Subgroups — C₅₃×#35034 #27242546

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2852	C₂	1	2	yes	maximal, complemented
2	C₅₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2847	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#2646	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2639	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2622	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2578	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2577	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2560	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2559	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2531	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2530	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2477	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2476	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2321	C₂	1	2	yes	maximal, complemented
18	C₅₃×#2290	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
22	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#120×C₅₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
30	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
31	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#400	C₂²	1	2	yes	complemented
36	C₅₃×#400	C₂²	1	2	yes	complemented
37	C₅₃×#400	C₂²	1	2	yes	complemented
38	C₅₃×#398	C₂²	1	2	yes	complemented
39	C₅₃×#398	C₂²	1	2	yes	complemented
40	C₅₃×#397	C₂²	1	2	yes	—
41	C₅₃×#397	C₂²	1	2	yes	—
42	C₅₃×#397	C₂²	1	2	yes	—
43	C₅₃×#397	C₂²	1	2	yes	—
44	C₅₃×#397	C₂²	1	2	yes	complemented
45	C₅₃×#394	C₂²	1	2	yes	—
46	C₅₃×#394	C₂²	1	2	yes	—
47	C₅₃×#394	C₂²	1	2	yes	—
48	C₅₃×#394	C₂²	1	2	yes	—
49	C₅₃×#394	C₂²	1	2	yes	complemented
50	C₅₃×#393	C₂²	1	2	yes	complemented
51	C₅₃×#391	C₂²	1	2	yes	complemented
52	C₅₃×#390	C₂²	1	2	yes	—
53	C₅₃×#390	C₂²	1	2	yes	—
54	C₅₃×#389	C₂²	1	2	yes	complemented
55	C₅₃×#388	C₂²	1	2	yes	—
56	C₅₃×#388	C₂²	1	2	yes	—
57	C₅₃×#388	C₂²	1	2	yes	—
58	C₅₃×#388	C₂²	1	2	yes	—
59	C₅₃×#388	C₂²	1	2	yes	complemented
60	C₅₃×#388	C₂²	1	2	yes	complemented
61	C₅₃×#388	C₂²	1	2	yes	complemented
62	C₅₃×#388	C₂²	1	2	yes	complemented
63	C₅₃×#388	C₂²	1	2	yes	complemented
64	C₅₃×#388	C₂²	1	2	yes	complemented
65	C₅₃×#387	C₂²	1	2	yes	complemented
66	C₅₃×#387	C₂²	1	2	yes	complemented
67	C₅₃×#387	C₂²	1	2	yes	complemented
68	C₅₃×#387	C₂²	1	2	yes	complemented
69	C₅₃×#387	C₂²	1	2	yes	complemented
70	C₅₃×#387	C₂²	1	2	yes	complemented
71	C₅₃×#387	C₂²	1	2	yes	complemented
72	C₅₃×#387	C₂²	1	2	yes	complemented
73	C₅₃×#386	C₂²	1	2	yes	—
74	C₅₃×#386	C₂²	1	2	yes	—
75	C₅₃×#386	C₂²	1	2	yes	—
76	C₅₃×#386	C₂²	1	2	yes	—
77	C₅₃×#386	C₂²	1	2	yes	—
78	C₅₃×#386	C₂²	1	2	yes	—
79	C₅₃×#386	C₂²	1	2	yes	—
80	C₅₃×#386	C₂²	1	2	yes	—
81	C₅₃×#386	C₂²	1	2	yes	complemented
82	C₅₃×#385	C₂²	1	2	yes	—
83	C₅₃×#385	C₂²	1	2	yes	—
84	C₅₃×#385	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	complemented
89	C₅₃×#383	C₂²	1	2	yes	complemented
90	C₅₃×#380	C₂²	1	1	yes	characteristic
91	C₅₃×#380	C₂²	1	1	yes	characteristic
92	C₅₃×#380	C₂²	1	1	yes	characteristic
93	C₅₃×#380	C₂²	1	1	yes	characteristic
94	C₅₃×#380	C₂²	1	1	yes	characteristic
95	C₅₃×#380	C₂²	1	1	yes	characteristic
96	C₅₃×#379	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
104	C₅₃×#376	C₂²	1	2	yes	complemented
105	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
106	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
107	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅₃	—	2	4	no	—
114	C₂³×C₄×C₅₃	—	4	2	no	—
115	C₂³×C₄×C₅₃	—	4	2	no	—
116	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
127	#126×C₅₃	—	4	4	no	—
128	C₂²⋊Q₈×C₅₃	—	2	4	no	—
129	C₂²⋊Q₈×C₅₃	—	4	2	no	—
130	C₂²⋊Q₈×C₅₃	—	4	2	no	—
131	#121×C₅₃	—	2	4	no	—
132	#121×C₅₃	—	4	2	no	—
133	#121×C₅₃	—	4	2	no	—
134	#120×C₅₃	—	2	8	no	—
135	C₄×D₄×C₅₃	—	2	8	no	—
136	#117×C₅₃	—	4	4	no	—
137	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
154	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
155	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
173	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₅₃	—	4	2	no	—
179	C₂×C₄²×C₅₃	—	4	2	no	—
180	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
187	#95×C₅₃	C₂³	1	2	yes	—
188	#95×C₅₃	C₂³	1	2	yes	—
189	#95×C₅₃	C₂³	1	2	yes	—
190	#95×C₅₃	C₂³	1	2	yes	—
191	#95×C₅₃	C₂³	1	2	yes	—
192	#95×C₅₃	C₂³	1	2	yes	—
193	#95×C₅₃	C₂³	1	2	yes	—
194	#95×C₅₃	C₂³	1	2	yes	—
195	#95×C₅₃	C₂³	1	2	yes	—
196	#95×C₅₃	C₂³	1	2	yes	—
197	#95×C₅₃	C₂³	1	2	yes	—
198	#95×C₅₃	C₂³	1	2	yes	—
199	#95×C₅₃	C₂³	1	2	yes	—
200	#95×C₅₃	C₂³	1	2	yes	—
201	#95×C₅₃	C₂³	1	2	yes	—
202	#95×C₅₃	C₂³	1	2	yes	—
203	#95×C₅₃	C₂³	1	2	yes	—
204	#95×C₅₃	C₂³	1	2	yes	—
205	#95×C₅₃	C₂³	1	2	yes	—
206	#95×C₅₃	C₂³	1	2	yes	—
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	C₂⁴×C₅₃	—	2	2	no	—
212	C₂⁴×C₅₃	—	2	2	no	—
213	C₂⁴×C₅₃	—	4	1	no	—
214	C₂⁴×C₅₃	—	4	1	no	—
215	C₂⁴×C₅₃	—	4	1	no	—
216	C₂⁴×C₅₃	—	4	1	no	—
217	C₂⁴×C₅₃	#41	1	4	yes	—
218	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
219	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
222	C₂×Q₈×C₅₃	—	2	2	no	—
223	C₂×Q₈×C₅₃	—	4	1	no	—
224	C₂×Q₈×C₅₃	—	4	1	no	—
225	C₂×D₄×C₅₃	—	2	4	no	—
226	C₂×D₄×C₅₃	—	2	4	no	—
227	C₂×D₄×C₅₃	—	2	4	no	—
228	C₂×D₄×C₅₃	—	2	4	no	—
229	C₂×D₄×C₅₃	—	2	4	no	—
230	C₂×D₄×C₅₃	—	2	2	no	—
231	C₂×D₄×C₅₃	—	4	1	no	—
232	C₂×D₄×C₅₃	—	4	1	no	—
233	C₂×D₄×C₅₃	—	4	2	no	—
234	C₂×D₄×C₅₃	—	4	2	no	—
235	C₂×D₄×C₅₃	—	4	2	no	—
236	C₂×D₄×C₅₃	—	4	2	no	—
237	C₂²×C₄×C₅₃	—	2	2	no	—
238	C₂²×C₄×C₅₃	—	2	2	no	—
239	C₂²×C₄×C₅₃	—	2	2	no	—
240	C₂²×C₄×C₅₃	—	2	2	no	—
241	C₂²×C₄×C₅₃	—	2	2	no	—
242	C₂²×C₄×C₅₃	—	2	2	no	—
243	C₂²×C₄×C₅₃	—	2	4	no	—
244	C₂²×C₄×C₅₃	—	2	2	no	—
245	C₂²×C₄×C₅₃	—	2	2	no	—
246	C₂²×C₄×C₅₃	—	2	2	no	—
247	C₂²×C₄×C₅₃	—	2	2	no	—
248	C₂²×C₄×C₅₃	—	2	2	no	—
249	C₂²×C₄×C₅₃	—	2	2	no	—
250	C₂²×C₄×C₅₃	—	2	2	no	—
251	C₂²×C₄×C₅₃	—	2	2	no	—
252	C₂²×C₄×C₅₃	—	4	1	no	—
253	C₂²×C₄×C₅₃	—	4	1	no	—
254	C₂²×C₄×C₅₃	—	4	1	no	—
255	C₂²×C₄×C₅₃	—	4	1	no	—
256	C₂²×C₄×C₅₃	—	4	2	no	—
257	C₂²×C₄×C₅₃	—	4	1	no	—
258	C₂²×C₄×C₅₃	—	4	1	no	—
259	C₂²×C₄×C₅₃	—	4	1	no	—
260	C₂²×C₄×C₅₃	—	4	1	no	—
261	C₂²×C₄×C₅₃	—	4	1	no	—
262	C₂²×C₄×C₅₃	—	4	1	no	—
263	C₂²×C₄×C₅₃	—	4	1	no	—
264	C₂²×C₄×C₅₃	—	4	2	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	16	no	—
269	C₂²×C₄×C₅₃	#41	1	4	yes	—
270	C₂²×C₄×C₅₃	#41	1	4	yes	—
271	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
285	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
286	C₄⋊C₄×C₅₃	—	2	4	no	—
287	C₄⋊C₄×C₅₃	—	2	2	no	—
288	C₄⋊C₄×C₅₃	—	2	4	no	—
289	C₄⋊C₄×C₅₃	—	2	2	no	—
290	C₄⋊C₄×C₅₃	—	2	4	no	—
291	C₄⋊C₄×C₅₃	—	2	4	no	—
292	C₄⋊C₄×C₅₃	—	4	2	no	—
293	C₄⋊C₄×C₅₃	—	4	2	no	—
294	C₄⋊C₄×C₅₃	—	4	2	no	—
295	C₄⋊C₄×C₅₃	—	4	2	no	—
296	C₄⋊C₄×C₅₃	—	4	1	no	—
297	C₄⋊C₄×C₅₃	—	4	1	no	—
298	C₄⋊C₄×C₅₃	—	4	1	no	—
299	C₄⋊C₄×C₅₃	—	4	1	no	—
300	C₄⋊C₄×C₅₃	—	4	2	no	—
301	C₄⋊C₄×C₅₃	—	4	2	no	—
302	C₂²⋊C₄×C₅₃	—	2	4	no	—
303	C₂²⋊C₄×C₅₃	—	2	4	no	—
304	C₂²⋊C₄×C₅₃	—	2	4	no	—
305	C₂²⋊C₄×C₅₃	—	2	4	no	—
306	C₂²⋊C₄×C₅₃	—	2	4	no	—
307	C₂²⋊C₄×C₅₃	—	2	4	no	—
308	C₂²⋊C₄×C₅₃	—	2	4	no	—
309	C₂²⋊C₄×C₅₃	—	2	4	no	—
310	C₂²⋊C₄×C₅₃	—	2	4	no	—
311	C₂²⋊C₄×C₅₃	—	2	4	no	—
312	C₂²⋊C₄×C₅₃	—	2	4	no	—
313	C₂²⋊C₄×C₅₃	—	2	4	no	—
314	C₂²⋊C₄×C₅₃	—	2	4	no	—
315	C₂²⋊C₄×C₅₃	—	4	2	no	—
316	C₂²⋊C₄×C₅₃	—	4	2	no	—
317	C₂²⋊C₄×C₅₃	—	4	2	no	—
318	C₂²⋊C₄×C₅₃	—	4	2	no	—
319	C₂²⋊C₄×C₅₃	—	4	2	no	—
320	C₂²⋊C₄×C₅₃	—	4	2	no	—
321	C₂²⋊C₄×C₅₃	—	4	2	no	—
322	C₂²⋊C₄×C₅₃	—	4	2	no	—
323	C₂²⋊C₄×C₅₃	—	4	2	no	—
324	C₂²⋊C₄×C₅₃	—	4	2	no	—
325	C₄²×C₅₃	—	2	4	no	—
326	C₄²×C₅₃	—	2	4	no	—
327	C₄²×C₅₃	—	2	4	no	—
328	C₄²×C₅₃	—	4	2	no	—
329	C₄²×C₅₃	—	4	2	no	—
330	C₄²×C₅₃	—	4	2	no	—
331	C₄²×C₅₃	—	4	2	no	—
332	C₂³×C₅₃	—	2	1	no	—
333	C₂³×C₅₃	—	2	1	no	—
334	C₂³×C₅₃	—	2	1	no	—
335	C₂³×C₅₃	—	2	1	no	—
336	C₂³×C₅₃	—	2	8	no	—
337	C₂³×C₅₃	—	2	1	no	—
338	C₂³×C₅₃	—	2	1	no	—
339	C₂³×C₅₃	—	2	1	no	—
340	C₂³×C₅₃	—	2	1	no	—
341	C₂³×C₅₃	—	2	1	no	—
342	C₂³×C₅₃	—	2	1	no	—
343	C₂³×C₅₃	—	2	1	no	—
344	C₂³×C₅₃	—	2	1	no	—
345	C₂³×C₅₃	—	2	1	no	—
346	C₂³×C₅₃	—	2	1	no	—
347	C₂³×C₅₃	—	2	1	no	—
348	C₂³×C₅₃	—	2	1	no	—
349	C₂³×C₅₃	—	2	2	no	—
350	C₂³×C₅₃	—	2	2	no	—
351	C₂³×C₅₃	—	2	2	no	—
352	C₂³×C₅₃	—	2	2	no	—
353	C₂³×C₅₃	—	2	2	no	—
354	C₂³×C₅₃	—	2	2	no	—
355	C₂³×C₅₃	—	2	2	no	—
356	C₂³×C₅₃	—	4	4	no	—
357	C₂³×C₅₃	—	4	4	no	—
358	C₂³×C₅₃	—	4	4	no	—
359	C₂³×C₅₃	—	4	4	no	—
360	C₂³×C₅₃	—	4	4	no	—
361	C₂³×C₅₃	—	4	4	no	—
362	C₂³×C₅₃	C₂×#41	1	2	yes	—
363	C₂³×C₅₃	C₂×#41	1	2	yes	—
364	C₂³×C₅₃	C₂×#41	1	2	yes	—
365	C₂³×C₅₃	C₂×#41	1	2	yes	—
366	C₂³×C₅₃	C₂×#41	1	2	yes	—
367	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
368	Q₈×C₅₃	—	8	2	no	—
369	D₄×C₅₃	—	4	8	no	—
370	D₄×C₅₃	—	8	2	no	—
371	D₄×C₅₃	—	8	4	no	—
372	D₄×C₅₃	—	8	4	no	—
373	C₂×C₄×C₅₃	—	2	8	no	—
374	C₂×C₄×C₅₃	—	2	1	no	—
375	C₂×C₄×C₅₃	—	2	1	no	—
376	C₂×C₄×C₅₃	—	2	1	no	—
377	C₂×C₄×C₅₃	—	2	1	no	—
378	C₂×C₄×C₅₃	—	2	1	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	2	no	—
383	C₂×C₄×C₅₃	—	2	2	no	—
384	C₂×C₄×C₅₃	—	2	2	no	—
385	C₂×C₄×C₅₃	—	2	2	no	—
386	C₂×C₄×C₅₃	—	2	2	no	—
387	C₂×C₄×C₅₃	—	2	2	no	—
388	C₂×C₄×C₅₃	—	2	2	no	—
389	C₂×C₄×C₅₃	—	2	2	no	—
390	C₂×C₄×C₅₃	—	2	2	no	—
391	C₂×C₄×C₅₃	—	2	2	no	—
392	C₂×C₄×C₅₃	—	2	2	no	—
393	C₂×C₄×C₅₃	—	2	2	no	—
394	C₂×C₄×C₅₃	—	2	2	no	—
395	C₂×C₄×C₅₃	—	2	2	no	—
396	C₂×C₄×C₅₃	—	2	2	no	—
397	C₂×C₄×C₅₃	—	2	2	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	2	no	—
402	C₂×C₄×C₅₃	—	2	2	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	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	2	no	—
412	C₂×C₄×C₅₃	—	2	2	no	—
413	C₂×C₄×C₅₃	—	2	2	no	—
414	C₂×C₄×C₅₃	—	4	4	no	—
415	C₂×C₄×C₅₃	—	4	4	no	—
416	C₂×C₄×C₅₃	—	4	4	no	—
417	C₂×C₄×C₅₃	—	4	4	no	—
418	C₂×C₄×C₅₃	—	4	4	no	—
419	C₂×C₄×C₅₃	—	4	4	no	—
420	C₂×C₄×C₅₃	—	4	8	no	—
421	C₂×C₄×C₅₃	—	4	4	no	—
422	C₂×C₄×C₅₃	—	4	4	no	—
423	C₂×C₄×C₅₃	—	4	4	no	—
424	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
425	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
426	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
427	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
428	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
429	#35034	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
430	C₂²×C₅₃	—	2	2	no	—
431	C₂²×C₅₃	—	2	2	no	—
432	C₂²×C₅₃	—	2	2	no	—
433	C₂²×C₅₃	—	2	2	no	—
434	C₂²×C₅₃	—	2	2	no	—
435	C₂²×C₅₃	—	2	2	no	—
436	C₂²×C₅₃	—	2	2	no	—
437	C₂²×C₅₃	—	2	2	no	—
438	C₂²×C₅₃	—	2	2	no	—
439	C₂²×C₅₃	—	2	2	no	—
440	C₂²×C₅₃	—	2	2	no	—
441	C₂²×C₅₃	—	2	2	no	—
442	C₂²×C₅₃	—	4	16	no	—
443	C₂²×C₅₃	—	4	1	no	—
444	C₂²×C₅₃	—	4	1	no	—
445	C₂²×C₅₃	—	4	1	no	—
446	C₂²×C₅₃	—	4	1	no	—
447	C₂²×C₅₃	—	4	1	no	—
448	C₂²×C₅₃	—	4	1	no	—
449	C₂²×C₅₃	—	4	1	no	—
450	C₂²×C₅₃	—	4	1	no	—
451	C₂²×C₅₃	—	4	2	no	—
452	C₂²×C₅₃	—	4	2	no	—
453	C₂²×C₅₃	—	4	2	no	—
454	C₂²×C₅₃	—	4	2	no	—
455	C₂²×C₅₃	—	4	2	no	—
456	C₂²×C₅₃	—	4	2	no	—
457	C₂²×C₅₃	—	4	2	no	—
458	C₂²×C₅₃	#529	1	4	yes	—
459	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
460	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
461	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
462	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
463	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
464	C₂²×C₅₃	#585	1	1	yes	characteristic
465	C₂²×C₅₃	#585	1	1	yes	characteristic
466	C₄×C₅₃	—	2	4	no	—
467	C₄×C₅₃	—	2	2	no	—
468	C₄×C₅₃	—	2	2	no	—
469	C₄×C₅₃	—	2	2	no	—
470	C₄×C₅₃	—	2	2	no	—
471	C₄×C₅₃	—	4	2	no	—
472	C₄×C₅₃	—	4	2	no	—
473	C₄×C₅₃	—	4	2	no	—
474	C₄×C₅₃	—	4	2	no	—
475	C₄×C₅₃	—	4	2	no	—
476	C₄×C₅₃	—	4	2	no	—
477	C₄×C₅₃	—	4	2	no	—
478	C₄×C₅₃	—	4	2	no	—
479	C₄×C₅₃	—	4	2	no	—
480	C₄×C₅₃	—	4	2	no	—
481	#2852	C₂×C₅₃	1	2	yes	complemented
482	#2848	C₂×C₅₃	1	1	yes	characteristic, complemented
483	#2847	C₂×C₅₃	1	1	yes	characteristic
484	#2646	C₂×C₅₃	1	1	yes	characteristic, complemented
485	#2639	C₂×C₅₃	1	1	yes	characteristic, complemented
486	#2622	C₂×C₅₃	1	2	yes	complemented
487	#2578	C₂×C₅₃	1	2	yes	complemented
488	#2577	C₂×C₅₃	1	2	yes	complemented
489	#2560	C₂×C₅₃	1	2	yes	complemented
490	#2559	C₂×C₅₃	1	2	yes	complemented
491	#2531	C₂×C₅₃	1	2	yes	complemented
492	#2530	C₂×C₅₃	1	2	yes	complemented
493	#2477	C₂×C₅₃	1	2	yes	complemented
494	#2476	C₂×C₅₃	1	2	yes	complemented
495	#2329	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#2325	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#2321	C₂×C₅₃	1	2	yes	complemented
498	#2290	C₂×C₅₃	1	2	yes	complemented
499	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
500	C₂×C₅₃	—	2	4	no	—
501	C₂×C₅₃	—	4	2	no	—
502	C₂×C₅₃	—	4	2	no	—
503	C₂×C₅₃	—	8	2	no	—
504	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
505	C₂×C₅₃	#3459	1	1	yes	characteristic
506	C₂×C₅₃	#3460	1	1	yes	characteristic
507	C₂×C₅₃	#3490	1	1	yes	characteristic
508	C₂×C₅₃	#3493	1	1	yes	characteristic
509	C₂×C₅₃	#3505	1	1	yes	characteristic
510	C₂×C₅₃	#3505	1	1	yes	characteristic
511	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
512	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
513	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
514	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
515	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
516	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
517	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
518	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
519	C₂×#120	C₂²×C₅₃	1	2	yes	—
520	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
521	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
522	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
523	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
524	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
525	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
526	#400	C₂²×C₅₃	1	2	yes	complemented
527	#400	C₂²×C₅₃	1	2	yes	complemented
528	#400	C₂²×C₅₃	1	2	yes	complemented
529	#398	C₂²×C₅₃	1	2	yes	complemented
530	#398	C₂²×C₅₃	1	2	yes	complemented
531	#397	C₂²×C₅₃	1	2	yes	—
532	#397	C₂²×C₅₃	1	2	yes	—
533	#397	C₂²×C₅₃	1	2	yes	—
534	#397	C₂²×C₅₃	1	2	yes	—
535	#397	C₂²×C₅₃	1	2	yes	complemented
536	#394	C₂²×C₅₃	1	2	yes	—
537	#394	C₂²×C₅₃	1	2	yes	—
538	#394	C₂²×C₅₃	1	2	yes	—
539	#394	C₂²×C₅₃	1	2	yes	—
540	#394	C₂²×C₅₃	1	2	yes	complemented
541	#393	C₂²×C₅₃	1	2	yes	complemented
542	#391	C₂²×C₅₃	1	2	yes	complemented
543	#390	C₂²×C₅₃	1	2	yes	—
544	#390	C₂²×C₅₃	1	2	yes	—
545	#389	C₂²×C₅₃	1	2	yes	complemented
546	#388	C₂²×C₅₃	1	2	yes	—
547	#388	C₂²×C₅₃	1	2	yes	—
548	#388	C₂²×C₅₃	1	2	yes	—
549	#388	C₂²×C₅₃	1	2	yes	—
550	#388	C₂²×C₅₃	1	2	yes	complemented
551	#388	C₂²×C₅₃	1	2	yes	complemented
552	#388	C₂²×C₅₃	1	2	yes	complemented
553	#388	C₂²×C₅₃	1	2	yes	complemented
554	#388	C₂²×C₅₃	1	2	yes	complemented
555	#388	C₂²×C₅₃	1	2	yes	complemented
556	#387	C₂²×C₅₃	1	2	yes	complemented
557	#387	C₂²×C₅₃	1	2	yes	complemented
558	#387	C₂²×C₅₃	1	2	yes	complemented
559	#387	C₂²×C₅₃	1	2	yes	complemented
560	#387	C₂²×C₅₃	1	2	yes	complemented
561	#387	C₂²×C₅₃	1	2	yes	complemented
562	#387	C₂²×C₅₃	1	2	yes	complemented
563	#387	C₂²×C₅₃	1	2	yes	complemented
564	#386	C₂²×C₅₃	1	2	yes	—
565	#386	C₂²×C₅₃	1	2	yes	—
566	#386	C₂²×C₅₃	1	2	yes	—
567	#386	C₂²×C₅₃	1	2	yes	—
568	#386	C₂²×C₅₃	1	2	yes	—
569	#386	C₂²×C₅₃	1	2	yes	—
570	#386	C₂²×C₅₃	1	2	yes	—
571	#386	C₂²×C₅₃	1	2	yes	—
572	#386	C₂²×C₅₃	1	2	yes	complemented
573	#385	C₂²×C₅₃	1	2	yes	—
574	#385	C₂²×C₅₃	1	2	yes	—
575	#385	C₂²×C₅₃	1	2	yes	—
576	#385	C₂²×C₅₃	1	2	yes	—
577	#385	C₂²×C₅₃	1	2	yes	—
578	#385	C₂²×C₅₃	1	2	yes	—
579	#385	C₂²×C₅₃	1	2	yes	complemented
580	#383	C₂²×C₅₃	1	2	yes	complemented
581	#380	C₂²×C₅₃	1	1	yes	characteristic
582	#380	C₂²×C₅₃	1	1	yes	characteristic
583	#380	C₂²×C₅₃	1	1	yes	characteristic
584	#380	C₂²×C₅₃	1	1	yes	characteristic
585	#380	C₂²×C₅₃	1	1	yes	characteristic
586	#380	C₂²×C₅₃	1	1	yes	characteristic
587	#379	C₂²×C₅₃	1	2	yes	—
588	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
589	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
590	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
591	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
592	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
593	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
594	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
595	#376	C₂²×C₅₃	1	2	yes	complemented
596	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
597	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
598	C₅₃	#35034	1	1	yes	characteristic, direct product factor, Sylow
599	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
600	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
602	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
603	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
604	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
605	C₂³×C₄	—	2	4	no	—
606	C₂³×C₄	—	4	2	no	—
607	C₂³×C₄	—	4	2	no	—
608	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
617	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
619	#126	—	4	4	no	—
620	C₂²⋊Q₈	—	2	4	no	—
621	C₂²⋊Q₈	—	4	2	no	—
622	C₂²⋊Q₈	—	4	2	no	—
623	#121	—	2	4	no	—
624	#121	—	4	2	no	—
625	#121	—	4	2	no	—
626	#120	—	2	8	no	—
627	C₄×D₄	—	2	8	no	—
628	#117	—	4	4	no	—
629	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
645	C₂×C₂²⋊C₄	—	2	4	no	—
646	C₂×C₂²⋊C₄	—	2	4	no	—
647	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
670	C₂×C₄²	—	4	2	no	—
671	C₂×C₄²	—	4	2	no	—
672	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
674	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
675	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
676	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
677	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
678	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
679	#95	C₂³×C₅₃	1	2	yes	—
680	#95	C₂³×C₅₃	1	2	yes	—
681	#95	C₂³×C₅₃	1	2	yes	—
682	#95	C₂³×C₅₃	1	2	yes	—
683	#95	C₂³×C₅₃	1	2	yes	—
684	#95	C₂³×C₅₃	1	2	yes	—
685	#95	C₂³×C₅₃	1	2	yes	—
686	#95	C₂³×C₅₃	1	2	yes	—
687	#95	C₂³×C₅₃	1	2	yes	—
688	#95	C₂³×C₅₃	1	2	yes	—
689	#95	C₂³×C₅₃	1	2	yes	—
690	#95	C₂³×C₅₃	1	2	yes	—
691	#95	C₂³×C₅₃	1	2	yes	—
692	#95	C₂³×C₅₃	1	2	yes	—
693	#95	C₂³×C₅₃	1	2	yes	—
694	#95	C₂³×C₅₃	1	2	yes	—
695	#95	C₂³×C₅₃	1	2	yes	—
696	#95	C₂³×C₅₃	1	2	yes	—
697	#95	C₂³×C₅₃	1	2	yes	—
698	#95	C₂³×C₅₃	1	2	yes	—
699	#95	C₂³×C₅₃	1	2	yes	—
700	#95	C₂³×C₅₃	1	2	yes	—
701	#95	C₂³×C₅₃	1	2	yes	—
702	#95	C₂³×C₅₃	1	2	yes	—
703	C₂⁴	—	2	2	no	—
704	C₂⁴	—	2	2	no	—
705	C₂⁴	—	4	1	no	—
706	C₂⁴	—	4	1	no	—
707	C₂⁴	—	4	1	no	—
708	C₂⁴	—	4	1	no	—
709	C₂⁴	#41×C₅₃	1	4	yes	—
710	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
711	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
712	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
713	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
714	C₂×Q₈	—	2	2	no	—
715	C₂×Q₈	—	4	1	no	—
716	C₂×Q₈	—	4	1	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	4	1	no	—
724	C₂×D₄	—	4	1	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	4	1	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	—	4	1	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	1	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	1	no	—
752	C₂²×C₄	—	4	1	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	1	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	—	4	1	no	—
760	C₂²×C₄	—	4	16	no	—
761	C₂²×C₄	#41×C₅₃	1	4	yes	—
762	C₂²×C₄	#41×C₅₃	1	4	yes	—
763	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	1	no	—
786	C₄⋊C₄	—	4	1	no	—
787	C₄⋊C₄	—	4	1	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₄²	—	2	4	no	—
818	C₄²	—	2	4	no	—
819	C₄²	—	2	4	no	—
820	C₄²	—	4	2	no	—
821	C₄²	—	4	2	no	—
822	C₄²	—	4	2	no	—
823	C₄²	—	4	2	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	8	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	4	4	no	—
849	C₂³	—	4	4	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	4	no	—
852	C₂³	—	4	4	no	—
853	C₂³	—	4	4	no	—
854	C₂³	C₂×#41×C₅₃	1	2	yes	—
855	C₂³	C₂×#41×C₅₃	1	2	yes	—
856	C₂³	C₂×#41×C₅₃	1	2	yes	—
857	C₂³	C₂×#41×C₅₃	1	2	yes	—
858	C₂³	C₂×#41×C₅₃	1	2	yes	—
859	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
860	Q₈	—	8	2	no	—
861	D₄	—	4	8	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	4	no	—
864	D₄	—	8	4	no	—
865	C₂×C₄	—	2	8	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	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	—	4	4	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	4	no	—
910	C₂×C₄	—	4	4	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	4	8	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
917	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
918	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
919	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
920	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	4	16	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	C₅₃×#529	1	4	yes	—
950	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
951	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
952	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
953	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
954	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
955	C₂²	C₅₃×#585	1	1	yes	characteristic
956	C₂²	C₅₃×#585	1	1	yes	characteristic
957	C₄	—	2	4	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₂	—	2	4	no	—
973	C₂	—	4	2	no	—
974	C₂	—	4	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₂×C₅₃×#529	1	1	yes	characteristic
977	C₂	C₅₃×#3459	1	1	yes	characteristic
978	C₂	C₅₃×#3460	1	1	yes	characteristic
979	C₂	C₅₃×#3490	1	1	yes	characteristic
980	C₂	C₅₃×#3493	1	1	yes	characteristic
981	C₂	C₅₃×#3505	1	1	yes	characteristic
982	C₂	C₅₃×#3505	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2847	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2852	C₂	semidirect
2. C₅₃×#2848	C₂	semidirect
4. C₅₃×#2646	C₂	semidirect
5. C₅₃×#2639	C₂	semidirect
6. C₅₃×#2622	C₂	semidirect
7. C₅₃×#2578	C₂	semidirect
8. C₅₃×#2577	C₂	semidirect
9. C₅₃×#2560	C₂	semidirect
10. C₅₃×#2559	C₂	semidirect
11. C₅₃×#2531	C₂	semidirect
12. C₅₃×#2530	C₂	semidirect
13. C₅₃×#2477	C₂	semidirect
14. C₅₃×#2476	C₂	semidirect
15. C₅₃×#2329	C₂	semidirect
16. C₅₃×#2325	C₂	semidirect
17. C₅₃×#2321	C₂	semidirect
18. C₅₃×#2290	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
21. C₂×#126×C₅₃	C₂²	semidirect
30. C₂×#117×C₅₃	C₂²	semidirect
35. C₅₃×#400	C₂²	semidirect
36. C₅₃×#400	C₂²	semidirect
37. C₅₃×#400	C₂²	semidirect
38. C₅₃×#398	C₂²	semidirect
39. C₅₃×#398	C₂²	semidirect
44. C₅₃×#397	C₂²	semidirect
49. C₅₃×#394	C₂²	semidirect
50. C₅₃×#393	C₂²	semidirect
51. C₅₃×#391	C₂²	semidirect
54. C₅₃×#389	C₂²	semidirect
59. C₅₃×#388	C₂²	semidirect
60. C₅₃×#388	C₂²	semidirect
61. C₅₃×#388	C₂²	semidirect
62. C₅₃×#388	C₂²	semidirect
63. C₅₃×#388	C₂²	semidirect
64. C₅₃×#388	C₂²	semidirect
65. C₅₃×#387	C₂²	semidirect
66. C₅₃×#387	C₂²	semidirect
67. C₅₃×#387	C₂²	semidirect
68. C₅₃×#387	C₂²	semidirect
69. C₅₃×#387	C₂²	semidirect
70. C₅₃×#387	C₂²	semidirect
71. C₅₃×#387	C₂²	semidirect
72. C₅₃×#387	C₂²	semidirect
81. C₅₃×#386	C₂²	semidirect
88. C₅₃×#385	C₂²	semidirect
89. C₅₃×#383	C₂²	semidirect
97. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
104. C₅₃×#376	C₂²	semidirect
429. #35034	C₅₃	direct (N × H)
481. #2852	C₂×C₅₃	semidirect
482. #2848	C₂×C₅₃	semidirect
484. #2646	C₂×C₅₃	semidirect
485. #2639	C₂×C₅₃	semidirect
486. #2622	C₂×C₅₃	semidirect
487. #2578	C₂×C₅₃	semidirect
488. #2577	C₂×C₅₃	semidirect
489. #2560	C₂×C₅₃	semidirect
490. #2559	C₂×C₅₃	semidirect
491. #2531	C₂×C₅₃	semidirect
492. #2530	C₂×C₅₃	semidirect
493. #2477	C₂×C₅₃	semidirect
494. #2476	C₂×C₅₃	semidirect
495. #2329	C₂×C₅₃	semidirect
496. #2325	C₂×C₅₃	semidirect
497. #2321	C₂×C₅₃	semidirect
498. #2290	C₂×C₅₃	semidirect
499. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
512. C₂×#126	C₂²×C₅₃	semidirect
521. C₂×#117	C₂²×C₅₃	semidirect
526. #400	C₂²×C₅₃	semidirect
527. #400	C₂²×C₅₃	semidirect
528. #400	C₂²×C₅₃	semidirect
529. #398	C₂²×C₅₃	semidirect
530. #398	C₂²×C₅₃	semidirect
535. #397	C₂²×C₅₃	semidirect
540. #394	C₂²×C₅₃	semidirect
541. #393	C₂²×C₅₃	semidirect
542. #391	C₂²×C₅₃	semidirect
545. #389	C₂²×C₅₃	semidirect
550. #388	C₂²×C₅₃	semidirect
551. #388	C₂²×C₅₃	semidirect
552. #388	C₂²×C₅₃	semidirect
553. #388	C₂²×C₅₃	semidirect
554. #388	C₂²×C₅₃	semidirect
555. #388	C₂²×C₅₃	semidirect
556. #387	C₂²×C₅₃	semidirect
557. #387	C₂²×C₅₃	semidirect
558. #387	C₂²×C₅₃	semidirect
559. #387	C₂²×C₅₃	semidirect
560. #387	C₂²×C₅₃	semidirect
561. #387	C₂²×C₅₃	semidirect
562. #387	C₂²×C₅₃	semidirect
563. #387	C₂²×C₅₃	semidirect
572. #386	C₂²×C₅₃	semidirect
579. #385	C₂²×C₅₃	semidirect
580. #383	C₂²×C₅₃	semidirect
588. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
594. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
595. #376	C₂²×C₅₃	semidirect
598. C₅₃	#35034	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×#2852	2
C₅₃×#2848	2
C₅₃×#2847	2
C₅₃×#2646	2
C₅₃×#2639	2
C₅₃×#2622	2
C₅₃×#2578	2
C₅₃×#2577	2
C₅₃×#2560	2
C₅₃×#2559	2
C₅₃×#2531	2
C₅₃×#2530	2
C₅₃×#2477	2
C₅₃×#2476	2
C₅₃×#2329	2
C₅₃×#2325	2
C₅₃×#2321	2
C₅₃×#2290	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
#35034	53

Subgroups — C53×#35034 #27242546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#35034 #27242546