Subgroups — #20288776

Order 6784.

1042 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811344	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811340	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811331	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811322	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811319	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811318	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811312	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811310	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811306	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811303	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811299	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811298	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811271	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811263	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811260	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811241	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811230	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811222	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811219	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811209	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811208	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811155	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811152	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811151	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811150	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#13133210	C₂	1	1	yes	maximal, characteristic, complemented
27	#126×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	#16811102	C₂	1	1	yes	maximal, characteristic, complemented
29	#16811096	C₂	1	1	yes	maximal, characteristic, complemented
30	#16811091	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11719945	C₂²	1	1	yes	characteristic
33	C₂×#11719947	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
35	#13133216	C₂²	1	1	yes	characteristic, complemented
36	#13133216	C₂²	1	1	yes	characteristic, complemented
37	#13133212	C₂²	1	1	yes	characteristic, complemented
38	#13133212	C₂²	1	1	yes	characteristic, complemented
39	#13133212	C₂²	1	1	yes	characteristic, complemented
40	#13133212	C₂²	1	1	yes	characteristic, complemented
41	#13133212	C₂²	1	1	yes	characteristic, complemented
42	#13133212	C₂²	1	1	yes	characteristic, complemented
43	#13133211	C₂²	1	1	yes	characteristic, complemented
44	#13133210	C₂²	1	1	yes	characteristic
45	#13133210	C₂²	1	1	yes	characteristic
46	#13133210	C₂²	1	1	yes	characteristic
47	#13133210	C₂²	1	1	yes	characteristic
48	#13133210	C₂²	1	1	yes	characteristic
49	#13133210	C₂²	1	1	yes	characteristic
50	#13133210	C₂²	1	1	yes	characteristic
51	#13133210	C₂²	1	1	yes	characteristic, complemented
52	#13133210	C₂²	1	1	yes	characteristic, complemented
53	#13133210	C₂²	1	1	yes	characteristic, complemented
54	#13133210	C₂²	1	1	yes	characteristic, complemented
55	#13133210	C₂²	1	1	yes	characteristic, complemented
56	#13133210	C₂²	1	1	yes	characteristic, complemented
57	#13133209	C₂²	1	1	yes	characteristic, complemented
58	#13133209	C₂²	1	1	yes	characteristic, complemented
59	#13133208	C₂²	1	1	yes	characteristic, complemented
60	#13133208	C₂²	1	1	yes	characteristic, complemented
61	#13133207	C₂²	1	1	yes	characteristic, complemented
62	#13133207	C₂²	1	1	yes	characteristic, complemented
63	#13133207	C₂²	1	1	yes	characteristic, complemented
64	#13133207	C₂²	1	1	yes	characteristic, complemented
65	#13133207	C₂²	1	1	yes	characteristic, complemented
66	#13133204	C₂²	1	1	yes	characteristic, complemented
67	#13133203	C₂²	1	1	yes	characteristic
68	#13133203	C₂²	1	1	yes	characteristic
69	#13133203	C₂²	1	1	yes	characteristic
70	#13133203	C₂²	1	1	yes	characteristic
71	#13133203	C₂²	1	1	yes	characteristic, complemented
72	#13133202	C₂²	1	1	yes	characteristic, complemented
73	#13133202	C₂²	1	1	yes	characteristic, complemented
74	#13133202	C₂²	1	1	yes	characteristic, complemented
75	#13133201	C₂²	1	1	yes	characteristic
76	#13133201	C₂²	1	1	yes	characteristic, complemented
77	#13133200	C₂²	1	1	yes	characteristic
78	#13133200	C₂²	1	1	yes	characteristic, complemented
79	#13133199	C₂²	1	1	yes	characteristic
80	#13133199	C₂²	1	1	yes	characteristic
81	#13133199	C₂²	1	1	yes	characteristic
82	#13133199	C₂²	1	1	yes	characteristic, complemented
83	#13133199	C₂²	1	1	yes	characteristic, complemented
84	#13133199	C₂²	1	1	yes	characteristic, complemented
85	#13133199	C₂²	1	1	yes	characteristic, complemented
86	#13133198	C₂²	1	1	yes	characteristic
87	#13133197	C₂²	1	1	yes	characteristic, complemented
88	#13133197	C₂²	1	1	yes	characteristic, complemented
89	#13133196	C₂²	1	1	yes	characteristic, complemented
90	#13133195	C₂²	1	1	yes	characteristic, complemented
91	#13133195	C₂²	1	1	yes	characteristic, complemented
92	#13133194	C₂²	1	1	yes	characteristic
93	#13133194	C₂²	1	1	yes	characteristic
94	#13133194	C₂²	1	1	yes	characteristic, complemented
95	#13133194	C₂²	1	1	yes	characteristic, complemented
96	#13133194	C₂²	1	1	yes	characteristic, complemented
97	#13133193	C₂²	1	1	yes	characteristic, complemented
98	#13133193	C₂²	1	1	yes	characteristic, complemented
99	#13133193	C₂²	1	1	yes	characteristic, complemented
100	#13133191	C₂²	1	1	yes	characteristic
101	#13133191	C₂²	1	1	yes	characteristic, complemented
102	#13133190	C₂²	1	1	yes	characteristic
103	#13133190	C₂²	1	1	yes	characteristic
104	#13133190	C₂²	1	1	yes	characteristic, complemented
105	#13133189	C₂²	1	1	yes	characteristic
106	#13133189	C₂²	1	1	yes	characteristic
107	#13133189	C₂²	1	1	yes	characteristic, complemented
108	#13133189	C₂²	1	1	yes	characteristic, complemented
109	#13133188	C₂²	1	1	yes	characteristic
110	#13133188	C₂²	1	1	yes	characteristic
111	#13133187	C₂²	1	1	yes	characteristic
112	#13133186	C₂²	1	1	yes	characteristic
113	#13133185	C₂²	1	1	yes	characteristic
114	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
117	#13133182	C₂²	1	1	yes	characteristic, complemented
118	#13133182	C₂²	1	1	yes	characteristic, complemented
119	#13133182	C₂²	1	1	yes	characteristic, complemented
120	#13133182	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
122	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
123	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
124	#13133179	C₂²	1	1	yes	characteristic, complemented
125	#13133179	C₂²	1	1	yes	characteristic, complemented
126	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
127	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
128	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
129	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
130	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
131	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
133	#13133177	C₂²	1	1	yes	characteristic
134	#13133177	C₂²	1	1	yes	characteristic
135	#13133177	C₂²	1	1	yes	characteristic
136	#13133177	C₂²	1	1	yes	characteristic
137	#13133177	C₂²	1	1	yes	characteristic
138	#13133177	C₂²	1	1	yes	characteristic
139	#13133177	C₂²	1	1	yes	characteristic, complemented
140	#13133177	C₂²	1	1	yes	characteristic, complemented
141	#13133177	C₂²	1	1	yes	characteristic, complemented
142	#13133177	C₂²	1	1	yes	characteristic, complemented
143	#13133177	C₂²	1	1	yes	characteristic, complemented
144	#13133176	C₂²	1	1	yes	characteristic, complemented
145	#13133176	C₂²	1	1	yes	characteristic, complemented
146	#13133175	C₂²	1	1	yes	characteristic, complemented
147	#13133174	C₂²	1	1	yes	characteristic, complemented
148	#13133174	C₂²	1	1	yes	characteristic, complemented
149	#13133174	C₂²	1	1	yes	characteristic, complemented
150	#13133174	C₂²	1	1	yes	characteristic, complemented
151	#13133173	C₂²	1	1	yes	characteristic
152	#13133173	C₂²	1	1	yes	characteristic
153	#13133173	C₂²	1	1	yes	characteristic, complemented
154	#13133173	C₂²	1	1	yes	characteristic, complemented
155	#13133173	C₂²	1	1	yes	characteristic, complemented
156	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
157	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
158	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
159	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
160	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
161	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
162	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
163	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
164	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
165	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
166	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
169	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
170	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
172	#126×C₅₃	C₂²	1	1	yes	characteristic
173	#126×C₅₃	C₂²	1	1	yes	characteristic
174	#124×C₅₃	C₂²	1	1	yes	characteristic
175	#123×C₅₃	C₂²	1	1	yes	characteristic
176	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
177	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	#120×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
188	C₂³×D₅₃	C₂³	1	1	yes	characteristic
189	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₅₃	—	2	4	no	—
199	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
209	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
210	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
211	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
212	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
213	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
214	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
216	#11719947	—	2	4	no	—
217	#11719945	—	2	4	no	—
218	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
219	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
231	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
232	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
233	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
234	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
235	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄²×C₅₃	C₂³	1	1	yes	characteristic
258	C₄²×C₅₃	C₂³	1	1	yes	characteristic
259	C₄²×C₅₃	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
274	#11719921	C₂³	1	1	yes	characteristic
275	#11719921	C₂³	1	1	yes	characteristic
276	#11719921	C₂³	1	1	yes	characteristic
277	#11719921	C₂³	1	1	yes	characteristic
278	#11719921	C₂³	1	1	yes	characteristic
279	#11719921	C₂³	1	1	yes	characteristic
280	#11719921	C₂³	1	1	yes	characteristic
281	#11719921	C₂³	1	1	yes	characteristic
282	#11719921	C₂³	1	1	yes	characteristic
283	#11719921	C₂³	1	1	yes	characteristic
284	#11719921	C₂³	1	1	yes	characteristic
285	#11719921	C₂³	1	1	yes	characteristic
286	#11719921	C₂³	1	1	yes	characteristic
287	#11719921	C₂³	1	1	yes	characteristic
288	#11719921	C₂³	1	1	yes	characteristic
289	#11719921	C₂³	1	1	yes	characteristic
290	#11719921	C₂³	1	1	yes	characteristic
291	#11719921	C₂³	1	1	yes	characteristic
292	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
293	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
295	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
296	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
304	#11719919	C₂³	1	1	yes	characteristic
305	#11719919	C₂³	1	1	yes	characteristic
306	#11719919	C₂³	1	1	yes	characteristic
307	#11719919	C₂³	1	1	yes	characteristic
308	#11719919	C₂³	1	1	yes	characteristic
309	#11719919	C₂³	1	1	yes	characteristic
310	#11719919	C₂³	1	1	yes	characteristic
311	#11719919	C₂³	1	1	yes	characteristic
312	#11719919	C₂³	1	1	yes	characteristic
313	#11719919	C₂³	1	1	yes	characteristic
314	#11719919	C₂³	1	1	yes	characteristic
315	#11719919	C₂³	1	1	yes	characteristic
316	#11719919	C₂³	1	1	yes	characteristic
317	#11719919	C₂³	1	1	yes	characteristic
318	#11719919	C₂³	1	1	yes	characteristic
319	#11719919	C₂³	1	1	yes	characteristic
320	#11719919	C₂³	1	1	yes	characteristic
321	#11719919	C₂³	1	1	yes	characteristic
322	#11719919	C₂³	1	1	yes	characteristic
323	#11719919	C₂³	1	1	yes	characteristic
324	#11719919	C₂³	1	1	yes	characteristic
325	#11719919	C₂³	1	1	yes	characteristic
326	#11719919	C₂³	1	1	yes	characteristic
327	#11719919	C₂³	1	1	yes	characteristic
328	#11719919	C₂³	1	1	yes	characteristic
329	#11719919	C₂³	1	1	yes	characteristic
330	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
331	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
332	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
333	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
334	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
335	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
336	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
337	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
338	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
339	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
340	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
341	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
342	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
343	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
344	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
345	C₂³×C₅₃	—	2	2	no	—
346	C₂³×C₅₃	—	4	1	no	—
347	C₂³×C₅₃	—	4	1	no	—
348	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²×D₅₃	—	2	2	no	—
353	C₂²×D₅₃	—	4	1	no	—
354	C₂²×D₅₃	—	4	1	no	—
355	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
356	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
358	Q₈×C₅₃	—	4	1	no	—
359	D₄×C₅₃	—	2	2	no	—
360	D₄×C₅₃	—	4	1	no	—
361	D₄×C₅₃	—	4	1	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	4	1	no	—
364	C₂×C₄×C₅₃	—	4	1	no	—
365	C₂×C₄×C₅₃	—	4	1	no	—
366	C₂×C₄×C₅₃	—	4	1	no	—
367	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²⋊D₅₃	—	2	2	no	—
379	C₂²⋊D₅₃	—	2	2	no	—
380	C₂²⋊D₅₃	—	2	2	no	—
381	C₂²⋊D₅₃	—	2	2	no	—
382	C₂²⋊D₅₃	—	2	2	no	—
383	C₂²⋊D₅₃	—	4	1	no	—
384	C₂²⋊D₅₃	—	4	1	no	—
385	C₂²⋊D₅₃	—	4	1	no	—
386	C₂²⋊D₅₃	—	4	1	no	—
387	C₂²⋊D₅₃	#41	1	4	yes	—
388	C₂×Dic₅₃	—	2	2	no	—
389	C₂×Dic₅₃	—	2	2	no	—
390	C₂×Dic₅₃	—	2	2	no	—
391	C₂×Dic₅₃	—	4	1	no	—
392	C₂×Dic₅₃	—	4	1	no	—
393	C₂×Dic₅₃	—	4	1	no	—
394	C₂×Dic₅₃	—	4	1	no	—
395	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
408	D₂₁₂	—	2	2	no	—
409	D₂₁₂	—	4	1	no	—
410	C₄×D₅₃	—	2	2	no	—
411	C₄×D₅₃	—	2	2	no	—
412	C₄×D₅₃	—	2	2	no	—
413	C₄×D₅₃	—	4	1	no	—
414	C₄×D₅₃	—	4	1	no	—
415	C₄×D₅₃	—	4	1	no	—
416	C₄×D₅₃	—	4	1	no	—
417	C₄×D₅₃	—	4	1	no	—
418	C₄×D₅₃	—	4	1	no	—
419	C₄×D₅₃	—	4	1	no	—
420	C₄×D₅₃	—	4	1	no	—
421	Dic₁₀₆	—	2	2	no	—
422	Dic₁₀₆	—	2	2	no	—
423	Dic₁₀₆	—	4	1	no	—
424	Dic₁₀₆	—	4	1	no	—
425	C₂²×C₅₃	—	2	1	no	—
426	C₂²×C₅₃	—	2	1	no	—
427	C₂²×C₅₃	—	2	1	no	—
428	C₂²×C₅₃	—	2	1	no	—
429	C₂²×C₅₃	—	2	1	no	—
430	C₂²×C₅₃	—	2	1	no	—
431	C₂²×C₅₃	—	2	1	no	—
432	C₂²×C₅₃	—	2	1	no	—
433	C₂²×C₅₃	—	2	1	no	—
434	C₂²×C₅₃	—	2	1	no	—
435	C₂²×C₅₃	—	2	1	no	—
436	C₂²×C₅₃	—	8	2	no	—
437	C₂²×C₅₃	C₂×#41	1	2	yes	—
438	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
439	C₂×D₅₃	—	2	1	no	—
440	C₂×D₅₃	—	2	1	no	—
441	C₂×D₅₃	—	2	1	no	—
442	C₂×D₅₃	—	2	1	no	—
443	C₂×D₅₃	—	2	1	no	—
444	C₂×D₅₃	—	2	1	no	—
445	C₂×D₅₃	—	2	1	no	—
446	C₂×D₅₃	—	2	1	no	—
447	C₂×D₅₃	—	8	2	no	—
448	C₂×D₅₃	C₂×#41	1	2	yes	—
449	C₄×C₅₃	—	2	1	no	—
450	C₄×C₅₃	—	2	1	no	—
451	C₄×C₅₃	—	2	1	no	—
452	C₄×C₅₃	—	2	1	no	—
453	C₄×C₅₃	—	2	1	no	—
454	C₄×C₅₃	—	2	1	no	—
455	C₄×C₅₃	—	2	1	no	—
456	C₄×C₅₃	—	2	1	no	—
457	C₄×C₅₃	—	2	1	no	—
458	C₄×C₅₃	—	2	1	no	—
459	C₄×C₅₃	—	2	1	no	—
460	Dic₅₃	—	2	1	no	—
461	Dic₅₃	—	2	1	no	—
462	Dic₅₃	—	2	1	no	—
463	Dic₅₃	—	2	1	no	—
464	Dic₅₃	—	2	1	no	—
465	Dic₅₃	—	2	1	no	—
466	Dic₅₃	—	2	1	no	—
467	Dic₅₃	—	2	1	no	—
468	Dic₅₃	—	2	1	no	—
469	Dic₅₃	—	2	1	no	—
470	Dic₅₃	—	2	1	no	—
471	Dic₅₃	—	2	1	no	—
472	Dic₅₃	C₂×#41	1	2	yes	—
473	#3521	—	53	1	no	maximal, Sylow
474	C₂×C₅₃	—	2	2	no	—
475	C₂×C₅₃	—	4	1	no	—
476	C₂×C₅₃	—	4	1	no	—
477	C₂×C₅₃	—	4	1	no	—
478	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
479	C₂×C₅₃	#585	1	1	yes	characteristic
480	C₂×C₅₃	#585	1	1	yes	characteristic
481	D₅₃	—	2	2	no	—
482	D₅₃	—	4	1	no	—
483	D₅₃	—	4	1	no	—
484	#556	—	53	1	no	—
485	#556	—	53	1	no	—
486	#554	—	53	1	no	—
487	#553	—	53	1	no	—
488	#553	—	53	1	no	—
489	#553	—	53	1	no	—
490	#552	—	53	1	no	—
491	#552	—	53	1	no	—
492	#552	—	53	1	no	—
493	#551	—	53	1	no	—
494	#551	—	53	1	no	—
495	#551	—	53	1	no	—
496	#551	D₅₃	1	1	yes	characteristic, complemented
497	#547	—	53	1	no	—
498	#546	—	53	1	no	—
499	#546	—	53	1	no	—
500	#542	—	53	1	no	—
501	#541	—	53	1	no	—
502	#539	—	53	1	no	—
503	#539	—	53	1	no	—
504	#538	—	53	1	no	—
505	#538	—	53	1	no	—
506	#529	—	53	1	no	—
507	#529	—	53	1	no	—
508	#529	—	53	1	no	—
509	#529	—	53	1	no	—
510	C₂×#126	—	53	1	no	—
511	C₂×#126	—	53	1	no	—
512	#520	—	53	1	no	—
513	#518	—	53	1	no	—
514	C₄×#41	—	53	1	no	—
515	C₅₃	#3521	1	1	yes	characteristic, complemented, Sylow
516	C₂×#41	—	53	1	no	—
517	C₂×#41	—	53	1	no	—
518	C₂²×D₄	—	53	1	no	—
519	C₄⋊Q₈	—	53	1	no	—
520	C₄⋊Q₈	—	53	1	no	—
521	#126	—	53	1	no	—
522	#126	—	53	1	no	—
523	#126	—	53	1	no	—
524	#126	—	53	1	no	—
525	#126	—	53	1	no	—
526	#126	—	53	1	no	—
527	#126	—	53	1	no	—
528	#126	—	53	1	no	—
529	#126	—	53	1	no	—
530	#126	—	53	1	no	—
531	#126	—	53	1	no	—
532	#126	—	53	1	no	—
533	#126	—	53	1	no	—
534	#126	—	53	1	no	—
535	#126	—	53	1	no	—
536	#126	—	53	1	no	—
537	#126	—	53	1	no	—
538	#126	—	53	1	no	—
539	#126	—	53	1	no	—
540	#126	—	53	1	no	—
541	#126	C₂×D₅₃	1	1	yes	characteristic
542	#126	C₂×D₅₃	1	1	yes	characteristic
543	#125	—	53	1	no	—
544	#125	—	53	1	no	—
545	#125	—	53	1	no	—
546	#125	—	53	1	no	—
547	#125	—	53	1	no	—
548	#125	—	53	1	no	—
549	#125	—	53	1	no	—
550	#125	—	53	1	no	—
551	#125	—	53	1	no	—
552	#124	—	53	1	no	—
553	#124	—	53	1	no	—
554	#124	—	53	1	no	—
555	#124	—	53	1	no	—
556	#124	—	53	1	no	—
557	#124	—	53	1	no	—
558	#124	C₂×D₅₃	1	1	yes	characteristic
559	#123	—	53	1	no	—
560	#123	—	53	1	no	—
561	#123	—	53	1	no	—
562	#123	—	53	1	no	—
563	#123	—	53	1	no	—
564	#123	—	53	1	no	—
565	#123	—	53	1	no	—
566	#123	—	53	1	no	—
567	#123	—	53	1	no	—
568	#123	—	53	1	no	—
569	#123	—	53	1	no	—
570	#123	—	53	1	no	—
571	#123	—	53	1	no	—
572	#123	—	53	1	no	—
573	#123	—	53	1	no	—
574	#123	C₂×D₅₃	1	1	yes	characteristic
575	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
576	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
577	C₂²⋊Q₈	—	53	1	no	—
578	C₂²⋊Q₈	—	53	1	no	—
579	C₂²⋊Q₈	—	53	1	no	—
580	C₂²⋊Q₈	—	53	1	no	—
581	C₂²⋊Q₈	—	53	1	no	—
582	C₂²⋊Q₈	—	53	1	no	—
583	C₂²⋊Q₈	—	53	1	no	—
584	C₂²⋊Q₈	—	53	1	no	—
585	C₂²⋊Q₈	—	53	1	no	—
586	C₂²⋊Q₈	—	53	1	no	—
587	C₂²⋊Q₈	—	53	1	no	—
588	C₂²⋊Q₈	—	53	1	no	—
589	C₂²⋊Q₈	—	53	1	no	—
590	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
591	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
592	#121	—	53	1	no	—
593	#121	—	53	1	no	—
594	#121	—	53	1	no	—
595	#121	—	53	1	no	—
596	#121	—	53	1	no	—
597	#121	—	53	1	no	—
598	#121	—	53	1	no	—
599	#121	—	53	1	no	—
600	#121	—	53	1	no	—
601	#121	—	53	1	no	—
602	#121	—	53	1	no	—
603	#120	—	53	1	no	—
604	#120	—	53	1	no	—
605	#120	—	53	1	no	—
606	#120	C₂×D₅₃	1	1	yes	characteristic
607	C₄×Q₈	—	53	1	no	—
608	C₄×Q₈	—	53	1	no	—
609	C₄×Q₈	—	53	1	no	—
610	C₄×Q₈	—	53	1	no	—
611	C₄×Q₈	—	53	1	no	—
612	C₄×Q₈	—	53	1	no	—
613	C₄×Q₈	—	53	1	no	—
614	C₄×D₄	—	53	1	no	—
615	C₄×D₄	—	53	1	no	—
616	C₄×D₄	—	53	1	no	—
617	C₄×D₄	—	53	1	no	—
618	C₄×D₄	—	53	1	no	—
619	C₄×D₄	—	53	1	no	—
620	C₄×D₄	—	53	1	no	—
621	C₄×D₄	—	53	1	no	—
622	C₄×D₄	—	53	1	no	—
623	C₄×D₄	—	53	1	no	—
624	C₄×D₄	—	53	1	no	—
625	C₄×D₄	—	53	1	no	—
626	C₄×D₄	—	53	1	no	—
627	C₄×D₄	—	53	1	no	—
628	C₄×D₄	—	53	1	no	—
629	C₄×D₄	—	53	1	no	—
630	C₄×D₄	—	53	1	no	—
631	C₄×D₄	—	53	1	no	—
632	C₄×D₄	—	53	1	no	—
633	C₄×D₄	—	53	1	no	—
634	C₄×D₄	—	53	1	no	—
635	C₄×D₄	—	53	1	no	—
636	C₄×D₄	—	53	1	no	—
637	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
638	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
639	#117	—	53	1	no	—
640	#117	—	53	1	no	—
641	#117	—	53	1	no	—
642	#117	—	53	1	no	—
643	#117	—	53	1	no	—
644	#117	—	53	1	no	—
645	#117	—	53	1	no	—
646	#117	—	53	1	no	—
647	#117	—	53	1	no	—
648	#117	—	53	1	no	—
649	#117	—	53	1	no	—
650	#117	—	53	1	no	—
651	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
652	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
653	C₂×C₄⋊C₄	—	53	1	no	—
654	C₂×C₄⋊C₄	—	53	1	no	—
655	C₂×C₄⋊C₄	—	53	1	no	—
656	C₂×C₄⋊C₄	—	53	1	no	—
657	C₂×C₄⋊C₄	—	53	1	no	—
658	C₂×C₄⋊C₄	—	53	1	no	—
659	C₂×C₄⋊C₄	—	53	1	no	—
660	C₂×C₂²⋊C₄	—	53	1	no	—
661	C₂×C₂²⋊C₄	—	53	1	no	—
662	C₂×C₂²⋊C₄	—	53	1	no	—
663	C₂×C₂²⋊C₄	—	53	1	no	—
664	C₂×C₂²⋊C₄	—	53	1	no	—
665	C₂×C₂²⋊C₄	—	53	1	no	—
666	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
668	C₂×C₄²	—	53	1	no	—
669	C₂×C₄²	—	53	1	no	—
670	C₂×C₄²	—	53	1	no	—
671	C₂⁴	—	53	1	no	—
672	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
673	#41	—	106	4	no	—
674	#41	—	106	4	no	—
675	C₂×Q₈	—	53	1	no	—
676	C₂×Q₈	—	53	1	no	—
677	C₂×Q₈	—	53	1	no	—
678	C₂×Q₈	—	53	1	no	—
679	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
680	C₂×D₄	—	53	1	no	—
681	C₂×D₄	—	53	1	no	—
682	C₂×D₄	—	53	1	no	—
683	C₂×D₄	—	53	1	no	—
684	C₂×D₄	—	53	1	no	—
685	C₂×D₄	—	53	1	no	—
686	C₂×D₄	—	53	1	no	—
687	C₂×D₄	—	53	1	no	—
688	C₂×D₄	—	53	1	no	—
689	C₂×D₄	—	53	1	no	—
690	C₂×D₄	—	53	1	no	—
691	C₂×D₄	—	53	1	no	—
692	C₂×D₄	—	106	4	no	—
693	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
694	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
695	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
696	C₂²×C₄	—	53	1	no	—
697	C₂²×C₄	—	53	1	no	—
698	C₂²×C₄	—	53	1	no	—
699	C₂²×C₄	—	53	1	no	—
700	C₂²×C₄	—	53	1	no	—
701	C₂²×C₄	—	53	1	no	—
702	C₂²×C₄	—	53	1	no	—
703	C₂²×C₄	—	53	1	no	—
704	C₂²×C₄	—	53	1	no	—
705	C₂²×C₄	—	53	1	no	—
706	C₂²×C₄	—	53	1	no	—
707	C₂²×C₄	—	53	1	no	—
708	C₂²×C₄	—	53	1	no	—
709	C₂²×C₄	—	53	1	no	—
710	C₂²×C₄	—	53	1	no	—
711	C₂²×C₄	—	53	1	no	—
712	C₂²×C₄	—	53	1	no	—
713	C₂²×C₄	—	53	1	no	—
714	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
715	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
716	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
719	C₄⋊C₄	—	53	1	no	—
720	C₄⋊C₄	—	53	1	no	—
721	C₄⋊C₄	—	53	1	no	—
722	C₄⋊C₄	—	53	1	no	—
723	C₄⋊C₄	—	53	1	no	—
724	C₄⋊C₄	—	53	1	no	—
725	C₄⋊C₄	—	53	1	no	—
726	C₄⋊C₄	—	53	1	no	—
727	C₄⋊C₄	—	53	1	no	—
728	C₄⋊C₄	—	53	1	no	—
729	C₄⋊C₄	—	53	1	no	—
730	C₄⋊C₄	—	53	1	no	—
731	C₄⋊C₄	—	53	1	no	—
732	C₄⋊C₄	—	53	1	no	—
733	C₄⋊C₄	—	53	1	no	—
734	C₄⋊C₄	—	53	1	no	—
735	C₄⋊C₄	—	53	1	no	—
736	C₄⋊C₄	—	53	1	no	—
737	C₄⋊C₄	—	53	1	no	—
738	C₄⋊C₄	—	53	1	no	—
739	C₄⋊C₄	—	53	1	no	—
740	C₄⋊C₄	—	53	1	no	—
741	C₄⋊C₄	—	53	1	no	—
742	C₄⋊C₄	—	53	1	no	—
743	C₄⋊C₄	—	53	1	no	—
744	C₄⋊C₄	—	53	1	no	—
745	C₄⋊C₄	—	53	1	no	—
746	C₄⋊C₄	—	53	1	no	—
747	C₄⋊C₄	—	53	1	no	—
748	C₄⋊C₄	—	53	1	no	—
749	C₄⋊C₄	—	53	1	no	—
750	C₄⋊C₄	—	53	1	no	—
751	C₄⋊C₄	—	53	1	no	—
752	C₄⋊C₄	—	53	1	no	—
753	C₄⋊C₄	—	53	1	no	—
754	C₄⋊C₄	—	53	1	no	—
755	C₄⋊C₄	—	53	1	no	—
756	C₄⋊C₄	—	53	1	no	—
757	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
764	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
765	C₂²⋊C₄	—	53	1	no	—
766	C₂²⋊C₄	—	53	1	no	—
767	C₂²⋊C₄	—	53	1	no	—
768	C₂²⋊C₄	—	53	1	no	—
769	C₂²⋊C₄	—	53	1	no	—
770	C₂²⋊C₄	—	53	1	no	—
771	C₂²⋊C₄	—	53	1	no	—
772	C₂²⋊C₄	—	53	1	no	—
773	C₂²⋊C₄	—	53	1	no	—
774	C₂²⋊C₄	—	53	1	no	—
775	C₂²⋊C₄	—	53	1	no	—
776	C₂²⋊C₄	—	53	1	no	—
777	C₂²⋊C₄	—	53	1	no	—
778	C₂²⋊C₄	—	53	1	no	—
779	C₂²⋊C₄	—	53	1	no	—
780	C₂²⋊C₄	—	53	1	no	—
781	C₂²⋊C₄	—	53	1	no	—
782	C₂²⋊C₄	—	53	1	no	—
783	C₂²⋊C₄	—	53	1	no	—
784	C₂²⋊C₄	—	53	1	no	—
785	C₂²⋊C₄	—	53	1	no	—
786	C₂²⋊C₄	—	53	1	no	—
787	C₂²⋊C₄	—	53	1	no	—
788	C₂²⋊C₄	—	53	1	no	—
789	C₂²⋊C₄	—	53	1	no	—
790	C₂²⋊C₄	—	53	1	no	—
791	C₂²⋊C₄	—	53	1	no	—
792	C₂²⋊C₄	—	53	1	no	—
793	C₂²⋊C₄	—	53	1	no	—
794	C₂²⋊C₄	—	53	1	no	—
795	C₂²⋊C₄	—	53	1	no	—
796	C₂²⋊C₄	—	53	1	no	—
797	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
811	C₄²	—	53	1	no	—
812	C₄²	—	53	1	no	—
813	C₄²	—	53	1	no	—
814	C₄²	—	53	1	no	—
815	C₄²	—	53	1	no	—
816	C₄²	—	53	1	no	—
817	C₄²	—	53	1	no	—
818	C₄²	—	53	1	no	—
819	C₄²	—	53	1	no	—
820	C₄²	—	53	1	no	—
821	C₄²	—	53	1	no	—
822	C₄²	—	53	1	no	—
823	C₄²	—	53	1	no	—
824	C₄²	—	53	1	no	—
825	C₄²	—	53	1	no	—
826	C₄²	C₂²×D₅₃	1	1	yes	characteristic
827	C₄²	C₂²×D₅₃	1	1	yes	characteristic
828	C₄²	C₂²×D₅₃	1	1	yes	characteristic
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	1	no	—
832	C₂³	—	53	1	no	—
833	C₂³	—	53	1	no	—
834	C₂³	—	53	1	no	—
835	C₂³	—	106	2	no	—
836	C₂³	—	212	1	no	—
837	C₂³	—	212	1	no	—
838	C₂³	C₂³×D₅₃	1	1	yes	characteristic
839	C₂³	C₂³×D₅₃	1	1	yes	characteristic
840	C₂³	C₂³×D₅₃	1	1	yes	characteristic
841	C₂³	C₂³×D₅₃	1	1	yes	characteristic
842	Q₈	—	4	1	no	—
843	Q₈	—	106	2	no	—
844	Q₈	—	106	2	no	—
845	Q₈	—	212	1	no	—
846	Q₈	—	212	1	no	—
847	D₄	—	2	2	no	—
848	D₄	—	4	1	no	—
849	D₄	—	4	1	no	—
850	D₄	—	53	4	no	—
851	D₄	—	106	2	no	—
852	D₄	—	106	2	no	—
853	D₄	—	106	2	no	—
854	D₄	—	106	2	no	—
855	D₄	—	106	2	no	—
856	D₄	—	106	2	no	—
857	D₄	—	212	1	no	—
858	D₄	—	212	1	no	—
859	D₄	—	212	1	no	—
860	D₄	—	212	1	no	—
861	D₄	—	212	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	53	1	no	—
868	C₂×C₄	—	53	1	no	—
869	C₂×C₄	—	53	1	no	—
870	C₂×C₄	—	53	1	no	—
871	C₂×C₄	—	53	1	no	—
872	C₂×C₄	—	53	1	no	—
873	C₂×C₄	—	53	1	no	—
874	C₂×C₄	—	53	1	no	—
875	C₂×C₄	—	53	1	no	—
876	C₂×C₄	—	53	1	no	—
877	C₂×C₄	—	53	1	no	—
878	C₂×C₄	—	53	1	no	—
879	C₂×C₄	—	53	1	no	—
880	C₂×C₄	—	106	2	no	—
881	C₂×C₄	—	106	2	no	—
882	C₂×C₄	—	106	2	no	—
883	C₂×C₄	—	106	2	no	—
884	C₂×C₄	—	106	2	no	—
885	C₂×C₄	—	106	2	no	—
886	C₂×C₄	—	212	1	no	—
887	C₂×C₄	—	212	1	no	—
888	C₂×C₄	—	212	1	no	—
889	C₂×C₄	—	212	1	no	—
890	C₂×C₄	—	212	1	no	—
891	C₂×C₄	—	212	1	no	—
892	C₂×C₄	—	212	1	no	—
893	C₂×C₄	—	212	1	no	—
894	C₂×C₄	—	212	1	no	—
895	C₂×C₄	—	212	1	no	—
896	C₂×C₄	—	212	1	no	—
897	C₂×C₄	—	212	1	no	—
898	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
899	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
908	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	8	2	no	—
921	C₂²	—	53	2	no	—
922	C₂²	—	106	1	no	—
923	C₂²	—	106	1	no	—
924	C₂²	—	106	1	no	—
925	C₂²	—	106	1	no	—
926	C₂²	—	106	1	no	—
927	C₂²	—	106	1	no	—
928	C₂²	—	106	1	no	—
929	C₂²	—	106	1	no	—
930	C₂²	—	424	2	no	—
931	C₂²	#41×D₅₃	1	2	yes	—
932	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	53	2	no	—
945	C₄	—	106	1	no	—
946	C₄	—	106	1	no	—
947	C₄	—	106	1	no	—
948	C₄	—	106	1	no	—
949	C₄	—	106	1	no	—
950	C₄	—	106	1	no	—
951	C₄	—	106	1	no	—
952	C₄	—	106	1	no	—
953	C₄	—	106	1	no	—
954	C₄	—	106	1	no	—
955	C₄	—	106	1	no	—
956	C₄	—	106	1	no	—
957	C₂	—	2	2	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	—	106	2	no	—
962	C₂	—	212	1	no	—
963	C₂	—	212	1	no	—
964	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
965	C₂	#16811458	1	1	yes	characteristic
966	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#551	C₂
hypercenter	#551	D₅₃
hypocenter	C₅₃	#3521
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #16811344	C₂	semidirect
2. #16811340	C₂	semidirect
3. #16811331	C₂	semidirect
4. #16811322	C₂	semidirect
5. #16811319	C₂	semidirect
6. #16811318	C₂	semidirect
7. #16811312	C₂	semidirect
8. #16811310	C₂	semidirect
9. #16811306	C₂	semidirect
10. #16811303	C₂	semidirect
11. #16811299	C₂	semidirect
12. #16811298	C₂	semidirect
13. #16811271	C₂	semidirect
14. #16811263	C₂	semidirect
15. #16811260	C₂	semidirect
16. #16811241	C₂	semidirect
17. #16811230	C₂	semidirect
18. #16811222	C₂	semidirect
19. #16811219	C₂	semidirect
20. #16811209	C₂	semidirect
21. #16811208	C₂	semidirect
22. #16811155	C₂	semidirect
23. #16811152	C₂	semidirect
24. #16811151	C₂	semidirect
25. #16811150	C₂	semidirect
26. C₂×#13133210	C₂	semidirect
27. #126×D₅₃	C₂	semidirect
28. #16811102	C₂	semidirect
29. #16811096	C₂	semidirect
30. #16811091	C₂	semidirect
31. C₅₃×#551	C₂	semidirect
35. #13133216	C₂²	semidirect
36. #13133216	C₂²	semidirect
37. #13133212	C₂²	semidirect
38. #13133212	C₂²	semidirect
39. #13133212	C₂²	semidirect
40. #13133212	C₂²	semidirect
41. #13133212	C₂²	semidirect
42. #13133212	C₂²	semidirect
43. #13133211	C₂²	semidirect
51. #13133210	C₂²	semidirect
52. #13133210	C₂²	semidirect
53. #13133210	C₂²	semidirect
54. #13133210	C₂²	semidirect
55. #13133210	C₂²	semidirect
56. #13133210	C₂²	semidirect
57. #13133209	C₂²	semidirect
58. #13133209	C₂²	semidirect
59. #13133208	C₂²	semidirect
60. #13133208	C₂²	semidirect
61. #13133207	C₂²	semidirect
62. #13133207	C₂²	semidirect
63. #13133207	C₂²	semidirect
64. #13133207	C₂²	semidirect
65. #13133207	C₂²	semidirect
66. #13133204	C₂²	semidirect
71. #13133203	C₂²	semidirect
72. #13133202	C₂²	semidirect
73. #13133202	C₂²	semidirect
74. #13133202	C₂²	semidirect
76. #13133201	C₂²	semidirect
78. #13133200	C₂²	semidirect
82. #13133199	C₂²	semidirect
83. #13133199	C₂²	semidirect
84. #13133199	C₂²	semidirect
85. #13133199	C₂²	semidirect
87. #13133197	C₂²	semidirect
88. #13133197	C₂²	semidirect
89. #13133196	C₂²	semidirect
90. #13133195	C₂²	semidirect
91. #13133195	C₂²	semidirect
94. #13133194	C₂²	semidirect
95. #13133194	C₂²	semidirect
96. #13133194	C₂²	semidirect
97. #13133193	C₂²	semidirect
98. #13133193	C₂²	semidirect
99. #13133193	C₂²	semidirect
101. #13133191	C₂²	semidirect
104. #13133190	C₂²	semidirect
107. #13133189	C₂²	semidirect
108. #13133189	C₂²	semidirect
114. Q₈×Dic₅₃	C₂²	semidirect
115. C₄×Dic₁₀₆	C₂²	semidirect
116. C₄×Dic₁₀₆	C₂²	semidirect
117. #13133182	C₂²	semidirect
118. #13133182	C₂²	semidirect
119. #13133182	C₂²	semidirect
120. #13133182	C₂²	semidirect
121. C₄×D₂₁₂	C₂²	semidirect
123. D₄×Dic₅₃	C₂²	semidirect
124. #13133179	C₂²	semidirect
125. #13133179	C₂²	semidirect
131. C₄×C₂²⋊D₅₃	C₂²	semidirect
132. C₄×C₂²⋊D₅₃	C₂²	semidirect
139. #13133177	C₂²	semidirect
140. #13133177	C₂²	semidirect
141. #13133177	C₂²	semidirect
142. #13133177	C₂²	semidirect
143. #13133177	C₂²	semidirect
144. #13133176	C₂²	semidirect
145. #13133176	C₂²	semidirect
146. #13133175	C₂²	semidirect
147. #13133174	C₂²	semidirect
148. #13133174	C₂²	semidirect
149. #13133174	C₂²	semidirect
150. #13133174	C₂²	semidirect
153. #13133173	C₂²	semidirect
154. #13133173	C₂²	semidirect
155. #13133173	C₂²	semidirect
156. C₂×C₄⋊Dic₅₃	C₂²	semidirect
157. C₂×#11719919	C₂²	semidirect
158. C₂×#11719919	C₂²	semidirect
159. C₂×#11719919	C₂²	semidirect
160. C₄⋊C₄×D₅₃	C₂²	semidirect
161. C₄⋊C₄×D₅₃	C₂²	semidirect
162. C₄⋊C₄×D₅₃	C₂²	semidirect
169. C₂×C₄×Dic₅₃	C₂²	semidirect
170. C₄²×D₅₃	C₂²	semidirect
171. C₄²×D₅₃	C₂²	semidirect
176. #123×C₅₃	C₂²	semidirect
177. #123×C₅₃	C₂²	semidirect
178. C₂²⋊Q₈×C₅₃	C₂²	semidirect
179. C₂²⋊Q₈×C₅₃	C₂²	semidirect
181. C₄×D₄×C₅₃	C₂²	semidirect
182. C₄×D₄×C₅₃	C₂²	semidirect
183. #117×C₅₃	C₂²	semidirect
184. #117×C₅₃	C₂²	semidirect
496. #551	D₅₃	semidirect
515. C₅₃	#3521	semidirect
575. #123	C₂×D₅₃	semidirect
576. #123	C₂×D₅₃	semidirect
590. C₂²⋊Q₈	C₂×D₅₃	semidirect
591. C₂²⋊Q₈	C₂×D₅₃	semidirect
637. C₄×D₄	C₂×D₅₃	semidirect
638. C₄×D₄	C₂×D₅₃	semidirect
651. #117	C₂×D₅₃	semidirect
652. #117	C₂×D₅₃	semidirect