Subgroups — C₅₃×#35016 #27242528

Order 13568.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2666	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2665	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2586	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2574	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2505	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2492	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2450	C₂	1	2	yes	maximal
13	C₅₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2417	C₂	1	1	yes	maximal, characteristic
18	C₅₃×#2409	C₂	1	1	yes	maximal, characteristic
19	C₅₃×#2329	C₂	1	2	yes	maximal, complemented
20	C₅₃×#2318	C₂	1	2	yes	maximal
21	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic
24	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#400	C₂²	1	2	yes	—
41	C₅₃×#400	C₂²	1	2	yes	—
42	C₅₃×#400	C₂²	1	2	yes	—
43	C₅₃×#400	C₂²	1	2	yes	—
44	C₅₃×#398	C₂²	1	2	yes	—
45	C₅₃×#398	C₂²	1	2	yes	—
46	C₅₃×#398	C₂²	1	2	yes	—
47	C₅₃×#398	C₂²	1	2	yes	—
48	C₅₃×#396	C₂²	1	2	yes	—
49	C₅₃×#396	C₂²	1	2	yes	—
50	C₅₃×#395	C₂²	1	2	yes	—
51	C₅₃×#395	C₂²	1	2	yes	—
52	C₅₃×#395	C₂²	1	2	yes	—
53	C₅₃×#395	C₂²	1	2	yes	—
54	C₅₃×#393	C₂²	1	2	yes	—
55	C₅₃×#393	C₂²	1	2	yes	—
56	C₅₃×#391	C₂²	1	1	yes	characteristic
57	C₅₃×#391	C₂²	1	1	yes	characteristic
58	C₅₃×#391	C₂²	1	1	yes	characteristic
59	C₅₃×#391	C₂²	1	1	yes	characteristic
60	C₅₃×#391	C₂²	1	1	yes	characteristic
61	C₅₃×#391	C₂²	1	1	yes	characteristic
62	C₅₃×#391	C₂²	1	2	yes	—
63	C₅₃×#391	C₂²	1	2	yes	—
64	C₅₃×#391	C₂²	1	1	yes	characteristic
65	C₅₃×#391	C₂²	1	2	yes	—
66	C₅₃×#391	C₂²	1	1	yes	characteristic
67	C₅₃×#391	C₂²	1	1	yes	characteristic
68	C₅₃×#391	C₂²	1	2	yes	—
69	C₅₃×#391	C₂²	1	1	yes	characteristic
70	C₅₃×#391	C₂²	1	2	yes	—
71	C₅₃×#389	C₂²	1	1	yes	characteristic
72	C₅₃×#389	C₂²	1	2	yes	—
73	C₅₃×#389	C₂²	1	1	yes	characteristic
74	C₅₃×#389	C₂²	1	2	yes	—
75	C₅₃×#389	C₂²	1	1	yes	characteristic
76	C₅₃×#389	C₂²	1	1	yes	characteristic
77	C₅₃×#389	C₂²	1	2	yes	—
78	C₅₃×#388	C₂²	1	2	yes	—
79	C₅₃×#388	C₂²	1	2	yes	—
80	C₅₃×#387	C₂²	1	2	yes	—
81	C₅₃×#387	C₂²	1	2	yes	—
82	C₅₃×#387	C₂²	1	2	yes	—
83	C₅₃×#387	C₂²	1	2	yes	—
84	C₅₃×#387	C₂²	1	2	yes	—
85	C₅₃×#387	C₂²	1	2	yes	—
86	C₅₃×#387	C₂²	1	2	yes	—
87	C₅₃×#387	C₂²	1	2	yes	—
88	C₅₃×#387	C₂²	1	2	yes	—
89	C₅₃×#387	C₂²	1	2	yes	—
90	C₅₃×#386	C₂²	1	2	yes	—
91	C₅₃×#386	C₂²	1	2	yes	—
92	C₅₃×#385	C₂²	1	2	yes	—
93	C₅₃×#385	C₂²	1	2	yes	—
94	C₅₃×#385	C₂²	1	2	yes	—
95	C₅₃×#385	C₂²	1	2	yes	—
96	C₅₃×#385	C₂²	1	2	yes	—
97	C₅₃×#385	C₂²	1	2	yes	—
98	C₅₃×#384	C₂²	1	1	yes	characteristic
99	C₅₃×#383	C₂²	1	2	yes	—
100	C₅₃×#382	C₂²	1	2	yes	—
101	C₅₃×#382	C₂²	1	2	yes	—
102	C₅₃×#381	C₂²	1	2	yes	—
103	C₅₃×#380	C₂²	1	1	yes	characteristic
104	C₅₃×#380	C₂²	1	2	yes	—
105	C₅₃×#380	C₂²	1	1	yes	characteristic
106	C₅₃×#380	C₂²	1	2	yes	—
107	C₅₃×#380	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
120	C₂×#95×C₅₃	C₂²	1	2	yes	—
121	C₂×#95×C₅₃	C₂²	1	2	yes	—
122	C₄³×C₅₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₅₃	—	2	4	no	—
124	C₂²×Q₈×C₅₃	—	4	2	no	—
125	C₂²×Q₈×C₅₃	—	4	2	no	—
126	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
130	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
131	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₄⋊Q₈×C₅₃	—	4	2	no	—
141	C₄⋊Q₈×C₅₃	—	4	2	no	—
142	C₄⋊Q₈×C₅₃	—	4	2	no	—
143	C₂²⋊Q₈×C₅₃	—	2	8	no	—
144	C₂²⋊Q₈×C₅₃	—	2	4	no	—
145	C₂²⋊Q₈×C₅₃	—	4	2	no	—
146	C₂²⋊Q₈×C₅₃	—	4	2	no	—
147	C₂²⋊Q₈×C₅₃	—	4	2	no	—
148	C₄×Q₈×C₅₃	—	4	2	no	—
149	C₄×D₄×C₅₃	—	2	4	no	—
150	C₄×D₄×C₅₃	—	2	4	no	—
151	C₄×D₄×C₅₃	Q₈	1	8	yes	complemented
152	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
153	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₅₃	—	4	2	no	—
191	C₂×C₄²×C₅₃	—	4	2	no	—
192	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
207	#95×C₅₃	C₂³	1	2	yes	—
208	#95×C₅₃	C₂³	1	2	yes	—
209	#95×C₅₃	C₂³	1	2	yes	—
210	#95×C₅₃	C₂³	1	2	yes	—
211	#95×C₅₃	C₂³	1	2	yes	—
212	#95×C₅₃	C₂³	1	2	yes	—
213	#95×C₅₃	C₂³	1	2	yes	—
214	#95×C₅₃	C₂³	1	2	yes	—
215	#95×C₅₃	C₂³	1	1	yes	characteristic
216	#95×C₅₃	C₂³	1	1	yes	characteristic
217	#95×C₅₃	C₂³	1	1	yes	characteristic
218	#95×C₅₃	C₂³	1	1	yes	characteristic
219	#95×C₅₃	C₂³	1	1	yes	characteristic
220	#95×C₅₃	C₂³	1	1	yes	characteristic
221	#95×C₅₃	C₂³	1	2	yes	—
222	#95×C₅₃	C₂³	1	2	yes	—
223	#95×C₅₃	C₂³	1	2	yes	—
224	#95×C₅₃	C₂³	1	2	yes	—
225	#95×C₅₃	C₂³	1	2	yes	—
226	#95×C₅₃	C₂³	1	2	yes	—
227	#95×C₅₃	C₂³	1	2	yes	—
228	#95×C₅₃	C₂³	1	2	yes	—
229	#95×C₅₃	C₂³	1	2	yes	—
230	#95×C₅₃	C₂³	1	2	yes	—
231	#95×C₅₃	C₂³	1	2	yes	—
232	#95×C₅₃	C₂³	1	2	yes	—
233	#95×C₅₃	C₂³	1	2	yes	—
234	#95×C₅₃	C₂³	1	2	yes	—
235	#95×C₅₃	C₂³	1	2	yes	—
236	#95×C₅₃	C₂³	1	2	yes	—
237	#95×C₅₃	C₂³	1	2	yes	—
238	#95×C₅₃	C₂³	1	2	yes	—
239	#95×C₅₃	C₂³	1	2	yes	—
240	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₅₃	—	2	2	no	—
243	C₂×Q₈×C₅₃	—	2	4	no	—
244	C₂×Q₈×C₅₃	—	2	2	no	—
245	C₂×Q₈×C₅₃	—	2	2	no	—
246	C₂×Q₈×C₅₃	—	2	4	no	—
247	C₂×Q₈×C₅₃	—	2	2	no	—
248	C₂×Q₈×C₅₃	—	2	2	no	—
249	C₂×Q₈×C₅₃	—	2	2	no	—
250	C₂×Q₈×C₅₃	—	2	2	no	—
251	C₂×Q₈×C₅₃	—	2	2	no	—
252	C₂×Q₈×C₅₃	—	2	2	no	—
253	C₂×Q₈×C₅₃	—	4	2	no	—
254	C₂×Q₈×C₅₃	—	4	2	no	—
255	C₂×Q₈×C₅₃	—	4	2	no	—
256	C₂×Q₈×C₅₃	—	4	2	no	—
257	C₂×Q₈×C₅₃	—	4	16	no	—
258	C₂×D₄×C₅₃	—	2	2	no	—
259	C₂×D₄×C₅₃	—	2	2	no	—
260	C₂×D₄×C₅₃	C₂×Q₈	1	4	yes	—
261	C₂²×C₄×C₅₃	—	2	2	no	—
262	C₂²×C₄×C₅₃	—	2	2	no	—
263	C₂²×C₄×C₅₃	—	2	2	no	—
264	C₂²×C₄×C₅₃	—	2	4	no	—
265	C₂²×C₄×C₅₃	—	2	4	no	—
266	C₂²×C₄×C₅₃	—	2	2	no	—
267	C₂²×C₄×C₅₃	—	2	2	no	—
268	C₂²×C₄×C₅₃	—	2	2	no	—
269	C₂²×C₄×C₅₃	—	2	2	no	—
270	C₂²×C₄×C₅₃	—	2	2	no	—
271	C₂²×C₄×C₅₃	—	2	2	no	—
272	C₂²×C₄×C₅₃	—	4	1	no	—
273	C₂²×C₄×C₅₃	—	4	1	no	—
274	C₂²×C₄×C₅₃	—	4	1	no	—
275	C₂²×C₄×C₅₃	—	4	1	no	—
276	C₂²×C₄×C₅₃	—	4	1	no	—
277	C₂²×C₄×C₅₃	—	4	1	no	—
278	C₂²×C₄×C₅₃	—	4	2	no	—
279	C₂²×C₄×C₅₃	—	4	2	no	—
280	C₂²×C₄×C₅₃	—	4	2	no	—
281	C₂²×C₄×C₅₃	—	4	2	no	—
282	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	—
283	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
284	C₂²×C₄×C₅₃	#41	1	4	yes	—
285	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₅₃	—	2	2	no	—
307	C₄⋊C₄×C₅₃	—	2	2	no	—
308	C₄⋊C₄×C₅₃	—	2	4	no	—
309	C₄⋊C₄×C₅₃	—	2	4	no	—
310	C₄⋊C₄×C₅₃	—	2	4	no	—
311	C₄⋊C₄×C₅₃	—	2	4	no	—
312	C₄⋊C₄×C₅₃	—	2	2	no	—
313	C₄⋊C₄×C₅₃	—	2	2	no	—
314	C₄⋊C₄×C₅₃	—	2	2	no	—
315	C₄⋊C₄×C₅₃	—	2	2	no	—
316	C₄⋊C₄×C₅₃	—	2	2	no	—
317	C₄⋊C₄×C₅₃	—	2	4	no	—
318	C₄⋊C₄×C₅₃	—	4	2	no	—
319	C₄⋊C₄×C₅₃	—	4	2	no	—
320	C₄⋊C₄×C₅₃	—	4	2	no	—
321	C₄⋊C₄×C₅₃	—	4	2	no	—
322	C₄⋊C₄×C₅₃	—	4	2	no	—
323	C₄⋊C₄×C₅₃	—	4	2	no	—
324	C₄⋊C₄×C₅₃	—	4	2	no	—
325	C₄⋊C₄×C₅₃	—	4	2	no	—
326	C₄⋊C₄×C₅₃	—	4	2	no	—
327	C₄⋊C₄×C₅₃	—	4	2	no	—
328	C₄⋊C₄×C₅₃	—	4	2	no	—
329	C₄⋊C₄×C₅₃	—	4	2	no	—
330	C₄⋊C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
331	C₂²⋊C₄×C₅₃	—	2	2	no	—
332	C₂²⋊C₄×C₅₃	—	2	4	no	—
333	C₂²⋊C₄×C₅₃	—	2	4	no	—
334	C₂²⋊C₄×C₅₃	—	2	2	no	—
335	C₂²⋊C₄×C₅₃	—	2	2	no	—
336	C₂²⋊C₄×C₅₃	—	4	2	no	—
337	C₂²⋊C₄×C₅₃	—	4	2	no	—
338	C₂²⋊C₄×C₅₃	—	4	2	no	—
339	C₂²⋊C₄×C₅₃	—	4	2	no	—
340	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	—
341	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
342	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
343	C₄²×C₅₃	—	2	2	no	—
344	C₄²×C₅₃	—	2	2	no	—
345	C₄²×C₅₃	—	2	2	no	—
346	C₄²×C₅₃	—	2	2	no	—
347	C₄²×C₅₃	—	2	2	no	—
348	C₄²×C₅₃	—	2	2	no	—
349	C₄²×C₅₃	—	2	2	no	—
350	C₄²×C₅₃	—	4	1	no	—
351	C₄²×C₅₃	—	4	1	no	—
352	C₄²×C₅₃	—	4	1	no	—
353	C₄²×C₅₃	—	4	1	no	—
354	C₄²×C₅₃	—	4	1	no	—
355	C₄²×C₅₃	—	4	2	no	—
356	C₄²×C₅₃	—	4	2	no	—
357	C₄²×C₅₃	C₂×Q₈	1	4	yes	complemented
358	C₂³×C₅₃	—	2	1	no	—
359	C₂³×C₅₃	—	2	1	no	—
360	C₂³×C₅₃	—	2	1	no	—
361	C₂³×C₅₃	—	2	1	no	—
362	C₂³×C₅₃	—	2	1	no	—
363	C₂³×C₅₃	—	2	1	no	—
364	C₂³×C₅₃	—	2	1	no	—
365	C₂³×C₅₃	—	2	1	no	—
366	C₂³×C₅₃	—	2	1	no	—
367	C₂³×C₅₃	—	2	1	no	—
368	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
369	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
370	C₂³×C₅₃	C₂×#41	1	2	yes	—
371	C₂³×C₅₃	C₂×#41	1	2	yes	—
372	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
373	Q₈×C₅₃	—	4	8	no	—
374	Q₈×C₅₃	—	4	4	no	—
375	Q₈×C₅₃	—	4	4	no	—
376	Q₈×C₅₃	—	4	4	no	—
377	Q₈×C₅₃	—	8	4	no	—
378	D₄×C₅₃	—	2	8	no	—
379	C₂×C₄×C₅₃	—	2	1	no	—
380	C₂×C₄×C₅₃	—	2	1	no	—
381	C₂×C₄×C₅₃	—	2	1	no	—
382	C₂×C₄×C₅₃	—	2	1	no	—
383	C₂×C₄×C₅₃	—	2	1	no	—
384	C₂×C₄×C₅₃	—	2	1	no	—
385	C₂×C₄×C₅₃	—	2	1	no	—
386	C₂×C₄×C₅₃	—	2	1	no	—
387	C₂×C₄×C₅₃	—	2	1	no	—
388	C₂×C₄×C₅₃	—	2	1	no	—
389	C₂×C₄×C₅₃	—	2	1	no	—
390	C₂×C₄×C₅₃	—	2	1	no	—
391	C₂×C₄×C₅₃	—	2	1	no	—
392	C₂×C₄×C₅₃	—	2	1	no	—
393	C₂×C₄×C₅₃	—	2	1	no	—
394	C₂×C₄×C₅₃	—	2	1	no	—
395	C₂×C₄×C₅₃	—	2	1	no	—
396	C₂×C₄×C₅₃	—	2	1	no	—
397	C₂×C₄×C₅₃	—	2	8	no	—
398	C₂×C₄×C₅₃	—	2	2	no	—
399	C₂×C₄×C₅₃	—	2	2	no	—
400	C₂×C₄×C₅₃	—	2	2	no	—
401	C₂×C₄×C₅₃	—	2	1	no	—
402	C₂×C₄×C₅₃	—	2	1	no	—
403	C₂×C₄×C₅₃	—	2	2	no	—
404	C₂×C₄×C₅₃	—	2	2	no	—
405	C₂×C₄×C₅₃	—	2	2	no	—
406	C₂×C₄×C₅₃	—	2	1	no	—
407	C₂×C₄×C₅₃	—	2	2	no	—
408	C₂×C₄×C₅₃	—	2	2	no	—
409	C₂×C₄×C₅₃	—	2	1	no	—
410	C₂×C₄×C₅₃	—	2	1	no	—
411	C₂×C₄×C₅₃	—	2	2	no	—
412	C₂×C₄×C₅₃	—	2	2	no	—
413	C₂×C₄×C₅₃	—	2	2	no	—
414	C₂×C₄×C₅₃	—	2	2	no	—
415	C₂×C₄×C₅₃	—	2	2	no	—
416	C₂×C₄×C₅₃	—	2	1	no	—
417	C₂×C₄×C₅₃	—	2	2	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	2	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	1	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	2	2	no	—
430	C₂×C₄×C₅₃	—	2	1	no	—
431	C₂×C₄×C₅₃	—	4	4	no	—
432	C₂×C₄×C₅₃	—	4	4	no	—
433	C₂×C₄×C₅₃	—	4	4	no	—
434	C₂×C₄×C₅₃	—	4	4	no	—
435	C₂×C₄×C₅₃	—	4	8	no	—
436	C₂×C₄×C₅₃	—	4	4	no	—
437	C₂×C₄×C₅₃	—	8	4	no	—
438	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
439	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
440	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
441	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
442	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
443	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
444	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
445	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
446	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
447	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
448	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
449	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
450	#35016	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂²×C₅₃	—	2	2	no	—
452	C₂²×C₅₃	—	2	2	no	—
453	C₂²×C₅₃	—	2	2	no	—
454	C₂²×C₅₃	—	2	2	no	—
455	C₂²×C₅₃	—	2	2	no	—
456	C₂²×C₅₃	—	2	2	no	—
457	C₂²×C₅₃	—	2	2	no	—
458	C₂²×C₅₃	—	2	2	no	—
459	C₂²×C₅₃	—	2	2	no	—
460	C₂²×C₅₃	—	4	1	no	—
461	C₂²×C₅₃	—	4	1	no	—
462	C₂²×C₅₃	—	4	1	no	—
463	C₂²×C₅₃	—	4	1	no	—
464	C₂²×C₅₃	#533	1	4	yes	—
465	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
466	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
467	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
468	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
471	C₂²×C₅₃	#585	1	1	yes	characteristic
472	C₄×C₅₃	—	2	2	no	—
473	C₄×C₅₃	—	2	2	no	—
474	C₄×C₅₃	—	2	2	no	—
475	C₄×C₅₃	—	2	2	no	—
476	C₄×C₅₃	—	2	2	no	—
477	C₄×C₅₃	—	2	2	no	—
478	C₄×C₅₃	—	2	2	no	—
479	C₄×C₅₃	—	2	2	no	—
480	C₄×C₅₃	—	2	2	no	—
481	C₄×C₅₃	—	4	1	no	—
482	C₄×C₅₃	—	4	2	no	—
483	C₄×C₅₃	—	4	2	no	—
484	C₄×C₅₃	—	4	2	no	—
485	C₄×C₅₃	—	4	1	no	—
486	C₄×C₅₃	—	4	2	no	—
487	C₄×C₅₃	—	4	2	no	—
488	C₄×C₅₃	—	4	2	no	—
489	C₄×C₅₃	—	4	2	no	—
490	C₄×C₅₃	—	4	2	no	—
491	C₄×C₅₃	—	4	1	no	—
492	C₄×C₅₃	#538	1	4	yes	—
493	#2863	C₂×C₅₃	1	1	yes	characteristic, complemented
494	#2862	C₂×C₅₃	1	1	yes	characteristic, complemented
495	#2857	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#2855	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#2666	C₂×C₅₃	1	2	yes	complemented
498	#2665	C₂×C₅₃	1	2	yes	complemented
499	#2586	C₂×C₅₃	1	2	yes	complemented
500	#2574	C₂×C₅₃	1	2	yes	complemented
501	#2511	C₂×C₅₃	1	1	yes	characteristic, complemented
502	#2505	C₂×C₅₃	1	2	yes	complemented
503	#2492	C₂×C₅₃	1	1	yes	characteristic, complemented
504	#2450	C₂×C₅₃	1	2	yes	—
505	#2446	C₂×C₅₃	1	1	yes	characteristic, complemented
506	#2440	C₂×C₅₃	1	1	yes	characteristic, complemented
507	#2434	C₂×C₅₃	1	1	yes	characteristic, complemented
508	#2429	C₂×C₅₃	1	1	yes	characteristic, complemented
509	#2417	C₂×C₅₃	1	1	yes	characteristic
510	#2409	C₂×C₅₃	1	1	yes	characteristic
511	#2329	C₂×C₅₃	1	2	yes	complemented
512	#2318	C₂×C₅₃	1	2	yes	—
513	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
514	C₂×#391	C₂×C₅₃	1	1	yes	characteristic, complemented
515	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic
516	C₂×C₅₃	—	2	4	no	—
517	C₂×C₅₃	—	4	2	no	—
518	C₂×C₅₃	C₂×#533	1	1	yes	characteristic
519	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
520	C₂×C₅₃	#3461	1	1	yes	characteristic
521	C₂×C₅₃	#3501	1	1	yes	characteristic
522	C₂×C₅₃	#3503	1	1	yes	characteristic
523	C₂×C₅₃	#3514	1	1	yes	characteristic
524	C₂×C₅₃	#3520	1	1	yes	characteristic
525	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
526	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
527	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
528	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
529	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
530	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
531	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
532	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
533	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
534	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
535	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
536	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
537	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
538	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
539	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
540	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
541	#400	C₂²×C₅₃	1	2	yes	—
542	#400	C₂²×C₅₃	1	2	yes	—
543	#400	C₂²×C₅₃	1	2	yes	—
544	#400	C₂²×C₅₃	1	2	yes	—
545	#398	C₂²×C₅₃	1	2	yes	—
546	#398	C₂²×C₅₃	1	2	yes	—
547	#398	C₂²×C₅₃	1	2	yes	—
548	#398	C₂²×C₅₃	1	2	yes	—
549	#396	C₂²×C₅₃	1	2	yes	—
550	#396	C₂²×C₅₃	1	2	yes	—
551	#395	C₂²×C₅₃	1	2	yes	—
552	#395	C₂²×C₅₃	1	2	yes	—
553	#395	C₂²×C₅₃	1	2	yes	—
554	#395	C₂²×C₅₃	1	2	yes	—
555	#393	C₂²×C₅₃	1	2	yes	—
556	#393	C₂²×C₅₃	1	2	yes	—
557	#391	C₂²×C₅₃	1	2	yes	—
558	#391	C₂²×C₅₃	1	2	yes	—
559	#391	C₂²×C₅₃	1	2	yes	—
560	#391	C₂²×C₅₃	1	2	yes	—
561	#391	C₂²×C₅₃	1	1	yes	characteristic
562	#391	C₂²×C₅₃	1	1	yes	characteristic
563	#391	C₂²×C₅₃	1	1	yes	characteristic
564	#391	C₂²×C₅₃	1	1	yes	characteristic
565	#391	C₂²×C₅₃	1	1	yes	characteristic
566	#391	C₂²×C₅₃	1	1	yes	characteristic
567	#391	C₂²×C₅₃	1	1	yes	characteristic
568	#391	C₂²×C₅₃	1	1	yes	characteristic
569	#391	C₂²×C₅₃	1	2	yes	—
570	#391	C₂²×C₅₃	1	1	yes	characteristic
571	#391	C₂²×C₅₃	1	1	yes	characteristic
572	#389	C₂²×C₅₃	1	2	yes	—
573	#389	C₂²×C₅₃	1	2	yes	—
574	#389	C₂²×C₅₃	1	2	yes	—
575	#389	C₂²×C₅₃	1	1	yes	characteristic
576	#389	C₂²×C₅₃	1	1	yes	characteristic
577	#389	C₂²×C₅₃	1	1	yes	characteristic
578	#389	C₂²×C₅₃	1	1	yes	characteristic
579	#388	C₂²×C₅₃	1	2	yes	—
580	#388	C₂²×C₅₃	1	2	yes	—
581	#387	C₂²×C₅₃	1	2	yes	—
582	#387	C₂²×C₅₃	1	2	yes	—
583	#387	C₂²×C₅₃	1	2	yes	—
584	#387	C₂²×C₅₃	1	2	yes	—
585	#387	C₂²×C₅₃	1	2	yes	—
586	#387	C₂²×C₅₃	1	2	yes	—
587	#387	C₂²×C₅₃	1	2	yes	—
588	#387	C₂²×C₅₃	1	2	yes	—
589	#387	C₂²×C₅₃	1	2	yes	—
590	#387	C₂²×C₅₃	1	2	yes	—
591	#386	C₂²×C₅₃	1	2	yes	—
592	#386	C₂²×C₅₃	1	2	yes	—
593	#385	C₂²×C₅₃	1	2	yes	—
594	#385	C₂²×C₅₃	1	2	yes	—
595	#385	C₂²×C₅₃	1	2	yes	—
596	#385	C₂²×C₅₃	1	2	yes	—
597	#385	C₂²×C₅₃	1	2	yes	—
598	#385	C₂²×C₅₃	1	2	yes	—
599	#384	C₂²×C₅₃	1	1	yes	characteristic
600	#383	C₂²×C₅₃	1	2	yes	—
601	#382	C₂²×C₅₃	1	2	yes	—
602	#382	C₂²×C₅₃	1	2	yes	—
603	#381	C₂²×C₅₃	1	2	yes	—
604	#380	C₂²×C₅₃	1	2	yes	—
605	#380	C₂²×C₅₃	1	2	yes	—
606	#380	C₂²×C₅₃	1	2	yes	—
607	#380	C₂²×C₅₃	1	1	yes	characteristic
608	#380	C₂²×C₅₃	1	1	yes	characteristic
609	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
610	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
611	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
612	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
613	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
614	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
615	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
616	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
617	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
618	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
619	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
620	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
621	C₂×#95	C₂²×C₅₃	1	2	yes	—
622	C₂×#95	C₂²×C₅₃	1	2	yes	—
623	C₄³	C₂²×C₅₃	1	1	yes	characteristic
624	C₅₃	#35016	1	1	yes	characteristic, direct product factor, Sylow
625	C₂²×Q₈	—	2	4	no	—
626	C₂²×Q₈	—	4	2	no	—
627	C₂²×Q₈	—	4	2	no	—
628	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
629	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
630	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
631	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
632	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
633	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
634	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
636	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
637	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
638	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
639	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
640	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
641	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
642	C₄⋊Q₈	—	4	2	no	—
643	C₄⋊Q₈	—	4	2	no	—
644	C₄⋊Q₈	—	4	2	no	—
645	C₂²⋊Q₈	—	2	4	no	—
646	C₂²⋊Q₈	—	2	8	no	—
647	C₂²⋊Q₈	—	4	2	no	—
648	C₂²⋊Q₈	—	4	2	no	—
649	C₂²⋊Q₈	—	4	2	no	—
650	C₄×Q₈	—	4	2	no	—
651	C₄×D₄	—	2	4	no	—
652	C₄×D₄	—	2	4	no	—
653	C₄×D₄	Q₈×C₅₃	1	8	yes	complemented
654	C₂×C₄⋊C₄	—	4	2	no	—
655	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
691	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
692	C₂×C₄²	—	4	2	no	—
693	C₂×C₄²	—	4	2	no	—
694	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
702	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
705	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
709	#95	C₂³×C₅₃	1	2	yes	—
710	#95	C₂³×C₅₃	1	2	yes	—
711	#95	C₂³×C₅₃	1	2	yes	—
712	#95	C₂³×C₅₃	1	2	yes	—
713	#95	C₂³×C₅₃	1	2	yes	—
714	#95	C₂³×C₅₃	1	2	yes	—
715	#95	C₂³×C₅₃	1	2	yes	—
716	#95	C₂³×C₅₃	1	2	yes	—
717	#95	C₂³×C₅₃	1	1	yes	characteristic
718	#95	C₂³×C₅₃	1	1	yes	characteristic
719	#95	C₂³×C₅₃	1	1	yes	characteristic
720	#95	C₂³×C₅₃	1	1	yes	characteristic
721	#95	C₂³×C₅₃	1	1	yes	characteristic
722	#95	C₂³×C₅₃	1	1	yes	characteristic
723	#95	C₂³×C₅₃	1	2	yes	—
724	#95	C₂³×C₅₃	1	2	yes	—
725	#95	C₂³×C₅₃	1	2	yes	—
726	#95	C₂³×C₅₃	1	2	yes	—
727	#95	C₂³×C₅₃	1	2	yes	—
728	#95	C₂³×C₅₃	1	2	yes	—
729	#95	C₂³×C₅₃	1	2	yes	—
730	#95	C₂³×C₅₃	1	2	yes	—
731	#95	C₂³×C₅₃	1	2	yes	—
732	#95	C₂³×C₅₃	1	2	yes	—
733	#95	C₂³×C₅₃	1	2	yes	—
734	#95	C₂³×C₅₃	1	2	yes	—
735	#95	C₂³×C₅₃	1	2	yes	—
736	#95	C₂³×C₅₃	1	2	yes	—
737	#95	C₂³×C₅₃	1	2	yes	—
738	#95	C₂³×C₅₃	1	2	yes	—
739	#95	C₂³×C₅₃	1	2	yes	—
740	#95	C₂³×C₅₃	1	2	yes	—
741	#95	C₂³×C₅₃	1	2	yes	—
742	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
743	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	4	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	2	2	no	—
750	C₂×Q₈	—	2	2	no	—
751	C₂×Q₈	—	2	2	no	—
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	2	no	—
755	C₂×Q₈	—	4	2	no	—
756	C₂×Q₈	—	4	2	no	—
757	C₂×Q₈	—	4	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	—	4	16	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	C₂×Q₈×C₅₃	1	4	yes	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	4	1	no	—
775	C₂²×C₄	—	4	1	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	—	4	1	no	—
778	C₂²×C₄	—	4	1	no	—
779	C₂²×C₄	—	4	1	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	C₂×Q₈×C₅₃	1	4	yes	—
785	C₂²×C₄	C₂×Q₈×C₅₃	1	4	yes	complemented
786	C₂²×C₄	#41×C₅₃	1	4	yes	—
787	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	4	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	—	4	2	no	—
823	C₄⋊C₄	—	4	2	no	—
824	C₄⋊C₄	—	4	2	no	—
825	C₄⋊C₄	—	4	2	no	—
826	C₄⋊C₄	—	4	2	no	—
827	C₄⋊C₄	—	4	2	no	—
828	C₄⋊C₄	—	4	2	no	—
829	C₄⋊C₄	—	4	2	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₄⋊C₄	C₂×Q₈×C₅₃	1	4	yes	complemented
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	C₂×Q₈×C₅₃	1	4	yes	—
843	C₂²⋊C₄	C₂×Q₈×C₅₃	1	4	yes	complemented
844	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	4	1	no	—
853	C₄²	—	4	1	no	—
854	C₄²	—	4	1	no	—
855	C₄²	—	4	1	no	—
856	C₄²	—	4	2	no	—
857	C₄²	—	4	2	no	—
858	C₄²	—	4	1	no	—
859	C₄²	C₂×Q₈×C₅₃	1	4	yes	complemented
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	C₂²×Q₈×C₅₃	1	2	yes	—
871	C₂³	C₂²×Q₈×C₅₃	1	2	yes	—
872	C₂³	C₂×#41×C₅₃	1	2	yes	—
873	C₂³	C₂×#41×C₅₃	1	2	yes	—
874	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
875	Q₈	—	4	8	no	—
876	Q₈	—	4	4	no	—
877	Q₈	—	4	4	no	—
878	Q₈	—	4	4	no	—
879	Q₈	—	8	4	no	—
880	D₄	—	2	8	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	8	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	4	4	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	8	no	—
938	C₂×C₄	—	4	4	no	—
939	C₂×C₄	—	8	4	no	—
940	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
941	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
942	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
943	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
944	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
945	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
946	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
947	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
948	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
949	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
950	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
951	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	1	no	—
965	C₂²	C₅₃×#533	1	4	yes	—
966	C₂²	C₂³×Q₈×C₅₃	1	1	yes	characteristic
967	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
968	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
969	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
970	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
971	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
972	C₂²	C₅₃×#585	1	1	yes	characteristic
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	C₅₃×#538	1	4	yes	—
994	C₂	—	2	4	no	—
995	C₂	—	4	2	no	—
996	C₂	C₂×C₅₃×#533	1	1	yes	characteristic
997	C₂	C₂×C₅₃×#538	1	1	yes	characteristic
998	C₂	C₅₃×#3461	1	1	yes	characteristic
999	C₂	C₅₃×#3501	1	1	yes	characteristic
1000	C₂	C₅₃×#3503	1	1	yes	characteristic
1001	C₂	C₅₃×#3514	1	1	yes	characteristic
1002	C₂	C₅₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂²×D₄×C₅₃	C₂³
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×#2863	C₂	semidirect
2. C₅₃×#2862	C₂	semidirect
3. C₅₃×#2857	C₂	semidirect
4. C₅₃×#2855	C₂	semidirect
5. C₅₃×#2666	C₂	semidirect
6. C₅₃×#2665	C₂	semidirect
7. C₅₃×#2586	C₂	semidirect
8. C₅₃×#2574	C₂	semidirect
9. C₅₃×#2511	C₂	semidirect
10. C₅₃×#2505	C₂	semidirect
11. C₅₃×#2492	C₂	semidirect
13. C₅₃×#2446	C₂	semidirect
14. C₅₃×#2440	C₂	semidirect
15. C₅₃×#2434	C₂	semidirect
16. C₅₃×#2429	C₂	semidirect
19. C₅₃×#2329	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
22. C₂×C₅₃×#391	C₂	semidirect
151. C₄×D₄×C₅₃	Q₈	semidirect
283. C₂²×C₄×C₅₃	C₂×Q₈	semidirect
330. C₄⋊C₄×C₅₃	C₂×Q₈	semidirect
341. C₂²⋊C₄×C₅₃	C₂×Q₈	semidirect
357. C₄²×C₅₃	C₂×Q₈	semidirect
450. #35016	C₅₃	direct (N × H)
493. #2863	C₂×C₅₃	semidirect
494. #2862	C₂×C₅₃	semidirect
495. #2857	C₂×C₅₃	semidirect
496. #2855	C₂×C₅₃	semidirect
497. #2666	C₂×C₅₃	semidirect
498. #2665	C₂×C₅₃	semidirect
499. #2586	C₂×C₅₃	semidirect
500. #2574	C₂×C₅₃	semidirect
501. #2511	C₂×C₅₃	semidirect
502. #2505	C₂×C₅₃	semidirect
503. #2492	C₂×C₅₃	semidirect
505. #2446	C₂×C₅₃	semidirect
506. #2440	C₂×C₅₃	semidirect
507. #2434	C₂×C₅₃	semidirect
508. #2429	C₂×C₅₃	semidirect
511. #2329	C₂×C₅₃	semidirect
513. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
514. C₂×#391	C₂×C₅₃	semidirect
624. C₅₃	#35016	direct (N × H)
653. C₄×D₄	Q₈×C₅₃	semidirect
785. C₂²×C₄	C₂×Q₈×C₅₃	semidirect
832. C₄⋊C₄	C₂×Q₈×C₅₃	semidirect
843. C₂²⋊C₄	C₂×Q₈×C₅₃	semidirect
859. C₄²	C₂×Q₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#2863	2
C₅₃×#2862	2
C₅₃×#2857	2
C₅₃×#2855	2
C₅₃×#2666	2
C₅₃×#2665	2
C₅₃×#2586	2
C₅₃×#2574	2
C₅₃×#2511	2
C₅₃×#2505	2
C₅₃×#2492	2
C₅₃×#2450	2
C₅₃×#2446	2
C₅₃×#2440	2
C₅₃×#2434	2
C₅₃×#2429	2
C₅₃×#2417	2
C₅₃×#2409	2
C₅₃×#2329	2
C₅₃×#2318	2
C₄×C₂²⋊Q₈×C₅₃	2
C₂×C₅₃×#391	2
C₄²×D₄×C₅₃	2
#35016	53

Subgroups — C53×#35016 #27242528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#35016 #27242528