Subgroups — C₅₃×#24901 #27232413

Order 13568.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₅₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1786	C₂	1	1	yes	maximal, characteristic
16	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
24	C₅₃×#450	—	2	4	no	—
25	C₄×SD₁₆×C₅₃	—	2	4	no	—
26	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#399	—	2	1	no	—
41	C₅₃×#398	—	2	1	no	—
42	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#390	C₂²	1	1	yes	characteristic
44	C₅₃×#390	C₂²	1	1	yes	characteristic
45	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#388	—	2	1	no	—
47	C₅₃×#387	—	2	1	no	—
48	C₅₃×#386	—	2	1	no	—
49	C₅₃×#386	—	2	1	no	—
50	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#380	C₂²	1	1	yes	characteristic
52	C₅₃×#380	C₂²	1	1	yes	characteristic
53	C₅₃×#379	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₅₃	—	2	1	no	—
62	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₅₃	—	2	2	no	—
64	C₂²×D₄×C₅₃	—	2	2	no	—
65	C₂²×D₄×C₅₃	—	2	2	no	—
66	C₂²×D₄×C₅₃	—	2	2	no	—
67	C₂²×D₄×C₅₃	—	2	1	no	—
68	C₂²×D₄×C₅₃	—	4	1	no	—
69	C₂²×D₄×C₅₃	—	4	1	no	—
70	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅₃	—	2	1	no	—
73	C₂³×C₄×C₅₃	—	2	1	no	—
74	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
75	C₂×SD₁₆×C₅₃	—	2	2	no	—
76	C₂×SD₁₆×C₅₃	—	2	2	no	—
77	C₂×SD₁₆×C₅₃	—	2	2	no	—
78	C₂×SD₁₆×C₅₃	—	2	2	no	—
79	C₂×SD₁₆×C₅₃	—	4	1	no	—
80	C₂×SD₁₆×C₅₃	D₄	1	4	yes	—
81	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
85	C₂²⋊Q₈×C₅₃	—	2	2	no	—
86	C₂²⋊Q₈×C₅₃	—	4	1	no	—
87	C₄×Q₈×C₅₃	—	2	2	no	—
88	C₄×Q₈×C₅₃	—	4	1	no	—
89	C₄×D₄×C₅₃	—	2	2	no	—
90	C₄×D₄×C₅₃	—	2	2	no	—
91	C₄×D₄×C₅₃	—	4	1	no	—
92	C₄×D₄×C₅₃	—	4	1	no	—
93	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
97	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
98	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
113	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₅₃	—	2	1	no	—
116	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
118	#106×C₅₃	—	2	2	no	—
119	#106×C₅₃	—	4	1	no	—
120	C₄⋊C₈×C₅₃	—	4	1	no	—
121	#103×C₅₃	—	2	2	no	—
122	#103×C₅₃	—	4	1	no	—
123	#102×C₅₃	—	2	2	no	—
124	#102×C₅₃	—	2	2	no	—
125	#102×C₅₃	—	2	2	no	—
126	#102×C₅₃	—	2	2	no	—
127	#102×C₅₃	—	2	2	no	—
128	#102×C₅₃	—	4	1	no	—
129	C₂²⋊C₈×C₅₃	—	2	2	no	—
130	C₂²⋊C₈×C₅₃	—	4	1	no	—
131	C₄×C₈×C₅₃	—	2	2	no	—
132	#95×C₅₃	—	2	1	no	—
133	#95×C₅₃	—	2	1	no	—
134	#95×C₅₃	—	2	1	no	—
135	#95×C₅₃	—	2	1	no	—
136	#95×C₅₃	—	2	1	no	—
137	#95×C₅₃	D₄	1	1	yes	characteristic
138	#95×C₅₃	D₄	1	1	yes	characteristic
139	C₂⁴×C₅₃	—	2	1	no	—
140	C₂⁴×C₅₃	—	2	4	no	—
141	C₂⁴×C₅₃	—	2	1	no	—
142	C₂⁴×C₅₃	—	4	2	no	—
143	C₂⁴×C₅₃	—	4	2	no	—
144	C₂⁴×C₅₃	—	4	2	no	—
145	C₂⁴×C₅₃	—	4	2	no	—
146	C₂⁴×C₅₃	—	8	1	no	—
147	C₂⁴×C₅₃	—	8	1	no	—
148	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₅₃	—	2	1	no	—
150	C₂×Q₈×C₅₃	—	2	1	no	—
151	C₂×Q₈×C₅₃	—	2	1	no	—
152	C₂×Q₈×C₅₃	—	2	1	no	—
153	C₂×Q₈×C₅₃	—	2	1	no	—
154	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₅₃	—	2	4	no	—
156	C₂×D₄×C₅₃	—	2	1	no	—
157	C₂×D₄×C₅₃	—	2	1	no	—
158	C₂×D₄×C₅₃	—	2	1	no	—
159	C₂×D₄×C₅₃	—	2	1	no	—
160	C₂×D₄×C₅₃	—	2	1	no	—
161	C₂×D₄×C₅₃	—	2	1	no	—
162	C₂×D₄×C₅₃	—	2	1	no	—
163	C₂×D₄×C₅₃	—	2	1	no	—
164	C₂×D₄×C₅₃	—	4	2	no	—
165	C₂×D₄×C₅₃	—	4	2	no	—
166	C₂×D₄×C₅₃	—	4	4	no	—
167	C₂×D₄×C₅₃	—	4	4	no	—
168	C₂×D₄×C₅₃	—	4	4	no	—
169	C₂×D₄×C₅₃	—	4	4	no	—
170	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
171	C₂×D₄×C₅₃	#41	1	2	yes	—
172	C₂×D₄×C₅₃	#41	1	2	yes	—
173	C₂×D₄×C₅₃	#41	1	2	yes	—
174	C₂²×C₄×C₅₃	—	2	1	no	—
175	C₂²×C₄×C₅₃	—	2	1	no	—
176	C₂²×C₄×C₅₃	—	2	1	no	—
177	C₂²×C₄×C₅₃	—	2	1	no	—
178	C₂²×C₄×C₅₃	—	2	1	no	—
179	C₂²×C₄×C₅₃	—	2	1	no	—
180	C₂²×C₄×C₅₃	—	2	1	no	—
181	C₂²×C₄×C₅₃	—	2	1	no	—
182	C₂²×C₄×C₅₃	—	2	1	no	—
183	C₂²×C₄×C₅₃	—	2	1	no	—
184	C₂²×C₄×C₅₃	—	2	1	no	—
185	C₂²×C₄×C₅₃	—	2	1	no	—
186	C₂²×C₄×C₅₃	—	4	2	no	—
187	C₂²×C₄×C₅₃	—	4	2	no	—
188	C₂²×C₄×C₅₃	—	4	2	no	—
189	C₂²×C₄×C₅₃	—	4	2	no	—
190	C₂²×C₄×C₅₃	—	8	1	no	—
191	C₂²×C₄×C₅₃	—	8	1	no	—
192	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₅₃	—	2	8	no	—
199	SD₁₆×C₅₃	—	4	4	no	—
200	C₂×C₈×C₅₃	—	2	1	no	—
201	C₂×C₈×C₅₃	—	2	1	no	—
202	C₂×C₈×C₅₃	—	2	1	no	—
203	C₂×C₈×C₅₃	—	2	1	no	—
204	C₂×C₈×C₅₃	—	2	1	no	—
205	C₂×C₈×C₅₃	—	2	1	no	—
206	C₂×C₈×C₅₃	—	2	1	no	—
207	C₂×C₈×C₅₃	—	2	1	no	—
208	C₂×C₈×C₅₃	—	2	1	no	—
209	C₂×C₈×C₅₃	—	2	1	no	—
210	C₂×C₈×C₅₃	—	2	1	no	—
211	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
212	C₄⋊C₄×C₅₃	—	2	1	no	—
213	C₄⋊C₄×C₅₃	—	2	1	no	—
214	C₄⋊C₄×C₅₃	—	2	1	no	—
215	C₄⋊C₄×C₅₃	—	2	1	no	—
216	C₄⋊C₄×C₅₃	—	2	1	no	—
217	C₄⋊C₄×C₅₃	—	2	1	no	—
218	C₄⋊C₄×C₅₃	—	2	1	no	—
219	C₄⋊C₄×C₅₃	—	2	1	no	—
220	C₄⋊C₄×C₅₃	—	2	1	no	—
221	C₄⋊C₄×C₅₃	—	2	1	no	—
222	C₄⋊C₄×C₅₃	—	4	2	no	—
223	C₄⋊C₄×C₅₃	—	4	2	no	—
224	C₄⋊C₄×C₅₃	—	4	2	no	—
225	C₄⋊C₄×C₅₃	—	8	1	no	—
226	C₄⋊C₄×C₅₃	—	8	1	no	—
227	C₂²⋊C₄×C₅₃	—	4	1	no	—
228	C₂²⋊C₄×C₅₃	—	4	2	no	—
229	C₂²⋊C₄×C₅₃	—	4	2	no	—
230	C₂²⋊C₄×C₅₃	—	4	2	no	—
231	C₂²⋊C₄×C₅₃	—	4	2	no	—
232	C₂²⋊C₄×C₅₃	—	4	2	no	—
233	C₂²⋊C₄×C₅₃	—	4	2	no	—
234	C₂²⋊C₄×C₅₃	—	8	1	no	—
235	C₂²⋊C₄×C₅₃	—	8	1	no	—
236	C₂²⋊C₄×C₅₃	—	8	1	no	—
237	C₂²⋊C₄×C₅₃	SD₁₆	1	4	yes	complemented
238	C₄²×C₅₃	—	2	1	no	—
239	C₄²×C₅₃	—	2	1	no	—
240	C₄²×C₅₃	—	2	1	no	—
241	C₄²×C₅₃	—	2	1	no	—
242	C₄²×C₅₃	—	4	2	no	—
243	C₂³×C₅₃	—	2	1	no	—
244	C₂³×C₅₃	—	2	2	no	—
245	C₂³×C₅₃	—	2	1	no	—
246	C₂³×C₅₃	—	2	2	no	—
247	C₂³×C₅₃	—	2	1	no	—
248	C₂³×C₅₃	—	2	2	no	—
249	C₂³×C₅₃	—	2	1	no	—
250	C₂³×C₅₃	—	2	1	no	—
251	C₂³×C₅₃	—	2	1	no	—
252	C₂³×C₅₃	—	2	2	no	—
253	C₂³×C₅₃	—	4	8	no	—
254	C₂³×C₅₃	—	4	8	no	—
255	C₂³×C₅₃	—	4	1	no	—
256	C₂³×C₅₃	—	4	1	no	—
257	C₂³×C₅₃	—	4	1	no	—
258	C₂³×C₅₃	—	4	1	no	—
259	C₂³×C₅₃	—	4	1	no	—
260	C₂³×C₅₃	—	4	1	no	—
261	C₂³×C₅₃	—	4	1	no	—
262	C₂³×C₅₃	—	4	1	no	—
263	C₂³×C₅₃	—	4	1	no	—
264	C₂³×C₅₃	—	4	1	no	—
265	C₂³×C₅₃	—	8	4	no	—
266	C₂³×C₅₃	—	8	4	no	—
267	C₂³×C₅₃	—	8	4	no	—
268	C₂³×C₅₃	—	8	4	no	—
269	C₂³×C₅₃	—	8	4	no	—
270	C₂³×C₅₃	C₂×SD₁₆	1	2	yes	—
271	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
272	Q₈×C₅₃	—	2	2	no	—
273	Q₈×C₅₃	—	2	2	no	—
274	Q₈×C₅₃	—	4	1	no	—
275	Q₈×C₅₃	—	4	1	no	—
276	D₄×C₅₃	—	2	2	no	—
277	D₄×C₅₃	—	2	2	no	—
278	D₄×C₅₃	—	2	2	no	—
279	D₄×C₅₃	—	2	2	no	—
280	D₄×C₅₃	—	2	2	no	—
281	D₄×C₅₃	—	4	8	no	—
282	D₄×C₅₃	—	4	1	no	—
283	D₄×C₅₃	—	4	1	no	—
284	D₄×C₅₃	#123	1	4	yes	—
285	C₂×C₄×C₅₃	—	2	1	no	—
286	C₂×C₄×C₅₃	—	2	1	no	—
287	C₂×C₄×C₅₃	—	2	1	no	—
288	C₂×C₄×C₅₃	—	2	1	no	—
289	C₂×C₄×C₅₃	—	2	1	no	—
290	C₂×C₄×C₅₃	—	2	1	no	—
291	C₂×C₄×C₅₃	—	2	2	no	—
292	C₂×C₄×C₅₃	—	2	1	no	—
293	C₂×C₄×C₅₃	—	2	1	no	—
294	C₂×C₄×C₅₃	—	2	1	no	—
295	C₂×C₄×C₅₃	—	2	1	no	—
296	C₂×C₄×C₅₃	—	2	1	no	—
297	C₂×C₄×C₅₃	—	2	1	no	—
298	C₂×C₄×C₅₃	—	2	1	no	—
299	C₂×C₄×C₅₃	—	4	1	no	—
300	C₂×C₄×C₅₃	—	4	1	no	—
301	C₂×C₄×C₅₃	—	4	1	no	—
302	C₂×C₄×C₅₃	—	4	1	no	—
303	C₂×C₄×C₅₃	—	4	1	no	—
304	C₂×C₄×C₅₃	—	4	1	no	—
305	C₂×C₄×C₅₃	—	4	1	no	—
306	C₂×C₄×C₅₃	—	4	1	no	—
307	C₂×C₄×C₅₃	—	4	1	no	—
308	C₂×C₄×C₅₃	—	4	1	no	—
309	C₂×C₄×C₅₃	—	4	1	no	—
310	C₂×C₄×C₅₃	—	4	1	no	—
311	C₂×C₄×C₅₃	—	4	1	no	—
312	C₂×C₄×C₅₃	—	4	1	no	—
313	C₂×C₄×C₅₃	—	4	1	no	—
314	C₂×C₄×C₅₃	—	4	1	no	—
315	C₂×C₄×C₅₃	—	4	1	no	—
316	C₂×C₄×C₅₃	—	4	1	no	—
317	C₂×C₄×C₅₃	—	4	1	no	—
318	C₂×C₄×C₅₃	—	4	1	no	—
319	C₂×C₄×C₅₃	—	4	1	no	—
320	C₂×C₄×C₅₃	—	8	4	no	—
321	C₂×C₄×C₅₃	—	8	4	no	—
322	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
323	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
324	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
329	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
330	C₈×C₅₃	—	2	2	no	—
331	C₈×C₅₃	—	4	1	no	—
332	C₈×C₅₃	—	4	1	no	—
333	C₈×C₅₃	—	4	1	no	—
334	#24901	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂²×C₅₃	—	2	2	no	—
336	C₂²×C₅₃	—	2	4	no	—
337	C₂²×C₅₃	—	2	2	no	—
338	C₂²×C₅₃	—	2	2	no	—
339	C₂²×C₅₃	—	4	2	no	—
340	C₂²×C₅₃	—	4	1	no	—
341	C₂²×C₅₃	—	4	2	no	—
342	C₂²×C₅₃	—	4	1	no	—
343	C₂²×C₅₃	—	4	1	no	—
344	C₂²×C₅₃	—	4	2	no	—
345	C₂²×C₅₃	—	4	2	no	—
346	C₂²×C₅₃	—	4	2	no	—
347	C₂²×C₅₃	—	4	1	no	—
348	C₂²×C₅₃	—	4	2	no	—
349	C₂²×C₅₃	—	4	2	no	—
350	C₂²×C₅₃	—	4	2	no	—
351	C₂²×C₅₃	—	4	2	no	—
352	C₂²×C₅₃	—	8	16	no	—
353	C₂²×C₅₃	—	8	1	no	—
354	C₂²×C₅₃	—	8	1	no	—
355	C₂²×C₅₃	—	8	1	no	—
356	C₂²×C₅₃	—	8	1	no	—
357	C₂²×C₅₃	#525	1	1	yes	characteristic
358	C₂²×C₅₃	D₄²	1	1	yes	characteristic
359	C₂²×C₅₃	#546	1	1	yes	characteristic
360	C₂²×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
361	C₂²×C₅₃	#575	1	1	yes	characteristic
362	C₂²×C₅₃	#576	1	1	yes	characteristic
363	C₂²×C₅₃	#577	1	1	yes	characteristic
364	C₄×C₅₃	—	2	2	no	—
365	C₄×C₅₃	—	2	2	no	—
366	C₄×C₅₃	—	4	1	no	—
367	C₄×C₅₃	—	4	2	no	—
368	C₄×C₅₃	—	4	1	no	—
369	C₄×C₅₃	—	4	1	no	—
370	C₄×C₅₃	—	8	1	no	—
371	C₄×C₅₃	—	8	1	no	—
372	C₄×C₅₃	—	8	1	no	—
373	C₄×C₅₃	—	8	1	no	—
374	C₄×C₅₃	—	8	1	no	—
375	C₄×C₅₃	C₂×#123	1	1	yes	characteristic
376	C₄×C₅₃	#538	1	1	yes	characteristic
377	C₄×C₅₃	#546	1	1	yes	characteristic
378	C₄×C₅₃	#551	1	1	yes	characteristic
379	C₂×#450	C₂×C₅₃	1	1	yes	characteristic
380	C₂×C₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
381	#2423	C₂×C₅₃	1	1	yes	characteristic, complemented
382	D₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic
383	#2094	C₂×C₅₃	1	1	yes	characteristic, complemented
384	#2077	C₂×C₅₃	1	1	yes	characteristic, complemented
385	#2055	C₂×C₅₃	1	1	yes	characteristic, complemented
386	#2035	C₂×C₅₃	1	1	yes	characteristic, complemented
387	#1934	C₂×C₅₃	1	1	yes	characteristic, complemented
388	#1923	C₂×C₅₃	1	1	yes	characteristic, complemented
389	#1880	C₂×C₅₃	1	1	yes	characteristic, complemented
390	#1877	C₂×C₅₃	1	1	yes	characteristic, complemented
391	#1864	C₂×C₅₃	1	1	yes	characteristic, complemented
392	#1802	C₂×C₅₃	1	1	yes	characteristic, complemented
393	#1786	C₂×C₅₃	1	1	yes	characteristic
394	C₂×C₅₃	—	4	2	no	—
395	C₂×C₅₃	—	4	4	no	—
396	C₂×C₅₃	—	8	2	no	—
397	C₂×C₅₃	#2418	1	1	yes	characteristic
398	C₂×C₅₃	#3101	1	1	yes	characteristic
399	C₂×C₅₃	#3118	1	1	yes	characteristic
400	C₂×C₅₃	#3268	1	1	yes	characteristic
401	C₂×C₅₃	D₄×SD₁₆	1	1	yes	characteristic
402	C₂×C₅₃	#3295	1	1	yes	characteristic
403	C₂×C₅₃	#3323	1	1	yes	characteristic
404	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
405	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
406	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
407	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
409	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	—	2	1	no	—
412	#450	—	2	4	no	—
413	C₄×SD₁₆	—	2	4	no	—
414	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
415	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
416	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
417	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
418	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
419	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
421	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
422	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
423	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
424	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
427	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
428	#399	—	2	1	no	—
429	#398	—	2	1	no	—
430	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
431	#390	C₂²×C₅₃	1	1	yes	characteristic
432	#390	C₂²×C₅₃	1	1	yes	characteristic
433	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
434	#388	—	2	1	no	—
435	#387	—	2	1	no	—
436	#386	—	2	1	no	—
437	#386	—	2	1	no	—
438	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
439	#380	C₂²×C₅₃	1	1	yes	characteristic
440	#380	C₂²×C₅₃	1	1	yes	characteristic
441	#379	—	2	1	no	—
442	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
443	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
444	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
445	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
446	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
447	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
448	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
449	C₅₃	#24901	1	1	yes	characteristic, direct product factor, Sylow
450	C₂⁵	—	2	1	no	—
451	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	2	2	no	—
454	C₂²×D₄	—	2	2	no	—
455	C₂²×D₄	—	2	2	no	—
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	—	4	1	no	—
458	C₂²×D₄	—	4	1	no	—
459	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
460	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	—	2	1	no	—
463	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	2	2	no	—
468	C₂×SD₁₆	—	4	1	no	—
469	C₂×SD₁₆	D₄×C₅₃	1	4	yes	—
470	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	4	1	no	—
476	C₄×Q₈	—	2	2	no	—
477	C₄×Q₈	—	4	1	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	4	1	no	—
481	C₄×D₄	—	4	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	4	4	no	—
502	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
504	C₂×C₄²	—	2	1	no	—
505	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
507	#106	—	2	2	no	—
508	#106	—	4	1	no	—
509	C₄⋊C₈	—	4	1	no	—
510	#103	—	2	2	no	—
511	#103	—	4	1	no	—
512	#102	—	2	2	no	—
513	#102	—	2	2	no	—
514	#102	—	2	2	no	—
515	#102	—	2	2	no	—
516	#102	—	2	2	no	—
517	#102	—	4	1	no	—
518	C₂²⋊C₈	—	2	2	no	—
519	C₂²⋊C₈	—	4	1	no	—
520	C₄×C₈	—	2	2	no	—
521	#95	—	2	1	no	—
522	#95	—	2	1	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	D₄×C₅₃	1	1	yes	characteristic
527	#95	D₄×C₅₃	1	1	yes	characteristic
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	4	no	—
530	C₂⁴	—	2	1	no	—
531	C₂⁴	—	4	2	no	—
532	C₂⁴	—	4	2	no	—
533	C₂⁴	—	4	2	no	—
534	C₂⁴	—	4	2	no	—
535	C₂⁴	—	8	1	no	—
536	C₂⁴	—	8	1	no	—
537	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
560	C₂×D₄	#41×C₅₃	1	2	yes	—
561	C₂×D₄	#41×C₅₃	1	2	yes	—
562	C₂×D₄	#41×C₅₃	1	2	yes	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	8	1	no	—
580	C₂²×C₄	—	8	1	no	—
581	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
587	SD₁₆	—	2	8	no	—
588	SD₁₆	—	4	4	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	8	1	no	—
615	C₄⋊C₄	—	8	1	no	—
616	C₂²⋊C₄	—	4	1	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	8	1	no	—
624	C₂²⋊C₄	—	8	1	no	—
625	C₂²⋊C₄	—	8	1	no	—
626	C₂²⋊C₄	SD₁₆×C₅₃	1	4	yes	complemented
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	4	2	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	4	8	no	—
643	C₂³	—	4	8	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	8	4	no	—
655	C₂³	—	8	4	no	—
656	C₂³	—	8	4	no	—
657	C₂³	—	8	4	no	—
658	C₂³	—	8	4	no	—
659	C₂³	C₂×SD₁₆×C₅₃	1	2	yes	—
660	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	4	1	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	2	no	—
670	D₄	—	4	8	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	1	no	—
673	D₄	#123×C₅₃	1	4	yes	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂×SD₁₆×C₅₃	1	2	yes	—
712	C₂×C₄	C₂×SD₁₆×C₅₃	1	2	yes	—
713	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
714	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
715	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
716	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
717	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
718	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
719	C₈	—	2	2	no	—
720	C₈	—	4	1	no	—
721	C₈	—	4	1	no	—
722	C₈	—	4	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	8	16	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	C₅₃×#525	1	1	yes	characteristic
746	C₂²	D₄²×C₅₃	1	1	yes	characteristic
747	C₂²	C₅₃×#546	1	1	yes	characteristic
748	C₂²	C₂²×SD₁₆×C₅₃	1	1	yes	characteristic
749	C₂²	C₅₃×#575	1	1	yes	characteristic
750	C₂²	C₅₃×#576	1	1	yes	characteristic
751	C₂²	C₅₃×#577	1	1	yes	characteristic
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	2	no	—
758	C₄	—	8	1	no	—
759	C₄	—	8	1	no	—
760	C₄	—	8	1	no	—
761	C₄	—	8	1	no	—
762	C₄	—	8	1	no	—
763	C₄	C₂×#123×C₅₃	1	1	yes	characteristic
764	C₄	C₅₃×#538	1	1	yes	characteristic
765	C₄	C₅₃×#546	1	1	yes	characteristic
766	C₄	C₅₃×#551	1	1	yes	characteristic
767	C₂	—	4	2	no	—
768	C₂	—	4	4	no	—
769	C₂	—	8	2	no	—
770	C₂	C₅₃×#2418	1	1	yes	characteristic
771	C₂	C₅₃×#3101	1	1	yes	characteristic
772	C₂	C₅₃×#3118	1	1	yes	characteristic
773	C₂	C₅₃×#3268	1	1	yes	characteristic
774	C₂	D₄×SD₁₆×C₅₃	1	1	yes	characteristic
775	C₂	C₅₃×#3295	1	1	yes	characteristic
776	C₂	C₅₃×#3323	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂³×D₄×C₅₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₄×C₂²⋊C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₅₃	C₂	semidirect
3. C₅₃×#2423	C₂	semidirect
5. C₅₃×#2094	C₂	semidirect
6. C₅₃×#2077	C₂	semidirect
7. C₅₃×#2055	C₂	semidirect
8. C₅₃×#2035	C₂	semidirect
9. C₅₃×#1934	C₂	semidirect
10. C₅₃×#1923	C₂	semidirect
11. C₅₃×#1880	C₂	semidirect
12. C₅₃×#1877	C₂	semidirect
13. C₅₃×#1864	C₂	semidirect
14. C₅₃×#1802	C₂	semidirect
20. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
26. C₂×#106×C₅₃	C₂²	semidirect
27. C₂×#106×C₅₃	C₂²	semidirect
28. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
29. C₂×#103×C₅₃	C₂²	semidirect
30. C₂×#103×C₅₃	C₂²	semidirect
39. C₂×C₄×C₈×C₅₃	C₂²	semidirect
42. C₅₃×#391	C₂²	semidirect
45. C₅₃×#389	C₂²	semidirect
50. C₅₃×#384	C₂²	semidirect
55. C₅₃×#340	C₂²	semidirect
56. C₅₃×#340	C₂²	semidirect
57. C₅₃×#340	C₂²	semidirect
58. C₅₃×#340	C₂²	semidirect
59. C₅₃×#336	C₂²	semidirect
60. C₅₃×#336	C₂²	semidirect
237. C₂²⋊C₄×C₅₃	SD₁₆	semidirect
334. #24901	C₅₃	direct (N × H)
380. C₂×C₄×SD₁₆	C₂×C₅₃	semidirect
381. #2423	C₂×C₅₃	semidirect
383. #2094	C₂×C₅₃	semidirect
384. #2077	C₂×C₅₃	semidirect
385. #2055	C₂×C₅₃	semidirect
386. #2035	C₂×C₅₃	semidirect
387. #1934	C₂×C₅₃	semidirect
388. #1923	C₂×C₅₃	semidirect
389. #1880	C₂×C₅₃	semidirect
390. #1877	C₂×C₅₃	semidirect
391. #1864	C₂×C₅₃	semidirect
392. #1802	C₂×C₅₃	semidirect
408. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
414. C₂×#106	C₂²×C₅₃	semidirect
415. C₂×#106	C₂²×C₅₃	semidirect
416. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
417. C₂×#103	C₂²×C₅₃	semidirect
418. C₂×#103	C₂²×C₅₃	semidirect
427. C₂×C₄×C₈	C₂²×C₅₃	semidirect
430. #391	C₂²×C₅₃	semidirect
433. #389	C₂²×C₅₃	semidirect
438. #384	C₂²×C₅₃	semidirect
443. #340	C₂²×C₅₃	semidirect
444. #340	C₂²×C₅₃	semidirect
445. #340	C₂²×C₅₃	semidirect
446. #340	C₂²×C₅₃	semidirect
447. #336	C₂²×C₅₃	semidirect
448. #336	C₂²×C₅₃	semidirect
449. C₅₃	#24901	direct (N × H)
626. C₂²⋊C₄	SD₁₆×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#450	2
C₂×C₄×SD₁₆×C₅₃	2
C₅₃×#2423	2
D₄×C₂²⋊C₄×C₅₃	2
C₅₃×#2094	2
C₅₃×#2077	2
C₅₃×#2055	2
C₅₃×#2035	2
C₅₃×#1934	2
C₅₃×#1923	2
C₅₃×#1880	2
C₅₃×#1877	2
C₅₃×#1864	2
C₅₃×#1802	2
C₅₃×#1786	2
#24901	53

Subgroups — C53×#24901 #27232413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#24901 #27232413