Subgroups — C₅₃×#61251 #27268763

Order 13568.

1842 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3475	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3357	C₂	1	2	yes	maximal, complemented
3	C₅₃×#3356	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3355	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3354	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3353	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3352	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3351	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3091	C₂	1	4	yes	maximal, complemented
11	C₅₃×#3076	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3054	C₂	1	2	yes	maximal, complemented
13	C₄×#135×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2911	C₂	1	2	yes	maximal, complemented
16	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	—
18	C₅₃×#556	C₂²	1	2	yes	—
19	C₅₃×#555	C₂²	1	2	yes	—
20	C₅₃×#554	C₂²	1	2	yes	—
21	C₅₃×#553	C₂²	1	4	yes	—
22	C₅₃×#552	—	2	2	no	—
23	C₅₃×#552	C₂²	1	4	yes	—
24	C₅₃×#551	—	2	4	no	—
25	C₅₃×#547	C₂²	1	2	yes	—
26	C₅₃×#546	—	2	2	no	—
27	C₅₃×#533	C₂²	1	2	yes	—
28	C₅₃×#529	—	2	2	no	—
29	C₅₃×#529	—	2	4	no	—
30	C₅₃×#525	C₂²	1	4	yes	—
31	C₄×#41×C₅₃	—	2	2	no	—
32	C₄×#41×C₅₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#117×C₅₃	C₂²	1	4	yes	—
35	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#499	C₂²	1	2	yes	complemented
38	C₅₃×#499	C₂²	1	2	yes	complemented
39	C₅₃×#498	C₂²	1	2	yes	complemented
40	C₅₃×#485	C₂²	1	4	yes	complemented
41	C₅₃×#485	C₂²	1	4	yes	complemented
42	C₅₃×#484	C₂²	1	4	yes	complemented
43	C₅₃×#483	C₂²	1	4	yes	complemented
44	C₅₃×#482	C₂²	1	4	yes	complemented
45	C₅₃×#482	C₂²	1	4	yes	complemented
46	C₅₃×#481	C₂²	1	4	yes	complemented
47	C₅₃×#480	C₂²	1	4	yes	complemented
48	C₅₃×#479	C₂²	1	4	yes	complemented
49	C₅₃×#478	C₂²	1	4	yes	complemented
50	C₅₃×#477	C₂²	1	2	yes	complemented
51	C₅₃×#476	C₂²	1	2	yes	complemented
52	C₅₃×#475	C₂²	1	2	yes	complemented
53	C₅₃×#474	C₂²	1	2	yes	complemented
54	C₅₃×#470	C₂²	1	4	yes	complemented
55	C₅₃×#469	C₂²	1	4	yes	complemented
56	C₅₃×#468	C₂²	1	4	yes	complemented
57	C₅₃×#468	C₂²	1	4	yes	complemented
58	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
61	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
62	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#436	C₂²	1	2	yes	—
65	C₅₃×#436	C₂²	1	2	yes	—
66	C₅₃×#436	C₂²	1	2	yes	—
67	C₅₃×#436	C₂²	1	2	yes	—
68	C₅₃×#428	C₂²	1	4	yes	complemented
69	C₅₃×#428	C₂²	1	4	yes	complemented
70	C₅₃×#428	C₂²	1	4	yes	complemented
71	C₅₃×#428	C₂²	1	4	yes	complemented
72	C₅₃×#427	C₂²	1	1	yes	characteristic
73	C₅₃×#427	C₂²	1	2	yes	—
74	C₅₃×#427	C₂²	1	4	yes	—
75	C₅₃×#427	C₂²	1	2	yes	—
76	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
77	C₅₃×#416	C₂²	1	2	yes	—
78	C₅₃×#416	C₂²	1	4	yes	—
79	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
81	C₂×#41×C₅₃	—	2	2	no	—
82	C₂×#41×C₅₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
85	#135×C₅₃	—	2	4	no	—
86	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
87	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
88	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₅₃	—	2	8	no	—
90	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
91	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
92	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
93	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
95	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
97	#126×C₅₃	—	2	4	no	—
98	#126×C₅₃	—	2	4	no	—
99	#126×C₅₃	—	2	4	no	—
100	#125×C₅₃	—	2	4	no	—
101	#125×C₅₃	—	2	2	no	—
102	#125×C₅₃	C₂³	1	4	yes	—
103	#124×C₅₃	—	2	4	no	—
104	#124×C₅₃	—	2	2	no	—
105	#123×C₅₃	—	2	4	no	—
106	#123×C₅₃	—	2	4	no	—
107	#123×C₅₃	—	2	4	no	—
108	#123×C₅₃	—	2	4	no	—
109	C₂²⋊Q₈×C₅₃	—	2	2	no	—
110	C₂²⋊Q₈×C₅₃	—	2	4	no	—
111	C₂²⋊Q₈×C₅₃	—	2	2	no	—
112	C₂²⋊Q₈×C₅₃	—	2	2	no	—
113	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
114	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
115	#121×C₅₃	—	2	4	no	—
116	#121×C₅₃	—	2	2	no	—
117	#121×C₅₃	C₂³	1	4	yes	—
118	#121×C₅₃	C₂³	1	4	yes	—
119	#120×C₅₃	—	2	4	no	—
120	C₄×Q₈×C₅₃	—	2	2	no	—
121	C₄×Q₈×C₅₃	—	2	2	no	—
122	C₄×Q₈×C₅₃	—	2	2	no	—
123	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
124	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
125	C₄×D₄×C₅₃	—	2	4	no	—
126	C₄×D₄×C₅₃	—	2	2	no	—
127	C₄×D₄×C₅₃	—	2	4	no	—
128	C₄×D₄×C₅₃	—	2	2	no	—
129	C₄×D₄×C₅₃	—	2	2	no	—
130	C₄×D₄×C₅₃	—	2	4	no	—
131	C₄×D₄×C₅₃	D₄	1	2	yes	—
132	C₄×D₄×C₅₃	D₄	1	2	yes	—
133	C₄×D₄×C₅₃	C₂³	1	2	yes	—
134	C₄×D₄×C₅₃	C₂³	1	2	yes	—
135	C₄×D₄×C₅₃	C₂³	1	2	yes	—
136	C₄×D₄×C₅₃	C₂³	1	2	yes	—
137	#117×C₅₃	—	2	2	no	—
138	#117×C₅₃	—	2	4	no	—
139	#117×C₅₃	—	2	2	no	—
140	#117×C₅₃	—	2	4	no	—
141	#117×C₅₃	—	2	4	no	—
142	#117×C₅₃	C₂³	1	4	yes	—
143	#117×C₅₃	C₂³	1	4	yes	—
144	#117×C₅₃	C₂³	1	2	yes	—
145	#117×C₅₃	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
151	C₂×C₄²×C₅₃	—	2	2	no	—
152	C₂×C₄²×C₅₃	—	2	4	no	—
153	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
154	#107×C₅₃	C₂³	1	2	yes	—
155	#107×C₅₃	C₂³	1	4	yes	—
156	#107×C₅₃	C₂³	1	2	yes	—
157	#107×C₅₃	C₂³	1	2	yes	—
158	#107×C₅₃	C₂³	1	2	yes	—
159	#107×C₅₃	C₂³	1	1	yes	characteristic
160	#107×C₅₃	C₂³	1	1	yes	characteristic
161	#107×C₅₃	C₂³	1	4	yes	—
162	#106×C₅₃	C₂³	1	4	yes	—
163	#106×C₅₃	C₂³	1	4	yes	—
164	#106×C₅₃	C₂³	1	4	yes	—
165	#106×C₅₃	C₂³	1	2	yes	—
166	#106×C₅₃	C₂³	1	4	yes	—
167	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
168	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
169	#103×C₅₃	C₂³	1	2	yes	—
170	#103×C₅₃	C₂³	1	2	yes	—
171	#103×C₅₃	C₂³	1	4	yes	—
172	#103×C₅₃	C₂³	1	4	yes	—
173	#102×C₅₃	C₂³	1	2	yes	—
174	#102×C₅₃	C₂³	1	2	yes	—
175	#102×C₅₃	C₂³	1	4	yes	—
176	#102×C₅₃	C₂³	1	4	yes	—
177	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
178	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
179	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
183	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
184	#41×C₅₃	—	2	4	no	—
185	#41×C₅₃	—	2	4	no	—
186	#41×C₅₃	—	4	8	no	—
187	C₂×Q₈×C₅₃	—	2	2	no	—
188	C₂×Q₈×C₅₃	—	2	2	no	—
189	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
190	C₂×D₄×C₅₃	—	2	2	no	—
191	C₂×D₄×C₅₃	—	2	4	no	—
192	C₂×D₄×C₅₃	—	2	4	no	—
193	C₂×D₄×C₅₃	—	4	2	no	—
194	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
195	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₅₃	—	2	4	no	—
198	C₂²×C₄×C₅₃	—	2	4	no	—
199	C₂²×C₄×C₅₃	—	2	4	no	—
200	C₂²×C₄×C₅₃	—	2	4	no	—
201	C₂²×C₄×C₅₃	—	2	2	no	—
202	C₂²×C₄×C₅₃	—	2	2	no	—
203	C₂²×C₄×C₅₃	—	2	2	no	—
204	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
210	Q₁₆×C₅₃	—	2	2	no	—
211	SD₁₆×C₅₃	—	2	4	no	—
212	D₈×C₅₃	—	2	2	no	—
213	M₁₆×C₅₃	—	2	8	no	—
214	M₁₆×C₅₃	—	2	8	no	—
215	C₂×C₈×C₅₃	—	2	4	no	—
216	C₂×C₈×C₅₃	—	2	2	no	—
217	C₂×C₈×C₅₃	#41	1	4	yes	complemented
218	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
219	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
220	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
221	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
222	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
223	C₄⋊C₄×C₅₃	—	2	4	no	—
224	C₄⋊C₄×C₅₃	—	2	4	no	—
225	C₄⋊C₄×C₅₃	—	2	2	no	—
226	C₄⋊C₄×C₅₃	—	2	4	no	—
227	C₄⋊C₄×C₅₃	—	2	4	no	—
228	C₄⋊C₄×C₅₃	—	2	2	no	—
229	C₄⋊C₄×C₅₃	—	2	2	no	—
230	C₄⋊C₄×C₅₃	—	2	4	no	—
231	C₄⋊C₄×C₅₃	—	2	4	no	—
232	C₄⋊C₄×C₅₃	—	2	2	no	—
233	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
236	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
237	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
238	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
239	C₂²⋊C₄×C₅₃	—	2	2	no	—
240	C₂²⋊C₄×C₅₃	—	2	4	no	—
241	C₂²⋊C₄×C₅₃	—	2	4	no	—
242	C₂²⋊C₄×C₅₃	—	2	4	no	—
243	C₂²⋊C₄×C₅₃	—	2	4	no	—
244	C₂²⋊C₄×C₅₃	—	2	4	no	—
245	C₂²⋊C₄×C₅₃	—	2	4	no	—
246	C₂²⋊C₄×C₅₃	—	2	2	no	—
247	C₂²⋊C₄×C₅₃	—	2	2	no	—
248	C₂²⋊C₄×C₅₃	—	2	4	no	—
249	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
250	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
251	C₄²×C₅₃	—	2	4	no	—
252	C₄²×C₅₃	—	2	2	no	—
253	C₄²×C₅₃	—	2	4	no	—
254	C₄²×C₅₃	—	2	2	no	—
255	C₄²×C₅₃	—	2	2	no	—
256	C₄²×C₅₃	—	2	4	no	—
257	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
261	C₂³×C₅₃	—	2	4	no	—
262	C₂³×C₅₃	—	2	2	no	—
263	C₂³×C₅₃	—	4	2	no	—
264	C₂³×C₅₃	—	4	2	no	—
265	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
266	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₅₃	—	2	2	no	—
268	Q₈×C₅₃	—	2	2	no	—
269	Q₈×C₅₃	—	4	4	no	—
270	Q₈×C₅₃	—	8	2	no	—
271	D₄×C₅₃	—	2	4	no	—
272	D₄×C₅₃	—	2	2	no	—
273	D₄×C₅₃	—	2	2	no	—
274	D₄×C₅₃	—	4	2	no	—
275	D₄×C₅₃	—	4	8	no	—
276	D₄×C₅₃	—	4	4	no	—
277	D₄×C₅₃	—	8	4	no	—
278	C₂×C₄×C₅₃	—	2	4	no	—
279	C₂×C₄×C₅₃	—	2	8	no	—
280	C₂×C₄×C₅₃	—	2	2	no	—
281	C₂×C₄×C₅₃	—	2	4	no	—
282	C₂×C₄×C₅₃	—	2	4	no	—
283	C₂×C₄×C₅₃	—	2	2	no	—
284	C₂×C₄×C₅₃	—	2	2	no	—
285	C₂×C₄×C₅₃	—	2	4	no	—
286	C₂×C₄×C₅₃	—	2	4	no	—
287	C₂×C₄×C₅₃	—	2	2	no	—
288	C₂×C₄×C₅₃	—	4	1	no	—
289	C₂×C₄×C₅₃	—	4	8	no	—
290	C₂×C₄×C₅₃	—	4	4	no	—
291	C₂×C₄×C₅₃	—	4	4	no	—
292	C₂×C₄×C₅₃	—	8	2	no	—
293	C₂×C₄×C₅₃	—	8	4	no	—
294	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
301	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
302	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
303	C₈×C₅₃	—	2	4	no	—
304	C₈×C₅₃	—	2	1	no	—
305	C₈×C₅₃	—	2	1	no	—
306	C₈×C₅₃	C₂×#41	1	2	yes	—
307	C₈×C₅₃	C₂×#41	1	2	yes	—
308	#61251	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂²×C₅₃	—	2	1	no	—
310	C₂²×C₅₃	—	2	1	no	—
311	C₂²×C₅₃	—	2	4	no	—
312	C₂²×C₅₃	—	2	4	no	—
313	C₂²×C₅₃	—	2	4	no	—
314	C₂²×C₅₃	—	4	2	no	—
315	C₂²×C₅₃	—	4	2	no	—
316	C₂²×C₅₃	—	4	2	no	—
317	C₂²×C₅₃	—	8	4	no	—
318	C₂²×C₅₃	#547	1	2	yes	—
319	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
320	C₄×C₅₃	—	2	1	no	—
321	C₄×C₅₃	—	2	1	no	—
322	C₄×C₅₃	—	2	4	no	—
323	C₄×C₅₃	—	2	1	no	—
324	C₄×C₅₃	—	4	2	no	—
325	C₄×C₅₃	—	4	4	no	—
326	C₄×C₅₃	—	4	2	no	—
327	C₄×C₅₃	—	4	2	no	—
328	C₄×C₅₃	—	4	4	no	—
329	C₄×C₅₃	#547	1	2	yes	—
330	C₄×C₅₃	#575	1	2	yes	—
331	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
332	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
333	#3475	C₂×C₅₃	1	2	yes	complemented
334	#3357	C₂×C₅₃	1	2	yes	complemented
335	#3356	C₂×C₅₃	1	2	yes	complemented
336	#3355	C₂×C₅₃	1	2	yes	complemented
337	#3354	C₂×C₅₃	1	2	yes	complemented
338	#3353	C₂×C₅₃	1	2	yes	complemented
339	#3352	C₂×C₅₃	1	2	yes	complemented
340	#3351	C₂×C₅₃	1	4	yes	complemented
341	#3160	C₂×C₅₃	1	1	yes	characteristic, complemented
342	#3091	C₂×C₅₃	1	4	yes	complemented
343	#3076	C₂×C₅₃	1	2	yes	complemented
344	#3054	C₂×C₅₃	1	2	yes	complemented
345	C₄×#135	C₂×C₅₃	1	1	yes	characteristic, complemented
346	C₂×#436	C₂×C₅₃	1	1	yes	characteristic, complemented
347	#2911	C₂×C₅₃	1	2	yes	complemented
348	C₂×C₅₃	—	2	2	no	—
349	C₂×C₅₃	—	4	4	no	—
350	C₂×C₅₃	—	8	2	no	—
351	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
352	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
353	C₂×C₅₃	#3584	1	1	yes	characteristic
354	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
355	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	—
356	#556	C₂²×C₅₃	1	2	yes	—
357	#555	C₂²×C₅₃	1	2	yes	—
358	#554	C₂²×C₅₃	1	2	yes	—
359	#553	C₂²×C₅₃	1	4	yes	—
360	#552	—	2	2	no	—
361	#552	C₂²×C₅₃	1	4	yes	—
362	#551	—	2	4	no	—
363	#547	C₂²×C₅₃	1	2	yes	—
364	#546	—	2	2	no	—
365	#533	C₂²×C₅₃	1	2	yes	—
366	#529	—	2	4	no	—
367	#529	—	2	2	no	—
368	#525	C₂²×C₅₃	1	4	yes	—
369	C₄×#41	—	2	2	no	—
370	C₄×#41	C₂²×C₅₃	1	2	yes	—
371	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
372	C₂×#117	C₂²×C₅₃	1	4	yes	—
373	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
374	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
375	#499	C₂²×C₅₃	1	2	yes	complemented
376	#499	C₂²×C₅₃	1	2	yes	complemented
377	#498	C₂²×C₅₃	1	2	yes	complemented
378	#485	C₂²×C₅₃	1	4	yes	complemented
379	#485	C₂²×C₅₃	1	4	yes	complemented
380	#484	C₂²×C₅₃	1	4	yes	complemented
381	#483	C₂²×C₅₃	1	4	yes	complemented
382	#482	C₂²×C₅₃	1	4	yes	complemented
383	#482	C₂²×C₅₃	1	4	yes	complemented
384	#481	C₂²×C₅₃	1	4	yes	complemented
385	#480	C₂²×C₅₃	1	4	yes	complemented
386	#479	C₂²×C₅₃	1	4	yes	complemented
387	#478	C₂²×C₅₃	1	4	yes	complemented
388	#477	C₂²×C₅₃	1	2	yes	complemented
389	#476	C₂²×C₅₃	1	2	yes	complemented
390	#475	C₂²×C₅₃	1	2	yes	complemented
391	#474	C₂²×C₅₃	1	2	yes	complemented
392	#470	C₂²×C₅₃	1	4	yes	complemented
393	#469	C₂²×C₅₃	1	4	yes	complemented
394	#468	C₂²×C₅₃	1	4	yes	complemented
395	#468	C₂²×C₅₃	1	4	yes	complemented
396	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
397	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
398	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
399	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
400	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
401	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
402	#436	C₂²×C₅₃	1	2	yes	—
403	#436	C₂²×C₅₃	1	2	yes	—
404	#436	C₂²×C₅₃	1	2	yes	—
405	#436	C₂²×C₅₃	1	2	yes	—
406	#428	C₂²×C₅₃	1	4	yes	complemented
407	#428	C₂²×C₅₃	1	4	yes	complemented
408	#428	C₂²×C₅₃	1	4	yes	complemented
409	#428	C₂²×C₅₃	1	4	yes	complemented
410	#427	C₂²×C₅₃	1	4	yes	—
411	#427	C₂²×C₅₃	1	2	yes	—
412	#427	C₂²×C₅₃	1	2	yes	—
413	#427	C₂²×C₅₃	1	1	yes	characteristic
414	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
415	#416	C₂²×C₅₃	1	4	yes	—
416	#416	C₂²×C₅₃	1	2	yes	—
417	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
418	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
419	C₅₃	#61251	1	1	yes	characteristic, direct product factor, Sylow
420	C₂×#41	—	2	2	no	—
421	C₂×#41	C₂³×C₅₃	1	2	yes	—
422	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
424	#135	—	2	4	no	—
425	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
426	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
427	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
428	C₂×M₁₆	—	2	8	no	—
429	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
430	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
431	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
432	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
434	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
435	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
436	#126	—	2	4	no	—
437	#126	—	2	4	no	—
438	#126	—	2	4	no	—
439	#125	—	2	4	no	—
440	#125	—	2	2	no	—
441	#125	C₂³×C₅₃	1	4	yes	—
442	#124	—	2	2	no	—
443	#124	—	2	4	no	—
444	#123	—	2	4	no	—
445	#123	—	2	4	no	—
446	#123	—	2	4	no	—
447	#123	—	2	4	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	4	no	—
452	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
453	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
454	#121	—	2	4	no	—
455	#121	—	2	2	no	—
456	#121	C₂³×C₅₃	1	4	yes	—
457	#121	C₂³×C₅₃	1	4	yes	—
458	#120	—	2	4	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
463	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	—	2	4	no	—
466	C₄×D₄	—	2	2	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	2	4	no	—
469	C₄×D₄	—	2	4	no	—
470	C₄×D₄	D₄×C₅₃	1	2	yes	—
471	C₄×D₄	D₄×C₅₃	1	2	yes	—
472	C₄×D₄	C₂³×C₅₃	1	2	yes	—
473	C₄×D₄	C₂³×C₅₃	1	2	yes	—
474	C₄×D₄	C₂³×C₅₃	1	2	yes	—
475	C₄×D₄	C₂³×C₅₃	1	2	yes	—
476	#117	—	2	4	no	—
477	#117	—	2	4	no	—
478	#117	—	2	2	no	—
479	#117	—	2	4	no	—
480	#117	—	2	2	no	—
481	#117	C₂³×C₅₃	1	2	yes	—
482	#117	C₂³×C₅₃	1	4	yes	—
483	#117	C₂³×C₅₃	1	4	yes	—
484	#117	C₂³×C₅₃	1	4	yes	—
485	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
488	C₂×C₂²⋊C₄	—	2	4	no	—
489	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
490	C₂×C₄²	—	2	4	no	—
491	C₂×C₄²	—	2	2	no	—
492	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
493	#107	C₂³×C₅₃	1	1	yes	characteristic
494	#107	C₂³×C₅₃	1	1	yes	characteristic
495	#107	C₂³×C₅₃	1	2	yes	—
496	#107	C₂³×C₅₃	1	2	yes	—
497	#107	C₂³×C₅₃	1	4	yes	—
498	#107	C₂³×C₅₃	1	4	yes	—
499	#107	C₂³×C₅₃	1	2	yes	—
500	#107	C₂³×C₅₃	1	2	yes	—
501	#106	C₂³×C₅₃	1	2	yes	—
502	#106	C₂³×C₅₃	1	4	yes	—
503	#106	C₂³×C₅₃	1	4	yes	—
504	#106	C₂³×C₅₃	1	4	yes	—
505	#106	C₂³×C₅₃	1	4	yes	—
506	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
507	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
508	#103	C₂³×C₅₃	1	2	yes	—
509	#103	C₂³×C₅₃	1	2	yes	—
510	#103	C₂³×C₅₃	1	4	yes	—
511	#103	C₂³×C₅₃	1	4	yes	—
512	#102	C₂³×C₅₃	1	2	yes	—
513	#102	C₂³×C₅₃	1	2	yes	—
514	#102	C₂³×C₅₃	1	4	yes	—
515	#102	C₂³×C₅₃	1	4	yes	—
516	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
517	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
518	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
519	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
520	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
521	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
522	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
523	#41	—	2	4	no	—
524	#41	—	2	4	no	—
525	#41	—	4	8	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
534	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
535	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
544	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
546	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
549	Q₁₆	—	2	2	no	—
550	SD₁₆	—	2	4	no	—
551	D₈	—	2	2	no	—
552	M₁₆	—	2	8	no	—
553	M₁₆	—	2	8	no	—
554	C₂×C₈	—	2	4	no	—
555	C₂×C₈	—	2	2	no	—
556	C₂×C₈	#41×C₅₃	1	4	yes	complemented
557	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
558	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
559	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
560	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
561	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
573	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
574	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
575	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
576	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
577	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
589	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	4	no	—
595	C₄²	—	2	2	no	—
596	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
597	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
598	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
599	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
600	C₂³	—	2	4	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	2	no	—
604	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
605	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
606	Q₈	—	2	2	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	4	4	no	—
609	Q₈	—	8	2	no	—
610	D₄	—	2	4	no	—
611	D₄	—	2	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	8	no	—
615	D₄	—	4	4	no	—
616	D₄	—	8	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	8	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	8	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	8	2	no	—
632	C₂×C₄	—	8	4	no	—
633	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
635	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
636	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
637	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
638	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
639	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
640	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
641	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
642	C₈	—	2	4	no	—
643	C₈	—	2	1	no	—
644	C₈	—	2	1	no	—
645	C₈	C₂×#41×C₅₃	1	2	yes	—
646	C₈	C₂×#41×C₅₃	1	2	yes	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	8	4	no	—
656	C₂²	C₅₃×#547	1	2	yes	—
657	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
658	C₄	—	2	4	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	4	no	—
667	C₄	C₅₃×#547	1	2	yes	—
668	C₄	C₅₃×#575	1	2	yes	—
669	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
670	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
671	C₂	—	2	2	no	—
672	C₂	—	4	4	no	—
673	C₂	—	8	2	no	—
674	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
675	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
676	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
socle	C₂²×C₅₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3475	C₂	semidirect
2. C₅₃×#3357	C₂	semidirect
3. C₅₃×#3356	C₂	semidirect
4. C₅₃×#3355	C₂	semidirect
5. C₅₃×#3354	C₂	semidirect
6. C₅₃×#3353	C₂	semidirect
7. C₅₃×#3352	C₂	semidirect
8. C₅₃×#3351	C₂	semidirect
9. C₅₃×#3160	C₂	semidirect
10. C₅₃×#3091	C₂	semidirect
11. C₅₃×#3076	C₂	semidirect
12. C₅₃×#3054	C₂	semidirect
13. C₄×#135×C₅₃	C₂	semidirect
14. C₂×C₅₃×#436	C₂	semidirect
15. C₅₃×#2911	C₂	semidirect
35. C₅₃×#500	C₂²	semidirect
36. C₅₃×#500	C₂²	semidirect
37. C₅₃×#499	C₂²	semidirect
38. C₅₃×#499	C₂²	semidirect
39. C₅₃×#498	C₂²	semidirect
40. C₅₃×#485	C₂²	semidirect
41. C₅₃×#485	C₂²	semidirect
42. C₅₃×#484	C₂²	semidirect
43. C₅₃×#483	C₂²	semidirect
44. C₅₃×#482	C₂²	semidirect
45. C₅₃×#482	C₂²	semidirect
46. C₅₃×#481	C₂²	semidirect
47. C₅₃×#480	C₂²	semidirect
48. C₅₃×#479	C₂²	semidirect
49. C₅₃×#478	C₂²	semidirect
50. C₅₃×#477	C₂²	semidirect
51. C₅₃×#476	C₂²	semidirect
52. C₅₃×#475	C₂²	semidirect
53. C₅₃×#474	C₂²	semidirect
54. C₅₃×#470	C₂²	semidirect
55. C₅₃×#469	C₂²	semidirect
56. C₅₃×#468	C₂²	semidirect
57. C₅₃×#468	C₂²	semidirect
58. C₄×Q₁₆×C₅₃	C₂²	semidirect
59. C₄×Q₁₆×C₅₃	C₂²	semidirect
60. C₄×SD₁₆×C₅₃	C₂²	semidirect
61. C₄×SD₁₆×C₅₃	C₂²	semidirect
62. C₄×D₈×C₅₃	C₂²	semidirect
63. C₄×D₈×C₅₃	C₂²	semidirect
68. C₅₃×#428	C₂²	semidirect
69. C₅₃×#428	C₂²	semidirect
70. C₅₃×#428	C₂²	semidirect
71. C₅₃×#428	C₂²	semidirect
217. C₂×C₈×C₅₃	#41	semidirect
308. #61251	C₅₃	direct (N × H)
333. #3475	C₂×C₅₃	semidirect
334. #3357	C₂×C₅₃	semidirect
335. #3356	C₂×C₅₃	semidirect
336. #3355	C₂×C₅₃	semidirect
337. #3354	C₂×C₅₃	semidirect
338. #3353	C₂×C₅₃	semidirect
339. #3352	C₂×C₅₃	semidirect
340. #3351	C₂×C₅₃	semidirect
341. #3160	C₂×C₅₃	semidirect
342. #3091	C₂×C₅₃	semidirect
343. #3076	C₂×C₅₃	semidirect
344. #3054	C₂×C₅₃	semidirect
345. C₄×#135	C₂×C₅₃	semidirect
346. C₂×#436	C₂×C₅₃	semidirect
347. #2911	C₂×C₅₃	semidirect
373. #500	C₂²×C₅₃	semidirect
374. #500	C₂²×C₅₃	semidirect
375. #499	C₂²×C₅₃	semidirect
376. #499	C₂²×C₅₃	semidirect
377. #498	C₂²×C₅₃	semidirect
378. #485	C₂²×C₅₃	semidirect
379. #485	C₂²×C₅₃	semidirect
380. #484	C₂²×C₅₃	semidirect
381. #483	C₂²×C₅₃	semidirect
382. #482	C₂²×C₅₃	semidirect
383. #482	C₂²×C₅₃	semidirect
384. #481	C₂²×C₅₃	semidirect
385. #480	C₂²×C₅₃	semidirect
386. #479	C₂²×C₅₃	semidirect
387. #478	C₂²×C₅₃	semidirect
388. #477	C₂²×C₅₃	semidirect
389. #476	C₂²×C₅₃	semidirect
390. #475	C₂²×C₅₃	semidirect
391. #474	C₂²×C₅₃	semidirect
392. #470	C₂²×C₅₃	semidirect
393. #469	C₂²×C₅₃	semidirect
394. #468	C₂²×C₅₃	semidirect
395. #468	C₂²×C₅₃	semidirect
396. C₄×Q₁₆	C₂²×C₅₃	semidirect
397. C₄×Q₁₆	C₂²×C₅₃	semidirect
398. C₄×SD₁₆	C₂²×C₅₃	semidirect
399. C₄×SD₁₆	C₂²×C₅₃	semidirect
400. C₄×D₈	C₂²×C₅₃	semidirect
401. C₄×D₈	C₂²×C₅₃	semidirect
406. #428	C₂²×C₅₃	semidirect
407. #428	C₂²×C₅₃	semidirect
408. #428	C₂²×C₅₃	semidirect
409. #428	C₂²×C₅₃	semidirect
419. C₅₃	#61251	direct (N × H)
556. C₂×C₈	#41×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3475	2
C₅₃×#3357	2
C₅₃×#3356	2
C₅₃×#3355	2
C₅₃×#3354	2
C₅₃×#3353	2
C₅₃×#3352	2
C₅₃×#3351	2
C₅₃×#3160	2
C₅₃×#3091	2
C₅₃×#3076	2
C₅₃×#3054	2
C₄×#135×C₅₃	2
C₂×C₅₃×#436	2
C₅₃×#2911	2
#61251	53

Subgroups — C53×#61251 #27268763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61251 #27268763