Subgroups — C₅₃×#61267 #27268779

Order 13568.

1870 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3494	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3355	C₂	1	4	yes	maximal, complemented
3	C₅₃×#3354	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3347	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3345	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3096	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3094	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3081	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#555	C₂²	1	4	yes	complemented
20	C₅₃×#553	C₂²	1	4	yes	complemented
21	C₅₃×#553	C₂²	1	4	yes	complemented
22	C₅₃×#551	—	2	4	no	—
23	C₅₃×#547	C₂²	1	4	yes	complemented
24	C₅₃×#546	—	2	4	no	—
25	C₅₃×#544	C₂²	1	2	yes	—
26	C₅₃×#542	—	2	2	no	—
27	C₅₃×#540	—	2	2	no	—
28	C₅₃×#535	C₂²	1	2	yes	—
29	C₅₃×#532	—	2	2	no	—
30	C₅₃×#529	—	2	2	no	—
31	C₅₃×#525	C₂²	1	1	yes	characteristic
32	C₂×#121×C₅₃	C₂²	1	2	yes	—
33	C₅₃×#520	C₂²	1	2	yes	—
34	C₅₃×#518	C₂²	1	2	yes	—
35	C₂×#117×C₅₃	C₂²	1	2	yes	—
36	C₅₃×#501	C₂²	1	4	yes	complemented
37	C₅₃×#499	C₂²	1	2	yes	complemented
38	C₅₃×#498	C₂²	1	2	yes	complemented
39	C₅₃×#482	C₂²	1	4	yes	complemented
40	C₅₃×#482	C₂²	1	4	yes	complemented
41	C₅₃×#482	C₂²	1	4	yes	complemented
42	C₅₃×#482	C₂²	1	4	yes	complemented
43	C₅₃×#481	C₂²	1	4	yes	complemented
44	C₅₃×#481	C₂²	1	4	yes	complemented
45	C₅₃×#480	C₂²	1	4	yes	complemented
46	C₅₃×#480	C₂²	1	4	yes	complemented
47	C₅₃×#478	C₂²	1	4	yes	complemented
48	C₅₃×#478	C₂²	1	4	yes	complemented
49	C₅₃×#476	C₂²	1	4	yes	complemented
50	C₅₃×#474	C₂²	1	4	yes	complemented
51	C₅₃×#469	C₂²	1	4	yes	—
52	C₅₃×#469	C₂²	1	4	yes	—
53	C₅₃×#469	C₂²	1	2	yes	complemented
54	C₅₃×#469	C₂²	1	2	yes	complemented
55	C₅₃×#466	C₂²	1	4	yes	complemented
56	C₅₃×#442	C₂²	1	2	yes	complemented
57	C₅₃×#442	C₂²	1	2	yes	complemented
58	C₄×D₈×C₅₃	C₂²	1	4	yes	complemented
59	C₅₃×#436	C₂²	1	4	yes	complemented
60	C₅₃×#435	C₂²	1	4	yes	complemented
61	C₅₃×#428	C₂²	1	2	yes	—
62	C₅₃×#428	C₂²	1	2	yes	—
63	C₅₃×#428	C₂²	1	2	yes	complemented
64	C₅₃×#428	C₂²	1	2	yes	complemented
65	C₅₃×#428	C₂²	1	2	yes	complemented
66	C₅₃×#428	C₂²	1	4	yes	complemented
67	C₅₃×#428	C₂²	1	2	yes	complemented
68	C₅₃×#427	C₂²	1	1	yes	characteristic
69	C₅₃×#427	C₂²	1	1	yes	characteristic
70	C₅₃×#427	C₂²	1	2	yes	—
71	C₅₃×#427	C₂²	1	2	yes	complemented
72	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
73	C₂×#106×C₅₃	C₂²	1	2	yes	complemented
74	C₅₃×#424	C₂²	1	1	yes	characteristic
75	C₅₃×#418	C₂²	1	2	yes	—
76	C₅₃×#418	C₂²	1	2	yes	—
77	C₂×#102×C₅₃	C₂²	1	2	yes	—
78	C₅₃×#408	C₂²	1	1	yes	characteristic
79	C₅₃×#407	C₂²	1	1	yes	characteristic
80	C₅₃×#405	C₂²	1	1	yes	characteristic
81	C₂×#41×C₅₃	—	2	4	no	—
82	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₅₃	—	2	2	no	—
84	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂×D₈×C₅₃	—	2	4	no	—
87	C₂×D₈×C₅₃	C₂³	1	2	yes	—
88	C₂×D₈×C₅₃	C₂³	1	2	yes	—
89	#131×C₅₃	—	2	4	no	—
90	C₂×M₁₆×C₅₃	—	2	4	no	—
91	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
92	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
93	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
95	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
98	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₅₃	—	2	2	no	—
100	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
101	#127×C₅₃	—	2	2	no	—
102	#126×C₅₃	—	2	4	no	—
103	#126×C₅₃	—	2	4	no	—
104	#125×C₅₃	—	2	2	no	—
105	#125×C₅₃	C₂³	1	4	yes	—
106	#124×C₅₃	—	2	4	no	—
107	#124×C₅₃	—	2	4	no	—
108	#124×C₅₃	—	2	2	no	—
109	#123×C₅₃	—	2	4	no	—
110	#123×C₅₃	—	2	4	no	—
111	#123×C₅₃	—	2	4	no	—
112	#123×C₅₃	—	2	4	no	—
113	#123×C₅₃	D₄	1	2	yes	—
114	C₂²⋊Q₈×C₅₃	—	2	4	no	—
115	C₂²⋊Q₈×C₅₃	—	2	4	no	—
116	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
117	#121×C₅₃	—	2	4	no	—
118	#121×C₅₃	—	2	4	no	—
119	#121×C₅₃	—	2	4	no	—
120	#121×C₅₃	—	2	2	no	—
121	#121×C₅₃	—	2	2	no	—
122	#121×C₅₃	D₄	1	2	yes	—
123	#121×C₅₃	C₂³	1	4	yes	—
124	#121×C₅₃	C₂³	1	4	yes	—
125	#121×C₅₃	C₂³	1	4	yes	—
126	#121×C₅₃	C₂³	1	4	yes	—
127	#120×C₅₃	—	2	4	no	—
128	#120×C₅₃	D₄	1	2	yes	—
129	C₄×Q₈×C₅₃	—	2	2	no	—
130	C₄×D₄×C₅₃	—	2	2	no	—
131	C₄×D₄×C₅₃	—	2	2	no	—
132	C₄×D₄×C₅₃	—	2	4	no	—
133	C₄×D₄×C₅₃	—	2	4	no	—
134	C₄×D₄×C₅₃	—	2	2	no	—
135	C₄×D₄×C₅₃	—	2	4	no	—
136	C₄×D₄×C₅₃	C₂³	1	4	yes	—
137	C₄×D₄×C₅₃	C₂³	1	4	yes	—
138	C₄×D₄×C₅₃	C₂³	1	4	yes	—
139	#117×C₅₃	—	2	4	no	—
140	#117×C₅₃	—	2	2	no	—
141	#117×C₅₃	—	2	2	no	—
142	#117×C₅₃	C₂³	1	2	yes	—
143	#117×C₅₃	C₂³	1	2	yes	—
144	#117×C₅₃	C₂³	1	2	yes	—
145	#117×C₅₃	C₂³	1	2	yes	—
146	#117×C₅₃	C₂³	1	4	yes	—
147	#117×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
153	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
154	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
155	C₂×C₄²×C₅₃	—	2	2	no	—
156	#107×C₅₃	C₂³	1	4	yes	—
157	#107×C₅₃	C₂³	1	2	yes	—
158	#107×C₅₃	C₂³	1	2	yes	—
159	#107×C₅₃	C₂³	1	2	yes	—
160	#107×C₅₃	C₂³	1	2	yes	—
161	#107×C₅₃	C₂³	1	4	yes	—
162	#106×C₅₃	C₂³	1	1	yes	characteristic
163	#106×C₅₃	C₂³	1	2	yes	—
164	#106×C₅₃	C₂³	1	4	yes	—
165	#106×C₅₃	C₂³	1	1	yes	characteristic
166	#106×C₅₃	C₂³	1	2	yes	—
167	#106×C₅₃	C₂³	1	1	yes	characteristic
168	#106×C₅₃	C₂³	1	4	yes	—
169	#106×C₅₃	C₂³	1	1	yes	characteristic
170	#106×C₅₃	C₂³	1	2	yes	—
171	#106×C₅₃	C₂³	1	2	yes	—
172	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
173	#102×C₅₃	C₂³	1	4	yes	—
174	#102×C₅₃	C₂³	1	4	yes	—
175	#102×C₅₃	C₂³	1	4	yes	—
176	#102×C₅₃	C₂³	1	4	yes	—
177	#102×C₅₃	C₂³	1	4	yes	—
178	#102×C₅₃	C₂³	1	4	yes	—
179	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
180	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
181	#97×C₅₃	C₂³	1	2	yes	—
182	C₄×C₈×C₅₃	C₂³	1	2	yes	—
183	C₂⁴×C₅₃	—	2	2	no	—
184	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
185	#41×C₅₃	—	2	2	no	—
186	#41×C₅₃	—	2	2	no	—
187	#41×C₅₃	—	8	8	no	—
188	C₂×Q₈×C₅₃	—	2	4	no	—
189	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₅₃	—	2	4	no	—
191	C₂×D₄×C₅₃	—	2	4	no	—
192	C₂×D₄×C₅₃	—	2	4	no	—
193	C₂×D₄×C₅₃	—	2	4	no	—
194	C₂×D₄×C₅₃	—	2	2	no	—
195	C₂×D₄×C₅₃	—	2	4	no	—
196	C₂×D₄×C₅₃	—	2	4	no	—
197	C₂×D₄×C₅₃	—	8	4	no	—
198	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
199	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
200	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
201	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₅₃	—	2	2	no	—
203	C₂²×C₄×C₅₃	—	2	2	no	—
204	C₂²×C₄×C₅₃	—	2	2	no	—
205	C₂²×C₄×C₅₃	—	2	2	no	—
206	C₂²×C₄×C₅₃	—	2	2	no	—
207	C₂²×C₄×C₅₃	—	2	4	no	—
208	C₂²×C₄×C₅₃	—	2	4	no	—
209	C₂²×C₄×C₅₃	—	2	4	no	—
210	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
215	D₈×C₅₃	—	2	4	no	—
216	D₈×C₅₃	—	2	4	no	—
217	M₁₆×C₅₃	—	2	2	no	—
218	M₁₆×C₅₃	—	2	2	no	—
219	M₁₆×C₅₃	—	2	4	no	—
220	M₁₆×C₅₃	—	2	4	no	—
221	M₁₆×C₅₃	—	2	4	no	—
222	C₂×C₈×C₅₃	—	2	2	no	—
223	C₂×C₈×C₅₃	—	2	4	no	—
224	C₂×C₈×C₅₃	#41	1	4	yes	complemented
225	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
226	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
227	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
228	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
229	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
230	C₄⋊C₄×C₅₃	—	2	2	no	—
231	C₄⋊C₄×C₅₃	—	2	2	no	—
232	C₄⋊C₄×C₅₃	—	2	2	no	—
233	C₄⋊C₄×C₅₃	—	2	4	no	—
234	C₄⋊C₄×C₅₃	—	2	4	no	—
235	C₄⋊C₄×C₅₃	—	2	4	no	—
236	C₄⋊C₄×C₅₃	—	2	4	no	—
237	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
238	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
239	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
240	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
241	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
242	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂²⋊C₄×C₅₃	—	2	2	no	—
245	C₂²⋊C₄×C₅₃	—	2	2	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	—	2	4	no	—
250	C₂²⋊C₄×C₅₃	—	2	4	no	—
251	C₂²⋊C₄×C₅₃	—	2	4	no	—
252	C₂²⋊C₄×C₅₃	—	2	4	no	—
253	C₂²⋊C₄×C₅₃	—	2	4	no	—
254	C₂²⋊C₄×C₅₃	—	2	4	no	—
255	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
256	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
257	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
258	C₄²×C₅₃	—	2	2	no	—
259	C₄²×C₅₃	—	2	2	no	—
260	C₄²×C₅₃	—	2	2	no	—
261	C₄²×C₅₃	—	2	2	no	—
262	C₄²×C₅₃	—	2	4	no	—
263	C₄²×C₅₃	C₂⁴	1	2	yes	—
264	C₂³×C₅₃	—	2	2	no	—
265	C₂³×C₅₃	—	2	4	no	—
266	C₂³×C₅₃	—	4	2	no	—
267	C₂³×C₅₃	—	4	4	no	—
268	C₂³×C₅₃	—	8	2	no	—
269	C₂³×C₅₃	—	8	2	no	—
270	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
271	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
272	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
273	Q₈×C₅₃	—	2	2	no	—
274	Q₈×C₅₃	—	8	4	no	—
275	D₄×C₅₃	—	2	4	no	—
276	D₄×C₅₃	—	2	2	no	—
277	D₄×C₅₃	—	2	4	no	—
278	D₄×C₅₃	—	2	4	no	—
279	D₄×C₅₃	—	4	4	no	—
280	D₄×C₅₃	—	4	8	no	—
281	D₄×C₅₃	—	4	4	no	—
282	D₄×C₅₃	—	8	4	no	—
283	D₄×C₅₃	—	8	4	no	—
284	D₄×C₅₃	—	8	4	no	—
285	C₂×C₄×C₅₃	—	2	2	no	—
286	C₂×C₄×C₅₃	—	2	4	no	—
287	C₂×C₄×C₅₃	—	2	2	no	—
288	C₂×C₄×C₅₃	—	2	2	no	—
289	C₂×C₄×C₅₃	—	2	2	no	—
290	C₂×C₄×C₅₃	—	2	2	no	—
291	C₂×C₄×C₅₃	—	2	2	no	—
292	C₂×C₄×C₅₃	—	2	2	no	—
293	C₂×C₄×C₅₃	—	2	4	no	—
294	C₂×C₄×C₅₃	—	2	2	no	—
295	C₂×C₄×C₅₃	—	2	2	no	—
296	C₂×C₄×C₅₃	—	4	4	no	—
297	C₂×C₄×C₅₃	—	8	4	no	—
298	C₂×C₄×C₅₃	—	8	4	no	—
299	C₂×C₄×C₅₃	—	8	2	no	—
300	C₂×C₄×C₅₃	—	8	2	no	—
301	C₂×C₄×C₅₃	—	8	4	no	—
302	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
303	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
307	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
308	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
309	C₈×C₅₃	—	2	2	no	—
310	C₈×C₅₃	—	2	2	no	—
311	C₈×C₅₃	—	2	2	no	—
312	C₈×C₅₃	C₂×#41	1	2	yes	—
313	C₈×C₅₃	C₂×#41	1	2	yes	—
314	#61267	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂²×C₅₃	—	2	2	no	—
316	C₂²×C₅₃	—	2	2	no	—
317	C₂²×C₅₃	—	2	4	no	—
318	C₂²×C₅₃	—	2	2	no	—
319	C₂²×C₅₃	—	2	2	no	—
320	C₂²×C₅₃	—	2	2	no	—
321	C₂²×C₅₃	—	4	4	no	—
322	C₂²×C₅₃	—	4	4	no	—
323	C₂²×C₅₃	—	4	4	no	—
324	C₂²×C₅₃	—	8	2	no	—
325	C₂²×C₅₃	—	16	4	no	—
326	C₂²×C₅₃	#547	1	2	yes	—
327	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
328	C₄×C₅₃	—	2	4	no	—
329	C₄×C₅₃	—	2	2	no	—
330	C₄×C₅₃	—	2	2	no	—
331	C₄×C₅₃	—	4	2	no	—
332	C₄×C₅₃	—	4	2	no	—
333	C₄×C₅₃	—	4	2	no	—
334	C₄×C₅₃	—	4	4	no	—
335	C₄×C₅₃	—	4	2	no	—
336	C₄×C₅₃	#547	1	2	yes	—
337	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
338	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
339	#3494	C₂×C₅₃	1	2	yes	complemented
340	#3355	C₂×C₅₃	1	4	yes	complemented
341	#3354	C₂×C₅₃	1	4	yes	complemented
342	#3347	C₂×C₅₃	1	4	yes	complemented
343	#3345	C₂×C₅₃	1	4	yes	complemented
344	#3163	C₂×C₅₃	1	1	yes	characteristic, complemented
345	#3096	C₂×C₅₃	1	2	yes	complemented
346	#3094	C₂×C₅₃	1	2	yes	complemented
347	#3081	C₂×C₅₃	1	2	yes	complemented
348	#3058	C₂×C₅₃	1	1	yes	characteristic, complemented
349	C₂×#469	C₂×C₅₃	1	1	yes	characteristic, complemented
350	#2948	C₂×C₅₃	1	1	yes	characteristic, complemented
351	#2930	C₂×C₅₃	1	1	yes	characteristic, complemented
352	#2912	C₂×C₅₃	1	1	yes	characteristic, complemented
353	#2911	C₂×C₅₃	1	1	yes	characteristic, complemented
354	C₂×C₅₃	—	2	2	no	—
355	C₂×C₅₃	—	4	2	no	—
356	C₂×C₅₃	—	4	2	no	—
357	C₂×C₅₃	—	8	4	no	—
358	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
359	C₂×C₅₃	#3585	1	2	yes	—
360	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
361	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
362	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
363	#555	C₂²×C₅₃	1	4	yes	complemented
364	#553	C₂²×C₅₃	1	4	yes	complemented
365	#553	C₂²×C₅₃	1	4	yes	complemented
366	#551	—	2	4	no	—
367	#547	C₂²×C₅₃	1	4	yes	complemented
368	#546	—	2	4	no	—
369	#544	C₂²×C₅₃	1	2	yes	—
370	#542	—	2	2	no	—
371	#540	—	2	2	no	—
372	#535	C₂²×C₅₃	1	2	yes	—
373	#532	—	2	2	no	—
374	#529	—	2	2	no	—
375	#525	C₂²×C₅₃	1	1	yes	characteristic
376	C₂×#121	C₂²×C₅₃	1	2	yes	—
377	#520	C₂²×C₅₃	1	2	yes	—
378	#518	C₂²×C₅₃	1	2	yes	—
379	C₂×#117	C₂²×C₅₃	1	2	yes	—
380	#501	C₂²×C₅₃	1	4	yes	complemented
381	#499	C₂²×C₅₃	1	2	yes	complemented
382	#498	C₂²×C₅₃	1	2	yes	complemented
383	#482	C₂²×C₅₃	1	4	yes	complemented
384	#482	C₂²×C₅₃	1	4	yes	complemented
385	#482	C₂²×C₅₃	1	4	yes	complemented
386	#482	C₂²×C₅₃	1	4	yes	complemented
387	#481	C₂²×C₅₃	1	4	yes	complemented
388	#481	C₂²×C₅₃	1	4	yes	complemented
389	#480	C₂²×C₅₃	1	4	yes	complemented
390	#480	C₂²×C₅₃	1	4	yes	complemented
391	#478	C₂²×C₅₃	1	4	yes	complemented
392	#478	C₂²×C₅₃	1	4	yes	complemented
393	#476	C₂²×C₅₃	1	4	yes	complemented
394	#474	C₂²×C₅₃	1	4	yes	complemented
395	#469	C₂²×C₅₃	1	4	yes	—
396	#469	C₂²×C₅₃	1	4	yes	—
397	#469	C₂²×C₅₃	1	2	yes	complemented
398	#469	C₂²×C₅₃	1	2	yes	complemented
399	#466	C₂²×C₅₃	1	4	yes	complemented
400	#442	C₂²×C₅₃	1	2	yes	complemented
401	#442	C₂²×C₅₃	1	2	yes	complemented
402	C₄×D₈	C₂²×C₅₃	1	4	yes	complemented
403	#436	C₂²×C₅₃	1	4	yes	complemented
404	#435	C₂²×C₅₃	1	4	yes	complemented
405	#428	C₂²×C₅₃	1	2	yes	—
406	#428	C₂²×C₅₃	1	2	yes	—
407	#428	C₂²×C₅₃	1	2	yes	complemented
408	#428	C₂²×C₅₃	1	2	yes	complemented
409	#428	C₂²×C₅₃	1	2	yes	complemented
410	#428	C₂²×C₅₃	1	4	yes	complemented
411	#428	C₂²×C₅₃	1	2	yes	complemented
412	#427	C₂²×C₅₃	1	2	yes	—
413	#427	C₂²×C₅₃	1	1	yes	characteristic
414	#427	C₂²×C₅₃	1	1	yes	characteristic
415	#427	C₂²×C₅₃	1	2	yes	complemented
416	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
417	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
418	#424	C₂²×C₅₃	1	1	yes	characteristic
419	#418	C₂²×C₅₃	1	2	yes	—
420	#418	C₂²×C₅₃	1	2	yes	—
421	C₂×#102	C₂²×C₅₃	1	2	yes	—
422	#408	C₂²×C₅₃	1	1	yes	characteristic
423	#407	C₂²×C₅₃	1	1	yes	characteristic
424	#405	C₂²×C₅₃	1	1	yes	characteristic
425	C₅₃	#61267	1	1	yes	characteristic, direct product factor, Sylow
426	C₂×#41	—	2	4	no	—
427	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
428	C₂²×D₄	—	2	2	no	—
429	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
430	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
431	C₂×D₈	—	2	4	no	—
432	C₂×D₈	C₂³×C₅₃	1	2	yes	—
433	C₂×D₈	C₂³×C₅₃	1	2	yes	—
434	#131	—	2	4	no	—
435	C₂×M₁₆	—	2	4	no	—
436	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
437	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
438	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
439	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
440	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
443	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
444	C₄⋊Q₈	—	2	2	no	—
445	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
446	#127	—	2	2	no	—
447	#126	—	2	4	no	—
448	#126	—	2	4	no	—
449	#125	—	2	2	no	—
450	#125	C₂³×C₅₃	1	4	yes	—
451	#124	—	2	2	no	—
452	#124	—	2	4	no	—
453	#124	—	2	4	no	—
454	#123	—	2	4	no	—
455	#123	—	2	4	no	—
456	#123	—	2	4	no	—
457	#123	—	2	4	no	—
458	#123	D₄×C₅₃	1	2	yes	—
459	C₂²⋊Q₈	—	2	4	no	—
460	C₂²⋊Q₈	—	2	4	no	—
461	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
462	#121	—	2	4	no	—
463	#121	—	2	4	no	—
464	#121	—	2	4	no	—
465	#121	—	2	2	no	—
466	#121	—	2	2	no	—
467	#121	D₄×C₅₃	1	2	yes	—
468	#121	C₂³×C₅₃	1	4	yes	—
469	#121	C₂³×C₅₃	1	4	yes	—
470	#121	C₂³×C₅₃	1	4	yes	—
471	#121	C₂³×C₅₃	1	4	yes	—
472	#120	—	2	4	no	—
473	#120	D₄×C₅₃	1	2	yes	—
474	C₄×Q₈	—	2	2	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	4	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	4	no	—
480	C₄×D₄	—	2	4	no	—
481	C₄×D₄	C₂³×C₅₃	1	4	yes	—
482	C₄×D₄	C₂³×C₅₃	1	4	yes	—
483	C₄×D₄	C₂³×C₅₃	1	4	yes	—
484	#117	—	2	2	no	—
485	#117	—	2	2	no	—
486	#117	—	2	4	no	—
487	#117	C₂³×C₅₃	1	2	yes	—
488	#117	C₂³×C₅₃	1	2	yes	—
489	#117	C₂³×C₅₃	1	2	yes	—
490	#117	C₂³×C₅₃	1	2	yes	—
491	#117	C₂³×C₅₃	1	4	yes	—
492	#117	C₂³×C₅₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
497	C₂×C₂²⋊C₄	—	2	2	no	—
498	C₂×C₂²⋊C₄	—	2	2	no	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₄²	—	2	2	no	—
501	#107	C₂³×C₅₃	1	2	yes	—
502	#107	C₂³×C₅₃	1	2	yes	—
503	#107	C₂³×C₅₃	1	2	yes	—
504	#107	C₂³×C₅₃	1	2	yes	—
505	#107	C₂³×C₅₃	1	4	yes	—
506	#107	C₂³×C₅₃	1	4	yes	—
507	#106	C₂³×C₅₃	1	2	yes	—
508	#106	C₂³×C₅₃	1	2	yes	—
509	#106	C₂³×C₅₃	1	1	yes	characteristic
510	#106	C₂³×C₅₃	1	4	yes	—
511	#106	C₂³×C₅₃	1	1	yes	characteristic
512	#106	C₂³×C₅₃	1	1	yes	characteristic
513	#106	C₂³×C₅₃	1	1	yes	characteristic
514	#106	C₂³×C₅₃	1	2	yes	—
515	#106	C₂³×C₅₃	1	2	yes	—
516	#106	C₂³×C₅₃	1	4	yes	—
517	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
518	#102	C₂³×C₅₃	1	4	yes	—
519	#102	C₂³×C₅₃	1	4	yes	—
520	#102	C₂³×C₅₃	1	4	yes	—
521	#102	C₂³×C₅₃	1	4	yes	—
522	#102	C₂³×C₅₃	1	4	yes	—
523	#102	C₂³×C₅₃	1	4	yes	—
524	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
525	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
526	#97	C₂³×C₅₃	1	2	yes	—
527	C₄×C₈	C₂³×C₅₃	1	2	yes	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
530	#41	—	2	2	no	—
531	#41	—	2	2	no	—
532	#41	—	8	8	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	8	4	no	—
543	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
544	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
545	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
546	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
556	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
560	D₈	—	2	4	no	—
561	D₈	—	2	4	no	—
562	M₁₆	—	2	2	no	—
563	M₁₆	—	2	2	no	—
564	M₁₆	—	2	4	no	—
565	M₁₆	—	2	4	no	—
566	M₁₆	—	2	4	no	—
567	C₂×C₈	—	2	2	no	—
568	C₂×C₈	—	2	4	no	—
569	C₂×C₈	#41×C₅₃	1	4	yes	complemented
570	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
571	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
572	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
573	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
574	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
583	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
584	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
585	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
586	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
587	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
588	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
601	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
602	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	4	no	—
608	C₄²	C₂⁴×C₅₃	1	2	yes	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	4	no	—
611	C₂³	—	4	2	no	—
612	C₂³	—	4	4	no	—
613	C₂³	—	8	2	no	—
614	C₂³	—	8	2	no	—
615	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
616	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
617	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
618	Q₈	—	2	2	no	—
619	Q₈	—	8	4	no	—
620	D₄	—	2	4	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	4	no	—
623	D₄	—	2	4	no	—
624	D₄	—	4	4	no	—
625	D₄	—	4	8	no	—
626	D₄	—	4	4	no	—
627	D₄	—	8	4	no	—
628	D₄	—	8	4	no	—
629	D₄	—	8	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	8	4	no	—
643	C₂×C₄	—	8	4	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	—	8	2	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
650	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
651	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
652	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
653	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
654	C₈	—	2	2	no	—
655	C₈	—	2	2	no	—
656	C₈	—	2	2	no	—
657	C₈	C₂×#41×C₅₃	1	2	yes	—
658	C₈	C₂×#41×C₅₃	1	2	yes	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	8	2	no	—
669	C₂²	—	16	4	no	—
670	C₂²	C₅₃×#547	1	2	yes	—
671	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
672	C₄	—	2	2	no	—
673	C₄	—	2	2	no	—
674	C₄	—	2	4	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	2	no	—
678	C₄	—	4	4	no	—
679	C₄	—	4	2	no	—
680	C₄	C₅₃×#547	1	2	yes	—
681	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
682	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
683	C₂	—	2	2	no	—
684	C₂	—	4	2	no	—
685	C₂	—	4	2	no	—
686	C₂	—	8	4	no	—
687	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
688	C₂	C₅₃×#3585	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3494	C₂	semidirect
2. C₅₃×#3355	C₂	semidirect
3. C₅₃×#3354	C₂	semidirect
4. C₅₃×#3347	C₂	semidirect
5. C₅₃×#3345	C₂	semidirect
6. C₅₃×#3163	C₂	semidirect
7. C₅₃×#3096	C₂	semidirect
8. C₅₃×#3094	C₂	semidirect
9. C₅₃×#3081	C₂	semidirect
10. C₅₃×#3058	C₂	semidirect
11. C₂×C₅₃×#469	C₂	semidirect
12. C₅₃×#2948	C₂	semidirect
13. C₅₃×#2930	C₂	semidirect
14. C₅₃×#2912	C₂	semidirect
15. C₅₃×#2911	C₂	semidirect
19. C₅₃×#555	C₂²	semidirect
20. C₅₃×#553	C₂²	semidirect
21. C₅₃×#553	C₂²	semidirect
23. C₅₃×#547	C₂²	semidirect
36. C₅₃×#501	C₂²	semidirect
37. C₅₃×#499	C₂²	semidirect
38. C₅₃×#498	C₂²	semidirect
39. C₅₃×#482	C₂²	semidirect
40. C₅₃×#482	C₂²	semidirect
41. C₅₃×#482	C₂²	semidirect
42. C₅₃×#482	C₂²	semidirect
43. C₅₃×#481	C₂²	semidirect
44. C₅₃×#481	C₂²	semidirect
45. C₅₃×#480	C₂²	semidirect
46. C₅₃×#480	C₂²	semidirect
47. C₅₃×#478	C₂²	semidirect
48. C₅₃×#478	C₂²	semidirect
49. C₅₃×#476	C₂²	semidirect
50. C₅₃×#474	C₂²	semidirect
53. C₅₃×#469	C₂²	semidirect
54. C₅₃×#469	C₂²	semidirect
55. C₅₃×#466	C₂²	semidirect
56. C₅₃×#442	C₂²	semidirect
57. C₅₃×#442	C₂²	semidirect
58. C₄×D₈×C₅₃	C₂²	semidirect
59. C₅₃×#436	C₂²	semidirect
60. C₅₃×#435	C₂²	semidirect
63. C₅₃×#428	C₂²	semidirect
64. C₅₃×#428	C₂²	semidirect
65. C₅₃×#428	C₂²	semidirect
66. C₅₃×#428	C₂²	semidirect
67. C₅₃×#428	C₂²	semidirect
71. C₅₃×#427	C₂²	semidirect
73. C₂×#106×C₅₃	C₂²	semidirect
224. C₂×C₈×C₅₃	#41	semidirect
314. #61267	C₅₃	direct (N × H)
339. #3494	C₂×C₅₃	semidirect
340. #3355	C₂×C₅₃	semidirect
341. #3354	C₂×C₅₃	semidirect
342. #3347	C₂×C₅₃	semidirect
343. #3345	C₂×C₅₃	semidirect
344. #3163	C₂×C₅₃	semidirect
345. #3096	C₂×C₅₃	semidirect
346. #3094	C₂×C₅₃	semidirect
347. #3081	C₂×C₅₃	semidirect
348. #3058	C₂×C₅₃	semidirect
349. C₂×#469	C₂×C₅₃	semidirect
350. #2948	C₂×C₅₃	semidirect
351. #2930	C₂×C₅₃	semidirect
352. #2912	C₂×C₅₃	semidirect
353. #2911	C₂×C₅₃	semidirect
363. #555	C₂²×C₅₃	semidirect
364. #553	C₂²×C₅₃	semidirect
365. #553	C₂²×C₅₃	semidirect
367. #547	C₂²×C₅₃	semidirect
380. #501	C₂²×C₅₃	semidirect
381. #499	C₂²×C₅₃	semidirect
382. #498	C₂²×C₅₃	semidirect
383. #482	C₂²×C₅₃	semidirect
384. #482	C₂²×C₅₃	semidirect
385. #482	C₂²×C₅₃	semidirect
386. #482	C₂²×C₅₃	semidirect
387. #481	C₂²×C₅₃	semidirect
388. #481	C₂²×C₅₃	semidirect
389. #480	C₂²×C₅₃	semidirect
390. #480	C₂²×C₅₃	semidirect
391. #478	C₂²×C₅₃	semidirect
392. #478	C₂²×C₅₃	semidirect
393. #476	C₂²×C₅₃	semidirect
394. #474	C₂²×C₅₃	semidirect
397. #469	C₂²×C₅₃	semidirect
398. #469	C₂²×C₅₃	semidirect
399. #466	C₂²×C₅₃	semidirect
400. #442	C₂²×C₅₃	semidirect
401. #442	C₂²×C₅₃	semidirect
402. C₄×D₈	C₂²×C₅₃	semidirect
403. #436	C₂²×C₅₃	semidirect
404. #435	C₂²×C₅₃	semidirect
407. #428	C₂²×C₅₃	semidirect
408. #428	C₂²×C₅₃	semidirect
409. #428	C₂²×C₅₃	semidirect
410. #428	C₂²×C₅₃	semidirect
411. #428	C₂²×C₅₃	semidirect
415. #427	C₂²×C₅₃	semidirect
417. C₂×#106	C₂²×C₅₃	semidirect
425. C₅₃	#61267	direct (N × H)
569. 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×#3494	2
C₅₃×#3355	2
C₅₃×#3354	2
C₅₃×#3347	2
C₅₃×#3345	2
C₅₃×#3163	2
C₅₃×#3096	2
C₅₃×#3094	2
C₅₃×#3081	2
C₅₃×#3058	2
C₂×C₅₃×#469	2
C₅₃×#2948	2
C₅₃×#2930	2
C₅₃×#2912	2
C₅₃×#2911	2
#61267	53

Subgroups — C53×#61267 #27268779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61267 #27268779