Subgroups — #27368243

Order 13568.

680 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#20284197	C₂	1	2	yes	maximal
3	#20283678	C₂	1	1	yes	maximal, characteristic
4	#20274234	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274232	C₂	1	2	yes	maximal, complemented
6	#20274230	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274228	C₂	1	1	yes	maximal, characteristic, complemented
8	#20274226	C₂	1	2	yes	maximal, complemented
9	#20273469	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273385	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1693	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133246	—	2	2	no	—
13	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
14	C₄×#11719947	C₂²	1	1	yes	characteristic
15	#16811028	C₂²	1	1	yes	characteristic
16	#16811027	—	2	1	no	—
17	#16811027	—	2	1	no	—
18	#16811026	C₂²	1	2	yes	—
19	#16810834	C₂²	1	2	yes	—
20	#16810832	—	2	2	no	—
21	#16810830	C₂²	1	2	yes	—
22	#16810828	C₂²	1	2	yes	—
23	#16810826	—	2	2	no	—
24	#16810753	C₂²	1	1	yes	characteristic
25	#16810750	C₂²	1	1	yes	characteristic
26	#16810701	C₂²	1	1	yes	characteristic
27	#16810697	—	2	1	no	—
28	#16810692	—	2	1	no	—
29	#16810675	C₂²	1	1	yes	characteristic
30	#16810673	—	2	1	no	—
31	#107×D₅₃	—	2	1	no	—
32	#107×D₅₃	—	2	1	no	—
33	#16810645	C₂²	1	2	yes	—
34	#16810630	—	2	2	no	—
35	M₁₆×Dic₅₃	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810374	C₂²	1	1	yes	characteristic
38	#16810373	C₂²	1	2	yes	—
39	#16810370	C₂²	1	2	yes	—
40	#16810369	C₂²	1	2	yes	—
41	#16810368	C₂²	1	2	yes	—
42	C₅₃×#500	C₂²	1	1	yes	characteristic
43	C₅₃×#461	C₂²	1	2	yes	—
44	C₅₃×#436	C₂²	1	1	yes	characteristic
45	C₅₃×#334	C₂²	1	1	yes	characteristic
46	C₅₃×#332	C₂²	1	2	yes	—
47	C₂×#11719947	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₅₃	—	2	2	no	—
49	#13133246	—	4	8	no	—
50	C₂×Dic₂₁₂	—	2	2	no	—
51	C₂×#11719925	—	2	2	no	—
52	C₂×#11719923	—	2	2	no	—
53	C₂×#11719917	—	2	1	no	—
54	C₂×#11719912	—	2	2	no	—
55	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
57	#13133217	C₂³	1	2	yes	—
58	#13133216	—	2	2	no	—
59	#13133216	—	2	2	no	—
60	#13133215	—	2	2	no	—
61	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
62	#13133182	D₄	1	1	yes	characteristic
63	D₄×Dic₅₃	D₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₅₃	—	2	1	no	—
65	#13133177	—	2	1	no	—
66	#13133175	D₄	1	1	yes	characteristic
67	#13133173	—	2	1	no	—
68	C₄⋊C₄×D₅₃	—	2	2	no	—
69	C₄⋊C₄×D₅₃	—	2	2	no	—
70	C₂×C₄×Dic₅₃	—	2	1	no	—
71	C₄²×D₅₃	C₂³	1	1	yes	characteristic
72	#13133151	—	2	1	no	—
73	#13133151	—	2	1	no	—
74	#13133150	—	2	2	no	—
75	#13133150	—	2	2	no	—
76	C₄⋊#88322	C₂³	1	1	yes	characteristic
77	C₄⋊#88322	C₂³	1	2	yes	—
78	#13133146	—	2	1	no	—
79	#13133146	—	2	2	no	—
80	#13133146	—	2	1	no	—
81	#13133142	—	2	2	no	—
82	#13133141	—	2	2	no	—
83	#13133140	—	2	2	no	—
84	C₂²⋊#88322	—	2	1	no	—
85	#13133129	—	2	1	no	—
86	#13133127	—	2	1	no	—
87	#13133127	—	2	1	no	—
88	C₄×#88322	C₂³	1	1	yes	characteristic
89	C₈×Dic₅₃	—	2	1	no	—
90	C₈×Dic₅₃	D₄	1	1	yes	characteristic
91	C₈×Dic₅₃	D₄	1	1	yes	characteristic
92	C₂×SD₁₆×C₅₃	—	2	2	no	—
93	C₂×M₁₆×C₅₃	—	2	1	no	—
94	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
95	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
96	#107×C₅₃	—	2	1	no	—
97	#107×C₅₃	—	2	1	no	—
98	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
99	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
100	#103×C₅₃	—	2	2	no	—
101	C₂²⋊C₈×C₅₃	—	2	1	no	—
102	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₂×Q₈×C₅₃	—	2	2	no	—
104	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₃	—	2	1	no	—
106	C₂×C₂²⋊D₅₃	—	2	1	no	—
107	C₂²×Dic₅₃	—	2	1	no	—
108	C₂²×Dic₅₃	—	2	1	no	—
109	Q₈×D₅₃	—	4	4	no	—
110	Q₈×D₅₃	—	4	4	no	—
111	#11719947	—	2	4	no	—
112	C₂×C₄×D₅₃	—	4	2	no	—
113	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
116	C₂×Dic₁₀₆	—	2	2	no	—
117	C₂×Dic₁₀₆	—	4	2	no	—
118	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
119	SD₁₆×C₅₃	—	4	4	no	—
120	M₁₆×C₅₃	—	4	2	no	—
121	C₂×C₈×C₅₃	—	2	1	no	—
122	C₂×C₈×C₅₃	—	2	2	no	—
123	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₅₃	—	2	2	no	—
126	C₄⋊C₄×C₅₃	—	2	2	no	—
127	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₅₃	—	2	1	no	—
129	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
130	C₂²⋊Dic₅₃	—	2	1	no	—
131	#11719925	—	4	4	no	—
132	#11719923	—	4	4	no	—
133	#11719921	—	2	1	no	—
134	C₄⋊Dic₅₃	—	2	2	no	—
135	C₄⋊Dic₅₃	—	2	2	no	—
136	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
137	#11719919	—	2	1	no	—
138	#11719919	—	2	1	no	—
139	#11719919	—	4	2	no	—
140	#11719919	—	4	2	no	—
141	C₄×Dic₅₃	—	2	1	no	—
142	C₄×Dic₅₃	—	2	1	no	—
143	C₄×Dic₅₃	—	2	1	no	—
144	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
145	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
146	C₄×Dic₅₃	#41	1	1	yes	characteristic
147	#11719917	—	4	2	no	—
148	C₂×#88322	—	2	1	no	—
149	C₂×#88322	—	2	2	no	—
150	C₂×#88322	C₂×D₄	1	1	yes	characteristic
151	C₂×#88322	C₂×D₄	1	1	yes	characteristic
152	Dic₂₁₂	—	4	4	no	—
153	#11719912	—	4	4	no	—
154	C₈×D₅₃	—	2	2	no	—
155	C₈×D₅₃	—	2	2	no	—
156	C₂³×C₅₃	—	2	1	no	—
157	C₂²×D₅₃	#121	1	1	yes	characteristic
158	Q₈×C₅₃	—	4	2	no	—
159	Q₈×C₅₃	—	4	2	no	—
160	D₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	—	2	1	no	—
162	C₂×C₄×C₅₃	—	4	1	no	—
163	C₂×C₄×C₅₃	—	4	1	no	—
164	C₂×C₄×C₅₃	—	4	2	no	—
165	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
168	C₂²⋊D₅₃	—	4	2	no	—
169	C₂×Dic₅₃	—	2	1	no	—
170	C₂×Dic₅₃	—	2	1	no	—
171	C₂×Dic₅₃	—	4	2	no	—
172	C₂×Dic₅₃	—	4	2	no	—
173	C₂×Dic₅₃	—	4	2	no	—
174	C₂×Dic₅₃	#121	1	1	yes	characteristic
175	C₂×Dic₅₃	#121	1	1	yes	characteristic
176	C₂×Dic₅₃	#121	1	1	yes	characteristic
177	C₄×D₅₃	—	2	1	no	—
178	C₄×D₅₃	—	2	1	no	—
179	C₄×D₅₃	—	2	2	no	—
180	C₄×D₅₃	—	8	4	no	—
181	C₄×D₅₃	AGL(1,ℤ/8)	1	4	yes	—
182	Dic₁₀₆	—	2	2	no	—
183	Dic₁₀₆	—	4	2	no	—
184	Dic₁₀₆	—	4	2	no	—
185	Dic₁₀₆	—	8	4	no	—
186	C₈×C₅₃	—	2	1	no	—
187	C₈×C₅₃	—	4	2	no	—
188	C₈×C₅₃	—	4	1	no	—
189	C₈×C₅₃	#137	1	2	yes	complemented
190	#88322	—	2	1	no	—
191	#88322	—	4	2	no	—
192	#88322	—	4	1	no	—
193	#88322	#137	1	2	yes	complemented
194	#19296	—	53	1	no	maximal, Sylow
195	C₂²×C₅₃	—	4	1	no	—
196	C₂²×C₅₃	—	4	1	no	—
197	C₂²×C₅₃	—	4	1	no	—
198	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
199	C₂×D₅₃	—	2	1	no	—
200	C₂×D₅₃	—	2	1	no	—
201	C₂×D₅₃	#469	1	2	yes	—
202	C₄×C₅₃	—	2	1	no	—
203	C₄×C₅₃	—	4	1	no	—
204	C₄×C₅₃	—	8	2	no	—
205	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
206	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
207	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
208	Dic₅₃	—	2	1	no	—
209	Dic₅₃	—	4	1	no	—
210	Dic₅₃	—	4	1	no	—
211	Dic₅₃	—	8	2	no	—
212	Dic₅₃	#469	1	2	yes	—
213	Dic₅₃	#473	1	2	yes	—
214	C₂×#500	—	53	1	no	—
215	#3039	—	53	2	no	—
216	#2965	—	53	1	no	—
217	#1694	—	53	1	no	—
218	#1694	—	53	1	no	—
219	#1694	—	53	2	no	—
220	#1693	—	53	2	no	—
221	#1693	—	53	1	no	—
222	#1693	D₅₃	1	1	yes	characteristic, complemented
223	#1566	—	53	1	no	—
224	#1546	—	53	2	no	—
225	C₂×C₅₃	—	8	1	no	—
226	C₂×C₅₃	#3039	1	1	yes	characteristic
227	C₂×C₅₃	C₂×#469	1	1	yes	characteristic
228	C₂×C₅₃	C₂×#473	1	1	yes	characteristic
229	D₅₃	—	2	2	no	—
230	C₂×#137	—	106	2	no	—
231	C₂×C₄⋊Q₈	—	53	2	no	—
232	C₄×#41	—	53	1	no	—
233	#500	—	53	2	no	—
234	#500	—	53	1	no	—
235	#500	—	106	1	no	—
236	#500	—	106	1	no	—
237	#500	C₂×D₅₃	1	1	yes	characteristic
238	#462	—	53	2	no	—
239	#462	—	53	2	no	—
240	#462	—	106	2	no	—
241	#461	—	53	2	no	—
242	#461	—	106	2	no	—
243	#461	C₂×D₅₃	1	2	yes	—
244	#446	—	53	1	no	—
245	#446	—	53	1	no	—
246	#436	—	53	1	no	—
247	#436	C₂×D₅₃	1	1	yes	characteristic
248	#435	—	106	1	no	—
249	#435	—	106	1	no	—
250	#431	—	53	1	no	—
251	#431	—	106	1	no	—
252	C₂×#107	—	106	1	no	—
253	C₂×#107	—	106	1	no	—
254	#423	—	53	2	no	—
255	#419	—	106	2	no	—
256	C₄×M₁₆	—	106	1	no	—
257	C₂×C₄×C₈	—	53	1	no	—
258	#334	—	53	2	no	—
259	#334	—	53	1	no	—
260	#334	C₂×D₅₃	1	1	yes	characteristic
261	#332	—	53	2	no	—
262	#332	—	53	2	no	—
263	#332	—	53	2	no	—
264	#332	C₂×D₅₃	1	2	yes	—
265	C₅₃	#19296	1	1	yes	characteristic, complemented, Sylow
266	C₂×#41	—	53	1	no	—
267	C₂²×Q₈	—	106	2	no	—
268	#137	—	212	8	no	—
269	C₂×Q₁₆	—	106	2	no	—
270	C₂×Q₁₆	—	106	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	106	2	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	106	2	no	—
275	C₂×M₁₆	—	106	1	no	—
276	C₂²×C₈	—	53	1	no	—
277	C₂²×C₈	—	53	1	no	—
278	C₄⋊Q₈	—	53	2	no	—
279	C₄⋊Q₈	—	106	2	no	—
280	C₄⋊Q₈	—	106	2	no	—
281	C₄⋊Q₈	—	106	2	no	—
282	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
283	C₄×Q₈	—	53	1	no	—
284	C₄×Q₈	—	53	1	no	—
285	C₄×D₄	—	53	1	no	—
286	C₄×D₄	—	106	1	no	—
287	C₄×D₄	—	106	1	no	—
288	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
289	#117	—	53	1	no	—
290	#117	—	106	1	no	—
291	C₂×C₄⋊C₄	—	106	2	no	—
292	C₂×C₄⋊C₄	—	106	2	no	—
293	C₂×C₄²	—	53	1	no	—
294	C₂×C₄²	—	106	1	no	—
295	#107	—	2	1	no	—
296	#107	—	2	1	no	—
297	#107	—	106	2	no	—
298	#107	—	106	2	no	—
299	#107	—	106	1	no	—
300	#107	—	106	1	no	—
301	C₄⋊C₈	—	53	1	no	—
302	C₄⋊C₈	—	53	2	no	—
303	C₄⋊C₈	—	106	2	no	—
304	C₄⋊C₈	—	106	1	no	—
305	C₄⋊C₈	—	106	1	no	—
306	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
307	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
308	#103	—	2	2	no	—
309	#103	—	106	2	no	—
310	#103	—	106	2	no	—
311	#103	—	106	2	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	106	1	no	—
314	C₂²⋊C₈	—	106	1	no	—
315	#97	—	106	1	no	—
316	#97	—	106	1	no	—
317	C₄×C₈	—	53	1	no	—
318	C₄×C₈	—	53	1	no	—
319	C₄×C₈	—	53	1	no	—
320	C₄×C₈	—	106	1	no	—
321	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
322	#41	—	106	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	53	1	no	—
325	C₂×Q₈	—	106	2	no	—
326	C₂×Q₈	—	212	2	no	—
327	C₂×Q₈	—	212	4	no	—
328	C₂×Q₈	—	212	4	no	—
329	C₂×D₄	—	106	1	no	—
330	C₂×D₄	D₄×D₅₃	1	1	yes	characteristic
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	53	1	no	—
333	C₂²×C₄	—	53	1	no	—
334	C₂²×C₄	—	53	1	no	—
335	C₂²×C₄	—	106	1	no	—
336	C₂²×C₄	—	106	1	no	—
337	C₂²×C₄	—	212	2	no	—
338	Q₁₆	—	212	4	no	—
339	Q₁₆	—	212	4	no	—
340	SD₁₆	—	4	4	no	—
341	SD₁₆	—	212	4	no	—
342	M₁₆	—	4	2	no	—
343	M₁₆	—	212	4	no	—
344	M₁₆	—	212	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	53	1	no	—
348	C₂×C₈	—	53	1	no	—
349	C₂×C₈	—	106	2	no	—
350	C₂×C₈	—	106	2	no	—
351	C₂×C₈	—	106	1	no	—
352	C₂×C₈	—	106	2	no	—
353	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
354	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	53	1	no	—
358	C₄⋊C₄	—	106	1	no	—
359	C₄⋊C₄	—	106	1	no	—
360	C₄⋊C₄	—	106	2	no	—
361	C₄⋊C₄	—	106	2	no	—
362	C₄⋊C₄	—	212	2	no	—
363	C₄⋊C₄	—	212	2	no	—
364	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	106	1	no	—
367	C₂²⋊C₄	—	106	1	no	—
368	C₄²	—	53	1	no	—
369	C₄²	—	53	1	no	—
370	C₄²	—	53	1	no	—
371	C₄²	—	106	1	no	—
372	C₄²	—	106	1	no	—
373	C₄²	—	106	1	no	—
374	C₄²	C₂³×D₅₃	1	1	yes	characteristic
375	C₂³	—	2	1	no	—
376	C₂³	—	53	1	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	106	2	no	—
380	Q₈	—	424	4	no	—
381	Q₈	—	212	2	no	—
382	Q₈	—	212	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	212	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	53	1	no	—
390	C₂×C₄	—	53	1	no	—
391	C₂×C₄	—	53	4	no	—
392	C₂×C₄	—	53	1	no	—
393	C₂×C₄	—	106	2	no	—
394	C₂×C₄	—	106	1	no	—
395	C₂×C₄	—	106	1	no	—
396	C₂×C₄	—	106	1	no	—
397	C₂×C₄	—	106	1	no	—
398	C₂×C₄	—	424	4	no	—
399	C₂×C₄	—	212	2	no	—
400	C₂×C₄	—	212	2	no	—
401	C₂×C₄	—	212	2	no	—
402	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
404	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
405	C₈	—	2	1	no	—
406	C₈	—	4	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	53	2	no	—
409	C₈	—	106	1	no	—
410	C₈	—	212	2	no	—
411	C₈	—	212	1	no	—
412	C₈	#13133246	1	2	yes	complemented
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	53	2	no	—
417	C₂²	—	106	1	no	—
418	C₂²	—	106	1	no	—
419	C₂²	#121×D₅₃	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	8	2	no	—
423	C₄	—	53	2	no	—
424	C₄	—	53	2	no	—
425	C₄	—	106	1	no	—
426	C₄	—	424	2	no	—
427	C₄	—	212	1	no	—
428	C₄	—	212	1	no	—
429	C₄	AGL(1,ℤ/8)×D₅₃	1	2	yes	—
430	C₄	#137×D₅₃	1	1	yes	characteristic
431	C₄	C₂×#13133246	1	1	yes	characteristic
432	C₂	—	8	1	no	—
433	C₂	—	106	2	no	—
434	C₂	#20284197	1	1	yes	characteristic
435	C₂	#469×D₅₃	1	1	yes	characteristic
436	C₂	#473×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1693	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×#11719947	D₄
hypercenter	#1693	D₅₃
hypocenter	C₅₃	#19296
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1693

Complements

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

N	H ≅ G/N	type
1. #500×D₅₃	C₂	semidirect
4. #20274234	C₂	semidirect
5. #20274232	C₂	semidirect
6. #20274230	C₂	semidirect
7. #20274228	C₂	semidirect
8. #20274226	C₂	semidirect
9. #20273469	C₂	semidirect
10. #20273385	C₂	semidirect
11. C₅₃×#1693	C₂	semidirect
189. C₈×C₅₃	#137	semidirect
193. #88322	#137	semidirect
222. #1693	D₅₃	semidirect
265. C₅₃	#19296	semidirect
412. C₈	#13133246	semidirect

Maximal subgroups

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

subgroup	index
#500×D₅₃	2
#20284197	2
#20283678	2
#20274234	2
#20274232	2
#20274230	2
#20274228	2
#20274226	2
#20273469	2
#20273385	2
C₅₃×#1693	2
#19296	53