Subgroups — C₅₃×#21290 #27228802

Order 13568.

862 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#442	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2319	C₂	1	2	yes	maximal, complemented
3	C₅₃×#1972	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1970	C₂	1	1	yes	maximal, characteristic
5	C₅₃×#1944	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1936	C₂	1	2	yes	maximal, complemented
8	C₅₃×#1934	C₂	1	2	yes	maximal, complemented
9	C₅₃×#1776	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#102×C₅₃	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
14	C₅₃×#442	C₄	1	8	yes	complemented
15	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
16	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
18	C₂×#102×C₅₃	C₂²	1	2	yes	—
19	C₂×#102×C₅₃	C₂²	1	2	yes	—
20	C₂×#102×C₅₃	C₂²	1	2	yes	—
21	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#390	C₂²	1	2	yes	—
28	C₅₃×#390	C₂²	1	2	yes	—
29	C₅₃×#389	C₂²	1	2	yes	—
30	C₅₃×#389	C₂²	1	2	yes	—
31	C₅₃×#388	—	2	2	no	—
32	C₅₃×#388	—	2	2	no	—
33	C₅₃×#381	—	2	2	no	—
34	C₅₃×#380	—	2	2	no	—
35	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
36	C₅₃×#376	C₂²	1	1	yes	characteristic
37	C₅₃×#340	C₂²	1	2	yes	—
38	C₅₃×#340	C₂²	1	2	yes	—
39	C₅₃×#340	C₂²	1	2	yes	—
40	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₅₃	—	2	2	no	—
42	C₂×D₈×C₅₃	—	2	2	no	—
43	C₂×D₈×C₅₃	—	2	2	no	—
44	C₂×D₈×C₅₃	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
49	C₄×D₄×C₅₃	—	2	4	no	—
50	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	—
51	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
53	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
61	C₂×C₄²×C₅₃	—	2	2	no	—
62	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
65	#107×C₅₃	—	2	2	no	—
66	#106×C₅₃	—	2	2	no	—
67	#106×C₅₃	C₂×C₄	1	4	yes	—
68	#102×C₅₃	—	2	4	no	—
69	#102×C₅₃	—	2	4	no	—
70	#102×C₅₃	C₂×C₄	1	8	yes	—
71	#97×C₅₃	—	2	2	no	—
72	#97×C₅₃	—	2	2	no	—
73	#97×C₅₃	C₂×C₄	1	4	yes	—
74	C₄×C₈×C₅₃	—	2	2	no	—
75	C₄×C₈×C₅₃	—	2	2	no	—
76	C₄×C₈×C₅₃	—	2	2	no	—
77	#95×C₅₃	—	2	2	no	—
78	#95×C₅₃	—	2	2	no	—
79	#95×C₅₃	—	2	2	no	—
80	#95×C₅₃	D₄	1	2	yes	—
81	#95×C₅₃	D₄	1	2	yes	—
82	C₂⁴×C₅₃	—	2	2	no	—
83	C₂×D₄×C₅₃	—	2	2	no	—
84	C₂×D₄×C₅₃	—	2	2	no	—
85	C₂×D₄×C₅₃	—	2	2	no	—
86	C₂×D₄×C₅₃	—	2	2	no	—
87	C₂×D₄×C₅₃	—	2	2	no	—
88	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₅₃	—	2	2	no	—
90	C₂²×C₄×C₅₃	—	2	8	no	—
91	C₂²×C₄×C₅₃	—	2	2	no	—
92	C₂²×C₄×C₅₃	—	2	2	no	—
93	C₂²×C₄×C₅₃	—	8	2	no	—
94	C₂²×C₄×C₅₃	—	8	2	no	—
95	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
100	D₈×C₅₃	—	2	8	no	—
101	C₂×C₈×C₅₃	—	2	1	no	—
102	C₂×C₈×C₅₃	—	2	1	no	—
103	C₂×C₈×C₅₃	—	2	1	no	—
104	C₂×C₈×C₅₃	—	2	1	no	—
105	C₂×C₈×C₅₃	—	2	1	no	—
106	C₂×C₈×C₅₃	—	2	1	no	—
107	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₅₃	#41	1	2	yes	—
110	C₂×C₈×C₅₃	#41	1	2	yes	—
111	C₂×C₈×C₅₃	#41	1	2	yes	—
112	C₂×C₈×C₅₃	#41	1	2	yes	—
113	C₄⋊C₄×C₅₃	—	2	2	no	—
114	C₄⋊C₄×C₅₃	—	2	2	no	—
115	C₄⋊C₄×C₅₃	—	2	2	no	—
116	C₄⋊C₄×C₅₃	—	2	2	no	—
117	C₄⋊C₄×C₅₃	—	2	2	no	—
118	C₄⋊C₄×C₅₃	—	8	2	no	—
119	C₄⋊C₄×C₅₃	—	8	2	no	—
120	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₅₃	—	2	8	no	—
122	C₂²⋊C₄×C₅₃	—	8	2	no	—
123	C₂²⋊C₄×C₅₃	—	8	2	no	—
124	C₂²⋊C₄×C₅₃	—	8	2	no	—
125	C₂²⋊C₄×C₅₃	—	8	2	no	—
126	C₄²×C₅₃	—	2	1	no	—
127	C₄²×C₅₃	—	2	1	no	—
128	C₄²×C₅₃	—	2	1	no	—
129	C₄²×C₅₃	—	2	1	no	—
130	C₄²×C₅₃	—	8	2	no	—
131	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
132	C₄²×C₅₃	#41	1	2	yes	—
133	C₂³×C₅₃	—	2	4	no	—
134	C₂³×C₅₃	—	4	2	no	—
135	C₂³×C₅₃	—	4	2	no	—
136	C₂³×C₅₃	—	4	2	no	—
137	C₂³×C₅₃	—	4	2	no	—
138	C₂³×C₅₃	—	4	2	no	—
139	C₂³×C₅₃	—	4	2	no	—
140	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
141	D₄×C₅₃	—	2	4	no	—
142	D₄×C₅₃	—	2	4	no	—
143	D₄×C₅₃	—	4	2	no	—
144	D₄×C₅₃	—	4	2	no	—
145	C₂×C₄×C₅₃	—	2	2	no	—
146	C₂×C₄×C₅₃	—	2	2	no	—
147	C₂×C₄×C₅₃	—	2	4	no	—
148	C₂×C₄×C₅₃	—	2	1	no	—
149	C₂×C₄×C₅₃	—	2	1	no	—
150	C₂×C₄×C₅₃	—	2	2	no	—
151	C₂×C₄×C₅₃	—	2	2	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	2	2	no	—
154	C₂×C₄×C₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	—	4	2	no	—
156	C₂×C₄×C₅₃	—	4	2	no	—
157	C₂×C₄×C₅₃	—	4	2	no	—
158	C₂×C₄×C₅₃	—	4	2	no	—
159	C₂×C₄×C₅₃	—	4	2	no	—
160	C₂×C₄×C₅₃	—	4	2	no	—
161	C₂×C₄×C₅₃	—	4	2	no	—
162	C₂×C₄×C₅₃	—	4	2	no	—
163	C₂×C₄×C₅₃	—	8	8	no	—
164	C₂×C₄×C₅₃	C₄×D₄	1	4	yes	—
165	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
171	C₈×C₅₃	—	2	2	no	—
172	C₈×C₅₃	—	2	2	no	—
173	C₈×C₅₃	—	2	2	no	—
174	C₈×C₅₃	#117	1	4	yes	—
175	#21290	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₅₃	—	4	4	no	—
177	C₂²×C₅₃	—	4	4	no	—
178	C₂²×C₅₃	—	4	4	no	—
179	C₂²×C₅₃	—	8	2	no	—
180	C₂²×C₅₃	—	8	2	no	—
181	C₂²×C₅₃	—	8	2	no	—
182	C₂²×C₅₃	—	8	2	no	—
183	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂²×C₅₃	#532	1	1	yes	characteristic
185	C₂²×C₅₃	#532	1	1	yes	characteristic
186	C₂²×C₅₃	#576	1	2	yes	—
187	C₂²×C₅₃	#577	1	2	yes	—
188	C₄×C₅₃	—	2	4	no	—
189	C₄×C₅₃	—	4	1	no	—
190	C₄×C₅₃	—	4	1	no	—
191	C₄×C₅₃	—	4	2	no	—
192	C₄×C₅₃	—	4	4	no	—
193	C₄×C₅₃	—	8	2	no	—
194	C₄×C₅₃	—	8	2	no	—
195	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
196	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
197	C₄×C₅₃	#529	1	1	yes	characteristic
198	C₄×C₅₃	#529	1	1	yes	characteristic
199	C₂×#442	C₂×C₅₃	1	1	yes	characteristic
200	#2319	C₂×C₅₃	1	2	yes	complemented
201	#1972	C₂×C₅₃	1	1	yes	characteristic
202	#1970	C₂×C₅₃	1	1	yes	characteristic
203	#1944	C₂×C₅₃	1	1	yes	characteristic, complemented
204	#1941	C₂×C₅₃	1	1	yes	characteristic, complemented
205	#1936	C₂×C₅₃	1	2	yes	complemented
206	#1934	C₂×C₅₃	1	2	yes	complemented
207	#1776	C₂×C₅₃	1	1	yes	characteristic, complemented
208	C₄×#102	C₂×C₅₃	1	2	yes	complemented
209	#1726	C₂×C₅₃	1	1	yes	characteristic, complemented
210	C₂×C₅₃	—	8	4	no	—
211	C₂×C₅₃	#2293	1	1	yes	characteristic
212	C₂×C₅₃	#2946	1	2	yes	—
213	C₂×C₅₃	#3173	1	1	yes	characteristic
214	C₂×C₅₃	#3176	1	1	yes	characteristic
215	C₂×C₅₃	#3179	1	2	yes	—
216	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
218	#442	C₄×C₅₃	1	8	yes	complemented
219	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
220	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
221	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
222	C₂×#102	C₂²×C₅₃	1	2	yes	—
223	C₂×#102	C₂²×C₅₃	1	2	yes	—
224	C₂×#102	C₂²×C₅₃	1	2	yes	—
225	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
226	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
227	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
231	#390	C₂²×C₅₃	1	2	yes	—
232	#390	C₂²×C₅₃	1	2	yes	—
233	#389	C₂²×C₅₃	1	2	yes	—
234	#389	C₂²×C₅₃	1	2	yes	—
235	#388	—	2	2	no	—
236	#388	—	2	2	no	—
237	#381	—	2	2	no	—
238	#380	—	2	2	no	—
239	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
240	#376	C₂²×C₅₃	1	1	yes	characteristic
241	#340	C₂²×C₅₃	1	2	yes	—
242	#340	C₂²×C₅₃	1	2	yes	—
243	#340	C₂²×C₅₃	1	2	yes	—
244	C₅₃	#21290	1	1	yes	characteristic, direct product factor, Sylow
245	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
246	C₂³×C₄	—	2	2	no	—
247	C₂×D₈	—	2	2	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×D₈	C₂×C₄×C₅₃	1	4	yes	—
250	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
254	C₄×D₄	—	2	4	no	—
255	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
270	#107	—	2	2	no	—
271	#106	—	2	2	no	—
272	#106	C₂×C₄×C₅₃	1	4	yes	—
273	#102	—	2	4	no	—
274	#102	—	2	4	no	—
275	#102	C₂×C₄×C₅₃	1	8	yes	—
276	#97	—	2	2	no	—
277	#97	—	2	2	no	—
278	#97	C₂×C₄×C₅₃	1	4	yes	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	D₄×C₅₃	1	2	yes	—
286	#95	D₄×C₅₃	1	2	yes	—
287	C₂⁴	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	8	2	no	—
299	C₂²×C₄	—	8	2	no	—
300	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
305	D₈	—	2	8	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
313	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
314	C₂×C₈	#41×C₅₃	1	2	yes	—
315	C₂×C₈	#41×C₅₃	1	2	yes	—
316	C₂×C₈	#41×C₅₃	1	2	yes	—
317	C₂×C₈	#41×C₅₃	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	8	2	no	—
324	C₄⋊C₄	—	8	2	no	—
325	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₂²⋊C₄	—	8	2	no	—
329	C₂²⋊C₄	—	8	2	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	8	2	no	—
336	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
337	C₄²	#41×C₅₃	1	2	yes	—
338	C₂³	—	2	4	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
346	D₄	—	2	4	no	—
347	D₄	—	2	4	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	8	no	—
369	C₂×C₄	C₄×D₄×C₅₃	1	4	yes	—
370	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	#117×C₅₃	1	4	yes	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
388	C₂²	C₅₃×#532	1	1	yes	characteristic
389	C₂²	C₅₃×#532	1	1	yes	characteristic
390	C₂²	C₅₃×#576	1	2	yes	—
391	C₂²	C₅₃×#577	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	C₂×#117×C₅₃	1	1	yes	characteristic
400	C₄	C₄×#41×C₅₃	1	1	yes	characteristic
401	C₄	C₅₃×#529	1	1	yes	characteristic
402	C₄	C₅₃×#529	1	1	yes	characteristic
403	C₂	—	8	4	no	—
404	C₂	C₅₃×#2293	1	1	yes	characteristic
405	C₂	C₅₃×#2946	1	2	yes	—
406	C₂	C₅₃×#3173	1	1	yes	characteristic
407	C₂	C₅₃×#3176	1	1	yes	characteristic
408	C₂	C₅₃×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂²×D₈×C₅₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₅₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2319	C₂	semidirect
5. C₅₃×#1944	C₂	semidirect
6. C₅₃×#1941	C₂	semidirect
7. C₅₃×#1936	C₂	semidirect
8. C₅₃×#1934	C₂	semidirect
9. C₅₃×#1776	C₂	semidirect
10. C₄×#102×C₅₃	C₂	semidirect
11. C₅₃×#1726	C₂	semidirect
14. C₅₃×#442	C₄	semidirect
175. #21290	C₅₃	direct (N × H)
200. #2319	C₂×C₅₃	semidirect
203. #1944	C₂×C₅₃	semidirect
204. #1941	C₂×C₅₃	semidirect
205. #1936	C₂×C₅₃	semidirect
206. #1934	C₂×C₅₃	semidirect
207. #1776	C₂×C₅₃	semidirect
208. C₄×#102	C₂×C₅₃	semidirect
209. #1726	C₂×C₅₃	semidirect
218. #442	C₄×C₅₃	semidirect
244. C₅₃	#21290	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×#442	2
C₅₃×#2319	2
C₅₃×#1972	2
C₅₃×#1970	2
C₅₃×#1944	2
C₅₃×#1941	2
C₅₃×#1936	2
C₅₃×#1934	2
C₅₃×#1776	2
C₄×#102×C₅₃	2
C₅₃×#1726	2
#21290	53

Subgroups — C53×#21290 #27228802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#21290 #27228802