Subgroups — C₅₃×#34456 #27241968

Order 13568.

2844 conjugacy classes of subgroups.

The subgroup lattice has 1710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2379	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2377	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×#2368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2359	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2358	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2358	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2342	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2342	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2337	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2321	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
33	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#546	C₄	1	16	yes	complemented
36	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#121×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×#120×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×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, complemented
52	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
62	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
63	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
64	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
65	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
66	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#390	C₂²	1	1	yes	characteristic
71	C₅₃×#390	C₂²	1	1	yes	characteristic
72	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#390	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, complemented
81	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#387	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×#386	C₂²	1	1	yes	characteristic
109	C₅₃×#386	C₂²	1	1	yes	characteristic
110	C₅₃×#386	C₂²	1	1	yes	characteristic
111	C₅₃×#386	C₂²	1	1	yes	characteristic
112	C₅₃×#386	C₂²	1	1	yes	characteristic
113	C₅₃×#386	C₂²	1	1	yes	characteristic
114	C₅₃×#386	C₂²	1	1	yes	characteristic
115	C₅₃×#386	C₂²	1	1	yes	characteristic
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, complemented
123	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
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, complemented
139	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#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×#383	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
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×#380	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#379	C₂²	1	1	yes	characteristic
168	C₅₃×#379	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
170	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
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, complemented
186	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
189	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×#41×C₅₃	—	4	2	no	—
191	C₂×#41×C₅₃	—	4	2	no	—
192	C₂×#41×C₅₃	C₂×C₄	1	8	yes	complemented
193	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
194	C₂²×D₄×C₅₃	—	4	2	no	—
195	C₂²×D₄×C₅₃	—	4	2	no	—
196	C₂²×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
197	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₅₃	—	4	2	no	—
207	C₂³×C₄×C₅₃	—	4	2	no	—
208	C₂³×C₄×C₅₃	—	4	2	no	—
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	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
219	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
221	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
224	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
229	#124×C₅₃	C₂×C₄	1	8	yes	complemented
230	#123×C₅₃	C₂×C₄	1	8	yes	complemented
231	#123×C₅₃	C₂×C₄	1	8	yes	complemented
232	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
233	#121×C₅₃	C₂×C₄	1	8	yes	complemented
234	#121×C₅₃	C₂×C₄	1	8	yes	complemented
235	#121×C₅₃	C₂×C₄	1	8	yes	complemented
236	#120×C₅₃	C₂×C₄	1	8	yes	complemented
237	#120×C₅₃	C₂×C₄	1	8	yes	complemented
238	C₄×D₄×C₅₃	—	4	2	no	—
239	C₄×D₄×C₅₃	—	4	2	no	—
240	C₄×D₄×C₅₃	—	4	2	no	—
241	C₄×D₄×C₅₃	—	4	2	no	—
242	C₄×D₄×C₅₃	—	4	2	no	—
243	C₄×D₄×C₅₃	—	4	2	no	—
244	C₄×D₄×C₅₃	—	4	2	no	—
245	C₄×D₄×C₅₃	—	4	2	no	—
246	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
247	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
248	#117×C₅₃	—	4	2	no	—
249	#117×C₅₃	—	4	2	no	—
250	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
251	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
277	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
278	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
279	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
280	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
281	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
282	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
323	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
326	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄×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	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄²×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	#95×C₅₃	C₂³	1	1	yes	characteristic
377	#95×C₅₃	C₂³	1	1	yes	characteristic
378	#95×C₅₃	C₂³	1	1	yes	characteristic
379	#95×C₅₃	C₂³	1	1	yes	characteristic
380	#95×C₅₃	C₂³	1	1	yes	characteristic
381	#95×C₅₃	C₂³	1	1	yes	characteristic
382	C₂⁴×C₅₃	—	2	2	no	—
383	C₂⁴×C₅₃	—	2	2	no	—
384	C₂⁴×C₅₃	—	2	2	no	—
385	C₂⁴×C₅₃	—	2	2	no	—
386	C₂⁴×C₅₃	—	2	2	no	—
387	C₂⁴×C₅₃	—	2	2	no	—
388	C₂⁴×C₅₃	—	4	1	no	—
389	C₂⁴×C₅₃	—	4	1	no	—
390	C₂⁴×C₅₃	—	4	1	no	—
391	C₂⁴×C₅₃	—	4	1	no	—
392	C₂⁴×C₅₃	—	4	1	no	—
393	C₂⁴×C₅₃	—	4	1	no	—
394	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
395	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
396	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
402	#41×C₅₃	—	4	16	no	—
403	C₂×Q₈×C₅₃	—	4	1	no	—
404	C₂×Q₈×C₅₃	—	4	1	no	—
405	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	complemented
406	C₂×D₄×C₅₃	—	2	2	no	—
407	C₂×D₄×C₅₃	—	2	2	no	—
408	C₂×D₄×C₅₃	—	2	2	no	—
409	C₂×D₄×C₅₃	—	2	2	no	—
410	C₂×D₄×C₅₃	—	2	2	no	—
411	C₂×D₄×C₅₃	—	2	2	no	—
412	C₂×D₄×C₅₃	—	2	2	no	—
413	C₂×D₄×C₅₃	—	2	2	no	—
414	C₂×D₄×C₅₃	—	4	1	no	—
415	C₂×D₄×C₅₃	—	4	1	no	—
416	C₂×D₄×C₅₃	—	4	1	no	—
417	C₂×D₄×C₅₃	—	4	1	no	—
418	C₂×D₄×C₅₃	—	4	1	no	—
419	C₂×D₄×C₅₃	—	4	1	no	—
420	C₂×D₄×C₅₃	—	4	1	no	—
421	C₂×D₄×C₅₃	—	4	1	no	—
422	C₂×D₄×C₅₃	—	4	1	no	—
423	C₂×D₄×C₅₃	—	4	1	no	—
424	C₂×D₄×C₅₃	—	4	16	no	—
425	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
426	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
427	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
428	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
429	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
430	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
431	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
432	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	complemented
433	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	complemented
434	C₂²×C₄×C₅₃	—	2	2	no	—
435	C₂²×C₄×C₅₃	—	2	2	no	—
436	C₂²×C₄×C₅₃	—	2	2	no	—
437	C₂²×C₄×C₅₃	—	2	2	no	—
438	C₂²×C₄×C₅₃	—	2	2	no	—
439	C₂²×C₄×C₅₃	—	2	2	no	—
440	C₂²×C₄×C₅₃	—	2	2	no	—
441	C₂²×C₄×C₅₃	—	2	2	no	—
442	C₂²×C₄×C₅₃	—	2	2	no	—
443	C₂²×C₄×C₅₃	—	2	2	no	—
444	C₂²×C₄×C₅₃	—	2	2	no	—
445	C₂²×C₄×C₅₃	—	2	2	no	—
446	C₂²×C₄×C₅₃	—	2	2	no	—
447	C₂²×C₄×C₅₃	—	2	2	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	1	no	—
457	C₂²×C₄×C₅₃	—	4	1	no	—
458	C₂²×C₄×C₅₃	—	4	1	no	—
459	C₂²×C₄×C₅₃	—	4	1	no	—
460	C₂²×C₄×C₅₃	—	4	1	no	—
461	C₂²×C₄×C₅₃	—	4	1	no	—
462	C₂²×C₄×C₅₃	—	4	1	no	—
463	C₂²×C₄×C₅₃	—	4	1	no	—
464	C₂²×C₄×C₅₃	—	4	1	no	—
465	C₂²×C₄×C₅₃	—	4	1	no	—
466	C₂²×C₄×C₅₃	—	4	1	no	—
467	C₂²×C₄×C₅₃	—	4	1	no	—
468	C₂²×C₄×C₅₃	—	4	1	no	—
469	C₂²×C₄×C₅₃	—	4	1	no	—
470	C₂²×C₄×C₅₃	—	4	1	no	—
471	C₂²×C₄×C₅₃	—	4	1	no	—
472	C₂²×C₄×C₅₃	—	4	1	no	—
473	C₂²×C₄×C₅₃	—	4	1	no	—
474	C₂²×C₄×C₅₃	—	4	1	no	—
475	C₂²×C₄×C₅₃	—	4	1	no	—
476	C₂²×C₄×C₅₃	—	4	1	no	—
477	C₂²×C₄×C₅₃	—	4	1	no	—
478	C₂²×C₄×C₅₃	—	4	1	no	—
479	C₂²×C₄×C₅₃	—	4	1	no	—
480	C₂²×C₄×C₅₃	—	4	1	no	—
481	C₂²×C₄×C₅₃	—	4	1	no	—
482	C₂²×C₄×C₅₃	—	4	1	no	—
483	C₂²×C₄×C₅₃	—	4	1	no	—
484	C₂²×C₄×C₅₃	—	4	1	no	—
485	C₂²×C₄×C₅₃	—	4	1	no	—
486	C₂²×C₄×C₅₃	—	4	1	no	—
487	C₂²×C₄×C₅₃	—	4	1	no	—
488	C₂²×C₄×C₅₃	—	4	16	no	—
489	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
490	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
491	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
492	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
493	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
494	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
495	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
502	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
505	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
507	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
510	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
511	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
512	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
513	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
515	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
516	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
517	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
518	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
519	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
520	C₄⋊C₄×C₅₃	—	2	2	no	—
521	C₄⋊C₄×C₅₃	—	2	2	no	—
522	C₄⋊C₄×C₅₃	—	4	1	no	—
523	C₄⋊C₄×C₅₃	—	4	1	no	—
524	C₄⋊C₄×C₅₃	—	4	1	no	—
525	C₄⋊C₄×C₅₃	—	4	1	no	—
526	C₄⋊C₄×C₅₃	—	4	1	no	—
527	C₄⋊C₄×C₅₃	—	4	1	no	—
528	C₄⋊C₄×C₅₃	—	4	1	no	—
529	C₄⋊C₄×C₅₃	—	4	1	no	—
530	C₄⋊C₄×C₅₃	—	4	1	no	—
531	C₄⋊C₄×C₅₃	—	4	1	no	—
532	C₄⋊C₄×C₅₃	—	4	1	no	—
533	C₄⋊C₄×C₅₃	—	4	1	no	—
534	C₄⋊C₄×C₅₃	—	4	1	no	—
535	C₄⋊C₄×C₅₃	—	4	1	no	—
536	C₄⋊C₄×C₅₃	—	4	1	no	—
537	C₄⋊C₄×C₅₃	—	4	1	no	—
538	C₄⋊C₄×C₅₃	—	4	1	no	—
539	C₄⋊C₄×C₅₃	—	4	1	no	—
540	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
541	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
542	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
543	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
544	C₂²⋊C₄×C₅₃	—	2	2	no	—
545	C₂²⋊C₄×C₅₃	—	2	2	no	—
546	C₂²⋊C₄×C₅₃	—	2	2	no	—
547	C₂²⋊C₄×C₅₃	—	2	2	no	—
548	C₂²⋊C₄×C₅₃	—	2	2	no	—
549	C₂²⋊C₄×C₅₃	—	2	2	no	—
550	C₂²⋊C₄×C₅₃	—	2	2	no	—
551	C₂²⋊C₄×C₅₃	—	2	2	no	—
552	C₂²⋊C₄×C₅₃	—	2	2	no	—
553	C₂²⋊C₄×C₅₃	—	2	2	no	—
554	C₂²⋊C₄×C₅₃	—	4	1	no	—
555	C₂²⋊C₄×C₅₃	—	4	1	no	—
556	C₂²⋊C₄×C₅₃	—	4	1	no	—
557	C₂²⋊C₄×C₅₃	—	4	1	no	—
558	C₂²⋊C₄×C₅₃	—	4	1	no	—
559	C₂²⋊C₄×C₅₃	—	4	1	no	—
560	C₂²⋊C₄×C₅₃	—	4	1	no	—
561	C₂²⋊C₄×C₅₃	—	4	1	no	—
562	C₂²⋊C₄×C₅₃	—	4	1	no	—
563	C₂²⋊C₄×C₅₃	—	4	1	no	—
564	C₂²⋊C₄×C₅₃	—	4	1	no	—
565	C₂²⋊C₄×C₅₃	—	4	1	no	—
566	C₂²⋊C₄×C₅₃	—	4	1	no	—
567	C₂²⋊C₄×C₅₃	—	4	1	no	—
568	C₂²⋊C₄×C₅₃	—	4	1	no	—
569	C₂²⋊C₄×C₅₃	—	4	1	no	—
570	C₂²⋊C₄×C₅₃	—	4	1	no	—
571	C₂²⋊C₄×C₅₃	—	4	1	no	—
572	C₂²⋊C₄×C₅₃	—	4	1	no	—
573	C₂²⋊C₄×C₅₃	—	4	1	no	—
574	C₂²⋊C₄×C₅₃	—	4	1	no	—
575	C₂²⋊C₄×C₅₃	—	4	1	no	—
576	C₂²⋊C₄×C₅₃	—	4	1	no	—
577	C₂²⋊C₄×C₅₃	—	4	1	no	—
578	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
579	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
580	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
581	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
582	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
583	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
584	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
585	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
586	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
587	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
588	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
589	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
590	C₄²×C₅₃	—	2	2	no	—
591	C₄²×C₅₃	—	4	1	no	—
592	C₄²×C₅₃	—	4	1	no	—
593	C₄²×C₅₃	—	4	1	no	—
594	C₄²×C₅₃	—	4	1	no	—
595	C₄²×C₅₃	—	4	1	no	—
596	C₄²×C₅₃	—	4	1	no	—
597	C₄²×C₅₃	—	4	1	no	—
598	C₄²×C₅₃	—	4	1	no	—
599	C₄²×C₅₃	—	4	1	no	—
600	C₄²×C₅₃	—	4	1	no	—
601	C₄²×C₅₃	—	4	1	no	—
602	C₄²×C₅₃	C₂²×C₄	1	4	yes	complemented
603	C₂³×C₅₃	—	2	1	no	—
604	C₂³×C₅₃	—	2	1	no	—
605	C₂³×C₅₃	—	2	1	no	—
606	C₂³×C₅₃	—	2	1	no	—
607	C₂³×C₅₃	—	2	1	no	—
608	C₂³×C₅₃	—	2	1	no	—
609	C₂³×C₅₃	—	2	1	no	—
610	C₂³×C₅₃	—	2	1	no	—
611	C₂³×C₅₃	—	2	8	no	—
612	C₂³×C₅₃	—	2	8	no	—
613	C₂³×C₅₃	—	2	1	no	—
614	C₂³×C₅₃	—	2	1	no	—
615	C₂³×C₅₃	—	2	1	no	—
616	C₂³×C₅₃	—	2	1	no	—
617	C₂³×C₅₃	—	2	1	no	—
618	C₂³×C₅₃	—	2	1	no	—
619	C₂³×C₅₃	—	2	1	no	—
620	C₂³×C₅₃	—	2	1	no	—
621	C₂³×C₅₃	—	2	1	no	—
622	C₂³×C₅₃	—	2	1	no	—
623	C₂³×C₅₃	—	2	1	no	—
624	C₂³×C₅₃	—	2	1	no	—
625	C₂³×C₅₃	—	2	1	no	—
626	C₂³×C₅₃	—	2	1	no	—
627	C₂³×C₅₃	—	2	1	no	—
628	C₂³×C₅₃	—	2	1	no	—
629	C₂³×C₅₃	—	2	1	no	—
630	C₂³×C₅₃	—	2	1	no	—
631	C₂³×C₅₃	—	2	1	no	—
632	C₂³×C₅₃	—	2	1	no	—
633	C₂³×C₅₃	—	2	1	no	—
634	C₂³×C₅₃	—	2	1	no	—
635	C₂³×C₅₃	—	2	1	no	—
636	C₂³×C₅₃	—	2	1	no	—
637	C₂³×C₅₃	—	2	8	no	—
638	C₂³×C₅₃	—	4	4	no	—
639	C₂³×C₅₃	—	4	4	no	—
640	C₂³×C₅₃	—	4	4	no	—
641	C₂³×C₅₃	—	4	4	no	—
642	C₂³×C₅₃	—	4	4	no	—
643	C₂³×C₅₃	—	4	4	no	—
644	C₂³×C₅₃	—	4	4	no	—
645	C₂³×C₅₃	—	8	2	no	—
646	C₂³×C₅₃	—	8	2	no	—
647	C₂³×C₅₃	—	8	2	no	—
648	C₂³×C₅₃	—	8	2	no	—
649	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
650	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
651	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
652	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
653	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
654	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
655	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
656	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
657	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
658	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
659	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
660	Q₈×C₅₃	—	4	4	no	—
661	D₄×C₅₃	—	2	8	no	—
662	D₄×C₅₃	—	2	8	no	—
663	D₄×C₅₃	—	2	8	no	—
664	D₄×C₅₃	—	2	8	no	—
665	D₄×C₅₃	—	4	4	no	—
666	D₄×C₅₃	—	4	4	no	—
667	D₄×C₅₃	—	4	4	no	—
668	D₄×C₅₃	—	4	4	no	—
669	D₄×C₅₃	—	4	4	no	—
670	C₂×C₄×C₅₃	—	2	8	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	—	2	1	no	—
695	C₂×C₄×C₅₃	—	2	1	no	—
696	C₂×C₄×C₅₃	—	2	1	no	—
697	C₂×C₄×C₅₃	—	2	1	no	—
698	C₂×C₄×C₅₃	—	2	1	no	—
699	C₂×C₄×C₅₃	—	2	1	no	—
700	C₂×C₄×C₅₃	—	2	1	no	—
701	C₂×C₄×C₅₃	—	2	1	no	—
702	C₂×C₄×C₅₃	—	2	1	no	—
703	C₂×C₄×C₅₃	—	2	1	no	—
704	C₂×C₄×C₅₃	—	2	1	no	—
705	C₂×C₄×C₅₃	—	2	1	no	—
706	C₂×C₄×C₅₃	—	2	1	no	—
707	C₂×C₄×C₅₃	—	2	1	no	—
708	C₂×C₄×C₅₃	—	2	1	no	—
709	C₂×C₄×C₅₃	—	2	1	no	—
710	C₂×C₄×C₅₃	—	2	1	no	—
711	C₂×C₄×C₅₃	—	2	1	no	—
712	C₂×C₄×C₅₃	—	2	1	no	—
713	C₂×C₄×C₅₃	—	2	1	no	—
714	C₂×C₄×C₅₃	—	2	1	no	—
715	C₂×C₄×C₅₃	—	2	1	no	—
716	C₂×C₄×C₅₃	—	2	1	no	—
717	C₂×C₄×C₅₃	—	2	1	no	—
718	C₂×C₄×C₅₃	—	2	1	no	—
719	C₂×C₄×C₅₃	—	2	1	no	—
720	C₂×C₄×C₅₃	—	2	1	no	—
721	C₂×C₄×C₅₃	—	2	1	no	—
722	C₂×C₄×C₅₃	—	2	1	no	—
723	C₂×C₄×C₅₃	—	2	1	no	—
724	C₂×C₄×C₅₃	—	2	1	no	—
725	C₂×C₄×C₅₃	—	2	1	no	—
726	C₂×C₄×C₅₃	—	2	1	no	—
727	C₂×C₄×C₅₃	—	2	1	no	—
728	C₂×C₄×C₅₃	—	2	1	no	—
729	C₂×C₄×C₅₃	—	2	1	no	—
730	C₂×C₄×C₅₃	—	2	1	no	—
731	C₂×C₄×C₅₃	—	2	1	no	—
732	C₂×C₄×C₅₃	—	2	1	no	—
733	C₂×C₄×C₅₃	—	2	1	no	—
734	C₂×C₄×C₅₃	—	2	1	no	—
735	C₂×C₄×C₅₃	—	2	1	no	—
736	C₂×C₄×C₅₃	—	4	4	no	—
737	C₂×C₄×C₅₃	—	4	4	no	—
738	C₂×C₄×C₅₃	—	4	4	no	—
739	C₂×C₄×C₅₃	—	4	4	no	—
740	C₂×C₄×C₅₃	—	4	4	no	—
741	C₂×C₄×C₅₃	—	4	4	no	—
742	C₂×C₄×C₅₃	—	4	4	no	—
743	C₂×C₄×C₅₃	—	4	4	no	—
744	C₂×C₄×C₅₃	—	4	4	no	—
745	C₂×C₄×C₅₃	—	4	4	no	—
746	C₂×C₄×C₅₃	—	4	4	no	—
747	C₂×C₄×C₅₃	—	8	2	no	—
748	C₂×C₄×C₅₃	—	8	2	no	—
749	C₂×C₄×C₅₃	—	8	2	no	—
750	C₂×C₄×C₅₃	—	8	2	no	—
751	C₂×C₄×C₅₃	—	8	2	no	—
752	C₂×C₄×C₅₃	—	8	2	no	—
753	C₂×C₄×C₅₃	—	8	2	no	—
754	C₂×C₄×C₅₃	—	8	2	no	—
755	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
756	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
757	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
758	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
759	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
760	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
761	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
762	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
763	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
764	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
765	#34456	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
766	C₂²×C₅₃	—	2	2	no	—
767	C₂²×C₅₃	—	2	2	no	—
768	C₂²×C₅₃	—	2	2	no	—
769	C₂²×C₅₃	—	2	2	no	—
770	C₂²×C₅₃	—	2	2	no	—
771	C₂²×C₅₃	—	2	2	no	—
772	C₂²×C₅₃	—	2	2	no	—
773	C₂²×C₅₃	—	2	2	no	—
774	C₂²×C₅₃	—	2	2	no	—
775	C₂²×C₅₃	—	2	2	no	—
776	C₂²×C₅₃	—	2	2	no	—
777	C₂²×C₅₃	—	2	2	no	—
778	C₂²×C₅₃	—	2	2	no	—
779	C₂²×C₅₃	—	2	2	no	—
780	C₂²×C₅₃	—	2	2	no	—
781	C₂²×C₅₃	—	2	2	no	—
782	C₂²×C₅₃	—	2	2	no	—
783	C₂²×C₅₃	—	2	2	no	—
784	C₂²×C₅₃	—	2	2	no	—
785	C₂²×C₅₃	—	2	2	no	—
786	C₂²×C₅₃	—	2	2	no	—
787	C₂²×C₅₃	—	2	2	no	—
788	C₂²×C₅₃	—	2	2	no	—
789	C₂²×C₅₃	—	2	2	no	—
790	C₂²×C₅₃	—	4	16	no	—
791	C₂²×C₅₃	—	4	1	no	—
792	C₂²×C₅₃	—	4	1	no	—
793	C₂²×C₅₃	—	4	1	no	—
794	C₂²×C₅₃	—	4	1	no	—
795	C₂²×C₅₃	—	4	1	no	—
796	C₂²×C₅₃	—	4	1	no	—
797	C₂²×C₅₃	—	4	1	no	—
798	C₂²×C₅₃	—	4	1	no	—
799	C₂²×C₅₃	—	4	1	no	—
800	C₂²×C₅₃	—	4	1	no	—
801	C₂²×C₅₃	—	4	1	no	—
802	C₂²×C₅₃	—	4	1	no	—
803	C₂²×C₅₃	—	4	1	no	—
804	C₂²×C₅₃	—	4	1	no	—
805	C₂²×C₅₃	—	4	1	no	—
806	C₂²×C₅₃	—	4	1	no	—
807	C₂²×C₅₃	—	8	8	no	—
808	C₂²×C₅₃	#518	1	4	yes	—
809	C₂²×C₅₃	#520	1	4	yes	—
810	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
811	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
812	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
813	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
814	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
815	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
816	C₂²×C₅₃	#585	1	1	yes	characteristic
817	C₄×C₅₃	—	2	2	no	—
818	C₄×C₅₃	—	2	2	no	—
819	C₄×C₅₃	—	2	2	no	—
820	C₄×C₅₃	—	2	2	no	—
821	C₄×C₅₃	—	2	2	no	—
822	C₄×C₅₃	—	2	2	no	—
823	C₄×C₅₃	—	2	2	no	—
824	C₄×C₅₃	—	2	2	no	—
825	C₄×C₅₃	—	2	2	no	—
826	C₄×C₅₃	—	2	2	no	—
827	C₄×C₅₃	—	4	1	no	—
828	C₄×C₅₃	—	4	1	no	—
829	C₄×C₅₃	—	4	1	no	—
830	C₄×C₅₃	—	4	1	no	—
831	C₄×C₅₃	—	4	1	no	—
832	C₄×C₅₃	—	4	1	no	—
833	C₄×C₅₃	—	4	1	no	—
834	C₄×C₅₃	—	4	1	no	—
835	C₄×C₅₃	—	4	1	no	—
836	C₄×C₅₃	—	4	1	no	—
837	C₄×C₅₃	—	4	1	no	—
838	C₄×C₅₃	—	4	1	no	—
839	C₄×C₅₃	—	4	1	no	—
840	C₄×C₅₃	—	4	1	no	—
841	C₄×C₅₃	—	4	1	no	—
842	C₂×#546	C₂×C₅₃	1	1	yes	characteristic
843	#2379	C₂×C₅₃	1	1	yes	characteristic, complemented
844	#2377	C₂×C₅₃	1	1	yes	characteristic, complemented
845	#2377	C₂×C₅₃	1	1	yes	characteristic, complemented
846	#2376	C₂×C₅₃	1	1	yes	characteristic, complemented
847	#2368	C₂×C₅₃	1	1	yes	characteristic, complemented
848	#2361	C₂×C₅₃	1	1	yes	characteristic, complemented
849	#2359	C₂×C₅₃	1	1	yes	characteristic, complemented
850	#2358	C₂×C₅₃	1	1	yes	characteristic, complemented
851	#2358	C₂×C₅₃	1	1	yes	characteristic, complemented
852	#2352	C₂×C₅₃	1	1	yes	characteristic, complemented
853	#2349	C₂×C₅₃	1	1	yes	characteristic, complemented
854	#2342	C₂×C₅₃	1	1	yes	characteristic, complemented
855	#2342	C₂×C₅₃	1	1	yes	characteristic, complemented
856	#2339	C₂×C₅₃	1	1	yes	characteristic, complemented
857	D₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
858	#2337	C₂×C₅₃	1	1	yes	characteristic, complemented
859	#2335	C₂×C₅₃	1	1	yes	characteristic, complemented
860	#2329	C₂×C₅₃	1	1	yes	characteristic, complemented
861	#2325	C₂×C₅₃	1	1	yes	characteristic, complemented
862	#2325	C₂×C₅₃	1	1	yes	characteristic, complemented
863	#2324	C₂×C₅₃	1	1	yes	characteristic, complemented
864	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
865	#2321	C₂×C₅₃	1	1	yes	characteristic, complemented
866	#2318	C₂×C₅₃	1	1	yes	characteristic, complemented
867	#2318	C₂×C₅₃	1	1	yes	characteristic, complemented
868	#2315	C₂×C₅₃	1	1	yes	characteristic, complemented
869	#2311	C₂×C₅₃	1	1	yes	characteristic, complemented
870	C₄×#120	C₂×C₅₃	1	1	yes	characteristic, complemented
871	C₂×#386	C₂×C₅₃	1	1	yes	characteristic, complemented
872	C₂×#385	C₂×C₅₃	1	1	yes	characteristic, complemented
873	C₂×C₅₃	—	2	4	no	—
874	C₂×C₅₃	—	2	4	no	—
875	C₂×C₅₃	—	4	2	no	—
876	C₂×C₅₃	—	4	2	no	—
877	C₂×C₅₃	—	4	2	no	—
878	C₂×C₅₃	—	4	2	no	—
879	C₂×C₅₃	C₂×#518	1	1	yes	characteristic
880	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
881	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
882	C₂×C₅₃	#3532	1	1	yes	characteristic
883	C₂×C₅₃	#3534	1	1	yes	characteristic
884	C₂×C₅₃	#3535	1	1	yes	characteristic
885	C₂×C₅₃	#3536	1	1	yes	characteristic
886	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
887	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
888	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
889	#546	C₄×C₅₃	1	16	yes	complemented
890	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
891	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
892	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
893	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
894	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
895	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
896	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
897	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
898	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
899	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
900	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
901	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
902	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
903	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
904	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
905	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
908	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
913	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
914	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
915	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
916	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
917	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
918	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
919	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
920	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
923	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	#390	C₂²×C₅₃	1	1	yes	characteristic
925	#390	C₂²×C₅₃	1	1	yes	characteristic
926	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
937	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
945	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
947	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#386	C₂²×C₅₃	1	1	yes	characteristic
963	#386	C₂²×C₅₃	1	1	yes	characteristic
964	#386	C₂²×C₅₃	1	1	yes	characteristic
965	#386	C₂²×C₅₃	1	1	yes	characteristic
966	#386	C₂²×C₅₃	1	1	yes	characteristic
967	#386	C₂²×C₅₃	1	1	yes	characteristic
968	#386	C₂²×C₅₃	1	1	yes	characteristic
969	#386	C₂²×C₅₃	1	1	yes	characteristic
970	#386	C₂²×C₅₃	1	1	yes	characteristic
971	#386	C₂²×C₅₃	1	1	yes	characteristic
972	#386	C₂²×C₅₃	1	1	yes	characteristic
973	#386	C₂²×C₅₃	1	1	yes	characteristic
974	#386	C₂²×C₅₃	1	1	yes	characteristic
975	#386	C₂²×C₅₃	1	1	yes	characteristic
976	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#385	C₂²×C₅₃	1	1	yes	characteristic
985	#385	C₂²×C₅₃	1	1	yes	characteristic
986	#385	C₂²×C₅₃	1	1	yes	characteristic
987	#385	C₂²×C₅₃	1	1	yes	characteristic
988	#385	C₂²×C₅₃	1	1	yes	characteristic
989	#385	C₂²×C₅₃	1	1	yes	characteristic
990	#385	C₂²×C₅₃	1	1	yes	characteristic
991	#385	C₂²×C₅₃	1	1	yes	characteristic
992	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#380	C₂²×C₅₃	1	1	yes	characteristic
1013	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#379	C₂²×C₅₃	1	1	yes	characteristic
1022	#379	C₂²×C₅₃	1	1	yes	characteristic
1023	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1027	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1028	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1029	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1030	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1031	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
1038	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
1039	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	C₅₃	#34456	1	1	yes	characteristic, direct product factor, Sylow
1043	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂×#41	—	4	2	no	—
1046	C₂×#41	—	4	2	no	—
1047	C₂×#41	C₂×C₄×C₅₃	1	8	yes	complemented
1048	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂²×D₄	—	4	2	no	—
1050	C₂²×D₄	—	4	2	no	—
1051	C₂²×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
1052	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1056	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1057	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂³×C₄	—	4	2	no	—
1062	C₂³×C₄	—	4	2	no	—
1063	C₂³×C₄	—	4	2	no	—
1064	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1084	#124	C₂×C₄×C₅₃	1	8	yes	complemented
1085	#123	C₂×C₄×C₅₃	1	8	yes	complemented
1086	#123	C₂×C₄×C₅₃	1	8	yes	complemented
1087	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
1088	#121	C₂×C₄×C₅₃	1	8	yes	complemented
1089	#121	C₂×C₄×C₅₃	1	8	yes	complemented
1090	#121	C₂×C₄×C₅₃	1	8	yes	complemented
1091	#120	C₂×C₄×C₅₃	1	8	yes	complemented
1092	#120	C₂×C₄×C₅₃	1	8	yes	complemented
1093	C₄×D₄	—	4	2	no	—
1094	C₄×D₄	—	4	2	no	—
1095	C₄×D₄	—	4	2	no	—
1096	C₄×D₄	—	4	2	no	—
1097	C₄×D₄	—	4	2	no	—
1098	C₄×D₄	—	4	2	no	—
1099	C₄×D₄	—	4	2	no	—
1100	C₄×D₄	—	4	2	no	—
1101	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
1102	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
1103	#117	—	4	2	no	—
1104	#117	—	4	2	no	—
1105	C₂×C₄⋊C₄	—	4	2	no	—
1106	C₂×C₄⋊C₄	—	4	2	no	—
1107	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1116	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1130	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂×C₂²⋊C₄	—	4	2	no	—
1132	C₂×C₂²⋊C₄	—	4	2	no	—
1133	C₂×C₂²⋊C₄	—	4	2	no	—
1134	C₂×C₂²⋊C₄	—	4	2	no	—
1135	C₂×C₂²⋊C₄	—	4	2	no	—
1136	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
1137	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
1138	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1140	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1141	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1145	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1147	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1148	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1149	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1150	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1151	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1152	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1153	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1154	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1155	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1156	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1157	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1158	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1159	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1160	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1161	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1162	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1163	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1164	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1165	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1166	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1167	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1168	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1169	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1170	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1171	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1173	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1177	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1178	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1179	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1181	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1182	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1183	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1184	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1186	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1187	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1188	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1189	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1190	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1191	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1192	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1193	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1194	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1195	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1196	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1197	#95	C₂³×C₅₃	1	1	yes	characteristic
1198	#95	C₂³×C₅₃	1	1	yes	characteristic
1199	#95	C₂³×C₅₃	1	1	yes	characteristic
1200	#95	C₂³×C₅₃	1	1	yes	characteristic
1201	#95	C₂³×C₅₃	1	1	yes	characteristic
1202	#95	C₂³×C₅₃	1	1	yes	characteristic
1203	#95	C₂³×C₅₃	1	1	yes	characteristic
1204	#95	C₂³×C₅₃	1	1	yes	characteristic
1205	#95	C₂³×C₅₃	1	1	yes	characteristic
1206	#95	C₂³×C₅₃	1	1	yes	characteristic
1207	#95	C₂³×C₅₃	1	1	yes	characteristic
1208	#95	C₂³×C₅₃	1	1	yes	characteristic
1209	#95	C₂³×C₅₃	1	1	yes	characteristic
1210	#95	C₂³×C₅₃	1	1	yes	characteristic
1211	#95	C₂³×C₅₃	1	1	yes	characteristic
1212	#95	C₂³×C₅₃	1	1	yes	characteristic
1213	#95	C₂³×C₅₃	1	1	yes	characteristic
1214	#95	C₂³×C₅₃	1	1	yes	characteristic
1215	#95	C₂³×C₅₃	1	1	yes	characteristic
1216	#95	C₂³×C₅₃	1	1	yes	characteristic
1217	#95	C₂³×C₅₃	1	1	yes	characteristic
1218	#95	C₂³×C₅₃	1	1	yes	characteristic
1219	#95	C₂³×C₅₃	1	1	yes	characteristic
1220	#95	C₂³×C₅₃	1	1	yes	characteristic
1221	#95	C₂³×C₅₃	1	1	yes	characteristic
1222	#95	C₂³×C₅₃	1	1	yes	characteristic
1223	#95	C₂³×C₅₃	1	1	yes	characteristic
1224	#95	C₂³×C₅₃	1	1	yes	characteristic
1225	#95	C₂³×C₅₃	1	1	yes	characteristic
1226	#95	C₂³×C₅₃	1	1	yes	characteristic
1227	#95	C₂³×C₅₃	1	1	yes	characteristic
1228	#95	C₂³×C₅₃	1	1	yes	characteristic
1229	#95	C₂³×C₅₃	1	1	yes	characteristic
1230	#95	C₂³×C₅₃	1	1	yes	characteristic
1231	#95	C₂³×C₅₃	1	1	yes	characteristic
1232	#95	C₂³×C₅₃	1	1	yes	characteristic
1233	#95	C₂³×C₅₃	1	1	yes	characteristic
1234	#95	C₂³×C₅₃	1	1	yes	characteristic
1235	#95	C₂³×C₅₃	1	1	yes	characteristic
1236	#95	C₂³×C₅₃	1	1	yes	characteristic
1237	C₂⁴	—	2	2	no	—
1238	C₂⁴	—	2	2	no	—
1239	C₂⁴	—	2	2	no	—
1240	C₂⁴	—	2	2	no	—
1241	C₂⁴	—	2	2	no	—
1242	C₂⁴	—	2	2	no	—
1243	C₂⁴	—	4	1	no	—
1244	C₂⁴	—	4	1	no	—
1245	C₂⁴	—	4	1	no	—
1246	C₂⁴	—	4	1	no	—
1247	C₂⁴	—	4	1	no	—
1248	C₂⁴	—	4	1	no	—
1249	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
1250	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
1251	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1252	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1253	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1254	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1255	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1256	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1257	#41	—	4	16	no	—
1258	C₂×Q₈	—	4	1	no	—
1259	C₂×Q₈	—	4	1	no	—
1260	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	complemented
1261	C₂×D₄	—	2	2	no	—
1262	C₂×D₄	—	2	2	no	—
1263	C₂×D₄	—	2	2	no	—
1264	C₂×D₄	—	2	2	no	—
1265	C₂×D₄	—	2	2	no	—
1266	C₂×D₄	—	2	2	no	—
1267	C₂×D₄	—	2	2	no	—
1268	C₂×D₄	—	2	2	no	—
1269	C₂×D₄	—	4	1	no	—
1270	C₂×D₄	—	4	1	no	—
1271	C₂×D₄	—	4	1	no	—
1272	C₂×D₄	—	4	1	no	—
1273	C₂×D₄	—	4	1	no	—
1274	C₂×D₄	—	4	1	no	—
1275	C₂×D₄	—	4	1	no	—
1276	C₂×D₄	—	4	1	no	—
1277	C₂×D₄	—	4	1	no	—
1278	C₂×D₄	—	4	1	no	—
1279	C₂×D₄	—	4	16	no	—
1280	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1281	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1282	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1283	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1284	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1285	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1286	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
1287	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1288	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1289	C₂²×C₄	—	2	2	no	—
1290	C₂²×C₄	—	2	2	no	—
1291	C₂²×C₄	—	2	2	no	—
1292	C₂²×C₄	—	2	2	no	—
1293	C₂²×C₄	—	2	2	no	—
1294	C₂²×C₄	—	2	2	no	—
1295	C₂²×C₄	—	2	2	no	—
1296	C₂²×C₄	—	2	2	no	—
1297	C₂²×C₄	—	2	2	no	—
1298	C₂²×C₄	—	2	2	no	—
1299	C₂²×C₄	—	2	2	no	—
1300	C₂²×C₄	—	2	2	no	—
1301	C₂²×C₄	—	2	2	no	—
1302	C₂²×C₄	—	2	2	no	—
1303	C₂²×C₄	—	4	1	no	—
1304	C₂²×C₄	—	4	1	no	—
1305	C₂²×C₄	—	4	1	no	—
1306	C₂²×C₄	—	4	1	no	—
1307	C₂²×C₄	—	4	1	no	—
1308	C₂²×C₄	—	4	1	no	—
1309	C₂²×C₄	—	4	1	no	—
1310	C₂²×C₄	—	4	1	no	—
1311	C₂²×C₄	—	4	1	no	—
1312	C₂²×C₄	—	4	1	no	—
1313	C₂²×C₄	—	4	1	no	—
1314	C₂²×C₄	—	4	1	no	—
1315	C₂²×C₄	—	4	1	no	—
1316	C₂²×C₄	—	4	1	no	—
1317	C₂²×C₄	—	4	1	no	—
1318	C₂²×C₄	—	4	1	no	—
1319	C₂²×C₄	—	4	1	no	—
1320	C₂²×C₄	—	4	1	no	—
1321	C₂²×C₄	—	4	1	no	—
1322	C₂²×C₄	—	4	1	no	—
1323	C₂²×C₄	—	4	1	no	—
1324	C₂²×C₄	—	4	1	no	—
1325	C₂²×C₄	—	4	1	no	—
1326	C₂²×C₄	—	4	1	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	16	no	—
1344	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1345	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1346	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
1347	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1348	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1349	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1350	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1351	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1352	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1353	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1354	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1355	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1356	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1357	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1358	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1359	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1360	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1361	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1362	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1363	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1364	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1365	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1366	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1367	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1368	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1369	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1370	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1371	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1372	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1373	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1374	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1375	C₄⋊C₄	—	2	2	no	—
1376	C₄⋊C₄	—	2	2	no	—
1377	C₄⋊C₄	—	4	1	no	—
1378	C₄⋊C₄	—	4	1	no	—
1379	C₄⋊C₄	—	4	1	no	—
1380	C₄⋊C₄	—	4	1	no	—
1381	C₄⋊C₄	—	4	1	no	—
1382	C₄⋊C₄	—	4	1	no	—
1383	C₄⋊C₄	—	4	1	no	—
1384	C₄⋊C₄	—	4	1	no	—
1385	C₄⋊C₄	—	4	1	no	—
1386	C₄⋊C₄	—	4	1	no	—
1387	C₄⋊C₄	—	4	1	no	—
1388	C₄⋊C₄	—	4	1	no	—
1389	C₄⋊C₄	—	4	1	no	—
1390	C₄⋊C₄	—	4	1	no	—
1391	C₄⋊C₄	—	4	1	no	—
1392	C₄⋊C₄	—	4	1	no	—
1393	C₄⋊C₄	—	4	1	no	—
1394	C₄⋊C₄	—	4	1	no	—
1395	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1396	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1397	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1398	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1399	C₂²⋊C₄	—	2	2	no	—
1400	C₂²⋊C₄	—	2	2	no	—
1401	C₂²⋊C₄	—	2	2	no	—
1402	C₂²⋊C₄	—	2	2	no	—
1403	C₂²⋊C₄	—	2	2	no	—
1404	C₂²⋊C₄	—	2	2	no	—
1405	C₂²⋊C₄	—	2	2	no	—
1406	C₂²⋊C₄	—	2	2	no	—
1407	C₂²⋊C₄	—	2	2	no	—
1408	C₂²⋊C₄	—	2	2	no	—
1409	C₂²⋊C₄	—	4	1	no	—
1410	C₂²⋊C₄	—	4	1	no	—
1411	C₂²⋊C₄	—	4	1	no	—
1412	C₂²⋊C₄	—	4	1	no	—
1413	C₂²⋊C₄	—	4	1	no	—
1414	C₂²⋊C₄	—	4	1	no	—
1415	C₂²⋊C₄	—	4	1	no	—
1416	C₂²⋊C₄	—	4	1	no	—
1417	C₂²⋊C₄	—	4	1	no	—
1418	C₂²⋊C₄	—	4	1	no	—
1419	C₂²⋊C₄	—	4	1	no	—
1420	C₂²⋊C₄	—	4	1	no	—
1421	C₂²⋊C₄	—	4	1	no	—
1422	C₂²⋊C₄	—	4	1	no	—
1423	C₂²⋊C₄	—	4	1	no	—
1424	C₂²⋊C₄	—	4	1	no	—
1425	C₂²⋊C₄	—	4	1	no	—
1426	C₂²⋊C₄	—	4	1	no	—
1427	C₂²⋊C₄	—	4	1	no	—
1428	C₂²⋊C₄	—	4	1	no	—
1429	C₂²⋊C₄	—	4	1	no	—
1430	C₂²⋊C₄	—	4	1	no	—
1431	C₂²⋊C₄	—	4	1	no	—
1432	C₂²⋊C₄	—	4	1	no	—
1433	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1434	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1435	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1436	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1437	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1438	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1439	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
1440	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1441	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1442	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1443	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1444	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
1445	C₄²	—	2	2	no	—
1446	C₄²	—	4	1	no	—
1447	C₄²	—	4	1	no	—
1448	C₄²	—	4	1	no	—
1449	C₄²	—	4	1	no	—
1450	C₄²	—	4	1	no	—
1451	C₄²	—	4	1	no	—
1452	C₄²	—	4	1	no	—
1453	C₄²	—	4	1	no	—
1454	C₄²	—	4	1	no	—
1455	C₄²	—	4	1	no	—
1456	C₄²	—	4	1	no	—
1457	C₄²	C₂²×C₄×C₅₃	1	4	yes	complemented
1458	C₂³	—	2	1	no	—
1459	C₂³	—	2	1	no	—
1460	C₂³	—	2	1	no	—
1461	C₂³	—	2	1	no	—
1462	C₂³	—	2	1	no	—
1463	C₂³	—	2	1	no	—
1464	C₂³	—	2	1	no	—
1465	C₂³	—	2	1	no	—
1466	C₂³	—	2	8	no	—
1467	C₂³	—	2	8	no	—
1468	C₂³	—	2	1	no	—
1469	C₂³	—	2	1	no	—
1470	C₂³	—	2	1	no	—
1471	C₂³	—	2	1	no	—
1472	C₂³	—	2	1	no	—
1473	C₂³	—	2	1	no	—
1474	C₂³	—	2	1	no	—
1475	C₂³	—	2	1	no	—
1476	C₂³	—	2	1	no	—
1477	C₂³	—	2	1	no	—
1478	C₂³	—	2	1	no	—
1479	C₂³	—	2	1	no	—
1480	C₂³	—	2	1	no	—
1481	C₂³	—	2	1	no	—
1482	C₂³	—	2	1	no	—
1483	C₂³	—	2	1	no	—
1484	C₂³	—	2	1	no	—
1485	C₂³	—	2	1	no	—
1486	C₂³	—	2	1	no	—
1487	C₂³	—	2	1	no	—
1488	C₂³	—	2	1	no	—
1489	C₂³	—	2	1	no	—
1490	C₂³	—	2	1	no	—
1491	C₂³	—	2	1	no	—
1492	C₂³	—	2	8	no	—
1493	C₂³	—	4	4	no	—
1494	C₂³	—	4	4	no	—
1495	C₂³	—	4	4	no	—
1496	C₂³	—	4	4	no	—
1497	C₂³	—	4	4	no	—
1498	C₂³	—	4	4	no	—
1499	C₂³	—	4	4	no	—
1500	C₂³	—	8	2	no	—
1501	C₂³	—	8	2	no	—
1502	C₂³	—	8	2	no	—
1503	C₂³	—	8	2	no	—
1504	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1505	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1506	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1507	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1508	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1509	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
1510	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1511	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1512	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1513	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1514	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1515	Q₈	—	4	4	no	—
1516	D₄	—	2	8	no	—
1517	D₄	—	2	8	no	—
1518	D₄	—	2	8	no	—
1519	D₄	—	2	8	no	—
1520	D₄	—	4	4	no	—
1521	D₄	—	4	4	no	—
1522	D₄	—	4	4	no	—
1523	D₄	—	4	4	no	—
1524	D₄	—	4	4	no	—
1525	C₂×C₄	—	2	8	no	—
1526	C₂×C₄	—	2	1	no	—
1527	C₂×C₄	—	2	1	no	—
1528	C₂×C₄	—	2	1	no	—
1529	C₂×C₄	—	2	1	no	—
1530	C₂×C₄	—	2	1	no	—
1531	C₂×C₄	—	2	1	no	—
1532	C₂×C₄	—	2	1	no	—
1533	C₂×C₄	—	2	1	no	—
1534	C₂×C₄	—	2	1	no	—
1535	C₂×C₄	—	2	1	no	—
1536	C₂×C₄	—	2	1	no	—
1537	C₂×C₄	—	2	1	no	—
1538	C₂×C₄	—	2	1	no	—
1539	C₂×C₄	—	2	1	no	—
1540	C₂×C₄	—	2	1	no	—
1541	C₂×C₄	—	2	1	no	—
1542	C₂×C₄	—	2	1	no	—
1543	C₂×C₄	—	2	1	no	—
1544	C₂×C₄	—	2	1	no	—
1545	C₂×C₄	—	2	1	no	—
1546	C₂×C₄	—	2	1	no	—
1547	C₂×C₄	—	2	1	no	—
1548	C₂×C₄	—	2	1	no	—
1549	C₂×C₄	—	2	1	no	—
1550	C₂×C₄	—	2	1	no	—
1551	C₂×C₄	—	2	1	no	—
1552	C₂×C₄	—	2	1	no	—
1553	C₂×C₄	—	2	1	no	—
1554	C₂×C₄	—	2	1	no	—
1555	C₂×C₄	—	2	1	no	—
1556	C₂×C₄	—	2	1	no	—
1557	C₂×C₄	—	2	1	no	—
1558	C₂×C₄	—	2	1	no	—
1559	C₂×C₄	—	2	1	no	—
1560	C₂×C₄	—	2	1	no	—
1561	C₂×C₄	—	2	1	no	—
1562	C₂×C₄	—	2	1	no	—
1563	C₂×C₄	—	2	1	no	—
1564	C₂×C₄	—	2	1	no	—
1565	C₂×C₄	—	2	1	no	—
1566	C₂×C₄	—	2	1	no	—
1567	C₂×C₄	—	2	1	no	—
1568	C₂×C₄	—	2	1	no	—
1569	C₂×C₄	—	2	1	no	—
1570	C₂×C₄	—	2	1	no	—
1571	C₂×C₄	—	2	1	no	—
1572	C₂×C₄	—	2	1	no	—
1573	C₂×C₄	—	2	1	no	—
1574	C₂×C₄	—	2	1	no	—
1575	C₂×C₄	—	2	1	no	—
1576	C₂×C₄	—	2	1	no	—
1577	C₂×C₄	—	2	1	no	—
1578	C₂×C₄	—	2	1	no	—
1579	C₂×C₄	—	2	1	no	—
1580	C₂×C₄	—	2	1	no	—
1581	C₂×C₄	—	2	1	no	—
1582	C₂×C₄	—	2	1	no	—
1583	C₂×C₄	—	2	1	no	—
1584	C₂×C₄	—	2	1	no	—
1585	C₂×C₄	—	2	1	no	—
1586	C₂×C₄	—	2	1	no	—
1587	C₂×C₄	—	2	1	no	—
1588	C₂×C₄	—	2	1	no	—
1589	C₂×C₄	—	2	1	no	—
1590	C₂×C₄	—	2	1	no	—
1591	C₂×C₄	—	4	4	no	—
1592	C₂×C₄	—	4	4	no	—
1593	C₂×C₄	—	4	4	no	—
1594	C₂×C₄	—	4	4	no	—
1595	C₂×C₄	—	4	4	no	—
1596	C₂×C₄	—	4	4	no	—
1597	C₂×C₄	—	4	4	no	—
1598	C₂×C₄	—	4	4	no	—
1599	C₂×C₄	—	4	4	no	—
1600	C₂×C₄	—	4	4	no	—
1601	C₂×C₄	—	4	4	no	—
1602	C₂×C₄	—	8	2	no	—
1603	C₂×C₄	—	8	2	no	—
1604	C₂×C₄	—	8	2	no	—
1605	C₂×C₄	—	8	2	no	—
1606	C₂×C₄	—	8	2	no	—
1607	C₂×C₄	—	8	2	no	—
1608	C₂×C₄	—	8	2	no	—
1609	C₂×C₄	—	8	2	no	—
1610	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1611	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1612	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1613	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1614	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1615	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1616	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1617	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1618	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1619	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1620	C₂²	—	2	2	no	—
1621	C₂²	—	2	2	no	—
1622	C₂²	—	2	2	no	—
1623	C₂²	—	2	2	no	—
1624	C₂²	—	2	2	no	—
1625	C₂²	—	2	2	no	—
1626	C₂²	—	2	2	no	—
1627	C₂²	—	2	2	no	—
1628	C₂²	—	2	2	no	—
1629	C₂²	—	2	2	no	—
1630	C₂²	—	2	2	no	—
1631	C₂²	—	2	2	no	—
1632	C₂²	—	2	2	no	—
1633	C₂²	—	2	2	no	—
1634	C₂²	—	2	2	no	—
1635	C₂²	—	2	2	no	—
1636	C₂²	—	2	2	no	—
1637	C₂²	—	2	2	no	—
1638	C₂²	—	2	2	no	—
1639	C₂²	—	2	2	no	—
1640	C₂²	—	2	2	no	—
1641	C₂²	—	2	2	no	—
1642	C₂²	—	2	2	no	—
1643	C₂²	—	2	2	no	—
1644	C₂²	—	4	16	no	—
1645	C₂²	—	4	1	no	—
1646	C₂²	—	4	1	no	—
1647	C₂²	—	4	1	no	—
1648	C₂²	—	4	1	no	—
1649	C₂²	—	4	1	no	—
1650	C₂²	—	4	1	no	—
1651	C₂²	—	4	1	no	—
1652	C₂²	—	4	1	no	—
1653	C₂²	—	4	1	no	—
1654	C₂²	—	4	1	no	—
1655	C₂²	—	4	1	no	—
1656	C₂²	—	4	1	no	—
1657	C₂²	—	4	1	no	—
1658	C₂²	—	4	1	no	—
1659	C₂²	—	4	1	no	—
1660	C₂²	—	4	1	no	—
1661	C₂²	—	8	8	no	—
1662	C₂²	C₅₃×#518	1	4	yes	—
1663	C₂²	C₅₃×#520	1	4	yes	—
1664	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
1665	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1666	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1667	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1668	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1669	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1670	C₂²	C₅₃×#585	1	1	yes	characteristic
1671	C₄	—	2	2	no	—
1672	C₄	—	2	2	no	—
1673	C₄	—	2	2	no	—
1674	C₄	—	2	2	no	—
1675	C₄	—	2	2	no	—
1676	C₄	—	2	2	no	—
1677	C₄	—	2	2	no	—
1678	C₄	—	2	2	no	—
1679	C₄	—	2	2	no	—
1680	C₄	—	2	2	no	—
1681	C₄	—	4	1	no	—
1682	C₄	—	4	1	no	—
1683	C₄	—	4	1	no	—
1684	C₄	—	4	1	no	—
1685	C₄	—	4	1	no	—
1686	C₄	—	4	1	no	—
1687	C₄	—	4	1	no	—
1688	C₄	—	4	1	no	—
1689	C₄	—	4	1	no	—
1690	C₄	—	4	1	no	—
1691	C₄	—	4	1	no	—
1692	C₄	—	4	1	no	—
1693	C₄	—	4	1	no	—
1694	C₄	—	4	1	no	—
1695	C₄	—	4	1	no	—
1696	C₂	—	2	4	no	—
1697	C₂	—	2	4	no	—
1698	C₂	—	4	2	no	—
1699	C₂	—	4	2	no	—
1700	C₂	—	4	2	no	—
1701	C₂	—	4	2	no	—
1702	C₂	C₂×C₅₃×#518	1	1	yes	characteristic
1703	C₂	C₂×C₅₃×#520	1	1	yes	characteristic
1704	C₂	C₄×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1705	C₂	C₅₃×#3532	1	1	yes	characteristic
1706	C₂	C₅₃×#3534	1	1	yes	characteristic
1707	C₂	C₅₃×#3535	1	1	yes	characteristic
1708	C₂	C₅₃×#3536	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×#546	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×#2379	C₂	semidirect
3. C₅₃×#2377	C₂	semidirect
4. C₅₃×#2377	C₂	semidirect
5. C₅₃×#2376	C₂	semidirect
6. C₅₃×#2368	C₂	semidirect
7. C₅₃×#2361	C₂	semidirect
8. C₅₃×#2359	C₂	semidirect
9. C₅₃×#2358	C₂	semidirect
10. C₅₃×#2358	C₂	semidirect
11. C₅₃×#2352	C₂	semidirect
12. C₅₃×#2349	C₂	semidirect
13. C₅₃×#2342	C₂	semidirect
14. C₅₃×#2342	C₂	semidirect
15. C₅₃×#2339	C₂	semidirect
16. D₄×C₂²⋊C₄×C₅₃	C₂	semidirect
17. C₅₃×#2337	C₂	semidirect
18. C₅₃×#2335	C₂	semidirect
19. C₅₃×#2329	C₂	semidirect
20. C₅₃×#2325	C₂	semidirect
21. C₅₃×#2325	C₂	semidirect
22. C₅₃×#2324	C₂	semidirect
23. C₅₃×#2322	C₂	semidirect
24. C₅₃×#2321	C₂	semidirect
25. C₅₃×#2318	C₂	semidirect
26. C₅₃×#2318	C₂	semidirect
27. C₅₃×#2315	C₂	semidirect
28. C₅₃×#2311	C₂	semidirect
29. C₄×#120×C₅₃	C₂	semidirect
30. C₂×C₅₃×#386	C₂	semidirect
31. C₂×C₅₃×#385	C₂	semidirect
35. C₅₃×#546	C₄	semidirect
51. C₂×C₄×D₄×C₅₃	C₂²	semidirect
52. C₂×C₄×D₄×C₅₃	C₂²	semidirect
53. C₂×C₄×D₄×C₅₃	C₂²	semidirect
54. C₂×C₄×D₄×C₅₃	C₂²	semidirect
55. C₂×#117×C₅₃	C₂²	semidirect
56. C₂×#117×C₅₃	C₂²	semidirect
57. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
58. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
66. C₅₃×#391	C₂²	semidirect
67. C₅₃×#391	C₂²	semidirect
68. C₅₃×#391	C₂²	semidirect
69. C₅₃×#391	C₂²	semidirect
72. C₅₃×#390	C₂²	semidirect
73. C₅₃×#390	C₂²	semidirect
74. C₅₃×#390	C₂²	semidirect
75. C₅₃×#390	C₂²	semidirect
76. C₅₃×#389	C₂²	semidirect
77. C₅₃×#389	C₂²	semidirect
78. C₅₃×#389	C₂²	semidirect
79. C₅₃×#389	C₂²	semidirect
80. C₅₃×#388	C₂²	semidirect
81. C₅₃×#388	C₂²	semidirect
82. C₅₃×#388	C₂²	semidirect
83. C₅₃×#388	C₂²	semidirect
84. C₅₃×#388	C₂²	semidirect
85. C₅₃×#388	C₂²	semidirect
86. C₅₃×#388	C₂²	semidirect
87. C₅₃×#388	C₂²	semidirect
88. C₅₃×#388	C₂²	semidirect
89. C₅₃×#388	C₂²	semidirect
90. C₅₃×#388	C₂²	semidirect
91. C₅₃×#388	C₂²	semidirect
92. C₅₃×#388	C₂²	semidirect
93. C₅₃×#388	C₂²	semidirect
94. C₅₃×#388	C₂²	semidirect
95. C₅₃×#388	C₂²	semidirect
96. C₅₃×#388	C₂²	semidirect
97. C₅₃×#388	C₂²	semidirect
98. C₅₃×#387	C₂²	semidirect
99. C₅₃×#387	C₂²	semidirect
100. C₅₃×#387	C₂²	semidirect
101. C₅₃×#387	C₂²	semidirect
102. C₅₃×#387	C₂²	semidirect
103. C₅₃×#387	C₂²	semidirect
104. C₅₃×#387	C₂²	semidirect
105. C₅₃×#387	C₂²	semidirect
106. C₅₃×#387	C₂²	semidirect
107. C₅₃×#387	C₂²	semidirect
122. C₅₃×#386	C₂²	semidirect
123. C₅₃×#386	C₂²	semidirect
124. C₅₃×#386	C₂²	semidirect
125. C₅₃×#386	C₂²	semidirect
126. C₅₃×#386	C₂²	semidirect
127. C₅₃×#386	C₂²	semidirect
128. C₅₃×#386	C₂²	semidirect
129. C₅₃×#386	C₂²	semidirect
138. C₅₃×#385	C₂²	semidirect
139. C₅₃×#385	C₂²	semidirect
140. C₅₃×#385	C₂²	semidirect
141. C₅₃×#385	C₂²	semidirect
142. C₅₃×#385	C₂²	semidirect
143. C₅₃×#385	C₂²	semidirect
144. C₅₃×#385	C₂²	semidirect
145. C₅₃×#385	C₂²	semidirect
146. C₅₃×#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×#383	C₂²	semidirect
153. C₅₃×#382	C₂²	semidirect
154. C₅₃×#382	C₂²	semidirect
155. C₅₃×#381	C₂²	semidirect
156. C₅₃×#381	C₂²	semidirect
157. C₅₃×#381	C₂²	semidirect
159. C₅₃×#380	C₂²	semidirect
160. C₅₃×#380	C₂²	semidirect
161. C₅₃×#380	C₂²	semidirect
162. C₅₃×#380	C₂²	semidirect
163. C₅₃×#380	C₂²	semidirect
164. C₅₃×#380	C₂²	semidirect
165. C₅₃×#380	C₂²	semidirect
166. C₅₃×#380	C₂²	semidirect
169. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
170. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
171. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
177. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
178. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
179. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
180. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
181. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
182. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
185. C₂×#95×C₅₃	C₂²	semidirect
186. C₂×#95×C₅₃	C₂²	semidirect
187. C₂×#95×C₅₃	C₂²	semidirect
192. C₂×#41×C₅₃	C₂×C₄	semidirect
196. C₂²×D₄×C₅₃	C₂×C₄	semidirect
229. #124×C₅₃	C₂×C₄	semidirect
230. #123×C₅₃	C₂×C₄	semidirect
231. #123×C₅₃	C₂×C₄	semidirect
232. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
233. #121×C₅₃	C₂×C₄	semidirect
234. #121×C₅₃	C₂×C₄	semidirect
235. #121×C₅₃	C₂×C₄	semidirect
236. #120×C₅₃	C₂×C₄	semidirect
237. #120×C₅₃	C₂×C₄	semidirect
246. C₄×D₄×C₅₃	C₂×C₄	semidirect
247. C₄×D₄×C₅₃	C₂×C₄	semidirect
281. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
282. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
405. C₂×Q₈×C₅₃	C₂²×C₄	semidirect
432. C₂×D₄×C₅₃	C₂²×C₄	semidirect
433. C₂×D₄×C₅₃	C₂²×C₄	semidirect
492. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
493. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
494. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
540. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
541. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
542. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
543. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
585. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
586. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
587. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
588. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
589. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
602. C₄²×C₅₃	C₂²×C₄	semidirect
765. #34456	C₅₃	direct (N × H)
843. #2379	C₂×C₅₃	semidirect
844. #2377	C₂×C₅₃	semidirect
845. #2377	C₂×C₅₃	semidirect
846. #2376	C₂×C₅₃	semidirect
847. #2368	C₂×C₅₃	semidirect
848. #2361	C₂×C₅₃	semidirect
849. #2359	C₂×C₅₃	semidirect
850. #2358	C₂×C₅₃	semidirect
851. #2358	C₂×C₅₃	semidirect
852. #2352	C₂×C₅₃	semidirect
853. #2349	C₂×C₅₃	semidirect
854. #2342	C₂×C₅₃	semidirect
855. #2342	C₂×C₅₃	semidirect
856. #2339	C₂×C₅₃	semidirect
857. D₄×C₂²⋊C₄	C₂×C₅₃	semidirect
858. #2337	C₂×C₅₃	semidirect
859. #2335	C₂×C₅₃	semidirect
860. #2329	C₂×C₅₃	semidirect
861. #2325	C₂×C₅₃	semidirect
862. #2325	C₂×C₅₃	semidirect
863. #2324	C₂×C₅₃	semidirect
864. #2322	C₂×C₅₃	semidirect
865. #2321	C₂×C₅₃	semidirect
866. #2318	C₂×C₅₃	semidirect
867. #2318	C₂×C₅₃	semidirect
868. #2315	C₂×C₅₃	semidirect
869. #2311	C₂×C₅₃	semidirect
870. C₄×#120	C₂×C₅₃	semidirect
871. C₂×#386	C₂×C₅₃	semidirect
872. C₂×#385	C₂×C₅₃	semidirect
889. #546	C₄×C₅₃	semidirect
905. C₂×C₄×D₄	C₂²×C₅₃	semidirect
906. C₂×C₄×D₄	C₂²×C₅₃	semidirect
907. C₂×C₄×D₄	C₂²×C₅₃	semidirect
908. C₂×C₄×D₄	C₂²×C₅₃	semidirect
909. C₂×#117	C₂²×C₅₃	semidirect
910. C₂×#117	C₂²×C₅₃	semidirect
911. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
912. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
920. #391	C₂²×C₅₃	semidirect
921. #391	C₂²×C₅₃	semidirect
922. #391	C₂²×C₅₃	semidirect
923. #391	C₂²×C₅₃	semidirect
926. #390	C₂²×C₅₃	semidirect
927. #390	C₂²×C₅₃	semidirect
928. #390	C₂²×C₅₃	semidirect
929. #390	C₂²×C₅₃	semidirect
930. #389	C₂²×C₅₃	semidirect
931. #389	C₂²×C₅₃	semidirect
932. #389	C₂²×C₅₃	semidirect
933. #389	C₂²×C₅₃	semidirect
934. #388	C₂²×C₅₃	semidirect
935. #388	C₂²×C₅₃	semidirect
936. #388	C₂²×C₅₃	semidirect
937. #388	C₂²×C₅₃	semidirect
938. #388	C₂²×C₅₃	semidirect
939. #388	C₂²×C₅₃	semidirect
940. #388	C₂²×C₅₃	semidirect
941. #388	C₂²×C₅₃	semidirect
942. #388	C₂²×C₅₃	semidirect
943. #388	C₂²×C₅₃	semidirect
944. #388	C₂²×C₅₃	semidirect
945. #388	C₂²×C₅₃	semidirect
946. #388	C₂²×C₅₃	semidirect
947. #388	C₂²×C₅₃	semidirect
948. #388	C₂²×C₅₃	semidirect
949. #388	C₂²×C₅₃	semidirect
950. #388	C₂²×C₅₃	semidirect
951. #388	C₂²×C₅₃	semidirect
952. #387	C₂²×C₅₃	semidirect
953. #387	C₂²×C₅₃	semidirect
954. #387	C₂²×C₅₃	semidirect
955. #387	C₂²×C₅₃	semidirect
956. #387	C₂²×C₅₃	semidirect
957. #387	C₂²×C₅₃	semidirect
958. #387	C₂²×C₅₃	semidirect
959. #387	C₂²×C₅₃	semidirect
960. #387	C₂²×C₅₃	semidirect
961. #387	C₂²×C₅₃	semidirect
976. #386	C₂²×C₅₃	semidirect
977. #386	C₂²×C₅₃	semidirect
978. #386	C₂²×C₅₃	semidirect
979. #386	C₂²×C₅₃	semidirect
980. #386	C₂²×C₅₃	semidirect
981. #386	C₂²×C₅₃	semidirect
982. #386	C₂²×C₅₃	semidirect
983. #386	C₂²×C₅₃	semidirect
992. #385	C₂²×C₅₃	semidirect
993. #385	C₂²×C₅₃	semidirect
994. #385	C₂²×C₅₃	semidirect
995. #385	C₂²×C₅₃	semidirect
996. #385	C₂²×C₅₃	semidirect
997. #385	C₂²×C₅₃	semidirect
998. #385	C₂²×C₅₃	semidirect
999. #385	C₂²×C₅₃	semidirect
1000. #385	C₂²×C₅₃	semidirect
1001. #385	C₂²×C₅₃	semidirect
1002. #385	C₂²×C₅₃	semidirect
1003. #385	C₂²×C₅₃	semidirect
1004. #385	C₂²×C₅₃	semidirect
1005. #385	C₂²×C₅₃	semidirect
1006. #383	C₂²×C₅₃	semidirect
1007. #382	C₂²×C₅₃	semidirect
1008. #382	C₂²×C₅₃	semidirect
1009. #381	C₂²×C₅₃	semidirect
1010. #381	C₂²×C₅₃	semidirect
1011. #381	C₂²×C₅₃	semidirect
1013. #380	C₂²×C₅₃	semidirect
1014. #380	C₂²×C₅₃	semidirect
1015. #380	C₂²×C₅₃	semidirect
1016. #380	C₂²×C₅₃	semidirect
1017. #380	C₂²×C₅₃	semidirect
1018. #380	C₂²×C₅₃	semidirect
1019. #380	C₂²×C₅₃	semidirect
1020. #380	C₂²×C₅₃	semidirect
1023. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
1024. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
1025. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
1031. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1032. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1033. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1034. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1035. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1036. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1039. C₂×#95	C₂²×C₅₃	semidirect
1040. C₂×#95	C₂²×C₅₃	semidirect
1041. C₂×#95	C₂²×C₅₃	semidirect
1042. C₅₃	#34456	direct (N × H)
1047. C₂×#41	C₂×C₄×C₅₃	semidirect
1051. C₂²×D₄	C₂×C₄×C₅₃	semidirect
1084. #124	C₂×C₄×C₅₃	semidirect
1085. #123	C₂×C₄×C₅₃	semidirect
1086. #123	C₂×C₄×C₅₃	semidirect
1087. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
1088. #121	C₂×C₄×C₅₃	semidirect
1089. #121	C₂×C₄×C₅₃	semidirect
1090. #121	C₂×C₄×C₅₃	semidirect
1091. #120	C₂×C₄×C₅₃	semidirect
1092. #120	C₂×C₄×C₅₃	semidirect
1101. C₄×D₄	C₂×C₄×C₅₃	semidirect
1102. C₄×D₄	C₂×C₄×C₅₃	semidirect
1136. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
1137. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
1260. C₂×Q₈	C₂²×C₄×C₅₃	semidirect
1287. C₂×D₄	C₂²×C₄×C₅₃	semidirect
1288. C₂×D₄	C₂²×C₄×C₅₃	semidirect
1347. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
1348. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
1349. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
1395. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1396. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1397. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1398. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
1440. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
1441. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
1442. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
1443. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
1444. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
1457. 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×#546	2
C₅₃×#2379	2
C₅₃×#2377	2
C₅₃×#2376	2
C₅₃×#2368	2
C₅₃×#2361	2
C₅₃×#2359	2
C₅₃×#2358	2
C₅₃×#2352	2
C₅₃×#2349	2
C₅₃×#2342	2
C₅₃×#2339	2
D₄×C₂²⋊C₄×C₅₃	2
C₅₃×#2337	2
C₅₃×#2335	2
C₅₃×#2329	2
C₅₃×#2325	2
C₅₃×#2324	2
C₅₃×#2322	2
C₅₃×#2321	2
C₅₃×#2318	2
C₅₃×#2315	2
C₅₃×#2311	2
C₄×#120×C₅₃	2
C₂×C₅₃×#386	2
C₂×C₅₃×#385	2
#34456	53

Subgroups — C53×#34456 #27241968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34456 #27241968