Subgroups — C₅₃×#36604 #27244116

Order 13568.

1888 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2854	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2597	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2596	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2585	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2569	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2554	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2543	C₂	1	1	yes	maximal, characteristic
9	C₅₃×#2525	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2516	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2481	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2443	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2374	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2373	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2364	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2353	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#123×C₅₃	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₅₃	C₂²	1	2	yes	—
21	C₂×#123×C₅₃	C₂²	1	2	yes	—
22	C₂×#123×C₅₃	C₂²	1	2	yes	—
23	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#121×C₅₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
29	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
31	C₅₃×#400	C₂²	1	2	yes	—
32	C₅₃×#400	C₂²	1	2	yes	—
33	C₅₃×#400	C₂²	1	2	yes	—
34	C₅₃×#399	C₂²	1	2	yes	—
35	C₅₃×#398	C₂²	1	2	yes	—
36	C₅₃×#398	C₂²	1	1	yes	characteristic
37	C₅₃×#398	C₂²	1	2	yes	—
38	C₅₃×#397	C₂²	1	2	yes	—
39	C₅₃×#397	C₂²	1	2	yes	—
40	C₅₃×#397	C₂²	1	1	yes	characteristic
41	C₅₃×#396	C₂²	1	2	yes	—
42	C₅₃×#394	C₂²	1	2	yes	—
43	C₅₃×#394	C₂²	1	1	yes	characteristic
44	C₅₃×#392	C₂²	1	1	yes	characteristic
45	C₅₃×#390	C₂²	1	2	yes	—
46	C₅₃×#390	C₂²	1	2	yes	—
47	C₅₃×#390	C₂²	1	2	yes	—
48	C₅₃×#389	C₂²	1	2	yes	—
49	C₅₃×#389	C₂²	1	2	yes	—
50	C₅₃×#389	C₂²	1	2	yes	—
51	C₅₃×#388	C₂²	1	2	yes	—
52	C₅₃×#388	C₂²	1	2	yes	—
53	C₅₃×#388	C₂²	1	2	yes	—
54	C₅₃×#388	C₂²	1	2	yes	—
55	C₅₃×#388	C₂²	1	2	yes	—
56	C₅₃×#388	C₂²	1	2	yes	—
57	C₅₃×#388	C₂²	1	2	yes	—
58	C₅₃×#388	C₂²	1	2	yes	—
59	C₅₃×#388	C₂²	1	2	yes	—
60	C₅₃×#388	C₂²	1	2	yes	—
61	C₅₃×#388	C₂²	1	2	yes	—
62	C₅₃×#388	C₂²	1	2	yes	—
63	C₅₃×#388	C₂²	1	2	yes	—
64	C₅₃×#388	C₂²	1	2	yes	—
65	C₅₃×#387	C₂²	1	2	yes	—
66	C₅₃×#387	C₂²	1	2	yes	—
67	C₅₃×#387	C₂²	1	2	yes	—
68	C₅₃×#387	C₂²	1	2	yes	—
69	C₅₃×#387	C₂²	1	2	yes	—
70	C₅₃×#387	C₂²	1	2	yes	—
71	C₅₃×#387	C₂²	1	2	yes	—
72	C₅₃×#387	C₂²	1	2	yes	—
73	C₅₃×#387	C₂²	1	2	yes	—
74	C₅₃×#387	C₂²	1	2	yes	—
75	C₅₃×#386	C₂²	1	1	yes	characteristic
76	C₅₃×#386	C₂²	1	2	yes	—
77	C₅₃×#386	C₂²	1	2	yes	—
78	C₅₃×#386	C₂²	1	2	yes	—
79	C₅₃×#386	C₂²	1	2	yes	—
80	C₅₃×#386	C₂²	1	2	yes	—
81	C₅₃×#386	C₂²	1	2	yes	—
82	C₅₃×#385	C₂²	1	2	yes	—
83	C₅₃×#385	C₂²	1	2	yes	—
84	C₅₃×#385	C₂²	1	1	yes	characteristic
85	C₅₃×#383	C₂²	1	1	yes	characteristic
86	C₅₃×#381	C₂²	1	1	yes	characteristic
87	C₅₃×#381	C₂²	1	1	yes	characteristic
88	C₅₃×#380	C₂²	1	2	yes	—
89	C₅₃×#380	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
104	C₅₃×#376	C₂²	1	1	yes	characteristic
105	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
106	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
107	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
113	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
118	#126×C₅₃	—	2	8	no	—
119	#123×C₅₃	—	2	8	no	—
120	#123×C₅₃	—	2	4	no	—
121	#123×C₅₃	—	2	8	no	—
122	#121×C₅₃	—	2	4	no	—
123	#121×C₅₃	—	4	4	no	—
124	C₄×D₄×C₅₃	—	2	4	no	—
125	C₄×D₄×C₅₃	—	4	4	no	—
126	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₅₃	—	2	4	no	—
166	C₂×C₄²×C₅₃	—	4	4	no	—
167	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
178	#95×C₅₃	C₂³	1	1	yes	characteristic
179	#95×C₅₃	C₂³	1	1	yes	characteristic
180	#95×C₅₃	C₂³	1	2	yes	—
181	#95×C₅₃	C₂³	1	2	yes	—
182	#95×C₅₃	C₂³	1	1	yes	characteristic
183	#95×C₅₃	C₂³	1	1	yes	characteristic
184	#95×C₅₃	C₂³	1	1	yes	characteristic
185	#95×C₅₃	C₂³	1	2	yes	—
186	#95×C₅₃	C₂³	1	2	yes	—
187	#95×C₅₃	C₂³	1	2	yes	—
188	#95×C₅₃	C₂³	1	1	yes	characteristic
189	#95×C₅₃	C₂³	1	2	yes	—
190	#95×C₅₃	C₂³	1	2	yes	—
191	#95×C₅₃	C₂³	1	2	yes	—
192	#95×C₅₃	C₂³	1	2	yes	—
193	#95×C₅₃	C₂³	1	2	yes	—
194	#95×C₅₃	C₂³	1	2	yes	—
195	#95×C₅₃	C₂³	1	2	yes	—
196	#95×C₅₃	C₂³	1	2	yes	—
197	#95×C₅₃	C₂³	1	2	yes	—
198	#95×C₅₃	C₂³	1	2	yes	—
199	#95×C₅₃	C₂³	1	2	yes	—
200	#95×C₅₃	C₂³	1	2	yes	—
201	#95×C₅₃	C₂³	1	2	yes	—
202	#95×C₅₃	C₂³	1	2	yes	—
203	#95×C₅₃	C₂³	1	2	yes	—
204	#95×C₅₃	C₂³	1	2	yes	—
205	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
206	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
207	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
208	C₂×D₄×C₅₃	—	2	2	no	—
209	C₂×D₄×C₅₃	—	2	4	no	—
210	C₂×D₄×C₅₃	—	2	2	no	—
211	C₂×D₄×C₅₃	—	2	4	no	—
212	C₂×D₄×C₅₃	—	2	4	no	—
213	C₂×D₄×C₅₃	—	2	2	no	—
214	C₂×D₄×C₅₃	—	2	2	no	—
215	C₂×D₄×C₅₃	—	2	4	no	—
216	C₂×D₄×C₅₃	—	4	2	no	—
217	C₂×D₄×C₅₃	—	4	2	no	—
218	C₂×D₄×C₅₃	—	4	2	no	—
219	C₂²×C₄×C₅₃	—	2	2	no	—
220	C₂²×C₄×C₅₃	—	2	2	no	—
221	C₂²×C₄×C₅₃	—	2	2	no	—
222	C₂²×C₄×C₅₃	—	2	4	no	—
223	C₂²×C₄×C₅₃	—	2	4	no	—
224	C₂²×C₄×C₅₃	—	2	4	no	—
225	C₂²×C₄×C₅₃	—	2	4	no	—
226	C₂²×C₄×C₅₃	—	2	4	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	—	2	4	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	—	4	2	no	—
235	C₂²×C₄×C₅₃	#41	1	4	yes	—
236	C₂²×C₄×C₅₃	#41	1	4	yes	—
237	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₅₃	—	2	4	no	—
254	C₄⋊C₄×C₅₃	—	2	4	no	—
255	C₄⋊C₄×C₅₃	—	2	4	no	—
256	C₄⋊C₄×C₅₃	—	2	2	no	—
257	C₄⋊C₄×C₅₃	—	2	2	no	—
258	C₄⋊C₄×C₅₃	—	2	4	no	—
259	C₄⋊C₄×C₅₃	—	2	4	no	—
260	C₄⋊C₄×C₅₃	—	2	4	no	—
261	C₄⋊C₄×C₅₃	—	2	4	no	—
262	C₄⋊C₄×C₅₃	—	2	4	no	—
263	C₄⋊C₄×C₅₃	—	2	4	no	—
264	C₄⋊C₄×C₅₃	—	4	2	no	—
265	C₄⋊C₄×C₅₃	—	4	2	no	—
266	C₄⋊C₄×C₅₃	—	4	2	no	—
267	C₄⋊C₄×C₅₃	—	4	2	no	—
268	C₄⋊C₄×C₅₃	—	4	2	no	—
269	C₄⋊C₄×C₅₃	#41	1	8	yes	—
270	C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂²⋊C₄×C₅₃	—	2	4	no	—
272	C₂²⋊C₄×C₅₃	—	2	2	no	—
273	C₂²⋊C₄×C₅₃	—	2	2	no	—
274	C₂²⋊C₄×C₅₃	—	2	2	no	—
275	C₂²⋊C₄×C₅₃	—	2	4	no	—
276	C₂²⋊C₄×C₅₃	—	2	4	no	—
277	C₂²⋊C₄×C₅₃	—	2	4	no	—
278	C₂²⋊C₄×C₅₃	—	2	4	no	—
279	C₂²⋊C₄×C₅₃	—	2	4	no	—
280	C₂²⋊C₄×C₅₃	—	2	4	no	—
281	C₂²⋊C₄×C₅₃	—	2	4	no	—
282	C₂²⋊C₄×C₅₃	—	2	4	no	—
283	C₂²⋊C₄×C₅₃	—	2	4	no	—
284	C₂²⋊C₄×C₅₃	—	2	4	no	—
285	C₂²⋊C₄×C₅₃	—	4	2	no	—
286	C₂²⋊C₄×C₅₃	—	4	2	no	—
287	C₂²⋊C₄×C₅₃	—	4	2	no	—
288	C₂²⋊C₄×C₅₃	—	4	2	no	—
289	C₂²⋊C₄×C₅₃	—	4	2	no	—
290	C₂²⋊C₄×C₅₃	—	4	2	no	—
291	C₄²×C₅₃	—	2	4	no	—
292	C₄²×C₅₃	—	2	4	no	—
293	C₄²×C₅₃	—	2	2	no	—
294	C₄²×C₅₃	—	2	4	no	—
295	C₄²×C₅₃	—	4	2	no	—
296	C₄²×C₅₃	—	4	2	no	—
297	C₄²×C₅₃	—	4	2	no	—
298	C₄²×C₅₃	—	4	2	no	—
299	C₄²×C₅₃	—	4	2	no	—
300	C₄²×C₅₃	—	4	2	no	—
301	C₄²×C₅₃	—	4	2	no	—
302	C₂³×C₅₃	—	2	2	no	—
303	C₂³×C₅₃	—	2	2	no	—
304	C₂³×C₅₃	—	2	1	no	—
305	C₂³×C₅₃	—	2	2	no	—
306	C₂³×C₅₃	—	2	2	no	—
307	C₂³×C₅₃	—	2	2	no	—
308	C₂³×C₅₃	—	2	1	no	—
309	C₂³×C₅₃	—	2	2	no	—
310	C₂³×C₅₃	—	2	2	no	—
311	C₂³×C₅₃	—	2	2	no	—
312	C₂³×C₅₃	—	2	1	no	—
313	C₂³×C₅₃	—	2	2	no	—
314	C₂³×C₅₃	—	2	2	no	—
315	C₂³×C₅₃	—	2	2	no	—
316	C₂³×C₅₃	C₂×#41	1	2	yes	—
317	C₂³×C₅₃	C₂×#41	1	2	yes	—
318	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
319	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
320	D₄×C₅₃	—	4	4	no	—
321	D₄×C₅₃	—	4	8	no	—
322	D₄×C₅₃	—	8	2	no	—
323	D₄×C₅₃	—	8	4	no	—
324	C₂×C₄×C₅₃	—	2	8	no	—
325	C₂×C₄×C₅₃	—	2	8	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	2	no	—
333	C₂×C₄×C₅₃	—	2	2	no	—
334	C₂×C₄×C₅₃	—	2	2	no	—
335	C₂×C₄×C₅₃	—	2	2	no	—
336	C₂×C₄×C₅₃	—	2	1	no	—
337	C₂×C₄×C₅₃	—	2	2	no	—
338	C₂×C₄×C₅₃	—	2	2	no	—
339	C₂×C₄×C₅₃	—	2	2	no	—
340	C₂×C₄×C₅₃	—	2	1	no	—
341	C₂×C₄×C₅₃	—	2	2	no	—
342	C₂×C₄×C₅₃	—	2	1	no	—
343	C₂×C₄×C₅₃	—	2	2	no	—
344	C₂×C₄×C₅₃	—	2	1	no	—
345	C₂×C₄×C₅₃	—	2	2	no	—
346	C₂×C₄×C₅₃	—	2	2	no	—
347	C₂×C₄×C₅₃	—	2	2	no	—
348	C₂×C₄×C₅₃	—	2	2	no	—
349	C₂×C₄×C₅₃	—	2	2	no	—
350	C₂×C₄×C₅₃	—	2	2	no	—
351	C₂×C₄×C₅₃	—	2	2	no	—
352	C₂×C₄×C₅₃	—	2	2	no	—
353	C₂×C₄×C₅₃	—	2	2	no	—
354	C₂×C₄×C₅₃	—	2	2	no	—
355	C₂×C₄×C₅₃	—	2	2	no	—
356	C₂×C₄×C₅₃	—	2	1	no	—
357	C₂×C₄×C₅₃	—	2	2	no	—
358	C₂×C₄×C₅₃	—	2	2	no	—
359	C₂×C₄×C₅₃	—	2	2	no	—
360	C₂×C₄×C₅₃	—	2	2	no	—
361	C₂×C₄×C₅₃	—	2	2	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	4	4	no	—
365	C₂×C₄×C₅₃	—	4	8	no	—
366	C₂×C₄×C₅₃	—	4	8	no	—
367	C₂×C₄×C₅₃	—	8	2	no	—
368	C₂×C₄×C₅₃	—	8	4	no	—
369	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
370	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
371	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
372	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
373	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
374	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
375	#36604	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
376	C₂²×C₅₃	—	2	2	no	—
377	C₂²×C₅₃	—	2	4	no	—
378	C₂²×C₅₃	—	2	2	no	—
379	C₂²×C₅₃	—	2	4	no	—
380	C₂²×C₅₃	—	4	2	no	—
381	C₂²×C₅₃	—	4	1	no	—
382	C₂²×C₅₃	—	4	1	no	—
383	C₂²×C₅₃	—	4	2	no	—
384	C₂²×C₅₃	—	4	2	no	—
385	C₂²×C₅₃	—	4	2	no	—
386	C₂²×C₅₃	—	4	2	no	—
387	C₂²×C₅₃	—	4	1	no	—
388	C₂²×C₅₃	—	4	2	no	—
389	C₂²×C₅₃	—	4	2	no	—
390	C₂²×C₅₃	—	4	2	no	—
391	C₂²×C₅₃	—	4	2	no	—
392	C₂²×C₅₃	#553	1	4	yes	—
393	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
394	C₂²×C₅₃	C₂²×#41	1	2	yes	—
395	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
396	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂²×C₅₃	#585	1	2	yes	—
398	C₄×C₅₃	—	2	4	no	—
399	C₄×C₅₃	—	2	4	no	—
400	C₄×C₅₃	—	2	2	no	—
401	C₄×C₅₃	—	2	2	no	—
402	C₄×C₅₃	—	2	4	no	—
403	C₄×C₅₃	—	2	4	no	—
404	C₄×C₅₃	—	4	1	no	—
405	C₄×C₅₃	—	4	1	no	—
406	C₄×C₅₃	—	4	2	no	—
407	C₄×C₅₃	—	4	2	no	—
408	C₄×C₅₃	—	4	2	no	—
409	C₄×C₅₃	—	4	2	no	—
410	C₄×C₅₃	—	4	1	no	—
411	C₄×C₅₃	—	4	2	no	—
412	C₄×C₅₃	—	4	2	no	—
413	C₄×C₅₃	—	4	2	no	—
414	#2854	C₂×C₅₃	1	1	yes	characteristic, complemented
415	#2854	C₂×C₅₃	1	2	yes	complemented
416	#2597	C₂×C₅₃	1	2	yes	complemented
417	#2596	C₂×C₅₃	1	2	yes	complemented
418	#2585	C₂×C₅₃	1	2	yes	complemented
419	#2569	C₂×C₅₃	1	1	yes	characteristic, complemented
420	#2554	C₂×C₅₃	1	2	yes	complemented
421	#2543	C₂×C₅₃	1	1	yes	characteristic
422	#2525	C₂×C₅₃	1	2	yes	complemented
423	#2516	C₂×C₅₃	1	2	yes	complemented
424	#2481	C₂×C₅₃	1	2	yes	complemented
425	#2443	C₂×C₅₃	1	2	yes	complemented
426	#2374	C₂×C₅₃	1	2	yes	complemented
427	#2373	C₂×C₅₃	1	2	yes	complemented
428	#2364	C₂×C₅₃	1	1	yes	characteristic, complemented
429	#2353	C₂×C₅₃	1	1	yes	characteristic, complemented
430	C₄×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
431	C₄×#123	C₂×C₅₃	1	2	yes	complemented
432	C₂×C₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
433	C₂×C₅₃	—	2	4	no	—
434	C₂×C₅₃	—	8	1	no	—
435	C₂×C₅₃	—	8	2	no	—
436	C₂×C₅₃	#3444	1	1	yes	characteristic
437	C₂×C₅₃	C₂×#553	1	1	yes	characteristic
438	C₂×C₅₃	#3480	1	2	yes	—
439	C₂×C₅₃	#3491	1	1	yes	characteristic
440	C₂×C₅₃	#3513	1	2	yes	—
441	C₂×#126	C₂²×C₅₃	1	2	yes	—
442	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
443	C₂×#123	C₂²×C₅₃	1	2	yes	—
444	C₂×#123	C₂²×C₅₃	1	2	yes	—
445	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
446	C₂×#121	C₂²×C₅₃	1	2	yes	—
447	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
448	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
449	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
450	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
451	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
452	#400	C₂²×C₅₃	1	2	yes	—
453	#400	C₂²×C₅₃	1	2	yes	—
454	#400	C₂²×C₅₃	1	2	yes	—
455	#399	C₂²×C₅₃	1	2	yes	—
456	#398	C₂²×C₅₃	1	2	yes	—
457	#398	C₂²×C₅₃	1	1	yes	characteristic
458	#398	C₂²×C₅₃	1	2	yes	—
459	#397	C₂²×C₅₃	1	1	yes	characteristic
460	#397	C₂²×C₅₃	1	2	yes	—
461	#397	C₂²×C₅₃	1	2	yes	—
462	#396	C₂²×C₅₃	1	2	yes	—
463	#394	C₂²×C₅₃	1	1	yes	characteristic
464	#394	C₂²×C₅₃	1	2	yes	—
465	#392	C₂²×C₅₃	1	1	yes	characteristic
466	#390	C₂²×C₅₃	1	2	yes	—
467	#390	C₂²×C₅₃	1	2	yes	—
468	#390	C₂²×C₅₃	1	2	yes	—
469	#389	C₂²×C₅₃	1	2	yes	—
470	#389	C₂²×C₅₃	1	2	yes	—
471	#389	C₂²×C₅₃	1	2	yes	—
472	#388	C₂²×C₅₃	1	2	yes	—
473	#388	C₂²×C₅₃	1	2	yes	—
474	#388	C₂²×C₅₃	1	2	yes	—
475	#388	C₂²×C₅₃	1	2	yes	—
476	#388	C₂²×C₅₃	1	2	yes	—
477	#388	C₂²×C₅₃	1	2	yes	—
478	#388	C₂²×C₅₃	1	2	yes	—
479	#388	C₂²×C₅₃	1	2	yes	—
480	#388	C₂²×C₅₃	1	2	yes	—
481	#388	C₂²×C₅₃	1	2	yes	—
482	#388	C₂²×C₅₃	1	2	yes	—
483	#388	C₂²×C₅₃	1	2	yes	—
484	#388	C₂²×C₅₃	1	2	yes	—
485	#388	C₂²×C₅₃	1	2	yes	—
486	#387	C₂²×C₅₃	1	2	yes	—
487	#387	C₂²×C₅₃	1	2	yes	—
488	#387	C₂²×C₅₃	1	2	yes	—
489	#387	C₂²×C₅₃	1	2	yes	—
490	#387	C₂²×C₅₃	1	2	yes	—
491	#387	C₂²×C₅₃	1	2	yes	—
492	#387	C₂²×C₅₃	1	2	yes	—
493	#387	C₂²×C₅₃	1	2	yes	—
494	#387	C₂²×C₅₃	1	2	yes	—
495	#387	C₂²×C₅₃	1	2	yes	—
496	#386	C₂²×C₅₃	1	2	yes	—
497	#386	C₂²×C₅₃	1	2	yes	—
498	#386	C₂²×C₅₃	1	2	yes	—
499	#386	C₂²×C₅₃	1	2	yes	—
500	#386	C₂²×C₅₃	1	2	yes	—
501	#386	C₂²×C₅₃	1	1	yes	characteristic
502	#386	C₂²×C₅₃	1	2	yes	—
503	#385	C₂²×C₅₃	1	2	yes	—
504	#385	C₂²×C₅₃	1	2	yes	—
505	#385	C₂²×C₅₃	1	1	yes	characteristic
506	#383	C₂²×C₅₃	1	1	yes	characteristic
507	#381	C₂²×C₅₃	1	1	yes	characteristic
508	#381	C₂²×C₅₃	1	1	yes	characteristic
509	#380	C₂²×C₅₃	1	1	yes	characteristic
510	#380	C₂²×C₅₃	1	2	yes	—
511	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
512	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
513	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
515	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
516	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
517	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
519	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
521	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
525	#376	C₂²×C₅₃	1	1	yes	characteristic
526	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
527	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
528	C₅₃	#36604	1	1	yes	characteristic, direct product factor, Sylow
529	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
531	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
532	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
535	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
536	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
538	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
540	#126	—	2	8	no	—
541	#123	—	2	4	no	—
542	#123	—	2	8	no	—
543	#123	—	2	8	no	—
544	#121	—	2	4	no	—
545	#121	—	4	4	no	—
546	C₄×D₄	—	2	4	no	—
547	C₄×D₄	—	4	4	no	—
548	C₂×C₄⋊C₄	—	2	8	no	—
549	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
571	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
587	C₂×C₄²	—	2	4	no	—
588	C₂×C₄²	—	4	4	no	—
589	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
591	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
592	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
593	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
594	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
595	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
596	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
597	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
598	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
599	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
600	#95	C₂³×C₅₃	1	1	yes	characteristic
601	#95	C₂³×C₅₃	1	1	yes	characteristic
602	#95	C₂³×C₅₃	1	2	yes	—
603	#95	C₂³×C₅₃	1	2	yes	—
604	#95	C₂³×C₅₃	1	1	yes	characteristic
605	#95	C₂³×C₅₃	1	1	yes	characteristic
606	#95	C₂³×C₅₃	1	1	yes	characteristic
607	#95	C₂³×C₅₃	1	2	yes	—
608	#95	C₂³×C₅₃	1	2	yes	—
609	#95	C₂³×C₅₃	1	2	yes	—
610	#95	C₂³×C₅₃	1	1	yes	characteristic
611	#95	C₂³×C₅₃	1	2	yes	—
612	#95	C₂³×C₅₃	1	2	yes	—
613	#95	C₂³×C₅₃	1	2	yes	—
614	#95	C₂³×C₅₃	1	2	yes	—
615	#95	C₂³×C₅₃	1	2	yes	—
616	#95	C₂³×C₅₃	1	2	yes	—
617	#95	C₂³×C₅₃	1	2	yes	—
618	#95	C₂³×C₅₃	1	2	yes	—
619	#95	C₂³×C₅₃	1	2	yes	—
620	#95	C₂³×C₅₃	1	2	yes	—
621	#95	C₂³×C₅₃	1	2	yes	—
622	#95	C₂³×C₅₃	1	2	yes	—
623	#95	C₂³×C₅₃	1	2	yes	—
624	#95	C₂³×C₅₃	1	2	yes	—
625	#95	C₂³×C₅₃	1	2	yes	—
626	#95	C₂³×C₅₃	1	2	yes	—
627	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
628	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
629	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	4	2	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	#41×C₅₃	1	4	yes	—
658	C₂²×C₄	#41×C₅₃	1	4	yes	—
659	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	#41×C₅₃	1	8	yes	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₄²	—	2	4	no	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	2	no	—
716	C₄²	—	2	4	no	—
717	C₄²	—	4	2	no	—
718	C₄²	—	4	2	no	—
719	C₄²	—	4	2	no	—
720	C₄²	—	4	2	no	—
721	C₄²	—	4	2	no	—
722	C₄²	—	4	2	no	—
723	C₄²	—	4	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	C₂×#41×C₅₃	1	2	yes	—
739	C₂³	C₂×#41×C₅₃	1	2	yes	—
740	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
741	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
742	D₄	—	4	4	no	—
743	D₄	—	4	8	no	—
744	D₄	—	8	2	no	—
745	D₄	—	8	4	no	—
746	C₂×C₄	—	2	8	no	—
747	C₂×C₄	—	2	8	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	8	no	—
788	C₂×C₄	—	4	8	no	—
789	C₂×C₄	—	8	2	no	—
790	C₂×C₄	—	8	4	no	—
791	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
792	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
793	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
794	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
795	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
796	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	1	no	—
813	C₂²	C₅₃×#553	1	4	yes	—
814	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
815	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
816	C₂²	C₂²×#41×C₅₃	1	2	yes	—
817	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
818	C₂²	C₅₃×#585	1	2	yes	—
819	C₄	—	2	4	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	4	no	—
823	C₄	—	2	4	no	—
824	C₄	—	2	4	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	1	no	—
835	C₂	—	2	4	no	—
836	C₂	—	8	1	no	—
837	C₂	—	8	2	no	—
838	C₂	C₅₃×#3444	1	1	yes	characteristic
839	C₂	C₂×C₅₃×#553	1	1	yes	characteristic
840	C₂	C₅₃×#3480	1	2	yes	—
841	C₂	C₅₃×#3491	1	1	yes	characteristic
842	C₂	C₅₃×#3513	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2543	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2854	C₂	semidirect
2. C₅₃×#2854	C₂	semidirect
3. C₅₃×#2597	C₂	semidirect
4. C₅₃×#2596	C₂	semidirect
5. C₅₃×#2585	C₂	semidirect
6. C₅₃×#2569	C₂	semidirect
7. C₅₃×#2554	C₂	semidirect
9. C₅₃×#2525	C₂	semidirect
10. C₅₃×#2516	C₂	semidirect
11. C₅₃×#2481	C₂	semidirect
12. C₅₃×#2443	C₂	semidirect
13. C₅₃×#2374	C₂	semidirect
14. C₅₃×#2373	C₂	semidirect
15. C₅₃×#2364	C₂	semidirect
16. C₅₃×#2353	C₂	semidirect
17. C₄×#123×C₅₃	C₂	semidirect
18. C₄×#123×C₅₃	C₂	semidirect
19. C₂×C₄×C₄⋊C₄×C₅₃	C₂	semidirect
375. #36604	C₅₃	direct (N × H)
414. #2854	C₂×C₅₃	semidirect
415. #2854	C₂×C₅₃	semidirect
416. #2597	C₂×C₅₃	semidirect
417. #2596	C₂×C₅₃	semidirect
418. #2585	C₂×C₅₃	semidirect
419. #2569	C₂×C₅₃	semidirect
420. #2554	C₂×C₅₃	semidirect
422. #2525	C₂×C₅₃	semidirect
423. #2516	C₂×C₅₃	semidirect
424. #2481	C₂×C₅₃	semidirect
425. #2443	C₂×C₅₃	semidirect
426. #2374	C₂×C₅₃	semidirect
427. #2373	C₂×C₅₃	semidirect
428. #2364	C₂×C₅₃	semidirect
429. #2353	C₂×C₅₃	semidirect
430. C₄×#123	C₂×C₅₃	semidirect
431. C₄×#123	C₂×C₅₃	semidirect
432. C₂×C₄×C₄⋊C₄	C₂×C₅₃	semidirect
528. C₅₃	#36604	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×#2854	2
C₅₃×#2597	2
C₅₃×#2596	2
C₅₃×#2585	2
C₅₃×#2569	2
C₅₃×#2554	2
C₅₃×#2543	2
C₅₃×#2525	2
C₅₃×#2516	2
C₅₃×#2481	2
C₅₃×#2443	2
C₅₃×#2374	2
C₅₃×#2373	2
C₅₃×#2364	2
C₅₃×#2353	2
C₄×#123×C₅₃	2
C₂×C₄×C₄⋊C₄×C₅₃	2
#36604	53

Subgroups — C53×#36604 #27244116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36604 #27244116