Subgroups — C₅₃×#22561 #27230073

Order 13568.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#408	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2297	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1780	C₂	1	1	yes	maximal, characteristic
13	C₅₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
21	C₅₃×#433	—	2	4	no	—
22	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#408	—	2	4	no	—
27	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊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×#97×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#391	C₄	1	1	yes	characteristic
42	C₅₃×#391	C₄	1	1	yes	characteristic
43	C₅₃×#390	C₄	1	1	yes	characteristic
44	C₅₃×#390	C₄	1	1	yes	characteristic
45	C₅₃×#386	C₄	1	1	yes	characteristic
46	C₅₃×#386	C₄	1	1	yes	characteristic
47	C₅₃×#386	C₄	1	1	yes	characteristic
48	C₅₃×#386	C₄	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
53	C₅₃×#336	C₂²	1	1	yes	characteristic
54	C₅₃×#336	C₂²	1	1	yes	characteristic
55	C₅₃×#336	C₂²	1	1	yes	characteristic
56	C₅₃×#336	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	C₂×#41×C₅₃	—	2	2	no	—
62	C₂×#41×C₅₃	—	2	2	no	—
63	C₂×#41×C₅₃	—	2	2	no	—
64	C₂×#41×C₅₃	—	2	2	no	—
65	C₂×#41×C₅₃	—	4	1	no	—
66	C₂×#41×C₅₃	—	4	1	no	—
67	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
70	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₅₃	—	2	2	no	—
77	C₂×M₁₆×C₅₃	—	2	2	no	—
78	C₂×M₁₆×C₅₃	—	4	1	no	—
79	C₂²×C₈×C₅₃	—	2	2	no	—
80	C₂²×C₈×C₅₃	—	2	2	no	—
81	C₂²×C₈×C₅₃	—	4	1	no	—
82	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
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	#117×C₅₃	—	2	2	no	—
91	#117×C₅₃	—	2	2	no	—
92	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₅₃	—	4	1	no	—
105	C₂×C₄²×C₅₃	—	4	1	no	—
106	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₅₃	—	2	2	no	—
113	C₄⋊C₈×C₅₃	—	2	2	no	—
114	C₄⋊C₈×C₅₃	—	4	1	no	—
115	C₄⋊C₈×C₅₃	—	4	1	no	—
116	C₂²⋊C₈×C₅₃	—	2	2	no	—
117	C₂²⋊C₈×C₅₃	—	2	2	no	—
118	C₂²⋊C₈×C₅₃	—	2	2	no	—
119	C₂²⋊C₈×C₅₃	—	2	2	no	—
120	C₂²⋊C₈×C₅₃	—	2	2	no	—
121	C₂²⋊C₈×C₅₃	—	2	2	no	—
122	C₂²⋊C₈×C₅₃	—	2	2	no	—
123	C₂²⋊C₈×C₅₃	—	4	1	no	—
124	C₂²⋊C₈×C₅₃	—	4	1	no	—
125	C₂²⋊C₈×C₅₃	D₄	1	4	yes	—
126	#97×C₅₃	—	2	2	no	—
127	#97×C₅₃	—	4	1	no	—
128	#97×C₅₃	—	4	1	no	—
129	C₄×C₈×C₅₃	—	2	2	no	—
130	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
131	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
132	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
133	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
134	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
135	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
136	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
137	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
138	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
140	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
141	#41×C₅₃	—	4	4	no	—
142	#41×C₅₃	—	4	4	no	—
143	#41×C₅₃	—	4	4	no	—
144	#41×C₅₃	—	4	4	no	—
145	C₂×Q₈×C₅₃	—	2	2	no	—
146	C₂×Q₈×C₅₃	—	2	2	no	—
147	C₂×Q₈×C₅₃	—	4	1	no	—
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	1	no	—
162	C₂²×C₄×C₅₃	—	2	1	no	—
163	C₂²×C₄×C₅₃	—	2	1	no	—
164	C₂²×C₄×C₅₃	—	2	1	no	—
165	C₂²×C₄×C₅₃	—	2	2	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	—	4	1	no	—
173	C₂²×C₄×C₅₃	—	4	1	no	—
174	C₂²×C₄×C₅₃	—	4	1	no	—
175	C₂²×C₄×C₅₃	—	4	1	no	—
176	C₂²×C₄×C₅₃	—	4	1	no	—
177	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₅₃	#41	1	2	yes	—
190	C₂²×C₄×C₅₃	#41	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	C₂×C₈×C₅₃	—	2	1	no	—
195	C₂×C₈×C₅₃	—	2	1	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	C₄⋊C₄×C₅₃	—	2	2	no	—
220	C₄⋊C₄×C₅₃	—	2	2	no	—
221	C₂²⋊C₄×C₅₃	—	2	2	no	—
222	C₂²⋊C₄×C₅₃	—	2	2	no	—
223	C₂²⋊C₄×C₅₃	—	2	2	no	—
224	C₂²⋊C₄×C₅₃	—	2	2	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	—	4	1	no	—
230	C₂²⋊C₄×C₅₃	—	4	1	no	—
231	C₄²×C₅₃	—	2	1	no	—
232	C₄²×C₅₃	—	2	1	no	—
233	C₄²×C₅₃	—	2	1	no	—
234	C₄²×C₅₃	—	2	1	no	—
235	C₄²×C₅₃	—	2	1	no	—
236	C₄²×C₅₃	—	2	1	no	—
237	C₄²×C₅₃	—	2	1	no	—
238	C₄²×C₅₃	—	2	1	no	—
239	C₄²×C₅₃	—	4	1	no	—
240	C₄²×C₅₃	—	4	1	no	—
241	C₂³×C₅₃	—	2	1	no	—
242	C₂³×C₅₃	—	2	1	no	—
243	C₂³×C₅₃	—	2	1	no	—
244	C₂³×C₅₃	—	2	1	no	—
245	C₂³×C₅₃	—	2	1	no	—
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	#117	1	2	yes	—
261	C₂³×C₅₃	C₄×D₄	1	2	yes	—
262	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
263	Q₈×C₅₃	—	4	4	no	—
264	D₄×C₅₃	—	4	4	no	—
265	D₄×C₅₃	—	4	4	no	—
266	D₄×C₅₃	—	4	4	no	—
267	C₂×C₄×C₅₃	—	2	1	no	—
268	C₂×C₄×C₅₃	—	2	1	no	—
269	C₂×C₄×C₅₃	—	2	1	no	—
270	C₂×C₄×C₅₃	—	2	1	no	—
271	C₂×C₄×C₅₃	—	2	1	no	—
272	C₂×C₄×C₅₃	—	2	1	no	—
273	C₂×C₄×C₅₃	—	2	2	no	—
274	C₂×C₄×C₅₃	—	2	2	no	—
275	C₂×C₄×C₅₃	—	2	2	no	—
276	C₂×C₄×C₅₃	—	2	2	no	—
277	C₂×C₄×C₅₃	—	2	2	no	—
278	C₂×C₄×C₅₃	—	2	2	no	—
279	C₂×C₄×C₅₃	—	2	2	no	—
280	C₂×C₄×C₅₃	—	2	2	no	—
281	C₂×C₄×C₅₃	—	2	1	no	—
282	C₂×C₄×C₅₃	—	2	1	no	—
283	C₂×C₄×C₅₃	—	2	1	no	—
284	C₂×C₄×C₅₃	—	2	1	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	—	2	1	no	—
304	C₂×C₄×C₅₃	—	2	1	no	—
305	C₂×C₄×C₅₃	—	4	4	no	—
306	C₂×C₄×C₅₃	—	4	4	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	#117	1	2	yes	—
312	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
313	C₂×C₄×C₅₃	#131	1	2	yes	—
314	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
320	C₈×C₅₃	—	2	2	no	—
321	C₈×C₅₃	—	2	2	no	—
322	C₈×C₅₃	—	4	1	no	—
323	C₈×C₅₃	—	4	1	no	—
324	C₈×C₅₃	—	4	1	no	—
325	C₈×C₅₃	—	4	1	no	—
326	C₈×C₅₃	—	4	1	no	—
327	C₈×C₅₃	—	4	1	no	—
328	#22561	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂²×C₅₃	—	2	2	no	—
330	C₂²×C₅₃	—	2	2	no	—
331	C₂²×C₅₃	—	2	2	no	—
332	C₂²×C₅₃	—	2	2	no	—
333	C₂²×C₅₃	—	2	2	no	—
334	C₂²×C₅₃	—	2	2	no	—
335	C₂²×C₅₃	—	4	1	no	—
336	C₂²×C₅₃	—	4	1	no	—
337	C₂²×C₅₃	—	4	1	no	—
338	C₂²×C₅₃	—	4	1	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	C₂×#117	1	1	yes	characteristic
351	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
352	C₂²×C₅₃	#518	1	1	yes	characteristic
353	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
354	C₂²×C₅₃	#568	1	1	yes	characteristic
355	C₂²×C₅₃	#568	1	1	yes	characteristic
356	C₂²×C₅₃	#568	1	1	yes	characteristic
357	C₄×C₅₃	—	2	2	no	—
358	C₄×C₅₃	—	2	2	no	—
359	C₄×C₅₃	—	2	2	no	—
360	C₄×C₅₃	—	4	1	no	—
361	C₄×C₅₃	—	4	1	no	—
362	C₄×C₅₃	—	4	1	no	—
363	C₄×C₅₃	—	4	1	no	—
364	C₄×C₅₃	—	4	1	no	—
365	C₄×C₅₃	—	4	1	no	—
366	C₄×C₅₃	—	4	1	no	—
367	C₄×C₅₃	—	4	1	no	—
368	C₄×C₅₃	#546	1	1	yes	characteristic
369	C₄×C₅₃	#546	1	1	yes	characteristic
370	C₄×C₅₃	#551	1	1	yes	characteristic
371	C₄×C₅₃	#551	1	1	yes	characteristic
372	C₂×#433	C₂×C₅₃	1	1	yes	characteristic, complemented
373	C₂×#408	C₂×C₅₃	1	1	yes	characteristic
374	#2297	C₂×C₅₃	1	1	yes	characteristic
375	#1924	C₂×C₅₃	1	1	yes	characteristic, complemented
376	#1924	C₂×C₅₃	1	1	yes	characteristic, complemented
377	#1924	C₂×C₅₃	1	1	yes	characteristic, complemented
378	#1923	C₂×C₅₃	1	1	yes	characteristic, complemented
379	#1851	C₂×C₅₃	1	1	yes	characteristic, complemented
380	#1850	C₂×C₅₃	1	1	yes	characteristic, complemented
381	#1818	C₂×C₅₃	1	1	yes	characteristic, complemented
382	#1797	C₂×C₅₃	1	1	yes	characteristic, complemented
383	#1780	C₂×C₅₃	1	1	yes	characteristic
384	#1753	C₂×C₅₃	1	1	yes	characteristic, complemented
385	#1752	C₂×C₅₃	1	1	yes	characteristic, complemented
386	#1749	C₂×C₅₃	1	1	yes	characteristic, complemented
387	C₂×C₅₃	—	4	2	no	—
388	C₂×C₅₃	—	4	2	no	—
389	C₂×C₅₃	—	8	1	no	—
390	C₂×C₅₃	#2342	1	1	yes	characteristic
391	C₂×C₅₃	#2923	1	1	yes	characteristic
392	C₂×C₅₃	#2925	1	1	yes	characteristic
393	C₂×C₅₃	#2932	1	1	yes	characteristic
394	C₂×C₅₃	#2935	1	1	yes	characteristic
395	C₂×C₅₃	#2976	1	1	yes	characteristic
396	C₂×C₅₃	#2978	1	1	yes	characteristic
397	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
398	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
399	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
400	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
401	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
402	#433	—	2	4	no	—
403	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
404	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
405	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
406	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
407	#408	—	2	4	no	—
408	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
409	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
410	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
411	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
412	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
413	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
414	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
415	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
417	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
418	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
419	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
420	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
421	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
422	#391	C₄×C₅₃	1	1	yes	characteristic
423	#391	C₄×C₅₃	1	1	yes	characteristic
424	#390	C₄×C₅₃	1	1	yes	characteristic
425	#390	C₄×C₅₃	1	1	yes	characteristic
426	#386	C₄×C₅₃	1	1	yes	characteristic
427	#386	C₄×C₅₃	1	1	yes	characteristic
428	#386	C₄×C₅₃	1	1	yes	characteristic
429	#386	C₄×C₅₃	1	1	yes	characteristic
430	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
431	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
432	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
433	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
434	#336	C₂²×C₅₃	1	1	yes	characteristic
435	#336	C₂²×C₅₃	1	1	yes	characteristic
436	#336	C₂²×C₅₃	1	1	yes	characteristic
437	#336	C₂²×C₅₃	1	1	yes	characteristic
438	#336	C₂²×C₅₃	1	1	yes	characteristic
439	#336	C₂²×C₅₃	1	1	yes	characteristic
440	#336	C₂²×C₅₃	1	1	yes	characteristic
441	#336	C₂²×C₅₃	1	1	yes	characteristic
442	C₅₃	#22561	1	1	yes	characteristic, direct product factor, Sylow
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	2	2	no	—
447	C₂×#41	—	4	1	no	—
448	C₂×#41	—	4	1	no	—
449	C₂²×Q₈	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	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
453	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
454	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
458	C₂×M₁₆	—	2	2	no	—
459	C₂×M₁₆	—	2	2	no	—
460	C₂×M₁₆	—	4	1	no	—
461	C₂²×C₈	—	2	2	no	—
462	C₂²×C₈	—	2	2	no	—
463	C₂²×C₈	—	4	1	no	—
464	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
465	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
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	#117	—	2	2	no	—
473	#117	—	2	2	no	—
474	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
486	C₂×C₄²	—	4	1	no	—
487	C₂×C₄²	—	4	1	no	—
488	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
489	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
494	C₄⋊C₈	—	2	2	no	—
495	C₄⋊C₈	—	2	2	no	—
496	C₄⋊C₈	—	4	1	no	—
497	C₄⋊C₈	—	4	1	no	—
498	C₂²⋊C₈	—	2	2	no	—
499	C₂²⋊C₈	—	2	2	no	—
500	C₂²⋊C₈	—	2	2	no	—
501	C₂²⋊C₈	—	2	2	no	—
502	C₂²⋊C₈	—	2	2	no	—
503	C₂²⋊C₈	—	2	2	no	—
504	C₂²⋊C₈	—	2	2	no	—
505	C₂²⋊C₈	—	4	1	no	—
506	C₂²⋊C₈	—	4	1	no	—
507	C₂²⋊C₈	D₄×C₅₃	1	4	yes	—
508	#97	—	2	2	no	—
509	#97	—	4	1	no	—
510	#97	—	4	1	no	—
511	C₄×C₈	—	2	2	no	—
512	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
513	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
514	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
515	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
516	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
517	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
518	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
519	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
520	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
521	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
522	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
523	#41	—	4	4	no	—
524	#41	—	4	4	no	—
525	#41	—	4	4	no	—
526	#41	—	4	4	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	4	1	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	4	1	no	—
537	C₂×D₄	—	4	1	no	—
538	C₂×D₄	—	4	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	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	1	no	—
549	C₂²×C₄	—	2	1	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	—	4	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	1	no	—
559	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
560	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
561	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
562	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
563	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
564	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
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	C₂×D₄×C₅₃	1	2	yes	—
571	C₂²×C₄	#41×C₅₃	1	2	yes	—
572	C₂²×C₄	#41×C₅₃	1	2	yes	—
573	C₂²×C₄	#41×C₅₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
575	M₁₆	—	4	4	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	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	—	4	4	no	—
599	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
600	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	4	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₂²⋊C₄	—	4	1	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₂²⋊C₄	—	4	1	no	—
612	C₂²⋊C₄	—	4	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	4	1	no	—
622	C₄²	—	4	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
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	#117×C₅₃	1	2	yes	—
643	C₂³	C₄×D₄×C₅₃	1	2	yes	—
644	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
645	Q₈	—	4	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	4	no	—
648	D₄	—	4	4	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	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	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	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	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	#117×C₅₃	1	2	yes	—
694	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
695	C₂×C₄	#131×C₅₃	1	2	yes	—
696	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
697	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
698	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
699	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
700	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
701	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
702	C₈	—	2	2	no	—
703	C₈	—	2	2	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₈	—	4	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	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	C₂×#117×C₅₃	1	1	yes	characteristic
732	C₂²	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
733	C₂²	C₅₃×#518	1	1	yes	characteristic
734	C₂²	C₂×#131×C₅₃	1	1	yes	characteristic
735	C₂²	C₅₃×#568	1	1	yes	characteristic
736	C₂²	C₅₃×#568	1	1	yes	characteristic
737	C₂²	C₅₃×#568	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	1	no	—
749	C₄	C₅₃×#546	1	1	yes	characteristic
750	C₄	C₅₃×#546	1	1	yes	characteristic
751	C₄	C₅₃×#551	1	1	yes	characteristic
752	C₄	C₅₃×#551	1	1	yes	characteristic
753	C₂	—	4	2	no	—
754	C₂	—	4	2	no	—
755	C₂	—	8	1	no	—
756	C₂	C₅₃×#2342	1	1	yes	characteristic
757	C₂	C₅₃×#2923	1	1	yes	characteristic
758	C₂	C₅₃×#2925	1	1	yes	characteristic
759	C₂	C₅₃×#2932	1	1	yes	characteristic
760	C₂	C₅₃×#2935	1	1	yes	characteristic
761	C₂	C₅₃×#2976	1	1	yes	characteristic
762	C₂	C₅₃×#2978	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	C₂²×#41×C₅₃	C₂²
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×#433	C₂	semidirect
4. C₅₃×#1924	C₂	semidirect
5. C₅₃×#1924	C₂	semidirect
6. C₅₃×#1924	C₂	semidirect
7. C₅₃×#1923	C₂	semidirect
8. C₅₃×#1851	C₂	semidirect
9. C₅₃×#1850	C₂	semidirect
10. C₅₃×#1818	C₂	semidirect
11. C₅₃×#1797	C₂	semidirect
13. C₅₃×#1753	C₂	semidirect
14. C₅₃×#1752	C₂	semidirect
15. C₅₃×#1749	C₂	semidirect
328. #22561	C₅₃	direct (N × H)
372. C₂×#433	C₂×C₅₃	semidirect
375. #1924	C₂×C₅₃	semidirect
376. #1924	C₂×C₅₃	semidirect
377. #1924	C₂×C₅₃	semidirect
378. #1923	C₂×C₅₃	semidirect
379. #1851	C₂×C₅₃	semidirect
380. #1850	C₂×C₅₃	semidirect
381. #1818	C₂×C₅₃	semidirect
382. #1797	C₂×C₅₃	semidirect
384. #1753	C₂×C₅₃	semidirect
385. #1752	C₂×C₅₃	semidirect
386. #1749	C₂×C₅₃	semidirect
442. C₅₃	#22561	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#433	2
C₂×C₅₃×#408	2
C₅₃×#2297	2
C₅₃×#1924	2
C₅₃×#1923	2
C₅₃×#1851	2
C₅₃×#1850	2
C₅₃×#1818	2
C₅₃×#1797	2
C₅₃×#1780	2
C₅₃×#1753	2
C₅₃×#1752	2
C₅₃×#1749	2
#22561	53

Subgroups — C53×#22561 #27230073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#22561 #27230073