Subgroups — C₅₃×#36762 #27244274

Order 13568.

1482 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2857	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2851	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2802	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2794	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2789	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2776	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2766	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2758	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2719	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2713	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2627	C₂	1	1	yes	maximal, characteristic
12	C₅₃×#2627	C₂	1	1	yes	maximal, characteristic
13	C₅₃×#2505	C₂	1	2	yes	maximal
14	C₅₃×#2493	C₂	1	2	yes	maximal
15	C₅₃×#2493	C₂	1	2	yes	maximal
16	C₅₃×#2473	C₂	1	2	yes	maximal
17	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic
18	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic
19	C₂×C₅₃×#387	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#125×C₅₃	C₂²	1	2	yes	—
22	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
28	C₅₃×#401	C₂²	1	2	yes	—
29	C₅₃×#401	C₂²	1	2	yes	—
30	C₅₃×#400	C₂²	1	2	yes	—
31	C₅₃×#400	C₂²	1	2	yes	—
32	C₅₃×#400	C₂²	1	2	yes	—
33	C₅₃×#400	C₂²	1	2	yes	—
34	C₅₃×#400	C₂²	1	2	yes	—
35	C₅₃×#400	C₂²	1	2	yes	—
36	C₅₃×#400	C₂²	1	2	yes	—
37	C₅₃×#400	C₂²	1	2	yes	—
38	C₅₃×#400	C₂²	1	2	yes	—
39	C₅₃×#400	C₂²	1	2	yes	—
40	C₅₃×#400	C₂²	1	2	yes	—
41	C₅₃×#400	C₂²	1	2	yes	—
42	C₅₃×#398	C₂²	1	2	yes	—
43	C₅₃×#398	C₂²	1	2	yes	—
44	C₅₃×#398	C₂²	1	2	yes	—
45	C₅₃×#398	C₂²	1	2	yes	—
46	C₅₃×#398	C₂²	1	2	yes	—
47	C₅₃×#398	C₂²	1	2	yes	—
48	C₅₃×#398	C₂²	1	2	yes	—
49	C₅₃×#398	C₂²	1	2	yes	—
50	C₅₃×#395	C₂²	1	2	yes	—
51	C₅₃×#395	C₂²	1	2	yes	—
52	C₅₃×#391	C₂²	1	2	yes	—
53	C₅₃×#391	C₂²	1	2	yes	—
54	C₅₃×#391	C₂²	1	1	yes	characteristic
55	C₅₃×#391	C₂²	1	1	yes	characteristic
56	C₅₃×#389	C₂²	1	2	yes	—
57	C₅₃×#389	C₂²	1	2	yes	—
58	C₅₃×#389	C₂²	1	2	yes	—
59	C₅₃×#389	C₂²	1	2	yes	—
60	C₅₃×#389	C₂²	1	2	yes	—
61	C₅₃×#389	C₂²	1	1	yes	characteristic
62	C₅₃×#389	C₂²	1	2	yes	—
63	C₅₃×#389	C₂²	1	1	yes	characteristic
64	C₅₃×#387	C₂²	1	2	yes	—
65	C₅₃×#387	C₂²	1	2	yes	—
66	C₅₃×#387	C₂²	1	2	yes	—
67	C₅₃×#387	C₂²	1	2	yes	—
68	C₅₃×#387	C₂²	1	2	yes	—
69	C₅₃×#387	C₂²	1	2	yes	—
70	C₅₃×#387	C₂²	1	2	yes	—
71	C₅₃×#387	C₂²	1	2	yes	—
72	C₅₃×#387	C₂²	1	2	yes	—
73	C₅₃×#387	C₂²	1	2	yes	—
74	C₅₃×#387	C₂²	1	2	yes	—
75	C₅₃×#387	C₂²	1	2	yes	—
76	C₅₃×#387	C₂²	1	2	yes	—
77	C₅₃×#387	C₂²	1	2	yes	—
78	C₅₃×#387	C₂²	1	2	yes	—
79	C₅₃×#387	C₂²	1	2	yes	—
80	C₅₃×#387	C₂²	1	2	yes	—
81	C₅₃×#387	C₂²	1	2	yes	—
82	C₅₃×#387	C₂²	1	2	yes	—
83	C₅₃×#387	C₂²	1	2	yes	—
84	C₅₃×#385	C₂²	1	2	yes	—
85	C₅₃×#385	C₂²	1	2	yes	—
86	C₅₃×#385	C₂²	1	2	yes	—
87	C₅₃×#385	C₂²	1	2	yes	—
88	C₅₃×#385	C₂²	1	2	yes	—
89	C₅₃×#385	C₂²	1	2	yes	—
90	C₅₃×#384	C₂²	1	1	yes	characteristic
91	C₅₃×#383	C₂²	1	2	yes	—
92	C₅₃×#383	C₂²	1	2	yes	—
93	C₅₃×#382	C₂²	1	2	yes	—
94	C₅₃×#382	C₂²	1	1	yes	characteristic
95	C₅₃×#381	C₂²	1	2	yes	—
96	C₅₃×#381	C₂²	1	2	yes	—
97	C₅₃×#380	C₂²	1	2	yes	—
98	C₅₃×#380	C₂²	1	2	yes	—
99	C₅₃×#380	C₂²	1	1	yes	characteristic
100	C₅₃×#380	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
103	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
104	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
105	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
106	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₅₃	—	4	2	no	—
117	#125×C₅₃	—	4	2	no	—
118	#125×C₅₃	—	4	4	no	—
119	C₂²⋊Q₈×C₅₃	—	2	4	no	—
120	C₂²⋊Q₈×C₅₃	—	2	4	no	—
121	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
122	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₅₃	—	4	2	no	—
156	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
164	#95×C₅₃	C₂³	1	2	yes	—
165	#95×C₅₃	C₂³	1	2	yes	—
166	#95×C₅₃	C₂³	1	2	yes	—
167	#95×C₅₃	C₂³	1	2	yes	—
168	#95×C₅₃	C₂³	1	2	yes	—
169	#95×C₅₃	C₂³	1	2	yes	—
170	#95×C₅₃	C₂³	1	2	yes	—
171	#95×C₅₃	C₂³	1	2	yes	—
172	#95×C₅₃	C₂³	1	2	yes	—
173	#95×C₅₃	C₂³	1	2	yes	—
174	#95×C₅₃	C₂³	1	2	yes	—
175	#95×C₅₃	C₂³	1	2	yes	—
176	#95×C₅₃	C₂³	1	2	yes	—
177	#95×C₅₃	C₂³	1	2	yes	—
178	#95×C₅₃	C₂³	1	2	yes	—
179	#95×C₅₃	C₂³	1	2	yes	—
180	#95×C₅₃	C₂³	1	2	yes	—
181	#95×C₅₃	C₂³	1	2	yes	—
182	#95×C₅₃	C₂³	1	2	yes	—
183	#95×C₅₃	C₂³	1	2	yes	—
184	#95×C₅₃	C₂³	1	2	yes	—
185	#95×C₅₃	C₂³	1	2	yes	—
186	#95×C₅₃	C₂³	1	2	yes	—
187	#95×C₅₃	C₂³	1	2	yes	—
188	#95×C₅₃	C₂³	1	2	yes	—
189	#95×C₅₃	C₂³	1	2	yes	—
190	#95×C₅₃	C₂³	1	2	yes	—
191	#95×C₅₃	C₂³	1	2	yes	—
192	#95×C₅₃	C₂³	1	2	yes	—
193	#95×C₅₃	C₂³	1	2	yes	—
194	#95×C₅₃	C₂³	1	2	yes	—
195	#95×C₅₃	C₂³	1	2	yes	—
196	#95×C₅₃	C₂³	1	2	yes	—
197	#95×C₅₃	C₂³	1	2	yes	—
198	#95×C₅₃	C₂³	1	2	yes	—
199	#95×C₅₃	C₂³	1	2	yes	—
200	#95×C₅₃	C₂³	1	2	yes	—
201	#95×C₅₃	C₂³	1	2	yes	—
202	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
203	C₂×Q₈×C₅₃	—	2	2	no	—
204	C₂×Q₈×C₅₃	—	2	2	no	—
205	C₂×Q₈×C₅₃	—	4	1	no	—
206	C₂×Q₈×C₅₃	—	4	1	no	—
207	C₂×Q₈×C₅₃	—	4	1	no	—
208	C₂×Q₈×C₅₃	—	4	1	no	—
209	C₂²×C₄×C₅₃	—	2	2	no	—
210	C₂²×C₄×C₅₃	—	2	2	no	—
211	C₂²×C₄×C₅₃	—	2	2	no	—
212	C₂²×C₄×C₅₃	—	2	2	no	—
213	C₂²×C₄×C₅₃	—	2	2	no	—
214	C₂²×C₄×C₅₃	—	2	2	no	—
215	C₂²×C₄×C₅₃	—	2	2	no	—
216	C₂²×C₄×C₅₃	—	2	2	no	—
217	C₂²×C₄×C₅₃	—	2	2	no	—
218	C₂²×C₄×C₅₃	—	2	2	no	—
219	C₂²×C₄×C₅₃	—	4	1	no	—
220	C₂²×C₄×C₅₃	—	4	1	no	—
221	C₂²×C₄×C₅₃	—	4	1	no	—
222	C₂²×C₄×C₅₃	—	4	1	no	—
223	C₂²×C₄×C₅₃	—	4	1	no	—
224	C₂²×C₄×C₅₃	—	4	1	no	—
225	C₂²×C₄×C₅₃	—	4	1	no	—
226	C₂²×C₄×C₅₃	—	4	1	no	—
227	C₂²×C₄×C₅₃	—	4	1	no	—
228	C₂²×C₄×C₅₃	—	4	1	no	—
229	C₂²×C₄×C₅₃	#41	1	4	yes	—
230	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₄⋊C₄×C₅₃	—	2	4	no	—
249	C₄⋊C₄×C₅₃	—	2	4	no	—
250	C₄⋊C₄×C₅₃	—	2	4	no	—
251	C₄⋊C₄×C₅₃	—	2	4	no	—
252	C₄⋊C₄×C₅₃	—	2	2	no	—
253	C₄⋊C₄×C₅₃	—	2	2	no	—
254	C₄⋊C₄×C₅₃	—	2	4	no	—
255	C₄⋊C₄×C₅₃	—	2	4	no	—
256	C₄⋊C₄×C₅₃	—	2	4	no	—
257	C₄⋊C₄×C₅₃	—	2	4	no	—
258	C₄⋊C₄×C₅₃	—	2	4	no	—
259	C₄⋊C₄×C₅₃	—	4	2	no	—
260	C₄⋊C₄×C₅₃	—	4	1	no	—
261	C₄⋊C₄×C₅₃	—	4	2	no	—
262	C₄⋊C₄×C₅₃	—	4	1	no	—
263	C₄⋊C₄×C₅₃	—	4	2	no	—
264	C₄⋊C₄×C₅₃	—	4	2	no	—
265	C₄⋊C₄×C₅₃	—	4	2	no	—
266	C₄⋊C₄×C₅₃	—	4	2	no	—
267	C₄⋊C₄×C₅₃	—	4	2	no	—
268	C₄⋊C₄×C₅₃	—	4	2	no	—
269	C₄⋊C₄×C₅₃	—	4	1	no	—
270	C₄⋊C₄×C₅₃	—	4	1	no	—
271	C₄⋊C₄×C₅₃	—	4	2	no	—
272	C₄⋊C₄×C₅₃	—	4	2	no	—
273	C₄⋊C₄×C₅₃	—	4	2	no	—
274	C₄⋊C₄×C₅₃	—	4	2	no	—
275	C₄⋊C₄×C₅₃	—	4	2	no	—
276	C₂²⋊C₄×C₅₃	—	2	4	no	—
277	C₂²⋊C₄×C₅₃	—	2	4	no	—
278	C₂²⋊C₄×C₅₃	—	2	4	no	—
279	C₂²⋊C₄×C₅₃	—	2	4	no	—
280	C₄²×C₅₃	—	2	2	no	—
281	C₄²×C₅₃	—	2	2	no	—
282	C₄²×C₅₃	—	4	1	no	—
283	C₄²×C₅₃	—	4	1	no	—
284	C₄²×C₅₃	—	4	2	no	—
285	C₄²×C₅₃	—	4	2	no	—
286	C₄²×C₅₃	—	4	2	no	—
287	C₄²×C₅₃	—	4	2	no	—
288	C₂³×C₅₃	—	2	1	no	—
289	C₂³×C₅₃	—	2	1	no	—
290	C₂³×C₅₃	—	2	1	no	—
291	C₂³×C₅₃	—	2	1	no	—
292	C₂³×C₅₃	C₂×#41	1	2	yes	—
293	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
294	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
295	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
296	Q₈×C₅₃	—	8	2	no	—
297	Q₈×C₅₃	—	8	2	no	—
298	C₂×C₄×C₅₃	—	2	1	no	—
299	C₂×C₄×C₅₃	—	2	1	no	—
300	C₂×C₄×C₅₃	—	2	1	no	—
301	C₂×C₄×C₅₃	—	2	1	no	—
302	C₂×C₄×C₅₃	—	2	1	no	—
303	C₂×C₄×C₅₃	—	2	1	no	—
304	C₂×C₄×C₅₃	—	2	1	no	—
305	C₂×C₄×C₅₃	—	2	1	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	2	no	—
308	C₂×C₄×C₅₃	—	2	2	no	—
309	C₂×C₄×C₅₃	—	2	2	no	—
310	C₂×C₄×C₅₃	—	2	2	no	—
311	C₂×C₄×C₅₃	—	2	2	no	—
312	C₂×C₄×C₅₃	—	2	1	no	—
313	C₂×C₄×C₅₃	—	2	1	no	—
314	C₂×C₄×C₅₃	—	2	2	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	2	2	no	—
317	C₂×C₄×C₅₃	—	2	2	no	—
318	C₂×C₄×C₅₃	—	2	2	no	—
319	C₂×C₄×C₅₃	—	2	2	no	—
320	C₂×C₄×C₅₃	—	2	2	no	—
321	C₂×C₄×C₅₃	—	2	2	no	—
322	C₂×C₄×C₅₃	—	2	1	no	—
323	C₂×C₄×C₅₃	—	2	2	no	—
324	C₂×C₄×C₅₃	—	2	1	no	—
325	C₂×C₄×C₅₃	—	2	1	no	—
326	C₂×C₄×C₅₃	—	2	2	no	—
327	C₂×C₄×C₅₃	—	2	2	no	—
328	C₂×C₄×C₅₃	—	2	2	no	—
329	C₂×C₄×C₅₃	—	2	2	no	—
330	C₂×C₄×C₅₃	—	2	2	no	—
331	C₂×C₄×C₅₃	—	2	2	no	—
332	C₂×C₄×C₅₃	—	2	2	no	—
333	C₂×C₄×C₅₃	—	2	2	no	—
334	C₂×C₄×C₅₃	—	2	2	no	—
335	C₂×C₄×C₅₃	—	2	2	no	—
336	C₂×C₄×C₅₃	—	2	2	no	—
337	C₂×C₄×C₅₃	—	2	2	no	—
338	C₂×C₄×C₅₃	—	2	2	no	—
339	C₂×C₄×C₅₃	—	2	1	no	—
340	C₂×C₄×C₅₃	—	2	2	no	—
341	C₂×C₄×C₅₃	—	2	2	no	—
342	C₂×C₄×C₅₃	—	2	2	no	—
343	C₂×C₄×C₅₃	—	2	2	no	—
344	C₂×C₄×C₅₃	—	2	2	no	—
345	C₂×C₄×C₅₃	—	2	2	no	—
346	C₂×C₄×C₅₃	—	2	2	no	—
347	C₂×C₄×C₅₃	—	2	2	no	—
348	C₂×C₄×C₅₃	—	4	4	no	—
349	C₂×C₄×C₅₃	—	4	4	no	—
350	C₂×C₄×C₅₃	—	4	4	no	—
351	C₂×C₄×C₅₃	—	4	4	no	—
352	C₂×C₄×C₅₃	—	4	4	no	—
353	C₂×C₄×C₅₃	—	8	2	no	—
354	C₂×C₄×C₅₃	—	8	2	no	—
355	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
356	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
357	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
358	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
359	#36762	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂²×C₅₃	—	2	2	no	—
361	C₂²×C₅₃	—	2	2	no	—
362	C₂²×C₅₃	—	2	2	no	—
363	C₂²×C₅₃	—	2	2	no	—
364	C₂²×C₅₃	—	2	2	no	—
365	C₂²×C₅₃	—	2	2	no	—
366	C₂²×C₅₃	#541	1	4	yes	—
367	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
368	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
370	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
371	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
372	C₂²×C₅₃	#585	1	1	yes	characteristic
373	C₂²×C₅₃	#585	1	1	yes	characteristic
374	C₄×C₅₃	—	2	2	no	—
375	C₄×C₅₃	—	2	2	no	—
376	C₄×C₅₃	—	2	2	no	—
377	C₄×C₅₃	—	2	2	no	—
378	C₄×C₅₃	—	4	2	no	—
379	C₄×C₅₃	—	4	2	no	—
380	C₄×C₅₃	—	4	2	no	—
381	C₄×C₅₃	—	4	2	no	—
382	C₄×C₅₃	—	4	2	no	—
383	C₄×C₅₃	—	4	2	no	—
384	C₄×C₅₃	—	4	2	no	—
385	C₄×C₅₃	—	4	1	no	—
386	C₄×C₅₃	—	4	2	no	—
387	C₄×C₅₃	—	4	2	no	—
388	C₄×C₅₃	—	4	1	no	—
389	C₄×C₅₃	—	4	2	no	—
390	C₄×C₅₃	—	4	2	no	—
391	C₄×C₅₃	—	4	2	no	—
392	#2857	C₂×C₅₃	1	1	yes	characteristic
393	#2851	C₂×C₅₃	1	1	yes	characteristic
394	#2802	C₂×C₅₃	1	2	yes	complemented
395	#2794	C₂×C₅₃	1	2	yes	complemented
396	#2789	C₂×C₅₃	1	2	yes	complemented
397	#2776	C₂×C₅₃	1	2	yes	complemented
398	#2766	C₂×C₅₃	1	2	yes	complemented
399	#2758	C₂×C₅₃	1	2	yes	complemented
400	#2719	C₂×C₅₃	1	2	yes	complemented
401	#2713	C₂×C₅₃	1	2	yes	complemented
402	#2627	C₂×C₅₃	1	1	yes	characteristic
403	#2627	C₂×C₅₃	1	1	yes	characteristic
404	#2505	C₂×C₅₃	1	2	yes	—
405	#2493	C₂×C₅₃	1	2	yes	—
406	#2493	C₂×C₅₃	1	2	yes	—
407	#2473	C₂×C₅₃	1	2	yes	—
408	#2329	C₂×C₅₃	1	1	yes	characteristic
409	#2329	C₂×C₅₃	1	1	yes	characteristic
410	C₂×#387	C₂×C₅₃	1	1	yes	characteristic
411	C₂×C₅₃	—	2	4	no	—
412	C₂×C₅₃	C₂×#541	1	1	yes	characteristic
413	C₂×C₅₃	#3505	1	1	yes	characteristic
414	C₂×C₅₃	#3507	1	1	yes	characteristic
415	C₂×C₅₃	#3535	1	1	yes	characteristic
416	C₂×C₅₃	#3538	1	1	yes	characteristic
417	C₂×C₅₃	#3563	1	1	yes	characteristic
418	C₂×C₅₃	#3564	1	1	yes	characteristic
419	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
420	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
421	C₂×#125	C₂²×C₅₃	1	2	yes	—
422	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
423	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
426	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
427	#401	C₂²×C₅₃	1	2	yes	—
428	#401	C₂²×C₅₃	1	2	yes	—
429	#400	C₂²×C₅₃	1	2	yes	—
430	#400	C₂²×C₅₃	1	2	yes	—
431	#400	C₂²×C₅₃	1	2	yes	—
432	#400	C₂²×C₅₃	1	2	yes	—
433	#400	C₂²×C₅₃	1	2	yes	—
434	#400	C₂²×C₅₃	1	2	yes	—
435	#400	C₂²×C₅₃	1	2	yes	—
436	#400	C₂²×C₅₃	1	2	yes	—
437	#400	C₂²×C₅₃	1	2	yes	—
438	#400	C₂²×C₅₃	1	2	yes	—
439	#400	C₂²×C₅₃	1	2	yes	—
440	#400	C₂²×C₅₃	1	2	yes	—
441	#398	C₂²×C₅₃	1	2	yes	—
442	#398	C₂²×C₅₃	1	2	yes	—
443	#398	C₂²×C₅₃	1	2	yes	—
444	#398	C₂²×C₅₃	1	2	yes	—
445	#398	C₂²×C₅₃	1	2	yes	—
446	#398	C₂²×C₅₃	1	2	yes	—
447	#398	C₂²×C₅₃	1	2	yes	—
448	#398	C₂²×C₅₃	1	2	yes	—
449	#395	C₂²×C₅₃	1	2	yes	—
450	#395	C₂²×C₅₃	1	2	yes	—
451	#391	C₂²×C₅₃	1	2	yes	—
452	#391	C₂²×C₅₃	1	2	yes	—
453	#391	C₂²×C₅₃	1	1	yes	characteristic
454	#391	C₂²×C₅₃	1	1	yes	characteristic
455	#389	C₂²×C₅₃	1	2	yes	—
456	#389	C₂²×C₅₃	1	2	yes	—
457	#389	C₂²×C₅₃	1	1	yes	characteristic
458	#389	C₂²×C₅₃	1	1	yes	characteristic
459	#389	C₂²×C₅₃	1	2	yes	—
460	#389	C₂²×C₅₃	1	2	yes	—
461	#389	C₂²×C₅₃	1	2	yes	—
462	#389	C₂²×C₅₃	1	2	yes	—
463	#387	C₂²×C₅₃	1	2	yes	—
464	#387	C₂²×C₅₃	1	2	yes	—
465	#387	C₂²×C₅₃	1	2	yes	—
466	#387	C₂²×C₅₃	1	2	yes	—
467	#387	C₂²×C₅₃	1	2	yes	—
468	#387	C₂²×C₅₃	1	2	yes	—
469	#387	C₂²×C₅₃	1	2	yes	—
470	#387	C₂²×C₅₃	1	2	yes	—
471	#387	C₂²×C₅₃	1	2	yes	—
472	#387	C₂²×C₅₃	1	2	yes	—
473	#387	C₂²×C₅₃	1	2	yes	—
474	#387	C₂²×C₅₃	1	2	yes	—
475	#387	C₂²×C₅₃	1	2	yes	—
476	#387	C₂²×C₅₃	1	2	yes	—
477	#387	C₂²×C₅₃	1	2	yes	—
478	#387	C₂²×C₅₃	1	2	yes	—
479	#387	C₂²×C₅₃	1	2	yes	—
480	#387	C₂²×C₅₃	1	2	yes	—
481	#387	C₂²×C₅₃	1	2	yes	—
482	#387	C₂²×C₅₃	1	2	yes	—
483	#385	C₂²×C₅₃	1	2	yes	—
484	#385	C₂²×C₅₃	1	2	yes	—
485	#385	C₂²×C₅₃	1	2	yes	—
486	#385	C₂²×C₅₃	1	2	yes	—
487	#385	C₂²×C₅₃	1	2	yes	—
488	#385	C₂²×C₅₃	1	2	yes	—
489	#384	C₂²×C₅₃	1	1	yes	characteristic
490	#383	C₂²×C₅₃	1	2	yes	—
491	#383	C₂²×C₅₃	1	2	yes	—
492	#382	C₂²×C₅₃	1	1	yes	characteristic
493	#382	C₂²×C₅₃	1	2	yes	—
494	#381	C₂²×C₅₃	1	2	yes	—
495	#381	C₂²×C₅₃	1	2	yes	—
496	#380	C₂²×C₅₃	1	1	yes	characteristic
497	#380	C₂²×C₅₃	1	1	yes	characteristic
498	#380	C₂²×C₅₃	1	2	yes	—
499	#380	C₂²×C₅₃	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
502	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
503	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
504	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
505	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
506	C₅₃	#36762	1	1	yes	characteristic, direct product factor, Sylow
507	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
508	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
516	C₄⋊Q₈	—	4	2	no	—
517	#125	—	4	2	no	—
518	#125	—	4	4	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂×C₄⋊C₄	—	2	4	no	—
522	C₂×C₄⋊C₄	—	4	2	no	—
523	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
555	C₂×C₄²	—	4	2	no	—
556	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
559	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
560	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
561	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
562	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
564	#95	C₂³×C₅₃	1	2	yes	—
565	#95	C₂³×C₅₃	1	2	yes	—
566	#95	C₂³×C₅₃	1	2	yes	—
567	#95	C₂³×C₅₃	1	2	yes	—
568	#95	C₂³×C₅₃	1	2	yes	—
569	#95	C₂³×C₅₃	1	2	yes	—
570	#95	C₂³×C₅₃	1	2	yes	—
571	#95	C₂³×C₅₃	1	2	yes	—
572	#95	C₂³×C₅₃	1	2	yes	—
573	#95	C₂³×C₅₃	1	2	yes	—
574	#95	C₂³×C₅₃	1	2	yes	—
575	#95	C₂³×C₅₃	1	2	yes	—
576	#95	C₂³×C₅₃	1	2	yes	—
577	#95	C₂³×C₅₃	1	2	yes	—
578	#95	C₂³×C₅₃	1	2	yes	—
579	#95	C₂³×C₅₃	1	2	yes	—
580	#95	C₂³×C₅₃	1	2	yes	—
581	#95	C₂³×C₅₃	1	2	yes	—
582	#95	C₂³×C₅₃	1	2	yes	—
583	#95	C₂³×C₅₃	1	2	yes	—
584	#95	C₂³×C₅₃	1	2	yes	—
585	#95	C₂³×C₅₃	1	2	yes	—
586	#95	C₂³×C₅₃	1	2	yes	—
587	#95	C₂³×C₅₃	1	2	yes	—
588	#95	C₂³×C₅₃	1	2	yes	—
589	#95	C₂³×C₅₃	1	2	yes	—
590	#95	C₂³×C₅₃	1	2	yes	—
591	#95	C₂³×C₅₃	1	2	yes	—
592	#95	C₂³×C₅₃	1	2	yes	—
593	#95	C₂³×C₅₃	1	2	yes	—
594	#95	C₂³×C₅₃	1	2	yes	—
595	#95	C₂³×C₅₃	1	2	yes	—
596	#95	C₂³×C₅₃	1	2	yes	—
597	#95	C₂³×C₅₃	1	2	yes	—
598	#95	C₂³×C₅₃	1	2	yes	—
599	#95	C₂³×C₅₃	1	2	yes	—
600	#95	C₂³×C₅₃	1	2	yes	—
601	#95	C₂³×C₅₃	1	2	yes	—
602	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	4	1	no	—
606	C₂×Q₈	—	4	1	no	—
607	C₂×Q₈	—	4	1	no	—
608	C₂×Q₈	—	4	1	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	—	4	1	no	—
622	C₂²×C₄	—	4	1	no	—
623	C₂²×C₄	—	4	1	no	—
624	C₂²×C₄	—	4	1	no	—
625	C₂²×C₄	—	4	1	no	—
626	C₂²×C₄	—	4	1	no	—
627	C₂²×C₄	—	4	1	no	—
628	C₂²×C₄	—	4	1	no	—
629	C₂²×C₄	#41×C₅₃	1	4	yes	—
630	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	1	no	—
661	C₄⋊C₄	—	4	1	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	1	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	4	1	no	—
683	C₄²	—	4	1	no	—
684	C₄²	—	4	2	no	—
685	C₄²	—	4	2	no	—
686	C₄²	—	4	2	no	—
687	C₄²	—	4	2	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	C₂×#41×C₅₃	1	2	yes	—
693	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
694	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
695	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
696	Q₈	—	8	2	no	—
697	Q₈	—	8	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	8	2	no	—
754	C₂×C₄	—	8	2	no	—
755	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
756	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
757	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
758	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	C₅₃×#541	1	4	yes	—
766	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
767	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
768	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
769	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
770	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
771	C₂²	C₅₃×#585	1	1	yes	characteristic
772	C₂²	C₅₃×#585	1	1	yes	characteristic
773	C₄	—	2	2	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₂	—	2	4	no	—
792	C₂	C₂×C₅₃×#541	1	1	yes	characteristic
793	C₂	C₅₃×#3505	1	1	yes	characteristic
794	C₂	C₅₃×#3507	1	1	yes	characteristic
795	C₂	C₅₃×#3535	1	1	yes	characteristic
796	C₂	C₅₃×#3538	1	1	yes	characteristic
797	C₂	C₅₃×#3563	1	1	yes	characteristic
798	C₂	C₅₃×#3564	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×#2794	C₂	semidirect
5. C₅₃×#2789	C₂	semidirect
6. C₅₃×#2776	C₂	semidirect
7. C₅₃×#2766	C₂	semidirect
8. C₅₃×#2758	C₂	semidirect
9. C₅₃×#2719	C₂	semidirect
10. C₅₃×#2713	C₂	semidirect
359. #36762	C₅₃	direct (N × H)
394. #2802	C₂×C₅₃	semidirect
395. #2794	C₂×C₅₃	semidirect
396. #2789	C₂×C₅₃	semidirect
397. #2776	C₂×C₅₃	semidirect
398. #2766	C₂×C₅₃	semidirect
399. #2758	C₂×C₅₃	semidirect
400. #2719	C₂×C₅₃	semidirect
401. #2713	C₂×C₅₃	semidirect
506. C₅₃	#36762	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×#2857	2
C₅₃×#2851	2
C₅₃×#2802	2
C₅₃×#2794	2
C₅₃×#2789	2
C₅₃×#2776	2
C₅₃×#2766	2
C₅₃×#2758	2
C₅₃×#2719	2
C₅₃×#2713	2
C₅₃×#2627	2
C₅₃×#2505	2
C₅₃×#2493	2
C₅₃×#2473	2
C₅₃×#2329	2
C₂×C₅₃×#387	2
#36762	53

Subgroups — C53×#36762 #27244274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36762 #27244274