Subgroups — C₅₃×#25156 #27232668

Order 13568.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
7	C₅₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
28	C₅₃×#461	—	2	4	no	—
29	C₅₃×#450	—	2	4	no	—
30	C₅₃×#450	—	2	4	no	—
31	C₄×SD₁₆×C₅₃	—	2	4	no	—
32	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#102×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×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#398	—	2	1	no	—
47	C₅₃×#396	—	2	1	no	—
48	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#390	C₂²	1	1	yes	characteristic
50	C₅₃×#390	C₂²	1	1	yes	characteristic
51	C₅₃×#389	—	2	1	no	—
52	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#388	—	2	1	no	—
54	C₅₃×#386	—	2	1	no	—
55	C₅₃×#386	—	2	1	no	—
56	C₅₃×#380	C₂²	1	1	yes	characteristic
57	C₅₃×#379	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
59	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₅₃	—	2	1	no	—
64	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₅₃	—	2	2	no	—
67	C₂²×D₄×C₅₃	—	2	2	no	—
68	C₂²×D₄×C₅₃	—	2	2	no	—
69	C₂²×D₄×C₅₃	—	2	2	no	—
70	C₂²×D₄×C₅₃	—	2	1	no	—
71	C₂²×D₄×C₅₃	—	4	1	no	—
72	C₂²×D₄×C₅₃	—	4	1	no	—
73	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅₃	—	2	1	no	—
76	C₂³×C₄×C₅₃	—	2	1	no	—
77	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
78	C₂×SD₁₆×C₅₃	—	2	2	no	—
79	C₂×SD₁₆×C₅₃	—	2	2	no	—
80	C₂×SD₁₆×C₅₃	—	2	2	no	—
81	C₂×SD₁₆×C₅₃	—	2	2	no	—
82	C₂×SD₁₆×C₅₃	—	2	2	no	—
83	C₂×SD₁₆×C₅₃	—	2	2	no	—
84	C₂×SD₁₆×C₅₃	—	2	2	no	—
85	C₂×SD₁₆×C₅₃	—	2	2	no	—
86	C₂×SD₁₆×C₅₃	—	2	2	no	—
87	C₂×SD₁₆×C₅₃	—	4	1	no	—
88	C₂×SD₁₆×C₅₃	—	4	1	no	—
89	C₂×SD₁₆×C₅₃	D₄	1	4	yes	—
90	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₄⋊Q₈×C₅₃	—	2	2	no	—
95	C₄⋊Q₈×C₅₃	—	4	1	no	—
96	C₂²⋊Q₈×C₅₃	—	2	2	no	—
97	C₂²⋊Q₈×C₅₃	—	2	2	no	—
98	C₂²⋊Q₈×C₅₃	—	4	1	no	—
99	C₂²⋊Q₈×C₅₃	—	4	1	no	—
100	C₄×Q₈×C₅₃	—	2	2	no	—
101	C₄×Q₈×C₅₃	—	4	1	no	—
102	C₄×D₄×C₅₃	—	2	2	no	—
103	C₄×D₄×C₅₃	—	2	2	no	—
104	C₄×D₄×C₅₃	—	4	1	no	—
105	C₄×D₄×C₅₃	—	4	1	no	—
106	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
108	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
109	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
110	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
111	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
112	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
126	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₅₃	—	2	1	no	—
129	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
131	#106×C₅₃	—	2	2	no	—
132	#106×C₅₃	—	4	1	no	—
133	C₄⋊C₈×C₅₃	—	2	2	no	—
134	#103×C₅₃	—	2	2	no	—
135	#103×C₅₃	—	2	2	no	—
136	#103×C₅₃	—	2	2	no	—
137	#103×C₅₃	—	4	1	no	—
138	#102×C₅₃	—	2	2	no	—
139	#102×C₅₃	—	2	2	no	—
140	#102×C₅₃	—	2	2	no	—
141	#102×C₅₃	D₄	1	4	yes	—
142	C₂²⋊C₈×C₅₃	—	2	2	no	—
143	C₂²⋊C₈×C₅₃	—	2	2	no	—
144	C₄×C₈×C₅₃	—	2	2	no	—
145	#95×C₅₃	—	2	1	no	—
146	#95×C₅₃	—	2	1	no	—
147	#95×C₅₃	—	2	1	no	—
148	#95×C₅₃	—	2	1	no	—
149	#95×C₅₃	D₄	1	1	yes	characteristic
150	#95×C₅₃	D₄	1	1	yes	characteristic
151	C₂⁴×C₅₃	—	2	1	no	—
152	C₂⁴×C₅₃	—	2	4	no	—
153	C₂⁴×C₅₃	—	2	1	no	—
154	C₂⁴×C₅₃	—	4	2	no	—
155	C₂⁴×C₅₃	—	4	2	no	—
156	C₂⁴×C₅₃	—	4	2	no	—
157	C₂⁴×C₅₃	—	4	2	no	—
158	C₂⁴×C₅₃	—	8	1	no	—
159	C₂⁴×C₅₃	—	8	1	no	—
160	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₅₃	—	2	1	no	—
162	C₂×Q₈×C₅₃	—	2	1	no	—
163	C₂×Q₈×C₅₃	—	2	1	no	—
164	C₂×Q₈×C₅₃	—	2	1	no	—
165	C₂×Q₈×C₅₃	—	2	1	no	—
166	C₂×Q₈×C₅₃	—	2	1	no	—
167	C₂×Q₈×C₅₃	—	2	1	no	—
168	C₂×Q₈×C₅₃	—	2	1	no	—
169	C₂×Q₈×C₅₃	—	2	1	no	—
170	C₂×Q₈×C₅₃	—	2	1	no	—
171	C₂×Q₈×C₅₃	—	2	1	no	—
172	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
173	C₂×D₄×C₅₃	—	2	4	no	—
174	C₂×D₄×C₅₃	—	2	1	no	—
175	C₂×D₄×C₅₃	—	2	1	no	—
176	C₂×D₄×C₅₃	—	2	1	no	—
177	C₂×D₄×C₅₃	—	2	1	no	—
178	C₂×D₄×C₅₃	—	2	1	no	—
179	C₂×D₄×C₅₃	—	2	1	no	—
180	C₂×D₄×C₅₃	—	2	1	no	—
181	C₂×D₄×C₅₃	—	2	1	no	—
182	C₂×D₄×C₅₃	—	4	2	no	—
183	C₂×D₄×C₅₃	—	4	2	no	—
184	C₂×D₄×C₅₃	—	4	4	no	—
185	C₂×D₄×C₅₃	—	4	4	no	—
186	C₂×D₄×C₅₃	—	4	4	no	—
187	C₂×D₄×C₅₃	—	4	4	no	—
188	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₅₃	#41	1	2	yes	—
191	C₂×D₄×C₅₃	#41	1	2	yes	—
192	C₂²×C₄×C₅₃	—	2	1	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	—	4	2	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	—	8	1	no	—
209	C₂²×C₄×C₅₃	—	8	1	no	—
210	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
216	SD₁₆×C₅₃	—	2	8	no	—
217	SD₁₆×C₅₃	—	4	4	no	—
218	SD₁₆×C₅₃	—	4	4	no	—
219	SD₁₆×C₅₃	—	4	4	no	—
220	C₂×C₈×C₅₃	—	2	1	no	—
221	C₂×C₈×C₅₃	—	2	1	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	C₂×D₄	1	2	yes	—
231	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
232	C₄⋊C₄×C₅₃	—	2	1	no	—
233	C₄⋊C₄×C₅₃	—	2	1	no	—
234	C₄⋊C₄×C₅₃	—	2	1	no	—
235	C₄⋊C₄×C₅₃	—	2	1	no	—
236	C₄⋊C₄×C₅₃	—	2	1	no	—
237	C₄⋊C₄×C₅₃	—	2	1	no	—
238	C₄⋊C₄×C₅₃	—	2	1	no	—
239	C₄⋊C₄×C₅₃	—	4	2	no	—
240	C₄⋊C₄×C₅₃	—	4	2	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	C₂×D₄	1	2	yes	—
246	C₂²⋊C₄×C₅₃	—	4	1	no	—
247	C₂²⋊C₄×C₅₃	—	4	2	no	—
248	C₂²⋊C₄×C₅₃	—	4	2	no	—
249	C₂²⋊C₄×C₅₃	—	4	2	no	—
250	C₂²⋊C₄×C₅₃	—	4	2	no	—
251	C₂²⋊C₄×C₅₃	—	4	2	no	—
252	C₂²⋊C₄×C₅₃	—	4	2	no	—
253	C₂²⋊C₄×C₅₃	—	4	2	no	—
254	C₂²⋊C₄×C₅₃	—	8	1	no	—
255	C₂²⋊C₄×C₅₃	—	8	1	no	—
256	C₂²⋊C₄×C₅₃	SD₁₆	1	4	yes	complemented
257	C₄²×C₅₃	—	2	1	no	—
258	C₄²×C₅₃	—	2	1	no	—
259	C₄²×C₅₃	—	2	1	no	—
260	C₄²×C₅₃	—	2	1	no	—
261	C₄²×C₅₃	—	4	2	no	—
262	C₂³×C₅₃	—	2	1	no	—
263	C₂³×C₅₃	—	2	2	no	—
264	C₂³×C₅₃	—	2	1	no	—
265	C₂³×C₅₃	—	2	1	no	—
266	C₂³×C₅₃	—	2	2	no	—
267	C₂³×C₅₃	—	2	2	no	—
268	C₂³×C₅₃	—	2	1	no	—
269	C₂³×C₅₃	—	2	1	no	—
270	C₂³×C₅₃	—	2	1	no	—
271	C₂³×C₅₃	—	2	2	no	—
272	C₂³×C₅₃	—	4	8	no	—
273	C₂³×C₅₃	—	4	8	no	—
274	C₂³×C₅₃	—	4	1	no	—
275	C₂³×C₅₃	—	4	1	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	—	8	4	no	—
285	C₂³×C₅₃	—	8	4	no	—
286	C₂³×C₅₃	—	8	4	no	—
287	C₂³×C₅₃	—	8	4	no	—
288	C₂³×C₅₃	—	8	4	no	—
289	C₂³×C₅₃	C₂×SD₁₆	1	2	yes	—
290	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
291	Q₈×C₅₃	—	2	2	no	—
292	Q₈×C₅₃	—	2	2	no	—
293	Q₈×C₅₃	—	4	1	no	—
294	Q₈×C₅₃	—	4	1	no	—
295	Q₈×C₅₃	—	4	1	no	—
296	Q₈×C₅₃	—	4	1	no	—
297	Q₈×C₅₃	—	4	1	no	—
298	Q₈×C₅₃	—	4	1	no	—
299	D₄×C₅₃	—	2	2	no	—
300	D₄×C₅₃	—	2	2	no	—
301	D₄×C₅₃	—	2	2	no	—
302	D₄×C₅₃	—	2	2	no	—
303	D₄×C₅₃	—	2	2	no	—
304	D₄×C₅₃	—	4	8	no	—
305	D₄×C₅₃	—	4	1	no	—
306	D₄×C₅₃	—	4	1	no	—
307	D₄×C₅₃	#121	1	4	yes	—
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	1	no	—
313	C₂×C₄×C₅₃	—	2	1	no	—
314	C₂×C₄×C₅₃	—	2	1	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	2	2	no	—
317	C₂×C₄×C₅₃	—	2	1	no	—
318	C₂×C₄×C₅₃	—	2	1	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	1	no	—
323	C₂×C₄×C₅₃	—	4	1	no	—
324	C₂×C₄×C₅₃	—	4	1	no	—
325	C₂×C₄×C₅₃	—	4	1	no	—
326	C₂×C₄×C₅₃	—	4	1	no	—
327	C₂×C₄×C₅₃	—	4	1	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	1	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	—	8	4	no	—
344	C₂×C₄×C₅₃	—	8	4	no	—
345	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
346	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
347	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
353	C₈×C₅₃	—	2	2	no	—
354	C₈×C₅₃	—	2	2	no	—
355	C₈×C₅₃	—	4	1	no	—
356	C₈×C₅₃	—	4	1	no	—
357	#25156	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₂²×C₅₃	—	2	2	no	—
359	C₂²×C₅₃	—	2	4	no	—
360	C₂²×C₅₃	—	2	2	no	—
361	C₂²×C₅₃	—	2	2	no	—
362	C₂²×C₅₃	—	4	2	no	—
363	C₂²×C₅₃	—	4	1	no	—
364	C₂²×C₅₃	—	4	2	no	—
365	C₂²×C₅₃	—	4	1	no	—
366	C₂²×C₅₃	—	4	1	no	—
367	C₂²×C₅₃	—	4	2	no	—
368	C₂²×C₅₃	—	4	1	no	—
369	C₂²×C₅₃	—	4	2	no	—
370	C₂²×C₅₃	—	4	2	no	—
371	C₂²×C₅₃	—	4	2	no	—
372	C₂²×C₅₃	—	4	2	no	—
373	C₂²×C₅₃	—	4	2	no	—
374	C₂²×C₅₃	—	4	2	no	—
375	C₂²×C₅₃	—	8	16	no	—
376	C₂²×C₅₃	—	8	1	no	—
377	C₂²×C₅₃	—	8	1	no	—
378	C₂²×C₅₃	—	8	1	no	—
379	C₂²×C₅₃	—	8	1	no	—
380	C₂²×C₅₃	#525	1	1	yes	characteristic
381	C₂²×C₅₃	D₄²	1	1	yes	characteristic
382	C₂²×C₅₃	D₄²	1	1	yes	characteristic
383	C₂²×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
384	C₂²×C₅₃	#575	1	1	yes	characteristic
385	C₂²×C₅₃	#577	1	1	yes	characteristic
386	C₂²×C₅₃	#577	1	1	yes	characteristic
387	C₄×C₅₃	—	2	2	no	—
388	C₄×C₅₃	—	2	2	no	—
389	C₄×C₅₃	—	4	1	no	—
390	C₄×C₅₃	—	4	2	no	—
391	C₄×C₅₃	—	4	1	no	—
392	C₄×C₅₃	—	4	2	no	—
393	C₄×C₅₃	—	4	1	no	—
394	C₄×C₅₃	—	8	1	no	—
395	C₄×C₅₃	—	8	1	no	—
396	C₄×C₅₃	—	8	1	no	—
397	C₄×C₅₃	—	8	1	no	—
398	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
399	C₄×C₅₃	#538	1	1	yes	characteristic
400	C₄×C₅₃	#546	1	1	yes	characteristic
401	C₄×C₅₃	#546	1	1	yes	characteristic
402	C₂×#461	C₂×C₅₃	1	1	yes	characteristic, complemented
403	C₂×#450	C₂×C₅₃	1	1	yes	characteristic
404	C₂×#450	C₂×C₅₃	1	1	yes	characteristic
405	C₂×C₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
406	#2429	C₂×C₅₃	1	1	yes	characteristic, complemented
407	D₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic
408	#2065	C₂×C₅₃	1	1	yes	characteristic, complemented
409	#2035	C₂×C₅₃	1	1	yes	characteristic, complemented
410	#2035	C₂×C₅₃	1	1	yes	characteristic, complemented
411	#2013	C₂×C₅₃	1	1	yes	characteristic, complemented
412	#1968	C₂×C₅₃	1	1	yes	characteristic, complemented
413	#1923	C₂×C₅₃	1	1	yes	characteristic, complemented
414	#1880	C₂×C₅₃	1	1	yes	characteristic, complemented
415	#1877	C₂×C₅₃	1	1	yes	characteristic, complemented
416	#1864	C₂×C₅₃	1	1	yes	characteristic, complemented
417	C₂×C₅₃	—	4	2	no	—
418	C₂×C₅₃	—	4	4	no	—
419	C₂×C₅₃	—	8	2	no	—
420	C₂×C₅₃	#2424	1	1	yes	characteristic
421	C₂×C₅₃	#3101	1	1	yes	characteristic
422	C₂×C₅₃	#3123	1	1	yes	characteristic
423	C₂×C₅₃	#3267	1	1	yes	characteristic
424	C₂×C₅₃	#3275	1	1	yes	characteristic
425	C₂×C₅₃	D₄×SD₁₆	1	1	yes	characteristic
426	C₂×C₅₃	D₄×SD₁₆	1	1	yes	characteristic
427	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
428	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
429	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
430	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
431	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
433	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
434	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
435	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
436	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
438	C₂²×C₂²⋊C₄	—	2	1	no	—
439	#461	—	2	4	no	—
440	#450	—	2	4	no	—
441	#450	—	2	4	no	—
442	C₄×SD₁₆	—	2	4	no	—
443	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
444	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
445	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
446	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
447	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
448	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
449	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
450	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
451	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
452	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
453	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
454	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
455	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
456	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
457	#398	—	2	1	no	—
458	#396	—	2	1	no	—
459	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
460	#390	C₂²×C₅₃	1	1	yes	characteristic
461	#390	C₂²×C₅₃	1	1	yes	characteristic
462	#389	—	2	1	no	—
463	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
464	#388	—	2	1	no	—
465	#386	—	2	1	no	—
466	#386	—	2	1	no	—
467	#380	C₂²×C₅₃	1	1	yes	characteristic
468	#379	—	2	1	no	—
469	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
470	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
471	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
472	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
473	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
474	C₅₃	#25156	1	1	yes	characteristic, direct product factor, Sylow
475	C₂⁵	—	2	1	no	—
476	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	—	2	2	no	—
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	4	1	no	—
484	C₂²×D₄	—	4	1	no	—
485	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
486	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
490	C₂×SD₁₆	—	2	2	no	—
491	C₂×SD₁₆	—	2	2	no	—
492	C₂×SD₁₆	—	2	2	no	—
493	C₂×SD₁₆	—	2	2	no	—
494	C₂×SD₁₆	—	2	2	no	—
495	C₂×SD₁₆	—	2	2	no	—
496	C₂×SD₁₆	—	2	2	no	—
497	C₂×SD₁₆	—	2	2	no	—
498	C₂×SD₁₆	—	2	2	no	—
499	C₂×SD₁₆	—	4	1	no	—
500	C₂×SD₁₆	—	4	1	no	—
501	C₂×SD₁₆	D₄×C₅₃	1	4	yes	—
502	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
506	C₄⋊Q₈	—	2	2	no	—
507	C₄⋊Q₈	—	4	1	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	2	no	—
510	C₂²⋊Q₈	—	4	1	no	—
511	C₂²⋊Q₈	—	4	1	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	4	1	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	4	1	no	—
517	C₄×D₄	—	4	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	4	4	no	—
538	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
540	C₂×C₄²	—	2	1	no	—
541	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
543	#106	—	2	2	no	—
544	#106	—	4	1	no	—
545	C₄⋊C₈	—	2	2	no	—
546	#103	—	2	2	no	—
547	#103	—	2	2	no	—
548	#103	—	2	2	no	—
549	#103	—	4	1	no	—
550	#102	—	2	2	no	—
551	#102	—	2	2	no	—
552	#102	—	2	2	no	—
553	#102	D₄×C₅₃	1	4	yes	—
554	C₂²⋊C₈	—	2	2	no	—
555	C₂²⋊C₈	—	2	2	no	—
556	C₄×C₈	—	2	2	no	—
557	#95	—	2	1	no	—
558	#95	—	2	1	no	—
559	#95	—	2	1	no	—
560	#95	—	2	1	no	—
561	#95	D₄×C₅₃	1	1	yes	characteristic
562	#95	D₄×C₅₃	1	1	yes	characteristic
563	C₂⁴	—	2	1	no	—
564	C₂⁴	—	2	4	no	—
565	C₂⁴	—	2	1	no	—
566	C₂⁴	—	4	2	no	—
567	C₂⁴	—	4	2	no	—
568	C₂⁴	—	4	2	no	—
569	C₂⁴	—	4	2	no	—
570	C₂⁴	—	8	1	no	—
571	C₂⁴	—	8	1	no	—
572	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
585	C₂×D₄	—	2	4	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	—	4	2	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
601	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
602	C₂×D₄	#41×C₅₃	1	2	yes	—
603	C₂×D₄	#41×C₅₃	1	2	yes	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
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	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	8	1	no	—
621	C₂²×C₄	—	8	1	no	—
622	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
628	SD₁₆	—	2	8	no	—
629	SD₁₆	—	4	4	no	—
630	SD₁₆	—	4	4	no	—
631	SD₁₆	—	4	4	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
643	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
658	C₂²⋊C₄	—	4	1	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	8	1	no	—
667	C₂²⋊C₄	—	8	1	no	—
668	C₂²⋊C₄	SD₁₆×C₅₃	1	4	yes	complemented
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	2	1	no	—
673	C₄²	—	4	2	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	4	8	no	—
685	C₂³	—	4	8	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	4	1	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	8	4	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	4	no	—
699	C₂³	—	8	4	no	—
700	C₂³	—	8	4	no	—
701	C₂³	C₂×SD₁₆×C₅₃	1	2	yes	—
702	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	4	1	no	—
706	Q₈	—	4	1	no	—
707	Q₈	—	4	1	no	—
708	Q₈	—	4	1	no	—
709	Q₈	—	4	1	no	—
710	Q₈	—	4	1	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	2	no	—
716	D₄	—	4	8	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	#121×C₅₃	1	4	yes	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	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	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	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	—	8	4	no	—
756	C₂×C₄	—	8	4	no	—
757	C₂×C₄	C₂×SD₁₆×C₅₃	1	2	yes	—
758	C₂×C₄	C₂×SD₁₆×C₅₃	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
761	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
762	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
763	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
764	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
765	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₈	—	4	1	no	—
768	C₈	—	4	1	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	8	16	no	—
787	C₂²	—	8	1	no	—
788	C₂²	—	8	1	no	—
789	C₂²	—	8	1	no	—
790	C₂²	—	8	1	no	—
791	C₂²	C₅₃×#525	1	1	yes	characteristic
792	C₂²	D₄²×C₅₃	1	1	yes	characteristic
793	C₂²	D₄²×C₅₃	1	1	yes	characteristic
794	C₂²	C₂²×SD₁₆×C₅₃	1	1	yes	characteristic
795	C₂²	C₅₃×#575	1	1	yes	characteristic
796	C₂²	C₅₃×#577	1	1	yes	characteristic
797	C₂²	C₅₃×#577	1	1	yes	characteristic
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	1	no	—
805	C₄	—	8	1	no	—
806	C₄	—	8	1	no	—
807	C₄	—	8	1	no	—
808	C₄	—	8	1	no	—
809	C₄	C₂×#121×C₅₃	1	1	yes	characteristic
810	C₄	C₅₃×#538	1	1	yes	characteristic
811	C₄	C₅₃×#546	1	1	yes	characteristic
812	C₄	C₅₃×#546	1	1	yes	characteristic
813	C₂	—	4	2	no	—
814	C₂	—	4	4	no	—
815	C₂	—	8	2	no	—
816	C₂	C₅₃×#2424	1	1	yes	characteristic
817	C₂	C₅₃×#3101	1	1	yes	characteristic
818	C₂	C₅₃×#3123	1	1	yes	characteristic
819	C₂	C₅₃×#3267	1	1	yes	characteristic
820	C₂	C₅₃×#3275	1	1	yes	characteristic
821	C₂	D₄×SD₁₆×C₅₃	1	1	yes	characteristic
822	C₂	D₄×SD₁₆×C₅₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#461	C₂	semidirect
4. C₂×C₄×SD₁₆×C₅₃	C₂	semidirect
5. C₅₃×#2429	C₂	semidirect
7. C₅₃×#2065	C₂	semidirect
8. C₅₃×#2035	C₂	semidirect
9. C₅₃×#2035	C₂	semidirect
10. C₅₃×#2013	C₂	semidirect
11. C₅₃×#1968	C₂	semidirect
12. C₅₃×#1923	C₂	semidirect
13. C₅₃×#1880	C₂	semidirect
14. C₅₃×#1877	C₂	semidirect
15. C₅₃×#1864	C₂	semidirect
21. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
24. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
32. C₂×#106×C₅₃	C₂²	semidirect
33. C₂×#106×C₅₃	C₂²	semidirect
34. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
35. C₂×#103×C₅₃	C₂²	semidirect
36. C₂×#103×C₅₃	C₂²	semidirect
37. C₂×#103×C₅₃	C₂²	semidirect
38. C₂×#103×C₅₃	C₂²	semidirect
45. C₂×C₄×C₈×C₅₃	C₂²	semidirect
48. C₅₃×#391	C₂²	semidirect
52. C₅₃×#389	C₂²	semidirect
59. C₅₃×#340	C₂²	semidirect
60. C₅₃×#340	C₂²	semidirect
61. C₅₃×#336	C₂²	semidirect
62. C₅₃×#336	C₂²	semidirect
256. C₂²⋊C₄×C₅₃	SD₁₆	semidirect
357. #25156	C₅₃	direct (N × H)
402. C₂×#461	C₂×C₅₃	semidirect
405. C₂×C₄×SD₁₆	C₂×C₅₃	semidirect
406. #2429	C₂×C₅₃	semidirect
408. #2065	C₂×C₅₃	semidirect
409. #2035	C₂×C₅₃	semidirect
410. #2035	C₂×C₅₃	semidirect
411. #2013	C₂×C₅₃	semidirect
412. #1968	C₂×C₅₃	semidirect
413. #1923	C₂×C₅₃	semidirect
414. #1880	C₂×C₅₃	semidirect
415. #1877	C₂×C₅₃	semidirect
416. #1864	C₂×C₅₃	semidirect
432. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
435. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
443. C₂×#106	C₂²×C₅₃	semidirect
444. C₂×#106	C₂²×C₅₃	semidirect
445. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
446. C₂×#103	C₂²×C₅₃	semidirect
447. C₂×#103	C₂²×C₅₃	semidirect
448. C₂×#103	C₂²×C₅₃	semidirect
449. C₂×#103	C₂²×C₅₃	semidirect
456. C₂×C₄×C₈	C₂²×C₅₃	semidirect
459. #391	C₂²×C₅₃	semidirect
463. #389	C₂²×C₅₃	semidirect
470. #340	C₂²×C₅₃	semidirect
471. #340	C₂²×C₅₃	semidirect
472. #336	C₂²×C₅₃	semidirect
473. #336	C₂²×C₅₃	semidirect
474. C₅₃	#25156	direct (N × H)
668. C₂²⋊C₄	SD₁₆×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×#461	2
C₂×C₅₃×#450	2
C₂×C₄×SD₁₆×C₅₃	2
C₅₃×#2429	2
D₄×C₂²⋊C₄×C₅₃	2
C₅₃×#2065	2
C₅₃×#2035	2
C₅₃×#2013	2
C₅₃×#1968	2
C₅₃×#1923	2
C₅₃×#1880	2
C₅₃×#1877	2
C₅₃×#1864	2
#25156	53

Subgroups — C53×#25156 #27232668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#25156 #27232668