Subgroups — D₄×C₁₆×D₅₃ #27537238

Order 13568.

806 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×D₅₃	C₂	1	2	yes	maximal, complemented
2	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×#11719908	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276534	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
7	#20276532	C₂	1	2	yes	maximal, complemented
8	C₄⋊C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²⋊C₁₆×D₅₃	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₅₃	C₂²	1	2	yes	—
13	C₄×D₄×D₅₃	C₄	1	1	yes	characteristic
14	C₂²×#11719908	C₂²	1	2	yes	complemented
15	C₂×C₁₆×D₅₃	—	2	8	no	—
16	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
17	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₅₃	C₂²	1	2	yes	complemented
20	C₂×C₁₆×D₅₃	C₂²	1	2	yes	complemented
21	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
22	D₄×#88322	C₄	1	1	yes	characteristic
23	#16810688	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	—
25	#16810686	C₄	1	2	yes	—
26	C₄⋊C₈×D₅₃	C₄	1	1	yes	characteristic
27	C₂²⋊C₈×D₅₃	C₄	1	2	yes	—
28	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
29	C₄⋊#11719908	C₂²	1	1	yes	characteristic, complemented
30	#16810441	C₂²	1	2	yes	complemented
31	C₂²⋊#11719908	C₂²	1	2	yes	complemented
32	#16810402	C₂²	1	2	yes	complemented
33	#16810402	C₂²	1	2	yes	complemented
34	C₄×#11719908	C₂²	1	1	yes	characteristic, complemented
35	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₆×C₅₃	C₂²	1	2	yes	complemented
38	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₅₃	C₈	1	1	yes	characteristic
43	C₂²×C₄×D₅₃	C₂×C₄	1	2	yes	—
44	C₂²×#88322	C₂×C₄	1	2	yes	—
45	C₂×C₈×D₅₃	—	2	4	no	—
46	C₂×C₈×D₅₃	—	2	4	no	—
47	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
50	C₂×C₈×D₅₃	C₂³	1	2	yes	—
51	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
52	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
53	D₄×Dic₅₃	C₈	1	1	yes	characteristic
54	#13133179	C₈	1	1	yes	characteristic
55	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
56	#13133177	C₈	1	2	yes	—
57	C₄⋊C₄×D₅₃	C₈	1	1	yes	characteristic
58	C₂²⋊C₄×D₅₃	C₈	1	2	yes	—
59	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×#11719908	—	2	4	no	—
61	C₂×#11719908	C₂³	1	2	yes	—
62	C₂×#11719908	C₂³	1	1	yes	characteristic
63	C₂×#11719908	C₂³	1	1	yes	characteristic
64	C₁₆×D₅₃	—	2	4	no	—
65	C₁₆×D₅₃	—	2	2	no	—
66	C₁₆×D₅₃	—	2	4	no	—
67	C₁₆×D₅₃	—	2	4	no	—
68	C₁₆×D₅₃	D₄	1	4	yes	direct product factor
69	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
70	#13133146	C₂×C₄	1	2	yes	—
71	C₂²⋊#88322	C₂×C₄	1	2	yes	—
72	#13133129	C₂×C₄	1	2	yes	—
73	#13133129	C₂×C₄	1	2	yes	—
74	C₄×#88322	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
78	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₆×C₅₃	—	2	4	no	—
80	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
81	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
82	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
85	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₂³×D₅₃	C₂×C₈	1	2	yes	—
87	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
89	C₂×C₂²⋊D₅₃	C₂×C₈	1	2	yes	—
90	C₂²×Dic₅₃	C₂×C₈	1	2	yes	—
91	D₄×D₅₃	C₁₆	1	8	yes	direct product factor
92	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₅₃	—	2	4	no	—
94	C₂×C₄×D₅₃	—	2	4	no	—
95	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
97	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
98	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
100	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₅₃	—	2	2	no	—
102	C₂×C₈×C₅₃	—	2	2	no	—
103	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
106	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
107	C₂²⋊C₄×C₅₃	C₂×C₈	1	2	yes	—
108	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²⋊Dic₅₃	C₂×C₈	1	2	yes	—
110	#11719921	C₂×C₈	1	2	yes	—
111	#11719921	C₂×C₈	1	2	yes	—
112	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
113	#11719919	C₂×C₈	1	2	yes	—
114	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
115	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
116	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×#88322	—	2	4	no	—
118	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
119	C₂×#88322	C₂²×C₄	1	2	yes	—
120	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₅₃	—	2	4	no	—
122	C₈×D₅₃	—	2	2	no	—
123	C₈×D₅₃	—	2	2	no	—
124	C₈×D₅₃	—	2	2	no	—
125	C₈×D₅₃	—	2	4	no	—
126	C₈×D₅₃	C₂×D₄	1	2	yes	—
127	C₈×D₅₃	#41	1	2	yes	—
128	C₁₆×C₅₃	—	2	2	no	—
129	C₁₆×C₅₃	—	2	1	no	—
130	C₁₆×C₅₃	C₂×D₄	1	2	yes	complemented
131	#11719908	—	2	2	no	—
132	#11719908	—	2	1	no	—
133	#11719908	C₂×D₄	1	2	yes	complemented
134	C₂³×C₅₃	C₂²×C₈	1	2	yes	—
135	C₂²×D₅₃	—	2	4	no	—
136	C₂²×D₅₃	—	2	4	no	—
137	C₂²×D₅₃	C₂×C₁₆	1	8	yes	complemented
138	C₂²×D₅₃	C₂²×C₈	1	2	yes	—
139	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
140	D₄×C₅₃	C₂×C₁₆	1	4	yes	complemented
141	C₂×C₄×C₅₃	—	2	2	no	—
142	C₂×C₄×C₅₃	—	2	2	no	—
143	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
144	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
145	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
147	C₂²⋊D₅₃	C₂×C₁₆	1	8	yes	complemented
148	C₂×Dic₅₃	—	2	4	no	—
149	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
150	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
151	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
152	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
153	D₂₁₂	C₂×C₁₆	1	4	yes	complemented
154	C₄×D₅₃	—	2	4	no	—
155	C₄×D₅₃	—	2	2	no	—
156	C₄×D₅₃	—	2	2	no	—
157	C₄×D₅₃	—	2	2	no	—
158	C₄×D₅₃	—	2	4	no	—
159	C₄×D₅₃	C₂×C₁₆	1	4	yes	complemented
160	C₄×D₅₃	C₄×D₄	1	2	yes	—
161	C₄×D₅₃	#131	1	2	yes	—
162	C₈×C₅₃	—	2	2	no	—
163	C₈×C₅₃	—	2	1	no	—
164	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
165	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
166	#88322	—	2	2	no	—
167	#88322	—	2	1	no	—
168	#88322	C₄×D₄	1	2	yes	—
169	C₂×D₄×C₁₆	—	53	1	no	maximal, Sylow
170	C₂²×C₅₃	—	2	2	no	—
171	C₂²×C₅₃	—	2	2	no	—
172	C₂²×C₅₃	C₂²×C₁₆	1	4	yes	complemented
173	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
174	C₂×D₅₃	—	2	2	no	—
175	C₂×D₅₃	—	2	2	no	—
176	C₂×D₅₃	—	2	16	no	—
177	C₂×D₅₃	C₈×D₄	1	2	yes	—
178	C₂×D₅₃	C₂²×C₁₆	1	2	yes	—
179	C₂×D₅₃	C₂²×C₁₆	1	4	yes	complemented
180	C₂×D₅₃	#504	1	2	yes	—
181	C₄×C₅₃	—	2	1	no	—
182	C₄×C₅₃	—	2	2	no	—
183	C₄×C₅₃	C₂²×C₁₆	1	2	yes	complemented
184	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
186	Dic₅₃	—	2	1	no	—
187	Dic₅₃	—	2	2	no	—
188	Dic₅₃	C₈×D₄	1	2	yes	—
189	Dic₅₃	C₂²×C₁₆	1	2	yes	complemented
190	C₂³×C₁₆	—	53	2	no	—
191	C₂×C₈×D₄	—	53	1	no	—
192	D₄×C₁₆	—	53	2	no	—
193	D₄×C₁₆	—	53	1	no	—
194	D₄×C₁₆	—	53	1	no	—
195	D₄×C₁₆	—	53	2	no	—
196	D₄×C₁₆	—	53	1	no	—
197	D₄×C₁₆	D₅₃	1	1	yes	characteristic, direct product factor
198	C₂×C₄⋊C₁₆	—	53	1	no	—
199	C₂×C₂²⋊C₁₆	—	53	2	no	—
200	C₂×C₄×C₁₆	—	53	1	no	—
201	C₂×C₅₃	—	2	4	no	—
202	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
203	C₂×C₅₃	C₂³×C₁₆	1	1	yes	characteristic
204	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
205	D₅₃	—	2	4	no	—
206	D₅₃	D₄×C₁₆	1	4	yes	direct product factor
207	C₂³×C₈	—	53	2	no	—
208	C₂×C₄×D₄	—	53	1	no	—
209	C₂²×C₁₆	—	53	1	no	—
210	C₂²×C₁₆	—	53	2	no	—
211	C₂²×C₁₆	—	53	1	no	—
212	C₂²×C₁₆	—	53	2	no	—
213	C₂²×C₁₆	—	53	2	no	—
214	C₂²×C₁₆	—	53	2	no	—
215	C₂²×C₁₆	—	106	8	no	—
216	C₂²×C₁₆	C₂×D₅₃	1	2	yes	complemented
217	C₈×D₄	—	53	2	no	—
218	C₈×D₄	—	53	1	no	—
219	C₈×D₄	—	53	1	no	—
220	C₈×D₄	—	53	2	no	—
221	C₈×D₄	—	53	1	no	—
222	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
223	C₂×C₄⋊C₈	—	53	1	no	—
224	C₂×C₂²⋊C₈	—	53	2	no	—
225	C₂×C₄×C₈	—	53	1	no	—
226	C₄⋊C₁₆	—	53	2	no	—
227	C₄⋊C₁₆	—	53	1	no	—
228	C₄⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
229	C₂²⋊C₁₆	—	53	2	no	—
230	C₂²⋊C₁₆	—	53	2	no	—
231	C₂²⋊C₁₆	—	53	2	no	—
232	C₂²⋊C₁₆	C₂×D₅₃	1	2	yes	complemented
233	C₄×C₁₆	—	53	1	no	—
234	C₄×C₁₆	—	53	1	no	—
235	C₄×C₁₆	—	53	1	no	—
236	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
237	C₅₃	C₂×D₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
238	C₂²×D₄	—	53	1	no	—
239	C₂³×C₄	—	53	2	no	—
240	C₂²×C₈	—	53	1	no	—
241	C₂²×C₈	—	53	2	no	—
242	C₂²×C₈	—	53	2	no	—
243	C₂²×C₈	—	53	2	no	—
244	C₂²×C₈	—	53	1	no	—
245	C₂²×C₈	—	53	2	no	—
246	C₂²×C₈	—	106	4	no	—
247	C₂²×C₈	—	106	4	no	—
248	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
249	C₄×D₄	—	53	1	no	—
250	C₄×D₄	—	53	2	no	—
251	C₄×D₄	—	53	1	no	—
252	C₄×D₄	—	53	2	no	—
253	C₄×D₄	—	53	1	no	—
254	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
255	C₂×C₄⋊C₄	—	53	1	no	—
256	C₂×C₂²⋊C₄	—	53	2	no	—
257	C₂×C₄²	—	53	1	no	—
258	C₂×C₁₆	—	2	4	no	—
259	C₂×C₁₆	—	53	1	no	—
260	C₂×C₁₆	—	53	4	no	—
261	C₂×C₁₆	—	53	1	no	—
262	C₂×C₁₆	—	53	2	no	—
263	C₂×C₁₆	—	106	4	no	—
264	C₂×C₁₆	—	106	2	no	—
265	C₂×C₁₆	—	106	4	no	—
266	C₂×C₁₆	—	106	4	no	—
267	C₂×C₁₆	—	106	4	no	—
268	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
269	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
270	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
271	C₄⋊C₈	—	53	2	no	—
272	C₄⋊C₈	—	53	1	no	—
273	C₄⋊C₈	C₄×D₅₃	1	1	yes	characteristic
274	C₂²⋊C₈	—	53	2	no	—
275	C₂²⋊C₈	—	53	2	no	—
276	C₂²⋊C₈	—	53	2	no	—
277	C₂²⋊C₈	C₄×D₅₃	1	2	yes	—
278	C₄×C₈	—	53	1	no	—
279	C₄×C₈	—	53	1	no	—
280	C₄×C₈	—	53	1	no	—
281	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
282	C₂⁴	—	53	2	no	—
283	C₂×D₄	—	53	2	no	—
284	C₂×D₄	—	53	8	no	—
285	C₂×D₄	—	53	1	no	—
286	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
287	C₂²×C₄	—	53	1	no	—
288	C₂²×C₄	—	53	1	no	—
289	C₂²×C₄	—	53	2	no	—
290	C₂²×C₄	—	53	1	no	—
291	C₂²×C₄	—	53	2	no	—
292	C₂²×C₄	—	53	2	no	—
293	C₂²×C₄	—	53	2	no	—
294	C₂²×C₄	—	106	4	no	—
295	C₂²×C₄	—	106	4	no	—
296	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	53	1	no	—
300	C₂×C₈	—	53	2	no	—
301	C₂×C₈	—	53	2	no	—
302	C₂×C₈	—	53	1	no	—
303	C₂×C₈	—	53	2	no	—
304	C₂×C₈	—	106	4	no	—
305	C₂×C₈	—	106	4	no	—
306	C₂×C₈	—	106	2	no	—
307	C₂×C₈	—	106	4	no	—
308	C₂×C₈	—	106	2	no	—
309	C₂×C₈	—	106	2	no	—
310	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
311	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
312	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
313	C₄⋊C₄	—	53	2	no	—
314	C₄⋊C₄	—	53	1	no	—
315	C₄⋊C₄	C₈×D₅₃	1	1	yes	characteristic
316	C₂²⋊C₄	—	53	2	no	—
317	C₂²⋊C₄	—	53	2	no	—
318	C₂²⋊C₄	—	53	2	no	—
319	C₂²⋊C₄	C₈×D₅₃	1	2	yes	—
320	C₄²	—	53	1	no	—
321	C₄²	—	53	1	no	—
322	C₄²	—	53	1	no	—
323	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
324	C₁₆	—	2	2	no	—
325	C₁₆	—	2	1	no	—
326	C₁₆	—	53	2	no	—
327	C₁₆	—	106	2	no	—
328	C₁₆	—	106	1	no	—
329	C₁₆	D₄×D₅₃	1	2	yes	direct product factor
330	C₂³	—	53	1	no	—
331	C₂³	—	53	8	no	—
332	C₂³	—	53	2	no	—
333	C₂³	—	106	4	no	—
334	C₂³	—	106	4	no	—
335	C₂³	C₂×C₈×D₅₃	1	2	yes	—
336	D₄	—	53	8	no	—
337	D₄	—	53	4	no	—
338	D₄	C₁₆×D₅₃	1	4	yes	direct product factor
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	53	1	no	—
342	C₂×C₄	—	53	1	no	—
343	C₂×C₄	—	53	4	no	—
344	C₂×C₄	—	53	2	no	—
345	C₂×C₄	—	53	2	no	—
346	C₂×C₄	—	53	1	no	—
347	C₂×C₄	—	53	2	no	—
348	C₂×C₄	—	106	4	no	—
349	C₂×C₄	—	106	2	no	—
350	C₂×C₄	—	106	4	no	—
351	C₂×C₄	—	106	4	no	—
352	C₂×C₄	—	106	2	no	—
353	C₂×C₄	—	106	2	no	—
354	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
356	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₈	—	2	1	no	—
360	C₈	—	53	2	no	—
361	C₈	—	106	2	no	—
362	C₈	—	106	1	no	—
363	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
364	C₈	#41×D₅₃	1	1	yes	characteristic
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	53	2	no	—
368	C₂²	—	53	2	no	—
369	C₂²	—	53	2	no	—
370	C₂²	—	53	4	no	—
371	C₂²	—	106	16	no	—
372	C₂²	—	106	2	no	—
373	C₂²	—	106	2	no	—
374	C₂²	C₂×C₁₆×D₅₃	1	4	yes	complemented
375	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	2	no	—
378	C₄	—	53	2	no	—
379	C₄	—	53	2	no	—
380	C₄	—	106	1	no	—
381	C₄	—	106	2	no	—
382	C₄	C₂×C₁₆×D₅₃	1	2	yes	complemented
383	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
384	C₄	#131×D₅₃	1	1	yes	characteristic
385	C₂	—	2	4	no	—
386	C₂	—	53	4	no	—
387	C₂	—	106	4	no	—
388	C₂	C₈×D₄×D₅₃	1	1	yes	characteristic
389	C₂	C₂²×C₁₆×D₅₃	1	1	yes	characteristic
390	C₂	#504×D₅₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₆×D₅₃	C₂	semidirect
3. C₁₆×D₂₁₂	C₂	semidirect
4. D₄×#11719908	C₂	semidirect
5. #20276534	C₂	semidirect
6. C₁₆×C₂²⋊D₅₃	C₂	semidirect
7. #20276532	C₂	semidirect
8. C₄⋊C₁₆×D₅₃	C₂	semidirect
9. C₂²⋊C₁₆×D₅₃	C₂	semidirect
10. C₄×C₁₆×D₅₃	C₂	semidirect
11. D₄×C₁₆×C₅₃	C₂	semidirect
14. C₂²×#11719908	C₂²	semidirect
19. C₂×C₁₆×D₅₃	C₂²	semidirect
20. C₂×C₁₆×D₅₃	C₂²	semidirect
29. C₄⋊#11719908	C₂²	semidirect
30. #16810441	C₂²	semidirect
31. C₂²⋊#11719908	C₂²	semidirect
32. #16810402	C₂²	semidirect
33. #16810402	C₂²	semidirect
34. C₄×#11719908	C₂²	semidirect
35. C₁₆×Dic₅₃	C₂²	semidirect
36. C₁₆×Dic₅₃	C₂²	semidirect
37. C₂²×C₁₆×C₅₃	C₂²	semidirect
39. C₅₃×C₄⋊C₁₆	C₂²	semidirect
40. C₅₃×C₂²⋊C₁₆	C₂²	semidirect
41. C₄×C₁₆×C₅₃	C₂²	semidirect
68. C₁₆×D₅₃	D₄	direct (N × H)
91. D₄×D₅₃	C₁₆	direct (N × H)
130. C₁₆×C₅₃	C₂×D₄	semidirect
133. #11719908	C₂×D₄	semidirect
137. C₂²×D₅₃	C₂×C₁₆	semidirect
140. D₄×C₅₃	C₂×C₁₆	semidirect
147. C₂²⋊D₅₃	C₂×C₁₆	semidirect
153. D₂₁₂	C₂×C₁₆	semidirect
159. C₄×D₅₃	C₂×C₁₆	semidirect
172. C₂²×C₅₃	C₂²×C₁₆	semidirect
179. C₂×D₅₃	C₂²×C₁₆	semidirect
183. C₄×C₅₃	C₂²×C₁₆	semidirect
189. Dic₅₃	C₂²×C₁₆	semidirect
197. D₄×C₁₆	D₅₃	direct (N × H)
206. D₅₃	D₄×C₁₆	direct (N × H)
216. C₂²×C₁₆	C₂×D₅₃	semidirect
228. C₄⋊C₁₆	C₂×D₅₃	semidirect
232. C₂²⋊C₁₆	C₂×D₅₃	semidirect
236. C₄×C₁₆	C₂×D₅₃	semidirect
237. C₅₃	C₂×D₄×C₁₆	semidirect
329. C₁₆	D₄×D₅₃	direct (N × H)
338. D₄	C₁₆×D₅₃	direct (N × H)
374. C₂²	C₂×C₁₆×D₅₃	semidirect
382. C₄	C₂×C₁₆×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₆×D₅₃	2
C₈×D₄×D₅₃	2
C₁₆×D₂₁₂	2
D₄×#11719908	2
#20276534	2
C₁₆×C₂²⋊D₅₃	2
#20276532	2
C₄⋊C₁₆×D₅₃	2
C₂²⋊C₁₆×D₅₃	2
C₄×C₁₆×D₅₃	2
D₄×C₁₆×C₅₃	2
C₂×D₄×C₁₆	53

Subgroups — D4×C16×D53 #27537238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₆×D₅₃ #27537238