Subgroups — C₅₃×#9675 #27217187

Order 13568.

600 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#124×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₄⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×Q₈⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₃×D₄⋊C₈	C₂	1	2	yes	maximal
6	C₂×#124×C₅₃	C₄	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₈×C₅₃	—	2	1	no	—
10	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₅₃	—	2	1	no	—
12	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	—
13	C₅₃×#391	C₄	1	1	yes	characteristic
14	C₅₃×#390	C₄	1	1	yes	characteristic
15	C₅₃×#388	—	2	1	no	—
16	C₅₃×#388	—	2	1	no	—
17	C₅₃×#382	C₄	1	1	yes	characteristic
18	C₄×C₂²⋊C₄×C₅₃	—	2	1	no	—
19	C₄×C₂²⋊C₄×C₅₃	—	2	1	no	—
20	C₄³×C₅₃	C₂²	1	1	yes	characteristic
21	C₅₃×#336	—	2	1	no	—
22	C₅₃×#336	—	2	1	no	—
23	C₅₃×Q₈⋊C₈	—	2	4	no	—
24	C₅₃×D₄⋊C₈	—	2	4	no	—
25	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₅₃	—	2	1	no	—
28	C₂²×C₈×C₅₃	—	2	2	no	—
29	C₂²×C₈×C₅₃	—	2	2	no	—
30	#124×C₅₃	—	2	2	no	—
31	#124×C₅₃	C₈	1	4	yes	complemented
32	C₄×Q₈×C₅₃	—	2	2	no	—
33	C₄×Q₈×C₅₃	—	2	2	no	—
34	C₄×D₄×C₅₃	—	2	2	no	—
35	C₄×D₄×C₅₃	—	2	2	no	—
36	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
37	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
44	C₂×C₄²×C₅₃	—	2	1	no	—
45	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
52	C₄⋊C₈×C₅₃	—	2	4	no	—
53	C₄⋊C₈×C₅₃	—	2	2	no	—
54	C₄⋊C₈×C₅₃	D₄	1	4	yes	—
55	C₄×C₈×C₅₃	—	2	2	no	—
56	C₄×C₈×C₅₃	—	2	2	no	—
57	C₄×C₈×C₅₃	—	4	2	no	—
58	#95×C₅₃	—	2	1	no	—
59	#95×C₅₃	—	2	1	no	—
60	#95×C₅₃	—	2	1	no	—
61	#95×C₅₃	—	2	1	no	—
62	C₂⁴×C₅₃	—	2	1	no	—
63	C₂×Q₈×C₅₃	—	2	1	no	—
64	C₂×Q₈×C₅₃	—	2	2	no	—
65	C₂×Q₈×C₅₃	—	2	2	no	—
66	C₂×Q₈×C₅₃	C₂×C₈	1	2	yes	—
67	C₂×D₄×C₅₃	—	2	2	no	—
68	C₂×D₄×C₅₃	—	2	1	no	—
69	C₂×D₄×C₅₃	—	2	2	no	—
70	C₂×D₄×C₅₃	C₂×C₈	1	2	yes	—
71	C₂²×C₄×C₅₃	—	2	1	no	—
72	C₂²×C₄×C₅₃	—	2	1	no	—
73	C₂²×C₄×C₅₃	—	2	1	no	—
74	C₂²×C₄×C₅₃	—	4	2	no	—
75	C₂²×C₄×C₅₃	—	4	2	no	—
76	C₂²×C₄×C₅₃	—	4	1	no	—
77	C₂²×C₄×C₅₃	—	4	1	no	—
78	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₈×C₅₃	—	2	4	no	—
86	C₂×C₈×C₅₃	—	2	4	no	—
87	C₂×C₈×C₅₃	—	4	2	no	—
88	C₂×C₈×C₅₃	—	4	2	no	—
89	C₂×C₈×C₅₃	—	4	2	no	—
90	C₂×C₈×C₅₃	—	4	2	no	—
91	C₄⋊C₄×C₅₃	—	2	2	no	—
92	C₄⋊C₄×C₅₃	—	2	2	no	—
93	C₄⋊C₄×C₅₃	—	4	1	no	—
94	C₄⋊C₄×C₅₃	—	4	1	no	—
95	C₂²⋊C₄×C₅₃	—	2	4	no	—
96	C₂²⋊C₄×C₅₃	—	2	4	no	—
97	C₂²⋊C₄×C₅₃	—	4	2	no	—
98	C₂²⋊C₄×C₅₃	—	4	2	no	—
99	C₂²⋊C₄×C₅₃	—	4	1	no	—
100	C₂²⋊C₄×C₅₃	—	4	1	no	—
101	C₄²×C₅₃	—	2	2	no	—
102	C₄²×C₅₃	—	2	2	no	—
103	C₄²×C₅₃	—	2	2	no	—
104	C₄²×C₅₃	—	2	1	no	—
105	C₄²×C₅₃	—	2	1	no	—
106	C₄²×C₅₃	—	4	1	no	—
107	C₄²×C₅₃	—	4	2	no	—
108	C₄²×C₅₃	C₂×C₈	1	2	yes	—
109	C₄²×C₅₃	M₁₆	1	2	yes	—
110	C₄²×C₅₃	C₂×D₄	1	2	yes	—
111	C₄²×C₅₃	#41	1	2	yes	—
112	C₂³×C₅₃	—	2	2	no	—
113	C₂³×C₅₃	—	4	1	no	—
114	C₂³×C₅₃	—	4	1	no	—
115	C₂³×C₅₃	—	4	1	no	—
116	C₂³×C₅₃	—	4	1	no	—
117	C₂³×C₅₃	—	4	1	no	—
118	C₂³×C₅₃	—	4	1	no	—
119	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	Q₈×C₅₃	—	2	4	no	—
121	Q₈×C₅₃	—	4	2	no	—
122	D₄×C₅₃	—	2	4	no	—
123	D₄×C₅₃	—	4	2	no	—
124	C₂×C₄×C₅₃	—	2	1	no	—
125	C₂×C₄×C₅₃	—	2	1	no	—
126	C₂×C₄×C₅₃	—	2	1	no	—
127	C₂×C₄×C₅₃	—	2	1	no	—
128	C₂×C₄×C₅₃	—	2	1	no	—
129	C₂×C₄×C₅₃	—	2	1	no	—
130	C₂×C₄×C₅₃	—	2	1	no	—
131	C₂×C₄×C₅₃	—	2	1	no	—
132	C₂×C₄×C₅₃	—	2	2	no	—
133	C₂×C₄×C₅₃	—	2	1	no	—
134	C₂×C₄×C₅₃	—	2	1	no	—
135	C₂×C₄×C₅₃	—	2	1	no	—
136	C₂×C₄×C₅₃	—	4	1	no	—
137	C₂×C₄×C₅₃	—	4	1	no	—
138	C₂×C₄×C₅₃	—	4	1	no	—
139	C₂×C₄×C₅₃	—	4	1	no	—
140	C₂×C₄×C₅₃	—	4	1	no	—
141	C₂×C₄×C₅₃	—	4	1	no	—
142	C₂×C₄×C₅₃	—	4	1	no	—
143	C₂×C₄×C₅₃	—	4	1	no	—
144	C₂×C₄×C₅₃	—	8	2	no	—
145	C₂×C₄×C₅₃	—	8	2	no	—
146	C₂×C₄×C₅₃	C₂²⋊C₈	1	2	yes	—
147	C₂×C₄×C₅₃	C₂²⋊C₈	1	2	yes	—
148	C₂×C₄×C₅₃	#104	1	2	yes	—
149	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₅₃	#121	1	2	yes	—
151	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
152	C₂×C₄×C₅₃	#127	1	1	yes	characteristic
153	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
155	C₂×C₄×C₅₃	#131	1	2	yes	—
156	C₂×C₄×C₅₃	#135	1	2	yes	—
157	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₅₃	#137	1	1	yes	characteristic
159	C₈×C₅₃	—	4	4	no	—
160	C₈×C₅₃	—	4	4	no	—
161	#9675	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂²×C₅₃	—	4	2	no	—
163	C₂²×C₅₃	—	4	2	no	—
164	C₂²×C₅₃	—	4	2	no	—
165	C₂²×C₅₃	—	8	1	no	—
166	C₂²×C₅₃	—	8	1	no	—
167	C₂²×C₅₃	—	8	1	no	—
168	C₂²×C₅₃	—	8	1	no	—
169	C₂²×C₅₃	#390	1	1	yes	characteristic
170	C₂²×C₅₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
171	C₂²×C₅₃	#408	1	1	yes	characteristic
172	C₂²×C₅₃	#416	1	1	yes	characteristic
173	C₂²×C₅₃	#417	1	1	yes	characteristic
174	C₂²×C₅₃	C₂×#104	1	1	yes	characteristic
175	C₂²×C₅₃	#421	1	1	yes	characteristic
176	C₄×C₅₃	—	2	1	no	—
177	C₄×C₅₃	—	2	1	no	—
178	C₄×C₅₃	—	2	2	no	—
179	C₄×C₅₃	—	2	2	no	—
180	C₄×C₅₃	—	2	2	no	—
181	C₄×C₅₃	—	4	2	no	—
182	C₄×C₅₃	—	4	1	no	—
183	C₄×C₅₃	—	8	1	no	—
184	C₄×C₅₃	—	8	1	no	—
185	C₄×C₅₃	C₈×D₄	1	2	yes	—
186	C₄×C₅₃	#436	1	2	yes	—
187	C₄×C₅₃	#463	1	2	yes	—
188	C₄×C₅₃	#464	1	2	yes	—
189	C₄×#124	C₂×C₅₃	1	1	yes	characteristic
190	C₄×C₄⋊C₈	C₂×C₅₃	1	1	yes	characteristic, complemented
191	C₄×C₄⋊C₈	C₂×C₅₃	1	1	yes	characteristic, complemented
192	C₂×Q₈⋊C₈	C₂×C₅₃	1	2	yes	complemented
193	C₂×D₄⋊C₈	C₂×C₅₃	1	2	yes	—
194	C₂×C₅₃	—	8	2	no	—
195	C₂×C₅₃	#1476	1	1	yes	characteristic
196	C₂×C₅₃	#1477	1	1	yes	characteristic
197	C₂×C₅₃	#1482	1	1	yes	characteristic
198	C₂×C₅₃	#1483	1	1	yes	characteristic
199	C₂×C₅₃	#1954	1	1	yes	characteristic
200	C₂×C₅₃	#1980	1	1	yes	characteristic
201	C₂×C₅₃	#1983	1	1	yes	characteristic
202	C₂×#124	C₄×C₅₃	1	1	yes	characteristic
203	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
204	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
205	C₂×C₄⋊C₈	—	2	1	no	—
206	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
207	C₂×C₄×C₈	—	2	1	no	—
208	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	—
209	#391	C₄×C₅₃	1	1	yes	characteristic
210	#390	C₄×C₅₃	1	1	yes	characteristic
211	#388	—	2	1	no	—
212	#388	—	2	1	no	—
213	#382	C₄×C₅₃	1	1	yes	characteristic
214	C₄×C₂²⋊C₄	—	2	1	no	—
215	C₄×C₂²⋊C₄	—	2	1	no	—
216	C₄³	C₂²×C₅₃	1	1	yes	characteristic
217	#336	—	2	1	no	—
218	#336	—	2	1	no	—
219	Q₈⋊C₈	—	2	4	no	—
220	D₄⋊C₈	—	2	4	no	—
221	C₅₃	#9675	1	1	yes	characteristic, direct product factor, Sylow
222	C₂²×Q₈	C₂×C₄×C₅₃	1	1	yes	characteristic
223	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
224	C₂³×C₄	—	2	1	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	#124	—	2	2	no	—
228	#124	C₈×C₅₃	1	4	yes	complemented
229	C₄×Q₈	—	2	2	no	—
230	C₄×Q₈	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₂²⋊C₄	—	2	1	no	—
239	C₂×C₂²⋊C₄	—	2	1	no	—
240	C₂×C₂²⋊C₄	—	2	1	no	—
241	C₂×C₄²	—	2	1	no	—
242	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
243	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
244	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
249	C₄⋊C₈	—	2	4	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	D₄×C₅₃	1	4	yes	—
252	C₄×C₈	—	2	2	no	—
253	C₄×C₈	—	2	2	no	—
254	C₄×C₈	—	4	2	no	—
255	#95	—	2	1	no	—
256	#95	—	2	1	no	—
257	#95	—	2	1	no	—
258	#95	—	2	1	no	—
259	C₂⁴	—	2	1	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	C₂×C₈×C₅₃	1	2	yes	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	C₂×C₈×C₅₃	1	2	yes	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
277	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	4	2	no	—
285	C₂×C₈	—	4	2	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	4	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	4	1	no	—
297	C₂²⋊C₄	—	4	1	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	4	1	no	—
304	C₄²	—	4	2	no	—
305	C₄²	C₂×C₈×C₅₃	1	2	yes	—
306	C₄²	M₁₆×C₅₃	1	2	yes	—
307	C₄²	C₂×D₄×C₅₃	1	2	yes	—
308	C₄²	#41×C₅₃	1	2	yes	—
309	C₂³	—	2	2	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	1	no	—
312	C₂³	—	4	1	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
317	Q₈	—	2	4	no	—
318	Q₈	—	4	2	no	—
319	D₄	—	2	4	no	—
320	D₄	—	4	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	C₂²⋊C₈×C₅₃	1	2	yes	—
344	C₂×C₄	C₂²⋊C₈×C₅₃	1	2	yes	—
345	C₂×C₄	#104×C₅₃	1	2	yes	—
346	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
347	C₂×C₄	#121×C₅₃	1	2	yes	—
348	C₂×C₄	#124×C₅₃	1	1	yes	characteristic
349	C₂×C₄	#127×C₅₃	1	1	yes	characteristic
350	C₂×C₄	C₂²×C₈×C₅₃	1	1	yes	characteristic
351	C₂×C₄	C₂×M₁₆×C₅₃	1	1	yes	characteristic
352	C₂×C₄	#131×C₅₃	1	2	yes	—
353	C₂×C₄	#135×C₅₃	1	2	yes	—
354	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
355	C₂×C₄	#137×C₅₃	1	1	yes	characteristic
356	C₈	—	4	4	no	—
357	C₈	—	4	4	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	8	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	1	no	—
365	C₂²	C₅₃×#390	1	1	yes	characteristic
366	C₂²	C₂×C₂²⋊C₈×C₅₃	1	1	yes	characteristic
367	C₂²	C₅₃×#408	1	1	yes	characteristic
368	C₂²	C₅₃×#416	1	1	yes	characteristic
369	C₂²	C₅₃×#417	1	1	yes	characteristic
370	C₂²	C₂×#104×C₅₃	1	1	yes	characteristic
371	C₂²	C₅₃×#421	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	C₈×D₄×C₅₃	1	2	yes	—
382	C₄	C₅₃×#436	1	2	yes	—
383	C₄	C₅₃×#463	1	2	yes	—
384	C₄	C₅₃×#464	1	2	yes	—
385	C₂	—	8	2	no	—
386	C₂	C₅₃×#1476	1	1	yes	characteristic
387	C₂	C₅₃×#1477	1	1	yes	characteristic
388	C₂	C₅₃×#1482	1	1	yes	characteristic
389	C₂	C₅₃×#1483	1	1	yes	characteristic
390	C₂	C₅₃×#1954	1	1	yes	characteristic
391	C₂	C₅₃×#1980	1	1	yes	characteristic
392	C₂	C₅₃×#1983	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₅₃
Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
socle	C₂³×C₅₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₅₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ C₄³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊C₈×C₅₃	C₂	semidirect
3. C₄×C₄⋊C₈×C₅₃	C₂	semidirect
4. C₂×C₅₃×Q₈⋊C₈	C₂	semidirect
31. #124×C₅₃	C₈	semidirect
161. #9675	C₅₃	direct (N × H)
190. C₄×C₄⋊C₈	C₂×C₅₃	semidirect
191. C₄×C₄⋊C₈	C₂×C₅₃	semidirect
192. C₂×Q₈⋊C₈	C₂×C₅₃	semidirect
221. C₅₃	#9675	direct (N × H)
228. #124	C₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×#124×C₅₃	2
C₄×C₄⋊C₈×C₅₃	2
C₂×C₅₃×Q₈⋊C₈	2
C₂×C₅₃×D₄⋊C₈	2
#9675	53

Subgroups — C53×#9675 #27217187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#9675 #27217187