Subgroups — C₅₃×#22540 #27230052

Order 13568.

1430 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#1982	C₂	1	3	yes	maximal, complemented
5	C₅₃×#1957	C₂	1	3	yes	maximal, complemented
6	C₅₃×#1802	C₂	1	3	yes	maximal, complemented
7	C₄×#102×C₅₃	C₂	1	3	yes	maximal, complemented
8	C₂²×#41×C₅₃	—	2	1	no	—
9	C₅₃×#550	—	2	4	no	—
10	C₅₃×#550	C₄	1	8	yes	complemented
11	C₂×#127×C₅₃	C₂²	1	3	yes	—
12	C₂×#121×C₅₃	—	2	3	no	—
13	C₂×C₄×Q₈×C₅₃	—	2	1	no	—
14	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	—
16	C₈×Q₈×C₅₃	—	2	4	no	—
17	C₂×C₄⋊C₈×C₅₃	C₂²	1	3	yes	—
18	C₂×#102×C₅₃	C₂²	1	3	yes	—
19	C₂×#102×C₅₃	C₂²	1	3	yes	—
20	C₂×#102×C₅₃	C₂²	1	6	yes	—
21	C₂×C₄×C₈×C₅₃	C₂²	1	3	yes	—
22	C₅₃×#389	—	2	3	no	—
23	C₅₃×#384	C₂²	1	3	yes	—
24	C₄×C₄⋊C₄×C₅₃	C₂²	1	3	yes	—
25	C₅₃×#340	C₂²	1	1	yes	characteristic
26	C₅₃×#340	C₂²	1	3	yes	—
27	C₂×#41×C₅₃	—	2	8	no	—
28	C₂×#41×C₅₃	—	4	4	no	—
29	C₂×#41×C₅₃	—	4	4	no	—
30	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₅₃	—	2	3	no	—
32	C₂²×D₄×C₅₃	—	2	3	no	—
33	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
34	C₂³×C₄×C₅₃	—	2	3	no	—
35	C₂²×C₈×C₅₃	C₂³	1	3	yes	—
36	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
37	#127×C₅₃	—	2	6	no	—
38	#127×C₅₃	C₂×C₄	1	12	yes	—
39	#121×C₅₃	—	2	24	no	—
40	C₄×Q₈×C₅₃	—	4	4	no	—
41	C₄×Q₈×C₅₃	C₂×C₄	1	4	yes	—
42	C₄×Q₈×C₅₃	D₄	1	4	yes	—
43	C₄×D₄×C₅₃	—	2	6	no	—
44	C₄×D₄×C₅₃	C₂×C₄	1	12	yes	—
45	C₂×C₄⋊C₄×C₅₃	—	2	3	no	—
46	C₂×C₄⋊C₄×C₅₃	—	2	3	no	—
47	C₂×C₄⋊C₄×C₅₃	D₄	1	3	yes	—
48	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
49	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₅₃	—	2	3	no	—
52	C₂×C₄²×C₅₃	—	2	3	no	—
53	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
54	C₄⋊C₈×C₅₃	—	2	6	no	—
55	#102×C₅₃	—	2	6	no	—
56	#102×C₅₃	—	2	6	no	—
57	#102×C₅₃	—	4	6	no	—
58	C₄×C₈×C₅₃	—	2	6	no	—
59	#95×C₅₃	—	2	3	no	—
60	C₂⁴×C₅₃	—	2	3	no	—
61	#41×C₅₃	—	4	32	no	—
62	C₂×Q₈×C₅₃	C₂²⋊C₄	1	4	yes	—
63	C₂×Q₈×C₅₃	D₈	1	4	yes	—
64	C₂×Q₈×C₅₃	SD₁₆	1	4	yes	—
65	C₂×D₄×C₅₃	—	2	12	no	—
66	C₂×D₄×C₅₃	—	2	12	no	—
67	C₂×D₄×C₅₃	—	2	3	no	—
68	C₂×D₄×C₅₃	—	2	3	no	—
69	C₂×D₄×C₅₃	—	2	3	no	—
70	C₂×D₄×C₅₃	—	2	3	no	—
71	C₂×D₄×C₅₃	—	2	3	no	—
72	C₂×D₄×C₅₃	—	4	6	no	—
73	C₂×D₄×C₅₃	—	4	6	no	—
74	C₂×D₄×C₅₃	—	8	3	no	—
75	C₂×D₄×C₅₃	—	8	3	no	—
76	C₂×D₄×C₅₃	C₂²×C₄	1	6	yes	—
77	C₂²×C₄×C₅₃	—	2	1	no	—
78	C₂²×C₄×C₅₃	—	2	1	no	—
79	C₂²×C₄×C₅₃	—	2	12	no	—
80	C₂²×C₄×C₅₃	—	2	3	no	—
81	C₂²×C₄×C₅₃	—	4	6	no	—
82	C₂²×C₄×C₅₃	—	4	6	no	—
83	C₂²×C₄×C₅₃	C₂×D₄	1	3	yes	—
84	C₂²×C₄×C₅₃	C₂×D₄	1	3	yes	—
85	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₅₃	—	2	1	no	—
87	C₂×C₈×C₅₃	—	2	1	no	—
88	C₂×C₈×C₅₃	—	2	3	no	—
89	C₂×C₈×C₅₃	—	2	3	no	—
90	C₂×C₈×C₅₃	—	2	3	no	—
91	C₂×C₈×C₅₃	#41	1	2	yes	complemented
92	C₄⋊C₄×C₅₃	—	2	1	no	—
93	C₄⋊C₄×C₅₃	—	2	1	no	—
94	C₄⋊C₄×C₅₃	—	2	3	no	—
95	C₄⋊C₄×C₅₃	—	2	3	no	—
96	C₄⋊C₄×C₅₃	—	4	6	no	—
97	C₄⋊C₄×C₅₃	—	8	3	no	—
98	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	12	yes	—
99	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
100	C₄⋊C₄×C₅₃	#41	1	2	yes	complemented
101	C₂²⋊C₄×C₅₃	—	2	12	no	—
102	C₄²×C₅₃	—	4	6	no	—
103	C₄²×C₅₃	C₂²×C₄	1	6	yes	—
104	C₄²×C₅₃	C₂×D₄	1	6	yes	—
105	C₂³×C₅₃	—	2	6	no	—
106	C₂³×C₅₃	—	4	3	no	—
107	C₂³×C₅₃	—	4	3	no	—
108	C₂³×C₅₃	—	4	3	no	—
109	C₂³×C₅₃	—	4	3	no	—
110	C₂³×C₅₃	—	4	3	no	—
111	C₂³×C₅₃	—	4	3	no	—
112	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
113	Q₈×C₅₃	#102	1	16	yes	complemented
114	D₄×C₅₃	—	2	6	no	—
115	D₄×C₅₃	—	2	6	no	—
116	D₄×C₅₃	—	4	3	no	—
117	D₄×C₅₃	—	4	3	no	—
118	D₄×C₅₃	—	4	24	no	—
119	D₄×C₅₃	—	8	12	no	—
120	C₂×C₄×C₅₃	—	2	3	no	—
121	C₂×C₄×C₅₃	—	2	3	no	—
122	C₂×C₄×C₅₃	—	2	2	no	—
123	C₂×C₄×C₅₃	—	2	2	no	—
124	C₂×C₄×C₅₃	—	4	1	no	—
125	C₂×C₄×C₅₃	—	4	1	no	—
126	C₂×C₄×C₅₃	—	4	1	no	—
127	C₂×C₄×C₅₃	—	4	1	no	—
128	C₂×C₄×C₅₃	—	4	24	no	—
129	C₂×C₄×C₅₃	—	4	3	no	—
130	C₂×C₄×C₅₃	—	4	3	no	—
131	C₂×C₄×C₅₃	—	4	3	no	—
132	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	6	yes	—
133	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	6	yes	—
134	C₂×C₄×C₅₃	C₂×D₈	1	6	yes	—
135	C₂×C₄×C₅₃	C₂×SD₁₆	1	6	yes	—
136	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
140	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
141	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
142	C₈×C₅₃	—	2	2	no	—
143	C₈×C₅₃	—	4	3	no	—
144	#22540	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂²×C₅₃	—	4	6	no	—
146	C₂²×C₅₃	—	4	6	no	—
147	C₂²×C₅₃	—	4	6	no	—
148	C₂²×C₅₃	—	8	3	no	—
149	C₂²×C₅₃	—	8	3	no	—
150	C₂²×C₅₃	—	8	3	no	—
151	C₂²×C₅₃	—	8	3	no	—
152	C₂²×C₅₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₅₃	#548	1	1	yes	characteristic
154	C₂²×C₅₃	#550	1	1	yes	characteristic
155	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
156	C₂²×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
157	C₂²×C₅₃	#576	1	1	yes	characteristic
158	C₂²×C₅₃	#577	1	1	yes	characteristic
159	C₄×C₅₃	—	2	6	no	—
160	C₄×C₅₃	—	4	2	no	—
161	C₄×C₅₃	—	4	2	no	—
162	C₄×C₅₃	—	8	3	no	—
163	C₄×C₅₃	C₂×#102	1	12	yes	—
164	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
165	C₄×C₅₃	#520	1	1	yes	characteristic
166	C₄×C₅₃	#548	1	1	yes	characteristic
167	C₄×C₅₃	#550	1	1	yes	characteristic
168	C₂×#550	C₂×C₅₃	1	1	yes	characteristic
169	C₂×C₈×Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
170	Q₈×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
171	#1982	C₂×C₅₃	1	3	yes	complemented
172	#1957	C₂×C₅₃	1	3	yes	complemented
173	#1802	C₂×C₅₃	1	3	yes	complemented
174	C₄×#102	C₂×C₅₃	1	3	yes	complemented
175	C₂×C₅₃	—	8	6	no	—
176	C₂×C₅₃	#2341	1	1	yes	characteristic
177	C₂×C₅₃	C₂²×#102	1	1	yes	characteristic
178	C₂×C₅₃	#2897	1	1	yes	characteristic
179	C₂×C₅₃	#3358	1	1	yes	characteristic
180	C₂×C₅₃	#3362	1	1	yes	characteristic
181	C₂×C₅₃	#3391	1	1	yes	characteristic
182	C₂×C₅₃	#3392	1	1	yes	characteristic
183	C₂²×#41	—	2	1	no	—
184	#550	—	2	4	no	—
185	#550	C₄×C₅₃	1	8	yes	complemented
186	C₂×#127	C₂²×C₅₃	1	3	yes	—
187	C₂×#121	—	2	3	no	—
188	C₂×C₄×Q₈	—	2	1	no	—
189	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
190	C₂×C₄×D₄	C₂²×C₅₃	1	3	yes	—
191	C₈×Q₈	—	2	4	no	—
192	C₂×C₄⋊C₈	C₂²×C₅₃	1	3	yes	—
193	C₂×#102	C₂²×C₅₃	1	3	yes	—
194	C₂×#102	C₂²×C₅₃	1	3	yes	—
195	C₂×#102	C₂²×C₅₃	1	6	yes	—
196	C₂×C₄×C₈	C₂²×C₅₃	1	3	yes	—
197	#389	—	2	3	no	—
198	#384	C₂²×C₅₃	1	3	yes	—
199	C₄×C₄⋊C₄	C₂²×C₅₃	1	3	yes	—
200	#340	C₂²×C₅₃	1	3	yes	—
201	#340	C₂²×C₅₃	1	1	yes	characteristic
202	C₅₃	#22540	1	1	yes	characteristic, direct product factor, Sylow
203	C₂×#41	—	2	8	no	—
204	C₂×#41	—	4	4	no	—
205	C₂×#41	—	4	4	no	—
206	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
207	C₂²×D₄	—	2	3	no	—
208	C₂²×D₄	—	2	3	no	—
209	C₂²×D₄	C₂³×C₅₃	1	3	yes	—
210	C₂³×C₄	—	2	3	no	—
211	C₂²×C₈	C₂³×C₅₃	1	3	yes	—
212	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
213	#127	—	2	6	no	—
214	#127	C₂×C₄×C₅₃	1	12	yes	—
215	#121	—	2	24	no	—
216	C₄×Q₈	—	4	4	no	—
217	C₄×Q₈	C₂×C₄×C₅₃	1	4	yes	—
218	C₄×Q₈	D₄×C₅₃	1	4	yes	—
219	C₄×D₄	—	2	6	no	—
220	C₄×D₄	C₂×C₄×C₅₃	1	12	yes	—
221	C₂×C₄⋊C₄	—	2	3	no	—
222	C₂×C₄⋊C₄	—	2	3	no	—
223	C₂×C₄⋊C₄	D₄×C₅₃	1	3	yes	—
224	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
225	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	2	3	no	—
228	C₂×C₄²	—	2	3	no	—
229	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
230	C₄⋊C₈	—	2	6	no	—
231	#102	—	2	6	no	—
232	#102	—	2	6	no	—
233	#102	—	4	6	no	—
234	C₄×C₈	—	2	6	no	—
235	#95	—	2	3	no	—
236	C₂⁴	—	2	3	no	—
237	#41	—	4	32	no	—
238	C₂×Q₈	C₂²⋊C₄×C₅₃	1	4	yes	—
239	C₂×Q₈	D₈×C₅₃	1	4	yes	—
240	C₂×Q₈	SD₁₆×C₅₃	1	4	yes	—
241	C₂×D₄	—	2	12	no	—
242	C₂×D₄	—	2	12	no	—
243	C₂×D₄	—	2	3	no	—
244	C₂×D₄	—	2	3	no	—
245	C₂×D₄	—	2	3	no	—
246	C₂×D₄	—	2	3	no	—
247	C₂×D₄	—	2	3	no	—
248	C₂×D₄	—	4	6	no	—
249	C₂×D₄	—	4	6	no	—
250	C₂×D₄	—	8	3	no	—
251	C₂×D₄	—	8	3	no	—
252	C₂×D₄	C₂²×C₄×C₅₃	1	6	yes	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	12	no	—
256	C₂²×C₄	—	2	3	no	—
257	C₂²×C₄	—	4	6	no	—
258	C₂²×C₄	—	4	6	no	—
259	C₂²×C₄	C₂×D₄×C₅₃	1	3	yes	—
260	C₂²×C₄	C₂×D₄×C₅₃	1	3	yes	—
261	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	3	no	—
265	C₂×C₈	—	2	3	no	—
266	C₂×C₈	—	2	3	no	—
267	C₂×C₈	#41×C₅₃	1	2	yes	complemented
268	C₄⋊C₄	—	2	1	no	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	—	2	3	no	—
271	C₄⋊C₄	—	2	3	no	—
272	C₄⋊C₄	—	4	6	no	—
273	C₄⋊C₄	—	8	3	no	—
274	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	12	yes	—
275	C₄⋊C₄	C₂²×C₄×C₅₃	1	2	yes	—
276	C₄⋊C₄	#41×C₅₃	1	2	yes	complemented
277	C₂²⋊C₄	—	2	12	no	—
278	C₄²	—	4	6	no	—
279	C₄²	C₂²×C₄×C₅₃	1	6	yes	—
280	C₄²	C₂×D₄×C₅₃	1	6	yes	—
281	C₂³	—	2	6	no	—
282	C₂³	—	4	3	no	—
283	C₂³	—	4	3	no	—
284	C₂³	—	4	3	no	—
285	C₂³	—	4	3	no	—
286	C₂³	—	4	3	no	—
287	C₂³	—	4	3	no	—
288	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
289	Q₈	#102×C₅₃	1	16	yes	complemented
290	D₄	—	2	6	no	—
291	D₄	—	2	6	no	—
292	D₄	—	4	3	no	—
293	D₄	—	4	3	no	—
294	D₄	—	4	24	no	—
295	D₄	—	8	12	no	—
296	C₂×C₄	—	2	3	no	—
297	C₂×C₄	—	2	3	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	—	4	1	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	24	no	—
305	C₂×C₄	—	4	3	no	—
306	C₂×C₄	—	4	3	no	—
307	C₂×C₄	—	4	3	no	—
308	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	6	yes	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	6	yes	—
310	C₂×C₄	C₂×D₈×C₅₃	1	6	yes	—
311	C₂×C₄	C₂×SD₁₆×C₅₃	1	6	yes	—
312	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
313	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
314	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
315	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
316	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
317	C₂×C₄	2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
318	C₈	—	2	2	no	—
319	C₈	—	4	3	no	—
320	C₂²	—	4	6	no	—
321	C₂²	—	4	6	no	—
322	C₂²	—	4	6	no	—
323	C₂²	—	8	3	no	—
324	C₂²	—	8	3	no	—
325	C₂²	—	8	3	no	—
326	C₂²	—	8	3	no	—
327	C₂²	C₂²×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
328	C₂²	C₅₃×#548	1	1	yes	characteristic
329	C₂²	C₅₃×#550	1	1	yes	characteristic
330	C₂²	C₂²×D₈×C₅₃	1	1	yes	characteristic
331	C₂²	C₂²×SD₁₆×C₅₃	1	1	yes	characteristic
332	C₂²	C₅₃×#576	1	1	yes	characteristic
333	C₂²	C₅₃×#577	1	1	yes	characteristic
334	C₄	—	2	6	no	—
335	C₄	—	4	2	no	—
336	C₄	—	4	2	no	—
337	C₄	—	8	3	no	—
338	C₄	C₂×#102×C₅₃	1	12	yes	—
339	C₄	C₄×#41×C₅₃	1	1	yes	characteristic
340	C₄	C₅₃×#520	1	1	yes	characteristic
341	C₄	C₅₃×#548	1	1	yes	characteristic
342	C₄	C₅₃×#550	1	1	yes	characteristic
343	C₂	—	8	6	no	—
344	C₂	C₅₃×#2341	1	1	yes	characteristic
345	C₂	C₂²×#102×C₅₃	1	1	yes	characteristic
346	C₂	C₅₃×#2897	1	1	yes	characteristic
347	C₂	C₅₃×#3358	1	1	yes	characteristic
348	C₂	C₅₃×#3362	1	1	yes	characteristic
349	C₂	C₅₃×#3391	1	1	yes	characteristic
350	C₂	C₅₃×#3392	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂×C₅₃×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄×Q₈×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Q₈×C₅₃	C₂	semidirect
3. Q₈×C₄⋊C₄×C₅₃	C₂	semidirect
4. C₅₃×#1982	C₂	semidirect
5. C₅₃×#1957	C₂	semidirect
6. C₅₃×#1802	C₂	semidirect
7. C₄×#102×C₅₃	C₂	semidirect
10. C₅₃×#550	C₄	semidirect
91. C₂×C₈×C₅₃	#41	semidirect
100. C₄⋊C₄×C₅₃	#41	semidirect
113. Q₈×C₅₃	#102	semidirect
144. #22540	C₅₃	direct (N × H)
169. C₂×C₈×Q₈	C₂×C₅₃	semidirect
170. Q₈×C₄⋊C₄	C₂×C₅₃	semidirect
171. #1982	C₂×C₅₃	semidirect
172. #1957	C₂×C₅₃	semidirect
173. #1802	C₂×C₅₃	semidirect
174. C₄×#102	C₂×C₅₃	semidirect
185. #550	C₄×C₅₃	semidirect
202. C₅₃	#22540	direct (N × H)
267. C₂×C₈	#41×C₅₃	semidirect
276. C₄⋊C₄	#41×C₅₃	semidirect
289. Q₈	#102×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#550	2
C₂×C₈×Q₈×C₅₃	2
Q₈×C₄⋊C₄×C₅₃	2
C₅₃×#1982	2
C₅₃×#1957	2
C₅₃×#1802	2
C₄×#102×C₅₃	2
#22540	53

Subgroups — C53×#22540 #27230052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#22540 #27230052