Subgroups — C₅₃×#34991 #27242503

Order 13568.

2878 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2852	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2638	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2636	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2633	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2630	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2480	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2473	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2466	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2463	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2460	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2455	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2449	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2449	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2443	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2437	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2425	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2419	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2418	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2412	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2410	C₂	1	1	yes	maximal, characteristic
26	C₅₃×#2405	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2318	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	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#539	—	2	8	no	—
36	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
52	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
54	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₅₃	—	2	8	no	—
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
68	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
70	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
71	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
72	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
73	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
74	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
75	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#394	C₂²	1	1	yes	characteristic
95	C₅₃×#394	C₂²	1	1	yes	characteristic
96	C₅₃×#394	C₂²	1	1	yes	characteristic
97	C₅₃×#394	C₂²	1	1	yes	characteristic
98	C₅₃×#394	C₂²	1	1	yes	characteristic
99	C₅₃×#394	C₂²	1	1	yes	characteristic
100	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#392	C₂²	1	1	yes	characteristic
106	C₅₃×#392	C₂²	1	1	yes	characteristic
107	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#386	C₂²	1	1	yes	characteristic
130	C₅₃×#386	C₂²	1	1	yes	characteristic
131	C₅₃×#386	C₂²	1	1	yes	characteristic
132	C₅₃×#386	C₂²	1	1	yes	characteristic
133	C₅₃×#386	C₂²	1	1	yes	characteristic
134	C₅₃×#386	C₂²	1	1	yes	characteristic
135	C₅₃×#386	C₂²	1	1	yes	characteristic
136	C₅₃×#386	C₂²	1	1	yes	characteristic
137	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#385	C₂²	1	1	yes	characteristic
144	C₅₃×#385	C₂²	1	1	yes	characteristic
145	C₅₃×#385	C₂²	1	1	yes	characteristic
146	C₅₃×#385	C₂²	1	1	yes	characteristic
147	C₅₃×#385	C₂²	1	1	yes	characteristic
148	C₅₃×#385	C₂²	1	1	yes	characteristic
149	C₅₃×#385	C₂²	1	1	yes	characteristic
150	C₅₃×#385	C₂²	1	1	yes	characteristic
151	C₅₃×#385	C₂²	1	1	yes	characteristic
152	C₅₃×#385	C₂²	1	1	yes	characteristic
153	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#380	C₂²	1	1	yes	characteristic
175	C₅₃×#380	C₂²	1	1	yes	characteristic
176	C₅₃×#380	C₂²	1	1	yes	characteristic
177	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#379	C₂²	1	1	yes	characteristic
181	C₅₃×#379	C₂²	1	1	yes	characteristic
182	C₅₃×#379	C₂²	1	1	yes	characteristic
183	C₅₃×#379	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
189	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
190	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²×D₄×C₅₃	—	2	4	no	—
193	C₂²×D₄×C₅₃	—	2	4	no	—
194	C₂²×D₄×C₅₃	—	2	4	no	—
195	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₅₃	—	2	4	no	—
205	C₂³×C₄×C₅₃	—	2	4	no	—
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	—	4	2	no	—
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	#126×C₅₃	—	2	4	no	—
229	#126×C₅₃	—	2	4	no	—
230	#125×C₅₃	—	2	4	no	—
231	#125×C₅₃	—	2	4	no	—
232	#123×C₅₃	—	2	4	no	—
233	#123×C₅₃	—	2	4	no	—
234	#123×C₅₃	—	2	4	no	—
235	#123×C₅₃	—	2	4	no	—
236	#123×C₅₃	—	2	4	no	—
237	#123×C₅₃	—	4	2	no	—
238	C₂²⋊Q₈×C₅₃	—	2	4	no	—
239	C₂²⋊Q₈×C₅₃	—	2	4	no	—
240	C₂²⋊Q₈×C₅₃	—	2	4	no	—
241	C₂²⋊Q₈×C₅₃	—	4	2	no	—
242	C₂²⋊Q₈×C₅₃	—	4	2	no	—
243	#121×C₅₃	—	2	4	no	—
244	#121×C₅₃	—	2	4	no	—
245	#120×C₅₃	—	2	4	no	—
246	#120×C₅₃	—	4	2	no	—
247	C₄×D₄×C₅₃	—	2	4	no	—
248	C₄×D₄×C₅₃	—	2	4	no	—
249	C₄×D₄×C₅₃	—	2	4	no	—
250	C₄×D₄×C₅₃	—	2	4	no	—
251	C₄×D₄×C₅₃	—	2	4	no	—
252	C₄×D₄×C₅₃	—	2	4	no	—
253	C₄×D₄×C₅₃	—	2	4	no	—
254	C₄×D₄×C₅₃	—	2	4	no	—
255	C₄×D₄×C₅₃	—	4	2	no	—
256	C₄×D₄×C₅₃	—	4	2	no	—
257	C₄×D₄×C₅₃	D₄	1	8	yes	complemented
258	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
259	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
260	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
296	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
297	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
298	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	—	2	4	no	—
348	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₄²×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	#95×C₅₃	C₂³	1	1	yes	characteristic
383	#95×C₅₃	C₂³	1	1	yes	characteristic
384	#95×C₅₃	C₂³	1	1	yes	characteristic
385	#95×C₅₃	C₂³	1	1	yes	characteristic
386	#95×C₅₃	C₂³	1	1	yes	characteristic
387	#95×C₅₃	C₂³	1	1	yes	characteristic
388	#95×C₅₃	C₂³	1	1	yes	characteristic
389	#95×C₅₃	C₂³	1	1	yes	characteristic
390	#95×C₅₃	C₂³	1	1	yes	characteristic
391	C₂⁴×C₅₃	—	2	2	no	—
392	C₂⁴×C₅₃	—	2	2	no	—
393	C₂⁴×C₅₃	—	2	2	no	—
394	C₂⁴×C₅₃	—	2	2	no	—
395	C₂⁴×C₅₃	—	2	2	no	—
396	C₂⁴×C₅₃	—	2	2	no	—
397	C₂⁴×C₅₃	—	2	2	no	—
398	C₂⁴×C₅₃	—	2	2	no	—
399	C₂⁴×C₅₃	—	2	2	no	—
400	C₂⁴×C₅₃	—	4	1	no	—
401	C₂⁴×C₅₃	—	4	1	no	—
402	C₂⁴×C₅₃	—	4	1	no	—
403	C₂⁴×C₅₃	—	4	1	no	—
404	C₂⁴×C₅₃	#41	1	4	yes	—
405	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂×Q₈×C₅₃	—	2	2	no	—
412	C₂×Q₈×C₅₃	—	4	1	no	—
413	C₂×Q₈×C₅₃	—	4	1	no	—
414	C₂×D₄×C₅₃	—	2	32	no	—
415	C₂×D₄×C₅₃	—	2	2	no	—
416	C₂×D₄×C₅₃	—	2	2	no	—
417	C₂×D₄×C₅₃	—	2	2	no	—
418	C₂×D₄×C₅₃	—	2	2	no	—
419	C₂×D₄×C₅₃	—	2	2	no	—
420	C₂×D₄×C₅₃	—	2	2	no	—
421	C₂×D₄×C₅₃	—	2	2	no	—
422	C₂×D₄×C₅₃	—	2	2	no	—
423	C₂×D₄×C₅₃	—	2	2	no	—
424	C₂×D₄×C₅₃	—	2	2	no	—
425	C₂×D₄×C₅₃	—	2	2	no	—
426	C₂×D₄×C₅₃	—	2	2	no	—
427	C₂×D₄×C₅₃	—	2	2	no	—
428	C₂×D₄×C₅₃	—	2	2	no	—
429	C₂×D₄×C₅₃	—	2	2	no	—
430	C₂×D₄×C₅₃	—	2	2	no	—
431	C₂×D₄×C₅₃	—	2	2	no	—
432	C₂×D₄×C₅₃	—	2	2	no	—
433	C₂×D₄×C₅₃	—	2	2	no	—
434	C₂×D₄×C₅₃	—	4	1	no	—
435	C₂×D₄×C₅₃	—	4	1	no	—
436	C₂×D₄×C₅₃	—	4	1	no	—
437	C₂×D₄×C₅₃	—	4	1	no	—
438	C₂×D₄×C₅₃	—	4	1	no	—
439	C₂×D₄×C₅₃	—	4	1	no	—
440	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
441	C₂×D₄×C₅₃	#41	1	4	yes	—
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	—	2	2	no	—
449	C₂²×C₄×C₅₃	—	2	2	no	—
450	C₂²×C₄×C₅₃	—	2	2	no	—
451	C₂²×C₄×C₅₃	—	2	2	no	—
452	C₂²×C₄×C₅₃	—	2	2	no	—
453	C₂²×C₄×C₅₃	—	2	2	no	—
454	C₂²×C₄×C₅₃	—	2	2	no	—
455	C₂²×C₄×C₅₃	—	2	2	no	—
456	C₂²×C₄×C₅₃	—	2	2	no	—
457	C₂²×C₄×C₅₃	—	2	2	no	—
458	C₂²×C₄×C₅₃	—	2	2	no	—
459	C₂²×C₄×C₅₃	—	2	2	no	—
460	C₂²×C₄×C₅₃	—	2	2	no	—
461	C₂²×C₄×C₅₃	—	2	2	no	—
462	C₂²×C₄×C₅₃	—	2	2	no	—
463	C₂²×C₄×C₅₃	—	2	2	no	—
464	C₂²×C₄×C₅₃	—	2	2	no	—
465	C₂²×C₄×C₅₃	—	2	2	no	—
466	C₂²×C₄×C₅₃	—	2	2	no	—
467	C₂²×C₄×C₅₃	—	2	2	no	—
468	C₂²×C₄×C₅₃	—	2	2	no	—
469	C₂²×C₄×C₅₃	—	2	2	no	—
470	C₂²×C₄×C₅₃	—	2	2	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	1	no	—
489	C₂²×C₄×C₅₃	—	4	1	no	—
490	C₂²×C₄×C₅₃	—	4	1	no	—
491	C₂²×C₄×C₅₃	—	4	1	no	—
492	C₂²×C₄×C₅₃	—	4	1	no	—
493	C₂²×C₄×C₅₃	—	4	1	no	—
494	C₂²×C₄×C₅₃	—	4	16	no	—
495	C₂²×C₄×C₅₃	—	4	16	no	—
496	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
497	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
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	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
521	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
522	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
523	C₄⋊C₄×C₅₃	—	2	2	no	—
524	C₄⋊C₄×C₅₃	—	2	2	no	—
525	C₄⋊C₄×C₅₃	—	2	2	no	—
526	C₄⋊C₄×C₅₃	—	2	2	no	—
527	C₄⋊C₄×C₅₃	—	2	2	no	—
528	C₄⋊C₄×C₅₃	—	2	2	no	—
529	C₄⋊C₄×C₅₃	—	2	2	no	—
530	C₄⋊C₄×C₅₃	—	2	2	no	—
531	C₄⋊C₄×C₅₃	—	2	2	no	—
532	C₄⋊C₄×C₅₃	—	2	2	no	—
533	C₄⋊C₄×C₅₃	—	2	2	no	—
534	C₄⋊C₄×C₅₃	—	2	2	no	—
535	C₄⋊C₄×C₅₃	—	2	2	no	—
536	C₄⋊C₄×C₅₃	—	2	2	no	—
537	C₄⋊C₄×C₅₃	—	2	2	no	—
538	C₄⋊C₄×C₅₃	—	2	2	no	—
539	C₄⋊C₄×C₅₃	—	2	2	no	—
540	C₄⋊C₄×C₅₃	—	2	2	no	—
541	C₄⋊C₄×C₅₃	—	2	2	no	—
542	C₄⋊C₄×C₅₃	—	2	2	no	—
543	C₄⋊C₄×C₅₃	—	2	2	no	—
544	C₄⋊C₄×C₅₃	—	2	2	no	—
545	C₄⋊C₄×C₅₃	—	4	1	no	—
546	C₄⋊C₄×C₅₃	—	4	1	no	—
547	C₄⋊C₄×C₅₃	—	4	1	no	—
548	C₄⋊C₄×C₅₃	—	4	1	no	—
549	C₄⋊C₄×C₅₃	—	4	1	no	—
550	C₄⋊C₄×C₅₃	—	4	1	no	—
551	C₄⋊C₄×C₅₃	—	4	1	no	—
552	C₄⋊C₄×C₅₃	—	4	1	no	—
553	C₄⋊C₄×C₅₃	—	4	1	no	—
554	C₄⋊C₄×C₅₃	—	4	1	no	—
555	C₄⋊C₄×C₅₃	—	4	1	no	—
556	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
557	C₂²⋊C₄×C₅₃	—	2	2	no	—
558	C₂²⋊C₄×C₅₃	—	2	2	no	—
559	C₂²⋊C₄×C₅₃	—	2	2	no	—
560	C₂²⋊C₄×C₅₃	—	2	2	no	—
561	C₂²⋊C₄×C₅₃	—	2	2	no	—
562	C₂²⋊C₄×C₅₃	—	2	2	no	—
563	C₂²⋊C₄×C₅₃	—	2	2	no	—
564	C₂²⋊C₄×C₅₃	—	2	2	no	—
565	C₂²⋊C₄×C₅₃	—	2	2	no	—
566	C₂²⋊C₄×C₅₃	—	2	2	no	—
567	C₂²⋊C₄×C₅₃	—	2	2	no	—
568	C₂²⋊C₄×C₅₃	—	2	2	no	—
569	C₂²⋊C₄×C₅₃	—	2	2	no	—
570	C₂²⋊C₄×C₅₃	—	2	2	no	—
571	C₂²⋊C₄×C₅₃	—	2	2	no	—
572	C₂²⋊C₄×C₅₃	—	2	2	no	—
573	C₂²⋊C₄×C₅₃	—	2	2	no	—
574	C₂²⋊C₄×C₅₃	—	2	2	no	—
575	C₂²⋊C₄×C₅₃	—	2	2	no	—
576	C₂²⋊C₄×C₅₃	—	2	2	no	—
577	C₂²⋊C₄×C₅₃	—	2	2	no	—
578	C₂²⋊C₄×C₅₃	—	2	2	no	—
579	C₂²⋊C₄×C₅₃	—	2	2	no	—
580	C₂²⋊C₄×C₅₃	—	2	2	no	—
581	C₂²⋊C₄×C₅₃	—	2	2	no	—
582	C₂²⋊C₄×C₅₃	—	2	2	no	—
583	C₂²⋊C₄×C₅₃	—	2	2	no	—
584	C₂²⋊C₄×C₅₃	—	2	2	no	—
585	C₂²⋊C₄×C₅₃	—	2	2	no	—
586	C₂²⋊C₄×C₅₃	—	2	2	no	—
587	C₂²⋊C₄×C₅₃	—	2	2	no	—
588	C₂²⋊C₄×C₅₃	—	4	1	no	—
589	C₂²⋊C₄×C₅₃	—	4	1	no	—
590	C₂²⋊C₄×C₅₃	—	4	1	no	—
591	C₂²⋊C₄×C₅₃	—	4	1	no	—
592	C₂²⋊C₄×C₅₃	—	4	1	no	—
593	C₂²⋊C₄×C₅₃	—	4	1	no	—
594	C₂²⋊C₄×C₅₃	—	4	1	no	—
595	C₂²⋊C₄×C₅₃	—	4	1	no	—
596	C₂²⋊C₄×C₅₃	—	4	1	no	—
597	C₂²⋊C₄×C₅₃	—	4	1	no	—
598	C₂²⋊C₄×C₅₃	—	4	1	no	—
599	C₂²⋊C₄×C₅₃	—	4	1	no	—
600	C₂²⋊C₄×C₅₃	—	4	1	no	—
601	C₂²⋊C₄×C₅₃	—	4	1	no	—
602	C₂²⋊C₄×C₅₃	—	4	1	no	—
603	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
604	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
605	C₄²×C₅₃	—	2	2	no	—
606	C₄²×C₅₃	—	2	2	no	—
607	C₄²×C₅₃	—	2	2	no	—
608	C₄²×C₅₃	—	2	2	no	—
609	C₄²×C₅₃	—	4	1	no	—
610	C₄²×C₅₃	—	4	1	no	—
611	C₄²×C₅₃	C₂×D₄	1	4	yes	—
612	C₂³×C₅₃	—	2	1	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	8	no	—
621	C₂³×C₅₃	—	2	8	no	—
622	C₂³×C₅₃	—	2	8	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	1	no	—
638	C₂³×C₅₃	—	2	1	no	—
639	C₂³×C₅₃	—	2	1	no	—
640	C₂³×C₅₃	—	2	1	no	—
641	C₂³×C₅₃	—	2	1	no	—
642	C₂³×C₅₃	—	2	1	no	—
643	C₂³×C₅₃	—	2	1	no	—
644	C₂³×C₅₃	—	2	1	no	—
645	C₂³×C₅₃	—	2	1	no	—
646	C₂³×C₅₃	—	2	1	no	—
647	C₂³×C₅₃	—	2	1	no	—
648	C₂³×C₅₃	—	4	4	no	—
649	C₂³×C₅₃	—	4	4	no	—
650	C₂³×C₅₃	—	4	4	no	—
651	C₂³×C₅₃	—	4	4	no	—
652	C₂³×C₅₃	—	4	4	no	—
653	C₂³×C₅₃	—	4	4	no	—
654	C₂³×C₅₃	—	4	4	no	—
655	C₂³×C₅₃	—	4	4	no	—
656	C₂³×C₅₃	—	4	4	no	—
657	C₂³×C₅₃	—	4	4	no	—
658	C₂³×C₅₃	—	4	4	no	—
659	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
660	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
661	C₂³×C₅₃	C₂×#41	1	2	yes	—
662	C₂³×C₅₃	C₂×#41	1	2	yes	—
663	C₂³×C₅₃	C₂×#41	1	2	yes	—
664	C₂³×C₅₃	C₂×#41	1	2	yes	—
665	C₂³×C₅₃	C₂×#41	1	2	yes	—
666	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
667	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
668	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
669	Q₈×C₅₃	—	8	2	no	—
670	D₄×C₅₃	—	2	8	no	—
671	D₄×C₅₃	—	2	8	no	—
672	D₄×C₅₃	—	2	8	no	—
673	D₄×C₅₃	—	2	8	no	—
674	D₄×C₅₃	—	4	4	no	—
675	D₄×C₅₃	—	4	4	no	—
676	D₄×C₅₃	—	4	4	no	—
677	D₄×C₅₃	—	8	2	no	—
678	D₄×C₅₃	—	8	2	no	—
679	C₂×C₄×C₅₃	—	2	8	no	—
680	C₂×C₄×C₅₃	—	2	8	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	—	2	1	no	—
737	C₂×C₄×C₅₃	—	2	1	no	—
738	C₂×C₄×C₅₃	—	2	1	no	—
739	C₂×C₄×C₅₃	—	2	1	no	—
740	C₂×C₄×C₅₃	—	2	1	no	—
741	C₂×C₄×C₅₃	—	2	1	no	—
742	C₂×C₄×C₅₃	—	2	1	no	—
743	C₂×C₄×C₅₃	—	2	1	no	—
744	C₂×C₄×C₅₃	—	2	1	no	—
745	C₂×C₄×C₅₃	—	2	1	no	—
746	C₂×C₄×C₅₃	—	2	1	no	—
747	C₂×C₄×C₅₃	—	2	1	no	—
748	C₂×C₄×C₅₃	—	2	1	no	—
749	C₂×C₄×C₅₃	—	4	4	no	—
750	C₂×C₄×C₅₃	—	4	4	no	—
751	C₂×C₄×C₅₃	—	4	4	no	—
752	C₂×C₄×C₅₃	—	4	4	no	—
753	C₂×C₄×C₅₃	—	4	4	no	—
754	C₂×C₄×C₅₃	—	4	4	no	—
755	C₂×C₄×C₅₃	—	4	4	no	—
756	C₂×C₄×C₅₃	—	4	4	no	—
757	C₂×C₄×C₅₃	—	4	4	no	—
758	C₂×C₄×C₅₃	—	4	4	no	—
759	C₂×C₄×C₅₃	—	4	4	no	—
760	C₂×C₄×C₅₃	—	4	4	no	—
761	C₂×C₄×C₅₃	—	4	4	no	—
762	C₂×C₄×C₅₃	—	8	2	no	—
763	C₂×C₄×C₅₃	—	8	2	no	—
764	C₂×C₄×C₅₃	—	8	2	no	—
765	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
766	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
767	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
768	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
769	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
770	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
771	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
772	#34991	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
791	C₂²×C₅₃	—	2	2	no	—
792	C₂²×C₅₃	—	2	2	no	—
793	C₂²×C₅₃	—	2	2	no	—
794	C₂²×C₅₃	—	4	16	no	—
795	C₂²×C₅₃	—	4	16	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	—	4	1	no	—
808	C₂²×C₅₃	—	4	1	no	—
809	C₂²×C₅₃	—	4	1	no	—
810	C₂²×C₅₃	—	4	1	no	—
811	C₂²×C₅₃	—	4	1	no	—
812	C₂²×C₅₃	—	4	1	no	—
813	C₂²×C₅₃	—	4	1	no	—
814	C₂²×C₅₃	—	4	1	no	—
815	C₂²×C₅₃	#525	1	4	yes	—
816	C₂²×C₅₃	#539	1	4	yes	complemented
817	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
818	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
819	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
820	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
821	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
822	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
823	C₂²×C₅₃	#585	1	1	yes	characteristic
824	C₄×C₅₃	—	2	2	no	—
825	C₄×C₅₃	—	2	2	no	—
826	C₄×C₅₃	—	2	2	no	—
827	C₄×C₅₃	—	2	2	no	—
828	C₄×C₅₃	—	2	2	no	—
829	C₄×C₅₃	—	2	2	no	—
830	C₄×C₅₃	—	2	2	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	C₄×C₅₃	—	4	1	no	—
843	C₄×C₅₃	—	4	1	no	—
844	C₄×C₅₃	—	4	1	no	—
845	C₄×C₅₃	—	4	1	no	—
846	C₄×C₅₃	—	4	1	no	—
847	C₄×C₅₃	—	4	1	no	—
848	C₄×C₅₃	—	4	1	no	—
849	C₂×#539	C₂×C₅₃	1	1	yes	characteristic, complemented
850	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
851	#2852	C₂×C₅₃	1	1	yes	characteristic, complemented
852	#2851	C₂×C₅₃	1	1	yes	characteristic, complemented
853	#2849	C₂×C₅₃	1	1	yes	characteristic, complemented
854	#2848	C₂×C₅₃	1	1	yes	characteristic, complemented
855	#2638	C₂×C₅₃	1	1	yes	characteristic, complemented
856	#2636	C₂×C₅₃	1	1	yes	characteristic, complemented
857	#2633	C₂×C₅₃	1	1	yes	characteristic, complemented
858	#2630	C₂×C₅₃	1	1	yes	characteristic, complemented
859	#2480	C₂×C₅₃	1	1	yes	characteristic, complemented
860	#2473	C₂×C₅₃	1	1	yes	characteristic, complemented
861	#2466	C₂×C₅₃	1	1	yes	characteristic, complemented
862	#2463	C₂×C₅₃	1	1	yes	characteristic, complemented
863	#2460	C₂×C₅₃	1	1	yes	characteristic, complemented
864	#2455	C₂×C₅₃	1	1	yes	characteristic, complemented
865	#2449	C₂×C₅₃	1	1	yes	characteristic, complemented
866	#2449	C₂×C₅₃	1	1	yes	characteristic, complemented
867	#2443	C₂×C₅₃	1	1	yes	characteristic, complemented
868	#2437	C₂×C₅₃	1	1	yes	characteristic, complemented
869	#2425	C₂×C₅₃	1	1	yes	characteristic, complemented
870	#2419	C₂×C₅₃	1	1	yes	characteristic, complemented
871	#2418	C₂×C₅₃	1	1	yes	characteristic, complemented
872	#2412	C₂×C₅₃	1	1	yes	characteristic, complemented
873	#2410	C₂×C₅₃	1	1	yes	characteristic
874	#2405	C₂×C₅₃	1	1	yes	characteristic, complemented
875	#2325	C₂×C₅₃	1	1	yes	characteristic, complemented
876	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#2318	C₂×C₅₃	1	1	yes	characteristic, complemented
878	C₄×#120	C₂×C₅₃	1	1	yes	characteristic, complemented
879	C₂×#385	C₂×C₅₃	1	1	yes	characteristic, complemented
880	C₂×C₅₃	—	2	4	no	—
881	C₂×C₅₃	—	2	4	no	—
882	C₂×C₅₃	—	4	2	no	—
883	C₂×C₅₃	—	4	2	no	—
884	C₂×C₅₃	—	4	2	no	—
885	C₂×C₅₃	—	8	1	no	—
886	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
887	C₂×C₅₃	C₂×#539	1	1	yes	characteristic
888	C₂×C₅₃	#3459	1	1	yes	characteristic
889	C₂×C₅₃	#3484	1	1	yes	characteristic
890	C₂×C₅₃	#3489	1	1	yes	characteristic
891	C₂×C₅₃	#3513	1	1	yes	characteristic
892	C₂×C₅₃	#3520	1	1	yes	characteristic
893	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
894	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
895	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
896	#539	—	2	8	no	—
897	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
898	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
899	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
900	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
901	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
902	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
903	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
904	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
905	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
908	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
913	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
914	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
915	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
916	C₂×C₄×D₄	—	2	8	no	—
917	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
918	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
919	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
920	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
921	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
922	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
923	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
924	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
925	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
926	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
929	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
932	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
933	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
934	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
935	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
936	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
937	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
945	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
947	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#394	C₂²×C₅₃	1	1	yes	characteristic
956	#394	C₂²×C₅₃	1	1	yes	characteristic
957	#394	C₂²×C₅₃	1	1	yes	characteristic
958	#394	C₂²×C₅₃	1	1	yes	characteristic
959	#394	C₂²×C₅₃	1	1	yes	characteristic
960	#394	C₂²×C₅₃	1	1	yes	characteristic
961	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#392	C₂²×C₅₃	1	1	yes	characteristic
967	#392	C₂²×C₅₃	1	1	yes	characteristic
968	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#386	C₂²×C₅₃	1	1	yes	characteristic
991	#386	C₂²×C₅₃	1	1	yes	characteristic
992	#386	C₂²×C₅₃	1	1	yes	characteristic
993	#386	C₂²×C₅₃	1	1	yes	characteristic
994	#386	C₂²×C₅₃	1	1	yes	characteristic
995	#386	C₂²×C₅₃	1	1	yes	characteristic
996	#386	C₂²×C₅₃	1	1	yes	characteristic
997	#386	C₂²×C₅₃	1	1	yes	characteristic
998	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#385	C₂²×C₅₃	1	1	yes	characteristic
1005	#385	C₂²×C₅₃	1	1	yes	characteristic
1006	#385	C₂²×C₅₃	1	1	yes	characteristic
1007	#385	C₂²×C₅₃	1	1	yes	characteristic
1008	#385	C₂²×C₅₃	1	1	yes	characteristic
1009	#385	C₂²×C₅₃	1	1	yes	characteristic
1010	#385	C₂²×C₅₃	1	1	yes	characteristic
1011	#385	C₂²×C₅₃	1	1	yes	characteristic
1012	#385	C₂²×C₅₃	1	1	yes	characteristic
1013	#385	C₂²×C₅₃	1	1	yes	characteristic
1014	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#380	C₂²×C₅₃	1	1	yes	characteristic
1036	#380	C₂²×C₅₃	1	1	yes	characteristic
1037	#380	C₂²×C₅₃	1	1	yes	characteristic
1038	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#379	C₂²×C₅₃	1	1	yes	characteristic
1042	#379	C₂²×C₅₃	1	1	yes	characteristic
1043	#379	C₂²×C₅₃	1	1	yes	characteristic
1044	#379	C₂²×C₅₃	1	1	yes	characteristic
1045	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1046	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	C₅₃	#34991	1	1	yes	characteristic, direct product factor, Sylow
1051	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂²×D₄	—	2	4	no	—
1055	C₂²×D₄	—	2	4	no	—
1056	C₂²×D₄	—	2	4	no	—
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	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂³×C₄	—	2	4	no	—
1067	C₂³×C₄	—	2	4	no	—
1068	C₂³×C₄	—	4	2	no	—
1069	C₂³×C₄	—	4	2	no	—
1070	C₂³×C₄	—	4	2	no	—
1071	C₂³×C₄	—	4	2	no	—
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	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1090	#126	—	2	4	no	—
1091	#126	—	2	4	no	—
1092	#125	—	2	4	no	—
1093	#125	—	2	4	no	—
1094	#123	—	2	4	no	—
1095	#123	—	2	4	no	—
1096	#123	—	2	4	no	—
1097	#123	—	2	4	no	—
1098	#123	—	2	4	no	—
1099	#123	—	4	2	no	—
1100	C₂²⋊Q₈	—	2	4	no	—
1101	C₂²⋊Q₈	—	2	4	no	—
1102	C₂²⋊Q₈	—	2	4	no	—
1103	C₂²⋊Q₈	—	4	2	no	—
1104	C₂²⋊Q₈	—	4	2	no	—
1105	#121	—	2	4	no	—
1106	#121	—	2	4	no	—
1107	#120	—	2	4	no	—
1108	#120	—	4	2	no	—
1109	C₄×D₄	—	2	4	no	—
1110	C₄×D₄	—	2	4	no	—
1111	C₄×D₄	—	2	4	no	—
1112	C₄×D₄	—	2	4	no	—
1113	C₄×D₄	—	2	4	no	—
1114	C₄×D₄	—	2	4	no	—
1115	C₄×D₄	—	2	4	no	—
1116	C₄×D₄	—	2	4	no	—
1117	C₄×D₄	—	4	2	no	—
1118	C₄×D₄	—	4	2	no	—
1119	C₄×D₄	D₄×C₅₃	1	8	yes	complemented
1120	C₂×C₄⋊C₄	—	2	4	no	—
1121	C₂×C₄⋊C₄	—	2	4	no	—
1122	C₂×C₄⋊C₄	—	4	2	no	—
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×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1140	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1141	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1145	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1147	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1148	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1149	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1150	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1151	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1152	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1153	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1154	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1155	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1156	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1157	C₂×C₂²⋊C₄	—	2	4	no	—
1158	C₂×C₂²⋊C₄	—	2	4	no	—
1159	C₂×C₂²⋊C₄	—	2	4	no	—
1160	C₂×C₂²⋊C₄	—	4	2	no	—
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×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1186	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1187	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1188	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1189	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1190	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1191	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1192	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1193	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1194	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1195	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1196	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1197	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1198	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1199	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1200	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1201	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1202	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1205	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1206	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1207	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1208	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1209	C₂×C₄²	—	2	4	no	—
1210	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1211	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1212	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1213	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1214	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1215	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1216	C₂×C₄²	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	#95	C₂³×C₅₃	1	1	yes	characteristic
1238	#95	C₂³×C₅₃	1	1	yes	characteristic
1239	#95	C₂³×C₅₃	1	1	yes	characteristic
1240	#95	C₂³×C₅₃	1	1	yes	characteristic
1241	#95	C₂³×C₅₃	1	1	yes	characteristic
1242	#95	C₂³×C₅₃	1	1	yes	characteristic
1243	#95	C₂³×C₅₃	1	1	yes	characteristic
1244	#95	C₂³×C₅₃	1	1	yes	characteristic
1245	#95	C₂³×C₅₃	1	1	yes	characteristic
1246	#95	C₂³×C₅₃	1	1	yes	characteristic
1247	#95	C₂³×C₅₃	1	1	yes	characteristic
1248	#95	C₂³×C₅₃	1	1	yes	characteristic
1249	#95	C₂³×C₅₃	1	1	yes	characteristic
1250	#95	C₂³×C₅₃	1	1	yes	characteristic
1251	#95	C₂³×C₅₃	1	1	yes	characteristic
1252	#95	C₂³×C₅₃	1	1	yes	characteristic
1253	C₂⁴	—	2	2	no	—
1254	C₂⁴	—	2	2	no	—
1255	C₂⁴	—	2	2	no	—
1256	C₂⁴	—	2	2	no	—
1257	C₂⁴	—	2	2	no	—
1258	C₂⁴	—	2	2	no	—
1259	C₂⁴	—	2	2	no	—
1260	C₂⁴	—	2	2	no	—
1261	C₂⁴	—	2	2	no	—
1262	C₂⁴	—	4	1	no	—
1263	C₂⁴	—	4	1	no	—
1264	C₂⁴	—	4	1	no	—
1265	C₂⁴	—	4	1	no	—
1266	C₂⁴	#41×C₅₃	1	4	yes	—
1267	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1268	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1269	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1270	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1271	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1272	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1273	C₂×Q₈	—	2	2	no	—
1274	C₂×Q₈	—	4	1	no	—
1275	C₂×Q₈	—	4	1	no	—
1276	C₂×D₄	—	2	32	no	—
1277	C₂×D₄	—	2	2	no	—
1278	C₂×D₄	—	2	2	no	—
1279	C₂×D₄	—	2	2	no	—
1280	C₂×D₄	—	2	2	no	—
1281	C₂×D₄	—	2	2	no	—
1282	C₂×D₄	—	2	2	no	—
1283	C₂×D₄	—	2	2	no	—
1284	C₂×D₄	—	2	2	no	—
1285	C₂×D₄	—	2	2	no	—
1286	C₂×D₄	—	2	2	no	—
1287	C₂×D₄	—	2	2	no	—
1288	C₂×D₄	—	2	2	no	—
1289	C₂×D₄	—	2	2	no	—
1290	C₂×D₄	—	2	2	no	—
1291	C₂×D₄	—	2	2	no	—
1292	C₂×D₄	—	2	2	no	—
1293	C₂×D₄	—	2	2	no	—
1294	C₂×D₄	—	2	2	no	—
1295	C₂×D₄	—	2	2	no	—
1296	C₂×D₄	—	4	1	no	—
1297	C₂×D₄	—	4	1	no	—
1298	C₂×D₄	—	4	1	no	—
1299	C₂×D₄	—	4	1	no	—
1300	C₂×D₄	—	4	1	no	—
1301	C₂×D₄	—	4	1	no	—
1302	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
1303	C₂×D₄	#41×C₅₃	1	4	yes	—
1304	C₂²×C₄	—	2	2	no	—
1305	C₂²×C₄	—	2	2	no	—
1306	C₂²×C₄	—	2	2	no	—
1307	C₂²×C₄	—	2	2	no	—
1308	C₂²×C₄	—	2	2	no	—
1309	C₂²×C₄	—	2	2	no	—
1310	C₂²×C₄	—	2	2	no	—
1311	C₂²×C₄	—	2	2	no	—
1312	C₂²×C₄	—	2	2	no	—
1313	C₂²×C₄	—	2	2	no	—
1314	C₂²×C₄	—	2	2	no	—
1315	C₂²×C₄	—	2	2	no	—
1316	C₂²×C₄	—	2	2	no	—
1317	C₂²×C₄	—	2	2	no	—
1318	C₂²×C₄	—	2	2	no	—
1319	C₂²×C₄	—	2	2	no	—
1320	C₂²×C₄	—	2	2	no	—
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	—	2	2	no	—
1328	C₂²×C₄	—	2	2	no	—
1329	C₂²×C₄	—	2	2	no	—
1330	C₂²×C₄	—	2	2	no	—
1331	C₂²×C₄	—	2	2	no	—
1332	C₂²×C₄	—	2	2	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	—	4	1	no	—
1350	C₂²×C₄	—	4	1	no	—
1351	C₂²×C₄	—	4	1	no	—
1352	C₂²×C₄	—	4	1	no	—
1353	C₂²×C₄	—	4	1	no	—
1354	C₂²×C₄	—	4	1	no	—
1355	C₂²×C₄	—	4	1	no	—
1356	C₂²×C₄	—	4	16	no	—
1357	C₂²×C₄	—	4	16	no	—
1358	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
1359	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
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	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1376	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1377	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1378	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1379	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1380	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1381	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1382	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1383	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1384	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1385	C₄⋊C₄	—	2	2	no	—
1386	C₄⋊C₄	—	2	2	no	—
1387	C₄⋊C₄	—	2	2	no	—
1388	C₄⋊C₄	—	2	2	no	—
1389	C₄⋊C₄	—	2	2	no	—
1390	C₄⋊C₄	—	2	2	no	—
1391	C₄⋊C₄	—	2	2	no	—
1392	C₄⋊C₄	—	2	2	no	—
1393	C₄⋊C₄	—	2	2	no	—
1394	C₄⋊C₄	—	2	2	no	—
1395	C₄⋊C₄	—	2	2	no	—
1396	C₄⋊C₄	—	2	2	no	—
1397	C₄⋊C₄	—	2	2	no	—
1398	C₄⋊C₄	—	2	2	no	—
1399	C₄⋊C₄	—	2	2	no	—
1400	C₄⋊C₄	—	2	2	no	—
1401	C₄⋊C₄	—	2	2	no	—
1402	C₄⋊C₄	—	2	2	no	—
1403	C₄⋊C₄	—	2	2	no	—
1404	C₄⋊C₄	—	2	2	no	—
1405	C₄⋊C₄	—	2	2	no	—
1406	C₄⋊C₄	—	2	2	no	—
1407	C₄⋊C₄	—	4	1	no	—
1408	C₄⋊C₄	—	4	1	no	—
1409	C₄⋊C₄	—	4	1	no	—
1410	C₄⋊C₄	—	4	1	no	—
1411	C₄⋊C₄	—	4	1	no	—
1412	C₄⋊C₄	—	4	1	no	—
1413	C₄⋊C₄	—	4	1	no	—
1414	C₄⋊C₄	—	4	1	no	—
1415	C₄⋊C₄	—	4	1	no	—
1416	C₄⋊C₄	—	4	1	no	—
1417	C₄⋊C₄	—	4	1	no	—
1418	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1419	C₂²⋊C₄	—	2	2	no	—
1420	C₂²⋊C₄	—	2	2	no	—
1421	C₂²⋊C₄	—	2	2	no	—
1422	C₂²⋊C₄	—	2	2	no	—
1423	C₂²⋊C₄	—	2	2	no	—
1424	C₂²⋊C₄	—	2	2	no	—
1425	C₂²⋊C₄	—	2	2	no	—
1426	C₂²⋊C₄	—	2	2	no	—
1427	C₂²⋊C₄	—	2	2	no	—
1428	C₂²⋊C₄	—	2	2	no	—
1429	C₂²⋊C₄	—	2	2	no	—
1430	C₂²⋊C₄	—	2	2	no	—
1431	C₂²⋊C₄	—	2	2	no	—
1432	C₂²⋊C₄	—	2	2	no	—
1433	C₂²⋊C₄	—	2	2	no	—
1434	C₂²⋊C₄	—	2	2	no	—
1435	C₂²⋊C₄	—	2	2	no	—
1436	C₂²⋊C₄	—	2	2	no	—
1437	C₂²⋊C₄	—	2	2	no	—
1438	C₂²⋊C₄	—	2	2	no	—
1439	C₂²⋊C₄	—	2	2	no	—
1440	C₂²⋊C₄	—	2	2	no	—
1441	C₂²⋊C₄	—	2	2	no	—
1442	C₂²⋊C₄	—	2	2	no	—
1443	C₂²⋊C₄	—	2	2	no	—
1444	C₂²⋊C₄	—	2	2	no	—
1445	C₂²⋊C₄	—	2	2	no	—
1446	C₂²⋊C₄	—	2	2	no	—
1447	C₂²⋊C₄	—	2	2	no	—
1448	C₂²⋊C₄	—	2	2	no	—
1449	C₂²⋊C₄	—	2	2	no	—
1450	C₂²⋊C₄	—	4	1	no	—
1451	C₂²⋊C₄	—	4	1	no	—
1452	C₂²⋊C₄	—	4	1	no	—
1453	C₂²⋊C₄	—	4	1	no	—
1454	C₂²⋊C₄	—	4	1	no	—
1455	C₂²⋊C₄	—	4	1	no	—
1456	C₂²⋊C₄	—	4	1	no	—
1457	C₂²⋊C₄	—	4	1	no	—
1458	C₂²⋊C₄	—	4	1	no	—
1459	C₂²⋊C₄	—	4	1	no	—
1460	C₂²⋊C₄	—	4	1	no	—
1461	C₂²⋊C₄	—	4	1	no	—
1462	C₂²⋊C₄	—	4	1	no	—
1463	C₂²⋊C₄	—	4	1	no	—
1464	C₂²⋊C₄	—	4	1	no	—
1465	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1466	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1467	C₄²	—	2	2	no	—
1468	C₄²	—	2	2	no	—
1469	C₄²	—	2	2	no	—
1470	C₄²	—	2	2	no	—
1471	C₄²	—	4	1	no	—
1472	C₄²	—	4	1	no	—
1473	C₄²	C₂×D₄×C₅₃	1	4	yes	—
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	8	no	—
1483	C₂³	—	2	8	no	—
1484	C₂³	—	2	8	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	1	no	—
1493	C₂³	—	2	1	no	—
1494	C₂³	—	2	1	no	—
1495	C₂³	—	2	1	no	—
1496	C₂³	—	2	1	no	—
1497	C₂³	—	2	1	no	—
1498	C₂³	—	2	1	no	—
1499	C₂³	—	2	1	no	—
1500	C₂³	—	2	1	no	—
1501	C₂³	—	2	1	no	—
1502	C₂³	—	2	1	no	—
1503	C₂³	—	2	1	no	—
1504	C₂³	—	2	1	no	—
1505	C₂³	—	2	1	no	—
1506	C₂³	—	2	1	no	—
1507	C₂³	—	2	1	no	—
1508	C₂³	—	2	1	no	—
1509	C₂³	—	2	1	no	—
1510	C₂³	—	4	4	no	—
1511	C₂³	—	4	4	no	—
1512	C₂³	—	4	4	no	—
1513	C₂³	—	4	4	no	—
1514	C₂³	—	4	4	no	—
1515	C₂³	—	4	4	no	—
1516	C₂³	—	4	4	no	—
1517	C₂³	—	4	4	no	—
1518	C₂³	—	4	4	no	—
1519	C₂³	—	4	4	no	—
1520	C₂³	—	4	4	no	—
1521	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1522	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1523	C₂³	C₂×#41×C₅₃	1	2	yes	—
1524	C₂³	C₂×#41×C₅₃	1	2	yes	—
1525	C₂³	C₂×#41×C₅₃	1	2	yes	—
1526	C₂³	C₂×#41×C₅₃	1	2	yes	—
1527	C₂³	C₂×#41×C₅₃	1	2	yes	—
1528	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1529	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1530	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1531	Q₈	—	8	2	no	—
1532	D₄	—	2	8	no	—
1533	D₄	—	2	8	no	—
1534	D₄	—	2	8	no	—
1535	D₄	—	2	8	no	—
1536	D₄	—	4	4	no	—
1537	D₄	—	4	4	no	—
1538	D₄	—	4	4	no	—
1539	D₄	—	8	2	no	—
1540	D₄	—	8	2	no	—
1541	C₂×C₄	—	2	8	no	—
1542	C₂×C₄	—	2	8	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	—	2	1	no	—
1592	C₂×C₄	—	2	1	no	—
1593	C₂×C₄	—	2	1	no	—
1594	C₂×C₄	—	2	1	no	—
1595	C₂×C₄	—	2	1	no	—
1596	C₂×C₄	—	2	1	no	—
1597	C₂×C₄	—	2	1	no	—
1598	C₂×C₄	—	2	1	no	—
1599	C₂×C₄	—	2	1	no	—
1600	C₂×C₄	—	2	1	no	—
1601	C₂×C₄	—	2	1	no	—
1602	C₂×C₄	—	2	1	no	—
1603	C₂×C₄	—	2	1	no	—
1604	C₂×C₄	—	2	1	no	—
1605	C₂×C₄	—	2	1	no	—
1606	C₂×C₄	—	2	1	no	—
1607	C₂×C₄	—	2	1	no	—
1608	C₂×C₄	—	2	1	no	—
1609	C₂×C₄	—	2	1	no	—
1610	C₂×C₄	—	2	1	no	—
1611	C₂×C₄	—	4	4	no	—
1612	C₂×C₄	—	4	4	no	—
1613	C₂×C₄	—	4	4	no	—
1614	C₂×C₄	—	4	4	no	—
1615	C₂×C₄	—	4	4	no	—
1616	C₂×C₄	—	4	4	no	—
1617	C₂×C₄	—	4	4	no	—
1618	C₂×C₄	—	4	4	no	—
1619	C₂×C₄	—	4	4	no	—
1620	C₂×C₄	—	4	4	no	—
1621	C₂×C₄	—	4	4	no	—
1622	C₂×C₄	—	4	4	no	—
1623	C₂×C₄	—	4	4	no	—
1624	C₂×C₄	—	8	2	no	—
1625	C₂×C₄	—	8	2	no	—
1626	C₂×C₄	—	8	2	no	—
1627	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1628	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1629	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1630	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1631	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1632	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1633	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
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	—	2	2	no	—
1645	C₂²	—	2	2	no	—
1646	C₂²	—	2	2	no	—
1647	C₂²	—	2	2	no	—
1648	C₂²	—	2	2	no	—
1649	C₂²	—	2	2	no	—
1650	C₂²	—	2	2	no	—
1651	C₂²	—	2	2	no	—
1652	C₂²	—	2	2	no	—
1653	C₂²	—	2	2	no	—
1654	C₂²	—	2	2	no	—
1655	C₂²	—	4	16	no	—
1656	C₂²	—	4	16	no	—
1657	C₂²	—	4	1	no	—
1658	C₂²	—	4	1	no	—
1659	C₂²	—	4	1	no	—
1660	C₂²	—	4	1	no	—
1661	C₂²	—	4	1	no	—
1662	C₂²	—	4	1	no	—
1663	C₂²	—	4	1	no	—
1664	C₂²	—	4	1	no	—
1665	C₂²	—	4	1	no	—
1666	C₂²	—	4	1	no	—
1667	C₂²	—	4	1	no	—
1668	C₂²	—	4	1	no	—
1669	C₂²	—	4	1	no	—
1670	C₂²	—	4	1	no	—
1671	C₂²	—	4	1	no	—
1672	C₂²	—	4	1	no	—
1673	C₂²	—	4	1	no	—
1674	C₂²	—	4	1	no	—
1675	C₂²	—	4	1	no	—
1676	C₂²	C₅₃×#525	1	4	yes	—
1677	C₂²	C₅₃×#539	1	4	yes	complemented
1678	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1679	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1680	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1681	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1682	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1683	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1684	C₂²	C₅₃×#585	1	1	yes	characteristic
1685	C₄	—	2	2	no	—
1686	C₄	—	2	2	no	—
1687	C₄	—	2	2	no	—
1688	C₄	—	2	2	no	—
1689	C₄	—	2	2	no	—
1690	C₄	—	2	2	no	—
1691	C₄	—	2	2	no	—
1692	C₄	—	4	1	no	—
1693	C₄	—	4	1	no	—
1694	C₄	—	4	1	no	—
1695	C₄	—	4	1	no	—
1696	C₄	—	4	1	no	—
1697	C₄	—	4	1	no	—
1698	C₄	—	4	1	no	—
1699	C₄	—	4	1	no	—
1700	C₄	—	4	1	no	—
1701	C₄	—	4	1	no	—
1702	C₄	—	4	1	no	—
1703	C₄	—	4	1	no	—
1704	C₄	—	4	1	no	—
1705	C₄	—	4	1	no	—
1706	C₄	—	4	1	no	—
1707	C₄	—	4	1	no	—
1708	C₄	—	4	1	no	—
1709	C₄	—	4	1	no	—
1710	C₂	—	2	4	no	—
1711	C₂	—	2	4	no	—
1712	C₂	—	4	2	no	—
1713	C₂	—	4	2	no	—
1714	C₂	—	4	2	no	—
1715	C₂	—	8	1	no	—
1716	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
1717	C₂	C₂×C₅₃×#539	1	1	yes	characteristic
1718	C₂	C₅₃×#3459	1	1	yes	characteristic
1719	C₂	C₅₃×#3484	1	1	yes	characteristic
1720	C₂	C₅₃×#3489	1	1	yes	characteristic
1721	C₂	C₅₃×#3513	1	1	yes	characteristic
1722	C₂	C₅₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2410	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#539	C₂	semidirect
2. C₂²×C₄×D₄×C₅₃	C₂	semidirect
3. C₅₃×#2852	C₂	semidirect
4. C₅₃×#2851	C₂	semidirect
5. C₅₃×#2849	C₂	semidirect
6. C₅₃×#2848	C₂	semidirect
7. C₅₃×#2638	C₂	semidirect
8. C₅₃×#2636	C₂	semidirect
9. C₅₃×#2633	C₂	semidirect
10. C₅₃×#2630	C₂	semidirect
11. C₅₃×#2480	C₂	semidirect
12. C₅₃×#2473	C₂	semidirect
13. C₅₃×#2466	C₂	semidirect
14. C₅₃×#2463	C₂	semidirect
15. C₅₃×#2460	C₂	semidirect
16. C₅₃×#2455	C₂	semidirect
17. C₅₃×#2449	C₂	semidirect
18. C₅₃×#2449	C₂	semidirect
19. C₅₃×#2443	C₂	semidirect
20. C₅₃×#2437	C₂	semidirect
21. C₅₃×#2425	C₂	semidirect
22. C₅₃×#2419	C₂	semidirect
23. C₅₃×#2418	C₂	semidirect
24. C₅₃×#2412	C₂	semidirect
26. C₅₃×#2405	C₂	semidirect
27. C₅₃×#2325	C₂	semidirect
28. C₅₃×#2322	C₂	semidirect
29. C₅₃×#2318	C₂	semidirect
30. C₄×#120×C₅₃	C₂	semidirect
31. C₂×C₅₃×#385	C₂	semidirect
36. C₂×#126×C₅₃	C₂²	semidirect
37. C₂×#126×C₅₃	C₂²	semidirect
38. C₂×#125×C₅₃	C₂²	semidirect
39. C₂×#125×C₅₃	C₂²	semidirect
42. C₂×#123×C₅₃	C₂²	semidirect
43. C₂×#123×C₅₃	C₂²	semidirect
44. C₂×#123×C₅₃	C₂²	semidirect
45. C₂×#123×C₅₃	C₂²	semidirect
47. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
48. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
49. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
50. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
65. C₂×C₄×D₄×C₅₃	C₂²	semidirect
66. C₂×C₄×D₄×C₅₃	C₂²	semidirect
68. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
69. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
75. C₅₃×#400	C₂²	semidirect
76. C₅₃×#399	C₂²	semidirect
77. C₅₃×#399	C₂²	semidirect
78. C₅₃×#399	C₂²	semidirect
79. C₅₃×#398	C₂²	semidirect
80. C₅₃×#398	C₂²	semidirect
81. C₅₃×#398	C₂²	semidirect
82. C₅₃×#398	C₂²	semidirect
83. C₅₃×#397	C₂²	semidirect
84. C₅₃×#397	C₂²	semidirect
85. C₅₃×#397	C₂²	semidirect
86. C₅₃×#397	C₂²	semidirect
87. C₅₃×#397	C₂²	semidirect
88. C₅₃×#397	C₂²	semidirect
89. C₅₃×#396	C₂²	semidirect
90. C₅₃×#396	C₂²	semidirect
91. C₅₃×#396	C₂²	semidirect
92. C₅₃×#396	C₂²	semidirect
93. C₅₃×#395	C₂²	semidirect
100. C₅₃×#394	C₂²	semidirect
101. C₅₃×#394	C₂²	semidirect
102. C₅₃×#394	C₂²	semidirect
103. C₅₃×#394	C₂²	semidirect
104. C₅₃×#393	C₂²	semidirect
107. C₅₃×#389	C₂²	semidirect
108. C₅₃×#389	C₂²	semidirect
109. C₅₃×#389	C₂²	semidirect
110. C₅₃×#389	C₂²	semidirect
111. C₅₃×#388	C₂²	semidirect
112. C₅₃×#388	C₂²	semidirect
113. C₅₃×#388	C₂²	semidirect
114. C₅₃×#388	C₂²	semidirect
115. C₅₃×#388	C₂²	semidirect
116. C₅₃×#388	C₂²	semidirect
117. C₅₃×#388	C₂²	semidirect
118. C₅₃×#388	C₂²	semidirect
119. C₅₃×#387	C₂²	semidirect
120. C₅₃×#387	C₂²	semidirect
121. C₅₃×#387	C₂²	semidirect
122. C₅₃×#387	C₂²	semidirect
123. C₅₃×#387	C₂²	semidirect
124. C₅₃×#387	C₂²	semidirect
125. C₅₃×#387	C₂²	semidirect
126. C₅₃×#387	C₂²	semidirect
127. C₅₃×#387	C₂²	semidirect
128. C₅₃×#387	C₂²	semidirect
137. C₅₃×#386	C₂²	semidirect
138. C₅₃×#386	C₂²	semidirect
139. C₅₃×#386	C₂²	semidirect
140. C₅₃×#386	C₂²	semidirect
141. C₅₃×#386	C₂²	semidirect
142. C₅₃×#386	C₂²	semidirect
153. C₅₃×#385	C₂²	semidirect
154. C₅₃×#385	C₂²	semidirect
155. C₅₃×#385	C₂²	semidirect
156. C₅₃×#385	C₂²	semidirect
157. C₅₃×#385	C₂²	semidirect
158. C₅₃×#385	C₂²	semidirect
159. C₅₃×#385	C₂²	semidirect
160. C₅₃×#385	C₂²	semidirect
161. C₅₃×#385	C₂²	semidirect
162. C₅₃×#385	C₂²	semidirect
163. C₅₃×#385	C₂²	semidirect
164. C₅₃×#385	C₂²	semidirect
165. C₅₃×#385	C₂²	semidirect
166. C₅₃×#385	C₂²	semidirect
167. C₅₃×#385	C₂²	semidirect
168. C₅₃×#385	C₂²	semidirect
169. C₅₃×#383	C₂²	semidirect
170. C₅₃×#382	C₂²	semidirect
171. C₅₃×#381	C₂²	semidirect
172. C₅₃×#381	C₂²	semidirect
173. C₅₃×#381	C₂²	semidirect
177. C₅₃×#380	C₂²	semidirect
178. C₅₃×#380	C₂²	semidirect
179. C₅₃×#380	C₂²	semidirect
185. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
186. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
187. C₂×#95×C₅₃	C₂²	semidirect
188. C₂×#95×C₅₃	C₂²	semidirect
257. C₄×D₄×C₅₃	D₄	semidirect
772. #34991	C₅₃	direct (N × H)
816. C₂²×C₅₃	#539	semidirect
849. C₂×#539	C₂×C₅₃	semidirect
850. C₂²×C₄×D₄	C₂×C₅₃	semidirect
851. #2852	C₂×C₅₃	semidirect
852. #2851	C₂×C₅₃	semidirect
853. #2849	C₂×C₅₃	semidirect
854. #2848	C₂×C₅₃	semidirect
855. #2638	C₂×C₅₃	semidirect
856. #2636	C₂×C₅₃	semidirect
857. #2633	C₂×C₅₃	semidirect
858. #2630	C₂×C₅₃	semidirect
859. #2480	C₂×C₅₃	semidirect
860. #2473	C₂×C₅₃	semidirect
861. #2466	C₂×C₅₃	semidirect
862. #2463	C₂×C₅₃	semidirect
863. #2460	C₂×C₅₃	semidirect
864. #2455	C₂×C₅₃	semidirect
865. #2449	C₂×C₅₃	semidirect
866. #2449	C₂×C₅₃	semidirect
867. #2443	C₂×C₅₃	semidirect
868. #2437	C₂×C₅₃	semidirect
869. #2425	C₂×C₅₃	semidirect
870. #2419	C₂×C₅₃	semidirect
871. #2418	C₂×C₅₃	semidirect
872. #2412	C₂×C₅₃	semidirect
874. #2405	C₂×C₅₃	semidirect
875. #2325	C₂×C₅₃	semidirect
876. #2322	C₂×C₅₃	semidirect
877. #2318	C₂×C₅₃	semidirect
878. C₄×#120	C₂×C₅₃	semidirect
879. C₂×#385	C₂×C₅₃	semidirect
897. C₂×#126	C₂²×C₅₃	semidirect
898. C₂×#126	C₂²×C₅₃	semidirect
899. C₂×#125	C₂²×C₅₃	semidirect
900. C₂×#125	C₂²×C₅₃	semidirect
903. C₂×#123	C₂²×C₅₃	semidirect
904. C₂×#123	C₂²×C₅₃	semidirect
905. C₂×#123	C₂²×C₅₃	semidirect
906. C₂×#123	C₂²×C₅₃	semidirect
908. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
909. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
910. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
911. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
926. C₂×C₄×D₄	C₂²×C₅₃	semidirect
927. C₂×C₄×D₄	C₂²×C₅₃	semidirect
929. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
930. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
936. #400	C₂²×C₅₃	semidirect
937. #399	C₂²×C₅₃	semidirect
938. #399	C₂²×C₅₃	semidirect
939. #399	C₂²×C₅₃	semidirect
940. #398	C₂²×C₅₃	semidirect
941. #398	C₂²×C₅₃	semidirect
942. #398	C₂²×C₅₃	semidirect
943. #398	C₂²×C₅₃	semidirect
944. #397	C₂²×C₅₃	semidirect
945. #397	C₂²×C₅₃	semidirect
946. #397	C₂²×C₅₃	semidirect
947. #397	C₂²×C₅₃	semidirect
948. #397	C₂²×C₅₃	semidirect
949. #397	C₂²×C₅₃	semidirect
950. #396	C₂²×C₅₃	semidirect
951. #396	C₂²×C₅₃	semidirect
952. #396	C₂²×C₅₃	semidirect
953. #396	C₂²×C₅₃	semidirect
954. #395	C₂²×C₅₃	semidirect
961. #394	C₂²×C₅₃	semidirect
962. #394	C₂²×C₅₃	semidirect
963. #394	C₂²×C₅₃	semidirect
964. #394	C₂²×C₅₃	semidirect
965. #393	C₂²×C₅₃	semidirect
968. #389	C₂²×C₅₃	semidirect
969. #389	C₂²×C₅₃	semidirect
970. #389	C₂²×C₅₃	semidirect
971. #389	C₂²×C₅₃	semidirect
972. #388	C₂²×C₅₃	semidirect
973. #388	C₂²×C₅₃	semidirect
974. #388	C₂²×C₅₃	semidirect
975. #388	C₂²×C₅₃	semidirect
976. #388	C₂²×C₅₃	semidirect
977. #388	C₂²×C₅₃	semidirect
978. #388	C₂²×C₅₃	semidirect
979. #388	C₂²×C₅₃	semidirect
980. #387	C₂²×C₅₃	semidirect
981. #387	C₂²×C₅₃	semidirect
982. #387	C₂²×C₅₃	semidirect
983. #387	C₂²×C₅₃	semidirect
984. #387	C₂²×C₅₃	semidirect
985. #387	C₂²×C₅₃	semidirect
986. #387	C₂²×C₅₃	semidirect
987. #387	C₂²×C₅₃	semidirect
988. #387	C₂²×C₅₃	semidirect
989. #387	C₂²×C₅₃	semidirect
998. #386	C₂²×C₅₃	semidirect
999. #386	C₂²×C₅₃	semidirect
1000. #386	C₂²×C₅₃	semidirect
1001. #386	C₂²×C₅₃	semidirect
1002. #386	C₂²×C₅₃	semidirect
1003. #386	C₂²×C₅₃	semidirect
1014. #385	C₂²×C₅₃	semidirect
1015. #385	C₂²×C₅₃	semidirect
1016. #385	C₂²×C₅₃	semidirect
1017. #385	C₂²×C₅₃	semidirect
1018. #385	C₂²×C₅₃	semidirect
1019. #385	C₂²×C₅₃	semidirect
1020. #385	C₂²×C₅₃	semidirect
1021. #385	C₂²×C₅₃	semidirect
1022. #385	C₂²×C₅₃	semidirect
1023. #385	C₂²×C₅₃	semidirect
1024. #385	C₂²×C₅₃	semidirect
1025. #385	C₂²×C₅₃	semidirect
1026. #385	C₂²×C₅₃	semidirect
1027. #385	C₂²×C₅₃	semidirect
1028. #385	C₂²×C₅₃	semidirect
1029. #385	C₂²×C₅₃	semidirect
1030. #383	C₂²×C₅₃	semidirect
1031. #382	C₂²×C₅₃	semidirect
1032. #381	C₂²×C₅₃	semidirect
1033. #381	C₂²×C₅₃	semidirect
1034. #381	C₂²×C₅₃	semidirect
1038. #380	C₂²×C₅₃	semidirect
1039. #380	C₂²×C₅₃	semidirect
1040. #380	C₂²×C₅₃	semidirect
1046. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1047. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1048. C₂×#95	C₂²×C₅₃	semidirect
1049. C₂×#95	C₂²×C₅₃	semidirect
1050. C₅₃	#34991	direct (N × H)
1119. C₄×D₄	D₄×C₅₃	semidirect
1677. C₂²	C₅₃×#539	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#539	2
C₂²×C₄×D₄×C₅₃	2
C₅₃×#2852	2
C₅₃×#2851	2
C₅₃×#2849	2
C₅₃×#2848	2
C₅₃×#2638	2
C₅₃×#2636	2
C₅₃×#2633	2
C₅₃×#2630	2
C₅₃×#2480	2
C₅₃×#2473	2
C₅₃×#2466	2
C₅₃×#2463	2
C₅₃×#2460	2
C₅₃×#2455	2
C₅₃×#2449	2
C₅₃×#2443	2
C₅₃×#2437	2
C₅₃×#2425	2
C₅₃×#2419	2
C₅₃×#2418	2
C₅₃×#2412	2
C₅₃×#2410	2
C₅₃×#2405	2
C₅₃×#2325	2
C₅₃×#2322	2
C₅₃×#2318	2
C₄×#120×C₅₃	2
C₂×C₅₃×#385	2
#34991	53

Subgroups — C53×#34991 #27242503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34991 #27242503