Subgroups — #28293111

Order 13568.

7474 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288553	C₂	1	4	yes	maximal, complemented
2	#20288546	C₂	1	8	yes	maximal, complemented
3	#20288543	C₂	1	4	yes	maximal, complemented
4	#20288542	C₂	1	8	yes	maximal, complemented
5	#20288414	C₂	1	1	yes	maximal, characteristic, complemented
6	#20288412	C₂	1	1	yes	maximal, characteristic, complemented
7	#20288408	C₂	1	2	yes	maximal, complemented
8	#20288406	C₂	1	8	yes	maximal, complemented
9	#20288404	C₂	1	1	yes	maximal, characteristic, complemented
10	#20288402	C₂	1	2	yes	maximal, complemented
11	#20288397	C₂	1	8	yes	maximal, complemented
12	#20288126	C₂	1	4	yes	maximal, complemented
13	#20288122	C₂	1	4	yes	maximal, complemented
14	#543×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16811183	C₂	1	2	yes	maximal, complemented
16	#534×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16811096	C₂	1	1	yes	maximal, characteristic, complemented
18	#518×D₅₃	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3490	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
21	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
22	#16811324	C₂²	1	8	yes	complemented
23	#16811323	C₂²	1	8	yes	complemented
24	#16811320	C₂²	1	4	yes	complemented
25	#16811320	C₂²	1	8	yes	complemented
26	#16811318	C₂²	1	8	yes	complemented
27	#16811318	C₂²	1	8	yes	complemented
28	#16811317	C₂²	1	4	yes	complemented
29	#16811315	C₂²	1	8	yes	complemented
30	#16811313	C₂²	1	8	yes	complemented
31	#16811312	C₂²	1	4	yes	complemented
32	#16811310	C₂²	1	8	yes	complemented
33	#16811309	C₂²	1	8	yes	complemented
34	#16811307	C₂²	1	4	yes	complemented
35	#16811306	C₂²	1	8	yes	complemented
36	#16811304	C₂²	1	8	yes	complemented
37	#16811304	C₂²	1	8	yes	complemented
38	#16811303	C₂²	1	8	yes	complemented
39	#16811302	C₂²	1	8	yes	complemented
40	#16811302	C₂²	1	8	yes	complemented
41	#16811301	C₂²	1	8	yes	complemented
42	#16811300	C₂²	1	8	yes	complemented
43	#16811299	C₂²	1	8	yes	complemented
44	#16811299	C₂²	1	8	yes	complemented
45	#16811299	C₂²	1	8	yes	complemented
46	#16811296	C₂²	1	8	yes	complemented
47	#16811283	C₂²	1	4	yes	complemented
48	#16811281	C₂²	1	8	yes	complemented
49	#16811280	C₂²	1	4	yes	complemented
50	#16811270	C₂²	1	4	yes	complemented
51	#16811267	C₂²	1	8	yes	complemented
52	#16811263	C₂²	1	8	yes	complemented
53	#16811262	C₂²	1	8	yes	complemented
54	#16811261	C₂²	1	4	yes	complemented
55	#16811260	C₂²	1	8	yes	complemented
56	#16811249	C₂²	1	2	yes	complemented
57	#16811249	C₂²	1	1	yes	characteristic, complemented
58	#16811248	C₂²	1	4	yes	complemented
59	#16811248	C₂²	1	8	yes	complemented
60	#16811222	C₂²	1	4	yes	complemented
61	#16811219	C₂²	1	8	yes	complemented
62	#16811218	C₂²	1	4	yes	complemented
63	#16811216	C₂²	1	8	yes	complemented
64	#16811216	C₂²	1	8	yes	complemented
65	#16811215	C₂²	1	8	yes	complemented
66	#16811214	C₂²	1	8	yes	complemented
67	#16811211	C₂²	1	4	yes	complemented
68	#16811209	C₂²	1	8	yes	complemented
69	#16811208	C₂²	1	8	yes	complemented
70	#16811207	C₂²	1	8	yes	complemented
71	#16811205	C₂²	1	8	yes	complemented
72	#16811205	C₂²	1	8	yes	complemented
73	#16811185	C₂²	1	1	yes	characteristic
74	#16811184	C₂²	1	4	yes	complemented
75	#16811183	C₂²	1	8	yes	—
76	#16811183	C₂²	1	4	yes	complemented
77	#16811183	C₂²	1	8	yes	complemented
78	#16811183	C₂²	1	4	yes	complemented
79	#16811183	C₂²	1	4	yes	complemented
80	#16811183	C₂²	1	4	yes	complemented
81	#16811183	C₂²	1	4	yes	complemented
82	#16811182	C₂²	1	2	yes	—
83	#16811181	C₂²	1	4	yes	complemented
84	#16811159	C₂²	1	4	yes	complemented
85	#16811156	C₂²	1	8	yes	complemented
86	#16811155	C₂²	1	8	yes	complemented
87	#16811154	C₂²	1	4	yes	complemented
88	#16811153	C₂²	1	8	yes	complemented
89	#16811152	C₂²	1	8	yes	complemented
90	#16811151	C₂²	1	8	yes	complemented
91	#16811134	C₂²	1	4	yes	complemented
92	#16811133	C₂²	1	8	yes	complemented
93	#16811132	C₂²	1	8	yes	complemented
94	#16811131	C₂²	1	8	yes	complemented
95	#16811130	C₂²	1	8	yes	complemented
96	#16811129	C₂²	1	8	yes	complemented
97	C₂×#13133201	C₂²	1	2	yes	complemented
98	C₂×#13133199	C₂²	1	4	yes	complemented
99	C₂×#13133198	C₂²	1	2	yes	complemented
100	#123×D₅₃	C₂²	1	4	yes	complemented
101	C₂²⋊Q₈×D₅₃	C₂²	1	8	yes	complemented
102	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
103	C₂×#13133190	C₂²	1	4	yes	complemented
104	C₂×#13133188	C₂²	1	4	yes	complemented
105	#121×D₅₃	C₂²	1	4	yes	complemented
106	C₂×#13133186	C₂²	1	2	yes	complemented
107	C₂×#13133185	C₂²	1	4	yes	complemented
108	#120×D₅₃	C₂²	1	4	yes	complemented
109	#16811098	C₂²	1	2	yes	complemented
110	#16811097	C₂²	1	4	yes	complemented
111	#16811096	C₂²	1	2	yes	complemented
112	#16811096	C₂²	1	2	yes	complemented
113	#16811096	C₂²	1	8	yes	complemented
114	#16811096	C₂²	1	4	yes	complemented
115	#16811096	C₂²	1	8	yes	complemented
116	#16811095	C₂²	1	8	yes	complemented
117	#16811095	C₂²	1	8	yes	complemented
118	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
119	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
120	C₂×#13133177	C₂²	1	2	yes	complemented
121	C₂×#13133177	C₂²	1	2	yes	complemented
122	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
123	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
124	C₂×#13133173	C₂²	1	1	yes	characteristic, complemented
125	C₂×#13133173	C₂²	1	1	yes	characteristic, complemented
126	#117×D₅₃	C₂²	1	4	yes	complemented
127	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
130	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
132	C₅₃×#551	C₂²	1	8	yes	complemented
133	C₅₃×#546	C₂²	1	8	yes	complemented
134	C₅₃×#543	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#538	C₂²	1	4	yes	complemented
136	C₅₃×#534	C₂²	1	1	yes	characteristic
137	C₅₃×#525	C₂²	1	4	yes	complemented
138	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
139	C₅₃×#518	C₂²	1	2	yes	complemented
140	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
141	C₂⁴×D₅₃	C₂³	1	2	yes	—
142	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
143	C₂×#11719945	C₂³	1	4	yes	complemented
144	C₂×#11719947	C₂³	1	8	yes	complemented
145	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
146	C₂²×D₂₁₂	C₂³	1	2	yes	—
147	C₂²×C₂²⋊D₅₃	—	2	8	no	—
148	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
149	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
150	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
151	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
152	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
153	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
154	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
155	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
156	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
157	C₂×D₄×D₅₃	—	2	16	no	—
158	C₂×D₄×D₅₃	C₂³	1	4	yes	—
159	C₂×D₄×D₅₃	C₂³	1	4	yes	—
160	C₂×D₄×D₅₃	C₂³	1	4	yes	—
161	C₂×D₄×D₅₃	C₂³	1	4	yes	—
162	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
163	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
164	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
165	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
166	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
167	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
168	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
169	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
170	#13133212	C₂³	1	8	yes	complemented
171	#13133212	C₂³	1	8	yes	complemented
172	#13133212	C₂³	1	8	yes	complemented
173	#13133211	C₂³	1	8	yes	complemented
174	#13133210	C₂³	1	8	yes	complemented
175	#13133210	C₂³	1	8	yes	complemented
176	#13133210	C₂³	1	8	yes	complemented
177	#13133210	C₂³	1	8	yes	complemented
178	#13133210	C₂³	1	8	yes	complemented
179	#13133210	C₂³	1	8	yes	complemented
180	#13133210	C₂³	1	8	yes	complemented
181	#13133209	C₂³	1	8	yes	complemented
182	#13133208	C₂³	1	4	yes	complemented
183	#13133208	C₂³	1	8	yes	complemented
184	#13133208	C₂³	1	4	yes	complemented
185	#13133207	C₂³	1	8	yes	complemented
186	#13133207	C₂³	1	8	yes	complemented
187	#13133207	C₂³	1	8	yes	complemented
188	#13133206	C₂³	1	4	yes	complemented
189	#13133204	C₂³	1	8	yes	complemented
190	#13133204	C₂³	1	4	yes	complemented
191	#13133203	C₂³	1	8	yes	complemented
192	#13133203	C₂³	1	8	yes	complemented
193	#13133203	C₂³	1	8	yes	complemented
194	#13133202	C₂³	1	8	yes	complemented
195	#13133202	C₂³	1	8	yes	complemented
196	#13133201	C₂³	1	4	yes	—
197	#13133201	C₂³	1	8	yes	—
198	#13133201	C₂³	1	8	yes	complemented
199	#13133201	C₂³	1	4	yes	complemented
200	#13133201	C₂³	1	4	yes	complemented
201	#13133200	C₂³	1	4	yes	—
202	#13133200	C₂³	1	8	yes	complemented
203	#13133200	C₂³	1	8	yes	complemented
204	#13133199	C₂³	1	8	yes	—
205	#13133199	C₂³	1	8	yes	—
206	#13133199	C₂³	1	8	yes	complemented
207	#13133199	C₂³	1	8	yes	complemented
208	#13133199	C₂³	1	8	yes	complemented
209	#13133199	C₂³	1	8	yes	complemented
210	#13133199	C₂³	1	8	yes	complemented
211	#13133199	C₂³	1	8	yes	complemented
212	#13133198	C₂³	1	8	yes	—
213	#13133198	C₂³	1	4	yes	—
214	#13133198	C₂³	1	8	yes	complemented
215	#13133198	C₂³	1	8	yes	complemented
216	#13133198	C₂³	1	8	yes	complemented
217	#13133198	C₂³	1	4	yes	complemented
218	#13133198	C₂³	1	4	yes	complemented
219	#13133197	C₂³	1	4	yes	complemented
220	#13133197	C₂³	1	8	yes	complemented
221	#13133196	C₂³	1	8	yes	complemented
222	#13133196	C₂³	1	4	yes	complemented
223	#13133196	C₂³	1	8	yes	complemented
224	#13133196	C₂³	1	4	yes	complemented
225	#13133195	C₂³	1	8	yes	complemented
226	#13133195	C₂³	1	8	yes	complemented
227	#13133195	C₂³	1	8	yes	complemented
228	#13133195	C₂³	1	8	yes	complemented
229	#13133194	C₂³	1	8	yes	complemented
230	#13133194	C₂³	1	8	yes	complemented
231	#13133194	C₂³	1	8	yes	complemented
232	#13133194	C₂³	1	8	yes	complemented
233	#13133194	C₂³	1	8	yes	complemented
234	#13133193	C₂³	1	8	yes	complemented
235	#13133193	C₂³	1	4	yes	complemented
236	#13133193	C₂³	1	8	yes	complemented
237	#13133192	C₂³	1	4	yes	complemented
238	#13133191	C₂³	1	4	yes	—
239	#13133191	C₂³	1	4	yes	complemented
240	#13133190	C₂³	1	8	yes	—
241	#13133190	C₂³	1	8	yes	—
242	#13133190	C₂³	1	8	yes	complemented
243	#13133190	C₂³	1	8	yes	complemented
244	#13133190	C₂³	1	8	yes	complemented
245	#13133190	C₂³	1	8	yes	complemented
246	#13133189	C₂³	1	8	yes	—
247	#13133189	C₂³	1	8	yes	complemented
248	#13133189	C₂³	1	8	yes	complemented
249	#13133188	C₂³	1	8	yes	—
250	#13133188	C₂³	1	8	yes	—
251	#13133188	C₂³	1	8	yes	complemented
252	#13133188	C₂³	1	8	yes	complemented
253	#13133188	C₂³	1	4	yes	complemented
254	#13133188	C₂³	1	8	yes	complemented
255	#13133187	C₂³	1	4	yes	—
256	#13133187	C₂³	1	8	yes	complemented
257	#13133186	C₂³	1	4	yes	—
258	#13133186	C₂³	1	8	yes	—
259	#13133186	C₂³	1	4	yes	complemented
260	#13133186	C₂³	1	4	yes	complemented
261	#13133185	C₂³	1	8	yes	—
262	#13133185	C₂³	1	8	yes	—
263	#13133185	C₂³	1	4	yes	—
264	#13133185	C₂³	1	8	yes	complemented
265	#13133185	C₂³	1	8	yes	complemented
266	#13133185	C₂³	1	8	yes	complemented
267	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
268	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
269	#13133182	C₂³	1	4	yes	complemented
270	C₄×D₂₁₂	C₂³	1	8	yes	complemented
271	C₄×D₂₁₂	C₂³	1	8	yes	complemented
272	D₄×Dic₅₃	C₂³	1	8	yes	—
273	D₄×Dic₅₃	C₂³	1	8	yes	complemented
274	D₄×Dic₅₃	C₂³	1	4	yes	complemented
275	D₄×Dic₅₃	C₂³	1	8	yes	complemented
276	#13133179	C₂³	1	4	yes	complemented
277	#13133179	C₂³	1	8	yes	complemented
278	#13133179	C₂³	1	8	yes	complemented
279	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
280	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
281	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
282	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
283	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
284	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
285	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
286	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
287	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
288	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
289	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
290	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
291	#13133177	C₂³	1	8	yes	—
292	#13133177	C₂³	1	8	yes	—
293	#13133177	C₂³	1	8	yes	complemented
294	#13133177	C₂³	1	8	yes	complemented
295	#13133177	C₂³	1	8	yes	complemented
296	#13133177	C₂³	1	8	yes	complemented
297	#13133177	C₂³	1	8	yes	complemented
298	#13133177	C₂³	1	8	yes	complemented
299	#13133177	C₂³	1	8	yes	complemented
300	#13133176	C₂³	1	8	yes	complemented
301	#13133176	C₂³	1	4	yes	complemented
302	#13133176	C₂³	1	4	yes	complemented
303	#13133175	C₂³	1	8	yes	complemented
304	#13133175	C₂³	1	8	yes	complemented
305	#13133174	C₂³	1	8	yes	complemented
306	#13133174	C₂³	1	8	yes	complemented
307	#13133173	C₂³	1	4	yes	complemented
308	#13133173	C₂³	1	8	yes	complemented
309	#13133173	C₂³	1	8	yes	complemented
310	#13133173	C₂³	1	8	yes	complemented
311	#13133173	C₂³	1	8	yes	complemented
312	#13133173	C₂³	1	4	yes	complemented
313	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
314	C₂×#11719919	C₂³	1	4	yes	complemented
315	C₂×#11719919	C₂³	1	2	yes	complemented
316	C₂×#11719919	C₂³	1	2	yes	complemented
317	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
318	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
319	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
320	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
321	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
323	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
324	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
325	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
326	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
327	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
328	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
329	C₂×#11719921	C₂³	1	2	yes	—
330	C₂×#11719921	C₂³	1	2	yes	—
331	C₂×#11719921	C₂³	1	4	yes	—
332	C₂×#11719921	C₂³	1	8	yes	complemented
333	C₂×#11719921	C₂³	1	4	yes	complemented
334	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
335	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
336	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
337	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
338	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
339	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
340	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
341	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
342	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
343	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
344	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
345	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
346	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
347	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
348	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
349	C₄²×D₅₃	C₂³	1	8	yes	complemented
350	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
352	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
353	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
354	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
355	#126×C₅₃	C₂³	1	8	yes	complemented
356	#124×C₅₃	C₂³	1	8	yes	complemented
357	#123×C₅₃	C₂³	1	4	yes	—
358	#123×C₅₃	C₂³	1	8	yes	complemented
359	#123×C₅₃	C₂³	1	8	yes	complemented
360	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
361	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
362	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
363	#121×C₅₃	C₂³	1	4	yes	—
364	#121×C₅₃	C₂³	1	4	yes	complemented
365	#121×C₅₃	C₂³	1	8	yes	complemented
366	#120×C₅₃	C₂³	1	8	yes	—
367	#120×C₅₃	C₂³	1	4	yes	—
368	#120×C₅₃	C₂³	1	4	yes	complemented
369	#120×C₅₃	C₂³	1	4	yes	complemented
370	C₄×D₄×C₅₃	C₂³	1	8	yes	—
371	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
372	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
373	#117×C₅₃	C₂³	1	4	yes	complemented
374	#117×C₅₃	C₂³	1	4	yes	complemented
375	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
376	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
377	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
378	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
379	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
380	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
381	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
382	C₂⁴×C₅₃	—	2	4	no	—
383	C₂⁴×C₅₃	—	8	2	no	—
384	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
385	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
386	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂³×D₅₃	—	2	8	no	—
390	C₂³×D₅₃	—	8	2	no	—
391	C₂³×D₅₃	—	8	4	no	—
392	C₂³×D₅₃	#41	1	8	yes	complemented
393	C₂³×D₅₃	C₂⁴	1	4	yes	—
394	C₂³×D₅₃	C₂⁴	1	2	yes	—
395	C₂³×D₅₃	C₂⁴	1	4	yes	—
396	C₂³×D₅₃	C₂⁴	1	2	yes	—
397	C₂³×D₅₃	C₂⁴	1	2	yes	—
398	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
399	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
400	#41×C₅₃	—	8	4	no	—
401	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
402	C₂×D₄×C₅₃	—	2	8	no	—
403	C₂×D₄×C₅₃	—	8	4	no	—
404	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
405	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
406	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
407	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
408	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
409	C₂²×C₄×C₅₃	—	8	2	no	—
410	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
412	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
413	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
414	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
415	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
416	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
417	C₂×C₂²⋊D₅₃	—	2	8	no	—
418	C₂×C₂²⋊D₅₃	—	2	8	no	—
419	C₂×C₂²⋊D₅₃	—	2	16	no	—
420	C₂×C₂²⋊D₅₃	—	2	16	no	—
421	C₂×C₂²⋊D₅₃	—	2	4	no	—
422	C₂×C₂²⋊D₅₃	—	2	4	no	—
423	C₂×C₂²⋊D₅₃	—	2	4	no	—
424	C₂×C₂²⋊D₅₃	—	2	4	no	—
425	C₂×C₂²⋊D₅₃	—	8	4	no	—
426	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
427	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
428	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
429	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
430	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
431	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
432	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
433	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
434	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
435	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
436	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
437	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
438	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
439	C₂²×Dic₅₃	—	2	4	no	—
440	C₂²×Dic₅₃	—	8	2	no	—
441	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
444	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
445	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
446	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
447	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
448	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
449	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
450	Q₈×D₅₃	—	8	4	no	—
451	#11719947	—	8	8	no	—
452	D₄×D₅₃	—	2	16	no	—
453	D₄×D₅₃	—	2	16	no	—
454	D₄×D₅₃	—	2	16	no	—
455	D₄×D₅₃	—	2	16	no	—
456	D₄×D₅₃	—	8	4	no	—
457	#11719945	—	8	4	no	—
458	C₂×D₂₁₂	—	2	8	no	—
459	C₂×D₂₁₂	C₂⁴	1	4	yes	—
460	C₂×D₂₁₂	C₂⁴	1	4	yes	—
461	C₂×D₂₁₂	C₂⁴	1	4	yes	—
462	C₂×C₄×D₅₃	—	2	8	no	—
463	C₂×C₄×D₅₃	—	8	2	no	—
464	C₂×C₄×D₅₃	—	8	4	no	—
465	C₂×C₄×D₅₃	—	8	2	no	—
466	C₂×C₄×D₅₃	—	8	8	no	—
467	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
468	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
469	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
470	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
471	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
472	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
473	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
474	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
475	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
476	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
477	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
478	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
479	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
480	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
481	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
482	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
483	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
484	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
485	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
486	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
487	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
488	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
489	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
490	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
491	C₄²×C₅₃	C₂⁴	1	8	yes	—
492	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
493	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
494	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
495	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
496	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
497	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
498	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
499	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
500	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
501	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
502	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
503	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
504	#11719921	C₂⁴	1	4	yes	—
505	#11719921	C₂⁴	1	8	yes	—
506	#11719921	C₂⁴	1	4	yes	—
507	#11719921	C₂⁴	1	8	yes	—
508	#11719921	C₂⁴	1	8	yes	—
509	#11719921	C₂⁴	1	8	yes	—
510	#11719921	C₂⁴	1	8	yes	—
511	#11719921	C₂⁴	1	8	yes	—
512	#11719921	C₂⁴	1	8	yes	—
513	#11719921	C₂⁴	1	8	yes	—
514	#11719921	C₂⁴	1	8	yes	—
515	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
516	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
517	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
518	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
519	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
520	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
521	#11719919	C₂⁴	1	8	yes	—
522	#11719919	C₂⁴	1	8	yes	—
523	#11719919	C₂⁴	1	8	yes	—
524	#11719919	C₂⁴	1	8	yes	—
525	#11719919	C₂⁴	1	8	yes	—
526	#11719919	C₂⁴	1	8	yes	—
527	#11719919	C₂⁴	1	8	yes	—
528	#11719919	C₂⁴	1	4	yes	—
529	#11719919	C₂⁴	1	4	yes	—
530	#11719919	C₂⁴	1	8	yes	—
531	#11719919	C₂⁴	1	8	yes	—
532	C₄×Dic₅₃	C₂⁴	1	8	yes	—
533	C₄×Dic₅₃	C₂⁴	1	8	yes	—
534	C₄×Dic₅₃	C₂⁴	1	8	yes	—
535	C₄×Dic₅₃	C₂⁴	1	4	yes	—
536	C₄×Dic₅₃	C₂⁴	1	8	yes	—
537	C₄×Dic₅₃	C₂⁴	1	4	yes	—
538	C₂³×C₅₃	—	2	2	no	—
539	C₂³×C₅₃	—	2	2	no	—
540	C₂³×C₅₃	—	2	8	no	—
541	C₂³×C₅₃	—	2	4	no	—
542	C₂³×C₅₃	—	4	2	no	—
543	C₂³×C₅₃	—	4	2	no	—
544	C₂³×C₅₃	—	4	2	no	—
545	C₂³×C₅₃	—	4	4	no	—
546	C₂³×C₅₃	—	4	4	no	—
547	C₂³×C₅₃	—	4	4	no	—
548	C₂³×C₅₃	—	8	8	no	—
549	C₂³×C₅₃	C₂×#41	1	4	yes	—
550	C₂³×C₅₃	C₂⁵	1	2	yes	—
551	C₂³×C₅₃	C₂⁵	1	4	yes	—
552	C₂³×C₅₃	C₂⁵	1	2	yes	—
553	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
554	C₂³×C₅₃	C₂⁵	1	2	yes	—
555	C₂²×D₅₃	—	2	4	no	—
556	C₂²×D₅₃	—	2	8	no	—
557	C₂²×D₅₃	—	2	8	no	—
558	C₂²×D₅₃	—	4	4	no	—
559	C₂²×D₅₃	—	4	2	no	—
560	C₂²×D₅₃	—	4	2	no	—
561	C₂²×D₅₃	—	4	8	no	—
562	C₂²×D₅₃	—	4	4	no	—
563	C₂²×D₅₃	—	4	8	no	—
564	C₂²×D₅₃	—	4	4	no	—
565	C₂²×D₅₃	—	8	8	no	—
566	C₂²×D₅₃	—	8	16	no	—
567	C₂²×D₅₃	C₂×#41	1	8	yes	—
568	C₂²×D₅₃	C₂×#41	1	8	yes	—
569	C₂²×D₅₃	C₂×#41	1	4	yes	—
570	C₂²×D₅₃	C₂×#41	1	4	yes	—
571	C₂²×D₅₃	C₂⁵	1	4	yes	—
572	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
573	C₂²×D₅₃	C₂⁵	1	2	yes	—
574	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
575	Q₈×C₅₃	—	4	4	no	—
576	D₄×C₅₃	—	2	8	no	—
577	D₄×C₅₃	—	2	8	no	—
578	D₄×C₅₃	—	4	4	no	—
579	D₄×C₅₃	—	4	8	no	—
580	D₄×C₅₃	—	4	8	no	—
581	C₂×C₄×C₅₃	—	2	4	no	—
582	C₂×C₄×C₅₃	—	4	2	no	—
583	C₂×C₄×C₅₃	—	4	2	no	—
584	C₂×C₄×C₅₃	—	4	4	no	—
585	C₂×C₄×C₅₃	—	4	8	no	—
586	C₂×C₄×C₅₃	—	4	4	no	—
587	C₂×C₄×C₅₃	—	4	4	no	—
588	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
589	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
590	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
591	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
592	C₂²⋊D₅₃	—	2	8	no	—
593	C₂²⋊D₅₃	—	2	8	no	—
594	C₂²⋊D₅₃	—	2	8	no	—
595	C₂²⋊D₅₃	—	2	8	no	—
596	C₂²⋊D₅₃	—	2	4	no	—
597	C₂²⋊D₅₃	—	2	4	no	—
598	C₂²⋊D₅₃	—	2	8	no	—
599	C₂²⋊D₅₃	—	2	8	no	—
600	C₂²⋊D₅₃	—	2	4	no	—
601	C₂²⋊D₅₃	—	2	4	no	—
602	C₂²⋊D₅₃	—	4	8	no	—
603	C₂²⋊D₅₃	—	4	8	no	—
604	C₂²⋊D₅₃	—	4	8	no	—
605	C₂×Dic₅₃	—	2	4	no	—
606	C₂×Dic₅₃	—	2	8	no	—
607	C₂×Dic₅₃	—	2	2	no	—
608	C₂×Dic₅₃	—	2	2	no	—
609	C₂×Dic₅₃	—	4	8	no	—
610	C₂×Dic₅₃	—	4	2	no	—
611	C₂×Dic₅₃	—	4	2	no	—
612	C₂×Dic₅₃	—	4	4	no	—
613	C₂×Dic₅₃	—	4	8	no	—
614	C₂×Dic₅₃	C₂⁵	1	8	yes	—
615	C₂×Dic₅₃	C₂⁵	1	4	yes	—
616	C₂×Dic₅₃	C₂⁵	1	4	yes	—
617	C₂×Dic₅₃	C₂⁵	1	4	yes	—
618	C₂×Dic₅₃	C₂⁵	1	2	yes	—
619	C₂×Dic₅₃	C₂⁵	1	2	yes	—
620	D₂₁₂	—	2	8	no	—
621	D₂₁₂	—	2	8	no	—
622	D₂₁₂	—	4	4	no	—
623	C₄×D₅₃	—	2	8	no	—
624	C₄×D₅₃	—	2	8	no	—
625	C₄×D₅₃	—	4	8	no	—
626	C₄×D₅₃	—	4	8	no	—
627	C₄×D₅₃	—	4	8	no	—
628	C₄×D₅₃	—	4	4	no	—
629	C₄×D₅₃	—	4	8	no	—
630	C₄×D₅₃	—	4	8	no	—
631	C₄×D₅₃	—	4	4	no	—
632	Dic₁₀₆	—	4	4	no	—
633	Dic₁₀₆	—	4	8	no	—
634	#62844	—	53	1	no	maximal, Sylow
635	C₂²×C₅₃	—	2	2	no	—
636	C₂²×C₅₃	—	2	4	no	—
637	C₂²×C₅₃	—	2	2	no	—
638	C₂²×C₅₃	—	2	2	no	—
639	C₂²×C₅₃	—	2	4	no	—
640	C₂²×C₅₃	—	2	4	no	—
641	C₂²×C₅₃	—	2	8	no	—
642	C₂²×C₅₃	—	2	2	no	—
643	C₂²×C₅₃	—	2	2	no	—
644	C₂²×C₅₃	—	4	4	no	—
645	C₂²×C₅₃	—	4	4	no	—
646	C₂²×C₅₃	—	4	4	no	—
647	C₂²×C₅₃	—	8	4	no	—
648	C₂²×C₅₃	—	8	8	no	—
649	C₂²×C₅₃	C₂²×#41	1	4	yes	—
650	C₂²×C₅₃	C₂²×#41	1	2	yes	—
651	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
652	C₂×D₅₃	—	2	2	no	—
653	C₂×D₅₃	—	2	4	no	—
654	C₂×D₅₃	—	2	2	no	—
655	C₂×D₅₃	—	2	4	no	—
656	C₂×D₅₃	—	2	8	no	—
657	C₂×D₅₃	—	4	8	no	—
658	C₂×D₅₃	—	4	4	no	—
659	C₂×D₅₃	—	4	8	no	—
660	C₂×D₅₃	—	4	4	no	—
661	C₂×D₅₃	—	4	16	no	—
662	C₂×D₅₃	—	8	8	no	—
663	C₂×D₅₃	—	8	4	no	—
664	C₂×D₅₃	C₂²×#41	1	2	yes	—
665	C₂×D₅₃	C₂²×#41	1	4	yes	—
666	C₂×D₅₃	C₂²×#41	1	2	yes	—
667	C₄×C₅₃	—	2	4	no	—
668	C₄×C₅₃	—	2	8	no	—
669	C₄×C₅₃	—	2	4	no	—
670	C₄×C₅₃	—	2	4	no	—
671	Dic₅₃	—	2	4	no	—
672	Dic₅₃	—	2	2	no	—
673	Dic₅₃	—	2	2	no	—
674	Dic₅₃	—	2	8	no	—
675	Dic₅₃	—	2	4	no	—
676	Dic₅₃	—	2	4	no	—
677	#3505	—	53	8	no	—
678	#3505	—	53	8	no	—
679	#3505	—	53	4	no	—
680	#3505	—	53	4	no	—
681	#3491	—	53	8	no	—
682	#3491	—	53	1	no	—
683	#3491	—	53	1	no	—
684	#3491	—	53	2	no	—
685	#3490	—	53	8	no	—
686	#3490	—	53	2	no	—
687	#3490	—	53	1	no	—
688	#3490	D₅₃	1	1	yes	characteristic, complemented
689	#3459	—	53	4	no	—
690	#3459	—	53	4	no	—
691	C₂×#543	—	53	1	no	—
692	C₂×#534	—	53	1	no	—
693	C₂×#534	—	53	2	no	—
694	C₂×#518	—	53	2	no	—
695	C₂×#518	—	53	1	no	—
696	C₂×C₅₃	—	2	4	no	—
697	C₂×C₅₃	—	2	2	no	—
698	C₂×C₅₃	—	4	4	no	—
699	C₂×C₅₃	—	4	2	no	—
700	C₂×C₅₃	—	4	2	no	—
701	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
702	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
703	D₅₃	—	2	4	no	—
704	D₅₃	—	2	2	no	—
705	D₅₃	—	2	2	no	—
706	D₅₃	—	4	4	no	—
707	C₂³×D₄	—	53	1	no	—
708	C₂³×D₄	—	53	2	no	—
709	#553	—	53	8	no	—
710	#553	—	53	8	no	—
711	#553	—	53	8	no	—
712	#553	—	53	8	no	—
713	#553	—	53	4	no	—
714	#553	—	53	8	no	—
715	#553	—	53	4	no	—
716	#552	—	53	8	no	—
717	#552	—	53	8	no	—
718	#552	—	53	4	no	—
719	#552	—	53	8	no	—
720	#552	—	53	8	no	—
721	#552	—	53	8	no	—
722	#552	—	53	4	no	—
723	#551	—	53	8	no	—
724	#551	—	53	8	no	—
725	#551	—	53	8	no	—
726	#551	—	53	8	no	—
727	#551	—	53	8	no	—
728	#551	—	53	8	no	—
729	#551	—	53	8	no	—
730	#551	—	53	8	no	—
731	#551	—	53	8	no	—
732	#551	—	53	8	no	—
733	#551	—	53	8	no	—
734	#551	C₂×D₅₃	1	8	yes	complemented
735	#548	—	53	4	no	—
736	#548	—	53	8	no	—
737	#548	—	53	4	no	—
738	#546	—	53	4	no	—
739	#546	—	53	8	no	—
740	#546	—	53	4	no	—
741	#546	—	53	8	no	—
742	#546	—	53	8	no	—
743	#546	—	53	8	no	—
744	#546	C₂×D₅₃	1	8	yes	complemented
745	#543	—	53	4	no	—
746	#543	—	53	8	no	—
747	#543	—	53	2	no	—
748	#543	—	53	1	no	—
749	#543	C₂×D₅₃	1	1	yes	characteristic, complemented
750	#539	—	53	8	no	—
751	#539	—	53	8	no	—
752	#539	—	53	8	no	—
753	#539	—	53	8	no	—
754	#539	—	53	4	no	—
755	#539	—	53	4	no	—
756	#539	—	53	8	no	—
757	#538	—	53	8	no	—
758	#538	—	53	8	no	—
759	#538	—	53	8	no	—
760	#538	—	53	8	no	—
761	#538	—	53	8	no	—
762	#538	—	53	4	no	—
763	#538	C₂×D₅₃	1	4	yes	complemented
764	#534	—	53	2	no	—
765	#534	—	53	4	no	—
766	#534	—	53	4	no	—
767	#534	—	53	8	no	—
768	#534	—	53	4	no	—
769	#534	—	53	8	no	—
770	#534	—	53	4	no	—
771	#534	—	53	4	no	—
772	#534	—	53	4	no	—
773	#534	—	53	4	no	—
774	#534	—	53	1	no	—
775	#534	C₂×D₅₃	1	1	yes	characteristic
776	#529	—	53	8	no	—
777	#529	—	53	8	no	—
778	#529	—	53	4	no	—
779	#529	—	53	4	no	—
780	#529	—	53	8	no	—
781	#529	—	53	8	no	—
782	#529	—	53	8	no	—
783	#525	—	53	8	no	—
784	#525	—	53	4	no	—
785	#525	—	53	8	no	—
786	#525	—	53	8	no	—
787	#525	—	53	8	no	—
788	#525	—	53	8	no	—
789	#525	C₂×D₅₃	1	4	yes	complemented
790	C₂×#123	—	53	2	no	—
791	C₂×#123	—	53	4	no	—
792	C₂×#123	—	53	2	no	—
793	C₂×#123	—	53	4	no	—
794	C₂×C₂²⋊Q₈	—	53	8	no	—
795	C₂×C₂²⋊Q₈	—	53	4	no	—
796	C₂×#121	—	53	4	no	—
797	C₂×#121	—	53	4	no	—
798	C₂×#121	—	53	4	no	—
799	C₂×#120	—	53	2	no	—
800	C₂×#120	—	53	4	no	—
801	C₂×#120	—	53	4	no	—
802	C₂×#120	C₂×D₅₃	1	2	yes	complemented
803	#518	—	53	2	no	—
804	#518	—	53	8	no	—
805	#518	—	53	8	no	—
806	#518	—	53	4	no	—
807	#518	—	53	2	no	—
808	#518	—	53	2	no	—
809	#518	—	53	8	no	—
810	#518	—	53	4	no	—
811	#518	—	53	8	no	—
812	#518	C₂×D₅₃	1	2	yes	complemented
813	C₂×C₄×D₄	—	53	2	no	—
814	C₂×C₄×D₄	—	53	2	no	—
815	C₂×C₄×D₄	—	53	8	no	—
816	C₂×C₄×D₄	—	53	8	no	—
817	C₂×C₄×D₄	—	53	2	no	—
818	C₂×C₄×D₄	—	53	2	no	—
819	C₂×#117	—	53	4	no	—
820	C₂×#117	—	53	1	no	—
821	C₂×#117	—	53	1	no	—
822	C₂²×C₂²⋊C₄	—	53	1	no	—
823	C₂²×C₂²⋊C₄	—	53	1	no	—
824	C₂²×C₂²⋊C₄	—	53	1	no	—
825	C₂²×C₂²⋊C₄	—	53	2	no	—
826	C₂²×C₂²⋊C₄	—	53	4	no	—
827	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
828	C₅₃	#62844	1	1	yes	characteristic, complemented, Sylow
829	C₂⁵	—	53	1	no	—
830	C₂⁵	—	53	2	no	—
831	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
832	C₂×#41	—	53	8	no	—
833	C₂×#41	—	53	4	no	—
834	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
835	C₂²×Q₈	—	53	4	no	—
836	C₂²×D₄	—	53	1	no	—
837	C₂²×D₄	—	53	1	no	—
838	C₂²×D₄	—	53	1	no	—
839	C₂²×D₄	—	53	1	no	—
840	C₂²×D₄	—	53	4	no	—
841	C₂²×D₄	—	53	2	no	—
842	C₂²×D₄	—	53	2	no	—
843	C₂²×D₄	—	53	4	no	—
844	C₂²×D₄	—	53	4	no	—
845	C₂²×D₄	—	53	4	no	—
846	C₂²×D₄	—	53	4	no	—
847	C₂²×D₄	—	53	4	no	—
848	C₂²×D₄	—	53	4	no	—
849	C₂²×D₄	—	53	4	no	—
850	C₂²×D₄	—	53	2	no	—
851	C₂²×D₄	—	106	16	no	—
852	C₂²×D₄	—	106	8	no	—
853	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
854	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
855	C₂³×C₄	—	53	1	no	—
856	C₂³×C₄	—	53	2	no	—
857	C₂³×C₄	—	53	2	no	—
858	C₂³×C₄	—	53	2	no	—
859	C₂³×C₄	—	53	2	no	—
860	C₂³×C₄	—	53	4	no	—
861	C₂³×C₄	—	53	8	no	—
862	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
863	#126	—	53	8	no	—
864	#126	—	53	8	no	—
865	#126	—	53	8	no	—
866	#126	—	53	8	no	—
867	#126	—	53	8	no	—
868	#126	—	53	8	no	—
869	#126	—	53	8	no	—
870	#126	—	53	8	no	—
871	#126	—	53	8	no	—
872	#126	—	53	8	no	—
873	#126	—	53	8	no	—
874	#126	C₂²×D₅₃	1	8	yes	complemented
875	#125	—	53	8	no	—
876	#125	—	53	8	no	—
877	#125	—	53	8	no	—
878	#125	—	53	8	no	—
879	#125	—	53	4	no	—
880	#125	—	53	4	no	—
881	#125	—	53	8	no	—
882	#124	—	53	4	no	—
883	#124	—	53	4	no	—
884	#124	—	53	8	no	—
885	#124	—	53	8	no	—
886	#124	—	53	8	no	—
887	#124	—	53	8	no	—
888	#124	C₂²×D₅₃	1	8	yes	complemented
889	#123	—	53	4	no	—
890	#123	—	53	4	no	—
891	#123	—	53	8	no	—
892	#123	—	53	4	no	—
893	#123	—	53	8	no	—
894	#123	—	53	8	no	—
895	#123	—	53	8	no	—
896	#123	—	53	4	no	—
897	#123	—	53	8	no	—
898	#123	—	53	8	no	—
899	#123	—	53	8	no	—
900	#123	—	53	8	no	—
901	#123	—	53	8	no	—
902	#123	—	53	8	no	—
903	#123	—	53	8	no	—
904	#123	—	53	4	no	—
905	#123	—	53	4	no	—
906	#123	—	53	8	no	—
907	#123	—	53	8	no	—
908	#123	—	53	8	no	—
909	#123	—	53	4	no	—
910	#123	—	53	8	no	—
911	#123	—	53	8	no	—
912	#123	—	53	8	no	—
913	#123	—	53	8	no	—
914	#123	C₂²×D₅₃	1	4	yes	—
915	#123	C₂²×D₅₃	1	8	yes	complemented
916	#123	C₂²×D₅₃	1	8	yes	complemented
917	C₂²⋊Q₈	—	53	8	no	—
918	C₂²⋊Q₈	—	53	4	no	—
919	C₂²⋊Q₈	—	53	8	no	—
920	C₂²⋊Q₈	—	53	4	no	—
921	C₂²⋊Q₈	—	53	8	no	—
922	C₂²⋊Q₈	—	53	8	no	—
923	C₂²⋊Q₈	—	53	4	no	—
924	C₂²⋊Q₈	—	53	8	no	—
925	C₂²⋊Q₈	—	53	8	no	—
926	C₂²⋊Q₈	—	53	8	no	—
927	C₂²⋊Q₈	—	53	8	no	—
928	C₂²⋊Q₈	—	53	4	no	—
929	C₂²⋊Q₈	—	53	8	no	—
930	C₂²⋊Q₈	—	53	8	no	—
931	C₂²⋊Q₈	—	53	8	no	—
932	C₂²⋊Q₈	—	53	8	no	—
933	C₂²⋊Q₈	—	53	8	no	—
934	C₂²⋊Q₈	—	53	8	no	—
935	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
936	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
937	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
938	#121	—	53	8	no	—
939	#121	—	53	8	no	—
940	#121	—	53	8	no	—
941	#121	—	53	4	no	—
942	#121	—	53	8	no	—
943	#121	—	53	8	no	—
944	#121	—	53	8	no	—
945	#121	—	53	8	no	—
946	#121	—	53	8	no	—
947	#121	—	53	4	no	—
948	#121	—	53	4	no	—
949	#121	—	53	4	no	—
950	#121	—	53	8	no	—
951	#121	—	53	8	no	—
952	#121	—	53	8	no	—
953	#121	—	53	8	no	—
954	#121	—	53	8	no	—
955	#121	—	53	8	no	—
956	#121	C₂²×D₅₃	1	4	yes	—
957	#121	C₂²×D₅₃	1	8	yes	complemented
958	#121	C₂²×D₅₃	1	4	yes	complemented
959	#120	—	53	4	no	—
960	#120	—	53	4	no	—
961	#120	—	53	4	no	—
962	#120	—	53	8	no	—
963	#120	—	53	8	no	—
964	#120	—	53	8	no	—
965	#120	—	53	8	no	—
966	#120	—	53	4	no	—
967	#120	—	53	8	no	—
968	#120	—	53	8	no	—
969	#120	—	53	8	no	—
970	#120	—	53	4	no	—
971	#120	C₂²×D₅₃	1	4	yes	—
972	#120	C₂²×D₅₃	1	8	yes	—
973	#120	C₂²×D₅₃	1	4	yes	complemented
974	#120	C₂²×D₅₃	1	4	yes	complemented
975	C₄×Q₈	—	53	4	no	—
976	C₄×Q₈	—	53	4	no	—
977	C₄×Q₈	—	53	8	no	—
978	C₄×D₄	—	53	8	no	—
979	C₄×D₄	—	53	8	no	—
980	C₄×D₄	—	53	4	no	—
981	C₄×D₄	—	53	8	no	—
982	C₄×D₄	—	53	8	no	—
983	C₄×D₄	—	53	8	no	—
984	C₄×D₄	—	53	8	no	—
985	C₄×D₄	—	53	8	no	—
986	C₄×D₄	—	53	8	no	—
987	C₄×D₄	—	53	4	no	—
988	C₄×D₄	—	53	4	no	—
989	C₄×D₄	—	53	8	no	—
990	C₄×D₄	—	53	4	no	—
991	C₄×D₄	—	53	4	no	—
992	C₄×D₄	—	53	8	no	—
993	C₄×D₄	—	53	8	no	—
994	C₄×D₄	—	53	8	no	—
995	C₄×D₄	—	53	8	no	—
996	C₄×D₄	—	53	4	no	—
997	C₄×D₄	—	53	8	no	—
998	C₄×D₄	—	53	8	no	—
999	C₄×D₄	—	53	8	no	—
1000	C₄×D₄	—	53	8	no	—
1001	C₄×D₄	—	53	8	no	—
1002	C₄×D₄	—	53	8	no	—
1003	C₄×D₄	—	53	8	no	—
1004	C₄×D₄	—	53	8	no	—
1005	C₄×D₄	—	53	8	no	—
1006	C₄×D₄	—	53	8	no	—
1007	C₄×D₄	—	53	8	no	—
1008	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1009	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1010	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1011	#117	—	53	4	no	—
1012	#117	—	53	8	no	—
1013	#117	—	53	4	no	—
1014	#117	—	53	8	no	—
1015	#117	—	53	8	no	—
1016	#117	—	53	4	no	—
1017	#117	—	53	8	no	—
1018	#117	—	53	4	no	—
1019	#117	—	53	8	no	—
1020	#117	—	53	8	no	—
1021	#117	—	53	8	no	—
1022	#117	—	53	8	no	—
1023	#117	—	53	8	no	—
1024	#117	C₂²×D₅₃	1	4	yes	complemented
1025	#117	C₂²×D₅₃	1	4	yes	complemented
1026	C₂×C₄⋊C₄	—	53	2	no	—
1027	C₂×C₄⋊C₄	—	53	2	no	—
1028	C₂×C₄⋊C₄	—	53	4	no	—
1029	C₂×C₄⋊C₄	—	53	4	no	—
1030	C₂×C₄⋊C₄	—	53	8	no	—
1031	C₂×C₄⋊C₄	—	53	4	no	—
1032	C₂×C₄⋊C₄	—	53	8	no	—
1033	C₂×C₄⋊C₄	—	53	4	no	—
1034	C₂×C₂²⋊C₄	—	53	1	no	—
1035	C₂×C₂²⋊C₄	—	53	1	no	—
1036	C₂×C₂²⋊C₄	—	53	2	no	—
1037	C₂×C₂²⋊C₄	—	53	2	no	—
1038	C₂×C₂²⋊C₄	—	53	4	no	—
1039	C₂×C₂²⋊C₄	—	53	8	no	—
1040	C₂×C₂²⋊C₄	—	53	4	no	—
1041	C₂×C₂²⋊C₄	—	53	4	no	—
1042	C₂×C₂²⋊C₄	—	53	2	no	—
1043	C₂×C₂²⋊C₄	—	53	2	no	—
1044	C₂×C₂²⋊C₄	—	53	4	no	—
1045	C₂×C₂²⋊C₄	—	53	8	no	—
1046	C₂×C₂²⋊C₄	—	53	4	no	—
1047	C₂×C₂²⋊C₄	—	53	4	no	—
1048	C₂×C₂²⋊C₄	—	53	4	no	—
1049	C₂×C₂²⋊C₄	—	53	4	no	—
1050	C₂×C₂²⋊C₄	—	53	4	no	—
1051	C₂×C₂²⋊C₄	—	53	8	no	—
1052	C₂×C₂²⋊C₄	—	53	4	no	—
1053	C₂×C₂²⋊C₄	—	53	4	no	—
1054	C₂×C₂²⋊C₄	—	53	4	no	—
1055	C₂×C₂²⋊C₄	—	53	4	no	—
1056	C₂×C₂²⋊C₄	—	53	4	no	—
1057	C₂×C₂²⋊C₄	—	53	4	no	—
1058	C₂×C₂²⋊C₄	—	53	8	no	—
1059	C₂×C₂²⋊C₄	—	53	8	no	—
1060	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1061	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1062	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1063	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1064	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1065	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
1066	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1067	C₂×C₄²	—	53	2	no	—
1068	C₂×C₄²	—	53	2	no	—
1069	C₂×C₄²	—	53	8	no	—
1070	C₂⁴	—	2	4	no	—
1071	C₂⁴	—	8	2	no	—
1072	C₂⁴	—	53	8	no	—
1073	C₂⁴	—	53	2	no	—
1074	C₂⁴	—	53	1	no	—
1075	C₂⁴	—	53	1	no	—
1076	C₂⁴	—	53	2	no	—
1077	C₂⁴	—	53	4	no	—
1078	C₂⁴	—	53	2	no	—
1079	C₂⁴	—	53	4	no	—
1080	C₂⁴	—	106	8	no	—
1081	C₂⁴	—	424	2	no	—
1082	C₂⁴	—	424	4	no	—
1083	C₂⁴	C₂³×D₅₃	1	2	yes	—
1084	C₂⁴	C₂³×D₅₃	1	4	yes	—
1085	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1086	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1087	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1088	#41	—	8	4	no	—
1089	#41	—	424	4	no	—
1090	#41	—	424	8	no	—
1091	C₂×Q₈	—	53	4	no	—
1092	C₂×Q₈	—	53	8	no	—
1093	C₂×Q₈	—	424	4	no	—
1094	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1095	C₂×D₄	—	2	8	no	—
1096	C₂×D₄	—	8	4	no	—
1097	C₂×D₄	—	53	2	no	—
1098	C₂×D₄	—	53	2	no	—
1099	C₂×D₄	—	53	4	no	—
1100	C₂×D₄	—	53	4	no	—
1101	C₂×D₄	—	53	4	no	—
1102	C₂×D₄	—	53	4	no	—
1103	C₂×D₄	—	53	4	no	—
1104	C₂×D₄	—	53	4	no	—
1105	C₂×D₄	—	53	2	no	—
1106	C₂×D₄	—	53	2	no	—
1107	C₂×D₄	—	53	8	no	—
1108	C₂×D₄	—	53	8	no	—
1109	C₂×D₄	—	53	8	no	—
1110	C₂×D₄	—	53	4	no	—
1111	C₂×D₄	—	53	4	no	—
1112	C₂×D₄	—	53	4	no	—
1113	C₂×D₄	—	106	8	no	—
1114	C₂×D₄	—	106	16	no	—
1115	C₂×D₄	—	106	16	no	—
1116	C₂×D₄	—	106	16	no	—
1117	C₂×D₄	—	106	16	no	—
1118	C₂×D₄	—	106	4	no	—
1119	C₂×D₄	—	106	4	no	—
1120	C₂×D₄	—	106	4	no	—
1121	C₂×D₄	—	106	4	no	—
1122	C₂×D₄	—	106	8	no	—
1123	C₂×D₄	—	106	16	no	—
1124	C₂×D₄	—	106	16	no	—
1125	C₂×D₄	—	106	8	no	—
1126	C₂×D₄	—	424	4	no	—
1127	C₂×D₄	—	424	4	no	—
1128	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1129	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1130	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1131	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1132	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1133	C₂²×C₄	—	8	2	no	—
1134	C₂²×C₄	—	53	1	no	—
1135	C₂²×C₄	—	53	1	no	—
1136	C₂²×C₄	—	53	4	no	—
1137	C₂²×C₄	—	53	2	no	—
1138	C₂²×C₄	—	53	2	no	—
1139	C₂²×C₄	—	53	2	no	—
1140	C₂²×C₄	—	53	4	no	—
1141	C₂²×C₄	—	53	8	no	—
1142	C₂²×C₄	—	53	8	no	—
1143	C₂²×C₄	—	53	4	no	—
1144	C₂²×C₄	—	53	4	no	—
1145	C₂²×C₄	—	53	8	no	—
1146	C₂²×C₄	—	53	8	no	—
1147	C₂²×C₄	—	53	4	no	—
1148	C₂²×C₄	—	53	4	no	—
1149	C₂²×C₄	—	53	8	no	—
1150	C₂²×C₄	—	53	8	no	—
1151	C₂²×C₄	—	53	8	no	—
1152	C₂²×C₄	—	106	8	no	—
1153	C₂²×C₄	—	106	4	no	—
1154	C₂²×C₄	—	424	2	no	—
1155	C₂²×C₄	—	424	2	no	—
1156	C₂²×C₄	—	424	4	no	—
1157	C₂²×C₄	—	424	8	no	—
1158	C₂²×C₄	—	424	2	no	—
1159	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1160	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1161	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1162	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1163	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1164	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1165	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1166	C₄⋊C₄	—	53	8	no	—
1167	C₄⋊C₄	—	53	8	no	—
1168	C₄⋊C₄	—	53	4	no	—
1169	C₄⋊C₄	—	53	4	no	—
1170	C₄⋊C₄	—	53	8	no	—
1171	C₄⋊C₄	—	53	8	no	—
1172	C₄⋊C₄	—	53	8	no	—
1173	C₄⋊C₄	—	53	8	no	—
1174	C₄⋊C₄	—	53	8	no	—
1175	C₄⋊C₄	—	53	4	no	—
1176	C₄⋊C₄	—	53	8	no	—
1177	C₄⋊C₄	—	53	8	no	—
1178	C₄⋊C₄	—	53	8	no	—
1179	C₄⋊C₄	—	53	8	no	—
1180	C₄⋊C₄	—	53	4	no	—
1181	C₄⋊C₄	—	53	8	no	—
1182	C₄⋊C₄	—	53	8	no	—
1183	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1184	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1185	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1186	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1187	C₂²⋊C₄	—	53	4	no	—
1188	C₂²⋊C₄	—	53	4	no	—
1189	C₂²⋊C₄	—	53	4	no	—
1190	C₂²⋊C₄	—	53	4	no	—
1191	C₂²⋊C₄	—	53	8	no	—
1192	C₂²⋊C₄	—	53	4	no	—
1193	C₂²⋊C₄	—	53	4	no	—
1194	C₂²⋊C₄	—	53	8	no	—
1195	C₂²⋊C₄	—	53	8	no	—
1196	C₂²⋊C₄	—	53	8	no	—
1197	C₂²⋊C₄	—	53	8	no	—
1198	C₂²⋊C₄	—	53	8	no	—
1199	C₂²⋊C₄	—	53	4	no	—
1200	C₂²⋊C₄	—	53	8	no	—
1201	C₂²⋊C₄	—	53	4	no	—
1202	C₂²⋊C₄	—	53	8	no	—
1203	C₂²⋊C₄	—	53	8	no	—
1204	C₂²⋊C₄	—	53	8	no	—
1205	C₂²⋊C₄	—	53	8	no	—
1206	C₂²⋊C₄	—	53	8	no	—
1207	C₂²⋊C₄	—	53	8	no	—
1208	C₂²⋊C₄	—	53	8	no	—
1209	C₂²⋊C₄	—	53	8	no	—
1210	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1211	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1212	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1213	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1214	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1215	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1216	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1217	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1218	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1219	C₄²	—	53	4	no	—
1220	C₄²	—	53	4	no	—
1221	C₄²	—	53	8	no	—
1222	C₄²	—	53	8	no	—
1223	C₄²	—	53	8	no	—
1224	C₄²	—	53	8	no	—
1225	C₄²	C₂³×D₅₃	1	8	yes	—
1226	C₂³	—	2	2	no	—
1227	C₂³	—	2	2	no	—
1228	C₂³	—	2	4	no	—
1229	C₂³	—	2	8	no	—
1230	C₂³	—	4	2	no	—
1231	C₂³	—	4	2	no	—
1232	C₂³	—	4	2	no	—
1233	C₂³	—	4	4	no	—
1234	C₂³	—	4	4	no	—
1235	C₂³	—	4	4	no	—
1236	C₂³	—	8	8	no	—
1237	C₂³	—	53	1	no	—
1238	C₂³	—	53	2	no	—
1239	C₂³	—	53	1	no	—
1240	C₂³	—	53	8	no	—
1241	C₂³	—	53	4	no	—
1242	C₂³	—	53	4	no	—
1243	C₂³	—	53	8	no	—
1244	C₂³	—	53	4	no	—
1245	C₂³	—	106	8	no	—
1246	C₂³	—	106	8	no	—
1247	C₂³	—	106	4	no	—
1248	C₂³	—	424	8	no	—
1249	C₂³	—	424	16	no	—
1250	C₂³	—	212	4	no	—
1251	C₂³	—	212	8	no	—
1252	C₂³	—	212	2	no	—
1253	C₂³	—	212	2	no	—
1254	C₂³	—	212	4	no	—
1255	C₂³	—	212	8	no	—
1256	C₂³	—	212	4	no	—
1257	C₂³	#41×D₅₃	1	4	yes	—
1258	C₂³	C₂⁴×D₅₃	1	4	yes	—
1259	C₂³	C₂⁴×D₅₃	1	2	yes	—
1260	C₂³	C₂⁴×D₅₃	1	2	yes	—
1261	C₂³	C₂⁴×D₅₃	1	2	yes	—
1262	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1263	Q₈	—	4	4	no	—
1264	Q₈	—	212	4	no	—
1265	Q₈	—	212	8	no	—
1266	D₄	—	2	8	no	—
1267	D₄	—	2	8	no	—
1268	D₄	—	4	8	no	—
1269	D₄	—	4	8	no	—
1270	D₄	—	4	4	no	—
1271	D₄	—	106	8	no	—
1272	D₄	—	106	8	no	—
1273	D₄	—	106	8	no	—
1274	D₄	—	106	8	no	—
1275	D₄	—	106	4	no	—
1276	D₄	—	106	4	no	—
1277	D₄	—	106	8	no	—
1278	D₄	—	106	8	no	—
1279	D₄	—	106	4	no	—
1280	D₄	—	106	4	no	—
1281	D₄	—	106	8	no	—
1282	D₄	—	106	8	no	—
1283	D₄	—	212	4	no	—
1284	D₄	—	212	8	no	—
1285	D₄	—	212	8	no	—
1286	D₄	—	212	8	no	—
1287	C₂×C₄	—	2	4	no	—
1288	C₂×C₄	—	4	2	no	—
1289	C₂×C₄	—	4	2	no	—
1290	C₂×C₄	—	4	4	no	—
1291	C₂×C₄	—	4	4	no	—
1292	C₂×C₄	—	4	4	no	—
1293	C₂×C₄	—	4	8	no	—
1294	C₂×C₄	—	53	4	no	—
1295	C₂×C₄	—	53	4	no	—
1296	C₂×C₄	—	53	2	no	—
1297	C₂×C₄	—	53	2	no	—
1298	C₂×C₄	—	53	8	no	—
1299	C₂×C₄	—	53	4	no	—
1300	C₂×C₄	—	106	8	no	—
1301	C₂×C₄	—	106	8	no	—
1302	C₂×C₄	—	106	4	no	—
1303	C₂×C₄	—	106	8	no	—
1304	C₂×C₄	—	106	2	no	—
1305	C₂×C₄	—	106	2	no	—
1306	C₂×C₄	—	212	8	no	—
1307	C₂×C₄	—	212	8	no	—
1308	C₂×C₄	—	212	4	no	—
1309	C₂×C₄	—	212	4	no	—
1310	C₂×C₄	—	212	8	no	—
1311	C₂×C₄	—	212	8	no	—
1312	C₂×C₄	—	212	8	no	—
1313	C₂×C₄	—	212	2	no	—
1314	C₂×C₄	—	212	2	no	—
1315	C₂×C₄	—	212	4	no	—
1316	C₂×C₄	—	212	8	no	—
1317	C₂×C₄	—	212	8	no	—
1318	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1319	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1320	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1321	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1322	C₂²	—	2	2	no	—
1323	C₂²	—	2	4	no	—
1324	C₂²	—	2	4	no	—
1325	C₂²	—	2	2	no	—
1326	C₂²	—	2	2	no	—
1327	C₂²	—	2	2	no	—
1328	C₂²	—	2	2	no	—
1329	C₂²	—	2	8	no	—
1330	C₂²	—	2	4	no	—
1331	C₂²	—	4	4	no	—
1332	C₂²	—	4	4	no	—
1333	C₂²	—	4	4	no	—
1334	C₂²	—	8	8	no	—
1335	C₂²	—	8	4	no	—
1336	C₂²	—	53	2	no	—
1337	C₂²	—	53	4	no	—
1338	C₂²	—	53	2	no	—
1339	C₂²	—	106	2	no	—
1340	C₂²	—	106	4	no	—
1341	C₂²	—	106	2	no	—
1342	C₂²	—	106	4	no	—
1343	C₂²	—	106	8	no	—
1344	C₂²	—	424	4	no	—
1345	C₂²	—	424	8	no	—
1346	C₂²	—	212	8	no	—
1347	C₂²	—	212	4	no	—
1348	C₂²	—	212	4	no	—
1349	C₂²	—	212	8	no	—
1350	C₂²	—	212	16	no	—
1351	C₂²	C₂×#41×D₅₃	1	4	yes	—
1352	C₂²	C₂×#41×D₅₃	1	2	yes	—
1353	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1354	C₄	—	2	4	no	—
1355	C₄	—	2	4	no	—
1356	C₄	—	2	4	no	—
1357	C₄	—	2	8	no	—
1358	C₄	—	106	4	no	—
1359	C₄	—	106	2	no	—
1360	C₄	—	106	2	no	—
1361	C₄	—	106	4	no	—
1362	C₄	—	106	8	no	—
1363	C₄	—	106	4	no	—
1364	C₂	—	2	2	no	—
1365	C₂	—	2	4	no	—
1366	C₂	—	4	2	no	—
1367	C₂	—	4	2	no	—
1368	C₂	—	4	4	no	—
1369	C₂	—	106	2	no	—
1370	C₂	—	106	4	no	—
1371	C₂	—	106	2	no	—
1372	C₂	—	212	4	no	—
1373	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1374	C₂	#20289525	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3490	C₂
hypercenter	#3490	D₅₃
hypocenter	C₅₃	#62844
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3490

Complements

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

N	H ≅ G/N	type
1. #20288553	C₂	semidirect
2. #20288546	C₂	semidirect
3. #20288543	C₂	semidirect
4. #20288542	C₂	semidirect
5. #20288414	C₂	semidirect
6. #20288412	C₂	semidirect
7. #20288408	C₂	semidirect
8. #20288406	C₂	semidirect
9. #20288404	C₂	semidirect
10. #20288402	C₂	semidirect
11. #20288397	C₂	semidirect
12. #20288126	C₂	semidirect
13. #20288122	C₂	semidirect
14. #543×D₅₃	C₂	semidirect
15. C₂×#16811183	C₂	semidirect
16. #534×D₅₃	C₂	semidirect
17. C₂×#16811096	C₂	semidirect
18. #518×D₅₃	C₂	semidirect
19. C₅₃×#3490	C₂	semidirect
22. #16811324	C₂²	semidirect
23. #16811323	C₂²	semidirect
24. #16811320	C₂²	semidirect
25. #16811320	C₂²	semidirect
26. #16811318	C₂²	semidirect
27. #16811318	C₂²	semidirect
28. #16811317	C₂²	semidirect
29. #16811315	C₂²	semidirect
30. #16811313	C₂²	semidirect
31. #16811312	C₂²	semidirect
32. #16811310	C₂²	semidirect
33. #16811309	C₂²	semidirect
34. #16811307	C₂²	semidirect
35. #16811306	C₂²	semidirect
36. #16811304	C₂²	semidirect
37. #16811304	C₂²	semidirect
38. #16811303	C₂²	semidirect
39. #16811302	C₂²	semidirect
40. #16811302	C₂²	semidirect
41. #16811301	C₂²	semidirect
42. #16811300	C₂²	semidirect
43. #16811299	C₂²	semidirect
44. #16811299	C₂²	semidirect
45. #16811299	C₂²	semidirect
46. #16811296	C₂²	semidirect
47. #16811283	C₂²	semidirect
48. #16811281	C₂²	semidirect
49. #16811280	C₂²	semidirect
50. #16811270	C₂²	semidirect
51. #16811267	C₂²	semidirect
52. #16811263	C₂²	semidirect
53. #16811262	C₂²	semidirect
54. #16811261	C₂²	semidirect
55. #16811260	C₂²	semidirect
56. #16811249	C₂²	semidirect
57. #16811249	C₂²	semidirect
58. #16811248	C₂²	semidirect
59. #16811248	C₂²	semidirect
60. #16811222	C₂²	semidirect
61. #16811219	C₂²	semidirect
62. #16811218	C₂²	semidirect
63. #16811216	C₂²	semidirect
64. #16811216	C₂²	semidirect
65. #16811215	C₂²	semidirect
66. #16811214	C₂²	semidirect
67. #16811211	C₂²	semidirect
68. #16811209	C₂²	semidirect
69. #16811208	C₂²	semidirect
70. #16811207	C₂²	semidirect
71. #16811205	C₂²	semidirect
72. #16811205	C₂²	semidirect
74. #16811184	C₂²	semidirect
76. #16811183	C₂²	semidirect
77. #16811183	C₂²	semidirect
78. #16811183	C₂²	semidirect
79. #16811183	C₂²	semidirect
80. #16811183	C₂²	semidirect
81. #16811183	C₂²	semidirect
83. #16811181	C₂²	semidirect
84. #16811159	C₂²	semidirect
85. #16811156	C₂²	semidirect
86. #16811155	C₂²	semidirect
87. #16811154	C₂²	semidirect
88. #16811153	C₂²	semidirect
89. #16811152	C₂²	semidirect
90. #16811151	C₂²	semidirect
91. #16811134	C₂²	semidirect
92. #16811133	C₂²	semidirect
93. #16811132	C₂²	semidirect
94. #16811131	C₂²	semidirect
95. #16811130	C₂²	semidirect
96. #16811129	C₂²	semidirect
97. C₂×#13133201	C₂²	semidirect
98. C₂×#13133199	C₂²	semidirect
99. C₂×#13133198	C₂²	semidirect
100. #123×D₅₃	C₂²	semidirect
101. C₂²⋊Q₈×D₅₃	C₂²	semidirect
102. C₂²⋊Q₈×D₅₃	C₂²	semidirect
103. C₂×#13133190	C₂²	semidirect
104. C₂×#13133188	C₂²	semidirect
105. #121×D₅₃	C₂²	semidirect
106. C₂×#13133186	C₂²	semidirect
107. C₂×#13133185	C₂²	semidirect
108. #120×D₅₃	C₂²	semidirect
109. #16811098	C₂²	semidirect
110. #16811097	C₂²	semidirect
111. #16811096	C₂²	semidirect
112. #16811096	C₂²	semidirect
113. #16811096	C₂²	semidirect
114. #16811096	C₂²	semidirect
115. #16811096	C₂²	semidirect
116. #16811095	C₂²	semidirect
117. #16811095	C₂²	semidirect
118. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
119. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
120. C₂×#13133177	C₂²	semidirect
121. C₂×#13133177	C₂²	semidirect
122. C₄×D₄×D₅₃	C₂²	semidirect
123. C₄×D₄×D₅₃	C₂²	semidirect
124. C₂×#13133173	C₂²	semidirect
125. C₂×#13133173	C₂²	semidirect
126. #117×D₅₃	C₂²	semidirect
127. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
131. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
132. C₅₃×#551	C₂²	semidirect
133. C₅₃×#546	C₂²	semidirect
134. C₅₃×#543	C₂²	semidirect
135. C₅₃×#538	C₂²	semidirect
137. C₅₃×#525	C₂²	semidirect
138. C₂×#120×C₅₃	C₂²	semidirect
139. C₅₃×#518	C₂²	semidirect
140. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
143. C₂×#11719945	C₂³	semidirect
144. C₂×#11719947	C₂³	semidirect
145. C₂×Q₈×D₅₃	C₂³	semidirect
156. C₂²×C₂²⋊D₅₃	C₂³	semidirect
162. C₂×D₄×D₅₃	C₂³	semidirect
164. C₂³×Dic₅₃	C₂³	semidirect
169. C₂²×C₄×D₅₃	C₂³	semidirect
170. #13133212	C₂³	semidirect
171. #13133212	C₂³	semidirect
172. #13133212	C₂³	semidirect
173. #13133211	C₂³	semidirect
174. #13133210	C₂³	semidirect
175. #13133210	C₂³	semidirect
176. #13133210	C₂³	semidirect
177. #13133210	C₂³	semidirect
178. #13133210	C₂³	semidirect
179. #13133210	C₂³	semidirect
180. #13133210	C₂³	semidirect
181. #13133209	C₂³	semidirect
182. #13133208	C₂³	semidirect
183. #13133208	C₂³	semidirect
184. #13133208	C₂³	semidirect
185. #13133207	C₂³	semidirect
186. #13133207	C₂³	semidirect
187. #13133207	C₂³	semidirect
188. #13133206	C₂³	semidirect
189. #13133204	C₂³	semidirect
190. #13133204	C₂³	semidirect
191. #13133203	C₂³	semidirect
192. #13133203	C₂³	semidirect
193. #13133203	C₂³	semidirect
194. #13133202	C₂³	semidirect
195. #13133202	C₂³	semidirect
198. #13133201	C₂³	semidirect
199. #13133201	C₂³	semidirect
200. #13133201	C₂³	semidirect
202. #13133200	C₂³	semidirect
203. #13133200	C₂³	semidirect
206. #13133199	C₂³	semidirect
207. #13133199	C₂³	semidirect
208. #13133199	C₂³	semidirect
209. #13133199	C₂³	semidirect
210. #13133199	C₂³	semidirect
211. #13133199	C₂³	semidirect
214. #13133198	C₂³	semidirect
215. #13133198	C₂³	semidirect
216. #13133198	C₂³	semidirect
217. #13133198	C₂³	semidirect
218. #13133198	C₂³	semidirect
219. #13133197	C₂³	semidirect
220. #13133197	C₂³	semidirect
221. #13133196	C₂³	semidirect
222. #13133196	C₂³	semidirect
223. #13133196	C₂³	semidirect
224. #13133196	C₂³	semidirect
225. #13133195	C₂³	semidirect
226. #13133195	C₂³	semidirect
227. #13133195	C₂³	semidirect
228. #13133195	C₂³	semidirect
229. #13133194	C₂³	semidirect
230. #13133194	C₂³	semidirect
231. #13133194	C₂³	semidirect
232. #13133194	C₂³	semidirect
233. #13133194	C₂³	semidirect
234. #13133193	C₂³	semidirect
235. #13133193	C₂³	semidirect
236. #13133193	C₂³	semidirect
237. #13133192	C₂³	semidirect
239. #13133191	C₂³	semidirect
242. #13133190	C₂³	semidirect
243. #13133190	C₂³	semidirect
244. #13133190	C₂³	semidirect
245. #13133190	C₂³	semidirect
247. #13133189	C₂³	semidirect
248. #13133189	C₂³	semidirect
251. #13133188	C₂³	semidirect
252. #13133188	C₂³	semidirect
253. #13133188	C₂³	semidirect
254. #13133188	C₂³	semidirect
256. #13133187	C₂³	semidirect
259. #13133186	C₂³	semidirect
260. #13133186	C₂³	semidirect
264. #13133185	C₂³	semidirect
265. #13133185	C₂³	semidirect
266. #13133185	C₂³	semidirect
267. Q₈×Dic₅₃	C₂³	semidirect
268. C₄×Dic₁₀₆	C₂³	semidirect
269. #13133182	C₂³	semidirect
270. C₄×D₂₁₂	C₂³	semidirect
271. C₄×D₂₁₂	C₂³	semidirect
273. D₄×Dic₅₃	C₂³	semidirect
274. D₄×Dic₅₃	C₂³	semidirect
275. D₄×Dic₅₃	C₂³	semidirect
276. #13133179	C₂³	semidirect
277. #13133179	C₂³	semidirect
278. #13133179	C₂³	semidirect
282. C₄×C₂²⋊D₅₃	C₂³	semidirect
283. C₄×C₂²⋊D₅₃	C₂³	semidirect
284. C₄×C₂²⋊D₅₃	C₂³	semidirect
285. C₄×C₂²⋊D₅₃	C₂³	semidirect
286. C₄×C₂²⋊D₅₃	C₂³	semidirect
287. C₄×C₂²⋊D₅₃	C₂³	semidirect
288. C₄×C₂²⋊D₅₃	C₂³	semidirect
289. C₄×C₂²⋊D₅₃	C₂³	semidirect
290. C₄×C₂²⋊D₅₃	C₂³	semidirect
293. #13133177	C₂³	semidirect
294. #13133177	C₂³	semidirect
295. #13133177	C₂³	semidirect
296. #13133177	C₂³	semidirect
297. #13133177	C₂³	semidirect
298. #13133177	C₂³	semidirect
299. #13133177	C₂³	semidirect
300. #13133176	C₂³	semidirect
301. #13133176	C₂³	semidirect
302. #13133176	C₂³	semidirect
303. #13133175	C₂³	semidirect
304. #13133175	C₂³	semidirect
305. #13133174	C₂³	semidirect
306. #13133174	C₂³	semidirect
307. #13133173	C₂³	semidirect
308. #13133173	C₂³	semidirect
309. #13133173	C₂³	semidirect
310. #13133173	C₂³	semidirect
311. #13133173	C₂³	semidirect
312. #13133173	C₂³	semidirect
313. C₂×C₄⋊Dic₅₃	C₂³	semidirect
314. C₂×#11719919	C₂³	semidirect
315. C₂×#11719919	C₂³	semidirect
316. C₂×#11719919	C₂³	semidirect
317. C₄⋊C₄×D₅₃	C₂³	semidirect
318. C₄⋊C₄×D₅₃	C₂³	semidirect
319. C₄⋊C₄×D₅₃	C₂³	semidirect
320. C₄⋊C₄×D₅₃	C₂³	semidirect
324. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
325. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
326. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
327. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
328. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
332. C₂×#11719921	C₂³	semidirect
333. C₂×#11719921	C₂³	semidirect
342. C₂²⋊C₄×D₅₃	C₂³	semidirect
343. C₂²⋊C₄×D₅₃	C₂³	semidirect
344. C₂²⋊C₄×D₅₃	C₂³	semidirect
345. C₂²⋊C₄×D₅₃	C₂³	semidirect
346. C₂²⋊C₄×D₅₃	C₂³	semidirect
347. C₂×C₄×Dic₅₃	C₂³	semidirect
348. C₂×C₄×Dic₅₃	C₂³	semidirect
349. C₄²×D₅₃	C₂³	semidirect
351. C₂×#41×C₅₃	C₂³	semidirect
353. C₂²×D₄×C₅₃	C₂³	semidirect
354. C₂³×C₄×C₅₃	C₂³	semidirect
355. #126×C₅₃	C₂³	semidirect
356. #124×C₅₃	C₂³	semidirect
358. #123×C₅₃	C₂³	semidirect
359. #123×C₅₃	C₂³	semidirect
360. C₂²⋊Q₈×C₅₃	C₂³	semidirect
361. C₂²⋊Q₈×C₅₃	C₂³	semidirect
362. C₂²⋊Q₈×C₅₃	C₂³	semidirect
364. #121×C₅₃	C₂³	semidirect
365. #121×C₅₃	C₂³	semidirect
368. #120×C₅₃	C₂³	semidirect
369. #120×C₅₃	C₂³	semidirect
371. C₄×D₄×C₅₃	C₂³	semidirect
372. C₄×D₄×C₅₃	C₂³	semidirect
373. #117×C₅₃	C₂³	semidirect
374. #117×C₅₃	C₂³	semidirect
378. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
379. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
380. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
381. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
392. C₂³×D₅₃	#41	semidirect
688. #3490	D₅₃	semidirect
734. #551	C₂×D₅₃	semidirect
744. #546	C₂×D₅₃	semidirect
749. #543	C₂×D₅₃	semidirect
763. #538	C₂×D₅₃	semidirect
789. #525	C₂×D₅₃	semidirect
802. C₂×#120	C₂×D₅₃	semidirect
812. #518	C₂×D₅₃	semidirect
827. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
828. C₅₃	#62844	semidirect
834. C₂×#41	C₂²×D₅₃	semidirect
854. C₂²×D₄	C₂²×D₅₃	semidirect
862. C₂³×C₄	C₂²×D₅₃	semidirect
874. #126	C₂²×D₅₃	semidirect
888. #124	C₂²×D₅₃	semidirect
915. #123	C₂²×D₅₃	semidirect
916. #123	C₂²×D₅₃	semidirect
935. C₂²⋊Q₈	C₂²×D₅₃	semidirect
936. C₂²⋊Q₈	C₂²×D₅₃	semidirect
937. C₂²⋊Q₈	C₂²×D₅₃	semidirect
957. #121	C₂²×D₅₃	semidirect
958. #121	C₂²×D₅₃	semidirect
973. #120	C₂²×D₅₃	semidirect
974. #120	C₂²×D₅₃	semidirect
1009. C₄×D₄	C₂²×D₅₃	semidirect
1010. C₄×D₄	C₂²×D₅₃	semidirect
1024. #117	C₂²×D₅₃	semidirect
1025. #117	C₂²×D₅₃	semidirect
1063. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1064. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1065. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1066. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288553	2
#20288546	2
#20288543	2
#20288542	2
#20288414	2
#20288412	2
#20288408	2
#20288406	2
#20288404	2
#20288402	2
#20288397	2
#20288126	2
#20288122	2
#543×D₅₃	2
C₂×#16811183	2
#534×D₅₃	2
C₂×#16811096	2
#518×D₅₃	2
C₅₃×#3490	2
#62844	53