Subgroups — #20288753

Order 6784.

1124 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811340	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811332	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811327	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811309	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811306	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811299	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811297	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811296	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811286	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811282	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811281	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811271	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	#16811239	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811237	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811222	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811217	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811216	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811214	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811176	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811150	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811132	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811129	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#13133194	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	#16811103	C₂	1	1	yes	maximal, characteristic, complemented
29	#16811102	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#13133177	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×#11719945	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11719947	C₂²	1	1	yes	characteristic
35	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
36	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
37	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
39	C₂³×Dic₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
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	#13133215	C₂²	1	1	yes	characteristic, complemented
45	#13133212	C₂²	1	1	yes	characteristic, complemented
46	#13133212	C₂²	1	1	yes	characteristic, complemented
47	#13133212	C₂²	1	1	yes	characteristic, complemented
48	#13133212	C₂²	1	1	yes	characteristic, complemented
49	#13133211	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	#13133209	C₂²	1	1	yes	characteristic, complemented
54	#13133208	C₂²	1	1	yes	characteristic, complemented
55	#13133208	C₂²	1	1	yes	characteristic, complemented
56	#13133208	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	#13133205	C₂²	1	1	yes	characteristic, complemented
61	#13133203	C₂²	1	1	yes	characteristic
62	#13133203	C₂²	1	1	yes	characteristic
63	#13133203	C₂²	1	1	yes	characteristic, complemented
64	#13133203	C₂²	1	1	yes	characteristic, complemented
65	#13133203	C₂²	1	1	yes	characteristic, complemented
66	#13133202	C₂²	1	1	yes	characteristic, complemented
67	#13133202	C₂²	1	1	yes	characteristic, complemented
68	#13133202	C₂²	1	1	yes	characteristic, complemented
69	#13133201	C₂²	1	1	yes	characteristic
70	#13133201	C₂²	1	1	yes	characteristic, complemented
71	#13133201	C₂²	1	1	yes	characteristic, complemented
72	#13133201	C₂²	1	1	yes	characteristic, complemented
73	#13133200	C₂²	1	1	yes	characteristic
74	#13133200	C₂²	1	1	yes	characteristic
75	#13133199	C₂²	1	1	yes	characteristic
76	#13133199	C₂²	1	1	yes	characteristic
77	#13133199	C₂²	1	1	yes	characteristic, complemented
78	#13133199	C₂²	1	1	yes	characteristic, complemented
79	#13133199	C₂²	1	1	yes	characteristic, complemented
80	#13133198	C₂²	1	1	yes	characteristic, complemented
81	#13133197	C₂²	1	1	yes	characteristic, complemented
82	#13133197	C₂²	1	1	yes	characteristic, complemented
83	#13133196	C₂²	1	1	yes	characteristic
84	#13133196	C₂²	1	1	yes	characteristic, complemented
85	#13133195	C₂²	1	1	yes	characteristic, complemented
86	#13133195	C₂²	1	1	yes	characteristic, complemented
87	#13133195	C₂²	1	1	yes	characteristic, complemented
88	#13133195	C₂²	1	1	yes	characteristic, complemented
89	#13133195	C₂²	1	1	yes	characteristic, complemented
90	#13133195	C₂²	1	1	yes	characteristic, complemented
91	#13133194	C₂²	1	1	yes	characteristic
92	#13133194	C₂²	1	1	yes	characteristic
93	#13133194	C₂²	1	1	yes	characteristic
94	#13133194	C₂²	1	1	yes	characteristic
95	#13133194	C₂²	1	1	yes	characteristic
96	#13133194	C₂²	1	1	yes	characteristic
97	#13133194	C₂²	1	1	yes	characteristic
98	#13133194	C₂²	1	1	yes	characteristic, complemented
99	#13133194	C₂²	1	1	yes	characteristic, complemented
100	#13133194	C₂²	1	1	yes	characteristic, complemented
101	#13133194	C₂²	1	1	yes	characteristic, complemented
102	#13133194	C₂²	1	1	yes	characteristic, complemented
103	#13133194	C₂²	1	1	yes	characteristic, complemented
104	#13133194	C₂²	1	1	yes	characteristic, complemented
105	#13133194	C₂²	1	1	yes	characteristic, complemented
106	#13133193	C₂²	1	1	yes	characteristic, complemented
107	#13133193	C₂²	1	1	yes	characteristic, complemented
108	#13133191	C₂²	1	1	yes	characteristic
109	#13133190	C₂²	1	1	yes	characteristic
110	#13133190	C₂²	1	1	yes	characteristic
111	#13133190	C₂²	1	1	yes	characteristic, complemented
112	#13133189	C₂²	1	1	yes	characteristic
113	#13133189	C₂²	1	1	yes	characteristic
114	#13133189	C₂²	1	1	yes	characteristic
115	#13133189	C₂²	1	1	yes	characteristic, complemented
116	#13133188	C₂²	1	1	yes	characteristic
117	#13133187	C₂²	1	1	yes	characteristic
118	#13133186	C₂²	1	1	yes	characteristic
119	#13133185	C₂²	1	1	yes	characteristic
120	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
124	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
125	#13133182	C₂²	1	1	yes	characteristic, complemented
126	#13133182	C₂²	1	1	yes	characteristic, complemented
127	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
129	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
130	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
131	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
133	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
134	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
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
140	#13133177	C₂²	1	1	yes	characteristic
141	#13133177	C₂²	1	1	yes	characteristic
142	#13133177	C₂²	1	1	yes	characteristic
143	#13133177	C₂²	1	1	yes	characteristic
144	#13133177	C₂²	1	1	yes	characteristic
145	#13133177	C₂²	1	1	yes	characteristic
146	#13133177	C₂²	1	1	yes	characteristic, complemented
147	#13133177	C₂²	1	1	yes	characteristic, complemented
148	#13133177	C₂²	1	1	yes	characteristic, complemented
149	#13133177	C₂²	1	1	yes	characteristic, complemented
150	#13133176	C₂²	1	1	yes	characteristic
151	#13133175	C₂²	1	1	yes	characteristic, complemented
152	#13133175	C₂²	1	1	yes	characteristic, complemented
153	#13133174	C₂²	1	1	yes	characteristic, complemented
154	#13133174	C₂²	1	1	yes	characteristic, complemented
155	#13133173	C₂²	1	1	yes	characteristic, complemented
156	#13133173	C₂²	1	1	yes	characteristic, complemented
157	#13133173	C₂²	1	1	yes	characteristic, complemented
158	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
159	C₂×#11719919	C₂²	1	1	yes	characteristic
160	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
161	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
162	C₂×#11719919	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	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
166	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
167	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
168	C₂×#11719921	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
171	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
172	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
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
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
182	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	#117×C₅₃	C₂²	1	1	yes	characteristic
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	—	4	2	no	—
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	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
221	Q₈×D₅₃	—	4	2	no	—
222	#11719947	—	2	4	no	—
223	#11719947	—	4	2	no	—
224	#11719945	—	2	4	no	—
225	#11719945	—	4	2	no	—
226	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
227	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₅₃	—	4	2	no	—
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×C₄×D₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
240	C₂×Dic₁₀₆	—	4	2	no	—
241	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
242	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
243	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
244	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
245	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
246	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
247	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
248	C₂×Dic₁₀₆	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	C₄⋊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	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₄²×C₅₃	C₂³	1	1	yes	characteristic
272	C₄²×C₅₃	C₂³	1	1	yes	characteristic
273	C₄²×C₅₃	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	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₅₃	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	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₅₃	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	#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	#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	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
349	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
350	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
351	C₂³×C₅₃	—	2	2	no	—
352	C₂³×C₅₃	—	2	2	no	—
353	C₂³×C₅₃	—	4	1	no	—
354	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂²×D₅₃	—	2	2	no	—
359	C₂²×D₅₃	—	2	2	no	—
360	C₂²×D₅₃	—	4	1	no	—
361	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
362	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
363	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
364	Q₈×C₅₃	—	4	1	no	—
365	D₄×C₅₃	—	2	2	no	—
366	D₄×C₅₃	—	2	2	no	—
367	D₄×C₅₃	—	4	1	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	4	1	no	—
371	C₂×C₄×C₅₃	—	4	1	no	—
372	C₂×C₄×C₅₃	—	4	1	no	—
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	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²⋊D₅₃	—	2	2	no	—
385	C₂²⋊D₅₃	—	2	2	no	—
386	C₂²⋊D₅₃	—	2	2	no	—
387	C₂²⋊D₅₃	—	2	2	no	—
388	C₂²⋊D₅₃	—	2	2	no	—
389	C₂²⋊D₅₃	—	2	2	no	—
390	C₂²⋊D₅₃	—	2	2	no	—
391	C₂²⋊D₅₃	—	4	1	no	—
392	C₂²⋊D₅₃	—	4	1	no	—
393	C₂²⋊D₅₃	#41	1	4	yes	complemented
394	C₂×Dic₅₃	—	2	2	no	—
395	C₂×Dic₅₃	—	2	2	no	—
396	C₂×Dic₅₃	—	2	2	no	—
397	C₂×Dic₅₃	—	2	2	no	—
398	C₂×Dic₅₃	—	2	2	no	—
399	C₂×Dic₅₃	—	2	2	no	—
400	C₂×Dic₅₃	—	4	1	no	—
401	C₂×Dic₅₃	—	4	1	no	—
402	C₂×Dic₅₃	—	4	1	no	—
403	C₂×Dic₅₃	—	4	1	no	—
404	C₂×Dic₅₃	—	4	1	no	—
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	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
417	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
418	D₂₁₂	—	2	2	no	—
419	D₂₁₂	—	4	1	no	—
420	C₄×D₅₃	—	2	2	no	—
421	C₄×D₅₃	—	2	2	no	—
422	C₄×D₅₃	—	2	2	no	—
423	C₄×D₅₃	—	2	2	no	—
424	C₄×D₅₃	—	2	2	no	—
425	C₄×D₅₃	—	4	1	no	—
426	C₄×D₅₃	—	4	1	no	—
427	C₄×D₅₃	—	4	1	no	—
428	C₄×D₅₃	—	4	1	no	—
429	C₄×D₅₃	—	4	1	no	—
430	C₄×D₅₃	—	4	1	no	—
431	Dic₁₀₆	—	2	2	no	—
432	Dic₁₀₆	—	2	2	no	—
433	Dic₁₀₆	—	2	2	no	—
434	Dic₁₀₆	—	2	2	no	—
435	Dic₁₀₆	—	2	2	no	—
436	Dic₁₀₆	—	4	1	no	—
437	Dic₁₀₆	—	4	1	no	—
438	Dic₁₀₆	—	4	1	no	—
439	C₂²×C₅₃	—	2	1	no	—
440	C₂²×C₅₃	—	2	1	no	—
441	C₂²×C₅₃	—	2	1	no	—
442	C₂²×C₅₃	—	2	1	no	—
443	C₂²×C₅₃	—	2	1	no	—
444	C₂²×C₅₃	—	2	1	no	—
445	C₂²×C₅₃	—	2	1	no	—
446	C₂²×C₅₃	—	2	1	no	—
447	C₂²×C₅₃	—	2	1	no	—
448	C₂²×C₅₃	—	2	1	no	—
449	C₂²×C₅₃	—	4	4	no	—
450	C₂²×C₅₃	C₂×#41	1	2	yes	—
451	C₂²×C₅₃	2₋¹⁺⁴	1	2	yes	—
452	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
453	C₂×D₅₃	—	2	1	no	—
454	C₂×D₅₃	—	2	1	no	—
455	C₂×D₅₃	—	2	1	no	—
456	C₂×D₅₃	—	2	1	no	—
457	C₂×D₅₃	—	2	1	no	—
458	C₂×D₅₃	—	2	1	no	—
459	C₂×D₅₃	—	2	1	no	—
460	C₂×D₅₃	—	2	1	no	—
461	C₂×D₅₃	—	4	4	no	—
462	C₂×D₅₃	C₂×#41	1	2	yes	—
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	C₄×C₅₃	—	2	1	no	—
469	C₄×C₅₃	—	2	1	no	—
470	C₄×C₅₃	—	2	1	no	—
471	C₄×C₅₃	—	2	1	no	—
472	C₄×C₅₃	—	2	1	no	—
473	C₄×C₅₃	—	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	Dic₅₃	—	2	1	no	—
481	Dic₅₃	—	2	1	no	—
482	Dic₅₃	—	2	1	no	—
483	Dic₅₃	—	2	1	no	—
484	Dic₅₃	—	2	1	no	—
485	Dic₅₃	C₂×#41	1	2	yes	—
486	Dic₅₃	H(5,𝔽₂)	1	2	yes	—
487	#3520	—	53	1	no	maximal, Sylow
488	C₂×C₅₃	—	2	2	no	—
489	C₂×C₅₃	—	2	2	no	—
490	C₂×C₅₃	—	4	1	no	—
491	C₂×C₅₃	—	4	1	no	—
492	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
493	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
495	D₅₃	—	2	2	no	—
496	D₅₃	—	4	1	no	—
497	D₅₃	—	4	1	no	—
498	#556	—	53	1	no	—
499	#554	—	53	1	no	—
500	#554	—	53	1	no	—
501	#552	—	53	1	no	—
502	#552	—	53	1	no	—
503	#551	—	53	1	no	—
504	#551	—	53	1	no	—
505	#551	—	53	1	no	—
506	#551	D₅₃	1	1	yes	characteristic, complemented
507	D₄×Q₈	—	53	1	no	—
508	#548	—	53	1	no	—
509	#548	—	53	1	no	—
510	#547	—	53	1	no	—
511	#547	—	53	1	no	—
512	#546	—	53	1	no	—
513	#546	—	53	1	no	—
514	#542	—	53	1	no	—
515	#542	—	53	1	no	—
516	#539	—	53	1	no	—
517	#539	—	53	1	no	—
518	#539	—	53	1	no	—
519	#539	—	53	1	no	—
520	#533	—	53	1	no	—
521	#529	—	53	1	no	—
522	#525	—	53	1	no	—
523	#525	—	53	1	no	—
524	C₂×C₂²⋊Q₈	—	53	1	no	—
525	C₂×C₂²⋊Q₈	—	53	1	no	—
526	#520	—	53	1	no	—
527	#520	—	53	1	no	—
528	C₂×C₄×D₄	—	53	1	no	—
529	C₅₃	#3520	1	1	yes	characteristic, complemented, Sylow
530	C₂×#41	—	53	1	no	—
531	C₂×#41	—	53	1	no	—
532	C₂×#41	—	53	1	no	—
533	C₂×#41	—	53	1	no	—
534	C₂²×Q₈	—	53	1	no	—
535	C₂²×Q₈	—	53	1	no	—
536	C₂²×D₄	—	53	1	no	—
537	C₂³×C₄	—	53	1	no	—
538	C₂³×C₄	—	53	1	no	—
539	C₄⋊Q₈	—	53	1	no	—
540	C₄⋊Q₈	—	53	1	no	—
541	C₄⋊Q₈	—	53	1	no	—
542	C₄⋊Q₈	—	53	1	no	—
543	#126	—	53	1	no	—
544	#126	—	53	1	no	—
545	#126	—	53	1	no	—
546	#126	—	53	1	no	—
547	#126	—	53	1	no	—
548	#126	—	53	1	no	—
549	#126	—	53	1	no	—
550	#126	—	53	1	no	—
551	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
552	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
553	#125	—	53	1	no	—
554	#125	—	53	1	no	—
555	#125	—	53	1	no	—
556	#125	—	53	1	no	—
557	#125	—	53	1	no	—
558	#125	—	53	1	no	—
559	#125	—	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	#124	—	53	1	no	—
566	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
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	C₂×D₅₃	1	1	yes	characteristic
583	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
584	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
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	—	53	1	no	—
591	C₂²⋊Q₈	—	53	1	no	—
592	C₂²⋊Q₈	—	53	1	no	—
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	C₂×D₅₃	1	1	yes	characteristic
613	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
614	#121	—	53	1	no	—
615	#121	—	53	1	no	—
616	#121	—	53	1	no	—
617	#121	—	53	1	no	—
618	#121	—	53	1	no	—
619	#121	—	53	1	no	—
620	#121	—	53	1	no	—
621	#121	—	53	1	no	—
622	#121	—	53	1	no	—
623	#120	—	53	1	no	—
624	#120	—	53	1	no	—
625	#120	—	53	1	no	—
626	#120	C₂×D₅₃	1	1	yes	characteristic
627	C₄×Q₈	—	53	1	no	—
628	C₄×Q₈	—	53	1	no	—
629	C₄×Q₈	—	53	1	no	—
630	C₄×Q₈	—	53	1	no	—
631	C₄×Q₈	—	53	1	no	—
632	C₄×Q₈	—	53	1	no	—
633	C₄×Q₈	—	53	1	no	—
634	C₄×D₄	—	53	1	no	—
635	C₄×D₄	—	53	1	no	—
636	C₄×D₄	—	53	1	no	—
637	C₄×D₄	—	53	1	no	—
638	C₄×D₄	—	53	1	no	—
639	C₄×D₄	—	53	1	no	—
640	C₄×D₄	—	53	1	no	—
641	C₄×D₄	—	53	1	no	—
642	C₄×D₄	—	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	—	53	1	no	—
656	C₄×D₄	—	53	1	no	—
657	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
658	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
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	#117	—	53	1	no	—
665	#117	—	53	1	no	—
666	#117	—	53	1	no	—
667	#117	C₂×D₅₃	1	1	yes	characteristic
668	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
669	C₂×C₄⋊C₄	—	53	1	no	—
670	C₂×C₄⋊C₄	—	53	1	no	—
671	C₂×C₄⋊C₄	—	53	1	no	—
672	C₂×C₄⋊C₄	—	53	1	no	—
673	C₂×C₄⋊C₄	—	53	1	no	—
674	C₂×C₄⋊C₄	—	53	1	no	—
675	C₂×C₄⋊C₄	—	53	1	no	—
676	C₂×C₄⋊C₄	—	53	1	no	—
677	C₂×C₄⋊C₄	—	53	1	no	—
678	C₂×C₂²⋊C₄	—	53	1	no	—
679	C₂×C₂²⋊C₄	—	53	1	no	—
680	C₂×C₂²⋊C₄	—	53	1	no	—
681	C₂×C₂²⋊C₄	—	53	1	no	—
682	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
684	C₂×C₄²	—	53	1	no	—
685	C₂⁴	—	53	1	no	—
686	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
687	#41	—	106	4	no	—
688	#41	—	106	4	no	—
689	#41	—	212	2	no	—
690	#41	—	212	2	no	—
691	C₂×Q₈	—	53	1	no	—
692	C₂×Q₈	—	53	1	no	—
693	C₂×Q₈	—	53	1	no	—
694	C₂×Q₈	—	53	1	no	—
695	C₂×Q₈	—	53	1	no	—
696	C₂×Q₈	—	53	1	no	—
697	C₂×Q₈	—	53	1	no	—
698	C₂×Q₈	—	53	1	no	—
699	C₂×Q₈	—	212	2	no	—
700	C₂×Q₈	—	212	2	no	—
701	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
702	C₂×D₄	—	53	1	no	—
703	C₂×D₄	—	53	1	no	—
704	C₂×D₄	—	53	1	no	—
705	C₂×D₄	—	53	1	no	—
706	C₂×D₄	—	53	1	no	—
707	C₂×D₄	—	53	1	no	—
708	C₂×D₄	—	53	1	no	—
709	C₂×D₄	—	53	1	no	—
710	C₂×D₄	—	53	1	no	—
711	C₂×D₄	—	53	1	no	—
712	C₂×D₄	—	53	1	no	—
713	C₂×D₄	—	53	1	no	—
714	C₂×D₄	—	106	4	no	—
715	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
716	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
717	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
728	C₂²×C₄	—	53	1	no	—
729	C₂²×C₄	—	53	1	no	—
730	C₂²×C₄	—	53	1	no	—
731	C₂²×C₄	—	53	1	no	—
732	C₂²×C₄	—	53	1	no	—
733	C₂²×C₄	—	53	1	no	—
734	C₂²×C₄	—	53	1	no	—
735	C₂²×C₄	—	53	1	no	—
736	C₂²×C₄	—	53	1	no	—
737	C₂²×C₄	—	53	1	no	—
738	C₂²×C₄	—	53	1	no	—
739	C₂²×C₄	—	53	1	no	—
740	C₂²×C₄	—	212	2	no	—
741	C₂²×C₄	—	212	2	no	—
742	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
743	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
744	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
745	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
746	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
770	C₄⋊C₄	—	53	1	no	—
771	C₄⋊C₄	—	53	1	no	—
772	C₄⋊C₄	—	53	1	no	—
773	C₄⋊C₄	—	53	1	no	—
774	C₄⋊C₄	—	53	1	no	—
775	C₄⋊C₄	—	53	1	no	—
776	C₄⋊C₄	—	53	1	no	—
777	C₄⋊C₄	—	53	1	no	—
778	C₄⋊C₄	—	53	1	no	—
779	C₄⋊C₄	—	53	1	no	—
780	C₄⋊C₄	—	53	1	no	—
781	C₄⋊C₄	—	53	1	no	—
782	C₄⋊C₄	—	53	1	no	—
783	C₄⋊C₄	—	53	1	no	—
784	C₄⋊C₄	—	53	1	no	—
785	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
786	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
820	C₂²⋊C₄	—	53	1	no	—
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	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
830	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
832	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
834	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
835	C₄²	—	53	1	no	—
836	C₄²	—	53	1	no	—
837	C₄²	—	53	1	no	—
838	C₄²	—	53	1	no	—
839	C₄²	—	53	1	no	—
840	C₄²	—	53	1	no	—
841	C₄²	—	53	1	no	—
842	C₄²	—	53	1	no	—
843	C₄²	—	53	1	no	—
844	C₄²	—	53	1	no	—
845	C₄²	—	53	1	no	—
846	C₄²	C₂²×D₅₃	1	1	yes	characteristic
847	C₄²	C₂²×D₅₃	1	1	yes	characteristic
848	C₄²	C₂²×D₅₃	1	1	yes	characteristic
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	53	1	no	—
853	C₂³	—	53	1	no	—
854	C₂³	—	53	1	no	—
855	C₂³	—	106	2	no	—
856	C₂³	—	106	2	no	—
857	C₂³	—	212	1	no	—
858	C₂³	C₂³×D₅₃	1	1	yes	characteristic
859	C₂³	C₂³×D₅₃	1	1	yes	characteristic
860	C₂³	C₂³×D₅₃	1	1	yes	characteristic
861	C₂³	C₂³×D₅₃	1	1	yes	characteristic
862	Q₈	—	4	1	no	—
863	Q₈	—	106	2	no	—
864	Q₈	—	106	2	no	—
865	Q₈	—	106	2	no	—
866	Q₈	—	106	2	no	—
867	Q₈	—	106	2	no	—
868	Q₈	—	212	1	no	—
869	Q₈	—	212	1	no	—
870	Q₈	—	212	1	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	4	1	no	—
874	D₄	—	53	4	no	—
875	D₄	—	106	2	no	—
876	D₄	—	106	2	no	—
877	D₄	—	106	2	no	—
878	D₄	—	106	2	no	—
879	D₄	—	106	2	no	—
880	D₄	—	106	2	no	—
881	D₄	—	106	2	no	—
882	D₄	—	106	2	no	—
883	D₄	—	212	1	no	—
884	D₄	—	212	1	no	—
885	D₄	—	212	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	53	1	no	—
892	C₂×C₄	—	53	1	no	—
893	C₂×C₄	—	53	1	no	—
894	C₂×C₄	—	53	1	no	—
895	C₂×C₄	—	53	1	no	—
896	C₂×C₄	—	53	1	no	—
897	C₂×C₄	—	53	1	no	—
898	C₂×C₄	—	53	1	no	—
899	C₂×C₄	—	53	1	no	—
900	C₂×C₄	—	53	1	no	—
901	C₂×C₄	—	53	1	no	—
902	C₂×C₄	—	53	1	no	—
903	C₂×C₄	—	53	1	no	—
904	C₂×C₄	—	106	2	no	—
905	C₂×C₄	—	106	2	no	—
906	C₂×C₄	—	106	2	no	—
907	C₂×C₄	—	106	2	no	—
908	C₂×C₄	—	106	2	no	—
909	C₂×C₄	—	106	2	no	—
910	C₂×C₄	—	106	2	no	—
911	C₂×C₄	—	106	2	no	—
912	C₂×C₄	—	106	2	no	—
913	C₂×C₄	—	106	2	no	—
914	C₂×C₄	—	106	2	no	—
915	C₂×C₄	—	212	1	no	—
916	C₂×C₄	—	212	1	no	—
917	C₂×C₄	—	212	1	no	—
918	C₂×C₄	—	212	1	no	—
919	C₂×C₄	—	212	1	no	—
920	C₂×C₄	—	212	1	no	—
921	C₂×C₄	—	212	1	no	—
922	C₂×C₄	—	212	1	no	—
923	C₂×C₄	—	212	1	no	—
924	C₂×C₄	—	212	1	no	—
925	C₂×C₄	—	212	1	no	—
926	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
927	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
928	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
929	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
930	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
931	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
932	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
933	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
934	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
935	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
936	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	4	4	no	—
948	C₂²	—	53	2	no	—
949	C₂²	—	106	1	no	—
950	C₂²	—	106	1	no	—
951	C₂²	—	106	1	no	—
952	C₂²	—	106	1	no	—
953	C₂²	—	106	1	no	—
954	C₂²	—	106	1	no	—
955	C₂²	—	106	1	no	—
956	C₂²	—	106	1	no	—
957	C₂²	—	212	4	no	—
958	C₂²	#41×D₅₃	1	2	yes	—
959	C₂²	#13133264	1	2	yes	—
960	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	53	2	no	—
973	C₄	—	53	2	no	—
974	C₄	—	106	1	no	—
975	C₄	—	106	1	no	—
976	C₄	—	106	1	no	—
977	C₄	—	106	1	no	—
978	C₄	—	106	1	no	—
979	C₄	—	106	1	no	—
980	C₄	—	106	1	no	—
981	C₄	—	106	1	no	—
982	C₄	—	106	1	no	—
983	C₄	—	106	1	no	—
984	C₄	—	106	1	no	—
985	C₂	—	2	2	no	—
986	C₂	—	2	2	no	—
987	C₂	—	4	1	no	—
988	C₂	—	4	1	no	—
989	C₂	—	106	2	no	—
990	C₂	—	212	1	no	—
991	C₂	—	212	1	no	—
992	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
993	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
994	C₂	C₂×#13133264	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	#3520
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. #16811340	C₂	semidirect
2. #16811332	C₂	semidirect
3. #16811327	C₂	semidirect
4. #16811309	C₂	semidirect
5. #16811306	C₂	semidirect
6. #16811299	C₂	semidirect
7. #16811297	C₂	semidirect
8. #16811296	C₂	semidirect
9. #16811286	C₂	semidirect
10. #16811282	C₂	semidirect
11. #16811281	C₂	semidirect
12. #16811271	C₂	semidirect
13. #16811271	C₂	semidirect
14. #16811263	C₂	semidirect
15. #16811260	C₂	semidirect
16. #16811239	C₂	semidirect
17. #16811237	C₂	semidirect
18. #16811222	C₂	semidirect
19. #16811217	C₂	semidirect
20. #16811216	C₂	semidirect
21. #16811214	C₂	semidirect
22. #16811176	C₂	semidirect
23. #16811150	C₂	semidirect
24. #16811132	C₂	semidirect
25. #16811129	C₂	semidirect
26. C₂×#13133194	C₂	semidirect
27. C₂²⋊Q₈×D₅₃	C₂	semidirect
28. #16811103	C₂	semidirect
29. #16811102	C₂	semidirect
30. C₂×#13133177	C₂	semidirect
31. C₅₃×#551	C₂	semidirect
33. C₂×#11719945	C₂²	semidirect
35. C₂×#11719947	C₂²	semidirect
36. C₂²×Dic₁₀₆	C₂²	semidirect
37. C₂×Q₈×D₅₃	C₂²	semidirect
41. #13133216	C₂²	semidirect
42. #13133216	C₂²	semidirect
43. #13133216	C₂²	semidirect
44. #13133215	C₂²	semidirect
45. #13133212	C₂²	semidirect
46. #13133212	C₂²	semidirect
47. #13133212	C₂²	semidirect
48. #13133212	C₂²	semidirect
49. #13133211	C₂²	semidirect
50. #13133210	C₂²	semidirect
51. #13133210	C₂²	semidirect
52. #13133210	C₂²	semidirect
53. #13133209	C₂²	semidirect
54. #13133208	C₂²	semidirect
55. #13133208	C₂²	semidirect
56. #13133208	C₂²	semidirect
57. #13133207	C₂²	semidirect
58. #13133207	C₂²	semidirect
59. #13133207	C₂²	semidirect
60. #13133205	C₂²	semidirect
63. #13133203	C₂²	semidirect
64. #13133203	C₂²	semidirect
65. #13133203	C₂²	semidirect
66. #13133202	C₂²	semidirect
67. #13133202	C₂²	semidirect
68. #13133202	C₂²	semidirect
70. #13133201	C₂²	semidirect
71. #13133201	C₂²	semidirect
72. #13133201	C₂²	semidirect
77. #13133199	C₂²	semidirect
78. #13133199	C₂²	semidirect
79. #13133199	C₂²	semidirect
80. #13133198	C₂²	semidirect
81. #13133197	C₂²	semidirect
82. #13133197	C₂²	semidirect
84. #13133196	C₂²	semidirect
85. #13133195	C₂²	semidirect
86. #13133195	C₂²	semidirect
87. #13133195	C₂²	semidirect
88. #13133195	C₂²	semidirect
89. #13133195	C₂²	semidirect
90. #13133195	C₂²	semidirect
98. #13133194	C₂²	semidirect
99. #13133194	C₂²	semidirect
100. #13133194	C₂²	semidirect
101. #13133194	C₂²	semidirect
102. #13133194	C₂²	semidirect
103. #13133194	C₂²	semidirect
104. #13133194	C₂²	semidirect
105. #13133194	C₂²	semidirect
106. #13133193	C₂²	semidirect
107. #13133193	C₂²	semidirect
111. #13133190	C₂²	semidirect
115. #13133189	C₂²	semidirect
120. C₄×Dic₁₀₆	C₂²	semidirect
121. C₄×Dic₁₀₆	C₂²	semidirect
122. C₄×Dic₁₀₆	C₂²	semidirect
123. C₄×Dic₁₀₆	C₂²	semidirect
124. C₄×Dic₁₀₆	C₂²	semidirect
125. #13133182	C₂²	semidirect
126. #13133182	C₂²	semidirect
127. C₄×D₂₁₂	C₂²	semidirect
128. C₄×D₂₁₂	C₂²	semidirect
131. D₄×Dic₅₃	C₂²	semidirect
134. C₄×C₂²⋊D₅₃	C₂²	semidirect
146. #13133177	C₂²	semidirect
147. #13133177	C₂²	semidirect
148. #13133177	C₂²	semidirect
149. #13133177	C₂²	semidirect
151. #13133175	C₂²	semidirect
152. #13133175	C₂²	semidirect
153. #13133174	C₂²	semidirect
154. #13133174	C₂²	semidirect
155. #13133173	C₂²	semidirect
156. #13133173	C₂²	semidirect
157. #13133173	C₂²	semidirect
158. C₂×C₄⋊Dic₅₃	C₂²	semidirect
160. C₂×#11719919	C₂²	semidirect
161. C₂×#11719919	C₂²	semidirect
162. C₂×#11719919	C₂²	semidirect
163. C₄⋊C₄×D₅₃	C₂²	semidirect
164. C₄⋊C₄×D₅₃	C₂²	semidirect
165. C₄⋊C₄×D₅₃	C₂²	semidirect
166. C₄⋊C₄×D₅₃	C₂²	semidirect
172. #126×C₅₃	C₂²	semidirect
173. #126×C₅₃	C₂²	semidirect
174. #124×C₅₃	C₂²	semidirect
176. #123×C₅₃	C₂²	semidirect
177. #123×C₅₃	C₂²	semidirect
179. C₂²⋊Q₈×C₅₃	C₂²	semidirect
182. C₄×D₄×C₅₃	C₂²	semidirect
184. #117×C₅₃	C₂²	semidirect
393. C₂²⋊D₅₃	#41	semidirect
506. #551	D₅₃	semidirect
529. C₅₃	#3520	semidirect
551. #126	C₂×D₅₃	semidirect
552. #126	C₂×D₅₃	semidirect
566. #124	C₂×D₅₃	semidirect
583. #123	C₂×D₅₃	semidirect
584. #123	C₂×D₅₃	semidirect
613. C₂²⋊Q₈	C₂×D₅₃	semidirect
658. C₄×D₄	C₂×D₅₃	semidirect
668. #117	C₂×D₅₃	semidirect