Subgroups — D₅₃×#1283 #27273770

Order 13568.

722 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20272566	C₂	1	1	yes	maximal, characteristic, complemented
5	#20272565	C₂	1	1	yes	maximal, characteristic, complemented
6	#20272564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₅₃	C₄	1	2	yes	—
9	C₂²×C₈×D₅₃	C₄	1	2	yes	—
10	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
11	#16810676	C₂²	1	1	yes	characteristic
12	#16810675	—	2	1	no	—
13	#16810674	—	2	1	no	—
14	#16810673	C₄	1	2	yes	—
15	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
16	C₂×#13133146	C₄	1	2	yes	—
17	C₄⋊C₈×D₅₃	—	2	1	no	—
18	C₄⋊C₈×D₅₃	—	2	1	no	—
19	C₄⋊C₈×D₅₃	—	2	1	no	—
20	C₄⋊C₈×D₅₃	—	2	1	no	—
21	C₄⋊C₈×D₅₃	—	2	1	no	—
22	C₂²⋊C₈×D₅₃	C₄	1	2	yes	—
23	C₄×#11719917	C₂²	1	1	yes	characteristic
24	#16810575	—	2	1	no	—
25	M₁₆×Dic₅₃	C₄	1	2	yes	—
26	C₄×#11719912	—	2	1	no	—
27	#97×D₅₃	—	2	1	no	—
28	C₄×C₈×D₅₃	—	2	1	no	—
29	C₄×C₈×D₅₃	—	2	1	no	—
30	C₅₃×#431	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
36	C₂×#11719917	C₂×C₄	1	2	yes	—
37	C₂×#11719912	—	2	2	no	—
38	M₁₆×D₅₃	—	2	4	no	—
39	M₁₆×D₅₃	C₈	1	8	yes	complemented
40	C₂²×#88322	C₂×C₄	1	2	yes	—
41	C₂×C₈×D₅₃	—	2	2	no	—
42	C₂×C₈×D₅₃	—	2	2	no	—
43	C₂×C₈×D₅₃	—	2	2	no	—
44	C₂×C₈×D₅₃	—	2	2	no	—
45	C₂×C₈×D₅₃	—	4	4	no	—
46	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₅₃	D₄	1	1	yes	characteristic
50	C₄²×D₅₃	D₄	1	1	yes	characteristic
51	C₄²×D₅₃	D₄	1	1	yes	characteristic
52	C₄²×D₅₃	D₄	1	1	yes	characteristic
53	C₄²×D₅₃	D₄	1	1	yes	characteristic
54	C₄²×D₅₃	D₄	1	1	yes	characteristic
55	C₄²×D₅₃	Q₈	1	1	yes	characteristic
56	C₄²×D₅₃	Q₈	1	1	yes	characteristic
57	C₄⋊#88322	—	2	1	no	—
58	C₄⋊#88322	—	2	1	no	—
59	C₄⋊#88322	—	2	1	no	—
60	#13133146	—	2	2	no	—
61	#13133146	—	2	2	no	—
62	#13133146	—	2	2	no	—
63	C₂²⋊#88322	C₂×C₄	1	2	yes	—
64	#13133129	—	2	2	no	—
65	#13133128	—	2	1	no	—
66	#13133127	—	2	2	no	—
67	C₄×#88322	—	2	1	no	—
68	C₄×#88322	—	2	1	no	—
69	C₈×Dic₅₃	—	2	2	no	—
70	C₈×Dic₅₃	—	2	2	no	—
71	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₅₃	—	2	1	no	—
75	C₄⋊C₈×C₅₃	—	2	1	no	—
76	C₄⋊C₈×C₅₃	—	2	1	no	—
77	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
78	#97×C₅₃	—	2	1	no	—
79	C₄×C₈×C₅₃	—	2	1	no	—
80	C₄×C₈×C₅₃	—	2	1	no	—
81	C₂³×D₅₃	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
86	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
87	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
88	C₂×C₄×D₅₃	—	2	2	no	—
89	C₂×C₄×D₅₃	—	2	2	no	—
90	C₂×C₄×D₅₃	—	4	2	no	—
91	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₂×C₈	1	4	yes	—
104	C₂×C₄×D₅₃	M₁₆	1	4	yes	—
105	M₁₆×C₅₃	—	2	2	no	—
106	M₁₆×C₅₃	C₂×C₈	1	4	yes	complemented
107	C₂×C₈×C₅₃	—	2	2	no	—
108	C₂×C₈×C₅₃	—	2	2	no	—
109	C₂×C₈×C₅₃	—	2	2	no	—
110	C₂×C₈×C₅₃	—	4	2	no	—
111	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
115	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
127	#11719917	—	2	2	no	—
128	#11719917	C₂×C₈	1	4	yes	complemented
129	C₂×#88322	—	2	2	no	—
130	C₂×#88322	—	2	2	no	—
131	C₂×#88322	—	2	2	no	—
132	C₂×#88322	—	4	2	no	—
133	#11719912	—	2	8	no	—
134	C₈×D₅₃	—	2	8	no	—
135	C₈×D₅₃	—	4	4	no	—
136	C₈×D₅₃	—	4	4	no	—
137	C₈×D₅₃	—	4	4	no	—
138	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
139	C₂²×D₅₃	—	2	2	no	—
140	C₂²×D₅₃	—	2	2	no	—
141	C₂²×D₅₃	#95	1	1	yes	characteristic
142	C₂²×D₅₃	#95	1	1	yes	characteristic
143	C₂²×D₅₃	C₄×C₈	1	2	yes	—
144	C₂²×D₅₃	#97	1	2	yes	—
145	C₂×C₄×C₅₃	—	2	1	no	—
146	C₂×C₄×C₅₃	—	2	1	no	—
147	C₂×C₄×C₅₃	—	4	1	no	—
148	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
156	C₂×Dic₅₃	—	2	2	no	—
157	C₂×Dic₅₃	—	4	1	no	—
158	C₂×Dic₅₃	#95	1	1	yes	characteristic
159	C₂×Dic₅₃	#95	1	1	yes	characteristic
160	C₂×Dic₅₃	#95	1	1	yes	characteristic
161	C₂×Dic₅₃	#95	1	1	yes	characteristic
162	C₂×Dic₅₃	#95	1	1	yes	characteristic
163	C₂×Dic₅₃	#95	1	1	yes	characteristic
164	C₂×Dic₅₃	C₄×C₈	1	2	yes	—
165	C₂×Dic₅₃	#97	1	2	yes	—
166	C₄×D₅₃	—	2	2	no	—
167	C₄×D₅₃	—	2	2	no	—
168	C₄×D₅₃	—	2	2	no	—
169	C₄×D₅₃	—	2	1	no	—
170	C₄×D₅₃	—	2	1	no	—
171	C₄×D₅₃	—	2	2	no	—
172	C₄×D₅₃	—	4	1	no	—
173	C₄×D₅₃	—	4	1	no	—
174	C₄×D₅₃	C₂²⋊C₈	1	4	yes	—
175	C₄×D₅₃	C₂²⋊C₈	1	4	yes	—
176	C₄×D₅₃	#100	1	2	yes	—
177	C₄×D₅₃	#101	1	2	yes	—
178	C₄×D₅₃	C₄⋊C₈	1	4	yes	—
179	C₄×D₅₃	C₄⋊C₈	1	4	yes	—
180	C₈×C₅₃	—	2	4	no	—
181	C₈×C₅₃	—	4	2	no	—
182	C₈×C₅₃	—	4	2	no	—
183	#88322	—	2	4	no	—
184	#88322	—	4	2	no	—
185	#88322	—	4	2	no	—
186	C₂×#1283	—	53	1	no	maximal, Sylow
187	C₂²×C₅₃	—	2	1	no	—
188	C₂²×C₅₃	—	2	1	no	—
189	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
190	C₂²×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
191	C₂²×C₅₃	C₂×#97	1	1	yes	characteristic
192	C₂×D₅₃	—	2	1	no	—
193	C₂×D₅₃	—	2	1	no	—
194	C₂×D₅₃	—	2	4	no	—
195	C₂×D₅₃	—	2	4	no	—
196	C₂×D₅₃	#336	1	2	yes	—
197	C₂×D₅₃	#336	1	2	yes	—
198	C₂×D₅₃	#343	1	2	yes	—
199	C₂×D₅₃	#344	1	2	yes	—
200	C₄×C₅₃	—	2	1	no	—
201	C₄×C₅₃	—	2	1	no	—
202	C₄×C₅₃	—	2	1	no	—
203	C₄×C₅₃	C₂×C₂²⋊C₈	1	2	yes	—
204	C₄×C₅₃	C₂×#100	1	1	yes	characteristic
205	C₄×C₅₃	C₂×#101	1	1	yes	characteristic
206	C₄×C₅₃	C₂×C₄⋊C₈	1	2	yes	—
207	Dic₅₃	—	2	1	no	—
208	Dic₅₃	—	2	1	no	—
209	Dic₅₃	—	2	1	no	—
210	Dic₅₃	#336	1	2	yes	—
211	Dic₅₃	#336	1	2	yes	—
212	Dic₅₃	#343	1	2	yes	—
213	C₂×#431	—	53	1	no	—
214	C₂²×C₄⋊C₈	—	53	1	no	—
215	C₂×C₄×M₁₆	—	53	1	no	—
216	#1283	—	53	1	no	—
217	#1283	—	53	1	no	—
218	#1283	—	53	1	no	—
219	#1283	D₅₃	1	1	yes	characteristic, direct product factor
220	C₂×C₅₃	—	2	1	no	—
221	C₂×C₅₃	—	2	1	no	—
222	C₂×C₅₃	C₂×#336	1	1	yes	characteristic
223	C₂×C₅₃	C₂×#343	1	1	yes	characteristic
224	C₂×C₅₃	C₂×#344	1	1	yes	characteristic
225	D₅₃	—	2	2	no	—
226	D₅₃	#1283	1	4	yes	direct product factor
227	C₂²×M₁₆	—	53	2	no	—
228	C₂³×C₈	—	53	2	no	—
229	C₂²×C₄²	—	53	1	no	—
230	#431	—	53	1	no	—
231	#431	—	53	2	no	—
232	#431	—	106	1	no	—
233	#431	—	106	1	no	—
234	#431	C₂×D₅₃	1	1	yes	characteristic
235	C₂×C₄⋊C₈	—	53	2	no	—
236	C₂×C₄⋊C₈	—	53	1	no	—
237	C₂×C₄⋊C₈	—	106	1	no	—
238	C₂×C₄⋊C₈	—	106	1	no	—
239	C₂×C₄⋊C₈	—	106	1	no	—
240	C₂×C₄⋊C₈	—	106	1	no	—
241	C₂×C₄⋊C₈	—	106	1	no	—
242	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
243	C₂×C₂²⋊C₈	—	53	2	no	—
244	C₄×M₁₆	—	53	2	no	—
245	C₄×M₁₆	—	53	1	no	—
246	C₄×M₁₆	—	106	1	no	—
247	C₄×M₁₆	—	106	1	no	—
248	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
249	C₂×#97	—	106	1	no	—
250	C₂×C₄×C₈	—	106	1	no	—
251	C₂×C₄×C₈	—	106	1	no	—
252	C₅₃	C₂×#1283	1	1	yes	characteristic, complemented, Sylow
253	C₂³×C₄	—	53	1	no	—
254	C₂³×C₄	—	53	1	no	—
255	C₂³×C₄	—	53	1	no	—
256	C₂×M₁₆	—	53	2	no	—
257	C₂×M₁₆	—	53	8	no	—
258	C₂×M₁₆	—	106	2	no	—
259	C₂×M₁₆	—	106	4	no	—
260	C₂×M₁₆	C₄×D₅₃	1	2	yes	—
261	C₂²×C₈	—	53	2	no	—
262	C₂²×C₈	—	106	2	no	—
263	C₂²×C₈	—	106	2	no	—
264	C₂²×C₈	—	106	2	no	—
265	C₂²×C₈	—	106	2	no	—
266	C₂²×C₈	—	212	4	no	—
267	C₂²×C₈	C₄×D₅₃	1	2	yes	—
268	C₂×C₄²	—	53	1	no	—
269	C₂×C₄²	—	53	1	no	—
270	C₂×C₄²	—	53	1	no	—
271	C₂×C₄²	—	53	1	no	—
272	C₂×C₄²	—	53	1	no	—
273	C₂×C₄²	—	53	1	no	—
274	C₂×C₄²	—	53	1	no	—
275	C₂×C₄²	—	53	1	no	—
276	C₂×C₄²	—	53	1	no	—
277	C₂×C₄²	—	53	1	no	—
278	C₂×C₄²	—	53	1	no	—
279	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	106	2	no	—
284	C₄⋊C₈	—	106	2	no	—
285	C₄⋊C₈	—	106	2	no	—
286	C₄⋊C₈	—	106	1	no	—
287	C₄⋊C₈	—	106	1	no	—
288	C₄⋊C₈	—	106	1	no	—
289	C₂²⋊C₈	—	53	2	no	—
290	C₂²⋊C₈	—	106	2	no	—
291	C₂²⋊C₈	C₄×D₅₃	1	2	yes	—
292	#97	—	2	1	no	—
293	#97	—	106	2	no	—
294	#97	—	106	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	—	106	2	no	—
298	C₄×C₈	—	106	2	no	—
299	C₄×C₈	—	106	1	no	—
300	C₄×C₈	—	106	1	no	—
301	C₂⁴	—	53	1	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	53	1	no	—
307	C₂²×C₄	—	53	1	no	—
308	C₂²×C₄	—	53	4	no	—
309	C₂²×C₄	—	53	4	no	—
310	C₂²×C₄	—	53	1	no	—
311	C₂²×C₄	—	53	1	no	—
312	C₂²×C₄	—	53	1	no	—
313	C₂²×C₄	—	53	1	no	—
314	C₂²×C₄	—	53	1	no	—
315	C₂²×C₄	—	53	1	no	—
316	C₂²×C₄	—	53	1	no	—
317	C₂²×C₄	—	53	1	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	106	2	no	—
320	C₂²×C₄	—	106	2	no	—
321	C₂²×C₄	—	212	2	no	—
322	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
325	M₁₆	—	2	2	no	—
326	M₁₆	—	53	4	no	—
327	M₁₆	—	106	8	no	—
328	M₁₆	—	106	2	no	—
329	M₁₆	C₈×D₅₃	1	4	yes	complemented
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	106	8	no	—
335	C₂×C₈	—	106	2	no	—
336	C₂×C₈	—	106	2	no	—
337	C₂×C₈	—	106	2	no	—
338	C₂×C₈	—	212	4	no	—
339	C₂×C₈	—	212	4	no	—
340	C₂×C₈	—	212	4	no	—
341	C₂×C₈	—	212	2	no	—
342	C₄²	—	53	1	no	—
343	C₄²	—	53	1	no	—
344	C₄²	—	53	1	no	—
345	C₄²	—	53	1	no	—
346	C₄²	—	53	1	no	—
347	C₄²	—	53	1	no	—
348	C₄²	—	53	1	no	—
349	C₄²	—	53	1	no	—
350	C₄²	—	53	1	no	—
351	C₄²	—	53	1	no	—
352	C₄²	—	53	1	no	—
353	C₄²	—	53	1	no	—
354	C₄²	D₄×D₅₃	1	1	yes	characteristic
355	C₄²	D₄×D₅₃	1	1	yes	characteristic
356	C₄²	D₄×D₅₃	1	1	yes	characteristic
357	C₄²	Q₈×D₅₃	1	1	yes	characteristic
358	C₂³	—	53	1	no	—
359	C₂³	—	53	2	no	—
360	C₂³	—	53	2	no	—
361	C₂³	—	53	1	no	—
362	C₂³	—	106	2	no	—
363	C₂³	—	106	2	no	—
364	C₂³	C₄²×D₅₃	1	1	yes	characteristic
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	53	2	no	—
369	C₂×C₄	—	53	2	no	—
370	C₂×C₄	—	53	1	no	—
371	C₂×C₄	—	53	1	no	—
372	C₂×C₄	—	53	1	no	—
373	C₂×C₄	—	53	4	no	—
374	C₂×C₄	—	53	4	no	—
375	C₂×C₄	—	53	2	no	—
376	C₂×C₄	—	53	2	no	—
377	C₂×C₄	—	53	4	no	—
378	C₂×C₄	—	53	4	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	106	2	no	—
383	C₂×C₄	—	106	2	no	—
384	C₂×C₄	—	106	2	no	—
385	C₂×C₄	—	106	2	no	—
386	C₂×C₄	—	106	2	no	—
387	C₂×C₄	—	106	1	no	—
388	C₂×C₄	—	106	1	no	—
389	C₂×C₄	—	212	1	no	—
390	C₂×C₄	—	212	1	no	—
391	C₂×C₄	—	212	1	no	—
392	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
393	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
394	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
395	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
396	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
397	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
398	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
399	C₂×C₄	M₁₆×D₅₃	1	2	yes	—
400	C₈	—	2	4	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	106	4	no	—
404	C₈	—	212	2	no	—
405	C₈	—	212	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	53	2	no	—
409	C₂²	—	53	2	no	—
410	C₂²	—	53	2	no	—
411	C₂²	—	53	2	no	—
412	C₂²	—	106	4	no	—
413	C₂²	—	106	4	no	—
414	C₂²	—	106	1	no	—
415	C₂²	—	106	1	no	—
416	C₂²	#95×D₅₃	1	1	yes	characteristic
417	C₂²	C₄×C₈×D₅₃	1	1	yes	characteristic
418	C₂²	#97×D₅₃	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	53	2	no	—
423	C₄	—	53	2	no	—
424	C₄	—	53	2	no	—
425	C₄	—	106	1	no	—
426	C₄	—	106	1	no	—
427	C₄	—	106	1	no	—
428	C₄	C₂²⋊C₈×D₅₃	1	2	yes	—
429	C₄	#100×D₅₃	1	1	yes	characteristic
430	C₄	#101×D₅₃	1	1	yes	characteristic
431	C₄	C₄⋊C₈×D₅₃	1	2	yes	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	53	4	no	—
435	C₂	—	106	2	no	—
436	C₂	#336×D₅₃	1	1	yes	characteristic
437	C₂	#343×D₅₃	1	1	yes	characteristic
438	C₂	#344×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₅₃
commutator	C₂²×C₅₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1283	C₂
socle	C₂²×C₅₃	C₂×#95
prime radical	C₂³×D₅₃	C₄²
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1283	D₅₃
hypocenter	C₅₃	C₂×#1283
LCS	G ▷ C₂²×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1283

Complements

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

N	H ≅ G/N	type
4. #20272566	C₂	semidirect
5. #20272565	C₂	semidirect
6. #20272564	C₂	semidirect
7. C₅₃×#1283	C₂	semidirect
39. M₁₆×D₅₃	C₈	semidirect
106. M₁₆×C₅₃	C₂×C₈	semidirect
128. #11719917	C₂×C₈	semidirect
219. #1283	D₅₃	direct (N × H)
226. D₅₃	#1283	direct (N × H)
252. C₅₃	C₂×#1283	semidirect
329. M₁₆	C₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#431×D₅₃	2
C₂×C₄⋊C₈×D₅₃	2
C₄×M₁₆×D₅₃	2
#20272566	2
#20272565	2
#20272564	2
C₅₃×#1283	2
C₂×#1283	53

Subgroups — D53×#1283 #27273770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1283 #27273770