Subgroups — C₅₃×#21434 #27228946

Order 13568.

688 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2298	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#1924	C₂	1	2	yes	maximal
3	C₅₃×#1923	C₂	1	2	yes	maximal
4	C₅₃×#1917	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1916	C₂	1	2	yes	maximal, complemented
6	C₅₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1750	C₂	1	1	yes	maximal, characteristic
9	C₅₃×#1750	C₂	1	1	yes	maximal, characteristic
10	C₅₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#97×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
17	C₂×#97×C₅₃	C₂²	1	2	yes	—
18	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₅₃×#388	C₄	1	2	yes	—
24	C₅₃×#388	C₄	1	2	yes	—
25	C₅₃×#387	C₄	1	2	yes	—
26	C₅₃×#387	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₅₃×#376	C₂²	1	1	yes	characteristic
32	C₄³×C₅₃	C₂²	1	1	yes	characteristic
33	C₅₃×#336	C₂²	1	2	yes	—
34	C₅₃×#336	C₂²	1	2	yes	—
35	C₅₃×#336	C₂²	1	2	yes	—
36	C₅₃×#336	C₂²	1	2	yes	—
37	C₅₃×#336	C₂²	1	2	yes	—
38	C₅₃×#336	C₂²	1	2	yes	—
39	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
44	#117×C₅₃	—	2	2	no	—
45	#117×C₅₃	—	2	2	no	—
46	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₅₃	—	2	4	no	—
63	C₄⋊C₈×C₅₃	—	2	4	no	—
64	C₂²⋊C₈×C₅₃	—	2	4	no	—
65	C₂²⋊C₈×C₅₃	—	2	4	no	—
66	#97×C₅₃	—	2	4	no	—
67	#97×C₅₃	—	2	2	no	—
68	#97×C₅₃	—	2	2	no	—
69	C₄×C₈×C₅₃	—	2	4	no	—
70	C₄×C₈×C₅₃	—	2	2	no	—
71	C₄×C₈×C₅₃	—	2	2	no	—
72	#95×C₅₃	C₂×C₄	1	2	yes	—
73	#95×C₅₃	C₂×C₄	1	2	yes	—
74	#95×C₅₃	C₂×C₄	1	2	yes	—
75	#95×C₅₃	C₂×C₄	1	2	yes	—
76	#95×C₅₃	C₂×C₄	1	2	yes	—
77	#95×C₅₃	C₂×C₄	1	2	yes	—
78	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	—	2	2	no	—
80	C₂²×C₄×C₅₃	—	2	2	no	—
81	C₂²×C₄×C₅₃	—	2	1	no	—
82	C₂²×C₄×C₅₃	—	2	1	no	—
83	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₅₃	—	2	2	no	—
94	C₂×C₈×C₅₃	—	2	2	no	—
95	C₂×C₈×C₅₃	—	2	2	no	—
96	C₂×C₈×C₅₃	—	2	2	no	—
97	C₂×C₈×C₅₃	—	2	2	no	—
98	C₂×C₈×C₅₃	—	2	2	no	—
99	C₂×C₈×C₅₃	—	2	2	no	—
100	C₂×C₈×C₅₃	—	2	2	no	—
101	C₂×C₈×C₅₃	—	2	2	no	—
102	C₂×C₈×C₅₃	—	2	2	no	—
103	C₂×C₈×C₅₃	#41	1	4	yes	—
104	C₂×C₈×C₅₃	#41	1	4	yes	—
105	C₄⋊C₄×C₅₃	—	2	2	no	—
106	C₄⋊C₄×C₅₃	—	2	2	no	—
107	C₄⋊C₄×C₅₃	—	2	4	no	—
108	C₄⋊C₄×C₅₃	—	4	2	no	—
109	C₂²⋊C₄×C₅₃	—	2	2	no	—
110	C₂²⋊C₄×C₅₃	—	2	2	no	—
111	C₂²⋊C₄×C₅₃	—	2	4	no	—
112	C₂²⋊C₄×C₅₃	—	4	2	no	—
113	C₄²×C₅₃	—	2	4	no	—
114	C₄²×C₅₃	—	2	2	no	—
115	C₄²×C₅₃	—	2	2	no	—
116	C₄²×C₅₃	—	2	2	no	—
117	C₄²×C₅₃	—	2	2	no	—
118	C₄²×C₅₃	—	2	1	no	—
119	C₄²×C₅₃	—	2	1	no	—
120	C₄²×C₅₃	—	4	2	no	—
121	C₄²×C₅₃	#41	1	2	yes	—
122	C₄²×C₅₃	#41	1	2	yes	—
123	C₂³×C₅₃	—	2	1	no	—
124	C₂³×C₅₃	—	2	1	no	—
125	C₂³×C₅₃	—	2	1	no	—
126	C₂³×C₅₃	—	2	2	no	—
127	C₂³×C₅₃	—	2	2	no	—
128	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
129	C₂×C₄×C₅₃	—	2	2	no	—
130	C₂×C₄×C₅₃	—	2	2	no	—
131	C₂×C₄×C₅₃	—	2	2	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	—	2	1	no	—
137	C₂×C₄×C₅₃	—	2	1	no	—
138	C₂×C₄×C₅₃	—	2	2	no	—
139	C₂×C₄×C₅₃	—	2	2	no	—
140	C₂×C₄×C₅₃	—	2	2	no	—
141	C₂×C₄×C₅₃	—	2	2	no	—
142	C₂×C₄×C₅₃	—	2	2	no	—
143	C₂×C₄×C₅₃	—	2	2	no	—
144	C₂×C₄×C₅₃	—	2	2	no	—
145	C₂×C₄×C₅₃	—	2	2	no	—
146	C₂×C₄×C₅₃	—	2	2	no	—
147	C₂×C₄×C₅₃	—	2	2	no	—
148	C₂×C₄×C₅₃	—	2	2	no	—
149	C₂×C₄×C₅₃	—	4	2	no	—
150	C₂×C₄×C₅₃	—	4	2	no	—
151	C₂×C₄×C₅₃	#117	1	2	yes	—
152	C₂×C₄×C₅₃	#117	1	2	yes	—
153	C₂×C₄×C₅₃	#131	1	4	yes	—
154	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
157	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
158	C₈×C₅₃	—	2	4	no	—
159	C₈×C₅₃	—	2	4	no	—
160	C₈×C₅₃	—	4	2	no	—
161	C₈×C₅₃	—	4	2	no	—
162	#21434	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₅₃	—	4	1	no	—
164	C₂²×C₅₃	—	4	1	no	—
165	C₂²×C₅₃	—	4	2	no	—
166	C₂²×C₅₃	—	4	2	no	—
167	C₂²×C₅₃	—	4	1	no	—
168	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
169	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
170	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
171	C₂²×C₅₃	C₂×#131	1	2	yes	—
172	C₂²×C₅₃	#568	1	2	yes	—
173	C₄×C₅₃	—	2	2	no	—
174	C₄×C₅₃	—	2	2	no	—
175	C₄×C₅₃	—	2	4	no	—
176	C₄×C₅₃	—	4	1	no	—
177	C₄×C₅₃	—	4	1	no	—
178	C₄×C₅₃	—	4	2	no	—
179	C₄×C₅₃	—	4	2	no	—
180	C₄×C₅₃	—	4	2	no	—
181	C₄×C₅₃	—	4	1	no	—
182	C₄×C₅₃	#529	1	2	yes	—
183	C₄×C₅₃	#529	1	2	yes	—
184	#2298	C₂×C₅₃	1	1	yes	characteristic
185	#1924	C₂×C₅₃	1	2	yes	—
186	#1923	C₂×C₅₃	1	2	yes	—
187	#1917	C₂×C₅₃	1	2	yes	complemented
188	#1916	C₂×C₅₃	1	2	yes	complemented
189	#1768	C₂×C₅₃	1	1	yes	characteristic, complemented
190	#1768	C₂×C₅₃	1	1	yes	characteristic, complemented
191	#1750	C₂×C₅₃	1	1	yes	characteristic
192	#1750	C₂×C₅₃	1	1	yes	characteristic
193	#1744	C₂×C₅₃	1	1	yes	characteristic, complemented
194	C₄×#97	C₂×C₅₃	1	1	yes	characteristic, complemented
195	C₂×C₅₃	—	8	1	no	—
196	C₂×C₅₃	#2298	1	1	yes	characteristic
197	C₂×C₅₃	#2922	1	1	yes	characteristic
198	C₂×C₅₃	#2923	1	1	yes	characteristic
199	C₂×C₅₃	#2968	1	2	yes	—
200	C₂×C₅₃	#2969	1	2	yes	—
201	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
204	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
205	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
206	C₂×#97	C₂²×C₅₃	1	2	yes	—
207	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
208	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	—
210	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
212	#388	C₄×C₅₃	1	2	yes	—
213	#388	C₄×C₅₃	1	2	yes	—
214	#387	C₄×C₅₃	1	2	yes	—
215	#387	C₄×C₅₃	1	2	yes	—
216	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
217	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
218	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
219	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
220	#376	C₂²×C₅₃	1	1	yes	characteristic
221	C₄³	C₂²×C₅₃	1	1	yes	characteristic
222	#336	C₂²×C₅₃	1	2	yes	—
223	#336	C₂²×C₅₃	1	2	yes	—
224	#336	C₂²×C₅₃	1	2	yes	—
225	#336	C₂²×C₅₃	1	2	yes	—
226	#336	C₂²×C₅₃	1	2	yes	—
227	#336	C₂²×C₅₃	1	2	yes	—
228	C₅₃	#21434	1	1	yes	characteristic, direct product factor, Sylow
229	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
231	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
232	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
233	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
234	#117	—	2	2	no	—
235	#117	—	2	2	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
244	C₂×C₄²	C₂×C₄×C₅₃	1	2	yes	—
245	C₂×C₄²	C₂×C₄×C₅₃	1	2	yes	—
246	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
252	C₄⋊C₈	—	2	4	no	—
253	C₄⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	2	4	no	—
255	C₂²⋊C₈	—	2	4	no	—
256	#97	—	2	4	no	—
257	#97	—	2	2	no	—
258	#97	—	2	2	no	—
259	C₄×C₈	—	2	4	no	—
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	—	2	2	no	—
262	#95	C₂×C₄×C₅₃	1	2	yes	—
263	#95	C₂×C₄×C₅₃	1	2	yes	—
264	#95	C₂×C₄×C₅₃	1	2	yes	—
265	#95	C₂×C₄×C₅₃	1	2	yes	—
266	#95	C₂×C₄×C₅₃	1	2	yes	—
267	#95	C₂×C₄×C₅₃	1	2	yes	—
268	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
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	C₂²×C₄×C₅₃	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
282	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	#41×C₅₃	1	4	yes	—
294	C₂×C₈	#41×C₅₃	1	4	yes	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₄²	—	2	4	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	2	1	no	—
310	C₄²	—	4	2	no	—
311	C₄²	#41×C₅₃	1	2	yes	—
312	C₄²	#41×C₅₃	1	2	yes	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	#117×C₅₃	1	2	yes	—
342	C₂×C₄	#117×C₅₃	1	2	yes	—
343	C₂×C₄	#131×C₅₃	1	4	yes	—
344	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
347	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
348	C₈	—	2	4	no	—
349	C₈	—	2	4	no	—
350	C₈	—	4	2	no	—
351	C₈	—	4	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	C₂×#117×C₅₃	1	1	yes	characteristic
358	C₂²	C₄×#41×C₅₃	1	1	yes	characteristic
359	C₂²	C₄×#41×C₅₃	1	1	yes	characteristic
360	C₂²	C₂×#131×C₅₃	1	2	yes	—
361	C₂²	C₅₃×#568	1	2	yes	—
362	C₄	—	2	4	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	1	no	—
371	C₄	C₅₃×#529	1	2	yes	—
372	C₄	C₅₃×#529	1	2	yes	—
373	C₂	—	8	1	no	—
374	C₂	C₅₃×#2298	1	1	yes	characteristic
375	C₂	C₅₃×#2922	1	1	yes	characteristic
376	C₂	C₅₃×#2923	1	1	yes	characteristic
377	C₂	C₅₃×#2968	1	2	yes	—
378	C₂	C₅₃×#2969	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂⁴×C₅₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅₃×#1917	C₂	semidirect
5. C₅₃×#1916	C₂	semidirect
6. C₅₃×#1768	C₂	semidirect
7. C₅₃×#1768	C₂	semidirect
10. C₅₃×#1744	C₂	semidirect
11. C₄×#97×C₅₃	C₂	semidirect
162. #21434	C₅₃	direct (N × H)
187. #1917	C₂×C₅₃	semidirect
188. #1916	C₂×C₅₃	semidirect
189. #1768	C₂×C₅₃	semidirect
190. #1768	C₂×C₅₃	semidirect
193. #1744	C₂×C₅₃	semidirect
194. C₄×#97	C₂×C₅₃	semidirect
228. C₅₃	#21434	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#2298	2
C₅₃×#1924	2
C₅₃×#1923	2
C₅₃×#1917	2
C₅₃×#1916	2
C₅₃×#1768	2
C₅₃×#1750	2
C₅₃×#1744	2
C₄×#97×C₅₃	2
#21434	53

Subgroups — C53×#21434 #27228946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#21434 #27228946