Subgroups — C₅₃×#21458 #27228970

Order 13568.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#447	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#102×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
20	C₅₃×#518	—	2	4	no	—
21	C₅₃×#518	—	2	4	no	—
22	C₂×C₄×D₄×C₅₃	—	2	1	no	—
23	C₂×C₄×D₄×C₅₃	—	2	1	no	—
24	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
32	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
33	C₅₃×#447	C₄	1	8	yes	complemented
34	C₅₃×#442	—	2	4	no	—
35	C₄×D₈×C₅₃	—	2	4	no	—
36	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#390	—	2	1	no	—
51	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#388	—	2	1	no	—
54	C₅₃×#386	—	2	1	no	—
55	C₅₃×#385	—	2	1	no	—
56	C₅₃×#380	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
64	C₂⁵×C₅₃	—	2	1	no	—
65	C₂²×D₄×C₅₃	—	2	2	no	—
66	C₂²×D₄×C₅₃	—	2	2	no	—
67	C₂²×D₄×C₅₃	—	2	2	no	—
68	C₂²×D₄×C₅₃	—	2	2	no	—
69	C₂²×D₄×C₅₃	—	2	1	no	—
70	C₂²×D₄×C₅₃	—	2	1	no	—
71	C₂²×D₄×C₅₃	—	2	2	no	—
72	C₂²×D₄×C₅₃	C₂×C₄	1	4	yes	complemented
73	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₅₃	—	2	1	no	—
77	C₂³×C₄×C₅₃	—	2	1	no	—
78	C₂³×C₄×C₅₃	—	2	1	no	—
79	C₂³×C₄×C₅₃	—	2	1	no	—
80	C₂³×C₄×C₅₃	—	2	1	no	—
81	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
82	C₂×D₈×C₅₃	—	2	2	no	—
83	C₂×D₈×C₅₃	—	2	2	no	—
84	C₂×D₈×C₅₃	—	2	2	no	—
85	C₂×D₈×C₅₃	—	2	2	no	—
86	C₂×D₈×C₅₃	C₂×C₄	1	4	yes	complemented
87	C₂×D₈×C₅₃	C₂×C₄	1	4	yes	complemented
88	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	#121×C₅₃	—	2	2	no	—
93	#121×C₅₃	C₂×C₄	1	4	yes	complemented
94	C₄×D₄×C₅₃	—	2	8	no	—
95	C₄×D₄×C₅₃	—	2	8	no	—
96	C₄×D₄×C₅₃	—	2	2	no	—
97	C₄×D₄×C₅₃	—	2	2	no	—
98	C₄×D₄×C₅₃	—	2	2	no	—
99	C₄×D₄×C₅₃	—	2	2	no	—
100	C₄×D₄×C₅₃	—	2	2	no	—
101	C₄×D₄×C₅₃	—	2	2	no	—
102	C₄×D₄×C₅₃	—	2	2	no	—
103	C₄×D₄×C₅₃	—	2	2	no	—
104	C₄×D₄×C₅₃	D₄	1	4	yes	complemented
105	C₄×D₄×C₅₃	D₄	1	4	yes	complemented
106	#117×C₅₃	—	2	2	no	—
107	#117×C₅₃	—	2	2	no	—
108	#117×C₅₃	—	2	2	no	—
109	#117×C₅₃	—	2	2	no	—
110	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
111	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
119	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₅₃	—	2	1	no	—
133	C₂×C₄²×C₅₃	—	2	1	no	—
134	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
136	#107×C₅₃	—	2	2	no	—
137	#106×C₅₃	—	2	2	no	—
138	#102×C₅₃	—	2	2	no	—
139	#102×C₅₃	—	2	2	no	—
140	#102×C₅₃	—	2	2	no	—
141	#102×C₅₃	—	2	2	no	—
142	#102×C₅₃	—	2	2	no	—
143	#102×C₅₃	—	2	2	no	—
144	#102×C₅₃	C₂×C₄	1	4	yes	complemented
145	#102×C₅₃	C₂×C₄	1	4	yes	complemented
146	C₂²⋊C₈×C₅₃	—	2	2	no	—
147	C₂²⋊C₈×C₅₃	C₂×C₄	1	4	yes	complemented
148	#97×C₅₃	—	2	2	no	—
149	C₄×C₈×C₅₃	—	2	2	no	—
150	#95×C₅₃	—	2	1	no	—
151	#95×C₅₃	—	2	1	no	—
152	#95×C₅₃	—	2	1	no	—
153	C₂⁴×C₅₃	—	2	4	no	—
154	C₂⁴×C₅₃	—	2	4	no	—
155	C₂⁴×C₅₃	—	2	1	no	—
156	C₂⁴×C₅₃	—	2	1	no	—
157	C₂⁴×C₅₃	—	2	4	no	—
158	C₂⁴×C₅₃	—	2	1	no	—
159	C₂⁴×C₅₃	—	8	1	no	—
160	C₂⁴×C₅₃	—	8	1	no	—
161	C₂⁴×C₅₃	—	8	1	no	—
162	C₂⁴×C₅₃	—	8	1	no	—
163	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₅₃	—	2	4	no	—
165	C₂×D₄×C₅₃	—	2	4	no	—
166	C₂×D₄×C₅₃	—	2	8	no	—
167	C₂×D₄×C₅₃	—	2	8	no	—
168	C₂×D₄×C₅₃	—	2	8	no	—
169	C₂×D₄×C₅₃	—	2	8	no	—
170	C₂×D₄×C₅₃	—	2	4	no	—
171	C₂×D₄×C₅₃	—	2	4	no	—
172	C₂×D₄×C₅₃	—	2	1	no	—
173	C₂×D₄×C₅₃	—	2	1	no	—
174	C₂×D₄×C₅₃	—	2	1	no	—
175	C₂×D₄×C₅₃	—	2	1	no	—
176	C₂×D₄×C₅₃	—	2	1	no	—
177	C₂×D₄×C₅₃	—	2	1	no	—
178	C₂×D₄×C₅₃	—	2	1	no	—
179	C₂×D₄×C₅₃	—	2	1	no	—
180	C₂×D₄×C₅₃	—	2	1	no	—
181	C₂×D₄×C₅₃	—	2	1	no	—
182	C₂×D₄×C₅₃	—	2	1	no	—
183	C₂×D₄×C₅₃	—	8	1	no	—
184	C₂×D₄×C₅₃	—	8	1	no	—
185	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
186	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
187	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
188	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₅₃	#41	1	2	yes	—
191	C₂×D₄×C₅₃	#41	1	2	yes	—
192	C₂²×C₄×C₅₃	—	2	1	no	—
193	C₂²×C₄×C₅₃	—	2	1	no	—
194	C₂²×C₄×C₅₃	—	2	1	no	—
195	C₂²×C₄×C₅₃	—	2	1	no	—
196	C₂²×C₄×C₅₃	—	2	1	no	—
197	C₂²×C₄×C₅₃	—	2	1	no	—
198	C₂²×C₄×C₅₃	—	2	1	no	—
199	C₂²×C₄×C₅₃	—	2	4	no	—
200	C₂²×C₄×C₅₃	—	2	4	no	—
201	C₂²×C₄×C₅₃	—	2	4	no	—
202	C₂²×C₄×C₅₃	—	2	4	no	—
203	C₂²×C₄×C₅₃	—	2	1	no	—
204	C₂²×C₄×C₅₃	—	2	1	no	—
205	C₂²×C₄×C₅₃	—	4	2	no	—
206	C₂²×C₄×C₅₃	—	8	1	no	—
207	C₂²×C₄×C₅₃	—	8	1	no	—
208	C₂²×C₄×C₅₃	—	8	1	no	—
209	C₂²×C₄×C₅₃	—	8	1	no	—
210	C₂²×C₄×C₅₃	—	8	1	no	—
211	C₂²×C₄×C₅₃	—	8	1	no	—
212	C₂²×C₄×C₅₃	—	8	1	no	—
213	C₂²×C₄×C₅₃	—	8	1	no	—
214	C₂²×C₄×C₅₃	—	8	1	no	—
215	C₂²×C₄×C₅₃	—	8	1	no	—
216	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
217	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₅₃	#41	1	2	yes	—
223	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
224	D₈×C₅₃	—	2	8	no	—
225	D₈×C₅₃	—	2	8	no	—
226	C₂×C₈×C₅₃	—	2	1	no	—
227	C₂×C₈×C₅₃	—	2	1	no	—
228	C₂×C₈×C₅₃	—	2	1	no	—
229	C₂×C₈×C₅₃	—	2	1	no	—
230	C₂×C₈×C₅₃	—	2	1	no	—
231	C₂×C₈×C₅₃	—	2	1	no	—
232	C₂×C₈×C₅₃	—	2	1	no	—
233	C₂×C₈×C₅₃	—	2	1	no	—
234	C₂×C₈×C₅₃	—	2	1	no	—
235	C₂×C₈×C₅₃	—	2	1	no	—
236	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
237	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
238	C₄⋊C₄×C₅₃	—	2	2	no	—
239	C₄⋊C₄×C₅₃	—	2	2	no	—
240	C₄⋊C₄×C₅₃	—	2	1	no	—
241	C₄⋊C₄×C₅₃	—	2	1	no	—
242	C₄⋊C₄×C₅₃	—	2	1	no	—
243	C₄⋊C₄×C₅₃	—	2	1	no	—
244	C₄⋊C₄×C₅₃	—	2	1	no	—
245	C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₄⋊C₄×C₅₃	—	2	1	no	—
247	C₄⋊C₄×C₅₃	—	8	1	no	—
248	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
249	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
251	C₂²⋊C₄×C₅₃	—	2	4	no	—
252	C₂²⋊C₄×C₅₃	—	2	4	no	—
253	C₂²⋊C₄×C₅₃	—	2	4	no	—
254	C₂²⋊C₄×C₅₃	—	2	4	no	—
255	C₂²⋊C₄×C₅₃	—	2	2	no	—
256	C₂²⋊C₄×C₅₃	—	2	2	no	—
257	C₂²⋊C₄×C₅₃	—	2	4	no	—
258	C₂²⋊C₄×C₅₃	—	2	4	no	—
259	C₂²⋊C₄×C₅₃	—	4	2	no	—
260	C₂²⋊C₄×C₅₃	—	8	1	no	—
261	C₂²⋊C₄×C₅₃	—	8	1	no	—
262	C₂²⋊C₄×C₅₃	—	8	1	no	—
263	C₄²×C₅₃	—	2	4	no	—
264	C₄²×C₅₃	—	2	1	no	—
265	C₄²×C₅₃	—	2	1	no	—
266	C₄²×C₅₃	—	8	1	no	—
267	C₄²×C₅₃	C₂×D₄	1	2	yes	—
268	C₄²×C₅₃	C₂×D₄	1	2	yes	—
269	C₂³×C₅₃	—	2	16	no	—
270	C₂³×C₅₃	—	2	2	no	—
271	C₂³×C₅₃	—	2	2	no	—
272	C₂³×C₅₃	—	2	2	no	—
273	C₂³×C₅₃	—	2	2	no	—
274	C₂³×C₅₃	—	2	1	no	—
275	C₂³×C₅₃	—	2	1	no	—
276	C₂³×C₅₃	—	2	2	no	—
277	C₂³×C₅₃	—	2	2	no	—
278	C₂³×C₅₃	—	2	1	no	—
279	C₂³×C₅₃	—	2	1	no	—
280	C₂³×C₅₃	—	2	1	no	—
281	C₂³×C₅₃	—	2	1	no	—
282	C₂³×C₅₃	—	2	2	no	—
283	C₂³×C₅₃	—	4	1	no	—
284	C₂³×C₅₃	—	4	1	no	—
285	C₂³×C₅₃	—	4	1	no	—
286	C₂³×C₅₃	—	4	1	no	—
287	C₂³×C₅₃	—	4	1	no	—
288	C₂³×C₅₃	—	4	1	no	—
289	C₂³×C₅₃	—	4	1	no	—
290	C₂³×C₅₃	—	4	1	no	—
291	C₂³×C₅₃	—	4	1	no	—
292	C₂³×C₅₃	—	4	1	no	—
293	C₂³×C₅₃	—	4	1	no	—
294	C₂³×C₅₃	—	4	1	no	—
295	C₂³×C₅₃	—	4	1	no	—
296	C₂³×C₅₃	—	4	1	no	—
297	C₂³×C₅₃	—	8	4	no	—
298	C₂³×C₅₃	—	8	4	no	—
299	C₂³×C₅₃	—	8	4	no	—
300	C₂³×C₅₃	—	8	4	no	—
301	C₂³×C₅₃	—	8	4	no	—
302	C₂³×C₅₃	—	8	4	no	—
303	C₂³×C₅₃	C₄×D₄	1	2	yes	—
304	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
305	D₄×C₅₃	—	2	16	no	—
306	D₄×C₅₃	—	2	2	no	—
307	D₄×C₅₃	—	2	2	no	—
308	D₄×C₅₃	—	2	2	no	—
309	D₄×C₅₃	—	2	2	no	—
310	D₄×C₅₃	—	2	2	no	—
311	D₄×C₅₃	—	2	2	no	—
312	D₄×C₅₃	—	2	2	no	—
313	D₄×C₅₃	—	2	2	no	—
314	D₄×C₅₃	—	4	1	no	—
315	D₄×C₅₃	—	4	1	no	—
316	D₄×C₅₃	—	8	4	no	—
317	D₄×C₅₃	C₄×D₄	1	4	yes	—
318	D₄×C₅₃	C₄×D₄	1	4	yes	—
319	C₂×C₄×C₅₃	—	2	1	no	—
320	C₂×C₄×C₅₃	—	2	1	no	—
321	C₂×C₄×C₅₃	—	2	1	no	—
322	C₂×C₄×C₅₃	—	2	1	no	—
323	C₂×C₄×C₅₃	—	2	1	no	—
324	C₂×C₄×C₅₃	—	2	1	no	—
325	C₂×C₄×C₅₃	—	2	2	no	—
326	C₂×C₄×C₅₃	—	2	2	no	—
327	C₂×C₄×C₅₃	—	2	2	no	—
328	C₂×C₄×C₅₃	—	2	2	no	—
329	C₂×C₄×C₅₃	—	2	2	no	—
330	C₂×C₄×C₅₃	—	2	2	no	—
331	C₂×C₄×C₅₃	—	2	2	no	—
332	C₂×C₄×C₅₃	—	2	1	no	—
333	C₂×C₄×C₅₃	—	2	1	no	—
334	C₂×C₄×C₅₃	—	2	1	no	—
335	C₂×C₄×C₅₃	—	2	1	no	—
336	C₂×C₄×C₅₃	—	2	1	no	—
337	C₂×C₄×C₅₃	—	2	1	no	—
338	C₂×C₄×C₅₃	—	4	1	no	—
339	C₂×C₄×C₅₃	—	4	1	no	—
340	C₂×C₄×C₅₃	—	4	1	no	—
341	C₂×C₄×C₅₃	—	4	1	no	—
342	C₂×C₄×C₅₃	—	4	1	no	—
343	C₂×C₄×C₅₃	—	4	1	no	—
344	C₂×C₄×C₅₃	—	4	1	no	—
345	C₂×C₄×C₅₃	—	4	1	no	—
346	C₂×C₄×C₅₃	—	4	1	no	—
347	C₂×C₄×C₅₃	—	4	1	no	—
348	C₂×C₄×C₅₃	—	4	1	no	—
349	C₂×C₄×C₅₃	—	4	1	no	—
350	C₂×C₄×C₅₃	—	8	4	no	—
351	C₂×C₄×C₅₃	—	8	4	no	—
352	C₂×C₄×C₅₃	—	8	4	no	—
353	C₂×C₄×C₅₃	—	8	4	no	—
354	C₂×C₄×C₅₃	—	8	4	no	—
355	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
356	C₂×C₄×C₅₃	#120	1	2	yes	—
357	C₂×C₄×C₅₃	#120	1	2	yes	—
358	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
359	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
363	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
364	C₈×C₅₃	—	2	2	no	—
365	C₈×C₅₃	—	2	2	no	—
366	C₈×C₅₃	—	4	1	no	—
367	C₈×C₅₃	—	4	1	no	—
368	#21458	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
369	C₂²×C₅₃	—	2	2	no	—
370	C₂²×C₅₃	—	2	2	no	—
371	C₂²×C₅₃	—	2	2	no	—
372	C₂²×C₅₃	—	2	4	no	—
373	C₂²×C₅₃	—	2	4	no	—
374	C₂²×C₅₃	—	4	1	no	—
375	C₂²×C₅₃	—	4	2	no	—
376	C₂²×C₅₃	—	4	2	no	—
377	C₂²×C₅₃	—	4	1	no	—
378	C₂²×C₅₃	—	4	2	no	—
379	C₂²×C₅₃	—	4	2	no	—
380	C₂²×C₅₃	—	4	2	no	—
381	C₂²×C₅₃	—	4	2	no	—
382	C₂²×C₅₃	—	4	2	no	—
383	C₂²×C₅₃	—	4	2	no	—
384	C₂²×C₅₃	—	4	2	no	—
385	C₂²×C₅₃	—	4	2	no	—
386	C₂²×C₅₃	—	4	1	no	—
387	C₂²×C₅₃	—	4	2	no	—
388	C₂²×C₅₃	—	4	2	no	—
389	C₂²×C₅₃	—	4	1	no	—
390	C₂²×C₅₃	—	4	2	no	—
391	C₂²×C₅₃	—	4	2	no	—
392	C₂²×C₅₃	—	4	2	no	—
393	C₂²×C₅₃	—	8	16	no	—
394	C₂²×C₅₃	—	8	1	no	—
395	C₂²×C₅₃	—	8	1	no	—
396	C₂²×C₅₃	—	8	1	no	—
397	C₂²×C₅₃	—	8	1	no	—
398	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
399	C₂²×C₅₃	C₂×#120	1	1	yes	characteristic
400	C₂²×C₅₃	#525	1	1	yes	characteristic
401	C₂²×C₅₃	#576	1	1	yes	characteristic
402	C₂²×C₅₃	#576	1	1	yes	characteristic
403	C₂²×C₅₃	#576	1	1	yes	characteristic
404	C₂²×C₅₃	#577	1	1	yes	characteristic
405	C₄×C₅₃	—	2	2	no	—
406	C₄×C₅₃	—	2	2	no	—
407	C₄×C₅₃	—	2	2	no	—
408	C₄×C₅₃	—	4	2	no	—
409	C₄×C₅₃	—	4	1	no	—
410	C₄×C₅₃	—	4	2	no	—
411	C₄×C₅₃	—	4	1	no	—
412	C₄×C₅₃	—	4	2	no	—
413	C₄×C₅₃	—	8	1	no	—
414	C₄×C₅₃	—	8	1	no	—
415	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
416	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
417	C₄×C₅₃	#525	1	1	yes	characteristic
418	C₄×C₅₃	#525	1	1	yes	characteristic
419	C₂×#518	C₂×C₅₃	1	1	yes	characteristic, complemented
420	C₂×#447	C₂×C₅₃	1	1	yes	characteristic
421	C₂×#442	C₂×C₅₃	1	1	yes	characteristic, complemented
422	C₂×C₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
423	#2324	C₂×C₅₃	1	1	yes	characteristic, complemented
424	#1879	C₂×C₅₃	1	1	yes	characteristic, complemented
425	#1879	C₂×C₅₃	1	1	yes	characteristic, complemented
426	#1875	C₂×C₅₃	1	1	yes	characteristic, complemented
427	#1864	C₂×C₅₃	1	1	yes	characteristic, complemented
428	#1862	C₂×C₅₃	1	1	yes	characteristic, complemented
429	#1854	C₂×C₅₃	1	1	yes	characteristic, complemented
430	#1786	C₂×C₅₃	1	1	yes	characteristic, complemented
431	#1762	C₂×C₅₃	1	1	yes	characteristic, complemented
432	C₄×#102	C₂×C₅₃	1	1	yes	characteristic, complemented
433	#1750	C₂×C₅₃	1	1	yes	characteristic, complemented
434	C₂×C₅₃	—	4	2	no	—
435	C₂×C₅₃	—	4	4	no	—
436	C₂×C₅₃	—	4	4	no	—
437	C₂×C₅₃	—	8	2	no	—
438	C₂×C₅₃	C₄×#120	1	1	yes	characteristic
439	C₂×C₅₃	#2946	1	1	yes	characteristic
440	C₂×C₅₃	#2948	1	1	yes	characteristic
441	C₂×C₅₃	#3008	1	1	yes	characteristic
442	C₂×C₅₃	#3012	1	1	yes	characteristic
443	C₂×C₅₃	#3118	1	1	yes	characteristic
444	C₂×C₅₃	#3122	1	1	yes	characteristic
445	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
446	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
447	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
448	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
449	#518	—	2	4	no	—
450	#518	—	2	4	no	—
451	C₂×C₄×D₄	—	2	1	no	—
452	C₂×C₄×D₄	—	2	1	no	—
453	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
456	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
458	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
459	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
460	C₂²×C₂²⋊C₄	—	2	1	no	—
461	C₂²×C₂²⋊C₄	—	2	1	no	—
462	#447	C₄×C₅₃	1	8	yes	complemented
463	#442	—	2	4	no	—
464	C₄×D₈	—	2	4	no	—
465	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
466	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
467	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
468	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
469	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
470	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
471	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
472	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
473	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
474	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
475	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
476	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
477	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
478	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
479	#390	—	2	1	no	—
480	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
481	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
482	#388	—	2	1	no	—
483	#386	—	2	1	no	—
484	#385	—	2	1	no	—
485	#380	C₂²×C₅₃	1	1	yes	characteristic
486	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
487	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
488	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
489	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
490	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
491	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
492	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
493	C₅₃	#21458	1	1	yes	characteristic, direct product factor, Sylow
494	C₂⁵	—	2	1	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	C₂×C₄×C₅₃	1	4	yes	complemented
503	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
512	C₂×D₈	—	2	2	no	—
513	C₂×D₈	—	2	2	no	—
514	C₂×D₈	—	2	2	no	—
515	C₂×D₈	—	2	2	no	—
516	C₂×D₈	C₂×C₄×C₅₃	1	4	yes	complemented
517	C₂×D₈	C₂×C₄×C₅₃	1	4	yes	complemented
518	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
520	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
522	#121	—	2	2	no	—
523	#121	C₂×C₄×C₅₃	1	4	yes	complemented
524	C₄×D₄	—	2	8	no	—
525	C₄×D₄	—	2	8	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	D₄×C₅₃	1	4	yes	complemented
535	C₄×D₄	D₄×C₅₃	1	4	yes	complemented
536	#117	—	2	2	no	—
537	#117	—	2	2	no	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	—	2	8	no	—
549	C₂×C₂²⋊C₄	—	2	8	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
562	C₂×C₄²	—	2	1	no	—
563	C₂×C₄²	—	2	1	no	—
564	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
566	#107	—	2	2	no	—
567	#106	—	2	2	no	—
568	#102	—	2	2	no	—
569	#102	—	2	2	no	—
570	#102	—	2	2	no	—
571	#102	—	2	2	no	—
572	#102	—	2	2	no	—
573	#102	—	2	2	no	—
574	#102	C₂×C₄×C₅₃	1	4	yes	complemented
575	#102	C₂×C₄×C₅₃	1	4	yes	complemented
576	C₂²⋊C₈	—	2	2	no	—
577	C₂²⋊C₈	C₂×C₄×C₅₃	1	4	yes	complemented
578	#97	—	2	2	no	—
579	C₄×C₈	—	2	2	no	—
580	#95	—	2	1	no	—
581	#95	—	2	1	no	—
582	#95	—	2	1	no	—
583	C₂⁴	—	2	4	no	—
584	C₂⁴	—	2	4	no	—
585	C₂⁴	—	2	1	no	—
586	C₂⁴	—	2	1	no	—
587	C₂⁴	—	2	4	no	—
588	C₂⁴	—	2	1	no	—
589	C₂⁴	—	8	1	no	—
590	C₂⁴	—	8	1	no	—
591	C₂⁴	—	8	1	no	—
592	C₂⁴	—	8	1	no	—
593	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	8	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	8	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	8	1	no	—
614	C₂×D₄	—	8	1	no	—
615	C₂×D₄	C₂²×C₄×C₅₃	1	2	yes	—
616	C₂×D₄	C₂²×C₄×C₅₃	1	2	yes	—
617	C₂×D₄	C₂²×C₄×C₅₃	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
619	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
620	C₂×D₄	#41×C₅₃	1	2	yes	—
621	C₂×D₄	#41×C₅₃	1	2	yes	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	8	1	no	—
637	C₂²×C₄	—	8	1	no	—
638	C₂²×C₄	—	8	1	no	—
639	C₂²×C₄	—	8	1	no	—
640	C₂²×C₄	—	8	1	no	—
641	C₂²×C₄	—	8	1	no	—
642	C₂²×C₄	—	8	1	no	—
643	C₂²×C₄	—	8	1	no	—
644	C₂²×C₄	—	8	1	no	—
645	C₂²×C₄	—	8	1	no	—
646	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
647	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
652	C₂²×C₄	#41×C₅₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
654	D₈	—	2	8	no	—
655	D₈	—	2	8	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
667	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	8	1	no	—
678	C₄⋊C₄	C₂²×C₄×C₅₃	1	2	yes	—
679	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
680	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	4	2	no	—
690	C₂²⋊C₄	—	8	1	no	—
691	C₂²⋊C₄	—	8	1	no	—
692	C₂²⋊C₄	—	8	1	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	1	no	—
695	C₄²	—	2	1	no	—
696	C₄²	—	8	1	no	—
697	C₄²	C₂×D₄×C₅₃	1	2	yes	—
698	C₄²	C₂×D₄×C₅₃	1	2	yes	—
699	C₂³	—	2	16	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	4	1	no	—
726	C₂³	—	4	1	no	—
727	C₂³	—	8	4	no	—
728	C₂³	—	8	4	no	—
729	C₂³	—	8	4	no	—
730	C₂³	—	8	4	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	C₄×D₄×C₅₃	1	2	yes	—
734	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
735	D₄	—	2	16	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	2	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	2	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	8	4	no	—
747	D₄	C₄×D₄×C₅₃	1	4	yes	—
748	D₄	C₄×D₄×C₅₃	1	4	yes	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	8	4	no	—
781	C₂×C₄	—	8	4	no	—
782	C₂×C₄	—	8	4	no	—
783	C₂×C₄	—	8	4	no	—
784	C₂×C₄	—	8	4	no	—
785	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
786	C₂×C₄	#120×C₅₃	1	2	yes	—
787	C₂×C₄	#120×C₅₃	1	2	yes	—
788	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
791	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
792	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
793	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
794	C₈	—	2	2	no	—
795	C₈	—	2	2	no	—
796	C₈	—	4	1	no	—
797	C₈	—	4	1	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	16	no	—
823	C₂²	—	8	1	no	—
824	C₂²	—	8	1	no	—
825	C₂²	—	8	1	no	—
826	C₂²	—	8	1	no	—
827	C₂²	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
828	C₂²	C₂×#120×C₅₃	1	1	yes	characteristic
829	C₂²	C₅₃×#525	1	1	yes	characteristic
830	C₂²	C₅₃×#576	1	1	yes	characteristic
831	C₂²	C₅₃×#576	1	1	yes	characteristic
832	C₂²	C₅₃×#576	1	1	yes	characteristic
833	C₂²	C₅₃×#577	1	1	yes	characteristic
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	2	no	—
842	C₄	—	8	1	no	—
843	C₄	—	8	1	no	—
844	C₄	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
845	C₄	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
846	C₄	C₅₃×#525	1	1	yes	characteristic
847	C₄	C₅₃×#525	1	1	yes	characteristic
848	C₂	—	4	2	no	—
849	C₂	—	4	4	no	—
850	C₂	—	4	4	no	—
851	C₂	—	8	2	no	—
852	C₂	C₄×#120×C₅₃	1	1	yes	characteristic
853	C₂	C₅₃×#2946	1	1	yes	characteristic
854	C₂	C₅₃×#2948	1	1	yes	characteristic
855	C₂	C₅₃×#3008	1	1	yes	characteristic
856	C₂	C₅₃×#3012	1	1	yes	characteristic
857	C₂	C₅₃×#3118	1	1	yes	characteristic
858	C₂	C₅₃×#3122	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂×C₅₃×#447	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×#117×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#518	C₂	semidirect
3. C₂×C₅₃×#442	C₂	semidirect
4. C₂×C₄×D₈×C₅₃	C₂	semidirect
5. C₅₃×#2324	C₂	semidirect
6. C₅₃×#1879	C₂	semidirect
7. C₅₃×#1879	C₂	semidirect
8. C₅₃×#1875	C₂	semidirect
9. C₅₃×#1864	C₂	semidirect
10. C₅₃×#1862	C₂	semidirect
11. C₅₃×#1854	C₂	semidirect
12. C₅₃×#1786	C₂	semidirect
13. C₅₃×#1762	C₂	semidirect
14. C₄×#102×C₅₃	C₂	semidirect
15. C₅₃×#1750	C₂	semidirect
28. C₂×C₄×D₄×C₅₃	C₂²	semidirect
33. C₅₃×#447	C₄	semidirect
36. C₂×#107×C₅₃	C₂²	semidirect
37. C₂×#106×C₅₃	C₂²	semidirect
44. C₂×#102×C₅₃	C₂²	semidirect
45. C₂×#102×C₅₃	C₂²	semidirect
48. C₂×#97×C₅₃	C₂²	semidirect
49. C₂×C₄×C₈×C₅₃	C₂²	semidirect
51. C₅₃×#390	C₂²	semidirect
52. C₅₃×#389	C₂²	semidirect
57. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
58. C₅₃×#340	C₂²	semidirect
59. C₅₃×#340	C₂²	semidirect
60. C₅₃×#340	C₂²	semidirect
61. C₅₃×#340	C₂²	semidirect
62. C₅₃×#336	C₂²	semidirect
63. C₅₃×#336	C₂²	semidirect
72. C₂²×D₄×C₅₃	C₂×C₄	semidirect
86. C₂×D₈×C₅₃	C₂×C₄	semidirect
87. C₂×D₈×C₅₃	C₂×C₄	semidirect
93. #121×C₅₃	C₂×C₄	semidirect
104. C₄×D₄×C₅₃	D₄	semidirect
105. C₄×D₄×C₅₃	D₄	semidirect
144. #102×C₅₃	C₂×C₄	semidirect
145. #102×C₅₃	C₂×C₄	semidirect
147. C₂²⋊C₈×C₅₃	C₂×C₄	semidirect
368. #21458	C₅₃	direct (N × H)
419. C₂×#518	C₂×C₅₃	semidirect
421. C₂×#442	C₂×C₅₃	semidirect
422. C₂×C₄×D₈	C₂×C₅₃	semidirect
423. #2324	C₂×C₅₃	semidirect
424. #1879	C₂×C₅₃	semidirect
425. #1879	C₂×C₅₃	semidirect
426. #1875	C₂×C₅₃	semidirect
427. #1864	C₂×C₅₃	semidirect
428. #1862	C₂×C₅₃	semidirect
429. #1854	C₂×C₅₃	semidirect
430. #1786	C₂×C₅₃	semidirect
431. #1762	C₂×C₅₃	semidirect
432. C₄×#102	C₂×C₅₃	semidirect
433. #1750	C₂×C₅₃	semidirect
457. C₂×C₄×D₄	C₂²×C₅₃	semidirect
462. #447	C₄×C₅₃	semidirect
465. C₂×#107	C₂²×C₅₃	semidirect
466. C₂×#106	C₂²×C₅₃	semidirect
473. C₂×#102	C₂²×C₅₃	semidirect
474. C₂×#102	C₂²×C₅₃	semidirect
477. C₂×#97	C₂²×C₅₃	semidirect
478. C₂×C₄×C₈	C₂²×C₅₃	semidirect
480. #390	C₂²×C₅₃	semidirect
481. #389	C₂²×C₅₃	semidirect
486. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
487. #340	C₂²×C₅₃	semidirect
488. #340	C₂²×C₅₃	semidirect
489. #340	C₂²×C₅₃	semidirect
490. #340	C₂²×C₅₃	semidirect
491. #336	C₂²×C₅₃	semidirect
492. #336	C₂²×C₅₃	semidirect
493. C₅₃	#21458	direct (N × H)
502. C₂²×D₄	C₂×C₄×C₅₃	semidirect
516. C₂×D₈	C₂×C₄×C₅₃	semidirect
517. C₂×D₈	C₂×C₄×C₅₃	semidirect
523. #121	C₂×C₄×C₅₃	semidirect
534. C₄×D₄	D₄×C₅₃	semidirect
535. C₄×D₄	D₄×C₅₃	semidirect
574. #102	C₂×C₄×C₅₃	semidirect
575. #102	C₂×C₄×C₅₃	semidirect
577. C₂²⋊C₈	C₂×C₄×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×#518	2
C₂×C₅₃×#447	2
C₂×C₅₃×#442	2
C₂×C₄×D₈×C₅₃	2
C₅₃×#2324	2
C₅₃×#1879	2
C₅₃×#1875	2
C₅₃×#1864	2
C₅₃×#1862	2
C₅₃×#1854	2
C₅₃×#1786	2
C₅₃×#1762	2
C₄×#102×C₅₃	2
C₅₃×#1750	2
#21458	53

Subgroups — C53×#21458 #27228970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#21458 #27228970