Subgroups — C₅₃×#22988 #27230500

Order 13568.

1050 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic
6	C₅₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×#121×C₅₃	C₄	1	1	yes	characteristic
21	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
25	C₅₃×#436	—	2	4	no	—
26	C₅₃×#435	—	2	4	no	—
27	C₅₃×#435	—	2	4	no	—
28	C₅₃×#423	—	2	4	no	—
29	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#390	C₄	1	1	yes	characteristic
48	C₅₃×#389	C₄	1	1	yes	characteristic
49	C₅₃×#388	C₄	1	1	yes	characteristic
50	C₅₃×#388	C₄	1	1	yes	characteristic
51	C₅₃×#386	C₄	1	1	yes	characteristic
52	C₅₃×#386	C₄	1	1	yes	characteristic
53	C₅₃×#380	C₄	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#336	C₂²	1	1	yes	characteristic
58	C₅₃×#336	C₂²	1	1	yes	characteristic
59	C₅₃×#336	C₂²	1	1	yes	characteristic
60	C₅₃×#336	C₂²	1	1	yes	characteristic
61	C₅₃×#336	C₂²	1	1	yes	characteristic
62	C₅₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₅₃	—	2	2	no	—
72	C₂×M₁₆×C₅₃	—	2	2	no	—
73	C₂×M₁₆×C₅₃	—	2	2	no	—
74	C₂×M₁₆×C₅₃	—	2	2	no	—
75	C₂×M₁₆×C₅₃	—	2	2	no	—
76	C₂×M₁₆×C₅₃	—	2	2	no	—
77	C₂×M₁₆×C₅₃	—	4	1	no	—
78	C₂×M₁₆×C₅₃	—	4	1	no	—
79	C₂×M₁₆×C₅₃	—	4	1	no	—
80	C₂²×C₈×C₅₃	—	2	2	no	—
81	C₂²×C₈×C₅₃	—	2	2	no	—
82	C₂²×C₈×C₅₃	—	4	1	no	—
83	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
91	#121×C₅₃	—	2	4	no	—
92	C₄×D₄×C₅₃	—	2	2	no	—
93	C₄×D₄×C₅₃	—	2	2	no	—
94	C₄×D₄×C₅₃	—	2	2	no	—
95	C₄×D₄×C₅₃	—	2	2	no	—
96	C₄×D₄×C₅₃	—	2	2	no	—
97	C₄×D₄×C₅₃	—	2	2	no	—
98	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₅₃	—	2	2	no	—
114	C₂×C₄²×C₅₃	—	2	2	no	—
115	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
121	C₄⋊C₈×C₅₃	—	2	2	no	—
122	C₄⋊C₈×C₅₃	—	2	2	no	—
123	C₄⋊C₈×C₅₃	—	2	2	no	—
124	C₄⋊C₈×C₅₃	—	2	2	no	—
125	C₄⋊C₈×C₅₃	—	2	2	no	—
126	C₄⋊C₈×C₅₃	D₄	1	4	yes	complemented
127	C₂²⋊C₈×C₅₃	—	2	2	no	—
128	C₂²⋊C₈×C₅₃	—	2	2	no	—
129	C₂²⋊C₈×C₅₃	—	2	2	no	—
130	C₂²⋊C₈×C₅₃	—	2	2	no	—
131	C₂²⋊C₈×C₅₃	—	2	2	no	—
132	C₂²⋊C₈×C₅₃	—	4	1	no	—
133	C₂²⋊C₈×C₅₃	—	4	1	no	—
134	C₂²⋊C₈×C₅₃	D₄	1	4	yes	complemented
135	#97×C₅₃	—	2	2	no	—
136	#97×C₅₃	—	2	2	no	—
137	#97×C₅₃	—	2	2	no	—
138	C₄×C₈×C₅₃	—	2	2	no	—
139	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
140	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
141	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
142	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
143	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
144	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
145	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
146	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
147	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₅₃	—	2	2	no	—
149	C₂×D₄×C₅₃	—	2	2	no	—
150	C₂×D₄×C₅₃	—	2	2	no	—
151	C₂×D₄×C₅₃	—	2	2	no	—
152	C₂×D₄×C₅₃	—	2	2	no	—
153	C₂×D₄×C₅₃	—	2	2	no	—
154	C₂×D₄×C₅₃	—	4	1	no	—
155	C₂×D₄×C₅₃	—	4	1	no	—
156	C₂×D₄×C₅₃	—	4	1	no	—
157	C₂²×C₄×C₅₃	—	2	1	no	—
158	C₂²×C₄×C₅₃	—	2	1	no	—
159	C₂²×C₄×C₅₃	—	2	1	no	—
160	C₂²×C₄×C₅₃	—	2	1	no	—
161	C₂²×C₄×C₅₃	—	2	2	no	—
162	C₂²×C₄×C₅₃	—	2	2	no	—
163	C₂²×C₄×C₅₃	—	2	2	no	—
164	C₂²×C₄×C₅₃	—	2	1	no	—
165	C₂²×C₄×C₅₃	—	2	1	no	—
166	C₂²×C₄×C₅₃	—	2	1	no	—
167	C₂²×C₄×C₅₃	—	2	1	no	—
168	C₂²×C₄×C₅₃	—	2	1	no	—
169	C₂²×C₄×C₅₃	—	2	1	no	—
170	C₂²×C₄×C₅₃	—	2	1	no	—
171	C₂²×C₄×C₅₃	—	2	1	no	—
172	C₂²×C₄×C₅₃	—	2	1	no	—
173	C₂²×C₄×C₅₃	—	2	1	no	—
174	C₂²×C₄×C₅₃	—	2	1	no	—
175	C₂²×C₄×C₅₃	—	2	1	no	—
176	C₂²×C₄×C₅₃	—	4	1	no	—
177	C₂²×C₄×C₅₃	—	4	1	no	—
178	C₂²×C₄×C₅₃	—	4	1	no	—
179	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₅₃	#41	1	2	yes	—
192	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
193	M₁₆×C₅₃	—	4	4	no	—
194	M₁₆×C₅₃	—	4	4	no	—
195	M₁₆×C₅₃	—	4	4	no	—
196	C₂×C₈×C₅₃	—	2	1	no	—
197	C₂×C₈×C₅₃	—	2	1	no	—
198	C₂×C₈×C₅₃	—	2	1	no	—
199	C₂×C₈×C₅₃	—	2	1	no	—
200	C₂×C₈×C₅₃	—	2	1	no	—
201	C₂×C₈×C₅₃	—	2	1	no	—
202	C₂×C₈×C₅₃	—	2	1	no	—
203	C₂×C₈×C₅₃	—	2	1	no	—
204	C₂×C₈×C₅₃	—	2	1	no	—
205	C₂×C₈×C₅₃	—	2	1	no	—
206	C₂×C₈×C₅₃	—	2	1	no	—
207	C₂×C₈×C₅₃	—	2	1	no	—
208	C₂×C₈×C₅₃	—	2	1	no	—
209	C₂×C₈×C₅₃	—	2	1	no	—
210	C₂×C₈×C₅₃	—	2	1	no	—
211	C₂×C₈×C₅₃	—	2	1	no	—
212	C₂×C₈×C₅₃	—	2	1	no	—
213	C₂×C₈×C₅₃	—	2	1	no	—
214	C₂×C₈×C₅₃	—	2	1	no	—
215	C₂×C₈×C₅₃	—	2	1	no	—
216	C₂×C₈×C₅₃	—	4	4	no	—
217	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
218	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
219	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
220	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
221	C₄⋊C₄×C₅₃	—	2	2	no	—
222	C₄⋊C₄×C₅₃	—	2	2	no	—
223	C₄⋊C₄×C₅₃	—	2	2	no	—
224	C₄⋊C₄×C₅₃	—	2	2	no	—
225	C₄⋊C₄×C₅₃	—	4	1	no	—
226	C₂²⋊C₄×C₅₃	—	2	2	no	—
227	C₂²⋊C₄×C₅₃	—	2	2	no	—
228	C₂²⋊C₄×C₅₃	—	2	2	no	—
229	C₂²⋊C₄×C₅₃	—	2	2	no	—
230	C₂²⋊C₄×C₅₃	—	2	2	no	—
231	C₂²⋊C₄×C₅₃	—	2	2	no	—
232	C₂²⋊C₄×C₅₃	—	2	2	no	—
233	C₂²⋊C₄×C₅₃	—	4	1	no	—
234	C₂²⋊C₄×C₅₃	—	4	1	no	—
235	C₂²⋊C₄×C₅₃	M₁₆	1	4	yes	complemented
236	C₄²×C₅₃	—	2	2	no	—
237	C₄²×C₅₃	—	2	2	no	—
238	C₄²×C₅₃	—	2	1	no	—
239	C₄²×C₅₃	—	2	1	no	—
240	C₄²×C₅₃	—	2	1	no	—
241	C₄²×C₅₃	—	2	1	no	—
242	C₄²×C₅₃	—	2	1	no	—
243	C₄²×C₅₃	—	2	1	no	—
244	C₄²×C₅₃	C₂×D₄	1	2	yes	—
245	C₄²×C₅₃	#41	1	2	yes	—
246	C₂³×C₅₃	—	2	1	no	—
247	C₂³×C₅₃	—	2	1	no	—
248	C₂³×C₅₃	—	2	1	no	—
249	C₂³×C₅₃	—	2	1	no	—
250	C₂³×C₅₃	—	2	1	no	—
251	C₂³×C₅₃	—	2	1	no	—
252	C₂³×C₅₃	—	2	1	no	—
253	C₂³×C₅₃	—	2	1	no	—
254	C₂³×C₅₃	—	2	1	no	—
255	C₂³×C₅₃	—	2	1	no	—
256	C₂³×C₅₃	—	2	1	no	—
257	C₂³×C₅₃	—	2	1	no	—
258	C₂³×C₅₃	—	2	1	no	—
259	C₂³×C₅₃	—	2	1	no	—
260	C₂³×C₅₃	—	2	1	no	—
261	C₂³×C₅₃	—	2	1	no	—
262	C₂³×C₅₃	—	2	1	no	—
263	C₂³×C₅₃	—	2	1	no	—
264	C₂³×C₅₃	—	2	1	no	—
265	C₂³×C₅₃	C₄×D₄	1	2	yes	—
266	C₂³×C₅₃	C₂×M₁₆	1	2	yes	—
267	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
268	D₄×C₅₃	—	4	4	no	—
269	D₄×C₅₃	—	4	4	no	—
270	D₄×C₅₃	—	4	4	no	—
271	C₂×C₄×C₅₃	—	2	1	no	—
272	C₂×C₄×C₅₃	—	2	1	no	—
273	C₂×C₄×C₅₃	—	2	1	no	—
274	C₂×C₄×C₅₃	—	2	1	no	—
275	C₂×C₄×C₅₃	—	2	1	no	—
276	C₂×C₄×C₅₃	—	2	1	no	—
277	C₂×C₄×C₅₃	—	2	1	no	—
278	C₂×C₄×C₅₃	—	2	1	no	—
279	C₂×C₄×C₅₃	—	2	1	no	—
280	C₂×C₄×C₅₃	—	2	1	no	—
281	C₂×C₄×C₅₃	—	2	2	no	—
282	C₂×C₄×C₅₃	—	2	2	no	—
283	C₂×C₄×C₅₃	—	2	2	no	—
284	C₂×C₄×C₅₃	—	2	2	no	—
285	C₂×C₄×C₅₃	—	2	1	no	—
286	C₂×C₄×C₅₃	—	2	1	no	—
287	C₂×C₄×C₅₃	—	2	1	no	—
288	C₂×C₄×C₅₃	—	2	1	no	—
289	C₂×C₄×C₅₃	—	2	1	no	—
290	C₂×C₄×C₅₃	—	2	1	no	—
291	C₂×C₄×C₅₃	—	2	1	no	—
292	C₂×C₄×C₅₃	—	2	1	no	—
293	C₂×C₄×C₅₃	—	2	1	no	—
294	C₂×C₄×C₅₃	—	2	1	no	—
295	C₂×C₄×C₅₃	—	2	1	no	—
296	C₂×C₄×C₅₃	—	2	1	no	—
297	C₂×C₄×C₅₃	—	2	1	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	—	4	4	no	—
304	C₂×C₄×C₅₃	—	4	4	no	—
305	C₂×C₄×C₅₃	—	4	1	no	—
306	C₂×C₄×C₅₃	—	4	1	no	—
307	C₂×C₄×C₅₃	—	4	1	no	—
308	C₂×C₄×C₅₃	—	4	1	no	—
309	C₂×C₄×C₅₃	—	4	1	no	—
310	C₂×C₄×C₅₃	—	4	1	no	—
311	C₂×C₄×C₅₃	—	4	1	no	—
312	C₂×C₄×C₅₃	—	4	1	no	—
313	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
314	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
315	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
316	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
317	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
318	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
324	C₈×C₅₃	—	2	2	no	—
325	C₈×C₅₃	—	2	2	no	—
326	C₈×C₅₃	—	2	2	no	—
327	C₈×C₅₃	—	2	2	no	—
328	C₈×C₅₃	—	4	1	no	—
329	C₈×C₅₃	—	4	1	no	—
330	C₈×C₅₃	—	4	1	no	—
331	C₈×C₅₃	—	4	1	no	—
332	#22988	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂²×C₅₃	—	2	2	no	—
334	C₂²×C₅₃	—	2	2	no	—
335	C₂²×C₅₃	—	2	2	no	—
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	2	2	no	—
338	C₂²×C₅₃	—	2	2	no	—
339	C₂²×C₅₃	—	4	1	no	—
340	C₂²×C₅₃	—	4	1	no	—
341	C₂²×C₅₃	—	4	1	no	—
342	C₂²×C₅₃	—	4	1	no	—
343	C₂²×C₅₃	—	4	1	no	—
344	C₂²×C₅₃	—	4	1	no	—
345	C₂²×C₅₃	—	4	1	no	—
346	C₂²×C₅₃	—	4	1	no	—
347	C₂²×C₅₃	—	4	1	no	—
348	C₂²×C₅₃	—	4	1	no	—
349	C₂²×C₅₃	—	4	1	no	—
350	C₂²×C₅₃	—	4	1	no	—
351	C₂²×C₅₃	—	4	1	no	—
352	C₂²×C₅₃	—	4	1	no	—
353	C₂²×C₅₃	—	4	1	no	—
354	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
355	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
356	C₂²×C₅₃	#520	1	1	yes	characteristic
357	C₂²×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
358	C₂²×C₅₃	#568	1	1	yes	characteristic
359	C₂²×C₅₃	#568	1	1	yes	characteristic
360	C₂²×C₅₃	#568	1	1	yes	characteristic
361	C₄×C₅₃	—	2	2	no	—
362	C₄×C₅₃	—	2	2	no	—
363	C₄×C₅₃	—	2	2	no	—
364	C₄×C₅₃	—	2	2	no	—
365	C₄×C₅₃	—	2	2	no	—
366	C₄×C₅₃	—	4	1	no	—
367	C₄×C₅₃	—	4	1	no	—
368	C₄×C₅₃	—	4	1	no	—
369	C₄×C₅₃	—	4	1	no	—
370	C₄×C₅₃	—	4	1	no	—
371	C₄×C₅₃	—	4	1	no	—
372	C₄×C₅₃	D₄²	1	1	yes	characteristic
373	C₄×C₅₃	#547	1	1	yes	characteristic
374	C₄×C₅₃	#548	1	1	yes	characteristic
375	C₄×C₅₃	#553	1	1	yes	characteristic
376	C₂×#436	C₂×C₅₃	1	1	yes	characteristic, complemented
377	C₂×#435	C₂×C₅₃	1	1	yes	characteristic, complemented
378	C₂×#435	C₂×C₅₃	1	1	yes	characteristic, complemented
379	C₂×#423	C₂×C₅₃	1	1	yes	characteristic, complemented
380	C₄×#121	C₂×C₅₃	1	1	yes	characteristic
381	#1955	C₂×C₅₃	1	1	yes	characteristic, complemented
382	#1940	C₂×C₅₃	1	1	yes	characteristic, complemented
383	#1924	C₂×C₅₃	1	1	yes	characteristic, complemented
384	#1923	C₂×C₅₃	1	1	yes	characteristic, complemented
385	#1870	C₂×C₅₃	1	1	yes	characteristic, complemented
386	#1870	C₂×C₅₃	1	1	yes	characteristic, complemented
387	#1851	C₂×C₅₃	1	1	yes	characteristic, complemented
388	#1850	C₂×C₅₃	1	1	yes	characteristic, complemented
389	#1771	C₂×C₅₃	1	1	yes	characteristic, complemented
390	#1749	C₂×C₅₃	1	1	yes	characteristic, complemented
391	C₂×C₅₃	—	4	2	no	—
392	C₂×C₅₃	—	4	2	no	—
393	C₂×C₅₃	—	8	1	no	—
394	C₂×C₅₃	#2361	1	1	yes	characteristic
395	C₂×C₅₃	#2930	1	1	yes	characteristic
396	C₂×C₅₃	#2932	1	1	yes	characteristic
397	C₂×C₅₃	D₄×M₁₆	1	1	yes	characteristic
398	C₂×C₅₃	D₄×M₁₆	1	1	yes	characteristic
399	C₂×C₅₃	#2989	1	1	yes	characteristic
400	C₂×C₅₃	#2995	1	1	yes	characteristic
401	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
402	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
403	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
404	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
405	C₂×#121	C₄×C₅₃	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
409	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
410	#436	—	2	4	no	—
411	#435	—	2	4	no	—
412	#435	—	2	4	no	—
413	#423	—	2	4	no	—
414	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
415	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
416	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
417	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
418	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
419	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
421	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
424	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
427	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
428	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
429	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
430	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
431	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
432	#390	C₄×C₅₃	1	1	yes	characteristic
433	#389	C₄×C₅₃	1	1	yes	characteristic
434	#388	C₄×C₅₃	1	1	yes	characteristic
435	#388	C₄×C₅₃	1	1	yes	characteristic
436	#386	C₄×C₅₃	1	1	yes	characteristic
437	#386	C₄×C₅₃	1	1	yes	characteristic
438	#380	C₄×C₅₃	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
440	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
442	#336	C₂²×C₅₃	1	1	yes	characteristic
443	#336	C₂²×C₅₃	1	1	yes	characteristic
444	#336	C₂²×C₅₃	1	1	yes	characteristic
445	#336	C₂²×C₅₃	1	1	yes	characteristic
446	#336	C₂²×C₅₃	1	1	yes	characteristic
447	#336	C₂²×C₅₃	1	1	yes	characteristic
448	C₅₃	#22988	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
450	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
451	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
452	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
453	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
457	C₂×M₁₆	—	2	2	no	—
458	C₂×M₁₆	—	2	2	no	—
459	C₂×M₁₆	—	2	2	no	—
460	C₂×M₁₆	—	2	2	no	—
461	C₂×M₁₆	—	2	2	no	—
462	C₂×M₁₆	—	2	2	no	—
463	C₂×M₁₆	—	4	1	no	—
464	C₂×M₁₆	—	4	1	no	—
465	C₂×M₁₆	—	4	1	no	—
466	C₂²×C₈	—	2	2	no	—
467	C₂²×C₈	—	2	2	no	—
468	C₂²×C₈	—	4	1	no	—
469	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
477	#121	—	2	4	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
499	C₂×C₄²	—	2	2	no	—
500	C₂×C₄²	—	2	2	no	—
501	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
502	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
507	C₄⋊C₈	—	2	2	no	—
508	C₄⋊C₈	—	2	2	no	—
509	C₄⋊C₈	—	2	2	no	—
510	C₄⋊C₈	—	2	2	no	—
511	C₄⋊C₈	—	2	2	no	—
512	C₄⋊C₈	D₄×C₅₃	1	4	yes	complemented
513	C₂²⋊C₈	—	2	2	no	—
514	C₂²⋊C₈	—	2	2	no	—
515	C₂²⋊C₈	—	2	2	no	—
516	C₂²⋊C₈	—	2	2	no	—
517	C₂²⋊C₈	—	2	2	no	—
518	C₂²⋊C₈	—	4	1	no	—
519	C₂²⋊C₈	—	4	1	no	—
520	C₂²⋊C₈	D₄×C₅₃	1	4	yes	complemented
521	#97	—	2	2	no	—
522	#97	—	2	2	no	—
523	#97	—	2	2	no	—
524	C₄×C₈	—	2	2	no	—
525	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
526	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
527	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
528	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
529	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
530	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
531	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
532	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
533	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	4	1	no	—
541	C₂×D₄	—	4	1	no	—
542	C₂×D₄	—	4	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	4	1	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
566	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
567	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
568	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
569	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
570	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
571	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
572	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
573	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
574	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
575	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
577	C₂²×C₄	#41×C₅₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
579	M₁₆	—	4	4	no	—
580	M₁₆	—	4	4	no	—
581	M₁₆	—	4	4	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	4	4	no	—
603	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
604	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
605	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
606	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	4	1	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	M₁₆×C₅₃	1	4	yes	complemented
622	C₄²	—	2	2	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	C₂×D₄×C₅₃	1	2	yes	—
631	C₄²	#41×C₅₃	1	2	yes	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	C₄×D₄×C₅₃	1	2	yes	—
652	C₂³	C₂×M₁₆×C₅₃	1	2	yes	—
653	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
654	D₄	—	4	4	no	—
655	D₄	—	4	4	no	—
656	D₄	—	4	4	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	4	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
700	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
701	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
702	C₂×C₄	C₂×M₁₆×C₅₃	1	2	yes	—
703	C₂×C₄	C₂×M₁₆×C₅₃	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
706	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
707	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
708	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
709	C₂×C₄	2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	2	no	—
713	C₈	—	2	2	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₈	—	4	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
740	C₂²	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
741	C₂²	C₅₃×#520	1	1	yes	characteristic
742	C₂²	C₂²×M₁₆×C₅₃	1	1	yes	characteristic
743	C₂²	C₅₃×#568	1	1	yes	characteristic
744	C₂²	C₅₃×#568	1	1	yes	characteristic
745	C₂²	C₅₃×#568	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	D₄²×C₅₃	1	1	yes	characteristic
758	C₄	C₅₃×#547	1	1	yes	characteristic
759	C₄	C₅₃×#548	1	1	yes	characteristic
760	C₄	C₅₃×#553	1	1	yes	characteristic
761	C₂	—	4	2	no	—
762	C₂	—	4	2	no	—
763	C₂	—	8	1	no	—
764	C₂	C₅₃×#2361	1	1	yes	characteristic
765	C₂	C₅₃×#2930	1	1	yes	characteristic
766	C₂	C₅₃×#2932	1	1	yes	characteristic
767	C₂	D₄×M₁₆×C₅₃	1	1	yes	characteristic
768	C₂	D₄×M₁₆×C₅₃	1	1	yes	characteristic
769	C₂	C₅₃×#2989	1	1	yes	characteristic
770	C₂	C₅₃×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂×#121×C₅₃	C₄
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. C₂×C₅₃×#436	C₂	semidirect
2. C₂×C₅₃×#435	C₂	semidirect
3. C₂×C₅₃×#435	C₂	semidirect
4. C₂×C₅₃×#423	C₂	semidirect
6. C₅₃×#1955	C₂	semidirect
7. C₅₃×#1940	C₂	semidirect
8. C₅₃×#1924	C₂	semidirect
9. C₅₃×#1923	C₂	semidirect
10. C₅₃×#1870	C₂	semidirect
11. C₅₃×#1870	C₂	semidirect
12. C₅₃×#1851	C₂	semidirect
13. C₅₃×#1850	C₂	semidirect
14. C₅₃×#1771	C₂	semidirect
15. C₅₃×#1749	C₂	semidirect
126. C₄⋊C₈×C₅₃	D₄	semidirect
134. C₂²⋊C₈×C₅₃	D₄	semidirect
235. C₂²⋊C₄×C₅₃	M₁₆	semidirect
332. #22988	C₅₃	direct (N × H)
376. C₂×#436	C₂×C₅₃	semidirect
377. C₂×#435	C₂×C₅₃	semidirect
378. C₂×#435	C₂×C₅₃	semidirect
379. C₂×#423	C₂×C₅₃	semidirect
381. #1955	C₂×C₅₃	semidirect
382. #1940	C₂×C₅₃	semidirect
383. #1924	C₂×C₅₃	semidirect
384. #1923	C₂×C₅₃	semidirect
385. #1870	C₂×C₅₃	semidirect
386. #1870	C₂×C₅₃	semidirect
387. #1851	C₂×C₅₃	semidirect
388. #1850	C₂×C₅₃	semidirect
389. #1771	C₂×C₅₃	semidirect
390. #1749	C₂×C₅₃	semidirect
448. C₅₃	#22988	direct (N × H)
512. C₄⋊C₈	D₄×C₅₃	semidirect
520. C₂²⋊C₈	D₄×C₅₃	semidirect
621. C₂²⋊C₄	M₁₆×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#436	2
C₂×C₅₃×#435	2
C₂×C₅₃×#423	2
C₄×#121×C₅₃	2
C₅₃×#1955	2
C₅₃×#1940	2
C₅₃×#1924	2
C₅₃×#1923	2
C₅₃×#1870	2
C₅₃×#1851	2
C₅₃×#1850	2
C₅₃×#1771	2
C₅₃×#1749	2
#22988	53

Subgroups — C53×#22988 #27230500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#22988 #27230500