Subgroups — C₅₃×#34479 #27241991

Order 13568.

2292 conjugacy classes of subgroups.

The subgroup lattice has 1522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#551	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2379	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×#2368	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2359	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2359	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2358	C₂	1	1	yes	maximal, characteristic
11	C₅₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2343	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2342	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2342	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2321	C₂	1	1	yes	maximal, characteristic
25	C₅₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅₃×#551	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×#124×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#123×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×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×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×#117×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
52	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
54	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
58	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
59	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#390	C₂²	1	1	yes	characteristic
64	C₅₃×#390	C₂²	1	1	yes	characteristic
65	C₅₃×#390	C₂²	1	1	yes	characteristic
66	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#388	C₂²	1	1	yes	characteristic
77	C₅₃×#388	C₂²	1	1	yes	characteristic
78	C₅₃×#388	C₂²	1	1	yes	characteristic
79	C₅₃×#388	C₂²	1	1	yes	characteristic
80	C₅₃×#388	C₂²	1	1	yes	characteristic
81	C₅₃×#388	C₂²	1	1	yes	characteristic
82	C₅₃×#388	C₂²	1	1	yes	characteristic
83	C₅₃×#388	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, complemented
99	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#386	C₂²	1	1	yes	characteristic
121	C₅₃×#386	C₂²	1	1	yes	characteristic
122	C₅₃×#386	C₂²	1	1	yes	characteristic
123	C₅₃×#386	C₂²	1	1	yes	characteristic
124	C₅₃×#386	C₂²	1	1	yes	characteristic
125	C₅₃×#386	C₂²	1	1	yes	characteristic
126	C₅₃×#385	C₂²	1	1	yes	characteristic
127	C₅₃×#385	C₂²	1	1	yes	characteristic
128	C₅₃×#385	C₂²	1	1	yes	characteristic
129	C₅₃×#385	C₂²	1	1	yes	characteristic
130	C₅₃×#385	C₂²	1	1	yes	characteristic
131	C₅₃×#385	C₂²	1	1	yes	characteristic
132	C₅₃×#385	C₂²	1	1	yes	characteristic
133	C₅₃×#385	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, complemented
142	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
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	C₅₃×#380	C₂²	1	1	yes	characteristic
161	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#379	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
164	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
165	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
166	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
167	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
168	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
169	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
170	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
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, complemented
182	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#376	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#376	C₂²	1	1	yes	characteristic, complemented
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, complemented
188	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×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	C₂²×D₄×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	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
206	#126×C₅₃	C₂×C₄	1	8	yes	complemented
207	#126×C₅₃	C₂×C₄	1	8	yes	complemented
208	#124×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	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
213	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
214	#120×C₅₃	C₂×C₄	1	8	yes	—
215	C₄×Q₈×C₅₃	—	4	2	no	—
216	C₄×D₄×C₅₃	—	4	2	no	—
217	C₄×D₄×C₅₃	—	4	2	no	—
218	C₄×D₄×C₅₃	—	4	2	no	—
219	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
220	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
221	#117×C₅₃	—	4	2	no	—
222	#117×C₅₃	—	4	2	no	—
223	#117×C₅₃	—	4	2	no	—
224	#117×C₅₃	C₂×C₄	1	8	yes	complemented
225	#117×C₅₃	C₂×C₄	1	8	yes	complemented
226	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
227	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₃	—	4	2	no	—
262	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
263	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
264	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
265	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
266	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₅₃	—	4	2	no	—
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	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
323	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
324	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₄²×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	—	2	2	no	—
371	C₂⁴×C₅₃	—	2	2	no	—
372	C₂⁴×C₅₃	—	4	1	no	—
373	C₂⁴×C₅₃	—	4	1	no	—
374	C₂⁴×C₅₃	—	4	1	no	—
375	C₂⁴×C₅₃	—	4	1	no	—
376	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
377	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂×Q₈×C₅₃	—	4	1	no	—
382	C₂×Q₈×C₅₃	—	4	1	no	—
383	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
384	C₂×D₄×C₅₃	—	2	2	no	—
385	C₂×D₄×C₅₃	—	2	2	no	—
386	C₂×D₄×C₅₃	—	4	1	no	—
387	C₂×D₄×C₅₃	—	4	1	no	—
388	C₂×D₄×C₅₃	—	4	1	no	—
389	C₂×D₄×C₅₃	—	4	1	no	—
390	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
391	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
392	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	2	no	—
395	C₂²×C₄×C₅₃	—	2	2	no	—
396	C₂²×C₄×C₅₃	—	2	2	no	—
397	C₂²×C₄×C₅₃	—	2	2	no	—
398	C₂²×C₄×C₅₃	—	2	2	no	—
399	C₂²×C₄×C₅₃	—	2	2	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	—	4	1	no	—
420	C₂²×C₄×C₅₃	—	4	1	no	—
421	C₂²×C₄×C₅₃	—	4	1	no	—
422	C₂²×C₄×C₅₃	—	4	1	no	—
423	C₂²×C₄×C₅₃	—	4	1	no	—
424	C₂²×C₄×C₅₃	—	4	1	no	—
425	C₂²×C₄×C₅₃	—	4	1	no	—
426	C₂²×C₄×C₅₃	—	4	1	no	—
427	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
428	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
429	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
430	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
431	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
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	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
459	C₄⋊C₄×C₅₃	—	2	2	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	—	4	1	no	—
481	C₄⋊C₄×C₅₃	—	4	1	no	—
482	C₄⋊C₄×C₅₃	—	4	1	no	—
483	C₄⋊C₄×C₅₃	—	4	1	no	—
484	C₄⋊C₄×C₅₃	—	4	1	no	—
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	C₂²⋊C₄×C₅₃	—	2	2	no	—
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	—	4	1	no	—
511	C₂²⋊C₄×C₅₃	—	4	1	no	—
512	C₂²⋊C₄×C₅₃	—	4	1	no	—
513	C₂²⋊C₄×C₅₃	—	4	1	no	—
514	C₂²⋊C₄×C₅₃	—	4	1	no	—
515	C₂²⋊C₄×C₅₃	—	4	1	no	—
516	C₂²⋊C₄×C₅₃	—	4	1	no	—
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	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
521	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
522	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
523	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
524	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
525	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
526	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
527	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
528	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
529	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
530	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
531	C₄²×C₅₃	—	2	2	no	—
532	C₄²×C₅₃	—	2	2	no	—
533	C₄²×C₅₃	—	2	2	no	—
534	C₄²×C₅₃	—	2	2	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	—	4	1	no	—
541	C₄²×C₅₃	—	4	1	no	—
542	C₄²×C₅₃	—	4	1	no	—
543	C₄²×C₅₃	—	4	1	no	—
544	C₄²×C₅₃	—	4	1	no	—
545	C₄²×C₅₃	—	4	1	no	—
546	C₄²×C₅₃	—	4	1	no	—
547	C₄²×C₅₃	—	4	1	no	—
548	C₄²×C₅₃	—	4	1	no	—
549	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
550	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
551	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
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	—	2	1	no	—
559	C₂³×C₅₃	—	2	1	no	—
560	C₂³×C₅₃	—	2	1	no	—
561	C₂³×C₅₃	—	2	1	no	—
562	C₂³×C₅₃	—	2	1	no	—
563	C₂³×C₅₃	—	2	1	no	—
564	C₂³×C₅₃	—	2	1	no	—
565	C₂³×C₅₃	—	2	1	no	—
566	C₂³×C₅₃	—	2	1	no	—
567	C₂³×C₅₃	—	2	1	no	—
568	C₂³×C₅₃	—	2	1	no	—
569	C₂³×C₅₃	—	2	1	no	—
570	C₂³×C₅₃	—	2	1	no	—
571	C₂³×C₅₃	—	2	1	no	—
572	C₂³×C₅₃	—	2	1	no	—
573	C₂³×C₅₃	—	2	1	no	—
574	C₂³×C₅₃	—	2	8	no	—
575	C₂³×C₅₃	—	4	4	no	—
576	C₂³×C₅₃	—	4	4	no	—
577	C₂³×C₅₃	—	8	2	no	—
578	C₂³×C₅₃	—	8	2	no	—
579	C₂³×C₅₃	—	8	2	no	—
580	C₂³×C₅₃	—	8	2	no	—
581	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
582	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
583	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
584	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
585	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
586	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
587	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
588	Q₈×C₅₃	—	4	4	no	—
589	D₄×C₅₃	—	2	8	no	—
590	D₄×C₅₃	—	4	4	no	—
591	D₄×C₅₃	—	4	4	no	—
592	C₂×C₄×C₅₃	—	2	8	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	—	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	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	2	1	no	—
652	C₂×C₄×C₅₃	—	2	1	no	—
653	C₂×C₄×C₅₃	—	2	1	no	—
654	C₂×C₄×C₅₃	—	2	1	no	—
655	C₂×C₄×C₅₃	—	2	1	no	—
656	C₂×C₄×C₅₃	—	2	1	no	—
657	C₂×C₄×C₅₃	—	2	1	no	—
658	C₂×C₄×C₅₃	—	2	1	no	—
659	C₂×C₄×C₅₃	—	2	1	no	—
660	C₂×C₄×C₅₃	—	2	1	no	—
661	C₂×C₄×C₅₃	—	2	1	no	—
662	C₂×C₄×C₅₃	—	4	4	no	—
663	C₂×C₄×C₅₃	—	4	4	no	—
664	C₂×C₄×C₅₃	—	4	4	no	—
665	C₂×C₄×C₅₃	—	4	4	no	—
666	C₂×C₄×C₅₃	—	4	4	no	—
667	C₂×C₄×C₅₃	—	4	4	no	—
668	C₂×C₄×C₅₃	—	8	2	no	—
669	C₂×C₄×C₅₃	—	8	2	no	—
670	C₂×C₄×C₅₃	—	8	2	no	—
671	C₂×C₄×C₅₃	—	8	2	no	—
672	C₂×C₄×C₅₃	—	8	2	no	—
673	C₂×C₄×C₅₃	—	8	2	no	—
674	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
675	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
676	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
677	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
678	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
679	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
680	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
681	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
682	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
683	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
684	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
685	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
686	#34479	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
687	C₂²×C₅₃	—	2	2	no	—
688	C₂²×C₅₃	—	2	2	no	—
689	C₂²×C₅₃	—	2	2	no	—
690	C₂²×C₅₃	—	2	2	no	—
691	C₂²×C₅₃	—	2	2	no	—
692	C₂²×C₅₃	—	2	2	no	—
693	C₂²×C₅₃	—	2	2	no	—
694	C₂²×C₅₃	—	2	2	no	—
695	C₂²×C₅₃	—	2	2	no	—
696	C₂²×C₅₃	—	2	2	no	—
697	C₂²×C₅₃	—	2	2	no	—
698	C₂²×C₅₃	—	2	2	no	—
699	C₂²×C₅₃	—	2	2	no	—
700	C₂²×C₅₃	—	2	2	no	—
701	C₂²×C₅₃	—	2	2	no	—
702	C₂²×C₅₃	—	4	1	no	—
703	C₂²×C₅₃	—	4	1	no	—
704	C₂²×C₅₃	—	4	1	no	—
705	C₂²×C₅₃	—	4	1	no	—
706	C₂²×C₅₃	—	4	1	no	—
707	C₂²×C₅₃	—	4	1	no	—
708	C₂²×C₅₃	—	4	1	no	—
709	C₂²×C₅₃	—	4	1	no	—
710	C₂²×C₅₃	—	4	1	no	—
711	C₂²×C₅₃	—	4	1	no	—
712	C₂²×C₅₃	—	4	1	no	—
713	C₂²×C₅₃	—	4	1	no	—
714	C₂²×C₅₃	—	8	8	no	—
715	C₂²×C₅₃	#520	1	4	yes	—
716	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
717	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
719	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
720	C₂²×C₅₃	#585	1	1	yes	characteristic
721	C₂²×C₅₃	#585	1	1	yes	characteristic
722	C₂²×C₅₃	#585	1	1	yes	characteristic
723	C₄×C₅₃	—	2	2	no	—
724	C₄×C₅₃	—	2	2	no	—
725	C₄×C₅₃	—	2	2	no	—
726	C₄×C₅₃	—	2	2	no	—
727	C₄×C₅₃	—	2	2	no	—
728	C₄×C₅₃	—	2	2	no	—
729	C₄×C₅₃	—	2	2	no	—
730	C₄×C₅₃	—	2	2	no	—
731	C₄×C₅₃	—	2	2	no	—
732	C₄×C₅₃	—	2	2	no	—
733	C₄×C₅₃	—	2	2	no	—
734	C₄×C₅₃	—	2	2	no	—
735	C₄×C₅₃	—	4	1	no	—
736	C₄×C₅₃	—	4	1	no	—
737	C₄×C₅₃	—	4	1	no	—
738	C₄×C₅₃	—	4	1	no	—
739	C₄×C₅₃	—	4	1	no	—
740	C₄×C₅₃	—	4	1	no	—
741	C₄×C₅₃	—	4	1	no	—
742	C₄×C₅₃	—	4	1	no	—
743	C₄×C₅₃	—	4	1	no	—
744	C₄×C₅₃	—	4	1	no	—
745	C₄×C₅₃	—	4	1	no	—
746	C₄×C₅₃	—	4	1	no	—
747	C₄×C₅₃	—	4	1	no	—
748	C₄×C₅₃	—	4	1	no	—
749	C₄×C₅₃	—	4	1	no	—
750	C₂×#551	C₂×C₅₃	1	1	yes	characteristic
751	#2383	C₂×C₅₃	1	1	yes	characteristic, complemented
752	#2379	C₂×C₅₃	1	1	yes	characteristic, complemented
753	#2378	C₂×C₅₃	1	1	yes	characteristic, complemented
754	#2376	C₂×C₅₃	1	1	yes	characteristic, complemented
755	#2373	C₂×C₅₃	1	1	yes	characteristic, complemented
756	#2368	C₂×C₅₃	1	1	yes	characteristic, complemented
757	#2359	C₂×C₅₃	1	1	yes	characteristic, complemented
758	#2359	C₂×C₅₃	1	1	yes	characteristic, complemented
759	#2358	C₂×C₅₃	1	1	yes	characteristic
760	#2354	C₂×C₅₃	1	1	yes	characteristic, complemented
761	#2349	C₂×C₅₃	1	1	yes	characteristic, complemented
762	#2346	C₂×C₅₃	1	1	yes	characteristic, complemented
763	#2343	C₂×C₅₃	1	1	yes	characteristic, complemented
764	#2342	C₂×C₅₃	1	1	yes	characteristic, complemented
765	#2342	C₂×C₅₃	1	1	yes	characteristic, complemented
766	#2335	C₂×C₅₃	1	1	yes	characteristic, complemented
767	#2335	C₂×C₅₃	1	1	yes	characteristic, complemented
768	#2334	C₂×C₅₃	1	1	yes	characteristic, complemented
769	#2334	C₂×C₅₃	1	1	yes	characteristic, complemented
770	#2326	C₂×C₅₃	1	1	yes	characteristic, complemented
771	#2323	C₂×C₅₃	1	1	yes	characteristic, complemented
772	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
773	#2321	C₂×C₅₃	1	1	yes	characteristic
774	#2318	C₂×C₅₃	1	1	yes	characteristic, complemented
775	#2317	C₂×C₅₃	1	1	yes	characteristic, complemented
776	#2315	C₂×C₅₃	1	1	yes	characteristic, complemented
777	#2314	C₂×C₅₃	1	1	yes	characteristic, complemented
778	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
779	#2290	C₂×C₅₃	1	1	yes	characteristic, complemented
780	C₂×#388	C₂×C₅₃	1	1	yes	characteristic, complemented
781	C₂×C₅₃	—	2	4	no	—
782	C₂×C₅₃	—	4	2	no	—
783	C₂×C₅₃	—	4	2	no	—
784	C₂×C₅₃	—	4	2	no	—
785	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
786	C₂×C₅₃	#3428	1	1	yes	characteristic
787	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
788	C₂×C₅₃	#3535	1	1	yes	characteristic
789	C₂×C₅₃	#3542	1	1	yes	characteristic
790	C₂×C₅₃	#3545	1	1	yes	characteristic
791	C₂×C₅₃	#3564	1	1	yes	characteristic
792	#551	C₄×C₅₃	1	16	yes	complemented
793	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
794	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
795	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
796	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
797	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
798	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
799	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
800	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
801	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
802	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
803	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
804	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
805	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
806	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
807	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
808	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
809	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
810	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
811	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
812	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
813	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
814	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
815	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
816	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
817	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
818	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
819	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
820	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
821	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
822	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
823	#390	C₂²×C₅₃	1	1	yes	characteristic
824	#390	C₂²×C₅₃	1	1	yes	characteristic
825	#390	C₂²×C₅₃	1	1	yes	characteristic
826	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
827	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
828	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
829	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
830	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
831	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
832	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
833	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
834	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
835	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
836	#388	C₂²×C₅₃	1	1	yes	characteristic
837	#388	C₂²×C₅₃	1	1	yes	characteristic
838	#388	C₂²×C₅₃	1	1	yes	characteristic
839	#388	C₂²×C₅₃	1	1	yes	characteristic
840	#388	C₂²×C₅₃	1	1	yes	characteristic
841	#388	C₂²×C₅₃	1	1	yes	characteristic
842	#388	C₂²×C₅₃	1	1	yes	characteristic
843	#388	C₂²×C₅₃	1	1	yes	characteristic
844	#388	C₂²×C₅₃	1	1	yes	characteristic
845	#388	C₂²×C₅₃	1	1	yes	characteristic
846	#388	C₂²×C₅₃	1	1	yes	characteristic
847	#388	C₂²×C₅₃	1	1	yes	characteristic
848	#388	C₂²×C₅₃	1	1	yes	characteristic
849	#388	C₂²×C₅₃	1	1	yes	characteristic
850	#388	C₂²×C₅₃	1	1	yes	characteristic
851	#388	C₂²×C₅₃	1	1	yes	characteristic
852	#388	C₂²×C₅₃	1	1	yes	characteristic
853	#388	C₂²×C₅₃	1	1	yes	characteristic
854	#388	C₂²×C₅₃	1	1	yes	characteristic
855	#388	C₂²×C₅₃	1	1	yes	characteristic
856	#388	C₂²×C₅₃	1	1	yes	characteristic
857	#388	C₂²×C₅₃	1	1	yes	characteristic
858	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
859	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
860	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
861	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
862	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
863	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
864	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
865	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
866	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
867	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
868	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
869	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
870	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
871	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
872	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
873	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
874	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
875	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
876	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
877	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
878	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
879	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
880	#386	C₂²×C₅₃	1	1	yes	characteristic
881	#386	C₂²×C₅₃	1	1	yes	characteristic
882	#386	C₂²×C₅₃	1	1	yes	characteristic
883	#386	C₂²×C₅₃	1	1	yes	characteristic
884	#386	C₂²×C₅₃	1	1	yes	characteristic
885	#386	C₂²×C₅₃	1	1	yes	characteristic
886	#385	C₂²×C₅₃	1	1	yes	characteristic
887	#385	C₂²×C₅₃	1	1	yes	characteristic
888	#385	C₂²×C₅₃	1	1	yes	characteristic
889	#385	C₂²×C₅₃	1	1	yes	characteristic
890	#385	C₂²×C₅₃	1	1	yes	characteristic
891	#385	C₂²×C₅₃	1	1	yes	characteristic
892	#385	C₂²×C₅₃	1	1	yes	characteristic
893	#385	C₂²×C₅₃	1	1	yes	characteristic
894	#385	C₂²×C₅₃	1	1	yes	characteristic
895	#385	C₂²×C₅₃	1	1	yes	characteristic
896	#385	C₂²×C₅₃	1	1	yes	characteristic
897	#385	C₂²×C₅₃	1	1	yes	characteristic
898	#385	C₂²×C₅₃	1	1	yes	characteristic
899	#385	C₂²×C₅₃	1	1	yes	characteristic
900	#385	C₂²×C₅₃	1	1	yes	characteristic
901	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
902	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
903	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
904	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
905	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
908	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
913	#381	C₂²×C₅₃	1	1	yes	characteristic
914	#381	C₂²×C₅₃	1	1	yes	characteristic
915	#380	C₂²×C₅₃	1	1	yes	characteristic
916	#380	C₂²×C₅₃	1	1	yes	characteristic
917	#380	C₂²×C₅₃	1	1	yes	characteristic
918	#380	C₂²×C₅₃	1	1	yes	characteristic
919	#380	C₂²×C₅₃	1	1	yes	characteristic
920	#380	C₂²×C₅₃	1	1	yes	characteristic
921	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	#379	C₂²×C₅₃	1	1	yes	characteristic
923	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
933	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
934	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
935	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
936	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
937	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
938	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
939	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
940	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
941	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#376	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#376	C₂²×C₅₃	1	1	yes	characteristic, complemented
945	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
946	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
947	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	C₅₃	#34479	1	1	yes	characteristic, direct product factor, Sylow
949	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
950	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
951	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
952	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
953	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
954	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
955	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
956	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
957	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
958	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
959	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
960	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
961	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
962	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
963	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
964	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
965	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
967	#126	C₂×C₄×C₅₃	1	8	yes	complemented
968	#126	C₂×C₄×C₅₃	1	8	yes	complemented
969	#124	C₂×C₄×C₅₃	1	8	yes	complemented
970	#123	C₂×C₄×C₅₃	1	8	yes	complemented
971	#123	C₂×C₄×C₅₃	1	8	yes	complemented
972	#123	C₂×C₄×C₅₃	1	8	yes	complemented
973	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
974	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
975	#120	C₂×C₄×C₅₃	1	8	yes	—
976	C₄×Q₈	—	4	2	no	—
977	C₄×D₄	—	4	2	no	—
978	C₄×D₄	—	4	2	no	—
979	C₄×D₄	—	4	2	no	—
980	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
981	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
982	#117	—	4	2	no	—
983	#117	—	4	2	no	—
984	#117	—	4	2	no	—
985	#117	C₂×C₄×C₅₃	1	8	yes	complemented
986	#117	C₂×C₄×C₅₃	1	8	yes	complemented
987	C₂×C₄⋊C₄	—	4	2	no	—
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×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1015	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	—	4	2	no	—
1023	C₂×C₂²⋊C₄	—	4	2	no	—
1024	C₂×C₂²⋊C₄	—	4	2	no	—
1025	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
1026	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
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×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1034	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1035	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1037	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1047	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1048	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1056	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1057	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂×C₄²	—	4	2	no	—
1066	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂×C₄²	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	#95	C₂³×C₅₃	1	1	yes	characteristic
1103	#95	C₂³×C₅₃	1	1	yes	characteristic
1104	#95	C₂³×C₅₃	1	1	yes	characteristic
1105	#95	C₂³×C₅₃	1	1	yes	characteristic
1106	#95	C₂³×C₅₃	1	1	yes	characteristic
1107	#95	C₂³×C₅₃	1	1	yes	characteristic
1108	#95	C₂³×C₅₃	1	1	yes	characteristic
1109	#95	C₂³×C₅₃	1	1	yes	characteristic
1110	#95	C₂³×C₅₃	1	1	yes	characteristic
1111	#95	C₂³×C₅₃	1	1	yes	characteristic
1112	#95	C₂³×C₅₃	1	1	yes	characteristic
1113	#95	C₂³×C₅₃	1	1	yes	characteristic
1114	#95	C₂³×C₅₃	1	1	yes	characteristic
1115	#95	C₂³×C₅₃	1	1	yes	characteristic
1116	#95	C₂³×C₅₃	1	1	yes	characteristic
1117	#95	C₂³×C₅₃	1	1	yes	characteristic
1118	#95	C₂³×C₅₃	1	1	yes	characteristic
1119	#95	C₂³×C₅₃	1	1	yes	characteristic
1120	#95	C₂³×C₅₃	1	1	yes	characteristic
1121	#95	C₂³×C₅₃	1	1	yes	characteristic
1122	#95	C₂³×C₅₃	1	1	yes	characteristic
1123	#95	C₂³×C₅₃	1	1	yes	characteristic
1124	#95	C₂³×C₅₃	1	1	yes	characteristic
1125	#95	C₂³×C₅₃	1	1	yes	characteristic
1126	#95	C₂³×C₅₃	1	1	yes	characteristic
1127	#95	C₂³×C₅₃	1	1	yes	characteristic
1128	#95	C₂³×C₅₃	1	1	yes	characteristic
1129	#95	C₂³×C₅₃	1	1	yes	characteristic
1130	#95	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂⁴	—	2	2	no	—
1132	C₂⁴	—	2	2	no	—
1133	C₂⁴	—	4	1	no	—
1134	C₂⁴	—	4	1	no	—
1135	C₂⁴	—	4	1	no	—
1136	C₂⁴	—	4	1	no	—
1137	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
1138	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1139	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1140	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1141	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1142	C₂×Q₈	—	4	1	no	—
1143	C₂×Q₈	—	4	1	no	—
1144	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	—
1145	C₂×D₄	—	2	2	no	—
1146	C₂×D₄	—	2	2	no	—
1147	C₂×D₄	—	4	1	no	—
1148	C₂×D₄	—	4	1	no	—
1149	C₂×D₄	—	4	1	no	—
1150	C₂×D₄	—	4	1	no	—
1151	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1152	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1153	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1154	C₂²×C₄	—	2	2	no	—
1155	C₂²×C₄	—	2	2	no	—
1156	C₂²×C₄	—	2	2	no	—
1157	C₂²×C₄	—	2	2	no	—
1158	C₂²×C₄	—	2	2	no	—
1159	C₂²×C₄	—	2	2	no	—
1160	C₂²×C₄	—	2	2	no	—
1161	C₂²×C₄	—	4	1	no	—
1162	C₂²×C₄	—	4	1	no	—
1163	C₂²×C₄	—	4	1	no	—
1164	C₂²×C₄	—	4	1	no	—
1165	C₂²×C₄	—	4	1	no	—
1166	C₂²×C₄	—	4	1	no	—
1167	C₂²×C₄	—	4	1	no	—
1168	C₂²×C₄	—	4	1	no	—
1169	C₂²×C₄	—	4	1	no	—
1170	C₂²×C₄	—	4	1	no	—
1171	C₂²×C₄	—	4	1	no	—
1172	C₂²×C₄	—	4	1	no	—
1173	C₂²×C₄	—	4	1	no	—
1174	C₂²×C₄	—	4	1	no	—
1175	C₂²×C₄	—	4	1	no	—
1176	C₂²×C₄	—	4	1	no	—
1177	C₂²×C₄	—	4	1	no	—
1178	C₂²×C₄	—	4	1	no	—
1179	C₂²×C₄	—	4	1	no	—
1180	C₂²×C₄	—	4	1	no	—
1181	C₂²×C₄	—	4	1	no	—
1182	C₂²×C₄	—	4	1	no	—
1183	C₂²×C₄	—	4	1	no	—
1184	C₂²×C₄	—	4	1	no	—
1185	C₂²×C₄	—	4	1	no	—
1186	C₂²×C₄	—	4	1	no	—
1187	C₂²×C₄	—	4	1	no	—
1188	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1189	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1190	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1191	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1192	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1193	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1194	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1195	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1196	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1197	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1198	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1199	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1200	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1201	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1202	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1203	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1204	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1205	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1206	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1207	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1208	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1209	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1210	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1211	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1212	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1213	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1214	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1215	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1216	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1217	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1218	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1219	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1220	C₄⋊C₄	—	2	2	no	—
1221	C₄⋊C₄	—	4	1	no	—
1222	C₄⋊C₄	—	4	1	no	—
1223	C₄⋊C₄	—	4	1	no	—
1224	C₄⋊C₄	—	4	1	no	—
1225	C₄⋊C₄	—	4	1	no	—
1226	C₄⋊C₄	—	4	1	no	—
1227	C₄⋊C₄	—	4	1	no	—
1228	C₄⋊C₄	—	4	1	no	—
1229	C₄⋊C₄	—	4	1	no	—
1230	C₄⋊C₄	—	4	1	no	—
1231	C₄⋊C₄	—	4	1	no	—
1232	C₄⋊C₄	—	4	1	no	—
1233	C₄⋊C₄	—	4	1	no	—
1234	C₄⋊C₄	—	4	1	no	—
1235	C₄⋊C₄	—	4	1	no	—
1236	C₄⋊C₄	—	4	1	no	—
1237	C₄⋊C₄	—	4	1	no	—
1238	C₄⋊C₄	—	4	1	no	—
1239	C₄⋊C₄	—	4	1	no	—
1240	C₄⋊C₄	—	4	1	no	—
1241	C₄⋊C₄	—	4	1	no	—
1242	C₄⋊C₄	—	4	1	no	—
1243	C₄⋊C₄	—	4	1	no	—
1244	C₄⋊C₄	—	4	1	no	—
1245	C₄⋊C₄	—	4	1	no	—
1246	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1247	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1248	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1249	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1250	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1251	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1252	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1253	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1254	C₂²⋊C₄	—	2	2	no	—
1255	C₂²⋊C₄	—	2	2	no	—
1256	C₂²⋊C₄	—	2	2	no	—
1257	C₂²⋊C₄	—	2	2	no	—
1258	C₂²⋊C₄	—	2	2	no	—
1259	C₂²⋊C₄	—	2	2	no	—
1260	C₂²⋊C₄	—	2	2	no	—
1261	C₂²⋊C₄	—	4	1	no	—
1262	C₂²⋊C₄	—	4	1	no	—
1263	C₂²⋊C₄	—	4	1	no	—
1264	C₂²⋊C₄	—	4	1	no	—
1265	C₂²⋊C₄	—	4	1	no	—
1266	C₂²⋊C₄	—	4	1	no	—
1267	C₂²⋊C₄	—	4	1	no	—
1268	C₂²⋊C₄	—	4	1	no	—
1269	C₂²⋊C₄	—	4	1	no	—
1270	C₂²⋊C₄	—	4	1	no	—
1271	C₂²⋊C₄	—	4	1	no	—
1272	C₂²⋊C₄	—	4	1	no	—
1273	C₂²⋊C₄	—	4	1	no	—
1274	C₂²⋊C₄	—	4	1	no	—
1275	C₂²⋊C₄	—	4	1	no	—
1276	C₂²⋊C₄	—	4	1	no	—
1277	C₂²⋊C₄	—	4	1	no	—
1278	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1279	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1280	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1281	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1282	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1283	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1284	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1285	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1286	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1287	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1288	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1289	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1290	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1291	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1292	C₄²	—	2	2	no	—
1293	C₄²	—	2	2	no	—
1294	C₄²	—	2	2	no	—
1295	C₄²	—	2	2	no	—
1296	C₄²	—	4	1	no	—
1297	C₄²	—	4	1	no	—
1298	C₄²	—	4	1	no	—
1299	C₄²	—	4	1	no	—
1300	C₄²	—	4	1	no	—
1301	C₄²	—	4	1	no	—
1302	C₄²	—	4	1	no	—
1303	C₄²	—	4	1	no	—
1304	C₄²	—	4	1	no	—
1305	C₄²	—	4	1	no	—
1306	C₄²	—	4	1	no	—
1307	C₄²	—	4	1	no	—
1308	C₄²	—	4	1	no	—
1309	C₄²	—	4	1	no	—
1310	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
1311	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
1312	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
1313	C₂³	—	2	1	no	—
1314	C₂³	—	2	1	no	—
1315	C₂³	—	2	1	no	—
1316	C₂³	—	2	1	no	—
1317	C₂³	—	2	1	no	—
1318	C₂³	—	2	1	no	—
1319	C₂³	—	2	1	no	—
1320	C₂³	—	2	1	no	—
1321	C₂³	—	2	1	no	—
1322	C₂³	—	2	1	no	—
1323	C₂³	—	2	1	no	—
1324	C₂³	—	2	1	no	—
1325	C₂³	—	2	1	no	—
1326	C₂³	—	2	1	no	—
1327	C₂³	—	2	1	no	—
1328	C₂³	—	2	1	no	—
1329	C₂³	—	2	1	no	—
1330	C₂³	—	2	1	no	—
1331	C₂³	—	2	1	no	—
1332	C₂³	—	2	1	no	—
1333	C₂³	—	2	1	no	—
1334	C₂³	—	2	1	no	—
1335	C₂³	—	2	8	no	—
1336	C₂³	—	4	4	no	—
1337	C₂³	—	4	4	no	—
1338	C₂³	—	8	2	no	—
1339	C₂³	—	8	2	no	—
1340	C₂³	—	8	2	no	—
1341	C₂³	—	8	2	no	—
1342	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1343	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1344	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1345	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1346	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1347	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1348	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1349	Q₈	—	4	4	no	—
1350	D₄	—	2	8	no	—
1351	D₄	—	4	4	no	—
1352	D₄	—	4	4	no	—
1353	C₂×C₄	—	2	8	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	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	2	1	no	—
1383	C₂×C₄	—	2	1	no	—
1384	C₂×C₄	—	2	1	no	—
1385	C₂×C₄	—	2	1	no	—
1386	C₂×C₄	—	2	1	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	2	1	no	—
1409	C₂×C₄	—	2	1	no	—
1410	C₂×C₄	—	2	1	no	—
1411	C₂×C₄	—	2	1	no	—
1412	C₂×C₄	—	2	1	no	—
1413	C₂×C₄	—	2	1	no	—
1414	C₂×C₄	—	2	1	no	—
1415	C₂×C₄	—	2	1	no	—
1416	C₂×C₄	—	2	1	no	—
1417	C₂×C₄	—	2	1	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	2	1	no	—
1422	C₂×C₄	—	2	1	no	—
1423	C₂×C₄	—	4	4	no	—
1424	C₂×C₄	—	4	4	no	—
1425	C₂×C₄	—	4	4	no	—
1426	C₂×C₄	—	4	4	no	—
1427	C₂×C₄	—	4	4	no	—
1428	C₂×C₄	—	4	4	no	—
1429	C₂×C₄	—	8	2	no	—
1430	C₂×C₄	—	8	2	no	—
1431	C₂×C₄	—	8	2	no	—
1432	C₂×C₄	—	8	2	no	—
1433	C₂×C₄	—	8	2	no	—
1434	C₂×C₄	—	8	2	no	—
1435	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1436	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1437	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1438	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1439	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1440	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1441	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1442	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1443	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1444	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1445	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1446	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1447	C₂²	—	2	2	no	—
1448	C₂²	—	2	2	no	—
1449	C₂²	—	2	2	no	—
1450	C₂²	—	2	2	no	—
1451	C₂²	—	2	2	no	—
1452	C₂²	—	2	2	no	—
1453	C₂²	—	2	2	no	—
1454	C₂²	—	2	2	no	—
1455	C₂²	—	2	2	no	—
1456	C₂²	—	2	2	no	—
1457	C₂²	—	2	2	no	—
1458	C₂²	—	2	2	no	—
1459	C₂²	—	2	2	no	—
1460	C₂²	—	2	2	no	—
1461	C₂²	—	2	2	no	—
1462	C₂²	—	4	1	no	—
1463	C₂²	—	4	1	no	—
1464	C₂²	—	4	1	no	—
1465	C₂²	—	4	1	no	—
1466	C₂²	—	4	1	no	—
1467	C₂²	—	4	1	no	—
1468	C₂²	—	4	1	no	—
1469	C₂²	—	4	1	no	—
1470	C₂²	—	4	1	no	—
1471	C₂²	—	4	1	no	—
1472	C₂²	—	4	1	no	—
1473	C₂²	—	4	1	no	—
1474	C₂²	—	8	8	no	—
1475	C₂²	C₅₃×#520	1	4	yes	—
1476	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
1477	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1478	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1479	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1480	C₂²	C₅₃×#585	1	1	yes	characteristic
1481	C₂²	C₅₃×#585	1	1	yes	characteristic
1482	C₂²	C₅₃×#585	1	1	yes	characteristic
1483	C₄	—	2	2	no	—
1484	C₄	—	2	2	no	—
1485	C₄	—	2	2	no	—
1486	C₄	—	2	2	no	—
1487	C₄	—	2	2	no	—
1488	C₄	—	2	2	no	—
1489	C₄	—	2	2	no	—
1490	C₄	—	2	2	no	—
1491	C₄	—	2	2	no	—
1492	C₄	—	2	2	no	—
1493	C₄	—	2	2	no	—
1494	C₄	—	2	2	no	—
1495	C₄	—	4	1	no	—
1496	C₄	—	4	1	no	—
1497	C₄	—	4	1	no	—
1498	C₄	—	4	1	no	—
1499	C₄	—	4	1	no	—
1500	C₄	—	4	1	no	—
1501	C₄	—	4	1	no	—
1502	C₄	—	4	1	no	—
1503	C₄	—	4	1	no	—
1504	C₄	—	4	1	no	—
1505	C₄	—	4	1	no	—
1506	C₄	—	4	1	no	—
1507	C₄	—	4	1	no	—
1508	C₄	—	4	1	no	—
1509	C₄	—	4	1	no	—
1510	C₂	—	2	4	no	—
1511	C₂	—	4	2	no	—
1512	C₂	—	4	2	no	—
1513	C₂	—	4	2	no	—
1514	C₂	C₂×C₅₃×#520	1	1	yes	characteristic
1515	C₂	C₅₃×#3428	1	1	yes	characteristic
1516	C₂	C₄×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1517	C₂	C₅₃×#3535	1	1	yes	characteristic
1518	C₂	C₅₃×#3542	1	1	yes	characteristic
1519	C₂	C₅₃×#3545	1	1	yes	characteristic
1520	C₂	C₅₃×#3564	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×#120×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×#2379	C₂	semidirect
4. C₅₃×#2378	C₂	semidirect
5. C₅₃×#2376	C₂	semidirect
6. C₅₃×#2373	C₂	semidirect
7. C₅₃×#2368	C₂	semidirect
8. C₅₃×#2359	C₂	semidirect
9. C₅₃×#2359	C₂	semidirect
11. C₅₃×#2354	C₂	semidirect
12. C₅₃×#2349	C₂	semidirect
13. C₅₃×#2346	C₂	semidirect
14. C₅₃×#2343	C₂	semidirect
15. C₅₃×#2342	C₂	semidirect
16. C₅₃×#2342	C₂	semidirect
17. C₅₃×#2335	C₂	semidirect
18. C₅₃×#2335	C₂	semidirect
19. C₅₃×#2334	C₂	semidirect
20. C₅₃×#2334	C₂	semidirect
21. C₅₃×#2326	C₂	semidirect
22. C₅₃×#2323	C₂	semidirect
23. C₅₃×#2322	C₂	semidirect
25. C₅₃×#2318	C₂	semidirect
26. C₅₃×#2317	C₂	semidirect
27. C₅₃×#2315	C₂	semidirect
28. C₅₃×#2314	C₂	semidirect
29. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
30. C₅₃×#2290	C₂	semidirect
31. C₂×C₅₃×#388	C₂	semidirect
32. C₅₃×#551	C₄	semidirect
42. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
52. C₂×#117×C₅₃	C₂²	semidirect
60. C₅₃×#391	C₂²	semidirect
61. C₅₃×#391	C₂²	semidirect
62. C₅₃×#391	C₂²	semidirect
66. C₅₃×#389	C₂²	semidirect
67. C₅₃×#389	C₂²	semidirect
68. C₅₃×#389	C₂²	semidirect
69. C₅₃×#389	C₂²	semidirect
70. C₅₃×#389	C₂²	semidirect
71. C₅₃×#389	C₂²	semidirect
72. C₅₃×#389	C₂²	semidirect
73. C₅₃×#389	C₂²	semidirect
74. C₅₃×#389	C₂²	semidirect
75. C₅₃×#389	C₂²	semidirect
98. C₅₃×#388	C₂²	semidirect
99. C₅₃×#388	C₂²	semidirect
100. C₅₃×#388	C₂²	semidirect
101. C₅₃×#388	C₂²	semidirect
102. C₅₃×#388	C₂²	semidirect
103. C₅₃×#388	C₂²	semidirect
104. C₅₃×#387	C₂²	semidirect
105. C₅₃×#387	C₂²	semidirect
106. C₅₃×#387	C₂²	semidirect
107. C₅₃×#387	C₂²	semidirect
108. C₅₃×#387	C₂²	semidirect
109. C₅₃×#387	C₂²	semidirect
110. C₅₃×#387	C₂²	semidirect
111. C₅₃×#387	C₂²	semidirect
112. C₅₃×#387	C₂²	semidirect
113. C₅₃×#387	C₂²	semidirect
114. C₅₃×#387	C₂²	semidirect
115. C₅₃×#387	C₂²	semidirect
116. C₅₃×#387	C₂²	semidirect
117. C₅₃×#387	C₂²	semidirect
118. C₅₃×#387	C₂²	semidirect
119. C₅₃×#387	C₂²	semidirect
141. C₅₃×#385	C₂²	semidirect
142. C₅₃×#385	C₂²	semidirect
143. C₅₃×#385	C₂²	semidirect
144. C₅₃×#385	C₂²	semidirect
145. C₅₃×#385	C₂²	semidirect
146. C₅₃×#384	C₂²	semidirect
147. C₅₃×#384	C₂²	semidirect
148. C₅₃×#383	C₂²	semidirect
149. C₅₃×#382	C₂²	semidirect
150. C₅₃×#382	C₂²	semidirect
151. C₅₃×#382	C₂²	semidirect
152. C₅₃×#382	C₂²	semidirect
161. C₅₃×#380	C₂²	semidirect
163. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
164. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
165. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
166. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
167. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
168. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
169. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
170. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
171. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
181. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
182. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
183. C₅₃×#376	C₂²	semidirect
184. C₅₃×#376	C₂²	semidirect
187. C₂×#95×C₅₃	C₂²	semidirect
206. #126×C₅₃	C₂×C₄	semidirect
207. #126×C₅₃	C₂×C₄	semidirect
208. #124×C₅₃	C₂×C₄	semidirect
209. #123×C₅₃	C₂×C₄	semidirect
210. #123×C₅₃	C₂×C₄	semidirect
211. #123×C₅₃	C₂×C₄	semidirect
212. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
213. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
219. C₄×D₄×C₅₃	C₂×C₄	semidirect
220. C₄×D₄×C₅₃	C₂×C₄	semidirect
224. #117×C₅₃	C₂×C₄	semidirect
225. #117×C₅₃	C₂×C₄	semidirect
264. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
265. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
686. #34479	C₅₃	direct (N × H)
751. #2383	C₂×C₅₃	semidirect
752. #2379	C₂×C₅₃	semidirect
753. #2378	C₂×C₅₃	semidirect
754. #2376	C₂×C₅₃	semidirect
755. #2373	C₂×C₅₃	semidirect
756. #2368	C₂×C₅₃	semidirect
757. #2359	C₂×C₅₃	semidirect
758. #2359	C₂×C₅₃	semidirect
760. #2354	C₂×C₅₃	semidirect
761. #2349	C₂×C₅₃	semidirect
762. #2346	C₂×C₅₃	semidirect
763. #2343	C₂×C₅₃	semidirect
764. #2342	C₂×C₅₃	semidirect
765. #2342	C₂×C₅₃	semidirect
766. #2335	C₂×C₅₃	semidirect
767. #2335	C₂×C₅₃	semidirect
768. #2334	C₂×C₅₃	semidirect
769. #2334	C₂×C₅₃	semidirect
770. #2326	C₂×C₅₃	semidirect
771. #2323	C₂×C₅₃	semidirect
772. #2322	C₂×C₅₃	semidirect
774. #2318	C₂×C₅₃	semidirect
775. #2317	C₂×C₅₃	semidirect
776. #2315	C₂×C₅₃	semidirect
777. #2314	C₂×C₅₃	semidirect
778. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
779. #2290	C₂×C₅₃	semidirect
780. C₂×#388	C₂×C₅₃	semidirect
792. #551	C₄×C₅₃	semidirect
802. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
812. C₂×#117	C₂²×C₅₃	semidirect
820. #391	C₂²×C₅₃	semidirect
821. #391	C₂²×C₅₃	semidirect
822. #391	C₂²×C₅₃	semidirect
826. #389	C₂²×C₅₃	semidirect
827. #389	C₂²×C₅₃	semidirect
828. #389	C₂²×C₅₃	semidirect
829. #389	C₂²×C₅₃	semidirect
830. #389	C₂²×C₅₃	semidirect
831. #389	C₂²×C₅₃	semidirect
832. #389	C₂²×C₅₃	semidirect
833. #389	C₂²×C₅₃	semidirect
834. #389	C₂²×C₅₃	semidirect
835. #389	C₂²×C₅₃	semidirect
858. #388	C₂²×C₅₃	semidirect
859. #388	C₂²×C₅₃	semidirect
860. #388	C₂²×C₅₃	semidirect
861. #388	C₂²×C₅₃	semidirect
862. #388	C₂²×C₅₃	semidirect
863. #388	C₂²×C₅₃	semidirect
864. #387	C₂²×C₅₃	semidirect
865. #387	C₂²×C₅₃	semidirect
866. #387	C₂²×C₅₃	semidirect
867. #387	C₂²×C₅₃	semidirect
868. #387	C₂²×C₅₃	semidirect
869. #387	C₂²×C₅₃	semidirect
870. #387	C₂²×C₅₃	semidirect
871. #387	C₂²×C₅₃	semidirect
872. #387	C₂²×C₅₃	semidirect
873. #387	C₂²×C₅₃	semidirect
874. #387	C₂²×C₅₃	semidirect
875. #387	C₂²×C₅₃	semidirect
876. #387	C₂²×C₅₃	semidirect
877. #387	C₂²×C₅₃	semidirect
878. #387	C₂²×C₅₃	semidirect
879. #387	C₂²×C₅₃	semidirect
901. #385	C₂²×C₅₃	semidirect
902. #385	C₂²×C₅₃	semidirect
903. #385	C₂²×C₅₃	semidirect
904. #385	C₂²×C₅₃	semidirect
905. #385	C₂²×C₅₃	semidirect
906. #384	C₂²×C₅₃	semidirect
907. #384	C₂²×C₅₃	semidirect
908. #383	C₂²×C₅₃	semidirect
909. #382	C₂²×C₅₃	semidirect
910. #382	C₂²×C₅₃	semidirect
911. #382	C₂²×C₅₃	semidirect
912. #382	C₂²×C₅₃	semidirect
921. #380	C₂²×C₅₃	semidirect
923. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
924. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
925. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
926. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
927. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
928. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
929. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
930. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
931. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
941. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
942. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
943. #376	C₂²×C₅₃	semidirect
944. #376	C₂²×C₅₃	semidirect
947. C₂×#95	C₂²×C₅₃	semidirect
948. C₅₃	#34479	direct (N × H)
967. #126	C₂×C₄×C₅₃	semidirect
968. #126	C₂×C₄×C₅₃	semidirect
969. #124	C₂×C₄×C₅₃	semidirect
970. #123	C₂×C₄×C₅₃	semidirect
971. #123	C₂×C₄×C₅₃	semidirect
972. #123	C₂×C₄×C₅₃	semidirect
973. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
974. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
980. C₄×D₄	C₂×C₄×C₅₃	semidirect
981. C₄×D₄	C₂×C₄×C₅₃	semidirect
985. #117	C₂×C₄×C₅₃	semidirect
986. #117	C₂×C₄×C₅₃	semidirect
1025. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
1026. C₂×C₂²⋊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×#551	2
C₅₃×#2383	2
C₅₃×#2379	2
C₅₃×#2378	2
C₅₃×#2376	2
C₅₃×#2373	2
C₅₃×#2368	2
C₅₃×#2359	2
C₅₃×#2358	2
C₅₃×#2354	2
C₅₃×#2349	2
C₅₃×#2346	2
C₅₃×#2343	2
C₅₃×#2342	2
C₅₃×#2335	2
C₅₃×#2334	2
C₅₃×#2326	2
C₅₃×#2323	2
C₅₃×#2322	2
C₅₃×#2321	2
C₅₃×#2318	2
C₅₃×#2317	2
C₅₃×#2315	2
C₅₃×#2314	2
C₄×C₂²⋊Q₈×C₅₃	2
C₅₃×#2290	2
C₂×C₅₃×#388	2
#34479	53

Subgroups — C53×#34479 #27241991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34479 #27241991