Subgroups — C₅₃×#61860 #27269372

Order 13568.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3388	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3384	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3373	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3371	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3244	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3241	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3125	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3119	C₂	1	2	yes	maximal, complemented
21	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#562	—	2	2	no	—
25	C₅₃×#559	C₂²	1	1	yes	characteristic
26	C₅₃×#559	C₂²	1	2	yes	—
27	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
28	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
29	C₅₃×#557	C₂²	1	2	yes	—
30	C₅₃×#557	C₂²	1	1	yes	characteristic
31	C₅₃×#554	—	2	1	no	—
32	C₅₃×#554	—	2	1	no	—
33	C₅₃×#554	C₂²	1	1	yes	characteristic
34	C₅₃×#554	C₂²	1	1	yes	characteristic
35	C₅₃×#554	C₂²	1	2	yes	—
36	C₅₃×#550	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₅₃	—	2	2	no	—
38	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
39	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#548	—	2	1	no	—
41	C₅₃×#547	—	2	1	no	—
42	C₅₃×#544	—	2	2	no	—
43	C₅₃×#544	C₂²	1	2	yes	—
44	C₅₃×#542	—	2	1	no	—
45	C₅₃×#542	C₂²	1	2	yes	—
46	C₅₃×#540	C₂²	1	2	yes	—
47	C₅₃×#539	—	2	2	no	—
48	C₅₃×#536	—	2	1	no	—
49	C₅₃×#533	—	2	1	no	—
50	C₅₃×#533	C₂²	1	1	yes	characteristic
51	C₅₃×#532	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊Q₈×C₅₃	—	2	1	no	—
53	C₂×C₄⋊Q₈×C₅₃	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×#501	C₂²	1	2	yes	—
59	C₅₃×#501	C₂²	1	2	yes	—
60	C₅₃×#499	C₂²	1	2	yes	—
61	C₅₃×#498	C₂²	1	1	yes	characteristic
62	C₅₃×#498	C₂²	1	1	yes	characteristic
63	C₅₃×#498	C₂²	1	2	yes	—
64	C₅₃×#490	C₂²	1	2	yes	—
65	C₅₃×#489	C₂²	1	2	yes	—
66	C₅₃×#489	C₂²	1	2	yes	—
67	C₅₃×#488	C₂²	1	2	yes	—
68	C₅₃×#486	C₂²	1	1	yes	characteristic
69	C₅₃×#486	C₂²	1	1	yes	characteristic
70	C₅₃×#486	C₂²	1	2	yes	—
71	C₅₃×#485	C₂²	1	1	yes	characteristic
72	C₅₃×#483	C₂²	1	2	yes	—
73	C₅₃×#482	C₂²	1	1	yes	characteristic
74	C₅₃×#482	C₂²	1	2	yes	—
75	C₅₃×#481	C₂²	1	2	yes	—
76	C₅₃×#481	C₂²	1	2	yes	—
77	C₅₃×#480	C₂²	1	2	yes	—
78	C₅₃×#479	C₂²	1	2	yes	—
79	C₅₃×#479	C₂²	1	1	yes	characteristic
80	C₅₃×#479	C₂²	1	2	yes	—
81	C₅₃×#478	C₂²	1	2	yes	—
82	C₅₃×#478	C₂²	1	2	yes	—
83	C₅₃×#478	C₂²	1	2	yes	—
84	C₅₃×#478	C₂²	1	1	yes	characteristic
85	C₅₃×#478	C₂²	1	2	yes	—
86	C₅₃×#477	C₂²	1	1	yes	characteristic
87	C₅₃×#477	C₂²	1	1	yes	characteristic
88	C₅₃×#476	C₂²	1	2	yes	—
89	C₅₃×#476	C₂²	1	2	yes	—
90	C₅₃×#476	C₂²	1	1	yes	characteristic
91	C₅₃×#476	C₂²	1	1	yes	characteristic
92	C₅₃×#476	C₂²	1	2	yes	—
93	C₅₃×#476	C₂²	1	2	yes	—
94	C₅₃×#476	C₂²	1	2	yes	—
95	C₅₃×#475	C₂²	1	2	yes	—
96	C₅₃×#475	C₂²	1	1	yes	characteristic
97	C₅₃×#475	C₂²	1	2	yes	—
98	C₅₃×#474	C₂²	1	2	yes	—
99	C₅₃×#474	C₂²	1	1	yes	characteristic
100	C₅₃×#464	C₂²	1	1	yes	characteristic
101	C₅₃×#464	C₂²	1	2	yes	—
102	C₅₃×#463	C₂²	1	1	yes	characteristic
103	C₅₃×#463	C₂²	1	2	yes	—
104	C₅₃×#460	C₂²	1	1	yes	characteristic
105	C₅₃×#460	C₂²	1	2	yes	—
106	C₅₃×#459	C₂²	1	1	yes	characteristic
107	C₅₃×#459	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	C₅₃×#446	C₂²	1	2	yes	—
113	C₅₃×#446	C₂²	1	2	yes	—
114	C₅₃×#446	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
117	C₅₃×#442	C₂²	1	2	yes	—
118	C₅₃×#442	C₂²	1	2	yes	—
119	C₅₃×#442	C₂²	1	2	yes	—
120	C₅₃×#441	C₂²	1	2	yes	—
121	C₅₃×#440	C₂²	1	2	yes	—
122	C₅₃×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
124	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
129	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₅₃	C₂²	1	2	yes	—
131	C₅₃×#433	C₂²	1	2	yes	—
132	C₅₃×#433	C₂²	1	2	yes	—
133	C₅₃×#432	C₂²	1	1	yes	characteristic
134	C₅₃×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₅₃	—	2	2	no	—
139	C₂²×Q₈×C₅₃	—	2	1	no	—
140	C₂²×Q₈×C₅₃	—	2	1	no	—
141	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
145	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₅₃	C₂³	1	2	yes	—
147	C₄⋊Q₈×C₅₃	—	2	2	no	—
148	C₄⋊Q₈×C₅₃	—	2	1	no	—
149	C₄⋊Q₈×C₅₃	—	2	1	no	—
150	C₄⋊Q₈×C₅₃	—	2	2	no	—
151	C₄⋊Q₈×C₅₃	—	2	2	no	—
152	C₄⋊Q₈×C₅₃	—	2	1	no	—
153	C₄⋊Q₈×C₅₃	—	2	1	no	—
154	C₄⋊Q₈×C₅₃	—	2	2	no	—
155	C₄⋊Q₈×C₅₃	—	2	1	no	—
156	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
165	#127×C₅₃	C₂³	1	1	yes	characteristic
166	#127×C₅₃	C₂³	1	2	yes	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	1	no	—
169	#125×C₅₃	—	2	2	no	—
170	#125×C₅₃	—	2	2	no	—
171	#125×C₅₃	—	2	2	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	D₄	1	2	yes	—
174	#125×C₅₃	C₂³	1	2	yes	—
175	#125×C₅₃	C₂³	1	2	yes	—
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	1	no	—
180	#124×C₅₃	—	2	1	no	—
181	#124×C₅₃	—	2	2	no	—
182	#124×C₅₃	C₂³	1	2	yes	—
183	#124×C₅₃	C₂³	1	1	yes	characteristic
184	#123×C₅₃	—	2	2	no	—
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	1	no	—
191	C₂²⋊Q₈×C₅₃	—	2	2	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	2	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	1	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	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	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	—	2	1	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
209	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	C₂³	1	1	yes	characteristic
216	#121×C₅₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₅₃	—	2	2	no	—
218	C₄×Q₈×C₅₃	—	2	1	no	—
219	C₄×Q₈×C₅₃	—	2	1	no	—
220	C₄×Q₈×C₅₃	—	2	1	no	—
221	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
228	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
230	C₄×D₄×C₅₃	—	2	2	no	—
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	1	no	—
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	C₂³	1	2	yes	—
247	#117×C₅₃	—	2	2	no	—
248	#117×C₅₃	—	2	1	no	—
249	#117×C₅₃	—	2	1	no	—
250	#117×C₅₃	C₂³	1	1	yes	characteristic
251	#117×C₅₃	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
253	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
258	C₂×C₄²×C₅₃	—	2	1	no	—
259	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
260	#107×C₅₃	C₂³	1	1	yes	characteristic
261	#107×C₅₃	C₂³	1	2	yes	—
262	#107×C₅₃	C₂³	1	2	yes	—
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	1	yes	characteristic
265	#106×C₅₃	C₂³	1	1	yes	characteristic
266	#106×C₅₃	C₂³	1	2	yes	—
267	#106×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
273	#106×C₅₃	C₂³	1	2	yes	—
274	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
279	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	#103×C₅₃	C₂³	1	1	yes	characteristic
283	#103×C₅₃	C₂³	1	1	yes	characteristic
284	#103×C₅₃	C₂³	1	2	yes	—
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	1	yes	characteristic
289	#102×C₅₃	C₂³	1	1	yes	characteristic
290	#102×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	#97×C₅₃	C₂³	1	2	yes	—
306	#97×C₅₃	C₂³	1	2	yes	—
307	#97×C₅₃	C₂³	1	2	yes	—
308	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	#41×C₅₃	—	2	2	no	—
313	#41×C₅₃	—	2	2	no	—
314	#41×C₅₃	—	8	2	no	—
315	#41×C₅₃	—	8	2	no	—
316	C₂×Q₈×C₅₃	—	2	1	no	—
317	C₂×Q₈×C₅₃	—	2	2	no	—
318	C₂×Q₈×C₅₃	—	2	2	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	1	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	2	2	no	—
323	C₂×Q₈×C₅₃	—	8	2	no	—
324	C₂×Q₈×C₅₃	—	8	2	no	—
325	C₂×Q₈×C₅₃	—	8	4	no	—
326	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
329	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	2	1	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	1	no	—
335	C₂×D₄×C₅₃	—	2	1	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
340	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	2	no	—
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	2	1	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	2	no	—
350	C₂²×C₄×C₅₃	—	2	2	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	Q₁₆×C₅₃	—	2	2	no	—
356	SD₁₆×C₅₃	—	2	2	no	—
357	SD₁₆×C₅₃	—	2	4	no	—
358	SD₁₆×C₅₃	—	2	2	no	—
359	D₈×C₅₃	—	2	2	no	—
360	D₈×C₅₃	—	2	4	no	—
361	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
365	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₅₃	—	2	1	no	—
368	C₄⋊C₄×C₅₃	—	2	1	no	—
369	C₄⋊C₄×C₅₃	—	2	1	no	—
370	C₄⋊C₄×C₅₃	—	2	2	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	1	no	—
379	C₄⋊C₄×C₅₃	—	2	1	no	—
380	C₄⋊C₄×C₅₃	—	2	1	no	—
381	C₄⋊C₄×C₅₃	—	2	1	no	—
382	C₄⋊C₄×C₅₃	—	2	1	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	2	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	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	2	yes	—
399	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²⋊C₄×C₅₃	—	2	1	no	—
407	C₂²⋊C₄×C₅₃	—	2	1	no	—
408	C₂²⋊C₄×C₅₃	—	2	2	no	—
409	C₂²⋊C₄×C₅₃	—	2	2	no	—
410	C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂²⋊C₄×C₅₃	—	2	1	no	—
414	C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	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	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
425	C₄²×C₅₃	—	2	1	no	—
426	C₄²×C₅₃	—	2	1	no	—
427	C₄²×C₅₃	—	2	1	no	—
428	C₄²×C₅₃	—	2	1	no	—
429	C₄²×C₅₃	—	2	2	no	—
430	C₄²×C₅₃	—	2	2	no	—
431	C₄²×C₅₃	—	2	2	no	—
432	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₄²×C₅₃	C₂⁴	1	2	yes	—
436	C₄²×C₅₃	C₂⁴	1	2	yes	—
437	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₂³×C₅₃	—	2	1	no	—
439	C₂³×C₅₃	—	2	2	no	—
440	C₂³×C₅₃	—	2	1	no	—
441	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
442	Q₈×C₅₃	—	2	2	no	—
443	Q₈×C₅₃	—	2	2	no	—
444	Q₈×C₅₃	—	2	1	no	—
445	Q₈×C₅₃	—	2	1	no	—
446	Q₈×C₅₃	—	2	1	no	—
447	Q₈×C₅₃	—	4	2	no	—
448	Q₈×C₅₃	—	4	4	no	—
449	Q₈×C₅₃	—	4	2	no	—
450	Q₈×C₅₃	—	8	1	no	—
451	Q₈×C₅₃	—	8	1	no	—
452	Q₈×C₅₃	—	8	2	no	—
453	Q₈×C₅₃	—	8	2	no	—
454	Q₈×C₅₃	—	8	2	no	—
455	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
456	D₄×C₅₃	—	2	4	no	—
457	D₄×C₅₃	—	2	1	no	—
458	D₄×C₅₃	—	2	1	no	—
459	D₄×C₅₃	—	2	2	no	—
460	D₄×C₅₃	—	2	1	no	—
461	D₄×C₅₃	—	2	2	no	—
462	D₄×C₅₃	—	4	2	no	—
463	D₄×C₅₃	—	8	1	no	—
464	D₄×C₅₃	—	8	2	no	—
465	D₄×C₅₃	—	8	2	no	—
466	D₄×C₅₃	—	8	1	no	—
467	D₄×C₅₃	—	8	2	no	—
468	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
469	C₂×C₄×C₅₃	—	2	4	no	—
470	C₂×C₄×C₅₃	—	2	1	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	1	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	1	no	—
475	C₂×C₄×C₅₃	—	2	2	no	—
476	C₂×C₄×C₅₃	—	2	1	no	—
477	C₂×C₄×C₅₃	—	2	2	no	—
478	C₂×C₄×C₅₃	—	2	2	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	1	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	4	1	no	—
483	C₂×C₄×C₅₃	—	4	2	no	—
484	C₂×C₄×C₅₃	—	4	2	no	—
485	C₂×C₄×C₅₃	—	4	2	no	—
486	C₂×C₄×C₅₃	—	8	2	no	—
487	C₂×C₄×C₅₃	—	8	2	no	—
488	C₂×C₄×C₅₃	—	8	2	no	—
489	C₂×C₄×C₅₃	—	8	2	no	—
490	C₂×C₄×C₅₃	—	8	2	no	—
491	C₂×C₄×C₅₃	—	8	2	no	—
492	C₂×C₄×C₅₃	—	8	2	no	—
493	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
503	C₈×C₅₃	—	2	1	no	—
504	C₈×C₅₃	—	2	2	no	—
505	C₈×C₅₃	—	2	1	no	—
506	C₈×C₅₃	—	2	2	no	—
507	C₈×C₅₃	—	2	1	no	—
508	C₈×C₅₃	—	2	1	no	—
509	#61860	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
510	C₂²×C₅₃	—	2	1	no	—
511	C₂²×C₅₃	—	2	1	no	—
512	C₂²×C₅₃	—	2	2	no	—
513	C₂²×C₅₃	—	2	1	no	—
514	C₂²×C₅₃	—	4	1	no	—
515	C₂²×C₅₃	—	4	1	no	—
516	C₂²×C₅₃	—	4	2	no	—
517	C₂²×C₅₃	—	4	1	no	—
518	C₂²×C₅₃	—	4	2	no	—
519	C₂²×C₅₃	—	4	1	no	—
520	C₂²×C₅₃	—	4	1	no	—
521	C₂²×C₅₃	—	4	2	no	—
522	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
523	C₄×C₅₃	—	2	1	no	—
524	C₄×C₅₃	—	2	1	no	—
525	C₄×C₅₃	—	2	2	no	—
526	C₄×C₅₃	—	2	2	no	—
527	C₄×C₅₃	—	2	1	no	—
528	C₄×C₅₃	—	2	2	no	—
529	C₄×C₅₃	—	2	1	no	—
530	C₄×C₅₃	—	2	2	no	—
531	C₄×C₅₃	—	2	2	no	—
532	C₄×C₅₃	—	4	1	no	—
533	C₄×C₅₃	—	4	1	no	—
534	C₄×C₅₃	—	4	2	no	—
535	C₄×C₅₃	—	4	2	no	—
536	C₄×C₅₃	—	4	1	no	—
537	C₄×C₅₃	—	4	1	no	—
538	C₄×C₅₃	—	4	1	no	—
539	C₄×C₅₃	—	4	2	no	—
540	C₄×C₅₃	#577	1	2	yes	—
541	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
542	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	#3554	C₂×C₅₃	1	1	yes	characteristic, complemented
544	#3503	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#3388	C₂×C₅₃	1	2	yes	complemented
546	#3387	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#3384	C₂×C₅₃	1	2	yes	complemented
548	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#3381	C₂×C₅₃	1	1	yes	characteristic, complemented
550	Q₈×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#3375	C₂×C₅₃	1	1	yes	characteristic, complemented
552	#3373	C₂×C₅₃	1	2	yes	complemented
553	#3371	C₂×C₅₃	1	2	yes	complemented
554	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#3362	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3361	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#3244	C₂×C₅₃	1	2	yes	complemented
558	#3241	C₂×C₅₃	1	2	yes	complemented
559	#3238	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3227	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#3125	C₂×C₅₃	1	2	yes	complemented
562	#3119	C₂×C₅₃	1	2	yes	complemented
563	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#2985	C₂×C₅₃	1	1	yes	characteristic, complemented
566	C₂×C₅₃	—	4	1	no	—
567	C₂×C₅₃	—	4	2	no	—
568	C₂×C₅₃	—	8	2	no	—
569	C₂×C₅₃	—	8	1	no	—
570	C₂×C₅₃	#3486	1	1	yes	characteristic
571	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
572	C₂×C₅₃	#3585	1	1	yes	characteristic
573	#562	—	2	2	no	—
574	#559	C₂²×C₅₃	1	1	yes	characteristic
575	#559	C₂²×C₅₃	1	2	yes	—
576	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
577	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
578	#557	C₂²×C₅₃	1	2	yes	—
579	#557	C₂²×C₅₃	1	1	yes	characteristic
580	#554	—	2	1	no	—
581	#554	—	2	1	no	—
582	#554	C₂²×C₅₃	1	1	yes	characteristic
583	#554	C₂²×C₅₃	1	1	yes	characteristic
584	#554	C₂²×C₅₃	1	2	yes	—
585	#550	C₂²×C₅₃	1	1	yes	characteristic
586	D₄×Q₈	—	2	2	no	—
587	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
588	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
589	#548	—	2	1	no	—
590	#547	—	2	1	no	—
591	#544	—	2	2	no	—
592	#544	C₂²×C₅₃	1	2	yes	—
593	#542	—	2	1	no	—
594	#542	C₂²×C₅₃	1	2	yes	—
595	#540	C₂²×C₅₃	1	2	yes	—
596	#539	—	2	2	no	—
597	#536	—	2	1	no	—
598	#533	—	2	1	no	—
599	#533	C₂²×C₅₃	1	1	yes	characteristic
600	#532	C₂²×C₅₃	1	1	yes	characteristic
601	C₂×C₄⋊Q₈	—	2	1	no	—
602	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
603	#529	C₂²×C₅₃	1	1	yes	characteristic
604	#520	C₂²×C₅₃	1	2	yes	—
605	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
606	#501	C₂²×C₅₃	1	2	yes	—
607	#501	C₂²×C₅₃	1	2	yes	—
608	#501	C₂²×C₅₃	1	2	yes	—
609	#499	C₂²×C₅₃	1	2	yes	—
610	#498	C₂²×C₅₃	1	1	yes	characteristic
611	#498	C₂²×C₅₃	1	2	yes	—
612	#498	C₂²×C₅₃	1	1	yes	characteristic
613	#490	C₂²×C₅₃	1	2	yes	—
614	#489	C₂²×C₅₃	1	2	yes	—
615	#489	C₂²×C₅₃	1	2	yes	—
616	#488	C₂²×C₅₃	1	2	yes	—
617	#486	C₂²×C₅₃	1	1	yes	characteristic
618	#486	C₂²×C₅₃	1	2	yes	—
619	#486	C₂²×C₅₃	1	1	yes	characteristic
620	#485	C₂²×C₅₃	1	1	yes	characteristic
621	#483	C₂²×C₅₃	1	2	yes	—
622	#482	C₂²×C₅₃	1	1	yes	characteristic
623	#482	C₂²×C₅₃	1	2	yes	—
624	#481	C₂²×C₅₃	1	2	yes	—
625	#481	C₂²×C₅₃	1	2	yes	—
626	#480	C₂²×C₅₃	1	2	yes	—
627	#479	C₂²×C₅₃	1	1	yes	characteristic
628	#479	C₂²×C₅₃	1	2	yes	—
629	#479	C₂²×C₅₃	1	2	yes	—
630	#478	C₂²×C₅₃	1	1	yes	characteristic
631	#478	C₂²×C₅₃	1	2	yes	—
632	#478	C₂²×C₅₃	1	2	yes	—
633	#478	C₂²×C₅₃	1	2	yes	—
634	#478	C₂²×C₅₃	1	2	yes	—
635	#477	C₂²×C₅₃	1	1	yes	characteristic
636	#477	C₂²×C₅₃	1	1	yes	characteristic
637	#476	C₂²×C₅₃	1	1	yes	characteristic
638	#476	C₂²×C₅₃	1	2	yes	—
639	#476	C₂²×C₅₃	1	1	yes	characteristic
640	#476	C₂²×C₅₃	1	2	yes	—
641	#476	C₂²×C₅₃	1	2	yes	—
642	#476	C₂²×C₅₃	1	2	yes	—
643	#476	C₂²×C₅₃	1	2	yes	—
644	#475	C₂²×C₅₃	1	1	yes	characteristic
645	#475	C₂²×C₅₃	1	2	yes	—
646	#475	C₂²×C₅₃	1	2	yes	—
647	#474	C₂²×C₅₃	1	1	yes	characteristic
648	#474	C₂²×C₅₃	1	2	yes	—
649	#464	C₂²×C₅₃	1	1	yes	characteristic
650	#464	C₂²×C₅₃	1	2	yes	—
651	#463	C₂²×C₅₃	1	1	yes	characteristic
652	#463	C₂²×C₅₃	1	2	yes	—
653	#460	C₂²×C₅₃	1	1	yes	characteristic
654	#460	C₂²×C₅₃	1	2	yes	—
655	#459	C₂²×C₅₃	1	1	yes	characteristic
656	#459	C₂²×C₅₃	1	2	yes	—
657	#452	C₂²×C₅₃	1	1	yes	characteristic
658	#449	C₂²×C₅₃	1	1	yes	characteristic
659	#449	C₂²×C₅₃	1	2	yes	—
660	#446	C₂²×C₅₃	1	1	yes	characteristic
661	#446	C₂²×C₅₃	1	2	yes	—
662	#446	C₂²×C₅₃	1	2	yes	—
663	#446	C₂²×C₅₃	1	1	yes	characteristic
664	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
665	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
666	#442	C₂²×C₅₃	1	2	yes	—
667	#442	C₂²×C₅₃	1	2	yes	—
668	#442	C₂²×C₅₃	1	2	yes	—
669	#441	C₂²×C₅₃	1	2	yes	—
670	#440	C₂²×C₅₃	1	2	yes	—
671	#440	C₂²×C₅₃	1	2	yes	—
672	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
676	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
677	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
678	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
679	C₄×D₈	C₂²×C₅₃	1	2	yes	—
680	#433	C₂²×C₅₃	1	2	yes	—
681	#433	C₂²×C₅₃	1	2	yes	—
682	#432	C₂²×C₅₃	1	1	yes	characteristic
683	#431	C₂²×C₅₃	1	1	yes	characteristic
684	C₅₃	#61860	1	1	yes	characteristic, direct product factor, Sylow
685	C₂×#41	—	2	1	no	—
686	C₂×#41	—	2	1	no	—
687	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
688	C₂²×Q₈	—	2	2	no	—
689	C₂²×Q₈	—	2	1	no	—
690	C₂²×Q₈	—	2	1	no	—
691	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
693	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
695	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
696	C₂×D₈	C₂³×C₅₃	1	2	yes	—
697	C₄⋊Q₈	—	2	2	no	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	—	2	2	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	—	2	1	no	—
705	C₄⋊Q₈	—	2	1	no	—
706	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
707	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
709	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
713	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
714	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
715	#127	C₂³×C₅₃	1	1	yes	characteristic
716	#127	C₂³×C₅₃	1	2	yes	—
717	#126	—	2	2	no	—
718	#126	—	2	1	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	D₄×C₅₃	1	2	yes	—
724	#125	C₂³×C₅₃	1	1	yes	characteristic
725	#125	C₂³×C₅₃	1	2	yes	—
726	#125	C₂³×C₅₃	1	2	yes	—
727	#125	C₂³×C₅₃	1	2	yes	—
728	#124	—	2	1	no	—
729	#124	—	2	2	no	—
730	#124	—	2	2	no	—
731	#124	—	2	1	no	—
732	#124	C₂³×C₅₃	1	1	yes	characteristic
733	#124	C₂³×C₅₃	1	2	yes	—
734	#123	—	2	1	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
757	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
758	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
760	#121	—	2	1	no	—
761	#121	—	2	2	no	—
762	#121	—	2	1	no	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	C₂³×C₅₃	1	1	yes	characteristic
766	#121	C₂³×C₅₃	1	2	yes	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
774	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
777	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
778	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₅₃	1	2	yes	—
791	C₄×D₄	C₂³×C₅₃	1	2	yes	—
792	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₅₃	1	2	yes	—
794	C₄×D₄	C₂³×C₅₃	1	2	yes	—
795	C₄×D₄	C₂³×C₅₃	1	2	yes	—
796	C₄×D₄	C₂³×C₅₃	1	2	yes	—
797	#117	—	2	2	no	—
798	#117	—	2	1	no	—
799	#117	—	2	1	no	—
800	#117	C₂³×C₅₃	1	1	yes	characteristic
801	#117	C₂³×C₅₃	1	2	yes	—
802	C₂×C₄⋊C₄	—	2	1	no	—
803	C₂×C₄⋊C₄	—	2	2	no	—
804	C₂×C₄⋊C₄	—	2	1	no	—
805	C₂×C₄⋊C₄	—	2	1	no	—
806	C₂×C₄⋊C₄	—	2	2	no	—
807	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
808	C₂×C₄²	—	2	1	no	—
809	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
810	#107	C₂³×C₅₃	1	2	yes	—
811	#107	C₂³×C₅₃	1	1	yes	characteristic
812	#107	C₂³×C₅₃	1	1	yes	characteristic
813	#107	C₂³×C₅₃	1	2	yes	—
814	#107	C₂³×C₅₃	1	2	yes	—
815	#106	C₂³×C₅₃	1	2	yes	—
816	#106	C₂³×C₅₃	1	2	yes	—
817	#106	C₂³×C₅₃	1	1	yes	characteristic
818	#106	C₂³×C₅₃	1	2	yes	—
819	#106	C₂³×C₅₃	1	1	yes	characteristic
820	#106	C₂³×C₅₃	1	2	yes	—
821	#106	C₂³×C₅₃	1	2	yes	—
822	#106	C₂³×C₅₃	1	2	yes	—
823	#106	C₂³×C₅₃	1	2	yes	—
824	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
829	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
830	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
831	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
832	#103	C₂³×C₅₃	1	1	yes	characteristic
833	#103	C₂³×C₅₃	1	2	yes	—
834	#103	C₂³×C₅₃	1	2	yes	—
835	#103	C₂³×C₅₃	1	1	yes	characteristic
836	#103	C₂³×C₅₃	1	1	yes	characteristic
837	#103	C₂³×C₅₃	1	1	yes	characteristic
838	#103	C₂³×C₅₃	1	2	yes	—
839	#102	C₂³×C₅₃	1	1	yes	characteristic
840	#102	C₂³×C₅₃	1	1	yes	characteristic
841	#102	C₂³×C₅₃	1	2	yes	—
842	#102	C₂³×C₅₃	1	1	yes	characteristic
843	#102	C₂³×C₅₃	1	2	yes	—
844	#102	C₂³×C₅₃	1	2	yes	—
845	#102	C₂³×C₅₃	1	1	yes	characteristic
846	#102	C₂³×C₅₃	1	2	yes	—
847	#102	C₂³×C₅₃	1	2	yes	—
848	#102	C₂³×C₅₃	1	2	yes	—
849	#102	C₂³×C₅₃	1	2	yes	—
850	#102	C₂³×C₅₃	1	2	yes	—
851	#102	C₂³×C₅₃	1	2	yes	—
852	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
853	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
854	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
855	#97	C₂³×C₅₃	1	2	yes	—
856	#97	C₂³×C₅₃	1	2	yes	—
857	#97	C₂³×C₅₃	1	2	yes	—
858	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
859	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
860	C₄×C₈	C₂³×C₅₃	1	2	yes	—
861	C₄×C₈	C₂³×C₅₃	1	2	yes	—
862	#41	—	2	2	no	—
863	#41	—	2	2	no	—
864	#41	—	8	2	no	—
865	#41	—	8	2	no	—
866	C₂×Q₈	—	2	1	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	2	2	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	2	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	8	2	no	—
874	C₂×Q₈	—	8	2	no	—
875	C₂×Q₈	—	8	4	no	—
876	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
877	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
878	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
879	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
880	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
889	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
903	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
905	Q₁₆	—	2	2	no	—
906	SD₁₆	—	2	2	no	—
907	SD₁₆	—	2	4	no	—
908	SD₁₆	—	2	2	no	—
909	D₈	—	2	2	no	—
910	D₈	—	2	4	no	—
911	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
913	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
915	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
947	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
948	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
955	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
974	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
983	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
984	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
985	C₄²	C₂⁴×C₅₃	1	2	yes	—
986	C₄²	C₂⁴×C₅₃	1	2	yes	—
987	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	2	no	—
991	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	4	2	no	—
998	Q₈	—	4	4	no	—
999	Q₈	—	4	2	no	—
1000	Q₈	—	8	2	no	—
1001	Q₈	—	8	1	no	—
1002	Q₈	—	8	1	no	—
1003	Q₈	—	8	2	no	—
1004	Q₈	—	8	2	no	—
1005	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
1006	D₄	—	2	4	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	2	2	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	1	no	—
1011	D₄	—	2	2	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	8	1	no	—
1014	D₄	—	8	2	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	1	no	—
1017	D₄	—	8	2	no	—
1018	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1019	C₂×C₄	—	2	4	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	4	1	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	—	8	2	no	—
1043	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1046	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1047	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1052	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1053	C₈	—	2	1	no	—
1054	C₈	—	2	2	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	2	2	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1072	C₄	—	2	1	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	1	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	2	no	—
1089	C₄	C₅₃×#577	1	2	yes	—
1090	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1091	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1092	C₂	—	4	1	no	—
1093	C₂	—	4	2	no	—
1094	C₂	—	8	1	no	—
1095	C₂	—	8	2	no	—
1096	C₂	C₅₃×#3486	1	1	yes	characteristic
1097	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1098	C₂	C₅₃×#3585	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3554	C₂	semidirect
2. C₅₃×#3503	C₂	semidirect
3. C₅₃×#3388	C₂	semidirect
4. C₅₃×#3387	C₂	semidirect
5. C₅₃×#3384	C₂	semidirect
6. C₅₃×#3384	C₂	semidirect
7. C₅₃×#3381	C₂	semidirect
8. Q₈×SD₁₆×C₅₃	C₂	semidirect
9. C₅₃×#3375	C₂	semidirect
10. C₅₃×#3373	C₂	semidirect
11. C₅₃×#3371	C₂	semidirect
12. C₅₃×#3366	C₂	semidirect
13. C₅₃×#3362	C₂	semidirect
14. C₅₃×#3361	C₂	semidirect
15. C₅₃×#3244	C₂	semidirect
16. C₅₃×#3241	C₂	semidirect
17. C₅₃×#3238	C₂	semidirect
18. C₅₃×#3227	C₂	semidirect
19. C₅₃×#3125	C₂	semidirect
20. C₅₃×#3119	C₂	semidirect
21. C₅₃×#3115	C₂	semidirect
22. C₅₃×#3102	C₂	semidirect
23. C₅₃×#2985	C₂	semidirect
509. #61860	C₅₃	direct (N × H)
543. #3554	C₂×C₅₃	semidirect
544. #3503	C₂×C₅₃	semidirect
545. #3388	C₂×C₅₃	semidirect
546. #3387	C₂×C₅₃	semidirect
547. #3384	C₂×C₅₃	semidirect
548. #3384	C₂×C₅₃	semidirect
549. #3381	C₂×C₅₃	semidirect
550. Q₈×SD₁₆	C₂×C₅₃	semidirect
551. #3375	C₂×C₅₃	semidirect
552. #3373	C₂×C₅₃	semidirect
553. #3371	C₂×C₅₃	semidirect
554. #3366	C₂×C₅₃	semidirect
555. #3362	C₂×C₅₃	semidirect
556. #3361	C₂×C₅₃	semidirect
557. #3244	C₂×C₅₃	semidirect
558. #3241	C₂×C₅₃	semidirect
559. #3238	C₂×C₅₃	semidirect
560. #3227	C₂×C₅₃	semidirect
561. #3125	C₂×C₅₃	semidirect
562. #3119	C₂×C₅₃	semidirect
563. #3115	C₂×C₅₃	semidirect
564. #3102	C₂×C₅₃	semidirect
565. #2985	C₂×C₅₃	semidirect
684. C₅₃	#61860	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×#3554	2
C₅₃×#3503	2
C₅₃×#3388	2
C₅₃×#3387	2
C₅₃×#3384	2
C₅₃×#3381	2
Q₈×SD₁₆×C₅₃	2
C₅₃×#3375	2
C₅₃×#3373	2
C₅₃×#3371	2
C₅₃×#3366	2
C₅₃×#3362	2
C₅₃×#3361	2
C₅₃×#3244	2
C₅₃×#3241	2
C₅₃×#3238	2
C₅₃×#3227	2
C₅₃×#3125	2
C₅₃×#3119	2
C₅₃×#3115	2
C₅₃×#3102	2
C₅₃×#2985	2
#61860	53

Subgroups — C53×#61860 #27269372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61860 #27269372