Subgroups — C₅₃×#34289 #27241801

Order 13568.

3032 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2364	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2359	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2359	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2344	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2325	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2322	C₂	1	2	yes	maximal, complemented
19	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#123×C₅₃	C₂	1	2	yes	maximal, complemented
21	C₅₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#387	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#547	C₄	1	16	yes	complemented
27	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#123×C₅₃	C₂²	1	2	yes	—
29	C₂×#123×C₅₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#121×C₅₃	C₂²	1	2	yes	—
33	C₅₃×#520	—	2	8	no	—
34	C₄×#41×C₅₃	—	2	8	no	—
35	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₃	C₂²	1	2	yes	—
51	C₂×#117×C₅₃	C₂²	1	2	yes	—
52	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
53	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
54	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
56	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
57	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
58	C₅₃×#391	C₂²	1	1	yes	characteristic
59	C₅₃×#391	C₂²	1	1	yes	characteristic
60	C₅₃×#391	C₂²	1	1	yes	characteristic
61	C₅₃×#391	C₂²	1	1	yes	characteristic
62	C₅₃×#389	C₂²	1	1	yes	characteristic
63	C₅₃×#389	C₂²	1	2	yes	—
64	C₅₃×#389	C₂²	1	2	yes	—
65	C₅₃×#389	C₂²	1	2	yes	—
66	C₅₃×#389	C₂²	1	1	yes	characteristic
67	C₅₃×#388	C₂²	1	1	yes	characteristic
68	C₅₃×#388	C₂²	1	1	yes	characteristic
69	C₅₃×#388	C₂²	1	2	yes	—
70	C₅₃×#388	C₂²	1	2	yes	—
71	C₅₃×#388	C₂²	1	2	yes	—
72	C₅₃×#388	C₂²	1	2	yes	—
73	C₅₃×#388	C₂²	1	2	yes	—
74	C₅₃×#387	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	1	yes	characteristic
83	C₅₃×#387	C₂²	1	2	yes	—
84	C₅₃×#387	C₂²	1	2	yes	—
85	C₅₃×#387	C₂²	1	2	yes	—
86	C₅₃×#387	C₂²	1	2	yes	—
87	C₅₃×#386	C₂²	1	1	yes	characteristic
88	C₅₃×#386	C₂²	1	1	yes	characteristic
89	C₅₃×#386	C₂²	1	2	yes	—
90	C₅₃×#386	C₂²	1	2	yes	—
91	C₅₃×#386	C₂²	1	2	yes	—
92	C₅₃×#386	C₂²	1	2	yes	—
93	C₅₃×#386	C₂²	1	2	yes	—
94	C₅₃×#385	C₂²	1	1	yes	characteristic
95	C₅₃×#385	C₂²	1	1	yes	characteristic
96	C₅₃×#385	C₂²	1	2	yes	—
97	C₅₃×#385	C₂²	1	2	yes	—
98	C₅₃×#385	C₂²	1	2	yes	—
99	C₅₃×#385	C₂²	1	2	yes	—
100	C₅₃×#382	C₂²	1	1	yes	characteristic
101	C₅₃×#381	C₂²	1	2	yes	—
102	C₅₃×#381	C₂²	1	2	yes	—
103	C₅₃×#380	C₂²	1	1	yes	characteristic
104	C₅₃×#380	C₂²	1	1	yes	characteristic
105	C₅₃×#380	C₂²	1	2	yes	—
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	2	yes	—
111	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
121	C₅₃×#376	C₂²	1	1	yes	characteristic
122	C₂×#95×C₅₃	C₂²	1	2	yes	—
123	C₂×#95×C₅₃	C₂²	1	2	yes	—
124	C₂×#95×C₅₃	C₂²	1	2	yes	—
125	C₂×#95×C₅₃	C₂²	1	2	yes	—
126	C₂×#41×C₅₃	—	2	4	no	—
127	C₂×#41×C₅₃	—	2	4	no	—
128	C₂×#41×C₅₃	—	2	4	no	—
129	C₂×#41×C₅₃	—	2	4	no	—
130	C₂×#41×C₅₃	C₂×C₄	1	8	yes	complemented
131	C₂×#41×C₅₃	C₂×C₄	1	8	yes	complemented
132	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
141	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
149	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
151	#123×C₅₃	C₂×C₄	1	16	yes	complemented
152	#123×C₅₃	C₂×C₄	1	16	yes	complemented
153	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
154	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
155	#121×C₅₃	C₂×C₄	1	16	yes	complemented
156	C₄×Q₈×C₅₃	—	2	4	no	—
157	C₄×Q₈×C₅₃	—	2	4	no	—
158	C₄×Q₈×C₅₃	—	2	4	no	—
159	C₄×Q₈×C₅₃	—	2	4	no	—
160	C₄×D₄×C₅₃	—	2	8	no	—
161	C₄×D₄×C₅₃	—	2	8	no	—
162	C₄×D₄×C₅₃	—	2	4	no	—
163	C₄×D₄×C₅₃	—	2	4	no	—
164	C₄×D₄×C₅₃	—	2	4	no	—
165	C₄×D₄×C₅₃	—	2	8	no	—
166	C₄×D₄×C₅₃	—	2	8	no	—
167	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
168	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
169	C₄×D₄×C₅₃	D₄	1	8	yes	complemented
170	#117×C₅₃	—	2	4	no	—
171	#117×C₅₃	—	2	8	no	—
172	#117×C₅₃	—	2	8	no	—
173	#117×C₅₃	—	2	4	no	—
174	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
175	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
176	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	16	yes	complemented
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
181	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
216	C₂×C₄²×C₅₃	—	2	4	no	—
217	C₂×C₄²×C₅₃	—	2	8	no	—
218	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
220	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
222	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
224	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
225	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
227	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
229	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
230	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
231	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
233	#95×C₅₃	C₂³	1	1	yes	characteristic
234	#95×C₅₃	C₂³	1	1	yes	characteristic
235	#95×C₅₃	C₂³	1	1	yes	characteristic
236	#95×C₅₃	C₂³	1	1	yes	characteristic
237	#95×C₅₃	C₂³	1	2	yes	—
238	#95×C₅₃	C₂³	1	2	yes	—
239	#95×C₅₃	C₂³	1	2	yes	—
240	#95×C₅₃	C₂³	1	2	yes	—
241	#95×C₅₃	C₂³	1	2	yes	—
242	#95×C₅₃	C₂³	1	2	yes	—
243	#95×C₅₃	C₂³	1	2	yes	—
244	#95×C₅₃	C₂³	1	2	yes	—
245	#95×C₅₃	C₂³	1	2	yes	—
246	#95×C₅₃	C₂³	1	2	yes	—
247	#95×C₅₃	C₂³	1	2	yes	—
248	#95×C₅₃	C₂³	1	2	yes	—
249	#95×C₅₃	C₂³	1	1	yes	characteristic
250	#95×C₅₃	C₂³	1	1	yes	characteristic
251	#95×C₅₃	C₂³	1	1	yes	characteristic
252	#95×C₅₃	C₂³	1	1	yes	characteristic
253	#95×C₅₃	C₂³	1	1	yes	characteristic
254	#95×C₅₃	C₂³	1	2	yes	—
255	#95×C₅₃	C₂³	1	2	yes	—
256	#95×C₅₃	C₂³	1	1	yes	characteristic
257	#95×C₅₃	C₂³	1	2	yes	—
258	#95×C₅₃	C₂³	1	2	yes	—
259	#95×C₅₃	C₂³	1	2	yes	—
260	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
263	#41×C₅₃	—	2	32	no	—
264	#41×C₅₃	—	2	32	no	—
265	C₂×Q₈×C₅₃	—	2	2	no	—
266	C₂×Q₈×C₅₃	—	2	2	no	—
267	C₂×Q₈×C₅₃	—	2	2	no	—
268	C₂×Q₈×C₅₃	—	2	2	no	—
269	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
270	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
271	C₂×D₄×C₅₃	—	2	4	no	—
272	C₂×D₄×C₅₃	—	2	4	no	—
273	C₂×D₄×C₅₃	—	2	4	no	—
274	C₂×D₄×C₅₃	—	2	4	no	—
275	C₂×D₄×C₅₃	—	4	1	no	—
276	C₂×D₄×C₅₃	—	4	1	no	—
277	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
278	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
279	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
280	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
281	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
282	C₂×D₄×C₅₃	#41	1	4	yes	—
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	4	no	—
287	C₂²×C₄×C₅₃	—	2	2	no	—
288	C₂²×C₄×C₅₃	—	2	2	no	—
289	C₂²×C₄×C₅₃	—	2	2	no	—
290	C₂²×C₄×C₅₃	—	2	2	no	—
291	C₂²×C₄×C₅₃	—	2	4	no	—
292	C₂²×C₄×C₅₃	—	2	4	no	—
293	C₂²×C₄×C₅₃	—	2	4	no	—
294	C₂²×C₄×C₅₃	—	2	2	no	—
295	C₂²×C₄×C₅₃	—	2	2	no	—
296	C₂²×C₄×C₅₃	—	2	2	no	—
297	C₂²×C₄×C₅₃	—	2	4	no	—
298	C₂²×C₄×C₅₃	—	2	4	no	—
299	C₂²×C₄×C₅₃	—	4	2	no	—
300	C₂²×C₄×C₅₃	—	4	2	no	—
301	C₂²×C₄×C₅₃	—	4	1	no	—
302	C₂²×C₄×C₅₃	—	4	2	no	—
303	C₂²×C₄×C₅₃	—	4	1	no	—
304	C₂²×C₄×C₅₃	—	4	1	no	—
305	C₂²×C₄×C₅₃	—	4	2	no	—
306	C₂²×C₄×C₅₃	—	4	2	no	—
307	C₂²×C₄×C₅₃	—	4	2	no	—
308	C₂²×C₄×C₅₃	—	4	2	no	—
309	C₂²×C₄×C₅₃	—	4	2	no	—
310	C₂²×C₄×C₅₃	—	4	2	no	—
311	C₂²×C₄×C₅₃	—	4	2	no	—
312	C₂²×C₄×C₅₃	—	4	2	no	—
313	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
314	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
315	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
316	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
317	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
318	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
319	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₄⋊C₄×C₅₃	—	2	2	no	—
340	C₄⋊C₄×C₅₃	—	2	4	no	—
341	C₄⋊C₄×C₅₃	—	2	4	no	—
342	C₄⋊C₄×C₅₃	—	2	4	no	—
343	C₄⋊C₄×C₅₃	—	2	2	no	—
344	C₄⋊C₄×C₅₃	—	2	2	no	—
345	C₄⋊C₄×C₅₃	—	2	4	no	—
346	C₄⋊C₄×C₅₃	—	2	4	no	—
347	C₄⋊C₄×C₅₃	—	2	2	no	—
348	C₄⋊C₄×C₅₃	—	2	2	no	—
349	C₄⋊C₄×C₅₃	—	2	2	no	—
350	C₄⋊C₄×C₅₃	—	4	2	no	—
351	C₄⋊C₄×C₅₃	—	4	2	no	—
352	C₄⋊C₄×C₅₃	—	4	1	no	—
353	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
354	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
355	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
356	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
357	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
358	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
359	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
360	C₂²⋊C₄×C₅₃	—	2	4	no	—
361	C₂²⋊C₄×C₅₃	—	2	4	no	—
362	C₂²⋊C₄×C₅₃	—	2	4	no	—
363	C₂²⋊C₄×C₅₃	—	2	2	no	—
364	C₂²⋊C₄×C₅₃	—	2	4	no	—
365	C₂²⋊C₄×C₅₃	—	2	2	no	—
366	C₂²⋊C₄×C₅₃	—	2	2	no	—
367	C₂²⋊C₄×C₅₃	—	4	2	no	—
368	C₂²⋊C₄×C₅₃	—	4	1	no	—
369	C₂²⋊C₄×C₅₃	—	4	1	no	—
370	C₂²⋊C₄×C₅₃	—	4	1	no	—
371	C₂²⋊C₄×C₅₃	—	4	2	no	—
372	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
373	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
374	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
375	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
376	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
377	C₂²⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
378	C₄²×C₅₃	—	2	2	no	—
379	C₄²×C₅₃	—	2	4	no	—
380	C₄²×C₅₃	—	2	2	no	—
381	C₄²×C₅₃	—	2	4	no	—
382	C₄²×C₅₃	—	2	2	no	—
383	C₄²×C₅₃	—	2	4	no	—
384	C₄²×C₅₃	—	2	4	no	—
385	C₄²×C₅₃	—	2	4	no	—
386	C₄²×C₅₃	—	2	2	no	—
387	C₄²×C₅₃	—	2	2	no	—
388	C₄²×C₅₃	—	4	2	no	—
389	C₄²×C₅₃	—	4	2	no	—
390	C₄²×C₅₃	—	4	2	no	—
391	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
392	C₄²×C₅₃	C₂×D₄	1	4	yes	—
393	C₂³×C₅₃	—	2	2	no	—
394	C₂³×C₅₃	—	2	2	no	—
395	C₂³×C₅₃	—	2	2	no	—
396	C₂³×C₅₃	—	2	2	no	—
397	C₂³×C₅₃	—	2	1	no	—
398	C₂³×C₅₃	—	2	1	no	—
399	C₂³×C₅₃	—	2	1	no	—
400	C₂³×C₅₃	—	2	1	no	—
401	C₂³×C₅₃	—	2	1	no	—
402	C₂³×C₅₃	—	2	1	no	—
403	C₂³×C₅₃	—	2	1	no	—
404	C₂³×C₅₃	—	2	1	no	—
405	C₂³×C₅₃	—	2	1	no	—
406	C₂³×C₅₃	—	2	1	no	—
407	C₂³×C₅₃	—	2	1	no	—
408	C₂³×C₅₃	—	2	1	no	—
409	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
410	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
411	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
412	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
413	C₂³×C₅₃	C₂×#41	1	4	yes	—
414	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
415	Q₈×C₅₃	—	2	8	no	—
416	Q₈×C₅₃	—	2	8	no	—
417	D₄×C₅₃	—	2	16	no	—
418	D₄×C₅₃	—	2	16	no	—
419	D₄×C₅₃	—	4	4	no	—
420	D₄×C₅₃	C₄×D₄	1	16	yes	—
421	C₂×C₄×C₅₃	—	2	16	no	—
422	C₂×C₄×C₅₃	—	2	16	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	1	no	—
425	C₂×C₄×C₅₃	—	2	1	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	1	no	—
429	C₂×C₄×C₅₃	—	2	1	no	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	2	no	—
432	C₂×C₄×C₅₃	—	2	1	no	—
433	C₂×C₄×C₅₃	—	2	1	no	—
434	C₂×C₄×C₅₃	—	2	1	no	—
435	C₂×C₄×C₅₃	—	2	1	no	—
436	C₂×C₄×C₅₃	—	2	1	no	—
437	C₂×C₄×C₅₃	—	2	1	no	—
438	C₂×C₄×C₅₃	—	2	1	no	—
439	C₂×C₄×C₅₃	—	2	2	no	—
440	C₂×C₄×C₅₃	—	2	2	no	—
441	C₂×C₄×C₅₃	—	2	1	no	—
442	C₂×C₄×C₅₃	—	2	2	no	—
443	C₂×C₄×C₅₃	—	2	2	no	—
444	C₂×C₄×C₅₃	—	2	1	no	—
445	C₂×C₄×C₅₃	—	2	8	no	—
446	C₂×C₄×C₅₃	—	2	8	no	—
447	C₂×C₄×C₅₃	—	2	1	no	—
448	C₂×C₄×C₅₃	—	2	2	no	—
449	C₂×C₄×C₅₃	—	2	1	no	—
450	C₂×C₄×C₅₃	—	2	2	no	—
451	C₂×C₄×C₅₃	—	2	1	no	—
452	C₂×C₄×C₅₃	—	2	1	no	—
453	C₂×C₄×C₅₃	—	2	2	no	—
454	C₂×C₄×C₅₃	—	2	1	no	—
455	C₂×C₄×C₅₃	—	2	2	no	—
456	C₂×C₄×C₅₃	—	2	1	no	—
457	C₂×C₄×C₅₃	—	2	1	no	—
458	C₂×C₄×C₅₃	—	2	1	no	—
459	C₂×C₄×C₅₃	—	2	2	no	—
460	C₂×C₄×C₅₃	—	2	1	no	—
461	C₂×C₄×C₅₃	—	2	1	no	—
462	C₂×C₄×C₅₃	—	2	2	no	—
463	C₂×C₄×C₅₃	—	2	1	no	—
464	C₂×C₄×C₅₃	—	2	2	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	1	no	—
467	C₂×C₄×C₅₃	—	2	2	no	—
468	C₂×C₄×C₅₃	—	2	1	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	2	1	no	—
471	C₂×C₄×C₅₃	—	4	8	no	—
472	C₂×C₄×C₅₃	—	4	8	no	—
473	C₂×C₄×C₅₃	—	4	4	no	—
474	C₂×C₄×C₅₃	—	4	8	no	—
475	C₂×C₄×C₅₃	—	4	4	no	—
476	C₂×C₄×C₅₃	—	8	4	no	—
477	C₂×C₄×C₅₃	—	8	4	no	—
478	C₂×C₄×C₅₃	—	8	4	no	—
479	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
480	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
481	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
482	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
483	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
484	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
485	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
486	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
487	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
489	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
492	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
493	#34289	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
494	C₂²×C₅₃	—	2	4	no	—
495	C₂²×C₅₃	—	2	4	no	—
496	C₂²×C₅₃	—	2	4	no	—
497	C₂²×C₅₃	—	2	4	no	—
498	C₂²×C₅₃	—	2	4	no	—
499	C₂²×C₅₃	—	2	4	no	—
500	C₂²×C₅₃	—	2	2	no	—
501	C₂²×C₅₃	—	2	2	no	—
502	C₂²×C₅₃	—	2	2	no	—
503	C₂²×C₅₃	—	2	2	no	—
504	C₂²×C₅₃	—	2	2	no	—
505	C₂²×C₅₃	—	2	2	no	—
506	C₂²×C₅₃	—	4	1	no	—
507	C₂²×C₅₃	—	4	1	no	—
508	C₂²×C₅₃	—	4	1	no	—
509	C₂²×C₅₃	—	4	1	no	—
510	C₂²×C₅₃	—	4	1	no	—
511	C₂²×C₅₃	—	4	1	no	—
512	C₂²×C₅₃	—	4	1	no	—
513	C₂²×C₅₃	—	4	1	no	—
514	C₂²×C₅₃	C₂×C₄×D₄	1	8	yes	—
515	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
516	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
517	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
518	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
519	C₂²×C₅₃	#585	1	1	yes	characteristic
520	C₂²×C₅₃	#585	1	1	yes	characteristic
521	C₂²×C₅₃	#585	1	1	yes	characteristic
522	C₄×C₅₃	—	2	2	no	—
523	C₄×C₅₃	—	2	2	no	—
524	C₄×C₅₃	—	2	4	no	—
525	C₄×C₅₃	—	2	4	no	—
526	C₄×C₅₃	—	2	2	no	—
527	C₄×C₅₃	—	2	4	no	—
528	C₄×C₅₃	—	2	2	no	—
529	C₄×C₅₃	—	2	2	no	—
530	C₄×C₅₃	—	2	4	no	—
531	C₄×C₅₃	—	2	2	no	—
532	C₄×C₅₃	—	2	2	no	—
533	C₄×C₅₃	—	4	1	no	—
534	C₄×C₅₃	—	4	2	no	—
535	C₄×C₅₃	—	4	1	no	—
536	C₄×C₅₃	—	4	1	no	—
537	C₄×C₅₃	—	4	2	no	—
538	C₄×C₅₃	—	4	1	no	—
539	C₄×C₅₃	—	4	2	no	—
540	C₄×C₅₃	—	4	1	no	—
541	C₄×C₅₃	C₂×C₄×D₄	1	4	yes	—
542	C₂×#547	C₂×C₅₃	1	1	yes	characteristic
543	C₂×#520	C₂×C₅₃	1	1	yes	characteristic, complemented
544	C₂×C₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#2365	C₂×C₅₃	1	1	yes	characteristic, complemented
546	#2364	C₂×C₅₃	1	2	yes	complemented
547	#2362	C₂×C₅₃	1	1	yes	characteristic, complemented
548	#2360	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#2359	C₂×C₅₃	1	2	yes	complemented
550	#2359	C₂×C₅₃	1	2	yes	complemented
551	#2352	C₂×C₅₃	1	1	yes	characteristic, complemented
552	#2349	C₂×C₅₃	1	1	yes	characteristic, complemented
553	#2344	C₂×C₅₃	1	2	yes	complemented
554	#2339	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#2339	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#2327	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#2325	C₂×C₅₃	1	2	yes	complemented
558	#2323	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#2322	C₂×C₅₃	1	2	yes	complemented
560	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
561	C₄×#123	C₂×C₅₃	1	2	yes	complemented
562	#2290	C₂×C₅₃	1	1	yes	characteristic, complemented
563	C₂×#387	C₂×C₅₃	1	2	yes	complemented
564	#2275	C₂×C₅₃	1	1	yes	characteristic, complemented
565	C₂×C₅₃	—	2	8	no	—
566	C₂×C₅₃	—	4	2	no	—
567	C₂×C₅₃	—	4	2	no	—
568	C₂×C₅₃	C₂²×C₄×D₄	1	1	yes	characteristic
569	C₂×C₅₃	#3428	1	1	yes	characteristic
570	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
571	C₂×C₅₃	#3485	1	1	yes	characteristic
572	C₂×C₅₃	#3489	1	1	yes	characteristic
573	C₂×C₅₃	#3515	1	1	yes	characteristic
574	C₂×C₅₃	#3521	1	1	yes	characteristic
575	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
576	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
577	#547	C₄×C₅₃	1	16	yes	complemented
578	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
579	C₂×#123	C₂²×C₅₃	1	2	yes	—
580	C₂×#123	C₂²×C₅₃	1	2	yes	—
581	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
582	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
583	C₂×#121	C₂²×C₅₃	1	2	yes	—
584	#520	—	2	8	no	—
585	C₄×#41	—	2	8	no	—
586	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
587	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
588	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
589	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
590	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
591	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
592	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
593	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
594	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
595	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
596	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
597	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
599	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
600	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
601	C₂×#117	C₂²×C₅₃	1	2	yes	—
602	C₂×#117	C₂²×C₅₃	1	2	yes	—
603	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
604	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
605	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
606	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
607	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
608	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
609	#391	C₂²×C₅₃	1	1	yes	characteristic
610	#391	C₂²×C₅₃	1	1	yes	characteristic
611	#391	C₂²×C₅₃	1	1	yes	characteristic
612	#391	C₂²×C₅₃	1	1	yes	characteristic
613	#389	C₂²×C₅₃	1	2	yes	—
614	#389	C₂²×C₅₃	1	2	yes	—
615	#389	C₂²×C₅₃	1	2	yes	—
616	#389	C₂²×C₅₃	1	1	yes	characteristic
617	#389	C₂²×C₅₃	1	1	yes	characteristic
618	#388	C₂²×C₅₃	1	2	yes	—
619	#388	C₂²×C₅₃	1	2	yes	—
620	#388	C₂²×C₅₃	1	2	yes	—
621	#388	C₂²×C₅₃	1	2	yes	—
622	#388	C₂²×C₅₃	1	2	yes	—
623	#388	C₂²×C₅₃	1	1	yes	characteristic
624	#388	C₂²×C₅₃	1	1	yes	characteristic
625	#387	C₂²×C₅₃	1	2	yes	—
626	#387	C₂²×C₅₃	1	2	yes	—
627	#387	C₂²×C₅₃	1	2	yes	—
628	#387	C₂²×C₅₃	1	2	yes	—
629	#387	C₂²×C₅₃	1	2	yes	—
630	#387	C₂²×C₅₃	1	2	yes	—
631	#387	C₂²×C₅₃	1	1	yes	characteristic
632	#387	C₂²×C₅₃	1	2	yes	—
633	#387	C₂²×C₅₃	1	2	yes	—
634	#387	C₂²×C₅₃	1	2	yes	—
635	#387	C₂²×C₅₃	1	2	yes	—
636	#387	C₂²×C₅₃	1	1	yes	characteristic
637	#387	C₂²×C₅₃	1	2	yes	—
638	#386	C₂²×C₅₃	1	2	yes	—
639	#386	C₂²×C₅₃	1	1	yes	characteristic
640	#386	C₂²×C₅₃	1	2	yes	—
641	#386	C₂²×C₅₃	1	2	yes	—
642	#386	C₂²×C₅₃	1	2	yes	—
643	#386	C₂²×C₅₃	1	2	yes	—
644	#386	C₂²×C₅₃	1	1	yes	characteristic
645	#385	C₂²×C₅₃	1	1	yes	characteristic
646	#385	C₂²×C₅₃	1	2	yes	—
647	#385	C₂²×C₅₃	1	2	yes	—
648	#385	C₂²×C₅₃	1	2	yes	—
649	#385	C₂²×C₅₃	1	2	yes	—
650	#385	C₂²×C₅₃	1	1	yes	characteristic
651	#382	C₂²×C₅₃	1	1	yes	characteristic
652	#381	C₂²×C₅₃	1	2	yes	—
653	#381	C₂²×C₅₃	1	2	yes	—
654	#380	C₂²×C₅₃	1	1	yes	characteristic
655	#380	C₂²×C₅₃	1	2	yes	—
656	#380	C₂²×C₅₃	1	1	yes	characteristic
657	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
658	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
659	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
660	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
661	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
662	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
663	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
664	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
665	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
666	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
667	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
668	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
669	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
670	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
671	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
672	#376	C₂²×C₅₃	1	1	yes	characteristic
673	C₂×#95	C₂²×C₅₃	1	2	yes	—
674	C₂×#95	C₂²×C₅₃	1	2	yes	—
675	C₂×#95	C₂²×C₅₃	1	2	yes	—
676	C₂×#95	C₂²×C₅₃	1	2	yes	—
677	C₅₃	#34289	1	1	yes	characteristic, direct product factor, Sylow
678	C₂×#41	—	2	4	no	—
679	C₂×#41	—	2	4	no	—
680	C₂×#41	—	2	4	no	—
681	C₂×#41	—	2	4	no	—
682	C₂×#41	C₂×C₄×C₅₃	1	8	yes	complemented
683	C₂×#41	C₂×C₄×C₅₃	1	8	yes	complemented
684	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
685	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
686	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
687	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
688	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
689	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
690	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
691	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
693	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
694	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
695	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
697	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
698	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
699	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
700	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
701	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
702	C₄⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
703	#123	C₂×C₄×C₅₃	1	16	yes	complemented
704	#123	C₂×C₄×C₅₃	1	16	yes	complemented
705	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
706	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
707	#121	C₂×C₄×C₅₃	1	16	yes	complemented
708	C₄×Q₈	—	2	4	no	—
709	C₄×Q₈	—	2	4	no	—
710	C₄×Q₈	—	2	4	no	—
711	C₄×Q₈	—	2	4	no	—
712	C₄×D₄	—	2	4	no	—
713	C₄×D₄	—	2	4	no	—
714	C₄×D₄	—	2	4	no	—
715	C₄×D₄	—	2	8	no	—
716	C₄×D₄	—	2	8	no	—
717	C₄×D₄	—	2	8	no	—
718	C₄×D₄	—	2	8	no	—
719	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
720	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
721	C₄×D₄	D₄×C₅₃	1	8	yes	complemented
722	#117	—	2	4	no	—
723	#117	—	2	8	no	—
724	#117	—	2	8	no	—
725	#117	—	2	4	no	—
726	C₂×C₄⋊C₄	—	2	8	no	—
727	C₂×C₄⋊C₄	—	2	4	no	—
728	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	16	yes	complemented
729	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
750	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
754	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
755	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
768	C₂×C₄²	—	2	8	no	—
769	C₂×C₄²	—	2	4	no	—
770	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
771	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
773	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
775	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
776	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
777	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
778	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
780	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
781	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
782	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
783	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
784	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
785	#95	C₂³×C₅₃	1	1	yes	characteristic
786	#95	C₂³×C₅₃	1	1	yes	characteristic
787	#95	C₂³×C₅₃	1	1	yes	characteristic
788	#95	C₂³×C₅₃	1	1	yes	characteristic
789	#95	C₂³×C₅₃	1	2	yes	—
790	#95	C₂³×C₅₃	1	2	yes	—
791	#95	C₂³×C₅₃	1	2	yes	—
792	#95	C₂³×C₅₃	1	2	yes	—
793	#95	C₂³×C₅₃	1	2	yes	—
794	#95	C₂³×C₅₃	1	2	yes	—
795	#95	C₂³×C₅₃	1	2	yes	—
796	#95	C₂³×C₅₃	1	2	yes	—
797	#95	C₂³×C₅₃	1	2	yes	—
798	#95	C₂³×C₅₃	1	2	yes	—
799	#95	C₂³×C₅₃	1	2	yes	—
800	#95	C₂³×C₅₃	1	2	yes	—
801	#95	C₂³×C₅₃	1	1	yes	characteristic
802	#95	C₂³×C₅₃	1	1	yes	characteristic
803	#95	C₂³×C₅₃	1	1	yes	characteristic
804	#95	C₂³×C₅₃	1	1	yes	characteristic
805	#95	C₂³×C₅₃	1	1	yes	characteristic
806	#95	C₂³×C₅₃	1	2	yes	—
807	#95	C₂³×C₅₃	1	2	yes	—
808	#95	C₂³×C₅₃	1	1	yes	characteristic
809	#95	C₂³×C₅₃	1	2	yes	—
810	#95	C₂³×C₅₃	1	2	yes	—
811	#95	C₂³×C₅₃	1	2	yes	—
812	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
813	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
814	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
815	#41	—	2	32	no	—
816	#41	—	2	32	no	—
817	C₂×Q₈	—	2	2	no	—
818	C₂×Q₈	—	2	2	no	—
819	C₂×Q₈	—	2	2	no	—
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	—
822	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	4	1	no	—
828	C₂×D₄	—	4	1	no	—
829	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
830	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
831	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
832	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
833	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
834	C₂×D₄	#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	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	4	no	—
850	C₂²×C₄	—	2	4	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	1	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
866	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
867	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
868	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
869	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
870	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
871	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	4	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	4	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	4	1	no	—
903	C₄⋊C₄	—	4	2	no	—
904	C₄⋊C₄	—	4	2	no	—
905	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
906	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
907	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
908	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
909	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
910	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
911	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	4	1	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	1	no	—
923	C₂²⋊C₄	—	4	1	no	—
924	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
925	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
926	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
927	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
928	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
929	C₂²⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
930	C₄²	—	2	2	no	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	4	no	—
933	C₄²	—	2	4	no	—
934	C₄²	—	2	2	no	—
935	C₄²	—	2	4	no	—
936	C₄²	—	2	4	no	—
937	C₄²	—	2	4	no	—
938	C₄²	—	2	2	no	—
939	C₄²	—	2	2	no	—
940	C₄²	—	4	2	no	—
941	C₄²	—	4	2	no	—
942	C₄²	—	4	2	no	—
943	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
944	C₄²	C₂×D₄×C₅₃	1	4	yes	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
962	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
963	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
964	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
965	C₂³	C₂×#41×C₅₃	1	4	yes	—
966	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
967	Q₈	—	2	8	no	—
968	Q₈	—	2	8	no	—
969	D₄	—	2	16	no	—
970	D₄	—	2	16	no	—
971	D₄	—	4	4	no	—
972	D₄	C₄×D₄×C₅₃	1	16	yes	—
973	C₂×C₄	—	2	16	no	—
974	C₂×C₄	—	2	16	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	8	no	—
998	C₂×C₄	—	2	8	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	4	8	no	—
1024	C₂×C₄	—	4	8	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	8	no	—
1027	C₂×C₄	—	4	4	no	—
1028	C₂×C₄	—	8	4	no	—
1029	C₂×C₄	—	8	4	no	—
1030	C₂×C₄	—	8	4	no	—
1031	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1032	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1033	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
1034	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1035	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1036	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
1037	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
1038	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1041	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
1042	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1043	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1044	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1045	C₂²	—	2	4	no	—
1046	C₂²	—	2	4	no	—
1047	C₂²	—	2	4	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	4	no	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	C₂×C₄×D₄×C₅₃	1	8	yes	—
1066	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
1067	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1068	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1069	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1070	C₂²	C₅₃×#585	1	1	yes	characteristic
1071	C₂²	C₅₃×#585	1	1	yes	characteristic
1072	C₂²	C₅₃×#585	1	1	yes	characteristic
1073	C₄	—	2	2	no	—
1074	C₄	—	2	4	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	4	no	—
1080	C₄	—	2	4	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	4	no	—
1083	C₄	—	2	2	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	C₂×C₄×D₄×C₅₃	1	4	yes	—
1093	C₂	—	2	8	no	—
1094	C₂	—	4	2	no	—
1095	C₂	—	4	2	no	—
1096	C₂	C₂²×C₄×D₄×C₅₃	1	1	yes	characteristic
1097	C₂	C₅₃×#3428	1	1	yes	characteristic
1098	C₂	C₄×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1099	C₂	C₅₃×#3485	1	1	yes	characteristic
1100	C₂	C₅₃×#3489	1	1	yes	characteristic
1101	C₂	C₅₃×#3515	1	1	yes	characteristic
1102	C₂	C₅₃×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂×C₅₃×#547	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#520	C₂	semidirect
3. C₂×C₄×#41×C₅₃	C₂	semidirect
4. C₅₃×#2365	C₂	semidirect
5. C₅₃×#2364	C₂	semidirect
6. C₅₃×#2362	C₂	semidirect
7. C₅₃×#2360	C₂	semidirect
8. C₅₃×#2359	C₂	semidirect
9. C₅₃×#2359	C₂	semidirect
10. C₅₃×#2352	C₂	semidirect
11. C₅₃×#2349	C₂	semidirect
12. C₅₃×#2344	C₂	semidirect
13. C₅₃×#2339	C₂	semidirect
14. C₅₃×#2339	C₂	semidirect
15. C₅₃×#2327	C₂	semidirect
16. C₅₃×#2325	C₂	semidirect
17. C₅₃×#2323	C₂	semidirect
18. C₅₃×#2322	C₂	semidirect
19. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
20. C₄×#123×C₅₃	C₂	semidirect
21. C₅₃×#2290	C₂	semidirect
22. C₂×C₅₃×#387	C₂	semidirect
23. C₅₃×#2275	C₂	semidirect
26. C₅₃×#547	C₄	semidirect
130. C₂×#41×C₅₃	C₂×C₄	semidirect
131. C₂×#41×C₅₃	C₂×C₄	semidirect
150. C₄⋊Q₈×C₅₃	C₂×C₄	semidirect
151. #123×C₅₃	C₂×C₄	semidirect
152. #123×C₅₃	C₂×C₄	semidirect
153. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
154. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
155. #121×C₅₃	C₂×C₄	semidirect
167. C₄×D₄×C₅₃	C₂×C₄	semidirect
168. C₄×D₄×C₅₃	C₂×C₄	semidirect
169. C₄×D₄×C₅₃	D₄	semidirect
176. C₂×C₄⋊C₄×C₅₃	C₂×C₄	semidirect
493. #34289	C₅₃	direct (N × H)
543. C₂×#520	C₂×C₅₃	semidirect
544. C₂×C₄×#41	C₂×C₅₃	semidirect
545. #2365	C₂×C₅₃	semidirect
546. #2364	C₂×C₅₃	semidirect
547. #2362	C₂×C₅₃	semidirect
548. #2360	C₂×C₅₃	semidirect
549. #2359	C₂×C₅₃	semidirect
550. #2359	C₂×C₅₃	semidirect
551. #2352	C₂×C₅₃	semidirect
552. #2349	C₂×C₅₃	semidirect
553. #2344	C₂×C₅₃	semidirect
554. #2339	C₂×C₅₃	semidirect
555. #2339	C₂×C₅₃	semidirect
556. #2327	C₂×C₅₃	semidirect
557. #2325	C₂×C₅₃	semidirect
558. #2323	C₂×C₅₃	semidirect
559. #2322	C₂×C₅₃	semidirect
560. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
561. C₄×#123	C₂×C₅₃	semidirect
562. #2290	C₂×C₅₃	semidirect
563. C₂×#387	C₂×C₅₃	semidirect
564. #2275	C₂×C₅₃	semidirect
577. #547	C₄×C₅₃	semidirect
677. C₅₃	#34289	direct (N × H)
682. C₂×#41	C₂×C₄×C₅₃	semidirect
683. C₂×#41	C₂×C₄×C₅₃	semidirect
702. C₄⋊Q₈	C₂×C₄×C₅₃	semidirect
703. #123	C₂×C₄×C₅₃	semidirect
704. #123	C₂×C₄×C₅₃	semidirect
705. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
706. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
707. #121	C₂×C₄×C₅₃	semidirect
719. C₄×D₄	C₂×C₄×C₅₃	semidirect
720. C₄×D₄	C₂×C₄×C₅₃	semidirect
721. C₄×D₄	D₄×C₅₃	semidirect
728. C₂×C₄⋊C₄	C₂×C₄×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×#547	2
C₂×C₅₃×#520	2
C₂×C₄×#41×C₅₃	2
C₅₃×#2365	2
C₅₃×#2364	2
C₅₃×#2362	2
C₅₃×#2360	2
C₅₃×#2359	2
C₅₃×#2352	2
C₅₃×#2349	2
C₅₃×#2344	2
C₅₃×#2339	2
C₅₃×#2327	2
C₅₃×#2325	2
C₅₃×#2323	2
C₅₃×#2322	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#123×C₅₃	2
C₅₃×#2290	2
C₂×C₅₃×#387	2
C₅₃×#2275	2
#34289	53

Subgroups — C53×#34289 #27241801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34289 #27241801