Subgroups — C₅₃×#35069 #27242581

Order 13568.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2865	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2864	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2852	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2655	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2652	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2650	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2649	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2588	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2587	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2576	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2575	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2530	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2505	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2493	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2488	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2481	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2478	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2477	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2449	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2444	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#2425	C₂	1	1	yes	maximal, characteristic
24	C₅₃×#2419	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2325	C₂	1	1	yes	maximal, characteristic
27	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#401	C₂²	1	1	yes	characteristic
48	C₅₃×#400	C₂²	1	1	yes	characteristic
49	C₅₃×#400	C₂²	1	1	yes	characteristic
50	C₅₃×#400	C₂²	1	1	yes	characteristic
51	C₅₃×#400	C₂²	1	1	yes	characteristic
52	C₅₃×#400	C₂²	1	1	yes	characteristic
53	C₅₃×#400	C₂²	1	1	yes	characteristic
54	C₅₃×#400	C₂²	1	1	yes	characteristic
55	C₅₃×#400	C₂²	1	1	yes	characteristic
56	C₅₃×#400	C₂²	1	1	yes	characteristic
57	C₅₃×#400	C₂²	1	1	yes	characteristic
58	C₅₃×#400	C₂²	1	1	yes	characteristic
59	C₅₃×#400	C₂²	1	1	yes	characteristic
60	C₅₃×#399	C₂²	1	1	yes	characteristic
61	C₅₃×#398	C₂²	1	1	yes	characteristic
62	C₅₃×#398	C₂²	1	1	yes	characteristic
63	C₅₃×#398	C₂²	1	1	yes	characteristic
64	C₅₃×#398	C₂²	1	1	yes	characteristic
65	C₅₃×#397	C₂²	1	1	yes	characteristic
66	C₅₃×#397	C₂²	1	1	yes	characteristic
67	C₅₃×#397	C₂²	1	1	yes	characteristic
68	C₅₃×#397	C₂²	1	1	yes	characteristic
69	C₅₃×#397	C₂²	1	1	yes	characteristic
70	C₅₃×#397	C₂²	1	1	yes	characteristic
71	C₅₃×#397	C₂²	1	1	yes	characteristic
72	C₅₃×#396	C₂²	1	1	yes	characteristic
73	C₅₃×#396	C₂²	1	1	yes	characteristic
74	C₅₃×#396	C₂²	1	1	yes	characteristic
75	C₅₃×#395	C₂²	1	1	yes	characteristic
76	C₅₃×#394	C₂²	1	1	yes	characteristic
77	C₅₃×#394	C₂²	1	1	yes	characteristic
78	C₅₃×#393	C₂²	1	1	yes	characteristic
79	C₅₃×#391	C₂²	1	1	yes	characteristic
80	C₅₃×#391	C₂²	1	1	yes	characteristic
81	C₅₃×#391	C₂²	1	1	yes	characteristic
82	C₅₃×#389	C₂²	1	1	yes	characteristic
83	C₅₃×#389	C₂²	1	1	yes	characteristic
84	C₅₃×#389	C₂²	1	1	yes	characteristic
85	C₅₃×#389	C₂²	1	1	yes	characteristic
86	C₅₃×#389	C₂²	1	1	yes	characteristic
87	C₅₃×#389	C₂²	1	1	yes	characteristic
88	C₅₃×#389	C₂²	1	1	yes	characteristic
89	C₅₃×#389	C₂²	1	1	yes	characteristic
90	C₅₃×#389	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×#388	C₂²	1	1	yes	characteristic
101	C₅₃×#388	C₂²	1	1	yes	characteristic
102	C₅₃×#388	C₂²	1	1	yes	characteristic
103	C₅₃×#388	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×#387	C₂²	1	1	yes	characteristic
129	C₅₃×#387	C₂²	1	1	yes	characteristic
130	C₅₃×#387	C₂²	1	1	yes	characteristic
131	C₅₃×#387	C₂²	1	1	yes	characteristic
132	C₅₃×#387	C₂²	1	1	yes	characteristic
133	C₅₃×#387	C₂²	1	1	yes	characteristic
134	C₅₃×#387	C₂²	1	1	yes	characteristic
135	C₅₃×#386	C₂²	1	1	yes	characteristic
136	C₅₃×#386	C₂²	1	1	yes	characteristic
137	C₅₃×#386	C₂²	1	1	yes	characteristic
138	C₅₃×#386	C₂²	1	1	yes	characteristic
139	C₅₃×#386	C₂²	1	1	yes	characteristic
140	C₅₃×#386	C₂²	1	1	yes	characteristic
141	C₅₃×#386	C₂²	1	1	yes	characteristic
142	C₅₃×#386	C₂²	1	1	yes	characteristic
143	C₅₃×#386	C₂²	1	1	yes	characteristic
144	C₅₃×#386	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×#385	C₂²	1	1	yes	characteristic
149	C₅₃×#385	C₂²	1	1	yes	characteristic
150	C₅₃×#385	C₂²	1	1	yes	characteristic
151	C₅₃×#385	C₂²	1	1	yes	characteristic
152	C₅₃×#385	C₂²	1	1	yes	characteristic
153	C₅₃×#385	C₂²	1	1	yes	characteristic
154	C₅₃×#385	C₂²	1	1	yes	characteristic
155	C₅₃×#385	C₂²	1	1	yes	characteristic
156	C₅₃×#385	C₂²	1	1	yes	characteristic
157	C₅₃×#385	C₂²	1	1	yes	characteristic
158	C₅₃×#385	C₂²	1	1	yes	characteristic
159	C₅₃×#383	C₂²	1	1	yes	characteristic
160	C₅₃×#382	C₂²	1	1	yes	characteristic
161	C₅₃×#382	C₂²	1	1	yes	characteristic
162	C₅₃×#381	C₂²	1	1	yes	characteristic
163	C₅₃×#381	C₂²	1	1	yes	characteristic
164	C₅₃×#381	C₂²	1	1	yes	characteristic
165	C₅₃×#381	C₂²	1	1	yes	characteristic
166	C₅₃×#380	C₂²	1	1	yes	characteristic
167	C₅₃×#380	C₂²	1	1	yes	characteristic
168	C₅₃×#380	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×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
172	C₄×C₄⋊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	C₅₃×#376	C₂²	1	1	yes	characteristic
182	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
183	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
184	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
185	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
186	C₄³×C₅₃	C₂²	1	1	yes	characteristic
187	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×D₄×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	C₂³×C₄×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	#126×C₅₃	—	4	2	no	—
203	#123×C₅₃	—	2	4	no	—
204	#123×C₅₃	—	2	4	no	—
205	C₂²⋊Q₈×C₅₃	—	2	4	no	—
206	C₂²⋊Q₈×C₅₃	—	4	2	no	—
207	#121×C₅₃	—	2	4	no	—
208	C₄×D₄×C₅₃	—	2	4	no	—
209	C₄×D₄×C₅₃	—	2	4	no	—
210	C₄×D₄×C₅₃	—	2	4	no	—
211	C₄×D₄×C₅₃	—	2	4	no	—
212	#117×C₅₃	—	4	2	no	—
213	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
214	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
215	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₄²×C₅₃	—	4	2	no	—
280	C₂×C₄²×C₅₃	—	4	2	no	—
281	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
297	#95×C₅₃	C₂³	1	1	yes	characteristic
298	#95×C₅₃	C₂³	1	1	yes	characteristic
299	#95×C₅₃	C₂³	1	1	yes	characteristic
300	#95×C₅₃	C₂³	1	1	yes	characteristic
301	#95×C₅₃	C₂³	1	1	yes	characteristic
302	#95×C₅₃	C₂³	1	1	yes	characteristic
303	#95×C₅₃	C₂³	1	1	yes	characteristic
304	#95×C₅₃	C₂³	1	1	yes	characteristic
305	#95×C₅₃	C₂³	1	1	yes	characteristic
306	#95×C₅₃	C₂³	1	1	yes	characteristic
307	#95×C₅₃	C₂³	1	1	yes	characteristic
308	#95×C₅₃	C₂³	1	1	yes	characteristic
309	#95×C₅₃	C₂³	1	1	yes	characteristic
310	#95×C₅₃	C₂³	1	1	yes	characteristic
311	#95×C₅₃	C₂³	1	1	yes	characteristic
312	#95×C₅₃	C₂³	1	1	yes	characteristic
313	#95×C₅₃	C₂³	1	1	yes	characteristic
314	#95×C₅₃	C₂³	1	1	yes	characteristic
315	#95×C₅₃	C₂³	1	1	yes	characteristic
316	#95×C₅₃	C₂³	1	1	yes	characteristic
317	#95×C₅₃	C₂³	1	1	yes	characteristic
318	#95×C₅₃	C₂³	1	1	yes	characteristic
319	#95×C₅₃	C₂³	1	1	yes	characteristic
320	#95×C₅₃	C₂³	1	1	yes	characteristic
321	#95×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	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂×Q₈×C₅₃	—	2	2	no	—
361	C₂×Q₈×C₅₃	—	4	1	no	—
362	C₂×Q₈×C₅₃	—	4	1	no	—
363	C₂×D₄×C₅₃	—	2	2	no	—
364	C₂×D₄×C₅₃	—	2	2	no	—
365	C₂×D₄×C₅₃	—	2	2	no	—
366	C₂×D₄×C₅₃	—	2	2	no	—
367	C₂×D₄×C₅₃	—	2	2	no	—
368	C₂×D₄×C₅₃	—	2	2	no	—
369	C₂×D₄×C₅₃	—	4	1	no	—
370	C₂×D₄×C₅₃	—	4	1	no	—
371	C₂×D₄×C₅₃	#41	1	4	yes	—
372	C₂²×C₄×C₅₃	—	2	2	no	—
373	C₂²×C₄×C₅₃	—	2	2	no	—
374	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	2	2	no	—
376	C₂²×C₄×C₅₃	—	2	2	no	—
377	C₂²×C₄×C₅₃	—	2	2	no	—
378	C₂²×C₄×C₅₃	—	2	2	no	—
379	C₂²×C₄×C₅₃	—	2	2	no	—
380	C₂²×C₄×C₅₃	—	2	2	no	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	—	2	2	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
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	—	4	1	no	—
389	C₂²×C₄×C₅₃	—	4	1	no	—
390	C₂²×C₄×C₅₃	—	4	1	no	—
391	C₂²×C₄×C₅₃	—	4	1	no	—
392	C₂²×C₄×C₅₃	—	4	1	no	—
393	C₂²×C₄×C₅₃	—	4	1	no	—
394	C₂²×C₄×C₅₃	—	4	1	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	#41	1	4	yes	—
405	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₅₃	—	2	2	no	—
434	C₄⋊C₄×C₅₃	—	2	2	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	—	2	2	no	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	—	2	2	no	—
440	C₄⋊C₄×C₅₃	—	2	2	no	—
441	C₄⋊C₄×C₅₃	—	2	2	no	—
442	C₄⋊C₄×C₅₃	—	2	2	no	—
443	C₄⋊C₄×C₅₃	—	2	2	no	—
444	C₄⋊C₄×C₅₃	—	2	2	no	—
445	C₄⋊C₄×C₅₃	—	2	2	no	—
446	C₄⋊C₄×C₅₃	—	2	2	no	—
447	C₄⋊C₄×C₅₃	—	2	2	no	—
448	C₄⋊C₄×C₅₃	—	2	2	no	—
449	C₄⋊C₄×C₅₃	—	2	2	no	—
450	C₄⋊C₄×C₅₃	—	2	2	no	—
451	C₄⋊C₄×C₅₃	—	2	2	no	—
452	C₄⋊C₄×C₅₃	—	2	2	no	—
453	C₄⋊C₄×C₅₃	—	4	1	no	—
454	C₄⋊C₄×C₅₃	—	4	1	no	—
455	C₄⋊C₄×C₅₃	—	4	1	no	—
456	C₄⋊C₄×C₅₃	—	4	1	no	—
457	C₄⋊C₄×C₅₃	—	4	1	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	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	2	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	2	2	no	—
474	C₂²⋊C₄×C₅₃	—	2	2	no	—
475	C₂²⋊C₄×C₅₃	—	2	2	no	—
476	C₂²⋊C₄×C₅₃	—	2	2	no	—
477	C₂²⋊C₄×C₅₃	—	2	2	no	—
478	C₂²⋊C₄×C₅₃	—	2	2	no	—
479	C₂²⋊C₄×C₅₃	—	2	2	no	—
480	C₂²⋊C₄×C₅₃	—	2	2	no	—
481	C₂²⋊C₄×C₅₃	—	2	2	no	—
482	C₂²⋊C₄×C₅₃	—	2	2	no	—
483	C₂²⋊C₄×C₅₃	—	2	2	no	—
484	C₂²⋊C₄×C₅₃	—	2	2	no	—
485	C₂²⋊C₄×C₅₃	—	2	2	no	—
486	C₂²⋊C₄×C₅₃	—	4	1	no	—
487	C₂²⋊C₄×C₅₃	—	4	1	no	—
488	C₂²⋊C₄×C₅₃	—	4	1	no	—
489	C₂²⋊C₄×C₅₃	—	4	1	no	—
490	C₂²⋊C₄×C₅₃	—	4	1	no	—
491	C₂²⋊C₄×C₅₃	—	4	1	no	—
492	C₂²⋊C₄×C₅₃	—	4	1	no	—
493	C₂²⋊C₄×C₅₃	—	4	1	no	—
494	C₂²⋊C₄×C₅₃	—	4	1	no	—
495	C₂²⋊C₄×C₅₃	—	4	1	no	—
496	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
497	C₄²×C₅₃	—	2	2	no	—
498	C₄²×C₅₃	—	2	2	no	—
499	C₄²×C₅₃	—	2	2	no	—
500	C₄²×C₅₃	—	2	2	no	—
501	C₄²×C₅₃	—	2	2	no	—
502	C₄²×C₅₃	—	2	2	no	—
503	C₄²×C₅₃	—	2	2	no	—
504	C₄²×C₅₃	—	2	2	no	—
505	C₄²×C₅₃	—	4	1	no	—
506	C₄²×C₅₃	—	4	1	no	—
507	C₄²×C₅₃	—	4	1	no	—
508	C₄²×C₅₃	—	4	1	no	—
509	C₄²×C₅₃	—	4	1	no	—
510	C₄²×C₅₃	—	4	1	no	—
511	C₄²×C₅₃	—	4	1	no	—
512	C₄²×C₅₃	—	4	1	no	—
513	C₂³×C₅₃	—	2	1	no	—
514	C₂³×C₅₃	—	2	1	no	—
515	C₂³×C₅₃	—	2	1	no	—
516	C₂³×C₅₃	—	2	1	no	—
517	C₂³×C₅₃	—	2	1	no	—
518	C₂³×C₅₃	—	2	1	no	—
519	C₂³×C₅₃	—	2	1	no	—
520	C₂³×C₅₃	—	2	1	no	—
521	C₂³×C₅₃	—	2	1	no	—
522	C₂³×C₅₃	—	2	1	no	—
523	C₂³×C₅₃	—	2	1	no	—
524	C₂³×C₅₃	—	2	1	no	—
525	C₂³×C₅₃	—	2	1	no	—
526	C₂³×C₅₃	—	2	1	no	—
527	C₂³×C₅₃	—	2	1	no	—
528	C₂³×C₅₃	—	2	1	no	—
529	C₂³×C₅₃	—	2	1	no	—
530	C₂³×C₅₃	C₂×#41	1	2	yes	—
531	C₂³×C₅₃	C₂×#41	1	2	yes	—
532	C₂³×C₅₃	C₂×#41	1	2	yes	—
533	C₂³×C₅₃	C₂×#41	1	2	yes	—
534	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
535	Q₈×C₅₃	—	8	2	no	—
536	D₄×C₅₃	—	2	8	no	—
537	D₄×C₅₃	—	4	4	no	—
538	D₄×C₅₃	—	8	2	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	1	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	—	4	4	no	—
617	C₂×C₄×C₅₃	—	4	4	no	—
618	C₂×C₄×C₅₃	—	4	4	no	—
619	C₂×C₄×C₅₃	—	4	4	no	—
620	C₂×C₄×C₅₃	—	4	4	no	—
621	C₂×C₄×C₅₃	—	4	4	no	—
622	C₂×C₄×C₅₃	—	4	4	no	—
623	C₂×C₄×C₅₃	—	4	4	no	—
624	C₂×C₄×C₅₃	—	4	4	no	—
625	C₂×C₄×C₅₃	—	8	2	no	—
626	C₂×C₄×C₅₃	—	8	2	no	—
627	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
628	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
629	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
630	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
631	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
632	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
633	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
634	#35069	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
635	C₂²×C₅₃	—	2	2	no	—
636	C₂²×C₅₃	—	2	2	no	—
637	C₂²×C₅₃	—	2	2	no	—
638	C₂²×C₅₃	—	2	2	no	—
639	C₂²×C₅₃	—	2	2	no	—
640	C₂²×C₅₃	—	2	2	no	—
641	C₂²×C₅₃	—	2	2	no	—
642	C₂²×C₅₃	—	2	2	no	—
643	C₂²×C₅₃	—	2	2	no	—
644	C₂²×C₅₃	—	4	1	no	—
645	C₂²×C₅₃	—	4	1	no	—
646	C₂²×C₅₃	—	4	1	no	—
647	C₂²×C₅₃	—	4	1	no	—
648	C₂²×C₅₃	—	4	1	no	—
649	C₂²×C₅₃	—	4	1	no	—
650	C₂²×C₅₃	—	4	1	no	—
651	C₂²×C₅₃	—	4	1	no	—
652	C₂²×C₅₃	—	4	1	no	—
653	C₂²×C₅₃	—	4	1	no	—
654	C₂²×C₅₃	—	4	1	no	—
655	C₂²×C₅₃	#529	1	4	yes	—
656	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
657	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
658	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
659	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
660	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
661	C₂²×C₅₃	#585	1	1	yes	characteristic
662	C₂²×C₅₃	#585	1	1	yes	characteristic
663	C₄×C₅₃	—	2	2	no	—
664	C₄×C₅₃	—	2	2	no	—
665	C₄×C₅₃	—	2	2	no	—
666	C₄×C₅₃	—	2	2	no	—
667	C₄×C₅₃	—	2	2	no	—
668	C₄×C₅₃	—	2	2	no	—
669	C₄×C₅₃	—	2	2	no	—
670	C₄×C₅₃	—	4	1	no	—
671	C₄×C₅₃	—	4	1	no	—
672	C₄×C₅₃	—	4	1	no	—
673	C₄×C₅₃	—	4	1	no	—
674	C₄×C₅₃	—	4	1	no	—
675	C₄×C₅₃	—	4	1	no	—
676	C₄×C₅₃	—	4	1	no	—
677	C₄×C₅₃	—	4	1	no	—
678	C₄×C₅₃	—	4	1	no	—
679	C₄×C₅₃	—	4	1	no	—
680	C₄×C₅₃	—	4	1	no	—
681	C₄×C₅₃	—	4	1	no	—
682	C₄×C₅₃	—	4	1	no	—
683	C₄×C₅₃	—	4	1	no	—
684	C₄×C₅₃	—	4	1	no	—
685	C₄×C₅₃	—	4	1	no	—
686	C₄×C₅₃	—	4	1	no	—
687	C₄×C₅₃	—	4	1	no	—
688	C₄×C₅₃	—	4	1	no	—
689	C₄×C₅₃	—	4	1	no	—
690	C₄×C₅₃	—	4	1	no	—
691	#2865	C₂×C₅₃	1	1	yes	characteristic, complemented
692	#2864	C₂×C₅₃	1	1	yes	characteristic, complemented
693	#2855	C₂×C₅₃	1	1	yes	characteristic, complemented
694	#2852	C₂×C₅₃	1	1	yes	characteristic, complemented
695	#2655	C₂×C₅₃	1	1	yes	characteristic, complemented
696	#2652	C₂×C₅₃	1	1	yes	characteristic, complemented
697	#2650	C₂×C₅₃	1	1	yes	characteristic, complemented
698	#2649	C₂×C₅₃	1	1	yes	characteristic, complemented
699	#2588	C₂×C₅₃	1	1	yes	characteristic, complemented
700	#2587	C₂×C₅₃	1	1	yes	characteristic, complemented
701	#2576	C₂×C₅₃	1	1	yes	characteristic, complemented
702	#2575	C₂×C₅₃	1	1	yes	characteristic, complemented
703	#2533	C₂×C₅₃	1	1	yes	characteristic, complemented
704	#2530	C₂×C₅₃	1	1	yes	characteristic, complemented
705	#2505	C₂×C₅₃	1	1	yes	characteristic, complemented
706	#2493	C₂×C₅₃	1	1	yes	characteristic, complemented
707	#2488	C₂×C₅₃	1	1	yes	characteristic, complemented
708	#2481	C₂×C₅₃	1	1	yes	characteristic, complemented
709	#2478	C₂×C₅₃	1	1	yes	characteristic, complemented
710	#2477	C₂×C₅₃	1	1	yes	characteristic, complemented
711	#2449	C₂×C₅₃	1	1	yes	characteristic, complemented
712	#2444	C₂×C₅₃	1	1	yes	characteristic
713	#2425	C₂×C₅₃	1	1	yes	characteristic
714	#2419	C₂×C₅₃	1	1	yes	characteristic, complemented
715	#2329	C₂×C₅₃	1	1	yes	characteristic, complemented
716	#2325	C₂×C₅₃	1	1	yes	characteristic
717	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
718	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
719	#2290	C₂×C₅₃	1	1	yes	characteristic, complemented
720	C₂×#387	C₂×C₅₃	1	1	yes	characteristic, complemented
721	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
722	C₂×C₅₃	—	2	4	no	—
723	C₂×C₅₃	—	4	2	no	—
724	C₂×C₅₃	—	8	1	no	—
725	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
726	C₂×C₅₃	#3459	1	1	yes	characteristic
727	C₂×C₅₃	#3461	1	1	yes	characteristic
728	C₂×C₅₃	#3513	1	1	yes	characteristic
729	C₂×C₅₃	#3515	1	1	yes	characteristic
730	C₂×C₅₃	#3520	1	1	yes	characteristic
731	C₂×C₅₃	#3521	1	1	yes	characteristic
732	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
733	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
734	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
735	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
736	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
737	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
738	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
739	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
740	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
741	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
742	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
743	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
744	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
745	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
746	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
747	#401	C₂²×C₅₃	1	1	yes	characteristic
748	#400	C₂²×C₅₃	1	1	yes	characteristic
749	#400	C₂²×C₅₃	1	1	yes	characteristic
750	#400	C₂²×C₅₃	1	1	yes	characteristic
751	#400	C₂²×C₅₃	1	1	yes	characteristic
752	#400	C₂²×C₅₃	1	1	yes	characteristic
753	#400	C₂²×C₅₃	1	1	yes	characteristic
754	#400	C₂²×C₅₃	1	1	yes	characteristic
755	#400	C₂²×C₅₃	1	1	yes	characteristic
756	#400	C₂²×C₅₃	1	1	yes	characteristic
757	#400	C₂²×C₅₃	1	1	yes	characteristic
758	#400	C₂²×C₅₃	1	1	yes	characteristic
759	#400	C₂²×C₅₃	1	1	yes	characteristic
760	#399	C₂²×C₅₃	1	1	yes	characteristic
761	#398	C₂²×C₅₃	1	1	yes	characteristic
762	#398	C₂²×C₅₃	1	1	yes	characteristic
763	#398	C₂²×C₅₃	1	1	yes	characteristic
764	#398	C₂²×C₅₃	1	1	yes	characteristic
765	#397	C₂²×C₅₃	1	1	yes	characteristic
766	#397	C₂²×C₅₃	1	1	yes	characteristic
767	#397	C₂²×C₅₃	1	1	yes	characteristic
768	#397	C₂²×C₅₃	1	1	yes	characteristic
769	#397	C₂²×C₅₃	1	1	yes	characteristic
770	#397	C₂²×C₅₃	1	1	yes	characteristic
771	#397	C₂²×C₅₃	1	1	yes	characteristic
772	#396	C₂²×C₅₃	1	1	yes	characteristic
773	#396	C₂²×C₅₃	1	1	yes	characteristic
774	#396	C₂²×C₅₃	1	1	yes	characteristic
775	#395	C₂²×C₅₃	1	1	yes	characteristic
776	#394	C₂²×C₅₃	1	1	yes	characteristic
777	#394	C₂²×C₅₃	1	1	yes	characteristic
778	#393	C₂²×C₅₃	1	1	yes	characteristic
779	#391	C₂²×C₅₃	1	1	yes	characteristic
780	#391	C₂²×C₅₃	1	1	yes	characteristic
781	#391	C₂²×C₅₃	1	1	yes	characteristic
782	#389	C₂²×C₅₃	1	1	yes	characteristic
783	#389	C₂²×C₅₃	1	1	yes	characteristic
784	#389	C₂²×C₅₃	1	1	yes	characteristic
785	#389	C₂²×C₅₃	1	1	yes	characteristic
786	#389	C₂²×C₅₃	1	1	yes	characteristic
787	#389	C₂²×C₅₃	1	1	yes	characteristic
788	#389	C₂²×C₅₃	1	1	yes	characteristic
789	#389	C₂²×C₅₃	1	1	yes	characteristic
790	#389	C₂²×C₅₃	1	1	yes	characteristic
791	#388	C₂²×C₅₃	1	1	yes	characteristic
792	#388	C₂²×C₅₃	1	1	yes	characteristic
793	#388	C₂²×C₅₃	1	1	yes	characteristic
794	#388	C₂²×C₅₃	1	1	yes	characteristic
795	#388	C₂²×C₅₃	1	1	yes	characteristic
796	#388	C₂²×C₅₃	1	1	yes	characteristic
797	#388	C₂²×C₅₃	1	1	yes	characteristic
798	#388	C₂²×C₅₃	1	1	yes	characteristic
799	#388	C₂²×C₅₃	1	1	yes	characteristic
800	#388	C₂²×C₅₃	1	1	yes	characteristic
801	#388	C₂²×C₅₃	1	1	yes	characteristic
802	#388	C₂²×C₅₃	1	1	yes	characteristic
803	#388	C₂²×C₅₃	1	1	yes	characteristic
804	#387	C₂²×C₅₃	1	1	yes	characteristic
805	#387	C₂²×C₅₃	1	1	yes	characteristic
806	#387	C₂²×C₅₃	1	1	yes	characteristic
807	#387	C₂²×C₅₃	1	1	yes	characteristic
808	#387	C₂²×C₅₃	1	1	yes	characteristic
809	#387	C₂²×C₅₃	1	1	yes	characteristic
810	#387	C₂²×C₅₃	1	1	yes	characteristic
811	#387	C₂²×C₅₃	1	1	yes	characteristic
812	#387	C₂²×C₅₃	1	1	yes	characteristic
813	#387	C₂²×C₅₃	1	1	yes	characteristic
814	#387	C₂²×C₅₃	1	1	yes	characteristic
815	#387	C₂²×C₅₃	1	1	yes	characteristic
816	#387	C₂²×C₅₃	1	1	yes	characteristic
817	#387	C₂²×C₅₃	1	1	yes	characteristic
818	#387	C₂²×C₅₃	1	1	yes	characteristic
819	#387	C₂²×C₅₃	1	1	yes	characteristic
820	#387	C₂²×C₅₃	1	1	yes	characteristic
821	#387	C₂²×C₅₃	1	1	yes	characteristic
822	#387	C₂²×C₅₃	1	1	yes	characteristic
823	#387	C₂²×C₅₃	1	1	yes	characteristic
824	#387	C₂²×C₅₃	1	1	yes	characteristic
825	#387	C₂²×C₅₃	1	1	yes	characteristic
826	#387	C₂²×C₅₃	1	1	yes	characteristic
827	#387	C₂²×C₅₃	1	1	yes	characteristic
828	#387	C₂²×C₅₃	1	1	yes	characteristic
829	#387	C₂²×C₅₃	1	1	yes	characteristic
830	#387	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	#386	C₂²×C₅₃	1	1	yes	characteristic
836	#386	C₂²×C₅₃	1	1	yes	characteristic
837	#386	C₂²×C₅₃	1	1	yes	characteristic
838	#386	C₂²×C₅₃	1	1	yes	characteristic
839	#386	C₂²×C₅₃	1	1	yes	characteristic
840	#386	C₂²×C₅₃	1	1	yes	characteristic
841	#386	C₂²×C₅₃	1	1	yes	characteristic
842	#386	C₂²×C₅₃	1	1	yes	characteristic
843	#386	C₂²×C₅₃	1	1	yes	characteristic
844	#386	C₂²×C₅₃	1	1	yes	characteristic
845	#385	C₂²×C₅₃	1	1	yes	characteristic
846	#385	C₂²×C₅₃	1	1	yes	characteristic
847	#385	C₂²×C₅₃	1	1	yes	characteristic
848	#385	C₂²×C₅₃	1	1	yes	characteristic
849	#385	C₂²×C₅₃	1	1	yes	characteristic
850	#385	C₂²×C₅₃	1	1	yes	characteristic
851	#385	C₂²×C₅₃	1	1	yes	characteristic
852	#385	C₂²×C₅₃	1	1	yes	characteristic
853	#385	C₂²×C₅₃	1	1	yes	characteristic
854	#385	C₂²×C₅₃	1	1	yes	characteristic
855	#385	C₂²×C₅₃	1	1	yes	characteristic
856	#385	C₂²×C₅₃	1	1	yes	characteristic
857	#385	C₂²×C₅₃	1	1	yes	characteristic
858	#385	C₂²×C₅₃	1	1	yes	characteristic
859	#383	C₂²×C₅₃	1	1	yes	characteristic
860	#382	C₂²×C₅₃	1	1	yes	characteristic
861	#382	C₂²×C₅₃	1	1	yes	characteristic
862	#381	C₂²×C₅₃	1	1	yes	characteristic
863	#381	C₂²×C₅₃	1	1	yes	characteristic
864	#381	C₂²×C₅₃	1	1	yes	characteristic
865	#381	C₂²×C₅₃	1	1	yes	characteristic
866	#380	C₂²×C₅₃	1	1	yes	characteristic
867	#380	C₂²×C₅₃	1	1	yes	characteristic
868	#380	C₂²×C₅₃	1	1	yes	characteristic
869	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
870	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
871	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
872	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
873	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
874	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
875	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
876	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
877	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
878	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
879	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
880	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
881	#376	C₂²×C₅₃	1	1	yes	characteristic
882	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
883	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
884	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
885	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
886	C₄³	C₂²×C₅₃	1	1	yes	characteristic
887	C₅₃	#35069	1	1	yes	characteristic, direct product factor, Sylow
888	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
889	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
890	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
891	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
892	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
893	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
894	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
895	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
896	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
897	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
898	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
899	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
900	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
901	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
902	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
903	#126	—	4	2	no	—
904	#123	—	2	4	no	—
905	#123	—	2	4	no	—
906	C₂²⋊Q₈	—	2	4	no	—
907	C₂²⋊Q₈	—	4	2	no	—
908	#121	—	2	4	no	—
909	C₄×D₄	—	2	4	no	—
910	C₄×D₄	—	2	4	no	—
911	C₄×D₄	—	2	4	no	—
912	C₄×D₄	—	2	4	no	—
913	#117	—	4	2	no	—
914	C₂×C₄⋊C₄	—	2	4	no	—
915	C₂×C₄⋊C₄	—	4	2	no	—
916	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
921	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
924	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
925	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
926	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
927	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
928	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
929	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
930	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
934	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
935	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
936	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
937	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
938	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
952	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
953	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
954	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
955	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
956	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
957	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
958	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
959	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
960	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
961	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
962	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
963	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
964	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
967	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
968	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
970	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
971	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
972	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
973	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
974	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
975	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
976	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
977	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
978	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
979	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
980	C₂×C₄²	—	4	2	no	—
981	C₂×C₄²	—	4	2	no	—
982	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
983	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
984	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
985	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
986	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
987	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
988	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
989	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
990	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
991	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
992	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
993	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
994	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
995	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
996	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
997	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
998	#95	C₂³×C₅₃	1	1	yes	characteristic
999	#95	C₂³×C₅₃	1	1	yes	characteristic
1000	#95	C₂³×C₅₃	1	1	yes	characteristic
1001	#95	C₂³×C₅₃	1	1	yes	characteristic
1002	#95	C₂³×C₅₃	1	1	yes	characteristic
1003	#95	C₂³×C₅₃	1	1	yes	characteristic
1004	#95	C₂³×C₅₃	1	1	yes	characteristic
1005	#95	C₂³×C₅₃	1	1	yes	characteristic
1006	#95	C₂³×C₅₃	1	1	yes	characteristic
1007	#95	C₂³×C₅₃	1	1	yes	characteristic
1008	#95	C₂³×C₅₃	1	1	yes	characteristic
1009	#95	C₂³×C₅₃	1	1	yes	characteristic
1010	#95	C₂³×C₅₃	1	1	yes	characteristic
1011	#95	C₂³×C₅₃	1	1	yes	characteristic
1012	#95	C₂³×C₅₃	1	1	yes	characteristic
1013	#95	C₂³×C₅₃	1	1	yes	characteristic
1014	#95	C₂³×C₅₃	1	1	yes	characteristic
1015	#95	C₂³×C₅₃	1	1	yes	characteristic
1016	#95	C₂³×C₅₃	1	1	yes	characteristic
1017	#95	C₂³×C₅₃	1	1	yes	characteristic
1018	#95	C₂³×C₅₃	1	1	yes	characteristic
1019	#95	C₂³×C₅₃	1	1	yes	characteristic
1020	#95	C₂³×C₅₃	1	1	yes	characteristic
1021	#95	C₂³×C₅₃	1	1	yes	characteristic
1022	#95	C₂³×C₅₃	1	1	yes	characteristic
1023	#95	C₂³×C₅₃	1	1	yes	characteristic
1024	#95	C₂³×C₅₃	1	1	yes	characteristic
1025	#95	C₂³×C₅₃	1	1	yes	characteristic
1026	#95	C₂³×C₅₃	1	1	yes	characteristic
1027	#95	C₂³×C₅₃	1	1	yes	characteristic
1028	#95	C₂³×C₅₃	1	1	yes	characteristic
1029	#95	C₂³×C₅₃	1	1	yes	characteristic
1030	#95	C₂³×C₅₃	1	1	yes	characteristic
1031	#95	C₂³×C₅₃	1	1	yes	characteristic
1032	#95	C₂³×C₅₃	1	1	yes	characteristic
1033	#95	C₂³×C₅₃	1	1	yes	characteristic
1034	#95	C₂³×C₅₃	1	1	yes	characteristic
1035	#95	C₂³×C₅₃	1	1	yes	characteristic
1036	#95	C₂³×C₅₃	1	1	yes	characteristic
1037	#95	C₂³×C₅₃	1	1	yes	characteristic
1038	#95	C₂³×C₅₃	1	1	yes	characteristic
1039	#95	C₂³×C₅₃	1	1	yes	characteristic
1040	#95	C₂³×C₅₃	1	1	yes	characteristic
1041	#95	C₂³×C₅₃	1	1	yes	characteristic
1042	#95	C₂³×C₅₃	1	1	yes	characteristic
1043	#95	C₂³×C₅₃	1	1	yes	characteristic
1044	#95	C₂³×C₅₃	1	1	yes	characteristic
1045	#95	C₂³×C₅₃	1	1	yes	characteristic
1046	#95	C₂³×C₅₃	1	1	yes	characteristic
1047	#95	C₂³×C₅₃	1	1	yes	characteristic
1048	#95	C₂³×C₅₃	1	1	yes	characteristic
1049	#95	C₂³×C₅₃	1	1	yes	characteristic
1050	#95	C₂³×C₅₃	1	1	yes	characteristic
1051	#95	C₂³×C₅₃	1	1	yes	characteristic
1052	#95	C₂³×C₅₃	1	1	yes	characteristic
1053	#95	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	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1059	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1060	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1061	C₂×Q₈	—	2	2	no	—
1062	C₂×Q₈	—	4	1	no	—
1063	C₂×Q₈	—	4	1	no	—
1064	C₂×D₄	—	2	2	no	—
1065	C₂×D₄	—	2	2	no	—
1066	C₂×D₄	—	2	2	no	—
1067	C₂×D₄	—	2	2	no	—
1068	C₂×D₄	—	2	2	no	—
1069	C₂×D₄	—	2	2	no	—
1070	C₂×D₄	—	4	1	no	—
1071	C₂×D₄	—	4	1	no	—
1072	C₂×D₄	#41×C₅₃	1	4	yes	—
1073	C₂²×C₄	—	2	2	no	—
1074	C₂²×C₄	—	2	2	no	—
1075	C₂²×C₄	—	2	2	no	—
1076	C₂²×C₄	—	2	2	no	—
1077	C₂²×C₄	—	2	2	no	—
1078	C₂²×C₄	—	2	2	no	—
1079	C₂²×C₄	—	2	2	no	—
1080	C₂²×C₄	—	2	2	no	—
1081	C₂²×C₄	—	2	2	no	—
1082	C₂²×C₄	—	2	2	no	—
1083	C₂²×C₄	—	2	2	no	—
1084	C₂²×C₄	—	2	2	no	—
1085	C₂²×C₄	—	2	2	no	—
1086	C₂²×C₄	—	2	2	no	—
1087	C₂²×C₄	—	2	2	no	—
1088	C₂²×C₄	—	2	2	no	—
1089	C₂²×C₄	—	4	1	no	—
1090	C₂²×C₄	—	4	1	no	—
1091	C₂²×C₄	—	4	1	no	—
1092	C₂²×C₄	—	4	1	no	—
1093	C₂²×C₄	—	4	1	no	—
1094	C₂²×C₄	—	4	1	no	—
1095	C₂²×C₄	—	4	1	no	—
1096	C₂²×C₄	—	4	1	no	—
1097	C₂²×C₄	—	4	1	no	—
1098	C₂²×C₄	—	4	1	no	—
1099	C₂²×C₄	—	4	1	no	—
1100	C₂²×C₄	—	4	1	no	—
1101	C₂²×C₄	—	4	1	no	—
1102	C₂²×C₄	—	4	1	no	—
1103	C₂²×C₄	—	4	1	no	—
1104	C₂²×C₄	—	4	1	no	—
1105	C₂²×C₄	#41×C₅₃	1	4	yes	—
1106	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1107	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1108	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1109	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1110	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1111	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1112	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1113	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1114	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1115	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1116	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1117	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1118	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1119	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1120	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1121	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1122	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1123	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1124	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1126	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1127	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1128	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1129	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1130	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1131	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1132	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1133	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1134	C₄⋊C₄	—	2	2	no	—
1135	C₄⋊C₄	—	2	2	no	—
1136	C₄⋊C₄	—	2	2	no	—
1137	C₄⋊C₄	—	2	2	no	—
1138	C₄⋊C₄	—	2	2	no	—
1139	C₄⋊C₄	—	2	2	no	—
1140	C₄⋊C₄	—	2	2	no	—
1141	C₄⋊C₄	—	2	2	no	—
1142	C₄⋊C₄	—	2	2	no	—
1143	C₄⋊C₄	—	2	2	no	—
1144	C₄⋊C₄	—	2	2	no	—
1145	C₄⋊C₄	—	2	2	no	—
1146	C₄⋊C₄	—	2	2	no	—
1147	C₄⋊C₄	—	2	2	no	—
1148	C₄⋊C₄	—	2	2	no	—
1149	C₄⋊C₄	—	2	2	no	—
1150	C₄⋊C₄	—	2	2	no	—
1151	C₄⋊C₄	—	2	2	no	—
1152	C₄⋊C₄	—	2	2	no	—
1153	C₄⋊C₄	—	2	2	no	—
1154	C₄⋊C₄	—	4	1	no	—
1155	C₄⋊C₄	—	4	1	no	—
1156	C₄⋊C₄	—	4	1	no	—
1157	C₄⋊C₄	—	4	1	no	—
1158	C₄⋊C₄	—	4	1	no	—
1159	C₄⋊C₄	—	4	1	no	—
1160	C₄⋊C₄	—	4	1	no	—
1161	C₄⋊C₄	—	4	1	no	—
1162	C₄⋊C₄	—	4	1	no	—
1163	C₄⋊C₄	—	4	1	no	—
1164	C₄⋊C₄	—	4	1	no	—
1165	C₄⋊C₄	—	4	1	no	—
1166	C₄⋊C₄	—	4	1	no	—
1167	C₄⋊C₄	—	4	1	no	—
1168	C₄⋊C₄	—	4	1	no	—
1169	C₄⋊C₄	—	4	1	no	—
1170	C₂²⋊C₄	—	2	2	no	—
1171	C₂²⋊C₄	—	2	2	no	—
1172	C₂²⋊C₄	—	2	2	no	—
1173	C₂²⋊C₄	—	2	2	no	—
1174	C₂²⋊C₄	—	2	2	no	—
1175	C₂²⋊C₄	—	2	2	no	—
1176	C₂²⋊C₄	—	2	2	no	—
1177	C₂²⋊C₄	—	2	2	no	—
1178	C₂²⋊C₄	—	2	2	no	—
1179	C₂²⋊C₄	—	2	2	no	—
1180	C₂²⋊C₄	—	2	2	no	—
1181	C₂²⋊C₄	—	2	2	no	—
1182	C₂²⋊C₄	—	2	2	no	—
1183	C₂²⋊C₄	—	2	2	no	—
1184	C₂²⋊C₄	—	2	2	no	—
1185	C₂²⋊C₄	—	2	2	no	—
1186	C₂²⋊C₄	—	2	2	no	—
1187	C₂²⋊C₄	—	4	1	no	—
1188	C₂²⋊C₄	—	4	1	no	—
1189	C₂²⋊C₄	—	4	1	no	—
1190	C₂²⋊C₄	—	4	1	no	—
1191	C₂²⋊C₄	—	4	1	no	—
1192	C₂²⋊C₄	—	4	1	no	—
1193	C₂²⋊C₄	—	4	1	no	—
1194	C₂²⋊C₄	—	4	1	no	—
1195	C₂²⋊C₄	—	4	1	no	—
1196	C₂²⋊C₄	—	4	1	no	—
1197	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
1198	C₄²	—	2	2	no	—
1199	C₄²	—	2	2	no	—
1200	C₄²	—	2	2	no	—
1201	C₄²	—	2	2	no	—
1202	C₄²	—	2	2	no	—
1203	C₄²	—	2	2	no	—
1204	C₄²	—	2	2	no	—
1205	C₄²	—	2	2	no	—
1206	C₄²	—	4	1	no	—
1207	C₄²	—	4	1	no	—
1208	C₄²	—	4	1	no	—
1209	C₄²	—	4	1	no	—
1210	C₄²	—	4	1	no	—
1211	C₄²	—	4	1	no	—
1212	C₄²	—	4	1	no	—
1213	C₄²	—	4	1	no	—
1214	C₂³	—	2	1	no	—
1215	C₂³	—	2	1	no	—
1216	C₂³	—	2	1	no	—
1217	C₂³	—	2	1	no	—
1218	C₂³	—	2	1	no	—
1219	C₂³	—	2	1	no	—
1220	C₂³	—	2	1	no	—
1221	C₂³	—	2	1	no	—
1222	C₂³	—	2	1	no	—
1223	C₂³	—	2	1	no	—
1224	C₂³	—	2	1	no	—
1225	C₂³	—	2	1	no	—
1226	C₂³	—	2	1	no	—
1227	C₂³	—	2	1	no	—
1228	C₂³	—	2	1	no	—
1229	C₂³	—	2	1	no	—
1230	C₂³	—	2	1	no	—
1231	C₂³	C₂×#41×C₅₃	1	2	yes	—
1232	C₂³	C₂×#41×C₅₃	1	2	yes	—
1233	C₂³	C₂×#41×C₅₃	1	2	yes	—
1234	C₂³	C₂×#41×C₅₃	1	2	yes	—
1235	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1236	Q₈	—	8	2	no	—
1237	D₄	—	2	8	no	—
1238	D₄	—	4	4	no	—
1239	D₄	—	8	2	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	2	1	no	—
1264	C₂×C₄	—	2	1	no	—
1265	C₂×C₄	—	2	1	no	—
1266	C₂×C₄	—	2	1	no	—
1267	C₂×C₄	—	2	1	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	2	1	no	—
1270	C₂×C₄	—	2	1	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	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	—	4	4	no	—
1318	C₂×C₄	—	4	4	no	—
1319	C₂×C₄	—	4	4	no	—
1320	C₂×C₄	—	4	4	no	—
1321	C₂×C₄	—	4	4	no	—
1322	C₂×C₄	—	4	4	no	—
1323	C₂×C₄	—	4	4	no	—
1324	C₂×C₄	—	4	4	no	—
1325	C₂×C₄	—	4	4	no	—
1326	C₂×C₄	—	8	2	no	—
1327	C₂×C₄	—	8	2	no	—
1328	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1329	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1330	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1331	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1332	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1333	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1334	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1335	C₂²	—	2	2	no	—
1336	C₂²	—	2	2	no	—
1337	C₂²	—	2	2	no	—
1338	C₂²	—	2	2	no	—
1339	C₂²	—	2	2	no	—
1340	C₂²	—	2	2	no	—
1341	C₂²	—	2	2	no	—
1342	C₂²	—	2	2	no	—
1343	C₂²	—	2	2	no	—
1344	C₂²	—	4	1	no	—
1345	C₂²	—	4	1	no	—
1346	C₂²	—	4	1	no	—
1347	C₂²	—	4	1	no	—
1348	C₂²	—	4	1	no	—
1349	C₂²	—	4	1	no	—
1350	C₂²	—	4	1	no	—
1351	C₂²	—	4	1	no	—
1352	C₂²	—	4	1	no	—
1353	C₂²	—	4	1	no	—
1354	C₂²	—	4	1	no	—
1355	C₂²	C₅₃×#529	1	4	yes	—
1356	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1357	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1358	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1359	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1360	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1361	C₂²	C₅₃×#585	1	1	yes	characteristic
1362	C₂²	C₅₃×#585	1	1	yes	characteristic
1363	C₄	—	2	2	no	—
1364	C₄	—	2	2	no	—
1365	C₄	—	2	2	no	—
1366	C₄	—	2	2	no	—
1367	C₄	—	2	2	no	—
1368	C₄	—	2	2	no	—
1369	C₄	—	2	2	no	—
1370	C₄	—	4	1	no	—
1371	C₄	—	4	1	no	—
1372	C₄	—	4	1	no	—
1373	C₄	—	4	1	no	—
1374	C₄	—	4	1	no	—
1375	C₄	—	4	1	no	—
1376	C₄	—	4	1	no	—
1377	C₄	—	4	1	no	—
1378	C₄	—	4	1	no	—
1379	C₄	—	4	1	no	—
1380	C₄	—	4	1	no	—
1381	C₄	—	4	1	no	—
1382	C₄	—	4	1	no	—
1383	C₄	—	4	1	no	—
1384	C₄	—	4	1	no	—
1385	C₄	—	4	1	no	—
1386	C₄	—	4	1	no	—
1387	C₄	—	4	1	no	—
1388	C₄	—	4	1	no	—
1389	C₄	—	4	1	no	—
1390	C₄	—	4	1	no	—
1391	C₂	—	2	4	no	—
1392	C₂	—	4	2	no	—
1393	C₂	—	8	1	no	—
1394	C₂	C₂×C₅₃×#529	1	1	yes	characteristic
1395	C₂	C₅₃×#3459	1	1	yes	characteristic
1396	C₂	C₅₃×#3461	1	1	yes	characteristic
1397	C₂	C₅₃×#3513	1	1	yes	characteristic
1398	C₂	C₅₃×#3515	1	1	yes	characteristic
1399	C₂	C₅₃×#3520	1	1	yes	characteristic
1400	C₂	C₅₃×#3521	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2865	C₂	semidirect
2. C₅₃×#2864	C₂	semidirect
3. C₅₃×#2855	C₂	semidirect
4. C₅₃×#2852	C₂	semidirect
5. C₅₃×#2655	C₂	semidirect
6. C₅₃×#2652	C₂	semidirect
7. C₅₃×#2650	C₂	semidirect
8. C₅₃×#2649	C₂	semidirect
9. C₅₃×#2588	C₂	semidirect
10. C₅₃×#2587	C₂	semidirect
11. C₅₃×#2576	C₂	semidirect
12. C₅₃×#2575	C₂	semidirect
13. C₅₃×#2533	C₂	semidirect
14. C₅₃×#2530	C₂	semidirect
15. C₅₃×#2505	C₂	semidirect
16. C₅₃×#2493	C₂	semidirect
17. C₅₃×#2488	C₂	semidirect
18. C₅₃×#2481	C₂	semidirect
19. C₅₃×#2478	C₂	semidirect
20. C₅₃×#2477	C₂	semidirect
21. C₅₃×#2449	C₂	semidirect
24. C₅₃×#2419	C₂	semidirect
25. C₅₃×#2329	C₂	semidirect
27. C₅₃×#2322	C₂	semidirect
28. C₅₃×#2322	C₂	semidirect
29. C₅₃×#2290	C₂	semidirect
30. C₂×C₅₃×#387	C₂	semidirect
31. C₄²×D₄×C₅₃	C₂	semidirect
634. #35069	C₅₃	direct (N × H)
691. #2865	C₂×C₅₃	semidirect
692. #2864	C₂×C₅₃	semidirect
693. #2855	C₂×C₅₃	semidirect
694. #2852	C₂×C₅₃	semidirect
695. #2655	C₂×C₅₃	semidirect
696. #2652	C₂×C₅₃	semidirect
697. #2650	C₂×C₅₃	semidirect
698. #2649	C₂×C₅₃	semidirect
699. #2588	C₂×C₅₃	semidirect
700. #2587	C₂×C₅₃	semidirect
701. #2576	C₂×C₅₃	semidirect
702. #2575	C₂×C₅₃	semidirect
703. #2533	C₂×C₅₃	semidirect
704. #2530	C₂×C₅₃	semidirect
705. #2505	C₂×C₅₃	semidirect
706. #2493	C₂×C₅₃	semidirect
707. #2488	C₂×C₅₃	semidirect
708. #2481	C₂×C₅₃	semidirect
709. #2478	C₂×C₅₃	semidirect
710. #2477	C₂×C₅₃	semidirect
711. #2449	C₂×C₅₃	semidirect
714. #2419	C₂×C₅₃	semidirect
715. #2329	C₂×C₅₃	semidirect
717. #2322	C₂×C₅₃	semidirect
718. #2322	C₂×C₅₃	semidirect
719. #2290	C₂×C₅₃	semidirect
720. C₂×#387	C₂×C₅₃	semidirect
721. C₄²×D₄	C₂×C₅₃	semidirect
887. C₅₃	#35069	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#2865	2
C₅₃×#2864	2
C₅₃×#2855	2
C₅₃×#2852	2
C₅₃×#2655	2
C₅₃×#2652	2
C₅₃×#2650	2
C₅₃×#2649	2
C₅₃×#2588	2
C₅₃×#2587	2
C₅₃×#2576	2
C₅₃×#2575	2
C₅₃×#2533	2
C₅₃×#2530	2
C₅₃×#2505	2
C₅₃×#2493	2
C₅₃×#2488	2
C₅₃×#2481	2
C₅₃×#2478	2
C₅₃×#2477	2
C₅₃×#2449	2
C₅₃×#2444	2
C₅₃×#2425	2
C₅₃×#2419	2
C₅₃×#2329	2
C₅₃×#2325	2
C₅₃×#2322	2
C₅₃×#2290	2
C₂×C₅₃×#387	2
C₄²×D₄×C₅₃	2
#35069	53

Subgroups — C53×#35069 #27242581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#35069 #27242581