Subgroups — #27356110

Order 13568.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285274	C₂	1	1	yes	maximal, characteristic
2	#20283816	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283781	C₂	1	1	yes	maximal, characteristic
4	#20273616	C₂	1	2	yes	maximal, complemented
5	#20273557	C₂	1	2	yes	maximal, complemented
6	#20273550	C₂	1	2	yes	maximal, complemented
7	#20273526	C₂	1	2	yes	maximal, complemented
8	#20273135	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273131	C₂	1	1	yes	maximal, characteristic
10	#20273004	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811180	C₂²	1	1	yes	characteristic
13	#16811173	C₂²	1	1	yes	characteristic
14	#16811021	C₄	1	1	yes	characteristic
15	#16810996	C₄	1	1	yes	characteristic
16	#16810974	C₄	1	1	yes	characteristic
17	#16810970	C₄	1	1	yes	characteristic
18	#16810852	C₄	1	2	yes	—
19	#16810852	C₄	1	2	yes	—
20	#16810753	—	2	1	no	—
21	#16810750	C₂²	1	2	yes	—
22	C₈×Dic₁₀₆	—	2	1	no	—
23	#16810747	C₂²	1	2	yes	—
24	C₄×#11719913	C₂²	1	2	yes	—
25	C₄×#11719913	C₂²	1	2	yes	—
26	#16810702	—	2	1	no	—
27	#16810700	C₂²	1	2	yes	—
28	C₈×D₂₁₂	—	2	1	no	—
29	#16810688	C₂²	1	2	yes	—
30	#16810681	—	2	2	no	—
31	#16810676	C₂²	1	1	yes	characteristic
32	#16810588	—	2	2	no	—
33	C₄×#11719917	C₂²	1	1	yes	characteristic
34	#16810353	C₂²	1	2	yes	—
35	#16810353	C₂²	1	2	yes	—
36	#16810350	C₂²	1	2	yes	—
37	#16810350	C₂²	1	2	yes	—
38	#16810345	C₂²	1	2	yes	—
39	#16810344	C₂²	1	2	yes	—
40	C₅₃×#431	C₂²	1	1	yes	characteristic
41	C₅₃×#431	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#335	C₂²	1	1	yes	characteristic
44	C₅₃×#335	C₂²	1	1	yes	characteristic
45	C₅₃×#334	C₂²	1	1	yes	characteristic
46	C₅₃×#334	C₂²	1	1	yes	characteristic
47	C₂×#11719945	—	2	1	no	—
48	C₂×#11719913	C₂×C₄	1	2	yes	—
49	C₂×#11719913	C₂×C₄	1	2	yes	—
50	C₂×#11719917	—	2	1	no	—
51	C₂×#11719912	—	2	2	no	—
52	C₂×C₈×D₅₃	—	2	2	no	—
53	#13133217	C₂×C₄	1	1	yes	characteristic
54	#13133217	C₂×C₄	1	1	yes	characteristic
55	#13133217	C₂×C₄	1	1	yes	characteristic
56	#13133214	C₂×C₄	1	1	yes	characteristic
57	#13133209	—	2	1	no	—
58	#13133205	—	2	1	no	—
59	#13133196	—	2	1	no	—
60	#13133196	C₂×C₄	1	2	yes	—
61	#13133191	—	2	1	no	—
62	#13133191	C₂×C₄	1	2	yes	—
63	C₄×Dic₁₀₆	—	2	1	no	—
64	C₄×Dic₁₀₆	C₂³	1	2	yes	—
65	C₄×D₂₁₂	—	2	1	no	—
66	C₄×D₂₁₂	C₂³	1	2	yes	—
67	#13133176	—	2	1	no	—
68	#13133149	C₂×C₄	1	2	yes	—
69	#13133149	C₂×C₄	1	2	yes	—
70	C₄⋊#88322	D₄	1	1	yes	characteristic
71	C₄⋊#88322	D₄	1	1	yes	characteristic
72	#13133146	—	2	2	no	—
73	#13133146	—	2	2	no	—
74	#13133142	C₂×C₄	1	2	yes	—
75	#13133142	C₂×C₄	1	2	yes	—
76	#13133139	C₂×C₄	1	2	yes	—
77	#13133139	C₂×C₄	1	2	yes	—
78	C₂²⋊#88322	D₄	1	2	yes	—
79	#13133129	—	2	2	no	—
80	#13133129	—	2	2	no	—
81	#13133128	—	2	1	no	—
82	#13133127	—	2	2	no	—
83	C₄×#88322	C₂³	1	2	yes	—
84	C₄×#88322	C₂³	1	2	yes	—
85	C₈×Dic₅₃	—	2	2	no	—
86	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²⋊C₈×C₅₃	—	2	1	no	—
94	C₂²⋊C₈×C₅₃	—	2	1	no	—
95	C₄×C₈×C₅₃	—	2	1	no	—
96	C₄×C₈×C₅₃	—	2	1	no	—
97	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
104	C₂×C₂²⋊D₅₃	—	2	2	no	—
105	#11719945	—	8	1	no	—
106	#11719945	—	8	1	no	—
107	C₂×D₂₁₂	—	2	1	no	—
108	C₂×D₂₁₂	—	2	1	no	—
109	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₅₃	—	2	2	no	—
111	C₂×Dic₁₀₆	—	2	1	no	—
112	C₂×Dic₁₀₆	—	2	1	no	—
113	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₅₃	—	2	2	no	—
115	C₂×C₈×C₅₃	—	2	1	no	—
116	C₂×C₈×C₅₃	—	2	1	no	—
117	C₂×C₈×C₅₃	—	2	1	no	—
118	C₂×C₈×C₅₃	—	2	1	no	—
119	C₂×C₈×C₅₃	—	4	1	no	—
120	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₅₃	#41	1	1	yes	characteristic
127	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
128	C₂²⋊Dic₅₃	—	2	2	no	—
129	#11719921	—	2	2	no	—
130	#11719921	—	2	2	no	—
131	C₄⋊Dic₅₃	—	2	1	no	—
132	C₄⋊Dic₅₃	—	2	1	no	—
133	C₄⋊Dic₅₃	—	2	1	no	—
134	C₄⋊Dic₅₃	—	2	1	no	—
135	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
136	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
137	#11719919	—	2	2	no	—
138	#11719919	—	2	2	no	—
139	C₄×Dic₅₃	—	2	2	no	—
140	#11719917	—	4	2	no	—
141	C₂×#88322	—	2	2	no	—
142	C₂×#88322	C₂×D₄	1	2	yes	—
143	C₂×#88322	C₂×D₄	1	2	yes	—
144	#11719913	—	2	4	no	—
145	#11719913	—	4	2	no	—
146	#11719912	—	8	2	no	—
147	C₈×D₅₃	—	8	2	no	—
148	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
149	C₂²×D₅₃	—	2	2	no	—
150	C₂×C₄×C₅₃	—	2	1	no	—
151	C₂×C₄×C₅₃	—	2	1	no	—
152	C₂×C₄×C₅₃	—	2	1	no	—
153	C₂×C₄×C₅₃	—	2	1	no	—
154	C₂×C₄×C₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
161	C₂²⋊D₅₃	—	8	2	no	—
162	C₂×Dic₅₃	—	2	2	no	—
163	C₂×Dic₅₃	—	2	2	no	—
164	C₂×Dic₅₃	—	2	2	no	—
165	D₂₁₂	—	2	2	no	—
166	D₂₁₂	—	2	2	no	—
167	D₂₁₂	—	4	2	no	—
168	D₂₁₂	—	8	1	no	—
169	C₄×D₅₃	—	4	2	no	—
170	C₄×D₅₃	—	4	2	no	—
171	Dic₁₀₆	—	2	2	no	—
172	Dic₁₀₆	—	2	2	no	—
173	Dic₁₀₆	—	4	2	no	—
174	Dic₁₀₆	—	8	1	no	—
175	C₈×C₅₃	—	2	1	no	—
176	C₈×C₅₃	—	2	1	no	—
177	C₈×C₅₃	—	2	1	no	—
178	C₈×C₅₃	—	4	1	no	—
179	C₈×C₅₃	—	4	1	no	—
180	C₈×C₅₃	—	4	1	no	—
181	C₈×C₅₃	—	4	1	no	—
182	C₈×C₅₃	#131	1	2	yes	—
183	#88322	—	2	2	no	—
184	#88322	—	2	2	no	—
185	#88322	—	4	2	no	—
186	#18089	—	53	1	no	maximal, Sylow
187	C₂²×C₅₃	—	2	1	no	—
188	C₂²×C₅₃	—	2	1	no	—
189	C₂²×C₅₃	—	2	1	no	—
190	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂×D₅₃	—	4	2	no	—
192	C₂×D₅₃	—	4	2	no	—
193	C₂×D₅₃	—	4	2	no	—
194	C₄×C₅₃	—	2	1	no	—
195	C₄×C₅₃	—	2	1	no	—
196	C₄×C₅₃	—	2	1	no	—
197	C₄×C₅₃	#444	1	2	yes	—
198	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
199	C₄×C₅₃	#568	1	1	yes	characteristic
200	C₄×C₅₃	#577	1	1	yes	characteristic
201	C₄×C₅₃	#577	1	1	yes	characteristic
202	Dic₅₃	—	4	2	no	—
203	Dic₅₃	—	4	2	no	—
204	Dic₅₃	—	4	2	no	—
205	#3167	—	53	1	no	—
206	#2986	—	53	1	no	—
207	#2979	—	53	1	no	—
208	#1592	—	53	2	no	—
209	#1583	—	53	2	no	—
210	#1582	—	53	2	no	—
211	SD₁₆⋊C₈	—	53	2	no	—
212	#1564	D₅₃	1	1	yes	characteristic, complemented
213	#1485	—	53	1	no	—
214	#1484	—	53	1	no	—
215	#1451	—	53	1	no	—
216	C₂×C₅₃	—	4	1	no	—
217	C₂×C₅₃	#2935	1	1	yes	characteristic
218	C₂×C₅₃	#2949	1	1	yes	characteristic
219	C₂×C₅₃	C₂×#444	1	1	yes	characteristic
220	D₅₃	—	8	2	no	—
221	#533	—	53	1	no	—
222	#532	—	53	1	no	—
223	#498	—	53	1	no	—
224	#492	—	53	1	no	—
225	#487	—	53	1	no	—
226	#486	—	53	1	no	—
227	#465	—	53	2	no	—
228	#465	—	53	2	no	—
229	#446	—	53	2	no	—
230	#446	—	106	1	no	—
231	C₈×Q₈	—	53	2	no	—
232	C₈×Q₈	—	106	1	no	—
233	C₄×SD₁₆	—	53	2	no	—
234	C₄×SD₁₆	—	53	2	no	—
235	#436	—	53	2	no	—
236	#436	—	106	1	no	—
237	C₈×D₄	—	53	2	no	—
238	C₈×D₄	—	106	1	no	—
239	#433	—	106	2	no	—
240	#431	—	53	1	no	—
241	#431	C₂×D₅₃	1	1	yes	characteristic
242	#431	C₂×D₅₃	1	1	yes	characteristic
243	#408	—	106	2	no	—
244	C₄×M₁₆	—	53	1	no	—
245	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
246	#335	C₂×D₅₃	1	1	yes	characteristic
247	#335	C₂×D₅₃	1	1	yes	characteristic
248	#334	C₂×D₅₃	1	1	yes	characteristic
249	#334	C₂×D₅₃	1	1	yes	characteristic
250	Q₈⋊C₈	—	53	2	no	—
251	Q₈⋊C₈	—	53	2	no	—
252	D₄⋊C₈	—	53	2	no	—
253	D₄⋊C₈	—	53	2	no	—
254	#322	—	53	2	no	—
255	#322	—	53	2	no	—
256	C₅₃	#18089	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	106	1	no	—
258	C₂×SD₁₆	—	53	2	no	—
259	C₂×SD₁₆	—	53	2	no	—
260	C₂×M₁₆	—	106	2	no	—
261	C₂×M₁₆	—	106	1	no	—
262	C₂²×C₈	—	106	2	no	—
263	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
265	C₄⋊Q₈	—	53	1	no	—
266	C₄⋊Q₈	—	53	1	no	—
267	C₄⋊Q₈	—	53	1	no	—
268	#127	—	53	1	no	—
269	#125	—	106	1	no	—
270	#124	—	106	1	no	—
271	C₂²⋊Q₈	—	53	2	no	—
272	C₂²⋊Q₈	—	106	1	no	—
273	#121	—	53	2	no	—
274	#121	—	106	1	no	—
275	C₄×Q₈	—	53	2	no	—
276	C₄×Q₈	—	106	1	no	—
277	C₄×D₄	—	53	2	no	—
278	C₄×D₄	—	106	1	no	—
279	#117	—	106	1	no	—
280	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
281	#106	—	53	2	no	—
282	#106	—	53	2	no	—
283	C₄⋊C₈	—	53	1	no	—
284	C₄⋊C₈	—	53	1	no	—
285	C₄⋊C₈	—	106	2	no	—
286	C₄⋊C₈	—	106	2	no	—
287	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
288	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
291	#103	—	53	2	no	—
292	#103	—	53	2	no	—
293	#102	—	53	2	no	—
294	#102	—	53	2	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	C₂²⋊C₈	—	53	2	no	—
298	C₂²⋊C₈	—	106	2	no	—
299	C₂²⋊C₈	—	106	2	no	—
300	#97	—	106	2	no	—
301	#97	—	106	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	—	53	2	no	—
305	C₄×C₈	—	53	2	no	—
306	C₄×C₈	—	106	2	no	—
307	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
308	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
311	#41	—	424	1	no	—
312	#41	—	424	1	no	—
313	C₂×Q₈	—	53	2	no	—
314	C₂×Q₈	—	106	1	no	—
315	C₂×Q₈	—	106	1	no	—
316	C₂×D₄	—	53	2	no	—
317	C₂×D₄	—	106	2	no	—
318	C₂×D₄	—	106	1	no	—
319	C₂×D₄	—	106	1	no	—
320	C₂²×C₄	—	106	2	no	—
321	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
323	C₂²×C₄	#11719949	1	1	yes	characteristic
324	SD₁₆	—	106	4	no	—
325	SD₁₆	—	212	2	no	—
326	M₁₆	—	424	2	no	—
327	M₁₆	—	212	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	53	2	no	—
335	C₂×C₈	—	53	2	no	—
336	C₂×C₈	—	106	2	no	—
337	C₂×C₈	—	424	2	no	—
338	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
341	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
342	C₄⋊C₄	—	53	2	no	—
343	C₄⋊C₄	—	53	2	no	—
344	C₄⋊C₄	—	106	1	no	—
345	C₄⋊C₄	—	106	1	no	—
346	C₄⋊C₄	—	106	1	no	—
347	C₄⋊C₄	—	106	2	no	—
348	C₄⋊C₄	—	106	1	no	—
349	C₄⋊C₄	—	106	2	no	—
350	C₂²⋊C₄	—	106	2	no	—
351	C₂²⋊C₄	—	106	2	no	—
352	C₂²⋊C₄	—	106	2	no	—
353	C₄²	—	106	2	no	—
354	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
355	C₄²	D₄×D₅₃	1	1	yes	characteristic
356	C₄²	#11719949	1	1	yes	characteristic
357	C₄²	C₂³×D₅₃	1	1	yes	characteristic
358	C₂³	—	106	2	no	—
359	C₂³	#13133179	1	1	yes	characteristic
360	Q₈	—	106	2	no	—
361	Q₈	—	106	2	no	—
362	Q₈	—	424	1	no	—
363	Q₈	—	212	2	no	—
364	D₄	—	106	2	no	—
365	D₄	—	106	2	no	—
366	D₄	—	424	1	no	—
367	D₄	—	424	2	no	—
368	D₄	—	212	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	106	2	no	—
375	C₂×C₄	—	106	2	no	—
376	C₂×C₄	—	106	2	no	—
377	C₂×C₄	—	212	2	no	—
378	C₂×C₄	—	212	2	no	—
379	C₂×C₄	#13133179	1	1	yes	characteristic
380	C₂×C₄	#13133179	1	1	yes	characteristic
381	C₂×C₄	#13133179	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
383	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
384	C₂×C₄	C₂×#11719949	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	1	no	—
392	C₈	—	106	2	no	—
393	C₈	—	106	2	no	—
394	C₈	—	212	2	no	—
395	C₈	#13133223	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	212	2	no	—
400	C₂²	—	212	2	no	—
401	C₂²	—	212	2	no	—
402	C₂²	C₂×#13133179	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	212	2	no	—
407	C₄	—	212	2	no	—
408	C₄	—	212	2	no	—
409	C₄	#16810744	1	2	yes	—
410	C₄	C₂×#13133223	1	1	yes	characteristic
411	C₄	#16811389	1	1	yes	characteristic
412	C₄	#16811430	1	1	yes	characteristic
413	C₄	#16811430	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	424	2	no	—
416	C₂	#20283458	1	1	yes	characteristic
417	C₂	#20283573	1	1	yes	characteristic
418	C₂	C₂×#16810744	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1564	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	#16811173	C₂²
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1564	D₅₃
hypocenter	C₅₃	#18089
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
2. #20283816	C₂	semidirect
4. #20273616	C₂	semidirect
5. #20273557	C₂	semidirect
6. #20273550	C₂	semidirect
7. #20273526	C₂	semidirect
8. #20273135	C₂	semidirect
10. #20273004	C₂	semidirect
11. C₅₃×#1564	C₂	semidirect
212. #1564	D₅₃	semidirect
256. C₅₃	#18089	semidirect

Maximal subgroups

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

subgroup	index
#20285274	2
#20283816	2
#20283781	2
#20273616	2
#20273557	2
#20273550	2
#20273526	2
#20273135	2
#20273131	2
#20273004	2
C₅₃×#1564	2
#18089	53