Subgroups — C₅₃×#62205 #27269717

Order 13568.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3345	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3335	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3316	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3301	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3263	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3244	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3125	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3084	C₂	1	2	yes	maximal, complemented
22	C₂×C₅₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#563	—	2	2	no	—
25	C₅₃×#559	—	2	1	no	—
26	C₅₃×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
28	C₅₃×#557	C₂²	1	1	yes	characteristic
29	C₅₃×#556	C₂²	1	1	yes	characteristic
30	C₅₃×#554	—	2	1	no	—
31	C₅₃×#554	C₂²	1	1	yes	characteristic
32	C₅₃×#554	C₂²	1	2	yes	—
33	C₅₃×#553	C₂²	1	2	yes	—
34	C₅₃×#550	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₅₃	—	2	1	no	—
36	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₅₃×#548	—	2	1	no	—
38	C₅₃×#548	C₂²	1	2	yes	—
39	C₅₃×#547	—	2	2	no	—
40	C₅₃×#547	C₂²	1	2	yes	—
41	C₅₃×#547	C₂²	1	1	yes	characteristic
42	C₅₃×#544	C₂²	1	2	yes	—
43	C₅₃×#542	—	2	2	no	—
44	C₅₃×#542	C₂²	1	2	yes	—
45	C₅₃×#542	C₂²	1	2	yes	—
46	C₅₃×#541	—	2	1	no	—
47	C₅₃×#539	—	2	2	no	—
48	C₅₃×#536	—	2	1	no	—
49	C₅₃×#532	—	2	1	no	—
50	C₅₃×#532	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
52	C₅₃×#529	—	2	1	no	—
53	C₅₃×#529	C₂²	1	1	yes	characteristic
54	C₅₃×#529	C₂²	1	1	yes	characteristic
55	C₅₃×#520	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	—
58	C₅₃×#498	C₂²	1	1	yes	characteristic
59	C₅₃×#498	C₂²	1	1	yes	characteristic
60	C₅₃×#498	C₂²	1	2	yes	—
61	C₅₃×#489	C₂²	1	2	yes	—
62	C₅₃×#488	C₂²	1	2	yes	—
63	C₅₃×#486	C₂²	1	1	yes	characteristic
64	C₅₃×#486	C₂²	1	1	yes	characteristic
65	C₅₃×#485	C₂²	1	2	yes	—
66	C₅₃×#483	C₂²	1	2	yes	—
67	C₅₃×#483	C₂²	1	1	yes	characteristic
68	C₅₃×#483	C₂²	1	2	yes	—
69	C₅₃×#482	C₂²	1	2	yes	—
70	C₅₃×#481	C₂²	1	2	yes	—
71	C₅₃×#481	C₂²	1	2	yes	—
72	C₅₃×#481	C₂²	1	2	yes	—
73	C₅₃×#481	C₂²	1	2	yes	—
74	C₅₃×#480	C₂²	1	1	yes	characteristic
75	C₅₃×#479	C₂²	1	1	yes	characteristic
76	C₅₃×#479	C₂²	1	2	yes	—
77	C₅₃×#479	C₂²	1	1	yes	characteristic
78	C₅₃×#478	C₂²	1	2	yes	—
79	C₅₃×#478	C₂²	1	2	yes	—
80	C₅₃×#477	C₂²	1	1	yes	characteristic
81	C₅₃×#476	C₂²	1	2	yes	—
82	C₅₃×#476	C₂²	1	2	yes	—
83	C₅₃×#476	C₂²	1	1	yes	characteristic
84	C₅₃×#476	C₂²	1	2	yes	—
85	C₅₃×#476	C₂²	1	2	yes	—
86	C₅₃×#475	C₂²	1	2	yes	—
87	C₅₃×#475	C₂²	1	2	yes	—
88	C₅₃×#475	C₂²	1	1	yes	characteristic
89	C₅₃×#475	C₂²	1	2	yes	—
90	C₅₃×#475	C₂²	1	1	yes	characteristic
91	C₅₃×#475	C₂²	1	1	yes	characteristic
92	C₅₃×#475	C₂²	1	2	yes	—
93	C₅₃×#475	C₂²	1	1	yes	characteristic
94	C₅₃×#470	C₂²	1	2	yes	—
95	C₅₃×#469	C₂²	1	2	yes	—
96	C₅₃×#466	C₂²	1	2	yes	—
97	C₅₃×#465	C₂²	1	2	yes	—
98	C₅₃×#465	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	—
100	C₅₃×#464	C₂²	1	1	yes	characteristic
101	C₅₃×#464	C₂²	1	2	yes	—
102	C₅₃×#464	C₂²	1	1	yes	characteristic
103	C₅₃×#463	C₂²	1	2	yes	—
104	C₅₃×#463	C₂²	1	2	yes	—
105	C₅₃×#460	C₂²	1	1	yes	characteristic
106	C₅₃×#459	C₂²	1	1	yes	characteristic
107	C₅₃×#452	C₂²	1	2	yes	—
108	C₅₃×#451	C₂²	1	1	yes	characteristic
109	C₅₃×#449	C₂²	1	2	yes	—
110	C₅₃×#448	C₂²	1	1	yes	characteristic
111	C₅₃×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
113	C₅₃×#442	C₂²	1	2	yes	—
114	C₅₃×#441	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
121	C₅₃×#436	C₂²	1	1	yes	characteristic
122	C₅₃×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₅₃	C₂²	1	2	yes	—
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
125	C₅₃×#433	C₂²	1	2	yes	—
126	C₅₃×#431	C₂²	1	1	yes	characteristic
127	C₅₃×#428	C₂²	1	2	yes	—
128	C₂×#106×C₅₃	C₂²	1	2	yes	—
129	C₂×#106×C₅₃	C₂²	1	2	yes	—
130	C₅₃×#424	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#417	C₂²	1	2	yes	—
133	C₅₃×#416	C₂²	1	2	yes	—
134	C₂×#103×C₅₃	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	—	2	2	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	C₂³	1	2	yes	—
139	C₂²×Q₈×C₅₃	—	2	1	no	—
140	C₂²×Q₈×C₅₃	—	2	1	no	—
141	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×D₈×C₅₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
150	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₅₃	—	2	1	no	—
152	C₄⋊Q₈×C₅₃	—	2	2	no	—
153	C₄⋊Q₈×C₅₃	—	2	2	no	—
154	C₄⋊Q₈×C₅₃	—	2	1	no	—
155	C₄⋊Q₈×C₅₃	—	2	1	no	—
156	C₄⋊Q₈×C₅₃	—	2	1	no	—
157	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
163	#127×C₅₃	—	2	1	no	—
164	#127×C₅₃	C₂³	1	1	yes	characteristic
165	#126×C₅₃	—	2	2	no	—
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	—	2	1	no	—
170	#126×C₅₃	D₄	1	2	yes	—
171	#125×C₅₃	—	2	1	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	—	2	2	no	—
174	#125×C₅₃	—	2	2	no	—
175	#125×C₅₃	D₄	1	1	yes	characteristic
176	#125×C₅₃	C₂³	1	2	yes	—
177	#125×C₅₃	C₂³	1	1	yes	characteristic
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	—	2	2	no	—
181	#124×C₅₃	—	2	1	no	—
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	—	2	1	no	—
184	#124×C₅₃	D₄	1	1	yes	characteristic
185	#124×C₅₃	C₂³	1	2	yes	—
186	#124×C₅₃	C₂³	1	1	yes	characteristic
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	2	no	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	1	no	—
195	#123×C₅₃	D₄	1	2	yes	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	1	no	—
198	C₂²⋊Q₈×C₅₃	—	2	1	no	—
199	C₂²⋊Q₈×C₅₃	—	2	2	no	—
200	C₂²⋊Q₈×C₅₃	—	2	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	2	no	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	2	no	—
207	C₂²⋊Q₈×C₅₃	—	2	2	no	—
208	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	2	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	D₄	1	1	yes	characteristic
217	#121×C₅₃	C₂³	1	1	yes	characteristic
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	2	yes	—
220	#121×C₅₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₅₃	—	2	1	no	—
222	C₄×Q₈×C₅₃	—	2	1	no	—
223	C₄×Q₈×C₅₃	—	2	1	no	—
224	C₄×Q₈×C₅₃	—	2	1	no	—
225	C₄×Q₈×C₅₃	—	2	1	no	—
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
232	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	—	2	2	no	—
237	C₄×D₄×C₅₃	—	2	2	no	—
238	C₄×D₄×C₅₃	—	2	2	no	—
239	C₄×D₄×C₅₃	—	2	2	no	—
240	C₄×D₄×C₅₃	—	2	1	no	—
241	C₄×D₄×C₅₃	—	2	1	no	—
242	C₄×D₄×C₅₃	—	2	2	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₅₃	C₂³	1	2	yes	—
248	C₄×D₄×C₅₃	C₂³	1	2	yes	—
249	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
250	#117×C₅₃	—	2	2	no	—
251	#117×C₅₃	—	2	1	no	—
252	#117×C₅₃	C₂³	1	2	yes	—
253	#117×C₅₃	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
261	C₂×C₄²×C₅₃	—	2	1	no	—
262	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	1	yes	characteristic
265	#107×C₅₃	C₂³	1	1	yes	characteristic
266	#106×C₅₃	C₂³	1	2	yes	—
267	#106×C₅₃	C₂³	1	1	yes	characteristic
268	#106×C₅₃	C₂³	1	2	yes	—
269	#106×C₅₃	C₂³	1	2	yes	—
270	#106×C₅₃	C₂³	1	2	yes	—
271	#106×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	1	yes	characteristic
276	#106×C₅₃	C₂³	1	2	yes	—
277	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
278	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	2	yes	—
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	#41×C₅₃	—	2	4	no	—
313	#41×C₅₃	—	4	2	no	—
314	#41×C₅₃	—	8	2	no	—
315	#41×C₅₃	—	8	4	no	—
316	#41×C₅₃	—	8	2	no	—
317	C₂×Q₈×C₅₃	—	2	1	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	2	1	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	—	2	2	no	—
325	C₂×Q₈×C₅₃	—	4	1	no	—
326	C₂×Q₈×C₅₃	—	8	2	no	—
327	C₂×Q₈×C₅₃	—	8	2	no	—
328	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₅₃	—	2	1	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	2	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	1	no	—
338	C₂×D₄×C₅₃	—	2	1	no	—
339	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
342	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	2	2	no	—
347	C₂²×C₄×C₅₃	—	2	2	no	—
348	C₂²×C₄×C₅₃	—	2	2	no	—
349	C₂²×C₄×C₅₃	—	2	1	no	—
350	C₂²×C₄×C₅₃	—	2	2	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	2	no	—
353	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
357	Q₁₆×C₅₃	—	2	2	no	—
358	Q₁₆×C₅₃	—	4	1	no	—
359	SD₁₆×C₅₃	—	2	2	no	—
360	SD₁₆×C₅₃	—	4	2	no	—
361	SD₁₆×C₅₃	—	4	1	no	—
362	D₈×C₅₃	—	4	2	no	—
363	M₁₆×C₅₃	—	4	2	no	—
364	C₂×C₈×C₅₃	—	4	2	no	—
365	C₂×C₈×C₅₃	—	4	2	no	—
366	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
371	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₅₃	—	2	1	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	1	no	—
376	C₄⋊C₄×C₅₃	—	2	1	no	—
377	C₄⋊C₄×C₅₃	—	2	1	no	—
378	C₄⋊C₄×C₅₃	—	2	1	no	—
379	C₄⋊C₄×C₅₃	—	2	2	no	—
380	C₄⋊C₄×C₅₃	—	2	1	no	—
381	C₄⋊C₄×C₅₃	—	2	1	no	—
382	C₄⋊C₄×C₅₃	—	2	2	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	1	no	—
385	C₄⋊C₄×C₅₃	—	2	1	no	—
386	C₄⋊C₄×C₅₃	—	2	1	no	—
387	C₄⋊C₄×C₅₃	—	2	2	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₄⋊C₄×C₅₃	—	2	2	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²⋊C₄×C₅₃	—	2	2	no	—
410	C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	1	no	—
425	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
430	C₄²×C₅₃	—	2	1	no	—
431	C₄²×C₅₃	—	2	1	no	—
432	C₄²×C₅₃	—	2	1	no	—
433	C₄²×C₅₃	—	2	1	no	—
434	C₄²×C₅₃	—	2	2	no	—
435	C₄²×C₅₃	—	2	1	no	—
436	C₄²×C₅₃	—	2	2	no	—
437	C₄²×C₅₃	—	2	2	no	—
438	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₄²×C₅₃	C₂⁴	1	2	yes	—
442	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂³×C₅₃	—	2	2	no	—
444	C₂³×C₅₃	—	2	1	no	—
445	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
446	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
447	Q₈×C₅₃	—	2	2	no	—
448	Q₈×C₅₃	—	2	1	no	—
449	Q₈×C₅₃	—	2	1	no	—
450	Q₈×C₅₃	—	2	1	no	—
451	Q₈×C₅₃	—	2	1	no	—
452	Q₈×C₅₃	—	2	1	no	—
453	Q₈×C₅₃	—	4	2	no	—
454	Q₈×C₅₃	—	4	2	no	—
455	Q₈×C₅₃	—	4	2	no	—
456	Q₈×C₅₃	—	8	2	no	—
457	Q₈×C₅₃	—	8	2	no	—
458	Q₈×C₅₃	—	8	1	no	—
459	Q₈×C₅₃	—	8	2	no	—
460	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
461	D₄×C₅₃	—	2	4	no	—
462	D₄×C₅₃	—	2	2	no	—
463	D₄×C₅₃	—	2	2	no	—
464	D₄×C₅₃	—	2	1	no	—
465	D₄×C₅₃	—	2	2	no	—
466	D₄×C₅₃	—	2	1	no	—
467	D₄×C₅₃	—	4	4	no	—
468	D₄×C₅₃	—	4	2	no	—
469	D₄×C₅₃	—	4	4	no	—
470	D₄×C₅₃	—	4	2	no	—
471	D₄×C₅₃	—	8	1	no	—
472	D₄×C₅₃	—	8	2	no	—
473	D₄×C₅₃	—	8	2	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	2	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	2	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	2	no	—
484	C₂×C₄×C₅₃	—	2	2	no	—
485	C₂×C₄×C₅₃	—	2	2	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	1	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	2	1	no	—
490	C₂×C₄×C₅₃	—	4	4	no	—
491	C₂×C₄×C₅₃	—	4	2	no	—
492	C₂×C₄×C₅₃	—	4	2	no	—
493	C₂×C₄×C₅₃	—	4	2	no	—
494	C₂×C₄×C₅₃	—	8	2	no	—
495	C₂×C₄×C₅₃	—	8	2	no	—
496	C₂×C₄×C₅₃	—	8	2	no	—
497	C₂×C₄×C₅₃	—	8	2	no	—
498	C₂×C₄×C₅₃	—	8	2	no	—
499	C₂×C₄×C₅₃	—	8	2	no	—
500	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
509	C₈×C₅₃	—	2	1	no	—
510	C₈×C₅₃	—	2	1	no	—
511	C₈×C₅₃	—	2	1	no	—
512	C₈×C₅₃	—	2	2	no	—
513	C₈×C₅₃	—	2	2	no	—
514	C₈×C₅₃	—	2	1	no	—
515	#62205	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂²×C₅₃	—	2	1	no	—
517	C₂²×C₅₃	—	2	1	no	—
518	C₂²×C₅₃	—	2	2	no	—
519	C₂²×C₅₃	—	2	2	no	—
520	C₂²×C₅₃	—	2	2	no	—
521	C₂²×C₅₃	—	4	2	no	—
522	C₂²×C₅₃	—	4	1	no	—
523	C₂²×C₅₃	—	4	1	no	—
524	C₂²×C₅₃	—	4	2	no	—
525	C₂²×C₅₃	—	4	1	no	—
526	C₂²×C₅₃	—	4	2	no	—
527	C₂²×C₅₃	#577	1	2	yes	—
528	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
529	C₄×C₅₃	—	2	2	no	—
530	C₄×C₅₃	—	2	1	no	—
531	C₄×C₅₃	—	2	2	no	—
532	C₄×C₅₃	—	2	1	no	—
533	C₄×C₅₃	—	2	1	no	—
534	C₄×C₅₃	—	2	1	no	—
535	C₄×C₅₃	—	2	2	no	—
536	C₄×C₅₃	—	2	2	no	—
537	C₄×C₅₃	—	4	1	no	—
538	C₄×C₅₃	—	4	1	no	—
539	C₄×C₅₃	—	4	1	no	—
540	C₄×C₅₃	—	4	1	no	—
541	C₄×C₅₃	—	4	1	no	—
542	C₄×C₅₃	—	4	2	no	—
543	C₄×C₅₃	—	4	2	no	—
544	C₄×C₅₃	—	4	2	no	—
545	C₄×C₅₃	—	4	1	no	—
546	C₄×C₅₃	#577	1	2	yes	—
547	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	C₄×C₅₃	#585	1	1	yes	characteristic
549	#3552	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3522	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#3387	C₂×C₅₃	1	1	yes	characteristic, complemented
552	Q₈×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
553	#3373	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#3365	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#3356	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3345	C₂×C₅₃	1	2	yes	complemented
557	#3335	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#3335	C₂×C₅₃	1	2	yes	complemented
559	#3332	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3316	C₂×C₅₃	1	2	yes	complemented
561	#3304	C₂×C₅₃	1	1	yes	characteristic, complemented
562	#3301	C₂×C₅₃	1	2	yes	complemented
563	#3263	C₂×C₅₃	1	2	yes	complemented
564	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3244	C₂×C₅₃	1	2	yes	complemented
566	#3227	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#3125	C₂×C₅₃	1	2	yes	complemented
568	#3108	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3084	C₂×C₅₃	1	2	yes	complemented
570	C₂×#475	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#2994	C₂×C₅₃	1	1	yes	characteristic, complemented
572	C₂×C₅₃	—	2	2	no	—
573	C₂×C₅₃	—	4	2	no	—
574	C₂×C₅₃	—	8	2	no	—
575	C₂×C₅₃	—	8	1	no	—
576	C₂×C₅₃	#3489	1	1	yes	characteristic
577	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
578	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
579	#563	—	2	2	no	—
580	#559	—	2	1	no	—
581	#559	C₂²×C₅₃	1	1	yes	characteristic
582	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
583	#557	C₂²×C₅₃	1	1	yes	characteristic
584	#556	C₂²×C₅₃	1	1	yes	characteristic
585	#554	—	2	1	no	—
586	#554	C₂²×C₅₃	1	1	yes	characteristic
587	#554	C₂²×C₅₃	1	2	yes	—
588	#553	C₂²×C₅₃	1	2	yes	—
589	#550	C₂²×C₅₃	1	1	yes	characteristic
590	D₄×Q₈	—	2	1	no	—
591	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
592	#548	—	2	1	no	—
593	#548	C₂²×C₅₃	1	2	yes	—
594	#547	—	2	2	no	—
595	#547	C₂²×C₅₃	1	1	yes	characteristic
596	#547	C₂²×C₅₃	1	2	yes	—
597	#544	C₂²×C₅₃	1	2	yes	—
598	#542	—	2	2	no	—
599	#542	C₂²×C₅₃	1	2	yes	—
600	#542	C₂²×C₅₃	1	2	yes	—
601	#541	—	2	1	no	—
602	#539	—	2	2	no	—
603	#536	—	2	1	no	—
604	#532	—	2	1	no	—
605	#532	C₂²×C₅₃	1	1	yes	characteristic
606	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
607	#529	—	2	1	no	—
608	#529	C₂²×C₅₃	1	1	yes	characteristic
609	#529	C₂²×C₅₃	1	1	yes	characteristic
610	#520	C₂²×C₅₃	1	2	yes	—
611	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
612	#501	C₂²×C₅₃	1	2	yes	—
613	#498	C₂²×C₅₃	1	2	yes	—
614	#498	C₂²×C₅₃	1	1	yes	characteristic
615	#498	C₂²×C₅₃	1	1	yes	characteristic
616	#489	C₂²×C₅₃	1	2	yes	—
617	#488	C₂²×C₅₃	1	2	yes	—
618	#486	C₂²×C₅₃	1	1	yes	characteristic
619	#486	C₂²×C₅₃	1	1	yes	characteristic
620	#485	C₂²×C₅₃	1	2	yes	—
621	#483	C₂²×C₅₃	1	1	yes	characteristic
622	#483	C₂²×C₅₃	1	2	yes	—
623	#483	C₂²×C₅₃	1	2	yes	—
624	#482	C₂²×C₅₃	1	2	yes	—
625	#481	C₂²×C₅₃	1	2	yes	—
626	#481	C₂²×C₅₃	1	2	yes	—
627	#481	C₂²×C₅₃	1	2	yes	—
628	#481	C₂²×C₅₃	1	2	yes	—
629	#480	C₂²×C₅₃	1	1	yes	characteristic
630	#479	C₂²×C₅₃	1	1	yes	characteristic
631	#479	C₂²×C₅₃	1	2	yes	—
632	#479	C₂²×C₅₃	1	1	yes	characteristic
633	#478	C₂²×C₅₃	1	2	yes	—
634	#478	C₂²×C₅₃	1	2	yes	—
635	#477	C₂²×C₅₃	1	1	yes	characteristic
636	#476	C₂²×C₅₃	1	2	yes	—
637	#476	C₂²×C₅₃	1	1	yes	characteristic
638	#476	C₂²×C₅₃	1	2	yes	—
639	#476	C₂²×C₅₃	1	2	yes	—
640	#476	C₂²×C₅₃	1	2	yes	—
641	#475	C₂²×C₅₃	1	1	yes	characteristic
642	#475	C₂²×C₅₃	1	1	yes	characteristic
643	#475	C₂²×C₅₃	1	2	yes	—
644	#475	C₂²×C₅₃	1	1	yes	characteristic
645	#475	C₂²×C₅₃	1	1	yes	characteristic
646	#475	C₂²×C₅₃	1	2	yes	—
647	#475	C₂²×C₅₃	1	2	yes	—
648	#475	C₂²×C₅₃	1	2	yes	—
649	#470	C₂²×C₅₃	1	2	yes	—
650	#469	C₂²×C₅₃	1	2	yes	—
651	#466	C₂²×C₅₃	1	2	yes	—
652	#465	C₂²×C₅₃	1	2	yes	—
653	#465	C₂²×C₅₃	1	2	yes	—
654	#465	C₂²×C₅₃	1	2	yes	—
655	#464	C₂²×C₅₃	1	1	yes	characteristic
656	#464	C₂²×C₅₃	1	1	yes	characteristic
657	#464	C₂²×C₅₃	1	2	yes	—
658	#463	C₂²×C₅₃	1	2	yes	—
659	#463	C₂²×C₅₃	1	2	yes	—
660	#460	C₂²×C₅₃	1	1	yes	characteristic
661	#459	C₂²×C₅₃	1	1	yes	characteristic
662	#452	C₂²×C₅₃	1	2	yes	—
663	#451	C₂²×C₅₃	1	1	yes	characteristic
664	#449	C₂²×C₅₃	1	2	yes	—
665	#448	C₂²×C₅₃	1	1	yes	characteristic
666	#446	C₂²×C₅₃	1	1	yes	characteristic
667	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
668	#442	C₂²×C₅₃	1	2	yes	—
669	#441	C₂²×C₅₃	1	2	yes	—
670	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
671	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
675	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
676	#436	C₂²×C₅₃	1	1	yes	characteristic
677	#435	C₂²×C₅₃	1	2	yes	—
678	C₈×D₄	C₂²×C₅₃	1	2	yes	—
679	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
680	#433	C₂²×C₅₃	1	2	yes	—
681	#431	C₂²×C₅₃	1	1	yes	characteristic
682	#428	C₂²×C₅₃	1	2	yes	—
683	C₂×#106	C₂²×C₅₃	1	2	yes	—
684	C₂×#106	C₂²×C₅₃	1	2	yes	—
685	#424	C₂²×C₅₃	1	2	yes	—
686	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
687	#417	C₂²×C₅₃	1	2	yes	—
688	#416	C₂²×C₅₃	1	2	yes	—
689	C₂×#103	C₂²×C₅₃	1	2	yes	—
690	C₅₃	#62205	1	1	yes	characteristic, direct product factor, Sylow
691	C₂×#41	—	2	2	no	—
692	C₂×#41	—	2	1	no	—
693	C₂×#41	—	2	1	no	—
694	C₂×#41	C₂³×C₅₃	1	2	yes	—
695	C₂²×Q₈	—	2	1	no	—
696	C₂²×Q₈	—	2	1	no	—
697	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
698	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
699	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
700	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
702	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
703	C₂×D₈	C₂³×C₅₃	1	2	yes	—
704	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
705	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
706	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	1	no	—
709	C₄⋊Q₈	—	2	2	no	—
710	C₄⋊Q₈	—	2	2	no	—
711	C₄⋊Q₈	—	2	1	no	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
714	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
718	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
719	#127	—	2	1	no	—
720	#127	C₂³×C₅₃	1	1	yes	characteristic
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	1	no	—
726	#126	D₄×C₅₃	1	2	yes	—
727	#125	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	D₄×C₅₃	1	1	yes	characteristic
732	#125	C₂³×C₅₃	1	1	yes	characteristic
733	#125	C₂³×C₅₃	1	2	yes	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	1	no	—
740	#124	D₄×C₅₃	1	1	yes	characteristic
741	#124	C₂³×C₅₃	1	1	yes	characteristic
742	#124	C₂³×C₅₃	1	2	yes	—
743	#123	—	2	1	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	D₄×C₅₃	1	2	yes	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	1	no	—
771	#121	—	2	2	no	—
772	#121	D₄×C₅₃	1	1	yes	characteristic
773	#121	C₂³×C₅₃	1	1	yes	characteristic
774	#121	C₂³×C₅₃	1	2	yes	—
775	#121	C₂³×C₅₃	1	2	yes	—
776	#121	C₂³×C₅₃	1	2	yes	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
787	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
789	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	C₂³×C₅₃	1	2	yes	—
801	C₄×D₄	C₂³×C₅₃	1	2	yes	—
802	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₅₃	1	2	yes	—
804	C₄×D₄	C₂³×C₅₃	1	2	yes	—
805	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
806	#117	—	2	2	no	—
807	#117	—	2	1	no	—
808	#117	C₂³×C₅₃	1	2	yes	—
809	#117	C₂³×C₅₃	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	—	2	2	no	—
813	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
815	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
816	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
817	C₂×C₄²	—	2	1	no	—
818	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
819	#107	C₂³×C₅₃	1	1	yes	characteristic
820	#107	C₂³×C₅₃	1	2	yes	—
821	#107	C₂³×C₅₃	1	1	yes	characteristic
822	#106	C₂³×C₅₃	1	2	yes	—
823	#106	C₂³×C₅₃	1	1	yes	characteristic
824	#106	C₂³×C₅₃	1	2	yes	—
825	#106	C₂³×C₅₃	1	2	yes	—
826	#106	C₂³×C₅₃	1	2	yes	—
827	#106	C₂³×C₅₃	1	2	yes	—
828	#106	C₂³×C₅₃	1	2	yes	—
829	#106	C₂³×C₅₃	1	2	yes	—
830	#106	C₂³×C₅₃	1	2	yes	—
831	#106	C₂³×C₅₃	1	1	yes	characteristic
832	#106	C₂³×C₅₃	1	2	yes	—
833	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
834	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
838	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
840	#103	C₂³×C₅₃	1	2	yes	—
841	#103	C₂³×C₅₃	1	2	yes	—
842	#103	C₂³×C₅₃	1	2	yes	—
843	#103	C₂³×C₅₃	1	2	yes	—
844	#103	C₂³×C₅₃	1	1	yes	characteristic
845	#103	C₂³×C₅₃	1	1	yes	characteristic
846	#103	C₂³×C₅₃	1	1	yes	characteristic
847	#103	C₂³×C₅₃	1	1	yes	characteristic
848	#103	C₂³×C₅₃	1	1	yes	characteristic
849	#103	C₂³×C₅₃	1	1	yes	characteristic
850	#103	C₂³×C₅₃	1	2	yes	—
851	#102	C₂³×C₅₃	1	2	yes	—
852	#102	C₂³×C₅₃	1	2	yes	—
853	#102	C₂³×C₅₃	1	2	yes	—
854	#102	C₂³×C₅₃	1	2	yes	—
855	#102	C₂³×C₅₃	1	1	yes	characteristic
856	#102	C₂³×C₅₃	1	2	yes	—
857	#102	C₂³×C₅₃	1	2	yes	—
858	#102	C₂³×C₅₃	1	1	yes	characteristic
859	#102	C₂³×C₅₃	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
861	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
862	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
864	#97	C₂³×C₅₃	1	2	yes	—
865	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
866	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₅₃	1	2	yes	—
868	#41	—	2	4	no	—
869	#41	—	4	2	no	—
870	#41	—	8	2	no	—
871	#41	—	8	4	no	—
872	#41	—	8	2	no	—
873	C₂×Q₈	—	2	1	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	4	1	no	—
882	C₂×Q₈	—	8	2	no	—
883	C₂×Q₈	—	8	2	no	—
884	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
885	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
887	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
896	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
897	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
898	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
910	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
913	Q₁₆	—	2	2	no	—
914	Q₁₆	—	4	1	no	—
915	SD₁₆	—	2	2	no	—
916	SD₁₆	—	4	1	no	—
917	SD₁₆	—	4	2	no	—
918	D₈	—	4	2	no	—
919	M₁₆	—	4	2	no	—
920	C₂×C₈	—	4	2	no	—
921	C₂×C₈	—	4	2	no	—
922	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
925	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
927	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
953	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
954	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
956	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
958	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
984	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
985	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
995	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
996	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
997	C₄²	C₂⁴×C₅₃	1	2	yes	—
998	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1002	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1003	Q₈	—	2	2	no	—
1004	Q₈	—	2	1	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	1	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	8	2	no	—
1013	Q₈	—	8	2	no	—
1014	Q₈	—	8	1	no	—
1015	Q₈	—	8	2	no	—
1016	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
1017	D₄	—	2	4	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	2	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	4	4	no	—
1024	D₄	—	4	2	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	8	1	no	—
1028	D₄	—	8	2	no	—
1029	D₄	—	8	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	—	8	2	no	—
1052	C₂×C₄	—	8	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1057	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1058	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1059	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1061	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	1	no	—
1068	C₈	—	2	2	no	—
1069	C₈	—	2	2	no	—
1070	C₈	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	C₅₃×#577	1	2	yes	—
1083	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1084	C₄	—	2	2	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	C₅₃×#577	1	2	yes	—
1102	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1103	C₄	C₅₃×#585	1	1	yes	characteristic
1104	C₂	—	2	2	no	—
1105	C₂	—	4	2	no	—
1106	C₂	—	8	2	no	—
1107	C₂	—	8	1	no	—
1108	C₂	C₅₃×#3489	1	1	yes	characteristic
1109	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1110	C₂	C₂×C₅₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3552	C₂	semidirect
2. C₅₃×#3522	C₂	semidirect
3. C₅₃×#3387	C₂	semidirect
4. Q₈×SD₁₆×C₅₃	C₂	semidirect
5. C₅₃×#3373	C₂	semidirect
6. C₅₃×#3365	C₂	semidirect
7. C₅₃×#3356	C₂	semidirect
8. C₅₃×#3345	C₂	semidirect
9. C₅₃×#3335	C₂	semidirect
10. C₅₃×#3335	C₂	semidirect
11. C₅₃×#3332	C₂	semidirect
12. C₅₃×#3316	C₂	semidirect
13. C₅₃×#3304	C₂	semidirect
14. C₅₃×#3301	C₂	semidirect
15. C₅₃×#3263	C₂	semidirect
16. C₅₃×#3247	C₂	semidirect
17. C₅₃×#3244	C₂	semidirect
18. C₅₃×#3227	C₂	semidirect
19. C₅₃×#3125	C₂	semidirect
20. C₅₃×#3108	C₂	semidirect
21. C₅₃×#3084	C₂	semidirect
22. C₂×C₅₃×#475	C₂	semidirect
23. C₅₃×#2994	C₂	semidirect
515. #62205	C₅₃	direct (N × H)
549. #3552	C₂×C₅₃	semidirect
550. #3522	C₂×C₅₃	semidirect
551. #3387	C₂×C₅₃	semidirect
552. Q₈×SD₁₆	C₂×C₅₃	semidirect
553. #3373	C₂×C₅₃	semidirect
554. #3365	C₂×C₅₃	semidirect
555. #3356	C₂×C₅₃	semidirect
556. #3345	C₂×C₅₃	semidirect
557. #3335	C₂×C₅₃	semidirect
558. #3335	C₂×C₅₃	semidirect
559. #3332	C₂×C₅₃	semidirect
560. #3316	C₂×C₅₃	semidirect
561. #3304	C₂×C₅₃	semidirect
562. #3301	C₂×C₅₃	semidirect
563. #3263	C₂×C₅₃	semidirect
564. #3247	C₂×C₅₃	semidirect
565. #3244	C₂×C₅₃	semidirect
566. #3227	C₂×C₅₃	semidirect
567. #3125	C₂×C₅₃	semidirect
568. #3108	C₂×C₅₃	semidirect
569. #3084	C₂×C₅₃	semidirect
570. C₂×#475	C₂×C₅₃	semidirect
571. #2994	C₂×C₅₃	semidirect
690. C₅₃	#62205	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×#3552	2
C₅₃×#3522	2
C₅₃×#3387	2
Q₈×SD₁₆×C₅₃	2
C₅₃×#3373	2
C₅₃×#3365	2
C₅₃×#3356	2
C₅₃×#3345	2
C₅₃×#3335	2
C₅₃×#3332	2
C₅₃×#3316	2
C₅₃×#3304	2
C₅₃×#3301	2
C₅₃×#3263	2
C₅₃×#3247	2
C₅₃×#3244	2
C₅₃×#3227	2
C₅₃×#3125	2
C₅₃×#3108	2
C₅₃×#3084	2
C₂×C₅₃×#475	2
C₅₃×#2994	2
#62205	53

Subgroups — C53×#62205 #27269717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62205 #27269717