Subgroups — #27537620

Order 13568.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283683	C₂	1	1	yes	maximal, characteristic
2	#20276622	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₆×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276544	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276541	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276537	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₆×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#20276521	C₂	1	1	yes	maximal, characteristic, complemented
10	#20276519	C₂	1	1	yes	maximal, characteristic, complemented
11	#20276515	C₂	1	1	yes	maximal, characteristic, complemented
12	#20276311	C₂	1	1	yes	maximal, characteristic, complemented
13	#20276310	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₆×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811153	C₄	1	1	yes	characteristic
17	C₂×#13133157	C₂²	1	1	yes	characteristic
18	C₂×#13133156	C₂²	1	1	yes	characteristic
19	C₂²×#11719908	C₂²	1	1	yes	characteristic
20	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
21	#16810752	C₄	1	1	yes	characteristic
22	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
23	#16810698	C₄	1	1	yes	characteristic
24	#16810695	C₄	1	1	yes	characteristic
25	#16810691	C₄	1	1	yes	characteristic
26	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
27	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
28	#16810683	C₄	1	1	yes	characteristic
29	#16810681	C₄	1	1	yes	characteristic
30	#16810677	C₄	1	1	yes	characteristic
31	#16810578	C₂²	1	1	yes	characteristic
32	#16810577	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
34	C₄⋊#11719908	C₂²	1	1	yes	characteristic
35	#16810441	C₂²	1	1	yes	characteristic
36	#16810441	C₂²	1	1	yes	characteristic
37	#16810441	C₂²	1	1	yes	characteristic
38	#16810441	C₂²	1	1	yes	characteristic
39	C₂²⋊#11719908	C₂²	1	1	yes	characteristic
40	C₂²⋊#11719908	C₂²	1	1	yes	characteristic
41	#16810402	C₂²	1	1	yes	characteristic
42	#16810402	C₂²	1	1	yes	characteristic
43	#16810399	C₂²	1	1	yes	characteristic
44	#16810398	C₂²	1	1	yes	characteristic
45	#16810398	C₂²	1	1	yes	characteristic
46	#16810398	C₂²	1	1	yes	characteristic
47	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
48	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
49	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
52	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
53	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₅₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₅₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₅₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
60	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
61	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
63	#13133212	C₈	1	1	yes	characteristic
64	#13133210	C₈	1	1	yes	characteristic
65	#13133207	C₈	1	1	yes	characteristic
66	#13133203	C₈	1	1	yes	characteristic
67	#13133201	C₈	1	1	yes	characteristic
68	#13133198	C₈	1	1	yes	characteristic
69	#13133194	C₈	1	1	yes	characteristic
70	#13133189	C₈	1	1	yes	characteristic
71	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
74	#13133176	C₂×C₄	1	1	yes	characteristic
75	#13133174	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
77	#13133157	—	2	2	no	—
78	#13133156	—	2	2	no	—
79	C₂×#11719908	—	2	2	no	—
80	C₂×#11719908	C₂³	1	1	yes	characteristic
81	C₂×#11719908	C₂³	1	1	yes	characteristic
82	C₂×#11719908	C₂³	1	1	yes	characteristic
83	C₂×#11719908	C₂³	1	1	yes	characteristic
84	C₁₆×D₅₃	—	2	2	no	—
85	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
86	#13133146	C₂×C₄	1	1	yes	characteristic
87	#13133146	C₂×C₄	1	1	yes	characteristic
88	#13133146	C₂×C₄	1	1	yes	characteristic
89	#13133146	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
92	#13133129	C₂×C₄	1	1	yes	characteristic
93	#13133129	C₂×C₄	1	1	yes	characteristic
94	#13133128	C₂×C₄	1	1	yes	characteristic
95	#13133127	C₂×C₄	1	1	yes	characteristic
96	#13133127	C₂×C₄	1	1	yes	characteristic
97	#13133127	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
101	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
102	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₁₆×C₅₃	—	2	2	no	—
107	C₂×C₁₆×C₅₃	—	2	2	no	—
108	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
109	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
110	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
111	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
115	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
117	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
120	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
121	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
122	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
125	C₂×C₈×C₅₃	—	2	1	no	—
126	C₂×C₈×C₅₃	—	2	1	no	—
127	C₂×C₈×C₅₃	—	2	1	no	—
128	C₂×C₈×C₅₃	—	2	1	no	—
129	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
133	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
134	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
135	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
136	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
138	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
139	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
140	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
141	#11719921	C₂×C₈	1	1	yes	characteristic
142	#11719921	C₂×C₈	1	1	yes	characteristic
143	#11719921	C₂×C₈	1	1	yes	characteristic
144	#11719921	C₂×C₈	1	1	yes	characteristic
145	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
146	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
147	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
148	#11719919	C₂×C₈	1	1	yes	characteristic
149	#11719919	C₂×C₈	1	1	yes	characteristic
150	#11719919	C₂×C₈	1	1	yes	characteristic
151	#11719919	C₂×C₈	1	1	yes	characteristic
152	#11719919	C₂×C₈	1	1	yes	characteristic
153	#11719919	C₂×C₈	1	1	yes	characteristic
154	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
159	#11719917	—	2	2	no	—
160	C₂×#88322	—	2	2	no	—
161	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
162	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
163	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
164	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
165	#11719912	—	2	2	no	—
166	C₈×D₅₃	—	2	1	no	—
167	C₈×D₅₃	—	2	1	no	—
168	C₁₆×C₅₃	—	2	1	no	—
169	C₁₆×C₅₃	—	2	1	no	—
170	C₁₆×C₅₃	—	2	1	no	—
171	C₁₆×C₅₃	#41	1	2	yes	—
172	#11719908	—	2	1	no	—
173	#11719908	—	2	1	no	—
174	#11719908	—	2	1	no	—
175	#11719908	#41	1	2	yes	—
176	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
177	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
178	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
179	D₄×C₅₃	—	2	2	no	—
180	C₂×C₄×C₅₃	—	2	1	no	—
181	C₂×C₄×C₅₃	—	2	1	no	—
182	C₂×C₄×C₅₃	—	2	1	no	—
183	C₂×C₄×C₅₃	—	2	1	no	—
184	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
185	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
189	C₂²⋊D₅₃	—	2	2	no	—
190	C₂²⋊D₅₃	—	2	2	no	—
191	C₂×Dic₅₃	—	2	2	no	—
192	C₂×Dic₅₃	—	2	2	no	—
193	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
194	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
195	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
196	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
197	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
198	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
200	C₄×D₅₃	—	2	1	no	—
201	C₄×D₅₃	—	2	1	no	—
202	Dic₁₀₆	—	2	2	no	—
203	C₈×C₅₃	—	2	1	no	—
204	C₈×C₅₃	—	2	1	no	—
205	C₈×C₅₃	—	2	1	no	—
206	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
207	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
208	#88322	—	2	1	no	—
209	#88322	—	2	1	no	—
210	#88322	—	2	1	no	—
211	#88322	#131	1	2	yes	—
212	#33480	—	53	1	no	maximal, Sylow
213	C₂²×C₅₃	—	2	1	no	—
214	C₂²×C₅₃	—	2	1	no	—
215	C₂²×C₅₃	—	2	1	no	—
216	C₂²×C₅₃	—	2	1	no	—
217	C₂²×C₅₃	—	2	1	no	—
218	C₂²×C₅₃	#504	1	2	yes	—
219	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
220	C₂×D₅₃	—	2	1	no	—
221	C₂×D₅₃	—	2	1	no	—
222	C₂×D₅₃	—	2	1	no	—
223	C₄×C₅₃	—	2	1	no	—
224	C₄×C₅₃	—	2	1	no	—
225	C₄×C₅₃	—	2	1	no	—
226	C₄×C₅₃	—	2	1	no	—
227	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
228	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
229	Dic₅₃	—	2	1	no	—
230	Dic₅₃	—	2	1	no	—
231	Dic₅₃	—	2	1	no	—
232	Dic₅₃	—	2	1	no	—
233	Dic₅₃	—	2	1	no	—
234	Dic₅₃	—	2	1	no	—
235	Dic₅₃	#504	1	2	yes	—
236	#2966	—	53	1	no	—
237	#2183	—	53	1	no	—
238	Q₈×C₁₆	—	53	1	no	—
239	#2169	—	53	1	no	—
240	#2168	—	53	1	no	—
241	#2168	—	53	1	no	—
242	D₄×C₁₆	—	53	1	no	—
243	D₄×C₁₆	—	53	1	no	—
244	D₄×C₁₆	D₅₃	1	1	yes	characteristic, complemented
245	#2164	—	53	1	no	—
246	#2164	—	53	1	no	—
247	#2163	—	53	1	no	—
248	#2108	—	53	1	no	—
249	#2108	—	53	1	no	—
250	C₂×C₄×C₁₆	—	53	1	no	—
251	C₂×C₅₃	—	2	2	no	—
252	C₂×C₅₃	—	4	1	no	—
253	C₂×C₅₃	C₈×#41	1	1	yes	characteristic
254	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
255	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
256	D₅₃	—	4	1	no	—
257	#529	—	53	1	no	—
258	C₂×M₃₂	—	53	1	no	—
259	C₂×M₃₂	—	53	1	no	—
260	C₂²×C₁₆	—	53	1	no	—
261	C₂²×C₁₆	—	53	1	no	—
262	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
263	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
264	#446	—	53	1	no	—
265	C₈×Q₈	—	53	1	no	—
266	#436	—	53	1	no	—
267	#435	—	53	1	no	—
268	#435	—	53	1	no	—
269	C₈×D₄	—	53	1	no	—
270	C₈×D₄	—	53	1	no	—
271	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
272	#433	—	53	1	no	—
273	#433	—	53	1	no	—
274	#432	—	53	1	no	—
275	#405	—	53	1	no	—
276	#405	—	53	1	no	—
277	C₂×C₄×C₈	—	53	1	no	—
278	C₄⋊C₁₆	—	53	1	no	—
279	C₄⋊C₁₆	—	53	1	no	—
280	C₄⋊C₁₆	—	53	1	no	—
281	C₄⋊C₁₆	—	53	1	no	—
282	C₄⋊C₁₆	—	53	1	no	—
283	C₄⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic
284	C₂²⋊C₁₆	—	53	1	no	—
285	C₂²⋊C₁₆	—	53	1	no	—
286	C₂²⋊C₁₆	—	53	1	no	—
287	C₂²⋊C₁₆	—	53	1	no	—
288	C₂²⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic
289	C₂²⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic
290	#346	—	53	1	no	—
291	#346	—	53	1	no	—
292	#346	—	53	1	no	—
293	#346	—	53	1	no	—
294	C₄×C₁₆	—	53	1	no	—
295	C₄×C₁₆	—	53	1	no	—
296	C₄×C₁₆	—	53	1	no	—
297	C₄×C₁₆	—	53	1	no	—
298	C₄×C₁₆	—	53	1	no	—
299	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic
300	C₅₃	#33480	1	1	yes	characteristic, complemented, Sylow
301	C₂×M₁₆	—	53	1	no	—
302	C₂×M₁₆	—	53	1	no	—
303	C₂²×C₈	—	53	1	no	—
304	C₂²×C₈	—	53	1	no	—
305	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
307	#126	—	53	1	no	—
308	#126	—	53	1	no	—
309	#125	—	53	1	no	—
310	#124	—	53	1	no	—
311	#123	—	53	1	no	—
312	#123	—	53	1	no	—
313	C₂²⋊Q₈	—	53	1	no	—
314	#121	—	53	1	no	—
315	C₄×Q₈	—	53	1	no	—
316	C₄×D₄	—	53	1	no	—
317	C₄×D₄	—	53	1	no	—
318	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
319	#117	—	53	1	no	—
320	#117	—	53	1	no	—
321	C₂×C₄²	—	53	1	no	—
322	M₃₂	—	106	2	no	—
323	M₃₂	—	106	2	no	—
324	C₂×C₁₆	—	2	2	no	—
325	C₂×C₁₆	—	2	2	no	—
326	C₂×C₁₆	—	53	1	no	—
327	C₂×C₁₆	—	53	1	no	—
328	C₂×C₁₆	—	53	1	no	—
329	C₂×C₁₆	—	53	1	no	—
330	C₂×C₁₆	—	106	2	no	—
331	C₂×C₁₆	—	106	2	no	—
332	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
333	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
334	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
335	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
336	C₄⋊C₈	—	53	1	no	—
337	C₄⋊C₈	—	53	1	no	—
338	C₄⋊C₈	—	53	1	no	—
339	C₄⋊C₈	—	53	1	no	—
340	C₄⋊C₈	—	53	1	no	—
341	C₄⋊C₈	C₄×D₅₃	1	1	yes	characteristic
342	C₂²⋊C₈	—	53	1	no	—
343	C₂²⋊C₈	—	53	1	no	—
344	C₂²⋊C₈	—	53	1	no	—
345	C₂²⋊C₈	—	53	1	no	—
346	C₂²⋊C₈	C₄×D₅₃	1	1	yes	characteristic
347	C₂²⋊C₈	C₄×D₅₃	1	1	yes	characteristic
348	#97	—	53	1	no	—
349	#97	—	53	1	no	—
350	#97	—	53	1	no	—
351	#97	—	53	1	no	—
352	C₄×C₈	—	53	1	no	—
353	C₄×C₈	—	53	1	no	—
354	C₄×C₈	—	53	1	no	—
355	C₄×C₈	—	53	1	no	—
356	C₄×C₈	—	53	1	no	—
357	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
358	C₂×Q₈	—	53	1	no	—
359	C₂×D₄	—	53	1	no	—
360	C₂×D₄	—	53	1	no	—
361	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
362	C₂²×C₄	—	53	1	no	—
363	C₂²×C₄	—	53	1	no	—
364	C₂²×C₄	—	53	1	no	—
365	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
367	M₁₆	—	106	2	no	—
368	M₁₆	—	106	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	53	1	no	—
374	C₂×C₈	—	53	1	no	—
375	C₂×C₈	—	53	1	no	—
376	C₂×C₈	—	53	1	no	—
377	C₂×C₈	—	106	2	no	—
378	C₂×C₈	—	106	1	no	—
379	C₂×C₈	—	106	1	no	—
380	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
381	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
382	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
383	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
384	C₄⋊C₄	—	53	1	no	—
385	C₄⋊C₄	—	53	1	no	—
386	C₄⋊C₄	—	53	1	no	—
387	C₄⋊C₄	—	53	1	no	—
388	C₄⋊C₄	—	53	1	no	—
389	C₄⋊C₄	—	53	1	no	—
390	C₄⋊C₄	—	53	1	no	—
391	C₄⋊C₄	—	53	1	no	—
392	C₄⋊C₄	—	53	1	no	—
393	C₄⋊C₄	C₈×D₅₃	1	1	yes	characteristic
394	C₂²⋊C₄	—	53	1	no	—
395	C₂²⋊C₄	—	53	1	no	—
396	C₂²⋊C₄	—	53	1	no	—
397	C₂²⋊C₄	—	53	1	no	—
398	C₂²⋊C₄	—	53	1	no	—
399	C₂²⋊C₄	—	53	1	no	—
400	C₂²⋊C₄	—	53	1	no	—
401	C₂²⋊C₄	—	53	1	no	—
402	C₂²⋊C₄	C₈×D₅₃	1	1	yes	characteristic
403	C₂²⋊C₄	C₈×D₅₃	1	1	yes	characteristic
404	C₄²	—	53	1	no	—
405	C₄²	—	53	1	no	—
406	C₄²	—	53	1	no	—
407	C₄²	—	53	1	no	—
408	C₄²	—	53	1	no	—
409	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
410	C₁₆	—	2	1	no	—
411	C₁₆	—	2	1	no	—
412	C₁₆	—	2	1	no	—
413	C₁₆	—	53	2	no	—
414	C₁₆	—	106	1	no	—
415	C₁₆	—	106	1	no	—
416	C₁₆	—	106	1	no	—
417	C₁₆	#11719947	1	2	yes	—
418	C₂³	—	53	1	no	—
419	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
420	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
421	Q₈	—	106	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	106	2	no	—
424	D₄	—	106	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	53	1	no	—
431	C₂×C₄	—	53	1	no	—
432	C₂×C₄	—	53	1	no	—
433	C₂×C₄	—	53	1	no	—
434	C₂×C₄	—	53	1	no	—
435	C₂×C₄	—	53	1	no	—
436	C₂×C₄	—	106	2	no	—
437	C₂×C₄	—	106	2	no	—
438	C₂×C₄	—	106	1	no	—
439	C₂×C₄	—	106	1	no	—
440	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
441	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
442	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
443	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	53	2	no	—
449	C₈	—	106	1	no	—
450	C₈	—	106	1	no	—
451	C₈	—	106	1	no	—
452	C₈	#41×D₅₃	1	1	yes	characteristic
453	C₈	C₂×#11719947	1	1	yes	characteristic
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	106	1	no	—
460	C₂²	—	106	1	no	—
461	C₂²	—	106	1	no	—
462	C₂²	#16811039	1	2	yes	—
463	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	53	2	no	—
469	C₄	—	106	1	no	—
470	C₄	—	106	1	no	—
471	C₄	—	106	1	no	—
472	C₄	—	106	1	no	—
473	C₄	—	106	1	no	—
474	C₄	—	106	1	no	—
475	C₄	C₄×#11719947	1	1	yes	characteristic
476	C₄	#131×D₅₃	1	1	yes	characteristic
477	C₂	—	2	2	no	—
478	C₂	—	4	1	no	—
479	C₂	—	212	1	no	—
480	C₂	C₈×#11719947	1	1	yes	characteristic
481	C₂	#504×D₅₃	1	1	yes	characteristic
482	C₂	C₂×#16811039	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₅₃
commutator, socle	C₂²×C₅₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	D₄×C₁₆×C₅₃	C₂
prime radical	#13133189	C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	D₄×C₁₆	D₅₃
hypocenter	C₅₃	#33480
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₁₆ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #20276622	C₂	semidirect
3. C₁₆×Dic₁₀₆	C₂	semidirect
4. #20276544	C₂	semidirect
5. #20276541	C₂	semidirect
6. #20276537	C₂	semidirect
7. C₁₆×C₂²⋊D₅₃	C₂	semidirect
8. C₁₆×C₂²⋊D₅₃	C₂	semidirect
9. #20276521	C₂	semidirect
10. #20276519	C₂	semidirect
11. #20276515	C₂	semidirect
12. #20276311	C₂	semidirect
13. #20276310	C₂	semidirect
14. C₂×C₁₆×Dic₅₃	C₂	semidirect
15. D₄×C₁₆×C₅₃	C₂	semidirect
244. D₄×C₁₆	D₅₃	semidirect
300. C₅₃	#33480	semidirect

Maximal subgroups

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

subgroup	index
#20283683	2
#20276622	2
C₁₆×Dic₁₀₆	2
#20276544	2
#20276541	2
#20276537	2
C₁₆×C₂²⋊D₅₃	2
#20276521	2
#20276519	2
#20276515	2
#20276311	2
#20276310	2
C₂×C₁₆×Dic₅₃	2
D₄×C₁₆×C₅₃	2
#33480	53