Subgroups — D₅₃×#1917 #27386138

Order 13568.

1070 conjugacy classes of subgroups.

The subgroup lattice has 672 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×#97×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20275282	C₂	1	1	yes	maximal, characteristic, complemented
5	#20275281	C₂	1	1	yes	maximal, characteristic, complemented
6	#20275280	C₂	1	1	yes	maximal, characteristic, complemented
7	#20275279	C₂	1	1	yes	maximal, characteristic, complemented
8	#20275278	C₂	1	1	yes	maximal, characteristic, complemented
9	#20275277	C₂	1	1	yes	maximal, characteristic, complemented
10	#20275276	C₂	1	1	yes	maximal, characteristic, complemented
11	#336×D₅₃	C₂	1	1	yes	maximal, characteristic
12	#336×D₅₃	C₂	1	1	yes	maximal, characteristic
13	#336×D₅₃	C₂	1	1	yes	maximal, characteristic
14	#336×D₅₃	C₂	1	1	yes	maximal, characteristic
15	C₅₃×#1917	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×D₅₃	C₄	1	1	yes	characteristic
21	C₂×C₄⋊C₄×D₅₃	C₄	1	1	yes	characteristic
22	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
26	C₂×#13133146	C₂²	1	1	yes	characteristic
27	C₂×#13133146	C₂²	1	1	yes	characteristic
28	C₄⋊C₈×D₅₃	—	2	4	no	—
29	C₂×#13133128	C₂²	1	1	yes	characteristic
30	C₂×#13133127	C₂²	1	1	yes	characteristic
31	C₂×#13133127	C₂²	1	1	yes	characteristic
32	#97×D₅₃	—	2	4	no	—
33	C₄⋊C₄×Dic₅₃	C₄	1	1	yes	characteristic
34	C₄⋊C₄×Dic₅₃	C₄	1	1	yes	characteristic
35	C₄×#11719919	C₂²	1	1	yes	characteristic
36	C₄×#11719919	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
38	#16810474	C₄	1	1	yes	characteristic
39	#16810474	C₄	1	1	yes	characteristic
40	#95×D₅₃	C₄	1	1	yes	characteristic
41	#95×D₅₃	C₄	1	1	yes	characteristic
42	#16810378	C₂²	1	1	yes	characteristic
43	#16810378	C₂²	1	1	yes	characteristic
44	#16810378	C₂²	1	1	yes	characteristic
45	#16810378	C₂²	1	1	yes	characteristic
46	#16810377	C₂²	1	1	yes	characteristic
47	#16810377	C₂²	1	1	yes	characteristic
48	#16810377	C₂²	1	1	yes	characteristic
49	#16810377	C₂²	1	1	yes	characteristic
50	#16810377	C₂²	1	1	yes	characteristic
51	#16810377	C₂²	1	1	yes	characteristic
52	#16810377	C₂²	1	1	yes	characteristic
53	#16810377	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#336	C₂²	1	1	yes	characteristic
58	C₅₃×#336	C₂²	1	1	yes	characteristic
59	C₅₃×#336	C₂²	1	1	yes	characteristic
60	C₅₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
68	C₂²×#88322	C₂³	1	1	yes	characteristic
69	C₂²×#88322	C₂³	1	1	yes	characteristic
70	C₂²×#88322	C₂³	1	1	yes	characteristic
71	C₂²×#88322	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₅₃	—	2	2	no	—
73	C₂×C₈×D₅₃	—	2	2	no	—
74	C₂×C₈×D₅₃	—	2	2	no	—
75	C₂×C₈×D₅₃	—	2	2	no	—
76	C₂×C₈×D₅₃	—	2	2	no	—
77	C₂×C₈×D₅₃	—	2	2	no	—
78	C₂×C₈×D₅₃	—	2	2	no	—
79	C₂×C₈×D₅₃	—	2	2	no	—
80	C₂×C₈×D₅₃	—	2	2	no	—
81	C₂×C₈×D₅₃	—	2	2	no	—
82	C₂×C₈×D₅₃	D₄	1	4	yes	—
83	C₂×C₈×D₅₃	Q₈	1	4	yes	—
84	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
87	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
88	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
89	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₄×D₅₃	—	2	4	no	—
91	C₄⋊C₄×D₅₃	—	2	4	no	—
92	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
101	C₄²×D₅₃	—	2	2	no	—
102	C₄²×D₅₃	—	2	2	no	—
103	C₄²×D₅₃	—	2	2	no	—
104	C₄²×D₅₃	—	2	2	no	—
105	C₄²×D₅₃	—	2	2	no	—
106	C₄²×D₅₃	—	2	2	no	—
107	C₄⋊#88322	—	2	2	no	—
108	#13133146	—	2	2	no	—
109	#13133146	—	2	2	no	—
110	#13133128	—	2	2	no	—
111	#13133127	—	2	2	no	—
112	#13133127	—	2	2	no	—
113	#13133124	C₂×C₄	1	1	yes	characteristic
114	#13133124	C₂×C₄	1	1	yes	characteristic
115	#13133124	C₂×C₄	1	1	yes	characteristic
116	#13133124	C₂×C₄	1	1	yes	characteristic
117	#13133124	C₂×C₄	1	1	yes	characteristic
118	#13133124	C₂×C₄	1	1	yes	characteristic
119	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₅₃	—	2	2	no	—
129	#97×C₅₃	—	2	2	no	—
130	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
131	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
132	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
140	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₅₃	—	2	2	no	—
148	C₂×C₄×D₅₃	—	2	2	no	—
149	C₂×C₄×D₅₃	—	2	2	no	—
150	C₂×C₄×D₅₃	—	2	2	no	—
151	C₂×C₄×D₅₃	—	2	2	no	—
152	C₂×C₄×D₅₃	—	2	2	no	—
153	C₂×C₄×D₅₃	—	2	2	no	—
154	C₂×C₄×D₅₃	—	2	2	no	—
155	C₂×C₄×D₅₃	—	2	2	no	—
156	C₂×C₄×D₅₃	—	2	2	no	—
157	C₂×C₄×D₅₃	—	2	2	no	—
158	C₂×C₄×D₅₃	—	2	2	no	—
159	C₂×C₄×D₅₃	—	2	2	no	—
160	C₂×C₄×D₅₃	—	2	2	no	—
161	C₂×C₄×D₅₃	—	2	2	no	—
162	C₂×C₄×D₅₃	—	2	2	no	—
163	C₂×C₄×D₅₃	M₁₆	1	4	yes	—
164	C₂×C₄×D₅₃	M₁₆	1	4	yes	—
165	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
166	C₂×C₄×D₅₃	C₂×Q₈	1	2	yes	—
167	C₂×C₄×D₅₃	#41	1	2	yes	—
168	C₂×C₄×D₅₃	#41	1	2	yes	—
169	C₂×C₄×D₅₃	#41	1	2	yes	—
170	C₂×C₄×D₅₃	#41	1	2	yes	—
171	C₂×C₈×C₅₃	—	2	1	no	—
172	C₂×C₈×C₅₃	—	2	1	no	—
173	C₂×C₈×C₅₃	—	2	1	no	—
174	C₂×C₈×C₅₃	—	2	1	no	—
175	C₂×C₈×C₅₃	—	2	1	no	—
176	C₂×C₈×C₅₃	—	2	1	no	—
177	C₂×C₈×C₅₃	—	2	1	no	—
178	C₂×C₈×C₅₃	—	2	1	no	—
179	C₂×C₈×C₅₃	—	2	1	no	—
180	C₂×C₈×C₅₃	—	2	1	no	—
181	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
182	C₂×C₈×C₅₃	C₂×Q₈	1	2	yes	—
183	C₄⋊C₄×C₅₃	—	2	2	no	—
184	C₄⋊C₄×C₅₃	—	2	2	no	—
185	C₄²×C₅₃	—	2	1	no	—
186	C₄²×C₅₃	—	2	1	no	—
187	C₄²×C₅₃	—	2	1	no	—
188	C₄²×C₅₃	—	2	1	no	—
189	C₄²×C₅₃	—	2	1	no	—
190	C₄²×C₅₃	—	2	1	no	—
191	C₄⋊Dic₅₃	—	2	2	no	—
192	C₄⋊Dic₅₃	—	2	2	no	—
193	#11719919	—	2	2	no	—
194	#11719919	—	2	2	no	—
195	#11719919	—	2	2	no	—
196	#11719919	—	2	2	no	—
197	C₄×Dic₅₃	—	2	1	no	—
198	C₄×Dic₅₃	—	2	1	no	—
199	C₄×Dic₅₃	—	2	1	no	—
200	C₄×Dic₅₃	—	2	1	no	—
201	C₄×Dic₅₃	—	2	1	no	—
202	C₄×Dic₅₃	—	2	1	no	—
203	C₄×Dic₅₃	—	2	2	no	—
204	C₄×Dic₅₃	—	2	2	no	—
205	C₄×Dic₅₃	—	2	2	no	—
206	C₄×Dic₅₃	—	2	2	no	—
207	C₄×Dic₅₃	—	2	2	no	—
208	C₄×Dic₅₃	—	2	2	no	—
209	C₂×#88322	—	2	1	no	—
210	C₂×#88322	—	2	1	no	—
211	C₂×#88322	—	2	1	no	—
212	C₂×#88322	—	2	1	no	—
213	C₂×#88322	—	2	1	no	—
214	C₂×#88322	—	2	1	no	—
215	C₂×#88322	—	2	1	no	—
216	C₂×#88322	—	2	1	no	—
217	C₂×#88322	—	2	1	no	—
218	C₂×#88322	—	2	1	no	—
219	C₂×#88322	C₂×D₄	1	2	yes	—
220	C₂×#88322	C₂×Q₈	1	2	yes	—
221	C₈×D₅₃	—	2	8	no	—
222	C₈×D₅₃	—	2	8	no	—
223	C₈×D₅₃	—	4	4	no	—
224	C₈×D₅₃	—	4	4	no	—
225	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
226	C₂²×D₅₃	#117	1	2	yes	—
227	C₂²×D₅₃	C₄×D₄	1	2	yes	—
228	C₂²×D₅₃	C₄×Q₈	1	2	yes	—
229	C₂²×D₅₃	C₂×M₁₆	1	2	yes	—
230	C₂²×D₅₃	C₂×M₁₆	1	2	yes	—
231	C₂²×D₅₃	#131	1	2	yes	—
232	C₂²×D₅₃	#131	1	2	yes	—
233	C₂×C₄×C₅₃	—	2	1	no	—
234	C₂×C₄×C₅₃	—	2	1	no	—
235	C₂×C₄×C₅₃	—	2	1	no	—
236	C₂×C₄×C₅₃	—	2	1	no	—
237	C₂×C₄×C₅₃	—	2	1	no	—
238	C₂×C₄×C₅₃	—	2	1	no	—
239	C₂×C₄×C₅₃	—	2	1	no	—
240	C₂×C₄×C₅₃	—	2	1	no	—
241	C₂×C₄×C₅₃	—	2	1	no	—
242	C₂×C₄×C₅₃	—	2	1	no	—
243	C₂×C₄×C₅₃	—	2	1	no	—
244	C₂×C₄×C₅₃	—	2	1	no	—
245	C₂×C₄×C₅₃	—	2	1	no	—
246	C₂×C₄×C₅₃	—	2	1	no	—
247	C₂×C₄×C₅₃	—	2	1	no	—
248	C₂×C₄×C₅₃	—	2	1	no	—
249	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
250	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
251	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
253	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
257	C₂×Dic₅₃	—	2	1	no	—
258	C₂×Dic₅₃	—	2	1	no	—
259	C₂×Dic₅₃	—	2	1	no	—
260	C₂×Dic₅₃	—	2	1	no	—
261	C₂×Dic₅₃	—	2	1	no	—
262	C₂×Dic₅₃	—	2	1	no	—
263	C₂×Dic₅₃	—	2	1	no	—
264	C₂×Dic₅₃	—	2	1	no	—
265	C₂×Dic₅₃	—	2	1	no	—
266	C₂×Dic₅₃	—	2	1	no	—
267	C₂×Dic₅₃	—	2	1	no	—
268	C₂×Dic₅₃	—	2	1	no	—
269	C₂×Dic₅₃	—	2	1	no	—
270	C₂×Dic₅₃	—	2	1	no	—
271	C₂×Dic₅₃	—	2	1	no	—
272	C₂×Dic₅₃	—	2	1	no	—
273	C₂×Dic₅₃	#117	1	2	yes	—
274	C₂×Dic₅₃	C₄×D₄	1	2	yes	—
275	C₂×Dic₅₃	C₄×Q₈	1	2	yes	—
276	C₂×Dic₅₃	C₂×M₁₆	1	2	yes	—
277	C₂×Dic₅₃	C₂×M₁₆	1	2	yes	—
278	C₄×D₅₃	—	2	8	no	—
279	C₄×D₅₃	—	2	8	no	—
280	C₄×D₅₃	—	4	4	no	—
281	C₄×D₅₃	—	4	4	no	—
282	C₄×D₅₃	—	4	4	no	—
283	C₄×D₅₃	—	4	4	no	—
284	C₄×D₅₃	C₂²⋊Q₈	1	4	yes	—
285	C₄×D₅₃	#123	1	4	yes	—
286	C₄×D₅₃	#125	1	4	yes	—
287	C₄×D₅₃	#126	1	4	yes	—
288	C₈×C₅₃	—	2	2	no	—
289	C₈×C₅₃	—	2	2	no	—
290	C₈×C₅₃	—	4	1	no	—
291	C₈×C₅₃	—	4	1	no	—
292	#88322	—	2	2	no	—
293	#88322	—	2	2	no	—
294	#88322	—	4	1	no	—
295	#88322	—	4	1	no	—
296	C₂×#1917	—	53	1	no	maximal, Sylow
297	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
298	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂²×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
300	C₂²×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
301	C₂²×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
302	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
303	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
304	C₂×D₅₃	#387	1	4	yes	—
305	C₂×D₅₃	#432	1	4	yes	—
306	C₂×D₅₃	#433	1	4	yes	—
307	C₂×D₅₃	#435	1	4	yes	—
308	C₂×D₅₃	#436	1	4	yes	—
309	C₂×D₅₃	#446	1	4	yes	—
310	C₂×D₅₃	#446	1	4	yes	—
311	C₄×C₅₃	—	2	2	no	—
312	C₄×C₅₃	—	2	2	no	—
313	C₄×C₅₃	—	4	1	no	—
314	C₄×C₅₃	—	4	1	no	—
315	C₄×C₅₃	—	4	1	no	—
316	C₄×C₅₃	—	4	1	no	—
317	C₄×C₅₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
318	C₄×C₅₃	C₂×#123	1	1	yes	characteristic
319	C₄×C₅₃	C₂×#125	1	1	yes	characteristic
320	C₄×C₅₃	C₂×#126	1	1	yes	characteristic
321	Dic₅₃	—	2	2	no	—
322	Dic₅₃	—	2	2	no	—
323	Dic₅₃	—	4	1	no	—
324	Dic₅₃	—	4	1	no	—
325	Dic₅₃	—	4	1	no	—
326	Dic₅₃	—	4	1	no	—
327	Dic₅₃	#387	1	4	yes	—
328	C₂²×C₄⋊C₈	—	53	1	no	—
329	C₂²×#97	—	53	1	no	—
330	C₂×C₄×C₄⋊C₄	—	53	1	no	—
331	#1917	—	53	1	no	—
332	#1917	—	53	1	no	—
333	#1917	—	53	1	no	—
334	#1917	—	53	1	no	—
335	#1917	—	53	1	no	—
336	#1917	—	53	1	no	—
337	#1917	—	53	1	no	—
338	#1917	D₅₃	1	1	yes	characteristic, direct product factor
339	C₂×#336	—	53	1	no	—
340	C₂×#336	—	53	1	no	—
341	C₂×#336	—	53	1	no	—
342	C₂×#336	—	53	1	no	—
343	C₂×C₅₃	C₂×#387	1	1	yes	characteristic
344	C₂×C₅₃	C₂×#432	1	1	yes	characteristic
345	C₂×C₅₃	C₂×#433	1	1	yes	characteristic
346	C₂×C₅₃	C₂×#435	1	1	yes	characteristic
347	C₂×C₅₃	C₂×#436	1	1	yes	characteristic
348	C₂×C₅₃	C₂×#446	1	1	yes	characteristic
349	C₂×C₅₃	C₂×#446	1	1	yes	characteristic
350	D₅₃	#1917	1	8	yes	direct product factor
351	C₂³×C₈	—	53	1	no	—
352	C₂³×C₈	—	53	1	no	—
353	C₂³×C₈	—	53	1	no	—
354	C₂³×C₈	—	53	1	no	—
355	C₂²×C₄⋊C₄	—	53	1	no	—
356	C₂²×C₄⋊C₄	—	53	1	no	—
357	C₂²×C₄²	—	53	1	no	—
358	C₂²×C₄²	—	53	1	no	—
359	C₂²×C₄²	—	53	1	no	—
360	C₂×C₄⋊C₈	—	53	1	no	—
361	C₂×C₄⋊C₈	—	53	1	no	—
362	C₂×C₄⋊C₈	—	53	1	no	—
363	C₂×C₄⋊C₈	—	106	4	no	—
364	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
365	C₂×#97	—	53	1	no	—
366	C₂×#97	—	53	1	no	—
367	C₂×#97	—	53	1	no	—
368	C₂×#97	—	106	4	no	—
369	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
370	C₄×C₄⋊C₄	—	53	1	no	—
371	C₄×C₄⋊C₄	—	53	1	no	—
372	C₄×C₄⋊C₄	—	53	1	no	—
373	C₄×C₄⋊C₄	—	53	1	no	—
374	C₄×C₄⋊C₄	—	53	1	no	—
375	C₄×C₄⋊C₄	—	53	1	no	—
376	C₄×C₄⋊C₄	—	53	1	no	—
377	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
378	C₂×#95	—	53	1	no	—
379	C₂×#95	—	53	1	no	—
380	#336	—	53	1	no	—
381	#336	—	53	1	no	—
382	#336	—	53	1	no	—
383	#336	—	53	1	no	—
384	#336	—	53	1	no	—
385	#336	—	53	1	no	—
386	#336	—	53	1	no	—
387	#336	—	53	1	no	—
388	#336	—	53	1	no	—
389	#336	—	53	1	no	—
390	#336	—	53	1	no	—
391	#336	—	53	1	no	—
392	#336	C₂×D₅₃	1	1	yes	characteristic
393	#336	C₂×D₅₃	1	1	yes	characteristic
394	#336	C₂×D₅₃	1	1	yes	characteristic
395	#336	C₂×D₅₃	1	1	yes	characteristic
396	C₅₃	C₂×#1917	1	1	yes	characteristic, complemented, Sylow
397	C₂³×C₄	—	53	1	no	—
398	C₂³×C₄	—	53	1	no	—
399	C₂³×C₄	—	53	1	no	—
400	C₂³×C₄	—	53	1	no	—
401	C₂³×C₄	—	53	1	no	—
402	C₂³×C₄	—	53	1	no	—
403	C₂³×C₄	—	53	1	no	—
404	C₂²×C₈	—	53	1	no	—
405	C₂²×C₈	—	53	1	no	—
406	C₂²×C₈	—	53	4	no	—
407	C₂²×C₈	—	53	4	no	—
408	C₂²×C₈	—	53	1	no	—
409	C₂²×C₈	—	53	1	no	—
410	C₂²×C₈	—	106	2	no	—
411	C₂²×C₈	—	106	2	no	—
412	C₂²×C₈	—	106	2	no	—
413	C₂²×C₈	—	106	2	no	—
414	C₂²×C₈	—	106	2	no	—
415	C₂²×C₈	—	106	2	no	—
416	C₂²×C₈	—	106	2	no	—
417	C₂²×C₈	—	106	2	no	—
418	C₂²×C₈	—	106	2	no	—
419	C₂²×C₈	—	106	2	no	—
420	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
421	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
422	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
423	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	—	53	1	no	—
425	C₂×C₄⋊C₄	—	53	1	no	—
426	C₂×C₄⋊C₄	—	53	1	no	—
427	C₂×C₄⋊C₄	—	53	1	no	—
428	C₂×C₄⋊C₄	—	53	1	no	—
429	C₂×C₄⋊C₄	—	53	1	no	—
430	C₂×C₄⋊C₄	—	106	4	no	—
431	C₂×C₄⋊C₄	—	106	4	no	—
432	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
434	C₂×C₄²	—	53	1	no	—
435	C₂×C₄²	—	53	1	no	—
436	C₂×C₄²	—	53	1	no	—
437	C₂×C₄²	—	53	1	no	—
438	C₂×C₄²	—	53	1	no	—
439	C₂×C₄²	—	53	1	no	—
440	C₂×C₄²	—	53	1	no	—
441	C₂×C₄²	—	53	1	no	—
442	C₂×C₄²	—	53	1	no	—
443	C₂×C₄²	—	106	2	no	—
444	C₂×C₄²	—	106	2	no	—
445	C₂×C₄²	—	106	2	no	—
446	C₂×C₄²	—	106	2	no	—
447	C₂×C₄²	—	106	2	no	—
448	C₂×C₄²	—	106	2	no	—
449	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
450	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
451	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
452	C₄⋊C₈	—	2	2	no	—
453	C₄⋊C₈	—	106	2	no	—
454	C₄⋊C₈	—	106	2	no	—
455	C₄⋊C₈	—	106	2	no	—
456	#97	—	2	2	no	—
457	#97	—	106	2	no	—
458	#97	—	106	2	no	—
459	#97	—	106	2	no	—
460	#95	—	53	1	no	—
461	#95	—	53	1	no	—
462	#95	—	53	1	no	—
463	#95	—	53	1	no	—
464	#95	—	53	1	no	—
465	#95	—	53	1	no	—
466	#95	C₄×D₅₃	1	1	yes	characteristic
467	#95	C₄×D₅₃	1	1	yes	characteristic
468	C₂⁴	—	53	1	no	—
469	C₂²×C₄	—	53	1	no	—
470	C₂²×C₄	—	53	2	no	—
471	C₂²×C₄	—	53	2	no	—
472	C₂²×C₄	—	53	2	no	—
473	C₂²×C₄	—	53	2	no	—
474	C₂²×C₄	—	53	2	no	—
475	C₂²×C₄	—	53	2	no	—
476	C₂²×C₄	—	53	1	no	—
477	C₂²×C₄	—	53	1	no	—
478	C₂²×C₄	—	53	4	no	—
479	C₂²×C₄	—	53	4	no	—
480	C₂²×C₄	—	53	1	no	—
481	C₂²×C₄	—	53	1	no	—
482	C₂²×C₄	—	53	1	no	—
483	C₂²×C₄	—	53	1	no	—
484	C₂²×C₄	—	106	2	no	—
485	C₂²×C₄	—	106	2	no	—
486	C₂²×C₄	—	106	2	no	—
487	C₂²×C₄	—	106	2	no	—
488	C₂²×C₄	—	106	2	no	—
489	C₂²×C₄	—	106	2	no	—
490	C₂²×C₄	—	106	2	no	—
491	C₂²×C₄	—	106	2	no	—
492	C₂²×C₄	—	106	2	no	—
493	C₂²×C₄	—	106	2	no	—
494	C₂²×C₄	—	106	2	no	—
495	C₂²×C₄	—	106	2	no	—
496	C₂²×C₄	—	106	2	no	—
497	C₂²×C₄	—	106	2	no	—
498	C₂²×C₄	—	106	2	no	—
499	C₂²×C₄	—	106	2	no	—
500	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
501	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
506	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	53	2	no	—
518	C₂×C₈	—	53	2	no	—
519	C₂×C₈	—	106	8	no	—
520	C₂×C₈	—	106	8	no	—
521	C₂×C₈	—	106	1	no	—
522	C₂×C₈	—	106	1	no	—
523	C₂×C₈	—	106	1	no	—
524	C₂×C₈	—	106	1	no	—
525	C₂×C₈	—	106	1	no	—
526	C₂×C₈	—	106	1	no	—
527	C₂×C₈	—	106	1	no	—
528	C₂×C₈	—	106	1	no	—
529	C₂×C₈	—	106	1	no	—
530	C₂×C₈	—	106	1	no	—
531	C₂×C₈	—	212	4	no	—
532	C₂×C₈	—	212	4	no	—
533	C₂×C₈	D₄×D₅₃	1	2	yes	—
534	C₂×C₈	Q₈×D₅₃	1	2	yes	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	106	2	no	—
538	C₄⋊C₄	—	106	2	no	—
539	C₄⋊C₄	—	106	2	no	—
540	C₄⋊C₄	—	106	2	no	—
541	C₄⋊C₄	—	106	2	no	—
542	C₄⋊C₄	—	106	2	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	106	2	no	—
550	C₄²	—	106	2	no	—
551	C₄²	—	106	2	no	—
552	C₄²	—	106	2	no	—
553	C₄²	—	106	2	no	—
554	C₄²	—	106	2	no	—
555	C₄²	—	106	1	no	—
556	C₄²	—	106	1	no	—
557	C₄²	—	106	1	no	—
558	C₄²	—	106	1	no	—
559	C₄²	—	106	1	no	—
560	C₄²	—	106	1	no	—
561	C₂³	—	53	2	no	—
562	C₂³	—	53	2	no	—
563	C₂³	—	53	2	no	—
564	C₂³	—	53	2	no	—
565	C₂³	—	53	2	no	—
566	C₂³	—	53	2	no	—
567	C₂³	—	53	2	no	—
568	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	53	2	no	—
586	C₂×C₄	—	53	2	no	—
587	C₂×C₄	—	53	2	no	—
588	C₂×C₄	—	53	4	no	—
589	C₂×C₄	—	53	4	no	—
590	C₂×C₄	—	53	4	no	—
591	C₂×C₄	—	53	4	no	—
592	C₂×C₄	—	53	2	no	—
593	C₂×C₄	—	53	2	no	—
594	C₂×C₄	—	106	8	no	—
595	C₂×C₄	—	106	8	no	—
596	C₂×C₄	—	106	1	no	—
597	C₂×C₄	—	106	1	no	—
598	C₂×C₄	—	106	1	no	—
599	C₂×C₄	—	106	1	no	—
600	C₂×C₄	—	106	1	no	—
601	C₂×C₄	—	106	1	no	—
602	C₂×C₄	—	106	1	no	—
603	C₂×C₄	—	106	1	no	—
604	C₂×C₄	—	106	1	no	—
605	C₂×C₄	—	106	1	no	—
606	C₂×C₄	—	106	1	no	—
607	C₂×C₄	—	106	1	no	—
608	C₂×C₄	—	106	1	no	—
609	C₂×C₄	—	106	1	no	—
610	C₂×C₄	—	106	1	no	—
611	C₂×C₄	—	106	1	no	—
612	C₂×C₄	—	212	4	no	—
613	C₂×C₄	—	212	4	no	—
614	C₂×C₄	—	212	4	no	—
615	C₂×C₄	—	212	4	no	—
616	C₂×C₄	M₁₆×D₅₃	1	2	yes	—
617	C₂×C₄	M₁₆×D₅₃	1	2	yes	—
618	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
619	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
620	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
621	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
622	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
623	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
624	C₈	—	2	2	no	—
625	C₈	—	2	2	no	—
626	C₈	—	4	1	no	—
627	C₈	—	4	1	no	—
628	C₈	—	106	2	no	—
629	C₈	—	106	2	no	—
630	C₈	—	212	1	no	—
631	C₈	—	212	1	no	—
632	C₂²	—	53	4	no	—
633	C₂²	—	53	4	no	—
634	C₂²	—	53	4	no	—
635	C₂²	—	53	4	no	—
636	C₂²	—	53	4	no	—
637	C₂²	—	53	4	no	—
638	C₂²	—	53	4	no	—
639	C₂²	#117×D₅₃	1	1	yes	characteristic
640	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
641	C₂²	C₄×Q₈×D₅₃	1	1	yes	characteristic
642	C₂²	C₂×M₁₆×D₅₃	1	1	yes	characteristic
643	C₂²	C₂×M₁₆×D₅₃	1	1	yes	characteristic
644	C₂²	#131×D₅₃	1	1	yes	characteristic
645	C₂²	#131×D₅₃	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	53	4	no	—
653	C₄	—	106	2	no	—
654	C₄	—	106	2	no	—
655	C₄	—	212	1	no	—
656	C₄	—	212	1	no	—
657	C₄	—	212	1	no	—
658	C₄	—	212	1	no	—
659	C₄	C₂²⋊Q₈×D₅₃	1	1	yes	characteristic
660	C₄	#123×D₅₃	1	1	yes	characteristic
661	C₄	#125×D₅₃	1	1	yes	characteristic
662	C₄	#126×D₅₃	1	1	yes	characteristic
663	C₂	—	53	8	no	—
664	C₂	#387×D₅₃	1	1	yes	characteristic
665	C₂	#432×D₅₃	1	1	yes	characteristic
666	C₂	#433×D₅₃	1	1	yes	characteristic
667	C₂	#435×D₅₃	1	1	yes	characteristic
668	C₂	#436×D₅₃	1	1	yes	characteristic
669	C₂	#446×D₅₃	1	1	yes	characteristic
670	C₂	#446×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅₃
commutator, socle	C₂³×C₅₃	C₂³×C₄
Fitting	C₅₃×#1917	C₂
prime radical	C₂³×D₅₃	C₂²×C₄
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1917	D₅₃
hypocenter	C₅₃	C₂×#1917
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1917

Complements

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

N	H ≅ G/N	type
4. #20275282	C₂	semidirect
5. #20275281	C₂	semidirect
6. #20275280	C₂	semidirect
7. #20275279	C₂	semidirect
8. #20275278	C₂	semidirect
9. #20275277	C₂	semidirect
10. #20275276	C₂	semidirect
15. C₅₃×#1917	C₂	semidirect
338. #1917	D₅₃	direct (N × H)
350. D₅₃	#1917	direct (N × H)
396. C₅₃	C₂×#1917	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×#97×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
#20275282	2
#20275281	2
#20275280	2
#20275279	2
#20275278	2
#20275277	2
#20275276	2
#336×D₅₃	2
C₅₃×#1917	2
C₂×#1917	53

Subgroups — D53×#1917 #27386138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1917 #27386138