Subgroups — #20288934

Order 6784.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811370	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811369	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811368	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811329	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811327	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811283	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811281	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811275	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811271	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811270	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811266	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811265	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811265	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811262	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811262	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811248	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811248	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811241	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811237	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811221	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811216	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811209	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811207	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811203	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811202	C₂	1	1	yes	maximal, characteristic, complemented
26	#16811202	C₂	1	1	yes	maximal, characteristic, complemented
27	#16811200	C₂	1	1	yes	maximal, characteristic, complemented
28	#16811131	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	#121×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#562	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
33	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
35	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
36	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
37	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
38	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
39	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
41	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
42	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
44	#13133216	C₂²	1	1	yes	characteristic, complemented
45	#13133215	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	#13133208	C₂²	1	1	yes	characteristic, complemented
51	#13133207	C₂²	1	1	yes	characteristic, complemented
52	#13133207	C₂²	1	1	yes	characteristic, complemented
53	#13133206	C₂²	1	1	yes	characteristic, complemented
54	#13133204	C₂²	1	1	yes	characteristic, complemented
55	#13133203	C₂²	1	1	yes	characteristic, complemented
56	#13133203	C₂²	1	1	yes	characteristic, complemented
57	#13133203	C₂²	1	1	yes	characteristic, complemented
58	#13133203	C₂²	1	1	yes	characteristic, complemented
59	#13133203	C₂²	1	1	yes	characteristic, complemented
60	#13133203	C₂²	1	1	yes	characteristic, complemented
61	#13133202	C₂²	1	1	yes	characteristic, complemented
62	#13133202	C₂²	1	1	yes	characteristic, complemented
63	#13133202	C₂²	1	1	yes	characteristic, complemented
64	#13133202	C₂²	1	1	yes	characteristic, complemented
65	#13133202	C₂²	1	1	yes	characteristic, complemented
66	#13133201	C₂²	1	1	yes	characteristic, complemented
67	#13133200	C₂²	1	1	yes	characteristic, complemented
68	#13133199	C₂²	1	1	yes	characteristic, complemented
69	#13133199	C₂²	1	1	yes	characteristic, complemented
70	#13133199	C₂²	1	1	yes	characteristic, complemented
71	#13133199	C₂²	1	1	yes	characteristic, complemented
72	#13133199	C₂²	1	1	yes	characteristic, complemented
73	#13133198	C₂²	1	1	yes	characteristic, complemented
74	#13133198	C₂²	1	1	yes	characteristic, complemented
75	#13133197	C₂²	1	1	yes	characteristic
76	#13133197	C₂²	1	1	yes	characteristic
77	#13133197	C₂²	1	1	yes	characteristic, complemented
78	#13133197	C₂²	1	1	yes	characteristic, complemented
79	#13133197	C₂²	1	1	yes	characteristic, complemented
80	#13133196	C₂²	1	1	yes	characteristic, complemented
81	#13133196	C₂²	1	1	yes	characteristic, complemented
82	#13133196	C₂²	1	1	yes	characteristic, complemented
83	#13133195	C₂²	1	1	yes	characteristic
84	#13133195	C₂²	1	1	yes	characteristic
85	#13133195	C₂²	1	1	yes	characteristic
86	#13133195	C₂²	1	1	yes	characteristic
87	#13133195	C₂²	1	1	yes	characteristic
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	#13133195	C₂²	1	1	yes	characteristic, complemented
92	#13133195	C₂²	1	1	yes	characteristic, complemented
93	#13133195	C₂²	1	1	yes	characteristic, complemented
94	#13133195	C₂²	1	1	yes	characteristic, complemented
95	#13133194	C₂²	1	1	yes	characteristic, complemented
96	#13133194	C₂²	1	1	yes	characteristic, complemented
97	#13133194	C₂²	1	1	yes	characteristic, complemented
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	#13133193	C₂²	1	1	yes	characteristic
104	#13133193	C₂²	1	1	yes	characteristic
105	#13133193	C₂²	1	1	yes	characteristic, complemented
106	#13133193	C₂²	1	1	yes	characteristic, complemented
107	#13133192	C₂²	1	1	yes	characteristic
108	#13133192	C₂²	1	1	yes	characteristic, complemented
109	#13133192	C₂²	1	1	yes	characteristic, complemented
110	#13133191	C₂²	1	1	yes	characteristic
111	#13133191	C₂²	1	1	yes	characteristic, complemented
112	#13133190	C₂²	1	1	yes	characteristic
113	#13133190	C₂²	1	1	yes	characteristic
114	#13133190	C₂²	1	1	yes	characteristic
115	#13133190	C₂²	1	1	yes	characteristic, complemented
116	#13133190	C₂²	1	1	yes	characteristic, complemented
117	#13133190	C₂²	1	1	yes	characteristic, complemented
118	#13133190	C₂²	1	1	yes	characteristic, complemented
119	#13133190	C₂²	1	1	yes	characteristic, complemented
120	#13133190	C₂²	1	1	yes	characteristic, complemented
121	#13133190	C₂²	1	1	yes	characteristic, complemented
122	#13133190	C₂²	1	1	yes	characteristic, complemented
123	#13133189	C₂²	1	1	yes	characteristic
124	#13133189	C₂²	1	1	yes	characteristic
125	#13133189	C₂²	1	1	yes	characteristic, complemented
126	#13133189	C₂²	1	1	yes	characteristic, complemented
127	#13133189	C₂²	1	1	yes	characteristic, complemented
128	#13133189	C₂²	1	1	yes	characteristic, complemented
129	#13133189	C₂²	1	1	yes	characteristic, complemented
130	#13133188	C₂²	1	1	yes	characteristic
131	#13133188	C₂²	1	1	yes	characteristic, complemented
132	#13133188	C₂²	1	1	yes	characteristic, complemented
133	#13133188	C₂²	1	1	yes	characteristic, complemented
134	#13133188	C₂²	1	1	yes	characteristic, complemented
135	#13133187	C₂²	1	1	yes	characteristic
136	#13133187	C₂²	1	1	yes	characteristic
137	#13133187	C₂²	1	1	yes	characteristic
138	#13133185	C₂²	1	1	yes	characteristic
139	#13133185	C₂²	1	1	yes	characteristic
140	#13133185	C₂²	1	1	yes	characteristic
141	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
142	#13133182	C₂²	1	1	yes	characteristic, complemented
143	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
144	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
145	#13133179	C₂²	1	1	yes	characteristic
146	#13133179	C₂²	1	1	yes	characteristic
147	#13133179	C₂²	1	1	yes	characteristic, complemented
148	#13133179	C₂²	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
150	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
152	#13133177	C₂²	1	1	yes	characteristic
153	#13133177	C₂²	1	1	yes	characteristic
154	#13133177	C₂²	1	1	yes	characteristic, complemented
155	#13133177	C₂²	1	1	yes	characteristic, complemented
156	#13133177	C₂²	1	1	yes	characteristic, complemented
157	#13133173	C₂²	1	1	yes	characteristic, complemented
158	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
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	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
164	C₂×#11719921	C₂²	1	1	yes	characteristic
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	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
177	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₂²⋊Q₈×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	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₅₃	C₂³	1	1	yes	characteristic
188	C₂³×D₅₃	C₂³	1	1	yes	characteristic
189	C₂³×D₅₃	C₂³	1	1	yes	characteristic
190	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₅₃	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	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₅₃	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	#11719949	—	4	2	no	—
222	Q₈×D₅₃	—	4	2	no	—
223	#11719947	—	4	2	no	—
224	#11719947	—	4	2	no	—
225	#11719947	—	4	2	no	—
226	D₄×D₅₃	—	4	2	no	—
227	D₄×D₅₃	—	4	2	no	—
228	D₄×D₅₃	—	4	2	no	—
229	#11719945	—	4	2	no	—
230	#11719945	—	4	2	no	—
231	#11719945	—	4	2	no	—
232	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
233	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
234	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
235	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
236	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
237	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
238	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₅₃	—	4	2	no	—
240	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
257	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
258	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
259	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
260	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
261	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
262	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
263	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
264	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₄²×C₅₃	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
289	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
290	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
291	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
292	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
293	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
294	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
295	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
296	C₂²⋊Dic₅₃	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	#11719921	C₂³	1	1	yes	characteristic
305	#11719921	C₂³	1	1	yes	characteristic
306	#11719921	C₂³	1	1	yes	characteristic
307	#11719921	C₂³	1	1	yes	characteristic
308	#11719921	C₂³	1	1	yes	characteristic
309	#11719921	C₂³	1	1	yes	characteristic
310	#11719921	C₂³	1	1	yes	characteristic
311	#11719921	C₂³	1	1	yes	characteristic
312	#11719921	C₂³	1	1	yes	characteristic
313	#11719921	C₂³	1	1	yes	characteristic
314	#11719921	C₂³	1	1	yes	characteristic
315	#11719921	C₂³	1	1	yes	characteristic
316	#11719921	C₂³	1	1	yes	characteristic
317	#11719921	C₂³	1	1	yes	characteristic
318	#11719921	C₂³	1	1	yes	characteristic
319	#11719921	C₂³	1	1	yes	characteristic
320	#11719921	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
324	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
325	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
326	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
327	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
328	C₄⋊Dic₅₃	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	#11719919	C₂³	1	1	yes	characteristic
341	#11719919	C₂³	1	1	yes	characteristic
342	#11719919	C₂³	1	1	yes	characteristic
343	#11719919	C₂³	1	1	yes	characteristic
344	#11719919	C₂³	1	1	yes	characteristic
345	#11719919	C₂³	1	1	yes	characteristic
346	#11719919	C₂³	1	1	yes	characteristic
347	#11719919	C₂³	1	1	yes	characteristic
348	#11719919	C₂³	1	1	yes	characteristic
349	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
350	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
351	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
352	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
353	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
361	C₂²×D₅₃	—	2	2	no	—
362	C₂²×D₅₃	—	4	1	no	—
363	C₂²×D₅₃	—	4	1	no	—
364	C₂²×D₅₃	—	4	1	no	—
365	C₂²×D₅₃	—	4	1	no	—
366	C₂²×D₅₃	—	4	1	no	—
367	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
372	Q₈×C₅₃	—	4	1	no	—
373	Q₈×C₅₃	—	4	1	no	—
374	D₄×C₅₃	—	4	1	no	—
375	D₄×C₅₃	—	4	1	no	—
376	D₄×C₅₃	—	4	1	no	—
377	D₄×C₅₃	—	4	1	no	—
378	D₄×C₅₃	—	4	1	no	—
379	D₄×C₅₃	—	4	1	no	—
380	C₂×C₄×C₅₃	—	4	1	no	—
381	C₂×C₄×C₅₃	—	4	1	no	—
382	C₂×C₄×C₅₃	—	4	1	no	—
383	C₂×C₄×C₅₃	—	4	1	no	—
384	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²⋊D₅₃	—	2	2	no	—
396	C₂²⋊D₅₃	—	2	2	no	—
397	C₂²⋊D₅₃	—	2	2	no	—
398	C₂²⋊D₅₃	—	2	2	no	—
399	C₂²⋊D₅₃	—	2	2	no	—
400	C₂²⋊D₅₃	—	2	2	no	—
401	C₂²⋊D₅₃	—	4	1	no	—
402	C₂²⋊D₅₃	—	4	1	no	—
403	C₂²⋊D₅₃	—	4	1	no	—
404	C₂²⋊D₅₃	—	4	1	no	—
405	C₂²⋊D₅₃	—	4	1	no	—
406	C₂²⋊D₅₃	—	4	1	no	—
407	C₂²⋊D₅₃	—	4	1	no	—
408	C₂²⋊D₅₃	—	4	1	no	—
409	C₂×Dic₅₃	—	2	2	no	—
410	C₂×Dic₅₃	—	2	2	no	—
411	C₂×Dic₅₃	—	4	1	no	—
412	C₂×Dic₅₃	—	4	1	no	—
413	C₂×Dic₅₃	—	4	1	no	—
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	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
419	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
421	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
424	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
425	D₂₁₂	—	2	2	no	—
426	D₂₁₂	—	2	2	no	—
427	D₂₁₂	—	2	2	no	—
428	D₂₁₂	—	2	2	no	—
429	D₂₁₂	—	4	1	no	—
430	D₂₁₂	—	4	1	no	—
431	D₂₁₂	—	4	1	no	—
432	C₄×D₅₃	—	2	2	no	—
433	C₄×D₅₃	—	2	2	no	—
434	C₄×D₅₃	—	2	2	no	—
435	C₄×D₅₃	—	2	2	no	—
436	C₄×D₅₃	—	2	2	no	—
437	C₄×D₅₃	—	4	1	no	—
438	C₄×D₅₃	—	4	1	no	—
439	C₄×D₅₃	—	4	1	no	—
440	C₄×D₅₃	—	4	1	no	—
441	C₄×D₅₃	—	4	1	no	—
442	C₄×D₅₃	—	4	1	no	—
443	C₄×D₅₃	—	4	1	no	—
444	C₄×D₅₃	—	4	1	no	—
445	C₄×D₅₃	—	4	1	no	—
446	C₄×D₅₃	—	4	1	no	—
447	C₄×D₅₃	—	4	1	no	—
448	C₄×D₅₃	—	4	1	no	—
449	Dic₁₀₆	—	2	2	no	—
450	Dic₁₀₆	—	2	2	no	—
451	Dic₁₀₆	—	4	1	no	—
452	Dic₁₀₆	—	4	1	no	—
453	Dic₁₀₆	—	4	1	no	—
454	Dic₁₀₆	—	4	1	no	—
455	Dic₁₀₆	—	4	1	no	—
456	C₂²×C₅₃	—	2	1	no	—
457	C₂²×C₅₃	—	2	1	no	—
458	C₂²×C₅₃	—	2	1	no	—
459	C₂²×C₅₃	—	2	1	no	—
460	C₂²×C₅₃	—	2	1	no	—
461	C₂²×C₅₃	—	2	1	no	—
462	C₂²×C₅₃	—	2	1	no	—
463	C₂²×C₅₃	—	2	1	no	—
464	C₂²×C₅₃	—	2	1	no	—
465	C₂²×C₅₃	—	2	1	no	—
466	C₂²×C₅₃	—	2	1	no	—
467	C₂²×C₅₃	—	2	1	no	—
468	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
469	C₂×D₅₃	—	2	1	no	—
470	C₂×D₅₃	—	2	1	no	—
471	C₂×D₅₃	—	2	1	no	—
472	C₂×D₅₃	—	2	1	no	—
473	C₂×D₅₃	—	2	1	no	—
474	C₂×D₅₃	—	2	1	no	—
475	C₂×D₅₃	—	2	1	no	—
476	C₂×D₅₃	—	2	1	no	—
477	C₂×D₅₃	—	2	1	no	—
478	C₂×D₅₃	—	2	1	no	—
479	C₂×D₅₃	—	2	1	no	—
480	C₂×D₅₃	—	2	1	no	—
481	C₂×D₅₃	—	2	1	no	—
482	C₂×D₅₃	—	4	4	no	—
483	C₂×D₅₃	—	8	2	no	—
484	C₂×D₅₃	—	8	2	no	—
485	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
486	C₂×D₅₃	2₋¹⁺⁴	1	2	yes	—
487	C₄×C₅₃	—	2	1	no	—
488	C₄×C₅₃	—	2	1	no	—
489	C₄×C₅₃	—	2	1	no	—
490	C₄×C₅₃	—	2	1	no	—
491	C₄×C₅₃	—	2	1	no	—
492	C₄×C₅₃	—	2	1	no	—
493	C₄×C₅₃	—	2	1	no	—
494	C₄×C₅₃	—	2	1	no	—
495	C₄×C₅₃	—	2	1	no	—
496	C₄×C₅₃	—	2	1	no	—
497	C₄×C₅₃	—	2	1	no	—
498	Dic₅₃	—	2	1	no	—
499	Dic₅₃	—	2	1	no	—
500	Dic₅₃	—	2	1	no	—
501	Dic₅₃	—	2	1	no	—
502	Dic₅₃	—	2	1	no	—
503	Dic₅₃	—	2	1	no	—
504	Dic₅₃	—	2	1	no	—
505	Dic₅₃	—	2	1	no	—
506	Dic₅₃	—	2	1	no	—
507	Dic₅₃	—	2	1	no	—
508	Dic₅₃	H(5,𝔽₂)	1	2	yes	—
509	#3536	—	53	1	no	maximal, Sylow
510	C₂×C₅₃	—	4	1	no	—
511	C₂×C₅₃	—	4	1	no	—
512	C₂×C₅₃	—	4	1	no	—
513	C₂×C₅₃	—	4	1	no	—
514	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
517	D₅₃	—	2	2	no	—
518	D₅₃	—	2	2	no	—
519	D₅₃	—	4	1	no	—
520	D₅₃	—	4	1	no	—
521	D₅₃	—	4	1	no	—
522	#562	—	53	1	no	—
523	#562	—	53	1	no	—
524	#562	—	53	1	no	—
525	#562	D₅₃	1	1	yes	characteristic, complemented
526	#554	—	53	1	no	—
527	#554	—	53	1	no	—
528	#548	—	53	1	no	—
529	#548	—	53	1	no	—
530	#547	—	53	1	no	—
531	#547	—	53	1	no	—
532	#546	—	53	1	no	—
533	#546	—	53	1	no	—
534	#546	—	53	1	no	—
535	#546	—	53	1	no	—
536	#546	—	53	1	no	—
537	#546	—	53	1	no	—
538	#543	—	53	1	no	—
539	#543	—	53	1	no	—
540	#542	—	53	1	no	—
541	#542	—	53	1	no	—
542	#539	—	53	1	no	—
543	#539	—	53	1	no	—
544	#538	—	53	1	no	—
545	#538	—	53	1	no	—
546	#537	—	53	1	no	—
547	#537	—	53	1	no	—
548	#537	—	53	1	no	—
549	#537	—	53	1	no	—
550	#525	—	53	1	no	—
551	C₂×C₂²⋊Q₈	—	53	1	no	—
552	C₂×#121	—	53	1	no	—
553	C₅₃	#3536	1	1	yes	characteristic, complemented, Sylow
554	C₂×#41	—	53	1	no	—
555	C₂×#41	—	53	1	no	—
556	C₂×#41	—	53	1	no	—
557	C₂×#41	—	53	1	no	—
558	C₂×#41	—	53	1	no	—
559	C₂×#41	—	53	1	no	—
560	C₂×#41	—	53	1	no	—
561	C₂²×Q₈	—	53	1	no	—
562	C₂²×D₄	—	53	1	no	—
563	C₂²×D₄	—	53	1	no	—
564	C₂²×D₄	—	53	1	no	—
565	C₂³×C₄	—	53	1	no	—
566	C₄⋊Q₈	—	53	1	no	—
567	C₄⋊Q₈	—	53	1	no	—
568	#126	—	53	1	no	—
569	#126	—	53	1	no	—
570	#126	—	53	1	no	—
571	#126	—	53	1	no	—
572	#125	—	53	1	no	—
573	#125	—	53	1	no	—
574	#125	—	53	1	no	—
575	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
576	#124	—	53	1	no	—
577	#124	—	53	1	no	—
578	#124	—	53	1	no	—
579	#124	—	53	1	no	—
580	#124	—	53	1	no	—
581	#124	—	53	1	no	—
582	#124	—	53	1	no	—
583	#124	—	53	1	no	—
584	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
585	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
586	#123	—	53	1	no	—
587	#123	—	53	1	no	—
588	#123	—	53	1	no	—
589	#123	—	53	1	no	—
590	#123	—	53	1	no	—
591	#123	—	53	1	no	—
592	#123	—	53	1	no	—
593	#123	—	53	1	no	—
594	#123	—	53	1	no	—
595	#123	—	53	1	no	—
596	#123	—	53	1	no	—
597	#123	—	53	1	no	—
598	#123	—	53	1	no	—
599	#123	—	53	1	no	—
600	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
601	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
602	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
603	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
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	—	53	1	no	—
625	C₂²⋊Q₈	—	53	1	no	—
626	C₂²⋊Q₈	—	53	1	no	—
627	C₂²⋊Q₈	—	53	1	no	—
628	C₂²⋊Q₈	—	53	1	no	—
629	C₂²⋊Q₈	—	53	1	no	—
630	C₂²⋊Q₈	—	53	1	no	—
631	C₂²⋊Q₈	—	53	1	no	—
632	C₂²⋊Q₈	—	53	1	no	—
633	C₂²⋊Q₈	—	53	1	no	—
634	C₂²⋊Q₈	—	53	1	no	—
635	C₂²⋊Q₈	—	53	1	no	—
636	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
637	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
638	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
639	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
640	#121	—	53	1	no	—
641	#121	—	53	1	no	—
642	#121	—	53	1	no	—
643	#121	—	53	1	no	—
644	#121	—	53	1	no	—
645	#121	—	53	1	no	—
646	#121	—	53	1	no	—
647	#121	—	53	1	no	—
648	#121	—	53	1	no	—
649	#121	—	53	1	no	—
650	#121	—	53	1	no	—
651	#121	—	53	1	no	—
652	#121	—	53	1	no	—
653	#121	—	53	1	no	—
654	#121	—	53	1	no	—
655	#121	—	53	1	no	—
656	#121	—	53	1	no	—
657	#121	—	53	1	no	—
658	#121	—	53	1	no	—
659	#121	—	53	1	no	—
660	#121	—	53	1	no	—
661	#121	—	53	1	no	—
662	#121	—	53	1	no	—
663	#121	—	53	1	no	—
664	#121	—	53	1	no	—
665	#121	—	53	1	no	—
666	#121	—	53	1	no	—
667	#121	—	53	1	no	—
668	#121	C₂×D₅₃	1	1	yes	characteristic
669	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
670	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
671	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
672	#120	—	53	1	no	—
673	#120	—	53	1	no	—
674	#120	—	53	1	no	—
675	#120	—	53	1	no	—
676	#120	—	53	1	no	—
677	#120	—	53	1	no	—
678	C₄×Q₈	—	53	1	no	—
679	C₄×Q₈	—	53	1	no	—
680	C₄×D₄	—	53	1	no	—
681	C₄×D₄	—	53	1	no	—
682	C₄×D₄	—	53	1	no	—
683	C₄×D₄	—	53	1	no	—
684	C₄×D₄	—	53	1	no	—
685	C₄×D₄	—	53	1	no	—
686	C₄×D₄	—	53	1	no	—
687	C₄×D₄	—	53	1	no	—
688	C₄×D₄	—	53	1	no	—
689	C₄×D₄	—	53	1	no	—
690	C₄×D₄	—	53	1	no	—
691	C₄×D₄	—	53	1	no	—
692	C₄×D₄	—	53	1	no	—
693	C₄×D₄	—	53	1	no	—
694	#117	—	53	1	no	—
695	C₂×C₄⋊C₄	—	53	1	no	—
696	C₂×C₄⋊C₄	—	53	1	no	—
697	C₂×C₄⋊C₄	—	53	1	no	—
698	C₂×C₄⋊C₄	—	53	1	no	—
699	C₂×C₄⋊C₄	—	53	1	no	—
700	C₂×C₄⋊C₄	—	53	1	no	—
701	C₂×C₂²⋊C₄	—	53	1	no	—
702	C₂×C₂²⋊C₄	—	53	1	no	—
703	C₂×C₂²⋊C₄	—	53	1	no	—
704	C₂×C₂²⋊C₄	—	53	1	no	—
705	C₂×C₂²⋊C₄	—	53	1	no	—
706	C₂×C₂²⋊C₄	—	53	1	no	—
707	C₂×C₂²⋊C₄	—	53	1	no	—
708	C₂×C₂²⋊C₄	—	53	1	no	—
709	C₂⁴	—	53	1	no	—
710	C₂⁴	—	53	1	no	—
711	C₂⁴	—	53	1	no	—
712	#41	—	212	2	no	—
713	#41	—	212	2	no	—
714	#41	—	212	2	no	—
715	#41	—	212	2	no	—
716	#41	—	212	2	no	—
717	#41	—	212	2	no	—
718	#41	—	212	2	no	—
719	C₂×Q₈	—	53	1	no	—
720	C₂×Q₈	—	53	1	no	—
721	C₂×Q₈	—	53	1	no	—
722	C₂×Q₈	—	53	1	no	—
723	C₂×Q₈	—	53	1	no	—
724	C₂×Q₈	—	53	1	no	—
725	C₂×Q₈	—	53	1	no	—
726	C₂×Q₈	—	212	2	no	—
727	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
728	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
729	C₂×D₄	—	53	1	no	—
730	C₂×D₄	—	53	1	no	—
731	C₂×D₄	—	53	1	no	—
732	C₂×D₄	—	53	1	no	—
733	C₂×D₄	—	53	1	no	—
734	C₂×D₄	—	53	1	no	—
735	C₂×D₄	—	53	1	no	—
736	C₂×D₄	—	53	1	no	—
737	C₂×D₄	—	53	1	no	—
738	C₂×D₄	—	53	1	no	—
739	C₂×D₄	—	53	1	no	—
740	C₂×D₄	—	53	1	no	—
741	C₂×D₄	—	53	1	no	—
742	C₂×D₄	—	53	1	no	—
743	C₂×D₄	—	53	1	no	—
744	C₂×D₄	—	53	1	no	—
745	C₂×D₄	—	53	1	no	—
746	C₂×D₄	—	53	1	no	—
747	C₂×D₄	—	53	1	no	—
748	C₂×D₄	—	53	1	no	—
749	C₂×D₄	—	53	1	no	—
750	C₂×D₄	—	212	2	no	—
751	C₂×D₄	—	212	2	no	—
752	C₂×D₄	—	212	2	no	—
753	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
754	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
755	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
756	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
757	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
758	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
759	C₂²×C₄	—	53	1	no	—
760	C₂²×C₄	—	53	1	no	—
761	C₂²×C₄	—	53	1	no	—
762	C₂²×C₄	—	53	1	no	—
763	C₂²×C₄	—	53	1	no	—
764	C₂²×C₄	—	53	1	no	—
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	—	212	2	no	—
782	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
783	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
784	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
785	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
786	C₄⋊C₄	—	53	1	no	—
787	C₄⋊C₄	—	53	1	no	—
788	C₄⋊C₄	—	53	1	no	—
789	C₄⋊C₄	—	53	1	no	—
790	C₄⋊C₄	—	53	1	no	—
791	C₄⋊C₄	—	53	1	no	—
792	C₄⋊C₄	—	53	1	no	—
793	C₄⋊C₄	—	53	1	no	—
794	C₄⋊C₄	—	53	1	no	—
795	C₄⋊C₄	—	53	1	no	—
796	C₄⋊C₄	—	53	1	no	—
797	C₄⋊C₄	—	53	1	no	—
798	C₄⋊C₄	—	53	1	no	—
799	C₄⋊C₄	—	53	1	no	—
800	C₄⋊C₄	—	53	1	no	—
801	C₄⋊C₄	—	53	1	no	—
802	C₄⋊C₄	—	53	1	no	—
803	C₄⋊C₄	—	53	1	no	—
804	C₄⋊C₄	—	53	1	no	—
805	C₄⋊C₄	—	53	1	no	—
806	C₄⋊C₄	—	53	1	no	—
807	C₄⋊C₄	—	53	1	no	—
808	C₄⋊C₄	—	53	1	no	—
809	C₄⋊C₄	—	53	1	no	—
810	C₄⋊C₄	—	53	1	no	—
811	C₄⋊C₄	—	53	1	no	—
812	C₄⋊C₄	—	53	1	no	—
813	C₄⋊C₄	—	53	1	no	—
814	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
815	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
816	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
817	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
818	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
819	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
820	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
821	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
822	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
823	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
824	C₂²⋊C₄	—	53	1	no	—
825	C₂²⋊C₄	—	53	1	no	—
826	C₂²⋊C₄	—	53	1	no	—
827	C₂²⋊C₄	—	53	1	no	—
828	C₂²⋊C₄	—	53	1	no	—
829	C₂²⋊C₄	—	53	1	no	—
830	C₂²⋊C₄	—	53	1	no	—
831	C₂²⋊C₄	—	53	1	no	—
832	C₂²⋊C₄	—	53	1	no	—
833	C₂²⋊C₄	—	53	1	no	—
834	C₂²⋊C₄	—	53	1	no	—
835	C₂²⋊C₄	—	53	1	no	—
836	C₂²⋊C₄	—	53	1	no	—
837	C₂²⋊C₄	—	53	1	no	—
838	C₂²⋊C₄	—	53	1	no	—
839	C₂²⋊C₄	—	53	1	no	—
840	C₂²⋊C₄	—	53	1	no	—
841	C₂²⋊C₄	—	53	1	no	—
842	C₂²⋊C₄	—	53	1	no	—
843	C₂²⋊C₄	—	53	1	no	—
844	C₂²⋊C₄	—	53	1	no	—
845	C₂²⋊C₄	—	53	1	no	—
846	C₂²⋊C₄	—	53	1	no	—
847	C₂²⋊C₄	—	53	1	no	—
848	C₂²⋊C₄	—	53	1	no	—
849	C₂²⋊C₄	—	53	1	no	—
850	C₂²⋊C₄	—	53	1	no	—
851	C₂²⋊C₄	—	53	1	no	—
852	C₂²⋊C₄	—	53	1	no	—
853	C₂²⋊C₄	—	53	1	no	—
854	C₂²⋊C₄	—	53	1	no	—
855	C₂²⋊C₄	—	53	1	no	—
856	C₂²⋊C₄	—	53	1	no	—
857	C₂²⋊C₄	—	53	1	no	—
858	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
859	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
860	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
861	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
862	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
863	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
864	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
865	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
866	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
867	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
868	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
869	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
870	C₄²	—	53	1	no	—
871	C₄²	—	53	1	no	—
872	C₄²	—	53	1	no	—
873	C₄²	—	53	1	no	—
874	C₄²	—	53	1	no	—
875	C₄²	C₂²×D₅₃	1	1	yes	characteristic
876	C₂³	—	53	1	no	—
877	C₂³	—	53	1	no	—
878	C₂³	—	53	1	no	—
879	C₂³	—	53	1	no	—
880	C₂³	—	53	1	no	—
881	C₂³	—	106	2	no	—
882	C₂³	—	106	2	no	—
883	C₂³	—	106	2	no	—
884	C₂³	—	106	2	no	—
885	C₂³	—	212	1	no	—
886	C₂³	—	212	1	no	—
887	C₂³	—	212	1	no	—
888	C₂³	—	212	1	no	—
889	C₂³	—	212	1	no	—
890	C₂³	C₂³×D₅₃	1	1	yes	characteristic
891	C₂³	C₂³×D₅₃	1	1	yes	characteristic
892	C₂³	C₂³×D₅₃	1	1	yes	characteristic
893	C₂³	C₂³×D₅₃	1	1	yes	characteristic
894	Q₈	—	4	1	no	—
895	Q₈	—	4	1	no	—
896	Q₈	—	106	2	no	—
897	Q₈	—	106	2	no	—
898	Q₈	—	212	1	no	—
899	Q₈	—	212	1	no	—
900	Q₈	—	212	1	no	—
901	Q₈	—	212	1	no	—
902	Q₈	—	212	1	no	—
903	D₄	—	4	1	no	—
904	D₄	—	4	1	no	—
905	D₄	—	4	1	no	—
906	D₄	—	4	1	no	—
907	D₄	—	4	1	no	—
908	D₄	—	4	1	no	—
909	D₄	—	106	2	no	—
910	D₄	—	106	2	no	—
911	D₄	—	106	2	no	—
912	D₄	—	106	2	no	—
913	D₄	—	106	2	no	—
914	D₄	—	106	2	no	—
915	D₄	—	106	2	no	—
916	D₄	—	106	2	no	—
917	D₄	—	106	2	no	—
918	D₄	—	106	2	no	—
919	D₄	—	212	1	no	—
920	D₄	—	212	1	no	—
921	D₄	—	212	1	no	—
922	D₄	—	212	1	no	—
923	D₄	—	212	1	no	—
924	D₄	—	212	1	no	—
925	D₄	—	212	1	no	—
926	D₄	—	212	1	no	—
927	D₄	—	212	1	no	—
928	D₄	—	212	1	no	—
929	D₄	—	212	1	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	53	1	no	—
935	C₂×C₄	—	53	1	no	—
936	C₂×C₄	—	53	1	no	—
937	C₂×C₄	—	53	1	no	—
938	C₂×C₄	—	53	1	no	—
939	C₂×C₄	—	53	1	no	—
940	C₂×C₄	—	53	1	no	—
941	C₂×C₄	—	53	1	no	—
942	C₂×C₄	—	53	1	no	—
943	C₂×C₄	—	53	1	no	—
944	C₂×C₄	—	53	1	no	—
945	C₂×C₄	—	106	2	no	—
946	C₂×C₄	—	106	2	no	—
947	C₂×C₄	—	106	2	no	—
948	C₂×C₄	—	106	2	no	—
949	C₂×C₄	—	106	2	no	—
950	C₂×C₄	—	106	2	no	—
951	C₂×C₄	—	106	2	no	—
952	C₂×C₄	—	212	1	no	—
953	C₂×C₄	—	212	1	no	—
954	C₂×C₄	—	212	1	no	—
955	C₂×C₄	—	212	1	no	—
956	C₂×C₄	—	212	1	no	—
957	C₂×C₄	—	212	1	no	—
958	C₂×C₄	—	212	1	no	—
959	C₂×C₄	—	212	1	no	—
960	C₂×C₄	—	212	1	no	—
961	C₂×C₄	—	212	1	no	—
962	C₂×C₄	—	212	1	no	—
963	C₂×C₄	—	212	1	no	—
964	C₂×C₄	—	212	1	no	—
965	C₂×C₄	—	212	1	no	—
966	C₂×C₄	—	212	1	no	—
967	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
968	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
969	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
970	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
971	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
972	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
973	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
974	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
975	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
976	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
977	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	53	2	no	—
991	C₂²	—	53	2	no	—
992	C₂²	—	106	1	no	—
993	C₂²	—	106	1	no	—
994	C₂²	—	106	1	no	—
995	C₂²	—	106	1	no	—
996	C₂²	—	106	1	no	—
997	C₂²	—	106	1	no	—
998	C₂²	—	106	1	no	—
999	C₂²	—	106	1	no	—
1000	C₂²	—	106	1	no	—
1001	C₂²	—	106	1	no	—
1002	C₂²	—	106	1	no	—
1003	C₂²	—	106	1	no	—
1004	C₂²	—	106	1	no	—
1005	C₂²	—	424	2	no	—
1006	C₂²	—	424	2	no	—
1007	C₂²	—	212	4	no	—
1008	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	53	2	no	—
1021	C₄	—	106	1	no	—
1022	C₄	—	106	1	no	—
1023	C₄	—	106	1	no	—
1024	C₄	—	106	1	no	—
1025	C₄	—	106	1	no	—
1026	C₄	—	106	1	no	—
1027	C₄	—	106	1	no	—
1028	C₄	—	106	1	no	—
1029	C₄	—	106	1	no	—
1030	C₄	—	106	1	no	—
1031	C₂	—	4	1	no	—
1032	C₂	—	4	1	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	1	no	—
1035	C₂	—	106	2	no	—
1036	C₂	—	106	2	no	—
1037	C₂	—	212	1	no	—
1038	C₂	—	212	1	no	—
1039	C₂	—	212	1	no	—
1040	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1041	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1042	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#562	C₂
hypercenter	#562	D₅₃
hypocenter	C₅₃	#3536
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #16811370	C₂	semidirect
2. #16811369	C₂	semidirect
3. #16811368	C₂	semidirect
4. #16811329	C₂	semidirect
5. #16811327	C₂	semidirect
6. #16811283	C₂	semidirect
7. #16811281	C₂	semidirect
8. #16811275	C₂	semidirect
9. #16811271	C₂	semidirect
10. #16811270	C₂	semidirect
11. #16811266	C₂	semidirect
12. #16811265	C₂	semidirect
13. #16811265	C₂	semidirect
14. #16811262	C₂	semidirect
15. #16811262	C₂	semidirect
16. #16811248	C₂	semidirect
17. #16811248	C₂	semidirect
18. #16811241	C₂	semidirect
19. #16811237	C₂	semidirect
20. #16811221	C₂	semidirect
21. #16811216	C₂	semidirect
22. #16811209	C₂	semidirect
23. #16811207	C₂	semidirect
24. #16811203	C₂	semidirect
25. #16811202	C₂	semidirect
26. #16811202	C₂	semidirect
27. #16811200	C₂	semidirect
28. #16811131	C₂	semidirect
29. C₂²⋊Q₈×D₅₃	C₂	semidirect
30. #121×D₅₃	C₂	semidirect
31. C₅₃×#562	C₂	semidirect
32. C₂×#11719949	C₂²	semidirect
33. C₂×#11719945	C₂²	semidirect
34. C₂×#11719945	C₂²	semidirect
35. C₂×#11719945	C₂²	semidirect
36. C₂×#11719947	C₂²	semidirect
37. C₂×#11719947	C₂²	semidirect
38. C₂×#11719947	C₂²	semidirect
39. C₂×Q₈×D₅₃	C₂²	semidirect
44. #13133216	C₂²	semidirect
45. #13133215	C₂²	semidirect
46. #13133212	C₂²	semidirect
47. #13133211	C₂²	semidirect
48. #13133210	C₂²	semidirect
49. #13133210	C₂²	semidirect
50. #13133208	C₂²	semidirect
51. #13133207	C₂²	semidirect
52. #13133207	C₂²	semidirect
53. #13133206	C₂²	semidirect
54. #13133204	C₂²	semidirect
55. #13133203	C₂²	semidirect
56. #13133203	C₂²	semidirect
57. #13133203	C₂²	semidirect
58. #13133203	C₂²	semidirect
59. #13133203	C₂²	semidirect
60. #13133203	C₂²	semidirect
61. #13133202	C₂²	semidirect
62. #13133202	C₂²	semidirect
63. #13133202	C₂²	semidirect
64. #13133202	C₂²	semidirect
65. #13133202	C₂²	semidirect
66. #13133201	C₂²	semidirect
67. #13133200	C₂²	semidirect
68. #13133199	C₂²	semidirect
69. #13133199	C₂²	semidirect
70. #13133199	C₂²	semidirect
71. #13133199	C₂²	semidirect
72. #13133199	C₂²	semidirect
73. #13133198	C₂²	semidirect
74. #13133198	C₂²	semidirect
77. #13133197	C₂²	semidirect
78. #13133197	C₂²	semidirect
79. #13133197	C₂²	semidirect
80. #13133196	C₂²	semidirect
81. #13133196	C₂²	semidirect
82. #13133196	C₂²	semidirect
88. #13133195	C₂²	semidirect
89. #13133195	C₂²	semidirect
90. #13133195	C₂²	semidirect
91. #13133195	C₂²	semidirect
92. #13133195	C₂²	semidirect
93. #13133195	C₂²	semidirect
94. #13133195	C₂²	semidirect
95. #13133194	C₂²	semidirect
96. #13133194	C₂²	semidirect
97. #13133194	C₂²	semidirect
98. #13133194	C₂²	semidirect
99. #13133194	C₂²	semidirect
100. #13133194	C₂²	semidirect
101. #13133194	C₂²	semidirect
102. #13133194	C₂²	semidirect
105. #13133193	C₂²	semidirect
106. #13133193	C₂²	semidirect
108. #13133192	C₂²	semidirect
109. #13133192	C₂²	semidirect
111. #13133191	C₂²	semidirect
115. #13133190	C₂²	semidirect
116. #13133190	C₂²	semidirect
117. #13133190	C₂²	semidirect
118. #13133190	C₂²	semidirect
119. #13133190	C₂²	semidirect
120. #13133190	C₂²	semidirect
121. #13133190	C₂²	semidirect
122. #13133190	C₂²	semidirect
125. #13133189	C₂²	semidirect
126. #13133189	C₂²	semidirect
127. #13133189	C₂²	semidirect
128. #13133189	C₂²	semidirect
129. #13133189	C₂²	semidirect
131. #13133188	C₂²	semidirect
132. #13133188	C₂²	semidirect
133. #13133188	C₂²	semidirect
134. #13133188	C₂²	semidirect
141. C₄×Dic₁₀₆	C₂²	semidirect
142. #13133182	C₂²	semidirect
144. C₄×D₂₁₂	C₂²	semidirect
147. #13133179	C₂²	semidirect
148. #13133179	C₂²	semidirect
150. C₄×C₂²⋊D₅₃	C₂²	semidirect
151. C₄×C₂²⋊D₅₃	C₂²	semidirect
154. #13133177	C₂²	semidirect
155. #13133177	C₂²	semidirect
156. #13133177	C₂²	semidirect
157. #13133173	C₂²	semidirect
158. C₂×#11719919	C₂²	semidirect
160. C₄⋊C₄×D₅₃	C₂²	semidirect
161. C₄⋊C₄×D₅₃	C₂²	semidirect
162. C₄⋊C₄×D₅₃	C₂²	semidirect
163. C₄⋊C₄×D₅₃	C₂²	semidirect
172. #125×C₅₃	C₂²	semidirect
173. #124×C₅₃	C₂²	semidirect
174. #124×C₅₃	C₂²	semidirect
175. #123×C₅₃	C₂²	semidirect
176. #123×C₅₃	C₂²	semidirect
177. #123×C₅₃	C₂²	semidirect
178. #123×C₅₃	C₂²	semidirect
179. C₂²⋊Q₈×C₅₃	C₂²	semidirect
180. C₂²⋊Q₈×C₅₃	C₂²	semidirect
181. C₂²⋊Q₈×C₅₃	C₂²	semidirect
182. C₂²⋊Q₈×C₅₃	C₂²	semidirect
184. #121×C₅₃	C₂²	semidirect
185. #121×C₅₃	C₂²	semidirect
186. #121×C₅₃	C₂²	semidirect
525. #562	D₅₃	semidirect
553. C₅₃	#3536	semidirect
575. #125	C₂×D₅₃	semidirect
584. #124	C₂×D₅₃	semidirect
585. #124	C₂×D₅₃	semidirect
600. #123	C₂×D₅₃	semidirect
601. #123	C₂×D₅₃	semidirect
602. #123	C₂×D₅₃	semidirect
603. #123	C₂×D₅₃	semidirect
636. C₂²⋊Q₈	C₂×D₅₃	semidirect
637. C₂²⋊Q₈	C₂×D₅₃	semidirect
638. C₂²⋊Q₈	C₂×D₅₃	semidirect
639. C₂²⋊Q₈	C₂×D₅₃	semidirect
669. #121	C₂×D₅₃	semidirect
670. #121	C₂×D₅₃	semidirect
671. #121	C₂×D₅₃	semidirect