Subgroups — C₅₃×#36760 #27244272

Order 13568.

1662 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2798	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2783	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2772	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2754	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2725	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2725	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2721	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2716	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2626	C₂	1	1	yes	maximal, characteristic
12	C₅₃×#2626	C₂	1	1	yes	maximal, characteristic
13	C₅₃×#2505	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2480	C₂	1	2	yes	maximal
15	C₅₃×#2480	C₂	1	2	yes	maximal
16	C₅₃×#2473	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×#126×C₅₃	C₂²	1	2	yes	—
22	C₂×#126×C₅₃	C₂²	1	2	yes	—
23	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
24	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#400	C₂²	1	2	yes	complemented
33	C₅₃×#400	C₂²	1	2	yes	complemented
34	C₅₃×#400	C₂²	1	2	yes	complemented
35	C₅₃×#400	C₂²	1	2	yes	complemented
36	C₅₃×#399	C₂²	1	2	yes	—
37	C₅₃×#399	C₂²	1	2	yes	—
38	C₅₃×#398	C₂²	1	2	yes	complemented
39	C₅₃×#398	C₂²	1	2	yes	complemented
40	C₅₃×#398	C₂²	1	2	yes	complemented
41	C₅₃×#398	C₂²	1	2	yes	complemented
42	C₅₃×#397	C₂²	1	2	yes	—
43	C₅₃×#397	C₂²	1	2	yes	—
44	C₅₃×#397	C₂²	1	2	yes	—
45	C₅₃×#397	C₂²	1	2	yes	—
46	C₅₃×#397	C₂²	1	2	yes	—
47	C₅₃×#397	C₂²	1	2	yes	—
48	C₅₃×#396	C₂²	1	2	yes	—
49	C₅₃×#396	C₂²	1	2	yes	—
50	C₅₃×#396	C₂²	1	2	yes	—
51	C₅₃×#396	C₂²	1	2	yes	—
52	C₅₃×#396	C₂²	1	2	yes	—
53	C₅₃×#396	C₂²	1	2	yes	—
54	C₅₃×#393	C₂²	1	2	yes	—
55	C₅₃×#393	C₂²	1	2	yes	—
56	C₅₃×#391	C₂²	1	2	yes	complemented
57	C₅₃×#391	C₂²	1	2	yes	complemented
58	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#389	C₂²	1	2	yes	complemented
61	C₅₃×#389	C₂²	1	2	yes	complemented
62	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#389	C₂²	1	2	yes	complemented
64	C₅₃×#389	C₂²	1	2	yes	complemented
65	C₅₃×#389	C₂²	1	2	yes	complemented
66	C₅₃×#389	C₂²	1	2	yes	complemented
67	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#388	C₂²	1	2	yes	—
69	C₅₃×#388	C₂²	1	2	yes	—
70	C₅₃×#388	C₂²	1	2	yes	—
71	C₅₃×#388	C₂²	1	2	yes	—
72	C₅₃×#388	C₂²	1	2	yes	—
73	C₅₃×#388	C₂²	1	2	yes	—
74	C₅₃×#388	C₂²	1	2	yes	—
75	C₅₃×#388	C₂²	1	2	yes	—
76	C₅₃×#388	C₂²	1	2	yes	—
77	C₅₃×#388	C₂²	1	2	yes	—
78	C₅₃×#387	C₂²	1	2	yes	complemented
79	C₅₃×#387	C₂²	1	2	yes	complemented
80	C₅₃×#387	C₂²	1	2	yes	complemented
81	C₅₃×#387	C₂²	1	2	yes	complemented
82	C₅₃×#387	C₂²	1	2	yes	complemented
83	C₅₃×#387	C₂²	1	2	yes	complemented
84	C₅₃×#387	C₂²	1	2	yes	complemented
85	C₅₃×#387	C₂²	1	2	yes	complemented
86	C₅₃×#387	C₂²	1	2	yes	complemented
87	C₅₃×#387	C₂²	1	2	yes	complemented
88	C₅₃×#385	C₂²	1	2	yes	—
89	C₅₃×#385	C₂²	1	2	yes	—
90	C₅₃×#385	C₂²	1	2	yes	—
91	C₅₃×#385	C₂²	1	2	yes	—
92	C₅₃×#385	C₂²	1	2	yes	—
93	C₅₃×#385	C₂²	1	2	yes	—
94	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#382	C₂²	1	2	yes	complemented
96	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#380	C₂²	1	2	yes	—
98	C₅₃×#380	C₂²	1	2	yes	—
99	C₅₃×#380	C₂²	1	1	yes	characteristic
100	C₅₃×#380	C₂²	1	1	yes	characteristic
101	C₅₃×#379	C₂²	1	2	yes	—
102	C₅₃×#379	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
105	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
106	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
107	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₅₃	—	4	2	no	—
117	#126×C₅₃	—	4	4	no	—
118	#126×C₅₃	—	4	4	no	—
119	#125×C₅₃	—	4	2	no	—
120	#125×C₅₃	—	4	4	no	—
121	C₂²⋊Q₈×C₅₃	—	2	4	no	—
122	C₂²⋊Q₈×C₅₃	—	2	4	no	—
123	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
151	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
152	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
153	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₅₃	—	4	2	no	—
172	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
180	#95×C₅₃	C₂³	1	2	yes	—
181	#95×C₅₃	C₂³	1	2	yes	—
182	#95×C₅₃	C₂³	1	2	yes	—
183	#95×C₅₃	C₂³	1	2	yes	—
184	#95×C₅₃	C₂³	1	2	yes	—
185	#95×C₅₃	C₂³	1	2	yes	—
186	#95×C₅₃	C₂³	1	2	yes	—
187	#95×C₅₃	C₂³	1	2	yes	—
188	#95×C₅₃	C₂³	1	2	yes	—
189	#95×C₅₃	C₂³	1	2	yes	—
190	#95×C₅₃	C₂³	1	2	yes	—
191	#95×C₅₃	C₂³	1	2	yes	—
192	#95×C₅₃	C₂³	1	2	yes	—
193	#95×C₅₃	C₂³	1	2	yes	—
194	#95×C₅₃	C₂³	1	2	yes	—
195	#95×C₅₃	C₂³	1	2	yes	—
196	#95×C₅₃	C₂³	1	2	yes	—
197	#95×C₅₃	C₂³	1	2	yes	—
198	#95×C₅₃	C₂³	1	2	yes	—
199	#95×C₅₃	C₂³	1	2	yes	—
200	#95×C₅₃	C₂³	1	2	yes	—
201	#95×C₅₃	C₂³	1	2	yes	—
202	#95×C₅₃	C₂³	1	2	yes	—
203	#95×C₅₃	C₂³	1	2	yes	—
204	#95×C₅₃	C₂³	1	2	yes	—
205	#95×C₅₃	C₂³	1	2	yes	—
206	C₂⁴×C₅₃	—	2	2	no	—
207	C₂⁴×C₅₃	—	2	2	no	—
208	C₂⁴×C₅₃	—	2	2	no	—
209	C₂⁴×C₅₃	—	4	1	no	—
210	C₂⁴×C₅₃	—	4	1	no	—
211	C₂⁴×C₅₃	—	4	1	no	—
212	C₂⁴×C₅₃	—	4	1	no	—
213	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
214	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
215	C₂×Q₈×C₅₃	—	2	2	no	—
216	C₂×Q₈×C₅₃	—	2	2	no	—
217	C₂×Q₈×C₅₃	—	4	1	no	—
218	C₂×Q₈×C₅₃	—	4	1	no	—
219	C₂×Q₈×C₅₃	—	4	1	no	—
220	C₂×Q₈×C₅₃	—	4	1	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	—	2	2	no	—
226	C₂²×C₄×C₅₃	—	2	2	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	—	4	1	no	—
229	C₂²×C₄×C₅₃	—	4	1	no	—
230	C₂²×C₄×C₅₃	—	4	1	no	—
231	C₂²×C₄×C₅₃	—	4	1	no	—
232	C₂²×C₄×C₅₃	—	4	1	no	—
233	C₂²×C₄×C₅₃	—	4	1	no	—
234	C₂²×C₄×C₅₃	—	4	1	no	—
235	C₂²×C₄×C₅₃	—	4	1	no	—
236	C₂²×C₄×C₅₃	—	4	1	no	—
237	C₂²×C₄×C₅₃	—	4	1	no	—
238	C₂²×C₄×C₅₃	#41	1	4	yes	—
239	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₄⋊C₄×C₅₃	—	2	4	no	—
257	C₄⋊C₄×C₅₃	—	2	4	no	—
258	C₄⋊C₄×C₅₃	—	2	2	no	—
259	C₄⋊C₄×C₅₃	—	2	2	no	—
260	C₄⋊C₄×C₅₃	—	2	4	no	—
261	C₄⋊C₄×C₅₃	—	2	4	no	—
262	C₄⋊C₄×C₅₃	—	2	4	no	—
263	C₄⋊C₄×C₅₃	—	2	4	no	—
264	C₄⋊C₄×C₅₃	—	2	4	no	—
265	C₄⋊C₄×C₅₃	—	4	2	no	—
266	C₄⋊C₄×C₅₃	—	4	1	no	—
267	C₄⋊C₄×C₅₃	—	4	1	no	—
268	C₄⋊C₄×C₅₃	—	4	2	no	—
269	C₄⋊C₄×C₅₃	—	4	2	no	—
270	C₄⋊C₄×C₅₃	—	4	2	no	—
271	C₄⋊C₄×C₅₃	—	4	2	no	—
272	C₄⋊C₄×C₅₃	—	4	2	no	—
273	C₄⋊C₄×C₅₃	—	4	1	no	—
274	C₄⋊C₄×C₅₃	—	4	1	no	—
275	C₄⋊C₄×C₅₃	—	4	2	no	—
276	C₄⋊C₄×C₅₃	—	4	2	no	—
277	C₄⋊C₄×C₅₃	—	4	2	no	—
278	C₄⋊C₄×C₅₃	—	4	2	no	—
279	C₄⋊C₄×C₅₃	—	4	2	no	—
280	C₄⋊C₄×C₅₃	—	4	2	no	—
281	C₄⋊C₄×C₅₃	—	4	2	no	—
282	C₂²⋊C₄×C₅₃	—	2	4	no	—
283	C₂²⋊C₄×C₅₃	—	2	4	no	—
284	C₂²⋊C₄×C₅₃	—	2	4	no	—
285	C₂²⋊C₄×C₅₃	—	2	4	no	—
286	C₂²⋊C₄×C₅₃	—	2	4	no	—
287	C₂²⋊C₄×C₅₃	—	2	4	no	—
288	C₂²⋊C₄×C₅₃	—	2	4	no	—
289	C₂²⋊C₄×C₅₃	—	2	4	no	—
290	C₂²⋊C₄×C₅₃	—	4	2	no	—
291	C₂²⋊C₄×C₅₃	—	4	2	no	—
292	C₂²⋊C₄×C₅₃	—	4	2	no	—
293	C₂²⋊C₄×C₅₃	—	4	2	no	—
294	C₂²⋊C₄×C₅₃	—	4	2	no	—
295	C₂²⋊C₄×C₅₃	—	4	2	no	—
296	C₂²⋊C₄×C₅₃	—	4	2	no	—
297	C₂²⋊C₄×C₅₃	—	4	2	no	—
298	C₂²⋊C₄×C₅₃	—	4	2	no	—
299	C₂²⋊C₄×C₅₃	—	4	2	no	—
300	C₄²×C₅₃	—	2	2	no	—
301	C₄²×C₅₃	—	2	2	no	—
302	C₄²×C₅₃	—	4	1	no	—
303	C₄²×C₅₃	—	4	1	no	—
304	C₄²×C₅₃	—	4	2	no	—
305	C₄²×C₅₃	—	4	2	no	—
306	C₄²×C₅₃	—	4	2	no	—
307	C₄²×C₅₃	—	4	2	no	—
308	C₂³×C₅₃	—	2	1	no	—
309	C₂³×C₅₃	—	2	1	no	—
310	C₂³×C₅₃	—	2	1	no	—
311	C₂³×C₅₃	—	2	1	no	—
312	C₂³×C₅₃	—	2	2	no	—
313	C₂³×C₅₃	—	2	2	no	—
314	C₂³×C₅₃	—	2	2	no	—
315	C₂³×C₅₃	—	2	2	no	—
316	C₂³×C₅₃	—	2	2	no	—
317	C₂³×C₅₃	—	2	2	no	—
318	C₂³×C₅₃	—	2	2	no	—
319	C₂³×C₅₃	—	4	4	no	—
320	C₂³×C₅₃	—	4	4	no	—
321	C₂³×C₅₃	—	4	4	no	—
322	C₂³×C₅₃	—	8	2	no	—
323	C₂³×C₅₃	—	8	2	no	—
324	C₂³×C₅₃	—	8	2	no	—
325	C₂³×C₅₃	—	8	2	no	—
326	C₂³×C₅₃	C₂×#41	1	2	yes	—
327	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
328	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
329	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
330	Q₈×C₅₃	—	8	2	no	—
331	Q₈×C₅₃	—	8	2	no	—
332	C₂×C₄×C₅₃	—	2	1	no	—
333	C₂×C₄×C₅₃	—	2	1	no	—
334	C₂×C₄×C₅₃	—	2	1	no	—
335	C₂×C₄×C₅₃	—	2	1	no	—
336	C₂×C₄×C₅₃	—	2	1	no	—
337	C₂×C₄×C₅₃	—	2	1	no	—
338	C₂×C₄×C₅₃	—	2	1	no	—
339	C₂×C₄×C₅₃	—	2	1	no	—
340	C₂×C₄×C₅₃	—	2	2	no	—
341	C₂×C₄×C₅₃	—	2	2	no	—
342	C₂×C₄×C₅₃	—	2	2	no	—
343	C₂×C₄×C₅₃	—	2	2	no	—
344	C₂×C₄×C₅₃	—	2	2	no	—
345	C₂×C₄×C₅₃	—	2	1	no	—
346	C₂×C₄×C₅₃	—	2	1	no	—
347	C₂×C₄×C₅₃	—	2	1	no	—
348	C₂×C₄×C₅₃	—	2	2	no	—
349	C₂×C₄×C₅₃	—	2	2	no	—
350	C₂×C₄×C₅₃	—	2	2	no	—
351	C₂×C₄×C₅₃	—	2	2	no	—
352	C₂×C₄×C₅₃	—	2	2	no	—
353	C₂×C₄×C₅₃	—	2	2	no	—
354	C₂×C₄×C₅₃	—	2	2	no	—
355	C₂×C₄×C₅₃	—	2	2	no	—
356	C₂×C₄×C₅₃	—	2	2	no	—
357	C₂×C₄×C₅₃	—	2	2	no	—
358	C₂×C₄×C₅₃	—	2	2	no	—
359	C₂×C₄×C₅₃	—	2	2	no	—
360	C₂×C₄×C₅₃	—	2	1	no	—
361	C₂×C₄×C₅₃	—	2	1	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	2	2	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	1	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	2	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	4	4	no	—
380	C₂×C₄×C₅₃	—	4	4	no	—
381	C₂×C₄×C₅₃	—	4	4	no	—
382	C₂×C₄×C₅₃	—	4	4	no	—
383	C₂×C₄×C₅₃	—	8	2	no	—
384	C₂×C₄×C₅₃	—	8	2	no	—
385	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
386	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
387	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
388	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
389	#36760	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂²×C₅₃	—	2	2	no	—
391	C₂²×C₅₃	—	2	2	no	—
392	C₂²×C₅₃	—	2	2	no	—
393	C₂²×C₅₃	—	2	2	no	—
394	C₂²×C₅₃	—	2	2	no	—
395	C₂²×C₅₃	—	2	2	no	—
396	C₂²×C₅₃	—	4	2	no	—
397	C₂²×C₅₃	—	4	2	no	—
398	C₂²×C₅₃	—	4	2	no	—
399	C₂²×C₅₃	—	4	2	no	—
400	C₂²×C₅₃	—	4	2	no	—
401	C₂²×C₅₃	—	4	2	no	—
402	C₂²×C₅₃	—	4	2	no	—
403	C₂²×C₅₃	—	8	8	no	—
404	C₂²×C₅₃	#541	1	4	yes	—
405	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
406	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
410	C₂²×C₅₃	#585	1	1	yes	characteristic
411	C₂²×C₅₃	#585	1	1	yes	characteristic
412	C₄×C₅₃	—	2	2	no	—
413	C₄×C₅₃	—	2	2	no	—
414	C₄×C₅₃	—	2	2	no	—
415	C₄×C₅₃	—	2	2	no	—
416	C₄×C₅₃	—	4	2	no	—
417	C₄×C₅₃	—	4	2	no	—
418	C₄×C₅₃	—	4	2	no	—
419	C₄×C₅₃	—	4	2	no	—
420	C₄×C₅₃	—	4	2	no	—
421	C₄×C₅₃	—	4	2	no	—
422	C₄×C₅₃	—	4	1	no	—
423	C₄×C₅₃	—	4	2	no	—
424	C₄×C₅₃	—	4	1	no	—
425	C₄×C₅₃	—	4	2	no	—
426	C₄×C₅₃	—	4	2	no	—
427	C₄×C₅₃	—	4	2	no	—
428	C₄×C₅₃	—	4	2	no	—
429	#2857	C₂×C₅₃	1	1	yes	characteristic, complemented
430	#2851	C₂×C₅₃	1	1	yes	characteristic, complemented
431	#2798	C₂×C₅₃	1	2	yes	complemented
432	#2783	C₂×C₅₃	1	2	yes	complemented
433	#2772	C₂×C₅₃	1	2	yes	complemented
434	#2754	C₂×C₅₃	1	2	yes	complemented
435	#2725	C₂×C₅₃	1	2	yes	complemented
436	#2725	C₂×C₅₃	1	2	yes	complemented
437	#2721	C₂×C₅₃	1	2	yes	complemented
438	#2716	C₂×C₅₃	1	2	yes	complemented
439	#2626	C₂×C₅₃	1	1	yes	characteristic
440	#2626	C₂×C₅₃	1	1	yes	characteristic
441	#2505	C₂×C₅₃	1	2	yes	complemented
442	#2480	C₂×C₅₃	1	2	yes	—
443	#2480	C₂×C₅₃	1	2	yes	—
444	#2473	C₂×C₅₃	1	2	yes	complemented
445	#2329	C₂×C₅₃	1	1	yes	characteristic, complemented
446	#2329	C₂×C₅₃	1	1	yes	characteristic, complemented
447	C₂×#388	C₂×C₅₃	1	1	yes	characteristic
448	C₂×C₅₃	—	2	4	no	—
449	C₂×C₅₃	—	8	2	no	—
450	C₂×C₅₃	C₂×#541	1	1	yes	characteristic
451	C₂×C₅₃	#3505	1	1	yes	characteristic
452	C₂×C₅₃	#3506	1	1	yes	characteristic
453	C₂×C₅₃	#3535	1	1	yes	characteristic
454	C₂×C₅₃	#3536	1	1	yes	characteristic
455	C₂×C₅₃	#3561	1	1	yes	characteristic
456	C₂×C₅₃	#3564	1	1	yes	characteristic
457	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
458	C₂×#126	C₂²×C₅₃	1	2	yes	—
459	C₂×#126	C₂²×C₅₃	1	2	yes	—
460	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
461	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
462	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
463	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
464	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
465	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
466	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
467	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
468	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
469	#400	C₂²×C₅₃	1	2	yes	complemented
470	#400	C₂²×C₅₃	1	2	yes	complemented
471	#400	C₂²×C₅₃	1	2	yes	complemented
472	#400	C₂²×C₅₃	1	2	yes	complemented
473	#399	C₂²×C₅₃	1	2	yes	—
474	#399	C₂²×C₅₃	1	2	yes	—
475	#398	C₂²×C₅₃	1	2	yes	complemented
476	#398	C₂²×C₅₃	1	2	yes	complemented
477	#398	C₂²×C₅₃	1	2	yes	complemented
478	#398	C₂²×C₅₃	1	2	yes	complemented
479	#397	C₂²×C₅₃	1	2	yes	—
480	#397	C₂²×C₅₃	1	2	yes	—
481	#397	C₂²×C₅₃	1	2	yes	—
482	#397	C₂²×C₅₃	1	2	yes	—
483	#397	C₂²×C₅₃	1	2	yes	—
484	#397	C₂²×C₅₃	1	2	yes	—
485	#396	C₂²×C₅₃	1	2	yes	—
486	#396	C₂²×C₅₃	1	2	yes	—
487	#396	C₂²×C₅₃	1	2	yes	—
488	#396	C₂²×C₅₃	1	2	yes	—
489	#396	C₂²×C₅₃	1	2	yes	—
490	#396	C₂²×C₅₃	1	2	yes	—
491	#393	C₂²×C₅₃	1	2	yes	—
492	#393	C₂²×C₅₃	1	2	yes	—
493	#391	C₂²×C₅₃	1	2	yes	complemented
494	#391	C₂²×C₅₃	1	2	yes	complemented
495	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
496	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
497	#389	C₂²×C₅₃	1	2	yes	complemented
498	#389	C₂²×C₅₃	1	2	yes	complemented
499	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
500	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
501	#389	C₂²×C₅₃	1	2	yes	complemented
502	#389	C₂²×C₅₃	1	2	yes	complemented
503	#389	C₂²×C₅₃	1	2	yes	complemented
504	#389	C₂²×C₅₃	1	2	yes	complemented
505	#388	C₂²×C₅₃	1	2	yes	—
506	#388	C₂²×C₅₃	1	2	yes	—
507	#388	C₂²×C₅₃	1	2	yes	—
508	#388	C₂²×C₅₃	1	2	yes	—
509	#388	C₂²×C₅₃	1	2	yes	—
510	#388	C₂²×C₅₃	1	2	yes	—
511	#388	C₂²×C₅₃	1	2	yes	—
512	#388	C₂²×C₅₃	1	2	yes	—
513	#388	C₂²×C₅₃	1	2	yes	—
514	#388	C₂²×C₅₃	1	2	yes	—
515	#387	C₂²×C₅₃	1	2	yes	complemented
516	#387	C₂²×C₅₃	1	2	yes	complemented
517	#387	C₂²×C₅₃	1	2	yes	complemented
518	#387	C₂²×C₅₃	1	2	yes	complemented
519	#387	C₂²×C₅₃	1	2	yes	complemented
520	#387	C₂²×C₅₃	1	2	yes	complemented
521	#387	C₂²×C₅₃	1	2	yes	complemented
522	#387	C₂²×C₅₃	1	2	yes	complemented
523	#387	C₂²×C₅₃	1	2	yes	complemented
524	#387	C₂²×C₅₃	1	2	yes	complemented
525	#385	C₂²×C₅₃	1	2	yes	—
526	#385	C₂²×C₅₃	1	2	yes	—
527	#385	C₂²×C₅₃	1	2	yes	—
528	#385	C₂²×C₅₃	1	2	yes	—
529	#385	C₂²×C₅₃	1	2	yes	—
530	#385	C₂²×C₅₃	1	2	yes	—
531	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
532	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
533	#382	C₂²×C₅₃	1	2	yes	complemented
534	#380	C₂²×C₅₃	1	1	yes	characteristic
535	#380	C₂²×C₅₃	1	1	yes	characteristic
536	#380	C₂²×C₅₃	1	2	yes	—
537	#380	C₂²×C₅₃	1	2	yes	—
538	#379	C₂²×C₅₃	1	2	yes	—
539	#379	C₂²×C₅₃	1	2	yes	—
540	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
541	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
542	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
543	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
544	C₅₃	#36760	1	1	yes	characteristic, direct product factor, Sylow
545	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
547	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
554	C₄⋊Q₈	—	4	2	no	—
555	#126	—	4	4	no	—
556	#126	—	4	4	no	—
557	#125	—	4	2	no	—
558	#125	—	4	4	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂×C₄⋊C₄	—	4	2	no	—
562	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
588	C₂×C₂²⋊C₄	—	2	4	no	—
589	C₂×C₂²⋊C₄	—	4	2	no	—
590	C₂×C₂²⋊C₄	—	4	2	no	—
591	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
609	C₂×C₄²	—	4	2	no	—
610	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
613	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
614	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
615	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
616	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
618	#95	C₂³×C₅₃	1	2	yes	—
619	#95	C₂³×C₅₃	1	2	yes	—
620	#95	C₂³×C₅₃	1	2	yes	—
621	#95	C₂³×C₅₃	1	2	yes	—
622	#95	C₂³×C₅₃	1	2	yes	—
623	#95	C₂³×C₅₃	1	2	yes	—
624	#95	C₂³×C₅₃	1	2	yes	—
625	#95	C₂³×C₅₃	1	2	yes	—
626	#95	C₂³×C₅₃	1	2	yes	—
627	#95	C₂³×C₅₃	1	2	yes	—
628	#95	C₂³×C₅₃	1	2	yes	—
629	#95	C₂³×C₅₃	1	2	yes	—
630	#95	C₂³×C₅₃	1	2	yes	—
631	#95	C₂³×C₅₃	1	2	yes	—
632	#95	C₂³×C₅₃	1	2	yes	—
633	#95	C₂³×C₅₃	1	2	yes	—
634	#95	C₂³×C₅₃	1	2	yes	—
635	#95	C₂³×C₅₃	1	2	yes	—
636	#95	C₂³×C₅₃	1	2	yes	—
637	#95	C₂³×C₅₃	1	2	yes	—
638	#95	C₂³×C₅₃	1	2	yes	—
639	#95	C₂³×C₅₃	1	2	yes	—
640	#95	C₂³×C₅₃	1	2	yes	—
641	#95	C₂³×C₅₃	1	2	yes	—
642	#95	C₂³×C₅₃	1	2	yes	—
643	#95	C₂³×C₅₃	1	2	yes	—
644	C₂⁴	—	2	2	no	—
645	C₂⁴	—	2	2	no	—
646	C₂⁴	—	2	2	no	—
647	C₂⁴	—	4	1	no	—
648	C₂⁴	—	4	1	no	—
649	C₂⁴	—	4	1	no	—
650	C₂⁴	—	4	1	no	—
651	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
652	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	4	1	no	—
656	C₂×Q₈	—	4	1	no	—
657	C₂×Q₈	—	4	1	no	—
658	C₂×Q₈	—	4	1	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	—	4	1	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	#41×C₅₃	1	4	yes	—
677	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	1	no	—
714	C₄⋊C₄	—	4	1	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	4	1	no	—
741	C₄²	—	4	1	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₄²	—	4	2	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	4	no	—
760	C₂³	—	8	2	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	2	no	—
763	C₂³	—	8	2	no	—
764	C₂³	C₂×#41×C₅₃	1	2	yes	—
765	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
766	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
767	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
768	Q₈	—	8	2	no	—
769	Q₈	—	8	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
824	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
825	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
826	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	8	8	no	—
841	C₂²	C₅₃×#541	1	4	yes	—
842	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
843	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
844	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
845	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
846	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
847	C₂²	C₅₃×#585	1	1	yes	characteristic
848	C₂²	C₅₃×#585	1	1	yes	characteristic
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₂	—	2	4	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂×C₅₃×#541	1	1	yes	characteristic
869	C₂	C₅₃×#3505	1	1	yes	characteristic
870	C₂	C₅₃×#3506	1	1	yes	characteristic
871	C₂	C₅₃×#3535	1	1	yes	characteristic
872	C₂	C₅₃×#3536	1	1	yes	characteristic
873	C₂	C₅₃×#3561	1	1	yes	characteristic
874	C₂	C₅₃×#3564	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2857	C₂	semidirect
2. C₅₃×#2851	C₂	semidirect
3. C₅₃×#2798	C₂	semidirect
4. C₅₃×#2783	C₂	semidirect
5. C₅₃×#2772	C₂	semidirect
6. C₅₃×#2754	C₂	semidirect
7. C₅₃×#2725	C₂	semidirect
8. C₅₃×#2725	C₂	semidirect
9. C₅₃×#2721	C₂	semidirect
10. C₅₃×#2716	C₂	semidirect
13. C₅₃×#2505	C₂	semidirect
16. C₅₃×#2473	C₂	semidirect
17. C₅₃×#2329	C₂	semidirect
18. C₅₃×#2329	C₂	semidirect
20. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
23. C₂×#125×C₅₃	C₂²	semidirect
24. C₂×#125×C₅₃	C₂²	semidirect
32. C₅₃×#400	C₂²	semidirect
33. C₅₃×#400	C₂²	semidirect
34. C₅₃×#400	C₂²	semidirect
35. C₅₃×#400	C₂²	semidirect
38. C₅₃×#398	C₂²	semidirect
39. C₅₃×#398	C₂²	semidirect
40. C₅₃×#398	C₂²	semidirect
41. C₅₃×#398	C₂²	semidirect
56. C₅₃×#391	C₂²	semidirect
57. C₅₃×#391	C₂²	semidirect
58. C₅₃×#391	C₂²	semidirect
59. C₅₃×#391	C₂²	semidirect
60. C₅₃×#389	C₂²	semidirect
61. C₅₃×#389	C₂²	semidirect
62. C₅₃×#389	C₂²	semidirect
63. C₅₃×#389	C₂²	semidirect
64. C₅₃×#389	C₂²	semidirect
65. C₅₃×#389	C₂²	semidirect
66. C₅₃×#389	C₂²	semidirect
67. C₅₃×#389	C₂²	semidirect
78. C₅₃×#387	C₂²	semidirect
79. C₅₃×#387	C₂²	semidirect
80. C₅₃×#387	C₂²	semidirect
81. C₅₃×#387	C₂²	semidirect
82. C₅₃×#387	C₂²	semidirect
83. C₅₃×#387	C₂²	semidirect
84. C₅₃×#387	C₂²	semidirect
85. C₅₃×#387	C₂²	semidirect
86. C₅₃×#387	C₂²	semidirect
87. C₅₃×#387	C₂²	semidirect
94. C₅₃×#384	C₂²	semidirect
95. C₅₃×#382	C₂²	semidirect
96. C₅₃×#382	C₂²	semidirect
389. #36760	C₅₃	direct (N × H)
429. #2857	C₂×C₅₃	semidirect
430. #2851	C₂×C₅₃	semidirect
431. #2798	C₂×C₅₃	semidirect
432. #2783	C₂×C₅₃	semidirect
433. #2772	C₂×C₅₃	semidirect
434. #2754	C₂×C₅₃	semidirect
435. #2725	C₂×C₅₃	semidirect
436. #2725	C₂×C₅₃	semidirect
437. #2721	C₂×C₅₃	semidirect
438. #2716	C₂×C₅₃	semidirect
441. #2505	C₂×C₅₃	semidirect
444. #2473	C₂×C₅₃	semidirect
445. #2329	C₂×C₅₃	semidirect
446. #2329	C₂×C₅₃	semidirect
457. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
460. C₂×#125	C₂²×C₅₃	semidirect
461. C₂×#125	C₂²×C₅₃	semidirect
469. #400	C₂²×C₅₃	semidirect
470. #400	C₂²×C₅₃	semidirect
471. #400	C₂²×C₅₃	semidirect
472. #400	C₂²×C₅₃	semidirect
475. #398	C₂²×C₅₃	semidirect
476. #398	C₂²×C₅₃	semidirect
477. #398	C₂²×C₅₃	semidirect
478. #398	C₂²×C₅₃	semidirect
493. #391	C₂²×C₅₃	semidirect
494. #391	C₂²×C₅₃	semidirect
495. #391	C₂²×C₅₃	semidirect
496. #391	C₂²×C₅₃	semidirect
497. #389	C₂²×C₅₃	semidirect
498. #389	C₂²×C₅₃	semidirect
499. #389	C₂²×C₅₃	semidirect
500. #389	C₂²×C₅₃	semidirect
501. #389	C₂²×C₅₃	semidirect
502. #389	C₂²×C₅₃	semidirect
503. #389	C₂²×C₅₃	semidirect
504. #389	C₂²×C₅₃	semidirect
515. #387	C₂²×C₅₃	semidirect
516. #387	C₂²×C₅₃	semidirect
517. #387	C₂²×C₅₃	semidirect
518. #387	C₂²×C₅₃	semidirect
519. #387	C₂²×C₅₃	semidirect
520. #387	C₂²×C₅₃	semidirect
521. #387	C₂²×C₅₃	semidirect
522. #387	C₂²×C₅₃	semidirect
523. #387	C₂²×C₅₃	semidirect
524. #387	C₂²×C₅₃	semidirect
531. #384	C₂²×C₅₃	semidirect
532. #382	C₂²×C₅₃	semidirect
533. #382	C₂²×C₅₃	semidirect
544. C₅₃	#36760	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#2857	2
C₅₃×#2851	2
C₅₃×#2798	2
C₅₃×#2783	2
C₅₃×#2772	2
C₅₃×#2754	2
C₅₃×#2725	2
C₅₃×#2721	2
C₅₃×#2716	2
C₅₃×#2626	2
C₅₃×#2505	2
C₅₃×#2480	2
C₅₃×#2473	2
C₅₃×#2329	2
C₂×C₅₃×#388	2
#36760	53

Subgroups — C53×#36760 #27244272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36760 #27244272