Subgroups — C₅₃×#34416 #27241928

Order 13568.

2522 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#538	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×#2377	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×#2367	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2364	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2359	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2353	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2337	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2321	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2321	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₅₃×#538	C₄	1	16	yes	complemented
34	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
63	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
64	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#390	C₂²	1	1	yes	characteristic
68	C₅₃×#390	C₂²	1	1	yes	characteristic
69	C₅₃×#390	C₂²	1	1	yes	characteristic
70	C₅₃×#390	C₂²	1	1	yes	characteristic
71	C₅₃×#390	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×#389	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
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, complemented
97	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
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×#386	C₂²	1	1	yes	characteristic
117	C₅₃×#386	C₂²	1	1	yes	characteristic
118	C₅₃×#386	C₂²	1	1	yes	characteristic
119	C₅₃×#386	C₂²	1	1	yes	characteristic
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×#386	C₂²	1	1	yes	characteristic
127	C₅₃×#386	C₂²	1	1	yes	characteristic
128	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
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
142	C₅₃×#385	C₂²	1	1	yes	characteristic
143	C₅₃×#385	C₂²	1	1	yes	characteristic
144	C₅₃×#385	C₂²	1	1	yes	characteristic
145	C₅₃×#385	C₂²	1	1	yes	characteristic
146	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#380	C₂²	1	1	yes	characteristic
158	C₅₃×#380	C₂²	1	1	yes	characteristic
159	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#379	C₂²	1	1	yes	characteristic
163	C₅₃×#379	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₂²⋊C₄×C₅₃	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	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₅₃	—	4	2	no	—
198	C₂³×C₄×C₅₃	—	4	2	no	—
199	C₂³×C₄×C₅₃	—	4	2	no	—
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	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
216	#126×C₅₃	C₂×C₄	1	8	yes	complemented
217	#126×C₅₃	C₂×C₄	1	8	yes	complemented
218	#124×C₅₃	C₂×C₄	1	8	yes	complemented
219	#124×C₅₃	C₂×C₄	1	8	yes	complemented
220	#123×C₅₃	C₂×C₄	1	8	yes	complemented
221	#123×C₅₃	C₂×C₄	1	8	yes	complemented
222	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
223	#121×C₅₃	C₂×C₄	1	8	yes	complemented
224	#121×C₅₃	C₂×C₄	1	8	yes	complemented
225	#121×C₅₃	C₂×C₄	1	8	yes	complemented
226	#120×C₅₃	C₂×C₄	1	8	yes	complemented
227	#120×C₅₃	C₂×C₄	1	8	yes	complemented
228	C₄×Q₈×C₅₃	—	4	2	no	—
229	C₄×D₄×C₅₃	—	4	2	no	—
230	C₄×D₄×C₅₃	—	4	2	no	—
231	C₄×D₄×C₅₃	—	4	2	no	—
232	C₄×D₄×C₅₃	—	4	2	no	—
233	C₄×D₄×C₅₃	—	4	2	no	—
234	C₄×D₄×C₅₃	—	4	2	no	—
235	C₄×D₄×C₅₃	—	4	2	no	—
236	C₄×D₄×C₅₃	—	4	2	no	—
237	C₄×D₄×C₅₃	—	4	2	no	—
238	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
239	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
240	#117×C₅₃	—	4	2	no	—
241	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
242	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
243	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
275	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₄×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	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₄²×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	#95×C₅₃	C₂³	1	1	yes	characteristic
371	#95×C₅₃	C₂³	1	1	yes	characteristic
372	#95×C₅₃	C₂³	1	1	yes	characteristic
373	#95×C₅₃	C₂³	1	1	yes	characteristic
374	#95×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	C₂⁴×C₅₃	—	2	2	no	—
377	C₂⁴×C₅₃	—	2	2	no	—
378	C₂⁴×C₅₃	—	4	1	no	—
379	C₂⁴×C₅₃	—	4	1	no	—
380	C₂⁴×C₅₃	—	4	1	no	—
381	C₂⁴×C₅₃	—	4	1	no	—
382	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
383	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×Q₈×C₅₃	—	4	1	no	—
389	C₂×Q₈×C₅₃	—	4	1	no	—
390	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	complemented
391	C₂×D₄×C₅₃	—	2	2	no	—
392	C₂×D₄×C₅₃	—	2	2	no	—
393	C₂×D₄×C₅₃	—	2	2	no	—
394	C₂×D₄×C₅₃	—	2	2	no	—
395	C₂×D₄×C₅₃	—	4	1	no	—
396	C₂×D₄×C₅₃	—	4	1	no	—
397	C₂×D₄×C₅₃	—	4	1	no	—
398	C₂×D₄×C₅₃	—	4	1	no	—
399	C₂×D₄×C₅₃	—	4	1	no	—
400	C₂×D₄×C₅₃	—	4	1	no	—
401	C₂×D₄×C₅₃	—	4	1	no	—
402	C₂×D₄×C₅₃	—	4	1	no	—
403	C₂×D₄×C₅₃	—	4	1	no	—
404	C₂×D₄×C₅₃	—	4	1	no	—
405	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
406	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
407	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
408	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
409	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
410	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
411	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	complemented
412	C₂²×C₄×C₅₃	—	2	2	no	—
413	C₂²×C₄×C₅₃	—	2	2	no	—
414	C₂²×C₄×C₅₃	—	2	2	no	—
415	C₂²×C₄×C₅₃	—	2	2	no	—
416	C₂²×C₄×C₅₃	—	2	2	no	—
417	C₂²×C₄×C₅₃	—	2	2	no	—
418	C₂²×C₄×C₅₃	—	2	2	no	—
419	C₂²×C₄×C₅₃	—	2	2	no	—
420	C₂²×C₄×C₅₃	—	2	2	no	—
421	C₂²×C₄×C₅₃	—	2	2	no	—
422	C₂²×C₄×C₅₃	—	2	2	no	—
423	C₂²×C₄×C₅₃	—	2	2	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	—	4	1	no	—
428	C₂²×C₄×C₅₃	—	4	1	no	—
429	C₂²×C₄×C₅₃	—	4	1	no	—
430	C₂²×C₄×C₅₃	—	4	1	no	—
431	C₂²×C₄×C₅₃	—	4	1	no	—
432	C₂²×C₄×C₅₃	—	4	1	no	—
433	C₂²×C₄×C₅₃	—	4	1	no	—
434	C₂²×C₄×C₅₃	—	4	1	no	—
435	C₂²×C₄×C₅₃	—	4	1	no	—
436	C₂²×C₄×C₅₃	—	4	1	no	—
437	C₂²×C₄×C₅₃	—	4	1	no	—
438	C₂²×C₄×C₅₃	—	4	1	no	—
439	C₂²×C₄×C₅₃	—	4	1	no	—
440	C₂²×C₄×C₅₃	—	4	1	no	—
441	C₂²×C₄×C₅₃	—	4	1	no	—
442	C₂²×C₄×C₅₃	—	4	1	no	—
443	C₂²×C₄×C₅₃	—	4	1	no	—
444	C₂²×C₄×C₅₃	—	4	1	no	—
445	C₂²×C₄×C₅₃	—	4	1	no	—
446	C₂²×C₄×C₅₃	—	4	1	no	—
447	C₂²×C₄×C₅₃	—	4	1	no	—
448	C₂²×C₄×C₅₃	—	4	1	no	—
449	C₂²×C₄×C₅₃	—	4	1	no	—
450	C₂²×C₄×C₅₃	—	4	1	no	—
451	C₂²×C₄×C₅₃	—	4	1	no	—
452	C₂²×C₄×C₅₃	—	4	1	no	—
453	C₂²×C₄×C₅₃	—	4	1	no	—
454	C₂²×C₄×C₅₃	—	4	1	no	—
455	C₂²×C₄×C₅₃	—	4	1	no	—
456	C₂²×C₄×C₅₃	—	4	16	no	—
457	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
458	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
459	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
460	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
461	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
469	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
470	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
471	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
472	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
473	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
474	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
475	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
476	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
478	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
479	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
481	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
482	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
483	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
484	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
485	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
486	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
487	C₄⋊C₄×C₅₃	—	2	2	no	—
488	C₄⋊C₄×C₅₃	—	2	2	no	—
489	C₄⋊C₄×C₅₃	—	2	2	no	—
490	C₄⋊C₄×C₅₃	—	2	2	no	—
491	C₄⋊C₄×C₅₃	—	2	2	no	—
492	C₄⋊C₄×C₅₃	—	2	2	no	—
493	C₄⋊C₄×C₅₃	—	4	1	no	—
494	C₄⋊C₄×C₅₃	—	4	1	no	—
495	C₄⋊C₄×C₅₃	—	4	1	no	—
496	C₄⋊C₄×C₅₃	—	4	1	no	—
497	C₄⋊C₄×C₅₃	—	4	1	no	—
498	C₄⋊C₄×C₅₃	—	4	1	no	—
499	C₄⋊C₄×C₅₃	—	4	1	no	—
500	C₄⋊C₄×C₅₃	—	4	1	no	—
501	C₄⋊C₄×C₅₃	—	4	1	no	—
502	C₄⋊C₄×C₅₃	—	4	1	no	—
503	C₄⋊C₄×C₅₃	—	4	1	no	—
504	C₄⋊C₄×C₅₃	—	4	1	no	—
505	C₄⋊C₄×C₅₃	—	4	1	no	—
506	C₄⋊C₄×C₅₃	—	4	1	no	—
507	C₄⋊C₄×C₅₃	—	4	1	no	—
508	C₄⋊C₄×C₅₃	—	4	1	no	—
509	C₄⋊C₄×C₅₃	—	4	1	no	—
510	C₄⋊C₄×C₅₃	—	4	1	no	—
511	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
512	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
513	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
514	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
515	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
516	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
517	C₂²⋊C₄×C₅₃	—	2	2	no	—
518	C₂²⋊C₄×C₅₃	—	2	2	no	—
519	C₂²⋊C₄×C₅₃	—	2	2	no	—
520	C₂²⋊C₄×C₅₃	—	2	2	no	—
521	C₂²⋊C₄×C₅₃	—	2	2	no	—
522	C₂²⋊C₄×C₅₃	—	2	2	no	—
523	C₂²⋊C₄×C₅₃	—	4	1	no	—
524	C₂²⋊C₄×C₅₃	—	4	1	no	—
525	C₂²⋊C₄×C₅₃	—	4	1	no	—
526	C₂²⋊C₄×C₅₃	—	4	1	no	—
527	C₂²⋊C₄×C₅₃	—	4	1	no	—
528	C₂²⋊C₄×C₅₃	—	4	1	no	—
529	C₂²⋊C₄×C₅₃	—	4	1	no	—
530	C₂²⋊C₄×C₅₃	—	4	1	no	—
531	C₂²⋊C₄×C₅₃	—	4	1	no	—
532	C₂²⋊C₄×C₅₃	—	4	1	no	—
533	C₂²⋊C₄×C₅₃	—	4	1	no	—
534	C₂²⋊C₄×C₅₃	—	4	1	no	—
535	C₂²⋊C₄×C₅₃	—	4	1	no	—
536	C₂²⋊C₄×C₅₃	—	4	1	no	—
537	C₂²⋊C₄×C₅₃	—	4	1	no	—
538	C₂²⋊C₄×C₅₃	—	4	1	no	—
539	C₂²⋊C₄×C₅₃	—	4	1	no	—
540	C₂²⋊C₄×C₅₃	—	4	1	no	—
541	C₂²⋊C₄×C₅₃	—	4	1	no	—
542	C₂²⋊C₄×C₅₃	—	4	1	no	—
543	C₂²⋊C₄×C₅₃	—	4	1	no	—
544	C₂²⋊C₄×C₅₃	—	4	1	no	—
545	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
546	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
547	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
548	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
549	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
550	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
551	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
552	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
553	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
554	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
555	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
556	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
557	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
558	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
559	C₄²×C₅₃	—	2	2	no	—
560	C₄²×C₅₃	—	2	2	no	—
561	C₄²×C₅₃	—	4	1	no	—
562	C₄²×C₅₃	—	4	1	no	—
563	C₄²×C₅₃	—	4	1	no	—
564	C₄²×C₅₃	—	4	1	no	—
565	C₄²×C₅₃	—	4	1	no	—
566	C₄²×C₅₃	—	4	1	no	—
567	C₄²×C₅₃	—	4	1	no	—
568	C₄²×C₅₃	—	4	1	no	—
569	C₄²×C₅₃	—	4	1	no	—
570	C₄²×C₅₃	—	4	1	no	—
571	C₄²×C₅₃	—	4	1	no	—
572	C₄²×C₅₃	—	4	1	no	—
573	C₄²×C₅₃	—	4	1	no	—
574	C₄²×C₅₃	—	4	1	no	—
575	C₄²×C₅₃	C₂²×C₄	1	4	yes	complemented
576	C₄²×C₅₃	C₂²×C₄	1	4	yes	complemented
577	C₂³×C₅₃	—	2	1	no	—
578	C₂³×C₅₃	—	2	1	no	—
579	C₂³×C₅₃	—	2	1	no	—
580	C₂³×C₅₃	—	2	1	no	—
581	C₂³×C₅₃	—	2	8	no	—
582	C₂³×C₅₃	—	2	1	no	—
583	C₂³×C₅₃	—	2	1	no	—
584	C₂³×C₅₃	—	2	1	no	—
585	C₂³×C₅₃	—	2	1	no	—
586	C₂³×C₅₃	—	2	1	no	—
587	C₂³×C₅₃	—	2	1	no	—
588	C₂³×C₅₃	—	2	1	no	—
589	C₂³×C₅₃	—	2	1	no	—
590	C₂³×C₅₃	—	2	1	no	—
591	C₂³×C₅₃	—	2	1	no	—
592	C₂³×C₅₃	—	2	1	no	—
593	C₂³×C₅₃	—	2	1	no	—
594	C₂³×C₅₃	—	2	1	no	—
595	C₂³×C₅₃	—	2	1	no	—
596	C₂³×C₅₃	—	2	1	no	—
597	C₂³×C₅₃	—	2	1	no	—
598	C₂³×C₅₃	—	2	1	no	—
599	C₂³×C₅₃	—	2	1	no	—
600	C₂³×C₅₃	—	2	1	no	—
601	C₂³×C₅₃	—	2	1	no	—
602	C₂³×C₅₃	—	2	1	no	—
603	C₂³×C₅₃	—	2	1	no	—
604	C₂³×C₅₃	—	2	1	no	—
605	C₂³×C₅₃	—	2	1	no	—
606	C₂³×C₅₃	—	4	4	no	—
607	C₂³×C₅₃	—	4	4	no	—
608	C₂³×C₅₃	—	4	4	no	—
609	C₂³×C₅₃	—	4	4	no	—
610	C₂³×C₅₃	—	4	4	no	—
611	C₂³×C₅₃	—	4	4	no	—
612	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
613	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
614	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
615	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
616	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
617	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
618	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
619	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
620	Q₈×C₅₃	—	4	4	no	—
621	D₄×C₅₃	—	2	8	no	—
622	D₄×C₅₃	—	2	8	no	—
623	D₄×C₅₃	—	4	4	no	—
624	D₄×C₅₃	—	4	4	no	—
625	D₄×C₅₃	—	4	4	no	—
626	D₄×C₅₃	—	4	4	no	—
627	D₄×C₅₃	—	4	4	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	2	1	no	—
639	C₂×C₄×C₅₃	—	2	1	no	—
640	C₂×C₄×C₅₃	—	2	1	no	—
641	C₂×C₄×C₅₃	—	2	1	no	—
642	C₂×C₄×C₅₃	—	2	1	no	—
643	C₂×C₄×C₅₃	—	2	1	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	2	1	no	—
646	C₂×C₄×C₅₃	—	2	1	no	—
647	C₂×C₄×C₅₃	—	2	1	no	—
648	C₂×C₄×C₅₃	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	2	1	no	—
652	C₂×C₄×C₅₃	—	2	1	no	—
653	C₂×C₄×C₅₃	—	2	1	no	—
654	C₂×C₄×C₅₃	—	2	1	no	—
655	C₂×C₄×C₅₃	—	2	1	no	—
656	C₂×C₄×C₅₃	—	2	1	no	—
657	C₂×C₄×C₅₃	—	2	1	no	—
658	C₂×C₄×C₅₃	—	2	1	no	—
659	C₂×C₄×C₅₃	—	2	1	no	—
660	C₂×C₄×C₅₃	—	2	1	no	—
661	C₂×C₄×C₅₃	—	2	1	no	—
662	C₂×C₄×C₅₃	—	2	1	no	—
663	C₂×C₄×C₅₃	—	2	1	no	—
664	C₂×C₄×C₅₃	—	2	1	no	—
665	C₂×C₄×C₅₃	—	2	1	no	—
666	C₂×C₄×C₅₃	—	2	1	no	—
667	C₂×C₄×C₅₃	—	2	1	no	—
668	C₂×C₄×C₅₃	—	2	1	no	—
669	C₂×C₄×C₅₃	—	2	1	no	—
670	C₂×C₄×C₅₃	—	2	1	no	—
671	C₂×C₄×C₅₃	—	2	1	no	—
672	C₂×C₄×C₅₃	—	2	1	no	—
673	C₂×C₄×C₅₃	—	2	1	no	—
674	C₂×C₄×C₅₃	—	2	1	no	—
675	C₂×C₄×C₅₃	—	2	1	no	—
676	C₂×C₄×C₅₃	—	2	1	no	—
677	C₂×C₄×C₅₃	—	2	1	no	—
678	C₂×C₄×C₅₃	—	2	1	no	—
679	C₂×C₄×C₅₃	—	2	1	no	—
680	C₂×C₄×C₅₃	—	2	1	no	—
681	C₂×C₄×C₅₃	—	2	1	no	—
682	C₂×C₄×C₅₃	—	2	1	no	—
683	C₂×C₄×C₅₃	—	2	1	no	—
684	C₂×C₄×C₅₃	—	2	1	no	—
685	C₂×C₄×C₅₃	—	2	1	no	—
686	C₂×C₄×C₅₃	—	2	1	no	—
687	C₂×C₄×C₅₃	—	2	1	no	—
688	C₂×C₄×C₅₃	—	2	1	no	—
689	C₂×C₄×C₅₃	—	2	1	no	—
690	C₂×C₄×C₅₃	—	2	1	no	—
691	C₂×C₄×C₅₃	—	2	1	no	—
692	C₂×C₄×C₅₃	—	2	1	no	—
693	C₂×C₄×C₅₃	—	2	1	no	—
694	C₂×C₄×C₅₃	—	4	4	no	—
695	C₂×C₄×C₅₃	—	4	4	no	—
696	C₂×C₄×C₅₃	—	4	4	no	—
697	C₂×C₄×C₅₃	—	4	4	no	—
698	C₂×C₄×C₅₃	—	4	4	no	—
699	C₂×C₄×C₅₃	—	4	4	no	—
700	C₂×C₄×C₅₃	—	4	4	no	—
701	C₂×C₄×C₅₃	—	4	4	no	—
702	C₂×C₄×C₅₃	—	4	4	no	—
703	C₂×C₄×C₅₃	—	4	4	no	—
704	C₂×C₄×C₅₃	—	8	2	no	—
705	C₂×C₄×C₅₃	—	8	2	no	—
706	C₂×C₄×C₅₃	—	8	2	no	—
707	C₂×C₄×C₅₃	—	8	2	no	—
708	C₂×C₄×C₅₃	—	8	2	no	—
709	C₂×C₄×C₅₃	—	8	2	no	—
710	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
711	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
712	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
713	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
714	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
715	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
716	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
717	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
718	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
719	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
720	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
721	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
722	#34416	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
723	C₂²×C₅₃	—	2	2	no	—
724	C₂²×C₅₃	—	2	2	no	—
725	C₂²×C₅₃	—	2	2	no	—
726	C₂²×C₅₃	—	2	2	no	—
727	C₂²×C₅₃	—	2	2	no	—
728	C₂²×C₅₃	—	2	2	no	—
729	C₂²×C₅₃	—	2	2	no	—
730	C₂²×C₅₃	—	2	2	no	—
731	C₂²×C₅₃	—	2	2	no	—
732	C₂²×C₅₃	—	2	2	no	—
733	C₂²×C₅₃	—	2	2	no	—
734	C₂²×C₅₃	—	2	2	no	—
735	C₂²×C₅₃	—	2	2	no	—
736	C₂²×C₅₃	—	2	2	no	—
737	C₂²×C₅₃	—	2	2	no	—
738	C₂²×C₅₃	—	2	2	no	—
739	C₂²×C₅₃	—	2	2	no	—
740	C₂²×C₅₃	—	2	2	no	—
741	C₂²×C₅₃	—	4	16	no	—
742	C₂²×C₅₃	—	4	1	no	—
743	C₂²×C₅₃	—	4	1	no	—
744	C₂²×C₅₃	—	4	1	no	—
745	C₂²×C₅₃	—	4	1	no	—
746	C₂²×C₅₃	—	4	1	no	—
747	C₂²×C₅₃	—	4	1	no	—
748	C₂²×C₅₃	—	4	1	no	—
749	C₂²×C₅₃	—	4	1	no	—
750	C₂²×C₅₃	—	4	1	no	—
751	C₂²×C₅₃	—	4	1	no	—
752	C₂²×C₅₃	—	4	1	no	—
753	C₂²×C₅₃	—	4	1	no	—
754	C₂²×C₅₃	—	4	1	no	—
755	C₂²×C₅₃	—	4	1	no	—
756	C₂²×C₅₃	—	4	1	no	—
757	C₂²×C₅₃	—	4	1	no	—
758	C₂²×C₅₃	#520	1	4	yes	—
759	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
760	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
762	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
763	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
764	C₂²×C₅₃	#585	1	1	yes	characteristic
765	C₂²×C₅₃	#585	1	1	yes	characteristic
766	C₄×C₅₃	—	2	2	no	—
767	C₄×C₅₃	—	2	2	no	—
768	C₄×C₅₃	—	2	2	no	—
769	C₄×C₅₃	—	2	2	no	—
770	C₄×C₅₃	—	2	2	no	—
771	C₄×C₅₃	—	2	2	no	—
772	C₄×C₅₃	—	2	2	no	—
773	C₄×C₅₃	—	2	2	no	—
774	C₄×C₅₃	—	2	2	no	—
775	C₄×C₅₃	—	2	2	no	—
776	C₄×C₅₃	—	2	2	no	—
777	C₄×C₅₃	—	2	2	no	—
778	C₄×C₅₃	—	4	1	no	—
779	C₄×C₅₃	—	4	1	no	—
780	C₄×C₅₃	—	4	1	no	—
781	C₄×C₅₃	—	4	1	no	—
782	C₄×C₅₃	—	4	1	no	—
783	C₄×C₅₃	—	4	1	no	—
784	C₄×C₅₃	—	4	1	no	—
785	C₄×C₅₃	—	4	1	no	—
786	C₄×C₅₃	—	4	1	no	—
787	C₄×C₅₃	—	4	1	no	—
788	C₄×C₅₃	—	4	1	no	—
789	C₄×C₅₃	—	4	1	no	—
790	C₄×C₅₃	—	4	1	no	—
791	C₄×C₅₃	—	4	1	no	—
792	C₂×#538	C₂×C₅₃	1	1	yes	characteristic
793	#2383	C₂×C₅₃	1	1	yes	characteristic, complemented
794	#2379	C₂×C₅₃	1	1	yes	characteristic, complemented
795	#2377	C₂×C₅₃	1	1	yes	characteristic, complemented
796	#2376	C₂×C₅₃	1	1	yes	characteristic, complemented
797	#2373	C₂×C₅₃	1	1	yes	characteristic, complemented
798	#2368	C₂×C₅₃	1	1	yes	characteristic, complemented
799	#2367	C₂×C₅₃	1	1	yes	characteristic, complemented
800	#2364	C₂×C₅₃	1	1	yes	characteristic, complemented
801	#2361	C₂×C₅₃	1	1	yes	characteristic, complemented
802	#2361	C₂×C₅₃	1	1	yes	characteristic, complemented
803	#2360	C₂×C₅₃	1	1	yes	characteristic, complemented
804	#2359	C₂×C₅₃	1	1	yes	characteristic, complemented
805	#2353	C₂×C₅₃	1	1	yes	characteristic, complemented
806	#2352	C₂×C₅₃	1	1	yes	characteristic, complemented
807	#2349	C₂×C₅₃	1	1	yes	characteristic, complemented
808	D₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
809	#2337	C₂×C₅₃	1	1	yes	characteristic, complemented
810	#2335	C₂×C₅₃	1	1	yes	characteristic, complemented
811	#2334	C₂×C₅₃	1	1	yes	characteristic, complemented
812	#2334	C₂×C₅₃	1	1	yes	characteristic, complemented
813	#2326	C₂×C₅₃	1	1	yes	characteristic, complemented
814	#2325	C₂×C₅₃	1	1	yes	characteristic, complemented
815	#2324	C₂×C₅₃	1	1	yes	characteristic, complemented
816	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
817	#2321	C₂×C₅₃	1	1	yes	characteristic, complemented
818	#2321	C₂×C₅₃	1	1	yes	characteristic, complemented
819	#2312	C₂×C₅₃	1	1	yes	characteristic, complemented
820	C₄×#120	C₂×C₅₃	1	1	yes	characteristic, complemented
821	C₄×#120	C₂×C₅₃	1	1	yes	characteristic, complemented
822	C₂×#385	C₂×C₅₃	1	1	yes	characteristic, complemented
823	C₂×C₅₃	—	2	4	no	—
824	C₂×C₅₃	—	4	2	no	—
825	C₂×C₅₃	—	4	2	no	—
826	C₂×C₅₃	—	4	2	no	—
827	C₂×C₅₃	—	4	2	no	—
828	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
829	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂×C₅₃	#3532	1	1	yes	characteristic
832	C₂×C₅₃	#3533	1	1	yes	characteristic
833	C₂×C₅₃	#3541	1	1	yes	characteristic
834	C₂×C₅₃	#3541	1	1	yes	characteristic
835	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
836	#538	C₄×C₅₃	1	16	yes	complemented
837	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
838	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
839	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
840	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
841	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
842	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
843	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
844	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
845	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
846	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
847	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
848	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
849	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
850	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
851	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
852	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
853	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
854	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
855	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
856	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
857	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
858	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
859	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
860	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
861	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
862	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
863	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
864	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
865	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
866	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
867	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
868	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
869	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
870	#390	C₂²×C₅₃	1	1	yes	characteristic
871	#390	C₂²×C₅₃	1	1	yes	characteristic
872	#390	C₂²×C₅₃	1	1	yes	characteristic
873	#390	C₂²×C₅₃	1	1	yes	characteristic
874	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
875	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
876	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
877	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
878	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
879	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
880	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
881	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
882	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
883	#388	C₂²×C₅₃	1	1	yes	characteristic
884	#388	C₂²×C₅₃	1	1	yes	characteristic
885	#388	C₂²×C₅₃	1	1	yes	characteristic
886	#388	C₂²×C₅₃	1	1	yes	characteristic
887	#388	C₂²×C₅₃	1	1	yes	characteristic
888	#388	C₂²×C₅₃	1	1	yes	characteristic
889	#388	C₂²×C₅₃	1	1	yes	characteristic
890	#388	C₂²×C₅₃	1	1	yes	characteristic
891	#388	C₂²×C₅₃	1	1	yes	characteristic
892	#388	C₂²×C₅₃	1	1	yes	characteristic
893	#388	C₂²×C₅₃	1	1	yes	characteristic
894	#388	C₂²×C₅₃	1	1	yes	characteristic
895	#388	C₂²×C₅₃	1	1	yes	characteristic
896	#388	C₂²×C₅₃	1	1	yes	characteristic
897	#388	C₂²×C₅₃	1	1	yes	characteristic
898	#388	C₂²×C₅₃	1	1	yes	characteristic
899	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
900	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
901	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
902	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
903	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
904	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
905	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
908	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
913	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
914	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
915	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
916	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
917	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	#386	C₂²×C₅₃	1	1	yes	characteristic
920	#386	C₂²×C₅₃	1	1	yes	characteristic
921	#386	C₂²×C₅₃	1	1	yes	characteristic
922	#386	C₂²×C₅₃	1	1	yes	characteristic
923	#386	C₂²×C₅₃	1	1	yes	characteristic
924	#386	C₂²×C₅₃	1	1	yes	characteristic
925	#386	C₂²×C₅₃	1	1	yes	characteristic
926	#386	C₂²×C₅₃	1	1	yes	characteristic
927	#386	C₂²×C₅₃	1	1	yes	characteristic
928	#386	C₂²×C₅₃	1	1	yes	characteristic
929	#386	C₂²×C₅₃	1	1	yes	characteristic
930	#386	C₂²×C₅₃	1	1	yes	characteristic
931	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#385	C₂²×C₅₃	1	1	yes	characteristic
934	#385	C₂²×C₅₃	1	1	yes	characteristic
935	#385	C₂²×C₅₃	1	1	yes	characteristic
936	#385	C₂²×C₅₃	1	1	yes	characteristic
937	#385	C₂²×C₅₃	1	1	yes	characteristic
938	#385	C₂²×C₅₃	1	1	yes	characteristic
939	#385	C₂²×C₅₃	1	1	yes	characteristic
940	#385	C₂²×C₅₃	1	1	yes	characteristic
941	#385	C₂²×C₅₃	1	1	yes	characteristic
942	#385	C₂²×C₅₃	1	1	yes	characteristic
943	#385	C₂²×C₅₃	1	1	yes	characteristic
944	#385	C₂²×C₅₃	1	1	yes	characteristic
945	#385	C₂²×C₅₃	1	1	yes	characteristic
946	#385	C₂²×C₅₃	1	1	yes	characteristic
947	#385	C₂²×C₅₃	1	1	yes	characteristic
948	#385	C₂²×C₅₃	1	1	yes	characteristic
949	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#380	C₂²×C₅₃	1	1	yes	characteristic
961	#380	C₂²×C₅₃	1	1	yes	characteristic
962	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#379	C₂²×C₅₃	1	1	yes	characteristic
966	#379	C₂²×C₅₃	1	1	yes	characteristic
967	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
975	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
976	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
977	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
978	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
979	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
980	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
981	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
982	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
983	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
984	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#376	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
989	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
990	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	C₅₃	#34416	1	1	yes	characteristic, direct product factor, Sylow
992	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
993	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
994	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
995	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
996	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
997	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
998	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
999	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1000	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1001	C₂³×C₄	—	4	2	no	—
1002	C₂³×C₄	—	4	2	no	—
1003	C₂³×C₄	—	4	2	no	—
1004	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1005	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1007	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1013	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1015	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1020	#126	C₂×C₄×C₅₃	1	8	yes	complemented
1021	#126	C₂×C₄×C₅₃	1	8	yes	complemented
1022	#124	C₂×C₄×C₅₃	1	8	yes	complemented
1023	#124	C₂×C₄×C₅₃	1	8	yes	complemented
1024	#123	C₂×C₄×C₅₃	1	8	yes	complemented
1025	#123	C₂×C₄×C₅₃	1	8	yes	complemented
1026	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
1027	#121	C₂×C₄×C₅₃	1	8	yes	complemented
1028	#121	C₂×C₄×C₅₃	1	8	yes	complemented
1029	#121	C₂×C₄×C₅₃	1	8	yes	complemented
1030	#120	C₂×C₄×C₅₃	1	8	yes	complemented
1031	#120	C₂×C₄×C₅₃	1	8	yes	complemented
1032	C₄×Q₈	—	4	2	no	—
1033	C₄×D₄	—	4	2	no	—
1034	C₄×D₄	—	4	2	no	—
1035	C₄×D₄	—	4	2	no	—
1036	C₄×D₄	—	4	2	no	—
1037	C₄×D₄	—	4	2	no	—
1038	C₄×D₄	—	4	2	no	—
1039	C₄×D₄	—	4	2	no	—
1040	C₄×D₄	—	4	2	no	—
1041	C₄×D₄	—	4	2	no	—
1042	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
1043	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
1044	#117	—	4	2	no	—
1045	C₂×C₄⋊C₄	—	4	2	no	—
1046	C₂×C₄⋊C₄	—	4	2	no	—
1047	C₂×C₄⋊C₄	—	4	2	no	—
1048	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1056	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1057	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×C₂²⋊C₄	—	4	2	no	—
1079	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
1080	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1090	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1103	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1106	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1116	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1130	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1140	#95	C₂³×C₅₃	1	1	yes	characteristic
1141	#95	C₂³×C₅₃	1	1	yes	characteristic
1142	#95	C₂³×C₅₃	1	1	yes	characteristic
1143	#95	C₂³×C₅₃	1	1	yes	characteristic
1144	#95	C₂³×C₅₃	1	1	yes	characteristic
1145	#95	C₂³×C₅₃	1	1	yes	characteristic
1146	#95	C₂³×C₅₃	1	1	yes	characteristic
1147	#95	C₂³×C₅₃	1	1	yes	characteristic
1148	#95	C₂³×C₅₃	1	1	yes	characteristic
1149	#95	C₂³×C₅₃	1	1	yes	characteristic
1150	#95	C₂³×C₅₃	1	1	yes	characteristic
1151	#95	C₂³×C₅₃	1	1	yes	characteristic
1152	#95	C₂³×C₅₃	1	1	yes	characteristic
1153	#95	C₂³×C₅₃	1	1	yes	characteristic
1154	#95	C₂³×C₅₃	1	1	yes	characteristic
1155	#95	C₂³×C₅₃	1	1	yes	characteristic
1156	#95	C₂³×C₅₃	1	1	yes	characteristic
1157	#95	C₂³×C₅₃	1	1	yes	characteristic
1158	#95	C₂³×C₅₃	1	1	yes	characteristic
1159	#95	C₂³×C₅₃	1	1	yes	characteristic
1160	#95	C₂³×C₅₃	1	1	yes	characteristic
1161	#95	C₂³×C₅₃	1	1	yes	characteristic
1162	#95	C₂³×C₅₃	1	1	yes	characteristic
1163	#95	C₂³×C₅₃	1	1	yes	characteristic
1164	#95	C₂³×C₅₃	1	1	yes	characteristic
1165	#95	C₂³×C₅₃	1	1	yes	characteristic
1166	#95	C₂³×C₅₃	1	1	yes	characteristic
1167	#95	C₂³×C₅₃	1	1	yes	characteristic
1168	#95	C₂³×C₅₃	1	1	yes	characteristic
1169	#95	C₂³×C₅₃	1	1	yes	characteristic
1170	#95	C₂³×C₅₃	1	1	yes	characteristic
1171	#95	C₂³×C₅₃	1	1	yes	characteristic
1172	#95	C₂³×C₅₃	1	1	yes	characteristic
1173	#95	C₂³×C₅₃	1	1	yes	characteristic
1174	#95	C₂³×C₅₃	1	1	yes	characteristic
1175	#95	C₂³×C₅₃	1	1	yes	characteristic
1176	#95	C₂³×C₅₃	1	1	yes	characteristic
1177	#95	C₂³×C₅₃	1	1	yes	characteristic
1178	#95	C₂³×C₅₃	1	1	yes	characteristic
1179	#95	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂⁴	—	2	2	no	—
1181	C₂⁴	—	2	2	no	—
1182	C₂⁴	—	4	1	no	—
1183	C₂⁴	—	4	1	no	—
1184	C₂⁴	—	4	1	no	—
1185	C₂⁴	—	4	1	no	—
1186	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
1187	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1188	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1189	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1190	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1191	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1192	C₂×Q₈	—	4	1	no	—
1193	C₂×Q₈	—	4	1	no	—
1194	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	complemented
1195	C₂×D₄	—	2	2	no	—
1196	C₂×D₄	—	2	2	no	—
1197	C₂×D₄	—	2	2	no	—
1198	C₂×D₄	—	2	2	no	—
1199	C₂×D₄	—	4	1	no	—
1200	C₂×D₄	—	4	1	no	—
1201	C₂×D₄	—	4	1	no	—
1202	C₂×D₄	—	4	1	no	—
1203	C₂×D₄	—	4	1	no	—
1204	C₂×D₄	—	4	1	no	—
1205	C₂×D₄	—	4	1	no	—
1206	C₂×D₄	—	4	1	no	—
1207	C₂×D₄	—	4	1	no	—
1208	C₂×D₄	—	4	1	no	—
1209	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1210	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1211	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1212	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1213	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1214	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1215	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1216	C₂²×C₄	—	2	2	no	—
1217	C₂²×C₄	—	2	2	no	—
1218	C₂²×C₄	—	2	2	no	—
1219	C₂²×C₄	—	2	2	no	—
1220	C₂²×C₄	—	2	2	no	—
1221	C₂²×C₄	—	2	2	no	—
1222	C₂²×C₄	—	2	2	no	—
1223	C₂²×C₄	—	2	2	no	—
1224	C₂²×C₄	—	2	2	no	—
1225	C₂²×C₄	—	2	2	no	—
1226	C₂²×C₄	—	2	2	no	—
1227	C₂²×C₄	—	2	2	no	—
1228	C₂²×C₄	—	4	1	no	—
1229	C₂²×C₄	—	4	1	no	—
1230	C₂²×C₄	—	4	1	no	—
1231	C₂²×C₄	—	4	1	no	—
1232	C₂²×C₄	—	4	1	no	—
1233	C₂²×C₄	—	4	1	no	—
1234	C₂²×C₄	—	4	1	no	—
1235	C₂²×C₄	—	4	1	no	—
1236	C₂²×C₄	—	4	1	no	—
1237	C₂²×C₄	—	4	1	no	—
1238	C₂²×C₄	—	4	1	no	—
1239	C₂²×C₄	—	4	1	no	—
1240	C₂²×C₄	—	4	1	no	—
1241	C₂²×C₄	—	4	1	no	—
1242	C₂²×C₄	—	4	1	no	—
1243	C₂²×C₄	—	4	1	no	—
1244	C₂²×C₄	—	4	1	no	—
1245	C₂²×C₄	—	4	1	no	—
1246	C₂²×C₄	—	4	1	no	—
1247	C₂²×C₄	—	4	1	no	—
1248	C₂²×C₄	—	4	1	no	—
1249	C₂²×C₄	—	4	1	no	—
1250	C₂²×C₄	—	4	1	no	—
1251	C₂²×C₄	—	4	1	no	—
1252	C₂²×C₄	—	4	1	no	—
1253	C₂²×C₄	—	4	1	no	—
1254	C₂²×C₄	—	4	1	no	—
1255	C₂²×C₄	—	4	1	no	—
1256	C₂²×C₄	—	4	1	no	—
1257	C₂²×C₄	—	4	1	no	—
1258	C₂²×C₄	—	4	1	no	—
1259	C₂²×C₄	—	4	1	no	—
1260	C₂²×C₄	—	4	16	no	—
1261	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1262	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1263	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1264	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1265	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1266	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1267	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1268	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1269	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1270	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1271	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1272	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1273	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1274	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1275	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1276	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1277	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1278	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1279	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1280	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1281	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1282	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1283	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1284	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1285	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1286	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1287	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1288	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1289	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1290	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1291	C₄⋊C₄	—	2	2	no	—
1292	C₄⋊C₄	—	2	2	no	—
1293	C₄⋊C₄	—	2	2	no	—
1294	C₄⋊C₄	—	2	2	no	—
1295	C₄⋊C₄	—	2	2	no	—
1296	C₄⋊C₄	—	2	2	no	—
1297	C₄⋊C₄	—	4	1	no	—
1298	C₄⋊C₄	—	4	1	no	—
1299	C₄⋊C₄	—	4	1	no	—
1300	C₄⋊C₄	—	4	1	no	—
1301	C₄⋊C₄	—	4	1	no	—
1302	C₄⋊C₄	—	4	1	no	—
1303	C₄⋊C₄	—	4	1	no	—
1304	C₄⋊C₄	—	4	1	no	—
1305	C₄⋊C₄	—	4	1	no	—
1306	C₄⋊C₄	—	4	1	no	—
1307	C₄⋊C₄	—	4	1	no	—
1308	C₄⋊C₄	—	4	1	no	—
1309	C₄⋊C₄	—	4	1	no	—
1310	C₄⋊C₄	—	4	1	no	—
1311	C₄⋊C₄	—	4	1	no	—
1312	C₄⋊C₄	—	4	1	no	—
1313	C₄⋊C₄	—	4	1	no	—
1314	C₄⋊C₄	—	4	1	no	—
1315	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1316	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1317	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1318	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1319	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1320	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1321	C₂²⋊C₄	—	2	2	no	—
1322	C₂²⋊C₄	—	2	2	no	—
1323	C₂²⋊C₄	—	2	2	no	—
1324	C₂²⋊C₄	—	2	2	no	—
1325	C₂²⋊C₄	—	2	2	no	—
1326	C₂²⋊C₄	—	2	2	no	—
1327	C₂²⋊C₄	—	4	1	no	—
1328	C₂²⋊C₄	—	4	1	no	—
1329	C₂²⋊C₄	—	4	1	no	—
1330	C₂²⋊C₄	—	4	1	no	—
1331	C₂²⋊C₄	—	4	1	no	—
1332	C₂²⋊C₄	—	4	1	no	—
1333	C₂²⋊C₄	—	4	1	no	—
1334	C₂²⋊C₄	—	4	1	no	—
1335	C₂²⋊C₄	—	4	1	no	—
1336	C₂²⋊C₄	—	4	1	no	—
1337	C₂²⋊C₄	—	4	1	no	—
1338	C₂²⋊C₄	—	4	1	no	—
1339	C₂²⋊C₄	—	4	1	no	—
1340	C₂²⋊C₄	—	4	1	no	—
1341	C₂²⋊C₄	—	4	1	no	—
1342	C₂²⋊C₄	—	4	1	no	—
1343	C₂²⋊C₄	—	4	1	no	—
1344	C₂²⋊C₄	—	4	1	no	—
1345	C₂²⋊C₄	—	4	1	no	—
1346	C₂²⋊C₄	—	4	1	no	—
1347	C₂²⋊C₄	—	4	1	no	—
1348	C₂²⋊C₄	—	4	1	no	—
1349	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1350	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1351	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1352	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1353	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1354	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1355	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1356	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1357	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1358	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1359	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1360	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1361	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1362	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1363	C₄²	—	2	2	no	—
1364	C₄²	—	2	2	no	—
1365	C₄²	—	4	1	no	—
1366	C₄²	—	4	1	no	—
1367	C₄²	—	4	1	no	—
1368	C₄²	—	4	1	no	—
1369	C₄²	—	4	1	no	—
1370	C₄²	—	4	1	no	—
1371	C₄²	—	4	1	no	—
1372	C₄²	—	4	1	no	—
1373	C₄²	—	4	1	no	—
1374	C₄²	—	4	1	no	—
1375	C₄²	—	4	1	no	—
1376	C₄²	—	4	1	no	—
1377	C₄²	—	4	1	no	—
1378	C₄²	—	4	1	no	—
1379	C₄²	C₂²×C₄×C₅₃	1	4	yes	complemented
1380	C₄²	C₂²×C₄×C₅₃	1	4	yes	complemented
1381	C₂³	—	2	1	no	—
1382	C₂³	—	2	1	no	—
1383	C₂³	—	2	1	no	—
1384	C₂³	—	2	1	no	—
1385	C₂³	—	2	8	no	—
1386	C₂³	—	2	1	no	—
1387	C₂³	—	2	1	no	—
1388	C₂³	—	2	1	no	—
1389	C₂³	—	2	1	no	—
1390	C₂³	—	2	1	no	—
1391	C₂³	—	2	1	no	—
1392	C₂³	—	2	1	no	—
1393	C₂³	—	2	1	no	—
1394	C₂³	—	2	1	no	—
1395	C₂³	—	2	1	no	—
1396	C₂³	—	2	1	no	—
1397	C₂³	—	2	1	no	—
1398	C₂³	—	2	1	no	—
1399	C₂³	—	2	1	no	—
1400	C₂³	—	2	1	no	—
1401	C₂³	—	2	1	no	—
1402	C₂³	—	2	1	no	—
1403	C₂³	—	2	1	no	—
1404	C₂³	—	2	1	no	—
1405	C₂³	—	2	1	no	—
1406	C₂³	—	2	1	no	—
1407	C₂³	—	2	1	no	—
1408	C₂³	—	2	1	no	—
1409	C₂³	—	2	1	no	—
1410	C₂³	—	4	4	no	—
1411	C₂³	—	4	4	no	—
1412	C₂³	—	4	4	no	—
1413	C₂³	—	4	4	no	—
1414	C₂³	—	4	4	no	—
1415	C₂³	—	4	4	no	—
1416	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1417	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1418	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1419	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1420	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1421	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1422	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1423	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1424	Q₈	—	4	4	no	—
1425	D₄	—	2	8	no	—
1426	D₄	—	2	8	no	—
1427	D₄	—	4	4	no	—
1428	D₄	—	4	4	no	—
1429	D₄	—	4	4	no	—
1430	D₄	—	4	4	no	—
1431	D₄	—	4	4	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	2	1	no	—
1445	C₂×C₄	—	2	1	no	—
1446	C₂×C₄	—	2	1	no	—
1447	C₂×C₄	—	2	1	no	—
1448	C₂×C₄	—	2	1	no	—
1449	C₂×C₄	—	2	1	no	—
1450	C₂×C₄	—	2	1	no	—
1451	C₂×C₄	—	2	1	no	—
1452	C₂×C₄	—	2	1	no	—
1453	C₂×C₄	—	2	1	no	—
1454	C₂×C₄	—	2	1	no	—
1455	C₂×C₄	—	2	1	no	—
1456	C₂×C₄	—	2	1	no	—
1457	C₂×C₄	—	2	1	no	—
1458	C₂×C₄	—	2	1	no	—
1459	C₂×C₄	—	2	1	no	—
1460	C₂×C₄	—	2	1	no	—
1461	C₂×C₄	—	2	1	no	—
1462	C₂×C₄	—	2	1	no	—
1463	C₂×C₄	—	2	1	no	—
1464	C₂×C₄	—	2	1	no	—
1465	C₂×C₄	—	2	1	no	—
1466	C₂×C₄	—	2	1	no	—
1467	C₂×C₄	—	2	1	no	—
1468	C₂×C₄	—	2	1	no	—
1469	C₂×C₄	—	2	1	no	—
1470	C₂×C₄	—	2	1	no	—
1471	C₂×C₄	—	2	1	no	—
1472	C₂×C₄	—	2	1	no	—
1473	C₂×C₄	—	2	1	no	—
1474	C₂×C₄	—	2	1	no	—
1475	C₂×C₄	—	2	1	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	1	no	—
1478	C₂×C₄	—	2	1	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	2	1	no	—
1482	C₂×C₄	—	2	1	no	—
1483	C₂×C₄	—	2	1	no	—
1484	C₂×C₄	—	2	1	no	—
1485	C₂×C₄	—	2	1	no	—
1486	C₂×C₄	—	2	1	no	—
1487	C₂×C₄	—	2	1	no	—
1488	C₂×C₄	—	2	1	no	—
1489	C₂×C₄	—	2	1	no	—
1490	C₂×C₄	—	2	1	no	—
1491	C₂×C₄	—	2	1	no	—
1492	C₂×C₄	—	2	1	no	—
1493	C₂×C₄	—	2	1	no	—
1494	C₂×C₄	—	2	1	no	—
1495	C₂×C₄	—	2	1	no	—
1496	C₂×C₄	—	2	1	no	—
1497	C₂×C₄	—	2	1	no	—
1498	C₂×C₄	—	4	4	no	—
1499	C₂×C₄	—	4	4	no	—
1500	C₂×C₄	—	4	4	no	—
1501	C₂×C₄	—	4	4	no	—
1502	C₂×C₄	—	4	4	no	—
1503	C₂×C₄	—	4	4	no	—
1504	C₂×C₄	—	4	4	no	—
1505	C₂×C₄	—	4	4	no	—
1506	C₂×C₄	—	4	4	no	—
1507	C₂×C₄	—	4	4	no	—
1508	C₂×C₄	—	8	2	no	—
1509	C₂×C₄	—	8	2	no	—
1510	C₂×C₄	—	8	2	no	—
1511	C₂×C₄	—	8	2	no	—
1512	C₂×C₄	—	8	2	no	—
1513	C₂×C₄	—	8	2	no	—
1514	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1515	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1516	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1517	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1518	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1519	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1520	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1521	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1522	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1523	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1524	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1525	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1526	C₂²	—	2	2	no	—
1527	C₂²	—	2	2	no	—
1528	C₂²	—	2	2	no	—
1529	C₂²	—	2	2	no	—
1530	C₂²	—	2	2	no	—
1531	C₂²	—	2	2	no	—
1532	C₂²	—	2	2	no	—
1533	C₂²	—	2	2	no	—
1534	C₂²	—	2	2	no	—
1535	C₂²	—	2	2	no	—
1536	C₂²	—	2	2	no	—
1537	C₂²	—	2	2	no	—
1538	C₂²	—	2	2	no	—
1539	C₂²	—	2	2	no	—
1540	C₂²	—	2	2	no	—
1541	C₂²	—	2	2	no	—
1542	C₂²	—	2	2	no	—
1543	C₂²	—	2	2	no	—
1544	C₂²	—	4	16	no	—
1545	C₂²	—	4	1	no	—
1546	C₂²	—	4	1	no	—
1547	C₂²	—	4	1	no	—
1548	C₂²	—	4	1	no	—
1549	C₂²	—	4	1	no	—
1550	C₂²	—	4	1	no	—
1551	C₂²	—	4	1	no	—
1552	C₂²	—	4	1	no	—
1553	C₂²	—	4	1	no	—
1554	C₂²	—	4	1	no	—
1555	C₂²	—	4	1	no	—
1556	C₂²	—	4	1	no	—
1557	C₂²	—	4	1	no	—
1558	C₂²	—	4	1	no	—
1559	C₂²	—	4	1	no	—
1560	C₂²	—	4	1	no	—
1561	C₂²	C₅₃×#520	1	4	yes	—
1562	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
1563	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1564	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1565	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1566	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1567	C₂²	C₅₃×#585	1	1	yes	characteristic
1568	C₂²	C₅₃×#585	1	1	yes	characteristic
1569	C₄	—	2	2	no	—
1570	C₄	—	2	2	no	—
1571	C₄	—	2	2	no	—
1572	C₄	—	2	2	no	—
1573	C₄	—	2	2	no	—
1574	C₄	—	2	2	no	—
1575	C₄	—	2	2	no	—
1576	C₄	—	2	2	no	—
1577	C₄	—	2	2	no	—
1578	C₄	—	2	2	no	—
1579	C₄	—	2	2	no	—
1580	C₄	—	2	2	no	—
1581	C₄	—	4	1	no	—
1582	C₄	—	4	1	no	—
1583	C₄	—	4	1	no	—
1584	C₄	—	4	1	no	—
1585	C₄	—	4	1	no	—
1586	C₄	—	4	1	no	—
1587	C₄	—	4	1	no	—
1588	C₄	—	4	1	no	—
1589	C₄	—	4	1	no	—
1590	C₄	—	4	1	no	—
1591	C₄	—	4	1	no	—
1592	C₄	—	4	1	no	—
1593	C₄	—	4	1	no	—
1594	C₄	—	4	1	no	—
1595	C₂	—	2	4	no	—
1596	C₂	—	4	2	no	—
1597	C₂	—	4	2	no	—
1598	C₂	—	4	2	no	—
1599	C₂	—	4	2	no	—
1600	C₂	C₂×C₅₃×#520	1	1	yes	characteristic
1601	C₂	C₄×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1602	C₂	C₄×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1603	C₂	C₅₃×#3532	1	1	yes	characteristic
1604	C₂	C₅₃×#3533	1	1	yes	characteristic
1605	C₂	C₅₃×#3541	1	1	yes	characteristic
1606	C₂	C₅₃×#3541	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×C₅₃×#538	C₂
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×#2377	C₂	semidirect
5. C₅₃×#2376	C₂	semidirect
6. C₅₃×#2373	C₂	semidirect
7. C₅₃×#2368	C₂	semidirect
8. C₅₃×#2367	C₂	semidirect
9. C₅₃×#2364	C₂	semidirect
10. C₅₃×#2361	C₂	semidirect
11. C₅₃×#2361	C₂	semidirect
12. C₅₃×#2360	C₂	semidirect
13. C₅₃×#2359	C₂	semidirect
14. C₅₃×#2353	C₂	semidirect
15. C₅₃×#2352	C₂	semidirect
16. C₅₃×#2349	C₂	semidirect
17. D₄×C₄⋊C₄×C₅₃	C₂	semidirect
18. C₅₃×#2337	C₂	semidirect
19. C₅₃×#2335	C₂	semidirect
20. C₅₃×#2334	C₂	semidirect
21. C₅₃×#2334	C₂	semidirect
22. C₅₃×#2326	C₂	semidirect
23. C₅₃×#2325	C₂	semidirect
24. C₅₃×#2324	C₂	semidirect
25. C₅₃×#2322	C₂	semidirect
26. C₅₃×#2321	C₂	semidirect
27. C₅₃×#2321	C₂	semidirect
28. C₅₃×#2312	C₂	semidirect
29. C₄×#120×C₅₃	C₂	semidirect
30. C₄×#120×C₅₃	C₂	semidirect
31. C₂×C₅₃×#385	C₂	semidirect
33. C₅₃×#538	C₄	semidirect
46. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
57. C₂×C₄×D₄×C₅₃	C₂²	semidirect
58. C₂×#117×C₅₃	C₂²	semidirect
61. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
64. C₅₃×#391	C₂²	semidirect
65. C₅₃×#391	C₂²	semidirect
66. C₅₃×#391	C₂²	semidirect
71. C₅₃×#390	C₂²	semidirect
72. C₅₃×#389	C₂²	semidirect
73. C₅₃×#389	C₂²	semidirect
74. C₅₃×#389	C₂²	semidirect
75. C₅₃×#389	C₂²	semidirect
76. C₅₃×#389	C₂²	semidirect
77. C₅₃×#389	C₂²	semidirect
78. C₅₃×#389	C₂²	semidirect
79. C₅₃×#389	C₂²	semidirect
96. C₅₃×#388	C₂²	semidirect
97. C₅₃×#388	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
128. C₅₃×#386	C₂²	semidirect
129. C₅₃×#386	C₂²	semidirect
146. C₅₃×#385	C₂²	semidirect
147. C₅₃×#385	C₂²	semidirect
148. C₅₃×#385	C₂²	semidirect
149. C₅₃×#385	C₂²	semidirect
150. C₅₃×#385	C₂²	semidirect
151. C₅₃×#385	C₂²	semidirect
152. C₅₃×#384	C₂²	semidirect
153. C₅₃×#383	C₂²	semidirect
154. C₅₃×#382	C₂²	semidirect
155. C₅₃×#382	C₂²	semidirect
156. C₅₃×#381	C₂²	semidirect
159. C₅₃×#380	C₂²	semidirect
160. C₅₃×#380	C₂²	semidirect
161. C₅₃×#380	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
181. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
182. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
183. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
184. C₅₃×#376	C₂²	semidirect
187. C₂×#95×C₅₃	C₂²	semidirect
216. #126×C₅₃	C₂×C₄	semidirect
217. #126×C₅₃	C₂×C₄	semidirect
218. #124×C₅₃	C₂×C₄	semidirect
219. #124×C₅₃	C₂×C₄	semidirect
220. #123×C₅₃	C₂×C₄	semidirect
221. #123×C₅₃	C₂×C₄	semidirect
222. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
223. #121×C₅₃	C₂×C₄	semidirect
224. #121×C₅₃	C₂×C₄	semidirect
225. #121×C₅₃	C₂×C₄	semidirect
226. #120×C₅₃	C₂×C₄	semidirect
227. #120×C₅₃	C₂×C₄	semidirect
238. C₄×D₄×C₅₃	C₂×C₄	semidirect
239. C₄×D₄×C₅₃	C₂×C₄	semidirect
275. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
390. C₂×Q₈×C₅₃	C₂²×C₄	semidirect
411. C₂×D₄×C₅₃	C₂²×C₄	semidirect
459. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
460. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
511. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
512. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
513. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
514. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
515. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
516. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
555. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
556. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
557. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
558. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
575. C₄²×C₅₃	C₂²×C₄	semidirect
576. C₄²×C₅₃	C₂²×C₄	semidirect
722. #34416	C₅₃	direct (N × H)
793. #2383	C₂×C₅₃	semidirect
794. #2379	C₂×C₅₃	semidirect
795. #2377	C₂×C₅₃	semidirect
796. #2376	C₂×C₅₃	semidirect
797. #2373	C₂×C₅₃	semidirect
798. #2368	C₂×C₅₃	semidirect
799. #2367	C₂×C₅₃	semidirect
800. #2364	C₂×C₅₃	semidirect
801. #2361	C₂×C₅₃	semidirect
802. #2361	C₂×C₅₃	semidirect
803. #2360	C₂×C₅₃	semidirect
804. #2359	C₂×C₅₃	semidirect
805. #2353	C₂×C₅₃	semidirect
806. #2352	C₂×C₅₃	semidirect
807. #2349	C₂×C₅₃	semidirect
808. D₄×C₄⋊C₄	C₂×C₅₃	semidirect
809. #2337	C₂×C₅₃	semidirect
810. #2335	C₂×C₅₃	semidirect
811. #2334	C₂×C₅₃	semidirect
812. #2334	C₂×C₅₃	semidirect
813. #2326	C₂×C₅₃	semidirect
814. #2325	C₂×C₅₃	semidirect
815. #2324	C₂×C₅₃	semidirect
816. #2322	C₂×C₅₃	semidirect
817. #2321	C₂×C₅₃	semidirect
818. #2321	C₂×C₅₃	semidirect
819. #2312	C₂×C₅₃	semidirect
820. C₄×#120	C₂×C₅₃	semidirect
821. C₄×#120	C₂×C₅₃	semidirect
822. C₂×#385	C₂×C₅₃	semidirect
836. #538	C₄×C₅₃	semidirect
849. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
860. C₂×C₄×D₄	C₂²×C₅₃	semidirect
861. C₂×#117	C₂²×C₅₃	semidirect
864. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
867. #391	C₂²×C₅₃	semidirect
868. #391	C₂²×C₅₃	semidirect
869. #391	C₂²×C₅₃	semidirect
874. #390	C₂²×C₅₃	semidirect
875. #389	C₂²×C₅₃	semidirect
876. #389	C₂²×C₅₃	semidirect
877. #389	C₂²×C₅₃	semidirect
878. #389	C₂²×C₅₃	semidirect
879. #389	C₂²×C₅₃	semidirect
880. #389	C₂²×C₅₃	semidirect
881. #389	C₂²×C₅₃	semidirect
882. #389	C₂²×C₅₃	semidirect
899. #388	C₂²×C₅₃	semidirect
900. #388	C₂²×C₅₃	semidirect
901. #388	C₂²×C₅₃	semidirect
902. #388	C₂²×C₅₃	semidirect
903. #388	C₂²×C₅₃	semidirect
904. #388	C₂²×C₅₃	semidirect
905. #388	C₂²×C₅₃	semidirect
906. #388	C₂²×C₅₃	semidirect
907. #387	C₂²×C₅₃	semidirect
908. #387	C₂²×C₅₃	semidirect
909. #387	C₂²×C₅₃	semidirect
910. #387	C₂²×C₅₃	semidirect
911. #387	C₂²×C₅₃	semidirect
912. #387	C₂²×C₅₃	semidirect
913. #387	C₂²×C₅₃	semidirect
914. #387	C₂²×C₅₃	semidirect
915. #387	C₂²×C₅₃	semidirect
916. #387	C₂²×C₅₃	semidirect
917. #387	C₂²×C₅₃	semidirect
918. #387	C₂²×C₅₃	semidirect
931. #386	C₂²×C₅₃	semidirect
932. #386	C₂²×C₅₃	semidirect
949. #385	C₂²×C₅₃	semidirect
950. #385	C₂²×C₅₃	semidirect
951. #385	C₂²×C₅₃	semidirect
952. #385	C₂²×C₅₃	semidirect
953. #385	C₂²×C₅₃	semidirect
954. #385	C₂²×C₅₃	semidirect
955. #384	C₂²×C₅₃	semidirect
956. #383	C₂²×C₅₃	semidirect
957. #382	C₂²×C₅₃	semidirect
958. #382	C₂²×C₅₃	semidirect
959. #381	C₂²×C₅₃	semidirect
962. #380	C₂²×C₅₃	semidirect
963. #380	C₂²×C₅₃	semidirect
964. #380	C₂²×C₅₃	semidirect
967. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
968. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
969. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
970. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
971. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
972. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
973. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
984. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
985. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
986. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
987. #376	C₂²×C₅₃	semidirect
990. C₂×#95	C₂²×C₅₃	semidirect
991. C₅₃	#34416	direct (N × H)
1020. #126	C₂×C₄×C₅₃	semidirect
1021. #126	C₂×C₄×C₅₃	semidirect
1022. #124	C₂×C₄×C₅₃	semidirect
1023. #124	C₂×C₄×C₅₃	semidirect
1024. #123	C₂×C₄×C₅₃	semidirect
1025. #123	C₂×C₄×C₅₃	semidirect
1026. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
1027. #121	C₂×C₄×C₅₃	semidirect
1028. #121	C₂×C₄×C₅₃	semidirect
1029. #121	C₂×C₄×C₅₃	semidirect
1030. #120	C₂×C₄×C₅₃	semidirect
1031. #120	C₂×C₄×C₅₃	semidirect
1042. C₄×D₄	C₂×C₄×C₅₃	semidirect
1043. C₄×D₄	C₂×C₄×C₅₃	semidirect
1079. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
1194. C₂×Q₈	C₂²×C₄×C₅₃	semidirect
1215. C₂×D₄	C₂²×C₄×C₅₃	semidirect
1263. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
1264. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
1315. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1316. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1317. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1318. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1319. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1320. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1359. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
1360. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
1361. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
1362. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
1379. C₄²	C₂²×C₄×C₅₃	semidirect
1380. C₄²	C₂²×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×#538	2
C₅₃×#2383	2
C₅₃×#2379	2
C₅₃×#2377	2
C₅₃×#2376	2
C₅₃×#2373	2
C₅₃×#2368	2
C₅₃×#2367	2
C₅₃×#2364	2
C₅₃×#2361	2
C₅₃×#2360	2
C₅₃×#2359	2
C₅₃×#2353	2
C₅₃×#2352	2
C₅₃×#2349	2
D₄×C₄⋊C₄×C₅₃	2
C₅₃×#2337	2
C₅₃×#2335	2
C₅₃×#2334	2
C₅₃×#2326	2
C₅₃×#2325	2
C₅₃×#2324	2
C₅₃×#2322	2
C₅₃×#2321	2
C₅₃×#2312	2
C₄×#120×C₅₃	2
C₂×C₅₃×#385	2
#34416	53

Subgroups — C53×#34416 #27241928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34416 #27241928