no	—
1272	C₂²×C₄	—	212	1	no	—
1273	C₂²×C₄	—	212	1	no	—
1274	C₂²×C₄	—	212	1	no	—
1275	C₂²×C₄	—	212	1	no	—
1276	C₂²×C₄	—	212	16	no	—
1277	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	—
1278	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	—
1279	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	complemented
1280	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	complemented
1281	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1282	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1283	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1284	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1285	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1286	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1287	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1288	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1289	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1290	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1291	C₄⋊C₄	—	106	2	no	—
1292	C₄⋊C₄	—	106	2	no	—
1293	C₄⋊C₄	—	106	2	no	—
1294	C₄⋊C₄	—	106	2	no	—
1295	C₄⋊C₄	—	106	2	no	—
1296	C₄⋊C₄	—	106	2	no	—
1297	C₄⋊C₄	—	212	1	no	—
1298	C₄⋊C₄	—	212	1	no	—
1299	C₄⋊C₄	—	212	1	no	—
1300	C₄⋊C₄	—	212	1	no	—
1301	C₄⋊C₄	—	212	1	no	—
1302	C₄⋊C₄	—	212	1	no	—
1303	C₄⋊C₄	—	212	1	no	—
1304	C₄⋊C₄	—	212	1	no	—
1305	C₄⋊C₄	—	212	1	no	—
1306	C₄⋊C₄	—	212	1	no	—
1307	C₄⋊C₄	—	212	1	no	—
1308	C₄⋊C₄	—	212	1	no	—
1309	C₄⋊C₄	—	212	1	no	—
1310	C₄⋊C₄	—	212	1	no	—
1311	C₄⋊C₄	—	212	1	no	—
1312	C₄⋊C₄	—	212	1	no	—
1313	C₄⋊C₄	—	212	1	no	—
1314	C₄⋊C₄	—	212	1	no	—
1315	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1316	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1317	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1318	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1319	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1320	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1321	C₂²⋊C₄	—	106	2	no	—
1322	C₂²⋊C₄	—	106	2	no	—
1323	C₂²⋊C₄	—	106	2	no	—
1324	C₂²⋊C₄	—	106	2	no	—
1325	C₂²⋊C₄	—	106	2	no	—
1326	C₂²⋊C₄	—	106	2	no	—
1327	C₂²⋊C₄	—	212	1	no	—
1328	C₂²⋊C₄	—	212	1	no	—
1329	C₂²⋊C₄	—	212	1	no	—
1330	C₂²⋊C₄	—	212	1	no	—
1331	C₂²⋊C₄	—	212	1	no	—
1332	C₂²⋊C₄	—	212	1	no	—
1333	C₂²⋊C₄	—	212	1	no	—
1334	C₂²⋊C₄	—	212	1	no	—
1335	C₂²⋊C₄	—	212	1	no	—
1336	C₂²⋊C₄	—	212	1	no	—
1337	C₂²⋊C₄	—	212	1	no	—
1338	C₂²⋊C₄	—	212	1	no	—
1339	C₂²⋊C₄	—	212	1	no	—
1340	C₂²⋊C₄	—	212	1	no	—
1341	C₂²⋊C₄	—	212	1	no	—
1342	C₂²⋊C₄	—	212	1	no	—
1343	C₂²⋊C₄	—	212	1	no	—
1344	C₂²⋊C₄	—	212	1	no	—
1345	C₂²⋊C₄	—	212	1	no	—
1346	C₂²⋊C₄	—	212	1	no	—
1347	C₂²⋊C₄	—	212	1	no	—
1348	C₂²⋊C₄	—	212	1	no	—
1349	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1350	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1351	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1352	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1353	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1354	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1355	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1356	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1357	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1358	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1359	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1360	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1361	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1362	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	complemented
1363	C₄²	—	106	2	no	—
1364	C₄²	—	106	2	no	—
1365	C₄²	—	212	1	no	—
1366	C₄²	—	212	1	no	—
1367	C₄²	—	212	1	no	—
1368	C₄²	—	212	1	no	—
1369	C₄²	—	212	1	no	—
1370	C₄²	—	212	1	no	—
1371	C₄²	—	212	1	no	—
1372	C₄²	—	212	1	no	—
1373	C₄²	—	212	1	no	—
1374	C₄²	—	212	1	no	—
1375	C₄²	—	212	1	no	—
1376	C₄²	—	212	1	no	—
1377	C₄²	—	212	1	no	—
1378	C₄²	—	212	1	no	—
1379	C₄²	C₂²×Dic₅₃	1	4	yes	complemented
1380	C₄²	C₂²×Dic₅₃	1	4	yes	complemented
1381	C₂³	—	2	1	no	—
1382	C₂³	—	2	1	no	—
1383	C₂³	—	2	1	no	—
1384	C₂³	—	2	1	no	—
1385	C₂³	—	2	8	no	—
1386	C₂³	—	2	1	no	—
1387	C₂³	—	2	1	no	—
1388	C₂³	—	2	1	no	—
1389	C₂³	—	2	1	no	—
1390	C₂³	—	2	1	no	—
1391	C₂³	—	2	1	no	—
1392	C₂³	—	2	1	no	—
1393	C₂³	—	2	1	no	—
1394	C₂³	—	2	1	no	—
1395	C₂³	—	2	1	no	—
1396	C₂³	—	2	1	no	—
1397	C₂³	—	2	1	no	—
1398	C₂³	—	2	1	no	—
1399	C₂³	—	2	1	no	—
1400	C₂³	—	2	1	no	—
1401	C₂³	—	2	1	no	—
1402	C₂³	—	2	1	no	—
1403	C₂³	—	2	1	no	—
1404	C₂³	—	2	1	no	—
1405	C₂³	—	2	1	no	—
1406	C₂³	—	2	1	no	—
1407	C₂³	—	2	1	no	—
1408	C₂³	—	2	1	no	—
1409	C₂³	—	2	1	no	—
1410	C₂³	—	4	4	no	—
1411	C₂³	—	4	4	no	—
1412	C₂³	—	4	4	no	—
1413	C₂³	—	4	4	no	—
1414	C₂³	—	4	4	no	—
1415	C₂³	—	4	4	no	—
1416	C₂³	C₂³×Dic₅₃	1	2	yes	—
1417	C₂³	C₂³×Dic₅₃	1	2	yes	—
1418	C₂³	C₂³×Dic₅₃	1	2	yes	—
1419	C₂³	C₂³×Dic₅₃	1	2	yes	—
1420	C₂³	C₂³×Dic₅₃	1	2	yes	—
1421	C₂³	#13133263	1	2	yes	—
1422	C₂³	#13133264	1	2	yes	—
1423	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1424	Q₈	—	4	4	no	—
1425	D₄	—	2	8	no	—
1426	D₄	—	2	8	no	—
1427	D₄	—	4	4	no	—
1428	D₄	—	4	4	no	—
1429	D₄	—	4	4	no	—
1430	D₄	—	4	4	no	—
1431	D₄	—	4	4	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	2	1	no	—
1445	C₂×C₄	—	2	1	no	—
1446	C₂×C₄	—	2	1	no	—
1447	C₂×C₄	—	2	1	no	—
1448	C₂×C₄	—	2	1	no	—
1449	C₂×C₄	—	2	1	no	—
1450	C₂×C₄	—	2	1	no	—
1451	C₂×C₄	—	2	1	no	—
1452	C₂×C₄	—	4	4	no	—
1453	C₂×C₄	—	4	4	no	—
1454	C₂×C₄	—	4	4	no	—
1455	C₂×C₄	—	4	4	no	—
1456	C₂×C₄	—	53	2	no	—
1457	C₂×C₄	—	53	2	no	—
1458	C₂×C₄	—	106	1	no	—
1459	C₂×C₄	—	106	1	no	—
1460	C₂×C₄	—	106	1	no	—
1461	C₂×C₄	—	106	1	no	—
1462	C₂×C₄	—	106	1	no	—
1463	C₂×C₄	—	106	1	no	—
1464	C₂×C₄	—	106	1	no	—
1465	C₂×C₄	—	106	1	no	—
1466	C₂×C₄	—	106	1	no	—
1467	C₂×C₄	—	106	1	no	—
1468	C₂×C₄	—	106	1	no	—
1469	C₂×C₄	—	106	1	no	—
1470	C₂×C₄	—	106	1	no	—
1471	C₂×C₄	—	106	1	no	—
1472	C₂×C₄	—	106	1	no	—
1473	C₂×C₄	—	106	1	no	—
1474	C₂×C₄	—	106	1	no	—
1475	C₂×C₄	—	106	1	no	—
1476	C₂×C₄	—	106	1	no	—
1477	C₂×C₄	—	106	1	no	—
1478	C₂×C₄	—	106	1	no	—
1479	C₂×C₄	—	106	1	no	—
1480	C₂×C₄	—	106	1	no	—
1481	C₂×C₄	—	106	1	no	—
1482	C₂×C₄	—	106	1	no	—
1483	C₂×C₄	—	106	1	no	—
1484	C₂×C₄	—	106	1	no	—
1485	C₂×C₄	—	106	1	no	—
1486	C₂×C₄	—	106	1	no	—
1487	C₂×C₄	—	106	1	no	—
1488	C₂×C₄	—	106	1	no	—
1489	C₂×C₄	—	106	1	no	—
1490	C₂×C₄	—	106	1	no	—
1491	C₂×C₄	—	106	1	no	—
1492	C₂×C₄	—	106	1	no	—
1493	C₂×C₄	—	106	1	no	—
1494	C₂×C₄	—	106	1	no	—
1495	C₂×C₄	—	106	1	no	—
1496	C₂×C₄	—	106	1	no	—
1497	C₂×C₄	—	106	1	no	—
1498	C₂×C₄	—	106	1	no	—
1499	C₂×C₄	—	106	1	no	—
1500	C₂×C₄	—	106	1	no	—
1501	C₂×C₄	—	106	1	no	—
1502	C₂×C₄	—	106	1	no	—
1503	C₂×C₄	—	106	1	no	—
1504	C₂×C₄	—	424	2	no	—
1505	C₂×C₄	—	424	2	no	—
1506	C₂×C₄	—	424	2	no	—
1507	C₂×C₄	—	424	2	no	—
1508	C₂×C₄	—	424	2	no	—
1509	C₂×C₄	—	424	2	no	—
1510	C₂×C₄	—	212	4	no	—
1511	C₂×C₄	—	212	4	no	—
1512	C₂×C₄	—	212	4	no	—
1513	C₂×C₄	—	212	4	no	—
1514	C₂×C₄	—	212	4	no	—
1515	C₂×C₄	—	212	4	no	—
1516	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1517	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1518	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1519	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1520	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1521	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1522	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1523	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1524	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1525	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1526	C₂²	—	2	2	no	—
1527	C₂²	—	2	2	no	—
1528	C₂²	—	2	2	no	—
1529	C₂²	—	2	2	no	—
1530	C₂²	—	2	2	no	—
1531	C₂²	—	2	2	no	—
1532	C₂²	—	2	2	no	—
1533	C₂²	—	2	2	no	—
1534	C₂²	—	2	2	no	—
1535	C₂²	—	2	2	no	—
1536	C₂²	—	2	2	no	—
1537	C₂²	—	2	2	no	—
1538	C₂²	—	2	2	no	—
1539	C₂²	—	2	2	no	—
1540	C₂²	—	2	2	no	—
1541	C₂²	—	2	2	no	—
1542	C₂²	—	2	2	no	—
1543	C₂²	—	2	2	no	—
1544	C₂²	—	4	16	no	—
1545	C₂²	—	4	1	no	—
1546	C₂²	—	4	1	no	—
1547	C₂²	—	4	1	no	—
1548	C₂²	—	4	1	no	—
1549	C₂²	—	4	1	no	—
1550	C₂²	—	4	1	no	—
1551	C₂²	—	4	1	no	—
1552	C₂²	—	4	1	no	—
1553	C₂²	—	4	1	no	—
1554	C₂²	—	4	1	no	—
1555	C₂²	—	4	1	no	—
1556	C₂²	—	4	1	no	—
1557	C₂²	—	4	1	no	—
1558	C₂²	—	4	1	no	—
1559	C₂²	—	4	1	no	—
1560	C₂²	—	4	1	no	—
1561	C₂²	#16811106	1	4	yes	—
1562	C₂²	C₂⁴×Dic₅₃	1	1	yes	characteristic
1563	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1564	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1565	C₂²	C₂×#13133263	1	1	yes	characteristic
1566	C₂²	C₂×#13133264	1	1	yes	characteristic
1567	C₂²	#16811458	1	1	yes	characteristic
1568	C₂²	#16811458	1	1	yes	characteristic
1569	C₄	—	2	2	no	—
1570	C₄	—	2	2	no	—
1571	C₄	—	2	2	no	—
1572	C₄	—	2	2	no	—
1573	C₄	—	2	2	no	—
1574	C₄	—	2	2	no	—
1575	C₄	—	2	2	no	—
1576	C₄	—	2	2	no	—
1577	C₄	—	2	2	no	—
1578	C₄	—	2	2	no	—
1579	C₄	—	106	2	no	—
1580	C₄	—	106	2	no	—
1581	C₄	—	212	1	no	—
1582	C₄	—	212	1	no	—
1583	C₄	—	212	1	no	—
1584	C₄	—	212	1	no	—
1585	C₄	—	212	1	no	—
1586	C₄	—	212	1	no	—
1587	C₄	—	212	1	no	—
1588	C₄	—	212	1	no	—
1589	C₄	—	212	1	no	—
1590	C₄	—	212	1	no	—
1591	C₄	—	212	1	no	—
1592	C₄	—	212	1	no	—
1593	C₄	—	212	1	no	—
1594	C₄	—	212	1	no	—
1595	C₂	—	2	4	no	—
1596	C₂	—	4	2	no	—
1597	C₂	—	4	2	no	—
1598	C₂	—	4	2	no	—
1599	C₂	—	4	2	no	—
1600	C₂	C₂×#16811106	1	1	yes	characteristic
1601	C₂	H(5,𝔽₂)×Dic₅₃	1	1	yes	characteristic
1602	C₂	H(5,𝔽₂)×Dic₅₃	1	1	yes	characteristic
1603	C₂	#20288866	1	1	yes	characteristic
1604	C₂	#20288883	1	1	yes	characteristic
1605	C₂	#20288995	1	1	yes	characteristic
1606	C₂	#20289003	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting, prime radical	C₂×C₅₃×#538	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#538	D₅₃
hypocenter	C₅₃	#34416
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#538

Complements

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

N	H ≅ G/N	type
1. #20277907	C₂	semidirect
2. #20277889	C₂	semidirect
3. #20277872	C₂	semidirect
4. #20277863	C₂	semidirect
5. #20277839	C₂	semidirect
6. #20277800	C₂	semidirect
7. #20277790	C₂	semidirect
8. #20277767	C₂	semidirect
9. #20277735	C₂	semidirect
10. #20277735	C₂	semidirect
11. #20277724	C₂	semidirect
12. #20277711	C₂	semidirect
13. #20277655	C₂	semidirect
14. #20277644	C₂	semidirect
15. #20277625	C₂	semidirect
16. D₄×C₄⋊Dic₅₃	C₂	semidirect
17. #20277530	C₂	semidirect
18. #20277509	C₂	semidirect
19. #20277494	C₂	semidirect
20. #20277494	C₂	semidirect
21. #20277428	C₂	semidirect
22. #20277420	C₂	semidirect
23. #20277410	C₂	semidirect
24. #20277387	C₂	semidirect
25. #20277376	C₂	semidirect
26. #20277376	C₂	semidirect
27. #20277313	C₂	semidirect
28. #120×Dic₅₃	C₂	semidirect
29. #120×Dic₅₃	C₂	semidirect
30. C₂×#16810498	C₂	semidirect
33. C₂×Q₈×Dic₅₃	C₂²	semidirect
42. C₂×D₄×Dic₅₃	C₂²	semidirect
43. C₂×#13133176	C₂²	semidirect
46. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
48. #16810530	C₂²	semidirect
49. #16810530	C₂²	semidirect
50. #16810530	C₂²	semidirect
55. #16810526	C₂²	semidirect
56. #16810522	C₂²	semidirect
57. #16810522	C₂²	semidirect
58. #16810522	C₂²	semidirect
59. #16810522	C₂²	semidirect
60. #16810522	C₂²	semidirect
61. #16810522	C₂²	semidirect
62. #16810522	C₂²	semidirect
63. #16810522	C₂²	semidirect
80. #16810516	C₂²	semidirect
81. #16810516	C₂²	semidirect
82. #16810516	C₂²	semidirect
83. #16810516	C₂²	semidirect
84. #16810516	C₂²	semidirect
85. #16810516	C₂²	semidirect
86. #16810516	C₂²	semidirect
87. #16810516	C₂²	semidirect
88. #16810509	C₂²	semidirect
89. #16810509	C₂²	semidirect
90. #16810509	C₂²	semidirect
91. #16810509	C₂²	semidirect
92. #16810509	C₂²	semidirect
93. #16810509	C₂²	semidirect
94. #16810509	C₂²	semidirect
95. #16810509	C₂²	semidirect
96. #16810509	C₂²	semidirect
97. #16810509	C₂²	semidirect
98. #16810509	C₂²	semidirect
99. #16810509	C₂²	semidirect
112. #16810503	C₂²	semidirect
113. #16810503	C₂²	semidirect
130. #16810498	C₂²	semidirect
131. #16810498	C₂²	semidirect
132. #16810498	C₂²	semidirect
133. #16810498	C₂²	semidirect
134. #16810498	C₂²	semidirect
135. #16810498	C₂²	semidirect
136. #16810493	C₂²	semidirect
137. #16810491	C₂²	semidirect
138. #16810489	C₂²	semidirect
139. #16810489	C₂²	semidirect
140. #16810486	C₂²	semidirect
143. #16810483	C₂²	semidirect
144. #16810483	C₂²	semidirect
145. #16810483	C₂²	semidirect
148. C₄⋊C₄×Dic₅₃	C₂²	semidirect
149. C₄⋊C₄×Dic₅₃	C₂²	semidirect
150. C₄⋊C₄×Dic₅₃	C₂²	semidirect
151. C₄⋊C₄×Dic₅₃	C₂²	semidirect
152. C₄×C₄⋊Dic₅₃	C₂²	semidirect
153. C₄×C₄⋊Dic₅₃	C₂²	semidirect
154. C₄×C₄⋊Dic₅₃	C₂²	semidirect
163. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
164. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
167. C₄×C₂²⋊Dic₅₃	C₂²	semidirect
168. #16810469	C₂²	semidirect
171. C₂×#13133124	C₂²	semidirect
172. C₅₃×#538	C₄	semidirect
339. #126×C₅₃	C₂×C₄	semidirect
340. #126×C₅₃	C₂×C₄	semidirect
341. #124×C₅₃	C₂×C₄	semidirect
342. #124×C₅₃	C₂×C₄	semidirect
343. #123×C₅₃	C₂×C₄	semidirect
344. #123×C₅₃	C₂×C₄	semidirect
345. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
346. #121×C₅₃	C₂×C₄	semidirect
347. #121×C₅₃	C₂×C₄	semidirect
348. #121×C₅₃	C₂×C₄	semidirect
349. #120×C₅₃	C₂×C₄	semidirect
350. #120×C₅₃	C₂×C₄	semidirect
351. C₄×D₄×C₅₃	C₂×C₄	semidirect
352. C₄×D₄×C₅₃	C₂×C₄	semidirect
359. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
390. C₂×Q₈×C₅₃	C₂²×C₄	semidirect
411. C₂×D₄×C₅₃	C₂²×C₄	semidirect
422. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
423. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
487. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
488. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
489. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
490. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
491. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
492. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
503. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
504. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
505. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
506. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
507. C₄²×C₅₃	C₂²×C₄	semidirect
508. C₄²×C₅₃	C₂²×C₄	semidirect
836. #538	Dic₅₃	semidirect
991. C₅₃	#34416	semidirect
1020. #126	C₂×Dic₅₃	semidirect
1021. #126	C₂×Dic₅₃	semidirect
1022. #124	C₂×Dic₅₃	semidirect
1023. #124	C₂×Dic₅₃	semidirect
1024. #123	C₂×Dic₅₃	semidirect
1025. #123	C₂×Dic₅₃	semidirect
1026. C₂²⋊Q₈	C₂×Dic₅₃	semidirect
1027. #121	C₂×Dic₅₃	semidirect
1028. #121	C₂×Dic₅₃	semidirect
1029. #121	C₂×Dic₅₃	semidirect
1030. #120	C₂×Dic₅₃	semidirect
1031. #120	C₂×Dic₅₃	semidirect
1042. C₄×D₄	C₂×Dic₅₃	semidirect
1043. C₄×D₄	C₂×Dic₅₃	semidirect
1107. C₂×C₂²⋊C₄	C₂×Dic₅₃	semidirect
1194. C₂×Q₈	C₂²×Dic₅₃	semidirect
1215. C₂×D₄	C₂²×Dic₅₃	semidirect
1279. C₂²×C₄	C₂²×Dic₅₃	semidirect
1280. C₂²×C₄	C₂²×Dic₅₃	semidirect
1315. C₄⋊C₄	C₂²×Dic₅₃	semidirect
1316. C₄⋊C₄	C₂²×Dic₅₃	semidirect
1317. C₄⋊C₄	C₂²×Dic₅₃	semidirect
1318. C₄⋊C₄	C₂²×Dic₅₃	semidirect
1319. C₄⋊C₄	C₂²×Dic₅₃	semidirect
1320. C₄⋊C₄	C₂²×Dic₅₃	semidirect
1359. C₂²⋊C₄	C₂²×Dic₅₃	semidirect
1360. C₂²⋊C₄	C₂²×Dic₅₃	semidirect
1361. C₂²⋊C₄	C₂²×Dic₅₃	semidirect
1362. C₂²⋊C₄	C₂²×Dic₅₃	semidirect
1379. C₄²	C₂²×Dic₅₃	semidirect
1380. C₄²	C₂²×Dic₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20277907	2
#20277889	2
#20277872	2
#20277863	2
#20277839	2
#20277800	2
#20277790	2
#20277767	2
#20277735	2
#20277724	2
#20277711	2
#20277655	2
#20277644	2
#20277625	2
D₄×C₄⋊Dic₅₃	2
#20277530	2
#20277509	2
#20277494	2
#20277428	2
#20277420	2
#20277410	2
#20277387	2
#20277376	2
#20277313	2
#120×Dic₅₃	2
C₂×#16810498	2
C₂×C₅₃×#538	2
#34416	53