Subgroups — #27368025

Order 13568.

638 conjugacy classes of subgroups.

The subgroup lattice has 432 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	#20284529	C₂	1	2	yes	maximal
3	C₈×#11719949	C₂	1	1	yes	maximal, characteristic
4	#20274119	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274117	C₂	1	2	yes	maximal, complemented
6	#20274115	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274113	C₂	1	2	yes	maximal, complemented
8	#20274111	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273472	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273394	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
13	C₄×#11719949	C₂²	1	1	yes	characteristic
14	#16811028	C₂²	1	1	yes	characteristic
15	#16811027	—	2	1	no	—
16	#16811027	—	2	1	no	—
17	#16811026	C₂²	1	2	yes	—
18	#16810918	C₂²	1	2	yes	—
19	#16810914	C₂²	1	2	yes	—
20	#16810910	C₂²	1	2	yes	—
21	#16810906	—	2	2	no	—
22	#16810902	—	2	2	no	—
23	Q₈×#88322	C₂²	1	1	yes	characteristic
24	C₈×D₂₁₂	—	2	1	no	—
25	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
26	#16810688	—	2	1	no	—
27	#16810688	C₂²	1	1	yes	characteristic
28	#16810675	—	2	1	no	—
29	#16810675	C₂²	1	1	yes	characteristic
30	#16810664	—	2	2	no	—
31	#107×D₅₃	—	2	1	no	—
32	#107×D₅₃	—	2	1	no	—
33	#16810645	C₂²	1	2	yes	—
34	#16810623	—	2	2	no	—
35	C₄×C₈×D₅₃	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810376	C₂²	1	1	yes	characteristic
38	#16810375	C₂²	1	2	yes	—
39	#16810372	C₂²	1	2	yes	—
40	#16810371	C₂²	1	2	yes	—
41	#16810371	C₂²	1	2	yes	—
42	C₅₃×#500	C₂²	1	1	yes	characteristic
43	C₅₃×#477	C₂²	1	2	yes	—
44	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#335	C₂²	1	1	yes	characteristic
46	C₅₃×#333	C₂²	1	2	yes	—
47	C₂×#11719949	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₅₃	—	2	2	no	—
49	C₂×#11719912	—	2	2	no	—
50	C₂×C₈×D₅₃	—	2	1	no	—
51	C₂×C₈×D₅₃	—	2	1	no	—
52	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
54	#13133217	C₂³	1	2	yes	—
55	#13133216	—	2	2	no	—
56	#13133216	—	2	2	no	—
57	#13133215	—	2	2	no	—
58	Q₈×Dic₅₃	D₄	1	1	yes	characteristic
59	C₄×D₂₁₂	—	2	1	no	—
60	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
61	#13133179	—	2	1	no	—
62	#13133179	D₄	1	1	yes	characteristic
63	#13133175	—	2	1	no	—
64	#13133175	D₄	1	1	yes	characteristic
65	C₄⋊C₄×D₅₃	—	2	2	no	—
66	C₄⋊C₄×D₅₃	—	2	2	no	—
67	C₄²×D₅₃	—	2	1	no	—
68	C₄²×D₅₃	C₂³	1	1	yes	characteristic
69	#13133151	—	2	1	no	—
70	#13133151	—	2	1	no	—
71	#13133150	—	2	2	no	—
72	#13133150	—	2	2	no	—
73	#13133150	—	2	2	no	—
74	#13133149	—	2	2	no	—
75	#13133148	—	2	2	no	—
76	C₄⋊#88322	—	2	1	no	—
77	C₄⋊#88322	C₂³	1	1	yes	characteristic
78	C₄⋊#88322	C₂³	1	2	yes	—
79	#13133146	—	2	2	no	—
80	#13133141	—	2	2	no	—
81	#13133139	—	2	2	no	—
82	#13133137	—	2	2	no	—
83	#13133129	—	2	1	no	—
84	#13133129	—	2	1	no	—
85	#13133129	—	2	1	no	—
86	C₄×#88322	—	2	1	no	—
87	C₄×#88322	C₂³	1	1	yes	characteristic
88	C₈×Dic₅₃	—	2	1	no	—
89	C₈×Dic₅₃	D₄	1	1	yes	characteristic
90	C₈×Dic₅₃	D₄	1	1	yes	characteristic
91	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
92	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
93	#107×C₅₃	—	2	1	no	—
94	#107×C₅₃	—	2	1	no	—
95	#107×C₅₃	—	2	2	no	—
96	C₄⋊C₈×C₅₃	—	2	1	no	—
97	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
99	#103×C₅₃	—	2	2	no	—
100	C₄×C₈×C₅₃	—	2	1	no	—
101	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₅₃	—	2	2	no	—
103	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
104	#11719949	—	2	2	no	—
105	#11719949	Q₁₆	1	4	yes	—
106	Q₈×D₅₃	—	8	4	no	—
107	C₂×D₂₁₂	—	2	1	no	—
108	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	—	2	1	no	—
110	C₂×C₄×D₅₃	—	2	1	no	—
111	C₂×C₄×D₅₃	—	2	1	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×C₈×C₅₃	—	2	1	no	—
119	C₂×C₈×C₅₃	—	2	2	no	—
120	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₅₃	—	2	1	no	—
123	C₄⋊C₄×C₅₃	—	2	2	no	—
124	C₄⋊C₄×C₅₃	—	2	2	no	—
125	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₅₃	—	2	1	no	—
127	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
128	#11719921	—	2	1	no	—
129	#11719921	—	2	1	no	—
130	#11719921	—	2	1	no	—
131	C₄⋊Dic₅₃	—	2	1	no	—
132	C₄⋊Dic₅₃	—	2	2	no	—
133	C₄⋊Dic₅₃	—	2	2	no	—
134	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
135	#11719919	—	4	2	no	—
136	#11719919	—	4	2	no	—
137	C₄×Dic₅₃	—	2	1	no	—
138	C₄×Dic₅₃	—	2	1	no	—
139	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₅₃	#41	1	1	yes	characteristic
142	C₂×#88322	—	2	1	no	—
143	C₂×#88322	—	2	2	no	—
144	C₂×#88322	C₂×D₄	1	1	yes	characteristic
145	C₂×#88322	C₂×D₄	1	1	yes	characteristic
146	#11719912	—	4	4	no	—
147	C₈×D₅₃	—	2	2	no	—
148	C₈×D₅₃	—	2	2	no	—
149	C₈×D₅₃	—	4	2	no	—
150	C₈×D₅₃	—	4	2	no	—
151	C₂²×D₅₃	—	2	1	no	—
152	C₂²×D₅₃	#121	1	1	yes	characteristic
153	Q₈×C₅₃	—	2	1	no	—
154	Q₈×C₅₃	—	8	2	no	—
155	Q₈×C₅₃	C₂×Q₁₆	1	2	yes	—
156	C₂×C₄×C₅₃	—	2	1	no	—
157	C₂×C₄×C₅₃	—	2	1	no	—
158	C₂×C₄×C₅₃	—	4	2	no	—
159	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
162	C₂×Dic₅₃	—	2	1	no	—
163	C₂×Dic₅₃	—	4	2	no	—
164	C₂×Dic₅₃	#121	1	1	yes	characteristic
165	C₂×Dic₅₃	#121	1	1	yes	characteristic
166	C₂×Dic₅₃	#121	1	1	yes	characteristic
167	D₂₁₂	—	2	4	no	—
168	D₂₁₂	—	2	1	no	—
169	D₂₁₂	C₂×Q₁₆	1	2	yes	—
170	C₄×D₅₃	—	2	1	no	—
171	C₄×D₅₃	—	2	1	no	—
172	C₄×D₅₃	—	2	4	no	—
173	C₄×D₅₃	—	2	2	no	—
174	C₄×D₅₃	—	4	1	no	—
175	C₄×D₅₃	—	4	1	no	—
176	C₄×D₅₃	—	4	2	no	—
177	C₄×D₅₃	—	8	4	no	—
178	C₄×D₅₃	C₂×Q₁₆	1	2	yes	—
179	C₄×D₅₃	#135	1	2	yes	—
180	Dic₁₀₆	—	8	4	no	—
181	Dic₁₀₆	—	8	2	no	—
182	C₈×C₅₃	—	2	1	no	—
183	C₈×C₅₃	—	4	2	no	—
184	C₈×C₅₃	—	4	1	no	—
185	C₈×C₅₃	#137	1	2	yes	—
186	#88322	—	2	1	no	—
187	#88322	—	4	2	no	—
188	#88322	—	4	1	no	—
189	#88322	#137	1	2	yes	—
190	#19272	—	53	1	no	maximal, Sylow
191	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
192	C₂×D₅₃	—	2	1	no	—
193	C₂×D₅₃	—	2	1	no	—
194	C₂×D₅₃	—	2	2	no	—
195	C₂×D₅₃	—	4	1	no	—
196	C₂×D₅₃	—	4	1	no	—
197	C₂×D₅₃	#467	1	2	yes	—
198	C₄×C₅₃	—	2	2	no	—
199	C₄×C₅₃	—	2	1	no	—
200	C₄×C₅₃	—	4	1	no	—
201	C₄×C₅₃	—	8	2	no	—
202	C₄×C₅₃	C₂²×Q₁₆	1	1	yes	characteristic
203	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
204	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
205	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
206	Dic₅₃	—	2	1	no	—
207	Dic₅₃	—	4	1	no	—
208	Dic₅₃	—	8	2	no	—
209	Dic₅₃	#467	1	2	yes	—
210	Dic₅₃	#472	1	2	yes	—
211	C₂×#500	—	53	1	no	—
212	#3079	—	53	2	no	—
213	C₈×#41	—	53	1	no	—
214	#1676	—	53	2	no	—
215	#1676	—	53	1	no	—
216	#1676	D₅₃	1	1	yes	characteristic, complemented
217	#1675	—	53	1	no	—
218	#1675	—	53	1	no	—
219	#1675	—	53	2	no	—
220	#1567	—	53	1	no	—
221	#1548	—	53	2	no	—
222	C₂×C₅₃	#3039	1	1	yes	characteristic
223	C₂×C₅₃	C₂×#467	1	1	yes	characteristic
224	C₂×C₅₃	C₂×#472	1	1	yes	characteristic
225	D₅₃	—	2	2	no	—
226	D₅₃	—	4	2	no	—
227	C₂×C₄⋊Q₈	—	53	2	no	—
228	C₄×#41	—	53	1	no	—
229	#500	—	53	2	no	—
230	#500	—	53	1	no	—
231	#500	—	106	1	no	—
232	#500	—	106	1	no	—
233	#500	C₂×D₅₃	1	1	yes	characteristic
234	#477	—	53	2	no	—
235	#477	C₂×D₅₃	1	2	yes	—
236	#476	—	53	2	no	—
237	#476	—	53	2	no	—
238	#475	—	106	2	no	—
239	#474	—	106	2	no	—
240	C₈×Q₈	—	53	1	no	—
241	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
242	C₈×D₄	—	53	1	no	—
243	C₈×D₄	—	53	1	no	—
244	C₈×D₄	—	106	1	no	—
245	C₈×D₄	—	106	1	no	—
246	#431	—	53	1	no	—
247	#431	—	106	1	no	—
248	#428	—	106	2	no	—
249	C₂×#107	—	106	1	no	—
250	C₂×#107	—	106	1	no	—
251	#423	—	53	2	no	—
252	#417	—	106	2	no	—
253	C₂×C₄×C₈	—	53	1	no	—
254	C₂×C₄×C₈	—	106	1	no	—
255	#335	—	53	2	no	—
256	#335	—	53	1	no	—
257	#335	C₂×D₅₃	1	1	yes	characteristic
258	#333	—	53	2	no	—
259	#333	—	53	2	no	—
260	#333	—	53	2	no	—
261	#333	C₂×D₅₃	1	2	yes	—
262	C₅₃	#19272	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	53	1	no	—
264	C₂²×Q₈	—	106	2	no	—
265	C₂×M₁₆	—	106	2	no	—
266	C₂²×C₈	—	53	1	no	—
267	C₂²×C₈	—	53	1	no	—
268	C₂²×C₈	—	106	1	no	—
269	C₂²×C₈	—	106	1	no	—
270	C₄⋊Q₈	—	53	2	no	—
271	C₄⋊Q₈	—	106	2	no	—
272	C₄⋊Q₈	—	106	2	no	—
273	C₄⋊Q₈	—	106	2	no	—
274	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
275	C₄×Q₈	—	53	1	no	—
276	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
277	C₄×D₄	—	53	1	no	—
278	C₄×D₄	—	53	1	no	—
279	C₄×D₄	—	106	1	no	—
280	C₄×D₄	—	106	1	no	—
281	#117	—	53	1	no	—
282	#117	—	106	1	no	—
283	C₂×C₄⋊C₄	—	106	2	no	—
284	C₂×C₄⋊C₄	—	106	2	no	—
285	C₂×C₄²	—	53	1	no	—
286	C₂×C₄²	—	106	1	no	—
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	2	no	—
290	#107	—	106	2	no	—
291	#107	—	106	2	no	—
292	#107	—	106	1	no	—
293	#107	—	106	1	no	—
294	#107	—	106	2	no	—
295	#106	—	106	2	no	—
296	#106	—	106	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	53	1	no	—
299	C₄⋊C₈	—	53	2	no	—
300	C₄⋊C₈	—	106	1	no	—
301	C₄⋊C₈	—	106	2	no	—
302	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
303	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
304	#103	—	2	2	no	—
305	#103	—	106	2	no	—
306	#102	—	106	2	no	—
307	#102	—	106	2	no	—
308	C₂²⋊C₈	—	106	1	no	—
309	C₂²⋊C₈	—	106	1	no	—
310	C₂²⋊C₈	—	106	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	53	1	no	—
313	C₄×C₈	—	53	1	no	—
314	C₄×C₈	—	53	1	no	—
315	C₄×C₈	—	106	1	no	—
316	C₄×C₈	—	106	1	no	—
317	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
318	#41	—	53	4	no	—
319	#41	—	106	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	106	2	no	—
322	C₂×Q₈	—	424	4	no	—
323	C₂×Q₈	—	212	2	no	—
324	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
325	C₂×D₄	—	53	1	no	—
326	C₂×D₄	—	106	1	no	—
327	C₂²×C₄	—	53	1	no	—
328	C₂²×C₄	—	53	1	no	—
329	C₂²×C₄	—	53	1	no	—
330	C₂²×C₄	—	106	1	no	—
331	C₂²×C₄	—	106	1	no	—
332	C₂²×C₄	—	106	1	no	—
333	C₂²×C₄	—	212	2	no	—
334	M₁₆	—	212	4	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	53	1	no	—
338	C₂×C₈	—	53	1	no	—
339	C₂×C₈	—	106	2	no	—
340	C₂×C₈	—	106	2	no	—
341	C₂×C₈	—	106	1	no	—
342	C₂×C₈	—	106	2	no	—
343	C₂×C₈	—	212	2	no	—
344	C₂×C₈	—	212	2	no	—
345	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
346	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	53	1	no	—
351	C₄⋊C₄	—	106	1	no	—
352	C₄⋊C₄	—	106	2	no	—
353	C₄⋊C₄	—	106	2	no	—
354	C₄⋊C₄	—	212	2	no	—
355	C₄⋊C₄	—	212	2	no	—
356	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
357	C₂²⋊C₄	—	106	1	no	—
358	C₂²⋊C₄	—	106	1	no	—
359	C₂²⋊C₄	—	106	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	53	1	no	—
362	C₄²	—	53	1	no	—
363	C₄²	—	53	1	no	—
364	C₄²	—	106	1	no	—
365	C₄²	—	106	1	no	—
366	C₄²	C₂³×D₅₃	1	1	yes	characteristic
367	C₂³	—	53	1	no	—
368	C₂³	—	106	1	no	—
369	Q₈	—	2	1	no	—
370	Q₈	—	8	2	no	—
371	Q₈	—	424	2	no	—
372	Q₈	—	424	4	no	—
373	Q₈	Q₁₆×D₅₃	1	2	yes	—
374	D₄	—	53	2	no	—
375	D₄	—	106	4	no	—
376	D₄	—	106	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	53	2	no	—
383	C₂×C₄	—	53	2	no	—
384	C₂×C₄	—	53	1	no	—
385	C₂×C₄	—	106	2	no	—
386	C₂×C₄	—	106	4	no	—
387	C₂×C₄	—	106	1	no	—
388	C₂×C₄	—	106	1	no	—
389	C₂×C₄	—	106	1	no	—
390	C₂×C₄	—	424	4	no	—
391	C₂×C₄	—	212	2	no	—
392	C₂×C₄	—	212	2	no	—
393	C₂×C₄	—	212	1	no	—
394	C₂×C₄	—	212	1	no	—
395	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
397	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	1	no	—
401	C₈	—	53	2	no	—
402	C₈	—	106	1	no	—
403	C₈	—	212	2	no	—
404	C₈	—	212	1	no	—
405	C₈	#13133249	1	2	yes	—
406	C₂²	—	53	2	no	—
407	C₂²	—	106	1	no	—
408	C₂²	—	106	1	no	—
409	C₂²	—	106	2	no	—
410	C₂²	—	212	1	no	—
411	C₂²	—	212	1	no	—
412	C₂²	#121×D₅₃	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	53	2	no	—
418	C₄	—	53	2	no	—
419	C₄	—	106	1	no	—
420	C₄	—	424	2	no	—
421	C₄	—	212	1	no	—
422	C₄	C₂×Q₁₆×D₅₃	1	1	yes	characteristic
423	C₄	#135×D₅₃	1	1	yes	characteristic
424	C₄	#137×D₅₃	1	1	yes	characteristic
425	C₄	C₂×#13133249	1	1	yes	characteristic
426	C₂	—	106	2	no	—
427	C₂	—	212	2	no	—
428	C₂	#20284199	1	1	yes	characteristic
429	C₂	#467×D₅₃	1	1	yes	characteristic
430	C₂	#472×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1676	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×#11719949	D₄
hypercenter	#1676	D₅₃
hypocenter	C₅₃	#19272
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1676

Complements

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

N	H ≅ G/N	type
1. #500×D₅₃	C₂	semidirect
4. #20274119	C₂	semidirect
5. #20274117	C₂	semidirect
6. #20274115	C₂	semidirect
7. #20274113	C₂	semidirect
8. #20274111	C₂	semidirect
9. #20273472	C₂	semidirect
10. #20273394	C₂	semidirect
11. C₅₃×#1676	C₂	semidirect
216. #1676	D₅₃	semidirect
262. C₅₃	#19272	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
#20284529	2
C₈×#11719949	2
#20274119	2
#20274117	2
#20274115	2
#20274113	2
#20274111	2
#20273472	2
#20273394	2
C₅₃×#1676	2
#19272	53