Subgroups — D₅₃×#3491 #28292138

Order 13568.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288414	C₂	1	1	yes	maximal, characteristic, complemented
2	#20288413	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288412	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288411	C₂	1	2	yes	maximal, complemented
5	#20288410	C₂	1	8	yes	maximal, complemented
6	#20288409	C₂	1	4	yes	maximal, complemented
7	#20288408	C₂	1	2	yes	maximal, complemented
8	#20288407	C₂	1	4	yes	maximal, complemented
9	#20288406	C₂	1	8	yes	maximal, complemented
10	#552×D₅₃	C₂	1	8	yes	maximal, complemented
11	#551×D₅₃	C₂	1	8	yes	maximal, complemented
12	#543×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#539×D₅₃	C₂	1	4	yes	maximal, complemented
14	#534×D₅₃	C₂	1	1	yes	maximal, characteristic
15	#529×D₅₃	C₂	1	4	yes	maximal, complemented
16	C₂×#123×D₅₃	C₂	1	2	yes	maximal, complemented
17	#518×D₅₃	C₂	1	2	yes	maximal, complemented
18	C₂×#117×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3491	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
21	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
22	#16811315	C₂²	1	8	yes	complemented
23	#16811314	C₂²	1	8	yes	complemented
24	#16811313	C₂²	1	8	yes	complemented
25	#16811312	C₂²	1	8	yes	complemented
26	#16811311	C₂²	1	8	yes	complemented
27	#16811310	C₂²	1	8	yes	complemented
28	#16811310	C₂²	1	8	yes	complemented
29	#16811309	C₂²	1	8	yes	complemented
30	#16811309	C₂²	1	8	yes	complemented
31	#16811308	C₂²	1	8	yes	complemented
32	#16811307	C₂²	1	8	yes	complemented
33	#16811306	C₂²	1	8	yes	complemented
34	#16811306	C₂²	1	8	yes	complemented
35	#16811305	C₂²	1	8	yes	complemented
36	#16811305	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	#16811300	C₂²	1	8	yes	complemented
44	#16811299	C₂²	1	8	yes	complemented
45	#16811299	C₂²	1	8	yes	complemented
46	#16811298	C₂²	1	8	yes	complemented
47	#16811298	C₂²	1	8	yes	complemented
48	#16811297	C₂²	1	8	yes	complemented
49	#16811297	C₂²	1	8	yes	complemented
50	#16811296	C₂²	1	8	yes	complemented
51	#16811296	C₂²	1	8	yes	complemented
52	#16811249	C₂²	1	2	yes	complemented
53	#16811249	C₂²	1	1	yes	characteristic, complemented
54	#16811248	C₂²	1	8	yes	complemented
55	#16811248	C₂²	1	4	yes	complemented
56	#16811222	C₂²	1	4	yes	complemented
57	#16811221	C₂²	1	8	yes	complemented
58	#16811220	C₂²	1	4	yes	complemented
59	#16811219	C₂²	1	8	yes	complemented
60	#16811218	C₂²	1	4	yes	complemented
61	#16811217	C₂²	1	8	yes	complemented
62	#16811216	C₂²	1	8	yes	complemented
63	#16811215	C₂²	1	8	yes	complemented
64	#16811214	C₂²	1	8	yes	complemented
65	#16811185	C₂²	1	1	yes	characteristic
66	#16811184	C₂²	1	4	yes	—
67	#16811183	C₂²	1	4	yes	—
68	#16811182	C₂²	1	2	yes	—
69	#16811181	C₂²	1	4	yes	—
70	#16811160	C₂²	1	4	yes	complemented
71	#16811159	C₂²	1	4	yes	complemented
72	#16811158	C₂²	1	4	yes	complemented
73	#16811157	C₂²	1	4	yes	complemented
74	#16811156	C₂²	1	8	yes	complemented
75	#16811155	C₂²	1	4	yes	complemented
76	#16811154	C₂²	1	4	yes	complemented
77	#16811153	C₂²	1	8	yes	complemented
78	#16811152	C₂²	1	4	yes	complemented
79	#16811151	C₂²	1	8	yes	complemented
80	#16811150	C₂²	1	8	yes	complemented
81	#126×D₅₃	C₂²	1	8	yes	complemented
82	#126×D₅₃	C₂²	1	8	yes	complemented
83	#125×D₅₃	C₂²	1	8	yes	complemented
84	#125×D₅₃	C₂²	1	4	yes	complemented
85	#124×D₅₃	C₂²	1	4	yes	complemented
86	C₂×#13133202	C₂²	1	4	yes	complemented
87	C₂×#13133201	C₂²	1	2	yes	complemented
88	C₂×#13133200	C₂²	1	2	yes	complemented
89	C₂×#13133199	C₂²	1	4	yes	complemented
90	C₂×#13133198	C₂²	1	2	yes	complemented
91	#123×D₅₃	C₂²	1	4	yes	—
92	#123×D₅₃	C₂²	1	8	yes	—
93	#123×D₅₃	C₂²	1	8	yes	complemented
94	#123×D₅₃	C₂²	1	4	yes	complemented
95	#123×D₅₃	C₂²	1	8	yes	complemented
96	#123×D₅₃	C₂²	1	4	yes	complemented
97	#123×D₅₃	C₂²	1	4	yes	complemented
98	#123×D₅₃	C₂²	1	4	yes	complemented
99	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
100	C₂²⋊Q₈×D₅₃	C₂²	1	8	yes	complemented
101	C₂²⋊Q₈×D₅₃	C₂²	1	8	yes	complemented
102	#121×D₅₃	C₂²	1	4	yes	—
103	#120×D₅₃	C₂²	1	4	yes	—
104	#16811098	C₂²	1	2	yes	complemented
105	#16811097	C₂²	1	4	yes	complemented
106	#16811096	C₂²	1	2	yes	complemented
107	#16811096	C₂²	1	2	yes	complemented
108	#16811096	C₂²	1	4	yes	complemented
109	#16811095	C₂²	1	8	yes	complemented
110	#16811095	C₂²	1	8	yes	complemented
111	C₄×Q₈×D₅₃	C₂²	1	4	yes	complemented
112	C₄×D₄×D₅₃	C₂²	1	8	yes	—
113	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
114	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
115	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
116	C₂×#13133175	C₂²	1	2	yes	complemented
117	C₂×#13133174	C₂²	1	2	yes	complemented
118	C₂×#13133173	C₂²	1	1	yes	characteristic, complemented
119	C₂×#13133173	C₂²	1	1	yes	characteristic, complemented
120	#117×D₅₃	C₂²	1	8	yes	complemented
121	#117×D₅₃	C₂²	1	4	yes	complemented
122	#117×D₅₃	C₂²	1	8	yes	complemented
123	#117×D₅₃	C₂²	1	8	yes	complemented
124	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₄×D₅₃	C₂²	1	4	yes	complemented
126	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
128	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
130	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
131	C₂×C₄²×D₅₃	C₂²	1	2	yes	complemented
132	C₅₃×#552	C₂²	1	8	yes	complemented
133	C₅₃×#551	C₂²	1	8	yes	complemented
134	C₅₃×#543	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#539	C₂²	1	4	yes	complemented
136	C₅₃×#534	C₂²	1	1	yes	characteristic
137	C₅₃×#529	C₂²	1	4	yes	complemented
138	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
139	C₅₃×#518	C₂²	1	2	yes	complemented
140	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
141	C₂⁴×D₅₃	C₂³	1	2	yes	—
142	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
143	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
144	C₂²×D₂₁₂	C₂³	1	2	yes	—
145	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
146	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
147	C₂×D₄×D₅₃	—	2	16	no	—
148	C₂×D₄×D₅₃	C₂³	1	4	yes	—
149	C₂×D₄×D₅₃	C₂³	1	4	yes	—
150	C₂×D₄×D₅₃	C₂³	1	4	yes	—
151	C₂×D₄×D₅₃	C₂³	1	4	yes	—
152	C₂×D₄×D₅₃	C₂³	1	4	yes	—
153	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
154	C₂²×C₄×D₅₃	—	2	8	no	—
155	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
156	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
157	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
158	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
159	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
160	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
161	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
162	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
163	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
164	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
165	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
166	#13133212	C₂³	1	8	yes	complemented
167	#13133212	C₂³	1	8	yes	complemented
168	#13133212	C₂³	1	8	yes	complemented
169	#13133212	C₂³	1	8	yes	complemented
170	#13133212	C₂³	1	8	yes	complemented
171	#13133212	C₂³	1	8	yes	complemented
172	#13133211	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	#13133209	C₂³	1	4	yes	complemented
181	#13133209	C₂³	1	8	yes	complemented
182	#13133208	C₂³	1	8	yes	complemented
183	#13133208	C₂³	1	4	yes	complemented
184	#13133208	C₂³	1	8	yes	complemented
185	#13133208	C₂³	1	4	yes	complemented
186	#13133207	C₂³	1	8	yes	complemented
187	#13133207	C₂³	1	8	yes	complemented
188	#13133207	C₂³	1	8	yes	complemented
189	#13133207	C₂³	1	8	yes	complemented
190	#13133207	C₂³	1	8	yes	complemented
191	#13133207	C₂³	1	8	yes	complemented
192	#13133206	C₂³	1	4	yes	complemented
193	#13133205	C₂³	1	4	yes	complemented
194	#13133204	C₂³	1	4	yes	complemented
195	#13133203	C₂³	1	8	yes	complemented
196	#13133203	C₂³	1	8	yes	complemented
197	#13133202	C₂³	1	8	yes	—
198	#13133202	C₂³	1	8	yes	—
199	#13133202	C₂³	1	8	yes	—
200	#13133202	C₂³	1	8	yes	complemented
201	#13133202	C₂³	1	8	yes	complemented
202	#13133202	C₂³	1	8	yes	complemented
203	#13133202	C₂³	1	8	yes	complemented
204	#13133201	C₂³	1	8	yes	—
205	#13133201	C₂³	1	4	yes	—
206	#13133201	C₂³	1	8	yes	complemented
207	#13133201	C₂³	1	4	yes	complemented
208	#13133201	C₂³	1	4	yes	complemented
209	#13133200	C₂³	1	8	yes	—
210	#13133200	C₂³	1	4	yes	—
211	#13133200	C₂³	1	8	yes	complemented
212	#13133200	C₂³	1	4	yes	complemented
213	#13133200	C₂³	1	4	yes	complemented
214	#13133199	C₂³	1	8	yes	—
215	#13133199	C₂³	1	8	yes	—
216	#13133199	C₂³	1	8	yes	—
217	#13133199	C₂³	1	8	yes	complemented
218	#13133199	C₂³	1	8	yes	complemented
219	#13133199	C₂³	1	8	yes	complemented
220	#13133199	C₂³	1	8	yes	complemented
221	#13133198	C₂³	1	8	yes	—
222	#13133198	C₂³	1	4	yes	—
223	#13133198	C₂³	1	8	yes	complemented
224	#13133198	C₂³	1	4	yes	complemented
225	#13133198	C₂³	1	4	yes	complemented
226	#13133197	C₂³	1	8	yes	complemented
227	#13133197	C₂³	1	8	yes	complemented
228	#13133197	C₂³	1	4	yes	complemented
229	#13133196	C₂³	1	8	yes	complemented
230	#13133196	C₂³	1	8	yes	complemented
231	#13133196	C₂³	1	4	yes	complemented
232	#13133195	C₂³	1	8	yes	complemented
233	#13133195	C₂³	1	8	yes	complemented
234	#13133195	C₂³	1	8	yes	complemented
235	#13133195	C₂³	1	8	yes	complemented
236	#13133195	C₂³	1	8	yes	complemented
237	#13133194	C₂³	1	8	yes	complemented
238	#13133194	C₂³	1	8	yes	complemented
239	#13133194	C₂³	1	8	yes	complemented
240	#13133194	C₂³	1	8	yes	complemented
241	#13133194	C₂³	1	8	yes	complemented
242	#13133193	C₂³	1	8	yes	complemented
243	#13133193	C₂³	1	8	yes	complemented
244	#13133193	C₂³	1	4	yes	complemented
245	#13133192	C₂³	1	4	yes	—
246	#13133191	C₂³	1	4	yes	—
247	#13133190	C₂³	1	8	yes	—
248	#13133189	C₂³	1	8	yes	—
249	#13133188	C₂³	1	4	yes	—
250	#13133187	C₂³	1	4	yes	—
251	#13133187	C₂³	1	8	yes	—
252	#13133186	C₂³	1	4	yes	—
253	#13133185	C₂³	1	4	yes	—
254	#13133185	C₂³	1	8	yes	—
255	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
256	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
257	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
258	#13133182	C₂³	1	4	yes	complemented
259	#13133182	C₂³	1	8	yes	complemented
260	C₄×D₂₁₂	C₂³	1	8	yes	—
261	C₄×D₂₁₂	C₂³	1	4	yes	complemented
262	C₄×D₂₁₂	C₂³	1	8	yes	complemented
263	D₄×Dic₅₃	C₂³	1	8	yes	—
264	D₄×Dic₅₃	C₂³	1	4	yes	complemented
265	D₄×Dic₅₃	C₂³	1	8	yes	complemented
266	#13133179	C₂³	1	8	yes	—
267	#13133179	C₂³	1	4	yes	complemented
268	#13133179	C₂³	1	8	yes	complemented
269	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
270	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
271	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
272	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
273	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
274	#13133177	C₂³	1	8	yes	—
275	#13133177	C₂³	1	8	yes	—
276	#13133177	C₂³	1	8	yes	complemented
277	#13133177	C₂³	1	8	yes	complemented
278	#13133177	C₂³	1	8	yes	complemented
279	#13133176	C₂³	1	8	yes	complemented
280	#13133176	C₂³	1	8	yes	complemented
281	#13133176	C₂³	1	4	yes	complemented
282	#13133175	C₂³	1	8	yes	complemented
283	#13133175	C₂³	1	8	yes	complemented
284	#13133175	C₂³	1	8	yes	complemented
285	#13133175	C₂³	1	8	yes	complemented
286	#13133175	C₂³	1	8	yes	complemented
287	#13133174	C₂³	1	8	yes	complemented
288	#13133174	C₂³	1	8	yes	complemented
289	#13133174	C₂³	1	8	yes	complemented
290	#13133174	C₂³	1	8	yes	complemented
291	#13133174	C₂³	1	8	yes	complemented
292	#13133173	C₂³	1	8	yes	complemented
293	#13133173	C₂³	1	8	yes	complemented
294	#13133173	C₂³	1	8	yes	complemented
295	#13133173	C₂³	1	8	yes	complemented
296	#13133173	C₂³	1	4	yes	complemented
297	#13133173	C₂³	1	4	yes	complemented
298	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
299	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
300	C₂×#11719919	C₂³	1	4	yes	complemented
301	C₂×#11719919	C₂³	1	4	yes	complemented
302	C₂×#11719919	C₂³	1	2	yes	complemented
303	C₂×#11719919	C₂³	1	2	yes	complemented
304	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
305	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
306	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
307	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
308	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
309	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
310	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
311	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
312	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
313	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
314	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
317	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
318	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
319	C₂×#11719921	C₂³	1	2	yes	—
320	C₂×#11719921	C₂³	1	2	yes	—
321	C₂×#11719921	C₂³	1	4	yes	—
322	C₂×#11719921	C₂³	1	4	yes	complemented
323	C₂×#11719921	C₂³	1	8	yes	complemented
324	C₂×#11719921	C₂³	1	4	yes	complemented
325	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
326	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
327	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
328	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
329	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
330	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
331	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
332	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
333	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
334	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
335	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
336	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
337	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
338	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
339	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
340	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
341	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
342	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
343	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
344	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
345	C₄²×D₅₃	C₂³	1	4	yes	—
346	C₄²×D₅₃	C₂³	1	4	yes	—
347	C₄²×D₅₃	C₂³	1	8	yes	—
348	C₄²×D₅₃	C₂³	1	4	yes	complemented
349	C₄²×D₅₃	C₂³	1	4	yes	complemented
350	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
351	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
352	#126×C₅₃	C₂³	1	8	yes	complemented
353	#126×C₅₃	C₂³	1	8	yes	complemented
354	#125×C₅₃	C₂³	1	4	yes	complemented
355	#125×C₅₃	C₂³	1	8	yes	complemented
356	#124×C₅₃	C₂³	1	4	yes	complemented
357	#123×C₅₃	C₂³	1	8	yes	—
358	#123×C₅₃	C₂³	1	4	yes	—
359	#123×C₅₃	C₂³	1	8	yes	complemented
360	#123×C₅₃	C₂³	1	4	yes	complemented
361	#123×C₅₃	C₂³	1	4	yes	complemented
362	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
363	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
364	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
365	#121×C₅₃	C₂³	1	4	yes	—
366	#120×C₅₃	C₂³	1	4	yes	—
367	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
368	C₄×D₄×C₅₃	C₂³	1	8	yes	—
369	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
370	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
371	#117×C₅₃	C₂³	1	8	yes	complemented
372	#117×C₅₃	C₂³	1	4	yes	complemented
373	#117×C₅₃	C₂³	1	8	yes	complemented
374	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
375	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
376	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
377	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
378	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
379	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
380	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
381	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
382	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
383	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂³×D₅₃	—	2	8	no	—
385	C₂³×D₅₃	—	4	4	no	—
386	C₂³×D₅₃	—	4	8	no	—
387	C₂³×D₅₃	#41	1	8	yes	—
388	C₂³×D₅₃	C₂⁴	1	4	yes	—
389	C₂³×D₅₃	C₂⁴	1	2	yes	—
390	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
391	C₂³×D₅₃	C₂⁴	1	4	yes	—
392	C₂³×D₅₃	C₂⁴	1	2	yes	—
393	C₂³×D₅₃	C₂⁴	1	2	yes	—
394	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
396	C₂×D₄×C₅₃	—	2	8	no	—
397	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
398	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
399	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
400	C₂²×C₄×C₅₃	—	2	4	no	—
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
403	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
408	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
409	C₂×C₂²⋊D₅₃	—	2	8	no	—
410	C₂×C₂²⋊D₅₃	—	2	8	no	—
411	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
412	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
413	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
414	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
415	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
416	C₂²×Dic₅₃	—	2	4	no	—
417	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
419	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
421	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
422	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
423	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
424	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
425	Q₈×D₅₃	—	4	8	no	—
426	D₄×D₅₃	—	2	16	no	—
427	D₄×D₅₃	—	2	16	no	—
428	D₄×D₅₃	—	2	16	no	—
429	D₄×D₅₃	—	2	16	no	—
430	D₄×D₅₃	—	4	8	no	—
431	C₂×D₂₁₂	—	2	8	no	—
432	C₂×D₂₁₂	C₂⁴	1	4	yes	—
433	C₂×D₂₁₂	C₂⁴	1	4	yes	—
434	C₂×D₂₁₂	C₂⁴	1	4	yes	—
435	C₂×C₄×D₅₃	—	2	16	no	—
436	C₂×C₄×D₅₃	—	2	4	no	—
437	C₂×C₄×D₅₃	—	2	4	no	—
438	C₂×C₄×D₅₃	—	2	16	no	—
439	C₂×C₄×D₅₃	—	2	4	no	—
440	C₂×C₄×D₅₃	—	2	4	no	—
441	C₂×C₄×D₅₃	—	2	8	no	—
442	C₂×C₄×D₅₃	—	4	4	no	—
443	C₂×C₄×D₅₃	—	4	16	no	—
444	C₂×C₄×D₅₃	—	4	8	no	—
445	C₂×C₄×D₅₃	—	4	4	no	—
446	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
447	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
448	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
449	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
450	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
451	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
452	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
453	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
454	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
455	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
456	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
457	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
458	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
459	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
460	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
461	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
462	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
463	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
464	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
465	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
466	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
467	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
468	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
469	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
470	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
471	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
472	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
473	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
474	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
475	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
476	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
477	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
478	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
479	C₄²×C₅₃	C₂⁴	1	4	yes	—
480	C₄²×C₅₃	C₂⁴	1	4	yes	—
481	C₄²×C₅₃	C₂⁴	1	8	yes	—
482	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
483	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
484	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
485	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
486	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
487	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
488	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
489	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
490	#11719921	C₂⁴	1	8	yes	—
491	#11719921	C₂⁴	1	8	yes	—
492	#11719921	C₂⁴	1	8	yes	—
493	#11719921	C₂⁴	1	8	yes	—
494	#11719921	C₂⁴	1	8	yes	—
495	#11719921	C₂⁴	1	8	yes	—
496	#11719921	C₂⁴	1	8	yes	—
497	#11719921	C₂⁴	1	8	yes	—
498	#11719921	C₂⁴	1	8	yes	—
499	#11719921	C₂⁴	1	8	yes	—
500	#11719921	C₂⁴	1	8	yes	—
501	#11719921	C₂⁴	1	8	yes	—
502	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
503	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
504	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
505	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
506	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
507	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
508	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
509	#11719919	C₂⁴	1	8	yes	—
510	#11719919	C₂⁴	1	8	yes	—
511	#11719919	C₂⁴	1	8	yes	—
512	#11719919	C₂⁴	1	8	yes	—
513	#11719919	C₂⁴	1	8	yes	—
514	#11719919	C₂⁴	1	8	yes	—
515	#11719919	C₂⁴	1	8	yes	—
516	#11719919	C₂⁴	1	8	yes	—
517	#11719919	C₂⁴	1	8	yes	—
518	#11719919	C₂⁴	1	8	yes	—
519	#11719919	C₂⁴	1	8	yes	—
520	#11719919	C₂⁴	1	8	yes	—
521	C₄×Dic₅₃	C₂⁴	1	4	yes	—
522	C₄×Dic₅₃	C₂⁴	1	4	yes	—
523	C₄×Dic₅₃	C₂⁴	1	4	yes	—
524	C₄×Dic₅₃	C₂⁴	1	4	yes	—
525	C₄×Dic₅₃	C₂⁴	1	4	yes	—
526	C₄×Dic₅₃	C₂⁴	1	4	yes	—
527	C₄×Dic₅₃	C₂⁴	1	8	yes	—
528	C₄×Dic₅₃	C₂⁴	1	8	yes	—
529	C₄×Dic₅₃	C₂⁴	1	8	yes	—
530	C₂³×C₅₃	—	2	4	no	—
531	C₂³×C₅₃	—	4	2	no	—
532	C₂³×C₅₃	—	4	4	no	—
533	C₂³×C₅₃	C₂×#41	1	4	yes	—
534	C₂³×C₅₃	C₂⁵	1	4	yes	—
535	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
536	C₂³×C₅₃	C₂⁵	1	2	yes	—
537	C₂²×D₅₃	—	2	4	no	—
538	C₂²×D₅₃	—	2	8	no	—
539	C₂²×D₅₃	—	2	4	no	—
540	C₂²×D₅₃	—	2	8	no	—
541	C₂²×D₅₃	—	2	16	no	—
542	C₂²×D₅₃	—	2	8	no	—
543	C₂²×D₅₃	—	4	16	no	—
544	C₂²×D₅₃	—	4	4	no	—
545	C₂²×D₅₃	—	4	2	no	—
546	C₂²×D₅₃	—	4	8	no	—
547	C₂²×D₅₃	—	4	4	no	—
548	C₂²×D₅₃	—	8	16	no	—
549	C₂²×D₅₃	C₂×#41	1	8	yes	—
550	C₂²×D₅₃	C₂×#41	1	4	yes	—
551	C₂²×D₅₃	C₂×#41	1	8	yes	—
552	C₂²×D₅₃	C₂×#41	1	4	yes	—
553	C₂²×D₅₃	C₂⁵	1	4	yes	—
554	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
555	C₂²×D₅₃	C₂⁵	1	2	yes	—
556	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
557	Q₈×C₅₃	—	4	4	no	—
558	D₄×C₅₃	—	2	8	no	—
559	D₄×C₅₃	—	2	8	no	—
560	D₄×C₅₃	—	4	4	no	—
561	C₂×C₄×C₅₃	—	2	8	no	—
562	C₂×C₄×C₅₃	—	2	2	no	—
563	C₂×C₄×C₅₃	—	2	2	no	—
564	C₂×C₄×C₅₃	—	2	4	no	—
565	C₂×C₄×C₅₃	—	4	4	no	—
566	C₂×C₄×C₅₃	—	4	8	no	—
567	C₂×C₄×C₅₃	—	4	2	no	—
568	C₂×C₄×C₅₃	—	4	2	no	—
569	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
570	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
571	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
572	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
573	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
574	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
575	C₂²⋊D₅₃	—	2	8	no	—
576	C₂²⋊D₅₃	—	2	8	no	—
577	C₂²⋊D₅₃	—	2	8	no	—
578	C₂²⋊D₅₃	—	2	8	no	—
579	C₂²⋊D₅₃	—	4	8	no	—
580	C₂×Dic₅₃	—	2	8	no	—
581	C₂×Dic₅₃	—	2	2	no	—
582	C₂×Dic₅₃	—	2	2	no	—
583	C₂×Dic₅₃	—	2	4	no	—
584	C₂×Dic₅₃	—	4	4	no	—
585	C₂×Dic₅₃	—	4	8	no	—
586	C₂×Dic₅₃	—	4	2	no	—
587	C₂×Dic₅₃	—	4	2	no	—
588	C₂×Dic₅₃	C₂⁵	1	8	yes	—
589	C₂×Dic₅₃	C₂⁵	1	4	yes	—
590	C₂×Dic₅₃	C₂⁵	1	2	yes	—
591	C₂×Dic₅₃	C₂⁵	1	4	yes	—
592	C₂×Dic₅₃	C₂⁵	1	2	yes	—
593	C₂×Dic₅₃	C₂⁵	1	4	yes	—
594	D₂₁₂	—	2	8	no	—
595	D₂₁₂	—	2	8	no	—
596	D₂₁₂	—	4	4	no	—
597	C₄×D₅₃	—	2	8	no	—
598	C₄×D₅₃	—	2	8	no	—
599	C₄×D₅₃	—	2	4	no	—
600	C₄×D₅₃	—	2	4	no	—
601	C₄×D₅₃	—	2	4	no	—
602	C₄×D₅₃	—	2	4	no	—
603	C₄×D₅₃	—	2	8	no	—
604	C₄×D₅₃	—	2	8	no	—
605	C₄×D₅₃	—	2	8	no	—
606	C₄×D₅₃	—	2	16	no	—
607	C₄×D₅₃	—	2	8	no	—
608	C₄×D₅₃	—	4	8	no	—
609	C₄×D₅₃	—	4	8	no	—
610	C₄×D₅₃	—	4	4	no	—
611	C₄×D₅₃	—	4	8	no	—
612	C₄×D₅₃	—	4	4	no	—
613	Dic₁₀₆	—	4	4	no	—
614	Dic₁₀₆	—	4	8	no	—
615	C₂×#3491	—	53	1	no	maximal, Sylow
616	C₂²×C₅₃	—	2	2	no	—
617	C₂²×C₅₃	—	2	4	no	—
618	C₂²×C₅₃	—	2	4	no	—
619	C₂²×C₅₃	—	2	8	no	—
620	C₂²×C₅₃	—	4	4	no	—
621	C₂²×C₅₃	—	8	4	no	—
622	C₂²×C₅₃	C₂²×#41	1	4	yes	—
623	C₂²×C₅₃	C₂²×#41	1	2	yes	—
624	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
625	C₂×D₅₃	—	2	2	no	—
626	C₂×D₅₃	—	2	4	no	—
627	C₂×D₅₃	—	2	16	no	—
628	C₂×D₅₃	—	2	8	no	—
629	C₂×D₅₃	—	2	4	no	—
630	C₂×D₅₃	—	2	8	no	—
631	C₂×D₅₃	—	4	4	no	—
632	C₂×D₅₃	—	4	8	no	—
633	C₂×D₅₃	—	4	16	no	—
634	C₂×D₅₃	—	8	8	no	—
635	C₂×D₅₃	—	8	4	no	—
636	C₂×D₅₃	C₂²×#41	1	4	yes	—
637	C₂×D₅₃	C₂²×#41	1	2	yes	—
638	C₂×D₅₃	C₂²×#41	1	2	yes	—
639	C₂×D₅₃	#585	1	4	yes	—
640	C₄×C₅₃	—	2	2	no	—
641	C₄×C₅₃	—	2	2	no	—
642	C₄×C₅₃	—	2	4	no	—
643	C₄×C₅₃	—	2	8	no	—
644	C₄×C₅₃	—	2	4	no	—
645	C₄×C₅₃	—	2	4	no	—
646	Dic₅₃	—	2	2	no	—
647	Dic₅₃	—	2	2	no	—
648	Dic₅₃	—	2	4	no	—
649	Dic₅₃	—	2	8	no	—
650	Dic₅₃	—	2	4	no	—
651	Dic₅₃	—	2	4	no	—
652	#3491	—	53	8	no	—
653	#3491	—	53	8	no	—
654	#3491	—	53	1	no	—
655	#3491	—	53	4	no	—
656	#3491	—	53	1	no	—
657	#3491	—	53	4	no	—
658	#3491	—	53	2	no	—
659	#3491	—	53	2	no	—
660	#3491	—	53	1	no	—
661	#3491	D₅₃	1	1	yes	characteristic, direct product factor
662	C₂×#552	—	53	8	no	—
663	C₂×#551	—	53	8	no	—
664	C₂×#543	—	53	1	no	—
665	C₂×#539	—	53	4	no	—
666	C₂×#534	—	53	1	no	—
667	C₂×#529	—	53	4	no	—
668	C₂²×#123	—	53	2	no	—
669	C₂×#518	—	53	2	no	—
670	C₂²×#117	—	53	1	no	—
671	C₂×C₅₃	—	2	4	no	—
672	C₂×C₅₃	—	2	2	no	—
673	C₂×C₅₃	—	4	4	no	—
674	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
675	C₂×C₅₃	C₂×#585	1	2	yes	—
676	D₅₃	—	2	4	no	—
677	D₅₃	—	2	2	no	—
678	D₅₃	—	4	4	no	—
679	D₅₃	#3491	1	4	yes	direct product factor
680	C₂³×D₄	—	53	2	no	—
681	C₂⁴×C₄	—	53	1	no	—
682	#552	—	53	8	no	—
683	#552	—	53	8	no	—
684	#552	—	53	8	no	—
685	#552	—	53	8	no	—
686	#552	—	53	8	no	—
687	#552	—	53	8	no	—
688	#552	—	53	8	no	—
689	#552	—	53	8	no	—
690	#552	—	53	8	no	—
691	#552	—	53	8	no	—
692	#552	—	53	8	no	—
693	#552	—	53	8	no	—
694	#552	—	53	8	no	—
695	#552	—	53	8	no	—
696	#552	—	53	8	no	—
697	#552	C₂×D₅₃	1	8	yes	complemented
698	#551	—	53	8	no	—
699	#551	—	53	8	no	—
700	#551	—	53	8	no	—
701	#551	—	53	8	no	—
702	#551	—	53	8	no	—
703	#551	—	53	8	no	—
704	#551	—	53	8	no	—
705	#551	—	53	8	no	—
706	#551	—	53	8	no	—
707	#551	—	53	8	no	—
708	#551	—	53	8	no	—
709	#551	—	53	8	no	—
710	#551	—	53	8	no	—
711	#551	—	53	8	no	—
712	#551	—	53	8	no	—
713	#551	C₂×D₅₃	1	8	yes	complemented
714	#543	—	53	4	no	—
715	#543	—	53	8	no	—
716	#543	—	53	2	no	—
717	#543	—	53	1	no	—
718	#543	C₂×D₅₃	1	1	yes	characteristic, complemented
719	#539	—	53	8	no	—
720	#539	—	53	8	no	—
721	#539	—	53	8	no	—
722	#539	—	53	8	no	—
723	#539	—	53	8	no	—
724	#539	—	53	4	no	—
725	#539	—	53	4	no	—
726	#539	—	53	8	no	—
727	#539	—	53	4	no	—
728	#539	C₂×D₅₃	1	4	yes	complemented
729	#534	—	53	2	no	—
730	#534	—	53	4	no	—
731	#534	—	53	4	no	—
732	#534	—	53	4	no	—
733	#534	—	53	1	no	—
734	#534	C₂×D₅₃	1	1	yes	characteristic
735	#529	—	53	8	no	—
736	#529	—	53	4	no	—
737	#529	—	53	4	no	—
738	#529	—	53	8	no	—
739	#529	—	53	4	no	—
740	#529	—	53	4	no	—
741	#529	—	53	4	no	—
742	#529	—	53	8	no	—
743	#529	—	53	4	no	—
744	#529	—	53	8	no	—
745	#529	—	53	4	no	—
746	#529	C₂×D₅₃	1	4	yes	complemented
747	C₂×#126	—	53	8	no	—
748	C₂×#126	—	53	8	no	—
749	C₂×#125	—	53	4	no	—
750	C₂×#125	—	53	8	no	—
751	C₂×#124	—	53	4	no	—
752	C₂×#123	—	53	2	no	—
753	C₂×#123	—	53	2	no	—
754	C₂×#123	—	53	8	no	—
755	C₂×#123	—	53	8	no	—
756	C₂×#123	—	53	4	no	—
757	C₂×#123	—	53	4	no	—
758	C₂×#123	—	53	4	no	—
759	C₂×#123	—	53	4	no	—
760	C₂×#123	—	53	4	no	—
761	C₂×#123	—	53	8	no	—
762	C₂×#123	—	53	4	no	—
763	C₂×#123	—	53	2	no	—
764	C₂×#123	—	53	4	no	—
765	C₂×#123	C₂×D₅₃	1	2	yes	complemented
766	C₂×C₂²⋊Q₈	—	53	4	no	—
767	C₂×C₂²⋊Q₈	—	53	8	no	—
768	C₂×C₂²⋊Q₈	—	53	8	no	—
769	C₂×#121	—	53	4	no	—
770	C₂×#120	—	53	4	no	—
771	#518	—	53	2	no	—
772	#518	—	53	8	no	—
773	#518	—	53	8	no	—
774	#518	—	53	4	no	—
775	#518	—	53	2	no	—
776	#518	—	53	2	no	—
777	#518	—	53	4	no	—
778	#518	C₂×D₅₃	1	2	yes	complemented
779	C₂×C₄×Q₈	—	53	4	no	—
780	C₂×C₄×D₄	—	53	8	no	—
781	C₂×C₄×D₄	—	53	8	no	—
782	C₂×C₄×D₄	—	53	4	no	—
783	C₂×#117	—	53	1	no	—
784	C₂×#117	—	53	8	no	—
785	C₂×#117	—	53	8	no	—
786	C₂×#117	—	53	4	no	—
787	C₂×#117	—	53	8	no	—
788	C₂×#117	—	53	2	no	—
789	C₂×#117	—	53	1	no	—
790	C₂×#117	—	53	1	no	—
791	C₂×#117	—	53	2	no	—
792	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
793	C₂²×C₄⋊C₄	—	53	2	no	—
794	C₂²×C₄⋊C₄	—	53	4	no	—
795	C₂²×C₂²⋊C₄	—	53	1	no	—
796	C₂²×C₂²⋊C₄	—	53	1	no	—
797	C₂²×C₂²⋊C₄	—	53	2	no	—
798	C₂²×C₂²⋊C₄	—	53	4	no	—
799	C₂²×C₂²⋊C₄	—	53	4	no	—
800	C₂²×C₄²	—	53	2	no	—
801	C₅₃	C₂×#3491	1	1	yes	characteristic, complemented, Sylow
802	C₂⁵	—	53	1	no	—
803	C₂⁵	—	53	2	no	—
804	C₂²×Q₈	—	53	4	no	—
805	C₂²×D₄	—	53	2	no	—
806	C₂²×D₄	—	53	2	no	—
807	C₂²×D₄	—	53	4	no	—
808	C₂²×D₄	—	53	4	no	—
809	C₂²×D₄	—	53	4	no	—
810	C₂²×D₄	—	53	4	no	—
811	C₂²×D₄	—	53	4	no	—
812	C₂²×D₄	—	53	2	no	—
813	C₂²×D₄	—	106	16	no	—
814	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
815	C₂³×C₄	—	53	1	no	—
816	C₂³×C₄	—	53	4	no	—
817	C₂³×C₄	—	53	2	no	—
818	C₂³×C₄	—	53	1	no	—
819	C₂³×C₄	—	53	1	no	—
820	C₂³×C₄	—	53	4	no	—
821	C₂³×C₄	—	53	1	no	—
822	C₂³×C₄	—	53	1	no	—
823	C₂³×C₄	—	53	4	no	—
824	C₂³×C₄	—	53	2	no	—
825	C₂³×C₄	—	53	2	no	—
826	C₂³×C₄	—	53	8	no	—
827	C₂³×C₄	—	106	8	no	—
828	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
829	#126	—	53	8	no	—
830	#126	—	53	8	no	—
831	#126	—	53	8	no	—
832	#126	—	53	8	no	—
833	#126	—	53	8	no	—
834	#126	—	53	8	no	—
835	#126	—	53	8	no	—
836	#126	—	53	8	no	—
837	#126	—	53	8	no	—
838	#126	—	53	8	no	—
839	#126	—	53	8	no	—
840	#126	—	53	8	no	—
841	#126	—	53	8	no	—
842	#126	—	53	8	no	—
843	#126	C₂²×D₅₃	1	8	yes	complemented
844	#126	C₂²×D₅₃	1	8	yes	complemented
845	#125	—	53	8	no	—
846	#125	—	53	8	no	—
847	#125	—	53	4	no	—
848	#125	—	53	4	no	—
849	#125	—	53	8	no	—
850	#125	—	53	8	no	—
851	#125	—	53	8	no	—
852	#125	—	53	8	no	—
853	#125	—	53	8	no	—
854	#125	—	53	8	no	—
855	#125	—	53	4	no	—
856	#125	—	53	8	no	—
857	#125	C₂²×D₅₃	1	4	yes	complemented
858	#125	C₂²×D₅₃	1	8	yes	complemented
859	#124	—	53	4	no	—
860	#124	—	53	4	no	—
861	#124	—	53	8	no	—
862	#124	—	53	8	no	—
863	#124	—	53	4	no	—
864	#124	C₂²×D₅₃	1	4	yes	complemented
865	#123	—	53	4	no	—
866	#123	—	53	4	no	—
867	#123	—	53	8	no	—
868	#123	—	53	4	no	—
869	#123	—	53	8	no	—
870	#123	—	53	4	no	—
871	#123	—	53	4	no	—
872	#123	—	53	8	no	—
873	#123	—	53	4	no	—
874	#123	—	53	8	no	—
875	#123	—	53	8	no	—
876	#123	—	53	8	no	—
877	#123	—	53	8	no	—
878	#123	—	53	8	no	—
879	#123	—	53	8	no	—
880	#123	—	53	8	no	—
881	#123	—	53	8	no	—
882	#123	—	53	8	no	—
883	#123	—	53	4	no	—
884	#123	—	53	8	no	—
885	#123	—	53	4	no	—
886	#123	—	53	8	no	—
887	#123	—	53	8	no	—
888	#123	—	53	8	no	—
889	#123	—	53	8	no	—
890	#123	—	53	4	no	—
891	#123	—	53	8	no	—
892	#123	—	53	8	no	—
893	#123	—	53	8	no	—
894	#123	C₂²×D₅₃	1	8	yes	—
895	#123	C₂²×D₅₃	1	4	yes	—
896	#123	C₂²×D₅₃	1	4	yes	complemented
897	#123	C₂²×D₅₃	1	4	yes	complemented
898	#123	C₂²×D₅₃	1	8	yes	complemented
899	C₂²⋊Q₈	—	53	4	no	—
900	C₂²⋊Q₈	—	53	8	no	—
901	C₂²⋊Q₈	—	53	8	no	—
902	C₂²⋊Q₈	—	53	4	no	—
903	C₂²⋊Q₈	—	53	8	no	—
904	C₂²⋊Q₈	—	53	8	no	—
905	C₂²⋊Q₈	—	53	8	no	—
906	C₂²⋊Q₈	—	53	4	no	—
907	C₂²⋊Q₈	—	53	8	no	—
908	C₂²⋊Q₈	—	53	8	no	—
909	C₂²⋊Q₈	—	53	8	no	—
910	C₂²⋊Q₈	—	53	8	no	—
911	C₂²⋊Q₈	—	53	8	no	—
912	C₂²⋊Q₈	—	53	8	no	—
913	C₂²⋊Q₈	—	53	8	no	—
914	C₂²⋊Q₈	—	53	8	no	—
915	C₂²⋊Q₈	—	53	8	no	—
916	C₂²⋊Q₈	—	53	8	no	—
917	C₂²⋊Q₈	—	53	8	no	—
918	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
919	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
920	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
921	#121	—	53	4	no	—
922	#121	—	53	8	no	—
923	#121	—	53	4	no	—
924	#121	—	53	4	no	—
925	#121	—	53	8	no	—
926	#121	C₂²×D₅₃	1	4	yes	—
927	#120	—	53	4	no	—
928	#120	—	53	4	no	—
929	#120	—	53	8	no	—
930	#120	—	53	8	no	—
931	#120	—	53	4	no	—
932	#120	C₂²×D₅₃	1	4	yes	—
933	C₄×Q₈	—	53	4	no	—
934	C₄×Q₈	—	53	4	no	—
935	C₄×Q₈	—	53	8	no	—
936	C₄×Q₈	—	53	8	no	—
937	C₄×Q₈	—	53	4	no	—
938	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
939	C₄×D₄	—	53	8	no	—
940	C₄×D₄	—	53	8	no	—
941	C₄×D₄	—	53	4	no	—
942	C₄×D₄	—	53	8	no	—
943	C₄×D₄	—	53	8	no	—
944	C₄×D₄	—	53	8	no	—
945	C₄×D₄	—	53	8	no	—
946	C₄×D₄	—	53	8	no	—
947	C₄×D₄	—	53	8	no	—
948	C₄×D₄	—	53	8	no	—
949	C₄×D₄	—	53	4	no	—
950	C₄×D₄	—	53	8	no	—
951	C₄×D₄	—	53	8	no	—
952	C₄×D₄	—	53	8	no	—
953	C₄×D₄	—	53	8	no	—
954	C₄×D₄	—	53	8	no	—
955	C₄×D₄	—	53	8	no	—
956	C₄×D₄	—	53	8	no	—
957	C₄×D₄	—	53	4	no	—
958	C₄×D₄	C₂²×D₅₃	1	8	yes	—
959	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
960	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
961	#117	—	53	8	no	—
962	#117	—	53	4	no	—
963	#117	—	53	8	no	—
964	#117	—	53	8	no	—
965	#117	—	53	8	no	—
966	#117	—	53	8	no	—
967	#117	—	53	8	no	—
968	#117	—	53	8	no	—
969	#117	—	53	8	no	—
970	#117	—	53	8	no	—
971	#117	—	53	4	no	—
972	#117	—	53	4	no	—
973	#117	—	53	8	no	—
974	#117	—	53	8	no	—
975	#117	—	53	8	no	—
976	#117	—	53	8	no	—
977	#117	—	53	8	no	—
978	#117	—	53	8	no	—
979	#117	—	53	8	no	—
980	#117	C₂²×D₅₃	1	8	yes	complemented
981	#117	C₂²×D₅₃	1	4	yes	complemented
982	#117	C₂²×D₅₃	1	8	yes	complemented
983	C₂×C₄⋊C₄	—	53	2	no	—
984	C₂×C₄⋊C₄	—	53	2	no	—
985	C₂×C₄⋊C₄	—	53	2	no	—
986	C₂×C₄⋊C₄	—	53	4	no	—
987	C₂×C₄⋊C₄	—	53	4	no	—
988	C₂×C₄⋊C₄	—	53	4	no	—
989	C₂×C₄⋊C₄	—	53	8	no	—
990	C₂×C₄⋊C₄	—	53	8	no	—
991	C₂×C₄⋊C₄	—	53	8	no	—
992	C₂×C₄⋊C₄	—	53	8	no	—
993	C₂×C₄⋊C₄	—	53	8	no	—
994	C₂×C₄⋊C₄	—	53	8	no	—
995	C₂×C₄⋊C₄	—	53	8	no	—
996	C₂×C₄⋊C₄	—	53	8	no	—
997	C₂×C₄⋊C₄	—	53	4	no	—
998	C₂×C₄⋊C₄	—	53	4	no	—
999	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1000	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1001	C₂×C₂²⋊C₄	—	53	1	no	—
1002	C₂×C₂²⋊C₄	—	53	1	no	—
1003	C₂×C₂²⋊C₄	—	53	2	no	—
1004	C₂×C₂²⋊C₄	—	53	4	no	—
1005	C₂×C₂²⋊C₄	—	53	4	no	—
1006	C₂×C₂²⋊C₄	—	53	2	no	—
1007	C₂×C₂²⋊C₄	—	53	2	no	—
1008	C₂×C₂²⋊C₄	—	53	4	no	—
1009	C₂×C₂²⋊C₄	—	53	8	no	—
1010	C₂×C₂²⋊C₄	—	53	4	no	—
1011	C₂×C₂²⋊C₄	—	53	4	no	—
1012	C₂×C₂²⋊C₄	—	53	4	no	—
1013	C₂×C₂²⋊C₄	—	53	4	no	—
1014	C₂×C₂²⋊C₄	—	53	4	no	—
1015	C₂×C₂²⋊C₄	—	53	4	no	—
1016	C₂×C₂²⋊C₄	—	53	4	no	—
1017	C₂×C₂²⋊C₄	—	53	8	no	—
1018	C₂×C₂²⋊C₄	—	53	4	no	—
1019	C₂×C₂²⋊C₄	—	53	8	no	—
1020	C₂×C₂²⋊C₄	—	53	4	no	—
1021	C₂×C₂²⋊C₄	—	53	4	no	—
1022	C₂×C₂²⋊C₄	—	53	4	no	—
1023	C₂×C₂²⋊C₄	—	53	4	no	—
1024	C₂×C₂²⋊C₄	—	53	8	no	—
1025	C₂×C₂²⋊C₄	—	53	8	no	—
1026	C₂×C₂²⋊C₄	—	53	8	no	—
1027	C₂×C₂²⋊C₄	—	53	8	no	—
1028	C₂×C₂²⋊C₄	—	53	8	no	—
1029	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1032	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1033	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1034	C₂×C₄²	—	53	2	no	—
1035	C₂×C₄²	—	53	2	no	—
1036	C₂×C₄²	—	53	2	no	—
1037	C₂×C₄²	—	53	4	no	—
1038	C₂×C₄²	—	53	8	no	—
1039	C₂×C₄²	—	53	4	no	—
1040	C₂×C₄²	—	53	4	no	—
1041	C₂×C₄²	—	53	4	no	—
1042	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
1043	C₂⁴	—	53	2	no	—
1044	C₂⁴	—	53	1	no	—
1045	C₂⁴	—	53	8	no	—
1046	C₂⁴	—	53	1	no	—
1047	C₂⁴	—	53	2	no	—
1048	C₂⁴	—	53	4	no	—
1049	C₂⁴	—	53	4	no	—
1050	C₂⁴	—	53	2	no	—
1051	C₂⁴	—	106	8	no	—
1052	C₂⁴	—	212	8	no	—
1053	C₂⁴	—	212	4	no	—
1054	C₂⁴	C₂³×D₅₃	1	2	yes	—
1055	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1056	C₂×Q₈	—	53	8	no	—
1057	C₂×Q₈	—	53	4	no	—
1058	C₂×Q₈	—	212	8	no	—
1059	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1060	C₂×D₄	—	2	8	no	—
1061	C₂×D₄	—	53	4	no	—
1062	C₂×D₄	—	53	4	no	—
1063	C₂×D₄	—	53	4	no	—
1064	C₂×D₄	—	53	4	no	—
1065	C₂×D₄	—	53	8	no	—
1066	C₂×D₄	—	53	4	no	—
1067	C₂×D₄	—	53	4	no	—
1068	C₂×D₄	—	53	4	no	—
1069	C₂×D₄	—	106	8	no	—
1070	C₂×D₄	—	106	16	no	—
1071	C₂×D₄	—	106	16	no	—
1072	C₂×D₄	—	106	16	no	—
1073	C₂×D₄	—	106	16	no	—
1074	C₂×D₄	—	106	8	no	—
1075	C₂×D₄	—	106	8	no	—
1076	C₂×D₄	—	212	8	no	—
1077	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1078	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1079	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1080	C₂²×C₄	—	2	4	no	—
1081	C₂²×C₄	—	53	1	no	—
1082	C₂²×C₄	—	53	4	no	—
1083	C₂²×C₄	—	53	2	no	—
1084	C₂²×C₄	—	53	1	no	—
1085	C₂²×C₄	—	53	2	no	—
1086	C₂²×C₄	—	53	2	no	—
1087	C₂²×C₄	—	53	4	no	—
1088	C₂²×C₄	—	53	8	no	—
1089	C₂²×C₄	—	53	2	no	—
1090	C₂²×C₄	—	53	4	no	—
1091	C₂²×C₄	—	53	2	no	—
1092	C₂²×C₄	—	53	4	no	—
1093	C₂²×C₄	—	53	4	no	—
1094	C₂²×C₄	—	53	8	no	—
1095	C₂²×C₄	—	53	2	no	—
1096	C₂²×C₄	—	53	4	no	—
1097	C₂²×C₄	—	53	4	no	—
1098	C₂²×C₄	—	53	4	no	—
1099	C₂²×C₄	—	53	2	no	—
1100	C₂²×C₄	—	53	4	no	—
1101	C₂²×C₄	—	53	4	no	—
1102	C₂²×C₄	—	53	8	no	—
1103	C₂²×C₄	—	53	8	no	—
1104	C₂²×C₄	—	53	8	no	—
1105	C₂²×C₄	—	106	16	no	—
1106	C₂²×C₄	—	106	4	no	—
1107	C₂²×C₄	—	106	4	no	—
1108	C₂²×C₄	—	106	16	no	—
1109	C₂²×C₄	—	106	4	no	—
1110	C₂²×C₄	—	106	4	no	—
1111	C₂²×C₄	—	106	8	no	—
1112	C₂²×C₄	—	106	4	no	—
1113	C₂²×C₄	—	212	4	no	—
1114	C₂²×C₄	—	212	16	no	—
1115	C₂²×C₄	—	212	8	no	—
1116	C₂²×C₄	—	212	4	no	—
1117	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1118	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1119	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1120	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1121	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1122	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1123	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1124	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1125	C₄⋊C₄	—	53	8	no	—
1126	C₄⋊C₄	—	53	8	no	—
1127	C₄⋊C₄	—	53	8	no	—
1128	C₄⋊C₄	—	53	8	no	—
1129	C₄⋊C₄	—	53	8	no	—
1130	C₄⋊C₄	—	53	8	no	—
1131	C₄⋊C₄	—	53	8	no	—
1132	C₄⋊C₄	—	53	8	no	—
1133	C₄⋊C₄	—	53	8	no	—
1134	C₄⋊C₄	—	53	8	no	—
1135	C₄⋊C₄	—	53	8	no	—
1136	C₄⋊C₄	—	53	8	no	—
1137	C₄⋊C₄	—	53	8	no	—
1138	C₄⋊C₄	—	53	8	no	—
1139	C₄⋊C₄	—	53	8	no	—
1140	C₄⋊C₄	—	53	8	no	—
1141	C₄⋊C₄	—	53	4	no	—
1142	C₄⋊C₄	—	53	8	no	—
1143	C₄⋊C₄	—	53	4	no	—
1144	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1145	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1146	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1147	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1148	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1149	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1150	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1151	C₂²⋊C₄	—	53	4	no	—
1152	C₂²⋊C₄	—	53	4	no	—
1153	C₂²⋊C₄	—	53	4	no	—
1154	C₂²⋊C₄	—	53	8	no	—
1155	C₂²⋊C₄	—	53	4	no	—
1156	C₂²⋊C₄	—	53	8	no	—
1157	C₂²⋊C₄	—	53	8	no	—
1158	C₂²⋊C₄	—	53	8	no	—
1159	C₂²⋊C₄	—	53	8	no	—
1160	C₂²⋊C₄	—	53	8	no	—
1161	C₂²⋊C₄	—	53	8	no	—
1162	C₂²⋊C₄	—	53	8	no	—
1163	C₂²⋊C₄	—	53	8	no	—
1164	C₂²⋊C₄	—	53	8	no	—
1165	C₂²⋊C₄	—	53	8	no	—
1166	C₂²⋊C₄	—	53	8	no	—
1167	C₂²⋊C₄	—	53	8	no	—
1168	C₂²⋊C₄	—	53	8	no	—
1169	C₂²⋊C₄	—	53	8	no	—
1170	C₂²⋊C₄	—	53	8	no	—
1171	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1172	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1173	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1174	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1175	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1176	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1177	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1178	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1179	C₄²	—	53	4	no	—
1180	C₄²	—	53	4	no	—
1181	C₄²	—	53	4	no	—
1182	C₄²	—	53	4	no	—
1183	C₄²	—	53	4	no	—
1184	C₄²	—	53	4	no	—
1185	C₄²	—	53	8	no	—
1186	C₄²	—	53	8	no	—
1187	C₄²	—	53	8	no	—
1188	C₄²	C₂³×D₅₃	1	4	yes	—
1189	C₄²	C₂³×D₅₃	1	4	yes	—
1190	C₄²	C₂³×D₅₃	1	8	yes	—
1191	C₂³	—	2	4	no	—
1192	C₂³	—	4	2	no	—
1193	C₂³	—	4	4	no	—
1194	C₂³	—	53	1	no	—
1195	C₂³	—	53	8	no	—
1196	C₂³	—	53	4	no	—
1197	C₂³	—	53	2	no	—
1198	C₂³	—	53	1	no	—
1199	C₂³	—	53	4	no	—
1200	C₂³	—	53	8	no	—
1201	C₂³	—	53	4	no	—
1202	C₂³	—	106	4	no	—
1203	C₂³	—	106	8	no	—
1204	C₂³	—	106	8	no	—
1205	C₂³	—	106	16	no	—
1206	C₂³	—	106	8	no	—
1207	C₂³	—	106	4	no	—
1208	C₂³	—	424	16	no	—
1209	C₂³	—	212	4	no	—
1210	C₂³	—	212	8	no	—
1211	C₂³	—	212	2	no	—
1212	C₂³	—	212	4	no	—
1213	C₂³	—	212	16	no	—
1214	C₂³	#41×D₅₃	1	4	yes	—
1215	C₂³	C₂⁴×D₅₃	1	4	yes	—
1216	C₂³	C₂⁴×D₅₃	1	2	yes	—
1217	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1218	Q₈	—	4	4	no	—
1219	Q₈	—	212	8	no	—
1220	Q₈	—	212	4	no	—
1221	D₄	—	2	8	no	—
1222	D₄	—	2	8	no	—
1223	D₄	—	4	4	no	—
1224	D₄	—	106	8	no	—
1225	D₄	—	106	8	no	—
1226	D₄	—	106	8	no	—
1227	D₄	—	106	8	no	—
1228	D₄	—	106	8	no	—
1229	D₄	—	106	8	no	—
1230	D₄	—	212	4	no	—
1231	D₄	—	212	8	no	—
1232	C₂×C₄	—	2	8	no	—
1233	C₂×C₄	—	2	2	no	—
1234	C₂×C₄	—	2	2	no	—
1235	C₂×C₄	—	2	4	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	4	8	no	—
1238	C₂×C₄	—	4	4	no	—
1239	C₂×C₄	—	4	2	no	—
1240	C₂×C₄	—	53	2	no	—
1241	C₂×C₄	—	53	4	no	—
1242	C₂×C₄	—	53	4	no	—
1243	C₂×C₄	—	53	4	no	—
1244	C₂×C₄	—	53	8	no	—
1245	C₂×C₄	—	53	2	no	—
1246	C₂×C₄	—	106	4	no	—
1247	C₂×C₄	—	106	4	no	—
1248	C₂×C₄	—	106	8	no	—
1249	C₂×C₄	—	106	8	no	—
1250	C₂×C₄	—	106	4	no	—
1251	C₂×C₄	—	106	4	no	—
1252	C₂×C₄	—	106	8	no	—
1253	C₂×C₄	—	106	8	no	—
1254	C₂×C₄	—	106	8	no	—
1255	C₂×C₄	—	106	16	no	—
1256	C₂×C₄	—	106	8	no	—
1257	C₂×C₄	—	106	8	no	—
1258	C₂×C₄	—	106	2	no	—
1259	C₂×C₄	—	106	2	no	—
1260	C₂×C₄	—	106	4	no	—
1261	C₂×C₄	—	212	4	no	—
1262	C₂×C₄	—	212	8	no	—
1263	C₂×C₄	—	212	8	no	—
1264	C₂×C₄	—	212	8	no	—
1265	C₂×C₄	—	212	4	no	—
1266	C₂×C₄	—	212	2	no	—
1267	C₂×C₄	—	212	8	no	—
1268	C₂×C₄	—	212	4	no	—
1269	C₂×C₄	—	212	2	no	—
1270	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1271	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1272	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1273	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1274	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1275	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	2	4	no	—
1278	C₂²	—	2	4	no	—
1279	C₂²	—	2	8	no	—
1280	C₂²	—	4	4	no	—
1281	C₂²	—	8	4	no	—
1282	C₂²	—	53	2	no	—
1283	C₂²	—	53	4	no	—
1284	C₂²	—	53	4	no	—
1285	C₂²	—	53	2	no	—
1286	C₂²	—	106	16	no	—
1287	C₂²	—	106	8	no	—
1288	C₂²	—	106	2	no	—
1289	C₂²	—	106	4	no	—
1290	C₂²	—	106	4	no	—
1291	C₂²	—	106	8	no	—
1292	C₂²	—	424	4	no	—
1293	C₂²	—	424	8	no	—
1294	C₂²	—	212	8	no	—
1295	C₂²	—	212	4	no	—
1296	C₂²	—	212	16	no	—
1297	C₂²	C₂×#41×D₅₃	1	4	yes	—
1298	C₂²	C₂×#41×D₅₃	1	2	yes	—
1299	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1300	C₄	—	2	2	no	—
1301	C₄	—	2	2	no	—
1302	C₄	—	2	4	no	—
1303	C₄	—	2	4	no	—
1304	C₄	—	2	8	no	—
1305	C₄	—	2	4	no	—
1306	C₄	—	106	2	no	—
1307	C₄	—	106	2	no	—
1308	C₄	—	106	4	no	—
1309	C₄	—	106	4	no	—
1310	C₄	—	106	8	no	—
1311	C₄	—	106	4	no	—
1312	C₂	—	2	4	no	—
1313	C₂	—	2	2	no	—
1314	C₂	—	4	4	no	—
1315	C₂	—	53	4	no	—
1316	C₂	—	106	4	no	—
1317	C₂	—	106	2	no	—
1318	C₂	—	212	4	no	—
1319	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1320	C₂	#585×D₅₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3491	C₂
prime radical	#534×D₅₃	C₂
hypercenter	#3491	D₅₃
hypocenter	C₅₃	C₂×#3491
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3491

Complements

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

N	H ≅ G/N	type
1. #20288414	C₂	semidirect
2. #20288413	C₂	semidirect
3. #20288412	C₂	semidirect
4. #20288411	C₂	semidirect
5. #20288410	C₂	semidirect
6. #20288409	C₂	semidirect
7. #20288408	C₂	semidirect
8. #20288407	C₂	semidirect
9. #20288406	C₂	semidirect
10. #552×D₅₃	C₂	semidirect
11. #551×D₅₃	C₂	semidirect
12. #543×D₅₃	C₂	semidirect
13. #539×D₅₃	C₂	semidirect
15. #529×D₅₃	C₂	semidirect
16. C₂×#123×D₅₃	C₂	semidirect
17. #518×D₅₃	C₂	semidirect
18. C₂×#117×D₅₃	C₂	semidirect
19. C₅₃×#3491	C₂	semidirect
22. #16811315	C₂²	semidirect
23. #16811314	C₂²	semidirect
24. #16811313	C₂²	semidirect
25. #16811312	C₂²	semidirect
26. #16811311	C₂²	semidirect
27. #16811310	C₂²	semidirect
28. #16811310	C₂²	semidirect
29. #16811309	C₂²	semidirect
30. #16811309	C₂²	semidirect
31. #16811308	C₂²	semidirect
32. #16811307	C₂²	semidirect
33. #16811306	C₂²	semidirect
34. #16811306	C₂²	semidirect
35. #16811305	C₂²	semidirect
36. #16811305	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. #16811300	C₂²	semidirect
44. #16811299	C₂²	semidirect
45. #16811299	C₂²	semidirect
46. #16811298	C₂²	semidirect
47. #16811298	C₂²	semidirect
48. #16811297	C₂²	semidirect
49. #16811297	C₂²	semidirect
50. #16811296	C₂²	semidirect
51. #16811296	C₂²	semidirect
52. #16811249	C₂²	semidirect
53. #16811249	C₂²	semidirect
54. #16811248	C₂²	semidirect
55. #16811248	C₂²	semidirect
56. #16811222	C₂²	semidirect
57. #16811221	C₂²	semidirect
58. #16811220	C₂²	semidirect
59. #16811219	C₂²	semidirect
60. #16811218	C₂²	semidirect
61. #16811217	C₂²	semidirect
62. #16811216	C₂²	semidirect
63. #16811215	C₂²	semidirect
64. #16811214	C₂²	semidirect
70. #16811160	C₂²	semidirect
71. #16811159	C₂²	semidirect
72. #16811158	C₂²	semidirect
73. #16811157	C₂²	semidirect
74. #16811156	C₂²	semidirect
75. #16811155	C₂²	semidirect
76. #16811154	C₂²	semidirect
77. #16811153	C₂²	semidirect
78. #16811152	C₂²	semidirect
79. #16811151	C₂²	semidirect
80. #16811150	C₂²	semidirect
81. #126×D₅₃	C₂²	semidirect
82. #126×D₅₃	C₂²	semidirect
83. #125×D₅₃	C₂²	semidirect
84. #125×D₅₃	C₂²	semidirect
85. #124×D₅₃	C₂²	semidirect
86. C₂×#13133202	C₂²	semidirect
87. C₂×#13133201	C₂²	semidirect
88. C₂×#13133200	C₂²	semidirect
89. C₂×#13133199	C₂²	semidirect
90. C₂×#13133198	C₂²	semidirect
93. #123×D₅₃	C₂²	semidirect
94. #123×D₅₃	C₂²	semidirect
95. #123×D₅₃	C₂²	semidirect
96. #123×D₅₃	C₂²	semidirect
97. #123×D₅₃	C₂²	semidirect
98. #123×D₅₃	C₂²	semidirect
99. C₂²⋊Q₈×D₅₃	C₂²	semidirect
100. C₂²⋊Q₈×D₅₃	C₂²	semidirect
101. C₂²⋊Q₈×D₅₃	C₂²	semidirect
104. #16811098	C₂²	semidirect
105. #16811097	C₂²	semidirect
106. #16811096	C₂²	semidirect
107. #16811096	C₂²	semidirect
108. #16811096	C₂²	semidirect
109. #16811095	C₂²	semidirect
110. #16811095	C₂²	semidirect
111. C₄×Q₈×D₅₃	C₂²	semidirect
113. C₄×D₄×D₅₃	C₂²	semidirect
114. C₄×D₄×D₅₃	C₂²	semidirect
115. C₂×#13133176	C₂²	semidirect
116. C₂×#13133175	C₂²	semidirect
117. C₂×#13133174	C₂²	semidirect
118. C₂×#13133173	C₂²	semidirect
119. C₂×#13133173	C₂²	semidirect
120. #117×D₅₃	C₂²	semidirect
121. #117×D₅₃	C₂²	semidirect
122. #117×D₅₃	C₂²	semidirect
123. #117×D₅₃	C₂²	semidirect
124. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
125. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
129. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
130. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
131. C₂×C₄²×D₅₃	C₂²	semidirect
132. C₅₃×#552	C₂²	semidirect
133. C₅₃×#551	C₂²	semidirect
134. C₅₃×#543	C₂²	semidirect
135. C₅₃×#539	C₂²	semidirect
137. C₅₃×#529	C₂²	semidirect
138. C₂×#123×C₅₃	C₂²	semidirect
139. C₅₃×#518	C₂²	semidirect
140. C₂×#117×C₅₃	C₂²	semidirect
166. #13133212	C₂³	semidirect
167. #13133212	C₂³	semidirect
168. #13133212	C₂³	semidirect
169. #13133212	C₂³	semidirect
170. #13133212	C₂³	semidirect
171. #13133212	C₂³	semidirect
172. #13133211	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. #13133209	C₂³	semidirect
181. #13133209	C₂³	semidirect
182. #13133208	C₂³	semidirect
183. #13133208	C₂³	semidirect
184. #13133208	C₂³	semidirect
185. #13133208	C₂³	semidirect
186. #13133207	C₂³	semidirect
187. #13133207	C₂³	semidirect
188. #13133207	C₂³	semidirect
189. #13133207	C₂³	semidirect
190. #13133207	C₂³	semidirect
191. #13133207	C₂³	semidirect
192. #13133206	C₂³	semidirect
193. #13133205	C₂³	semidirect
194. #13133204	C₂³	semidirect
195. #13133203	C₂³	semidirect
196. #13133203	C₂³	semidirect
200. #13133202	C₂³	semidirect
201. #13133202	C₂³	semidirect
202. #13133202	C₂³	semidirect
203. #13133202	C₂³	semidirect
206. #13133201	C₂³	semidirect
207. #13133201	C₂³	semidirect
208. #13133201	C₂³	semidirect
211. #13133200	C₂³	semidirect
212. #13133200	C₂³	semidirect
213. #13133200	C₂³	semidirect
217. #13133199	C₂³	semidirect
218. #13133199	C₂³	semidirect
219. #13133199	C₂³	semidirect
220. #13133199	C₂³	semidirect
223. #13133198	C₂³	semidirect
224. #13133198	C₂³	semidirect
225. #13133198	C₂³	semidirect
226. #13133197	C₂³	semidirect
227. #13133197	C₂³	semidirect
228. #13133197	C₂³	semidirect
229. #13133196	C₂³	semidirect
230. #13133196	C₂³	semidirect
231. #13133196	C₂³	semidirect
232. #13133195	C₂³	semidirect
233. #13133195	C₂³	semidirect
234. #13133195	C₂³	semidirect
235. #13133195	C₂³	semidirect
236. #13133195	C₂³	semidirect
237. #13133194	C₂³	semidirect
238. #13133194	C₂³	semidirect
239. #13133194	C₂³	semidirect
240. #13133194	C₂³	semidirect
241. #13133194	C₂³	semidirect
242. #13133193	C₂³	semidirect
243. #13133193	C₂³	semidirect
244. #13133193	C₂³	semidirect
255. Q₈×Dic₅₃	C₂³	semidirect
256. C₄×Dic₁₀₆	C₂³	semidirect
257. C₄×Dic₁₀₆	C₂³	semidirect
258. #13133182	C₂³	semidirect
259. #13133182	C₂³	semidirect
261. C₄×D₂₁₂	C₂³	semidirect
262. C₄×D₂₁₂	C₂³	semidirect
264. D₄×Dic₅₃	C₂³	semidirect
265. D₄×Dic₅₃	C₂³	semidirect
267. #13133179	C₂³	semidirect
268. #13133179	C₂³	semidirect
271. C₄×C₂²⋊D₅₃	C₂³	semidirect
272. C₄×C₂²⋊D₅₃	C₂³	semidirect
273. C₄×C₂²⋊D₅₃	C₂³	semidirect
276. #13133177	C₂³	semidirect
277. #13133177	C₂³	semidirect
278. #13133177	C₂³	semidirect
279. #13133176	C₂³	semidirect
280. #13133176	C₂³	semidirect
281. #13133176	C₂³	semidirect
282. #13133175	C₂³	semidirect
283. #13133175	C₂³	semidirect
284. #13133175	C₂³	semidirect
285. #13133175	C₂³	semidirect
286. #13133175	C₂³	semidirect
287. #13133174	C₂³	semidirect
288. #13133174	C₂³	semidirect
289. #13133174	C₂³	semidirect
290. #13133174	C₂³	semidirect
291. #13133174	C₂³	semidirect
292. #13133173	C₂³	semidirect
293. #13133173	C₂³	semidirect
294. #13133173	C₂³	semidirect
295. #13133173	C₂³	semidirect
296. #13133173	C₂³	semidirect
297. #13133173	C₂³	semidirect
298. C₂×C₄⋊Dic₅₃	C₂³	semidirect
299. C₂×C₄⋊Dic₅₃	C₂³	semidirect
300. C₂×#11719919	C₂³	semidirect
301. C₂×#11719919	C₂³	semidirect
302. C₂×#11719919	C₂³	semidirect
303. C₂×#11719919	C₂³	semidirect
311. C₄⋊C₄×D₅₃	C₂³	semidirect
312. C₄⋊C₄×D₅₃	C₂³	semidirect
313. C₄⋊C₄×D₅₃	C₂³	semidirect
317. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
318. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
322. C₂×#11719921	C₂³	semidirect
323. C₂×#11719921	C₂³	semidirect
324. C₂×#11719921	C₂³	semidirect
337. C₂²⋊C₄×D₅₃	C₂³	semidirect
338. C₂²⋊C₄×D₅₃	C₂³	semidirect
339. C₂²⋊C₄×D₅₃	C₂³	semidirect
340. C₂²⋊C₄×D₅₃	C₂³	semidirect
341. C₂²⋊C₄×D₅₃	C₂³	semidirect
342. C₂×C₄×Dic₅₃	C₂³	semidirect
343. C₂×C₄×Dic₅₃	C₂³	semidirect
344. C₂×C₄×Dic₅₃	C₂³	semidirect
348. C₄²×D₅₃	C₂³	semidirect
349. C₄²×D₅₃	C₂³	semidirect
352. #126×C₅₃	C₂³	semidirect
353. #126×C₅₃	C₂³	semidirect
354. #125×C₅₃	C₂³	semidirect
355. #125×C₅₃	C₂³	semidirect
356. #124×C₅₃	C₂³	semidirect
359. #123×C₅₃	C₂³	semidirect
360. #123×C₅₃	C₂³	semidirect
361. #123×C₅₃	C₂³	semidirect
362. C₂²⋊Q₈×C₅₃	C₂³	semidirect
363. C₂²⋊Q₈×C₅₃	C₂³	semidirect
364. C₂²⋊Q₈×C₅₃	C₂³	semidirect
367. C₄×Q₈×C₅₃	C₂³	semidirect
369. C₄×D₄×C₅₃	C₂³	semidirect
370. C₄×D₄×C₅₃	C₂³	semidirect
371. #117×C₅₃	C₂³	semidirect
372. #117×C₅₃	C₂³	semidirect
373. #117×C₅₃	C₂³	semidirect
374. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
375. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
379. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
380. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
381. C₂×C₄²×C₅₃	C₂³	semidirect
661. #3491	D₅₃	direct (N × H)
679. D₅₃	#3491	direct (N × H)
697. #552	C₂×D₅₃	semidirect
713. #551	C₂×D₅₃	semidirect
718. #543	C₂×D₅₃	semidirect
728. #539	C₂×D₅₃	semidirect
746. #529	C₂×D₅₃	semidirect
765. C₂×#123	C₂×D₅₃	semidirect
778. #518	C₂×D₅₃	semidirect
792. C₂×#117	C₂×D₅₃	semidirect
801. C₅₃	C₂×#3491	semidirect
843. #126	C₂²×D₅₃	semidirect
844. #126	C₂²×D₅₃	semidirect
857. #125	C₂²×D₅₃	semidirect
858. #125	C₂²×D₅₃	semidirect
864. #124	C₂²×D₅₃	semidirect
896. #123	C₂²×D₅₃	semidirect
897. #123	C₂²×D₅₃	semidirect
898. #123	C₂²×D₅₃	semidirect
918. C₂²⋊Q₈	C₂²×D₅₃	semidirect
919. C₂²⋊Q₈	C₂²×D₅₃	semidirect
920. C₂²⋊Q₈	C₂²×D₅₃	semidirect
938. C₄×Q₈	C₂²×D₅₃	semidirect
959. C₄×D₄	C₂²×D₅₃	semidirect
960. C₄×D₄	C₂²×D₅₃	semidirect
980. #117	C₂²×D₅₃	semidirect
981. #117	C₂²×D₅₃	semidirect
982. #117	C₂²×D₅₃	semidirect
999. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1000. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1032. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1033. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1042. C₂×C₄²	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288414	2
#20288413	2
#20288412	2
#20288411	2
#20288410	2
#20288409	2
#20288408	2
#20288407	2
#20288406	2
#552×D₅₃	2
#551×D₅₃	2
#543×D₅₃	2
#539×D₅₃	2
#534×D₅₃	2
#529×D₅₃	2
C₂×#123×D₅₃	2
#518×D₅₃	2
C₂×#117×D₅₃	2
C₅₃×#3491	2
C₂×#3491	53

Subgroups — D53×#3491 #28292138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3491 #28292138