Subgroups — C₅₃×#11268 #27218780

Order 13568.

798 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#382	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#340	C₂	1	2	yes	maximal
3	C₂×C₅₃×#340	C₂	1	2	yes	maximal
4	C₂×C₅₃×#336	C₂	1	1	yes	maximal, characteristic
5	C₅₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₅₃	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
11	C₅₃×#382	—	2	4	no	—
12	C₂×#95×C₅₃	—	2	2	no	—
13	C₂×#95×C₅₃	—	2	2	no	—
14	C₅₃×#340	—	2	4	no	—
15	C₅₃×#340	—	2	4	no	—
16	C₅₃×#336	C₄	1	4	yes	complemented
17	C₂³×C₄×C₅₃	—	2	2	no	—
18	C₂³×C₄×C₅₃	—	2	1	no	—
19	C₂³×C₄×C₅₃	—	2	1	no	—
20	C₂³×C₄×C₅₃	D₄	1	2	yes	—
21	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
22	C₂²×C₈×C₅₃	—	2	2	no	—
23	C₂²×C₈×C₅₃	—	2	2	no	—
24	C₂²×C₈×C₅₃	—	2	2	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	C₂×C₄	1	4	yes	—
29	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
30	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
31	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
32	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
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	D₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₅₃	D₄	1	4	yes	—
42	C₂×C₄⋊C₄×C₅₃	Q₈	1	2	yes	—
43	C₂×C₄²×C₅₃	—	2	2	no	—
44	C₂×C₄²×C₅₃	—	2	2	no	—
45	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₅₃	Q₈	1	2	yes	—
47	#95×C₅₃	—	2	8	no	—
48	#95×C₅₃	—	4	4	no	—
49	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₅₃	—	2	2	no	—
51	C₂²×C₄×C₅₃	—	2	2	no	—
52	C₂²×C₄×C₅₃	—	2	2	no	—
53	C₂²×C₄×C₅₃	—	2	2	no	—
54	C₂²×C₄×C₅₃	—	2	2	no	—
55	C₂²×C₄×C₅₃	—	2	2	no	—
56	C₂²×C₄×C₅₃	—	2	4	no	—
57	C₂²×C₄×C₅₃	—	2	2	no	—
58	C₂²×C₄×C₅₃	—	2	2	no	—
59	C₂²×C₄×C₅₃	—	4	1	no	—
60	C₂²×C₄×C₅₃	—	4	2	no	—
61	C₂²×C₄×C₅₃	—	4	1	no	—
62	C₂²×C₄×C₅₃	—	4	1	no	—
63	C₂²×C₄×C₅₃	—	4	2	no	—
64	C₂²×C₄×C₅₃	—	4	1	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	C₄⋊C₄	1	4	yes	—
74	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	#41	1	2	yes	—
80	C₂²×C₄×C₅₃	#41	1	2	yes	—
81	C₂²×C₄×C₅₃	#41	1	2	yes	—
82	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
84	C₂×C₈×C₅₃	—	2	4	no	—
85	C₂×C₈×C₅₃	—	2	4	no	—
86	C₂×C₈×C₅₃	—	2	4	no	—
87	C₂×C₈×C₅₃	—	4	2	no	—
88	C₂×C₈×C₅₃	—	4	2	no	—
89	C₂×C₈×C₅₃	—	4	2	no	—
90	C₂×C₈×C₅₃	—	4	2	no	—
91	C₄⋊C₄×C₅₃	—	2	4	no	—
92	C₄⋊C₄×C₅₃	—	2	4	no	—
93	C₄⋊C₄×C₅₃	—	2	4	no	—
94	C₄⋊C₄×C₅₃	—	2	4	no	—
95	C₄⋊C₄×C₅₃	—	4	2	no	—
96	C₄⋊C₄×C₅₃	—	4	2	no	—
97	C₄⋊C₄×C₅₃	—	4	2	no	—
98	C₄⋊C₄×C₅₃	—	4	2	no	—
99	C₄²×C₅₃	—	2	4	no	—
100	C₄²×C₅₃	—	2	4	no	—
101	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂³×C₅₃	#120	1	1	yes	characteristic
103	C₂³×C₅₃	#121	1	1	yes	characteristic
104	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
105	C₂³×C₅₃	#123	1	1	yes	characteristic
106	C₂³×C₅₃	#124	1	1	yes	characteristic
107	C₂³×C₅₃	#124	1	1	yes	characteristic
108	C₂³×C₅₃	#135	1	2	yes	—
109	C₂³×C₅₃	#135	1	2	yes	—
110	C₂³×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
111	C₂³×C₅₃	#137	1	2	yes	—
112	C₂×C₄×C₅₃	—	2	4	no	—
113	C₂×C₄×C₅₃	—	2	4	no	—
114	C₂×C₄×C₅₃	—	2	4	no	—
115	C₂×C₄×C₅₃	—	4	2	no	—
116	C₂×C₄×C₅₃	—	4	2	no	—
117	C₂×C₄×C₅₃	—	4	2	no	—
118	C₂×C₄×C₅₃	—	4	2	no	—
119	C₂×C₄×C₅₃	—	4	2	no	—
120	C₂×C₄×C₅₃	—	4	4	no	—
121	C₂×C₄×C₅₃	—	4	2	no	—
122	C₂×C₄×C₅₃	—	4	4	no	—
123	C₂×C₄×C₅₃	—	4	4	no	—
124	C₂×C₄×C₅₃	—	4	4	no	—
125	C₂×C₄×C₅₃	—	4	4	no	—
126	C₂×C₄×C₅₃	—	8	2	no	—
127	C₂×C₄×C₅₃	—	8	2	no	—
128	C₂×C₄×C₅₃	—	8	2	no	—
129	C₂×C₄×C₅₃	—	8	2	no	—
130	C₂×C₄×C₅₃	—	8	1	no	—
131	C₂×C₄×C₅₃	—	8	1	no	—
132	C₂×C₄×C₅₃	—	8	2	no	—
133	C₂×C₄×C₅₃	—	8	2	no	—
134	C₂×C₄×C₅₃	—	8	1	no	—
135	C₂×C₄×C₅₃	—	8	1	no	—
136	C₂×C₄×C₅₃	#117	1	2	yes	—
137	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
138	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
140	C₂×C₄×C₅₃	#121	1	2	yes	—
141	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
142	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₅₃	#123	1	2	yes	—
144	C₂×C₄×C₅₃	#123	1	2	yes	—
145	C₂×C₄×C₅₃	#124	1	2	yes	—
146	C₂×C₄×C₅₃	#125	1	2	yes	—
147	C₂×C₄×C₅₃	#125	1	2	yes	—
148	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
149	C₂×C₄×C₅₃	#126	1	2	yes	—
150	C₂×C₄×C₅₃	#126	1	2	yes	—
151	C₂×C₄×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
152	C₈×C₅₃	—	4	4	no	—
153	#11268	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂²×C₅₃	#382	1	1	yes	characteristic
155	C₂²×C₅₃	#385	1	1	yes	characteristic
156	C₂²×C₅₃	#389	1	1	yes	characteristic
157	C₂²×C₅₃	#393	1	1	yes	characteristic
158	C₂²×C₅₃	#394	1	1	yes	characteristic
159	C₂²×C₅₃	#397	1	1	yes	characteristic
160	C₂²×C₅₃	#400	1	1	yes	characteristic
161	C₂²×C₅₃	#427	1	2	yes	—
162	C₂²×C₅₃	#428	1	2	yes	—
163	C₂²×C₅₃	#449	1	2	yes	—
164	C₂²×C₅₃	#452	1	2	yes	—
165	C₂²×C₅₃	#463	1	2	yes	—
166	C₂²×C₅₃	#464	1	2	yes	—
167	C₂²×C₅₃	#478	1	2	yes	—
168	C₂²×C₅₃	#479	1	2	yes	—
169	C₂²×C₅₃	#482	1	2	yes	—
170	C₂²×C₅₃	#485	1	2	yes	—
171	C₂²×C₅₃	#488	1	1	yes	characteristic
172	C₂²×C₅₃	#488	1	1	yes	characteristic
173	C₂²×C₅₃	#488	1	2	yes	—
174	C₂²×C₅₃	#489	1	2	yes	—
175	C₂²×C₅₃	#490	1	1	yes	characteristic
176	C₂²×C₅₃	#491	1	1	yes	characteristic
177	C₄×C₅₃	—	4	4	no	—
178	C₄×C₅₃	—	8	2	no	—
179	C₄×C₅₃	—	8	2	no	—
180	C₄×C₅₃	—	8	4	no	—
181	C₄×C₅₃	#387	1	2	yes	—
182	C₄×C₅₃	#388	1	2	yes	—
183	C₄×C₅₃	#398	1	2	yes	—
184	C₄×C₅₃	#400	1	2	yes	—
185	C₂×#382	C₂×C₅₃	1	1	yes	characteristic
186	C₂×#340	C₂×C₅₃	1	2	yes	—
187	C₂×#340	C₂×C₅₃	1	2	yes	—
188	C₂×#336	C₂×C₅₃	1	1	yes	characteristic
189	C₄⋊#95	C₂×C₅₃	1	1	yes	characteristic
190	C₂×C₅₃	#1442	1	1	yes	characteristic
191	C₂×C₅₃	#1835	1	1	yes	characteristic
192	C₂×C₅₃	#1836	1	1	yes	characteristic
193	C₂×C₅₃	#1854	1	2	yes	—
194	C₂×C₅₃	#1949	1	2	yes	—
195	C₂×C₅₃	#2025	1	1	yes	characteristic
196	C₂×C₅₃	#2026	1	1	yes	characteristic
197	C₂×C₅₃	#2042	1	2	yes	—
198	C₂×C₅₃	#2073	1	1	yes	characteristic
199	C₂×C₅₃	#2074	1	1	yes	characteristic
200	C₂×C₅₃	#2101	1	2	yes	—
201	C₂³×C₈	C₂²×C₅₃	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
205	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
206	#382	—	2	4	no	—
207	C₂×#95	—	2	2	no	—
208	C₂×#95	—	2	2	no	—
209	#340	—	2	4	no	—
210	#340	—	2	4	no	—
211	#336	C₄×C₅₃	1	4	yes	complemented
212	C₅₃	#11268	1	1	yes	characteristic, direct product factor, Sylow
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	—	2	1	no	—
215	C₂³×C₄	—	2	1	no	—
216	C₂³×C₄	D₄×C₅₃	1	2	yes	—
217	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	C₂×C₄×C₅₃	1	4	yes	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
237	C₂×C₄⋊C₄	D₄×C₅₃	1	4	yes	—
238	C₂×C₄⋊C₄	Q₈×C₅₃	1	2	yes	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	C₂×C₄×C₅₃	1	2	yes	—
242	C₂×C₄²	Q₈×C₅₃	1	2	yes	—
243	#95	—	2	8	no	—
244	#95	—	4	4	no	—
245	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	—	4	1	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	C₄⋊C₄×C₅₃	1	4	yes	—
270	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
273	C₂²×C₄	C₂×Q₈×C₅₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×Q₈×C₅₃	1	1	yes	characteristic
275	C₂²×C₄	#41×C₅₃	1	2	yes	—
276	C₂²×C₄	#41×C₅₃	1	2	yes	—
277	C₂²×C₄	#41×C₅₃	1	2	yes	—
278	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
279	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	4	2	no	—
284	C₂×C₈	—	4	2	no	—
285	C₂×C₈	—	4	2	no	—
286	C₂×C₈	—	4	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄²	—	2	4	no	—
296	C₄²	—	2	4	no	—
297	C₂³	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
298	C₂³	#120×C₅₃	1	1	yes	characteristic
299	C₂³	#121×C₅₃	1	1	yes	characteristic
300	C₂³	C₂²⋊Q₈×C₅₃	1	1	yes	characteristic
301	C₂³	#123×C₅₃	1	1	yes	characteristic
302	C₂³	#124×C₅₃	1	1	yes	characteristic
303	C₂³	#124×C₅₃	1	1	yes	characteristic
304	C₂³	#135×C₅₃	1	2	yes	—
305	C₂³	#135×C₅₃	1	2	yes	—
306	C₂³	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
307	C₂³	#137×C₅₃	1	2	yes	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	8	1	no	—
323	C₂×C₄	—	8	2	no	—
324	C₂×C₄	—	8	1	no	—
325	C₂×C₄	—	8	2	no	—
326	C₂×C₄	—	8	1	no	—
327	C₂×C₄	—	8	1	no	—
328	C₂×C₄	—	8	2	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	—	8	2	no	—
332	C₂×C₄	#117×C₅₃	1	2	yes	—
333	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
334	C₂×C₄	C₄×D₄×C₅₃	1	1	yes	characteristic
335	C₂×C₄	C₄×Q₈×C₅₃	1	1	yes	characteristic
336	C₂×C₄	#121×C₅₃	1	2	yes	—
337	C₂×C₄	C₂²⋊Q₈×C₅₃	1	2	yes	—
338	C₂×C₄	C₂²⋊Q₈×C₅₃	1	2	yes	—
339	C₂×C₄	#123×C₅₃	1	2	yes	—
340	C₂×C₄	#123×C₅₃	1	2	yes	—
341	C₂×C₄	#124×C₅₃	1	2	yes	—
342	C₂×C₄	#125×C₅₃	1	2	yes	—
343	C₂×C₄	#125×C₅₃	1	2	yes	—
344	C₂×C₄	#125×C₅₃	1	1	yes	characteristic
345	C₂×C₄	#126×C₅₃	1	2	yes	—
346	C₂×C₄	#126×C₅₃	1	2	yes	—
347	C₂×C₄	C₄⋊Q₈×C₅₃	1	1	yes	characteristic
348	C₈	—	4	4	no	—
349	C₂²	C₅₃×#382	1	1	yes	characteristic
350	C₂²	C₅₃×#385	1	1	yes	characteristic
351	C₂²	C₅₃×#389	1	1	yes	characteristic
352	C₂²	C₅₃×#393	1	1	yes	characteristic
353	C₂²	C₅₃×#394	1	1	yes	characteristic
354	C₂²	C₅₃×#397	1	1	yes	characteristic
355	C₂²	C₅₃×#400	1	1	yes	characteristic
356	C₂²	C₅₃×#427	1	2	yes	—
357	C₂²	C₅₃×#428	1	2	yes	—
358	C₂²	C₅₃×#449	1	2	yes	—
359	C₂²	C₅₃×#452	1	2	yes	—
360	C₂²	C₅₃×#463	1	2	yes	—
361	C₂²	C₅₃×#464	1	2	yes	—
362	C₂²	C₅₃×#478	1	2	yes	—
363	C₂²	C₅₃×#479	1	2	yes	—
364	C₂²	C₅₃×#482	1	2	yes	—
365	C₂²	C₅₃×#485	1	2	yes	—
366	C₂²	C₅₃×#488	1	1	yes	characteristic
367	C₂²	C₅₃×#488	1	1	yes	characteristic
368	C₂²	C₅₃×#488	1	2	yes	—
369	C₂²	C₅₃×#489	1	2	yes	—
370	C₂²	C₅₃×#490	1	1	yes	characteristic
371	C₂²	C₅₃×#491	1	1	yes	characteristic
372	C₄	—	4	4	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	4	no	—
375	C₄	—	8	2	no	—
376	C₄	C₅₃×#387	1	2	yes	—
377	C₄	C₅₃×#388	1	2	yes	—
378	C₄	C₅₃×#398	1	2	yes	—
379	C₄	C₅₃×#400	1	2	yes	—
380	C₂	C₅₃×#1442	1	1	yes	characteristic
381	C₂	C₅₃×#1835	1	1	yes	characteristic
382	C₂	C₅₃×#1836	1	1	yes	characteristic
383	C₂	C₅₃×#1854	1	2	yes	—
384	C₂	C₅₃×#1949	1	2	yes	—
385	C₂	C₅₃×#2025	1	1	yes	characteristic
386	C₂	C₅₃×#2026	1	1	yes	characteristic
387	C₂	C₅₃×#2042	1	2	yes	—
388	C₂	C₅₃×#2073	1	1	yes	characteristic
389	C₂	C₅₃×#2074	1	1	yes	characteristic
390	C₂	C₅₃×#2101	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×#336	C₄	semidirect
153. #11268	C₅₃	direct (N × H)
211. #336	C₄×C₅₃	semidirect
212. C₅₃	#11268	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#382	2
C₂×C₅₃×#340	2
C₂×C₅₃×#336	2
C₅₃×C₄⋊#95	2
#11268	53

Subgroups — C53×#11268 #27218780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#11268 #27218780