Subgroups — C₅₃×#34800 #27242312

Order 13568.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2532	C₂	1	2	yes	maximal, complemented
2	C₅₃×#2526	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2518	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2508	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2500	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2485	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2459	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2439	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2414	C₂	1	1	yes	maximal, characteristic
13	C₅₃×#2398	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2392	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#124×C₅₃	C₂	1	2	yes	maximal, complemented
17	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2298	C₂	1	2	yes	maximal, complemented
20	C₅₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#117×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#124×C₅₃	C₂²	1	2	yes	—
26	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
35	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#117×C₅₃	C₂²	1	2	yes	—
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×#398	C₂²	1	2	yes	—
43	C₅₃×#397	C₂²	1	2	yes	—
44	C₅₃×#397	C₂²	1	2	yes	—
45	C₅₃×#397	C₂²	1	2	yes	—
46	C₅₃×#396	C₂²	1	2	yes	—
47	C₅₃×#396	C₂²	1	2	yes	—
48	C₅₃×#394	C₂²	1	2	yes	—
49	C₅₃×#394	C₂²	1	2	yes	—
50	C₅₃×#394	C₂²	1	2	yes	—
51	C₅₃×#394	C₂²	1	2	yes	—
52	C₅₃×#394	C₂²	1	2	yes	—
53	C₅₃×#393	C₂²	1	2	yes	—
54	C₅₃×#393	C₂²	1	2	yes	—
55	C₅₃×#392	C₂²	1	2	yes	—
56	C₅₃×#391	C₂²	1	2	yes	—
57	C₅₃×#391	C₂²	1	2	yes	—
58	C₅₃×#390	C₂²	1	1	yes	characteristic
59	C₅₃×#390	C₂²	1	1	yes	characteristic
60	C₅₃×#390	C₂²	1	1	yes	characteristic
61	C₅₃×#390	C₂²	1	1	yes	characteristic
62	C₅₃×#390	C₂²	1	2	yes	—
63	C₅₃×#389	C₂²	1	1	yes	characteristic
64	C₅₃×#389	C₂²	1	1	yes	characteristic
65	C₅₃×#389	C₂²	1	1	yes	characteristic
66	C₅₃×#389	C₂²	1	1	yes	characteristic
67	C₅₃×#389	C₂²	1	1	yes	characteristic
68	C₅₃×#389	C₂²	1	1	yes	characteristic
69	C₅₃×#389	C₂²	1	2	yes	—
70	C₅₃×#388	C₂²	1	2	yes	—
71	C₅₃×#388	C₂²	1	2	yes	—
72	C₅₃×#388	C₂²	1	2	yes	—
73	C₅₃×#388	C₂²	1	2	yes	—
74	C₅₃×#388	C₂²	1	2	yes	—
75	C₅₃×#388	C₂²	1	2	yes	—
76	C₅₃×#388	C₂²	1	2	yes	—
77	C₅₃×#388	C₂²	1	2	yes	—
78	C₅₃×#388	C₂²	1	2	yes	—
79	C₅₃×#388	C₂²	1	2	yes	—
80	C₅₃×#388	C₂²	1	2	yes	—
81	C₅₃×#388	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×#386	C₂²	1	2	yes	—
87	C₅₃×#386	C₂²	1	2	yes	—
88	C₅₃×#384	C₂²	1	1	yes	characteristic
89	C₅₃×#383	C₂²	1	2	yes	—
90	C₅₃×#382	C₂²	1	1	yes	characteristic
91	C₅₃×#382	C₂²	1	1	yes	characteristic
92	C₅₃×#382	C₂²	1	2	yes	—
93	C₅₃×#381	C₂²	1	2	yes	—
94	C₅₃×#380	C₂²	1	1	yes	characteristic
95	C₅₃×#380	C₂²	1	1	yes	characteristic
96	C₅₃×#380	C₂²	1	1	yes	characteristic
97	C₅₃×#380	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
107	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
108	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
110	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
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	2	yes	—
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
119	C₅₃×#376	C₂²	1	2	yes	—
120	C₅₃×#376	C₂²	1	2	yes	—
121	C₄³×C₅₃	C₂²	1	2	yes	—
122	C₄³×C₅₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
127	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
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	C₄⋊Q₈×C₅₃	—	2	4	no	—
136	#124×C₅₃	—	2	8	no	—
137	#121×C₅₃	—	2	4	no	—
138	#121×C₅₃	—	2	4	no	—
139	C₄×Q₈×C₅₃	—	4	4	no	—
140	C₄×D₄×C₅₃	—	2	4	no	—
141	C₄×D₄×C₅₃	—	2	4	no	—
142	C₄×D₄×C₅₃	—	2	4	no	—
143	C₄×D₄×C₅₃	—	2	4	no	—
144	C₄×D₄×C₅₃	—	4	4	no	—
145	C₄×D₄×C₅₃	—	4	4	no	—
146	#117×C₅₃	—	2	4	no	—
147	#117×C₅₃	—	2	8	no	—
148	#117×C₅₃	—	2	4	no	—
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
188	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅₃	—	2	4	no	—
192	C₂×C₄²×C₅₃	—	2	4	no	—
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	2	yes	—
198	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
210	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
213	#95×C₅₃	C₂³	1	2	yes	—
214	#95×C₅₃	C₂³	1	2	yes	—
215	#95×C₅₃	C₂³	1	2	yes	—
216	#95×C₅₃	C₂³	1	2	yes	—
217	#95×C₅₃	C₂³	1	2	yes	—
218	#95×C₅₃	C₂³	1	2	yes	—
219	#95×C₅₃	C₂³	1	2	yes	—
220	#95×C₅₃	C₂³	1	2	yes	—
221	#95×C₅₃	C₂³	1	1	yes	characteristic
222	#95×C₅₃	C₂³	1	1	yes	characteristic
223	#95×C₅₃	C₂³	1	1	yes	characteristic
224	#95×C₅₃	C₂³	1	1	yes	characteristic
225	#95×C₅₃	C₂³	1	1	yes	characteristic
226	#95×C₅₃	C₂³	1	1	yes	characteristic
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	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
239	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₅₃	—	2	4	no	—
242	C₂×Q₈×C₅₃	—	2	4	no	—
243	C₂×Q₈×C₅₃	—	4	2	no	—
244	C₂×D₄×C₅₃	—	2	2	no	—
245	C₂×D₄×C₅₃	—	2	2	no	—
246	C₂×D₄×C₅₃	—	2	4	no	—
247	C₂×D₄×C₅₃	—	2	4	no	—
248	C₂×D₄×C₅₃	—	2	2	no	—
249	C₂×D₄×C₅₃	—	2	2	no	—
250	C₂×D₄×C₅₃	—	2	4	no	—
251	C₂×D₄×C₅₃	—	2	2	no	—
252	C₂×D₄×C₅₃	—	2	2	no	—
253	C₂×D₄×C₅₃	—	4	2	no	—
254	C₂×D₄×C₅₃	—	4	2	no	—
255	C₂×D₄×C₅₃	—	4	2	no	—
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	2	2	no	—
258	C₂²×C₄×C₅₃	—	2	2	no	—
259	C₂²×C₄×C₅₃	—	2	2	no	—
260	C₂²×C₄×C₅₃	—	2	2	no	—
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	2	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	4	no	—
270	C₂²×C₄×C₅₃	—	2	2	no	—
271	C₂²×C₄×C₅₃	—	2	2	no	—
272	C₂²×C₄×C₅₃	—	2	2	no	—
273	C₂²×C₄×C₅₃	—	2	4	no	—
274	C₂²×C₄×C₅₃	—	4	1	no	—
275	C₂²×C₄×C₅₃	—	4	1	no	—
276	C₂²×C₄×C₅₃	#41	1	4	yes	—
277	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₅₃	—	2	4	no	—
298	C₄⋊C₄×C₅₃	—	2	4	no	—
299	C₄⋊C₄×C₅₃	—	2	2	no	—
300	C₄⋊C₄×C₅₃	—	2	2	no	—
301	C₄⋊C₄×C₅₃	—	2	2	no	—
302	C₄⋊C₄×C₅₃	—	2	2	no	—
303	C₄⋊C₄×C₅₃	—	2	2	no	—
304	C₄⋊C₄×C₅₃	—	2	2	no	—
305	C₄⋊C₄×C₅₃	—	2	2	no	—
306	C₄⋊C₄×C₅₃	—	2	2	no	—
307	C₄⋊C₄×C₅₃	—	2	4	no	—
308	C₄⋊C₄×C₅₃	—	2	2	no	—
309	C₄⋊C₄×C₅₃	—	4	2	no	—
310	C₄⋊C₄×C₅₃	—	4	2	no	—
311	C₄⋊C₄×C₅₃	—	4	2	no	—
312	C₄⋊C₄×C₅₃	—	4	2	no	—
313	C₄⋊C₄×C₅₃	—	4	2	no	—
314	C₄⋊C₄×C₅₃	—	4	2	no	—
315	C₄⋊C₄×C₅₃	#41	1	4	yes	—
316	C₂²⋊C₄×C₅₃	—	2	4	no	—
317	C₂²⋊C₄×C₅₃	—	2	2	no	—
318	C₂²⋊C₄×C₅₃	—	2	4	no	—
319	C₂²⋊C₄×C₅₃	—	2	4	no	—
320	C₂²⋊C₄×C₅₃	—	2	4	no	—
321	C₂²⋊C₄×C₅₃	—	2	4	no	—
322	C₂²⋊C₄×C₅₃	—	2	4	no	—
323	C₂²⋊C₄×C₅₃	—	2	2	no	—
324	C₂²⋊C₄×C₅₃	—	2	2	no	—
325	C₂²⋊C₄×C₅₃	—	2	2	no	—
326	C₂²⋊C₄×C₅₃	—	2	2	no	—
327	C₂²⋊C₄×C₅₃	—	2	4	no	—
328	C₂²⋊C₄×C₅₃	—	2	4	no	—
329	C₂²⋊C₄×C₅₃	—	2	4	no	—
330	C₂²⋊C₄×C₅₃	—	2	4	no	—
331	C₂²⋊C₄×C₅₃	—	4	2	no	—
332	C₂²⋊C₄×C₅₃	—	4	2	no	—
333	C₂²⋊C₄×C₅₃	—	4	2	no	—
334	C₂²⋊C₄×C₅₃	—	4	2	no	—
335	C₂²⋊C₄×C₅₃	—	4	2	no	—
336	C₂²⋊C₄×C₅₃	—	4	2	no	—
337	C₂²⋊C₄×C₅₃	—	4	2	no	—
338	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
339	C₄²×C₅₃	—	2	2	no	—
340	C₄²×C₅₃	—	2	2	no	—
341	C₄²×C₅₃	—	2	2	no	—
342	C₄²×C₅₃	—	2	2	no	—
343	C₄²×C₅₃	—	2	2	no	—
344	C₄²×C₅₃	—	2	2	no	—
345	C₄²×C₅₃	—	2	4	no	—
346	C₄²×C₅₃	—	2	4	no	—
347	C₄²×C₅₃	—	2	4	no	—
348	C₄²×C₅₃	—	2	2	no	—
349	C₄²×C₅₃	—	2	2	no	—
350	C₄²×C₅₃	—	2	4	no	—
351	C₄²×C₅₃	—	2	2	no	—
352	C₄²×C₅₃	—	2	4	no	—
353	C₄²×C₅₃	—	2	4	no	—
354	C₄²×C₅₃	—	2	2	no	—
355	C₄²×C₅₃	—	4	1	no	—
356	C₄²×C₅₃	—	4	2	no	—
357	C₄²×C₅₃	#41	1	4	yes	—
358	C₄²×C₅₃	#41	1	4	yes	—
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	—	2	1	no	—
369	C₂³×C₅₃	—	2	1	no	—
370	C₂³×C₅₃	—	2	1	no	—
371	C₂³×C₅₃	—	2	2	no	—
372	C₂³×C₅₃	—	2	2	no	—
373	C₂³×C₅₃	—	2	2	no	—
374	C₂³×C₅₃	—	2	2	no	—
375	C₂³×C₅₃	—	2	2	no	—
376	C₂³×C₅₃	—	2	2	no	—
377	C₂³×C₅₃	—	2	2	no	—
378	C₂³×C₅₃	C₂×#41	1	2	yes	—
379	C₂³×C₅₃	C₂×#41	1	2	yes	—
380	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
381	Q₈×C₅₃	—	4	8	no	—
382	D₄×C₅₃	—	2	8	no	—
383	D₄×C₅₃	—	4	8	no	—
384	D₄×C₅₃	—	4	8	no	—
385	D₄×C₅₃	—	4	4	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	2	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	2	no	—
396	C₂×C₄×C₅₃	—	2	1	no	—
397	C₂×C₄×C₅₃	—	2	1	no	—
398	C₂×C₄×C₅₃	—	2	1	no	—
399	C₂×C₄×C₅₃	—	2	1	no	—
400	C₂×C₄×C₅₃	—	2	8	no	—
401	C₂×C₄×C₅₃	—	2	1	no	—
402	C₂×C₄×C₅₃	—	2	1	no	—
403	C₂×C₄×C₅₃	—	2	1	no	—
404	C₂×C₄×C₅₃	—	2	1	no	—
405	C₂×C₄×C₅₃	—	2	1	no	—
406	C₂×C₄×C₅₃	—	2	1	no	—
407	C₂×C₄×C₅₃	—	2	2	no	—
408	C₂×C₄×C₅₃	—	2	1	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	1	no	—
429	C₂×C₄×C₅₃	—	2	1	no	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	1	no	—
432	C₂×C₄×C₅₃	—	2	2	no	—
433	C₂×C₄×C₅₃	—	2	2	no	—
434	C₂×C₄×C₅₃	—	4	4	no	—
435	C₂×C₄×C₅₃	—	4	4	no	—
436	C₂×C₄×C₅₃	—	4	4	no	—
437	C₂×C₄×C₅₃	—	4	4	no	—
438	C₂×C₄×C₅₃	—	4	4	no	—
439	C₂×C₄×C₅₃	—	4	8	no	—
440	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
441	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
442	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
443	C₂×C₄×C₅₃	C₂×#41	1	4	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	C₂×#41	1	2	yes	—
448	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
449	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
450	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
451	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
452	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
453	#34800	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	4	1	no	—
465	C₂²×C₅₃	—	4	1	no	—
466	C₂²×C₅₃	—	4	1	no	—
467	C₂²×C₅₃	—	4	1	no	—
468	C₂²×C₅₃	—	4	2	no	—
469	C₂²×C₅₃	—	4	2	no	—
470	C₂²×C₅₃	—	4	2	no	—
471	C₂²×C₅₃	—	4	2	no	—
472	C₂²×C₅₃	—	4	2	no	—
473	C₂²×C₅₃	—	4	2	no	—
474	C₂²×C₅₃	—	4	2	no	—
475	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
476	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
477	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
478	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
479	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
480	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂²×C₅₃	#585	1	1	yes	characteristic
482	C₄×C₅₃	—	2	2	no	—
483	C₄×C₅₃	—	2	2	no	—
484	C₄×C₅₃	—	2	2	no	—
485	C₄×C₅₃	—	2	2	no	—
486	C₄×C₅₃	—	2	2	no	—
487	C₄×C₅₃	—	2	4	no	—
488	C₄×C₅₃	—	2	2	no	—
489	C₄×C₅₃	—	4	1	no	—
490	C₄×C₅₃	—	4	2	no	—
491	C₄×C₅₃	—	4	1	no	—
492	C₄×C₅₃	—	4	2	no	—
493	C₄×C₅₃	—	4	2	no	—
494	C₄×C₅₃	—	4	1	no	—
495	C₄×C₅₃	—	4	1	no	—
496	C₄×C₅₃	—	4	2	no	—
497	C₄×C₅₃	—	4	1	no	—
498	C₄×C₅₃	—	4	2	no	—
499	C₄×C₅₃	—	4	2	no	—
500	C₄×C₅₃	#529	1	4	yes	—
501	C₄×C₅₃	#555	1	4	yes	—
502	#2532	C₂×C₅₃	1	2	yes	complemented
503	#2526	C₂×C₅₃	1	2	yes	complemented
504	#2518	C₂×C₅₃	1	2	yes	complemented
505	#2513	C₂×C₅₃	1	1	yes	characteristic, complemented
506	#2508	C₂×C₅₃	1	1	yes	characteristic, complemented
507	#2500	C₂×C₅₃	1	1	yes	characteristic, complemented
508	#2497	C₂×C₅₃	1	1	yes	characteristic, complemented
509	#2491	C₂×C₅₃	1	1	yes	characteristic, complemented
510	#2485	C₂×C₅₃	1	1	yes	characteristic, complemented
511	#2459	C₂×C₅₃	1	2	yes	complemented
512	#2439	C₂×C₅₃	1	1	yes	characteristic, complemented
513	#2414	C₂×C₅₃	1	1	yes	characteristic
514	#2398	C₂×C₅₃	1	2	yes	complemented
515	#2392	C₂×C₅₃	1	2	yes	complemented
516	C₄×C₄⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
517	C₄×#124	C₂×C₅₃	1	2	yes	complemented
518	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
519	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
520	#2298	C₂×C₅₃	1	2	yes	complemented
521	#2293	C₂×C₅₃	1	1	yes	characteristic, complemented
522	#2283	C₂×C₅₃	1	1	yes	characteristic, complemented
523	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
524	C₄×#117	C₂×C₅₃	1	1	yes	characteristic, complemented
525	C₂×C₅₃	—	4	2	no	—
526	C₂×C₅₃	—	4	2	no	—
527	C₂×C₅₃	—	8	2	no	—
528	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
529	C₂×C₅₃	#3444	1	1	yes	characteristic
530	C₂×C₅₃	#3460	1	1	yes	characteristic
531	C₂×C₅₃	C₂×#555	1	1	yes	characteristic
532	C₂×C₅₃	#3475	1	1	yes	characteristic
533	C₂×C₅₃	#3480	1	1	yes	characteristic
534	C₂×C₅₃	#3481	1	1	yes	characteristic
535	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
536	C₂×#124	C₂²×C₅₃	1	2	yes	—
537	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
538	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
539	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
540	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
541	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
542	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
543	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
544	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
545	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
546	C₂×#117	C₂²×C₅₃	1	2	yes	—
547	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
548	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
549	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
550	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
551	#400	C₂²×C₅₃	1	2	yes	—
552	#400	C₂²×C₅₃	1	2	yes	—
553	#398	C₂²×C₅₃	1	2	yes	—
554	#397	C₂²×C₅₃	1	2	yes	—
555	#397	C₂²×C₅₃	1	2	yes	—
556	#397	C₂²×C₅₃	1	2	yes	—
557	#396	C₂²×C₅₃	1	2	yes	—
558	#396	C₂²×C₅₃	1	2	yes	—
559	#394	C₂²×C₅₃	1	2	yes	—
560	#394	C₂²×C₅₃	1	2	yes	—
561	#394	C₂²×C₅₃	1	2	yes	—
562	#394	C₂²×C₅₃	1	2	yes	—
563	#394	C₂²×C₅₃	1	2	yes	—
564	#393	C₂²×C₅₃	1	2	yes	—
565	#393	C₂²×C₅₃	1	2	yes	—
566	#392	C₂²×C₅₃	1	2	yes	—
567	#391	C₂²×C₅₃	1	2	yes	—
568	#391	C₂²×C₅₃	1	2	yes	—
569	#390	C₂²×C₅₃	1	1	yes	characteristic
570	#390	C₂²×C₅₃	1	2	yes	—
571	#390	C₂²×C₅₃	1	1	yes	characteristic
572	#390	C₂²×C₅₃	1	1	yes	characteristic
573	#390	C₂²×C₅₃	1	1	yes	characteristic
574	#389	C₂²×C₅₃	1	1	yes	characteristic
575	#389	C₂²×C₅₃	1	1	yes	characteristic
576	#389	C₂²×C₅₃	1	2	yes	—
577	#389	C₂²×C₅₃	1	1	yes	characteristic
578	#389	C₂²×C₅₃	1	1	yes	characteristic
579	#389	C₂²×C₅₃	1	1	yes	characteristic
580	#389	C₂²×C₅₃	1	1	yes	characteristic
581	#388	C₂²×C₅₃	1	2	yes	—
582	#388	C₂²×C₅₃	1	2	yes	—
583	#388	C₂²×C₅₃	1	2	yes	—
584	#388	C₂²×C₅₃	1	2	yes	—
585	#388	C₂²×C₅₃	1	2	yes	—
586	#388	C₂²×C₅₃	1	2	yes	—
587	#388	C₂²×C₅₃	1	2	yes	—
588	#388	C₂²×C₅₃	1	2	yes	—
589	#388	C₂²×C₅₃	1	2	yes	—
590	#388	C₂²×C₅₃	1	2	yes	—
591	#388	C₂²×C₅₃	1	2	yes	—
592	#388	C₂²×C₅₃	1	2	yes	—
593	#387	C₂²×C₅₃	1	2	yes	—
594	#387	C₂²×C₅₃	1	2	yes	—
595	#387	C₂²×C₅₃	1	2	yes	—
596	#387	C₂²×C₅₃	1	2	yes	—
597	#386	C₂²×C₅₃	1	2	yes	—
598	#386	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	1	yes	characteristic
602	#382	C₂²×C₅₃	1	1	yes	characteristic
603	#382	C₂²×C₅₃	1	2	yes	—
604	#381	C₂²×C₅₃	1	2	yes	—
605	#380	C₂²×C₅₃	1	1	yes	characteristic
606	#380	C₂²×C₅₃	1	1	yes	characteristic
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×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
615	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
616	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
617	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
618	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
619	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
620	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
621	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
622	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
623	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
624	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
625	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
626	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
627	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
628	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
629	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
630	#376	C₂²×C₅₃	1	2	yes	—
631	#376	C₂²×C₅₃	1	2	yes	—
632	C₄³	C₂²×C₅₃	1	1	yes	characteristic
633	C₄³	C₂²×C₅₃	1	2	yes	—
634	C₅₃	#34800	1	1	yes	characteristic, direct product factor, Sylow
635	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
636	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
637	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
638	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
639	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
640	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
641	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
642	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
643	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
646	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
647	C₄⋊Q₈	—	2	4	no	—
648	#124	—	2	8	no	—
649	#121	—	2	4	no	—
650	#121	—	2	4	no	—
651	C₄×Q₈	—	4	4	no	—
652	C₄×D₄	—	2	4	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	—	2	4	no	—
655	C₄×D₄	—	2	4	no	—
656	C₄×D₄	—	4	4	no	—
657	C₄×D₄	—	4	4	no	—
658	#117	—	2	4	no	—
659	#117	—	2	4	no	—
660	#117	—	2	8	no	—
661	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×C₄²	—	2	4	no	—
704	C₂×C₄²	—	2	4	no	—
705	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
706	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
707	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
708	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
709	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
710	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
714	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
723	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
734	#95	C₂³×C₅₃	1	1	yes	characteristic
735	#95	C₂³×C₅₃	1	1	yes	characteristic
736	#95	C₂³×C₅₃	1	1	yes	characteristic
737	#95	C₂³×C₅₃	1	1	yes	characteristic
738	#95	C₂³×C₅₃	1	1	yes	characteristic
739	#95	C₂³×C₅₃	1	2	yes	—
740	#95	C₂³×C₅₃	1	2	yes	—
741	#95	C₂³×C₅₃	1	2	yes	—
742	#95	C₂³×C₅₃	1	2	yes	—
743	#95	C₂³×C₅₃	1	2	yes	—
744	#95	C₂³×C₅₃	1	2	yes	—
745	#95	C₂³×C₅₃	1	2	yes	—
746	#95	C₂³×C₅₃	1	2	yes	—
747	#95	C₂³×C₅₃	1	2	yes	—
748	#95	C₂³×C₅₃	1	2	yes	—
749	#95	C₂³×C₅₃	1	2	yes	—
750	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
751	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
752	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
753	C₂×Q₈	—	2	4	no	—
754	C₂×Q₈	—	2	4	no	—
755	C₂×Q₈	—	4	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	2	no	—
767	C₂×D₄	—	4	2	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	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	4	no	—
786	C₂²×C₄	—	4	1	no	—
787	C₂²×C₄	—	4	1	no	—
788	C₂²×C₄	#41×C₅₃	1	4	yes	—
789	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
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	2	yes	—
806	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	4	no	—
814	C₄⋊C₄	—	2	2	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	—	2	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	#41×C₅₃	1	4	yes	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	4	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	4	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	—	4	2	no	—
845	C₂²⋊C₄	—	4	2	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	4	no	—
858	C₄²	—	2	4	no	—
859	C₄²	—	2	4	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	4	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	4	no	—
865	C₄²	—	2	4	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	4	2	no	—
868	C₄²	—	4	1	no	—
869	C₄²	#41×C₅₃	1	4	yes	—
870	C₄²	#41×C₅₃	1	4	yes	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	2	no	—
890	C₂³	C₂×#41×C₅₃	1	2	yes	—
891	C₂³	C₂×#41×C₅₃	1	2	yes	—
892	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
893	Q₈	—	4	8	no	—
894	D₄	—	2	8	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	8	no	—
897	D₄	—	4	4	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	8	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	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	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	4	4	no	—
947	C₂×C₄	—	4	4	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	4	no	—
951	C₂×C₄	—	4	8	no	—
952	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
953	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
954	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
955	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
956	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
957	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
958	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
959	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
960	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
961	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
962	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
963	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
964	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
965	C₂²	—	2	2	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
987	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
988	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
989	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
990	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
991	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
992	C₂²	C₅₃×#585	1	1	yes	characteristic
993	C₄	—	2	2	no	—
994	C₄	—	2	2	no	—
995	C₄	—	2	2	no	—
996	C₄	—	2	4	no	—
997	C₄	—	2	2	no	—
998	C₄	—	2	2	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	1	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	1	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	1	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	2	no	—
1009	C₄	—	4	1	no	—
1010	C₄	—	4	2	no	—
1011	C₄	C₅₃×#529	1	4	yes	—
1012	C₄	C₅₃×#555	1	4	yes	—
1013	C₂	—	4	2	no	—
1014	C₂	—	4	2	no	—
1015	C₂	—	8	2	no	—
1016	C₂	C₂×C₅₃×#529	1	1	yes	characteristic
1017	C₂	C₅₃×#3444	1	1	yes	characteristic
1018	C₂	C₅₃×#3460	1	1	yes	characteristic
1019	C₂	C₂×C₅₃×#555	1	1	yes	characteristic
1020	C₂	C₅₃×#3475	1	1	yes	characteristic
1021	C₂	C₅₃×#3480	1	1	yes	characteristic
1022	C₂	C₅₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
prime radical	C₅₃×#2414	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2532	C₂	semidirect
2. C₅₃×#2526	C₂	semidirect
3. C₅₃×#2518	C₂	semidirect
4. C₅₃×#2513	C₂	semidirect
5. C₅₃×#2508	C₂	semidirect
6. C₅₃×#2500	C₂	semidirect
7. C₅₃×#2497	C₂	semidirect
8. C₅₃×#2491	C₂	semidirect
9. C₅₃×#2485	C₂	semidirect
10. C₅₃×#2459	C₂	semidirect
11. C₅₃×#2439	C₂	semidirect
13. C₅₃×#2398	C₂	semidirect
14. C₅₃×#2392	C₂	semidirect
15. C₄×C₄⋊Q₈×C₅₃	C₂	semidirect
16. C₄×#124×C₅₃	C₂	semidirect
17. C₄×#121×C₅₃	C₂	semidirect
18. C₄×#121×C₅₃	C₂	semidirect
19. C₅₃×#2298	C₂	semidirect
20. C₅₃×#2293	C₂	semidirect
21. C₅₃×#2283	C₂	semidirect
22. C₄²×D₄×C₅₃	C₂	semidirect
23. C₄×#117×C₅₃	C₂	semidirect
453. #34800	C₅₃	direct (N × H)
502. #2532	C₂×C₅₃	semidirect
503. #2526	C₂×C₅₃	semidirect
504. #2518	C₂×C₅₃	semidirect
505. #2513	C₂×C₅₃	semidirect
506. #2508	C₂×C₅₃	semidirect
507. #2500	C₂×C₅₃	semidirect
508. #2497	C₂×C₅₃	semidirect
509. #2491	C₂×C₅₃	semidirect
510. #2485	C₂×C₅₃	semidirect
511. #2459	C₂×C₅₃	semidirect
512. #2439	C₂×C₅₃	semidirect
514. #2398	C₂×C₅₃	semidirect
515. #2392	C₂×C₅₃	semidirect
516. C₄×C₄⋊Q₈	C₂×C₅₃	semidirect
517. C₄×#124	C₂×C₅₃	semidirect
518. C₄×#121	C₂×C₅₃	semidirect
519. C₄×#121	C₂×C₅₃	semidirect
520. #2298	C₂×C₅₃	semidirect
521. #2293	C₂×C₅₃	semidirect
522. #2283	C₂×C₅₃	semidirect
523. C₄²×D₄	C₂×C₅₃	semidirect
524. C₄×#117	C₂×C₅₃	semidirect
634. C₅₃	#34800	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×#2532	2
C₅₃×#2526	2
C₅₃×#2518	2
C₅₃×#2513	2
C₅₃×#2508	2
C₅₃×#2500	2
C₅₃×#2497	2
C₅₃×#2491	2
C₅₃×#2485	2
C₅₃×#2459	2
C₅₃×#2439	2
C₅₃×#2414	2
C₅₃×#2398	2
C₅₃×#2392	2
C₄×C₄⋊Q₈×C₅₃	2
C₄×#124×C₅₃	2
C₄×#121×C₅₃	2
C₅₃×#2298	2
C₅₃×#2293	2
C₅₃×#2283	2
C₄²×D₄×C₅₃	2
C₄×#117×C₅₃	2
#34800	53

Subgroups — C53×#34800 #27242312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34800 #27242312