Subgroups — C₅₃×#36866 #27244378

Order 13568.

1454 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2855	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2851	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2802	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2776	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2771	C₂	1	1	yes	maximal, characteristic
6	C₅₃×#2767	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2765	C₂	1	1	yes	maximal, characteristic
8	C₅₃×#2765	C₂	1	1	yes	maximal, characteristic
9	C₅₃×#2764	C₂	1	1	yes	maximal, characteristic
10	C₅₃×#2762	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2755	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2747	C₂	1	1	yes	maximal, characteristic
13	C₅₃×#2726	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2713	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2713	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2704	C₂	1	1	yes	maximal, characteristic
17	C₅₃×#2690	C₂	1	1	yes	maximal, characteristic
18	C₅₃×#2677	C₂	1	1	yes	maximal, characteristic
19	C₅₃×#2666	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2655	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2577	C₂	1	1	yes	maximal, characteristic
22	C₅₃×#2574	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#2530	C₂	1	1	yes	maximal, characteristic
24	C₅₃×#2528	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2524	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2522	C₂	1	1	yes	maximal, characteristic
27	C₅₃×#2462	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic
32	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#401	C₂²	1	1	yes	characteristic
42	C₅₃×#401	C₂²	1	1	yes	characteristic
43	C₅₃×#400	C₂²	1	1	yes	characteristic
44	C₅₃×#400	C₂²	1	1	yes	characteristic
45	C₅₃×#400	C₂²	1	1	yes	characteristic
46	C₅₃×#400	C₂²	1	1	yes	characteristic
47	C₅₃×#400	C₂²	1	1	yes	characteristic
48	C₅₃×#400	C₂²	1	1	yes	characteristic
49	C₅₃×#400	C₂²	1	1	yes	characteristic
50	C₅₃×#400	C₂²	1	1	yes	characteristic
51	C₅₃×#400	C₂²	1	1	yes	characteristic
52	C₅₃×#400	C₂²	1	1	yes	characteristic
53	C₅₃×#400	C₂²	1	1	yes	characteristic
54	C₅₃×#400	C₂²	1	1	yes	characteristic
55	C₅₃×#400	C₂²	1	1	yes	characteristic
56	C₅₃×#400	C₂²	1	1	yes	characteristic
57	C₅₃×#400	C₂²	1	1	yes	characteristic
58	C₅₃×#399	C₂²	1	1	yes	characteristic
59	C₅₃×#398	C₂²	1	1	yes	characteristic
60	C₅₃×#398	C₂²	1	1	yes	characteristic
61	C₅₃×#398	C₂²	1	1	yes	characteristic
62	C₅₃×#398	C₂²	1	1	yes	characteristic
63	C₅₃×#398	C₂²	1	1	yes	characteristic
64	C₅₃×#398	C₂²	1	1	yes	characteristic
65	C₅₃×#398	C₂²	1	1	yes	characteristic
66	C₅₃×#398	C₂²	1	1	yes	characteristic
67	C₅₃×#398	C₂²	1	1	yes	characteristic
68	C₅₃×#398	C₂²	1	1	yes	characteristic
69	C₅₃×#398	C₂²	1	1	yes	characteristic
70	C₅₃×#398	C₂²	1	1	yes	characteristic
71	C₅₃×#398	C₂²	1	1	yes	characteristic
72	C₅₃×#398	C₂²	1	1	yes	characteristic
73	C₅₃×#398	C₂²	1	1	yes	characteristic
74	C₅₃×#398	C₂²	1	1	yes	characteristic
75	C₅₃×#398	C₂²	1	1	yes	characteristic
76	C₅₃×#398	C₂²	1	1	yes	characteristic
77	C₅₃×#397	C₂²	1	1	yes	characteristic
78	C₅₃×#397	C₂²	1	1	yes	characteristic
79	C₅₃×#397	C₂²	1	1	yes	characteristic
80	C₅₃×#397	C₂²	1	1	yes	characteristic
81	C₅₃×#396	C₂²	1	1	yes	characteristic
82	C₅₃×#396	C₂²	1	1	yes	characteristic
83	C₅₃×#395	C₂²	1	1	yes	characteristic
84	C₅₃×#395	C₂²	1	1	yes	characteristic
85	C₅₃×#395	C₂²	1	1	yes	characteristic
86	C₅₃×#395	C₂²	1	1	yes	characteristic
87	C₅₃×#395	C₂²	1	1	yes	characteristic
88	C₅₃×#393	C₂²	1	1	yes	characteristic
89	C₅₃×#391	C₂²	1	1	yes	characteristic
90	C₅₃×#391	C₂²	1	1	yes	characteristic
91	C₅₃×#391	C₂²	1	1	yes	characteristic
92	C₅₃×#391	C₂²	1	1	yes	characteristic
93	C₅₃×#391	C₂²	1	1	yes	characteristic
94	C₅₃×#391	C₂²	1	1	yes	characteristic
95	C₅₃×#391	C₂²	1	1	yes	characteristic
96	C₅₃×#391	C₂²	1	1	yes	characteristic
97	C₅₃×#389	C₂²	1	1	yes	characteristic
98	C₅₃×#389	C₂²	1	1	yes	characteristic
99	C₅₃×#389	C₂²	1	1	yes	characteristic
100	C₅₃×#389	C₂²	1	1	yes	characteristic
101	C₅₃×#389	C₂²	1	1	yes	characteristic
102	C₅₃×#389	C₂²	1	1	yes	characteristic
103	C₅₃×#389	C₂²	1	1	yes	characteristic
104	C₅₃×#389	C₂²	1	1	yes	characteristic
105	C₅₃×#389	C₂²	1	1	yes	characteristic
106	C₅₃×#389	C₂²	1	1	yes	characteristic
107	C₅₃×#389	C₂²	1	1	yes	characteristic
108	C₅₃×#389	C₂²	1	1	yes	characteristic
109	C₅₃×#389	C₂²	1	1	yes	characteristic
110	C₅₃×#389	C₂²	1	1	yes	characteristic
111	C₅₃×#388	C₂²	1	1	yes	characteristic
112	C₅₃×#388	C₂²	1	1	yes	characteristic
113	C₅₃×#388	C₂²	1	1	yes	characteristic
114	C₅₃×#388	C₂²	1	1	yes	characteristic
115	C₅₃×#388	C₂²	1	1	yes	characteristic
116	C₅₃×#388	C₂²	1	1	yes	characteristic
117	C₅₃×#388	C₂²	1	1	yes	characteristic
118	C₅₃×#388	C₂²	1	1	yes	characteristic
119	C₅₃×#387	C₂²	1	1	yes	characteristic
120	C₅₃×#387	C₂²	1	1	yes	characteristic
121	C₅₃×#387	C₂²	1	1	yes	characteristic
122	C₅₃×#387	C₂²	1	1	yes	characteristic
123	C₅₃×#387	C₂²	1	1	yes	characteristic
124	C₅₃×#387	C₂²	1	1	yes	characteristic
125	C₅₃×#387	C₂²	1	1	yes	characteristic
126	C₅₃×#387	C₂²	1	1	yes	characteristic
127	C₅₃×#387	C₂²	1	1	yes	characteristic
128	C₅₃×#387	C₂²	1	1	yes	characteristic
129	C₅₃×#387	C₂²	1	1	yes	characteristic
130	C₅₃×#387	C₂²	1	1	yes	characteristic
131	C₅₃×#387	C₂²	1	1	yes	characteristic
132	C₅₃×#387	C₂²	1	1	yes	characteristic
133	C₅₃×#387	C₂²	1	1	yes	characteristic
134	C₅₃×#387	C₂²	1	1	yes	characteristic
135	C₅₃×#387	C₂²	1	1	yes	characteristic
136	C₅₃×#387	C₂²	1	1	yes	characteristic
137	C₅₃×#387	C₂²	1	1	yes	characteristic
138	C₅₃×#387	C₂²	1	1	yes	characteristic
139	C₅₃×#387	C₂²	1	1	yes	characteristic
140	C₅₃×#387	C₂²	1	1	yes	characteristic
141	C₅₃×#387	C₂²	1	1	yes	characteristic
142	C₅₃×#387	C₂²	1	1	yes	characteristic
143	C₅₃×#387	C₂²	1	1	yes	characteristic
144	C₅₃×#387	C₂²	1	1	yes	characteristic
145	C₅₃×#387	C₂²	1	1	yes	characteristic
146	C₅₃×#387	C₂²	1	1	yes	characteristic
147	C₅₃×#387	C₂²	1	1	yes	characteristic
148	C₅₃×#387	C₂²	1	1	yes	characteristic
149	C₅₃×#387	C₂²	1	1	yes	characteristic
150	C₅₃×#387	C₂²	1	1	yes	characteristic
151	C₅₃×#387	C₂²	1	1	yes	characteristic
152	C₅₃×#387	C₂²	1	1	yes	characteristic
153	C₅₃×#387	C₂²	1	1	yes	characteristic
154	C₅₃×#387	C₂²	1	1	yes	characteristic
155	C₅₃×#387	C₂²	1	1	yes	characteristic
156	C₅₃×#387	C₂²	1	1	yes	characteristic
157	C₅₃×#385	C₂²	1	1	yes	characteristic
158	C₅₃×#385	C₂²	1	1	yes	characteristic
159	C₅₃×#385	C₂²	1	1	yes	characteristic
160	C₅₃×#385	C₂²	1	1	yes	characteristic
161	C₅₃×#385	C₂²	1	1	yes	characteristic
162	C₅₃×#385	C₂²	1	1	yes	characteristic
163	C₅₃×#385	C₂²	1	1	yes	characteristic
164	C₅₃×#385	C₂²	1	1	yes	characteristic
165	C₅₃×#383	C₂²	1	1	yes	characteristic
166	C₅₃×#383	C₂²	1	1	yes	characteristic
167	C₅₃×#383	C₂²	1	1	yes	characteristic
168	C₅₃×#382	C₂²	1	1	yes	characteristic
169	C₅₃×#382	C₂²	1	1	yes	characteristic
170	C₅₃×#382	C₂²	1	1	yes	characteristic
171	C₅₃×#382	C₂²	1	1	yes	characteristic
172	C₅₃×#381	C₂²	1	1	yes	characteristic
173	C₅₃×#381	C₂²	1	1	yes	characteristic
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
178	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
179	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
180	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
182	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
183	C₄×C₄⋊C₄×C₅₃	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
186	C₅₃×#376	C₂²	1	1	yes	characteristic
187	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₄⋊Q₈×C₅₃	—	2	4	no	—
194	C₄⋊Q₈×C₅₃	—	4	2	no	—
195	#125×C₅₃	—	2	4	no	—
196	#125×C₅₃	—	4	2	no	—
197	#125×C₅₃	—	4	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	4	no	—
199	C₂²⋊Q₈×C₅₃	—	4	2	no	—
200	C₄×Q₈×C₅₃	—	4	2	no	—
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄²×C₅₃	—	4	2	no	—
265	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
281	#95×C₅₃	C₂³	1	1	yes	characteristic
282	#95×C₅₃	C₂³	1	1	yes	characteristic
283	#95×C₅₃	C₂³	1	1	yes	characteristic
284	#95×C₅₃	C₂³	1	1	yes	characteristic
285	#95×C₅₃	C₂³	1	1	yes	characteristic
286	#95×C₅₃	C₂³	1	1	yes	characteristic
287	#95×C₅₃	C₂³	1	1	yes	characteristic
288	#95×C₅₃	C₂³	1	1	yes	characteristic
289	#95×C₅₃	C₂³	1	1	yes	characteristic
290	#95×C₅₃	C₂³	1	1	yes	characteristic
291	#95×C₅₃	C₂³	1	1	yes	characteristic
292	#95×C₅₃	C₂³	1	1	yes	characteristic
293	#95×C₅₃	C₂³	1	1	yes	characteristic
294	#95×C₅₃	C₂³	1	1	yes	characteristic
295	#95×C₅₃	C₂³	1	1	yes	characteristic
296	#95×C₅₃	C₂³	1	1	yes	characteristic
297	#95×C₅₃	C₂³	1	1	yes	characteristic
298	#95×C₅₃	C₂³	1	1	yes	characteristic
299	#95×C₅₃	C₂³	1	1	yes	characteristic
300	#95×C₅₃	C₂³	1	1	yes	characteristic
301	#95×C₅₃	C₂³	1	1	yes	characteristic
302	#95×C₅₃	C₂³	1	1	yes	characteristic
303	#95×C₅₃	C₂³	1	1	yes	characteristic
304	#95×C₅₃	C₂³	1	1	yes	characteristic
305	#95×C₅₃	C₂³	1	1	yes	characteristic
306	#95×C₅₃	C₂³	1	1	yes	characteristic
307	#95×C₅₃	C₂³	1	1	yes	characteristic
308	#95×C₅₃	C₂³	1	1	yes	characteristic
309	#95×C₅₃	C₂³	1	1	yes	characteristic
310	#95×C₅₃	C₂³	1	1	yes	characteristic
311	#95×C₅₃	C₂³	1	1	yes	characteristic
312	#95×C₅₃	C₂³	1	1	yes	characteristic
313	#95×C₅₃	C₂³	1	1	yes	characteristic
314	#95×C₅₃	C₂³	1	1	yes	characteristic
315	#95×C₅₃	C₂³	1	1	yes	characteristic
316	#95×C₅₃	C₂³	1	1	yes	characteristic
317	#95×C₅₃	C₂³	1	1	yes	characteristic
318	#95×C₅₃	C₂³	1	1	yes	characteristic
319	#95×C₅₃	C₂³	1	1	yes	characteristic
320	#95×C₅₃	C₂³	1	1	yes	characteristic
321	#95×C₅₃	C₂³	1	1	yes	characteristic
322	#95×C₅₃	C₂³	1	1	yes	characteristic
323	#95×C₅₃	C₂³	1	1	yes	characteristic
324	#95×C₅₃	C₂³	1	1	yes	characteristic
325	#95×C₅₃	C₂³	1	1	yes	characteristic
326	#95×C₅₃	C₂³	1	1	yes	characteristic
327	#95×C₅₃	C₂³	1	1	yes	characteristic
328	#95×C₅₃	C₂³	1	1	yes	characteristic
329	#95×C₅₃	C₂³	1	1	yes	characteristic
330	#95×C₅₃	C₂³	1	1	yes	characteristic
331	#95×C₅₃	C₂³	1	1	yes	characteristic
332	#95×C₅₃	C₂³	1	1	yes	characteristic
333	#95×C₅₃	C₂³	1	1	yes	characteristic
334	#95×C₅₃	C₂³	1	1	yes	characteristic
335	#95×C₅₃	C₂³	1	1	yes	characteristic
336	#95×C₅₃	C₂³	1	1	yes	characteristic
337	#95×C₅₃	C₂³	1	1	yes	characteristic
338	#95×C₅₃	C₂³	1	1	yes	characteristic
339	#95×C₅₃	C₂³	1	1	yes	characteristic
340	#95×C₅₃	C₂³	1	1	yes	characteristic
341	#95×C₅₃	C₂³	1	1	yes	characteristic
342	#95×C₅₃	C₂³	1	1	yes	characteristic
343	#95×C₅₃	C₂³	1	1	yes	characteristic
344	#95×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×Q₈×C₅₃	—	2	2	no	—
353	C₂×Q₈×C₅₃	—	2	2	no	—
354	C₂×Q₈×C₅₃	—	2	2	no	—
355	C₂×Q₈×C₅₃	—	2	2	no	—
356	C₂×Q₈×C₅₃	—	4	1	no	—
357	C₂×Q₈×C₅₃	—	4	1	no	—
358	C₂×Q₈×C₅₃	—	4	1	no	—
359	C₂×Q₈×C₅₃	—	4	1	no	—
360	C₂×Q₈×C₅₃	—	4	1	no	—
361	C₂²×C₄×C₅₃	—	2	2	no	—
362	C₂²×C₄×C₅₃	—	2	2	no	—
363	C₂²×C₄×C₅₃	—	2	2	no	—
364	C₂²×C₄×C₅₃	—	2	2	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	4	1	no	—
367	C₂²×C₄×C₅₃	—	4	1	no	—
368	C₂²×C₄×C₅₃	—	4	1	no	—
369	C₂²×C₄×C₅₃	—	4	1	no	—
370	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	—	2	2	no	—
401	C₄⋊C₄×C₅₃	—	2	2	no	—
402	C₄⋊C₄×C₅₃	—	2	2	no	—
403	C₄⋊C₄×C₅₃	—	2	2	no	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	—	2	2	no	—
406	C₄⋊C₄×C₅₃	—	2	2	no	—
407	C₄⋊C₄×C₅₃	—	2	2	no	—
408	C₄⋊C₄×C₅₃	—	2	2	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	2	no	—
411	C₄⋊C₄×C₅₃	—	2	2	no	—
412	C₄⋊C₄×C₅₃	—	2	2	no	—
413	C₄⋊C₄×C₅₃	—	2	2	no	—
414	C₄⋊C₄×C₅₃	—	2	2	no	—
415	C₄⋊C₄×C₅₃	—	2	2	no	—
416	C₄⋊C₄×C₅₃	—	2	2	no	—
417	C₄⋊C₄×C₅₃	—	2	2	no	—
418	C₄⋊C₄×C₅₃	—	2	2	no	—
419	C₄⋊C₄×C₅₃	—	2	2	no	—
420	C₄⋊C₄×C₅₃	—	2	2	no	—
421	C₄⋊C₄×C₅₃	—	4	1	no	—
422	C₄⋊C₄×C₅₃	—	4	1	no	—
423	C₄⋊C₄×C₅₃	—	4	1	no	—
424	C₄⋊C₄×C₅₃	—	4	1	no	—
425	C₄⋊C₄×C₅₃	—	4	1	no	—
426	C₄⋊C₄×C₅₃	—	4	1	no	—
427	C₄⋊C₄×C₅₃	—	4	1	no	—
428	C₄⋊C₄×C₅₃	—	4	1	no	—
429	C₄⋊C₄×C₅₃	—	4	1	no	—
430	C₄⋊C₄×C₅₃	—	4	1	no	—
431	C₄⋊C₄×C₅₃	—	4	1	no	—
432	C₄⋊C₄×C₅₃	—	4	1	no	—
433	C₄⋊C₄×C₅₃	—	4	1	no	—
434	C₄⋊C₄×C₅₃	—	4	1	no	—
435	C₄⋊C₄×C₅₃	—	4	1	no	—
436	C₄⋊C₄×C₅₃	—	4	1	no	—
437	C₄⋊C₄×C₅₃	—	4	1	no	—
438	C₄⋊C₄×C₅₃	—	4	1	no	—
439	C₄⋊C₄×C₅₃	—	4	1	no	—
440	C₄⋊C₄×C₅₃	—	4	1	no	—
441	C₄⋊C₄×C₅₃	—	4	1	no	—
442	C₄⋊C₄×C₅₃	—	4	1	no	—
443	C₄⋊C₄×C₅₃	—	4	1	no	—
444	C₄⋊C₄×C₅₃	—	4	1	no	—
445	C₄⋊C₄×C₅₃	—	4	1	no	—
446	C₄⋊C₄×C₅₃	—	4	1	no	—
447	C₄⋊C₄×C₅₃	—	4	1	no	—
448	C₄⋊C₄×C₅₃	—	4	1	no	—
449	C₄⋊C₄×C₅₃	—	4	1	no	—
450	C₄⋊C₄×C₅₃	#41	1	4	yes	—
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	—	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	C₄²×C₅₃	—	2	2	no	—
464	C₄²×C₅₃	—	2	2	no	—
465	C₄²×C₅₃	—	2	2	no	—
466	C₄²×C₅₃	—	2	2	no	—
467	C₄²×C₅₃	—	2	2	no	—
468	C₄²×C₅₃	—	2	2	no	—
469	C₄²×C₅₃	—	4	1	no	—
470	C₄²×C₅₃	—	4	1	no	—
471	C₄²×C₅₃	—	4	1	no	—
472	C₄²×C₅₃	—	4	1	no	—
473	C₄²×C₅₃	—	4	1	no	—
474	C₄²×C₅₃	—	4	1	no	—
475	C₄²×C₅₃	—	4	1	no	—
476	C₄²×C₅₃	—	4	1	no	—
477	C₄²×C₅₃	—	4	1	no	—
478	C₄²×C₅₃	—	4	1	no	—
479	C₂³×C₅₃	—	2	1	no	—
480	C₂³×C₅₃	—	2	1	no	—
481	C₂³×C₅₃	—	2	1	no	—
482	C₂³×C₅₃	—	2	1	no	—
483	C₂³×C₅₃	—	2	1	no	—
484	C₂³×C₅₃	—	2	1	no	—
485	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
486	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
487	Q₈×C₅₃	—	4	4	no	—
488	Q₈×C₅₃	—	8	2	no	—
489	Q₈×C₅₃	—	8	2	no	—
490	C₂×C₄×C₅₃	—	2	1	no	—
491	C₂×C₄×C₅₃	—	2	1	no	—
492	C₂×C₄×C₅₃	—	2	1	no	—
493	C₂×C₄×C₅₃	—	2	1	no	—
494	C₂×C₄×C₅₃	—	2	1	no	—
495	C₂×C₄×C₅₃	—	2	1	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	1	no	—
498	C₂×C₄×C₅₃	—	2	1	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	2	1	no	—
502	C₂×C₄×C₅₃	—	2	1	no	—
503	C₂×C₄×C₅₃	—	2	1	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	1	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	1	no	—
512	C₂×C₄×C₅₃	—	2	1	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	—	2	1	no	—
517	C₂×C₄×C₅₃	—	2	1	no	—
518	C₂×C₄×C₅₃	—	2	1	no	—
519	C₂×C₄×C₅₃	—	2	1	no	—
520	C₂×C₄×C₅₃	—	2	1	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	1	no	—
523	C₂×C₄×C₅₃	—	2	1	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	1	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	1	no	—
532	C₂×C₄×C₅₃	—	2	1	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	—	2	1	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	1	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	1	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	4	4	no	—
575	C₂×C₄×C₅₃	—	4	4	no	—
576	C₂×C₄×C₅₃	—	4	4	no	—
577	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
578	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
579	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
580	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
581	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
582	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
583	#36866	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
584	C₂²×C₅₃	—	2	2	no	—
585	C₂²×C₅₃	—	2	2	no	—
586	C₂²×C₅₃	—	2	2	no	—
587	C₂²×C₅₃	—	4	1	no	—
588	C₂²×C₅₃	—	4	1	no	—
589	C₂²×C₅₃	—	4	1	no	—
590	C₂²×C₅₃	—	4	1	no	—
591	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
592	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
594	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
595	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
596	C₂²×C₅₃	#585	1	1	yes	characteristic
597	C₂²×C₅₃	#585	1	1	yes	characteristic
598	C₄×C₅₃	—	2	2	no	—
599	C₄×C₅₃	—	2	2	no	—
600	C₄×C₅₃	—	2	2	no	—
601	C₄×C₅₃	—	2	2	no	—
602	C₄×C₅₃	—	2	2	no	—
603	C₄×C₅₃	—	2	2	no	—
604	C₄×C₅₃	—	4	1	no	—
605	C₄×C₅₃	—	4	1	no	—
606	C₄×C₅₃	—	4	1	no	—
607	C₄×C₅₃	—	4	1	no	—
608	C₄×C₅₃	—	4	1	no	—
609	C₄×C₅₃	—	4	1	no	—
610	C₄×C₅₃	—	4	1	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	—	4	1	no	—
613	C₄×C₅₃	—	4	1	no	—
614	C₄×C₅₃	—	4	1	no	—
615	C₄×C₅₃	—	4	1	no	—
616	C₄×C₅₃	—	4	1	no	—
617	C₄×C₅₃	—	4	1	no	—
618	C₄×C₅₃	—	4	1	no	—
619	C₄×C₅₃	—	4	1	no	—
620	C₄×C₅₃	—	4	1	no	—
621	C₄×C₅₃	—	4	1	no	—
622	C₄×C₅₃	—	4	1	no	—
623	C₄×C₅₃	—	4	1	no	—
624	C₄×C₅₃	—	4	1	no	—
625	C₄×C₅₃	—	4	1	no	—
626	C₄×C₅₃	—	4	1	no	—
627	C₄×C₅₃	—	4	1	no	—
628	#2855	C₂×C₅₃	1	1	yes	characteristic
629	#2851	C₂×C₅₃	1	1	yes	characteristic
630	#2802	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#2776	C₂×C₅₃	1	1	yes	characteristic, complemented
632	#2771	C₂×C₅₃	1	1	yes	characteristic
633	#2767	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#2765	C₂×C₅₃	1	1	yes	characteristic
635	#2765	C₂×C₅₃	1	1	yes	characteristic
636	#2764	C₂×C₅₃	1	1	yes	characteristic
637	#2762	C₂×C₅₃	1	1	yes	characteristic, complemented
638	#2755	C₂×C₅₃	1	1	yes	characteristic, complemented
639	#2747	C₂×C₅₃	1	1	yes	characteristic
640	#2726	C₂×C₅₃	1	1	yes	characteristic, complemented
641	#2713	C₂×C₅₃	1	1	yes	characteristic, complemented
642	#2713	C₂×C₅₃	1	1	yes	characteristic, complemented
643	#2704	C₂×C₅₃	1	1	yes	characteristic
644	#2690	C₂×C₅₃	1	1	yes	characteristic
645	#2677	C₂×C₅₃	1	1	yes	characteristic
646	#2666	C₂×C₅₃	1	1	yes	characteristic, complemented
647	#2655	C₂×C₅₃	1	1	yes	characteristic, complemented
648	#2577	C₂×C₅₃	1	1	yes	characteristic
649	#2574	C₂×C₅₃	1	1	yes	characteristic
650	#2530	C₂×C₅₃	1	1	yes	characteristic
651	#2528	C₂×C₅₃	1	1	yes	characteristic, complemented
652	#2524	C₂×C₅₃	1	1	yes	characteristic, complemented
653	#2522	C₂×C₅₃	1	1	yes	characteristic
654	#2462	C₂×C₅₃	1	1	yes	characteristic, complemented
655	#2446	C₂×C₅₃	1	1	yes	characteristic, complemented
656	#2336	C₂×C₅₃	1	1	yes	characteristic, complemented
657	#2331	C₂×C₅₃	1	1	yes	characteristic, complemented
658	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic
659	C₂×C₅₃	—	4	2	no	—
660	C₂×C₅₃	#3461	1	1	yes	characteristic
661	C₂×C₅₃	#3513	1	1	yes	characteristic
662	C₂×C₅₃	#3523	1	1	yes	characteristic
663	C₂×C₅₃	#3538	1	1	yes	characteristic
664	C₂×C₅₃	#3541	1	1	yes	characteristic
665	C₂×C₅₃	#3563	1	1	yes	characteristic
666	C₂×C₅₃	#3565	1	1	yes	characteristic
667	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
668	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
669	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
670	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
671	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
672	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
673	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
674	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
675	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
676	#401	C₂²×C₅₃	1	1	yes	characteristic
677	#401	C₂²×C₅₃	1	1	yes	characteristic
678	#400	C₂²×C₅₃	1	1	yes	characteristic
679	#400	C₂²×C₅₃	1	1	yes	characteristic
680	#400	C₂²×C₅₃	1	1	yes	characteristic
681	#400	C₂²×C₅₃	1	1	yes	characteristic
682	#400	C₂²×C₅₃	1	1	yes	characteristic
683	#400	C₂²×C₅₃	1	1	yes	characteristic
684	#400	C₂²×C₅₃	1	1	yes	characteristic
685	#400	C₂²×C₅₃	1	1	yes	characteristic
686	#400	C₂²×C₅₃	1	1	yes	characteristic
687	#400	C₂²×C₅₃	1	1	yes	characteristic
688	#400	C₂²×C₅₃	1	1	yes	characteristic
689	#400	C₂²×C₅₃	1	1	yes	characteristic
690	#400	C₂²×C₅₃	1	1	yes	characteristic
691	#400	C₂²×C₅₃	1	1	yes	characteristic
692	#400	C₂²×C₅₃	1	1	yes	characteristic
693	#399	C₂²×C₅₃	1	1	yes	characteristic
694	#398	C₂²×C₅₃	1	1	yes	characteristic
695	#398	C₂²×C₅₃	1	1	yes	characteristic
696	#398	C₂²×C₅₃	1	1	yes	characteristic
697	#398	C₂²×C₅₃	1	1	yes	characteristic
698	#398	C₂²×C₅₃	1	1	yes	characteristic
699	#398	C₂²×C₅₃	1	1	yes	characteristic
700	#398	C₂²×C₅₃	1	1	yes	characteristic
701	#398	C₂²×C₅₃	1	1	yes	characteristic
702	#398	C₂²×C₅₃	1	1	yes	characteristic
703	#398	C₂²×C₅₃	1	1	yes	characteristic
704	#398	C₂²×C₅₃	1	1	yes	characteristic
705	#398	C₂²×C₅₃	1	1	yes	characteristic
706	#398	C₂²×C₅₃	1	1	yes	characteristic
707	#398	C₂²×C₅₃	1	1	yes	characteristic
708	#398	C₂²×C₅₃	1	1	yes	characteristic
709	#398	C₂²×C₅₃	1	1	yes	characteristic
710	#398	C₂²×C₅₃	1	1	yes	characteristic
711	#398	C₂²×C₅₃	1	1	yes	characteristic
712	#397	C₂²×C₅₃	1	1	yes	characteristic
713	#397	C₂²×C₅₃	1	1	yes	characteristic
714	#397	C₂²×C₅₃	1	1	yes	characteristic
715	#397	C₂²×C₅₃	1	1	yes	characteristic
716	#396	C₂²×C₅₃	1	1	yes	characteristic
717	#396	C₂²×C₅₃	1	1	yes	characteristic
718	#395	C₂²×C₅₃	1	1	yes	characteristic
719	#395	C₂²×C₅₃	1	1	yes	characteristic
720	#395	C₂²×C₅₃	1	1	yes	characteristic
721	#395	C₂²×C₅₃	1	1	yes	characteristic
722	#395	C₂²×C₅₃	1	1	yes	characteristic
723	#393	C₂²×C₅₃	1	1	yes	characteristic
724	#391	C₂²×C₅₃	1	1	yes	characteristic
725	#391	C₂²×C₅₃	1	1	yes	characteristic
726	#391	C₂²×C₅₃	1	1	yes	characteristic
727	#391	C₂²×C₅₃	1	1	yes	characteristic
728	#391	C₂²×C₅₃	1	1	yes	characteristic
729	#391	C₂²×C₅₃	1	1	yes	characteristic
730	#391	C₂²×C₅₃	1	1	yes	characteristic
731	#391	C₂²×C₅₃	1	1	yes	characteristic
732	#389	C₂²×C₅₃	1	1	yes	characteristic
733	#389	C₂²×C₅₃	1	1	yes	characteristic
734	#389	C₂²×C₅₃	1	1	yes	characteristic
735	#389	C₂²×C₅₃	1	1	yes	characteristic
736	#389	C₂²×C₅₃	1	1	yes	characteristic
737	#389	C₂²×C₅₃	1	1	yes	characteristic
738	#389	C₂²×C₅₃	1	1	yes	characteristic
739	#389	C₂²×C₅₃	1	1	yes	characteristic
740	#389	C₂²×C₅₃	1	1	yes	characteristic
741	#389	C₂²×C₅₃	1	1	yes	characteristic
742	#389	C₂²×C₅₃	1	1	yes	characteristic
743	#389	C₂²×C₅₃	1	1	yes	characteristic
744	#389	C₂²×C₅₃	1	1	yes	characteristic
745	#389	C₂²×C₅₃	1	1	yes	characteristic
746	#388	C₂²×C₅₃	1	1	yes	characteristic
747	#388	C₂²×C₅₃	1	1	yes	characteristic
748	#388	C₂²×C₅₃	1	1	yes	characteristic
749	#388	C₂²×C₅₃	1	1	yes	characteristic
750	#388	C₂²×C₅₃	1	1	yes	characteristic
751	#388	C₂²×C₅₃	1	1	yes	characteristic
752	#388	C₂²×C₅₃	1	1	yes	characteristic
753	#388	C₂²×C₅₃	1	1	yes	characteristic
754	#387	C₂²×C₅₃	1	1	yes	characteristic
755	#387	C₂²×C₅₃	1	1	yes	characteristic
756	#387	C₂²×C₅₃	1	1	yes	characteristic
757	#387	C₂²×C₅₃	1	1	yes	characteristic
758	#387	C₂²×C₅₃	1	1	yes	characteristic
759	#387	C₂²×C₅₃	1	1	yes	characteristic
760	#387	C₂²×C₅₃	1	1	yes	characteristic
761	#387	C₂²×C₅₃	1	1	yes	characteristic
762	#387	C₂²×C₅₃	1	1	yes	characteristic
763	#387	C₂²×C₅₃	1	1	yes	characteristic
764	#387	C₂²×C₅₃	1	1	yes	characteristic
765	#387	C₂²×C₅₃	1	1	yes	characteristic
766	#387	C₂²×C₅₃	1	1	yes	characteristic
767	#387	C₂²×C₅₃	1	1	yes	characteristic
768	#387	C₂²×C₅₃	1	1	yes	characteristic
769	#387	C₂²×C₅₃	1	1	yes	characteristic
770	#387	C₂²×C₅₃	1	1	yes	characteristic
771	#387	C₂²×C₅₃	1	1	yes	characteristic
772	#387	C₂²×C₅₃	1	1	yes	characteristic
773	#387	C₂²×C₅₃	1	1	yes	characteristic
774	#387	C₂²×C₅₃	1	1	yes	characteristic
775	#387	C₂²×C₅₃	1	1	yes	characteristic
776	#387	C₂²×C₅₃	1	1	yes	characteristic
777	#387	C₂²×C₅₃	1	1	yes	characteristic
778	#387	C₂²×C₅₃	1	1	yes	characteristic
779	#387	C₂²×C₅₃	1	1	yes	characteristic
780	#387	C₂²×C₅₃	1	1	yes	characteristic
781	#387	C₂²×C₅₃	1	1	yes	characteristic
782	#387	C₂²×C₅₃	1	1	yes	characteristic
783	#387	C₂²×C₅₃	1	1	yes	characteristic
784	#387	C₂²×C₅₃	1	1	yes	characteristic
785	#387	C₂²×C₅₃	1	1	yes	characteristic
786	#387	C₂²×C₅₃	1	1	yes	characteristic
787	#387	C₂²×C₅₃	1	1	yes	characteristic
788	#387	C₂²×C₅₃	1	1	yes	characteristic
789	#387	C₂²×C₅₃	1	1	yes	characteristic
790	#387	C₂²×C₅₃	1	1	yes	characteristic
791	#387	C₂²×C₅₃	1	1	yes	characteristic
792	#385	C₂²×C₅₃	1	1	yes	characteristic
793	#385	C₂²×C₅₃	1	1	yes	characteristic
794	#385	C₂²×C₅₃	1	1	yes	characteristic
795	#385	C₂²×C₅₃	1	1	yes	characteristic
796	#385	C₂²×C₅₃	1	1	yes	characteristic
797	#385	C₂²×C₅₃	1	1	yes	characteristic
798	#385	C₂²×C₅₃	1	1	yes	characteristic
799	#385	C₂²×C₅₃	1	1	yes	characteristic
800	#383	C₂²×C₅₃	1	1	yes	characteristic
801	#383	C₂²×C₅₃	1	1	yes	characteristic
802	#383	C₂²×C₅₃	1	1	yes	characteristic
803	#382	C₂²×C₅₃	1	1	yes	characteristic
804	#382	C₂²×C₅₃	1	1	yes	characteristic
805	#382	C₂²×C₅₃	1	1	yes	characteristic
806	#382	C₂²×C₅₃	1	1	yes	characteristic
807	#381	C₂²×C₅₃	1	1	yes	characteristic
808	#381	C₂²×C₅₃	1	1	yes	characteristic
809	#380	C₂²×C₅₃	1	1	yes	characteristic
810	#380	C₂²×C₅₃	1	1	yes	characteristic
811	#380	C₂²×C₅₃	1	1	yes	characteristic
812	#380	C₂²×C₅₃	1	1	yes	characteristic
813	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
814	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
815	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
816	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
817	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
818	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
819	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
820	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
821	#376	C₂²×C₅₃	1	1	yes	characteristic
822	C₅₃	#36866	1	1	yes	characteristic, direct product factor, Sylow
823	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
824	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
825	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
826	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
827	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
828	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
829	C₄⋊Q₈	—	2	4	no	—
830	C₄⋊Q₈	—	4	2	no	—
831	#125	—	2	4	no	—
832	#125	—	4	2	no	—
833	#125	—	4	2	no	—
834	C₂²⋊Q₈	—	2	4	no	—
835	C₂²⋊Q₈	—	4	2	no	—
836	C₄×Q₈	—	4	2	no	—
837	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
845	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
846	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
847	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
848	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
850	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
853	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
854	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
855	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
856	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
857	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
858	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
859	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
861	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
862	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
863	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
864	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
865	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
866	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
875	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
876	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
888	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
889	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
890	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
891	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
892	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
893	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
894	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
895	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
896	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
897	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
898	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
899	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
900	C₂×C₄²	—	4	2	no	—
901	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
902	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
903	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
904	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
905	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
906	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
907	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
908	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
909	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
910	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
911	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
912	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
913	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
914	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
915	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
916	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
917	#95	C₂³×C₅₃	1	1	yes	characteristic
918	#95	C₂³×C₅₃	1	1	yes	characteristic
919	#95	C₂³×C₅₃	1	1	yes	characteristic
920	#95	C₂³×C₅₃	1	1	yes	characteristic
921	#95	C₂³×C₅₃	1	1	yes	characteristic
922	#95	C₂³×C₅₃	1	1	yes	characteristic
923	#95	C₂³×C₅₃	1	1	yes	characteristic
924	#95	C₂³×C₅₃	1	1	yes	characteristic
925	#95	C₂³×C₅₃	1	1	yes	characteristic
926	#95	C₂³×C₅₃	1	1	yes	characteristic
927	#95	C₂³×C₅₃	1	1	yes	characteristic
928	#95	C₂³×C₅₃	1	1	yes	characteristic
929	#95	C₂³×C₅₃	1	1	yes	characteristic
930	#95	C₂³×C₅₃	1	1	yes	characteristic
931	#95	C₂³×C₅₃	1	1	yes	characteristic
932	#95	C₂³×C₅₃	1	1	yes	characteristic
933	#95	C₂³×C₅₃	1	1	yes	characteristic
934	#95	C₂³×C₅₃	1	1	yes	characteristic
935	#95	C₂³×C₅₃	1	1	yes	characteristic
936	#95	C₂³×C₅₃	1	1	yes	characteristic
937	#95	C₂³×C₅₃	1	1	yes	characteristic
938	#95	C₂³×C₅₃	1	1	yes	characteristic
939	#95	C₂³×C₅₃	1	1	yes	characteristic
940	#95	C₂³×C₅₃	1	1	yes	characteristic
941	#95	C₂³×C₅₃	1	1	yes	characteristic
942	#95	C₂³×C₅₃	1	1	yes	characteristic
943	#95	C₂³×C₅₃	1	1	yes	characteristic
944	#95	C₂³×C₅₃	1	1	yes	characteristic
945	#95	C₂³×C₅₃	1	1	yes	characteristic
946	#95	C₂³×C₅₃	1	1	yes	characteristic
947	#95	C₂³×C₅₃	1	1	yes	characteristic
948	#95	C₂³×C₅₃	1	1	yes	characteristic
949	#95	C₂³×C₅₃	1	1	yes	characteristic
950	#95	C₂³×C₅₃	1	1	yes	characteristic
951	#95	C₂³×C₅₃	1	1	yes	characteristic
952	#95	C₂³×C₅₃	1	1	yes	characteristic
953	#95	C₂³×C₅₃	1	1	yes	characteristic
954	#95	C₂³×C₅₃	1	1	yes	characteristic
955	#95	C₂³×C₅₃	1	1	yes	characteristic
956	#95	C₂³×C₅₃	1	1	yes	characteristic
957	#95	C₂³×C₅₃	1	1	yes	characteristic
958	#95	C₂³×C₅₃	1	1	yes	characteristic
959	#95	C₂³×C₅₃	1	1	yes	characteristic
960	#95	C₂³×C₅₃	1	1	yes	characteristic
961	#95	C₂³×C₅₃	1	1	yes	characteristic
962	#95	C₂³×C₅₃	1	1	yes	characteristic
963	#95	C₂³×C₅₃	1	1	yes	characteristic
964	#95	C₂³×C₅₃	1	1	yes	characteristic
965	#95	C₂³×C₅₃	1	1	yes	characteristic
966	#95	C₂³×C₅₃	1	1	yes	characteristic
967	#95	C₂³×C₅₃	1	1	yes	characteristic
968	#95	C₂³×C₅₃	1	1	yes	characteristic
969	#95	C₂³×C₅₃	1	1	yes	characteristic
970	#95	C₂³×C₅₃	1	1	yes	characteristic
971	#95	C₂³×C₅₃	1	1	yes	characteristic
972	#95	C₂³×C₅₃	1	1	yes	characteristic
973	#95	C₂³×C₅₃	1	1	yes	characteristic
974	#95	C₂³×C₅₃	1	1	yes	characteristic
975	#95	C₂³×C₅₃	1	1	yes	characteristic
976	#95	C₂³×C₅₃	1	1	yes	characteristic
977	#95	C₂³×C₅₃	1	1	yes	characteristic
978	#95	C₂³×C₅₃	1	1	yes	characteristic
979	#95	C₂³×C₅₃	1	1	yes	characteristic
980	#95	C₂³×C₅₃	1	1	yes	characteristic
981	#95	C₂³×C₅₃	1	1	yes	characteristic
982	#95	C₂³×C₅₃	1	1	yes	characteristic
983	#95	C₂³×C₅₃	1	1	yes	characteristic
984	#95	C₂³×C₅₃	1	1	yes	characteristic
985	#95	C₂³×C₅₃	1	1	yes	characteristic
986	#95	C₂³×C₅₃	1	1	yes	characteristic
987	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
988	C₂×Q₈	—	2	2	no	—
989	C₂×Q₈	—	2	2	no	—
990	C₂×Q₈	—	2	2	no	—
991	C₂×Q₈	—	2	2	no	—
992	C₂×Q₈	—	4	1	no	—
993	C₂×Q₈	—	4	1	no	—
994	C₂×Q₈	—	4	1	no	—
995	C₂×Q₈	—	4	1	no	—
996	C₂×Q₈	—	4	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	4	1	no	—
1003	C₂²×C₄	—	4	1	no	—
1004	C₂²×C₄	—	4	1	no	—
1005	C₂²×C₄	—	4	1	no	—
1006	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1022	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1024	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1027	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1028	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1029	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1030	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1031	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1032	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1035	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	4	1	no	—
1058	C₄⋊C₄	—	4	1	no	—
1059	C₄⋊C₄	—	4	1	no	—
1060	C₄⋊C₄	—	4	1	no	—
1061	C₄⋊C₄	—	4	1	no	—
1062	C₄⋊C₄	—	4	1	no	—
1063	C₄⋊C₄	—	4	1	no	—
1064	C₄⋊C₄	—	4	1	no	—
1065	C₄⋊C₄	—	4	1	no	—
1066	C₄⋊C₄	—	4	1	no	—
1067	C₄⋊C₄	—	4	1	no	—
1068	C₄⋊C₄	—	4	1	no	—
1069	C₄⋊C₄	—	4	1	no	—
1070	C₄⋊C₄	—	4	1	no	—
1071	C₄⋊C₄	—	4	1	no	—
1072	C₄⋊C₄	—	4	1	no	—
1073	C₄⋊C₄	—	4	1	no	—
1074	C₄⋊C₄	—	4	1	no	—
1075	C₄⋊C₄	—	4	1	no	—
1076	C₄⋊C₄	—	4	1	no	—
1077	C₄⋊C₄	—	4	1	no	—
1078	C₄⋊C₄	—	4	1	no	—
1079	C₄⋊C₄	—	4	1	no	—
1080	C₄⋊C₄	—	4	1	no	—
1081	C₄⋊C₄	—	4	1	no	—
1082	C₄⋊C₄	—	4	1	no	—
1083	C₄⋊C₄	—	4	1	no	—
1084	C₄⋊C₄	—	4	1	no	—
1085	C₄⋊C₄	—	4	1	no	—
1086	C₄⋊C₄	#41×C₅₃	1	4	yes	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	4	1	no	—
1094	C₂²⋊C₄	—	4	1	no	—
1095	C₂²⋊C₄	—	4	1	no	—
1096	C₂²⋊C₄	—	4	1	no	—
1097	C₂²⋊C₄	—	4	1	no	—
1098	C₂²⋊C₄	—	4	1	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	—	2	2	no	—
1101	C₄²	—	2	2	no	—
1102	C₄²	—	2	2	no	—
1103	C₄²	—	2	2	no	—
1104	C₄²	—	2	2	no	—
1105	C₄²	—	4	1	no	—
1106	C₄²	—	4	1	no	—
1107	C₄²	—	4	1	no	—
1108	C₄²	—	4	1	no	—
1109	C₄²	—	4	1	no	—
1110	C₄²	—	4	1	no	—
1111	C₄²	—	4	1	no	—
1112	C₄²	—	4	1	no	—
1113	C₄²	—	4	1	no	—
1114	C₄²	—	4	1	no	—
1115	C₂³	—	2	1	no	—
1116	C₂³	—	2	1	no	—
1117	C₂³	—	2	1	no	—
1118	C₂³	—	2	1	no	—
1119	C₂³	—	2	1	no	—
1120	C₂³	—	2	1	no	—
1121	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1122	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1123	Q₈	—	4	4	no	—
1124	Q₈	—	8	2	no	—
1125	Q₈	—	8	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	4	4	no	—
1211	C₂×C₄	—	4	4	no	—
1212	C₂×C₄	—	4	4	no	—
1213	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1214	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1215	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1216	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1217	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1218	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1219	C₂²	—	2	2	no	—
1220	C₂²	—	2	2	no	—
1221	C₂²	—	2	2	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1227	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1228	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1229	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1230	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1231	C₂²	C₅₃×#585	1	1	yes	characteristic
1232	C₂²	C₅₃×#585	1	1	yes	characteristic
1233	C₄	—	2	2	no	—
1234	C₄	—	2	2	no	—
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	2	2	no	—
1238	C₄	—	2	2	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	1	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	1	no	—
1263	C₂	—	4	2	no	—
1264	C₂	C₅₃×#3461	1	1	yes	characteristic
1265	C₂	C₅₃×#3513	1	1	yes	characteristic
1266	C₂	C₅₃×#3523	1	1	yes	characteristic
1267	C₂	C₅₃×#3538	1	1	yes	characteristic
1268	C₂	C₅₃×#3541	1	1	yes	characteristic
1269	C₂	C₅₃×#3563	1	1	yes	characteristic
1270	C₂	C₅₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂⁴×C₅₃	C₂⁴
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
3. C₅₃×#2802	C₂	semidirect
4. C₅₃×#2776	C₂	semidirect
6. C₅₃×#2767	C₂	semidirect
10. C₅₃×#2762	C₂	semidirect
11. C₅₃×#2755	C₂	semidirect
13. C₅₃×#2726	C₂	semidirect
14. C₅₃×#2713	C₂	semidirect
15. C₅₃×#2713	C₂	semidirect
19. C₅₃×#2666	C₂	semidirect
20. C₅₃×#2655	C₂	semidirect
24. C₅₃×#2528	C₂	semidirect
25. C₅₃×#2524	C₂	semidirect
27. C₅₃×#2462	C₂	semidirect
28. C₅₃×#2446	C₂	semidirect
29. C₅₃×#2336	C₂	semidirect
30. C₅₃×#2331	C₂	semidirect
583. #36866	C₅₃	direct (N × H)
630. #2802	C₂×C₅₃	semidirect
631. #2776	C₂×C₅₃	semidirect
633. #2767	C₂×C₅₃	semidirect
637. #2762	C₂×C₅₃	semidirect
638. #2755	C₂×C₅₃	semidirect
640. #2726	C₂×C₅₃	semidirect
641. #2713	C₂×C₅₃	semidirect
642. #2713	C₂×C₅₃	semidirect
646. #2666	C₂×C₅₃	semidirect
647. #2655	C₂×C₅₃	semidirect
651. #2528	C₂×C₅₃	semidirect
652. #2524	C₂×C₅₃	semidirect
654. #2462	C₂×C₅₃	semidirect
655. #2446	C₂×C₅₃	semidirect
656. #2336	C₂×C₅₃	semidirect
657. #2331	C₂×C₅₃	semidirect
822. C₅₃	#36866	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#2855	2
C₅₃×#2851	2
C₅₃×#2802	2
C₅₃×#2776	2
C₅₃×#2771	2
C₅₃×#2767	2
C₅₃×#2765	2
C₅₃×#2764	2
C₅₃×#2762	2
C₅₃×#2755	2
C₅₃×#2747	2
C₅₃×#2726	2
C₅₃×#2713	2
C₅₃×#2704	2
C₅₃×#2690	2
C₅₃×#2677	2
C₅₃×#2666	2
C₅₃×#2655	2
C₅₃×#2577	2
C₅₃×#2574	2
C₅₃×#2530	2
C₅₃×#2528	2
C₅₃×#2524	2
C₅₃×#2522	2
C₅₃×#2462	2
C₅₃×#2446	2
C₅₃×#2336	2
C₅₃×#2331	2
C₄×C₂²⋊Q₈×C₅₃	2
#36866	53

Subgroups — C53×#36866 #27244378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36866 #27244378