Subgroups — C₅₃×#25533 #27233045

Order 13568.

1444 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₃	—	2	1	no	—
17	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#547	—	2	4	no	—
20	C₅₃×#547	—	2	4	no	—
21	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×#123×C₅₃	—	2	1	no	—
23	C₂×#123×C₅₃	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
25	C₂×#121×C₅₃	—	2	1	no	—
26	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#480	—	2	4	no	—
36	C₅₃×#466	—	2	4	no	—
37	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
49	C₅₃×#396	—	2	1	no	—
50	C₅₃×#394	—	2	1	no	—
51	C₅₃×#390	C₂²	1	1	yes	characteristic
52	C₅₃×#389	C₂²	1	1	yes	characteristic
53	C₅₃×#386	—	2	1	no	—
54	C₅₃×#380	C₂²	1	1	yes	characteristic
55	C₅₃×#340	C₂²	1	1	yes	characteristic
56	C₅₃×#340	C₂²	1	1	yes	characteristic
57	C₅₃×#340	C₂²	1	1	yes	characteristic
58	C₅₃×#340	C₂²	1	1	yes	characteristic
59	C₅₃×#340	C₂²	1	1	yes	characteristic
60	C₅₃×#340	C₂²	1	1	yes	characteristic
61	C₅₃×#336	C₂²	1	1	yes	characteristic
62	C₅₃×#336	C₂²	1	1	yes	characteristic
63	C₂×#41×C₅₃	—	2	8	no	—
64	C₂×#41×C₅₃	—	4	4	no	—
65	C₂×#41×C₅₃	—	4	4	no	—
66	C₂²×Q₈×C₅₃	—	2	1	no	—
67	C₂²×D₄×C₅₃	—	2	1	no	—
68	C₂²×D₄×C₅₃	—	2	1	no	—
69	C₂²×D₄×C₅₃	—	2	1	no	—
70	C₂²×D₄×C₅₃	—	2	1	no	—
71	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
72	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅₃	—	2	1	no	—
75	C₂³×C₄×C₅₃	—	2	1	no	—
76	C₂³×C₄×C₅₃	—	2	1	no	—
77	C₂³×C₄×C₅₃	—	2	1	no	—
78	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
80	C₂×D₈×C₅₃	—	2	2	no	—
81	C₂×D₈×C₅₃	—	2	2	no	—
82	C₂×D₈×C₅₃	—	4	1	no	—
83	C₂²×C₈×C₅₃	—	2	2	no	—
84	C₂²×C₈×C₅₃	—	2	2	no	—
85	C₂²×C₈×C₅₃	—	4	1	no	—
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	C₄⋊Q₈×C₅₃	—	2	2	no	—
91	C₄⋊Q₈×C₅₃	—	2	2	no	—
92	#123×C₅₃	—	2	8	no	—
93	#123×C₅₃	—	2	8	no	—
94	C₂²⋊Q₈×C₅₃	—	2	8	no	—
95	#121×C₅₃	—	2	2	no	—
96	#121×C₅₃	—	2	2	no	—
97	#121×C₅₃	—	2	2	no	—
98	#121×C₅₃	—	2	2	no	—
99	#121×C₅₃	—	2	2	no	—
100	#121×C₅₃	—	2	2	no	—
101	#121×C₅₃	—	4	1	no	—
102	#121×C₅₃	—	4	4	no	—
103	#121×C₅₃	D₄	1	4	yes	complemented
104	C₄×D₄×C₅₃	—	2	2	no	—
105	C₄×D₄×C₅₃	—	2	2	no	—
106	C₄×D₄×C₅₃	—	2	2	no	—
107	C₄×D₄×C₅₃	—	2	2	no	—
108	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
109	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
110	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
111	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
112	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
113	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
114	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
115	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
116	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
117	C₂×C₄⋊C₄×C₅₃	—	4	1	no	—
118	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₅₃	D₄	1	4	yes	complemented
120	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
136	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
137	#107×C₅₃	—	2	2	no	—
138	#107×C₅₃	—	2	2	no	—
139	#107×C₅₃	—	2	2	no	—
140	#102×C₅₃	—	2	2	no	—
141	#102×C₅₃	—	2	2	no	—
142	#102×C₅₃	—	2	2	no	—
143	#102×C₅₃	—	2	2	no	—
144	#102×C₅₃	—	2	2	no	—
145	#102×C₅₃	—	4	1	no	—
146	C₂²⋊C₈×C₅₃	—	2	2	no	—
147	C₂²⋊C₈×C₅₃	—	2	2	no	—
148	C₂²⋊C₈×C₅₃	—	4	1	no	—
149	#95×C₅₃	—	2	1	no	—
150	#95×C₅₃	—	2	1	no	—
151	C₂⁴×C₅₃	—	2	1	no	—
152	C₂⁴×C₅₃	—	2	1	no	—
153	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
154	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
155	#41×C₅₃	—	4	32	no	—
156	C₂×Q₈×C₅₃	—	2	4	no	—
157	C₂×Q₈×C₅₃	—	4	2	no	—
158	C₂×Q₈×C₅₃	—	4	2	no	—
159	C₂×D₄×C₅₃	—	2	2	no	—
160	C₂×D₄×C₅₃	—	2	2	no	—
161	C₂×D₄×C₅₃	—	2	4	no	—
162	C₂×D₄×C₅₃	—	2	4	no	—
163	C₂×D₄×C₅₃	—	2	1	no	—
164	C₂×D₄×C₅₃	—	2	1	no	—
165	C₂×D₄×C₅₃	—	2	1	no	—
166	C₂×D₄×C₅₃	—	2	1	no	—
167	C₂×D₄×C₅₃	—	2	1	no	—
168	C₂×D₄×C₅₃	—	2	1	no	—
169	C₂×D₄×C₅₃	—	2	1	no	—
170	C₂×D₄×C₅₃	—	2	1	no	—
171	C₂×D₄×C₅₃	—	2	1	no	—
172	C₂×D₄×C₅₃	—	2	1	no	—
173	C₂×D₄×C₅₃	—	2	1	no	—
174	C₂×D₄×C₅₃	—	4	2	no	—
175	C₂×D₄×C₅₃	—	4	2	no	—
176	C₂×D₄×C₅₃	—	4	2	no	—
177	C₂×D₄×C₅₃	—	4	2	no	—
178	C₂×D₄×C₅₃	—	4	2	no	—
179	C₂×D₄×C₅₃	—	4	2	no	—
180	C₂×D₄×C₅₃	—	4	2	no	—
181	C₂×D₄×C₅₃	—	4	2	no	—
182	C₂×D₄×C₅₃	—	4	2	no	—
183	C₂×D₄×C₅₃	—	8	1	no	—
184	C₂×D₄×C₅₃	D₈	1	4	yes	complemented
185	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₅₃	—	2	1	no	—
187	C₂²×C₄×C₅₃	—	2	1	no	—
188	C₂²×C₄×C₅₃	—	2	1	no	—
189	C₂²×C₄×C₅₃	—	2	1	no	—
190	C₂²×C₄×C₅₃	—	2	4	no	—
191	C₂²×C₄×C₅₃	—	2	4	no	—
192	C₂²×C₄×C₅₃	—	2	4	no	—
193	C₂²×C₄×C₅₃	—	2	1	no	—
194	C₂²×C₄×C₅₃	—	2	1	no	—
195	C₂²×C₄×C₅₃	—	2	1	no	—
196	C₂²×C₄×C₅₃	—	2	1	no	—
197	C₂²×C₄×C₅₃	—	2	1	no	—
198	C₂²×C₄×C₅₃	—	2	1	no	—
199	C₂²×C₄×C₅₃	—	2	1	no	—
200	C₂²×C₄×C₅₃	—	2	1	no	—
201	C₂²×C₄×C₅₃	—	2	1	no	—
202	C₂²×C₄×C₅₃	—	2	1	no	—
203	C₂²×C₄×C₅₃	—	2	1	no	—
204	C₂²×C₄×C₅₃	—	2	1	no	—
205	C₂²×C₄×C₅₃	—	4	2	no	—
206	C₂²×C₄×C₅₃	—	4	2	no	—
207	C₂²×C₄×C₅₃	—	4	2	no	—
208	C₂²×C₄×C₅₃	—	4	2	no	—
209	C₂²×C₄×C₅₃	—	4	2	no	—
210	C₂²×C₄×C₅₃	—	4	2	no	—
211	C₂²×C₄×C₅₃	—	4	2	no	—
212	C₂²×C₄×C₅₃	—	4	2	no	—
213	C₂²×C₄×C₅₃	—	8	1	no	—
214	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
221	D₈×C₅₃	—	4	4	no	—
222	C₂×C₈×C₅₃	—	2	1	no	—
223	C₂×C₈×C₅₃	—	2	1	no	—
224	C₂×C₈×C₅₃	—	2	1	no	—
225	C₂×C₈×C₅₃	—	2	1	no	—
226	C₂×C₈×C₅₃	—	2	1	no	—
227	C₂×C₈×C₅₃	—	2	1	no	—
228	C₂×C₈×C₅₃	—	2	1	no	—
229	C₂×C₈×C₅₃	—	2	1	no	—
230	C₂×C₈×C₅₃	—	2	1	no	—
231	C₂×C₈×C₅₃	—	2	1	no	—
232	C₂×C₈×C₅₃	—	2	1	no	—
233	C₂×C₈×C₅₃	—	4	4	no	—
234	C₂×C₈×C₅₃	#41	1	2	yes	complemented
235	C₄⋊C₄×C₅₃	—	2	4	no	—
236	C₄⋊C₄×C₅₃	—	2	4	no	—
237	C₄⋊C₄×C₅₃	—	2	4	no	—
238	C₄⋊C₄×C₅₃	—	2	2	no	—
239	C₄⋊C₄×C₅₃	—	2	1	no	—
240	C₄⋊C₄×C₅₃	—	2	1	no	—
241	C₄⋊C₄×C₅₃	—	2	1	no	—
242	C₄⋊C₄×C₅₃	—	2	1	no	—
243	C₄⋊C₄×C₅₃	—	2	1	no	—
244	C₄⋊C₄×C₅₃	—	2	1	no	—
245	C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₄⋊C₄×C₅₃	—	2	1	no	—
247	C₄⋊C₄×C₅₃	—	4	2	no	—
248	C₄⋊C₄×C₅₃	—	4	2	no	—
249	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
251	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
252	C₄⋊C₄×C₅₃	#41	1	2	yes	complemented
253	C₂²⋊C₄×C₅₃	—	2	4	no	—
254	C₂²⋊C₄×C₅₃	—	2	4	no	—
255	C₂²⋊C₄×C₅₃	—	2	2	no	—
256	C₂²⋊C₄×C₅₃	—	2	4	no	—
257	C₂²⋊C₄×C₅₃	—	2	2	no	—
258	C₂²⋊C₄×C₅₃	—	4	2	no	—
259	C₂²⋊C₄×C₅₃	—	4	2	no	—
260	C₂²⋊C₄×C₅₃	—	4	2	no	—
261	C₂²⋊C₄×C₅₃	—	4	2	no	—
262	C₂²⋊C₄×C₅₃	—	8	1	no	—
263	C₄²×C₅₃	—	2	1	no	—
264	C₄²×C₅₃	—	2	1	no	—
265	C₂³×C₅₃	—	2	1	no	—
266	C₂³×C₅₃	—	2	1	no	—
267	C₂³×C₅₃	—	2	1	no	—
268	C₂³×C₅₃	—	2	1	no	—
269	C₂³×C₅₃	—	2	1	no	—
270	C₂³×C₅₃	—	2	1	no	—
271	C₂³×C₅₃	—	2	1	no	—
272	C₂³×C₅₃	—	2	1	no	—
273	C₂³×C₅₃	—	2	1	no	—
274	C₂³×C₅₃	—	2	1	no	—
275	C₂³×C₅₃	—	2	2	no	—
276	C₂³×C₅₃	—	4	1	no	—
277	C₂³×C₅₃	—	4	1	no	—
278	C₂³×C₅₃	—	4	1	no	—
279	C₂³×C₅₃	—	4	1	no	—
280	C₂³×C₅₃	—	4	1	no	—
281	C₂³×C₅₃	—	4	1	no	—
282	C₂³×C₅₃	—	4	1	no	—
283	C₂³×C₅₃	—	4	1	no	—
284	C₂³×C₅₃	—	4	1	no	—
285	C₂³×C₅₃	—	4	1	no	—
286	C₂³×C₅₃	—	4	1	no	—
287	C₂³×C₅₃	—	4	1	no	—
288	C₂³×C₅₃	—	4	1	no	—
289	C₂³×C₅₃	#120	1	2	yes	—
290	C₂³×C₅₃	C₂×D₈	1	2	yes	—
291	C₂³×C₅₃	C₂×D₈	1	2	yes	—
292	C₂³×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
293	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₅₃	—	4	8	no	—
295	D₄×C₅₃	—	2	8	no	—
296	D₄×C₅₃	—	2	2	no	—
297	D₄×C₅₃	—	2	2	no	—
298	D₄×C₅₃	—	4	8	no	—
299	D₄×C₅₃	—	4	8	no	—
300	D₄×C₅₃	—	4	1	no	—
301	D₄×C₅₃	—	4	1	no	—
302	D₄×C₅₃	—	4	1	no	—
303	D₄×C₅₃	—	4	1	no	—
304	D₄×C₅₃	—	4	1	no	—
305	D₄×C₅₃	—	4	1	no	—
306	D₄×C₅₃	—	8	4	no	—
307	D₄×C₅₃	—	8	4	no	—
308	C₂×C₄×C₅₃	—	2	1	no	—
309	C₂×C₄×C₅₃	—	2	1	no	—
310	C₂×C₄×C₅₃	—	2	1	no	—
311	C₂×C₄×C₅₃	—	2	1	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	1	no	—
320	C₂×C₄×C₅₃	—	2	1	no	—
321	C₂×C₄×C₅₃	—	2	1	no	—
322	C₂×C₄×C₅₃	—	2	2	no	—
323	C₂×C₄×C₅₃	—	2	1	no	—
324	C₂×C₄×C₅₃	—	2	1	no	—
325	C₂×C₄×C₅₃	—	2	1	no	—
326	C₂×C₄×C₅₃	—	4	8	no	—
327	C₂×C₄×C₅₃	—	4	8	no	—
328	C₂×C₄×C₅₃	—	4	1	no	—
329	C₂×C₄×C₅₃	—	4	1	no	—
330	C₂×C₄×C₅₃	—	4	1	no	—
331	C₂×C₄×C₅₃	—	4	1	no	—
332	C₂×C₄×C₅₃	—	4	1	no	—
333	C₂×C₄×C₅₃	—	4	1	no	—
334	C₂×C₄×C₅₃	—	4	1	no	—
335	C₂×C₄×C₅₃	—	4	1	no	—
336	C₂×C₄×C₅₃	—	4	8	no	—
337	C₂×C₄×C₅₃	—	4	1	no	—
338	C₂×C₄×C₅₃	—	4	1	no	—
339	C₂×C₄×C₅₃	—	4	1	no	—
340	C₂×C₄×C₅₃	—	4	1	no	—
341	C₂×C₄×C₅₃	—	4	1	no	—
342	C₂×C₄×C₅₃	—	4	1	no	—
343	C₂×C₄×C₅₃	—	4	1	no	—
344	C₂×C₄×C₅₃	—	4	1	no	—
345	C₂×C₄×C₅₃	—	4	1	no	—
346	C₂×C₄×C₅₃	—	4	1	no	—
347	C₂×C₄×C₅₃	—	8	4	no	—
348	C₂×C₄×C₅₃	#120	1	2	yes	—
349	C₂×C₄×C₅₃	C₂×D₈	1	2	yes	—
350	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
353	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
354	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
356	C₈×C₅₃	—	2	2	no	—
357	C₈×C₅₃	—	4	1	no	—
358	C₈×C₅₃	—	4	1	no	—
359	C₈×C₅₃	—	4	1	no	—
360	#25533	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
367	C₂²×C₅₃	—	2	2	no	—
368	C₂²×C₅₃	—	2	2	no	—
369	C₂²×C₅₃	—	2	2	no	—
370	C₂²×C₅₃	—	4	1	no	—
371	C₂²×C₅₃	—	4	1	no	—
372	C₂²×C₅₃	—	4	1	no	—
373	C₂²×C₅₃	—	4	1	no	—
374	C₂²×C₅₃	—	4	2	no	—
375	C₂²×C₅₃	—	4	2	no	—
376	C₂²×C₅₃	—	4	2	no	—
377	C₂²×C₅₃	—	8	1	no	—
378	C₂²×C₅₃	—	8	1	no	—
379	C₂²×C₅₃	—	8	1	no	—
380	C₂²×C₅₃	—	8	1	no	—
381	C₂²×C₅₃	—	8	1	no	—
382	C₂²×C₅₃	—	8	1	no	—
383	C₂²×C₅₃	—	8	1	no	—
384	C₂²×C₅₃	—	8	1	no	—
385	C₂²×C₅₃	—	8	1	no	—
386	C₂²×C₅₃	—	8	1	no	—
387	C₂²×C₅₃	—	8	1	no	—
388	C₂²×C₅₃	#447	1	4	yes	—
389	C₂²×C₅₃	C₂×#120	1	1	yes	characteristic
390	C₂²×C₅₃	#546	1	1	yes	characteristic
391	C₂²×C₅₃	#547	1	1	yes	characteristic
392	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
393	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂²×C₅₃	#577	1	1	yes	characteristic
395	C₂²×C₅₃	#578	1	1	yes	characteristic
396	C₄×C₅₃	—	2	2	no	—
397	C₄×C₅₃	—	2	2	no	—
398	C₄×C₅₃	—	4	1	no	—
399	C₄×C₅₃	—	4	2	no	—
400	C₄×C₅₃	—	4	2	no	—
401	C₄×C₅₃	—	4	2	no	—
402	C₄×C₅₃	—	4	1	no	—
403	C₄×C₅₃	—	4	2	no	—
404	C₄×C₅₃	—	8	1	no	—
405	C₄×C₅₃	—	8	1	no	—
406	C₄×C₅₃	#532	1	1	yes	characteristic
407	C₄×C₅₃	#537	1	1	yes	characteristic
408	C₄×C₅₃	#546	1	1	yes	characteristic
409	C₄×C₅₃	#547	1	1	yes	characteristic
410	C₂×#547	C₂×C₅₃	1	1	yes	characteristic, complemented
411	C₂×#480	C₂×C₅₃	1	1	yes	characteristic, complemented
412	C₂×#466	C₂×C₅₃	1	1	yes	characteristic, complemented
413	#2416	C₂×C₅₃	1	1	yes	characteristic, complemented
414	#2057	C₂×C₅₃	1	1	yes	characteristic, complemented
415	#2033	C₂×C₅₃	1	1	yes	characteristic, complemented
416	#2023	C₂×C₅₃	1	1	yes	characteristic, complemented
417	#1999	C₂×C₅₃	1	1	yes	characteristic, complemented
418	#1879	C₂×C₅₃	1	1	yes	characteristic, complemented
419	#1874	C₂×C₅₃	1	1	yes	characteristic, complemented
420	#1874	C₂×C₅₃	1	1	yes	characteristic, complemented
421	#1869	C₂×C₅₃	1	1	yes	characteristic, complemented
422	#1862	C₂×C₅₃	1	1	yes	characteristic, complemented
423	#1852	C₂×C₅₃	1	1	yes	characteristic, complemented
424	C₂×#340	C₂×C₅₃	1	1	yes	characteristic, complemented
425	C₂×C₅₃	—	2	4	no	—
426	C₂×C₅₃	—	4	2	no	—
427	C₂×C₅₃	—	8	2	no	—
428	C₂×C₅₃	—	16	1	no	—
429	C₂×C₅₃	#2430	1	1	yes	characteristic
430	C₂×C₅₃	C₂×#447	1	1	yes	characteristic
431	C₂×C₅₃	#3013	1	1	yes	characteristic
432	C₂×C₅₃	#3294	1	1	yes	characteristic
433	C₂×C₅₃	#3308	1	1	yes	characteristic
434	C₂×C₅₃	#3334	1	1	yes	characteristic
435	C₂×C₅₃	#3345	1	1	yes	characteristic
436	C₂²×#41	—	2	1	no	—
437	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
438	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
439	#547	—	2	4	no	—
440	#547	—	2	4	no	—
441	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
442	C₂×#123	—	2	1	no	—
443	C₂×#123	—	2	1	no	—
444	C₂×C₂²⋊Q₈	—	2	1	no	—
445	C₂×#121	—	2	1	no	—
446	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
447	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
448	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
449	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
450	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
452	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
453	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
454	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
455	#480	—	2	4	no	—
456	#466	—	2	4	no	—
457	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
458	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
459	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
460	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
461	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
462	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
463	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
464	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
465	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
466	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
467	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
468	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
469	#396	—	2	1	no	—
470	#394	—	2	1	no	—
471	#390	C₂²×C₅₃	1	1	yes	characteristic
472	#389	C₂²×C₅₃	1	1	yes	characteristic
473	#386	—	2	1	no	—
474	#380	C₂²×C₅₃	1	1	yes	characteristic
475	#340	C₂²×C₅₃	1	1	yes	characteristic
476	#340	C₂²×C₅₃	1	1	yes	characteristic
477	#340	C₂²×C₅₃	1	1	yes	characteristic
478	#340	C₂²×C₅₃	1	1	yes	characteristic
479	#340	C₂²×C₅₃	1	1	yes	characteristic
480	#340	C₂²×C₅₃	1	1	yes	characteristic
481	#336	C₂²×C₅₃	1	1	yes	characteristic
482	#336	C₂²×C₅₃	1	1	yes	characteristic
483	C₅₃	#25533	1	1	yes	characteristic, direct product factor, Sylow
484	C₂×#41	—	2	8	no	—
485	C₂×#41	—	4	4	no	—
486	C₂×#41	—	4	4	no	—
487	C₂²×Q₈	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
494	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
495	C₂³×C₄	—	2	1	no	—
496	C₂³×C₄	—	2	1	no	—
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
501	C₂×D₈	—	2	2	no	—
502	C₂×D₈	—	2	2	no	—
503	C₂×D₈	—	4	1	no	—
504	C₂²×C₈	—	2	2	no	—
505	C₂²×C₈	—	2	2	no	—
506	C₂²×C₈	—	4	1	no	—
507	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	—	2	2	no	—
513	#123	—	2	8	no	—
514	#123	—	2	8	no	—
515	C₂²⋊Q₈	—	2	8	no	—
516	#121	—	2	2	no	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	—	4	1	no	—
523	#121	—	4	4	no	—
524	#121	D₄×C₅₃	1	4	yes	complemented
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	2	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	2	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	4	1	no	—
539	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	D₄×C₅₃	1	4	yes	complemented
541	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
558	#107	—	2	2	no	—
559	#107	—	2	2	no	—
560	#107	—	2	2	no	—
561	#102	—	2	2	no	—
562	#102	—	2	2	no	—
563	#102	—	2	2	no	—
564	#102	—	2	2	no	—
565	#102	—	2	2	no	—
566	#102	—	4	1	no	—
567	C₂²⋊C₈	—	2	2	no	—
568	C₂²⋊C₈	—	2	2	no	—
569	C₂²⋊C₈	—	4	1	no	—
570	#95	—	2	1	no	—
571	#95	—	2	1	no	—
572	C₂⁴	—	2	1	no	—
573	C₂⁴	—	2	1	no	—
574	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
575	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
576	#41	—	4	32	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	4	2	no	—
579	C₂×Q₈	—	4	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂×D₄	—	4	2	no	—
600	C₂×D₄	—	4	2	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	8	1	no	—
605	C₂×D₄	D₈×C₅₃	1	4	yes	complemented
606	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	8	1	no	—
635	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
639	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
640	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
642	D₈	—	4	4	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	4	4	no	—
655	C₂×C₈	#41×C₅₃	1	2	yes	complemented
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
672	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
673	C₄⋊C₄	#41×C₅₃	1	2	yes	complemented
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	8	1	no	—
684	C₄²	—	2	1	no	—
685	C₄²	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	4	1	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	#120×C₅₃	1	2	yes	—
711	C₂³	C₂×D₈×C₅₃	1	2	yes	—
712	C₂³	C₂×D₈×C₅₃	1	2	yes	—
713	C₂³	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
714	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
715	Q₈	—	4	8	no	—
716	D₄	—	2	8	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	4	8	no	—
720	D₄	—	4	8	no	—
721	D₄	—	4	1	no	—
722	D₄	—	4	1	no	—
723	D₄	—	4	1	no	—
724	D₄	—	4	1	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	1	no	—
727	D₄	—	8	4	no	—
728	D₄	—	8	4	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	4	8	no	—
748	C₂×C₄	—	4	8	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	8	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	8	4	no	—
769	C₂×C₄	#120×C₅₃	1	2	yes	—
770	C₂×C₄	C₂×D₈×C₅₃	1	2	yes	—
771	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
773	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
774	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
775	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
776	C₂×C₄	2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
777	C₈	—	2	2	no	—
778	C₈	—	4	1	no	—
779	C₈	—	4	1	no	—
780	C₈	—	4	1	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	8	1	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	8	1	no	—
808	C₂²	C₅₃×#447	1	4	yes	—
809	C₂²	C₂×#120×C₅₃	1	1	yes	characteristic
810	C₂²	C₅₃×#546	1	1	yes	characteristic
811	C₂²	C₅₃×#547	1	1	yes	characteristic
812	C₂²	C₂²×D₈×C₅₃	1	1	yes	characteristic
813	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
814	C₂²	C₅₃×#577	1	1	yes	characteristic
815	C₂²	C₅₃×#578	1	1	yes	characteristic
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	2	no	—
824	C₄	—	8	1	no	—
825	C₄	—	8	1	no	—
826	C₄	C₅₃×#532	1	1	yes	characteristic
827	C₄	C₅₃×#537	1	1	yes	characteristic
828	C₄	C₅₃×#546	1	1	yes	characteristic
829	C₄	C₅₃×#547	1	1	yes	characteristic
830	C₂	—	2	4	no	—
831	C₂	—	4	2	no	—
832	C₂	—	8	2	no	—
833	C₂	—	16	1	no	—
834	C₂	C₅₃×#2430	1	1	yes	characteristic
835	C₂	C₂×C₅₃×#447	1	1	yes	characteristic
836	C₂	C₅₃×#3013	1	1	yes	characteristic
837	C₂	C₅₃×#3294	1	1	yes	characteristic
838	C₂	C₅₃×#3308	1	1	yes	characteristic
839	C₂	C₅₃×#3334	1	1	yes	characteristic
840	C₂	C₅₃×#3345	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#547	C₂	semidirect
2. C₂×C₅₃×#480	C₂	semidirect
3. C₂×C₅₃×#466	C₂	semidirect
4. C₅₃×#2416	C₂	semidirect
5. C₅₃×#2057	C₂	semidirect
6. C₅₃×#2033	C₂	semidirect
7. C₅₃×#2023	C₂	semidirect
8. C₅₃×#1999	C₂	semidirect
9. C₅₃×#1879	C₂	semidirect
10. C₅₃×#1874	C₂	semidirect
11. C₅₃×#1874	C₂	semidirect
12. C₅₃×#1869	C₂	semidirect
13. C₅₃×#1862	C₂	semidirect
14. C₅₃×#1852	C₂	semidirect
15. C₂×C₅₃×#340	C₂	semidirect
103. #121×C₅₃	D₄	semidirect
119. C₂×C₄⋊C₄×C₅₃	D₄	semidirect
184. C₂×D₄×C₅₃	D₈	semidirect
234. C₂×C₈×C₅₃	#41	semidirect
252. C₄⋊C₄×C₅₃	#41	semidirect
360. #25533	C₅₃	direct (N × H)
410. C₂×#547	C₂×C₅₃	semidirect
411. C₂×#480	C₂×C₅₃	semidirect
412. C₂×#466	C₂×C₅₃	semidirect
413. #2416	C₂×C₅₃	semidirect
414. #2057	C₂×C₅₃	semidirect
415. #2033	C₂×C₅₃	semidirect
416. #2023	C₂×C₅₃	semidirect
417. #1999	C₂×C₅₃	semidirect
418. #1879	C₂×C₅₃	semidirect
419. #1874	C₂×C₅₃	semidirect
420. #1874	C₂×C₅₃	semidirect
421. #1869	C₂×C₅₃	semidirect
422. #1862	C₂×C₅₃	semidirect
423. #1852	C₂×C₅₃	semidirect
424. C₂×#340	C₂×C₅₃	semidirect
483. C₅₃	#25533	direct (N × H)
524. #121	D₄×C₅₃	semidirect
540. C₂×C₄⋊C₄	D₄×C₅₃	semidirect
605. C₂×D₄	D₈×C₅₃	semidirect
655. C₂×C₈	#41×C₅₃	semidirect
673. C₄⋊C₄	#41×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×#547	2
C₂×C₅₃×#480	2
C₂×C₅₃×#466	2
C₅₃×#2416	2
C₅₃×#2057	2
C₅₃×#2033	2
C₅₃×#2023	2
C₅₃×#1999	2
C₅₃×#1879	2
C₅₃×#1874	2
C₅₃×#1869	2
C₅₃×#1862	2
C₅₃×#1852	2
C₂×C₅₃×#340	2
#25533	53

Subgroups — C53×#25533 #27233045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#25533 #27233045