Subgroups — #20288923

Order 6784.

1038 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811376	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811375	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811370	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811368	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811329	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811328	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811309	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811305	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811302	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811301	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811298	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811298	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811278	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811274	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811270	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811265	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811253	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811248	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811241	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811238	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811221	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811219	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811219	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811216	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811209	C₂	1	1	yes	maximal, characteristic, complemented
26	#16811196	C₂	1	1	yes	maximal, characteristic, complemented
27	#16811196	C₂	1	1	yes	maximal, characteristic, complemented
28	#16811132	C₂	1	1	yes	maximal, characteristic, complemented
29	#123×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11719945	C₂²	1	1	yes	characteristic
33	C₂×#11719945	C₂²	1	1	yes	characteristic
34	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
35	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
38	#13133217	C₂²	1	1	yes	characteristic, complemented
39	#13133216	C₂²	1	1	yes	characteristic, complemented
40	#13133216	C₂²	1	1	yes	characteristic, complemented
41	#13133216	C₂²	1	1	yes	characteristic, complemented
42	#13133216	C₂²	1	1	yes	characteristic, complemented
43	#13133216	C₂²	1	1	yes	characteristic, complemented
44	#13133212	C₂²	1	1	yes	characteristic, complemented
45	#13133212	C₂²	1	1	yes	characteristic, complemented
46	#13133212	C₂²	1	1	yes	characteristic, complemented
47	#13133211	C₂²	1	1	yes	characteristic, complemented
48	#13133210	C₂²	1	1	yes	characteristic, complemented
49	#13133210	C₂²	1	1	yes	characteristic, complemented
50	#13133210	C₂²	1	1	yes	characteristic, complemented
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	#13133208	C₂²	1	1	yes	characteristic, complemented
55	#13133208	C₂²	1	1	yes	characteristic, complemented
56	#13133207	C₂²	1	1	yes	characteristic, complemented
57	#13133207	C₂²	1	1	yes	characteristic, complemented
58	#13133207	C₂²	1	1	yes	characteristic, complemented
59	#13133207	C₂²	1	1	yes	characteristic, complemented
60	#13133207	C₂²	1	1	yes	characteristic, complemented
61	#13133207	C₂²	1	1	yes	characteristic, complemented
62	#13133204	C₂²	1	1	yes	characteristic
63	#13133204	C₂²	1	1	yes	characteristic, complemented
64	#13133203	C₂²	1	1	yes	characteristic
65	#13133203	C₂²	1	1	yes	characteristic, complemented
66	#13133203	C₂²	1	1	yes	characteristic, complemented
67	#13133203	C₂²	1	1	yes	characteristic, complemented
68	#13133203	C₂²	1	1	yes	characteristic, complemented
69	#13133203	C₂²	1	1	yes	characteristic, complemented
70	#13133202	C₂²	1	1	yes	characteristic
71	#13133202	C₂²	1	1	yes	characteristic
72	#13133202	C₂²	1	1	yes	characteristic
73	#13133202	C₂²	1	1	yes	characteristic
74	#13133202	C₂²	1	1	yes	characteristic, complemented
75	#13133202	C₂²	1	1	yes	characteristic, complemented
76	#13133202	C₂²	1	1	yes	characteristic, complemented
77	#13133202	C₂²	1	1	yes	characteristic, complemented
78	#13133201	C₂²	1	1	yes	characteristic
79	#13133200	C₂²	1	1	yes	characteristic
80	#13133200	C₂²	1	1	yes	characteristic, complemented
81	#13133200	C₂²	1	1	yes	characteristic, complemented
82	#13133199	C₂²	1	1	yes	characteristic
83	#13133199	C₂²	1	1	yes	characteristic
84	#13133199	C₂²	1	1	yes	characteristic
85	#13133199	C₂²	1	1	yes	characteristic
86	#13133199	C₂²	1	1	yes	characteristic
87	#13133199	C₂²	1	1	yes	characteristic, complemented
88	#13133199	C₂²	1	1	yes	characteristic, complemented
89	#13133199	C₂²	1	1	yes	characteristic, complemented
90	#13133199	C₂²	1	1	yes	characteristic, complemented
91	#13133199	C₂²	1	1	yes	characteristic, complemented
92	#13133198	C₂²	1	1	yes	characteristic
93	#13133198	C₂²	1	1	yes	characteristic, complemented
94	#13133197	C₂²	1	1	yes	characteristic
95	#13133197	C₂²	1	1	yes	characteristic
96	#13133197	C₂²	1	1	yes	characteristic
97	#13133197	C₂²	1	1	yes	characteristic, complemented
98	#13133197	C₂²	1	1	yes	characteristic, complemented
99	#13133197	C₂²	1	1	yes	characteristic, complemented
100	#13133196	C₂²	1	1	yes	characteristic, complemented
101	#13133196	C₂²	1	1	yes	characteristic, complemented
102	#13133196	C₂²	1	1	yes	characteristic, complemented
103	#13133196	C₂²	1	1	yes	characteristic, complemented
104	#13133196	C₂²	1	1	yes	characteristic, complemented
105	#13133196	C₂²	1	1	yes	characteristic, complemented
106	#13133195	C₂²	1	1	yes	characteristic
107	#13133195	C₂²	1	1	yes	characteristic
108	#13133195	C₂²	1	1	yes	characteristic
109	#13133195	C₂²	1	1	yes	characteristic
110	#13133195	C₂²	1	1	yes	characteristic
111	#13133195	C₂²	1	1	yes	characteristic, complemented
112	#13133195	C₂²	1	1	yes	characteristic, complemented
113	#13133195	C₂²	1	1	yes	characteristic, complemented
114	#13133195	C₂²	1	1	yes	characteristic, complemented
115	#13133195	C₂²	1	1	yes	characteristic, complemented
116	#13133195	C₂²	1	1	yes	characteristic, complemented
117	#13133194	C₂²	1	1	yes	characteristic, complemented
118	#13133194	C₂²	1	1	yes	characteristic, complemented
119	#13133194	C₂²	1	1	yes	characteristic, complemented
120	#13133194	C₂²	1	1	yes	characteristic, complemented
121	#13133194	C₂²	1	1	yes	characteristic, complemented
122	#13133193	C₂²	1	1	yes	characteristic
123	#13133193	C₂²	1	1	yes	characteristic, complemented
124	#13133193	C₂²	1	1	yes	characteristic, complemented
125	#13133192	C₂²	1	1	yes	characteristic
126	#13133191	C₂²	1	1	yes	characteristic, complemented
127	#13133190	C₂²	1	1	yes	characteristic
128	#13133190	C₂²	1	1	yes	characteristic
129	#13133189	C₂²	1	1	yes	characteristic
130	#13133189	C₂²	1	1	yes	characteristic, complemented
131	#13133188	C₂²	1	1	yes	characteristic
132	#13133188	C₂²	1	1	yes	characteristic
133	#13133188	C₂²	1	1	yes	characteristic, complemented
134	#13133187	C₂²	1	1	yes	characteristic
135	#13133187	C₂²	1	1	yes	characteristic
136	#13133185	C₂²	1	1	yes	characteristic
137	#13133185	C₂²	1	1	yes	characteristic
138	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
139	#13133182	C₂²	1	1	yes	characteristic, complemented
140	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
141	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
142	#13133179	C₂²	1	1	yes	characteristic
143	#13133179	C₂²	1	1	yes	characteristic
144	#13133179	C₂²	1	1	yes	characteristic
145	#13133179	C₂²	1	1	yes	characteristic, complemented
146	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
147	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
148	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
151	#13133177	C₂²	1	1	yes	characteristic
152	#13133175	C₂²	1	1	yes	characteristic
153	#13133175	C₂²	1	1	yes	characteristic, complemented
154	#13133175	C₂²	1	1	yes	characteristic, complemented
155	#13133174	C₂²	1	1	yes	characteristic
156	#13133174	C₂²	1	1	yes	characteristic, complemented
157	#13133174	C₂²	1	1	yes	characteristic, complemented
158	#13133173	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
160	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
161	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
162	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
163	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
164	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
165	C₂×#11719921	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	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
172	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	#123×C₅₃	C₂²	1	1	yes	characteristic
177	#123×C₅₃	C₂²	1	1	yes	characteristic
178	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	#121×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₅₃	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	C₂³	1	1	yes	characteristic
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	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
207	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
208	Q₈×D₅₃	—	4	2	no	—
209	D₄×D₅₃	—	4	2	no	—
210	#11719945	—	4	2	no	—
211	#11719945	—	4	2	no	—
212	#11719945	—	4	2	no	—
213	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
214	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
215	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
216	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₅₃	—	4	2	no	—
218	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₅₃	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×C₄×D₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
234	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
235	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
236	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
237	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
238	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
239	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
240	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
241	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
242	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₄²×C₅₃	C₂³	1	1	yes	characteristic
267	C₄²×C₅₃	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	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₅₃	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	#11719921	C₂³	1	1	yes	characteristic
293	#11719921	C₂³	1	1	yes	characteristic
294	#11719921	C₂³	1	1	yes	characteristic
295	#11719921	C₂³	1	1	yes	characteristic
296	#11719921	C₂³	1	1	yes	characteristic
297	#11719921	C₂³	1	1	yes	characteristic
298	#11719921	C₂³	1	1	yes	characteristic
299	#11719921	C₂³	1	1	yes	characteristic
300	#11719921	C₂³	1	1	yes	characteristic
301	#11719921	C₂³	1	1	yes	characteristic
302	#11719921	C₂³	1	1	yes	characteristic
303	#11719921	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
309	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
310	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
315	C₄⋊Dic₅₃	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	#11719919	C₂³	1	1	yes	characteristic
331	#11719919	C₂³	1	1	yes	characteristic
332	#11719919	C₂³	1	1	yes	characteristic
333	#11719919	C₂³	1	1	yes	characteristic
334	#11719919	C₂³	1	1	yes	characteristic
335	#11719919	C₂³	1	1	yes	characteristic
336	#11719919	C₂³	1	1	yes	characteristic
337	#11719919	C₂³	1	1	yes	characteristic
338	#11719919	C₂³	1	1	yes	characteristic
339	#11719919	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	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
346	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
347	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
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	C₂²×D₅₃	—	2	2	no	—
352	C₂²×D₅₃	—	2	2	no	—
353	C₂²×D₅₃	—	2	2	no	—
354	C₂²×D₅₃	—	4	1	no	—
355	C₂²×D₅₃	—	4	1	no	—
356	C₂²×D₅₃	—	4	1	no	—
357	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
358	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
359	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
360	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
361	Q₈×C₅₃	—	4	1	no	—
362	D₄×C₅₃	—	4	1	no	—
363	D₄×C₅₃	—	4	1	no	—
364	D₄×C₅₃	—	4	1	no	—
365	C₂×C₄×C₅₃	—	4	1	no	—
366	C₂×C₄×C₅₃	—	4	1	no	—
367	C₂×C₄×C₅₃	—	4	1	no	—
368	C₂×C₄×C₅₃	—	4	1	no	—
369	C₂×C₄×C₅₃	—	4	1	no	—
370	C₂×C₄×C₅₃	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	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²⋊D₅₃	—	2	2	no	—
383	C₂²⋊D₅₃	—	2	2	no	—
384	C₂²⋊D₅₃	—	2	2	no	—
385	C₂²⋊D₅₃	—	4	1	no	—
386	C₂²⋊D₅₃	—	4	1	no	—
387	C₂²⋊D₅₃	—	4	1	no	—
388	C₂²⋊D₅₃	—	4	1	no	—
389	C₂²⋊D₅₃	—	4	1	no	—
390	C₂×Dic₅₃	—	4	1	no	—
391	C₂×Dic₅₃	—	4	1	no	—
392	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
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	D₂₁₂	—	2	2	no	—
405	D₂₁₂	—	2	2	no	—
406	D₂₁₂	—	2	2	no	—
407	D₂₁₂	—	4	1	no	—
408	C₄×D₅₃	—	2	2	no	—
409	C₄×D₅₃	—	2	2	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	C₄×D₅₃	—	4	1	no	—
422	C₄×D₅₃	—	4	1	no	—
423	C₄×D₅₃	—	4	1	no	—
424	Dic₁₀₆	—	4	1	no	—
425	Dic₁₀₆	—	4	1	no	—
426	Dic₁₀₆	—	4	1	no	—
427	Dic₁₀₆	—	4	1	no	—
428	Dic₁₀₆	—	4	1	no	—
429	Dic₁₀₆	—	4	1	no	—
430	Dic₁₀₆	—	4	1	no	—
431	Dic₁₀₆	—	4	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	—	2	1	no	—
437	C₂²×C₅₃	—	2	1	no	—
438	C₂²×C₅₃	—	2	1	no	—
439	C₂²×C₅₃	—	2	1	no	—
440	C₂²×C₅₃	—	2	1	no	—
441	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
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	—	2	1	no	—
448	C₂×D₅₃	—	2	1	no	—
449	C₂×D₅₃	—	2	1	no	—
450	C₂×D₅₃	—	2	1	no	—
451	C₂×D₅₃	—	2	1	no	—
452	C₂×D₅₃	—	4	4	no	—
453	C₂×D₅₃	—	8	2	no	—
454	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
455	C₂×D₅₃	2₋¹⁺⁴	1	2	yes	—
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	C₄×C₅₃	—	2	1	no	—
461	C₄×C₅₃	—	2	1	no	—
462	C₄×C₅₃	—	2	1	no	—
463	C₄×C₅₃	—	2	1	no	—
464	C₄×C₅₃	—	2	1	no	—
465	C₄×C₅₃	—	2	1	no	—
466	C₄×C₅₃	—	2	1	no	—
467	C₄×C₅₃	—	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	—	2	1	no	—
473	Dic₅₃	—	2	1	no	—
474	Dic₅₃	—	2	1	no	—
475	Dic₅₃	—	2	1	no	—
476	Dic₅₃	—	2	1	no	—
477	Dic₅₃	—	2	1	no	—
478	Dic₅₃	—	2	1	no	—
479	Dic₅₃	—	2	1	no	—
480	#3535	—	53	1	no	maximal, Sylow
481	C₂×C₅₃	—	4	1	no	—
482	C₂×C₅₃	—	4	1	no	—
483	C₂×C₅₃	—	4	1	no	—
484	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
485	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
486	C₂×C₅₃	#585	1	1	yes	characteristic
487	D₅₃	—	2	2	no	—
488	D₅₃	—	2	2	no	—
489	D₅₃	—	4	1	no	—
490	D₅₃	—	4	1	no	—
491	#563	—	53	1	no	—
492	#563	—	53	1	no	—
493	#562	—	53	1	no	—
494	#562	—	53	1	no	—
495	#554	—	53	1	no	—
496	#554	—	53	1	no	—
497	#552	—	53	1	no	—
498	#552	—	53	1	no	—
499	#551	—	53	1	no	—
500	#551	—	53	1	no	—
501	#551	—	53	1	no	—
502	#551	—	53	1	no	—
503	#547	—	53	1	no	—
504	#547	—	53	1	no	—
505	#546	—	53	1	no	—
506	#546	—	53	1	no	—
507	#544	—	53	1	no	—
508	#543	—	53	1	no	—
509	#542	—	53	1	no	—
510	#542	—	53	1	no	—
511	#539	—	53	1	no	—
512	#539	—	53	1	no	—
513	#539	—	53	1	no	—
514	#539	—	53	1	no	—
515	#539	D₅₃	1	1	yes	characteristic, complemented
516	#538	—	53	1	no	—
517	#536	—	53	1	no	—
518	#536	—	53	1	no	—
519	#525	—	53	1	no	—
520	C₂×#123	—	53	1	no	—
521	C₂×C₂²⋊Q₈	—	53	1	no	—
522	C₅₃	#3535	1	1	yes	characteristic, complemented, Sylow
523	C₂×#41	—	53	1	no	—
524	C₂×#41	—	53	1	no	—
525	C₂×#41	—	53	1	no	—
526	C₂²×Q₈	—	53	1	no	—
527	C₂²×D₄	—	53	1	no	—
528	C₂³×C₄	—	53	1	no	—
529	C₄⋊Q₈	—	53	1	no	—
530	C₄⋊Q₈	—	53	1	no	—
531	C₄⋊Q₈	—	53	1	no	—
532	C₄⋊Q₈	—	53	1	no	—
533	C₄⋊Q₈	—	53	1	no	—
534	C₄⋊Q₈	—	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	—	53	1	no	—
542	#126	—	53	1	no	—
543	#126	—	53	1	no	—
544	#126	—	53	1	no	—
545	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
546	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
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	#125	—	53	1	no	—
553	#125	—	53	1	no	—
554	#125	—	53	1	no	—
555	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
556	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
557	#124	—	53	1	no	—
558	#124	—	53	1	no	—
559	#124	—	53	1	no	—
560	#124	—	53	1	no	—
561	#124	—	53	1	no	—
562	#124	—	53	1	no	—
563	#124	—	53	1	no	—
564	#124	—	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	—	53	1	no	—
575	#123	—	53	1	no	—
576	#123	—	53	1	no	—
577	#123	—	53	1	no	—
578	#123	—	53	1	no	—
579	#123	—	53	1	no	—
580	#123	—	53	1	no	—
581	#123	—	53	1	no	—
582	#123	—	53	1	no	—
583	#123	—	53	1	no	—
584	#123	—	53	1	no	—
585	#123	—	53	1	no	—
586	#123	—	53	1	no	—
587	#123	—	53	1	no	—
588	#123	—	53	1	no	—
589	#123	C₂×D₅₃	1	1	yes	characteristic
590	#123	C₂×D₅₃	1	1	yes	characteristic
591	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
592	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
593	C₂²⋊Q₈	—	53	1	no	—
594	C₂²⋊Q₈	—	53	1	no	—
595	C₂²⋊Q₈	—	53	1	no	—
596	C₂²⋊Q₈	—	53	1	no	—
597	C₂²⋊Q₈	—	53	1	no	—
598	C₂²⋊Q₈	—	53	1	no	—
599	C₂²⋊Q₈	—	53	1	no	—
600	C₂²⋊Q₈	—	53	1	no	—
601	C₂²⋊Q₈	—	53	1	no	—
602	C₂²⋊Q₈	—	53	1	no	—
603	C₂²⋊Q₈	—	53	1	no	—
604	C₂²⋊Q₈	—	53	1	no	—
605	C₂²⋊Q₈	—	53	1	no	—
606	C₂²⋊Q₈	—	53	1	no	—
607	C₂²⋊Q₈	—	53	1	no	—
608	C₂²⋊Q₈	—	53	1	no	—
609	C₂²⋊Q₈	—	53	1	no	—
610	C₂²⋊Q₈	—	53	1	no	—
611	C₂²⋊Q₈	—	53	1	no	—
612	C₂²⋊Q₈	—	53	1	no	—
613	C₂²⋊Q₈	—	53	1	no	—
614	C₂²⋊Q₈	—	53	1	no	—
615	C₂²⋊Q₈	—	53	1	no	—
616	C₂²⋊Q₈	—	53	1	no	—
617	C₂²⋊Q₈	—	53	1	no	—
618	C₂²⋊Q₈	—	53	1	no	—
619	C₂²⋊Q₈	—	53	1	no	—
620	C₂²⋊Q₈	—	53	1	no	—
621	C₂²⋊Q₈	—	53	1	no	—
622	C₂²⋊Q₈	—	53	1	no	—
623	C₂²⋊Q₈	—	53	1	no	—
624	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
625	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
626	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
627	#121	—	53	1	no	—
628	#121	—	53	1	no	—
629	#121	—	53	1	no	—
630	#121	—	53	1	no	—
631	#121	—	53	1	no	—
632	#121	—	53	1	no	—
633	#121	—	53	1	no	—
634	#121	—	53	1	no	—
635	#121	—	53	1	no	—
636	#121	C₂×D₅₃	1	1	yes	characteristic
637	#120	—	53	1	no	—
638	#120	—	53	1	no	—
639	#120	—	53	1	no	—
640	#120	—	53	1	no	—
641	C₄×Q₈	—	53	1	no	—
642	C₄×Q₈	—	53	1	no	—
643	C₄×D₄	—	53	1	no	—
644	C₄×D₄	—	53	1	no	—
645	C₄×D₄	—	53	1	no	—
646	C₄×D₄	—	53	1	no	—
647	C₄×D₄	—	53	1	no	—
648	C₄×D₄	—	53	1	no	—
649	C₄×D₄	—	53	1	no	—
650	C₄×D₄	—	53	1	no	—
651	C₄×D₄	—	53	1	no	—
652	C₄×D₄	—	53	1	no	—
653	C₄×D₄	—	53	1	no	—
654	C₄×D₄	—	53	1	no	—
655	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
656	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
657	#117	—	53	1	no	—
658	#117	—	53	1	no	—
659	#117	—	53	1	no	—
660	#117	—	53	1	no	—
661	#117	—	53	1	no	—
662	#117	—	53	1	no	—
663	#117	—	53	1	no	—
664	C₂×C₄⋊C₄	—	53	1	no	—
665	C₂×C₄⋊C₄	—	53	1	no	—
666	C₂×C₄⋊C₄	—	53	1	no	—
667	C₂×C₄⋊C₄	—	53	1	no	—
668	C₂×C₄⋊C₄	—	53	1	no	—
669	C₂×C₄⋊C₄	—	53	1	no	—
670	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
671	C₂×C₂²⋊C₄	—	53	1	no	—
672	C₂×C₂²⋊C₄	—	53	1	no	—
673	C₂×C₂²⋊C₄	—	53	1	no	—
674	C₂×C₂²⋊C₄	—	53	1	no	—
675	C₂×C₂²⋊C₄	—	53	1	no	—
676	C₂×C₂²⋊C₄	—	53	1	no	—
677	C₂×C₂²⋊C₄	—	53	1	no	—
678	C₂⁴	—	53	1	no	—
679	C₂⁴	—	53	1	no	—
680	#41	—	212	2	no	—
681	#41	—	212	2	no	—
682	#41	—	212	2	no	—
683	C₂×Q₈	—	53	1	no	—
684	C₂×Q₈	—	53	1	no	—
685	C₂×Q₈	—	53	1	no	—
686	C₂×Q₈	—	53	1	no	—
687	C₂×Q₈	—	53	1	no	—
688	C₂×Q₈	—	53	1	no	—
689	C₂×Q₈	—	53	1	no	—
690	C₂×Q₈	—	53	1	no	—
691	C₂×Q₈	—	212	2	no	—
692	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
693	C₂×D₄	—	53	1	no	—
694	C₂×D₄	—	53	1	no	—
695	C₂×D₄	—	53	1	no	—
696	C₂×D₄	—	53	1	no	—
697	C₂×D₄	—	53	1	no	—
698	C₂×D₄	—	53	1	no	—
699	C₂×D₄	—	53	1	no	—
700	C₂×D₄	—	53	1	no	—
701	C₂×D₄	—	53	1	no	—
702	C₂×D₄	—	53	1	no	—
703	C₂×D₄	—	53	1	no	—
704	C₂×D₄	—	53	1	no	—
705	C₂×D₄	—	212	2	no	—
706	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
707	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
708	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
715	C₂²×C₄	—	53	1	no	—
716	C₂²×C₄	—	53	1	no	—
717	C₂²×C₄	—	53	1	no	—
718	C₂²×C₄	—	53	1	no	—
719	C₂²×C₄	—	53	1	no	—
720	C₂²×C₄	—	53	1	no	—
721	C₂²×C₄	—	53	1	no	—
722	C₂²×C₄	—	53	1	no	—
723	C₂²×C₄	—	53	1	no	—
724	C₂²×C₄	—	53	1	no	—
725	C₂²×C₄	—	53	1	no	—
726	C₂²×C₄	—	53	1	no	—
727	C₂²×C₄	—	212	2	no	—
728	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
729	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
758	C₄⋊C₄	—	53	1	no	—
759	C₄⋊C₄	—	53	1	no	—
760	C₄⋊C₄	—	53	1	no	—
761	C₄⋊C₄	—	53	1	no	—
762	C₄⋊C₄	—	53	1	no	—
763	C₄⋊C₄	—	53	1	no	—
764	C₄⋊C₄	—	53	1	no	—
765	C₄⋊C₄	—	53	1	no	—
766	C₄⋊C₄	—	53	1	no	—
767	C₄⋊C₄	—	53	1	no	—
768	C₄⋊C₄	—	53	1	no	—
769	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
798	C₂²⋊C₄	—	53	1	no	—
799	C₂²⋊C₄	—	53	1	no	—
800	C₂²⋊C₄	—	53	1	no	—
801	C₂²⋊C₄	—	53	1	no	—
802	C₂²⋊C₄	—	53	1	no	—
803	C₂²⋊C₄	—	53	1	no	—
804	C₂²⋊C₄	—	53	1	no	—
805	C₂²⋊C₄	—	53	1	no	—
806	C₂²⋊C₄	—	53	1	no	—
807	C₂²⋊C₄	—	53	1	no	—
808	C₂²⋊C₄	—	53	1	no	—
809	C₂²⋊C₄	—	53	1	no	—
810	C₂²⋊C₄	—	53	1	no	—
811	C₂²⋊C₄	—	53	1	no	—
812	C₂²⋊C₄	—	53	1	no	—
813	C₂²⋊C₄	—	53	1	no	—
814	C₂²⋊C₄	—	53	1	no	—
815	C₂²⋊C₄	—	53	1	no	—
816	C₂²⋊C₄	—	53	1	no	—
817	C₂²⋊C₄	—	53	1	no	—
818	C₂²⋊C₄	—	53	1	no	—
819	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
829	C₄²	—	53	1	no	—
830	C₄²	—	53	1	no	—
831	C₄²	—	53	1	no	—
832	C₄²	—	53	1	no	—
833	C₄²	—	53	1	no	—
834	C₄²	—	53	1	no	—
835	C₄²	—	53	1	no	—
836	C₄²	—	53	1	no	—
837	C₄²	C₂²×D₅₃	1	1	yes	characteristic
838	C₄²	C₂²×D₅₃	1	1	yes	characteristic
839	C₂³	—	53	1	no	—
840	C₂³	—	53	1	no	—
841	C₂³	—	53	1	no	—
842	C₂³	—	53	1	no	—
843	C₂³	—	106	2	no	—
844	C₂³	—	106	2	no	—
845	C₂³	—	106	2	no	—
846	C₂³	—	212	1	no	—
847	C₂³	—	212	1	no	—
848	C₂³	—	212	1	no	—
849	C₂³	C₂³×D₅₃	1	1	yes	characteristic
850	C₂³	C₂³×D₅₃	1	1	yes	characteristic
851	C₂³	C₂³×D₅₃	1	1	yes	characteristic
852	Q₈	—	4	1	no	—
853	Q₈	—	212	1	no	—
854	Q₈	—	212	1	no	—
855	Q₈	—	212	1	no	—
856	Q₈	—	212	1	no	—
857	Q₈	—	212	1	no	—
858	Q₈	—	212	1	no	—
859	Q₈	—	212	1	no	—
860	Q₈	—	212	1	no	—
861	D₄	—	4	1	no	—
862	D₄	—	4	1	no	—
863	D₄	—	4	1	no	—
864	D₄	—	106	2	no	—
865	D₄	—	106	2	no	—
866	D₄	—	106	2	no	—
867	D₄	—	106	2	no	—
868	D₄	—	106	2	no	—
869	D₄	—	106	2	no	—
870	D₄	—	212	1	no	—
871	D₄	—	212	1	no	—
872	D₄	—	212	1	no	—
873	D₄	—	212	1	no	—
874	D₄	—	212	1	no	—
875	D₄	—	212	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	53	1	no	—
882	C₂×C₄	—	53	1	no	—
883	C₂×C₄	—	53	1	no	—
884	C₂×C₄	—	53	1	no	—
885	C₂×C₄	—	53	1	no	—
886	C₂×C₄	—	53	1	no	—
887	C₂×C₄	—	53	1	no	—
888	C₂×C₄	—	53	1	no	—
889	C₂×C₄	—	53	1	no	—
890	C₂×C₄	—	53	1	no	—
891	C₂×C₄	—	53	1	no	—
892	C₂×C₄	—	53	1	no	—
893	C₂×C₄	—	106	2	no	—
894	C₂×C₄	—	106	2	no	—
895	C₂×C₄	—	106	2	no	—
896	C₂×C₄	—	106	2	no	—
897	C₂×C₄	—	106	2	no	—
898	C₂×C₄	—	212	1	no	—
899	C₂×C₄	—	212	1	no	—
900	C₂×C₄	—	212	1	no	—
901	C₂×C₄	—	212	1	no	—
902	C₂×C₄	—	212	1	no	—
903	C₂×C₄	—	212	1	no	—
904	C₂×C₄	—	212	1	no	—
905	C₂×C₄	—	212	1	no	—
906	C₂×C₄	—	212	1	no	—
907	C₂×C₄	—	212	1	no	—
908	C₂×C₄	—	212	1	no	—
909	C₂×C₄	—	212	1	no	—
910	C₂×C₄	—	212	1	no	—
911	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
922	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	53	2	no	—
933	C₂²	—	53	2	no	—
934	C₂²	—	106	1	no	—
935	C₂²	—	106	1	no	—
936	C₂²	—	106	1	no	—
937	C₂²	—	106	1	no	—
938	C₂²	—	106	1	no	—
939	C₂²	—	106	1	no	—
940	C₂²	—	106	1	no	—
941	C₂²	—	106	1	no	—
942	C₂²	—	106	1	no	—
943	C₂²	—	106	1	no	—
944	C₂²	—	424	2	no	—
945	C₂²	—	212	4	no	—
946	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	106	1	no	—
960	C₄	—	106	1	no	—
961	C₄	—	106	1	no	—
962	C₄	—	106	1	no	—
963	C₄	—	106	1	no	—
964	C₄	—	106	1	no	—
965	C₄	—	106	1	no	—
966	C₄	—	106	1	no	—
967	C₄	—	106	1	no	—
968	C₄	—	106	1	no	—
969	C₄	—	106	1	no	—
970	C₄	—	106	1	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	106	2	no	—
975	C₂	—	106	2	no	—
976	C₂	—	212	1	no	—
977	C₂	—	212	1	no	—
978	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
979	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
980	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#539	C₂
hypercenter	#539	D₅₃
hypocenter	C₅₃	#3535
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #16811376	C₂	semidirect
2. #16811375	C₂	semidirect
3. #16811370	C₂	semidirect
4. #16811368	C₂	semidirect
5. #16811329	C₂	semidirect
6. #16811328	C₂	semidirect
7. #16811309	C₂	semidirect
8. #16811305	C₂	semidirect
9. #16811302	C₂	semidirect
10. #16811301	C₂	semidirect
11. #16811298	C₂	semidirect
12. #16811298	C₂	semidirect
13. #16811278	C₂	semidirect
14. #16811274	C₂	semidirect
15. #16811270	C₂	semidirect
16. #16811265	C₂	semidirect
17. #16811253	C₂	semidirect
18. #16811248	C₂	semidirect
19. #16811241	C₂	semidirect
20. #16811238	C₂	semidirect
21. #16811221	C₂	semidirect
22. #16811219	C₂	semidirect
23. #16811219	C₂	semidirect
24. #16811216	C₂	semidirect
25. #16811209	C₂	semidirect
26. #16811196	C₂	semidirect
27. #16811196	C₂	semidirect
28. #16811132	C₂	semidirect
29. #123×D₅₃	C₂	semidirect
30. C₂²⋊Q₈×D₅₃	C₂	semidirect
31. C₅₃×#539	C₂	semidirect
34. C₂×#11719945	C₂²	semidirect
35. C₂×Q₈×D₅₃	C₂²	semidirect
38. #13133217	C₂²	semidirect
39. #13133216	C₂²	semidirect
40. #13133216	C₂²	semidirect
41. #13133216	C₂²	semidirect
42. #13133216	C₂²	semidirect
43. #13133216	C₂²	semidirect
44. #13133212	C₂²	semidirect
45. #13133212	C₂²	semidirect
46. #13133212	C₂²	semidirect
47. #13133211	C₂²	semidirect
48. #13133210	C₂²	semidirect
49. #13133210	C₂²	semidirect
50. #13133210	C₂²	semidirect
51. #13133210	C₂²	semidirect
52. #13133210	C₂²	semidirect
53. #13133210	C₂²	semidirect
54. #13133208	C₂²	semidirect
55. #13133208	C₂²	semidirect
56. #13133207	C₂²	semidirect
57. #13133207	C₂²	semidirect
58. #13133207	C₂²	semidirect
59. #13133207	C₂²	semidirect
60. #13133207	C₂²	semidirect
61. #13133207	C₂²	semidirect
63. #13133204	C₂²	semidirect
65. #13133203	C₂²	semidirect
66. #13133203	C₂²	semidirect
67. #13133203	C₂²	semidirect
68. #13133203	C₂²	semidirect
69. #13133203	C₂²	semidirect
74. #13133202	C₂²	semidirect
75. #13133202	C₂²	semidirect
76. #13133202	C₂²	semidirect
77. #13133202	C₂²	semidirect
80. #13133200	C₂²	semidirect
81. #13133200	C₂²	semidirect
87. #13133199	C₂²	semidirect
88. #13133199	C₂²	semidirect
89. #13133199	C₂²	semidirect
90. #13133199	C₂²	semidirect
91. #13133199	C₂²	semidirect
93. #13133198	C₂²	semidirect
97. #13133197	C₂²	semidirect
98. #13133197	C₂²	semidirect
99. #13133197	C₂²	semidirect
100. #13133196	C₂²	semidirect
101. #13133196	C₂²	semidirect
102. #13133196	C₂²	semidirect
103. #13133196	C₂²	semidirect
104. #13133196	C₂²	semidirect
105. #13133196	C₂²	semidirect
111. #13133195	C₂²	semidirect
112. #13133195	C₂²	semidirect
113. #13133195	C₂²	semidirect
114. #13133195	C₂²	semidirect
115. #13133195	C₂²	semidirect
116. #13133195	C₂²	semidirect
117. #13133194	C₂²	semidirect
118. #13133194	C₂²	semidirect
119. #13133194	C₂²	semidirect
120. #13133194	C₂²	semidirect
121. #13133194	C₂²	semidirect
123. #13133193	C₂²	semidirect
124. #13133193	C₂²	semidirect
126. #13133191	C₂²	semidirect
130. #13133189	C₂²	semidirect
133. #13133188	C₂²	semidirect
138. C₄×Dic₁₀₆	C₂²	semidirect
139. #13133182	C₂²	semidirect
141. C₄×D₂₁₂	C₂²	semidirect
145. #13133179	C₂²	semidirect
149. C₄×C₂²⋊D₅₃	C₂²	semidirect
150. C₄×C₂²⋊D₅₃	C₂²	semidirect
153. #13133175	C₂²	semidirect
154. #13133175	C₂²	semidirect
156. #13133174	C₂²	semidirect
157. #13133174	C₂²	semidirect
158. #13133173	C₂²	semidirect
161. C₄⋊C₄×D₅₃	C₂²	semidirect
162. C₄⋊C₄×D₅₃	C₂²	semidirect
163. C₄⋊C₄×D₅₃	C₂²	semidirect
164. C₄⋊C₄×D₅₃	C₂²	semidirect
172. #126×C₅₃	C₂²	semidirect
173. #126×C₅₃	C₂²	semidirect
174. #125×C₅₃	C₂²	semidirect
175. #125×C₅₃	C₂²	semidirect
178. #123×C₅₃	C₂²	semidirect
179. #123×C₅₃	C₂²	semidirect
180. C₂²⋊Q₈×C₅₃	C₂²	semidirect
181. C₂²⋊Q₈×C₅₃	C₂²	semidirect
182. C₂²⋊Q₈×C₅₃	C₂²	semidirect
184. C₄×D₄×C₅₃	C₂²	semidirect
185. C₄×D₄×C₅₃	C₂²	semidirect
186. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
515. #539	D₅₃	semidirect
522. C₅₃	#3535	semidirect
545. #126	C₂×D₅₃	semidirect
546. #126	C₂×D₅₃	semidirect
555. #125	C₂×D₅₃	semidirect
556. #125	C₂×D₅₃	semidirect
591. #123	C₂×D₅₃	semidirect
592. #123	C₂×D₅₃	semidirect
624. C₂²⋊Q₈	C₂×D₅₃	semidirect
625. C₂²⋊Q₈	C₂×D₅₃	semidirect
626. C₂²⋊Q₈	C₂×D₅₃	semidirect
655. C₄×D₄	C₂×D₅₃	semidirect
656. C₄×D₄	C₂×D₅₃	semidirect
670. C₂×C₄⋊C₄	C₂×D₅₃	semidirect