Subgroups — D₅₃×#2162 #27537153

Order 13568.

726 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20276514	C₂	1	1	yes	maximal, characteristic, complemented
3	#20276513	C₂	1	2	yes	maximal, complemented
4	#20276512	C₂	1	2	yes	maximal, complemented
5	#20276511	C₂	1	2	yes	maximal, complemented
6	C₄⋊C₁₆×D₅₃	C₂	1	2	yes	maximal, complemented
7	C₂²⋊C₁₆×D₅₃	C₂	1	2	yes	maximal
8	C₄×C₁₆×D₅₃	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₅₃	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₅₃	C₄	1	1	yes	characteristic
13	C₂×C₁₆×D₅₃	C₂²	1	4	yes	—
14	C₂×C₄×#88322	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
17	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
18	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
19	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
20	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
21	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
22	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
23	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
25	C₄⋊#11719908	C₂²	1	2	yes	complemented
26	#16810441	C₂²	1	4	yes	complemented
27	C₂²⋊#11719908	C₂²	1	2	yes	—
28	#16810402	C₂²	1	4	yes	—
29	C₄×#11719908	C₂²	1	2	yes	complemented
30	C₁₆×Dic₅₃	C₂²	1	4	yes	complemented
31	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
33	C₅₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₄×C₁₆×C₅₃	C₂²	1	2	yes	complemented
35	C₂²×C₄×D₅₃	C₈	1	1	yes	characteristic
36	C₂²×C₄×D₅₃	C₈	1	1	yes	characteristic
37	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
39	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×D₅₃	—	2	4	no	—
41	C₂×C₈×D₅₃	—	2	4	no	—
42	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
50	C₂×C₄×Dic₅₃	C₈	1	1	yes	characteristic
51	C₂×C₄×Dic₅₃	C₈	1	1	yes	characteristic
52	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₅₃	C₈	1	1	yes	characteristic
54	C₄²×D₅₃	C₈	1	1	yes	characteristic
55	C₄²×D₅₃	C₈	1	1	yes	characteristic
56	C₄²×D₅₃	C₈	1	1	yes	characteristic
57	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂×#11719908	C₂³	1	4	yes	—
62	C₁₆×D₅₃	—	2	8	no	—
63	C₄×#88322	C₂×C₄	1	1	yes	characteristic
64	C₄×#88322	C₂×C₄	1	1	yes	characteristic
65	C₄×#88322	C₂×C₄	1	1	yes	characteristic
66	C₄×#88322	C₂×C₄	1	1	yes	characteristic
67	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
69	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
74	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₆×C₅₃	C₂³	1	4	yes	—
79	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
83	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
88	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
89	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₅₃	—	2	4	no	—
91	C₂×C₄×D₅₃	—	2	2	no	—
92	C₂×C₄×D₅₃	—	2	2	no	—
93	C₂×C₄×D₅₃	C₁₆	1	8	yes	complemented
94	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₅₃	—	2	2	no	—
107	C₂×C₈×C₅₃	—	2	2	no	—
108	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
112	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
113	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
114	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
117	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
118	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
119	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
120	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
121	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
122	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
123	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
124	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
125	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
126	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×#88322	—	2	2	no	—
129	C₂×#88322	—	2	2	no	—
130	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
131	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
132	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
133	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₅₃	—	2	2	no	—
135	C₈×D₅₃	—	2	2	no	—
136	C₈×D₅₃	—	2	2	no	—
137	C₈×D₅₃	—	2	2	no	—
138	C₈×D₅₃	—	2	2	no	—
139	C₈×D₅₃	—	2	2	no	—
140	C₈×D₅₃	M₁₆	1	4	yes	—
141	C₈×D₅₃	#41	1	4	yes	—
142	C₁₆×C₅₃	—	2	4	no	—
143	#11719908	—	2	4	no	—
144	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
145	C₂²×D₅₃	—	2	2	no	—
146	C₂²×D₅₃	—	2	2	no	—
147	C₂²×D₅₃	C₂×C₁₆	1	4	yes	—
148	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₅₃	—	2	1	no	—
151	C₂×C₄×C₅₃	—	2	1	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	C₂×C₁₆	1	4	yes	complemented
154	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×Dic₅₃	—	2	2	no	—
161	C₂×Dic₅₃	—	2	2	no	—
162	C₂×Dic₅₃	C₂×C₁₆	1	4	yes	complemented
163	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
165	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
168	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
169	C₄×D₅₃	—	2	2	no	—
170	C₄×D₅₃	—	2	2	no	—
171	C₄×D₅₃	—	2	1	no	—
172	C₄×D₅₃	—	2	1	no	—
173	C₄×D₅₃	—	2	2	no	—
174	C₄×D₅₃	—	2	2	no	—
175	C₄×D₅₃	—	2	2	no	—
176	C₄×D₅₃	C₂×C₁₆	1	4	yes	—
177	C₄×D₅₃	C₂×C₁₆	1	4	yes	—
178	C₄×D₅₃	C₂×C₁₆	1	4	yes	complemented
179	C₄×D₅₃	C₂×C₁₆	1	4	yes	complemented
180	C₄×D₅₃	M₃₂	1	4	yes	—
181	C₄×D₅₃	#117	1	2	yes	—
182	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
183	C₈×C₅₃	—	2	1	no	—
184	C₈×C₅₃	—	2	1	no	—
185	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
186	C₈×C₅₃	C₂×#41	1	2	yes	—
187	#88322	—	2	1	no	—
188	#88322	—	2	1	no	—
189	#88322	#117	1	2	yes	—
190	#88322	C₂×M₁₆	1	2	yes	—
191	C₂×#2162	—	53	1	no	maximal, Sylow
192	C₂²×C₅₃	—	2	1	no	—
193	C₂²×C₅₃	—	2	1	no	—
194	C₂²×C₅₃	C₂²×C₁₆	1	2	yes	—
195	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
196	C₂×D₅₃	—	2	1	no	—
197	C₂×D₅₃	—	2	1	no	—
198	C₂×D₅₃	—	2	8	no	—
199	C₂×D₅₃	#431	1	2	yes	—
200	C₂×D₅₃	C₂²×C₁₆	1	2	yes	—
201	C₂×D₅₃	C₂²×C₁₆	1	2	yes	—
202	C₂×D₅₃	C₂×M₃₂	1	2	yes	—
203	C₄×C₅₃	—	2	1	no	—
204	C₄×C₅₃	—	2	1	no	—
205	C₄×C₅₃	C₂²×C₁₆	1	2	yes	—
206	C₄×C₅₃	C₂²×C₁₆	1	2	yes	—
207	C₄×C₅₃	C₂×M₃₂	1	2	yes	—
208	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
209	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
210	Dic₅₃	—	2	1	no	—
211	Dic₅₃	—	2	1	no	—
212	Dic₅₃	#431	1	2	yes	—
213	Dic₅₃	C₂²×C₁₆	1	2	yes	—
214	Dic₅₃	C₂²×C₁₆	1	2	yes	—
215	Dic₅₃	C₂×M₃₂	1	2	yes	—
216	C₂²×C₄×C₈	—	53	1	no	—
217	#2162	—	53	1	no	—
218	#2162	—	53	2	no	—
219	#2162	—	53	2	no	—
220	#2162	—	53	2	no	—
221	#2162	D₅₃	1	1	yes	characteristic, direct product factor
222	C₂×C₄⋊C₁₆	—	53	2	no	—
223	C₂×C₂²⋊C₁₆	—	53	2	no	—
224	C₂×C₄×C₁₆	—	53	2	no	—
225	C₂×C₅₃	—	2	2	no	—
226	C₂×C₅₃	C₂×#431	1	1	yes	characteristic
227	C₂×C₅₃	C₂³×C₁₆	1	1	yes	characteristic
228	C₂×C₅₃	C₂²×M₃₂	1	1	yes	characteristic
229	D₅₃	—	2	2	no	—
230	D₅₃	#2162	1	4	yes	direct product factor
231	C₂³×C₈	—	53	1	no	—
232	C₂³×C₈	—	53	1	no	—
233	C₂²×C₄²	—	53	1	no	—
234	C₂²×C₁₆	—	53	4	no	—
235	C₂×C₄×C₈	—	53	1	no	—
236	C₂×C₄×C₈	—	53	1	no	—
237	C₂×C₄×C₈	—	53	1	no	—
238	C₂×C₄×C₈	—	53	1	no	—
239	C₂×C₄×C₈	—	53	1	no	—
240	C₂×C₄×C₈	—	53	1	no	—
241	C₂×C₄×C₈	—	53	1	no	—
242	C₂×C₄×C₈	—	53	1	no	—
243	C₂×C₄×C₈	—	53	1	no	—
244	C₂×C₄×C₈	—	53	1	no	—
245	C₂×C₄×C₈	—	53	1	no	—
246	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
247	C₄⋊C₁₆	—	53	4	no	—
248	C₄⋊C₁₆	—	53	2	no	—
249	C₄⋊C₁₆	C₂×D₅₃	1	2	yes	complemented
250	C₂²⋊C₁₆	—	53	2	no	—
251	C₂²⋊C₁₆	—	53	4	no	—
252	C₂²⋊C₁₆	C₂×D₅₃	1	2	yes	—
253	C₄×C₁₆	—	53	4	no	—
254	C₄×C₁₆	—	53	2	no	—
255	C₄×C₁₆	C₂×D₅₃	1	2	yes	complemented
256	C₅₃	C₂×#2162	1	1	yes	characteristic, complemented, Sylow
257	C₂³×C₄	—	53	1	no	—
258	C₂³×C₄	—	53	1	no	—
259	C₂³×C₄	—	53	1	no	—
260	C₂²×C₈	—	53	1	no	—
261	C₂²×C₈	—	53	1	no	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	—	53	1	no	—
265	C₂²×C₈	—	53	1	no	—
266	C₂²×C₈	—	53	1	no	—
267	C₂²×C₈	—	53	1	no	—
268	C₂²×C₈	—	53	1	no	—
269	C₂²×C₈	—	53	1	no	—
270	C₂²×C₈	—	106	4	no	—
271	C₂²×C₈	—	106	4	no	—
272	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
273	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
280	C₂×C₄²	—	53	1	no	—
281	C₂×C₄²	—	53	1	no	—
282	C₂×C₄²	—	53	1	no	—
283	C₂×C₄²	—	53	1	no	—
284	C₂×C₄²	—	53	1	no	—
285	C₂×C₄²	C₄×D₅₃	1	1	yes	characteristic
286	C₂×C₁₆	—	53	4	no	—
287	C₂×C₁₆	—	106	8	no	—
288	C₂×C₁₆	C₂²×D₅₃	1	4	yes	—
289	C₄×C₈	—	53	1	no	—
290	C₄×C₈	—	53	1	no	—
291	C₄×C₈	—	53	1	no	—
292	C₄×C₈	—	53	1	no	—
293	C₄×C₈	—	53	1	no	—
294	C₄×C₈	—	53	1	no	—
295	C₄×C₈	—	53	1	no	—
296	C₄×C₈	—	53	1	no	—
297	C₄×C₈	—	53	1	no	—
298	C₄×C₈	—	53	1	no	—
299	C₄×C₈	—	53	1	no	—
300	C₄×C₈	—	53	1	no	—
301	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
302	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
305	C₂⁴	—	53	1	no	—
306	C₂²×C₄	—	53	1	no	—
307	C₂²×C₄	—	53	8	no	—
308	C₂²×C₄	—	53	1	no	—
309	C₂²×C₄	—	53	1	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	—	53	1	no	—
320	C₂²×C₄	—	53	1	no	—
321	C₂²×C₄	—	53	1	no	—
322	C₂²×C₄	—	106	2	no	—
323	C₂²×C₄	—	106	2	no	—
324	C₂²×C₄	—	106	4	no	—
325	C₂²×C₄	C₈×D₅₃	1	1	yes	characteristic
326	C₂²×C₄	C₈×D₅₃	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	53	1	no	—
331	C₂×C₈	—	53	1	no	—
332	C₂×C₈	—	53	4	no	—
333	C₂×C₈	—	53	4	no	—
334	C₂×C₈	—	53	1	no	—
335	C₂×C₈	—	53	1	no	—
336	C₂×C₈	—	106	2	no	—
337	C₂×C₈	—	106	2	no	—
338	C₂×C₈	—	106	2	no	—
339	C₂×C₈	—	106	2	no	—
340	C₂×C₈	—	106	2	no	—
341	C₂×C₈	—	106	2	no	—
342	C₂×C₈	—	106	2	no	—
343	C₂×C₈	—	106	2	no	—
344	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
345	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
346	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
347	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
355	C₄²	—	53	1	no	—
356	C₄²	—	53	1	no	—
357	C₄²	—	53	1	no	—
358	C₄²	—	53	1	no	—
359	C₄²	—	53	1	no	—
360	C₄²	C₈×D₅₃	1	1	yes	characteristic
361	C₄²	C₈×D₅₃	1	1	yes	characteristic
362	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
363	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
364	C₁₆	—	2	4	no	—
365	C₁₆	—	106	4	no	—
366	C₂³	—	53	1	no	—
367	C₂³	—	53	4	no	—
368	C₂³	—	53	1	no	—
369	C₂³	—	106	2	no	—
370	C₂³	—	106	2	no	—
371	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	53	4	no	—
376	C₂×C₄	—	53	1	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	4	no	—
381	C₂×C₄	—	53	4	no	—
382	C₂×C₄	—	53	4	no	—
383	C₂×C₄	—	53	4	no	—
384	C₂×C₄	—	53	4	no	—
385	C₂×C₄	—	53	2	no	—
386	C₂×C₄	—	53	2	no	—
387	C₂×C₄	—	53	1	no	—
388	C₂×C₄	—	53	1	no	—
389	C₂×C₄	—	106	2	no	—
390	C₂×C₄	—	106	2	no	—
391	C₂×C₄	—	106	2	no	—
392	C₂×C₄	—	106	2	no	—
393	C₂×C₄	—	106	2	no	—
394	C₂×C₄	—	106	2	no	—
395	C₂×C₄	—	106	2	no	—
396	C₂×C₄	—	106	1	no	—
397	C₂×C₄	—	106	1	no	—
398	C₂×C₄	C₁₆×D₅₃	1	4	yes	complemented
399	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
400	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
401	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
402	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
403	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	53	2	no	—
408	C₈	—	53	2	no	—
409	C₈	—	106	1	no	—
410	C₈	—	106	1	no	—
411	C₈	M₁₆×D₅₃	1	2	yes	—
412	C₈	#41×D₅₃	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	53	2	no	—
416	C₂²	—	53	2	no	—
417	C₂²	—	53	2	no	—
418	C₂²	—	53	2	no	—
419	C₂²	—	106	8	no	—
420	C₂²	—	106	1	no	—
421	C₂²	—	106	1	no	—
422	C₂²	C₂×C₁₆×D₅₃	1	2	yes	—
423	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	53	2	no	—
427	C₄	—	53	2	no	—
428	C₄	—	53	2	no	—
429	C₄	—	53	2	no	—
430	C₄	—	106	1	no	—
431	C₄	—	106	1	no	—
432	C₄	C₂×C₁₆×D₅₃	1	2	yes	—
433	C₄	C₂×C₁₆×D₅₃	1	2	yes	—
434	C₄	M₃₂×D₅₃	1	2	yes	—
435	C₄	#117×D₅₃	1	1	yes	characteristic
436	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	53	4	no	—
439	C₂	—	106	2	no	—
440	C₂	#431×D₅₃	1	1	yes	characteristic
441	C₂	C₂²×C₁₆×D₅₃	1	1	yes	characteristic
442	C₂	C₂×M₃₂×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₅₃
commutator	C₂×C₅₃	C₂³×C₁₆
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#2162	C₂
socle	C₂²×C₅₃	C₂³×C₈
prime radical	C₂³×D₅₃	C₂×C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2162	D₅₃
hypocenter	C₅₃	C₂×#2162
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄×C₈ ◁ #2162

Complements

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

N	H ≅ G/N	type
2. #20276514	C₂	semidirect
3. #20276513	C₂	semidirect
4. #20276512	C₂	semidirect
5. #20276511	C₂	semidirect
6. C₄⋊C₁₆×D₅₃	C₂	semidirect
8. C₄×C₁₆×D₅₃	C₂	semidirect
9. C₅₃×#2162	C₂	semidirect
25. C₄⋊#11719908	C₂²	semidirect
26. #16810441	C₂²	semidirect
29. C₄×#11719908	C₂²	semidirect
30. C₁₆×Dic₅₃	C₂²	semidirect
32. C₅₃×C₄⋊C₁₆	C₂²	semidirect
34. C₄×C₁₆×C₅₃	C₂²	semidirect
93. C₂×C₄×D₅₃	C₁₆	semidirect
153. C₂×C₄×C₅₃	C₂×C₁₆	semidirect
162. C₂×Dic₅₃	C₂×C₁₆	semidirect
178. C₄×D₅₃	C₂×C₁₆	semidirect
179. C₄×D₅₃	C₂×C₁₆	semidirect
221. #2162	D₅₃	direct (N × H)
230. D₅₃	#2162	direct (N × H)
249. C₄⋊C₁₆	C₂×D₅₃	semidirect
255. C₄×C₁₆	C₂×D₅₃	semidirect
256. C₅₃	C₂×#2162	semidirect
398. C₂×C₄	C₁₆×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×D₅₃	2
#20276514	2
#20276513	2
#20276512	2
#20276511	2
C₄⋊C₁₆×D₅₃	2
C₂²⋊C₁₆×D₅₃	2
C₄×C₁₆×D₅₃	2
C₅₃×#2162	2
C₂×#2162	53

Subgroups — D53×#2162 #27537153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2162 #27537153