Subgroups — C₅₃×#9293 #27216805

Order 13568.

558 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3205	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#1545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#1517	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#1286	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1275	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#131×C₅₃	—	2	1	no	—
9	C₅₃×#532	C₂²	1	1	yes	characteristic
10	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
11	C₅₃×#493	C₄	1	2	yes	complemented
12	C₅₃×#486	C₄	1	2	yes	complemented
13	C₅₃×#459	—	2	2	no	—
14	C₅₃×#447	—	2	2	no	—
15	C₅₃×#435	—	2	2	no	—
16	C₅₃×#435	—	2	2	no	—
17	C₅₃×#431	C₂²	1	1	yes	characteristic
18	C₅₃×#431	C₂²	1	1	yes	characteristic
19	C₅₃×#423	C₂²	1	1	yes	characteristic
20	C₂×#102×C₅₃	—	2	1	no	—
21	C₂×#102×C₅₃	—	2	1	no	—
22	C₅₃×#408	—	2	1	no	—
23	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
24	C₅₃×#382	C₂²	1	1	yes	characteristic
25	C₅₃×#331	—	2	2	no	—
26	C₅₃×#327	—	2	2	no	—
27	C₂×#41×C₅₃	—	2	1	no	—
28	C₂²×D₄×C₅₃	—	2	1	no	—
29	C₂²×D₄×C₅₃	—	2	1	no	—
30	C₂²×D₄×C₅₃	—	2	1	no	—
31	C₂×D₈×C₅₃	—	2	4	no	—
32	#131×C₅₃	—	4	2	no	—
33	#131×C₅₃	—	4	2	no	—
34	C₂×M₁₆×C₅₃	—	2	2	no	—
35	C₂×M₁₆×C₅₃	—	2	1	no	—
36	C₂²×C₈×C₅₃	—	2	2	no	—
37	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
39	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
40	#127×C₅₃	—	2	1	no	—
41	#127×C₅₃	—	2	1	no	—
42	#127×C₅₃	—	2	1	no	—
43	#127×C₅₃	C₂×C₄	1	2	yes	—
44	#127×C₅₃	C₂×C₄	1	1	yes	characteristic
45	#124×C₅₃	—	2	1	no	—
46	#121×C₅₃	—	2	1	no	—
47	#121×C₅₃	D₄	1	2	yes	—
48	C₄×D₄×C₅₃	—	2	1	no	—
49	C₄×D₄×C₅₃	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
51	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
52	C₄⋊C₈×C₅₃	—	2	1	no	—
53	C₄⋊C₈×C₅₃	—	2	1	no	—
54	C₄⋊C₈×C₅₃	—	2	1	no	—
55	C₄⋊C₈×C₅₃	D₄	1	2	yes	—
56	#102×C₅₃	—	2	4	no	—
57	#102×C₅₃	—	4	2	no	—
58	#102×C₅₃	—	4	2	no	—
59	C₂²⋊C₈×C₅₃	—	2	4	no	—
60	C₂²⋊C₈×C₅₃	—	2	1	no	—
61	C₂²⋊C₈×C₅₃	—	2	1	no	—
62	#97×C₅₃	—	2	1	no	—
63	#97×C₅₃	—	2	1	no	—
64	C₄×C₈×C₅₃	—	2	1	no	—
65	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
66	#95×C₅₃	—	2	1	no	—
67	#95×C₅₃	—	2	1	no	—
68	C₂⁴×C₅₃	—	4	1	no	—
69	#41×C₅₃	—	4	1	no	—
70	#41×C₅₃	—	4	1	no	—
71	#41×C₅₃	—	4	1	no	—
72	#41×C₅₃	—	4	1	no	—
73	C₂×Q₈×C₅₃	—	2	1	no	—
74	C₂×D₄×C₅₃	—	2	2	no	—
75	C₂×D₄×C₅₃	—	2	2	no	—
76	C₂×D₄×C₅₃	—	2	1	no	—
77	C₂×D₄×C₅₃	—	2	2	no	—
78	C₂×D₄×C₅₃	—	2	1	no	—
79	C₂×D₄×C₅₃	—	2	2	no	—
80	C₂×D₄×C₅₃	—	4	1	no	—
81	C₂×D₄×C₅₃	—	4	1	no	—
82	C₂×D₄×C₅₃	—	4	1	no	—
83	C₂×D₄×C₅₃	—	4	1	no	—
84	C₂×D₄×C₅₃	—	4	1	no	—
85	C₂×D₄×C₅₃	—	4	1	no	—
86	C₂×D₄×C₅₃	—	4	1	no	—
87	C₂×D₄×C₅₃	—	8	2	no	—
88	C₂×D₄×C₅₃	—	8	2	no	—
89	C₂×D₄×C₅₃	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₅₃	—	2	2	no	—
91	C₂²×C₄×C₅₃	—	4	1	no	—
92	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
95	D₈×C₅₃	—	8	4	no	—
96	M₁₆×C₅₃	—	4	4	no	—
97	M₁₆×C₅₃	—	4	1	no	—
98	M₁₆×C₅₃	—	4	1	no	—
99	C₂×C₈×C₅₃	—	2	1	no	—
100	C₂×C₈×C₅₃	—	2	1	no	—
101	C₂×C₈×C₅₃	—	2	2	no	—
102	C₂×C₈×C₅₃	—	2	1	no	—
103	C₂×C₈×C₅₃	—	2	2	no	—
104	C₂×C₈×C₅₃	—	2	1	no	—
105	C₂×C₈×C₅₃	—	2	1	no	—
106	C₂×C₈×C₅₃	—	4	4	no	—
107	C₂×C₈×C₅₃	—	4	1	no	—
108	C₂×C₈×C₅₃	D₈	1	2	yes	complemented
109	C₄⋊C₄×C₅₃	—	2	1	no	—
110	C₄⋊C₄×C₅₃	—	4	1	no	—
111	C₄⋊C₄×C₅₃	—	4	1	no	—
112	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
113	C₂²⋊C₄×C₅₃	—	2	2	no	—
114	C₂²⋊C₄×C₅₃	—	2	2	no	—
115	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₅₃	#41	1	1	yes	characteristic
119	C₂³×C₅₃	—	2	2	no	—
120	C₂³×C₅₃	—	4	2	no	—
121	C₂³×C₅₃	—	8	2	no	—
122	C₂³×C₅₃	—	8	2	no	—
123	C₂³×C₅₃	—	8	1	no	—
124	C₂³×C₅₃	—	8	1	no	—
125	C₂³×C₅₃	#121	1	1	yes	characteristic
126	Q₈×C₅₃	—	4	1	no	—
127	Q₈×C₅₃	—	4	1	no	—
128	D₄×C₅₃	—	4	2	no	—
129	D₄×C₅₃	—	4	4	no	—
130	D₄×C₅₃	—	4	2	no	—
131	D₄×C₅₃	—	4	2	no	—
132	D₄×C₅₃	—	4	1	no	—
133	D₄×C₅₃	—	4	2	no	—
134	D₄×C₅₃	—	4	1	no	—
135	D₄×C₅₃	—	4	2	no	—
136	D₄×C₅₃	—	8	1	no	—
137	D₄×C₅₃	—	8	2	no	—
138	D₄×C₅₃	—	8	2	no	—
139	D₄×C₅₃	—	8	2	no	—
140	D₄×C₅₃	—	8	1	no	—
141	D₄×C₅₃	—	8	1	no	—
142	C₂×C₄×C₅₃	—	2	2	no	—
143	C₂×C₄×C₅₃	—	4	1	no	—
144	C₂×C₄×C₅₃	—	4	1	no	—
145	C₂×C₄×C₅₃	—	4	2	no	—
146	C₂×C₄×C₅₃	—	4	2	no	—
147	C₂×C₄×C₅₃	—	8	1	no	—
148	C₂×C₄×C₅₃	—	8	1	no	—
149	C₂×C₄×C₅₃	—	8	1	no	—
150	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
154	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
155	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
158	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₈×C₅₃	—	2	2	no	—
161	C₈×C₅₃	—	4	2	no	—
162	C₈×C₅₃	—	4	2	no	—
163	C₈×C₅₃	—	4	1	no	—
164	C₈×C₅₃	—	8	1	no	—
165	#9293	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂²×C₅₃	—	2	1	no	—
167	C₂²×C₅₃	—	2	1	no	—
168	C₂²×C₅₃	—	4	2	no	—
169	C₂²×C₅₃	—	4	2	no	—
170	C₂²×C₅₃	—	4	2	no	—
171	C₂²×C₅₃	—	8	2	no	—
172	C₂²×C₅₃	—	8	2	no	—
173	C₂²×C₅₃	—	8	2	no	—
174	C₂²×C₅₃	—	16	2	no	—
175	C₂²×C₅₃	—	16	2	no	—
176	C₂²×C₅₃	#386	1	1	yes	characteristic
177	C₂²×C₅₃	#459	1	1	yes	characteristic
178	C₂²×C₅₃	#463	1	1	yes	characteristic
179	C₄×C₅₃	—	2	1	no	—
180	C₄×C₅₃	—	2	1	no	—
181	C₄×C₅₃	—	2	1	no	—
182	C₄×C₅₃	—	2	1	no	—
183	C₄×C₅₃	—	4	2	no	—
184	C₄×C₅₃	—	16	1	no	—
185	C₄×C₅₃	C₄×D₈	1	1	yes	characteristic
186	C₄×C₅₃	#442	1	1	yes	characteristic
187	C₄×C₅₃	#447	1	1	yes	characteristic
188	C₄×C₅₃	#449	1	1	yes	characteristic
189	#3205	C₂×C₅₃	1	1	yes	characteristic
190	#2932	C₂×C₅₃	1	1	yes	characteristic, complemented
191	#1961	C₂×C₅₃	1	1	yes	characteristic, complemented
192	#1545	C₂×C₅₃	1	1	yes	characteristic, complemented
193	#1517	C₂×C₅₃	1	1	yes	characteristic, complemented
194	#1286	C₂×C₅₃	1	1	yes	characteristic, complemented
195	#1275	C₂×C₅₃	1	1	yes	characteristic, complemented
196	C₂×C₅₃	—	2	1	no	—
197	C₂×C₅₃	—	2	1	no	—
198	C₂×C₅₃	—	8	2	no	—
199	C₂×C₅₃	—	16	2	no	—
200	C₂×C₅₃	#1879	1	1	yes	characteristic
201	C₂×C₅₃	#1903	1	1	yes	characteristic
202	C₂×C₅₃	#1910	1	1	yes	characteristic
203	C₂×#131	—	2	1	no	—
204	#532	C₂²×C₅₃	1	1	yes	characteristic
205	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
206	#493	C₄×C₅₃	1	2	yes	complemented
207	#486	C₄×C₅₃	1	2	yes	complemented
208	#459	—	2	2	no	—
209	#447	—	2	2	no	—
210	#435	—	2	2	no	—
211	#435	—	2	2	no	—
212	#431	C₂²×C₅₃	1	1	yes	characteristic
213	#431	C₂²×C₅₃	1	1	yes	characteristic
214	#423	C₂²×C₅₃	1	1	yes	characteristic
215	C₂×#102	—	2	1	no	—
216	C₂×#102	—	2	1	no	—
217	#408	—	2	1	no	—
218	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
219	#382	C₂²×C₅₃	1	1	yes	characteristic
220	#331	—	2	2	no	—
221	#327	—	2	2	no	—
222	C₅₃	#9293	1	1	yes	characteristic, direct product factor, Sylow
223	C₂×#41	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂×D₈	—	2	4	no	—
228	#131	—	4	2	no	—
229	#131	—	4	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	1	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	D₄×C₅₃	1	1	yes	characteristic
234	C₂²×C₈	D₄×C₅₃	1	1	yes	characteristic
235	C₄⋊Q₈	C₂×C₄×C₅₃	1	1	yes	characteristic
236	#127	—	2	1	no	—
237	#127	—	2	1	no	—
238	#127	—	2	1	no	—
239	#127	C₂×C₄×C₅₃	1	2	yes	—
240	#127	C₂×C₄×C₅₃	1	1	yes	characteristic
241	#124	—	2	1	no	—
242	#121	—	2	1	no	—
243	#121	D₄×C₅₃	1	2	yes	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	D₄×C₅₃	1	2	yes	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	D₄×C₅₃	1	2	yes	—
252	#102	—	2	4	no	—
253	#102	—	4	2	no	—
254	#102	—	4	2	no	—
255	C₂²⋊C₈	—	2	4	no	—
256	C₂²⋊C₈	—	2	1	no	—
257	C₂²⋊C₈	—	2	1	no	—
258	#97	—	2	1	no	—
259	#97	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	C₂×C₄×C₅₃	1	2	yes	—
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	C₂⁴	—	4	1	no	—
265	#41	—	4	1	no	—
266	#41	—	4	1	no	—
267	#41	—	4	1	no	—
268	#41	—	4	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂×D₄	—	8	2	no	—
284	C₂×D₄	—	8	2	no	—
285	C₂×D₄	C₂²⋊C₄×C₅₃	1	2	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
290	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
291	D₈	—	8	4	no	—
292	M₁₆	—	4	4	no	—
293	M₁₆	—	4	1	no	—
294	M₁₆	—	4	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	4	4	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	D₈×C₅₃	1	2	yes	complemented
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₄²	C₂²×C₄×C₅₃	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
313	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
314	C₄²	#41×C₅₃	1	1	yes	characteristic
315	C₂³	—	2	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	8	2	no	—
318	C₂³	—	8	2	no	—
319	C₂³	—	8	1	no	—
320	C₂³	—	8	1	no	—
321	C₂³	#121×C₅₃	1	1	yes	characteristic
322	Q₈	—	4	1	no	—
323	Q₈	—	4	1	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	2	no	—
332	D₄	—	8	1	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	2	no	—
335	D₄	—	8	2	no	—
336	D₄	—	8	1	no	—
337	D₄	—	8	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	8	1	no	—
345	C₂×C₄	—	8	1	no	—
346	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
347	C₂×C₄	C₄×D₄×C₅₃	1	1	yes	characteristic
348	C₂×C₄	C₄×D₄×C₅₃	1	1	yes	characteristic
349	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
350	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
351	C₂×C₄	#123×C₅₃	1	1	yes	characteristic
352	C₂×C₄	C₂×D₈×C₅₃	1	1	yes	characteristic
353	C₂×C₄	#135×C₅₃	1	1	yes	characteristic
354	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
355	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
356	C₈	—	2	2	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₈	—	4	1	no	—
360	C₈	—	8	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	16	2	no	—
370	C₂²	—	16	2	no	—
371	C₂²	C₅₃×#386	1	1	yes	characteristic
372	C₂²	C₅₃×#459	1	1	yes	characteristic
373	C₂²	C₅₃×#463	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	16	1	no	—
380	C₄	C₄×D₈×C₅₃	1	1	yes	characteristic
381	C₄	C₅₃×#442	1	1	yes	characteristic
382	C₄	C₅₃×#447	1	1	yes	characteristic
383	C₄	C₅₃×#449	1	1	yes	characteristic
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	—	8	2	no	—
387	C₂	—	16	2	no	—
388	C₂	C₅₃×#1879	1	1	yes	characteristic
389	C₂	C₅₃×#1903	1	1	yes	characteristic
390	C₂	C₅₃×#1910	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	#386
commutator	C₄²	C₂²×C₄×C₅₃
Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
prime radical	C₅₃×#3205	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2932	C₂	semidirect
3. C₅₃×#1961	C₂	semidirect
4. C₅₃×#1545	C₂	semidirect
5. C₅₃×#1517	C₂	semidirect
6. C₅₃×#1286	C₂	semidirect
7. C₅₃×#1275	C₂	semidirect
11. C₅₃×#493	C₄	semidirect
12. C₅₃×#486	C₄	semidirect
108. C₂×C₈×C₅₃	D₈	semidirect
165. #9293	C₅₃	direct (N × H)
190. #2932	C₂×C₅₃	semidirect
191. #1961	C₂×C₅₃	semidirect
192. #1545	C₂×C₅₃	semidirect
193. #1517	C₂×C₅₃	semidirect
194. #1286	C₂×C₅₃	semidirect
195. #1275	C₂×C₅₃	semidirect
206. #493	C₄×C₅₃	semidirect
207. #486	C₄×C₅₃	semidirect
222. C₅₃	#9293	direct (N × H)
304. C₂×C₈	D₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3205	2
C₅₃×#2932	2
C₅₃×#1961	2
C₅₃×#1545	2
C₅₃×#1517	2
C₅₃×#1286	2
C₅₃×#1275	2
#9293	53

Subgroups — C53×#9293 #27216805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#9293 #27216805