Subgroups — C₅₃×#11202 #27218714

Order 13568.

934 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₃×#336	C₂	1	2	yes	maximal
4	C₂×C₅₃×#336	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅₃×#336	C₂	1	2	yes	maximal
6	C₂³×C₈×C₅₃	C₂²	1	2	yes	—
7	C₂³×C₈×C₅₃	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₅₃	C₄	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₅₃	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₅₃	—	2	4	no	—
14	C₂×C₄⋊C₈×C₅₃	—	2	2	no	—
15	C₄×C₄⋊C₄×C₅₃	—	2	2	no	—
16	C₄×C₄⋊C₄×C₅₃	—	2	2	no	—
17	C₂×#95×C₅₃	C₄	1	1	yes	characteristic
18	C₂×#95×C₅₃	C₄	1	1	yes	characteristic
19	C₅₃×#336	—	2	4	no	—
20	C₅₃×#336	—	2	2	no	—
21	C₅₃×#336	—	2	4	no	—
22	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₅₃	—	2	2	no	—
30	C₂²×C₈×C₅₃	—	2	2	no	—
31	C₂²×C₈×C₅₃	—	2	2	no	—
32	C₂²×C₈×C₅₃	—	2	2	no	—
33	C₂²×C₈×C₅₃	—	2	2	no	—
34	C₂²×C₈×C₅₃	—	2	2	no	—
35	C₂²×C₈×C₅₃	—	2	2	no	—
36	C₂²×C₈×C₅₃	—	2	2	no	—
37	C₂²×C₈×C₅₃	—	2	2	no	—
38	C₂²×C₈×C₅₃	—	2	2	no	—
39	C₂²×C₈×C₅₃	—	2	2	no	—
40	C₂²×C₈×C₅₃	—	2	2	no	—
41	C₂²×C₈×C₅₃	D₄	1	4	yes	—
42	C₂²×C₈×C₅₃	Q₈	1	4	yes	—
43	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
46	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₅₃	C₈	1	4	yes	complemented
49	C₂×C₄²×C₅₃	—	2	1	no	—
50	C₂×C₄²×C₅₃	—	2	1	no	—
51	C₂×C₄²×C₅₃	—	2	2	no	—
52	C₂×C₄²×C₅₃	—	2	2	no	—
53	C₂×C₄²×C₅₃	—	2	1	no	—
54	C₂×C₄²×C₅₃	—	2	1	no	—
55	C₂×C₄²×C₅₃	—	2	1	no	—
56	C₂×C₄²×C₅₃	—	2	1	no	—
57	C₂×C₄²×C₅₃	—	2	2	no	—
58	C₂×C₄²×C₅₃	—	2	2	no	—
59	C₂×C₄²×C₅₃	D₄	1	2	yes	—
60	C₂×C₄²×C₅₃	D₄	1	2	yes	—
61	C₂×C₄²×C₅₃	D₄	1	2	yes	—
62	C₂×C₄²×C₅₃	Q₈	1	2	yes	—
63	C₄⋊C₈×C₅₃	—	2	8	no	—
64	#95×C₅₃	—	2	2	no	—
65	#95×C₅₃	—	2	2	no	—
66	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₅₃	—	2	1	no	—
68	C₂²×C₄×C₅₃	—	2	1	no	—
69	C₂²×C₄×C₅₃	—	2	2	no	—
70	C₂²×C₄×C₅₃	—	2	1	no	—
71	C₂²×C₄×C₅₃	—	2	1	no	—
72	C₂²×C₄×C₅₃	—	2	2	no	—
73	C₂²×C₄×C₅₃	—	2	1	no	—
74	C₂²×C₄×C₅₃	—	2	1	no	—
75	C₂²×C₄×C₅₃	—	2	1	no	—
76	C₂²×C₄×C₅₃	—	2	1	no	—
77	C₂²×C₄×C₅₃	—	2	2	no	—
78	C₂²×C₄×C₅₃	—	2	2	no	—
79	C₂²×C₄×C₅₃	—	2	2	no	—
80	C₂²×C₄×C₅₃	—	2	1	no	—
81	C₂²×C₄×C₅₃	—	2	1	no	—
82	C₂²×C₄×C₅₃	—	2	1	no	—
83	C₂²×C₄×C₅₃	—	2	1	no	—
84	C₂²×C₄×C₅₃	—	2	2	no	—
85	C₂²×C₄×C₅₃	—	2	2	no	—
86	C₂²×C₄×C₅₃	—	2	2	no	—
87	C₂²×C₄×C₅₃	—	2	2	no	—
88	C₂²×C₄×C₅₃	—	2	2	no	—
89	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₅₃	C₂×C₈	1	2	yes	—
94	C₂²×C₄×C₅₃	C₂×C₈	1	2	yes	—
95	C₂²×C₄×C₅₃	C₂×C₈	1	2	yes	—
96	C₂²×C₄×C₅₃	M₁₆	1	2	yes	—
97	C₂²×C₄×C₅₃	M₁₆	1	2	yes	—
98	C₂²×C₄×C₅₃	M₁₆	1	2	yes	—
99	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
106	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	#41	1	2	yes	—
108	C₂²×C₄×C₅₃	#41	1	2	yes	—
109	C₂×C₈×C₅₃	—	2	4	no	—
110	C₂×C₈×C₅₃	—	2	4	no	—
111	C₂×C₈×C₅₃	—	2	4	no	—
112	C₂×C₈×C₅₃	—	2	4	no	—
113	C₂×C₈×C₅₃	—	2	4	no	—
114	C₂×C₈×C₅₃	—	2	4	no	—
115	C₂×C₈×C₅₃	—	4	2	no	—
116	C₂×C₈×C₅₃	—	4	2	no	—
117	C₂×C₈×C₅₃	—	4	2	no	—
118	C₂×C₈×C₅₃	—	4	2	no	—
119	C₂×C₈×C₅₃	—	4	2	no	—
120	C₂×C₈×C₅₃	—	4	2	no	—
121	C₂×C₈×C₅₃	—	4	2	no	—
122	C₂×C₈×C₅₃	—	4	2	no	—
123	C₄⋊C₄×C₅₃	—	2	8	no	—
124	C₄⋊C₄×C₅₃	—	2	8	no	—
125	C₄²×C₅₃	—	2	2	no	—
126	C₄²×C₅₃	—	2	2	no	—
127	C₄²×C₅₃	—	2	2	no	—
128	C₄²×C₅₃	—	2	4	no	—
129	C₄²×C₅₃	—	2	2	no	—
130	C₄²×C₅₃	—	2	2	no	—
131	C₄²×C₅₃	—	2	2	no	—
132	C₄²×C₅₃	—	4	1	no	—
133	C₄²×C₅₃	—	4	2	no	—
134	C₄²×C₅₃	—	4	1	no	—
135	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂³×C₅₃	#117	1	1	yes	characteristic
138	C₂³×C₅₃	C₄×D₄	1	2	yes	—
139	C₂³×C₅₃	C₄×Q₈	1	2	yes	—
140	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
141	C₂³×C₅₃	C₂×M₁₆	1	1	yes	characteristic
142	C₂³×C₅₃	C₂×M₁₆	1	1	yes	characteristic
143	C₂³×C₅₃	C₂×M₁₆	1	1	yes	characteristic
144	C₂³×C₅₃	#131	1	2	yes	—
145	C₂³×C₅₃	#131	1	2	yes	—
146	C₂×C₄×C₅₃	—	2	2	no	—
147	C₂×C₄×C₅₃	—	2	2	no	—
148	C₂×C₄×C₅₃	—	2	2	no	—
149	C₂×C₄×C₅₃	—	2	2	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	4	no	—
155	C₂×C₄×C₅₃	—	2	4	no	—
156	C₂×C₄×C₅₃	—	2	2	no	—
157	C₂×C₄×C₅₃	—	2	2	no	—
158	C₂×C₄×C₅₃	—	2	2	no	—
159	C₂×C₄×C₅₃	—	2	2	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	—	2	2	no	—
162	C₂×C₄×C₅₃	—	2	4	no	—
163	C₂×C₄×C₅₃	—	2	4	no	—
164	C₂×C₄×C₅₃	—	2	4	no	—
165	C₂×C₄×C₅₃	—	4	1	no	—
166	C₂×C₄×C₅₃	—	4	1	no	—
167	C₂×C₄×C₅₃	—	4	1	no	—
168	C₂×C₄×C₅₃	—	4	1	no	—
169	C₂×C₄×C₅₃	—	4	1	no	—
170	C₂×C₄×C₅₃	—	4	1	no	—
171	C₂×C₄×C₅₃	—	4	2	no	—
172	C₂×C₄×C₅₃	—	4	2	no	—
173	C₂×C₄×C₅₃	—	4	2	no	—
174	C₂×C₄×C₅₃	—	4	2	no	—
175	C₂×C₄×C₅₃	—	4	2	no	—
176	C₂×C₄×C₅₃	C₂²⋊C₈	1	4	yes	—
177	C₂×C₄×C₅₃	C₄⋊C₈	1	4	yes	complemented
178	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
179	C₂×C₄×C₅₃	#121	1	2	yes	—
180	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
181	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₅₃	#121	1	2	yes	—
183	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
186	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
187	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₅₃	#123	1	2	yes	—
189	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
190	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
191	C₂×C₄×C₅₃	#125	1	2	yes	—
192	C₂×C₄×C₅₃	#125	1	2	yes	—
193	C₂×C₄×C₅₃	#126	1	2	yes	—
194	C₂×C₄×C₅₃	C₄⋊Q₈	1	2	yes	—
195	C₂×C₄×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
196	C₈×C₅₃	—	4	4	no	—
197	C₈×C₅₃	—	4	4	no	—
198	#11202	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₅₃	#380	1	1	yes	characteristic
200	C₂²×C₅₃	#386	1	1	yes	characteristic
201	C₂²×C₅₃	#387	1	2	yes	—
202	C₂²×C₅₃	#389	1	2	yes	—
203	C₂²×C₅₃	#391	1	1	yes	characteristic
204	C₂²×C₅₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
205	C₂²×C₅₃	#407	1	1	yes	characteristic
206	C₂²×C₅₃	#408	1	1	yes	characteristic
207	C₂²×C₅₃	#408	1	1	yes	characteristic
208	C₂²×C₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic
209	C₂²×C₅₃	#423	1	1	yes	characteristic
210	C₂²×C₅₃	#424	1	2	yes	—
211	C₂²×C₅₃	#431	1	1	yes	characteristic
212	C₂²×C₅₃	#432	1	1	yes	characteristic
213	C₂²×C₅₃	#433	1	2	yes	—
214	C₂²×C₅₃	C₈×D₄	1	2	yes	—
215	C₂²×C₅₃	#435	1	2	yes	—
216	C₂²×C₅₃	#435	1	2	yes	—
217	C₂²×C₅₃	#436	1	2	yes	—
218	C₂²×C₅₃	C₈×Q₈	1	2	yes	—
219	C₂²×C₅₃	#446	1	2	yes	—
220	C₂²×C₅₃	#446	1	2	yes	—
221	C₂²×C₅₃	#446	1	2	yes	—
222	C₄×C₅₃	—	2	4	no	—
223	C₄×C₅₃	—	2	4	no	—
224	C₄×C₅₃	—	4	2	no	—
225	C₄×C₅₃	—	4	2	no	—
226	C₄×C₅₃	—	4	2	no	—
227	C₄×C₅₃	—	4	2	no	—
228	C₄×C₅₃	#394	1	1	yes	characteristic
229	C₄×C₅₃	#395	1	1	yes	characteristic
230	C₄×C₅₃	#396	1	2	yes	—
231	C₄×C₅₃	#398	1	1	yes	characteristic
232	C₄×C₅₃	#398	1	2	yes	—
233	C₄×C₅₃	#400	1	1	yes	characteristic
234	C₂²×C₄⋊C₈	C₂×C₅₃	1	1	yes	characteristic
235	C₂×C₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic
236	C₂×#336	C₂×C₅₃	1	2	yes	—
237	C₂×#336	C₂×C₅₃	1	2	yes	—
238	C₂×#336	C₂×C₅₃	1	1	yes	characteristic
239	C₂×C₅₃	#1441	1	1	yes	characteristic
240	C₂×C₅₃	#1797	1	1	yes	characteristic
241	C₂×C₅₃	#1798	1	1	yes	characteristic
242	C₂×C₅₃	#1869	1	1	yes	characteristic
243	C₂×C₅₃	#1870	1	1	yes	characteristic
244	C₂×C₅₃	#1916	1	2	yes	—
245	C₂×C₅₃	#1917	1	2	yes	—
246	C₂×C₅₃	#1939	1	2	yes	—
247	C₂×C₅₃	#1940	1	2	yes	—
248	C₂×C₅₃	#1984	1	1	yes	characteristic
249	C₂×C₅₃	#1985	1	1	yes	characteristic
250	C₂³×C₈	C₂²×C₅₃	1	2	yes	—
251	C₂³×C₈	C₂²×C₅₃	1	2	yes	—
252	C₂²×C₄⋊C₄	C₄×C₅₃	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	C₄×C₅₃	1	1	yes	characteristic
254	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
255	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
256	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
257	C₂×C₄⋊C₈	—	2	4	no	—
258	C₂×C₄⋊C₈	—	2	2	no	—
259	C₄×C₄⋊C₄	—	2	2	no	—
260	C₄×C₄⋊C₄	—	2	2	no	—
261	C₂×#95	C₄×C₅₃	1	1	yes	characteristic
262	C₂×#95	C₄×C₅₃	1	1	yes	characteristic
263	#336	—	2	4	no	—
264	#336	—	2	2	no	—
265	#336	—	2	4	no	—
266	C₅₃	#11202	1	1	yes	characteristic, direct product factor, Sylow
267	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
268	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
269	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
270	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
271	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
272	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	D₄×C₅₃	1	4	yes	—
287	C₂²×C₈	Q₈×C₅₃	1	4	yes	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	C₈×C₅₃	1	4	yes	complemented
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	D₄×C₅₃	1	2	yes	—
305	C₂×C₄²	D₄×C₅₃	1	2	yes	—
306	C₂×C₄²	D₄×C₅₃	1	2	yes	—
307	C₂×C₄²	Q₈×C₅₃	1	2	yes	—
308	C₄⋊C₈	—	2	8	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
335	C₂²×C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
336	C₂²×C₄	C₄⋊C₄×C₅₃	1	2	yes	—
337	C₂²×C₄	C₄⋊C₄×C₅₃	1	2	yes	—
338	C₂²×C₄	C₂×C₈×C₅₃	1	2	yes	—
339	C₂²×C₄	C₂×C₈×C₅₃	1	2	yes	—
340	C₂²×C₄	C₂×C₈×C₅₃	1	2	yes	—
341	C₂²×C₄	M₁₆×C₅₃	1	2	yes	—
342	C₂²×C₄	M₁₆×C₅₃	1	2	yes	—
343	C₂²×C₄	M₁₆×C₅₃	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×Q₈×C₅₃	1	2	yes	—
349	C₂²×C₄	C₂×Q₈×C₅₃	1	1	yes	characteristic
350	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
351	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
352	C₂²×C₄	#41×C₅₃	1	2	yes	—
353	C₂²×C₄	#41×C₅₃	1	2	yes	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	—	4	2	no	—
361	C₂×C₈	—	4	2	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	4	2	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	1	no	—
378	C₄²	—	4	2	no	—
379	C₄²	—	4	1	no	—
380	C₂³	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
381	C₂³	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
382	C₂³	#117×C₅₃	1	1	yes	characteristic
383	C₂³	C₄×D₄×C₅₃	1	2	yes	—
384	C₂³	C₄×Q₈×C₅₃	1	2	yes	—
385	C₂³	C₂²×C₈×C₅₃	1	1	yes	characteristic
386	C₂³	C₂×M₁₆×C₅₃	1	1	yes	characteristic
387	C₂³	C₂×M₁₆×C₅₃	1	1	yes	characteristic
388	C₂³	C₂×M₁₆×C₅₃	1	1	yes	characteristic
389	C₂³	#131×C₅₃	1	2	yes	—
390	C₂³	#131×C₅₃	1	2	yes	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	C₂²⋊C₈×C₅₃	1	4	yes	—
422	C₂×C₄	C₄⋊C₈×C₅₃	1	4	yes	complemented
423	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
424	C₂×C₄	#121×C₅₃	1	2	yes	—
425	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
426	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
427	C₂×C₄	#121×C₅₃	1	2	yes	—
428	C₂×C₄	C₂²⋊Q₈×C₅₃	1	2	yes	—
429	C₂×C₄	C₂²⋊Q₈×C₅₃	1	1	yes	characteristic
430	C₂×C₄	C₂²⋊Q₈×C₅₃	1	2	yes	—
431	C₂×C₄	C₂²⋊Q₈×C₅₃	1	2	yes	—
432	C₂×C₄	C₂²⋊Q₈×C₅₃	1	1	yes	characteristic
433	C₂×C₄	#123×C₅₃	1	2	yes	—
434	C₂×C₄	#123×C₅₃	1	1	yes	characteristic
435	C₂×C₄	#124×C₅₃	1	1	yes	characteristic
436	C₂×C₄	#125×C₅₃	1	2	yes	—
437	C₂×C₄	#125×C₅₃	1	2	yes	—
438	C₂×C₄	#126×C₅₃	1	2	yes	—
439	C₂×C₄	C₄⋊Q₈×C₅₃	1	2	yes	—
440	C₂×C₄	C₄⋊Q₈×C₅₃	1	1	yes	characteristic
441	C₈	—	4	4	no	—
442	C₈	—	4	4	no	—
443	C₂²	C₅₃×#380	1	1	yes	characteristic
444	C₂²	C₅₃×#386	1	1	yes	characteristic
445	C₂²	C₅₃×#387	1	2	yes	—
446	C₂²	C₅₃×#389	1	2	yes	—
447	C₂²	C₅₃×#391	1	1	yes	characteristic
448	C₂²	C₂×C₂²⋊C₈×C₅₃	1	1	yes	characteristic
449	C₂²	C₅₃×#407	1	1	yes	characteristic
450	C₂²	C₅₃×#408	1	1	yes	characteristic
451	C₂²	C₅₃×#408	1	1	yes	characteristic
452	C₂²	C₂×C₄⋊C₈×C₅₃	1	1	yes	characteristic
453	C₂²	C₅₃×#423	1	1	yes	characteristic
454	C₂²	C₅₃×#424	1	2	yes	—
455	C₂²	C₅₃×#431	1	1	yes	characteristic
456	C₂²	C₅₃×#432	1	1	yes	characteristic
457	C₂²	C₅₃×#433	1	2	yes	—
458	C₂²	C₈×D₄×C₅₃	1	2	yes	—
459	C₂²	C₅₃×#435	1	2	yes	—
460	C₂²	C₅₃×#435	1	2	yes	—
461	C₂²	C₅₃×#436	1	2	yes	—
462	C₂²	C₈×Q₈×C₅₃	1	2	yes	—
463	C₂²	C₅₃×#446	1	2	yes	—
464	C₂²	C₅₃×#446	1	2	yes	—
465	C₂²	C₅₃×#446	1	2	yes	—
466	C₄	—	2	4	no	—
467	C₄	—	2	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	C₅₃×#394	1	1	yes	characteristic
473	C₄	C₅₃×#395	1	1	yes	characteristic
474	C₄	C₅₃×#396	1	2	yes	—
475	C₄	C₅₃×#398	1	1	yes	characteristic
476	C₄	C₅₃×#398	1	2	yes	—
477	C₄	C₅₃×#400	1	1	yes	characteristic
478	C₂	C₅₃×#1441	1	1	yes	characteristic
479	C₂	C₅₃×#1797	1	1	yes	characteristic
480	C₂	C₅₃×#1798	1	1	yes	characteristic
481	C₂	C₅₃×#1869	1	1	yes	characteristic
482	C₂	C₅₃×#1870	1	1	yes	characteristic
483	C₂	C₅₃×#1916	1	2	yes	—
484	C₂	C₅₃×#1917	1	2	yes	—
485	C₂	C₅₃×#1939	1	2	yes	—
486	C₂	C₅₃×#1940	1	2	yes	—
487	C₂	C₅₃×#1984	1	1	yes	characteristic
488	C₂	C₅₃×#1985	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₅₃	C₂³
commutator	C₂³	C₂²×C₈×C₅₃
Frattini, cosocle	C₂³×C₄	C₂³×C₅₃
socle, prime radical	C₂⁴×C₅₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
48. C₂×C₄⋊C₄×C₅₃	C₈	semidirect
177. C₂×C₄×C₅₃	C₄⋊C₈	semidirect
198. #11202	C₅₃	direct (N × H)
266. C₅₃	#11202	direct (N × H)
293. C₂×C₄⋊C₄	C₈×C₅₃	semidirect
422. C₂×C₄	C₄⋊C₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₈×C₅₃	2
C₂×C₄×C₄⋊C₄×C₅₃	2
C₂×C₅₃×#336	2
#11202	53

Subgroups — C53×#11202 #27218714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#11202 #27218714