Subgroups — #28318466

Order 13568.

990 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#432	C₂	1	1	yes	maximal, characteristic
2	#20291162	C₂	1	1	yes	maximal, characteristic
3	#20290509	C₂	1	2	yes	maximal, complemented
4	C₈×C₄⋊#6157	C₂	1	2	yes	maximal, complemented
5	#20290451	C₂	1	2	yes	maximal
6	C₈×C₂²⋊#6157	C₂	1	2	yes	maximal
7	#20290433	C₂	1	2	yes	maximal, complemented
8	#20290371	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
10	#16811646	C₄	1	2	yes	complemented
11	#16811645	C₄	1	2	yes	complemented
12	#16811644	C₄	1	2	yes	complemented
13	#16811643	C₄	1	2	yes	complemented
14	D₅₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
15	D₅₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
16	#16811582	C₂²	1	2	yes	—
17	C₂×#13133271	C₂²	1	4	yes	—
18	C₂×C₈×#6157	C₂²	1	4	yes	—
19	#16811568	C₄	1	2	yes	—
20	#16811567	C₄	1	2	yes	—
21	#16811566	C₄	1	2	yes	—
22	#16811565	C₄	1	2	yes	—
23	C₄×C₄⋊#6157	C₂²	1	2	yes	—
24	C₄×C₂²⋊#6157	C₂²	1	2	yes	—
25	#16811559	C₂²	1	2	yes	—
26	(C₂×#6157)⋊C₈	C₂²	1	4	yes	—
27	(C₂×#6157)⋊C₈	C₂²	1	4	yes	—
28	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×#88322	C₄	1	1	yes	characteristic, complemented
32	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic, complemented
33	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic, complemented
34	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic, complemented
35	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic, complemented
36	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic, complemented
37	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic, complemented
38	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
39	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₅₃	C₄	1	1	yes	characteristic, complemented
43	C₂×D₅₃⋊C₈	C₂³	1	4	yes	—
44	C₂×C₄⋊#6157	C₂×C₄	1	4	yes	—
45	C₂×C₂²⋊#6157	C₂×C₄	1	4	yes	—
46	C₂×C₄×#6157	C₂³	1	4	yes	—
47	#13133284	C₂×C₄	1	4	yes	—
48	C₄⋊#88324	C₂×C₄	1	4	yes	—
49	#13133274	C₂×C₄	1	4	yes	—
50	C₂²⋊#88324	C₂×C₄	1	4	yes	—
51	#13133272	C₂×C₄	1	4	yes	—
52	#13133272	C₂×C₄	1	4	yes	—
53	#13133271	—	2	8	no	—
54	C₈×#6157	—	2	8	no	—
55	(C₂×#6157)⋊C₄	C₂×C₄	1	4	yes	—
56	(C₂×#6157)⋊C₄	C₂×C₄	1	4	yes	—
57	(C₂×#6157)⋊C₄	C₂×C₄	1	4	yes	—
58	(C₂×#6157)⋊C₄	C₂×C₄	1	4	yes	—
59	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
62	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
63	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅₃	—	2	4	no	—
65	C₂×C₈×D₅₃	—	2	4	no	—
66	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
73	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
79	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
80	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₅₃	C₂³	1	1	yes	characteristic
84	C₄²×D₅₃	C₂³	1	1	yes	characteristic
85	C₄×#88322	C₂×C₄	1	1	yes	characteristic
86	C₄×#88322	C₂×C₄	1	1	yes	characteristic
87	C₄×#88322	C₂×C₄	1	1	yes	characteristic
88	C₄×#88322	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
90	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
101	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
104	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×#6157	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
108	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
110	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
111	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₅₃	—	2	4	no	—
113	C₂×C₄×D₅₃	—	2	4	no	—
114	C₂×C₄×D₅₃	—	2	2	no	—
115	C₂×C₄×D₅₃	—	2	2	no	—
116	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
117	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
118	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
119	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
120	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
128	C₂²⋊#6157	—	2	8	no	—
129	C₂×#88324	C₂²×C₄	1	8	yes	—
130	C₄⋊#6157	—	2	8	no	—
131	C₄×#6157	—	2	4	no	—
132	C₄×#6157	—	2	4	no	—
133	D₅₃⋊C₈	—	2	4	no	—
134	D₅₃⋊C₈	—	2	4	no	—
135	C₂×C₈×C₅₃	—	2	2	no	—
136	C₂×C₈×C₅₃	—	2	2	no	—
137	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₅₃	C₄²	1	1	yes	characteristic
142	C₄²×C₅₃	C₄²	1	1	yes	characteristic
143	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
146	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
147	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
148	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
149	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
150	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
151	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×#88322	—	2	2	no	—
158	C₂×#88322	—	2	2	no	—
159	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
160	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
161	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
162	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
163	C₈×D₅₃	—	2	2	no	—
164	C₈×D₅₃	—	2	2	no	—
165	C₈×D₅₃	—	2	2	no	—
166	C₈×D₅₃	—	2	2	no	—
167	C₈×D₅₃	—	2	2	no	—
168	C₈×D₅₃	—	2	2	no	—
169	C₈×D₅₃	#41	1	4	yes	—
170	C₈×D₅₃	#41	1	4	yes	—
171	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
172	C₂²×D₅₃	—	2	2	no	—
173	C₂²×D₅₃	—	2	2	no	—
174	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
175	C₂²×D₅₃	#131	1	4	yes	—
176	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×#6157	—	2	8	no	—
178	C₂×#6157	—	2	8	no	—
179	C₂×#6157	—	2	8	no	—
180	C₂×C₄×C₅₃	—	2	2	no	—
181	C₂×C₄×C₅₃	—	2	1	no	—
182	C₂×C₄×C₅₃	—	2	1	no	—
183	C₂×C₄×C₅₃	—	2	2	no	—
184	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
186	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
187	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
190	C₂×Dic₅₃	—	2	2	no	—
191	C₂×Dic₅₃	—	2	2	no	—
192	C₂×Dic₅₃	—	2	2	no	—
193	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
194	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
195	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
196	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
197	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
198	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
199	C₄×D₅₃	—	2	2	no	—
200	C₄×D₅₃	—	2	2	no	—
201	C₄×D₅₃	—	2	2	no	—
202	C₄×D₅₃	—	2	2	no	—
203	C₄×D₅₃	—	2	2	no	—
204	C₄×D₅₃	—	2	2	no	—
205	C₄×D₅₃	—	2	1	no	—
206	C₄×D₅₃	—	2	1	no	—
207	C₄×D₅₃	—	2	2	no	—
208	C₄×D₅₃	—	2	2	no	—
209	C₄×D₅₃	—	2	2	no	—
210	C₄×D₅₃	#131	1	4	yes	—
211	C₄×D₅₃	C₂×#41	1	2	yes	—
212	C₄×D₅₃	C₂×#41	1	2	yes	—
213	#88324	—	2	8	no	—
214	C₈×C₅₃	—	2	1	no	—
215	C₈×C₅₃	—	2	1	no	—
216	C₈×C₅₃	#117	1	2	yes	—
217	C₈×C₅₃	#117	1	2	yes	—
218	#88322	—	2	1	no	—
219	#88322	—	2	1	no	—
220	#88322	#117	1	2	yes	—
221	#88322	#117	1	2	yes	—
222	#20476	—	53	1	no	maximal, Sylow
223	C₂²×C₅₃	—	2	1	no	—
224	C₂²×C₅₃	—	2	1	no	—
225	C₂²×C₅₃	#405	1	2	yes	—
226	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
227	C₂×D₅₃	—	2	1	no	—
228	C₂×D₅₃	—	2	1	no	—
229	C₂×D₅₃	—	2	8	no	—
230	C₂×D₅₃	#405	1	2	yes	—
231	C₂×D₅₃	C₄×#41	1	2	yes	—
232	C₂×D₅₃	C₂×#131	1	2	yes	—
233	C₂×D₅₃	C₂×#131	1	2	yes	—
234	#6157	—	4	8	no	—
235	C₄×C₅₃	—	2	1	no	—
236	C₄×C₅₃	—	2	1	no	—
237	C₄×C₅₃	—	2	1	no	—
238	C₄×C₅₃	—	2	1	no	—
239	C₄×C₅₃	#405	1	2	yes	—
240	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
241	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
242	Dic₅₃	—	2	1	no	—
243	Dic₅₃	—	2	1	no	—
244	Dic₅₃	—	2	1	no	—
245	Dic₅₃	—	2	1	no	—
246	Dic₅₃	#405	1	2	yes	—
247	Dic₅₃	C₄×#41	1	2	yes	—
248	C₂×#432	—	53	1	no	—
249	C₂²×C₄×C₈	—	53	1	no	—
250	#2283	—	53	1	no	—
251	#1770	—	53	2	no	—
252	C₈×C₄⋊C₄	—	53	2	no	—
253	#1752	—	53	2	no	—
254	C₈×C₂²⋊C₄	—	53	2	no	—
255	#1746	—	53	2	no	—
256	#1726	—	53	2	no	—
257	C₂×C₅₃	—	2	2	no	—
258	C₂×C₅₃	C₄×#117	1	1	yes	characteristic
259	C₂×C₅₃	C₂×#405	1	1	yes	characteristic
260	C₂×C₅₃	C₂×#405	1	1	yes	characteristic
261	D₅₃	—	2	2	no	—
262	D₅₃	#2966	1	4	yes	—
263	C₂³×C₈	—	53	1	no	—
264	C₂³×C₈	—	53	1	no	—
265	C₂²×C₄²	—	53	1	no	—
266	#432	—	53	2	no	—
267	#432	—	53	2	no	—
268	#432	—	53	2	no	—
269	#432	—	53	2	no	—
270	C₂×C₄⋊C₈	—	53	2	no	—
271	C₂×C₂²⋊C₈	—	53	2	no	—
272	C₂×#97	—	53	2	no	—
273	C₂×#97	—	53	4	no	—
274	C₂×C₄×C₈	—	53	1	no	—
275	C₂×C₄×C₈	—	53	1	no	—
276	C₂×C₄×C₈	—	53	1	no	—
277	C₂×C₄×C₈	—	53	1	no	—
278	C₂×C₄×C₈	—	53	1	no	—
279	C₂×C₄×C₈	—	53	1	no	—
280	C₂×C₄×C₈	—	53	1	no	—
281	C₂×C₄×C₈	—	53	1	no	—
282	C₂×C₄×C₈	—	53	1	no	—
283	C₂×C₄×C₈	—	53	1	no	—
284	C₂×C₄×C₈	—	53	1	no	—
285	C₂×C₄×C₈	—	53	4	no	—
286	C₂×C₄×C₈	#6157	1	1	yes	characteristic, complemented
287	#383	—	53	2	no	—
288	#382	—	53	2	no	—
289	#381	—	53	2	no	—
290	#380	—	53	2	no	—
291	C₄×C₄⋊C₄	—	53	2	no	—
292	C₄×C₂²⋊C₄	—	53	2	no	—
293	#376	—	53	2	no	—
294	#336	—	53	4	no	—
295	#336	—	53	4	no	—
296	C₅₃	#20476	1	1	yes	characteristic, complemented, Sylow
297	C₂³×C₄	—	53	1	no	—
298	C₂³×C₄	—	53	1	no	—
299	C₂³×C₄	—	53	1	no	—
300	C₂²×C₈	—	53	1	no	—
301	C₂²×C₈	—	53	1	no	—
302	C₂²×C₈	—	53	4	no	—
303	C₂²×C₈	—	53	1	no	—
304	C₂²×C₈	—	53	1	no	—
305	C₂²×C₈	—	53	1	no	—
306	C₂²×C₈	—	53	1	no	—
307	C₂²×C₈	—	53	1	no	—
308	C₂²×C₈	—	53	1	no	—
309	C₂²×C₈	—	53	1	no	—
310	C₂²×C₈	—	53	1	no	—
311	C₂²×C₈	—	106	4	no	—
312	C₂²×C₈	—	106	4	no	—
313	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
314	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	53	4	no	—
316	C₂×C₂²⋊C₄	—	53	4	no	—
317	C₂×C₄²	—	53	1	no	—
318	C₂×C₄²	—	53	1	no	—
319	C₂×C₄²	—	53	1	no	—
320	C₂×C₄²	—	53	1	no	—
321	C₂×C₄²	—	53	1	no	—
322	C₂×C₄²	—	53	1	no	—
323	C₂×C₄²	—	53	1	no	—
324	C₂×C₄²	—	53	1	no	—
325	C₂×C₄²	—	53	1	no	—
326	C₂×C₄²	—	53	1	no	—
327	C₂×C₄²	—	53	1	no	—
328	C₂×C₄²	—	53	4	no	—
329	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
330	C₄⋊C₈	—	53	4	no	—
331	C₄⋊C₈	—	53	4	no	—
332	C₂²⋊C₈	—	53	4	no	—
333	C₂²⋊C₈	—	53	4	no	—
334	#97	—	53	4	no	—
335	#97	—	53	4	no	—
336	#97	—	106	8	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	—	53	1	no	—
342	C₄×C₈	—	53	1	no	—
343	C₄×C₈	—	53	1	no	—
344	C₄×C₈	—	53	1	no	—
345	C₄×C₈	—	53	1	no	—
346	C₄×C₈	—	53	1	no	—
347	C₄×C₈	—	53	1	no	—
348	C₄×C₈	—	53	1	no	—
349	C₄×C₈	—	106	8	no	—
350	C₄×C₈	C₂×#6157	1	1	yes	characteristic
351	C₄×C₈	C₂×#6157	1	1	yes	characteristic
352	C₄×C₈	C₂×#6157	1	1	yes	characteristic
353	C₄×C₈	C₂×#6157	1	1	yes	characteristic
354	#95	—	53	4	no	—
355	#95	—	53	4	no	—
356	#95	—	53	4	no	—
357	#95	—	53	4	no	—
358	C₂⁴	—	53	1	no	—
359	C₂²×C₄	—	53	1	no	—
360	C₂²×C₄	—	53	1	no	—
361	C₂²×C₄	—	53	1	no	—
362	C₂²×C₄	—	53	1	no	—
363	C₂²×C₄	—	53	1	no	—
364	C₂²×C₄	—	53	1	no	—
365	C₂²×C₄	—	53	1	no	—
366	C₂²×C₄	—	53	1	no	—
367	C₂²×C₄	—	53	1	no	—
368	C₂²×C₄	—	53	1	no	—
369	C₂²×C₄	—	53	1	no	—
370	C₂²×C₄	—	53	1	no	—
371	C₂²×C₄	—	53	1	no	—
372	C₂²×C₄	—	53	1	no	—
373	C₂²×C₄	—	53	1	no	—
374	C₂²×C₄	—	53	8	no	—
375	C₂²×C₄	—	106	2	no	—
376	C₂²×C₄	—	106	2	no	—
377	C₂²×C₄	—	106	4	no	—
378	C₂²×C₄	—	106	4	no	—
379	C₂²×C₄	C₄×#6157	1	1	yes	characteristic
380	C₂²×C₄	C₄×#6157	1	1	yes	characteristic
381	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	53	1	no	—
385	C₂×C₈	—	53	1	no	—
386	C₂×C₈	—	53	4	no	—
387	C₂×C₈	—	53	4	no	—
388	C₂×C₈	—	53	8	no	—
389	C₂×C₈	—	53	1	no	—
390	C₂×C₈	—	53	1	no	—
391	C₂×C₈	—	106	2	no	—
392	C₂×C₈	—	106	2	no	—
393	C₂×C₈	—	106	2	no	—
394	C₂×C₈	—	106	2	no	—
395	C₂×C₈	—	106	2	no	—
396	C₂×C₈	—	106	2	no	—
397	C₂×C₈	—	106	4	no	—
398	C₂×C₈	—	106	4	no	—
399	C₂×C₈	—	106	2	no	—
400	C₂×C₈	—	106	2	no	—
401	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
402	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
403	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
404	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
405	C₄⋊C₄	—	106	8	no	—
406	C₂²⋊C₄	—	106	8	no	—
407	C₄²	—	53	1	no	—
408	C₄²	—	53	1	no	—
409	C₄²	—	53	1	no	—
410	C₄²	—	53	1	no	—
411	C₄²	—	53	1	no	—
412	C₄²	—	53	1	no	—
413	C₄²	—	53	1	no	—
414	C₄²	—	53	1	no	—
415	C₄²	—	53	1	no	—
416	C₄²	—	53	1	no	—
417	C₄²	—	53	1	no	—
418	C₄²	—	53	1	no	—
419	C₄²	—	106	4	no	—
420	C₄²	—	106	4	no	—
421	C₄²	C₄×#6157	1	1	yes	characteristic
422	C₄²	C₄×#6157	1	1	yes	characteristic
423	C₄²	C₂²×#6157	1	1	yes	characteristic
424	C₄²	C₂²×#6157	1	1	yes	characteristic
425	C₂³	—	53	1	no	—
426	C₂³	—	53	4	no	—
427	C₂³	—	53	1	no	—
428	C₂³	—	106	2	no	—
429	C₂³	—	106	2	no	—
430	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	53	1	no	—
436	C₂×C₄	—	53	1	no	—
437	C₂×C₄	—	53	4	no	—
438	C₂×C₄	—	53	2	no	—
439	C₂×C₄	—	53	2	no	—
440	C₂×C₄	—	53	1	no	—
441	C₂×C₄	—	53	1	no	—
442	C₂×C₄	—	53	1	no	—
443	C₂×C₄	—	53	1	no	—
444	C₂×C₄	—	106	2	no	—
445	C₂×C₄	—	106	2	no	—
446	C₂×C₄	—	106	2	no	—
447	C₂×C₄	—	106	2	no	—
448	C₂×C₄	—	106	2	no	—
449	C₂×C₄	—	106	2	no	—
450	C₂×C₄	—	106	2	no	—
451	C₂×C₄	—	106	2	no	—
452	C₂×C₄	—	106	2	no	—
453	C₂×C₄	—	106	2	no	—
454	C₂×C₄	—	106	2	no	—
455	C₂×C₄	—	106	2	no	—
456	C₂×C₄	—	106	1	no	—
457	C₂×C₄	—	106	1	no	—
458	C₂×C₄	—	106	8	no	—
459	C₂×C₄	—	106	8	no	—
460	C₂×C₄	—	106	8	no	—
461	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
462	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
463	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
464	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
465	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
466	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
467	C₈	—	2	1	no	—
468	C₈	—	2	1	no	—
469	C₈	—	53	2	no	—
470	C₈	—	53	2	no	—
471	C₈	—	106	8	no	—
472	C₈	—	106	1	no	—
473	C₈	—	106	1	no	—
474	C₈	#13133296	1	2	yes	—
475	C₈	#13133296	1	2	yes	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	53	2	no	—
479	C₂²	—	53	2	no	—
480	C₂²	—	53	2	no	—
481	C₂²	—	53	2	no	—
482	C₂²	—	106	8	no	—
483	C₂²	—	106	1	no	—
484	C₂²	—	106	1	no	—
485	C₂²	#16811586	1	2	yes	—
486	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	53	2	no	—
492	C₄	—	53	2	no	—
493	C₄	—	106	1	no	—
494	C₄	—	106	1	no	—
495	C₄	—	106	1	no	—
496	C₄	—	106	1	no	—
497	C₄	—	212	8	no	—
498	C₄	#16811586	1	2	yes	—
499	C₄	C₂×#13133296	1	1	yes	characteristic
500	C₄	C₂×#13133296	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	53	4	no	—
503	C₂	—	106	2	no	—
504	C₂	C₄×#13133296	1	1	yes	characteristic
505	C₂	C₂×#16811586	1	1	yes	characteristic
506	C₂	C₂×#16811586	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×C₄×C₈×C₅₃	C₄
prime radical	C₂³×D₅₃	C₂²×C₄
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×C₄×C₈	#6157
hypocenter	C₅₃	#20476
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #20290509	C₂	semidirect
4. C₈×C₄⋊#6157	C₂	semidirect
7. #20290433	C₂	semidirect
8. #20290371	C₂	semidirect
10. #16811646	C₄	semidirect
11. #16811645	C₄	semidirect
12. #16811644	C₄	semidirect
13. #16811643	C₄	semidirect
31. C₂×C₄×#88322	C₄	semidirect
32. C₂×C₈×Dic₅₃	C₄	semidirect
33. C₂×C₈×Dic₅₃	C₄	semidirect
34. C₄×C₈×D₅₃	C₄	semidirect
35. C₄×C₈×D₅₃	C₄	semidirect
36. C₄×C₈×D₅₃	C₄	semidirect
37. C₄×C₈×D₅₃	C₄	semidirect
42. C₂×C₄×C₈×C₅₃	C₄	semidirect
286. C₂×C₄×C₈	#6157	semidirect
296. C₅₃	#20476	semidirect

Maximal subgroups

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

subgroup	index
D₅₃⋊#432	2
#20291162	2
#20290509	2
C₈×C₄⋊#6157	2
#20290451	2
C₈×C₂²⋊#6157	2
#20290433	2
#20290371	2
C₂×C₄×C₈×D₅₃	2
#20476	53