Subgroups — D₅₃×#1279 #27273614

Order 13568.

974 conjugacy classes of subgroups.

The subgroup lattice has 414 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	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20272556	C₂	1	1	yes	maximal, characteristic, complemented
5	#20272555	C₂	1	1	yes	maximal, characteristic, complemented
6	#20272554	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₅₃	—	2	1	no	—
9	C₂²×C₈×D₅₃	—	2	1	no	—
10	C₂×C₄⋊C₄×D₅₃	C₄	1	2	yes	—
11	C₂×C₄²×D₅₃	—	2	1	no	—
12	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
14	C₂×#13133146	—	2	1	no	—
15	C₄⋊C₈×D₅₃	—	2	2	no	—
16	C₄⋊C₈×D₅₃	C₄	1	4	yes	complemented
17	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₅₃	—	2	1	no	—
19	C₄×C₈×D₅₃	—	2	2	no	—
20	C₄×C₈×D₅₃	C₄	1	4	yes	complemented
21	C₄⋊C₄×Dic₅₃	C₄	1	2	yes	—
22	C₄×#11719919	—	2	1	no	—
23	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
24	#16810474	—	2	1	no	—
25	#95×D₅₃	—	2	1	no	—
26	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₅₃	—	2	2	no	—
30	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
33	C₂²×#88322	—	2	1	no	—
34	C₂²×#88322	—	2	1	no	—
35	C₂×C₈×D₅₃	—	2	8	no	—
36	C₂×C₈×D₅₃	—	2	4	no	—
37	C₂×C₈×D₅₃	—	2	4	no	—
38	C₂×C₈×D₅₃	—	4	2	no	—
39	C₂×C₈×D₅₃	—	4	2	no	—
40	C₂×C₄⋊Dic₅₃	C₂×C₄	1	2	yes	—
41	C₂×#11719919	—	2	2	no	—
42	C₄⋊C₄×D₅₃	—	2	4	no	—
43	C₄⋊C₄×D₅₃	C₈	1	8	yes	complemented
44	C₂×C₄×Dic₅₃	—	2	1	no	—
45	C₂×C₄×Dic₅₃	—	2	2	no	—
46	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
49	C₄²×D₅₃	—	4	2	no	—
50	C₄²×D₅₃	—	4	2	no	—
51	C₄²×D₅₃	C₂×C₄	1	2	yes	—
52	C₄²×D₅₃	C₂×C₄	1	2	yes	—
53	C₄²×D₅₃	D₄	1	2	yes	—
54	C₄²×D₅₃	Q₈	1	2	yes	—
55	C₄⋊#88322	—	2	1	no	—
56	C₄⋊#88322	C₂×C₄	1	2	yes	complemented
57	#13133146	—	2	4	no	—
58	C₄×#88322	—	2	1	no	—
59	C₄×#88322	C₂×C₄	1	2	yes	complemented
60	C₈×Dic₅₃	—	2	4	no	—
61	#13133124	—	2	1	no	—
62	#13133124	—	2	2	no	—
63	C₂²×C₈×C₅₃	—	2	1	no	—
64	C₂²×C₈×C₅₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₅₃	—	2	1	no	—
67	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₅₃	—	2	1	no	—
69	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	complemented
70	C₄×C₈×C₅₃	—	2	1	no	—
71	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
72	#95×C₅₃	—	2	1	no	—
73	C₂³×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	—	2	2	no	—
75	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×Dic₅₃	—	2	2	no	—
79	C₂²×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₅₃	—	2	4	no	—
83	C₂×C₄×D₅₃	—	2	8	no	—
84	C₂×C₄×D₅₃	—	4	4	no	—
85	C₂×C₄×D₅₃	—	4	4	no	—
86	C₂×C₄×D₅₃	C₄²	1	2	yes	—
87	C₂×C₄×D₅₃	C₂²⋊C₄	1	2	yes	—
88	C₂×C₄×D₅₃	C₂²⋊C₄	1	2	yes	—
89	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
90	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
91	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
92	C₂×C₄×D₅₃	C₂×C₈	1	4	yes	—
93	C₂×C₄×D₅₃	M₁₆	1	4	yes	—
94	C₂×C₄×D₅₃	D₈	1	2	yes	—
95	C₂×C₄×D₅₃	SD₁₆	1	2	yes	—
96	C₂×C₄×D₅₃	SD₁₆	1	2	yes	—
97	C₂×C₄×D₅₃	Q₁₆	1	2	yes	—
98	C₂×C₈×C₅₃	—	2	4	no	—
99	C₂×C₈×C₅₃	—	2	2	no	—
100	C₂×C₈×C₅₃	—	2	2	no	—
101	C₂×C₈×C₅₃	—	4	1	no	—
102	C₂×C₈×C₅₃	—	4	1	no	—
103	C₄⋊C₄×C₅₃	—	2	2	no	—
104	C₄⋊C₄×C₅₃	C₂×C₈	1	4	yes	complemented
105	C₄²×C₅₃	—	4	1	no	—
106	C₄²×C₅₃	—	4	1	no	—
107	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
111	C₄⋊Dic₅₃	—	2	2	no	—
112	C₄⋊Dic₅₃	C₂×C₈	1	4	yes	complemented
113	#11719919	—	2	8	no	—
114	C₄×Dic₅₃	—	4	1	no	—
115	C₄×Dic₅₃	—	4	1	no	—
116	C₄×Dic₅₃	—	4	4	no	—
117	C₄×Dic₅₃	C₄²	1	2	yes	—
118	C₄×Dic₅₃	C₂²⋊C₄	1	2	yes	—
119	C₄×Dic₅₃	C₂²⋊C₄	1	2	yes	—
120	C₄×Dic₅₃	C₄⋊C₄	1	2	yes	—
121	C₄×Dic₅₃	C₄⋊C₄	1	2	yes	—
122	C₄×Dic₅₃	C₄⋊C₄	1	2	yes	—
123	C₂×#88322	—	2	4	no	—
124	C₂×#88322	—	2	2	no	—
125	C₂×#88322	—	2	2	no	—
126	C₂×#88322	—	4	1	no	—
127	C₂×#88322	—	4	1	no	—
128	C₈×D₅₃	—	2	16	no	—
129	C₈×D₅₃	—	4	8	no	—
130	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×D₅₃	#95	1	2	yes	—
132	C₂²×D₅₃	C₂²⋊C₈	1	4	yes	—
133	C₂²×D₅₃	#102	1	2	yes	—
134	C₂²×D₅₃	#103	1	2	yes	—
135	C₂²×D₅₃	#104	1	4	yes	—
136	C₂×C₄×C₅₃	—	2	2	no	—
137	C₂×C₄×C₅₃	—	2	4	no	—
138	C₂×C₄×C₅₃	—	4	2	no	—
139	C₂×C₄×C₅₃	—	4	2	no	—
140	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
147	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
148	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
152	C₂×Dic₅₃	—	2	2	no	—
153	C₂×Dic₅₃	—	2	4	no	—
154	C₂×Dic₅₃	—	4	2	no	—
155	C₂×Dic₅₃	—	4	2	no	—
156	C₂×Dic₅₃	#95	1	2	yes	—
157	C₂×Dic₅₃	#95	1	2	yes	—
158	C₂×Dic₅₃	#95	1	2	yes	—
159	C₂×Dic₅₃	C₂²⋊C₈	1	4	yes	—
160	C₂×Dic₅₃	#102	1	2	yes	—
161	C₂×Dic₅₃	#103	1	2	yes	—
162	C₄×D₅₃	—	2	4	no	—
163	C₄×D₅₃	—	2	4	no	—
164	C₄×D₅₃	—	4	16	no	—
165	C₄×D₅₃	C₄×C₈	1	4	yes	—
166	C₄×D₅₃	#97	1	4	yes	—
167	C₄×D₅₃	#102	1	4	yes	—
168	C₄×D₅₃	#103	1	4	yes	—
169	C₄×D₅₃	C₄⋊C₈	1	8	yes	—
170	C₄×D₅₃	#106	1	4	yes	—
171	C₄×D₅₃	#107	1	4	yes	—
172	C₈×C₅₃	—	2	4	no	—
173	C₈×C₅₃	—	4	2	no	—
174	#88322	—	2	4	no	—
175	#88322	—	4	2	no	—
176	C₂×#1279	—	53	1	no	maximal, Sylow
177	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
178	C₂²×C₅₃	C₂×C₂²⋊C₈	1	2	yes	—
179	C₂²×C₅₃	C₂×#102	1	1	yes	characteristic
180	C₂²×C₅₃	C₂×#103	1	1	yes	characteristic
181	C₂²×C₅₃	C₂×#104	1	2	yes	—
182	C₂×D₅₃	D₄⋊C₈	1	8	yes	—
183	C₂×D₅₃	Q₈⋊C₈	1	8	yes	—
184	C₂×D₅₃	#336	1	4	yes	—
185	C₂×D₅₃	#339	1	4	yes	—
186	C₂×D₅₃	#340	1	4	yes	—
187	C₄×C₅₃	—	2	1	no	—
188	C₄×C₅₃	—	2	1	no	—
189	C₄×C₅₃	—	4	4	no	—
190	C₄×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
191	C₄×C₅₃	C₂×#97	1	1	yes	characteristic
192	C₄×C₅₃	C₂×#102	1	1	yes	characteristic
193	C₄×C₅₃	C₂×#103	1	1	yes	characteristic
194	C₄×C₅₃	C₂×C₄⋊C₈	1	2	yes	—
195	C₄×C₅₃	C₂×#106	1	1	yes	characteristic
196	C₄×C₅₃	C₂×#107	1	1	yes	characteristic
197	Dic₅₃	—	2	2	no	—
198	Dic₅₃	—	4	4	no	—
199	Dic₅₃	#336	1	4	yes	—
200	Dic₅₃	#340	1	4	yes	—
201	C₂²×C₄⋊C₈	—	53	1	no	—
202	C₂²×C₄×C₈	—	53	1	no	—
203	C₂×C₄×C₄⋊C₄	—	53	1	no	—
204	#1279	—	53	1	no	—
205	#1279	—	53	1	no	—
206	#1279	—	53	1	no	—
207	#1279	D₅₃	1	1	yes	characteristic, direct product factor
208	C₂×C₅₃	C₂×D₄⋊C₈	1	2	yes	—
209	C₂×C₅₃	C₂×Q₈⋊C₈	1	2	yes	—
210	C₂×C₅₃	C₂×#336	1	1	yes	characteristic
211	C₂×C₅₃	C₂×#339	1	1	yes	characteristic
212	C₂×C₅₃	C₂×#340	1	1	yes	characteristic
213	D₅₃	#1279	1	8	yes	direct product factor
214	C₂³×C₈	—	106	1	no	—
215	C₂³×C₈	—	106	1	no	—
216	C₂²×C₄⋊C₄	—	53	2	no	—
217	C₂²×C₄²	—	53	1	no	—
218	C₂²×C₄²	—	106	1	no	—
219	C₂×C₄⋊C₈	—	53	1	no	—
220	C₂×C₄⋊C₈	—	53	4	no	—
221	C₂×C₄⋊C₈	—	106	2	no	—
222	C₂×C₄⋊C₈	—	106	1	no	—
223	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
224	C₂×C₄×C₈	—	53	1	no	—
225	C₂×C₄×C₈	—	53	4	no	—
226	C₂×C₄×C₈	—	106	2	no	—
227	C₂×C₄×C₈	—	106	1	no	—
228	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
229	C₄×C₄⋊C₄	—	53	2	no	—
230	C₄×C₄⋊C₄	—	53	1	no	—
231	C₄×C₄⋊C₄	—	106	1	no	—
232	C₄×C₄⋊C₄	—	106	1	no	—
233	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
234	C₂×#95	—	106	1	no	—
235	C₅₃	C₂×#1279	1	1	yes	characteristic, complemented, Sylow
236	C₂³×C₄	—	53	1	no	—
237	C₂³×C₄	—	53	1	no	—
238	C₂³×C₄	—	53	1	no	—
239	C₂³×C₄	—	106	2	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	106	4	no	—
243	C₂²×C₈	—	106	8	no	—
244	C₂²×C₈	—	106	4	no	—
245	C₂²×C₈	—	106	1	no	—
246	C₂²×C₈	—	106	1	no	—
247	C₂²×C₈	—	212	2	no	—
248	C₂²×C₈	—	212	2	no	—
249	C₂×C₄⋊C₄	—	53	2	no	—
250	C₂×C₄⋊C₄	—	53	8	no	—
251	C₂×C₄⋊C₄	—	106	4	no	—
252	C₂×C₄⋊C₄	—	106	2	no	—
253	C₂×C₄⋊C₄	C₄×D₅₃	1	2	yes	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	—	53	1	no	—
256	C₂×C₄²	—	53	1	no	—
257	C₂×C₄²	—	53	1	no	—
258	C₂×C₄²	—	53	2	no	—
259	C₂×C₄²	—	53	2	no	—
260	C₂×C₄²	—	53	2	no	—
261	C₂×C₄²	—	53	2	no	—
262	C₂×C₄²	—	106	2	no	—
263	C₂×C₄²	—	106	1	no	—
264	C₂×C₄²	—	212	2	no	—
265	C₂×C₄²	—	212	2	no	—
266	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	53	2	no	—
269	C₄⋊C₈	—	106	4	no	—
270	C₄⋊C₈	—	106	1	no	—
271	C₄⋊C₈	C₄×D₅₃	1	2	yes	complemented
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	53	2	no	—
274	C₄×C₈	—	106	4	no	—
275	C₄×C₈	—	106	1	no	—
276	C₄×C₈	C₄×D₅₃	1	2	yes	complemented
277	#95	—	2	1	no	—
278	#95	—	106	2	no	—
279	#95	—	106	1	no	—
280	C₂⁴	—	53	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	53	1	no	—
283	C₂²×C₄	—	53	1	no	—
284	C₂²×C₄	—	53	2	no	—
285	C₂²×C₄	—	53	2	no	—
286	C₂²×C₄	—	53	2	no	—
287	C₂²×C₄	—	53	2	no	—
288	C₂²×C₄	—	53	4	no	—
289	C₂²×C₄	—	53	4	no	—
290	C₂²×C₄	—	53	2	no	—
291	C₂²×C₄	—	53	2	no	—
292	C₂²×C₄	—	53	2	no	—
293	C₂²×C₄	—	53	2	no	—
294	C₂²×C₄	—	53	1	no	—
295	C₂²×C₄	—	53	2	no	—
296	C₂²×C₄	—	53	2	no	—
297	C₂²×C₄	—	106	4	no	—
298	C₂²×C₄	—	106	8	no	—
299	C₂²×C₄	—	106	2	no	—
300	C₂²×C₄	—	212	4	no	—
301	C₂²×C₄	—	212	4	no	—
302	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
303	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
304	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	106	16	no	—
311	C₂×C₈	—	106	4	no	—
312	C₂×C₈	—	106	2	no	—
313	C₂×C₈	—	106	2	no	—
314	C₂×C₈	—	212	8	no	—
315	C₂×C₈	—	212	1	no	—
316	C₂×C₈	—	212	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	53	4	no	—
319	C₄⋊C₄	—	106	8	no	—
320	C₄⋊C₄	—	106	2	no	—
321	C₄⋊C₄	C₈×D₅₃	1	4	yes	complemented
322	C₄²	—	4	1	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	53	2	no	—
325	C₄²	—	53	2	no	—
326	C₄²	—	53	2	no	—
327	C₄²	—	53	2	no	—
328	C₄²	—	53	2	no	—
329	C₄²	—	53	2	no	—
330	C₄²	—	212	4	no	—
331	C₄²	—	212	1	no	—
332	C₄²	—	212	1	no	—
333	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
334	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
335	C₄²	D₄×D₅₃	1	1	yes	characteristic
336	C₄²	Q₈×D₅₃	1	1	yes	characteristic
337	C₂³	—	53	4	no	—
338	C₂³	—	53	2	no	—
339	C₂³	—	53	2	no	—
340	C₂³	—	53	4	no	—
341	C₂³	—	53	2	no	—
342	C₂³	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	53	4	no	—
348	C₂×C₄	—	53	2	no	—
349	C₂×C₄	—	53	2	no	—
350	C₂×C₄	—	53	2	no	—
351	C₂×C₄	—	53	2	no	—
352	C₂×C₄	—	53	4	no	—
353	C₂×C₄	—	53	4	no	—
354	C₂×C₄	—	53	4	no	—
355	C₂×C₄	—	53	4	no	—
356	C₂×C₄	—	53	8	no	—
357	C₂×C₄	—	53	4	no	—
358	C₂×C₄	—	53	4	no	—
359	C₂×C₄	—	53	2	no	—
360	C₂×C₄	—	106	4	no	—
361	C₂×C₄	—	106	4	no	—
362	C₂×C₄	—	106	2	no	—
363	C₂×C₄	—	106	4	no	—
364	C₂×C₄	—	212	16	no	—
365	C₂×C₄	—	212	2	no	—
366	C₂×C₄	—	212	2	no	—
367	C₂×C₄	C₄²×D₅₃	1	1	yes	characteristic
368	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
369	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
370	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
371	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
372	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
374	C₂×C₄	M₁₆×D₅₃	1	2	yes	—
375	C₂×C₄	D₈×D₅₃	1	1	yes	characteristic
376	C₂×C₄	SD₁₆×D₅₃	1	1	yes	characteristic
377	C₂×C₄	SD₁₆×D₅₃	1	1	yes	characteristic
378	C₂×C₄	Q₁₆×D₅₃	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	4	2	no	—
381	C₈	—	106	4	no	—
382	C₈	—	212	2	no	—
383	C₂²	—	53	8	no	—
384	C₂²	—	53	8	no	—
385	C₂²	—	53	4	no	—
386	C₂²	—	53	4	no	—
387	C₂²	—	53	4	no	—
388	C₂²	#95×D₅₃	1	1	yes	characteristic
389	C₂²	C₂²⋊C₈×D₅₃	1	2	yes	—
390	C₂²	#102×D₅₃	1	1	yes	characteristic
391	C₂²	#103×D₅₃	1	1	yes	characteristic
392	C₂²	#104×D₅₃	1	2	yes	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	4	no	—
396	C₄	—	53	4	no	—
397	C₄	—	53	4	no	—
398	C₄	—	106	2	no	—
399	C₄	—	212	4	no	—
400	C₄	C₄×C₈×D₅₃	1	1	yes	characteristic
401	C₄	#97×D₅₃	1	1	yes	characteristic
402	C₄	#102×D₅₃	1	1	yes	characteristic
403	C₄	#103×D₅₃	1	1	yes	characteristic
404	C₄	C₄⋊C₈×D₅₃	1	2	yes	—
405	C₄	#106×D₅₃	1	1	yes	characteristic
406	C₄	#107×D₅₃	1	1	yes	characteristic
407	C₂	—	53	8	no	—
408	C₂	D₄⋊C₈×D₅₃	1	2	yes	—
409	C₂	Q₈⋊C₈×D₅₃	1	2	yes	—
410	C₂	#336×D₅₃	1	1	yes	characteristic
411	C₂	#339×D₅₃	1	1	yes	characteristic
412	C₂	#340×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₃
commutator	C₄×C₅₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1279	C₂
socle	C₂³×C₅₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₅₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1279	D₅₃
hypocenter	C₅₃	C₂×#1279
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #20272556	C₂	semidirect
5. #20272555	C₂	semidirect
6. #20272554	C₂	semidirect
7. C₅₃×#1279	C₂	semidirect
16. C₄⋊C₈×D₅₃	C₄	semidirect
20. C₄×C₈×D₅₃	C₄	semidirect
43. C₄⋊C₄×D₅₃	C₈	semidirect
56. C₄⋊#88322	C₂×C₄	semidirect
59. C₄×#88322	C₂×C₄	semidirect
69. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
71. C₄×C₈×C₅₃	C₂×C₄	semidirect
104. C₄⋊C₄×C₅₃	C₂×C₈	semidirect
112. C₄⋊Dic₅₃	C₂×C₈	semidirect
207. #1279	D₅₃	direct (N × H)
213. D₅₃	#1279	direct (N × H)
235. C₅₃	C₂×#1279	semidirect
271. C₄⋊C₈	C₄×D₅₃	semidirect
276. C₄×C₈	C₄×D₅₃	semidirect
321. C₄⋊C₄	C₈×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
C₂×C₄×C₈×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
#20272556	2
#20272555	2
#20272554	2
C₅₃×#1279	2
C₂×#1279	53

Subgroups — D53×#1279 #27273614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1279 #27273614