Subgroups — C₅₃×#36679 #27244191

Order 13568.

1506 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2841	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2839	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2838	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2833	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2831	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2827	C₂	1	2	yes	maximal
9	C₅₃×#2817	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2814	C₂	1	2	yes	maximal
11	C₅₃×#2402	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2401	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2401	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2399	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2398	C₂	1	1	yes	maximal, characteristic
16	C₅₃×#2396	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2395	C₂	1	1	yes	maximal, characteristic
18	C₄×C₂²⋊Q₈×C₅₃	C₂	1	2	yes	maximal, complemented
19	C₄×#123×C₅₃	C₂	1	1	yes	maximal, characteristic
20	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#401	C₂²	1	2	yes	—
28	C₅₃×#401	C₂²	1	2	yes	—
29	C₅₃×#400	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	1	yes	characteristic
42	C₅₃×#399	C₂²	1	2	yes	—
43	C₅₃×#399	C₂²	1	1	yes	characteristic
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×#398	C₂²	1	2	yes	—
51	C₅₃×#398	C₂²	1	1	yes	characteristic
52	C₅₃×#398	C₂²	1	2	yes	—
53	C₅₃×#398	C₂²	1	2	yes	—
54	C₅₃×#398	C₂²	1	2	yes	—
55	C₅₃×#397	C₂²	1	2	yes	—
56	C₅₃×#397	C₂²	1	2	yes	—
57	C₅₃×#397	C₂²	1	2	yes	—
58	C₅₃×#397	C₂²	1	2	yes	—
59	C₅₃×#397	C₂²	1	1	yes	characteristic
60	C₅₃×#397	C₂²	1	1	yes	characteristic
61	C₅₃×#397	C₂²	1	2	yes	—
62	C₅₃×#397	C₂²	1	2	yes	—
63	C₅₃×#397	C₂²	1	1	yes	characteristic
64	C₅₃×#397	C₂²	1	2	yes	—
65	C₅₃×#396	C₂²	1	2	yes	—
66	C₅₃×#396	C₂²	1	2	yes	—
67	C₅₃×#396	C₂²	1	2	yes	—
68	C₅₃×#396	C₂²	1	2	yes	—
69	C₅₃×#395	C₂²	1	2	yes	—
70	C₅₃×#395	C₂²	1	2	yes	—
71	C₅₃×#395	C₂²	1	2	yes	—
72	C₅₃×#395	C₂²	1	2	yes	—
73	C₅₃×#395	C₂²	1	2	yes	—
74	C₅₃×#394	C₂²	1	2	yes	—
75	C₅₃×#394	C₂²	1	2	yes	—
76	C₅₃×#393	C₂²	1	2	yes	—
77	C₅₃×#393	C₂²	1	1	yes	characteristic
78	C₅₃×#393	C₂²	1	1	yes	characteristic
79	C₅₃×#391	C₂²	1	2	yes	—
80	C₅₃×#389	C₂²	1	2	yes	—
81	C₅₃×#388	C₂²	1	2	yes	—
82	C₅₃×#387	C₂²	1	2	yes	—
83	C₅₃×#387	C₂²	1	2	yes	—
84	C₅₃×#387	C₂²	1	2	yes	—
85	C₅₃×#386	C₂²	1	1	yes	characteristic
86	C₅₃×#385	C₂²	1	1	yes	characteristic
87	C₅₃×#385	C₂²	1	2	yes	—
88	C₅₃×#385	C₂²	1	2	yes	—
89	C₅₃×#381	C₂²	1	1	yes	characteristic
90	C₅₃×#380	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
105	C₅₃×#376	C₂²	1	1	yes	characteristic
106	C₅₃×#376	C₂²	1	2	yes	—
107	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×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	#123×C₅₃	—	2	4	no	—
115	C₂²⋊Q₈×C₅₃	—	2	8	no	—
116	C₄×Q₈×C₅₃	—	4	4	no	—
117	C₄×Q₈×C₅₃	—	4	2	no	—
118	C₄×D₄×C₅₃	—	4	2	no	—
119	#117×C₅₃	—	4	2	no	—
120	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
136	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₅₃	—	4	2	no	—
159	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
167	#95×C₅₃	C₂³	1	1	yes	characteristic
168	#95×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
184	#95×C₅₃	C₂³	1	1	yes	characteristic
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	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
202	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
203	C₂×Q₈×C₅₃	—	2	4	no	—
204	C₂×Q₈×C₅₃	—	4	2	no	—
205	C₂×Q₈×C₅₃	—	4	1	no	—
206	C₂×Q₈×C₅₃	—	4	2	no	—
207	C₂×Q₈×C₅₃	—	4	2	no	—
208	C₂×D₄×C₅₃	—	2	2	no	—
209	C₂×D₄×C₅₃	—	4	1	no	—
210	C₂×D₄×C₅₃	—	4	1	no	—
211	C₂²×C₄×C₅₃	—	2	2	no	—
212	C₂²×C₄×C₅₃	—	2	2	no	—
213	C₂²×C₄×C₅₃	—	2	4	no	—
214	C₂²×C₄×C₅₃	—	2	4	no	—
215	C₂²×C₄×C₅₃	—	4	1	no	—
216	C₂²×C₄×C₅₃	—	4	1	no	—
217	C₂²×C₄×C₅₃	—	4	1	no	—
218	C₂²×C₄×C₅₃	—	4	2	no	—
219	C₂²×C₄×C₅₃	#41	1	4	yes	—
220	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₅₃	C₂⁴	1	2	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	1	yes	characteristic
234	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
237	C₄⋊C₄×C₅₃	—	2	4	no	—
238	C₄⋊C₄×C₅₃	—	2	4	no	—
239	C₄⋊C₄×C₅₃	—	2	4	no	—
240	C₄⋊C₄×C₅₃	—	2	4	no	—
241	C₄⋊C₄×C₅₃	—	4	2	no	—
242	C₄⋊C₄×C₅₃	—	4	2	no	—
243	C₄⋊C₄×C₅₃	—	4	2	no	—
244	C₄⋊C₄×C₅₃	—	4	2	no	—
245	C₄⋊C₄×C₅₃	—	4	2	no	—
246	C₄⋊C₄×C₅₃	—	4	2	no	—
247	C₄⋊C₄×C₅₃	—	4	2	no	—
248	C₄⋊C₄×C₅₃	—	4	2	no	—
249	C₄⋊C₄×C₅₃	—	4	2	no	—
250	C₄⋊C₄×C₅₃	—	4	2	no	—
251	C₄⋊C₄×C₅₃	—	4	2	no	—
252	C₄⋊C₄×C₅₃	—	4	2	no	—
253	C₄⋊C₄×C₅₃	—	4	1	no	—
254	C₄⋊C₄×C₅₃	—	4	1	no	—
255	C₄⋊C₄×C₅₃	—	4	1	no	—
256	C₄⋊C₄×C₅₃	—	4	2	no	—
257	C₄⋊C₄×C₅₃	—	4	2	no	—
258	C₄⋊C₄×C₅₃	—	4	2	no	—
259	C₄⋊C₄×C₅₃	—	4	2	no	—
260	C₄⋊C₄×C₅₃	—	4	1	no	—
261	C₂²⋊C₄×C₅₃	—	2	4	no	—
262	C₂²⋊C₄×C₅₃	—	2	4	no	—
263	C₂²⋊C₄×C₅₃	—	2	2	no	—
264	C₂²⋊C₄×C₅₃	—	2	4	no	—
265	C₂²⋊C₄×C₅₃	—	4	2	no	—
266	C₂²⋊C₄×C₅₃	—	4	2	no	—
267	C₂²⋊C₄×C₅₃	—	4	2	no	—
268	C₂²⋊C₄×C₅₃	—	4	2	no	—
269	C₂²⋊C₄×C₅₃	—	4	2	no	—
270	C₂²⋊C₄×C₅₃	—	4	2	no	—
271	C₂²⋊C₄×C₅₃	—	4	1	no	—
272	C₂²⋊C₄×C₅₃	—	4	2	no	—
273	C₂²⋊C₄×C₅₃	—	4	1	no	—
274	C₂²⋊C₄×C₅₃	—	4	1	no	—
275	C₄²×C₅₃	—	2	4	no	—
276	C₄²×C₅₃	—	2	4	no	—
277	C₄²×C₅₃	—	2	2	no	—
278	C₄²×C₅₃	—	2	4	no	—
279	C₄²×C₅₃	—	2	4	no	—
280	C₄²×C₅₃	—	2	4	no	—
281	C₄²×C₅₃	—	2	4	no	—
282	C₄²×C₅₃	—	4	2	no	—
283	C₂³×C₅₃	—	2	1	no	—
284	C₂³×C₅₃	—	2	2	no	—
285	C₂³×C₅₃	—	2	1	no	—
286	C₂³×C₅₃	—	2	2	no	—
287	C₂³×C₅₃	—	2	1	no	—
288	C₂³×C₅₃	—	2	1	no	—
289	C₂³×C₅₃	—	2	2	no	—
290	C₂³×C₅₃	—	2	1	no	—
291	C₂³×C₅₃	—	2	2	no	—
292	C₂³×C₅₃	C₂×#41	1	2	yes	—
293	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
294	Q₈×C₅₃	—	4	8	no	—
295	Q₈×C₅₃	—	4	4	no	—
296	D₄×C₅₃	—	4	4	no	—
297	C₂×C₄×C₅₃	—	2	2	no	—
298	C₂×C₄×C₅₃	—	2	2	no	—
299	C₂×C₄×C₅₃	—	2	1	no	—
300	C₂×C₄×C₅₃	—	2	2	no	—
301	C₂×C₄×C₅₃	—	2	2	no	—
302	C₂×C₄×C₅₃	—	2	2	no	—
303	C₂×C₄×C₅₃	—	2	2	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	1	no	—
306	C₂×C₄×C₅₃	—	2	1	no	—
307	C₂×C₄×C₅₃	—	2	2	no	—
308	C₂×C₄×C₅₃	—	2	1	no	—
309	C₂×C₄×C₅₃	—	2	1	no	—
310	C₂×C₄×C₅₃	—	2	2	no	—
311	C₂×C₄×C₅₃	—	2	2	no	—
312	C₂×C₄×C₅₃	—	2	2	no	—
313	C₂×C₄×C₅₃	—	2	2	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	2	no	—
323	C₂×C₄×C₅₃	—	2	2	no	—
324	C₂×C₄×C₅₃	—	2	1	no	—
325	C₂×C₄×C₅₃	—	2	2	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	2	no	—
340	C₂×C₄×C₅₃	—	2	2	no	—
341	C₂×C₄×C₅₃	—	4	4	no	—
342	C₂×C₄×C₅₃	—	4	4	no	—
343	C₂×C₄×C₅₃	—	4	4	no	—
344	C₂×C₄×C₅₃	—	4	4	no	—
345	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
346	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
347	C₂×C₄×C₅₃	2₋¹⁺⁴	1	4	yes	—
348	#36679	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₂²×C₅₃	—	2	2	no	—
350	C₂²×C₅₃	—	2	4	no	—
351	C₂²×C₅₃	—	4	1	no	—
352	C₂²×C₅₃	—	4	1	no	—
353	C₂²×C₅₃	—	4	2	no	—
354	C₂²×C₅₃	—	4	1	no	—
355	C₂²×C₅₃	—	4	2	no	—
356	C₂²×C₅₃	—	4	1	no	—
357	C₂²×C₅₃	—	4	1	no	—
358	C₂²×C₅₃	—	4	2	no	—
359	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
360	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
361	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
362	C₂²×C₅₃	#585	1	1	yes	characteristic
363	C₂²×C₅₃	#585	1	2	yes	—
364	C₄×C₅₃	—	2	4	no	—
365	C₄×C₅₃	—	4	1	no	—
366	C₄×C₅₃	—	4	2	no	—
367	C₄×C₅₃	—	4	2	no	—
368	C₄×C₅₃	—	4	2	no	—
369	C₄×C₅₃	—	4	2	no	—
370	C₄×C₅₃	—	4	2	no	—
371	C₄×C₅₃	—	4	1	no	—
372	C₄×C₅₃	—	4	1	no	—
373	C₄×C₅₃	—	4	2	no	—
374	C₄×C₅₃	—	4	2	no	—
375	C₄×C₅₃	—	4	1	no	—
376	C₄×C₅₃	—	4	2	no	—
377	C₄×C₅₃	—	4	2	no	—
378	C₄×C₅₃	—	4	2	no	—
379	C₄×C₅₃	—	4	2	no	—
380	C₄×C₅₃	#563	1	4	yes	—
381	#2841	C₂×C₅₃	1	1	yes	characteristic, complemented
382	#2839	C₂×C₅₃	1	2	yes	complemented
383	#2838	C₂×C₅₃	1	2	yes	complemented
384	#2835	C₂×C₅₃	1	1	yes	characteristic, complemented
385	#2834	C₂×C₅₃	1	1	yes	characteristic, complemented
386	#2833	C₂×C₅₃	1	2	yes	complemented
387	#2831	C₂×C₅₃	1	2	yes	complemented
388	#2827	C₂×C₅₃	1	2	yes	—
389	#2817	C₂×C₅₃	1	1	yes	characteristic, complemented
390	#2814	C₂×C₅₃	1	2	yes	—
391	#2402	C₂×C₅₃	1	2	yes	complemented
392	#2401	C₂×C₅₃	1	2	yes	complemented
393	#2401	C₂×C₅₃	1	2	yes	complemented
394	#2399	C₂×C₅₃	1	2	yes	complemented
395	#2398	C₂×C₅₃	1	1	yes	characteristic
396	#2396	C₂×C₅₃	1	2	yes	complemented
397	#2395	C₂×C₅₃	1	1	yes	characteristic
398	C₄×C₂²⋊Q₈	C₂×C₅₃	1	2	yes	complemented
399	C₄×#123	C₂×C₅₃	1	1	yes	characteristic
400	C₂×C₅₃	—	4	2	no	—
401	C₂×C₅₃	—	8	1	no	—
402	C₂×C₅₃	#3459	1	1	yes	characteristic
403	C₂×C₅₃	#3461	1	2	yes	—
404	C₂×C₅₃	C₂×#563	1	1	yes	characteristic
405	C₂×C₅₃	#3529	1	1	yes	characteristic
406	C₂×C₅₃	#3531	1	2	yes	—
407	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
408	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
409	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
410	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
412	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
413	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
414	#401	C₂²×C₅₃	1	2	yes	—
415	#401	C₂²×C₅₃	1	2	yes	—
416	#400	C₂²×C₅₃	1	2	yes	—
417	#400	C₂²×C₅₃	1	2	yes	—
418	#400	C₂²×C₅₃	1	2	yes	—
419	#400	C₂²×C₅₃	1	2	yes	—
420	#400	C₂²×C₅₃	1	2	yes	—
421	#400	C₂²×C₅₃	1	2	yes	—
422	#400	C₂²×C₅₃	1	2	yes	—
423	#400	C₂²×C₅₃	1	2	yes	—
424	#400	C₂²×C₅₃	1	2	yes	—
425	#400	C₂²×C₅₃	1	2	yes	—
426	#400	C₂²×C₅₃	1	2	yes	—
427	#400	C₂²×C₅₃	1	2	yes	—
428	#400	C₂²×C₅₃	1	1	yes	characteristic
429	#399	C₂²×C₅₃	1	2	yes	—
430	#399	C₂²×C₅₃	1	1	yes	characteristic
431	#398	C₂²×C₅₃	1	2	yes	—
432	#398	C₂²×C₅₃	1	2	yes	—
433	#398	C₂²×C₅₃	1	2	yes	—
434	#398	C₂²×C₅₃	1	2	yes	—
435	#398	C₂²×C₅₃	1	1	yes	characteristic
436	#398	C₂²×C₅₃	1	2	yes	—
437	#398	C₂²×C₅₃	1	2	yes	—
438	#398	C₂²×C₅₃	1	2	yes	—
439	#398	C₂²×C₅₃	1	2	yes	—
440	#398	C₂²×C₅₃	1	2	yes	—
441	#398	C₂²×C₅₃	1	2	yes	—
442	#397	C₂²×C₅₃	1	2	yes	—
443	#397	C₂²×C₅₃	1	1	yes	characteristic
444	#397	C₂²×C₅₃	1	1	yes	characteristic
445	#397	C₂²×C₅₃	1	2	yes	—
446	#397	C₂²×C₅₃	1	2	yes	—
447	#397	C₂²×C₅₃	1	1	yes	characteristic
448	#397	C₂²×C₅₃	1	2	yes	—
449	#397	C₂²×C₅₃	1	2	yes	—
450	#397	C₂²×C₅₃	1	2	yes	—
451	#397	C₂²×C₅₃	1	2	yes	—
452	#396	C₂²×C₅₃	1	2	yes	—
453	#396	C₂²×C₅₃	1	2	yes	—
454	#396	C₂²×C₅₃	1	2	yes	—
455	#396	C₂²×C₅₃	1	2	yes	—
456	#395	C₂²×C₅₃	1	2	yes	—
457	#395	C₂²×C₅₃	1	2	yes	—
458	#395	C₂²×C₅₃	1	2	yes	—
459	#395	C₂²×C₅₃	1	2	yes	—
460	#395	C₂²×C₅₃	1	2	yes	—
461	#394	C₂²×C₅₃	1	2	yes	—
462	#394	C₂²×C₅₃	1	2	yes	—
463	#393	C₂²×C₅₃	1	2	yes	—
464	#393	C₂²×C₅₃	1	1	yes	characteristic
465	#393	C₂²×C₅₃	1	1	yes	characteristic
466	#391	C₂²×C₅₃	1	2	yes	—
467	#389	C₂²×C₅₃	1	2	yes	—
468	#388	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	#386	C₂²×C₅₃	1	1	yes	characteristic
473	#385	C₂²×C₅₃	1	2	yes	—
474	#385	C₂²×C₅₃	1	2	yes	—
475	#385	C₂²×C₅₃	1	1	yes	characteristic
476	#381	C₂²×C₅₃	1	1	yes	characteristic
477	#380	C₂²×C₅₃	1	2	yes	—
478	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
483	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
485	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
487	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
492	#376	C₂²×C₅₃	1	1	yes	characteristic
493	#376	C₂²×C₅₃	1	2	yes	—
494	C₅₃	#36679	1	1	yes	characteristic, direct product factor, Sylow
495	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
496	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
502	#123	—	2	4	no	—
503	C₂²⋊Q₈	—	2	8	no	—
504	C₄×Q₈	—	4	4	no	—
505	C₄×Q₈	—	4	2	no	—
506	C₄×D₄	—	4	2	no	—
507	#117	—	4	2	no	—
508	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
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	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
546	C₂×C₄²	—	4	2	no	—
547	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
548	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
550	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
551	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
552	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
553	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
554	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
555	#95	C₂³×C₅₃	1	1	yes	characteristic
556	#95	C₂³×C₅₃	1	1	yes	characteristic
557	#95	C₂³×C₅₃	1	2	yes	—
558	#95	C₂³×C₅₃	1	2	yes	—
559	#95	C₂³×C₅₃	1	2	yes	—
560	#95	C₂³×C₅₃	1	2	yes	—
561	#95	C₂³×C₅₃	1	2	yes	—
562	#95	C₂³×C₅₃	1	2	yes	—
563	#95	C₂³×C₅₃	1	2	yes	—
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	1	yes	characteristic
572	#95	C₂³×C₅₃	1	1	yes	characteristic
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	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
590	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
591	C₂×Q₈	—	2	4	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂×Q₈	—	4	1	no	—
594	C₂×Q₈	—	4	2	no	—
595	C₂×Q₈	—	4	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	4	1	no	—
598	C₂×D₄	—	4	1	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	4	1	no	—
604	C₂²×C₄	—	4	1	no	—
605	C₂²×C₄	—	4	1	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	#41×C₅₃	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	4	1	no	—
630	C₄⋊C₄	—	4	1	no	—
631	C₄⋊C₄	—	4	1	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	1	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	1	no	—
655	C₂²⋊C₄	—	4	1	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	1	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	4	no	—
665	C₄²	—	2	2	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	4	2	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	1	no	—
680	C₂³	C₂×#41×C₅₃	1	2	yes	—
681	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
682	Q₈	—	4	8	no	—
683	Q₈	—	4	4	no	—
684	D₄	—	4	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	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	2	no	—
713	C₂×C₄	—	2	2	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	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	4	4	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
734	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
735	C₂×C₄	2₋¹⁺⁴×C₅₃	1	4	yes	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	2	no	—
746	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
747	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
748	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
749	C₂²	C₅₃×#585	1	1	yes	characteristic
750	C₂²	C₅₃×#585	1	2	yes	—
751	C₄	—	2	4	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	C₅₃×#563	1	4	yes	—
768	C₂	—	4	2	no	—
769	C₂	—	8	1	no	—
770	C₂	C₅₃×#3459	1	1	yes	characteristic
771	C₂	C₅₃×#3461	1	2	yes	—
772	C₂	C₂×C₅₃×#563	1	1	yes	characteristic
773	C₂	C₅₃×#3529	1	1	yes	characteristic
774	C₂	C₅₃×#3531	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×D₄×C₅₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2841	C₂	semidirect
2. C₅₃×#2839	C₂	semidirect
3. C₅₃×#2838	C₂	semidirect
4. C₅₃×#2835	C₂	semidirect
5. C₅₃×#2834	C₂	semidirect
6. C₅₃×#2833	C₂	semidirect
7. C₅₃×#2831	C₂	semidirect
9. C₅₃×#2817	C₂	semidirect
11. C₅₃×#2402	C₂	semidirect
12. C₅₃×#2401	C₂	semidirect
13. C₅₃×#2401	C₂	semidirect
14. C₅₃×#2399	C₂	semidirect
16. C₅₃×#2396	C₂	semidirect
18. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
348. #36679	C₅₃	direct (N × H)
381. #2841	C₂×C₅₃	semidirect
382. #2839	C₂×C₅₃	semidirect
383. #2838	C₂×C₅₃	semidirect
384. #2835	C₂×C₅₃	semidirect
385. #2834	C₂×C₅₃	semidirect
386. #2833	C₂×C₅₃	semidirect
387. #2831	C₂×C₅₃	semidirect
389. #2817	C₂×C₅₃	semidirect
391. #2402	C₂×C₅₃	semidirect
392. #2401	C₂×C₅₃	semidirect
393. #2401	C₂×C₅₃	semidirect
394. #2399	C₂×C₅₃	semidirect
396. #2396	C₂×C₅₃	semidirect
398. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
494. C₅₃	#36679	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×#2841	2
C₅₃×#2839	2
C₅₃×#2838	2
C₅₃×#2835	2
C₅₃×#2834	2
C₅₃×#2833	2
C₅₃×#2831	2
C₅₃×#2827	2
C₅₃×#2817	2
C₅₃×#2814	2
C₅₃×#2402	2
C₅₃×#2401	2
C₅₃×#2399	2
C₅₃×#2398	2
C₅₃×#2396	2
C₅₃×#2395	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#123×C₅₃	2
#36679	53

Subgroups — C53×#36679 #27244191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36679 #27244191