Subgroups — C₅₃×#62186 #27269698

Order 13568.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1126 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×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3355	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3346	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3333	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3257	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3241	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3124	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3083	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#563	—	2	2	no	—
25	C₅₃×#557	C₂²	1	1	yes	characteristic
26	C₅₃×#557	C₂²	1	1	yes	characteristic
27	C₅₃×#556	C₂²	1	1	yes	characteristic
28	C₅₃×#554	C₂²	1	2	yes	—
29	C₅₃×#553	—	2	2	no	—
30	C₅₃×#553	C₂²	1	2	yes	—
31	C₅₃×#553	C₂²	1	2	yes	—
32	C₅₃×#550	—	2	1	no	—
33	C₅₃×#550	C₂²	1	1	yes	characteristic
34	C₅₃×#550	C₂²	1	2	yes	—
35	C₅₃×#550	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₅₃	—	2	1	no	—
37	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#548	—	2	1	no	—
39	C₅₃×#547	—	2	1	no	—
40	C₅₃×#547	C₂²	1	1	yes	characteristic
41	C₅₃×#547	C₂²	1	1	yes	characteristic
42	C₅₃×#544	C₂²	1	2	yes	—
43	C₅₃×#542	C₂²	1	2	yes	—
44	C₅₃×#541	—	2	1	no	—
45	C₅₃×#540	—	2	2	no	—
46	C₅₃×#540	C₂²	1	2	yes	—
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	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	—
58	C₅₃×#500	C₂²	1	1	yes	characteristic
59	C₅₃×#500	C₂²	1	1	yes	characteristic
60	C₅₃×#499	C₂²	1	2	yes	—
61	C₅₃×#490	C₂²	1	2	yes	—
62	C₅₃×#486	C₂²	1	1	yes	characteristic
63	C₅₃×#486	C₂²	1	1	yes	characteristic
64	C₅₃×#486	C₂²	1	2	yes	—
65	C₅₃×#485	C₂²	1	1	yes	characteristic
66	C₅₃×#484	C₂²	1	2	yes	—
67	C₅₃×#482	C₂²	1	2	yes	—
68	C₅₃×#482	C₂²	1	2	yes	—
69	C₅₃×#482	C₂²	1	1	yes	characteristic
70	C₅₃×#481	C₂²	1	2	yes	—
71	C₅₃×#480	C₂²	1	2	yes	—
72	C₅₃×#480	C₂²	1	2	yes	—
73	C₅₃×#480	C₂²	1	2	yes	—
74	C₅₃×#480	C₂²	1	2	yes	—
75	C₅₃×#479	C₂²	1	2	yes	—
76	C₅₃×#479	C₂²	1	2	yes	—
77	C₅₃×#479	C₂²	1	1	yes	characteristic
78	C₅₃×#478	C₂²	1	1	yes	characteristic
79	C₅₃×#478	C₂²	1	2	yes	—
80	C₅₃×#478	C₂²	1	2	yes	—
81	C₅₃×#478	C₂²	1	2	yes	—
82	C₅₃×#477	C₂²	1	2	yes	—
83	C₅₃×#477	C₂²	1	2	yes	—
84	C₅₃×#476	C₂²	1	2	yes	—
85	C₅₃×#475	C₂²	1	1	yes	characteristic
86	C₅₃×#475	C₂²	1	1	yes	characteristic
87	C₅₃×#475	C₂²	1	1	yes	characteristic
88	C₅₃×#474	C₂²	1	2	yes	—
89	C₅₃×#474	C₂²	1	2	yes	—
90	C₅₃×#474	C₂²	1	1	yes	characteristic
91	C₅₃×#474	C₂²	1	1	yes	characteristic
92	C₅₃×#474	C₂²	1	1	yes	characteristic
93	C₅₃×#474	C₂²	1	2	yes	—
94	C₅₃×#469	C₂²	1	2	yes	—
95	C₅₃×#469	C₂²	1	2	yes	—
96	C₅₃×#468	C₂²	1	2	yes	—
97	C₅₃×#468	C₂²	1	2	yes	—
98	C₅₃×#466	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	—
100	C₅₃×#464	C₂²	1	1	yes	characteristic
101	C₅₃×#463	C₂²	1	2	yes	—
102	C₅₃×#463	C₂²	1	1	yes	characteristic
103	C₅₃×#460	C₂²	1	1	yes	characteristic
104	C₅₃×#460	C₂²	1	2	yes	—
105	C₅₃×#459	C₂²	1	1	yes	characteristic
106	C₅₃×#459	C₂²	1	2	yes	—
107	C₅₃×#452	C₂²	1	2	yes	—
108	C₅₃×#452	C₂²	1	1	yes	characteristic
109	C₅₃×#449	C₂²	1	1	yes	characteristic
110	C₅₃×#449	C₂²	1	2	yes	—
111	C₅₃×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
113	C₅₃×#440	C₂²	1	2	yes	—
114	C₅₃×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	2	yes	—
121	C₅₃×#436	C₂²	1	1	yes	characteristic
122	C₅₃×#436	C₂²	1	2	yes	—
123	C₅₃×#435	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	C₅₃×#428	C₂²	1	2	yes	—
129	C₂×#107×C₅₃	C₂²	1	2	yes	—
130	C₅₃×#424	C₂²	1	2	yes	—
131	C₅₃×#423	C₂²	1	1	yes	characteristic
132	C₅₃×#417	C₂²	1	2	yes	—
133	C₅₃×#417	C₂²	1	2	yes	—
134	C₅₃×#416	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×#41×C₅₃	C₂³	1	2	yes	—
141	C₂²×Q₈×C₅₃	—	2	1	no	—
142	C₂²×Q₈×C₅₃	—	2	1	no	—
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	1	yes	characteristic
148	C₂×D₈×C₅₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₅₃	—	2	2	no	—
153	C₄⋊Q₈×C₅₃	—	2	1	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	#127×C₅₃	—	2	1	no	—
163	#127×C₅₃	—	2	2	no	—
164	#127×C₅₃	C₂³	1	1	yes	characteristic
165	#127×C₅₃	C₂³	1	2	yes	—
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	—	2	2	no	—
170	#126×C₅₃	—	2	1	no	—
171	#126×C₅₃	D₄	1	2	yes	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	—	2	2	no	—
174	#125×C₅₃	—	2	2	no	—
175	#125×C₅₃	—	2	2	no	—
176	#125×C₅₃	D₄	1	1	yes	characteristic
177	#125×C₅₃	C₂³	1	2	yes	—
178	#125×C₅₃	C₂³	1	2	yes	—
179	#125×C₅₃	C₂³	1	1	yes	characteristic
180	#124×C₅₃	—	2	2	no	—
181	#124×C₅₃	—	2	1	no	—
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	D₄	1	1	yes	characteristic
184	#124×C₅₃	C₂³	1	1	yes	characteristic
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	—	2	2	no	—
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	1	no	—
193	#123×C₅₃	D₄	1	2	yes	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	1	no	—
197	C₂²⋊Q₈×C₅₃	—	2	1	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	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	D₄	1	1	yes	characteristic
204	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
205	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
206	#121×C₅₃	—	2	1	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	2	no	—
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	#121×C₅₃	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	2	no	—
233	C₄×D₄×C₅₃	—	2	2	no	—
234	C₄×D₄×C₅₃	—	2	2	no	—
235	C₄×D₄×C₅₃	—	2	2	no	—
236	C₄×D₄×C₅₃	—	2	2	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	—	2	2	no	—
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	—	2	1	no	—
241	C₄×D₄×C₅₃	—	2	1	no	—
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
249	C₄×D₄×C₅₃	C₂³	1	2	yes	—
250	#117×C₅₃	—	2	2	no	—
251	#117×C₅₃	—	2	1	no	—
252	#117×C₅₃	—	2	1	no	—
253	#117×C₅₃	C₂³	1	1	yes	characteristic
254	#117×C₅₃	C₂³	1	2	yes	—
255	#117×C₅₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
257	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
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	1	yes	characteristic
264	#107×C₅₃	C₂³	1	1	yes	characteristic
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	2	yes	—
269	#107×C₅₃	C₂³	1	2	yes	—
270	#107×C₅₃	C₂³	1	2	yes	—
271	#107×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	1	yes	characteristic
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
286	#103×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	1	yes	characteristic
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	1	yes	characteristic
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×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	1	yes	characteristic
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	1	yes	characteristic
303	#102×C₅₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	2	yes	—
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	#41×C₅₃	—	2	2	no	—
313	#41×C₅₃	—	2	4	no	—
314	#41×C₅₃	—	4	2	no	—
315	#41×C₅₃	—	4	1	no	—
316	#41×C₅₃	—	8	2	no	—
317	#41×C₅₃	—	8	2	no	—
318	#41×C₅₃	—	8	2	no	—
319	#41×C₅₃	—	8	2	no	—
320	C₂×Q₈×C₅₃	—	2	1	no	—
321	C₂×Q₈×C₅₃	—	2	1	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	—	8	2	no	—
326	C₂×Q₈×C₅₃	—	8	2	no	—
327	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	2	2	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	—	2	2	no	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
344	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	1	no	—
353	C₂²×C₄×C₅₃	—	2	1	no	—
354	C₂²×C₄×C₅₃	—	2	2	no	—
355	C₂²×C₄×C₅₃	—	2	2	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
361	Q₁₆×C₅₃	—	2	2	no	—
362	SD₁₆×C₅₃	—	2	2	no	—
363	SD₁₆×C₅₃	—	4	2	no	—
364	SD₁₆×C₅₃	—	4	1	no	—
365	D₈×C₅₃	—	4	1	no	—
366	D₈×C₅₃	—	4	2	no	—
367	M₁₆×C₅₃	—	4	2	no	—
368	M₁₆×C₅₃	—	4	2	no	—
369	C₂×C₈×C₅₃	—	4	2	no	—
370	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
374	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₅₃	—	2	1	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	2	no	—
379	C₄⋊C₄×C₅₃	—	2	1	no	—
380	C₄⋊C₄×C₅₃	—	2	2	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	1	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
410	C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	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	1	no	—
419	C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	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	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
432	C₄²×C₅₃	—	2	1	no	—
433	C₄²×C₅₃	—	2	1	no	—
434	C₄²×C₅₃	—	2	1	no	—
435	C₄²×C₅₃	—	2	2	no	—
436	C₄²×C₅₃	—	2	1	no	—
437	C₄²×C₅₃	—	2	2	no	—
438	C₄²×C₅₃	—	2	2	no	—
439	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₅₃	C₂⁴	1	2	yes	—
443	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂³×C₅₃	—	2	1	no	—
445	C₂³×C₅₃	—	2	2	no	—
446	C₂³×C₅₃	—	2	1	no	—
447	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
449	Q₈×C₅₃	—	2	2	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	2₋¹⁺⁴	1	2	yes	—
459	D₄×C₅₃	—	2	2	no	—
460	D₄×C₅₃	—	2	2	no	—
461	D₄×C₅₃	—	2	1	no	—
462	D₄×C₅₃	—	2	1	no	—
463	D₄×C₅₃	—	2	2	no	—
464	D₄×C₅₃	—	2	1	no	—
465	D₄×C₅₃	—	2	1	no	—
466	D₄×C₅₃	—	4	2	no	—
467	D₄×C₅₃	—	4	4	no	—
468	D₄×C₅₃	—	4	2	no	—
469	D₄×C₅₃	—	4	2	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	D₄×C₅₃	—	8	2	no	—
475	D₄×C₅₃	—	8	2	no	—
476	D₄×C₅₃	—	8	2	no	—
477	D₄×C₅₃	—	8	2	no	—
478	C₂×C₄×C₅₃	—	2	1	no	—
479	C₂×C₄×C₅₃	—	2	2	no	—
480	C₂×C₄×C₅₃	—	2	1	no	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	2	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	2	no	—
487	C₂×C₄×C₅₃	—	2	2	no	—
488	C₂×C₄×C₅₃	—	2	2	no	—
489	C₂×C₄×C₅₃	—	2	1	no	—
490	C₂×C₄×C₅₃	—	2	1	no	—
491	C₂×C₄×C₅₃	—	2	1	no	—
492	C₂×C₄×C₅₃	—	4	1	no	—
493	C₂×C₄×C₅₃	—	4	2	no	—
494	C₂×C₄×C₅₃	—	4	4	no	—
495	C₂×C₄×C₅₃	—	4	2	no	—
496	C₂×C₄×C₅₃	—	4	2	no	—
497	C₂×C₄×C₅₃	—	8	1	no	—
498	C₂×C₄×C₅₃	—	8	2	no	—
499	C₂×C₄×C₅₃	—	8	2	no	—
500	C₂×C₄×C₅₃	—	8	2	no	—
501	C₂×C₄×C₅₃	—	8	2	no	—
502	C₂×C₄×C₅₃	—	8	2	no	—
503	C₂×C₄×C₅₃	—	8	2	no	—
504	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
513	C₈×C₅₃	—	2	1	no	—
514	C₈×C₅₃	—	2	1	no	—
515	C₈×C₅₃	—	2	1	no	—
516	C₈×C₅₃	—	2	2	no	—
517	C₈×C₅₃	—	2	2	no	—
518	C₈×C₅₃	—	2	1	no	—
519	#62186	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
520	C₂²×C₅₃	—	2	1	no	—
521	C₂²×C₅₃	—	2	2	no	—
522	C₂²×C₅₃	—	2	2	no	—
523	C₂²×C₅₃	—	2	1	no	—
524	C₂²×C₅₃	—	2	1	no	—
525	C₂²×C₅₃	—	2	2	no	—
526	C₂²×C₅₃	—	4	1	no	—
527	C₂²×C₅₃	—	4	1	no	—
528	C₂²×C₅₃	—	4	2	no	—
529	C₂²×C₅₃	—	4	1	no	—
530	C₂²×C₅₃	—	4	2	no	—
531	C₂²×C₅₃	—	4	1	no	—
532	C₂²×C₅₃	—	4	1	no	—
533	C₂²×C₅₃	—	4	1	no	—
534	C₂²×C₅₃	—	4	2	no	—
535	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
536	C₄×C₅₃	—	2	1	no	—
537	C₄×C₅₃	—	2	1	no	—
538	C₄×C₅₃	—	2	2	no	—
539	C₄×C₅₃	—	2	2	no	—
540	C₄×C₅₃	—	2	1	no	—
541	C₄×C₅₃	—	2	2	no	—
542	C₄×C₅₃	—	2	1	no	—
543	C₄×C₅₃	—	2	2	no	—
544	C₄×C₅₃	—	4	1	no	—
545	C₄×C₅₃	—	4	1	no	—
546	C₄×C₅₃	—	4	1	no	—
547	C₄×C₅₃	—	4	1	no	—
548	C₄×C₅₃	—	4	1	no	—
549	C₄×C₅₃	—	4	2	no	—
550	C₄×C₅₃	—	4	2	no	—
551	C₄×C₅₃	—	4	2	no	—
552	C₄×C₅₃	#576	1	2	yes	—
553	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	C₄×C₅₃	#585	1	1	yes	characteristic
555	#3552	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3517	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#3386	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#3383	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#3368	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3358	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#3355	C₂×C₅₃	1	2	yes	complemented
562	#3353	C₂×C₅₃	1	1	yes	characteristic, complemented
563	#3346	C₂×C₅₃	1	2	yes	complemented
564	#3334	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3333	C₂×C₅₃	1	2	yes	complemented
566	#3332	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#3309	C₂×C₅₃	1	2	yes	complemented
568	#3304	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3257	C₂×C₅₃	1	2	yes	complemented
570	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#3241	C₂×C₅₃	1	2	yes	complemented
572	#3226	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3124	C₂×C₅₃	1	2	yes	complemented
574	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#3083	C₂×C₅₃	1	2	yes	complemented
576	#3079	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
578	C₂×C₅₃	—	4	1	no	—
579	C₂×C₅₃	—	4	2	no	—
580	C₂×C₅₃	—	8	1	no	—
581	C₂×C₅₃	—	8	1	no	—
582	C₂×C₅₃	—	8	2	no	—
583	C₂×C₅₃	#3489	1	1	yes	characteristic
584	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
585	C₂×C₅₃	#3586	1	1	yes	characteristic
586	#563	—	2	2	no	—
587	#557	C₂²×C₅₃	1	1	yes	characteristic
588	#557	C₂²×C₅₃	1	1	yes	characteristic
589	#556	C₂²×C₅₃	1	1	yes	characteristic
590	#554	C₂²×C₅₃	1	2	yes	—
591	#553	—	2	2	no	—
592	#553	C₂²×C₅₃	1	2	yes	—
593	#553	C₂²×C₅₃	1	2	yes	—
594	#550	—	2	1	no	—
595	#550	C₂²×C₅₃	1	1	yes	characteristic
596	#550	C₂²×C₅₃	1	2	yes	—
597	#550	C₂²×C₅₃	1	1	yes	characteristic
598	D₄×Q₈	—	2	1	no	—
599	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
600	#548	—	2	1	no	—
601	#547	—	2	1	no	—
602	#547	C₂²×C₅₃	1	1	yes	characteristic
603	#547	C₂²×C₅₃	1	1	yes	characteristic
604	#544	C₂²×C₅₃	1	2	yes	—
605	#542	C₂²×C₅₃	1	2	yes	—
606	#541	—	2	1	no	—
607	#540	—	2	2	no	—
608	#540	C₂²×C₅₃	1	2	yes	—
609	#539	—	2	2	no	—
610	#536	—	2	1	no	—
611	#532	—	2	1	no	—
612	#532	C₂²×C₅₃	1	1	yes	characteristic
613	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
614	#529	—	2	1	no	—
615	#529	C₂²×C₅₃	1	1	yes	characteristic
616	#529	C₂²×C₅₃	1	1	yes	characteristic
617	#520	C₂²×C₅₃	1	2	yes	—
618	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
619	#501	C₂²×C₅₃	1	2	yes	—
620	#500	C₂²×C₅₃	1	1	yes	characteristic
621	#500	C₂²×C₅₃	1	1	yes	characteristic
622	#499	C₂²×C₅₃	1	2	yes	—
623	#490	C₂²×C₅₃	1	2	yes	—
624	#486	C₂²×C₅₃	1	1	yes	characteristic
625	#486	C₂²×C₅₃	1	2	yes	—
626	#486	C₂²×C₅₃	1	1	yes	characteristic
627	#485	C₂²×C₅₃	1	1	yes	characteristic
628	#484	C₂²×C₅₃	1	2	yes	—
629	#482	C₂²×C₅₃	1	2	yes	—
630	#482	C₂²×C₅₃	1	1	yes	characteristic
631	#482	C₂²×C₅₃	1	2	yes	—
632	#481	C₂²×C₅₃	1	2	yes	—
633	#480	C₂²×C₅₃	1	2	yes	—
634	#480	C₂²×C₅₃	1	2	yes	—
635	#480	C₂²×C₅₃	1	2	yes	—
636	#480	C₂²×C₅₃	1	2	yes	—
637	#479	C₂²×C₅₃	1	1	yes	characteristic
638	#479	C₂²×C₅₃	1	2	yes	—
639	#479	C₂²×C₅₃	1	2	yes	—
640	#478	C₂²×C₅₃	1	2	yes	—
641	#478	C₂²×C₅₃	1	2	yes	—
642	#478	C₂²×C₅₃	1	2	yes	—
643	#478	C₂²×C₅₃	1	1	yes	characteristic
644	#477	C₂²×C₅₃	1	2	yes	—
645	#477	C₂²×C₅₃	1	2	yes	—
646	#476	C₂²×C₅₃	1	2	yes	—
647	#475	C₂²×C₅₃	1	1	yes	characteristic
648	#475	C₂²×C₅₃	1	1	yes	characteristic
649	#475	C₂²×C₅₃	1	1	yes	characteristic
650	#474	C₂²×C₅₃	1	1	yes	characteristic
651	#474	C₂²×C₅₃	1	1	yes	characteristic
652	#474	C₂²×C₅₃	1	1	yes	characteristic
653	#474	C₂²×C₅₃	1	2	yes	—
654	#474	C₂²×C₅₃	1	2	yes	—
655	#474	C₂²×C₅₃	1	2	yes	—
656	#469	C₂²×C₅₃	1	2	yes	—
657	#469	C₂²×C₅₃	1	2	yes	—
658	#468	C₂²×C₅₃	1	2	yes	—
659	#468	C₂²×C₅₃	1	2	yes	—
660	#466	C₂²×C₅₃	1	2	yes	—
661	#465	C₂²×C₅₃	1	2	yes	—
662	#464	C₂²×C₅₃	1	1	yes	characteristic
663	#463	C₂²×C₅₃	1	1	yes	characteristic
664	#463	C₂²×C₅₃	1	2	yes	—
665	#460	C₂²×C₅₃	1	2	yes	—
666	#460	C₂²×C₅₃	1	1	yes	characteristic
667	#459	C₂²×C₅₃	1	1	yes	characteristic
668	#459	C₂²×C₅₃	1	2	yes	—
669	#452	C₂²×C₅₃	1	1	yes	characteristic
670	#452	C₂²×C₅₃	1	2	yes	—
671	#449	C₂²×C₅₃	1	2	yes	—
672	#449	C₂²×C₅₃	1	1	yes	characteristic
673	#446	C₂²×C₅₃	1	1	yes	characteristic
674	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
675	#440	C₂²×C₅₃	1	2	yes	—
676	#440	C₂²×C₅₃	1	2	yes	—
677	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
678	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
681	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
682	C₄×D₈	C₂²×C₅₃	1	2	yes	—
683	#436	C₂²×C₅₃	1	1	yes	characteristic
684	#436	C₂²×C₅₃	1	2	yes	—
685	#435	C₂²×C₅₃	1	2	yes	—
686	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
687	#433	C₂²×C₅₃	1	2	yes	—
688	#431	C₂²×C₅₃	1	1	yes	characteristic
689	#428	C₂²×C₅₃	1	2	yes	—
690	#428	C₂²×C₅₃	1	2	yes	—
691	C₂×#107	C₂²×C₅₃	1	2	yes	—
692	#424	C₂²×C₅₃	1	2	yes	—
693	#423	C₂²×C₅₃	1	1	yes	characteristic
694	#417	C₂²×C₅₃	1	2	yes	—
695	#417	C₂²×C₅₃	1	2	yes	—
696	#416	C₂²×C₅₃	1	2	yes	—
697	C₅₃	#62186	1	1	yes	characteristic, direct product factor, Sylow
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	—	2	1	no	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×#41	C₂³×C₅₃	1	2	yes	—
704	C₂²×Q₈	—	2	1	no	—
705	C₂²×Q₈	—	2	1	no	—
706	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
710	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
711	C₂×D₈	C₂³×C₅₃	1	2	yes	—
712	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
713	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
714	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	2	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
725	#127	—	2	1	no	—
726	#127	—	2	2	no	—
727	#127	C₂³×C₅₃	1	1	yes	characteristic
728	#127	C₂³×C₅₃	1	2	yes	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	1	no	—
734	#126	D₄×C₅₃	1	2	yes	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	2	no	—
739	#125	D₄×C₅₃	1	1	yes	characteristic
740	#125	C₂³×C₅₃	1	1	yes	characteristic
741	#125	C₂³×C₅₃	1	2	yes	—
742	#125	C₂³×C₅₃	1	2	yes	—
743	#124	—	2	1	no	—
744	#124	—	2	2	no	—
745	#124	—	2	1	no	—
746	#124	D₄×C₅₃	1	1	yes	characteristic
747	#124	C₂³×C₅₃	1	1	yes	characteristic
748	#123	—	2	1	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	D₄×C₅₃	1	2	yes	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	—	2	1	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	D₄×C₅₃	1	1	yes	characteristic
780	#121	C₂³×C₅₃	1	1	yes	characteristic
781	#121	C₂³×C₅₃	1	2	yes	—
782	#121	C₂³×C₅₃	1	2	yes	—
783	#121	C₂³×C₅₃	1	2	yes	—
784	#121	C₂³×C₅₃	1	2	yes	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
791	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
793	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₅₃	1	2	yes	—
808	C₄×D₄	C₂³×C₅₃	1	2	yes	—
809	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₅₃	1	2	yes	—
811	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₅₃	1	2	yes	—
813	#117	—	2	2	no	—
814	#117	—	2	1	no	—
815	#117	—	2	1	no	—
816	#117	C₂³×C₅₃	1	1	yes	characteristic
817	#117	C₂³×C₅₃	1	2	yes	—
818	#117	C₂³×C₅₃	1	2	yes	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	—	2	2	no	—
821	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
823	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
824	C₂×C₄²	—	2	1	no	—
825	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
826	#107	C₂³×C₅₃	1	1	yes	characteristic
827	#107	C₂³×C₅₃	1	2	yes	—
828	#107	C₂³×C₅₃	1	2	yes	—
829	#107	C₂³×C₅₃	1	2	yes	—
830	#107	C₂³×C₅₃	1	2	yes	—
831	#107	C₂³×C₅₃	1	2	yes	—
832	#107	C₂³×C₅₃	1	2	yes	—
833	#107	C₂³×C₅₃	1	1	yes	characteristic
834	#107	C₂³×C₅₃	1	2	yes	—
835	#106	C₂³×C₅₃	1	1	yes	characteristic
836	#106	C₂³×C₅₃	1	2	yes	—
837	#106	C₂³×C₅₃	1	2	yes	—
838	#106	C₂³×C₅₃	1	2	yes	—
839	#106	C₂³×C₅₃	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
841	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
845	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
846	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
847	#103	C₂³×C₅₃	1	1	yes	characteristic
848	#103	C₂³×C₅₃	1	2	yes	—
849	#103	C₂³×C₅₃	1	1	yes	characteristic
850	#103	C₂³×C₅₃	1	2	yes	—
851	#103	C₂³×C₅₃	1	1	yes	characteristic
852	#103	C₂³×C₅₃	1	1	yes	characteristic
853	#103	C₂³×C₅₃	1	2	yes	—
854	#102	C₂³×C₅₃	1	2	yes	—
855	#102	C₂³×C₅₃	1	2	yes	—
856	#102	C₂³×C₅₃	1	2	yes	—
857	#102	C₂³×C₅₃	1	2	yes	—
858	#102	C₂³×C₅₃	1	2	yes	—
859	#102	C₂³×C₅₃	1	2	yes	—
860	#102	C₂³×C₅₃	1	1	yes	characteristic
861	#102	C₂³×C₅₃	1	2	yes	—
862	#102	C₂³×C₅₃	1	1	yes	characteristic
863	#102	C₂³×C₅₃	1	1	yes	characteristic
864	#102	C₂³×C₅₃	1	1	yes	characteristic
865	#102	C₂³×C₅₃	1	2	yes	—
866	#102	C₂³×C₅₃	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
871	#97	C₂³×C₅₃	1	2	yes	—
872	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₅₃	1	2	yes	—
875	#41	—	2	2	no	—
876	#41	—	2	4	no	—
877	#41	—	4	2	no	—
878	#41	—	4	1	no	—
879	#41	—	8	2	no	—
880	#41	—	8	2	no	—
881	#41	—	8	2	no	—
882	#41	—	8	2	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	8	2	no	—
889	C₂×Q₈	—	8	2	no	—
890	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
905	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
906	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
907	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
908	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
921	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
924	Q₁₆	—	2	2	no	—
925	SD₁₆	—	2	2	no	—
926	SD₁₆	—	4	2	no	—
927	SD₁₆	—	4	1	no	—
928	D₈	—	4	1	no	—
929	D₈	—	4	2	no	—
930	M₁₆	—	4	2	no	—
931	M₁₆	—	4	2	no	—
932	C₂×C₈	—	4	2	no	—
933	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
937	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
964	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1003	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₅₃	1	2	yes	—
1006	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1011	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	4	2	no	—
1017	Q₈	—	4	2	no	—
1018	Q₈	—	4	2	no	—
1019	Q₈	—	8	2	no	—
1020	Q₈	—	8	2	no	—
1021	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	2	2	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	2	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	8	1	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	D₄	—	8	2	no	—
1039	D₄	—	8	2	no	—
1040	D₄	—	8	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	4	1	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1075	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	2	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	C₅₃×#576	1	2	yes	—
1115	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1116	C₄	C₅₃×#585	1	1	yes	characteristic
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	8	1	no	—
1120	C₂	—	8	2	no	—
1121	C₂	—	8	1	no	—
1122	C₂	C₅₃×#3489	1	1	yes	characteristic
1123	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1124	C₂	C₅₃×#3586	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×#3517	C₂	semidirect
3. C₅₃×#3386	C₂	semidirect
4. C₅₃×#3383	C₂	semidirect
5. C₅₃×#3368	C₂	semidirect
6. C₅₃×#3358	C₂	semidirect
7. C₅₃×#3355	C₂	semidirect
8. C₅₃×#3353	C₂	semidirect
9. C₅₃×#3346	C₂	semidirect
10. C₅₃×#3334	C₂	semidirect
11. C₅₃×#3333	C₂	semidirect
12. C₅₃×#3332	C₂	semidirect
13. C₅₃×#3309	C₂	semidirect
14. C₅₃×#3304	C₂	semidirect
15. C₅₃×#3257	C₂	semidirect
16. C₅₃×#3251	C₂	semidirect
17. C₅₃×#3241	C₂	semidirect
18. C₅₃×#3226	C₂	semidirect
19. C₅₃×#3124	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3083	C₂	semidirect
22. C₅₃×#3079	C₂	semidirect
23. C₅₃×#2993	C₂	semidirect
519. #62186	C₅₃	direct (N × H)
555. #3552	C₂×C₅₃	semidirect
556. #3517	C₂×C₅₃	semidirect
557. #3386	C₂×C₅₃	semidirect
558. #3383	C₂×C₅₃	semidirect
559. #3368	C₂×C₅₃	semidirect
560. #3358	C₂×C₅₃	semidirect
561. #3355	C₂×C₅₃	semidirect
562. #3353	C₂×C₅₃	semidirect
563. #3346	C₂×C₅₃	semidirect
564. #3334	C₂×C₅₃	semidirect
565. #3333	C₂×C₅₃	semidirect
566. #3332	C₂×C₅₃	semidirect
567. #3309	C₂×C₅₃	semidirect
568. #3304	C₂×C₅₃	semidirect
569. #3257	C₂×C₅₃	semidirect
570. #3251	C₂×C₅₃	semidirect
571. #3241	C₂×C₅₃	semidirect
572. #3226	C₂×C₅₃	semidirect
573. #3124	C₂×C₅₃	semidirect
574. #3102	C₂×C₅₃	semidirect
575. #3083	C₂×C₅₃	semidirect
576. #3079	C₂×C₅₃	semidirect
577. #2993	C₂×C₅₃	semidirect
697. C₅₃	#62186	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×#3517	2
C₅₃×#3386	2
C₅₃×#3383	2
C₅₃×#3368	2
C₅₃×#3358	2
C₅₃×#3355	2
C₅₃×#3353	2
C₅₃×#3346	2
C₅₃×#3334	2
C₅₃×#3333	2
C₅₃×#3332	2
C₅₃×#3309	2
C₅₃×#3304	2
C₅₃×#3257	2
C₅₃×#3251	2
C₅₃×#3241	2
C₅₃×#3226	2
C₅₃×#3124	2
C₅₃×#3102	2
C₅₃×#3083	2
C₅₃×#3079	2
C₅₃×#2993	2
#62186	53

Subgroups — C53×#62186 #27269698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62186 #27269698