Subgroups — C₅₃×#11256 #27218768

Order 13568.

814 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#107×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#340	C₂	1	2	yes	maximal
3	C₂×C₅₃×#340	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₃×#336	C₂	1	1	yes	maximal, characteristic
5	C₅₃×C₄⋊#95	C₂	1	2	yes	maximal
6	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
11	C₂×#107×C₅₃	—	2	2	no	—
12	C₂×#107×C₅₃	—	2	4	no	—
13	C₂×#95×C₅₃	—	2	2	no	—
14	C₂×#95×C₅₃	—	2	2	no	—
15	C₅₃×#340	—	2	4	no	—
16	C₅₃×#340	C₄	1	4	yes	complemented
17	C₅₃×#336	—	2	2	no	—
18	C₂³×C₄×C₅₃	—	2	2	no	—
19	C₂³×C₄×C₅₃	—	2	2	no	—
20	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
23	C₂²×C₈×C₅₃	—	2	2	no	—
24	C₂²×C₈×C₅₃	—	2	1	no	—
25	C₂²×C₈×C₅₃	—	2	2	no	—
26	C₂²×C₈×C₅₃	—	2	2	no	—
27	C₂²×C₈×C₅₃	—	2	2	no	—
28	C₂²×C₈×C₅₃	—	2	1	no	—
29	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
30	C₂²×C₈×C₅₃	D₄	1	2	yes	—
31	C₂²×C₈×C₅₃	Q₈	1	2	yes	—
32	C₂²×C₈×C₅₃	Q₈	1	2	yes	—
33	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
34	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
36	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
37	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
38	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₅₃	D₄	1	4	yes	—
45	C₂×C₄²×C₅₃	—	2	1	no	—
46	C₂×C₄²×C₅₃	—	2	1	no	—
47	C₂×C₄²×C₅₃	—	2	2	no	—
48	C₂×C₄²×C₅₃	—	2	2	no	—
49	#107×C₅₃	—	2	8	no	—
50	#95×C₅₃	—	4	4	no	—
51	#95×C₅₃	—	4	4	no	—
52	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₅₃	—	2	1	no	—
54	C₂²×C₄×C₅₃	—	2	1	no	—
55	C₂²×C₄×C₅₃	—	2	2	no	—
56	C₂²×C₄×C₅₃	—	2	2	no	—
57	C₂²×C₄×C₅₃	—	2	1	no	—
58	C₂²×C₄×C₅₃	—	2	1	no	—
59	C₂²×C₄×C₅₃	—	2	2	no	—
60	C₂²×C₄×C₅₃	—	2	2	no	—
61	C₂²×C₄×C₅₃	—	2	4	no	—
62	C₂²×C₄×C₅₃	—	2	4	no	—
63	C₂²×C₄×C₅₃	—	4	2	no	—
64	C₂²×C₄×C₅₃	—	4	2	no	—
65	C₂²×C₄×C₅₃	—	4	2	no	—
66	C₂²×C₄×C₅₃	—	4	2	no	—
67	C₂²×C₄×C₅₃	—	4	2	no	—
68	C₂²×C₄×C₅₃	—	4	2	no	—
69	C₂²×C₄×C₅₃	—	4	2	no	—
70	C₂²×C₄×C₅₃	—	4	2	no	—
71	C₂²×C₄×C₅₃	—	4	2	no	—
72	C₂²×C₄×C₅₃	—	4	2	no	—
73	C₂²×C₄×C₅₃	—	4	2	no	—
74	C₂²×C₄×C₅₃	—	4	2	no	—
75	C₂²×C₄×C₅₃	D₈	1	2	yes	—
76	C₂²×C₄×C₅₃	Q₁₆	1	2	yes	—
77	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	#41	1	2	yes	—
83	C₂²×C₄×C₅₃	#41	1	2	yes	—
84	C₂²×C₄×C₅₃	#41	1	2	yes	—
85	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
87	C₂×C₈×C₅₃	—	2	4	no	—
88	C₂×C₈×C₅₃	—	2	2	no	—
89	C₂×C₈×C₅₃	—	2	4	no	—
90	C₂×C₈×C₅₃	—	2	2	no	—
91	C₂×C₈×C₅₃	—	2	4	no	—
92	C₂×C₈×C₅₃	—	2	2	no	—
93	C₂×C₈×C₅₃	—	4	1	no	—
94	C₂×C₈×C₅₃	—	4	1	no	—
95	C₂×C₈×C₅₃	—	4	2	no	—
96	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	—
97	C₄⋊C₄×C₅₃	—	2	4	no	—
98	C₄⋊C₄×C₅₃	—	2	4	no	—
99	C₄⋊C₄×C₅₃	—	2	4	no	—
100	C₄⋊C₄×C₅₃	—	2	4	no	—
101	C₄⋊C₄×C₅₃	—	4	2	no	—
102	C₄⋊C₄×C₅₃	—	4	2	no	—
103	C₄⋊C₄×C₅₃	—	4	2	no	—
104	C₄⋊C₄×C₅₃	—	4	2	no	—
105	C₄²×C₅₃	—	4	1	no	—
106	C₄²×C₅₃	—	4	1	no	—
107	C₄²×C₅₃	—	4	2	no	—
108	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
109	C₂³×C₅₃	#121	1	2	yes	—
110	C₂³×C₅₃	#121	1	1	yes	characteristic
111	C₂³×C₅₃	#123	1	2	yes	—
112	C₂³×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
113	C₂³×C₅₃	C₂×D₈	1	1	yes	characteristic
114	C₂³×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
115	C₂³×C₅₃	#135	1	1	yes	characteristic
116	C₂³×C₅₃	#135	1	1	yes	characteristic
117	C₂³×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
118	C₂³×C₅₃	#137	1	2	yes	—
119	C₂×C₄×C₅₃	—	2	2	no	—
120	C₂×C₄×C₅₃	—	2	2	no	—
121	C₂×C₄×C₅₃	—	2	4	no	—
122	C₂×C₄×C₅₃	—	2	4	no	—
123	C₂×C₄×C₅₃	—	4	1	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	2	no	—
128	C₂×C₄×C₅₃	—	4	2	no	—
129	C₂×C₄×C₅₃	—	4	4	no	—
130	C₂×C₄×C₅₃	—	4	4	no	—
131	C₂×C₄×C₅₃	—	4	4	no	—
132	C₂×C₄×C₅₃	—	4	4	no	—
133	C₂×C₄×C₅₃	—	4	4	no	—
134	C₂×C₄×C₅₃	—	4	4	no	—
135	C₂×C₄×C₅₃	—	8	2	no	—
136	C₂×C₄×C₅₃	—	8	2	no	—
137	C₂×C₄×C₅₃	—	8	2	no	—
138	C₂×C₄×C₅₃	—	8	2	no	—
139	C₂×C₄×C₅₃	—	8	2	no	—
140	C₂×C₄×C₅₃	—	8	2	no	—
141	C₂×C₄×C₅₃	—	8	2	no	—
142	C₂×C₄×C₅₃	—	8	2	no	—
143	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₅₃	#117	1	2	yes	—
145	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
150	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
152	C₂×C₄×C₅₃	#123	1	2	yes	—
153	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
154	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
155	C₂×C₄×C₅₃	#124	1	2	yes	—
156	C₂×C₄×C₅₃	#125	1	2	yes	—
157	C₂×C₄×C₅₃	#125	1	2	yes	—
158	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
159	C₂×C₄×C₅₃	#126	1	2	yes	—
160	C₂×C₄×C₅₃	#126	1	2	yes	—
161	C₈×C₅₃	—	2	4	no	—
162	C₈×C₅₃	—	4	2	no	—
163	#11256	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₅₃	#388	1	2	yes	—
165	C₂²×C₅₃	#389	1	1	yes	characteristic
166	C₂²×C₅₃	#394	1	1	yes	characteristic
167	C₂²×C₅₃	#397	1	1	yes	characteristic
168	C₂²×C₅₃	#398	1	2	yes	—
169	C₂²×C₅₃	C₄×D₈	1	1	yes	characteristic
170	C₂²×C₅₃	C₄×Q₁₆	1	1	yes	characteristic
171	C₂²×C₅₃	#440	1	2	yes	—
172	C₂²×C₅₃	#459	1	2	yes	—
173	C₂²×C₅₃	#462	1	2	yes	—
174	C₂²×C₅₃	#463	1	2	yes	—
175	C₂²×C₅₃	#464	1	2	yes	—
176	C₂²×C₅₃	#466	1	1	yes	characteristic
177	C₂²×C₅₃	#467	1	1	yes	characteristic
178	C₂²×C₅₃	#469	1	1	yes	characteristic
179	C₂²×C₅₃	#470	1	1	yes	characteristic
180	C₂²×C₅₃	#480	1	2	yes	—
181	C₂²×C₅₃	#482	1	2	yes	—
182	C₂²×C₅₃	#484	1	2	yes	—
183	C₂²×C₅₃	#485	1	2	yes	—
184	C₂²×C₅₃	#499	1	1	yes	characteristic
185	C₂²×C₅₃	#500	1	1	yes	characteristic
186	C₂²×C₅₃	#501	1	2	yes	—
187	C₄×C₅₃	—	4	2	no	—
188	C₄×C₅₃	—	4	2	no	—
189	C₄×C₅₃	—	8	4	no	—
190	C₄×C₅₃	—	8	4	no	—
191	C₄×C₅₃	#382	1	1	yes	characteristic
192	C₄×C₅₃	#385	1	1	yes	characteristic
193	C₄×C₅₃	#387	1	2	yes	—
194	C₄×C₅₃	#393	1	1	yes	characteristic
195	C₄×C₅₃	#400	1	2	yes	—
196	C₄×C₅₃	#400	1	1	yes	characteristic
197	C₂²×#107	C₂×C₅₃	1	1	yes	characteristic
198	C₂×#340	C₂×C₅₃	1	2	yes	—
199	C₂×#340	C₂×C₅₃	1	1	yes	characteristic
200	C₂×#336	C₂×C₅₃	1	1	yes	characteristic
201	C₄⋊#95	C₂×C₅₃	1	2	yes	—
202	C₂×C₅₃	#1442	1	1	yes	characteristic
203	C₂×C₅₃	#1925	1	2	yes	—
204	C₂×C₅₃	#1928	1	2	yes	—
205	C₂×C₅₃	#1942	1	1	yes	characteristic
206	C₂×C₅₃	#1944	1	1	yes	characteristic
207	C₂×C₅₃	#2054	1	1	yes	characteristic
208	C₂×C₅₃	#2056	1	1	yes	characteristic
209	C₂×C₅₃	#2075	1	1	yes	characteristic
210	C₂×C₅₃	#2076	1	1	yes	characteristic
211	C₂×C₅₃	#2083	1	2	yes	—
212	C₂×C₅₃	#2085	1	2	yes	—
213	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
214	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
215	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
217	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
218	C₂×#107	—	2	2	no	—
219	C₂×#107	—	2	4	no	—
220	C₂×#95	—	2	2	no	—
221	C₂×#95	—	2	2	no	—
222	#340	—	2	4	no	—
223	#340	C₄×C₅₃	1	4	yes	complemented
224	#336	—	2	2	no	—
225	C₅₃	#11256	1	1	yes	characteristic, direct product factor, Sylow
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	—	2	2	no	—
228	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
229	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	C₂×C₄×C₅₃	1	2	yes	—
238	C₂²×C₈	D₄×C₅₃	1	2	yes	—
239	C₂²×C₈	Q₈×C₅₃	1	2	yes	—
240	C₂²×C₈	Q₈×C₅₃	1	2	yes	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	4	yes	—
252	C₂×C₄⋊C₄	D₄×C₅₃	1	4	yes	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	1	no	—
257	#107	—	2	8	no	—
258	#95	—	4	4	no	—
259	#95	—	4	4	no	—
260	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	D₈×C₅₃	1	2	yes	—
284	C₂²×C₄	Q₁₆×C₅₃	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
288	C₂²×C₄	C₂×Q₈×C₅₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×Q₈×C₅₃	1	1	yes	characteristic
290	C₂²×C₄	#41×C₅₃	1	2	yes	—
291	C₂²×C₄	#41×C₅₃	1	2	yes	—
292	C₂²×C₄	#41×C₅₃	1	2	yes	—
293	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
294	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	C₄⋊C₄×C₅₃	1	4	yes	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄²	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	4	2	no	—
316	C₂³	C₄×D₄×C₅₃	1	1	yes	characteristic
317	C₂³	#121×C₅₃	1	2	yes	—
318	C₂³	#121×C₅₃	1	1	yes	characteristic
319	C₂³	#123×C₅₃	1	2	yes	—
320	C₂³	C₄⋊Q₈×C₅₃	1	1	yes	characteristic
321	C₂³	C₂×D₈×C₅₃	1	1	yes	characteristic
322	C₂³	C₂×Q₁₆×C₅₃	1	1	yes	characteristic
323	C₂³	#135×C₅₃	1	1	yes	characteristic
324	C₂³	#135×C₅₃	1	1	yes	characteristic
325	C₂³	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
326	C₂³	#137×C₅₃	1	2	yes	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
352	C₂×C₄	#117×C₅₃	1	2	yes	—
353	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
354	C₂×C₄	C₄×Q₈×C₅₃	1	1	yes	characteristic
355	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
356	C₂×C₄	C₂²⋊Q₈×C₅₃	1	2	yes	—
357	C₂×C₄	C₂²⋊Q₈×C₅₃	1	2	yes	—
358	C₂×C₄	C₂²⋊Q₈×C₅₃	1	1	yes	characteristic
359	C₂×C₄	#123×C₅₃	1	1	yes	characteristic
360	C₂×C₄	#123×C₅₃	1	2	yes	—
361	C₂×C₄	#124×C₅₃	1	1	yes	characteristic
362	C₂×C₄	#124×C₅₃	1	1	yes	characteristic
363	C₂×C₄	#124×C₅₃	1	2	yes	—
364	C₂×C₄	#125×C₅₃	1	2	yes	—
365	C₂×C₄	#125×C₅₃	1	2	yes	—
366	C₂×C₄	#125×C₅₃	1	1	yes	characteristic
367	C₂×C₄	#126×C₅₃	1	2	yes	—
368	C₂×C₄	#126×C₅₃	1	2	yes	—
369	C₈	—	2	4	no	—
370	C₈	—	4	2	no	—
371	C₂²	C₅₃×#388	1	2	yes	—
372	C₂²	C₅₃×#389	1	1	yes	characteristic
373	C₂²	C₅₃×#394	1	1	yes	characteristic
374	C₂²	C₅₃×#397	1	1	yes	characteristic
375	C₂²	C₅₃×#398	1	2	yes	—
376	C₂²	C₄×D₈×C₅₃	1	1	yes	characteristic
377	C₂²	C₄×Q₁₆×C₅₃	1	1	yes	characteristic
378	C₂²	C₅₃×#440	1	2	yes	—
379	C₂²	C₅₃×#459	1	2	yes	—
380	C₂²	C₅₃×#462	1	2	yes	—
381	C₂²	C₅₃×#463	1	2	yes	—
382	C₂²	C₅₃×#464	1	2	yes	—
383	C₂²	C₅₃×#466	1	1	yes	characteristic
384	C₂²	C₅₃×#467	1	1	yes	characteristic
385	C₂²	C₅₃×#469	1	1	yes	characteristic
386	C₂²	C₅₃×#470	1	1	yes	characteristic
387	C₂²	C₅₃×#480	1	2	yes	—
388	C₂²	C₅₃×#482	1	2	yes	—
389	C₂²	C₅₃×#484	1	2	yes	—
390	C₂²	C₅₃×#485	1	2	yes	—
391	C₂²	C₅₃×#499	1	1	yes	characteristic
392	C₂²	C₅₃×#500	1	1	yes	characteristic
393	C₂²	C₅₃×#501	1	2	yes	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	4	no	—
397	C₄	—	8	4	no	—
398	C₄	C₅₃×#382	1	1	yes	characteristic
399	C₄	C₅₃×#385	1	1	yes	characteristic
400	C₄	C₅₃×#387	1	2	yes	—
401	C₄	C₅₃×#393	1	1	yes	characteristic
402	C₄	C₅₃×#400	1	2	yes	—
403	C₄	C₅₃×#400	1	1	yes	characteristic
404	C₂	C₅₃×#1442	1	1	yes	characteristic
405	C₂	C₅₃×#1925	1	2	yes	—
406	C₂	C₅₃×#1928	1	2	yes	—
407	C₂	C₅₃×#1942	1	1	yes	characteristic
408	C₂	C₅₃×#1944	1	1	yes	characteristic
409	C₂	C₅₃×#2054	1	1	yes	characteristic
410	C₂	C₅₃×#2056	1	1	yes	characteristic
411	C₂	C₅₃×#2075	1	1	yes	characteristic
412	C₂	C₅₃×#2076	1	1	yes	characteristic
413	C₂	C₅₃×#2083	1	2	yes	—
414	C₂	C₅₃×#2085	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅₃	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₅₃
Frattini, cosocle	C₂³×C₄	C₂³×C₅₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₅₃×#340	C₄	semidirect
163. #11256	C₅₃	direct (N × H)
223. #340	C₄×C₅₃	semidirect
225. C₅₃	#11256	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#107×C₅₃	2
C₂×C₅₃×#340	2
C₂×C₅₃×#336	2
C₅₃×C₄⋊#95	2
#11256	53

Subgroups — C53×#11256 #27218768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#11256 #27218768