Subgroups — C₅₃×#2419 #20271356

Order 6784.

560 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#123×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#386	C₂	1	1	yes	maximal, characteristic
10	C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#95×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
21	#123×C₅₃	—	2	4	no	—
22	C₄×D₄×C₅₃	—	2	4	no	—
23	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
39	#95×C₅₃	C₂²	1	1	yes	characteristic
40	#95×C₅₃	C₂²	1	1	yes	characteristic
41	#95×C₅₃	C₂²	1	1	yes	characteristic
42	#95×C₅₃	C₂²	1	1	yes	characteristic
43	#95×C₅₃	C₂²	1	1	yes	characteristic
44	#95×C₅₃	C₂²	1	1	yes	characteristic
45	#95×C₅₃	C₂²	1	1	yes	characteristic
46	#95×C₅₃	C₂²	1	1	yes	characteristic
47	#95×C₅₃	C₂²	1	1	yes	characteristic
48	#95×C₅₃	C₂²	1	1	yes	characteristic
49	#95×C₅₃	C₂²	1	1	yes	characteristic
50	#95×C₅₃	C₂²	1	1	yes	characteristic
51	#95×C₅₃	C₂²	1	1	yes	characteristic
52	#95×C₅₃	C₂²	1	1	yes	characteristic
53	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
54	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
55	C₂×D₄×C₅₃	—	2	2	no	—
56	C₂×D₄×C₅₃	—	2	2	no	—
57	C₂×D₄×C₅₃	D₄	1	4	yes	—
58	C₂²×C₄×C₅₃	—	2	2	no	—
59	C₂²×C₄×C₅₃	—	2	2	no	—
60	C₂²×C₄×C₅₃	—	2	2	no	—
61	C₂²×C₄×C₅₃	—	2	2	no	—
62	C₂²×C₄×C₅₃	—	2	2	no	—
63	C₂²×C₄×C₅₃	—	2	2	no	—
64	C₂²×C₄×C₅₃	—	2	2	no	—
65	C₂²×C₄×C₅₃	—	2	2	no	—
66	C₂²×C₄×C₅₃	—	2	2	no	—
67	C₂²×C₄×C₅₃	—	4	1	no	—
68	C₂²×C₄×C₅₃	—	4	1	no	—
69	C₂²×C₄×C₅₃	—	4	1	no	—
70	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₄×C₅₃	—	2	2	no	—
84	C₄⋊C₄×C₅₃	—	2	2	no	—
85	C₄⋊C₄×C₅₃	—	2	2	no	—
86	C₄⋊C₄×C₅₃	—	2	2	no	—
87	C₄⋊C₄×C₅₃	—	2	2	no	—
88	C₄⋊C₄×C₅₃	—	4	1	no	—
89	C₄⋊C₄×C₅₃	—	4	1	no	—
90	C₂²⋊C₄×C₅₃	—	2	2	no	—
91	C₂²⋊C₄×C₅₃	—	2	2	no	—
92	C₂²⋊C₄×C₅₃	—	2	2	no	—
93	C₂²⋊C₄×C₅₃	—	2	2	no	—
94	C₂²⋊C₄×C₅₃	—	2	2	no	—
95	C₂²⋊C₄×C₅₃	—	2	2	no	—
96	C₂²⋊C₄×C₅₃	—	2	2	no	—
97	C₂²⋊C₄×C₅₃	—	4	1	no	—
98	C₄²×C₅₃	—	2	2	no	—
99	C₂³×C₅₃	—	2	1	no	—
100	C₂³×C₅₃	—	2	1	no	—
101	C₂³×C₅₃	—	2	1	no	—
102	C₂³×C₅₃	—	2	1	no	—
103	C₂³×C₅₃	—	2	1	no	—
104	C₂³×C₅₃	—	2	1	no	—
105	C₂³×C₅₃	—	2	1	no	—
106	C₂³×C₅₃	—	2	1	no	—
107	C₂³×C₅₃	—	2	1	no	—
108	C₂³×C₅₃	—	2	1	no	—
109	C₂³×C₅₃	C₂×D₄	1	2	yes	—
110	C₂³×C₅₃	C₂×D₄	1	2	yes	—
111	C₂³×C₅₃	#41	1	2	yes	—
112	C₂³×C₅₃	#41	1	2	yes	—
113	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
114	D₄×C₅₃	—	2	8	no	—
115	C₂×C₄×C₅₃	—	2	1	no	—
116	C₂×C₄×C₅₃	—	2	1	no	—
117	C₂×C₄×C₅₃	—	2	1	no	—
118	C₂×C₄×C₅₃	—	2	1	no	—
119	C₂×C₄×C₅₃	—	2	1	no	—
120	C₂×C₄×C₅₃	—	2	1	no	—
121	C₂×C₄×C₅₃	—	2	1	no	—
122	C₂×C₄×C₅₃	—	2	1	no	—
123	C₂×C₄×C₅₃	—	2	1	no	—
124	C₂×C₄×C₅₃	—	2	1	no	—
125	C₂×C₄×C₅₃	—	2	1	no	—
126	C₂×C₄×C₅₃	—	2	1	no	—
127	C₂×C₄×C₅₃	—	2	1	no	—
128	C₂×C₄×C₅₃	—	2	1	no	—
129	C₂×C₄×C₅₃	—	2	1	no	—
130	C₂×C₄×C₅₃	—	2	1	no	—
131	C₂×C₄×C₅₃	—	2	1	no	—
132	C₂×C₄×C₅₃	—	2	1	no	—
133	C₂×C₄×C₅₃	—	2	1	no	—
134	C₂×C₄×C₅₃	—	2	1	no	—
135	C₂×C₄×C₅₃	—	2	1	no	—
136	C₂×C₄×C₅₃	—	2	1	no	—
137	C₂×C₄×C₅₃	—	2	1	no	—
138	C₂×C₄×C₅₃	—	2	1	no	—
139	C₂×C₄×C₅₃	—	2	1	no	—
140	C₂×C₄×C₅₃	—	2	1	no	—
141	C₂×C₄×C₅₃	—	2	1	no	—
142	C₂×C₄×C₅₃	—	2	1	no	—
143	C₂×C₄×C₅₃	—	2	1	no	—
144	C₂×C₄×C₅₃	—	2	1	no	—
145	C₂×C₄×C₅₃	—	2	1	no	—
146	C₂×C₄×C₅₃	—	2	1	no	—
147	C₂×C₄×C₅₃	—	2	1	no	—
148	C₂×C₄×C₅₃	—	2	1	no	—
149	C₂×C₄×C₅₃	—	2	1	no	—
150	C₂×C₄×C₅₃	—	2	1	no	—
151	C₂×C₄×C₅₃	—	4	4	no	—
152	C₂×C₄×C₅₃	—	4	4	no	—
153	C₂×C₄×C₅₃	—	4	4	no	—
154	C₂×C₄×C₅₃	—	4	4	no	—
155	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
156	C₂×C₄×C₅₃	#41	1	2	yes	—
157	C₂×C₄×C₅₃	#41	1	2	yes	—
158	C₂²×C₅₃	—	2	2	no	—
159	C₂²×C₅₃	—	2	2	no	—
160	C₂²×C₅₃	—	2	2	no	—
161	C₂²×C₅₃	—	2	2	no	—
162	C₂²×C₅₃	—	2	2	no	—
163	C₂²×C₅₃	—	2	2	no	—
164	C₂²×C₅₃	—	2	2	no	—
165	C₂²×C₅₃	—	2	2	no	—
166	C₂²×C₅₃	—	2	2	no	—
167	C₂²×C₅₃	—	4	1	no	—
168	C₂²×C₅₃	—	4	1	no	—
169	C₂²×C₅₃	—	4	1	no	—
170	C₂²×C₅₃	—	4	1	no	—
171	C₂²×C₅₃	#123	1	4	yes	—
172	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
173	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
174	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
175	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
176	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
177	C₂²×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂²×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
179	C₄×C₅₃	—	2	2	no	—
180	C₄×C₅₃	—	2	2	no	—
181	C₄×C₅₃	—	2	2	no	—
182	C₄×C₅₃	—	4	1	no	—
183	C₄×C₅₃	—	4	1	no	—
184	C₄×C₅₃	—	4	1	no	—
185	C₄×C₅₃	—	4	1	no	—
186	C₄×C₅₃	—	4	1	no	—
187	C₄×C₅₃	—	4	1	no	—
188	C₄×C₅₃	—	4	1	no	—
189	C₄×C₅₃	—	4	1	no	—
190	C₄×C₅₃	—	4	1	no	—
191	C₄×C₅₃	—	4	1	no	—
192	#2419	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂×C₅₃	—	2	4	no	—
194	C₂×C₅₃	—	4	2	no	—
195	C₂×C₅₃	C₂×#123	1	1	yes	characteristic
196	C₂×C₅₃	#529	1	1	yes	characteristic
197	C₂×C₅₃	#539	1	1	yes	characteristic
198	C₂×C₅₃	#546	1	1	yes	characteristic
199	C₂×C₅₃	#547	1	1	yes	characteristic
200	C₂×C₅₃	#551	1	1	yes	characteristic
201	C₂×C₅₃	#552	1	1	yes	characteristic
202	C₂×#123	C₂×C₅₃	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic
204	#400	C₂×C₅₃	1	1	yes	characteristic, complemented
205	#398	C₂×C₅₃	1	1	yes	characteristic, complemented
206	#397	C₂×C₅₃	1	1	yes	characteristic, complemented
207	#397	C₂×C₅₃	1	1	yes	characteristic, complemented
208	#387	C₂×C₅₃	1	1	yes	characteristic, complemented
209	#387	C₂×C₅₃	1	1	yes	characteristic, complemented
210	#386	C₂×C₅₃	1	1	yes	characteristic
211	#385	C₂×C₅₃	1	1	yes	characteristic, complemented
212	#385	C₂×C₅₃	1	1	yes	characteristic, complemented
213	#381	C₂×C₅₃	1	1	yes	characteristic, complemented
214	#381	C₂×C₅₃	1	1	yes	characteristic, complemented
215	#380	C₂×C₅₃	1	1	yes	characteristic, complemented
216	C₂×#95	C₂×C₅₃	1	1	yes	characteristic, complemented
217	C₅₃	#2419	1	1	yes	characteristic, direct product factor, Sylow
218	C₂²×D₄	C₂²×C₅₃	1	1	yes	characteristic
219	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic
220	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic
221	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic
222	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic
223	#123	—	2	4	no	—
224	C₄×D₄	—	2	4	no	—
225	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
236	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
240	C₂×C₄²	C₂²×C₅₃	1	1	yes	characteristic
241	#95	C₂²×C₅₃	1	1	yes	characteristic
242	#95	C₂²×C₅₃	1	1	yes	characteristic
243	#95	C₂²×C₅₃	1	1	yes	characteristic
244	#95	C₂²×C₅₃	1	1	yes	characteristic
245	#95	C₂²×C₅₃	1	1	yes	characteristic
246	#95	C₂²×C₅₃	1	1	yes	characteristic
247	#95	C₂²×C₅₃	1	1	yes	characteristic
248	#95	C₂²×C₅₃	1	1	yes	characteristic
249	#95	C₂²×C₅₃	1	1	yes	characteristic
250	#95	C₂²×C₅₃	1	1	yes	characteristic
251	#95	C₂²×C₅₃	1	1	yes	characteristic
252	#95	C₂²×C₅₃	1	1	yes	characteristic
253	#95	C₂²×C₅₃	1	1	yes	characteristic
254	#95	C₂²×C₅₃	1	1	yes	characteristic
255	C₂⁴	C₂³×C₅₃	1	1	yes	characteristic
256	C₂⁴	C₂³×C₅₃	1	1	yes	characteristic
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	D₄×C₅₃	1	4	yes	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
273	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
275	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
276	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
277	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
279	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
281	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	4	1	no	—
300	C₄²	—	2	2	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	C₂×D₄×C₅₃	1	2	yes	—
312	C₂³	C₂×D₄×C₅₃	1	2	yes	—
313	C₂³	#41×C₅₃	1	2	yes	—
314	C₂³	#41×C₅₃	1	2	yes	—
315	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
316	D₄	—	2	8	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	C₂×D₄×C₅₃	1	2	yes	—
358	C₂×C₄	#41×C₅₃	1	2	yes	—
359	C₂×C₄	#41×C₅₃	1	2	yes	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	#123×C₅₃	1	4	yes	—
374	C₂²	C₂²×D₄×C₅₃	1	1	yes	characteristic
375	C₂²	C₂×#41×C₅₃	1	1	yes	characteristic
376	C₂²	C₂×#41×C₅₃	1	1	yes	characteristic
377	C₂²	C₂×#41×C₅₃	1	1	yes	characteristic
378	C₂²	C₂×#41×C₅₃	1	1	yes	characteristic
379	C₂²	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
380	C₂²	2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₂	—	2	4	no	—
395	C₂	—	4	2	no	—
396	C₂	C₂×#123×C₅₃	1	1	yes	characteristic
397	C₂	C₅₃×#529	1	1	yes	characteristic
398	C₂	C₅₃×#539	1	1	yes	characteristic
399	C₂	C₅₃×#546	1	1	yes	characteristic
400	C₂	C₅₃×#547	1	1	yes	characteristic
401	C₂	C₅₃×#551	1	1	yes	characteristic
402	C₂	C₅₃×#552	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₅₃×#400	C₂	semidirect
4. C₅₃×#398	C₂	semidirect
5. C₅₃×#397	C₂	semidirect
6. C₅₃×#397	C₂	semidirect
7. C₅₃×#387	C₂	semidirect
8. C₅₃×#387	C₂	semidirect
10. C₅₃×#385	C₂	semidirect
11. C₅₃×#385	C₂	semidirect
12. C₅₃×#381	C₂	semidirect
13. C₅₃×#381	C₂	semidirect
14. C₅₃×#380	C₂	semidirect
15. C₂×#95×C₅₃	C₂	semidirect
192. #2419	C₅₃	direct (N × H)
204. #400	C₂×C₅₃	semidirect
205. #398	C₂×C₅₃	semidirect
206. #397	C₂×C₅₃	semidirect
207. #397	C₂×C₅₃	semidirect
208. #387	C₂×C₅₃	semidirect
209. #387	C₂×C₅₃	semidirect
211. #385	C₂×C₅₃	semidirect
212. #385	C₂×C₅₃	semidirect
213. #381	C₂×C₅₃	semidirect
214. #381	C₂×C₅₃	semidirect
215. #380	C₂×C₅₃	semidirect
216. C₂×#95	C₂×C₅₃	semidirect
217. C₅₃	#2419	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×#123×C₅₃	2
C₂×C₄×D₄×C₅₃	2
C₅₃×#400	2
C₅₃×#398	2
C₅₃×#397	2
C₅₃×#387	2
C₅₃×#386	2
C₅₃×#385	2
C₅₃×#381	2
C₅₃×#380	2
C₂×#95×C₅₃	2
#2419	53

Subgroups — C53×#2419 #20271356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#2419 #20271356