Subgroups — C₅₃×#34417 #27241929

Order 13568.

2202 conjugacy classes of subgroups.

The subgroup lattice has 1464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#539	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2378	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2368	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2364	C₂	1	1	yes	maximal, characteristic
10	C₅₃×#2361	C₂	1	1	yes	maximal, characteristic
11	C₅₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2359	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2353	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅₃×#539	C₄	1	16	yes	complemented
33	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
54	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
58	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
59	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#391	C₂²	1	1	yes	characteristic
61	C₅₃×#391	C₂²	1	1	yes	characteristic
62	C₅₃×#391	C₂²	1	1	yes	characteristic
63	C₅₃×#390	C₂²	1	1	yes	characteristic
64	C₅₃×#389	C₂²	1	1	yes	characteristic
65	C₅₃×#389	C₂²	1	1	yes	characteristic
66	C₅₃×#389	C₂²	1	1	yes	characteristic
67	C₅₃×#389	C₂²	1	1	yes	characteristic
68	C₅₃×#389	C₂²	1	1	yes	characteristic
69	C₅₃×#389	C₂²	1	1	yes	characteristic
70	C₅₃×#389	C₂²	1	1	yes	characteristic
71	C₅₃×#389	C₂²	1	1	yes	characteristic
72	C₅₃×#389	C₂²	1	1	yes	characteristic
73	C₅₃×#389	C₂²	1	1	yes	characteristic
74	C₅₃×#389	C₂²	1	1	yes	characteristic
75	C₅₃×#389	C₂²	1	1	yes	characteristic
76	C₅₃×#389	C₂²	1	1	yes	characteristic
77	C₅₃×#389	C₂²	1	1	yes	characteristic
78	C₅₃×#389	C₂²	1	1	yes	characteristic
79	C₅₃×#389	C₂²	1	1	yes	characteristic
80	C₅₃×#389	C₂²	1	1	yes	characteristic
81	C₅₃×#389	C₂²	1	1	yes	characteristic
82	C₅₃×#389	C₂²	1	1	yes	characteristic
83	C₅₃×#389	C₂²	1	1	yes	characteristic
84	C₅₃×#388	C₂²	1	1	yes	characteristic
85	C₅₃×#388	C₂²	1	1	yes	characteristic
86	C₅₃×#388	C₂²	1	1	yes	characteristic
87	C₅₃×#388	C₂²	1	1	yes	characteristic
88	C₅₃×#388	C₂²	1	1	yes	characteristic
89	C₅₃×#388	C₂²	1	1	yes	characteristic
90	C₅₃×#388	C₂²	1	1	yes	characteristic
91	C₅₃×#388	C₂²	1	1	yes	characteristic
92	C₅₃×#388	C₂²	1	1	yes	characteristic
93	C₅₃×#388	C₂²	1	1	yes	characteristic
94	C₅₃×#388	C₂²	1	1	yes	characteristic
95	C₅₃×#388	C₂²	1	1	yes	characteristic
96	C₅₃×#388	C₂²	1	1	yes	characteristic
97	C₅₃×#388	C₂²	1	1	yes	characteristic
98	C₅₃×#388	C₂²	1	1	yes	characteristic
99	C₅₃×#388	C₂²	1	1	yes	characteristic
100	C₅₃×#387	C₂²	1	1	yes	characteristic
101	C₅₃×#387	C₂²	1	1	yes	characteristic
102	C₅₃×#387	C₂²	1	1	yes	characteristic
103	C₅₃×#387	C₂²	1	1	yes	characteristic
104	C₅₃×#387	C₂²	1	1	yes	characteristic
105	C₅₃×#387	C₂²	1	1	yes	characteristic
106	C₅₃×#387	C₂²	1	1	yes	characteristic
107	C₅₃×#387	C₂²	1	1	yes	characteristic
108	C₅₃×#387	C₂²	1	1	yes	characteristic
109	C₅₃×#387	C₂²	1	1	yes	characteristic
110	C₅₃×#387	C₂²	1	1	yes	characteristic
111	C₅₃×#387	C₂²	1	1	yes	characteristic
112	C₅₃×#387	C₂²	1	1	yes	characteristic
113	C₅₃×#387	C₂²	1	1	yes	characteristic
114	C₅₃×#387	C₂²	1	1	yes	characteristic
115	C₅₃×#387	C₂²	1	1	yes	characteristic
116	C₅₃×#387	C₂²	1	1	yes	characteristic
117	C₅₃×#387	C₂²	1	1	yes	characteristic
118	C₅₃×#387	C₂²	1	1	yes	characteristic
119	C₅₃×#387	C₂²	1	1	yes	characteristic
120	C₅₃×#387	C₂²	1	1	yes	characteristic
121	C₅₃×#387	C₂²	1	1	yes	characteristic
122	C₅₃×#387	C₂²	1	1	yes	characteristic
123	C₅₃×#387	C₂²	1	1	yes	characteristic
124	C₅₃×#387	C₂²	1	1	yes	characteristic
125	C₅₃×#387	C₂²	1	1	yes	characteristic
126	C₅₃×#387	C₂²	1	1	yes	characteristic
127	C₅₃×#387	C₂²	1	1	yes	characteristic
128	C₅₃×#386	C₂²	1	1	yes	characteristic
129	C₅₃×#386	C₂²	1	1	yes	characteristic
130	C₅₃×#386	C₂²	1	1	yes	characteristic
131	C₅₃×#386	C₂²	1	1	yes	characteristic
132	C₅₃×#386	C₂²	1	1	yes	characteristic
133	C₅₃×#386	C₂²	1	1	yes	characteristic
134	C₅₃×#385	C₂²	1	1	yes	characteristic
135	C₅₃×#385	C₂²	1	1	yes	characteristic
136	C₅₃×#385	C₂²	1	1	yes	characteristic
137	C₅₃×#385	C₂²	1	1	yes	characteristic
138	C₅₃×#385	C₂²	1	1	yes	characteristic
139	C₅₃×#385	C₂²	1	1	yes	characteristic
140	C₅₃×#385	C₂²	1	1	yes	characteristic
141	C₅₃×#385	C₂²	1	1	yes	characteristic
142	C₅₃×#385	C₂²	1	1	yes	characteristic
143	C₅₃×#385	C₂²	1	1	yes	characteristic
144	C₅₃×#385	C₂²	1	1	yes	characteristic
145	C₅₃×#385	C₂²	1	1	yes	characteristic
146	C₅₃×#385	C₂²	1	1	yes	characteristic
147	C₅₃×#385	C₂²	1	1	yes	characteristic
148	C₅₃×#384	C₂²	1	1	yes	characteristic
149	C₅₃×#383	C₂²	1	1	yes	characteristic
150	C₅₃×#382	C₂²	1	1	yes	characteristic
151	C₅₃×#382	C₂²	1	1	yes	characteristic
152	C₅₃×#381	C₂²	1	1	yes	characteristic
153	C₅₃×#381	C₂²	1	1	yes	characteristic
154	C₅₃×#381	C₂²	1	1	yes	characteristic
155	C₅₃×#380	C₂²	1	1	yes	characteristic
156	C₅₃×#380	C₂²	1	1	yes	characteristic
157	C₅₃×#380	C₂²	1	1	yes	characteristic
158	C₅₃×#380	C₂²	1	1	yes	characteristic
159	C₅₃×#380	C₂²	1	1	yes	characteristic
160	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
161	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
162	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
170	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
171	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₅₃×#376	C₂²	1	1	yes	characteristic
185	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
187	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
188	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
205	#126×C₅₃	C₂×C₄	1	8	yes	complemented
206	#126×C₅₃	C₂×C₄	1	8	yes	complemented
207	#125×C₅₃	C₂×C₄	1	8	yes	complemented
208	#125×C₅₃	C₂×C₄	1	8	yes	complemented
209	#123×C₅₃	C₂×C₄	1	8	yes	complemented
210	#123×C₅₃	C₂×C₄	1	8	yes	complemented
211	#123×C₅₃	C₂×C₄	1	8	yes	complemented
212	#123×C₅₃	C₂×C₄	1	8	yes	complemented
213	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
214	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
215	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
216	#121×C₅₃	C₂×C₄	1	8	yes	—
217	C₄×Q₈×C₅₃	—	4	2	no	—
218	C₄×D₄×C₅₃	—	4	2	no	—
219	C₄×D₄×C₅₃	—	4	2	no	—
220	C₄×D₄×C₅₃	—	4	2	no	—
221	C₄×D₄×C₅₃	—	4	2	no	—
222	C₄×D₄×C₅₃	—	4	2	no	—
223	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
224	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
225	#117×C₅₃	—	4	2	no	—
226	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
227	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
228	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
229	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
230	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
231	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₅₃	—	4	2	no	—
300	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
319	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
320	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
321	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
322	#95×C₅₃	C₂³	1	1	yes	characteristic
323	#95×C₅₃	C₂³	1	1	yes	characteristic
324	#95×C₅₃	C₂³	1	1	yes	characteristic
325	#95×C₅₃	C₂³	1	1	yes	characteristic
326	#95×C₅₃	C₂³	1	1	yes	characteristic
327	#95×C₅₃	C₂³	1	1	yes	characteristic
328	#95×C₅₃	C₂³	1	1	yes	characteristic
329	#95×C₅₃	C₂³	1	1	yes	characteristic
330	#95×C₅₃	C₂³	1	1	yes	characteristic
331	#95×C₅₃	C₂³	1	1	yes	characteristic
332	#95×C₅₃	C₂³	1	1	yes	characteristic
333	#95×C₅₃	C₂³	1	1	yes	characteristic
334	#95×C₅₃	C₂³	1	1	yes	characteristic
335	#95×C₅₃	C₂³	1	1	yes	characteristic
336	#95×C₅₃	C₂³	1	1	yes	characteristic
337	#95×C₅₃	C₂³	1	1	yes	characteristic
338	#95×C₅₃	C₂³	1	1	yes	characteristic
339	#95×C₅₃	C₂³	1	1	yes	characteristic
340	#95×C₅₃	C₂³	1	1	yes	characteristic
341	#95×C₅₃	C₂³	1	1	yes	characteristic
342	#95×C₅₃	C₂³	1	1	yes	characteristic
343	#95×C₅₃	C₂³	1	1	yes	characteristic
344	#95×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	#95×C₅₃	C₂³	1	1	yes	characteristic
368	#95×C₅₃	C₂³	1	1	yes	characteristic
369	#95×C₅₃	C₂³	1	1	yes	characteristic
370	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×Q₈×C₅₃	—	4	1	no	—
374	C₂×Q₈×C₅₃	—	4	1	no	—
375	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
376	C₂×D₄×C₅₃	—	2	2	no	—
377	C₂×D₄×C₅₃	—	2	2	no	—
378	C₂×D₄×C₅₃	—	2	2	no	—
379	C₂×D₄×C₅₃	—	2	2	no	—
380	C₂×D₄×C₅₃	—	4	1	no	—
381	C₂×D₄×C₅₃	—	4	1	no	—
382	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
383	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
384	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
385	C₂²×C₄×C₅₃	—	2	2	no	—
386	C₂²×C₄×C₅₃	—	2	2	no	—
387	C₂²×C₄×C₅₃	—	2	2	no	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	2	no	—
390	C₂²×C₄×C₅₃	—	2	2	no	—
391	C₂²×C₄×C₅₃	—	2	2	no	—
392	C₂²×C₄×C₅₃	—	2	2	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	2	no	—
395	C₂²×C₄×C₅₃	—	4	1	no	—
396	C₂²×C₄×C₅₃	—	4	1	no	—
397	C₂²×C₄×C₅₃	—	4	1	no	—
398	C₂²×C₄×C₅₃	—	4	1	no	—
399	C₂²×C₄×C₅₃	—	4	1	no	—
400	C₂²×C₄×C₅₃	—	4	1	no	—
401	C₂²×C₄×C₅₃	—	4	1	no	—
402	C₂²×C₄×C₅₃	—	4	1	no	—
403	C₂²×C₄×C₅₃	—	4	1	no	—
404	C₂²×C₄×C₅₃	—	4	1	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	—	4	1	no	—
410	C₂²×C₄×C₅₃	—	4	1	no	—
411	C₂²×C₄×C₅₃	—	4	1	no	—
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	C₂²×C₄	1	4	yes	—
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	—
423	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
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×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₅₃	—	2	2	no	—
453	C₄⋊C₄×C₅₃	—	2	2	no	—
454	C₄⋊C₄×C₅₃	—	2	2	no	—
455	C₄⋊C₄×C₅₃	—	2	2	no	—
456	C₄⋊C₄×C₅₃	—	2	2	no	—
457	C₄⋊C₄×C₅₃	—	2	2	no	—
458	C₄⋊C₄×C₅₃	—	4	1	no	—
459	C₄⋊C₄×C₅₃	—	4	1	no	—
460	C₄⋊C₄×C₅₃	—	4	1	no	—
461	C₄⋊C₄×C₅₃	—	4	1	no	—
462	C₄⋊C₄×C₅₃	—	4	1	no	—
463	C₄⋊C₄×C₅₃	—	4	1	no	—
464	C₄⋊C₄×C₅₃	—	4	1	no	—
465	C₄⋊C₄×C₅₃	—	4	1	no	—
466	C₄⋊C₄×C₅₃	—	4	1	no	—
467	C₄⋊C₄×C₅₃	—	4	1	no	—
468	C₄⋊C₄×C₅₃	—	4	1	no	—
469	C₄⋊C₄×C₅₃	—	4	1	no	—
470	C₄⋊C₄×C₅₃	—	4	1	no	—
471	C₄⋊C₄×C₅₃	—	4	1	no	—
472	C₄⋊C₄×C₅₃	—	4	1	no	—
473	C₄⋊C₄×C₅₃	—	4	1	no	—
474	C₄⋊C₄×C₅₃	—	4	1	no	—
475	C₄⋊C₄×C₅₃	—	4	1	no	—
476	C₄⋊C₄×C₅₃	—	4	1	no	—
477	C₄⋊C₄×C₅₃	—	4	1	no	—
478	C₄⋊C₄×C₅₃	—	4	1	no	—
479	C₄⋊C₄×C₅₃	—	4	1	no	—
480	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
481	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
482	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
483	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
484	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
485	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
486	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
487	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
488	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
489	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
490	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
491	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
492	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
493	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
494	C₂²⋊C₄×C₅₃	—	2	2	no	—
495	C₂²⋊C₄×C₅₃	—	2	2	no	—
496	C₂²⋊C₄×C₅₃	—	2	2	no	—
497	C₂²⋊C₄×C₅₃	—	2	2	no	—
498	C₂²⋊C₄×C₅₃	—	2	2	no	—
499	C₂²⋊C₄×C₅₃	—	2	2	no	—
500	C₂²⋊C₄×C₅₃	—	4	1	no	—
501	C₂²⋊C₄×C₅₃	—	4	1	no	—
502	C₂²⋊C₄×C₅₃	—	4	1	no	—
503	C₂²⋊C₄×C₅₃	—	4	1	no	—
504	C₂²⋊C₄×C₅₃	—	4	1	no	—
505	C₂²⋊C₄×C₅₃	—	4	1	no	—
506	C₂²⋊C₄×C₅₃	—	4	1	no	—
507	C₂²⋊C₄×C₅₃	—	4	1	no	—
508	C₂²⋊C₄×C₅₃	—	4	1	no	—
509	C₂²⋊C₄×C₅₃	—	4	1	no	—
510	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
511	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
512	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
513	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
514	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
515	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
516	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
517	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
518	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
519	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
520	C₄²×C₅₃	—	2	2	no	—
521	C₄²×C₅₃	—	2	2	no	—
522	C₄²×C₅₃	—	4	1	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	C₄²×C₅₃	—	4	1	no	—
528	C₄²×C₅₃	—	4	1	no	—
529	C₄²×C₅₃	—	4	1	no	—
530	C₄²×C₅₃	—	4	1	no	—
531	C₄²×C₅₃	—	4	1	no	—
532	C₄²×C₅₃	—	4	1	no	—
533	C₄²×C₅₃	—	4	1	no	—
534	C₄²×C₅₃	—	4	1	no	—
535	C₄²×C₅₃	—	4	1	no	—
536	C₄²×C₅₃	—	4	1	no	—
537	C₄²×C₅₃	—	4	1	no	—
538	C₄²×C₅₃	—	4	1	no	—
539	C₄²×C₅₃	—	4	1	no	—
540	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
541	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
542	C₂³×C₅₃	—	2	1	no	—
543	C₂³×C₅₃	—	2	1	no	—
544	C₂³×C₅₃	—	2	1	no	—
545	C₂³×C₅₃	—	2	1	no	—
546	C₂³×C₅₃	—	2	1	no	—
547	C₂³×C₅₃	—	2	1	no	—
548	C₂³×C₅₃	—	2	1	no	—
549	C₂³×C₅₃	—	2	1	no	—
550	C₂³×C₅₃	—	2	1	no	—
551	C₂³×C₅₃	—	2	1	no	—
552	C₂³×C₅₃	—	2	1	no	—
553	C₂³×C₅₃	—	2	1	no	—
554	C₂³×C₅₃	—	2	1	no	—
555	C₂³×C₅₃	—	2	1	no	—
556	C₂³×C₅₃	—	2	1	no	—
557	C₂³×C₅₃	—	2	1	no	—
558	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
559	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
560	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
561	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
562	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
563	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
564	Q₈×C₅₃	—	4	4	no	—
565	D₄×C₅₃	—	2	8	no	—
566	D₄×C₅₃	—	2	8	no	—
567	D₄×C₅₃	—	4	4	no	—
568	C₂×C₄×C₅₃	—	2	8	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	1	no	—
579	C₂×C₄×C₅₃	—	2	1	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	1	no	—
614	C₂×C₄×C₅₃	—	2	1	no	—
615	C₂×C₄×C₅₃	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	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	—	4	4	no	—
640	C₂×C₄×C₅₃	—	4	4	no	—
641	C₂×C₄×C₅₃	—	4	4	no	—
642	C₂×C₄×C₅₃	—	4	4	no	—
643	C₂×C₄×C₅₃	—	4	4	no	—
644	C₂×C₄×C₅₃	—	4	4	no	—
645	C₂×C₄×C₅₃	—	8	2	no	—
646	C₂×C₄×C₅₃	—	8	2	no	—
647	C₂×C₄×C₅₃	—	8	2	no	—
648	C₂×C₄×C₅₃	—	8	2	no	—
649	C₂×C₄×C₅₃	—	8	2	no	—
650	C₂×C₄×C₅₃	—	8	2	no	—
651	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
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×C₄×C₅₃	C₂³×C₄	1	2	yes	—
663	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
664	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
665	#34417	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
666	C₂²×C₅₃	—	2	2	no	—
667	C₂²×C₅₃	—	2	2	no	—
668	C₂²×C₅₃	—	2	2	no	—
669	C₂²×C₅₃	—	2	2	no	—
670	C₂²×C₅₃	—	2	2	no	—
671	C₂²×C₅₃	—	2	2	no	—
672	C₂²×C₅₃	—	2	2	no	—
673	C₂²×C₅₃	—	2	2	no	—
674	C₂²×C₅₃	—	2	2	no	—
675	C₂²×C₅₃	—	2	2	no	—
676	C₂²×C₅₃	—	2	2	no	—
677	C₂²×C₅₃	—	2	2	no	—
678	C₂²×C₅₃	—	4	1	no	—
679	C₂²×C₅₃	—	4	1	no	—
680	C₂²×C₅₃	—	4	1	no	—
681	C₂²×C₅₃	—	4	1	no	—
682	C₂²×C₅₃	—	4	1	no	—
683	C₂²×C₅₃	—	4	1	no	—
684	C₂²×C₅₃	—	4	1	no	—
685	C₂²×C₅₃	—	4	1	no	—
686	C₂²×C₅₃	#520	1	4	yes	—
687	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
688	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
689	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
690	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
691	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
692	C₂²×C₅₃	#585	1	1	yes	characteristic
693	C₂²×C₅₃	#585	1	1	yes	characteristic
694	C₄×C₅₃	—	2	2	no	—
695	C₄×C₅₃	—	2	2	no	—
696	C₄×C₅₃	—	2	2	no	—
697	C₄×C₅₃	—	2	2	no	—
698	C₄×C₅₃	—	2	2	no	—
699	C₄×C₅₃	—	2	2	no	—
700	C₄×C₅₃	—	2	2	no	—
701	C₄×C₅₃	—	2	2	no	—
702	C₄×C₅₃	—	2	2	no	—
703	C₄×C₅₃	—	2	2	no	—
704	C₄×C₅₃	—	2	2	no	—
705	C₄×C₅₃	—	2	2	no	—
706	C₄×C₅₃	—	2	2	no	—
707	C₄×C₅₃	—	2	2	no	—
708	C₄×C₅₃	—	4	1	no	—
709	C₄×C₅₃	—	4	1	no	—
710	C₄×C₅₃	—	4	1	no	—
711	C₄×C₅₃	—	4	1	no	—
712	C₄×C₅₃	—	4	1	no	—
713	C₄×C₅₃	—	4	1	no	—
714	C₄×C₅₃	—	4	1	no	—
715	C₄×C₅₃	—	4	1	no	—
716	C₄×C₅₃	—	4	1	no	—
717	C₄×C₅₃	—	4	1	no	—
718	C₄×C₅₃	—	4	1	no	—
719	C₄×C₅₃	—	4	1	no	—
720	C₄×C₅₃	—	4	1	no	—
721	C₄×C₅₃	—	4	1	no	—
722	C₂×#539	C₂×C₅₃	1	1	yes	characteristic
723	#2383	C₂×C₅₃	1	1	yes	characteristic, complemented
724	#2382	C₂×C₅₃	1	1	yes	characteristic, complemented
725	#2378	C₂×C₅₃	1	1	yes	characteristic, complemented
726	#2376	C₂×C₅₃	1	1	yes	characteristic, complemented
727	#2373	C₂×C₅₃	1	1	yes	characteristic, complemented
728	#2370	C₂×C₅₃	1	1	yes	characteristic, complemented
729	#2368	C₂×C₅₃	1	1	yes	characteristic, complemented
730	#2364	C₂×C₅₃	1	1	yes	characteristic
731	#2361	C₂×C₅₃	1	1	yes	characteristic
732	#2360	C₂×C₅₃	1	1	yes	characteristic, complemented
733	#2360	C₂×C₅₃	1	1	yes	characteristic, complemented
734	#2359	C₂×C₅₃	1	1	yes	characteristic, complemented
735	#2353	C₂×C₅₃	1	1	yes	characteristic, complemented
736	#2352	C₂×C₅₃	1	1	yes	characteristic, complemented
737	#2349	C₂×C₅₃	1	1	yes	characteristic, complemented
738	D₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
739	#2336	C₂×C₅₃	1	1	yes	characteristic, complemented
740	#2335	C₂×C₅₃	1	1	yes	characteristic, complemented
741	#2334	C₂×C₅₃	1	1	yes	characteristic, complemented
742	#2334	C₂×C₅₃	1	1	yes	characteristic, complemented
743	#2330	C₂×C₅₃	1	1	yes	characteristic, complemented
744	#2329	C₂×C₅₃	1	1	yes	characteristic, complemented
745	#2323	C₂×C₅₃	1	1	yes	characteristic, complemented
746	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
747	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
748	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
749	#2313	C₂×C₅₃	1	1	yes	characteristic, complemented
750	C₄×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
751	C₄×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
752	C₂×#389	C₂×C₅₃	1	1	yes	characteristic, complemented
753	C₂×C₅₃	—	2	4	no	—
754	C₂×C₅₃	—	4	2	no	—
755	C₂×C₅₃	—	4	2	no	—
756	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
757	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
758	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
759	C₂×C₅₃	#3534	1	1	yes	characteristic
760	C₂×C₅₃	#3535	1	1	yes	characteristic
761	C₂×C₅₃	#3552	1	1	yes	characteristic
762	C₂×C₅₃	#3553	1	1	yes	characteristic
763	#539	C₄×C₅₃	1	16	yes	complemented
764	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
765	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
766	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
767	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
768	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
769	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
770	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
771	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
772	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
773	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
774	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
775	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
776	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
777	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
778	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
779	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
780	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
781	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
782	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
783	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
784	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
785	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
786	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
787	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
788	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
789	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
790	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
791	#391	C₂²×C₅₃	1	1	yes	characteristic
792	#391	C₂²×C₅₃	1	1	yes	characteristic
793	#391	C₂²×C₅₃	1	1	yes	characteristic
794	#390	C₂²×C₅₃	1	1	yes	characteristic
795	#389	C₂²×C₅₃	1	1	yes	characteristic
796	#389	C₂²×C₅₃	1	1	yes	characteristic
797	#389	C₂²×C₅₃	1	1	yes	characteristic
798	#389	C₂²×C₅₃	1	1	yes	characteristic
799	#389	C₂²×C₅₃	1	1	yes	characteristic
800	#389	C₂²×C₅₃	1	1	yes	characteristic
801	#389	C₂²×C₅₃	1	1	yes	characteristic
802	#389	C₂²×C₅₃	1	1	yes	characteristic
803	#389	C₂²×C₅₃	1	1	yes	characteristic
804	#389	C₂²×C₅₃	1	1	yes	characteristic
805	#389	C₂²×C₅₃	1	1	yes	characteristic
806	#389	C₂²×C₅₃	1	1	yes	characteristic
807	#389	C₂²×C₅₃	1	1	yes	characteristic
808	#389	C₂²×C₅₃	1	1	yes	characteristic
809	#389	C₂²×C₅₃	1	1	yes	characteristic
810	#389	C₂²×C₅₃	1	1	yes	characteristic
811	#389	C₂²×C₅₃	1	1	yes	characteristic
812	#389	C₂²×C₅₃	1	1	yes	characteristic
813	#389	C₂²×C₅₃	1	1	yes	characteristic
814	#389	C₂²×C₅₃	1	1	yes	characteristic
815	#388	C₂²×C₅₃	1	1	yes	characteristic
816	#388	C₂²×C₅₃	1	1	yes	characteristic
817	#388	C₂²×C₅₃	1	1	yes	characteristic
818	#388	C₂²×C₅₃	1	1	yes	characteristic
819	#388	C₂²×C₅₃	1	1	yes	characteristic
820	#388	C₂²×C₅₃	1	1	yes	characteristic
821	#388	C₂²×C₅₃	1	1	yes	characteristic
822	#388	C₂²×C₅₃	1	1	yes	characteristic
823	#388	C₂²×C₅₃	1	1	yes	characteristic
824	#388	C₂²×C₅₃	1	1	yes	characteristic
825	#388	C₂²×C₅₃	1	1	yes	characteristic
826	#388	C₂²×C₅₃	1	1	yes	characteristic
827	#388	C₂²×C₅₃	1	1	yes	characteristic
828	#388	C₂²×C₅₃	1	1	yes	characteristic
829	#388	C₂²×C₅₃	1	1	yes	characteristic
830	#388	C₂²×C₅₃	1	1	yes	characteristic
831	#387	C₂²×C₅₃	1	1	yes	characteristic
832	#387	C₂²×C₅₃	1	1	yes	characteristic
833	#387	C₂²×C₅₃	1	1	yes	characteristic
834	#387	C₂²×C₅₃	1	1	yes	characteristic
835	#387	C₂²×C₅₃	1	1	yes	characteristic
836	#387	C₂²×C₅₃	1	1	yes	characteristic
837	#387	C₂²×C₅₃	1	1	yes	characteristic
838	#387	C₂²×C₅₃	1	1	yes	characteristic
839	#387	C₂²×C₅₃	1	1	yes	characteristic
840	#387	C₂²×C₅₃	1	1	yes	characteristic
841	#387	C₂²×C₅₃	1	1	yes	characteristic
842	#387	C₂²×C₅₃	1	1	yes	characteristic
843	#387	C₂²×C₅₃	1	1	yes	characteristic
844	#387	C₂²×C₅₃	1	1	yes	characteristic
845	#387	C₂²×C₅₃	1	1	yes	characteristic
846	#387	C₂²×C₅₃	1	1	yes	characteristic
847	#387	C₂²×C₅₃	1	1	yes	characteristic
848	#387	C₂²×C₅₃	1	1	yes	characteristic
849	#387	C₂²×C₅₃	1	1	yes	characteristic
850	#387	C₂²×C₅₃	1	1	yes	characteristic
851	#387	C₂²×C₅₃	1	1	yes	characteristic
852	#387	C₂²×C₅₃	1	1	yes	characteristic
853	#387	C₂²×C₅₃	1	1	yes	characteristic
854	#387	C₂²×C₅₃	1	1	yes	characteristic
855	#387	C₂²×C₅₃	1	1	yes	characteristic
856	#387	C₂²×C₅₃	1	1	yes	characteristic
857	#387	C₂²×C₅₃	1	1	yes	characteristic
858	#387	C₂²×C₅₃	1	1	yes	characteristic
859	#386	C₂²×C₅₃	1	1	yes	characteristic
860	#386	C₂²×C₅₃	1	1	yes	characteristic
861	#386	C₂²×C₅₃	1	1	yes	characteristic
862	#386	C₂²×C₅₃	1	1	yes	characteristic
863	#386	C₂²×C₅₃	1	1	yes	characteristic
864	#386	C₂²×C₅₃	1	1	yes	characteristic
865	#385	C₂²×C₅₃	1	1	yes	characteristic
866	#385	C₂²×C₅₃	1	1	yes	characteristic
867	#385	C₂²×C₅₃	1	1	yes	characteristic
868	#385	C₂²×C₅₃	1	1	yes	characteristic
869	#385	C₂²×C₅₃	1	1	yes	characteristic
870	#385	C₂²×C₅₃	1	1	yes	characteristic
871	#385	C₂²×C₅₃	1	1	yes	characteristic
872	#385	C₂²×C₅₃	1	1	yes	characteristic
873	#385	C₂²×C₅₃	1	1	yes	characteristic
874	#385	C₂²×C₅₃	1	1	yes	characteristic
875	#385	C₂²×C₅₃	1	1	yes	characteristic
876	#385	C₂²×C₅₃	1	1	yes	characteristic
877	#385	C₂²×C₅₃	1	1	yes	characteristic
878	#385	C₂²×C₅₃	1	1	yes	characteristic
879	#384	C₂²×C₅₃	1	1	yes	characteristic
880	#383	C₂²×C₅₃	1	1	yes	characteristic
881	#382	C₂²×C₅₃	1	1	yes	characteristic
882	#382	C₂²×C₅₃	1	1	yes	characteristic
883	#381	C₂²×C₅₃	1	1	yes	characteristic
884	#381	C₂²×C₅₃	1	1	yes	characteristic
885	#381	C₂²×C₅₃	1	1	yes	characteristic
886	#380	C₂²×C₅₃	1	1	yes	characteristic
887	#380	C₂²×C₅₃	1	1	yes	characteristic
888	#380	C₂²×C₅₃	1	1	yes	characteristic
889	#380	C₂²×C₅₃	1	1	yes	characteristic
890	#380	C₂²×C₅₃	1	1	yes	characteristic
891	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
892	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
893	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
894	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
895	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
896	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
897	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
898	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
899	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
900	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
901	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
902	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
903	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
904	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
905	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
906	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
907	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
908	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
909	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
910	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
911	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
912	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
913	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
914	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
915	#376	C₂²×C₅₃	1	1	yes	characteristic
916	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
917	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
918	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
919	C₅₃	#34417	1	1	yes	characteristic, direct product factor, Sylow
920	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
921	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
922	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
923	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
924	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
925	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
926	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
927	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
928	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
929	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
930	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
931	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
932	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
933	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
934	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
935	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
936	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
937	#126	C₂×C₄×C₅₃	1	8	yes	complemented
938	#126	C₂×C₄×C₅₃	1	8	yes	complemented
939	#125	C₂×C₄×C₅₃	1	8	yes	complemented
940	#125	C₂×C₄×C₅₃	1	8	yes	complemented
941	#123	C₂×C₄×C₅₃	1	8	yes	complemented
942	#123	C₂×C₄×C₅₃	1	8	yes	complemented
943	#123	C₂×C₄×C₅₃	1	8	yes	complemented
944	#123	C₂×C₄×C₅₃	1	8	yes	complemented
945	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
946	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
947	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
948	#121	C₂×C₄×C₅₃	1	8	yes	—
949	C₄×Q₈	—	4	2	no	—
950	C₄×D₄	—	4	2	no	—
951	C₄×D₄	—	4	2	no	—
952	C₄×D₄	—	4	2	no	—
953	C₄×D₄	—	4	2	no	—
954	C₄×D₄	—	4	2	no	—
955	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
956	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
957	#117	—	4	2	no	—
958	C₂×C₄⋊C₄	—	4	2	no	—
959	C₂×C₄⋊C₄	—	4	2	no	—
960	C₂×C₄⋊C₄	—	4	2	no	—
961	C₂×C₄⋊C₄	—	4	2	no	—
962	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
963	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
970	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
973	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
976	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
977	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
978	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
979	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
980	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
981	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
982	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
983	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
984	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
985	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
986	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
987	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
989	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
990	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
991	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
994	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
995	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
996	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
998	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
999	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1000	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1001	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1002	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1004	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1005	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1007	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1013	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1015	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1031	C₂×C₄²	—	4	2	no	—
1032	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1033	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1034	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1035	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1036	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1037	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1038	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1039	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1040	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1041	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1042	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1043	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1046	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1047	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1048	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1054	#95	C₂³×C₅₃	1	1	yes	characteristic
1055	#95	C₂³×C₅₃	1	1	yes	characteristic
1056	#95	C₂³×C₅₃	1	1	yes	characteristic
1057	#95	C₂³×C₅₃	1	1	yes	characteristic
1058	#95	C₂³×C₅₃	1	1	yes	characteristic
1059	#95	C₂³×C₅₃	1	1	yes	characteristic
1060	#95	C₂³×C₅₃	1	1	yes	characteristic
1061	#95	C₂³×C₅₃	1	1	yes	characteristic
1062	#95	C₂³×C₅₃	1	1	yes	characteristic
1063	#95	C₂³×C₅₃	1	1	yes	characteristic
1064	#95	C₂³×C₅₃	1	1	yes	characteristic
1065	#95	C₂³×C₅₃	1	1	yes	characteristic
1066	#95	C₂³×C₅₃	1	1	yes	characteristic
1067	#95	C₂³×C₅₃	1	1	yes	characteristic
1068	#95	C₂³×C₅₃	1	1	yes	characteristic
1069	#95	C₂³×C₅₃	1	1	yes	characteristic
1070	#95	C₂³×C₅₃	1	1	yes	characteristic
1071	#95	C₂³×C₅₃	1	1	yes	characteristic
1072	#95	C₂³×C₅₃	1	1	yes	characteristic
1073	#95	C₂³×C₅₃	1	1	yes	characteristic
1074	#95	C₂³×C₅₃	1	1	yes	characteristic
1075	#95	C₂³×C₅₃	1	1	yes	characteristic
1076	#95	C₂³×C₅₃	1	1	yes	characteristic
1077	#95	C₂³×C₅₃	1	1	yes	characteristic
1078	#95	C₂³×C₅₃	1	1	yes	characteristic
1079	#95	C₂³×C₅₃	1	1	yes	characteristic
1080	#95	C₂³×C₅₃	1	1	yes	characteristic
1081	#95	C₂³×C₅₃	1	1	yes	characteristic
1082	#95	C₂³×C₅₃	1	1	yes	characteristic
1083	#95	C₂³×C₅₃	1	1	yes	characteristic
1084	#95	C₂³×C₅₃	1	1	yes	characteristic
1085	#95	C₂³×C₅₃	1	1	yes	characteristic
1086	#95	C₂³×C₅₃	1	1	yes	characteristic
1087	#95	C₂³×C₅₃	1	1	yes	characteristic
1088	#95	C₂³×C₅₃	1	1	yes	characteristic
1089	#95	C₂³×C₅₃	1	1	yes	characteristic
1090	#95	C₂³×C₅₃	1	1	yes	characteristic
1091	#95	C₂³×C₅₃	1	1	yes	characteristic
1092	#95	C₂³×C₅₃	1	1	yes	characteristic
1093	#95	C₂³×C₅₃	1	1	yes	characteristic
1094	#95	C₂³×C₅₃	1	1	yes	characteristic
1095	#95	C₂³×C₅₃	1	1	yes	characteristic
1096	#95	C₂³×C₅₃	1	1	yes	characteristic
1097	#95	C₂³×C₅₃	1	1	yes	characteristic
1098	#95	C₂³×C₅₃	1	1	yes	characteristic
1099	#95	C₂³×C₅₃	1	1	yes	characteristic
1100	#95	C₂³×C₅₃	1	1	yes	characteristic
1101	#95	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1103	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1104	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1105	C₂×Q₈	—	4	1	no	—
1106	C₂×Q₈	—	4	1	no	—
1107	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	—
1108	C₂×D₄	—	2	2	no	—
1109	C₂×D₄	—	2	2	no	—
1110	C₂×D₄	—	2	2	no	—
1111	C₂×D₄	—	2	2	no	—
1112	C₂×D₄	—	4	1	no	—
1113	C₂×D₄	—	4	1	no	—
1114	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1115	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1116	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1117	C₂²×C₄	—	2	2	no	—
1118	C₂²×C₄	—	2	2	no	—
1119	C₂²×C₄	—	2	2	no	—
1120	C₂²×C₄	—	2	2	no	—
1121	C₂²×C₄	—	2	2	no	—
1122	C₂²×C₄	—	2	2	no	—
1123	C₂²×C₄	—	2	2	no	—
1124	C₂²×C₄	—	2	2	no	—
1125	C₂²×C₄	—	2	2	no	—
1126	C₂²×C₄	—	2	2	no	—
1127	C₂²×C₄	—	4	1	no	—
1128	C₂²×C₄	—	4	1	no	—
1129	C₂²×C₄	—	4	1	no	—
1130	C₂²×C₄	—	4	1	no	—
1131	C₂²×C₄	—	4	1	no	—
1132	C₂²×C₄	—	4	1	no	—
1133	C₂²×C₄	—	4	1	no	—
1134	C₂²×C₄	—	4	1	no	—
1135	C₂²×C₄	—	4	1	no	—
1136	C₂²×C₄	—	4	1	no	—
1137	C₂²×C₄	—	4	1	no	—
1138	C₂²×C₄	—	4	1	no	—
1139	C₂²×C₄	—	4	1	no	—
1140	C₂²×C₄	—	4	1	no	—
1141	C₂²×C₄	—	4	1	no	—
1142	C₂²×C₄	—	4	1	no	—
1143	C₂²×C₄	—	4	1	no	—
1144	C₂²×C₄	—	4	1	no	—
1145	C₂²×C₄	—	4	1	no	—
1146	C₂²×C₄	—	4	1	no	—
1147	C₂²×C₄	—	4	1	no	—
1148	C₂²×C₄	—	4	1	no	—
1149	C₂²×C₄	—	4	1	no	—
1150	C₂²×C₄	—	4	1	no	—
1151	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1152	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1153	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1154	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1155	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1156	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1157	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1158	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1159	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1160	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1161	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1162	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1163	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1164	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1165	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1166	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1167	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1168	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1169	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1170	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1171	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1172	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1173	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1174	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1175	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1176	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1177	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1178	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1179	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1180	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1181	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1182	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1183	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1184	C₄⋊C₄	—	2	2	no	—
1185	C₄⋊C₄	—	2	2	no	—
1186	C₄⋊C₄	—	2	2	no	—
1187	C₄⋊C₄	—	2	2	no	—
1188	C₄⋊C₄	—	2	2	no	—
1189	C₄⋊C₄	—	2	2	no	—
1190	C₄⋊C₄	—	4	1	no	—
1191	C₄⋊C₄	—	4	1	no	—
1192	C₄⋊C₄	—	4	1	no	—
1193	C₄⋊C₄	—	4	1	no	—
1194	C₄⋊C₄	—	4	1	no	—
1195	C₄⋊C₄	—	4	1	no	—
1196	C₄⋊C₄	—	4	1	no	—
1197	C₄⋊C₄	—	4	1	no	—
1198	C₄⋊C₄	—	4	1	no	—
1199	C₄⋊C₄	—	4	1	no	—
1200	C₄⋊C₄	—	4	1	no	—
1201	C₄⋊C₄	—	4	1	no	—
1202	C₄⋊C₄	—	4	1	no	—
1203	C₄⋊C₄	—	4	1	no	—
1204	C₄⋊C₄	—	4	1	no	—
1205	C₄⋊C₄	—	4	1	no	—
1206	C₄⋊C₄	—	4	1	no	—
1207	C₄⋊C₄	—	4	1	no	—
1208	C₄⋊C₄	—	4	1	no	—
1209	C₄⋊C₄	—	4	1	no	—
1210	C₄⋊C₄	—	4	1	no	—
1211	C₄⋊C₄	—	4	1	no	—
1212	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1213	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1214	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1215	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1216	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1217	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1218	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1219	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1220	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1221	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1222	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1223	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1224	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1225	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1226	C₂²⋊C₄	—	2	2	no	—
1227	C₂²⋊C₄	—	2	2	no	—
1228	C₂²⋊C₄	—	2	2	no	—
1229	C₂²⋊C₄	—	2	2	no	—
1230	C₂²⋊C₄	—	2	2	no	—
1231	C₂²⋊C₄	—	2	2	no	—
1232	C₂²⋊C₄	—	4	1	no	—
1233	C₂²⋊C₄	—	4	1	no	—
1234	C₂²⋊C₄	—	4	1	no	—
1235	C₂²⋊C₄	—	4	1	no	—
1236	C₂²⋊C₄	—	4	1	no	—
1237	C₂²⋊C₄	—	4	1	no	—
1238	C₂²⋊C₄	—	4	1	no	—
1239	C₂²⋊C₄	—	4	1	no	—
1240	C₂²⋊C₄	—	4	1	no	—
1241	C₂²⋊C₄	—	4	1	no	—
1242	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1243	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1244	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1245	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1246	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1247	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1248	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1249	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1250	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1251	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1252	C₄²	—	2	2	no	—
1253	C₄²	—	2	2	no	—
1254	C₄²	—	4	1	no	—
1255	C₄²	—	4	1	no	—
1256	C₄²	—	4	1	no	—
1257	C₄²	—	4	1	no	—
1258	C₄²	—	4	1	no	—
1259	C₄²	—	4	1	no	—
1260	C₄²	—	4	1	no	—
1261	C₄²	—	4	1	no	—
1262	C₄²	—	4	1	no	—
1263	C₄²	—	4	1	no	—
1264	C₄²	—	4	1	no	—
1265	C₄²	—	4	1	no	—
1266	C₄²	—	4	1	no	—
1267	C₄²	—	4	1	no	—
1268	C₄²	—	4	1	no	—
1269	C₄²	—	4	1	no	—
1270	C₄²	—	4	1	no	—
1271	C₄²	—	4	1	no	—
1272	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
1273	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
1274	C₂³	—	2	1	no	—
1275	C₂³	—	2	1	no	—
1276	C₂³	—	2	1	no	—
1277	C₂³	—	2	1	no	—
1278	C₂³	—	2	1	no	—
1279	C₂³	—	2	1	no	—
1280	C₂³	—	2	1	no	—
1281	C₂³	—	2	1	no	—
1282	C₂³	—	2	1	no	—
1283	C₂³	—	2	1	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	1	no	—
1290	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1291	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1292	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1293	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1294	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1295	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1296	Q₈	—	4	4	no	—
1297	D₄	—	2	8	no	—
1298	D₄	—	2	8	no	—
1299	D₄	—	4	4	no	—
1300	C₂×C₄	—	2	8	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	4	4	no	—
1372	C₂×C₄	—	4	4	no	—
1373	C₂×C₄	—	4	4	no	—
1374	C₂×C₄	—	4	4	no	—
1375	C₂×C₄	—	4	4	no	—
1376	C₂×C₄	—	4	4	no	—
1377	C₂×C₄	—	8	2	no	—
1378	C₂×C₄	—	8	2	no	—
1379	C₂×C₄	—	8	2	no	—
1380	C₂×C₄	—	8	2	no	—
1381	C₂×C₄	—	8	2	no	—
1382	C₂×C₄	—	8	2	no	—
1383	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1384	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1385	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1386	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1387	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1388	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1389	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1390	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1391	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1392	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1393	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1394	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1395	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1396	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1397	C₂²	—	2	2	no	—
1398	C₂²	—	2	2	no	—
1399	C₂²	—	2	2	no	—
1400	C₂²	—	2	2	no	—
1401	C₂²	—	2	2	no	—
1402	C₂²	—	2	2	no	—
1403	C₂²	—	2	2	no	—
1404	C₂²	—	2	2	no	—
1405	C₂²	—	2	2	no	—
1406	C₂²	—	2	2	no	—
1407	C₂²	—	2	2	no	—
1408	C₂²	—	2	2	no	—
1409	C₂²	—	4	1	no	—
1410	C₂²	—	4	1	no	—
1411	C₂²	—	4	1	no	—
1412	C₂²	—	4	1	no	—
1413	C₂²	—	4	1	no	—
1414	C₂²	—	4	1	no	—
1415	C₂²	—	4	1	no	—
1416	C₂²	—	4	1	no	—
1417	C₂²	C₅₃×#520	1	4	yes	—
1418	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
1419	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1420	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1421	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1422	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1423	C₂²	C₅₃×#585	1	1	yes	characteristic
1424	C₂²	C₅₃×#585	1	1	yes	characteristic
1425	C₄	—	2	2	no	—
1426	C₄	—	2	2	no	—
1427	C₄	—	2	2	no	—
1428	C₄	—	2	2	no	—
1429	C₄	—	2	2	no	—
1430	C₄	—	2	2	no	—
1431	C₄	—	2	2	no	—
1432	C₄	—	2	2	no	—
1433	C₄	—	2	2	no	—
1434	C₄	—	2	2	no	—
1435	C₄	—	2	2	no	—
1436	C₄	—	2	2	no	—
1437	C₄	—	2	2	no	—
1438	C₄	—	2	2	no	—
1439	C₄	—	4	1	no	—
1440	C₄	—	4	1	no	—
1441	C₄	—	4	1	no	—
1442	C₄	—	4	1	no	—
1443	C₄	—	4	1	no	—
1444	C₄	—	4	1	no	—
1445	C₄	—	4	1	no	—
1446	C₄	—	4	1	no	—
1447	C₄	—	4	1	no	—
1448	C₄	—	4	1	no	—
1449	C₄	—	4	1	no	—
1450	C₄	—	4	1	no	—
1451	C₄	—	4	1	no	—
1452	C₄	—	4	1	no	—
1453	C₂	—	2	4	no	—
1454	C₂	—	4	2	no	—
1455	C₂	—	4	2	no	—
1456	C₂	C₂×C₅₃×#520	1	1	yes	characteristic
1457	C₂	C₄×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1458	C₂	C₄×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1459	C₂	C₅₃×#3534	1	1	yes	characteristic
1460	C₂	C₅₃×#3535	1	1	yes	characteristic
1461	C₂	C₅₃×#3552	1	1	yes	characteristic
1462	C₂	C₅₃×#3553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂×#121×C₅₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2383	C₂	semidirect
3. C₅₃×#2382	C₂	semidirect
4. C₅₃×#2378	C₂	semidirect
5. C₅₃×#2376	C₂	semidirect
6. C₅₃×#2373	C₂	semidirect
7. C₅₃×#2370	C₂	semidirect
8. C₅₃×#2368	C₂	semidirect
11. C₅₃×#2360	C₂	semidirect
12. C₅₃×#2360	C₂	semidirect
13. C₅₃×#2359	C₂	semidirect
14. C₅₃×#2353	C₂	semidirect
15. C₅₃×#2352	C₂	semidirect
16. C₅₃×#2349	C₂	semidirect
17. D₄×C₄⋊C₄×C₅₃	C₂	semidirect
18. C₅₃×#2336	C₂	semidirect
19. C₅₃×#2335	C₂	semidirect
20. C₅₃×#2334	C₂	semidirect
21. C₅₃×#2334	C₂	semidirect
22. C₅₃×#2330	C₂	semidirect
23. C₅₃×#2329	C₂	semidirect
24. C₅₃×#2323	C₂	semidirect
25. C₅₃×#2322	C₂	semidirect
26. C₅₃×#2322	C₂	semidirect
27. C₅₃×#2322	C₂	semidirect
28. C₅₃×#2313	C₂	semidirect
29. C₄×#123×C₅₃	C₂	semidirect
30. C₄×#123×C₅₃	C₂	semidirect
31. C₂×C₅₃×#389	C₂	semidirect
32. C₅₃×#539	C₄	semidirect
205. #126×C₅₃	C₂×C₄	semidirect
206. #126×C₅₃	C₂×C₄	semidirect
207. #125×C₅₃	C₂×C₄	semidirect
208. #125×C₅₃	C₂×C₄	semidirect
209. #123×C₅₃	C₂×C₄	semidirect
210. #123×C₅₃	C₂×C₄	semidirect
211. #123×C₅₃	C₂×C₄	semidirect
212. #123×C₅₃	C₂×C₄	semidirect
213. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
214. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
215. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
223. C₄×D₄×C₅₃	C₂×C₄	semidirect
224. C₄×D₄×C₅₃	C₂×C₄	semidirect
230. C₂×C₄⋊C₄×C₅₃	C₂×C₄	semidirect
665. #34417	C₅₃	direct (N × H)
723. #2383	C₂×C₅₃	semidirect
724. #2382	C₂×C₅₃	semidirect
725. #2378	C₂×C₅₃	semidirect
726. #2376	C₂×C₅₃	semidirect
727. #2373	C₂×C₅₃	semidirect
728. #2370	C₂×C₅₃	semidirect
729. #2368	C₂×C₅₃	semidirect
732. #2360	C₂×C₅₃	semidirect
733. #2360	C₂×C₅₃	semidirect
734. #2359	C₂×C₅₃	semidirect
735. #2353	C₂×C₅₃	semidirect
736. #2352	C₂×C₅₃	semidirect
737. #2349	C₂×C₅₃	semidirect
738. D₄×C₄⋊C₄	C₂×C₅₃	semidirect
739. #2336	C₂×C₅₃	semidirect
740. #2335	C₂×C₅₃	semidirect
741. #2334	C₂×C₅₃	semidirect
742. #2334	C₂×C₅₃	semidirect
743. #2330	C₂×C₅₃	semidirect
744. #2329	C₂×C₅₃	semidirect
745. #2323	C₂×C₅₃	semidirect
746. #2322	C₂×C₅₃	semidirect
747. #2322	C₂×C₅₃	semidirect
748. #2322	C₂×C₅₃	semidirect
749. #2313	C₂×C₅₃	semidirect
750. C₄×#123	C₂×C₅₃	semidirect
751. C₄×#123	C₂×C₅₃	semidirect
752. C₂×#389	C₂×C₅₃	semidirect
763. #539	C₄×C₅₃	semidirect
919. C₅₃	#34417	direct (N × H)
937. #126	C₂×C₄×C₅₃	semidirect
938. #126	C₂×C₄×C₅₃	semidirect
939. #125	C₂×C₄×C₅₃	semidirect
940. #125	C₂×C₄×C₅₃	semidirect
941. #123	C₂×C₄×C₅₃	semidirect
942. #123	C₂×C₄×C₅₃	semidirect
943. #123	C₂×C₄×C₅₃	semidirect
944. #123	C₂×C₄×C₅₃	semidirect
945. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
946. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
947. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
955. C₄×D₄	C₂×C₄×C₅₃	semidirect
956. C₄×D₄	C₂×C₄×C₅₃	semidirect
962. C₂×C₄⋊C₄	C₂×C₄×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#539	2
C₅₃×#2383	2
C₅₃×#2382	2
C₅₃×#2378	2
C₅₃×#2376	2
C₅₃×#2373	2
C₅₃×#2370	2
C₅₃×#2368	2
C₅₃×#2364	2
C₅₃×#2361	2
C₅₃×#2360	2
C₅₃×#2359	2
C₅₃×#2353	2
C₅₃×#2352	2
C₅₃×#2349	2
D₄×C₄⋊C₄×C₅₃	2
C₅₃×#2336	2
C₅₃×#2335	2
C₅₃×#2334	2
C₅₃×#2330	2
C₅₃×#2329	2
C₅₃×#2323	2
C₅₃×#2322	2
C₅₃×#2313	2
C₄×#123×C₅₃	2
C₂×C₅₃×#389	2
#34417	53

Subgroups — C53×#34417 #27241929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34417 #27241929