Subgroups — #27290047

Order 13568.

1006 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#16810378	C₂	1	1	yes	maximal, characteristic
4	C₂×#16810377	C₂	1	1	yes	maximal, characteristic
5	C₂×#16810377	C₂	1	1	yes	maximal, characteristic
6	C₂×#16810377	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅₃×#336	C₂	1	1	yes	maximal, characteristic
8	C₂³×#88322	C₂²	1	1	yes	characteristic
9	C₂³×#88322	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₅₃	C₄	1	2	yes	—
11	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₅₃	—	2	2	no	—
14	C₂×C₈×Dic₅₃	—	2	2	no	—
15	C₂×C₈×Dic₅₃	—	2	2	no	—
16	C₄×C₄⋊Dic₅₃	—	2	2	no	—
17	C₄×C₄⋊Dic₅₃	—	2	2	no	—
18	C₂×#13133124	C₄	1	2	yes	—
19	#16810378	C₄	1	4	yes	complemented
20	#16810377	—	2	2	no	—
21	#16810377	—	2	2	no	—
22	#16810377	—	2	2	no	—
23	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#336	C₄	1	4	yes	complemented
27	C₂³×Dic₅₃	C₂×C₄	1	2	yes	—
28	C₂³×Dic₅₃	C₂×C₄	1	2	yes	—
29	C₂²×#88322	—	2	1	no	—
30	C₂²×#88322	—	2	1	no	—
31	C₂²×#88322	—	2	1	no	—
32	C₂²×#88322	—	2	1	no	—
33	C₂²×#88322	—	2	1	no	—
34	C₂²×#88322	—	2	1	no	—
35	C₂²×#88322	—	2	1	no	—
36	C₂²×#88322	—	2	1	no	—
37	C₂²×#88322	—	2	1	no	—
38	C₂²×#88322	—	2	1	no	—
39	C₂²×#88322	C₂×C₄	1	2	yes	—
40	C₂²×#88322	C₂×C₄	1	2	yes	—
41	C₂²×#88322	D₄	1	2	yes	—
42	C₂²×#88322	Q₈	1	2	yes	—
43	C₂×C₄⋊Dic₅₃	—	2	4	no	—
44	C₂×C₄⋊Dic₅₃	—	2	4	no	—
45	C₂×C₄⋊Dic₅₃	C₈	1	8	yes	complemented
46	C₂×C₄×Dic₅₃	—	2	1	no	—
47	C₂×C₄×Dic₅₃	—	2	1	no	—
48	C₂×C₄×Dic₅₃	—	2	1	no	—
49	C₂×C₄×Dic₅₃	—	2	1	no	—
50	C₂×C₄×Dic₅₃	—	2	1	no	—
51	C₂×C₄×Dic₅₃	—	2	1	no	—
52	C₂×C₄×Dic₅₃	—	2	1	no	—
53	C₂×C₄×Dic₅₃	—	2	1	no	—
54	C₂×C₄×Dic₅₃	—	2	1	no	—
55	C₂×C₄×Dic₅₃	—	2	1	no	—
56	C₂×C₄×Dic₅₃	D₄	1	2	yes	—
57	C₂×C₄×Dic₅₃	D₄	1	2	yes	—
58	C₈×Dic₅₃	—	2	8	no	—
59	#13133124	—	2	4	no	—
60	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₅₃	—	2	1	no	—
64	C₂²×C₈×C₅₃	—	2	1	no	—
65	C₂²×C₈×C₅₃	—	2	1	no	—
66	C₂²×C₈×C₅₃	—	2	1	no	—
67	C₂²×C₈×C₅₃	—	2	1	no	—
68	C₂²×C₈×C₅₃	—	2	1	no	—
69	C₂²×C₈×C₅₃	—	2	1	no	—
70	C₂²×C₈×C₅₃	—	2	1	no	—
71	C₂²×C₈×C₅₃	—	2	1	no	—
72	C₂²×C₈×C₅₃	—	2	1	no	—
73	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
74	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
75	C₂²×C₈×C₅₃	D₄	1	2	yes	—
76	C₂²×C₈×C₅₃	Q₈	1	2	yes	—
77	C₂×C₄²×C₅₃	—	2	1	no	—
78	C₂×C₄²×C₅₃	—	2	1	no	—
79	C₂×C₄²×C₅₃	—	2	1	no	—
80	C₂×C₄²×C₅₃	—	2	1	no	—
81	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
83	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	—	2	1	no	—
85	C₂²×C₄×C₅₃	—	2	1	no	—
86	C₂²×C₄×C₅₃	—	2	2	no	—
87	C₂²×C₄×C₅₃	—	2	1	no	—
88	C₂²×C₄×C₅₃	—	2	1	no	—
89	C₂²×C₄×C₅₃	—	2	2	no	—
90	C₂²×C₄×C₅₃	—	2	2	no	—
91	C₂²×C₄×C₅₃	C₄²	1	2	yes	—
92	C₂²×C₄×C₅₃	C₄²	1	2	yes	—
93	C₂²×C₄×C₅₃	C₂×C₈	1	4	yes	—
94	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	#41	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	1	yes	characteristic
108	C₂²×Dic₅₃	—	2	2	no	—
109	C₂²×Dic₅₃	—	2	2	no	—
110	C₂²×Dic₅₃	—	2	2	no	—
111	C₂²×Dic₅₃	—	2	2	no	—
112	C₂²×Dic₅₃	—	2	2	no	—
113	C₂²×Dic₅₃	—	2	2	no	—
114	C₂²×Dic₅₃	—	2	2	no	—
115	C₂²×Dic₅₃	—	2	2	no	—
116	C₂²×Dic₅₃	—	2	2	no	—
117	C₂²×Dic₅₃	—	2	2	no	—
118	C₂²×Dic₅₃	C₂²⋊C₄	1	4	yes	—
119	C₂²×Dic₅₃	C₂×C₈	1	4	yes	—
120	C₂²×Dic₅₃	C₂×C₈	1	4	yes	—
121	C₂²×Dic₅₃	M₁₆	1	4	yes	—
122	C₂×C₈×C₅₃	—	2	2	no	—
123	C₂×C₈×C₅₃	—	2	2	no	—
124	C₂×C₈×C₅₃	—	2	2	no	—
125	C₂×C₈×C₅₃	—	2	2	no	—
126	C₂×C₈×C₅₃	—	2	2	no	—
127	C₂×C₈×C₅₃	—	2	2	no	—
128	C₂×C₈×C₅₃	—	2	2	no	—
129	C₂×C₈×C₅₃	—	2	2	no	—
130	C₂×C₈×C₅₃	—	2	2	no	—
131	C₂×C₈×C₅₃	—	4	1	no	—
132	C₂×C₈×C₅₃	—	4	1	no	—
133	C₂×C₈×C₅₃	—	4	1	no	—
134	C₂×C₈×C₅₃	—	4	1	no	—
135	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	complemented
136	C₄²×C₅₃	—	2	2	no	—
137	C₄²×C₅₃	—	2	2	no	—
138	C₄²×C₅₃	—	2	2	no	—
139	C₄²×C₅₃	—	2	2	no	—
140	C₄⋊Dic₅₃	—	2	16	no	—
141	C₄×Dic₅₃	—	2	2	no	—
142	C₄×Dic₅₃	—	2	2	no	—
143	C₄×Dic₅₃	—	2	2	no	—
144	C₄×Dic₅₃	—	2	2	no	—
145	C₄×Dic₅₃	—	4	1	no	—
146	C₄×Dic₅₃	—	4	1	no	—
147	C₄×Dic₅₃	—	4	1	no	—
148	C₄×Dic₅₃	—	4	1	no	—
149	C₂×#88322	—	2	2	no	—
150	C₂×#88322	—	2	2	no	—
151	C₂×#88322	—	2	2	no	—
152	C₂×#88322	—	2	2	no	—
153	C₂×#88322	—	2	2	no	—
154	C₂×#88322	—	2	2	no	—
155	C₂×#88322	—	2	2	no	—
156	C₂×#88322	—	2	2	no	—
157	C₂×#88322	—	2	2	no	—
158	C₂×#88322	—	4	1	no	—
159	C₂×#88322	—	4	1	no	—
160	C₂×#88322	—	4	1	no	—
161	C₂×#88322	—	4	1	no	—
162	C₂×#88322	C₄⋊C₄	1	4	yes	complemented
163	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
164	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂³×C₅₃	#117	1	1	yes	characteristic
166	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
167	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
168	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
169	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
170	C₂³×C₅₃	C₂²×C₈	1	2	yes	—
171	C₂³×C₅₃	C₂×M₁₆	1	2	yes	—
172	C₂³×C₅₃	#131	1	2	yes	—
173	C₂³×C₅₃	#131	1	2	yes	—
174	C₂×C₄×C₅₃	—	2	2	no	—
175	C₂×C₄×C₅₃	—	2	2	no	—
176	C₂×C₄×C₅₃	—	2	4	no	—
177	C₂×C₄×C₅₃	—	2	4	no	—
178	C₂×C₄×C₅₃	—	2	2	no	—
179	C₂×C₄×C₅₃	—	2	2	no	—
180	C₂×C₄×C₅₃	—	2	2	no	—
181	C₂×C₄×C₅₃	—	4	2	no	—
182	C₂×C₄×C₅₃	—	4	2	no	—
183	C₂×C₄×C₅₃	C₄×C₈	1	4	yes	complemented
184	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
187	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
188	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
197	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
198	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
199	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
204	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
205	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
206	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
207	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
208	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
209	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
210	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
211	C₂×C₄×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
212	C₂×Dic₅₃	—	2	4	no	—
213	C₂×Dic₅₃	—	2	4	no	—
214	C₂×Dic₅₃	—	2	4	no	—
215	C₂×Dic₅₃	—	2	4	no	—
216	C₂×Dic₅₃	—	2	4	no	—
217	C₂×Dic₅₃	—	2	4	no	—
218	C₂×Dic₅₃	—	2	4	no	—
219	C₂×Dic₅₃	—	2	4	no	—
220	C₂×Dic₅₃	—	2	4	no	—
221	C₂×Dic₅₃	—	4	2	no	—
222	C₂×Dic₅₃	—	4	2	no	—
223	C₂×Dic₅₃	—	4	2	no	—
224	C₂×Dic₅₃	—	4	2	no	—
225	C₂×Dic₅₃	C₂²⋊C₈	1	8	yes	—
226	C₈×C₅₃	—	2	4	no	—
227	C₈×C₅₃	—	4	2	no	—
228	#88322	—	2	4	no	—
229	#88322	—	4	2	no	—
230	#10874	—	53	1	no	maximal, Sylow
231	C₂²×C₅₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
232	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
233	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
234	C₂²×C₅₃	#386	1	1	yes	characteristic
235	C₂²×C₅₃	#387	1	1	yes	characteristic
236	C₂²×C₅₃	#387	1	1	yes	characteristic
237	C₂²×C₅₃	#391	1	1	yes	characteristic
238	C₂²×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
239	C₂²×C₅₃	C₄×M₁₆	1	1	yes	characteristic
240	C₂²×C₅₃	#405	1	1	yes	characteristic
241	C₂²×C₅₃	#405	1	1	yes	characteristic
242	C₂²×C₅₃	C₂×C₂²⋊C₈	1	2	yes	—
243	C₂²×C₅₃	#408	1	2	yes	—
244	C₂²×C₅₃	#431	1	2	yes	—
245	C₂²×C₅₃	#433	1	2	yes	—
246	C₂²×C₅₃	C₈×D₄	1	2	yes	—
247	C₂²×C₅₃	C₈×D₄	1	2	yes	—
248	C₂²×C₅₃	#435	1	2	yes	—
249	C₂²×C₅₃	#435	1	2	yes	—
250	C₂²×C₅₃	C₈×Q₈	1	2	yes	—
251	C₂²×C₅₃	C₈×Q₈	1	2	yes	—
252	C₂²×C₅₃	#446	1	2	yes	—
253	C₂²×C₅₃	#446	1	2	yes	—
254	C₄×C₅₃	—	2	4	no	—
255	C₄×C₅₃	—	4	2	no	—
256	C₄×C₅₃	#385	1	1	yes	characteristic
257	C₄×C₅₃	#385	1	1	yes	characteristic
258	C₄×C₅₃	#387	1	1	yes	characteristic
259	C₄×C₅₃	#387	1	1	yes	characteristic
260	C₄×C₅₃	#388	1	1	yes	characteristic
261	C₄×C₅₃	#388	1	1	yes	characteristic
262	C₄×C₅₃	#389	1	1	yes	characteristic
263	C₄×C₅₃	#389	1	1	yes	characteristic
264	Dic₅₃	—	2	8	no	—
265	Dic₅₃	—	4	4	no	—
266	C₂²×C₄×C₈	—	53	1	no	—
267	C₂×C₄×C₄⋊C₄	—	53	1	no	—
268	C₂×#336	—	53	1	no	—
269	C₂×#336	—	53	1	no	—
270	C₂×#336	—	53	1	no	—
271	C₂×#336	—	53	1	no	—
272	C₂×#336	D₅₃	1	1	yes	characteristic
273	C₂×C₅₃	#1436	1	1	yes	characteristic
274	C₂×C₅₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
275	C₂×C₅₃	#1750	1	1	yes	characteristic
276	C₂×C₅₃	C₈×C₄⋊C₄	1	1	yes	characteristic
277	C₂×C₅₃	C₈×C₄⋊C₄	1	1	yes	characteristic
278	C₂×C₅₃	#1771	1	1	yes	characteristic
279	C₂×C₅₃	#1771	1	1	yes	characteristic
280	C₂×C₅₃	#1869	1	2	yes	—
281	C₂×C₅₃	#1916	1	2	yes	—
282	C₂×C₅₃	#1916	1	2	yes	—
283	C₂×C₅₃	#1984	1	2	yes	—
284	C₂³×C₈	—	53	1	no	—
285	C₂³×C₈	—	53	1	no	—
286	C₂³×C₈	C₂×D₅₃	1	1	yes	characteristic
287	C₂³×C₈	C₂×D₅₃	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	—	53	2	no	—
289	C₂²×C₄²	—	53	1	no	—
290	C₂²×C₄²	—	53	1	no	—
291	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
292	C₂×C₄×C₈	—	106	2	no	—
293	C₂×C₄×C₈	—	106	2	no	—
294	C₂×C₄×C₈	—	106	2	no	—
295	C₄×C₄⋊C₄	—	106	2	no	—
296	C₄×C₄⋊C₄	—	106	2	no	—
297	C₂×#95	—	53	2	no	—
298	#336	—	53	4	no	—
299	#336	—	106	2	no	—
300	#336	—	106	2	no	—
301	#336	—	106	2	no	—
302	#336	Dic₅₃	1	4	yes	complemented
303	C₅₃	#10874	1	1	yes	characteristic, complemented, Sylow
304	C₂³×C₄	—	53	2	no	—
305	C₂³×C₄	—	53	2	no	—
306	C₂³×C₄	C₄×D₅₃	1	1	yes	characteristic
307	C₂³×C₄	C₄×D₅₃	1	1	yes	characteristic
308	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₂²×C₈	—	2	1	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	—	2	1	no	—
319	C₂²×C₈	—	53	2	no	—
320	C₂²×C₈	—	53	2	no	—
321	C₂²×C₈	—	53	2	no	—
322	C₂²×C₈	—	53	2	no	—
323	C₂²×C₈	—	106	1	no	—
324	C₂²×C₈	—	106	1	no	—
325	C₂²×C₈	—	106	1	no	—
326	C₂²×C₈	—	106	1	no	—
327	C₂²×C₈	—	106	1	no	—
328	C₂²×C₈	—	106	1	no	—
329	C₂²×C₈	—	106	1	no	—
330	C₂²×C₈	—	106	1	no	—
331	C₂²×C₈	—	106	1	no	—
332	C₂²×C₈	—	106	1	no	—
333	C₂²×C₈	Dic₁₀₆	1	2	yes	—
334	C₂²×C₈	D₂₁₂	1	2	yes	—
335	C₂²×C₈	C₂×Dic₅₃	1	2	yes	—
336	C₂²×C₈	C₂×Dic₅₃	1	2	yes	—
337	C₂×C₄⋊C₄	—	53	8	no	—
338	C₂×C₄⋊C₄	—	106	4	no	—
339	C₂×C₄⋊C₄	—	106	4	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	—	53	2	no	—
345	C₂×C₄²	—	53	2	no	—
346	C₂×C₄²	—	106	1	no	—
347	C₂×C₄²	—	106	1	no	—
348	C₂×C₄²	—	106	1	no	—
349	C₂×C₄²	—	106	1	no	—
350	C₂×C₄²	—	106	1	no	—
351	C₂×C₄²	—	106	1	no	—
352	C₂×C₄²	—	106	1	no	—
353	C₂×C₄²	—	106	1	no	—
354	C₂×C₄²	—	106	1	no	—
355	C₂×C₄²	—	106	1	no	—
356	C₂×C₄²	C₄×D₅₃	1	2	yes	—
357	C₂×C₄²	C₂×Dic₅₃	1	2	yes	—
358	C₄×C₈	—	106	8	no	—
359	#95	—	106	4	no	—
360	C₂⁴	C₂×C₄×D₅₃	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	53	4	no	—
369	C₂²×C₄	—	53	4	no	—
370	C₂²×C₄	—	53	4	no	—
371	C₂²×C₄	—	53	4	no	—
372	C₂²×C₄	—	106	2	no	—
373	C₂²×C₄	—	106	2	no	—
374	C₂²×C₄	—	106	2	no	—
375	C₂²×C₄	—	106	2	no	—
376	C₂²×C₄	—	106	2	no	—
377	C₂²×C₄	—	106	2	no	—
378	C₂²×C₄	—	106	2	no	—
379	C₂²×C₄	—	106	2	no	—
380	C₂²×C₄	—	106	2	no	—
381	C₂²×C₄	—	106	2	no	—
382	C₂²×C₄	C₈×D₅₃	1	4	yes	—
383	C₂²×C₄	C₄×Dic₅₃	1	2	yes	—
384	C₂²×C₄	C₄×Dic₅₃	1	2	yes	—
385	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
388	C₂²×C₄	#11719945	1	1	yes	characteristic
389	C₂²×C₄	#11719945	1	1	yes	characteristic
390	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
391	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
392	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
393	C₂²×C₄	#11719947	1	1	yes	characteristic
394	C₂²×C₄	#11719947	1	1	yes	characteristic
395	C₂²×C₄	#11719947	1	1	yes	characteristic
396	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
397	C₂²×C₄	#11719949	1	1	yes	characteristic
398	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	4	1	no	—
409	C₂×C₈	—	4	1	no	—
410	C₂×C₈	—	4	1	no	—
411	C₂×C₈	—	4	1	no	—
412	C₂×C₈	—	53	4	no	—
413	C₂×C₈	—	106	2	no	—
414	C₂×C₈	—	106	2	no	—
415	C₂×C₈	—	106	2	no	—
416	C₂×C₈	—	106	2	no	—
417	C₂×C₈	—	106	2	no	—
418	C₂×C₈	—	106	2	no	—
419	C₂×C₈	—	106	2	no	—
420	C₂×C₈	—	106	2	no	—
421	C₂×C₈	—	106	2	no	—
422	C₂×C₈	—	212	1	no	—
423	C₂×C₈	—	212	1	no	—
424	C₂×C₈	—	212	1	no	—
425	C₂×C₈	—	212	1	no	—
426	C₂×C₈	C₄⋊Dic₅₃	1	4	yes	complemented
427	C₄⋊C₄	—	106	16	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	106	2	no	—
433	C₄²	—	106	2	no	—
434	C₄²	—	106	2	no	—
435	C₄²	—	106	2	no	—
436	C₄²	—	212	1	no	—
437	C₄²	—	212	1	no	—
438	C₄²	—	212	1	no	—
439	C₄²	—	212	1	no	—
440	C₂³	C₂×C₄×Dic₅₃	1	1	yes	characteristic
441	C₂³	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
442	C₂³	#13133173	1	1	yes	characteristic
443	C₂³	#13133179	1	1	yes	characteristic
444	C₂³	C₄×D₂₁₂	1	1	yes	characteristic
445	C₂³	#13133182	1	1	yes	characteristic
446	C₂³	C₄×Dic₁₀₆	1	1	yes	characteristic
447	C₂³	C₂×C₈×D₅₃	1	2	yes	—
448	C₂³	M₁₆×D₅₃	1	2	yes	—
449	C₂³	#13133223	1	2	yes	—
450	C₂³	#13133225	1	2	yes	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	53	8	no	—
461	C₂×C₄	—	106	4	no	—
462	C₂×C₄	—	106	4	no	—
463	C₂×C₄	—	106	4	no	—
464	C₂×C₄	—	106	4	no	—
465	C₂×C₄	—	106	4	no	—
466	C₂×C₄	—	106	4	no	—
467	C₂×C₄	—	106	4	no	—
468	C₂×C₄	—	106	4	no	—
469	C₂×C₄	—	106	4	no	—
470	C₂×C₄	—	212	2	no	—
471	C₂×C₄	—	212	2	no	—
472	C₂×C₄	—	212	2	no	—
473	C₂×C₄	—	212	2	no	—
474	C₂×C₄	C₈×Dic₅₃	1	4	yes	complemented
475	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
476	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
477	C₂×C₄	#13133175	1	1	yes	characteristic
478	C₂×C₄	#13133176	1	1	yes	characteristic
479	C₂×C₄	#13133177	1	1	yes	characteristic
480	C₂×C₄	#13133177	1	1	yes	characteristic
481	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
482	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
483	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
484	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
485	C₂×C₄	C₄×Dic₁₀₆	1	1	yes	characteristic
486	C₂×C₄	Q₈×Dic₅₃	1	1	yes	characteristic
487	C₂×C₄	#13133187	1	1	yes	characteristic
488	C₂×C₄	#13133190	1	1	yes	characteristic
489	C₂×C₄	#13133192	1	1	yes	characteristic
490	C₂×C₄	#13133194	1	1	yes	characteristic
491	C₂×C₄	#13133194	1	1	yes	characteristic
492	C₂×C₄	#13133195	1	1	yes	characteristic
493	C₂×C₄	#13133197	1	1	yes	characteristic
494	C₂×C₄	#13133199	1	1	yes	characteristic
495	C₂×C₄	#13133201	1	1	yes	characteristic
496	C₂×C₄	#13133202	1	1	yes	characteristic
497	C₂×C₄	#13133203	1	1	yes	characteristic
498	C₂×C₄	#13133207	1	1	yes	characteristic
499	C₂×C₄	#13133208	1	1	yes	characteristic
500	C₂×C₄	#13133210	1	1	yes	characteristic
501	C₂×C₄	#13133212	1	1	yes	characteristic
502	C₂×C₄	#13133216	1	1	yes	characteristic
503	C₈	—	2	4	no	—
504	C₈	—	4	2	no	—
505	C₈	—	106	4	no	—
506	C₈	—	212	2	no	—
507	C₂²	C₂²⋊C₄×Dic₅₃	1	1	yes	characteristic
508	C₂²	C₄×C₄⋊Dic₅₃	1	1	yes	characteristic
509	C₂²	C₄⋊C₄×Dic₅₃	1	1	yes	characteristic
510	C₂²	#16810501	1	1	yes	characteristic
511	C₂²	#16810506	1	1	yes	characteristic
512	C₂²	#16810508	1	1	yes	characteristic
513	C₂²	#16810527	1	1	yes	characteristic
514	C₂²	C₂×C₈×Dic₅₃	1	1	yes	characteristic
515	C₂²	M₁₆×Dic₅₃	1	1	yes	characteristic
516	C₂²	#16810578	1	1	yes	characteristic
517	C₂²	#16810581	1	1	yes	characteristic
518	C₂²	C₂²⋊C₈×D₅₃	1	2	yes	—
519	C₂²	#16810588	1	2	yes	—
520	C₂²	#16810673	1	2	yes	—
521	C₂²	#16810681	1	2	yes	—
522	C₂²	#16810688	1	2	yes	—
523	C₂²	C₈×D₂₁₂	1	2	yes	—
524	C₂²	#16810693	1	2	yes	—
525	C₂²	#16810696	1	2	yes	—
526	C₂²	#16810747	1	2	yes	—
527	C₂²	C₈×Dic₁₀₆	1	2	yes	—
528	C₂²	#16810751	1	2	yes	—
529	C₂²	#16810752	1	2	yes	—
530	C₄	—	2	4	no	—
531	C₄	—	4	2	no	—
532	C₄	—	106	8	no	—
533	C₄	—	212	4	no	—
534	C₄	#16810497	1	1	yes	characteristic
535	C₄	#16810498	1	1	yes	characteristic
536	C₄	#16810509	1	1	yes	characteristic
537	C₄	#16810510	1	1	yes	characteristic
538	C₄	#16810515	1	1	yes	characteristic
539	C₄	#16810516	1	1	yes	characteristic
540	C₄	#16810520	1	1	yes	characteristic
541	C₄	#16810522	1	1	yes	characteristic
542	C₂	#20272949	1	1	yes	characteristic
543	C₂	C₂²⋊C₈×Dic₅₃	1	1	yes	characteristic
544	C₂	#20274483	1	1	yes	characteristic
545	C₂	C₈×C₄⋊Dic₅₃	1	1	yes	characteristic
546	C₂	#20274580	1	1	yes	characteristic
547	C₂	#20274587	1	1	yes	characteristic
548	C₂	#20274592	1	1	yes	characteristic
549	C₂	#20275006	1	2	yes	—
550	C₂	#20275271	1	2	yes	—
551	C₂	#20275273	1	2	yes	—
552	C₂	#20275649	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₅₃
commutator	C₂²×C₅₃	C₂×C₄×C₈
Fitting	C₂×C₅₃×#336	C₂
socle, prime radical	C₂⁴×C₅₃	C₂²×C₄
cosocle	C₂³×C₄×C₅₃	C₂³
hypercenter	C₂×#336	D₅₃
hypocenter	C₅₃	#10874
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
19. #16810378	C₄	semidirect
26. C₅₃×#336	C₄	semidirect
45. C₂×C₄⋊Dic₅₃	C₈	semidirect
135. C₂×C₈×C₅₃	C₄⋊C₄	semidirect
162. C₂×#88322	C₄⋊C₄	semidirect
183. C₂×C₄×C₅₃	C₄×C₈	semidirect
302. #336	Dic₅₃	semidirect
303. C₅₃	#10874	semidirect
426. C₂×C₈	C₄⋊Dic₅₃	semidirect
474. C₂×C₄	C₈×Dic₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₅₃	2
C₂×C₄×C₄⋊Dic₅₃	2
C₂×#16810378	2
C₂×#16810377	2
C₂×C₅₃×#336	2
#10874	53