Subgroups — C₅₃×#61477 #27268989

Order 13568.

1772 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3515	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3331	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3315	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3283	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3177	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3120	C₂	1	4	yes	maximal, complemented
14	C₅₃×#3116	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2951	C₂	1	2	yes	maximal, complemented
17	C₄×#135×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#135×C₅₃	C₂²	1	2	yes	—
20	C₅₃×#557	C₂²	1	2	yes	—
21	C₅₃×#554	C₂²	1	2	yes	—
22	C₅₃×#554	C₂²	1	2	yes	—
23	C₅₃×#553	—	2	2	no	—
24	C₅₃×#552	—	2	4	no	—
25	C₅₃×#552	—	2	2	no	—
26	C₅₃×#552	C₂²	1	4	yes	—
27	C₅₃×#547	C₂²	1	4	yes	—
28	C₅₃×#547	C₂²	1	2	yes	—
29	C₅₃×#541	C₂²	1	4	yes	—
30	C₅₃×#539	—	2	4	no	—
31	C₅₃×#533	C₂²	1	2	yes	—
32	C₅₃×#529	—	2	2	no	—
33	C₅₃×#529	C₂²	1	1	yes	characteristic
34	C₂×#125×C₅₃	—	2	2	no	—
35	C₅₃×#520	C₂²	1	4	yes	—
36	C₄×#41×C₅₃	C₂²	1	2	yes	—
37	C₅₃×#500	C₂²	1	1	yes	characteristic
38	C₅₃×#499	C₂²	1	2	yes	—
39	C₅₃×#494	C₂²	1	1	yes	characteristic
40	C₅₃×#494	C₂²	1	2	yes	—
41	C₅₃×#491	C₂²	1	4	yes	—
42	C₅₃×#487	C₂²	1	2	yes	—
43	C₅₃×#485	C₂²	1	4	yes	—
44	C₅₃×#484	C₂²	1	4	yes	—
45	C₅₃×#483	C₂²	1	4	yes	—
46	C₅₃×#479	C₂²	1	4	yes	—
47	C₅₃×#478	C₂²	1	4	yes	—
48	C₅₃×#477	C₂²	1	2	yes	—
49	C₅₃×#476	C₂²	1	2	yes	—
50	C₅₃×#470	C₂²	1	4	yes	—
51	C₅₃×#467	C₂²	1	2	yes	—
52	C₅₃×#467	C₂²	1	2	yes	—
53	C₅₃×#467	C₂²	1	2	yes	—
54	C₅₃×#467	C₂²	1	2	yes	—
55	C₅₃×#462	C₂²	1	4	yes	—
56	C₅₃×#462	C₂²	1	2	yes	—
57	C₅₃×#461	C₂²	1	2	yes	—
58	C₅₃×#461	C₂²	1	4	yes	—
59	C₅₃×#452	C₂²	1	4	yes	—
60	C₅₃×#452	C₂²	1	4	yes	—
61	C₅₃×#452	C₂²	1	4	yes	—
62	C₅₃×#446	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
64	C₅₃×#441	C₂²	1	4	yes	—
65	C₅₃×#440	C₂²	1	4	yes	—
66	C₅₃×#440	C₂²	1	4	yes	—
67	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
68	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
69	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
70	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
71	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
72	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
73	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
74	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
75	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
76	C₄×D₈×C₅₃	C₂²	1	2	yes	—
77	C₅₃×#436	C₂²	1	1	yes	characteristic
78	C₅₃×#435	C₂²	1	2	yes	—
79	C₈×D₄×C₅₃	C₂²	1	2	yes	—
80	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
81	C₅₃×#433	C₂²	1	2	yes	—
82	C₅₃×#432	C₂²	1	1	yes	characteristic
83	C₅₃×#427	C₂²	1	1	yes	characteristic
84	C₂×#107×C₅₃	C₂²	1	2	yes	—
85	C₅₃×#417	C₂²	1	4	yes	—
86	C₅₃×#416	C₂²	1	2	yes	—
87	C₅₃×#405	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
89	C₂×#41×C₅₃	C₂³	1	2	yes	—
90	C₂×#41×C₅₃	C₂³	1	4	yes	—
91	#135×C₅₃	—	2	4	no	—
92	#135×C₅₃	—	2	8	no	—
93	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
94	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
95	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
99	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
101	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
107	#126×C₅₃	—	2	4	no	—
108	#126×C₅₃	—	2	4	no	—
109	#126×C₅₃	—	2	4	no	—
110	#126×C₅₃	D₄	1	2	yes	—
111	#125×C₅₃	—	2	4	no	—
112	#125×C₅₃	—	2	4	no	—
113	#125×C₅₃	—	2	2	no	—
114	#125×C₅₃	—	2	2	no	—
115	#125×C₅₃	—	2	4	no	—
116	#125×C₅₃	—	2	4	no	—
117	#125×C₅₃	—	2	2	no	—
118	#125×C₅₃	D₄	1	1	yes	characteristic
119	#125×C₅₃	C₂³	1	4	yes	—
120	#124×C₅₃	D₄	1	1	yes	characteristic
121	#123×C₅₃	—	2	4	no	—
122	#123×C₅₃	—	2	4	no	—
123	#123×C₅₃	—	2	4	no	—
124	#123×C₅₃	—	2	4	no	—
125	#123×C₅₃	D₄	1	2	yes	—
126	C₂²⋊Q₈×C₅₃	—	2	4	no	—
127	C₂²⋊Q₈×C₅₃	—	2	4	no	—
128	C₂²⋊Q₈×C₅₃	—	2	2	no	—
129	C₂²⋊Q₈×C₅₃	—	2	2	no	—
130	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
131	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
132	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
133	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
134	#121×C₅₃	—	2	2	no	—
135	#121×C₅₃	—	2	4	no	—
136	#121×C₅₃	D₄	1	1	yes	characteristic
137	C₄×Q₈×C₅₃	—	2	2	no	—
138	C₄×Q₈×C₅₃	—	2	2	no	—
139	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
140	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
141	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
142	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
143	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
144	C₄×D₄×C₅₃	—	2	4	no	—
145	C₄×D₄×C₅₃	—	2	4	no	—
146	C₄×D₄×C₅₃	—	2	2	no	—
147	C₄×D₄×C₅₃	—	2	2	no	—
148	C₄×D₄×C₅₃	—	2	2	no	—
149	C₄×D₄×C₅₃	C₂³	1	2	yes	—
150	C₄×D₄×C₅₃	C₂³	1	2	yes	—
151	C₄×D₄×C₅₃	C₂³	1	4	yes	—
152	C₄×D₄×C₅₃	C₂³	1	2	yes	—
153	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
154	#117×C₅₃	—	2	4	no	—
155	#117×C₅₃	—	2	4	no	—
156	#117×C₅₃	—	2	2	no	—
157	#117×C₅₃	—	2	2	no	—
158	#117×C₅₃	C₂³	1	2	yes	—
159	#117×C₅₃	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
161	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
162	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
163	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
164	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
165	C₂×C₄²×C₅₃	—	2	2	no	—
166	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
167	#107×C₅₃	C₂³	1	4	yes	—
168	#107×C₅₃	C₂³	1	1	yes	characteristic
169	#107×C₅₃	C₂³	1	2	yes	—
170	#107×C₅₃	C₂³	1	2	yes	—
171	#107×C₅₃	C₂³	1	1	yes	characteristic
172	#106×C₅₃	C₂³	1	4	yes	—
173	#106×C₅₃	C₂³	1	2	yes	—
174	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
177	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
178	#103×C₅₃	C₂³	1	4	yes	—
179	#103×C₅₃	C₂³	1	4	yes	—
180	#103×C₅₃	C₂³	1	4	yes	—
181	#103×C₅₃	C₂³	1	4	yes	—
182	#103×C₅₃	C₂³	1	2	yes	—
183	#103×C₅₃	C₂³	1	4	yes	—
184	#103×C₅₃	C₂³	1	2	yes	—
185	#102×C₅₃	C₂³	1	2	yes	—
186	#102×C₅₃	C₂³	1	2	yes	—
187	#102×C₅₃	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
191	#97×C₅₃	C₂³	1	2	yes	—
192	#97×C₅₃	C₂³	1	2	yes	—
193	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₅₃	C₂³	1	2	yes	—
195	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
198	#41×C₅₃	—	2	4	no	—
199	#41×C₅₃	—	2	8	no	—
200	#41×C₅₃	—	4	2	no	—
201	#41×C₅₃	—	4	4	no	—
202	C₂×Q₈×C₅₃	—	2	2	no	—
203	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
204	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
205	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
206	C₂×D₄×C₅₃	—	2	4	no	—
207	C₂×D₄×C₅₃	—	2	2	no	—
208	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
210	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₅₃	—	2	4	no	—
212	C₂²×C₄×C₅₃	—	2	2	no	—
213	C₂²×C₄×C₅₃	—	2	2	no	—
214	C₂²×C₄×C₅₃	—	2	4	no	—
215	C₂²×C₄×C₅₃	—	2	2	no	—
216	C₂²×C₄×C₅₃	—	2	4	no	—
217	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
221	Q₁₆×C₅₃	—	2	4	no	—
222	Q₁₆×C₅₃	—	2	2	no	—
223	Q₁₆×C₅₃	—	4	2	no	—
224	Q₁₆×C₅₃	—	4	4	no	—
225	SD₁₆×C₅₃	—	2	4	no	—
226	SD₁₆×C₅₃	—	2	8	no	—
227	D₈×C₅₃	#41	1	4	yes	—
228	M₁₆×C₅₃	—	4	2	no	—
229	C₂×C₈×C₅₃	—	2	2	no	—
230	C₂×C₈×C₅₃	—	2	4	no	—
231	C₂×C₈×C₅₃	—	4	1	no	—
232	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
237	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
238	C₄⋊C₄×C₅₃	—	2	4	no	—
239	C₄⋊C₄×C₅₃	—	2	2	no	—
240	C₄⋊C₄×C₅₃	—	2	2	no	—
241	C₄⋊C₄×C₅₃	—	2	4	no	—
242	C₄⋊C₄×C₅₃	—	2	4	no	—
243	C₄⋊C₄×C₅₃	—	2	4	no	—
244	C₄⋊C₄×C₅₃	—	2	4	no	—
245	C₄⋊C₄×C₅₃	—	2	4	no	—
246	C₄⋊C₄×C₅₃	—	2	4	no	—
247	C₄⋊C₄×C₅₃	—	2	4	no	—
248	C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₄⋊C₄×C₅₃	—	2	2	no	—
250	C₄⋊C₄×C₅₃	—	2	4	no	—
251	C₄⋊C₄×C₅₃	—	2	2	no	—
252	C₄⋊C₄×C₅₃	—	2	4	no	—
253	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
255	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
257	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
262	C₂²⋊C₄×C₅₃	—	2	4	no	—
263	C₂²⋊C₄×C₅₃	—	2	4	no	—
264	C₂²⋊C₄×C₅₃	—	2	2	no	—
265	C₂²⋊C₄×C₅₃	—	2	4	no	—
266	C₂²⋊C₄×C₅₃	—	2	2	no	—
267	C₂²⋊C₄×C₅₃	—	2	4	no	—
268	C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
270	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
273	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
274	C₄²×C₅₃	—	2	2	no	—
275	C₄²×C₅₃	—	2	2	no	—
276	C₄²×C₅₃	—	2	2	no	—
277	C₄²×C₅₃	—	2	4	no	—
278	C₄²×C₅₃	—	2	4	no	—
279	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
283	C₄²×C₅₃	C₂⁴	1	2	yes	—
284	C₂³×C₅₃	—	2	2	no	—
285	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
286	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₅₃	—	2	2	no	—
288	Q₈×C₅₃	—	2	4	no	—
289	Q₈×C₅₃	—	2	2	no	—
290	Q₈×C₅₃	—	2	4	no	—
291	Q₈×C₅₃	—	2	2	no	—
292	Q₈×C₅₃	—	8	2	no	—
293	D₄×C₅₃	—	2	2	no	—
294	D₄×C₅₃	—	2	2	no	—
295	D₄×C₅₃	—	4	2	no	—
296	D₄×C₅₃	—	4	4	no	—
297	D₄×C₅₃	—	4	8	no	—
298	D₄×C₅₃	C₂×#41	1	4	yes	—
299	C₂×C₄×C₅₃	—	2	2	no	—
300	C₂×C₄×C₅₃	—	2	1	no	—
301	C₂×C₄×C₅₃	—	2	2	no	—
302	C₂×C₄×C₅₃	—	2	1	no	—
303	C₂×C₄×C₅₃	—	2	2	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	4	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	4	no	—
308	C₂×C₄×C₅₃	—	2	2	no	—
309	C₂×C₄×C₅₃	—	4	1	no	—
310	C₂×C₄×C₅₃	—	4	4	no	—
311	C₂×C₄×C₅₃	—	4	8	no	—
312	C₂×C₄×C₅₃	—	4	4	no	—
313	C₂×C₄×C₅₃	—	8	2	no	—
314	C₂×C₄×C₅₃	—	8	4	no	—
315	C₂×C₄×C₅₃	—	8	4	no	—
316	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
325	C₈×C₅₃	—	2	1	no	—
326	C₈×C₅₃	—	2	2	no	—
327	C₈×C₅₃	—	2	1	no	—
328	C₈×C₅₃	—	2	1	no	—
329	C₈×C₅₃	—	2	2	no	—
330	C₈×C₅₃	C₂×#41	1	2	yes	—
331	#61477	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂²×C₅₃	—	2	1	no	—
333	C₂²×C₅₃	—	2	2	no	—
334	C₂²×C₅₃	—	2	1	no	—
335	C₂²×C₅₃	—	2	2	no	—
336	C₂²×C₅₃	—	2	4	no	—
337	C₂²×C₅₃	—	2	1	no	—
338	C₂²×C₅₃	—	2	2	no	—
339	C₂²×C₅₃	—	4	2	no	—
340	C₂²×C₅₃	—	4	2	no	—
341	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
342	C₄×C₅₃	—	2	1	no	—
343	C₄×C₅₃	—	2	1	no	—
344	C₄×C₅₃	—	2	2	no	—
345	C₄×C₅₃	—	2	1	no	—
346	C₄×C₅₃	—	2	2	no	—
347	C₄×C₅₃	—	2	1	no	—
348	C₄×C₅₃	—	2	2	no	—
349	C₄×C₅₃	—	4	2	no	—
350	C₄×C₅₃	—	4	4	no	—
351	C₄×C₅₃	—	4	2	no	—
352	C₄×C₅₃	—	4	4	no	—
353	C₄×C₅₃	—	4	2	no	—
354	C₄×C₅₃	#578	1	2	yes	—
355	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
356	C₄×C₅₃	#585	1	1	yes	characteristic
357	#3515	C₂×C₅₃	1	2	yes	complemented
358	#3395	C₂×C₅₃	1	1	yes	characteristic, complemented
359	#3380	C₂×C₅₃	1	1	yes	characteristic, complemented
360	#3372	C₂×C₅₃	1	2	yes	complemented
361	#3338	C₂×C₅₃	1	1	yes	characteristic, complemented
362	#3336	C₂×C₅₃	1	2	yes	complemented
363	#3331	C₂×C₅₃	1	2	yes	complemented
364	#3315	C₂×C₅₃	1	4	yes	complemented
365	#3283	C₂×C₅₃	1	1	yes	characteristic, complemented
366	#3283	C₂×C₅₃	1	2	yes	complemented
367	#3177	C₂×C₅₃	1	2	yes	complemented
368	#3170	C₂×C₅₃	1	1	yes	characteristic, complemented
369	#3120	C₂×C₅₃	1	4	yes	complemented
370	#3116	C₂×C₅₃	1	2	yes	complemented
371	#2966	C₂×C₅₃	1	1	yes	characteristic, complemented
372	#2951	C₂×C₅₃	1	2	yes	complemented
373	C₄×#135	C₂×C₅₃	1	1	yes	characteristic, complemented
374	C₂×C₅₃	—	4	1	no	—
375	C₂×C₅₃	—	4	2	no	—
376	C₂×C₅₃	—	4	4	no	—
377	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
378	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
379	C₂×C₅₃	#3584	1	1	yes	characteristic
380	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
381	C₂×#135	C₂²×C₅₃	1	2	yes	—
382	#557	C₂²×C₅₃	1	2	yes	—
383	#554	C₂²×C₅₃	1	2	yes	—
384	#554	C₂²×C₅₃	1	2	yes	—
385	#553	—	2	2	no	—
386	#552	—	2	4	no	—
387	#552	—	2	2	no	—
388	#552	C₂²×C₅₃	1	4	yes	—
389	#547	C₂²×C₅₃	1	2	yes	—
390	#547	C₂²×C₅₃	1	4	yes	—
391	#541	C₂²×C₅₃	1	4	yes	—
392	#539	—	2	4	no	—
393	#533	C₂²×C₅₃	1	2	yes	—
394	#529	—	2	2	no	—
395	#529	C₂²×C₅₃	1	1	yes	characteristic
396	C₂×#125	—	2	2	no	—
397	#520	C₂²×C₅₃	1	4	yes	—
398	C₄×#41	C₂²×C₅₃	1	2	yes	—
399	#500	C₂²×C₅₃	1	1	yes	characteristic
400	#499	C₂²×C₅₃	1	2	yes	—
401	#494	C₂²×C₅₃	1	1	yes	characteristic
402	#494	C₂²×C₅₃	1	2	yes	—
403	#491	C₂²×C₅₃	1	4	yes	—
404	#487	C₂²×C₅₃	1	2	yes	—
405	#485	C₂²×C₅₃	1	4	yes	—
406	#484	C₂²×C₅₃	1	4	yes	—
407	#483	C₂²×C₅₃	1	4	yes	—
408	#479	C₂²×C₅₃	1	4	yes	—
409	#478	C₂²×C₅₃	1	4	yes	—
410	#477	C₂²×C₅₃	1	2	yes	—
411	#476	C₂²×C₅₃	1	2	yes	—
412	#470	C₂²×C₅₃	1	4	yes	—
413	#467	C₂²×C₅₃	1	2	yes	—
414	#467	C₂²×C₅₃	1	2	yes	—
415	#467	C₂²×C₅₃	1	2	yes	—
416	#467	C₂²×C₅₃	1	2	yes	—
417	#462	C₂²×C₅₃	1	2	yes	—
418	#462	C₂²×C₅₃	1	4	yes	—
419	#461	C₂²×C₅₃	1	2	yes	—
420	#461	C₂²×C₅₃	1	4	yes	—
421	#452	C₂²×C₅₃	1	4	yes	—
422	#452	C₂²×C₅₃	1	4	yes	—
423	#452	C₂²×C₅₃	1	4	yes	—
424	#446	C₂²×C₅₃	1	1	yes	characteristic
425	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
426	#441	C₂²×C₅₃	1	4	yes	—
427	#440	C₂²×C₅₃	1	4	yes	—
428	#440	C₂²×C₅₃	1	4	yes	—
429	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
430	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
431	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
432	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
433	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
434	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
435	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
436	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
437	C₄×D₈	C₂²×C₅₃	1	2	yes	—
438	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
439	#436	C₂²×C₅₃	1	1	yes	characteristic
440	#435	C₂²×C₅₃	1	2	yes	—
441	C₈×D₄	C₂²×C₅₃	1	2	yes	—
442	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
443	#433	C₂²×C₅₃	1	2	yes	—
444	#432	C₂²×C₅₃	1	1	yes	characteristic
445	#427	C₂²×C₅₃	1	1	yes	characteristic
446	C₂×#107	C₂²×C₅₃	1	2	yes	—
447	#417	C₂²×C₅₃	1	4	yes	—
448	#416	C₂²×C₅₃	1	2	yes	—
449	#405	C₂²×C₅₃	1	2	yes	—
450	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
451	C₅₃	#61477	1	1	yes	characteristic, direct product factor, Sylow
452	C₂×#41	C₂³×C₅₃	1	2	yes	—
453	C₂×#41	C₂³×C₅₃	1	4	yes	—
454	#135	—	2	4	no	—
455	#135	—	2	8	no	—
456	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
457	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
458	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
459	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
460	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
461	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
462	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
463	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
464	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
465	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
466	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
469	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
470	#126	—	2	4	no	—
471	#126	—	2	4	no	—
472	#126	—	2	4	no	—
473	#126	D₄×C₅₃	1	2	yes	—
474	#125	—	2	4	no	—
475	#125	—	2	4	no	—
476	#125	—	2	2	no	—
477	#125	—	2	2	no	—
478	#125	—	2	4	no	—
479	#125	—	2	4	no	—
480	#125	—	2	2	no	—
481	#125	D₄×C₅₃	1	1	yes	characteristic
482	#125	C₂³×C₅₃	1	4	yes	—
483	#124	D₄×C₅₃	1	1	yes	characteristic
484	#123	—	2	4	no	—
485	#123	—	2	4	no	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	D₄×C₅₃	1	2	yes	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
494	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
495	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
496	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
497	#121	—	2	2	no	—
498	#121	—	2	4	no	—
499	#121	D₄×C₅₃	1	1	yes	characteristic
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
503	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
504	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
505	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
506	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	4	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	C₂³×C₅₃	1	2	yes	—
513	C₄×D₄	C₂³×C₅₃	1	2	yes	—
514	C₄×D₄	C₂³×C₅₃	1	4	yes	—
515	C₄×D₄	C₂³×C₅₃	1	2	yes	—
516	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
517	#117	—	2	2	no	—
518	#117	—	2	4	no	—
519	#117	—	2	4	no	—
520	#117	—	2	2	no	—
521	#117	C₂³×C₅₃	1	2	yes	—
522	#117	C₂³×C₅₃	1	2	yes	—
523	C₂×C₄⋊C₄	—	2	4	no	—
524	C₂×C₄⋊C₄	—	2	2	no	—
525	C₂×C₄⋊C₄	—	2	4	no	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
528	C₂×C₄²	—	2	2	no	—
529	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
530	#107	C₂³×C₅₃	1	1	yes	characteristic
531	#107	C₂³×C₅₃	1	2	yes	—
532	#107	C₂³×C₅₃	1	4	yes	—
533	#107	C₂³×C₅₃	1	1	yes	characteristic
534	#107	C₂³×C₅₃	1	2	yes	—
535	#106	C₂³×C₅₃	1	2	yes	—
536	#106	C₂³×C₅₃	1	4	yes	—
537	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
538	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
539	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
540	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
541	#103	C₂³×C₅₃	1	2	yes	—
542	#103	C₂³×C₅₃	1	2	yes	—
543	#103	C₂³×C₅₃	1	4	yes	—
544	#103	C₂³×C₅₃	1	4	yes	—
545	#103	C₂³×C₅₃	1	4	yes	—
546	#103	C₂³×C₅₃	1	4	yes	—
547	#103	C₂³×C₅₃	1	4	yes	—
548	#102	C₂³×C₅₃	1	2	yes	—
549	#102	C₂³×C₅₃	1	2	yes	—
550	#102	C₂³×C₅₃	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
553	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
554	#97	C₂³×C₅₃	1	2	yes	—
555	#97	C₂³×C₅₃	1	2	yes	—
556	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
557	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
560	C₄×C₈	C₂³×C₅₃	1	2	yes	—
561	#41	—	2	4	no	—
562	#41	—	2	8	no	—
563	#41	—	4	2	no	—
564	#41	—	4	4	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
567	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
568	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
572	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
573	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
584	Q₁₆	—	2	2	no	—
585	Q₁₆	—	2	4	no	—
586	Q₁₆	—	4	2	no	—
587	Q₁₆	—	4	4	no	—
588	SD₁₆	—	2	4	no	—
589	SD₁₆	—	2	8	no	—
590	D₈	#41×C₅₃	1	4	yes	—
591	M₁₆	—	4	2	no	—
592	C₂×C₈	—	2	2	no	—
593	C₂×C₈	—	2	4	no	—
594	C₂×C₈	—	4	1	no	—
595	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
596	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
597	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
598	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
599	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
600	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
618	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
620	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
621	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
633	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
634	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
635	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
636	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	4	no	—
642	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
644	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
645	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
646	C₄²	C₂⁴×C₅₃	1	2	yes	—
647	C₂³	—	2	2	no	—
648	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
649	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	2	4	no	—
653	Q₈	—	2	4	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	8	2	no	—
656	D₄	—	2	2	no	—
657	D₄	—	2	2	no	—
658	D₄	—	4	2	no	—
659	D₄	—	4	4	no	—
660	D₄	—	4	8	no	—
661	D₄	C₂×#41×C₅₃	1	4	yes	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	8	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	8	2	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
681	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
683	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
687	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
688	C₈	—	2	1	no	—
689	C₈	—	2	2	no	—
690	C₈	—	2	1	no	—
691	C₈	—	2	1	no	—
692	C₈	—	2	2	no	—
693	C₈	C₂×#41×C₅₃	1	2	yes	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
704	C₄	—	2	1	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	4	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	4	no	—
716	C₄	C₅₃×#578	1	2	yes	—
717	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
718	C₄	C₅₃×#585	1	1	yes	characteristic
719	C₂	—	4	1	no	—
720	C₂	—	4	2	no	—
721	C₂	—	4	4	no	—
722	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
723	C₂	C₂×C₅₃×#578	1	1	yes	characteristic
724	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3515	C₂	semidirect
2. C₅₃×#3395	C₂	semidirect
3. C₅₃×#3380	C₂	semidirect
4. C₅₃×#3372	C₂	semidirect
5. C₅₃×#3338	C₂	semidirect
6. C₅₃×#3336	C₂	semidirect
7. C₅₃×#3331	C₂	semidirect
8. C₅₃×#3315	C₂	semidirect
9. C₅₃×#3283	C₂	semidirect
10. C₅₃×#3283	C₂	semidirect
11. C₅₃×#3177	C₂	semidirect
12. C₅₃×#3170	C₂	semidirect
13. C₅₃×#3120	C₂	semidirect
14. C₅₃×#3116	C₂	semidirect
15. C₅₃×#2966	C₂	semidirect
16. C₅₃×#2951	C₂	semidirect
17. C₄×#135×C₅₃	C₂	semidirect
331. #61477	C₅₃	direct (N × H)
357. #3515	C₂×C₅₃	semidirect
358. #3395	C₂×C₅₃	semidirect
359. #3380	C₂×C₅₃	semidirect
360. #3372	C₂×C₅₃	semidirect
361. #3338	C₂×C₅₃	semidirect
362. #3336	C₂×C₅₃	semidirect
363. #3331	C₂×C₅₃	semidirect
364. #3315	C₂×C₅₃	semidirect
365. #3283	C₂×C₅₃	semidirect
366. #3283	C₂×C₅₃	semidirect
367. #3177	C₂×C₅₃	semidirect
368. #3170	C₂×C₅₃	semidirect
369. #3120	C₂×C₅₃	semidirect
370. #3116	C₂×C₅₃	semidirect
371. #2966	C₂×C₅₃	semidirect
372. #2951	C₂×C₅₃	semidirect
373. C₄×#135	C₂×C₅₃	semidirect
451. C₅₃	#61477	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3515	2
C₅₃×#3395	2
C₅₃×#3380	2
C₅₃×#3372	2
C₅₃×#3338	2
C₅₃×#3336	2
C₅₃×#3331	2
C₅₃×#3315	2
C₅₃×#3283	2
C₅₃×#3177	2
C₅₃×#3170	2
C₅₃×#3120	2
C₅₃×#3116	2
C₅₃×#2966	2
C₅₃×#2951	2
C₄×#135×C₅₃	2
#61477	53

Subgroups — C53×#61477 #27268989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61477 #27268989