Subgroups — #27537302

Order 13568.

734 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133156	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20276545	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276544	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276542	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276541	C₂	1	1	yes	maximal, characteristic, complemented
8	#20276539	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₆×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#20276532	C₂	1	1	yes	maximal, characteristic, complemented
11	#20276469	C₂	1	1	yes	maximal, characteristic, complemented
12	#20276324	C₂	1	1	yes	maximal, characteristic, complemented
13	#20276324	C₂	1	1	yes	maximal, characteristic, complemented
14	#20276308	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₅₃	C₄	1	1	yes	characteristic
19	C₂×#13133157	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13133156	—	2	4	no	—
21	C₂×#13133156	C₂²	1	1	yes	characteristic
22	C₂×#13133156	C₂²	1	1	yes	characteristic
23	C₂×#13133156	C₂²	1	1	yes	characteristic
24	C₂×#13133156	C₂²	1	1	yes	characteristic
25	C₂×#13133156	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13133156	C₂²	1	1	yes	characteristic, complemented
27	M₃₂×D₅₃	—	2	4	no	—
28	C₂²×#11719908	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
32	D₄×#88322	C₄	1	1	yes	characteristic
33	#16810688	C₄	1	1	yes	characteristic
34	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
35	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
36	#16810686	C₄	1	1	yes	characteristic
37	#16810686	C₄	1	1	yes	characteristic
38	C₄⋊C₈×D₅₃	C₄	1	1	yes	characteristic
39	C₂²⋊C₈×D₅₃	C₄	1	1	yes	characteristic
40	C₂²⋊C₈×D₅₃	C₄	1	1	yes	characteristic
41	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
42	C₄⋊#11719908	C₂²	1	1	yes	characteristic, complemented
43	#16810441	C₂²	1	1	yes	characteristic, complemented
44	#16810441	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊#11719908	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊#11719908	C₂²	1	1	yes	characteristic, complemented
47	#16810402	C₂²	1	1	yes	characteristic, complemented
48	#16810402	C₂²	1	1	yes	characteristic, complemented
49	#16810402	C₂²	1	1	yes	characteristic, complemented
50	#16810402	C₂²	1	1	yes	characteristic, complemented
51	#16810399	C₂²	1	1	yes	characteristic, complemented
52	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#346	C₂²	1	1	yes	characteristic, complemented
61	C₂×D₄×D₅₃	C₈	1	1	yes	characteristic
62	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
65	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅₃	—	2	2	no	—
67	C₂×C₈×D₅₃	—	2	2	no	—
68	C₂×C₈×D₅₃	—	2	2	no	—
69	C₂×C₈×D₅₃	—	2	2	no	—
70	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
77	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
78	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
79	D₄×Dic₅₃	C₈	1	1	yes	characteristic
80	#13133179	C₈	1	1	yes	characteristic
81	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
83	#13133177	C₈	1	1	yes	characteristic
84	#13133177	C₈	1	1	yes	characteristic
85	C₄⋊C₄×D₅₃	C₈	1	1	yes	characteristic
86	C₂²⋊C₄×D₅₃	C₈	1	1	yes	characteristic
87	C₂²⋊C₄×D₅₃	C₈	1	1	yes	characteristic
88	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
89	#13133157	—	2	2	no	—
90	#13133156	—	2	2	no	—
91	#13133156	—	2	2	no	—
92	#13133156	—	2	2	no	—
93	#13133156	—	2	2	no	—
94	#13133156	—	2	2	no	—
95	#13133156	D₄	1	4	yes	complemented
96	C₂×#11719908	—	2	2	no	—
97	C₂×#11719908	C₂³	1	1	yes	characteristic
98	C₂×#11719908	C₂³	1	1	yes	characteristic
99	C₂×#11719908	C₂³	1	1	yes	characteristic
100	C₂×#11719908	C₂³	1	1	yes	characteristic
101	C₁₆×D₅₃	—	2	2	no	—
102	C₁₆×D₅₃	—	2	2	no	—
103	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
104	#13133146	C₂×C₄	1	1	yes	characteristic
105	#13133146	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
108	#13133129	C₂×C₄	1	1	yes	characteristic
109	#13133129	C₂×C₄	1	1	yes	characteristic
110	#13133129	C₂×C₄	1	1	yes	characteristic
111	#13133129	C₂×C₄	1	1	yes	characteristic
112	C₄×#88322	C₂×C₄	1	1	yes	characteristic
113	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
114	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
118	M₃₂×C₅₃	—	2	2	no	—
119	C₂×C₁₆×C₅₃	—	2	2	no	—
120	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
121	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
122	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
127	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
128	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
129	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
130	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
131	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
135	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
136	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
137	D₄×D₅₃	—	2	4	no	—
138	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
139	C₂×C₄×D₅₃	—	2	2	no	—
140	C₂×C₄×D₅₃	—	2	2	no	—
141	C₂×C₄×D₅₃	—	2	2	no	—
142	C₂×C₄×D₅₃	—	2	2	no	—
143	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
147	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
148	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
149	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₅₃	—	2	1	no	—
153	C₂×C₈×C₅₃	—	2	1	no	—
154	C₂×C₈×C₅₃	—	2	1	no	—
155	C₂×C₈×C₅₃	—	2	1	no	—
156	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
160	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
161	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
162	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
163	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
164	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
165	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
166	#11719921	C₂×C₈	1	1	yes	characteristic
167	#11719921	C₂×C₈	1	1	yes	characteristic
168	#11719921	C₂×C₈	1	1	yes	characteristic
169	#11719921	C₂×C₈	1	1	yes	characteristic
170	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
171	#11719919	C₂×C₈	1	1	yes	characteristic
172	#11719919	C₂×C₈	1	1	yes	characteristic
173	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
174	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
176	C₂×#88322	—	2	2	no	—
177	C₂×#88322	—	2	2	no	—
178	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
179	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
180	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
181	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
182	C₈×D₅₃	—	2	2	no	—
183	C₈×D₅₃	—	2	2	no	—
184	C₈×D₅₃	—	2	2	no	—
185	C₈×D₅₃	—	2	1	no	—
186	C₈×D₅₃	—	2	1	no	—
187	C₈×D₅₃	—	2	1	no	—
188	C₈×D₅₃	—	2	1	no	—
189	C₈×D₅₃	—	2	2	no	—
190	C₈×D₅₃	—	2	2	no	—
191	C₈×D₅₃	C₂×D₄	1	2	yes	—
192	C₈×D₅₃	#41	1	2	yes	—
193	C₁₆×C₅₃	—	2	1	no	—
194	C₁₆×C₅₃	—	2	1	no	—
195	C₁₆×C₅₃	—	2	1	no	—
196	C₁₆×C₅₃	C₂×D₄	1	2	yes	complemented
197	#11719908	—	2	1	no	—
198	#11719908	—	2	1	no	—
199	#11719908	—	2	1	no	—
200	#11719908	C₂×D₄	1	2	yes	complemented
201	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
202	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
203	C₂²×D₅₃	—	2	2	no	—
204	C₂²×D₅₃	—	2	2	no	—
205	C₂²×D₅₃	—	2	2	no	—
206	C₂²×D₅₃	—	2	2	no	—
207	C₂²×D₅₃	—	4	1	no	—
208	C₂²×D₅₃	—	4	1	no	—
209	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
210	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
211	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
212	D₄×C₅₃	—	2	2	no	—
213	C₂×C₄×C₅₃	—	2	1	no	—
214	C₂×C₄×C₅₃	—	2	1	no	—
215	C₂×C₄×C₅₃	—	2	1	no	—
216	C₂×C₄×C₅₃	—	2	1	no	—
217	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
218	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
219	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
220	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
221	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
222	C₂²⋊D₅₃	—	2	2	no	—
223	C₂²⋊D₅₃	M₃₂	1	4	yes	complemented
224	C₂×Dic₅₃	—	2	2	no	—
225	C₂×Dic₅₃	—	2	2	no	—
226	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
227	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
228	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
229	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
230	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
231	D₂₁₂	—	2	2	no	—
232	C₄×D₅₃	—	2	2	no	—
233	C₄×D₅₃	—	2	2	no	—
234	C₄×D₅₃	—	2	1	no	—
235	C₄×D₅₃	—	2	1	no	—
236	C₄×D₅₃	—	2	1	no	—
237	C₄×D₅₃	—	2	1	no	—
238	C₄×D₅₃	—	2	2	no	—
239	C₄×D₅₃	—	2	2	no	—
240	C₄×D₅₃	—	2	2	no	—
241	C₄×D₅₃	—	4	1	no	—
242	C₄×D₅₃	C₄×D₄	1	2	yes	—
243	C₄×D₅₃	#131	1	2	yes	—
244	C₈×C₅₃	—	2	1	no	—
245	C₈×C₅₃	—	2	1	no	—
246	C₈×C₅₃	—	2	1	no	—
247	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
248	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
249	#88322	—	2	1	no	—
250	#88322	—	2	1	no	—
251	#88322	—	2	1	no	—
252	#88322	C₄×D₄	1	2	yes	—
253	D₄×M₃₂	—	53	1	no	maximal, Sylow
254	C₂²×C₅₃	—	2	1	no	—
255	C₂²×C₅₃	—	2	1	no	—
256	C₂²×C₅₃	—	2	1	no	—
257	C₂²×C₅₃	—	2	1	no	—
258	C₂²×C₅₃	—	2	1	no	—
259	C₂²×C₅₃	C₂×M₃₂	1	2	yes	complemented
260	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
261	C₂×D₅₃	—	2	1	no	—
262	C₂×D₅₃	—	2	1	no	—
263	C₂×D₅₃	—	2	1	no	—
264	C₂×D₅₃	—	2	1	no	—
265	C₂×D₅₃	—	2	1	no	—
266	C₂×D₅₃	—	2	1	no	—
267	C₂×D₅₃	—	2	1	no	—
268	C₂×D₅₃	—	4	4	no	—
269	C₂×D₅₃	—	4	4	no	—
270	C₂×D₅₃	C₈×D₄	1	2	yes	—
271	C₂×D₅₃	C₂×M₃₂	1	2	yes	complemented
272	C₄×C₅₃	—	2	1	no	—
273	C₄×C₅₃	—	2	1	no	—
274	C₄×C₅₃	—	2	1	no	—
275	C₄×C₅₃	—	2	1	no	—
276	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
277	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
278	Dic₅₃	—	2	1	no	—
279	Dic₅₃	—	2	1	no	—
280	Dic₅₃	—	2	1	no	—
281	Dic₅₃	C₈×D₄	1	2	yes	—
282	Dic₅₃	C₂×M₃₂	1	2	yes	complemented
283	C₂²×M₃₂	—	53	1	no	—
284	C₂²×M₃₂	—	53	1	no	—
285	C₂×C₈×D₄	—	53	1	no	—
286	#2169	—	53	1	no	—
287	#2169	—	53	1	no	—
288	#2168	—	53	1	no	—
289	#2168	—	53	1	no	—
290	#2168	—	53	1	no	—
291	#2168	D₅₃	1	1	yes	characteristic, complemented
292	D₄×C₁₆	—	53	1	no	—
293	D₄×C₁₆	—	53	1	no	—
294	#2150	—	53	1	no	—
295	#2112	—	53	1	no	—
296	#2112	—	53	1	no	—
297	C₄×M₃₂	—	53	1	no	—
298	C₂×C₅₃	—	2	2	no	—
299	C₂×C₅₃	—	4	1	no	—
300	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
301	C₂×C₅₃	C₂²×M₃₂	1	1	yes	characteristic
302	C₂×C₅₃	#3407	1	1	yes	characteristic
303	D₅₃	—	2	2	no	—
304	D₅₃	—	2	2	no	—
305	D₅₃	—	4	1	no	—
306	C₂³×C₈	—	53	1	no	—
307	C₂³×C₈	—	53	1	no	—
308	C₂×C₄×D₄	—	53	1	no	—
309	C₂×M₃₂	—	53	1	no	—
310	C₂×M₃₂	—	53	1	no	—
311	C₂×M₃₂	—	53	1	no	—
312	C₂×M₃₂	—	53	1	no	—
313	C₂×M₃₂	—	53	1	no	—
314	C₂×M₃₂	—	53	1	no	—
315	C₂×M₃₂	—	53	1	no	—
316	C₂×M₃₂	—	106	4	no	—
317	C₂×M₃₂	—	106	4	no	—
318	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic, complemented
319	C₂²×C₁₆	—	53	1	no	—
320	C₂²×C₁₆	—	53	1	no	—
321	C₂²×C₁₆	—	53	1	no	—
322	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
323	C₈×D₄	—	53	1	no	—
324	C₈×D₄	—	53	1	no	—
325	C₈×D₄	—	53	1	no	—
326	C₈×D₄	—	53	1	no	—
327	C₈×D₄	—	53	1	no	—
328	C₈×D₄	—	53	1	no	—
329	C₈×D₄	—	53	1	no	—
330	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
331	C₂×C₄⋊C₈	—	53	1	no	—
332	C₂×C₂²⋊C₈	—	53	1	no	—
333	C₂×C₂²⋊C₈	—	53	1	no	—
334	C₂×C₄×C₈	—	53	1	no	—
335	C₄⋊C₁₆	—	53	1	no	—
336	C₄⋊C₁₆	—	53	1	no	—
337	C₄⋊C₁₆	—	53	1	no	—
338	C₄⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
339	C₂²⋊C₁₆	—	53	1	no	—
340	C₂²⋊C₁₆	—	53	1	no	—
341	C₂²⋊C₁₆	—	53	1	no	—
342	C₂²⋊C₁₆	—	53	1	no	—
343	C₂²⋊C₁₆	—	53	1	no	—
344	C₂²⋊C₁₆	—	53	1	no	—
345	C₂²⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
346	C₂²⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
347	#346	—	53	1	no	—
348	#346	C₂×D₅₃	1	1	yes	characteristic, complemented
349	C₄×C₁₆	—	53	1	no	—
350	C₄×C₁₆	—	53	1	no	—
351	C₅₃	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
352	C₂²×D₄	—	53	1	no	—
353	C₂³×C₄	—	53	1	no	—
354	C₂³×C₄	—	53	1	no	—
355	C₂²×C₈	—	53	1	no	—
356	C₂²×C₈	—	53	1	no	—
357	C₂²×C₈	—	53	1	no	—
358	C₂²×C₈	—	53	1	no	—
359	C₂²×C₈	—	53	1	no	—
360	C₂²×C₈	—	53	1	no	—
361	C₂²×C₈	—	53	1	no	—
362	C₂²×C₈	—	53	1	no	—
363	C₂²×C₈	—	53	1	no	—
364	C₂²×C₈	—	53	1	no	—
365	C₂²×C₈	—	106	2	no	—
366	C₂²×C₈	—	106	2	no	—
367	C₂²×C₈	—	106	2	no	—
368	C₂²×C₈	—	106	2	no	—
369	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
370	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
371	C₄×D₄	—	53	1	no	—
372	C₄×D₄	—	53	1	no	—
373	C₄×D₄	—	53	1	no	—
374	C₄×D₄	—	53	1	no	—
375	C₄×D₄	—	53	1	no	—
376	C₄×D₄	—	53	1	no	—
377	C₄×D₄	—	53	1	no	—
378	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	—	53	1	no	—
380	C₂×C₂²⋊C₄	—	53	1	no	—
381	C₂×C₂²⋊C₄	—	53	1	no	—
382	C₂×C₄²	—	53	1	no	—
383	M₃₂	—	2	2	no	—
384	M₃₂	—	53	4	no	—
385	M₃₂	—	106	2	no	—
386	M₃₂	—	106	2	no	—
387	M₃₂	—	106	2	no	—
388	M₃₂	—	106	2	no	—
389	M₃₂	—	106	2	no	—
390	M₃₂	—	106	2	no	—
391	C₂×C₁₆	—	2	2	no	—
392	C₂×C₁₆	—	53	1	no	—
393	C₂×C₁₆	—	53	1	no	—
394	C₂×C₁₆	—	53	1	no	—
395	C₂×C₁₆	—	53	1	no	—
396	C₂×C₁₆	—	106	2	no	—
397	C₂×C₁₆	—	106	2	no	—
398	C₂×C₁₆	—	106	2	no	—
399	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
400	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
401	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
402	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
403	C₄⋊C₈	—	53	1	no	—
404	C₄⋊C₈	—	53	1	no	—
405	C₄⋊C₈	—	53	1	no	—
406	C₄⋊C₈	C₄×D₅₃	1	1	yes	characteristic
407	C₂²⋊C₈	—	53	1	no	—
408	C₂²⋊C₈	—	53	1	no	—
409	C₂²⋊C₈	—	53	1	no	—
410	C₂²⋊C₈	—	53	1	no	—
411	C₂²⋊C₈	—	53	1	no	—
412	C₂²⋊C₈	—	53	1	no	—
413	C₂²⋊C₈	C₄×D₅₃	1	1	yes	characteristic
414	C₂²⋊C₈	C₄×D₅₃	1	1	yes	characteristic
415	C₄×C₈	—	53	1	no	—
416	C₄×C₈	—	53	1	no	—
417	C₄×C₈	—	53	1	no	—
418	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
419	C₂⁴	—	53	1	no	—
420	C₂⁴	—	53	1	no	—
421	C₂×D₄	—	53	1	no	—
422	C₂×D₄	—	53	1	no	—
423	C₂×D₄	—	53	1	no	—
424	C₂×D₄	—	106	4	no	—
425	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
426	C₂²×C₄	—	53	1	no	—
427	C₂²×C₄	—	53	1	no	—
428	C₂²×C₄	—	53	1	no	—
429	C₂²×C₄	—	53	1	no	—
430	C₂²×C₄	—	53	1	no	—
431	C₂²×C₄	—	53	1	no	—
432	C₂²×C₄	—	53	1	no	—
433	C₂²×C₄	—	53	1	no	—
434	C₂²×C₄	—	53	1	no	—
435	C₂²×C₄	—	53	1	no	—
436	C₂²×C₄	—	53	1	no	—
437	C₂²×C₄	—	106	2	no	—
438	C₂²×C₄	—	106	2	no	—
439	C₂²×C₄	—	106	2	no	—
440	C₂²×C₄	—	106	2	no	—
441	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	53	1	no	—
448	C₂×C₈	—	53	2	no	—
449	C₂×C₈	—	53	2	no	—
450	C₂×C₈	—	53	1	no	—
451	C₂×C₈	—	53	1	no	—
452	C₂×C₈	—	53	1	no	—
453	C₂×C₈	—	106	2	no	—
454	C₂×C₈	—	106	2	no	—
455	C₂×C₈	—	106	2	no	—
456	C₂×C₈	—	106	2	no	—
457	C₂×C₈	—	106	2	no	—
458	C₂×C₈	—	106	2	no	—
459	C₂×C₈	—	106	2	no	—
460	C₂×C₈	—	106	1	no	—
461	C₂×C₈	—	106	1	no	—
462	C₂×C₈	—	106	1	no	—
463	C₂×C₈	—	106	1	no	—
464	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
465	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
466	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
467	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
468	C₄⋊C₄	—	53	1	no	—
469	C₄⋊C₄	—	53	1	no	—
470	C₄⋊C₄	—	53	1	no	—
471	C₄⋊C₄	C₈×D₅₃	1	1	yes	characteristic
472	C₂²⋊C₄	—	53	1	no	—
473	C₂²⋊C₄	—	53	1	no	—
474	C₂²⋊C₄	—	53	1	no	—
475	C₂²⋊C₄	—	53	1	no	—
476	C₂²⋊C₄	—	53	1	no	—
477	C₂²⋊C₄	—	53	1	no	—
478	C₂²⋊C₄	C₈×D₅₃	1	1	yes	characteristic
479	C₂²⋊C₄	C₈×D₅₃	1	1	yes	characteristic
480	C₄²	—	53	1	no	—
481	C₄²	—	53	1	no	—
482	C₄²	—	53	1	no	—
483	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
484	C₁₆	—	2	1	no	—
485	C₁₆	—	2	1	no	—
486	C₁₆	—	2	1	no	—
487	C₁₆	—	53	2	no	—
488	C₁₆	—	106	1	no	—
489	C₁₆	—	106	1	no	—
490	C₁₆	—	106	1	no	—
491	C₁₆	D₄×D₅₃	1	2	yes	complemented
492	C₂³	—	53	1	no	—
493	C₂³	—	53	1	no	—
494	C₂³	—	53	1	no	—
495	C₂³	—	106	2	no	—
496	C₂³	—	106	2	no	—
497	C₂³	—	106	2	no	—
498	C₂³	—	106	2	no	—
499	C₂³	—	212	1	no	—
500	C₂³	—	212	1	no	—
501	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
502	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
503	D₄	—	2	2	no	—
504	D₄	—	53	4	no	—
505	D₄	—	106	2	no	—
506	D₄	—	106	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	53	1	no	—
512	C₂×C₄	—	53	1	no	—
513	C₂×C₄	—	53	2	no	—
514	C₂×C₄	—	53	2	no	—
515	C₂×C₄	—	53	1	no	—
516	C₂×C₄	—	53	1	no	—
517	C₂×C₄	—	53	1	no	—
518	C₂×C₄	—	106	2	no	—
519	C₂×C₄	—	106	2	no	—
520	C₂×C₄	—	106	2	no	—
521	C₂×C₄	—	106	2	no	—
522	C₂×C₄	—	106	2	no	—
523	C₂×C₄	—	106	2	no	—
524	C₂×C₄	—	106	2	no	—
525	C₂×C₄	—	106	1	no	—
526	C₂×C₄	—	106	1	no	—
527	C₂×C₄	—	106	1	no	—
528	C₂×C₄	—	106	1	no	—
529	C₂×C₄	—	212	1	no	—
530	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
531	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
532	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
533	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
534	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	53	2	no	—
539	C₈	—	106	1	no	—
540	C₈	—	106	1	no	—
541	C₈	—	106	1	no	—
542	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
543	C₈	#41×D₅₃	1	1	yes	characteristic
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	53	2	no	—
550	C₂²	—	53	2	no	—
551	C₂²	—	106	1	no	—
552	C₂²	—	106	1	no	—
553	C₂²	—	106	1	no	—
554	C₂²	—	106	1	no	—
555	C₂²	—	106	1	no	—
556	C₂²	—	106	1	no	—
557	C₂²	—	106	1	no	—
558	C₂²	—	212	4	no	—
559	C₂²	—	212	4	no	—
560	C₂²	M₃₂×D₅₃	1	2	yes	complemented
561	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	53	2	no	—
567	C₄	—	53	2	no	—
568	C₄	—	106	1	no	—
569	C₄	—	106	1	no	—
570	C₄	—	106	1	no	—
571	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
572	C₄	#131×D₅₃	1	1	yes	characteristic
573	C₂	—	2	2	no	—
574	C₂	—	4	1	no	—
575	C₂	—	106	2	no	—
576	C₂	—	106	2	no	—
577	C₂	—	212	1	no	—
578	C₂	C₈×D₄×D₅₃	1	1	yes	characteristic
579	C₂	C₂×M₃₂×D₅₃	1	1	yes	characteristic
580	C₂	#20287816	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₅₃×#2168	C₂
prime radical	C₂×D₄×D₅₃	C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2168	D₅₃
hypocenter	C₅₃	D₄×M₃₂
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
1. C₂²×#13133156	C₂	semidirect
2. C₂×M₃₂×D₅₃	C₂	semidirect
4. #20276545	C₂	semidirect
5. #20276544	C₂	semidirect
6. #20276542	C₂	semidirect
7. #20276541	C₂	semidirect
8. #20276539	C₂	semidirect
9. C₁₆×C₂²⋊D₅₃	C₂	semidirect
10. #20276532	C₂	semidirect
11. #20276469	C₂	semidirect
12. #20276324	C₂	semidirect
13. #20276324	C₂	semidirect
14. #20276308	C₂	semidirect
15. C₅₃×#2168	C₂	semidirect
19. C₂×#13133157	C₂²	semidirect
25. C₂×#13133156	C₂²	semidirect
26. C₂×#13133156	C₂²	semidirect
28. C₂²×#11719908	C₂²	semidirect
29. C₂×C₁₆×D₅₃	C₂²	semidirect
30. C₂×C₁₆×D₅₃	C₂²	semidirect
42. C₄⋊#11719908	C₂²	semidirect
43. #16810441	C₂²	semidirect
44. #16810441	C₂²	semidirect
45. C₂²⋊#11719908	C₂²	semidirect
46. C₂²⋊#11719908	C₂²	semidirect
47. #16810402	C₂²	semidirect
48. #16810402	C₂²	semidirect
49. #16810402	C₂²	semidirect
50. #16810402	C₂²	semidirect
51. #16810399	C₂²	semidirect
52. C₁₆×Dic₅₃	C₂²	semidirect
53. C₁₆×Dic₅₃	C₂²	semidirect
54. C₂×M₃₂×C₅₃	C₂²	semidirect
55. C₂²×C₁₆×C₅₃	C₂²	semidirect
57. C₅₃×C₄⋊C₁₆	C₂²	semidirect
58. C₅₃×C₂²⋊C₁₆	C₂²	semidirect
59. C₅₃×C₂²⋊C₁₆	C₂²	semidirect
60. C₅₃×#346	C₂²	semidirect
95. #13133156	D₄	semidirect
196. C₁₆×C₅₃	C₂×D₄	semidirect
200. #11719908	C₂×D₄	semidirect
223. C₂²⋊D₅₃	M₃₂	semidirect
259. C₂²×C₅₃	C₂×M₃₂	semidirect
271. C₂×D₅₃	C₂×M₃₂	semidirect
282. Dic₅₃	C₂×M₃₂	semidirect
291. #2168	D₅₃	semidirect
318. C₂×M₃₂	C₂×D₅₃	semidirect
322. C₂²×C₁₆	C₂×D₅₃	semidirect
338. C₄⋊C₁₆	C₂×D₅₃	semidirect
345. C₂²⋊C₁₆	C₂×D₅₃	semidirect
346. C₂²⋊C₁₆	C₂×D₅₃	semidirect
348. #346	C₂×D₅₃	semidirect
351. C₅₃	D₄×M₃₂	semidirect
491. C₁₆	D₄×D₅₃	semidirect
560. C₂²	M₃₂×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13133156	2
C₂×M₃₂×D₅₃	2
C₈×D₄×D₅₃	2
#20276545	2
#20276544	2
#20276542	2
#20276541	2
#20276539	2
C₁₆×C₂²⋊D₅₃	2
#20276532	2
#20276469	2
#20276324	2
#20276308	2
C₅₃×#2168	2
D₄×M₃₂	53