Subgroups — C₅₃×#22657 #27230169

Order 13568.

982 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#427	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2354	C₂	1	2	yes	maximal
4	C₅₃×#1947	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1854	C₂	1	4	yes	maximal, complemented
6	C₅₃×#1844	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1807	C₂	1	2	yes	maximal, complemented
8	C₄×#106×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₅₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
11	C₂×#117×C₅₃	C₂²	1	4	yes	—
12	C₈×D₄×C₅₃	C₄	1	8	yes	complemented
13	C₅₃×#427	—	2	8	no	—
14	C₂×#107×C₅₃	C₂²	1	4	yes	—
15	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
16	C₂×#106×C₅₃	C₂²	1	2	yes	—
17	C₂×#106×C₅₃	C₂²	1	2	yes	—
18	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₅₃×#390	—	2	2	no	—
23	C₅₃×#388	—	2	4	no	—
24	C₅₃×#384	C₂²	1	2	yes	—
25	C₅₃×#380	C₂²	1	4	yes	—
26	C₄×C₄⋊C₄×C₅₃	—	2	2	no	—
27	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
28	C₅₃×#340	C₂²	1	4	yes	—
29	C₅₃×#340	C₂²	1	2	yes	—
30	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
32	C₂²×C₈×C₅₃	—	2	4	no	—
33	C₂²×C₈×C₅₃	—	2	4	no	—
34	C₂²×C₈×C₅₃	C₂×C₄	1	8	yes	—
35	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
36	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
38	C₄×D₄×C₅₃	C₂×C₄	1	4	yes	—
39	C₄×D₄×C₅₃	Q₈	1	4	yes	—
40	#117×C₅₃	—	2	8	no	—
41	#117×C₅₃	—	4	4	no	—
42	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
46	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
47	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
48	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
51	C₂×C₄²×C₅₃	—	2	4	no	—
52	C₂×C₄²×C₅₃	—	2	2	no	—
53	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
54	#107×C₅₃	—	2	8	no	—
55	#106×C₅₃	—	2	4	no	—
56	#106×C₅₃	—	2	2	no	—
57	#106×C₅₃	—	4	2	no	—
58	#106×C₅₃	D₄	1	4	yes	complemented
59	C₄⋊C₈×C₅₃	C₂×C₄	1	4	yes	—
60	C₂²⋊C₈×C₅₃	C₂×C₄	1	8	yes	—
61	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	—
62	#95×C₅₃	—	2	4	no	—
63	#95×C₅₃	—	2	2	no	—
64	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
65	C₂×D₄×C₅₃	—	2	4	no	—
66	C₂×D₄×C₅₃	C₄⋊C₄	1	4	yes	—
67	C₂²×C₄×C₅₃	—	2	2	no	—
68	C₂²×C₄×C₅₃	—	2	2	no	—
69	C₂²×C₄×C₅₃	—	2	2	no	—
70	C₂²×C₄×C₅₃	—	2	2	no	—
71	C₂²×C₄×C₅₃	—	2	2	no	—
72	C₂²×C₄×C₅₃	—	2	2	no	—
73	C₂²×C₄×C₅₃	—	2	4	no	—
74	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	—
79	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
80	C₂×C₈×C₅₃	—	2	2	no	—
81	C₂×C₈×C₅₃	—	2	2	no	—
82	C₂×C₈×C₅₃	—	2	1	no	—
83	C₂×C₈×C₅₃	—	2	1	no	—
84	C₂×C₈×C₅₃	—	2	16	no	—
85	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
86	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
87	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
89	C₂×C₈×C₅₃	#41	1	2	yes	—
90	C₄⋊C₄×C₅₃	—	2	2	no	—
91	C₄⋊C₄×C₅₃	—	2	4	no	—
92	C₄⋊C₄×C₅₃	—	2	2	no	—
93	C₄⋊C₄×C₅₃	—	2	4	no	—
94	C₄⋊C₄×C₅₃	—	2	2	no	—
95	C₄⋊C₄×C₅₃	—	4	4	no	—
96	C₄⋊C₄×C₅₃	—	8	2	no	—
97	C₄⋊C₄×C₅₃	C₄⋊C₄	1	4	yes	—
98	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
99	C₂²⋊C₄×C₅₃	—	4	8	no	—
100	C₂²⋊C₄×C₅₃	—	8	4	no	—
101	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	8	yes	—
102	C₄²×C₅₃	—	4	8	no	—
103	C₄²×C₅₃	—	4	4	no	—
104	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
105	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
106	C₂³×C₅₃	—	2	2	no	—
107	C₂³×C₅₃	—	2	2	no	—
108	C₂³×C₅₃	—	2	4	no	—
109	C₂³×C₅₃	—	2	4	no	—
110	C₂³×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
111	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
112	D₄×C₅₃	—	2	8	no	—
113	C₂×C₄×C₅₃	—	2	2	no	—
114	C₂×C₄×C₅₃	—	2	2	no	—
115	C₂×C₄×C₅₃	—	2	2	no	—
116	C₂×C₄×C₅₃	—	2	4	no	—
117	C₂×C₄×C₅₃	—	2	4	no	—
118	C₂×C₄×C₅₃	—	2	4	no	—
119	C₂×C₄×C₅₃	—	2	4	no	—
120	C₂×C₄×C₅₃	—	2	4	no	—
121	C₂×C₄×C₅₃	—	4	2	no	—
122	C₂×C₄×C₅₃	—	4	2	no	—
123	C₂×C₄×C₅₃	—	4	4	no	—
124	C₂×C₄×C₅₃	—	4	2	no	—
125	C₂×C₄×C₅₃	—	4	2	no	—
126	C₂×C₄×C₅₃	—	4	4	no	—
127	C₂×C₄×C₅₃	—	4	2	no	—
128	C₂×C₄×C₅₃	—	4	4	no	—
129	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
130	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
132	C₂×C₄×C₅₃	#135	1	4	yes	—
133	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
137	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
138	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
139	C₈×C₅₃	—	2	4	no	—
140	C₈×C₅₃	—	2	2	no	—
141	C₈×C₅₃	C₄×D₄	1	4	yes	—
142	#22657	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂²×C₅₃	—	2	4	no	—
144	C₂²×C₅₃	—	2	4	no	—
145	C₂²×C₅₃	—	2	4	no	—
146	C₂²×C₅₃	—	4	4	no	—
147	C₂²×C₅₃	—	4	4	no	—
148	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
149	C₂²×C₅₃	D₄²	1	1	yes	characteristic
150	C₂²×C₅₃	#547	1	1	yes	characteristic
151	C₂²×C₅₃	C₂×#135	1	2	yes	—
152	C₂²×C₅₃	#577	1	2	yes	—
153	C₄×C₅₃	—	2	4	no	—
154	C₄×C₅₃	—	2	2	no	—
155	C₄×C₅₃	—	4	4	no	—
156	C₄×C₅₃	—	8	2	no	—
157	C₄×C₅₃	—	8	4	no	—
158	C₄×C₅₃	#427	1	4	yes	complemented
159	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
160	C₄×C₅₃	#520	1	1	yes	characteristic
161	C₄×C₅₃	D₄×Q₈	1	1	yes	characteristic
162	C₄×C₅₃	#554	1	1	yes	characteristic
163	C₂×C₈×D₄	C₂×C₅₃	1	1	yes	characteristic
164	C₂×#427	C₂×C₅₃	1	2	yes	complemented
165	#2354	C₂×C₅₃	1	2	yes	—
166	#1947	C₂×C₅₃	1	2	yes	complemented
167	#1854	C₂×C₅₃	1	4	yes	complemented
168	#1844	C₂×C₅₃	1	1	yes	characteristic, complemented
169	#1807	C₂×C₅₃	1	2	yes	complemented
170	C₄×#106	C₂×C₅₃	1	1	yes	characteristic, complemented
171	C₂×C₅₃	—	4	4	no	—
172	C₂×C₅₃	D₄×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
174	C₂×C₅₃	#2912	1	1	yes	characteristic
175	C₂×C₅₃	#3284	1	2	yes	—
176	C₂×C₅₃	#3340	1	2	yes	—
177	C₂³×C₈	C₂²×C₅₃	1	2	yes	—
178	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
179	C₂×#117	C₂²×C₅₃	1	4	yes	—
180	C₈×D₄	C₄×C₅₃	1	8	yes	complemented
181	#427	—	2	8	no	—
182	C₂×#107	C₂²×C₅₃	1	4	yes	—
183	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
184	C₂×#106	C₂²×C₅₃	1	2	yes	—
185	C₂×#106	C₂²×C₅₃	1	2	yes	—
186	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
188	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
190	#390	—	2	2	no	—
191	#388	—	2	4	no	—
192	#384	C₂²×C₅₃	1	2	yes	—
193	#380	C₂²×C₅₃	1	4	yes	—
194	C₄×C₄⋊C₄	—	2	2	no	—
195	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
196	#340	C₂²×C₅₃	1	4	yes	—
197	#340	C₂²×C₅₃	1	2	yes	—
198	C₅₃	#22657	1	1	yes	characteristic, direct product factor, Sylow
199	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
200	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
201	C₂²×C₈	—	2	4	no	—
202	C₂²×C₈	—	2	4	no	—
203	C₂²×C₈	C₂×C₄×C₅₃	1	8	yes	—
204	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
205	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
206	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
207	C₄×D₄	C₂×C₄×C₅₃	1	4	yes	—
208	C₄×D₄	Q₈×C₅₃	1	4	yes	—
209	#117	—	2	8	no	—
210	#117	—	4	4	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
215	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
216	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
217	C₂×C₂²⋊C₄	—	2	4	no	—
218	C₂×C₂²⋊C₄	—	2	4	no	—
219	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
220	C₂×C₄²	—	2	4	no	—
221	C₂×C₄²	—	2	2	no	—
222	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
223	#107	—	2	8	no	—
224	#106	—	2	4	no	—
225	#106	—	2	2	no	—
226	#106	—	4	2	no	—
227	#106	D₄×C₅₃	1	4	yes	complemented
228	C₄⋊C₈	C₂×C₄×C₅₃	1	4	yes	—
229	C₂²⋊C₈	C₂×C₄×C₅₃	1	8	yes	—
230	C₄×C₈	C₂×C₄×C₅₃	1	4	yes	—
231	#95	—	2	4	no	—
232	#95	—	2	2	no	—
233	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
234	C₂×D₄	—	2	4	no	—
235	C₂×D₄	C₄⋊C₄×C₅₃	1	4	yes	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
244	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
245	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
246	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
247	C₂²×C₄	C₂×Q₈×C₅₃	1	4	yes	—
248	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	1	no	—
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	16	no	—
254	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
255	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
256	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
257	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
258	C₂×C₈	#41×C₅₃	1	2	yes	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	—	2	4	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	—	2	4	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₄⋊C₄	—	4	4	no	—
265	C₄⋊C₄	—	8	2	no	—
266	C₄⋊C₄	C₄⋊C₄×C₅₃	1	4	yes	—
267	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
268	C₂²⋊C₄	—	4	8	no	—
269	C₂²⋊C₄	—	8	4	no	—
270	C₂²⋊C₄	C₄⋊C₄×C₅₃	1	8	yes	—
271	C₄²	—	4	8	no	—
272	C₄²	—	4	4	no	—
273	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
274	C₄²	C₂×Q₈×C₅₃	1	2	yes	—
275	C₂³	—	2	2	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	4	no	—
278	C₂³	—	2	4	no	—
279	C₂³	C₂×C₄⋊C₄×C₅₃	1	4	yes	—
280	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
281	D₄	—	2	8	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	4	4	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
299	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	4	yes	—
300	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
301	C₂×C₄	#135×C₅₃	1	4	yes	—
302	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
303	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
304	C₂×C₄	C₂²×Q₈×C₅₃	1	1	yes	characteristic
305	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
306	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
307	C₂×C₄	2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
308	C₈	—	2	4	no	—
309	C₈	—	2	2	no	—
310	C₈	C₄×D₄×C₅₃	1	4	yes	—
311	C₂²	—	2	4	no	—
312	C₂²	—	2	4	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	4	4	no	—
315	C₂²	—	4	4	no	—
316	C₂²	C₂²×C₄⋊C₄×C₅₃	1	1	yes	characteristic
317	C₂²	D₄²×C₅₃	1	1	yes	characteristic
318	C₂²	C₅₃×#547	1	1	yes	characteristic
319	C₂²	C₂×#135×C₅₃	1	2	yes	—
320	C₂²	C₅₃×#577	1	2	yes	—
321	C₄	—	2	4	no	—
322	C₄	—	2	2	no	—
323	C₄	—	4	4	no	—
324	C₄	—	8	4	no	—
325	C₄	—	8	2	no	—
326	C₄	C₅₃×#427	1	4	yes	complemented
327	C₄	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
328	C₄	C₅₃×#520	1	1	yes	characteristic
329	C₄	D₄×Q₈×C₅₃	1	1	yes	characteristic
330	C₄	C₅₃×#554	1	1	yes	characteristic
331	C₂	—	4	4	no	—
332	C₂	D₄×C₄⋊C₄×C₅₃	1	1	yes	characteristic
333	C₂	C₂×C₅₃×#427	1	1	yes	characteristic
334	C₂	C₅₃×#2912	1	1	yes	characteristic
335	C₂	C₅₃×#3284	1	2	yes	—
336	C₂	C₅₃×#3340	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#427	C₂	semidirect
4. C₅₃×#1947	C₂	semidirect
5. C₅₃×#1854	C₂	semidirect
6. C₅₃×#1844	C₂	semidirect
7. C₅₃×#1807	C₂	semidirect
8. C₄×#106×C₅₃	C₂	semidirect
12. C₈×D₄×C₅₃	C₄	semidirect
58. #106×C₅₃	D₄	semidirect
142. #22657	C₅₃	direct (N × H)
158. C₄×C₅₃	#427	semidirect
164. C₂×#427	C₂×C₅₃	semidirect
166. #1947	C₂×C₅₃	semidirect
167. #1854	C₂×C₅₃	semidirect
168. #1844	C₂×C₅₃	semidirect
169. #1807	C₂×C₅₃	semidirect
170. C₄×#106	C₂×C₅₃	semidirect
180. C₈×D₄	C₄×C₅₃	semidirect
198. C₅₃	#22657	direct (N × H)
227. #106	D₄×C₅₃	semidirect
326. C₄	C₅₃×#427	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₅₃	2
C₂×C₅₃×#427	2
C₅₃×#2354	2
C₅₃×#1947	2
C₅₃×#1854	2
C₅₃×#1844	2
C₅₃×#1807	2
C₄×#106×C₅₃	2
#22657	53

Subgroups — C53×#22657 #27230169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#22657 #27230169