Subgroups — C₅₃×#36570 #27244082

Order 13568.

1976 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2587	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2579	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2574	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2522	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2508	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2450	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2449	C₂	1	2	yes	maximal, complemented
16	C₅₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2368	C₂	1	2	yes	maximal, complemented
18	C₅₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2349	C₂	1	2	yes	maximal, complemented
20	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic
21	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic
22	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
29	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×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	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#400	C₂²	1	2	yes	—
42	C₅₃×#399	C₂²	1	2	yes	—
43	C₅₃×#398	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×#396	C₂²	1	2	yes	—
48	C₅₃×#396	C₂²	1	2	yes	—
49	C₅₃×#396	C₂²	1	2	yes	—
50	C₅₃×#396	C₂²	1	2	yes	—
51	C₅₃×#395	C₂²	1	2	yes	—
52	C₅₃×#393	C₂²	1	2	yes	—
53	C₅₃×#391	C₂²	1	2	yes	—
54	C₅₃×#391	C₂²	1	2	yes	—
55	C₅₃×#390	C₂²	1	1	yes	characteristic
56	C₅₃×#390	C₂²	1	1	yes	characteristic
57	C₅₃×#390	C₂²	1	1	yes	characteristic
58	C₅₃×#389	C₂²	1	2	yes	—
59	C₅₃×#389	C₂²	1	1	yes	characteristic
60	C₅₃×#389	C₂²	1	1	yes	characteristic
61	C₅₃×#389	C₂²	1	1	yes	characteristic
62	C₅₃×#389	C₂²	1	1	yes	characteristic
63	C₅₃×#389	C₂²	1	1	yes	characteristic
64	C₅₃×#389	C₂²	1	1	yes	characteristic
65	C₅₃×#389	C₂²	1	2	yes	—
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×#389	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×#387	C₂²	1	2	yes	—
75	C₅₃×#387	C₂²	1	2	yes	—
76	C₅₃×#387	C₂²	1	2	yes	—
77	C₅₃×#387	C₂²	1	2	yes	—
78	C₅₃×#387	C₂²	1	2	yes	—
79	C₅₃×#387	C₂²	1	2	yes	—
80	C₅₃×#387	C₂²	1	2	yes	—
81	C₅₃×#387	C₂²	1	2	yes	—
82	C₅₃×#386	C₂²	1	2	yes	—
83	C₅₃×#386	C₂²	1	2	yes	—
84	C₅₃×#386	C₂²	1	2	yes	—
85	C₅₃×#385	C₂²	1	2	yes	—
86	C₅₃×#385	C₂²	1	2	yes	—
87	C₅₃×#385	C₂²	1	2	yes	—
88	C₅₃×#385	C₂²	1	2	yes	—
89	C₅₃×#385	C₂²	1	2	yes	—
90	C₅₃×#385	C₂²	1	2	yes	—
91	C₅₃×#385	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×#384	C₂²	1	1	yes	characteristic
96	C₅₃×#382	C₂²	1	1	yes	characteristic
97	C₅₃×#382	C₂²	1	2	yes	—
98	C₅₃×#382	C₂²	1	1	yes	characteristic
99	C₅₃×#380	C₂²	1	2	yes	—
100	C₅₃×#380	C₂²	1	2	yes	—
101	C₅₃×#380	C₂²	1	1	yes	characteristic
102	C₅₃×#380	C₂²	1	1	yes	characteristic
103	C₅₃×#380	C₂²	1	1	yes	characteristic
104	C₅₃×#380	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
113	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊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	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
120	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
121	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×#95×C₅₃	C₂²	1	2	yes	—
123	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
132	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₅₃	—	4	2	no	—
137	#125×C₅₃	—	2	4	no	—
138	#125×C₅₃	—	4	2	no	—
139	C₂²⋊Q₈×C₅₃	—	2	8	no	—
140	C₂²⋊Q₈×C₅₃	—	4	4	no	—
141	#121×C₅₃	Q₈	1	8	yes	complemented
142	C₄×D₄×C₅₃	—	2	4	no	—
143	C₄×D₄×C₅₃	—	2	8	no	—
144	C₄×D₄×C₅₃	—	4	4	no	—
145	C₄×D₄×C₅₃	—	4	4	no	—
146	C₄×D₄×C₅₃	—	4	2	no	—
147	C₄×D₄×C₅₃	—	4	2	no	—
148	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
149	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
164	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊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	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	2	yes	—
191	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
194	C₂×C₄²×C₅₃	—	2	4	no	—
195	C₂×C₄²×C₅₃	—	4	2	no	—
196	C₂×C₄²×C₅₃	—	4	2	no	—
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	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	1	yes	characteristic
208	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
210	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
211	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
212	#95×C₅₃	C₂³	1	1	yes	characteristic
213	#95×C₅₃	C₂³	1	1	yes	characteristic
214	#95×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
240	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₅₃	—	2	4	no	—
242	C₂×Q₈×C₅₃	—	4	2	no	—
243	C₂×Q₈×C₅₃	—	4	2	no	—
244	C₂×D₄×C₅₃	—	2	4	no	—
245	C₂×D₄×C₅₃	—	2	4	no	—
246	C₂×D₄×C₅₃	—	2	2	no	—
247	C₂×D₄×C₅₃	—	2	2	no	—
248	C₂×D₄×C₅₃	C₂×Q₈	1	8	yes	—
249	C₂×D₄×C₅₃	C₂×Q₈	1	4	yes	—
250	C₂²×C₄×C₅₃	—	2	2	no	—
251	C₂²×C₄×C₅₃	—	2	2	no	—
252	C₂²×C₄×C₅₃	—	2	2	no	—
253	C₂²×C₄×C₅₃	—	2	2	no	—
254	C₂²×C₄×C₅₃	—	2	2	no	—
255	C₂²×C₄×C₅₃	—	2	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	4	no	—
263	C₂²×C₄×C₅₃	—	2	4	no	—
264	C₂²×C₄×C₅₃	—	2	4	no	—
265	C₂²×C₄×C₅₃	—	4	1	no	—
266	C₂²×C₄×C₅₃	—	4	1	no	—
267	C₂²×C₄×C₅₃	—	4	1	no	—
268	C₂²×C₄×C₅₃	—	4	1	no	—
269	C₂²×C₄×C₅₃	—	4	1	no	—
270	C₂²×C₄×C₅₃	—	4	1	no	—
271	C₂²×C₄×C₅₃	—	4	1	no	—
272	C₂²×C₄×C₅₃	—	4	2	no	—
273	C₂²×C₄×C₅₃	—	4	2	no	—
274	C₂²×C₄×C₅₃	—	4	2	no	—
275	C₂²×C₄×C₅₃	—	4	2	no	—
276	C₂²×C₄×C₅₃	—	4	2	no	—
277	C₂²×C₄×C₅₃	—	4	2	no	—
278	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	—
279	C₂²×C₄×C₅₃	#41	1	4	yes	—
280	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
287	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	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	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	2	no	—
308	C₄⋊C₄×C₅₃	—	2	4	no	—
309	C₄⋊C₄×C₅₃	—	2	2	no	—
310	C₄⋊C₄×C₅₃	—	2	4	no	—
311	C₄⋊C₄×C₅₃	—	2	4	no	—
312	C₄⋊C₄×C₅₃	—	2	4	no	—
313	C₄⋊C₄×C₅₃	—	2	4	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	2	no	—
318	C₄⋊C₄×C₅₃	—	2	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	—
331	C₄⋊C₄×C₅₃	#41	1	4	yes	—
332	C₂²⋊C₄×C₅₃	—	2	4	no	—
333	C₂²⋊C₄×C₅₃	—	2	4	no	—
334	C₂²⋊C₄×C₅₃	—	2	4	no	—
335	C₂²⋊C₄×C₅₃	—	2	4	no	—
336	C₂²⋊C₄×C₅₃	—	2	4	no	—
337	C₂²⋊C₄×C₅₃	—	2	4	no	—
338	C₂²⋊C₄×C₅₃	—	2	4	no	—
339	C₂²⋊C₄×C₅₃	—	4	2	no	—
340	C₂²⋊C₄×C₅₃	—	4	2	no	—
341	C₂²⋊C₄×C₅₃	—	4	2	no	—
342	C₂²⋊C₄×C₅₃	—	4	2	no	—
343	C₂²⋊C₄×C₅₃	—	4	2	no	—
344	C₂²⋊C₄×C₅₃	C₂×Q₈	1	8	yes	—
345	C₄²×C₅₃	—	2	2	no	—
346	C₄²×C₅₃	—	2	2	no	—
347	C₄²×C₅₃	—	2	2	no	—
348	C₄²×C₅₃	—	2	4	no	—
349	C₄²×C₅₃	—	2	2	no	—
350	C₄²×C₅₃	—	2	2	no	—
351	C₄²×C₅₃	—	2	2	no	—
352	C₄²×C₅₃	—	2	2	no	—
353	C₄²×C₅₃	—	4	1	no	—
354	C₄²×C₅₃	—	4	1	no	—
355	C₄²×C₅₃	—	4	1	no	—
356	C₄²×C₅₃	—	4	1	no	—
357	C₄²×C₅₃	—	4	2	no	—
358	C₄²×C₅₃	—	4	2	no	—
359	C₄²×C₅₃	#41	1	4	yes	—
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	2	no	—
365	C₂³×C₅₃	—	2	2	no	—
366	C₂³×C₅₃	—	2	2	no	—
367	C₂³×C₅₃	—	2	2	no	—
368	C₂³×C₅₃	—	2	2	no	—
369	C₂³×C₅₃	—	2	2	no	—
370	C₂³×C₅₃	C₂²×Q₈	1	4	yes	—
371	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
372	C₂³×C₅₃	C₂×#41	1	2	yes	—
373	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
374	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
375	Q₈×C₅₃	—	8	4	no	—
376	D₄×C₅₃	—	2	16	no	—
377	D₄×C₅₃	—	2	8	no	—
378	C₂×C₄×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	2	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	2	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	1	no	—
400	C₂×C₄×C₅₃	—	2	2	no	—
401	C₂×C₄×C₅₃	—	2	2	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	2	no	—
407	C₂×C₄×C₅₃	—	2	2	no	—
408	C₂×C₄×C₅₃	—	2	2	no	—
409	C₂×C₄×C₅₃	—	2	2	no	—
410	C₂×C₄×C₅₃	—	2	2	no	—
411	C₂×C₄×C₅₃	—	2	1	no	—
412	C₂×C₄×C₅₃	—	2	1	no	—
413	C₂×C₄×C₅₃	—	2	1	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	1	no	—
418	C₂×C₄×C₅₃	—	2	1	no	—
419	C₂×C₄×C₅₃	—	2	1	no	—
420	C₂×C₄×C₅₃	—	2	2	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	2	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	1	no	—
426	C₂×C₄×C₅₃	—	2	1	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	1	no	—
429	C₂×C₄×C₅₃	—	2	2	no	—
430	C₂×C₄×C₅₃	—	2	2	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	4	no	—
436	C₂×C₄×C₅₃	—	8	4	no	—
437	C₂×C₄×C₅₃	—	8	4	no	—
438	C₂×C₄×C₅₃	—	8	4	no	—
439	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
440	C₂×C₄×C₅₃	C₂²×Q₈	1	4	yes	—
441	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
442	C₂×C₄×C₅₃	C₂×#41	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	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	H(5,𝔽₂)	1	2	yes	—
451	#36570	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	4	no	—
459	C₂²×C₅₃	—	2	4	no	—
460	C₂²×C₅₃	—	2	4	no	—
461	C₂²×C₅₃	—	4	2	no	—
462	C₂²×C₅₃	—	4	2	no	—
463	C₂²×C₅₃	—	4	2	no	—
464	C₂²×C₅₃	—	4	2	no	—
465	C₂²×C₅₃	#554	1	4	yes	—
466	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
467	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
468	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
469	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
470	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂²×C₅₃	#585	1	1	yes	characteristic
473	C₄×C₅₃	—	2	2	no	—
474	C₄×C₅₃	—	2	2	no	—
475	C₄×C₅₃	—	2	2	no	—
476	C₄×C₅₃	—	2	4	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	—	2	2	no	—
482	C₄×C₅₃	—	4	2	no	—
483	C₄×C₅₃	—	4	2	no	—
484	C₄×C₅₃	—	4	1	no	—
485	C₄×C₅₃	—	4	2	no	—
486	C₄×C₅₃	—	4	1	no	—
487	C₄×C₅₃	—	4	1	no	—
488	C₄×C₅₃	—	4	2	no	—
489	C₄×C₅₃	—	4	1	no	—
490	C₄×C₅₃	—	4	1	no	—
491	C₄×C₅₃	—	4	2	no	—
492	C₄×C₅₃	—	4	2	no	—
493	C₄×C₅₃	#554	1	4	yes	—
494	#2857	C₂×C₅₃	1	1	yes	characteristic, complemented
495	#2851	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#2851	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#2587	C₂×C₅₃	1	2	yes	complemented
498	#2579	C₂×C₅₃	1	2	yes	complemented
499	#2574	C₂×C₅₃	1	2	yes	complemented
500	#2566	C₂×C₅₃	1	1	yes	characteristic, complemented
501	#2550	C₂×C₅₃	1	1	yes	characteristic, complemented
502	#2522	C₂×C₅₃	1	2	yes	complemented
503	#2508	C₂×C₅₃	1	1	yes	characteristic, complemented
504	#2507	C₂×C₅₃	1	1	yes	characteristic, complemented
505	#2454	C₂×C₅₃	1	1	yes	characteristic, complemented
506	#2452	C₂×C₅₃	1	1	yes	characteristic, complemented
507	#2450	C₂×C₅₃	1	2	yes	complemented
508	#2449	C₂×C₅₃	1	2	yes	complemented
509	#2370	C₂×C₅₃	1	1	yes	characteristic, complemented
510	#2368	C₂×C₅₃	1	2	yes	complemented
511	#2349	C₂×C₅₃	1	1	yes	characteristic, complemented
512	#2349	C₂×C₅₃	1	2	yes	complemented
513	C₄×#121	C₂×C₅₃	1	1	yes	characteristic
514	C₄×#121	C₂×C₅₃	1	1	yes	characteristic
515	C₄×#121	C₂×C₅₃	1	1	yes	characteristic
516	C₂×C₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
517	C₂×C₅₃	—	2	4	no	—
518	C₂×C₅₃	—	4	4	no	—
519	C₂×C₅₃	#3444	1	1	yes	characteristic
520	C₂×C₅₃	C₂×#554	1	1	yes	characteristic
521	C₂×C₅₃	C₂×#554	1	1	yes	characteristic
522	C₂×C₅₃	Q₈×#41	1	1	yes	characteristic
523	C₂×C₅₃	#3494	1	1	yes	characteristic
524	C₂×C₅₃	#3505	1	1	yes	characteristic
525	C₂×C₅₃	#3519	1	1	yes	characteristic
526	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
527	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
528	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
529	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
530	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
531	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
532	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
533	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
534	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
535	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
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×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
540	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
541	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
542	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
543	#400	C₂²×C₅₃	1	2	yes	—
544	#399	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	#396	C₂²×C₅₃	1	2	yes	—
552	#396	C₂²×C₅₃	1	2	yes	—
553	#395	C₂²×C₅₃	1	2	yes	—
554	#393	C₂²×C₅₃	1	2	yes	—
555	#391	C₂²×C₅₃	1	2	yes	—
556	#391	C₂²×C₅₃	1	2	yes	—
557	#390	C₂²×C₅₃	1	1	yes	characteristic
558	#390	C₂²×C₅₃	1	1	yes	characteristic
559	#390	C₂²×C₅₃	1	1	yes	characteristic
560	#389	C₂²×C₅₃	1	2	yes	—
561	#389	C₂²×C₅₃	1	2	yes	—
562	#389	C₂²×C₅₃	1	2	yes	—
563	#389	C₂²×C₅₃	1	1	yes	characteristic
564	#389	C₂²×C₅₃	1	1	yes	characteristic
565	#389	C₂²×C₅₃	1	1	yes	characteristic
566	#389	C₂²×C₅₃	1	1	yes	characteristic
567	#389	C₂²×C₅₃	1	1	yes	characteristic
568	#389	C₂²×C₅₃	1	1	yes	characteristic
569	#389	C₂²×C₅₃	1	2	yes	—
570	#389	C₂²×C₅₃	1	1	yes	characteristic
571	#389	C₂²×C₅₃	1	1	yes	characteristic
572	#389	C₂²×C₅₃	1	1	yes	characteristic
573	#388	C₂²×C₅₃	1	2	yes	—
574	#388	C₂²×C₅₃	1	2	yes	—
575	#388	C₂²×C₅₃	1	2	yes	—
576	#387	C₂²×C₅₃	1	2	yes	—
577	#387	C₂²×C₅₃	1	2	yes	—
578	#387	C₂²×C₅₃	1	2	yes	—
579	#387	C₂²×C₅₃	1	2	yes	—
580	#387	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	#386	C₂²×C₅₃	1	2	yes	—
585	#386	C₂²×C₅₃	1	2	yes	—
586	#386	C₂²×C₅₃	1	2	yes	—
587	#385	C₂²×C₅₃	1	2	yes	—
588	#385	C₂²×C₅₃	1	2	yes	—
589	#385	C₂²×C₅₃	1	2	yes	—
590	#385	C₂²×C₅₃	1	2	yes	—
591	#385	C₂²×C₅₃	1	2	yes	—
592	#385	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	#384	C₂²×C₅₃	1	1	yes	characteristic
598	#382	C₂²×C₅₃	1	1	yes	characteristic
599	#382	C₂²×C₅₃	1	2	yes	—
600	#382	C₂²×C₅₃	1	1	yes	characteristic
601	#380	C₂²×C₅₃	1	2	yes	—
602	#380	C₂²×C₅₃	1	2	yes	—
603	#380	C₂²×C₅₃	1	1	yes	characteristic
604	#380	C₂²×C₅₃	1	1	yes	characteristic
605	#380	C₂²×C₅₃	1	1	yes	characteristic
606	#380	C₂²×C₅₃	1	2	yes	—
607	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
608	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
609	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
610	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
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×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
619	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
620	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
621	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
622	C₂×#95	C₂²×C₅₃	1	2	yes	—
623	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
624	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
625	C₅₃	#36570	1	1	yes	characteristic, direct product factor, Sylow
626	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
627	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
628	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
633	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
634	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
636	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
637	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
638	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
639	C₄⋊Q₈	—	4	2	no	—
640	#125	—	2	4	no	—
641	#125	—	4	2	no	—
642	C₂²⋊Q₈	—	2	8	no	—
643	C₂²⋊Q₈	—	4	4	no	—
644	#121	Q₈×C₅₃	1	8	yes	complemented
645	C₄×D₄	—	2	8	no	—
646	C₄×D₄	—	2	4	no	—
647	C₄×D₄	—	4	2	no	—
648	C₄×D₄	—	4	2	no	—
649	C₄×D₄	—	4	4	no	—
650	C₄×D₄	—	4	4	no	—
651	C₂×C₄⋊C₄	—	2	4	no	—
652	C₂×C₄⋊C₄	—	2	4	no	—
653	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
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	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	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	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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	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×C₄²	—	2	4	no	—
698	C₂×C₄²	—	4	2	no	—
699	C₂×C₄²	—	4	2	no	—
700	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
701	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
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	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	1	yes	characteristic
714	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
715	#95	C₂³×C₅₃	1	1	yes	characteristic
716	#95	C₂³×C₅₃	1	1	yes	characteristic
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	2	yes	—
743	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
744	C₂×Q₈	—	2	4	no	—
745	C₂×Q₈	—	4	2	no	—
746	C₂×Q₈	—	4	2	no	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	C₂×Q₈×C₅₃	1	8	yes	—
752	C₂×D₄	C₂×Q₈×C₅₃	1	4	yes	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	1	no	—
772	C₂²×C₄	—	4	1	no	—
773	C₂²×C₄	—	4	1	no	—
774	C₂²×C₄	—	4	1	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	C₂×Q₈×C₅₃	1	4	yes	—
782	C₂²×C₄	#41×C₅₃	1	4	yes	—
783	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
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	2	no	—
813	C₄⋊C₄	—	2	4	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	2	4	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	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	—	4	2	no	—
833	C₄⋊C₄	C₂×Q₈×C₅₃	1	4	yes	—
834	C₄⋊C₄	#41×C₅₃	1	4	yes	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	4	no	—
839	C₂²⋊C₄	—	2	4	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	4	no	—
842	C₂²⋊C₄	—	4	2	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	C₂×Q₈×C₅₃	1	8	yes	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	4	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	4	1	no	—
857	C₄²	—	4	1	no	—
858	C₄²	—	4	1	no	—
859	C₄²	—	4	1	no	—
860	C₄²	—	4	2	no	—
861	C₄²	—	4	2	no	—
862	C₄²	#41×C₅₃	1	4	yes	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	C₂²×Q₈×C₅₃	1	4	yes	—
874	C₂³	C₂²×Q₈×C₅₃	1	2	yes	—
875	C₂³	C₂×#41×C₅₃	1	2	yes	—
876	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
877	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
878	Q₈	—	8	4	no	—
879	D₄	—	2	16	no	—
880	D₄	—	2	8	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	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	2	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	1	no	—
900	C₂×C₄	—	2	8	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	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	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	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	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	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	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	4	no	—
939	C₂×C₄	—	8	4	no	—
940	C₂×C₄	—	8	4	no	—
941	C₂×C₄	—	8	4	no	—
942	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
943	C₂×C₄	C₂²×Q₈×C₅₃	1	4	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	C₂×#41×C₅₃	1	2	yes	—
950	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
951	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
952	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
953	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
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	4	no	—
961	C₂²	—	2	4	no	—
962	C₂²	—	2	4	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	C₅₃×#554	1	4	yes	—
968	C₂²	C₂³×Q₈×C₅₃	1	1	yes	characteristic
969	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
970	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
971	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
972	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
973	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
974	C₂²	C₅₃×#585	1	1	yes	characteristic
975	C₄	—	2	2	no	—
976	C₄	—	2	4	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	—	2	2	no	—
983	C₄	—	2	2	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	C₅₃×#554	1	4	yes	—
996	C₂	—	2	4	no	—
997	C₂	—	4	4	no	—
998	C₂	C₅₃×#3444	1	1	yes	characteristic
999	C₂	C₂×C₅₃×#554	1	1	yes	characteristic
1000	C₂	C₂×C₅₃×#554	1	1	yes	characteristic
1001	C₂	Q₈×#41×C₅₃	1	1	yes	characteristic
1002	C₂	C₅₃×#3494	1	1	yes	characteristic
1003	C₂	C₅₃×#3505	1	1	yes	characteristic
1004	C₂	C₅₃×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂×#121×C₅₃	C₂²
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×#2857	C₂	semidirect
2. C₅₃×#2851	C₂	semidirect
3. C₅₃×#2851	C₂	semidirect
4. C₅₃×#2587	C₂	semidirect
5. C₅₃×#2579	C₂	semidirect
6. C₅₃×#2574	C₂	semidirect
7. C₅₃×#2566	C₂	semidirect
8. C₅₃×#2550	C₂	semidirect
9. C₅₃×#2522	C₂	semidirect
10. C₅₃×#2508	C₂	semidirect
11. C₅₃×#2507	C₂	semidirect
12. C₅₃×#2454	C₂	semidirect
13. C₅₃×#2452	C₂	semidirect
14. C₅₃×#2450	C₂	semidirect
15. C₅₃×#2449	C₂	semidirect
16. C₅₃×#2370	C₂	semidirect
17. C₅₃×#2368	C₂	semidirect
18. C₅₃×#2349	C₂	semidirect
19. C₅₃×#2349	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₅₃	C₂	semidirect
141. #121×C₅₃	Q₈	semidirect
451. #36570	C₅₃	direct (N × H)
494. #2857	C₂×C₅₃	semidirect
495. #2851	C₂×C₅₃	semidirect
496. #2851	C₂×C₅₃	semidirect
497. #2587	C₂×C₅₃	semidirect
498. #2579	C₂×C₅₃	semidirect
499. #2574	C₂×C₅₃	semidirect
500. #2566	C₂×C₅₃	semidirect
501. #2550	C₂×C₅₃	semidirect
502. #2522	C₂×C₅₃	semidirect
503. #2508	C₂×C₅₃	semidirect
504. #2507	C₂×C₅₃	semidirect
505. #2454	C₂×C₅₃	semidirect
506. #2452	C₂×C₅₃	semidirect
507. #2450	C₂×C₅₃	semidirect
508. #2449	C₂×C₅₃	semidirect
509. #2370	C₂×C₅₃	semidirect
510. #2368	C₂×C₅₃	semidirect
511. #2349	C₂×C₅₃	semidirect
512. #2349	C₂×C₅₃	semidirect
516. C₂×C₄×C₄⋊C₄	C₂×C₅₃	semidirect
625. C₅₃	#36570	direct (N × H)
644. #121	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×#2857	2
C₅₃×#2851	2
C₅₃×#2587	2
C₅₃×#2579	2
C₅₃×#2574	2
C₅₃×#2566	2
C₅₃×#2550	2
C₅₃×#2522	2
C₅₃×#2508	2
C₅₃×#2507	2
C₅₃×#2454	2
C₅₃×#2452	2
C₅₃×#2450	2
C₅₃×#2449	2
C₅₃×#2370	2
C₅₃×#2368	2
C₅₃×#2349	2
C₄×#121×C₅₃	2
C₂×C₄×C₄⋊C₄×C₅₃	2
#36570	53

Subgroups — C53×#36570 #27244082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36570 #27244082