Subgroups — C₅₃×#22874 #27230386

Order 13568.

1314 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
6	C₅₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#102×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
26	C₅₃×#450	C₄	1	8	yes	complemented
27	C₄×SD₁₆×C₅₃	—	2	4	no	—
28	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#102×C₅₃	—	2	4	no	—
33	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#390	C₂²	1	1	yes	characteristic
44	C₅₃×#390	C₂²	1	1	yes	characteristic
45	C₅₃×#389	—	2	1	no	—
46	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#387	—	2	1	no	—
48	C₅₃×#386	—	2	1	no	—
49	C₅₃×#386	—	2	1	no	—
50	C₅₃×#385	—	2	1	no	—
51	C₅₃×#380	C₂²	1	1	yes	characteristic
52	C₅₃×#379	—	2	1	no	—
53	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₄×C₂²⋊C₄×C₅₃	—	2	1	no	—
55	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
62	C₂⁵×C₅₃	—	2	1	no	—
63	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₅₃	—	2	2	no	—
65	C₂²×D₄×C₅₃	—	2	2	no	—
66	C₂²×D₄×C₅₃	—	2	1	no	—
67	C₂²×D₄×C₅₃	—	2	2	no	—
68	C₂²×D₄×C₅₃	—	4	1	no	—
69	C₂²×D₄×C₅₃	—	4	1	no	—
70	C₂²×D₄×C₅₃	C₂×C₄	1	4	yes	—
71	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅₃	—	2	1	no	—
74	C₂³×C₄×C₅₃	—	2	1	no	—
75	C₂³×C₄×C₅₃	—	2	1	no	—
76	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
77	C₂×SD₁₆×C₅₃	—	2	2	no	—
78	C₂×SD₁₆×C₅₃	—	2	2	no	—
79	C₂×SD₁₆×C₅₃	—	4	1	no	—
80	C₂×SD₁₆×C₅₃	—	4	1	no	—
81	C₂×SD₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
82	C₂×SD₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
83	C₂²×C₈×C₅₃	—	2	2	no	—
84	C₂²×C₈×C₅₃	—	2	2	no	—
85	C₂²×C₈×C₅₃	—	4	1	no	—
86	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²⋊Q₈×C₅₃	—	2	2	no	—
91	C₂²⋊Q₈×C₅₃	C₂×C₄	1	4	yes	complemented
92	C₄×Q₈×C₅₃	—	2	2	no	—
93	C₄×Q₈×C₅₃	—	4	1	no	—
94	C₄×D₄×C₅₃	—	2	2	no	—
95	C₄×D₄×C₅₃	—	2	2	no	—
96	C₄×D₄×C₅₃	—	4	1	no	—
97	C₄×D₄×C₅₃	—	4	1	no	—
98	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
99	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
101	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
102	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
103	C₂×C₄⋊C₄×C₅₃	—	4	1	no	—
104	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
118	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₅₃	—	2	1	no	—
121	C₂×C₄²×C₅₃	—	2	1	no	—
122	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
124	#106×C₅₃	—	2	2	no	—
125	#106×C₅₃	—	4	1	no	—
126	#103×C₅₃	—	2	2	no	—
127	#103×C₅₃	—	4	1	no	—
128	#102×C₅₃	—	2	2	no	—
129	#102×C₅₃	—	2	2	no	—
130	#102×C₅₃	—	2	2	no	—
131	#102×C₅₃	C₂×C₄	1	4	yes	complemented
132	#102×C₅₃	C₂×C₄	1	4	yes	complemented
133	#102×C₅₃	D₄	1	4	yes	—
134	C₂²⋊C₈×C₅₃	C₂×C₄	1	4	yes	complemented
135	C₄×C₈×C₅₃	—	2	2	no	—
136	C₄×C₈×C₅₃	—	4	1	no	—
137	#95×C₅₃	—	2	1	no	—
138	#95×C₅₃	—	2	1	no	—
139	#95×C₅₃	—	2	1	no	—
140	#95×C₅₃	—	2	1	no	—
141	#95×C₅₃	—	2	1	no	—
142	#95×C₅₃	D₄	1	1	yes	characteristic
143	#95×C₅₃	D₄	1	1	yes	characteristic
144	C₂⁴×C₅₃	—	2	1	no	—
145	C₂⁴×C₅₃	—	2	1	no	—
146	C₂⁴×C₅₃	—	2	4	no	—
147	C₂⁴×C₅₃	—	4	2	no	—
148	C₂⁴×C₅₃	—	4	2	no	—
149	C₂⁴×C₅₃	—	4	2	no	—
150	C₂⁴×C₅₃	—	4	2	no	—
151	C₂⁴×C₅₃	—	8	1	no	—
152	C₂⁴×C₅₃	—	8	1	no	—
153	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₅₃	—	2	1	no	—
155	C₂×Q₈×C₅₃	—	2	1	no	—
156	C₂×Q₈×C₅₃	—	2	1	no	—
157	C₂×Q₈×C₅₃	—	2	1	no	—
158	C₂×Q₈×C₅₃	—	2	1	no	—
159	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₅₃	—	2	8	no	—
161	C₂×D₄×C₅₃	—	2	4	no	—
162	C₂×D₄×C₅₃	—	2	1	no	—
163	C₂×D₄×C₅₃	—	2	1	no	—
164	C₂×D₄×C₅₃	—	2	1	no	—
165	C₂×D₄×C₅₃	—	2	1	no	—
166	C₂×D₄×C₅₃	—	2	1	no	—
167	C₂×D₄×C₅₃	—	2	1	no	—
168	C₂×D₄×C₅₃	—	2	1	no	—
169	C₂×D₄×C₅₃	—	2	1	no	—
170	C₂×D₄×C₅₃	—	4	4	no	—
171	C₂×D₄×C₅₃	—	4	4	no	—
172	C₂×D₄×C₅₃	—	4	4	no	—
173	C₂×D₄×C₅₃	—	4	2	no	—
174	C₂×D₄×C₅₃	—	4	2	no	—
175	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
176	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
177	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
178	C₂×D₄×C₅₃	#41	1	2	yes	—
179	C₂²×C₄×C₅₃	—	2	1	no	—
180	C₂²×C₄×C₅₃	—	2	1	no	—
181	C₂²×C₄×C₅₃	—	2	1	no	—
182	C₂²×C₄×C₅₃	—	2	1	no	—
183	C₂²×C₄×C₅₃	—	2	1	no	—
184	C₂²×C₄×C₅₃	—	2	1	no	—
185	C₂²×C₄×C₅₃	—	2	1	no	—
186	C₂²×C₄×C₅₃	—	2	1	no	—
187	C₂²×C₄×C₅₃	—	2	1	no	—
188	C₂²×C₄×C₅₃	—	2	1	no	—
189	C₂²×C₄×C₅₃	—	4	2	no	—
190	C₂²×C₄×C₅₃	—	4	2	no	—
191	C₂²×C₄×C₅₃	—	4	2	no	—
192	C₂²×C₄×C₅₃	—	4	2	no	—
193	C₂²×C₄×C₅₃	—	4	2	no	—
194	C₂²×C₄×C₅₃	—	4	2	no	—
195	C₂²×C₄×C₅₃	—	8	1	no	—
196	C₂²×C₄×C₅₃	—	8	1	no	—
197	C₂²×C₄×C₅₃	—	8	1	no	—
198	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
199	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₅₃	#41	1	2	yes	—
205	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
206	SD₁₆×C₅₃	—	2	8	no	—
207	SD₁₆×C₅₃	—	4	4	no	—
208	C₂×C₈×C₅₃	—	2	1	no	—
209	C₂×C₈×C₅₃	—	2	1	no	—
210	C₂×C₈×C₅₃	—	2	1	no	—
211	C₂×C₈×C₅₃	—	2	1	no	—
212	C₂×C₈×C₅₃	—	2	1	no	—
213	C₂×C₈×C₅₃	—	2	1	no	—
214	C₂×C₈×C₅₃	—	2	1	no	—
215	C₂×C₈×C₅₃	—	2	1	no	—
216	C₂×C₈×C₅₃	—	2	1	no	—
217	C₂×C₈×C₅₃	—	4	4	no	—
218	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
219	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
220	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
221	C₄⋊C₄×C₅₃	—	2	4	no	—
222	C₄⋊C₄×C₅₃	—	2	1	no	—
223	C₄⋊C₄×C₅₃	—	2	1	no	—
224	C₄⋊C₄×C₅₃	—	2	1	no	—
225	C₄⋊C₄×C₅₃	—	2	1	no	—
226	C₄⋊C₄×C₅₃	—	2	1	no	—
227	C₄⋊C₄×C₅₃	—	2	1	no	—
228	C₄⋊C₄×C₅₃	—	2	1	no	—
229	C₄⋊C₄×C₅₃	—	2	1	no	—
230	C₄⋊C₄×C₅₃	—	4	2	no	—
231	C₄⋊C₄×C₅₃	—	4	2	no	—
232	C₄⋊C₄×C₅₃	—	8	1	no	—
233	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
234	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
235	C₂²⋊C₄×C₅₃	—	2	4	no	—
236	C₂²⋊C₄×C₅₃	—	2	2	no	—
237	C₂²⋊C₄×C₅₃	—	4	2	no	—
238	C₂²⋊C₄×C₅₃	—	4	2	no	—
239	C₂²⋊C₄×C₅₃	—	4	2	no	—
240	C₂²⋊C₄×C₅₃	—	4	2	no	—
241	C₂²⋊C₄×C₅₃	—	4	2	no	—
242	C₂²⋊C₄×C₅₃	—	8	1	no	—
243	C₂²⋊C₄×C₅₃	—	8	1	no	—
244	C₂²⋊C₄×C₅₃	SD₁₆	1	4	yes	complemented
245	C₄²×C₅₃	—	2	1	no	—
246	C₄²×C₅₃	—	2	1	no	—
247	C₄²×C₅₃	—	2	1	no	—
248	C₄²×C₅₃	—	2	1	no	—
249	C₄²×C₅₃	—	4	2	no	—
250	C₄²×C₅₃	—	8	1	no	—
251	C₂³×C₅₃	—	2	1	no	—
252	C₂³×C₅₃	—	2	1	no	—
253	C₂³×C₅₃	—	2	1	no	—
254	C₂³×C₅₃	—	2	1	no	—
255	C₂³×C₅₃	—	2	2	no	—
256	C₂³×C₅₃	—	2	2	no	—
257	C₂³×C₅₃	—	2	2	no	—
258	C₂³×C₅₃	—	2	2	no	—
259	C₂³×C₅₃	—	4	8	no	—
260	C₂³×C₅₃	—	4	1	no	—
261	C₂³×C₅₃	—	4	1	no	—
262	C₂³×C₅₃	—	4	1	no	—
263	C₂³×C₅₃	—	4	1	no	—
264	C₂³×C₅₃	—	4	1	no	—
265	C₂³×C₅₃	—	4	1	no	—
266	C₂³×C₅₃	—	4	1	no	—
267	C₂³×C₅₃	—	4	1	no	—
268	C₂³×C₅₃	—	4	1	no	—
269	C₂³×C₅₃	—	4	1	no	—
270	C₂³×C₅₃	—	4	8	no	—
271	C₂³×C₅₃	—	8	4	no	—
272	C₂³×C₅₃	—	8	4	no	—
273	C₂³×C₅₃	—	8	4	no	—
274	C₂³×C₅₃	—	8	4	no	—
275	C₂³×C₅₃	—	8	4	no	—
276	C₂³×C₅₃	C₄×D₄	1	2	yes	—
277	C₂³×C₅₃	C₂×SD₁₆	1	2	yes	—
278	C₂³×C₅₃	#135	1	2	yes	—
279	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₅₃	—	2	2	no	—
281	Q₈×C₅₃	—	2	2	no	—
282	Q₈×C₅₃	—	4	1	no	—
283	Q₈×C₅₃	—	4	1	no	—
284	D₄×C₅₃	—	2	2	no	—
285	D₄×C₅₃	—	2	2	no	—
286	D₄×C₅₃	—	2	2	no	—
287	D₄×C₅₃	—	2	2	no	—
288	D₄×C₅₃	—	2	2	no	—
289	D₄×C₅₃	—	4	8	no	—
290	D₄×C₅₃	—	4	1	no	—
291	D₄×C₅₃	—	4	1	no	—
292	D₄×C₅₃	C₄×D₄	1	4	yes	—
293	C₂×C₄×C₅₃	—	2	1	no	—
294	C₂×C₄×C₅₃	—	2	1	no	—
295	C₂×C₄×C₅₃	—	2	1	no	—
296	C₂×C₄×C₅₃	—	2	1	no	—
297	C₂×C₄×C₅₃	—	2	1	no	—
298	C₂×C₄×C₅₃	—	2	1	no	—
299	C₂×C₄×C₅₃	—	2	2	no	—
300	C₂×C₄×C₅₃	—	2	2	no	—
301	C₂×C₄×C₅₃	—	2	2	no	—
302	C₂×C₄×C₅₃	—	2	2	no	—
303	C₂×C₄×C₅₃	—	2	2	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	2	no	—
306	C₂×C₄×C₅₃	—	2	1	no	—
307	C₂×C₄×C₅₃	—	2	1	no	—
308	C₂×C₄×C₅₃	—	2	1	no	—
309	C₂×C₄×C₅₃	—	2	1	no	—
310	C₂×C₄×C₅₃	—	2	1	no	—
311	C₂×C₄×C₅₃	—	2	1	no	—
312	C₂×C₄×C₅₃	—	4	1	no	—
313	C₂×C₄×C₅₃	—	4	1	no	—
314	C₂×C₄×C₅₃	—	4	1	no	—
315	C₂×C₄×C₅₃	—	4	1	no	—
316	C₂×C₄×C₅₃	—	4	1	no	—
317	C₂×C₄×C₅₃	—	4	1	no	—
318	C₂×C₄×C₅₃	—	4	1	no	—
319	C₂×C₄×C₅₃	—	4	1	no	—
320	C₂×C₄×C₅₃	—	4	1	no	—
321	C₂×C₄×C₅₃	—	4	1	no	—
322	C₂×C₄×C₅₃	—	4	1	no	—
323	C₂×C₄×C₅₃	—	4	1	no	—
324	C₂×C₄×C₅₃	—	4	1	no	—
325	C₂×C₄×C₅₃	—	4	1	no	—
326	C₂×C₄×C₅₃	—	4	1	no	—
327	C₂×C₄×C₅₃	—	8	4	no	—
328	C₂×C₄×C₅₃	—	8	4	no	—
329	C₂×C₄×C₅₃	—	8	4	no	—
330	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
331	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
332	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
333	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
334	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
339	C₈×C₅₃	—	2	2	no	—
340	C₈×C₅₃	—	2	2	no	—
341	C₈×C₅₃	—	2	2	no	—
342	C₈×C₅₃	—	4	1	no	—
343	#22874	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂²×C₅₃	—	2	2	no	—
345	C₂²×C₅₃	—	2	2	no	—
346	C₂²×C₅₃	—	2	2	no	—
347	C₂²×C₅₃	—	2	2	no	—
348	C₂²×C₅₃	—	2	2	no	—
349	C₂²×C₅₃	—	2	2	no	—
350	C₂²×C₅₃	—	2	4	no	—
351	C₂²×C₅₃	—	4	2	no	—
352	C₂²×C₅₃	—	4	2	no	—
353	C₂²×C₅₃	—	4	2	no	—
354	C₂²×C₅₃	—	4	2	no	—
355	C₂²×C₅₃	—	4	2	no	—
356	C₂²×C₅₃	—	4	2	no	—
357	C₂²×C₅₃	—	4	2	no	—
358	C₂²×C₅₃	—	4	2	no	—
359	C₂²×C₅₃	—	4	2	no	—
360	C₂²×C₅₃	—	8	16	no	—
361	C₂²×C₅₃	—	8	1	no	—
362	C₂²×C₅₃	—	8	1	no	—
363	C₂²×C₅₃	—	8	1	no	—
364	C₂²×C₅₃	—	8	1	no	—
365	C₂²×C₅₃	C₄×SD₁₆	1	4	yes	complemented
366	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
367	C₂²×C₅₃	D₄²	1	1	yes	characteristic
368	C₂²×C₅₃	#546	1	1	yes	characteristic
369	C₂²×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
370	C₂²×C₅₃	C₂×#135	1	1	yes	characteristic
371	C₂²×C₅₃	#576	1	1	yes	characteristic
372	C₂²×C₅₃	#577	1	1	yes	characteristic
373	C₄×C₅₃	—	2	2	no	—
374	C₄×C₅₃	—	2	2	no	—
375	C₄×C₅₃	—	2	2	no	—
376	C₄×C₅₃	—	4	2	no	—
377	C₄×C₅₃	—	4	2	no	—
378	C₄×C₅₃	—	4	1	no	—
379	C₄×C₅₃	—	4	2	no	—
380	C₄×C₅₃	—	4	1	no	—
381	C₄×C₅₃	—	8	1	no	—
382	C₄×C₅₃	—	8	1	no	—
383	C₄×C₅₃	—	8	1	no	—
384	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
385	C₄×C₅₃	#518	1	1	yes	characteristic
386	C₄×C₅₃	#546	1	1	yes	characteristic
387	C₄×C₅₃	#551	1	1	yes	characteristic
388	C₂×#450	C₂×C₅₃	1	1	yes	characteristic
389	C₂×C₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
390	C₂²×#102	C₂×C₅₃	1	1	yes	characteristic
391	#2360	C₂×C₅₃	1	1	yes	characteristic, complemented
392	D₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic
393	#1968	C₂×C₅₃	1	1	yes	characteristic, complemented
394	#1934	C₂×C₅₃	1	1	yes	characteristic, complemented
395	#1926	C₂×C₅₃	1	1	yes	characteristic, complemented
396	#1892	C₂×C₅₃	1	1	yes	characteristic, complemented
397	#1880	C₂×C₅₃	1	1	yes	characteristic, complemented
398	#1877	C₂×C₅₃	1	1	yes	characteristic, complemented
399	#1864	C₂×C₅₃	1	1	yes	characteristic, complemented
400	#1853	C₂×C₅₃	1	1	yes	characteristic, complemented
401	C₄×#102	C₂×C₅₃	1	1	yes	characteristic, complemented
402	C₈×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
403	C₂×C₅₃	—	2	4	no	—
404	C₂×C₅₃	—	4	4	no	—
405	C₂×C₅₃	—	8	2	no	—
406	C₂×C₅₃	#2358	1	1	yes	characteristic
407	C₂×C₅₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
408	C₂×C₅₃	#2946	1	1	yes	characteristic
409	C₂×C₅₃	#3280	1	1	yes	characteristic
410	C₂×C₅₃	D₄×SD₁₆	1	1	yes	characteristic
411	C₂×C₅₃	#3295	1	1	yes	characteristic
412	C₂×C₅₃	#3296	1	1	yes	characteristic
413	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
414	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
415	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
416	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
417	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
419	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
421	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	—	2	1	no	—
423	#450	C₄×C₅₃	1	8	yes	complemented
424	C₄×SD₁₆	—	2	4	no	—
425	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
426	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
427	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
428	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
429	C₂×#102	—	2	4	no	—
430	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
431	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
432	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
433	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
434	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
435	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
437	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
438	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
439	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
440	#390	C₂²×C₅₃	1	1	yes	characteristic
441	#390	C₂²×C₅₃	1	1	yes	characteristic
442	#389	—	2	1	no	—
443	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
444	#387	—	2	1	no	—
445	#386	—	2	1	no	—
446	#386	—	2	1	no	—
447	#385	—	2	1	no	—
448	#380	C₂²×C₅₃	1	1	yes	characteristic
449	#379	—	2	1	no	—
450	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
451	C₄×C₂²⋊C₄	—	2	1	no	—
452	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
453	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
454	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
455	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
456	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
457	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
458	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
459	C₅₃	#22874	1	1	yes	characteristic, direct product factor, Sylow
460	C₂⁵	—	2	1	no	—
461	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
462	C₂²×D₄	—	2	2	no	—
463	C₂²×D₄	—	2	2	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	2	no	—
466	C₂²×D₄	—	4	1	no	—
467	C₂²×D₄	—	4	1	no	—
468	C₂²×D₄	C₂×C₄×C₅₃	1	4	yes	—
469	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	2	2	no	—
477	C₂×SD₁₆	—	4	1	no	—
478	C₂×SD₁₆	—	4	1	no	—
479	C₂×SD₁₆	C₂×C₄×C₅₃	1	4	yes	complemented
480	C₂×SD₁₆	C₂×C₄×C₅₃	1	4	yes	complemented
481	C₂²×C₈	—	2	2	no	—
482	C₂²×C₈	—	2	2	no	—
483	C₂²×C₈	—	4	1	no	—
484	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	C₂×C₄×C₅₃	1	4	yes	complemented
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	—	4	1	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	4	1	no	—
495	C₄×D₄	—	4	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	4	1	no	—
502	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	4	4	no	—
516	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
522	#106	—	2	2	no	—
523	#106	—	4	1	no	—
524	#103	—	2	2	no	—
525	#103	—	4	1	no	—
526	#102	—	2	2	no	—
527	#102	—	2	2	no	—
528	#102	—	2	2	no	—
529	#102	C₂×C₄×C₅₃	1	4	yes	complemented
530	#102	C₂×C₄×C₅₃	1	4	yes	complemented
531	#102	D₄×C₅₃	1	4	yes	—
532	C₂²⋊C₈	C₂×C₄×C₅₃	1	4	yes	complemented
533	C₄×C₈	—	2	2	no	—
534	C₄×C₈	—	4	1	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	#95	—	2	1	no	—
538	#95	—	2	1	no	—
539	#95	—	2	1	no	—
540	#95	D₄×C₅₃	1	1	yes	characteristic
541	#95	D₄×C₅₃	1	1	yes	characteristic
542	C₂⁴	—	2	1	no	—
543	C₂⁴	—	2	1	no	—
544	C₂⁴	—	2	4	no	—
545	C₂⁴	—	4	2	no	—
546	C₂⁴	—	4	2	no	—
547	C₂⁴	—	4	2	no	—
548	C₂⁴	—	4	2	no	—
549	C₂⁴	—	8	1	no	—
550	C₂⁴	—	8	1	no	—
551	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	C₂²×C₄×C₅₃	1	2	yes	—
558	C₂×D₄	—	2	8	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	C₂²×C₄×C₅₃	1	2	yes	—
574	C₂×D₄	C₂²×C₄×C₅₃	1	2	yes	—
575	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
576	C₂×D₄	#41×C₅₃	1	2	yes	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	8	1	no	—
594	C₂²×C₄	—	8	1	no	—
595	C₂²×C₄	—	8	1	no	—
596	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
597	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
602	C₂²×C₄	#41×C₅₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
604	SD₁₆	—	2	8	no	—
605	SD₁₆	—	4	4	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	4	4	no	—
616	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
617	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
618	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	8	1	no	—
631	C₄⋊C₄	C₂²×C₄×C₅₃	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	8	1	no	—
641	C₂²⋊C₄	—	8	1	no	—
642	C₂²⋊C₄	SD₁₆×C₅₃	1	4	yes	complemented
643	C₄²	—	2	1	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	2	1	no	—
646	C₄²	—	2	1	no	—
647	C₄²	—	4	2	no	—
648	C₄²	—	8	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	4	8	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	8	no	—
669	C₂³	—	8	4	no	—
670	C₂³	—	8	4	no	—
671	C₂³	—	8	4	no	—
672	C₂³	—	8	4	no	—
673	C₂³	—	8	4	no	—
674	C₂³	C₄×D₄×C₅₃	1	2	yes	—
675	C₂³	C₂×SD₁₆×C₅₃	1	2	yes	—
676	C₂³	#135×C₅₃	1	2	yes	—
677	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	4	1	no	—
681	Q₈	—	4	1	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	2	no	—
687	D₄	—	4	8	no	—
688	D₄	—	4	1	no	—
689	D₄	—	4	1	no	—
690	D₄	C₄×D₄×C₅₃	1	4	yes	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	—	8	4	no	—
728	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
729	C₂×C₄	C₂×SD₁₆×C₅₃	1	2	yes	—
730	C₂×C₄	C₂×SD₁₆×C₅₃	1	2	yes	—
731	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
733	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
734	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
735	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
736	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
737	C₈	—	2	2	no	—
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	4	1	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	8	16	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	C₄×SD₁₆×C₅₃	1	4	yes	complemented
763	C₂²	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
764	C₂²	D₄²×C₅₃	1	1	yes	characteristic
765	C₂²	C₅₃×#546	1	1	yes	characteristic
766	C₂²	C₂²×SD₁₆×C₅₃	1	1	yes	characteristic
767	C₂²	C₂×#135×C₅₃	1	1	yes	characteristic
768	C₂²	C₅₃×#576	1	1	yes	characteristic
769	C₂²	C₅₃×#577	1	1	yes	characteristic
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	2	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	2	no	—
778	C₄	—	8	1	no	—
779	C₄	—	8	1	no	—
780	C₄	—	8	1	no	—
781	C₄	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
782	C₄	C₅₃×#518	1	1	yes	characteristic
783	C₄	C₅₃×#546	1	1	yes	characteristic
784	C₄	C₅₃×#551	1	1	yes	characteristic
785	C₂	—	2	4	no	—
786	C₂	—	4	4	no	—
787	C₂	—	8	2	no	—
788	C₂	C₅₃×#2358	1	1	yes	characteristic
789	C₂	C₂×C₄×SD₁₆×C₅₃	1	1	yes	characteristic
790	C₂	C₅₃×#2946	1	1	yes	characteristic
791	C₂	C₅₃×#3280	1	1	yes	characteristic
792	C₂	D₄×SD₁₆×C₅₃	1	1	yes	characteristic
793	C₂	C₅₃×#3295	1	1	yes	characteristic
794	C₂	C₅₃×#3296	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂³×D₄×C₅₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₄×C₂²⋊C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₅₃	C₂	semidirect
4. C₅₃×#2360	C₂	semidirect
6. C₅₃×#1968	C₂	semidirect
7. C₅₃×#1934	C₂	semidirect
8. C₅₃×#1926	C₂	semidirect
9. C₅₃×#1892	C₂	semidirect
10. C₅₃×#1880	C₂	semidirect
11. C₅₃×#1877	C₂	semidirect
12. C₅₃×#1864	C₂	semidirect
13. C₅₃×#1853	C₂	semidirect
14. C₄×#102×C₅₃	C₂	semidirect
15. C₈×C₂²⋊C₄×C₅₃	C₂	semidirect
21. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
26. C₅₃×#450	C₄	semidirect
28. C₂×#106×C₅₃	C₂²	semidirect
29. C₂×#106×C₅₃	C₂²	semidirect
30. C₂×#103×C₅₃	C₂²	semidirect
31. C₂×#103×C₅₃	C₂²	semidirect
40. C₂×C₄×C₈×C₅₃	C₂²	semidirect
41. C₂×C₄×C₈×C₅₃	C₂²	semidirect
42. C₅₃×#391	C₂²	semidirect
46. C₅₃×#389	C₂²	semidirect
53. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
56. C₅₃×#340	C₂²	semidirect
57. C₅₃×#340	C₂²	semidirect
58. C₅₃×#340	C₂²	semidirect
59. C₅₃×#340	C₂²	semidirect
60. C₅₃×#336	C₂²	semidirect
61. C₅₃×#336	C₂²	semidirect
81. C₂×SD₁₆×C₅₃	C₂×C₄	semidirect
82. C₂×SD₁₆×C₅₃	C₂×C₄	semidirect
91. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
131. #102×C₅₃	C₂×C₄	semidirect
132. #102×C₅₃	C₂×C₄	semidirect
134. C₂²⋊C₈×C₅₃	C₂×C₄	semidirect
244. C₂²⋊C₄×C₅₃	SD₁₆	semidirect
343. #22874	C₅₃	direct (N × H)
365. C₂²×C₅₃	C₄×SD₁₆	semidirect
389. C₂×C₄×SD₁₆	C₂×C₅₃	semidirect
391. #2360	C₂×C₅₃	semidirect
393. #1968	C₂×C₅₃	semidirect
394. #1934	C₂×C₅₃	semidirect
395. #1926	C₂×C₅₃	semidirect
396. #1892	C₂×C₅₃	semidirect
397. #1880	C₂×C₅₃	semidirect
398. #1877	C₂×C₅₃	semidirect
399. #1864	C₂×C₅₃	semidirect
400. #1853	C₂×C₅₃	semidirect
401. C₄×#102	C₂×C₅₃	semidirect
402. C₈×C₂²⋊C₄	C₂×C₅₃	semidirect
418. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
423. #450	C₄×C₅₃	semidirect
425. C₂×#106	C₂²×C₅₃	semidirect
426. C₂×#106	C₂²×C₅₃	semidirect
427. C₂×#103	C₂²×C₅₃	semidirect
428. C₂×#103	C₂²×C₅₃	semidirect
437. C₂×C₄×C₈	C₂²×C₅₃	semidirect
438. C₂×C₄×C₈	C₂²×C₅₃	semidirect
439. #391	C₂²×C₅₃	semidirect
443. #389	C₂²×C₅₃	semidirect
450. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
453. #340	C₂²×C₅₃	semidirect
454. #340	C₂²×C₅₃	semidirect
455. #340	C₂²×C₅₃	semidirect
456. #340	C₂²×C₅₃	semidirect
457. #336	C₂²×C₅₃	semidirect
458. #336	C₂²×C₅₃	semidirect
459. C₅₃	#22874	direct (N × H)
479. C₂×SD₁₆	C₂×C₄×C₅₃	semidirect
480. C₂×SD₁₆	C₂×C₄×C₅₃	semidirect
489. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
529. #102	C₂×C₄×C₅₃	semidirect
530. #102	C₂×C₄×C₅₃	semidirect
532. C₂²⋊C₈	C₂×C₄×C₅₃	semidirect
642. C₂²⋊C₄	SD₁₆×C₅₃	semidirect
762. C₂²	C₄×SD₁₆×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#450	2
C₂×C₄×SD₁₆×C₅₃	2
C₂²×#102×C₅₃	2
C₅₃×#2360	2
D₄×C₂²⋊C₄×C₅₃	2
C₅₃×#1968	2
C₅₃×#1934	2
C₅₃×#1926	2
C₅₃×#1892	2
C₅₃×#1880	2
C₅₃×#1877	2
C₅₃×#1864	2
C₅₃×#1853	2
C₄×#102×C₅₃	2
C₈×C₂²⋊C₄×C₅₃	2
#22874	53

Subgroups — C53×#22874 #27230386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#22874 #27230386