Subgroups — C₅₃×#24259 #27231771

Order 13568.

1566 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1959	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
21	C₅₃×#546	—	2	4	no	—
22	C₅₃×#546	—	2	4	no	—
23	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×#123×C₅₃	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#121×C₅₃	—	2	1	no	—
29	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#120×C₅₃	—	2	1	no	—
31	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
35	C₅₃×#464	—	2	4	no	—
36	C₅₃×#452	—	2	4	no	—
37	C₅₃×#450	—	2	4	no	—
38	C₅₃×#440	—	2	4	no	—
39	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#396	—	2	1	no	—
57	C₅₃×#396	—	2	1	no	—
58	C₅₃×#390	—	2	1	no	—
59	C₅₃×#389	—	2	1	no	—
60	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#380	C₂²	1	1	yes	characteristic
62	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₅₃	—	2	1	no	—
66	C₂×#41×C₅₃	—	2	2	no	—
67	C₂×#41×C₅₃	—	2	2	no	—
68	C₂×#41×C₅₃	—	2	2	no	—
69	C₂×#41×C₅₃	—	2	2	no	—
70	C₂×#41×C₅₃	—	4	1	no	—
71	C₂×#41×C₅₃	—	4	1	no	—
72	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₅₃	—	2	1	no	—
75	C₂²×D₄×C₅₃	—	2	1	no	—
76	C₂²×D₄×C₅₃	—	2	2	no	—
77	C₂²×D₄×C₅₃	—	2	2	no	—
78	C₂²×D₄×C₅₃	—	2	2	no	—
79	C₂²×D₄×C₅₃	—	2	2	no	—
80	C₂²×D₄×C₅₃	—	2	1	no	—
81	C₂²×D₄×C₅₃	—	4	1	no	—
82	C₂²×D₄×C₅₃	—	4	1	no	—
83	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
84	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅₃	—	2	1	no	—
87	C₂³×C₄×C₅₃	—	2	1	no	—
88	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂×Q₁₆×C₅₃	—	2	2	no	—
91	C₂×Q₁₆×C₅₃	—	2	2	no	—
92	C₂×Q₁₆×C₅₃	—	4	1	no	—
93	C₂×SD₁₆×C₅₃	—	2	2	no	—
94	C₂×SD₁₆×C₅₃	—	2	2	no	—
95	C₂×SD₁₆×C₅₃	—	2	2	no	—
96	C₂×SD₁₆×C₅₃	—	2	2	no	—
97	C₂×SD₁₆×C₅₃	—	4	1	no	—
98	C₂×SD₁₆×C₅₃	D₄	1	4	yes	complemented
99	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
103	#124×C₅₃	—	2	2	no	—
104	#124×C₅₃	D₄	1	4	yes	—
105	#123×C₅₃	—	2	8	no	—
106	C₂²⋊Q₈×C₅₃	—	2	2	no	—
107	C₂²⋊Q₈×C₅₃	—	2	2	no	—
108	C₂²⋊Q₈×C₅₃	—	2	2	no	—
109	C₂²⋊Q₈×C₅₃	—	2	2	no	—
110	C₂²⋊Q₈×C₅₃	—	4	1	no	—
111	C₂²⋊Q₈×C₅₃	—	4	1	no	—
112	#121×C₅₃	—	2	8	no	—
113	#121×C₅₃	—	2	2	no	—
114	#121×C₅₃	—	2	2	no	—
115	#120×C₅₃	—	2	8	no	—
116	C₄×Q₈×C₅₃	—	2	2	no	—
117	C₄×Q₈×C₅₃	—	2	2	no	—
118	C₄×D₄×C₅₃	—	2	2	no	—
119	C₄×D₄×C₅₃	—	2	2	no	—
120	C₄×D₄×C₅₃	—	2	2	no	—
121	C₄×D₄×C₅₃	D₄	1	4	yes	—
122	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
123	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
124	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
125	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
126	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
127	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
128	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
134	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
145	C₂×C₄²×C₅₃	—	2	1	no	—
146	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
147	#107×C₅₃	—	2	2	no	—
148	C₄⋊C₈×C₅₃	—	2	2	no	—
149	#103×C₅₃	—	2	2	no	—
150	#103×C₅₃	—	2	2	no	—
151	#103×C₅₃	—	2	2	no	—
152	#103×C₅₃	—	4	1	no	—
153	#102×C₅₃	—	2	2	no	—
154	#102×C₅₃	—	2	2	no	—
155	#102×C₅₃	—	2	2	no	—
156	#102×C₅₃	—	2	2	no	—
157	#102×C₅₃	—	2	2	no	—
158	#102×C₅₃	—	4	1	no	—
159	C₂²⋊C₈×C₅₃	—	2	2	no	—
160	C₂²⋊C₈×C₅₃	—	2	2	no	—
161	C₂²⋊C₈×C₅₃	—	4	1	no	—
162	C₂²⋊C₈×C₅₃	—	4	1	no	—
163	#97×C₅₃	—	2	2	no	—
164	#95×C₅₃	—	2	1	no	—
165	#95×C₅₃	—	2	1	no	—
166	C₂⁴×C₅₃	—	2	1	no	—
167	C₂⁴×C₅₃	—	2	4	no	—
168	C₂⁴×C₅₃	—	2	1	no	—
169	C₂⁴×C₅₃	—	4	2	no	—
170	C₂⁴×C₅₃	—	4	2	no	—
171	C₂⁴×C₅₃	—	4	2	no	—
172	C₂⁴×C₅₃	—	4	2	no	—
173	C₂⁴×C₅₃	—	8	1	no	—
174	C₂⁴×C₅₃	—	8	1	no	—
175	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
176	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
177	#41×C₅₃	—	4	4	no	—
178	#41×C₅₃	—	4	4	no	—
179	#41×C₅₃	—	4	4	no	—
180	#41×C₅₃	—	4	4	no	—
181	C₂×Q₈×C₅₃	—	2	1	no	—
182	C₂×Q₈×C₅₃	—	2	1	no	—
183	C₂×Q₈×C₅₃	—	2	1	no	—
184	C₂×Q₈×C₅₃	—	2	1	no	—
185	C₂×Q₈×C₅₃	—	2	1	no	—
186	C₂×Q₈×C₅₃	—	2	1	no	—
187	C₂×Q₈×C₅₃	—	2	1	no	—
188	C₂×Q₈×C₅₃	—	2	1	no	—
189	C₂×Q₈×C₅₃	—	2	1	no	—
190	C₂×Q₈×C₅₃	—	2	1	no	—
191	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
192	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
193	C₂×D₄×C₅₃	—	2	4	no	—
194	C₂×D₄×C₅₃	—	2	4	no	—
195	C₂×D₄×C₅₃	—	2	2	no	—
196	C₂×D₄×C₅₃	—	2	4	no	—
197	C₂×D₄×C₅₃	—	2	2	no	—
198	C₂×D₄×C₅₃	—	2	1	no	—
199	C₂×D₄×C₅₃	—	2	1	no	—
200	C₂×D₄×C₅₃	—	2	1	no	—
201	C₂×D₄×C₅₃	—	2	1	no	—
202	C₂×D₄×C₅₃	—	2	1	no	—
203	C₂×D₄×C₅₃	—	2	1	no	—
204	C₂×D₄×C₅₃	—	2	1	no	—
205	C₂×D₄×C₅₃	—	2	1	no	—
206	C₂×D₄×C₅₃	—	4	1	no	—
207	C₂×D₄×C₅₃	—	4	2	no	—
208	C₂×D₄×C₅₃	—	4	2	no	—
209	C₂×D₄×C₅₃	—	4	4	no	—
210	C₂×D₄×C₅₃	—	4	4	no	—
211	C₂×D₄×C₅₃	—	4	4	no	—
212	C₂×D₄×C₅₃	—	4	2	no	—
213	C₂×D₄×C₅₃	—	4	2	no	—
214	C₂×D₄×C₅₃	—	4	4	no	—
215	C₂×D₄×C₅₃	—	8	1	no	—
216	C₂×D₄×C₅₃	—	8	1	no	—
217	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₅₃	#41	1	2	yes	—
221	C₂²×C₄×C₅₃	—	2	4	no	—
222	C₂²×C₄×C₅₃	—	2	1	no	—
223	C₂²×C₄×C₅₃	—	2	1	no	—
224	C₂²×C₄×C₅₃	—	2	1	no	—
225	C₂²×C₄×C₅₃	—	2	1	no	—
226	C₂²×C₄×C₅₃	—	2	1	no	—
227	C₂²×C₄×C₅₃	—	2	1	no	—
228	C₂²×C₄×C₅₃	—	2	1	no	—
229	C₂²×C₄×C₅₃	—	2	1	no	—
230	C₂²×C₄×C₅₃	—	2	1	no	—
231	C₂²×C₄×C₅₃	—	2	1	no	—
232	C₂²×C₄×C₅₃	—	2	1	no	—
233	C₂²×C₄×C₅₃	—	2	1	no	—
234	C₂²×C₄×C₅₃	—	2	1	no	—
235	C₂²×C₄×C₅₃	—	2	1	no	—
236	C₂²×C₄×C₅₃	—	2	1	no	—
237	C₂²×C₄×C₅₃	—	2	4	no	—
238	C₂²×C₄×C₅₃	—	2	1	no	—
239	C₂²×C₄×C₅₃	—	2	1	no	—
240	C₂²×C₄×C₅₃	—	2	1	no	—
241	C₂²×C₄×C₅₃	—	4	2	no	—
242	C₂²×C₄×C₅₃	—	4	2	no	—
243	C₂²×C₄×C₅₃	—	8	1	no	—
244	C₂²×C₄×C₅₃	—	8	1	no	—
245	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
250	Q₁₆×C₅₃	—	4	4	no	—
251	SD₁₆×C₅₃	—	2	8	no	—
252	SD₁₆×C₅₃	—	4	4	no	—
253	C₂×C₈×C₅₃	—	2	1	no	—
254	C₂×C₈×C₅₃	—	2	1	no	—
255	C₂×C₈×C₅₃	—	2	1	no	—
256	C₂×C₈×C₅₃	—	2	1	no	—
257	C₂×C₈×C₅₃	—	2	1	no	—
258	C₂×C₈×C₅₃	—	2	1	no	—
259	C₂×C₈×C₅₃	—	2	1	no	—
260	C₂×C₈×C₅₃	—	2	1	no	—
261	C₂×C₈×C₅₃	—	2	1	no	—
262	C₂×C₈×C₅₃	—	2	1	no	—
263	C₂×C₈×C₅₃	—	2	1	no	—
264	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₅₃	—	2	4	no	—
266	C₄⋊C₄×C₅₃	—	2	2	no	—
267	C₄⋊C₄×C₅₃	—	2	1	no	—
268	C₄⋊C₄×C₅₃	—	2	1	no	—
269	C₄⋊C₄×C₅₃	—	2	1	no	—
270	C₄⋊C₄×C₅₃	—	2	1	no	—
271	C₄⋊C₄×C₅₃	—	2	1	no	—
272	C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₄⋊C₄×C₅₃	—	2	1	no	—
274	C₄⋊C₄×C₅₃	—	4	2	no	—
275	C₄⋊C₄×C₅₃	—	4	2	no	—
276	C₄⋊C₄×C₅₃	—	4	2	no	—
277	C₄⋊C₄×C₅₃	—	4	2	no	—
278	C₄⋊C₄×C₅₃	—	8	1	no	—
279	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
280	C₂²⋊C₄×C₅₃	—	2	4	no	—
281	C₂²⋊C₄×C₅₃	—	2	4	no	—
282	C₂²⋊C₄×C₅₃	—	2	2	no	—
283	C₂²⋊C₄×C₅₃	—	2	4	no	—
284	C₂²⋊C₄×C₅₃	—	2	4	no	—
285	C₂²⋊C₄×C₅₃	—	2	4	no	—
286	C₂²⋊C₄×C₅₃	—	2	2	no	—
287	C₂²⋊C₄×C₅₃	—	4	2	no	—
288	C₂²⋊C₄×C₅₃	—	4	2	no	—
289	C₂²⋊C₄×C₅₃	—	8	1	no	—
290	C₂²⋊C₄×C₅₃	—	8	1	no	—
291	C₄²×C₅₃	—	4	2	no	—
292	C₄²×C₅₃	C₂×D₄	1	2	yes	—
293	C₄²×C₅₃	C₂×D₄	1	2	yes	—
294	C₂³×C₅₃	—	2	2	no	—
295	C₂³×C₅₃	—	2	1	no	—
296	C₂³×C₅₃	—	2	1	no	—
297	C₂³×C₅₃	—	2	2	no	—
298	C₂³×C₅₃	—	2	1	no	—
299	C₂³×C₅₃	—	2	2	no	—
300	C₂³×C₅₃	—	2	1	no	—
301	C₂³×C₅₃	—	2	1	no	—
302	C₂³×C₅₃	—	2	1	no	—
303	C₂³×C₅₃	—	2	1	no	—
304	C₂³×C₅₃	—	2	2	no	—
305	C₂³×C₅₃	—	2	1	no	—
306	C₂³×C₅₃	—	2	1	no	—
307	C₂³×C₅₃	—	2	1	no	—
308	C₂³×C₅₃	—	2	1	no	—
309	C₂³×C₅₃	—	2	1	no	—
310	C₂³×C₅₃	—	2	1	no	—
311	C₂³×C₅₃	—	4	8	no	—
312	C₂³×C₅₃	—	4	8	no	—
313	C₂³×C₅₃	—	4	1	no	—
314	C₂³×C₅₃	—	4	1	no	—
315	C₂³×C₅₃	—	4	1	no	—
316	C₂³×C₅₃	—	4	1	no	—
317	C₂³×C₅₃	—	4	1	no	—
318	C₂³×C₅₃	—	4	1	no	—
319	C₂³×C₅₃	—	4	1	no	—
320	C₂³×C₅₃	—	4	1	no	—
321	C₂³×C₅₃	—	4	1	no	—
322	C₂³×C₅₃	—	4	1	no	—
323	C₂³×C₅₃	—	8	4	no	—
324	C₂³×C₅₃	—	8	4	no	—
325	C₂³×C₅₃	—	8	4	no	—
326	C₂³×C₅₃	—	8	4	no	—
327	C₂³×C₅₃	—	8	4	no	—
328	C₂³×C₅₃	#137	1	2	yes	—
329	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₅₃	—	2	2	no	—
331	Q₈×C₅₃	—	2	2	no	—
332	Q₈×C₅₃	—	2	2	no	—
333	Q₈×C₅₃	—	2	2	no	—
334	Q₈×C₅₃	—	4	1	no	—
335	Q₈×C₅₃	—	4	1	no	—
336	Q₈×C₅₃	—	4	1	no	—
337	Q₈×C₅₃	—	4	1	no	—
338	D₄×C₅₃	—	2	2	no	—
339	D₄×C₅₃	—	2	2	no	—
340	D₄×C₅₃	—	2	2	no	—
341	D₄×C₅₃	—	2	2	no	—
342	D₄×C₅₃	—	2	2	no	—
343	D₄×C₅₃	—	4	4	no	—
344	D₄×C₅₃	—	4	8	no	—
345	D₄×C₅₃	—	4	8	no	—
346	D₄×C₅₃	—	4	1	no	—
347	D₄×C₅₃	—	4	1	no	—
348	D₄×C₅₃	—	8	4	no	—
349	D₄×C₅₃	#121	1	4	yes	—
350	C₂×C₄×C₅₃	—	2	1	no	—
351	C₂×C₄×C₅₃	—	2	1	no	—
352	C₂×C₄×C₅₃	—	2	1	no	—
353	C₂×C₄×C₅₃	—	2	1	no	—
354	C₂×C₄×C₅₃	—	2	1	no	—
355	C₂×C₄×C₅₃	—	2	2	no	—
356	C₂×C₄×C₅₃	—	2	2	no	—
357	C₂×C₄×C₅₃	—	2	1	no	—
358	C₂×C₄×C₅₃	—	2	1	no	—
359	C₂×C₄×C₅₃	—	2	1	no	—
360	C₂×C₄×C₅₃	—	2	2	no	—
361	C₂×C₄×C₅₃	—	2	1	no	—
362	C₂×C₄×C₅₃	—	2	1	no	—
363	C₂×C₄×C₅₃	—	4	8	no	—
364	C₂×C₄×C₅₃	—	4	1	no	—
365	C₂×C₄×C₅₃	—	4	1	no	—
366	C₂×C₄×C₅₃	—	4	1	no	—
367	C₂×C₄×C₅₃	—	4	1	no	—
368	C₂×C₄×C₅₃	—	4	1	no	—
369	C₂×C₄×C₅₃	—	4	1	no	—
370	C₂×C₄×C₅₃	—	4	1	no	—
371	C₂×C₄×C₅₃	—	4	1	no	—
372	C₂×C₄×C₅₃	—	4	1	no	—
373	C₂×C₄×C₅₃	—	4	1	no	—
374	C₂×C₄×C₅₃	—	4	1	no	—
375	C₂×C₄×C₅₃	—	4	1	no	—
376	C₂×C₄×C₅₃	—	4	1	no	—
377	C₂×C₄×C₅₃	—	4	1	no	—
378	C₂×C₄×C₅₃	—	4	1	no	—
379	C₂×C₄×C₅₃	—	4	1	no	—
380	C₂×C₄×C₅₃	—	4	1	no	—
381	C₂×C₄×C₅₃	—	4	1	no	—
382	C₂×C₄×C₅₃	—	4	1	no	—
383	C₂×C₄×C₅₃	—	4	1	no	—
384	C₂×C₄×C₅₃	—	4	1	no	—
385	C₂×C₄×C₅₃	—	4	1	no	—
386	C₂×C₄×C₅₃	—	4	1	no	—
387	C₂×C₄×C₅₃	—	8	4	no	—
388	C₂×C₄×C₅₃	#120	1	2	yes	—
389	C₂×C₄×C₅₃	#120	1	2	yes	—
390	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
394	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
395	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
396	C₈×C₅₃	—	2	2	no	—
397	C₈×C₅₃	—	4	1	no	—
398	C₈×C₅₃	—	4	1	no	—
399	C₈×C₅₃	—	4	1	no	—
400	#24259	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂²×C₅₃	—	2	4	no	—
402	C₂²×C₅₃	—	2	2	no	—
403	C₂²×C₅₃	—	2	2	no	—
404	C₂²×C₅₃	—	2	2	no	—
405	C₂²×C₅₃	—	4	1	no	—
406	C₂²×C₅₃	—	4	2	no	—
407	C₂²×C₅₃	—	4	2	no	—
408	C₂²×C₅₃	—	4	2	no	—
409	C₂²×C₅₃	—	4	1	no	—
410	C₂²×C₅₃	—	4	1	no	—
411	C₂²×C₅₃	—	4	2	no	—
412	C₂²×C₅₃	—	4	1	no	—
413	C₂²×C₅₃	—	4	2	no	—
414	C₂²×C₅₃	—	4	2	no	—
415	C₂²×C₅₃	—	4	1	no	—
416	C₂²×C₅₃	—	4	2	no	—
417	C₂²×C₅₃	—	4	1	no	—
418	C₂²×C₅₃	—	4	2	no	—
419	C₂²×C₅₃	—	4	1	no	—
420	C₂²×C₅₃	—	4	1	no	—
421	C₂²×C₅₃	—	4	2	no	—
422	C₂²×C₅₃	—	4	1	no	—
423	C₂²×C₅₃	—	4	1	no	—
424	C₂²×C₅₃	—	4	1	no	—
425	C₂²×C₅₃	—	8	16	no	—
426	C₂²×C₅₃	—	8	1	no	—
427	C₂²×C₅₃	—	8	1	no	—
428	C₂²×C₅₃	—	8	1	no	—
429	C₂²×C₅₃	—	8	1	no	—
430	C₂²×C₅₃	C₂×#120	1	1	yes	characteristic
431	C₂²×C₅₃	D₄²	1	1	yes	characteristic
432	C₂²×C₅₃	#546	1	1	yes	characteristic
433	C₂²×C₅₃	C₂×#137	1	1	yes	characteristic
434	C₂²×C₅₃	#575	1	1	yes	characteristic
435	C₂²×C₅₃	#576	1	1	yes	characteristic
436	C₂²×C₅₃	#577	1	1	yes	characteristic
437	C₄×C₅₃	—	2	2	no	—
438	C₄×C₅₃	—	2	2	no	—
439	C₄×C₅₃	—	4	1	no	—
440	C₄×C₅₃	—	4	1	no	—
441	C₄×C₅₃	—	4	2	no	—
442	C₄×C₅₃	—	4	2	no	—
443	C₄×C₅₃	—	4	2	no	—
444	C₄×C₅₃	—	8	1	no	—
445	C₄×C₅₃	—	8	1	no	—
446	C₄×C₅₃	—	8	1	no	—
447	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
448	C₄×C₅₃	#535	1	1	yes	characteristic
449	C₄×C₅₃	D₄²	1	1	yes	characteristic
450	C₄×C₅₃	#546	1	1	yes	characteristic
451	C₂×#546	C₂×C₅₃	1	1	yes	characteristic
452	C₂×#464	C₂×C₅₃	1	1	yes	characteristic, complemented
453	C₂×#452	C₂×C₅₃	1	1	yes	characteristic, complemented
454	C₂×#450	C₂×C₅₃	1	1	yes	characteristic, complemented
455	C₂×#440	C₂×C₅₃	1	1	yes	characteristic, complemented
456	#2538	C₂×C₅₃	1	1	yes	characteristic, complemented
457	#2036	C₂×C₅₃	1	1	yes	characteristic, complemented
458	#2033	C₂×C₅₃	1	1	yes	characteristic, complemented
459	#2001	C₂×C₅₃	1	1	yes	characteristic, complemented
460	#2000	C₂×C₅₃	1	1	yes	characteristic, complemented
461	#1959	C₂×C₅₃	1	1	yes	characteristic, complemented
462	#1955	C₂×C₅₃	1	1	yes	characteristic, complemented
463	#1802	C₂×C₅₃	1	1	yes	characteristic, complemented
464	#1788	C₂×C₅₃	1	1	yes	characteristic, complemented
465	#1786	C₂×C₅₃	1	1	yes	characteristic, complemented
466	C₂×C₅₃	—	4	2	no	—
467	C₂×C₅₃	—	4	4	no	—
468	C₂×C₅₃	—	8	1	no	—
469	C₂×C₅₃	—	8	2	no	—
470	C₂×C₅₃	#2408	1	1	yes	characteristic
471	C₂×C₅₃	#3007	1	1	yes	characteristic
472	C₂×C₅₃	#3012	1	1	yes	characteristic
473	C₂×C₅₃	#3266	1	1	yes	characteristic
474	C₂×C₅₃	#3268	1	1	yes	characteristic
475	C₂×C₅₃	#3311	1	1	yes	characteristic
476	C₂×C₅₃	#3314	1	1	yes	characteristic
477	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
478	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
479	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
480	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
481	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
482	#546	—	2	4	no	—
483	#546	—	2	4	no	—
484	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
485	C₂×#123	—	2	1	no	—
486	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
487	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
488	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
489	C₂×#121	—	2	1	no	—
490	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
491	C₂×#120	—	2	1	no	—
492	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
493	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
494	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
495	C₂²×C₂²⋊C₄	—	2	1	no	—
496	#464	—	2	4	no	—
497	#452	—	2	4	no	—
498	#450	—	2	4	no	—
499	#440	—	2	4	no	—
500	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
501	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
502	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
503	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
504	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
505	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
506	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
507	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
508	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
509	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
510	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
511	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
512	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
514	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
515	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
516	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
517	#396	—	2	1	no	—
518	#396	—	2	1	no	—
519	#390	—	2	1	no	—
520	#389	—	2	1	no	—
521	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
522	#380	C₂²×C₅₃	1	1	yes	characteristic
523	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
524	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
525	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
526	C₅₃	#24259	1	1	yes	characteristic, direct product factor, Sylow
527	C₂⁵	—	2	1	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	—	2	2	no	—
530	C₂×#41	—	2	2	no	—
531	C₂×#41	—	2	2	no	—
532	C₂×#41	—	4	1	no	—
533	C₂×#41	—	4	1	no	—
534	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
535	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	—	2	2	no	—
539	C₂²×D₄	—	2	2	no	—
540	C₂²×D₄	—	2	2	no	—
541	C₂²×D₄	—	2	2	no	—
542	C₂²×D₄	—	2	1	no	—
543	C₂²×D₄	—	4	1	no	—
544	C₂²×D₄	—	4	1	no	—
545	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
548	C₂³×C₄	—	2	1	no	—
549	C₂³×C₄	—	2	1	no	—
550	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
552	C₂×Q₁₆	—	2	2	no	—
553	C₂×Q₁₆	—	2	2	no	—
554	C₂×Q₁₆	—	4	1	no	—
555	C₂×SD₁₆	—	2	2	no	—
556	C₂×SD₁₆	—	2	2	no	—
557	C₂×SD₁₆	—	2	2	no	—
558	C₂×SD₁₆	—	2	2	no	—
559	C₂×SD₁₆	—	4	1	no	—
560	C₂×SD₁₆	D₄×C₅₃	1	4	yes	complemented
561	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
562	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
563	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
564	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
565	#124	—	2	2	no	—
566	#124	D₄×C₅₃	1	4	yes	—
567	#123	—	2	8	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	4	1	no	—
573	C₂²⋊Q₈	—	4	1	no	—
574	#121	—	2	8	no	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#120	—	2	8	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	D₄×C₅₃	1	4	yes	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	—	2	8	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
607	C₂×C₄²	—	2	1	no	—
608	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
609	#107	—	2	2	no	—
610	C₄⋊C₈	—	2	2	no	—
611	#103	—	2	2	no	—
612	#103	—	2	2	no	—
613	#103	—	2	2	no	—
614	#103	—	4	1	no	—
615	#102	—	2	2	no	—
616	#102	—	2	2	no	—
617	#102	—	2	2	no	—
618	#102	—	2	2	no	—
619	#102	—	2	2	no	—
620	#102	—	4	1	no	—
621	C₂²⋊C₈	—	2	2	no	—
622	C₂²⋊C₈	—	2	2	no	—
623	C₂²⋊C₈	—	4	1	no	—
624	C₂²⋊C₈	—	4	1	no	—
625	#97	—	2	2	no	—
626	#95	—	2	1	no	—
627	#95	—	2	1	no	—
628	C₂⁴	—	2	1	no	—
629	C₂⁴	—	2	4	no	—
630	C₂⁴	—	2	1	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	—	4	2	no	—
634	C₂⁴	—	4	2	no	—
635	C₂⁴	—	8	1	no	—
636	C₂⁴	—	8	1	no	—
637	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
638	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
639	#41	—	4	4	no	—
640	#41	—	4	4	no	—
641	#41	—	4	4	no	—
642	#41	—	4	4	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
654	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	4	1	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	4	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	4	no	—
677	C₂×D₄	—	8	1	no	—
678	C₂×D₄	—	8	1	no	—
679	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
680	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
681	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
682	C₂×D₄	#41×C₅₃	1	2	yes	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	8	1	no	—
706	C₂²×C₄	—	8	1	no	—
707	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
712	Q₁₆	—	4	4	no	—
713	SD₁₆	—	2	8	no	—
714	SD₁₆	—	4	4	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	—	2	1	no	—
717	C₂×C₈	—	2	1	no	—
718	C₂×C₈	—	2	1	no	—
719	C₂×C₈	—	2	1	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	2	1	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	8	1	no	—
741	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	8	1	no	—
752	C₂²⋊C₄	—	8	1	no	—
753	C₄²	—	4	2	no	—
754	C₄²	C₂×D₄×C₅₃	1	2	yes	—
755	C₄²	C₂×D₄×C₅₃	1	2	yes	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	4	8	no	—
774	C₂³	—	4	8	no	—
775	C₂³	—	4	1	no	—
776	C₂³	—	4	1	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	—	4	1	no	—
781	C₂³	—	4	1	no	—
782	C₂³	—	4	1	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	1	no	—
785	C₂³	—	8	4	no	—
786	C₂³	—	8	4	no	—
787	C₂³	—	8	4	no	—
788	C₂³	—	8	4	no	—
789	C₂³	—	8	4	no	—
790	C₂³	#137×C₅₃	1	2	yes	—
791	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
792	Q₈	—	2	2	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	2	2	no	—
796	Q₈	—	4	1	no	—
797	Q₈	—	4	1	no	—
798	Q₈	—	4	1	no	—
799	Q₈	—	4	1	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	8	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	1	no	—
809	D₄	—	4	1	no	—
810	D₄	—	8	4	no	—
811	D₄	#121×C₅₃	1	4	yes	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	4	8	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	1	no	—
848	C₂×C₄	—	4	1	no	—
849	C₂×C₄	—	8	4	no	—
850	C₂×C₄	#120×C₅₃	1	2	yes	—
851	C₂×C₄	#120×C₅₃	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
855	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
856	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
857	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
858	C₈	—	2	2	no	—
859	C₈	—	4	1	no	—
860	C₈	—	4	1	no	—
861	C₈	—	4	1	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	8	16	no	—
887	C₂²	—	8	1	no	—
888	C₂²	—	8	1	no	—
889	C₂²	—	8	1	no	—
890	C₂²	—	8	1	no	—
891	C₂²	C₂×#120×C₅₃	1	1	yes	characteristic
892	C₂²	D₄²×C₅₃	1	1	yes	characteristic
893	C₂²	C₅₃×#546	1	1	yes	characteristic
894	C₂²	C₂×#137×C₅₃	1	1	yes	characteristic
895	C₂²	C₅₃×#575	1	1	yes	characteristic
896	C₂²	C₅₃×#576	1	1	yes	characteristic
897	C₂²	C₅₃×#577	1	1	yes	characteristic
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	8	1	no	—
906	C₄	—	8	1	no	—
907	C₄	—	8	1	no	—
908	C₄	C₂×#121×C₅₃	1	1	yes	characteristic
909	C₄	C₅₃×#535	1	1	yes	characteristic
910	C₄	D₄²×C₅₃	1	1	yes	characteristic
911	C₄	C₅₃×#546	1	1	yes	characteristic
912	C₂	—	4	2	no	—
913	C₂	—	4	4	no	—
914	C₂	—	8	1	no	—
915	C₂	—	8	2	no	—
916	C₂	C₅₃×#2408	1	1	yes	characteristic
917	C₂	C₅₃×#3007	1	1	yes	characteristic
918	C₂	C₅₃×#3012	1	1	yes	characteristic
919	C₂	C₅₃×#3266	1	1	yes	characteristic
920	C₂	C₅₃×#3268	1	1	yes	characteristic
921	C₂	C₅₃×#3311	1	1	yes	characteristic
922	C₂	C₅₃×#3314	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂×C₅₃×#546	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#464	C₂	semidirect
3. C₂×C₅₃×#452	C₂	semidirect
4. C₂×C₅₃×#450	C₂	semidirect
5. C₂×C₅₃×#440	C₂	semidirect
6. C₅₃×#2538	C₂	semidirect
7. C₅₃×#2036	C₂	semidirect
8. C₅₃×#2033	C₂	semidirect
9. C₅₃×#2001	C₂	semidirect
10. C₅₃×#2000	C₂	semidirect
11. C₅₃×#1959	C₂	semidirect
12. C₅₃×#1955	C₂	semidirect
13. C₅₃×#1802	C₂	semidirect
14. C₅₃×#1788	C₂	semidirect
15. C₅₃×#1786	C₂	semidirect
18. C₂²×Q₁₆×C₅₃	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
31. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
39. C₂×#107×C₅₃	C₂²	semidirect
40. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
41. C₂×#103×C₅₃	C₂²	semidirect
42. C₂×#103×C₅₃	C₂²	semidirect
43. C₂×#103×C₅₃	C₂²	semidirect
44. C₂×#103×C₅₃	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
54. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
55. C₂×#97×C₅₃	C₂²	semidirect
60. C₅₃×#384	C₂²	semidirect
62. C₅₃×#380	C₂²	semidirect
63. C₅₃×#340	C₂²	semidirect
64. C₅₃×#340	C₂²	semidirect
98. C₂×SD₁₆×C₅₃	D₄	semidirect
400. #24259	C₅₃	direct (N × H)
452. C₂×#464	C₂×C₅₃	semidirect
453. C₂×#452	C₂×C₅₃	semidirect
454. C₂×#450	C₂×C₅₃	semidirect
455. C₂×#440	C₂×C₅₃	semidirect
456. #2538	C₂×C₅₃	semidirect
457. #2036	C₂×C₅₃	semidirect
458. #2033	C₂×C₅₃	semidirect
459. #2001	C₂×C₅₃	semidirect
460. #2000	C₂×C₅₃	semidirect
461. #1959	C₂×C₅₃	semidirect
462. #1955	C₂×C₅₃	semidirect
463. #1802	C₂×C₅₃	semidirect
464. #1788	C₂×C₅₃	semidirect
465. #1786	C₂×C₅₃	semidirect
479. C₂²×Q₁₆	C₂²×C₅₃	semidirect
488. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
492. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
500. C₂×#107	C₂²×C₅₃	semidirect
501. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
502. C₂×#103	C₂²×C₅₃	semidirect
503. C₂×#103	C₂²×C₅₃	semidirect
504. C₂×#103	C₂²×C₅₃	semidirect
505. C₂×#103	C₂²×C₅₃	semidirect
514. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
515. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
516. C₂×#97	C₂²×C₅₃	semidirect
521. #384	C₂²×C₅₃	semidirect
523. #380	C₂²×C₅₃	semidirect
524. #340	C₂²×C₅₃	semidirect
525. #340	C₂²×C₅₃	semidirect
526. C₅₃	#24259	direct (N × H)
560. C₂×SD₁₆	D₄×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×#546	2
C₂×C₅₃×#464	2
C₂×C₅₃×#452	2
C₂×C₅₃×#450	2
C₂×C₅₃×#440	2
C₅₃×#2538	2
C₅₃×#2036	2
C₅₃×#2033	2
C₅₃×#2001	2
C₅₃×#2000	2
C₅₃×#1959	2
C₅₃×#1955	2
C₅₃×#1802	2
C₅₃×#1788	2
C₅₃×#1786	2
#24259	53

Subgroups — C53×#24259 #27231771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#24259 #27231771