Subgroups — D₅₃×#3282 #28259312

Order 13568.

2934 conjugacy classes of subgroups.

The subgroup lattice has 2094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#135×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×SD₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#548×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#546×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#20286429	C₂	1	1	yes	maximal, characteristic, complemented
6	#20286428	C₂	1	1	yes	maximal, characteristic, complemented
7	#20286427	C₂	1	1	yes	maximal, characteristic, complemented
8	#20286426	C₂	1	1	yes	maximal, characteristic, complemented
9	#20286425	C₂	1	1	yes	maximal, characteristic, complemented
10	#20286424	C₂	1	1	yes	maximal, characteristic, complemented
11	#20286423	C₂	1	1	yes	maximal, characteristic, complemented
12	#20286422	C₂	1	1	yes	maximal, characteristic, complemented
13	#20286421	C₂	1	1	yes	maximal, characteristic, complemented
14	#20286420	C₂	1	1	yes	maximal, characteristic, complemented
15	#20286419	C₂	1	1	yes	maximal, characteristic, complemented
16	#20286418	C₂	1	1	yes	maximal, characteristic, complemented
17	#20286417	C₂	1	1	yes	maximal, characteristic, complemented
18	#20286416	C₂	1	1	yes	maximal, characteristic, complemented
19	#20286415	C₂	1	1	yes	maximal, characteristic, complemented
20	#495×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#465×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#465×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#464×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	#463×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	#452×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
26	#449×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
27	#451×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	#447×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×SD₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
35	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
36	C₂×#13133240	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13133239	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13133238	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133238	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13133237	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13133237	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13133236	C₂²	1	1	yes	characteristic, complemented
43	#135×D₅₃	—	2	8	no	—
44	C₂×Q₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×Q₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#11719913	C₂²	1	1	yes	characteristic, complemented
47	C₂²×#11719923	C₂²	1	1	yes	characteristic, complemented
48	C₂²×#11719924	C₂²	1	1	yes	characteristic, complemented
49	C₂×SD₁₆×D₅₃	—	2	8	no	—
50	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic
53	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic
54	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
60	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
61	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
62	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
63	#16811285	C₂²	1	1	yes	characteristic, complemented
64	#16811284	C₂²	1	1	yes	characteristic, complemented
65	#16811283	—	2	1	no	—
66	#16811283	C₂²	1	1	yes	characteristic, complemented
67	#16811282	—	2	1	no	—
68	#16811282	C₂²	1	1	yes	characteristic, complemented
69	#16811281	—	2	1	no	—
70	#16811281	C₂²	1	1	yes	characteristic, complemented
71	#16811280	C₂²	1	1	yes	characteristic, complemented
72	#16811279	—	2	1	no	—
73	#16811279	C₂²	1	1	yes	characteristic, complemented
74	#16811270	C₂²	1	1	yes	characteristic, complemented
75	#16811269	C₂²	1	1	yes	characteristic, complemented
76	#16811268	C₂²	1	1	yes	characteristic, complemented
77	#16811267	C₂²	1	1	yes	characteristic, complemented
78	#16811266	C₂²	1	1	yes	characteristic, complemented
79	#16811265	—	2	1	no	—
80	#16811264	C₂²	1	1	yes	characteristic, complemented
81	#16811263	—	2	1	no	—
82	#16811262	—	2	1	no	—
83	#16811261	C₂²	1	1	yes	characteristic, complemented
84	#16811260	—	2	1	no	—
85	#124×D₅₃	—	2	1	no	—
86	#124×D₅₃	C₂²	1	1	yes	characteristic
87	#124×D₅₃	C₂²	1	1	yes	characteristic, complemented
88	#123×D₅₃	—	2	1	no	—
89	C₂²⋊Q₈×D₅₃	—	2	1	no	—
90	C₂²⋊Q₈×D₅₃	C₂²	1	1	yes	characteristic
91	C₂²⋊Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
92	#121×D₅₃	—	2	1	no	—
93	#121×D₅₃	—	2	1	no	—
94	#121×D₅₃	C₂²	1	1	yes	characteristic
95	#121×D₅₃	C₂²	1	1	yes	characteristic
96	#120×D₅₃	—	2	1	no	—
97	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₄×D₅₃	—	2	1	no	—
99	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
100	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×D₅₃	—	2	1	no	—
102	#16811008	C₂²	1	1	yes	characteristic, complemented
103	#16811007	C₂²	1	1	yes	characteristic, complemented
104	#16811006	C₂²	1	1	yes	characteristic, complemented
105	#16811005	C₂²	1	1	yes	characteristic, complemented
106	#16811005	C₂²	1	1	yes	characteristic, complemented
107	#16811004	C₂²	1	1	yes	characteristic, complemented
108	#16811004	C₂²	1	1	yes	characteristic, complemented
109	#16810855	C₂²	1	1	yes	characteristic, complemented
110	#16810855	C₂²	1	1	yes	characteristic, complemented
111	#16810854	C₂²	1	1	yes	characteristic, complemented
112	#16810854	C₂²	1	1	yes	characteristic, complemented
113	#16810853	C₂²	1	1	yes	characteristic, complemented
114	#16810853	C₂²	1	1	yes	characteristic, complemented
115	#16810852	C₂²	1	1	yes	characteristic, complemented
116	#16810852	C₂²	1	1	yes	characteristic, complemented
117	#16810851	C₂²	1	1	yes	characteristic, complemented
118	#16810851	C₂²	1	1	yes	characteristic, complemented
119	#16810850	C₂²	1	1	yes	characteristic, complemented
120	#16810850	C₂²	1	1	yes	characteristic, complemented
121	#16810849	C₂²	1	1	yes	characteristic, complemented
122	#16810849	C₂²	1	1	yes	characteristic, complemented
123	#16810848	C₂²	1	1	yes	characteristic, complemented
124	#16810847	C₂²	1	1	yes	characteristic, complemented
125	#16810846	C₂²	1	1	yes	characteristic, complemented
126	#16810845	C₂²	1	1	yes	characteristic, complemented
127	#16810844	C₂²	1	1	yes	characteristic, complemented
128	#16810843	C₂²	1	1	yes	characteristic, complemented
129	#16810842	C₂²	1	1	yes	characteristic, complemented
130	#16810841	C₂²	1	1	yes	characteristic, complemented
131	#16810840	C₂²	1	1	yes	characteristic, complemented
132	#16810839	C₂²	1	1	yes	characteristic, complemented
133	#16810838	C₂²	1	1	yes	characteristic, complemented
134	#16810837	C₂²	1	1	yes	characteristic, complemented
135	#16810836	C₂²	1	1	yes	characteristic, complemented
136	#16810835	C₂²	1	1	yes	characteristic, complemented
137	#16810788	C₂²	1	1	yes	characteristic, complemented
138	#16810787	C₂²	1	1	yes	characteristic, complemented
139	#16810786	C₂²	1	1	yes	characteristic, complemented
140	#16810785	C₂²	1	1	yes	characteristic, complemented
141	#16810784	C₂²	1	1	yes	characteristic, complemented
142	#16810783	C₂²	1	1	yes	characteristic, complemented
143	#16810782	C₂²	1	1	yes	characteristic, complemented
144	#16810781	C₂²	1	1	yes	characteristic, complemented
145	#16810780	C₂²	1	1	yes	characteristic, complemented
146	#16810780	C₂²	1	1	yes	characteristic, complemented
147	#16810779	C₂²	1	1	yes	characteristic, complemented
148	#16810778	C₂²	1	1	yes	characteristic, complemented
149	#16810777	C₂²	1	1	yes	characteristic, complemented
150	#16810777	C₂²	1	1	yes	characteristic, complemented
151	#16810771	C₂²	1	1	yes	characteristic, complemented
152	#16810770	C₂²	1	1	yes	characteristic, complemented
153	#16810769	C₂²	1	1	yes	characteristic, complemented
154	#16810768	C₂²	1	1	yes	characteristic, complemented
155	#16810767	C₂²	1	1	yes	characteristic, complemented
156	#16810766	C₂²	1	1	yes	characteristic, complemented
157	#16810765	C₂²	1	1	yes	characteristic, complemented
158	#16810759	C₂²	1	1	yes	characteristic, complemented
159	#16810758	C₂²	1	1	yes	characteristic, complemented
160	#16810758	C₂²	1	1	yes	characteristic, complemented
161	#16810757	C₂²	1	1	yes	characteristic, complemented
162	#16810756	C₂²	1	1	yes	characteristic, complemented
163	#16810755	C₂²	1	1	yes	characteristic, complemented
164	#16810755	C₂²	1	1	yes	characteristic, complemented
165	#16810714	C₂²	1	1	yes	characteristic, complemented
166	C₄×#11719913	C₂²	1	1	yes	characteristic, complemented
167	SD₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
168	C₄×#11719924	C₂²	1	1	yes	characteristic, complemented
169	#16810710	C₂²	1	1	yes	characteristic, complemented
170	C₄×#11719923	C₂²	1	1	yes	characteristic, complemented
171	#16810708	C₂²	1	1	yes	characteristic, complemented
172	C₈×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
173	D₄×#88322	C₂²	1	1	yes	characteristic, complemented
174	#16810688	C₂²	1	1	yes	characteristic, complemented
175	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
177	#16810686	C₂²	1	1	yes	characteristic, complemented
178	#16810686	C₂²	1	1	yes	characteristic, complemented
179	#106×D₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
181	#103×D₅₃	C₂²	1	1	yes	characteristic, complemented
182	#103×D₅₃	C₂²	1	1	yes	characteristic, complemented
183	#103×D₅₃	C₂²	1	1	yes	characteristic, complemented
184	#102×D₅₃	C₂²	1	1	yes	characteristic
185	#102×D₅₃	C₂²	1	1	yes	characteristic
186	#102×D₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
188	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
189	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
190	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
191	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
202	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
203	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
204	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
205	C₂⁴×D₅₃	—	2	1	no	—
206	C₂×#11719949	C₂³	1	1	yes	characteristic
207	C₂×#11719949	C₂³	1	1	yes	characteristic, complemented
208	C₂×#11719945	—	2	1	no	—
209	C₂×#11719945	—	2	1	no	—
210	C₂×#11719945	C₂³	1	1	yes	characteristic
211	C₂×#11719945	C₂³	1	1	yes	characteristic, complemented
212	C₂×#11719947	—	2	1	no	—
213	C₂×#11719947	—	2	1	no	—
214	C₂×#11719947	C₂³	1	1	yes	characteristic
215	C₂×#11719947	C₂³	1	1	yes	characteristic, complemented
216	#41×D₅₃	—	2	4	no	—
217	#41×D₅₃	—	2	4	no	—
218	#41×D₅₃	—	4	2	no	—
219	#41×D₅₃	—	4	2	no	—
220	C₂²×Dic₁₀₆	—	2	1	no	—
221	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
222	C₂×Q₈×D₅₃	—	2	1	no	—
223	C₂×Q₈×D₅₃	—	2	1	no	—
224	C₂×Q₈×D₅₃	—	2	4	no	—
225	C₂×Q₈×D₅₃	—	4	2	no	—
226	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
227	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
228	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
229	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
230	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
231	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
232	C₂²×C₂²⋊D₅₃	—	2	1	no	—
233	C₂×D₄×D₅₃	—	2	4	no	—
234	C₂×D₄×D₅₃	—	2	1	no	—
235	C₂×D₄×D₅₃	—	2	1	no	—
236	C₂×D₄×D₅₃	—	2	1	no	—
237	C₂×D₄×D₅₃	—	2	1	no	—
238	C₂×D₄×D₅₃	—	2	1	no	—
239	C₂×D₄×D₅₃	—	2	1	no	—
240	C₂×D₄×D₅₃	—	4	2	no	—
241	C₂×D₄×D₅₃	D₄	1	1	yes	characteristic
242	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
243	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
244	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
245	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
246	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
247	C₂²×C₄×D₅₃	—	2	1	no	—
248	C₂²×C₄×D₅₃	—	2	1	no	—
249	C₂²×C₄×D₅₃	—	2	1	no	—
250	C₂²×C₄×D₅₃	—	2	1	no	—
251	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
252	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
253	#13133240	—	2	4	no	—
254	#13133239	—	2	4	no	—
255	#13133238	—	2	4	no	—
256	#13133238	—	2	4	no	—
257	#13133237	—	2	4	no	—
258	#13133237	—	2	4	no	—
259	#13133236	—	2	4	no	—
260	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic, complemented
261	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic, complemented
262	C₂×#11719925	C₂³	1	1	yes	characteristic, complemented
263	C₂×#11719925	C₂³	1	1	yes	characteristic, complemented
264	C₂×#11719925	C₂³	1	1	yes	characteristic, complemented
265	C₂×#11719925	C₂³	1	1	yes	characteristic, complemented
266	Q₁₆×D₅₃	—	2	4	no	—
267	Q₁₆×D₅₃	—	4	2	no	—
268	C₂×#11719913	—	2	4	no	—
269	C₂×#11719913	C₂³	1	1	yes	characteristic
270	C₂×#11719913	C₂³	1	1	yes	characteristic
271	C₂×#11719913	C₂³	1	1	yes	characteristic
272	C₂×#11719913	C₂³	1	1	yes	characteristic
273	C₂×#11719913	C₂³	1	1	yes	characteristic, complemented
274	C₂×#11719923	—	2	4	no	—
275	C₂×#11719923	C₂³	1	1	yes	characteristic
276	C₂×#11719923	C₂³	1	1	yes	characteristic
277	C₂×#11719923	C₂³	1	1	yes	characteristic
278	C₂×#11719923	C₂³	1	1	yes	characteristic
279	C₂×#11719923	C₂³	1	1	yes	characteristic, complemented
280	C₂×#11719924	—	2	4	no	—
281	C₂×#11719924	C₂³	1	1	yes	characteristic
282	C₂×#11719924	C₂³	1	1	yes	characteristic
283	C₂×#11719924	C₂³	1	1	yes	characteristic
284	C₂×#11719924	C₂³	1	1	yes	characteristic
285	C₂×#11719924	C₂³	1	1	yes	characteristic, complemented
286	SD₁₆×D₅₃	—	2	4	no	—
287	SD₁₆×D₅₃	—	2	4	no	—
288	SD₁₆×D₅₃	—	2	4	no	—
289	SD₁₆×D₅₃	—	2	4	no	—
290	SD₁₆×D₅₃	—	2	4	no	—
291	SD₁₆×D₅₃	—	2	4	no	—
292	SD₁₆×D₅₃	—	2	4	no	—
293	SD₁₆×D₅₃	—	2	4	no	—
294	SD₁₆×D₅₃	D₄	1	8	yes	complemented
295	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
296	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
297	C₂×#11719922	C₂³	1	1	yes	characteristic
298	C₂×#11719922	C₂³	1	1	yes	characteristic
299	C₂×#11719922	C₂³	1	1	yes	characteristic
300	C₂×#11719922	C₂³	1	1	yes	characteristic
301	D₈×D₅₃	—	2	4	no	—
302	D₈×D₅₃	—	4	2	no	—
303	C₂²×#88322	C₂³	1	1	yes	characteristic
304	C₂²×#88322	C₂³	1	1	yes	characteristic, complemented
305	C₂×C₈×D₅₃	—	2	4	no	—
306	C₂×C₈×D₅₃	—	2	4	no	—
307	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic, complemented
314	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic, complemented
315	#13133206	—	2	1	no	—
316	#13133206	C₂³	1	1	yes	characteristic
317	#13133206	C₂³	1	1	yes	characteristic, complemented
318	#13133205	—	2	1	no	—
319	#13133205	C₂³	1	1	yes	characteristic
320	#13133205	C₂³	1	1	yes	characteristic, complemented
321	#13133204	—	2	1	no	—
322	#13133204	C₂³	1	1	yes	characteristic
323	#13133204	C₂³	1	1	yes	characteristic, complemented
324	#13133203	—	2	1	no	—
325	#13133203	—	2	1	no	—
326	#13133203	—	2	1	no	—
327	#13133203	—	2	1	no	—
328	#13133203	—	2	1	no	—
329	#13133203	—	2	1	no	—
330	#13133203	—	2	1	no	—
331	#13133203	—	2	1	no	—
332	#13133202	—	2	1	no	—
333	#13133202	—	2	1	no	—
334	#13133201	—	2	1	no	—
335	#13133200	—	2	1	no	—
336	#13133199	—	2	1	no	—
337	#13133199	—	2	1	no	—
338	#13133198	—	2	1	no	—
339	#13133197	—	2	1	no	—
340	#13133197	C₂³	1	1	yes	characteristic
341	#13133197	C₂³	1	1	yes	characteristic, complemented
342	#13133196	—	2	1	no	—
343	#13133196	C₂³	1	1	yes	characteristic
344	#13133196	C₂³	1	1	yes	characteristic, complemented
345	#13133195	—	2	1	no	—
346	#13133195	—	2	1	no	—
347	#13133195	—	2	1	no	—
348	#13133195	—	2	1	no	—
349	#13133194	—	2	1	no	—
350	#13133194	—	2	1	no	—
351	#13133194	—	2	1	no	—
352	#13133194	—	2	1	no	—
353	#13133193	—	2	1	no	—
354	#13133193	C₂³	1	1	yes	characteristic
355	#13133193	C₂³	1	1	yes	characteristic, complemented
356	#13133192	—	2	1	no	—
357	#13133192	—	2	1	no	—
358	#13133192	C₂³	1	1	yes	characteristic
359	#13133192	C₂³	1	1	yes	characteristic
360	#13133191	—	2	1	no	—
361	#13133191	—	2	1	no	—
362	#13133191	C₂³	1	1	yes	characteristic
363	#13133191	C₂³	1	1	yes	characteristic
364	#13133190	—	2	1	no	—
365	#13133190	—	2	1	no	—
366	#13133190	—	2	1	no	—
367	#13133190	—	2	1	no	—
368	#13133190	—	2	1	no	—
369	#13133190	—	2	1	no	—
370	#13133189	—	2	1	no	—
371	#13133189	—	2	1	no	—
372	#13133189	—	2	1	no	—
373	#13133189	—	2	1	no	—
374	#13133189	—	2	1	no	—
375	#13133189	—	2	1	no	—
376	#13133188	—	2	1	no	—
377	#13133188	—	2	1	no	—
378	#13133188	C₂³	1	1	yes	characteristic
379	#13133188	C₂³	1	1	yes	characteristic
380	#13133187	—	2	1	no	—
381	#13133187	—	2	1	no	—
382	#13133187	—	2	1	no	—
383	#13133186	—	2	1	no	—
384	#13133185	—	2	1	no	—
385	#13133185	—	2	1	no	—
386	#13133185	—	2	1	no	—
387	Q₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
388	C₄×Dic₁₀₆	—	2	1	no	—
389	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
390	#13133182	—	2	1	no	—
391	#13133182	C₂³	1	1	yes	characteristic, complemented
392	C₄×D₂₁₂	—	2	1	no	—
393	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
394	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
395	D₄×Dic₅₃	—	2	1	no	—
396	D₄×Dic₅₃	D₄	1	1	yes	characteristic
397	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
398	#13133179	—	2	1	no	—
399	#13133179	D₄	1	1	yes	characteristic
400	#13133179	C₂³	1	1	yes	characteristic
401	C₄×C₂²⋊D₅₃	—	2	1	no	—
402	C₄×C₂²⋊D₅₃	—	2	1	no	—
403	C₄×C₂²⋊D₅₃	—	2	1	no	—
404	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
405	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
406	#13133177	—	2	1	no	—
407	#13133177	—	2	1	no	—
408	#13133177	—	2	1	no	—
409	#13133177	D₄	1	1	yes	characteristic
410	#13133177	D₄	1	1	yes	characteristic
411	C₄⋊C₄×D₅₃	—	2	1	no	—
412	C₄⋊C₄×D₅₃	—	2	1	no	—
413	C₄⋊C₄×D₅₃	—	2	1	no	—
414	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
415	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
416	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
417	C₂×C₂²⋊Dic₅₃	—	2	1	no	—
418	C₂×#11719921	—	2	1	no	—
419	C₂×#11719921	—	2	1	no	—
420	C₂²⋊C₄×D₅₃	—	2	1	no	—
421	C₂²⋊C₄×D₅₃	—	2	1	no	—
422	C₂²⋊C₄×D₅₃	—	2	1	no	—
423	C₂²⋊C₄×D₅₃	—	2	1	no	—
424	C₂²⋊C₄×D₅₃	—	2	1	no	—
425	C₂²⋊C₄×D₅₃	—	2	1	no	—
426	C₂²⋊C₄×D₅₃	—	2	1	no	—
427	C₂²⋊C₄×D₅₃	—	2	1	no	—
428	C₂²⋊C₄×D₅₃	—	2	1	no	—
429	C₂²⋊C₄×D₅₃	—	2	1	no	—
430	C₂²⋊C₄×D₅₃	—	2	1	no	—
431	C₂²⋊C₄×D₅₃	—	2	1	no	—
432	C₂²⋊C₄×D₅₃	—	2	1	no	—
433	C₂²⋊C₄×D₅₃	D₄	1	1	yes	characteristic
434	C₂²⋊C₄×D₅₃	D₄	1	1	yes	characteristic
435	C₄²×D₅₃	—	2	1	no	—
436	C₄²×D₅₃	C₂³	1	1	yes	characteristic
437	#13133149	C₂³	1	1	yes	characteristic, complemented
438	#13133148	C₂³	1	1	yes	characteristic, complemented
439	#13133148	C₂³	1	1	yes	characteristic, complemented
440	C₄⋊#88322	C₂³	1	1	yes	characteristic, complemented
441	#13133146	C₂³	1	1	yes	characteristic, complemented
442	#13133146	C₂³	1	1	yes	characteristic, complemented
443	#13133142	C₂³	1	1	yes	characteristic, complemented
444	#13133142	C₂³	1	1	yes	characteristic, complemented
445	#13133142	C₂³	1	1	yes	characteristic, complemented
446	#13133141	C₂³	1	1	yes	characteristic, complemented
447	#13133141	C₂³	1	1	yes	characteristic, complemented
448	#13133141	C₂³	1	1	yes	characteristic, complemented
449	#13133140	C₂³	1	1	yes	characteristic, complemented
450	#13133140	C₂³	1	1	yes	characteristic, complemented
451	#13133140	C₂³	1	1	yes	characteristic, complemented
452	#13133139	C₂³	1	1	yes	characteristic
453	#13133139	C₂³	1	1	yes	characteristic
454	#13133139	C₂³	1	1	yes	characteristic, complemented
455	#13133138	C₂³	1	1	yes	characteristic
456	#13133138	C₂³	1	1	yes	characteristic
457	#13133138	C₂³	1	1	yes	characteristic, complemented
458	#13133137	C₂³	1	1	yes	characteristic
459	#13133137	C₂³	1	1	yes	characteristic
460	#13133137	C₂³	1	1	yes	characteristic, complemented
461	C₂²⋊#88322	C₂³	1	1	yes	characteristic
462	C₂²⋊#88322	C₂³	1	1	yes	characteristic, complemented
463	#13133129	C₂³	1	1	yes	characteristic
464	#13133129	C₂³	1	1	yes	characteristic
465	#13133129	C₂³	1	1	yes	characteristic, complemented
466	#13133129	C₂³	1	1	yes	characteristic, complemented
467	C₄×#88322	C₂³	1	1	yes	characteristic, complemented
468	C₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
469	C₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
470	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
471	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic, complemented
472	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
473	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
474	#135×C₅₃	—	2	4	no	—
475	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
476	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
477	C₂×SD₁₆×C₅₃	—	2	4	no	—
478	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
479	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
480	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
481	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
482	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
483	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
485	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
486	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
487	#124×C₅₃	—	2	1	no	—
488	#124×C₅₃	C₂³	1	1	yes	characteristic
489	#124×C₅₃	C₂³	1	1	yes	characteristic, complemented
490	#123×C₅₃	—	2	1	no	—
491	C₂²⋊Q₈×C₅₃	—	2	1	no	—
492	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
493	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
494	#121×C₅₃	—	2	1	no	—
495	#121×C₅₃	—	2	1	no	—
496	#121×C₅₃	C₂³	1	1	yes	characteristic
497	#121×C₅₃	C₂³	1	1	yes	characteristic
498	#120×C₅₃	—	2	1	no	—
499	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
500	C₄×D₄×C₅₃	—	2	1	no	—
501	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
502	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
503	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
504	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
505	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
506	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
507	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
508	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
509	#102×C₅₃	C₂³	1	1	yes	characteristic
510	#102×C₅₃	C₂³	1	1	yes	characteristic
511	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
512	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
513	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
514	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
515	C₂⁴×C₅₃	—	2	1	no	—
516	C₂³×D₅₃	—	2	1	no	—
517	C₂³×D₅₃	—	2	1	no	—
518	C₂³×D₅₃	—	2	1	no	—
519	C₂³×D₅₃	—	2	1	no	—
520	C₂³×D₅₃	—	2	1	no	—
521	C₂³×D₅₃	—	2	1	no	—
522	C₂³×D₅₃	—	4	4	no	—
523	C₂³×D₅₃	—	4	4	no	—
524	C₂³×D₅₃	—	8	2	no	—
525	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
526	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
527	#41×C₅₃	—	2	2	no	—
528	#41×C₅₃	—	2	2	no	—
529	#41×C₅₃	—	4	1	no	—
530	#41×C₅₃	—	4	1	no	—
531	C₂×Q₈×C₅₃	—	2	1	no	—
532	C₂×Q₈×C₅₃	—	2	2	no	—
533	C₂×Q₈×C₅₃	—	4	1	no	—
534	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
535	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
536	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂×D₄×C₅₃	—	2	2	no	—
538	C₂×D₄×C₅₃	—	2	1	no	—
539	C₂×D₄×C₅₃	—	2	1	no	—
540	C₂×D₄×C₅₃	—	2	1	no	—
541	C₂×D₄×C₅₃	—	2	1	no	—
542	C₂×D₄×C₅₃	—	2	1	no	—
543	C₂×D₄×C₅₃	—	4	1	no	—
544	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
545	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
546	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
547	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
548	C₂²×C₄×C₅₃	—	2	1	no	—
549	C₂²×C₄×C₅₃	—	2	1	no	—
550	C₂²×C₄×C₅₃	—	2	1	no	—
551	C₂²×C₄×C₅₃	—	2	1	no	—
552	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
553	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
554	C₂×C₂²⋊D₅₃	—	2	1	no	—
555	C₂×C₂²⋊D₅₃	—	2	1	no	—
556	C₂×C₂²⋊D₅₃	—	2	1	no	—
557	C₂×C₂²⋊D₅₃	—	2	1	no	—
558	C₂×C₂²⋊D₅₃	—	2	1	no	—
559	C₂×C₂²⋊D₅₃	—	2	1	no	—
560	C₂×C₂²⋊D₅₃	—	2	1	no	—
561	C₂×C₂²⋊D₅₃	—	2	1	no	—
562	C₂×C₂²⋊D₅₃	—	2	1	no	—
563	C₂×C₂²⋊D₅₃	—	2	1	no	—
564	C₂×C₂²⋊D₅₃	—	2	1	no	—
565	C₂×C₂²⋊D₅₃	—	2	1	no	—
566	C₂×C₂²⋊D₅₃	—	2	1	no	—
567	C₂×C₂²⋊D₅₃	—	4	4	no	—
568	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
569	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
570	C₂²×Dic₅₃	—	2	1	no	—
571	C₂²×Dic₅₃	—	2	1	no	—
572	C₂²×Dic₅₃	—	2	1	no	—
573	C₂²×Dic₅₃	—	2	1	no	—
574	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
575	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
576	#11719949	—	2	2	no	—
577	#11719949	—	2	2	no	—
578	#11719949	—	4	1	no	—
579	#11719949	—	4	1	no	—
580	Q₈×D₅₃	—	2	2	no	—
581	Q₈×D₅₃	—	2	2	no	—
582	Q₈×D₅₃	—	2	2	no	—
583	Q₈×D₅₃	—	2	2	no	—
584	Q₈×D₅₃	—	2	2	no	—
585	Q₈×D₅₃	—	2	2	no	—
586	Q₈×D₅₃	—	2	2	no	—
587	Q₈×D₅₃	—	4	1	no	—
588	Q₈×D₅₃	—	4	1	no	—
589	Q₈×D₅₃	—	4	4	no	—
590	Q₈×D₅₃	—	4	4	no	—
591	Q₈×D₅₃	C₂×D₄	1	4	yes	—
592	#11719947	—	2	2	no	—
593	#11719947	—	2	2	no	—
594	#11719947	—	4	1	no	—
595	#11719947	—	4	1	no	—
596	#11719947	—	4	4	no	—
597	#11719947	—	4	4	no	—
598	D₄×D₅₃	—	2	4	no	—
599	D₄×D₅₃	—	2	2	no	—
600	D₄×D₅₃	—	2	2	no	—
601	D₄×D₅₃	—	2	2	no	—
602	D₄×D₅₃	—	2	2	no	—
603	D₄×D₅₃	—	2	2	no	—
604	D₄×D₅₃	—	2	2	no	—
605	D₄×D₅₃	—	2	2	no	—
606	D₄×D₅₃	—	4	1	no	—
607	D₄×D₅₃	—	4	1	no	—
608	D₄×D₅₃	—	4	4	no	—
609	D₄×D₅₃	—	4	4	no	—
610	D₄×D₅₃	—	4	4	no	—
611	D₄×D₅₃	—	4	4	no	—
612	D₄×D₅₃	—	4	4	no	—
613	D₄×D₅₃	—	8	2	no	—
614	D₄×D₅₃	C₂×D₄	1	4	yes	—
615	#11719945	—	2	2	no	—
616	#11719945	—	2	2	no	—
617	#11719945	—	4	4	no	—
618	#11719945	—	4	1	no	—
619	#11719945	—	4	1	no	—
620	#11719945	—	4	4	no	—
621	C₂×D₂₁₂	—	2	2	no	—
622	C₂×D₂₁₂	—	2	1	no	—
623	C₂×D₂₁₂	—	2	1	no	—
624	C₂×D₂₁₂	—	2	1	no	—
625	C₂×D₂₁₂	—	2	1	no	—
626	C₂×D₂₁₂	—	2	1	no	—
627	C₂×D₂₁₂	—	4	1	no	—
628	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
629	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
630	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
631	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
632	C₂×C₄×D₅₃	—	2	1	no	—
633	C₂×C₄×D₅₃	—	2	2	no	—
634	C₂×C₄×D₅₃	—	2	2	no	—
635	C₂×C₄×D₅₃	—	2	2	no	—
636	C₂×C₄×D₅₃	—	2	2	no	—
637	C₂×C₄×D₅₃	—	2	1	no	—
638	C₂×C₄×D₅₃	—	2	1	no	—
639	C₂×C₄×D₅₃	—	2	1	no	—
640	C₂×C₄×D₅₃	—	2	1	no	—
641	C₂×C₄×D₅₃	—	2	1	no	—
642	C₂×C₄×D₅₃	—	2	1	no	—
643	C₂×C₄×D₅₃	—	2	1	no	—
644	C₂×C₄×D₅₃	—	2	1	no	—
645	C₂×C₄×D₅₃	—	2	1	no	—
646	C₂×C₄×D₅₃	—	2	1	no	—
647	C₂×C₄×D₅₃	—	2	1	no	—
648	C₂×C₄×D₅₃	—	2	1	no	—
649	C₂×C₄×D₅₃	—	4	4	no	—
650	C₂×C₄×D₅₃	—	4	4	no	—
651	C₂×C₄×D₅₃	—	4	4	no	—
652	C₂×C₄×D₅₃	—	8	2	no	—
653	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
654	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
660	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
661	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
662	C₂×Dic₁₀₆	—	2	1	no	—
663	C₂×Dic₁₀₆	—	2	2	no	—
664	C₂×Dic₁₀₆	—	2	1	no	—
665	C₂×Dic₁₀₆	—	2	1	no	—
666	C₂×Dic₁₀₆	—	2	1	no	—
667	C₂×Dic₁₀₆	—	2	1	no	—
668	C₂×Dic₁₀₆	—	2	1	no	—
669	C₂×Dic₁₀₆	—	4	1	no	—
670	C₂×Dic₁₀₆	—	4	4	no	—
671	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
672	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
673	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
674	Q₁₆×C₅₃	—	2	2	no	—
675	Q₁₆×C₅₃	—	4	1	no	—
676	SD₁₆×C₅₃	—	2	2	no	—
677	SD₁₆×C₅₃	—	2	2	no	—
678	SD₁₆×C₅₃	—	2	2	no	—
679	SD₁₆×C₅₃	—	2	2	no	—
680	SD₁₆×C₅₃	C₂×D₄	1	4	yes	complemented
681	D₈×C₅₃	—	2	2	no	—
682	D₈×C₅₃	—	4	1	no	—
683	C₂×C₈×C₅₃	—	2	2	no	—
684	C₂×C₈×C₅₃	—	2	2	no	—
685	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
686	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
687	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
688	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
689	C₄⋊C₄×C₅₃	—	2	1	no	—
690	C₄⋊C₄×C₅₃	—	2	1	no	—
691	C₄⋊C₄×C₅₃	—	2	1	no	—
692	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
693	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
694	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
695	C₂²⋊C₄×C₅₃	—	2	1	no	—
696	C₂²⋊C₄×C₅₃	—	2	1	no	—
697	C₂²⋊C₄×C₅₃	—	2	1	no	—
698	C₂²⋊C₄×C₅₃	—	2	1	no	—
699	C₂²⋊C₄×C₅₃	—	2	1	no	—
700	C₂²⋊C₄×C₅₃	—	2	1	no	—
701	C₂²⋊C₄×C₅₃	—	2	1	no	—
702	C₂²⋊C₄×C₅₃	—	2	1	no	—
703	C₂²⋊C₄×C₅₃	—	2	1	no	—
704	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
705	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
706	C₄²×C₅₃	—	2	1	no	—
707	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
708	C₂²⋊Dic₅₃	—	2	1	no	—
709	C₂²⋊Dic₅₃	—	2	1	no	—
710	C₂²⋊Dic₅₃	—	2	1	no	—
711	C₂²⋊Dic₅₃	—	2	1	no	—
712	C₂²⋊Dic₅₃	—	2	1	no	—
713	C₂²⋊Dic₅₃	—	2	1	no	—
714	C₂²⋊Dic₅₃	—	2	1	no	—
715	C₂²⋊Dic₅₃	—	2	1	no	—
716	C₂²⋊Dic₅₃	—	2	1	no	—
717	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
718	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
719	#11719925	—	2	2	no	—
720	#11719925	—	2	2	no	—
721	#11719925	—	4	1	no	—
722	#11719925	—	4	1	no	—
723	#11719924	—	2	2	no	—
724	#11719924	—	2	2	no	—
725	#11719924	—	2	2	no	—
726	#11719924	—	2	2	no	—
727	#11719924	C₂×D₄	1	4	yes	complemented
728	#11719923	—	2	2	no	—
729	#11719923	—	2	2	no	—
730	#11719923	—	2	2	no	—
731	#11719923	—	2	2	no	—
732	#11719923	C₂×D₄	1	4	yes	complemented
733	#11719922	—	2	2	no	—
734	#11719922	—	2	2	no	—
735	#11719922	—	4	1	no	—
736	#11719922	—	4	1	no	—
737	#11719921	—	2	1	no	—
738	#11719921	—	2	1	no	—
739	#11719921	—	2	1	no	—
740	#11719921	—	2	1	no	—
741	#11719921	—	2	1	no	—
742	#11719921	—	2	1	no	—
743	#11719921	—	2	1	no	—
744	#11719921	—	2	1	no	—
745	#11719921	—	2	1	no	—
746	#11719921	—	2	1	no	—
747	#11719921	—	2	1	no	—
748	#11719921	—	2	1	no	—
749	#11719921	—	2	1	no	—
750	#11719921	—	2	1	no	—
751	#11719921	—	2	1	no	—
752	#11719921	—	2	1	no	—
753	#11719921	—	2	1	no	—
754	#11719921	—	2	1	no	—
755	#11719921	C₂×D₄	1	1	yes	characteristic
756	#11719921	C₂×D₄	1	1	yes	characteristic
757	#11719921	C₂×D₄	1	1	yes	characteristic
758	#11719921	C₂×D₄	1	1	yes	characteristic
759	C₄⋊Dic₅₃	—	2	1	no	—
760	C₄⋊Dic₅₃	—	2	1	no	—
761	C₄⋊Dic₅₃	—	2	1	no	—
762	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
763	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
764	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
765	#11719919	—	2	1	no	—
766	#11719919	—	2	1	no	—
767	#11719919	—	2	1	no	—
768	#11719919	—	2	1	no	—
769	#11719919	—	2	1	no	—
770	#11719919	—	2	1	no	—
771	#11719919	—	2	1	no	—
772	#11719919	—	2	1	no	—
773	#11719919	C₂×D₄	1	1	yes	characteristic
774	#11719919	C₂×D₄	1	1	yes	characteristic
775	C₄×Dic₅₃	—	2	1	no	—
776	C₄×Dic₅₃	—	2	1	no	—
777	C₄×Dic₅₃	—	2	1	no	—
778	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
779	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
780	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
781	C₂×#88322	—	2	2	no	—
782	C₂×#88322	—	2	2	no	—
783	C₂×#88322	C₂⁴	1	1	yes	characteristic
784	C₂×#88322	C₂⁴	1	1	yes	characteristic
785	C₂×#88322	C₂⁴	1	1	yes	characteristic
786	C₂×#88322	C₂⁴	1	1	yes	characteristic
787	Dic₂₁₂	—	2	2	no	—
788	Dic₂₁₂	—	4	1	no	—
789	D₄₂₄	—	2	2	no	—
790	D₄₂₄	—	4	1	no	—
791	#11719913	—	2	2	no	—
792	#11719913	—	2	2	no	—
793	#11719913	—	2	2	no	—
794	#11719913	—	2	2	no	—
795	#11719913	C₂×D₄	1	4	yes	complemented
796	C₈×D₅₃	—	2	2	no	—
797	C₈×D₅₃	—	2	2	no	—
798	C₈×D₅₃	—	2	2	no	—
799	C₈×D₅₃	—	2	2	no	—
800	C₈×D₅₃	—	2	2	no	—
801	C₈×D₅₃	—	2	2	no	—
802	C₈×D₅₃	—	2	2	no	—
803	C₈×D₅₃	C₂×D₄	1	4	yes	—
804	C₂³×C₅₃	—	2	1	no	—
805	C₂³×C₅₃	—	2	1	no	—
806	C₂³×C₅₃	—	2	1	no	—
807	C₂³×C₅₃	—	4	2	no	—
808	C₂³×C₅₃	—	4	2	no	—
809	C₂³×C₅₃	—	8	1	no	—
810	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
811	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
812	C₂²×D₅₃	—	2	2	no	—
813	C₂²×D₅₃	—	2	2	no	—
814	C₂²×D₅₃	—	2	1	no	—
815	C₂²×D₅₃	—	2	2	no	—
816	C₂²×D₅₃	—	2	4	no	—
817	C₂²×D₅₃	—	2	2	no	—
818	C₂²×D₅₃	—	2	2	no	—
819	C₂²×D₅₃	—	2	1	no	—
820	C₂²×D₅₃	—	2	1	no	—
821	C₂²×D₅₃	—	4	2	no	—
822	C₂²×D₅₃	—	4	2	no	—
823	C₂²×D₅₃	—	4	2	no	—
824	C₂²×D₅₃	—	4	2	no	—
825	C₂²×D₅₃	—	4	2	no	—
826	C₂²×D₅₃	—	4	2	no	—
827	C₂²×D₅₃	—	4	2	no	—
828	C₂²×D₅₃	—	4	2	no	—
829	C₂²×D₅₃	—	4	2	no	—
830	C₂²×D₅₃	—	4	2	no	—
831	C₂²×D₅₃	—	4	2	no	—
832	C₂²×D₅₃	—	4	2	no	—
833	C₂²×D₅₃	—	4	2	no	—
834	C₂²×D₅₃	—	4	2	no	—
835	C₂²×D₅₃	—	8	1	no	—
836	C₂²×D₅₃	—	8	1	no	—
837	C₂²×D₅₃	—	8	16	no	—
838	C₂²×D₅₃	—	8	1	no	—
839	C₂²×D₅₃	#135	1	4	yes	complemented
840	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
841	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
842	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
843	Q₈×C₅₃	—	2	1	no	—
844	Q₈×C₅₃	—	2	1	no	—
845	Q₈×C₅₃	—	2	1	no	—
846	Q₈×C₅₃	—	2	1	no	—
847	Q₈×C₅₃	—	2	1	no	—
848	Q₈×C₅₃	—	4	2	no	—
849	Q₈×C₅₃	C₂²×D₄	1	2	yes	—
850	D₄×C₅₃	—	2	2	no	—
851	D₄×C₅₃	—	2	1	no	—
852	D₄×C₅₃	—	2	1	no	—
853	D₄×C₅₃	—	2	1	no	—
854	D₄×C₅₃	—	2	1	no	—
855	D₄×C₅₃	—	2	1	no	—
856	D₄×C₅₃	—	4	2	no	—
857	D₄×C₅₃	—	4	2	no	—
858	D₄×C₅₃	—	4	2	no	—
859	D₄×C₅₃	—	4	2	no	—
860	D₄×C₅₃	—	8	1	no	—
861	D₄×C₅₃	C₂²×D₄	1	2	yes	—
862	C₂×C₄×C₅₃	—	2	1	no	—
863	C₂×C₄×C₅₃	—	2	1	no	—
864	C₂×C₄×C₅₃	—	2	1	no	—
865	C₂×C₄×C₅₃	—	2	1	no	—
866	C₂×C₄×C₅₃	—	2	1	no	—
867	C₂×C₄×C₅₃	—	2	1	no	—
868	C₂×C₄×C₅₃	—	2	1	no	—
869	C₂×C₄×C₅₃	—	2	1	no	—
870	C₂×C₄×C₅₃	—	2	1	no	—
871	C₂×C₄×C₅₃	—	4	2	no	—
872	C₂×C₄×C₅₃	—	4	2	no	—
873	C₂×C₄×C₅₃	—	4	2	no	—
874	C₂×C₄×C₅₃	—	8	1	no	—
875	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
876	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
877	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
878	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
879	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
880	C₂²⋊D₅₃	—	2	2	no	—
881	C₂²⋊D₅₃	—	2	2	no	—
882	C₂²⋊D₅₃	—	2	4	no	—
883	C₂²⋊D₅₃	—	4	2	no	—
884	C₂²⋊D₅₃	—	4	2	no	—
885	C₂²⋊D₅₃	—	4	2	no	—
886	C₂²⋊D₅₃	—	4	2	no	—
887	C₂²⋊D₅₃	—	4	2	no	—
888	C₂²⋊D₅₃	—	4	2	no	—
889	C₂²⋊D₅₃	—	4	2	no	—
890	C₂²⋊D₅₃	—	4	2	no	—
891	C₂²⋊D₅₃	—	4	2	no	—
892	C₂²⋊D₅₃	—	4	2	no	—
893	C₂²⋊D₅₃	—	8	1	no	—
894	C₂²⋊D₅₃	—	8	1	no	—
895	C₂×Dic₅₃	—	2	1	no	—
896	C₂×Dic₅₃	—	2	2	no	—
897	C₂×Dic₅₃	—	2	2	no	—
898	C₂×Dic₅₃	—	2	1	no	—
899	C₂×Dic₅₃	—	2	1	no	—
900	C₂×Dic₅₃	—	2	1	no	—
901	C₂×Dic₅₃	—	2	1	no	—
902	C₂×Dic₅₃	—	4	2	no	—
903	C₂×Dic₅₃	—	4	2	no	—
904	C₂×Dic₅₃	—	4	2	no	—
905	C₂×Dic₅₃	—	8	1	no	—
906	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
907	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
908	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
909	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
910	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
911	D₂₁₂	—	2	2	no	—
912	D₂₁₂	—	2	1	no	—
913	D₂₁₂	—	2	1	no	—
914	D₂₁₂	—	2	1	no	—
915	D₂₁₂	—	2	1	no	—
916	D₂₁₂	—	2	1	no	—
917	D₂₁₂	—	4	2	no	—
918	D₂₁₂	—	4	2	no	—
919	D₂₁₂	—	4	2	no	—
920	D₂₁₂	—	4	2	no	—
921	D₂₁₂	—	8	1	no	—
922	D₂₁₂	C₂²×D₄	1	2	yes	—
923	C₄×D₅₃	—	2	2	no	—
924	C₄×D₅₃	—	2	2	no	—
925	C₄×D₅₃	—	2	4	no	—
926	C₄×D₅₃	—	2	2	no	—
927	C₄×D₅₃	—	2	2	no	—
928	C₄×D₅₃	—	2	1	no	—
929	C₄×D₅₃	—	2	1	no	—
930	C₄×D₅₃	—	2	1	no	—
931	C₄×D₅₃	—	2	1	no	—
932	C₄×D₅₃	—	2	2	no	—
933	C₄×D₅₃	—	2	2	no	—
934	C₄×D₅₃	—	4	2	no	—
935	C₄×D₅₃	—	4	2	no	—
936	C₄×D₅₃	—	4	2	no	—
937	C₄×D₅₃	—	4	2	no	—
938	C₄×D₅₃	—	4	2	no	—
939	C₄×D₅₃	—	4	2	no	—
940	C₄×D₅₃	—	4	2	no	—
941	C₄×D₅₃	—	4	2	no	—
942	C₄×D₅₃	—	4	2	no	—
943	C₄×D₅₃	—	4	2	no	—
944	C₄×D₅₃	—	8	1	no	—
945	C₄×D₅₃	—	8	1	no	—
946	C₄×D₅₃	C₂²×D₄	1	2	yes	—
947	C₄×D₅₃	H(5,𝔽₂)	1	2	yes	—
948	Dic₁₀₆	—	2	1	no	—
949	Dic₁₀₆	—	2	4	no	—
950	Dic₁₀₆	—	2	1	no	—
951	Dic₁₀₆	—	2	1	no	—
952	Dic₁₀₆	—	2	1	no	—
953	Dic₁₀₆	—	2	1	no	—
954	Dic₁₀₆	—	4	2	no	—
955	Dic₁₀₆	—	4	2	no	—
956	Dic₁₀₆	—	4	2	no	—
957	Dic₁₀₆	—	4	2	no	—
958	Dic₁₀₆	—	4	2	no	—
959	Dic₁₀₆	C₂²×D₄	1	2	yes	—
960	C₈×C₅₃	—	2	1	no	—
961	C₈×C₅₃	—	2	1	no	—
962	C₈×C₅₃	—	2	1	no	—
963	C₈×C₅₃	C₂²×D₄	1	2	yes	—
964	#88322	—	2	1	no	—
965	#88322	—	2	1	no	—
966	#88322	—	2	1	no	—
967	#88322	C₂²×D₄	1	2	yes	—
968	C₂×#3282	—	53	1	no	maximal, Sylow
969	C₂²×C₅₃	—	2	1	no	—
970	C₂²×C₅₃	—	2	1	no	—
971	C₂²×C₅₃	—	2	1	no	—
972	C₂²×C₅₃	—	2	2	no	—
973	C₂²×C₅₃	—	2	1	no	—
974	C₂²×C₅₃	—	2	1	no	—
975	C₂²×C₅₃	—	4	1	no	—
976	C₂²×C₅₃	—	4	1	no	—
977	C₂²×C₅₃	—	4	1	no	—
978	C₂²×C₅₃	—	4	1	no	—
979	C₂²×C₅₃	—	4	1	no	—
980	C₂²×C₅₃	—	4	1	no	—
981	C₂²×C₅₃	—	4	1	no	—
982	C₂²×C₅₃	—	4	1	no	—
983	C₂²×C₅₃	—	8	4	no	—
984	C₂²×C₅₃	C₂×#135	1	2	yes	complemented
985	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
986	C₂×D₅₃	—	2	1	no	—
987	C₂×D₅₃	—	2	1	no	—
988	C₂×D₅₃	—	2	8	no	—
989	C₂×D₅₃	—	2	1	no	—
990	C₂×D₅₃	—	2	2	no	—
991	C₂×D₅₃	—	2	1	no	—
992	C₂×D₅₃	—	2	1	no	—
993	C₂×D₅₃	—	4	1	no	—
994	C₂×D₅₃	—	4	1	no	—
995	C₂×D₅₃	—	4	4	no	—
996	C₂×D₅₃	—	4	8	no	—
997	C₂×D₅₃	—	4	1	no	—
998	C₂×D₅₃	—	4	1	no	—
999	C₂×D₅₃	—	4	1	no	—
1000	C₂×D₅₃	—	4	1	no	—
1001	C₂×D₅₃	—	4	1	no	—
1002	C₂×D₅₃	—	4	1	no	—
1003	C₂×D₅₃	—	8	4	no	—
1004	C₂×D₅₃	—	8	4	no	—
1005	C₂×D₅₃	—	8	4	no	—
1006	C₂×D₅₃	—	8	4	no	—
1007	C₂×D₅₃	—	8	4	no	—
1008	C₂×D₅₃	D₄²	1	2	yes	—
1009	C₂×D₅₃	C₂×#135	1	2	yes	—
1010	C₂×D₅₃	C₂×#135	1	2	yes	complemented
1011	C₂×D₅₃	#577	1	2	yes	—
1012	C₄×C₅₃	—	2	2	no	—
1013	C₄×C₅₃	—	2	1	no	—
1014	C₄×C₅₃	—	2	1	no	—
1015	C₄×C₅₃	—	2	1	no	—
1016	C₄×C₅₃	—	2	1	no	—
1017	C₄×C₅₃	—	4	1	no	—
1018	C₄×C₅₃	—	4	1	no	—
1019	C₄×C₅₃	—	4	1	no	—
1020	C₄×C₅₃	—	4	1	no	—
1021	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
1022	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1023	Dic₅₃	—	2	2	no	—
1024	Dic₅₃	—	2	1	no	—
1025	Dic₅₃	—	2	1	no	—
1026	Dic₅₃	—	2	1	no	—
1027	Dic₅₃	—	2	1	no	—
1028	Dic₅₃	—	4	1	no	—
1029	Dic₅₃	—	4	1	no	—
1030	Dic₅₃	—	4	1	no	—
1031	Dic₅₃	—	4	1	no	—
1032	Dic₅₃	D₄²	1	2	yes	—
1033	C₂²×#135	—	53	1	no	—
1034	C₂³×SD₁₆	—	53	1	no	—
1035	C₂×#548	—	53	1	no	—
1036	C₂×#546	—	53	1	no	—
1037	#3282	—	53	1	no	—
1038	#3282	—	53	1	no	—
1039	#3282	—	53	1	no	—
1040	#3282	—	53	1	no	—
1041	#3282	—	53	1	no	—
1042	#3282	—	53	1	no	—
1043	#3282	—	53	1	no	—
1044	#3282	—	53	1	no	—
1045	#3282	—	53	1	no	—
1046	#3282	—	53	1	no	—
1047	#3282	—	53	1	no	—
1048	#3282	—	53	1	no	—
1049	#3282	—	53	1	no	—
1050	#3282	—	53	1	no	—
1051	#3282	—	53	1	no	—
1052	#3282	D₅₃	1	1	yes	characteristic, direct product factor
1053	C₂×#495	—	53	1	no	—
1054	C₂×#465	—	53	1	no	—
1055	C₂×#465	—	53	1	no	—
1056	C₂×#464	—	53	1	no	—
1057	C₂×#463	—	53	1	no	—
1058	C₂×#452	—	53	1	no	—
1059	C₂×#449	—	53	1	no	—
1060	C₂×#451	—	53	1	no	—
1061	C₂×#447	—	53	1	no	—
1062	C₂×C₄×SD₁₆	—	53	1	no	—
1063	C₂×C₈×D₄	—	53	1	no	—
1064	C₂×C₅₃	—	2	2	no	—
1065	C₂×C₅₃	—	4	2	no	—
1066	C₂×C₅₃	—	4	1	no	—
1067	C₂×C₅₃	—	8	1	no	—
1068	C₂×C₅₃	—	8	1	no	—
1069	C₂×C₅₃	C₂×D₄²	1	1	yes	characteristic
1070	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
1071	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
1072	D₅₃	—	2	2	no	—
1073	D₅₃	—	4	1	no	—
1074	D₅₃	—	4	2	no	—
1075	D₅₃	—	8	1	no	—
1076	D₅₃	—	8	1	no	—
1077	D₅₃	#3282	1	4	yes	direct product factor
1078	C₂²×#41	—	53	1	no	—
1079	C₂²×#41	—	53	1	no	—
1080	C₂³×Q₈	—	53	1	no	—
1081	C₂³×D₄	—	53	1	no	—
1082	C₂×#135	—	53	1	no	—
1083	C₂×#135	—	53	1	no	—
1084	C₂×#135	—	53	1	no	—
1085	C₂×#135	—	53	1	no	—
1086	C₂×#135	—	53	1	no	—
1087	C₂×#135	—	53	1	no	—
1088	C₂×#135	—	53	1	no	—
1089	C₂×#135	—	106	8	no	—
1090	C₂×#135	C₂×D₅₃	1	1	yes	characteristic, complemented
1091	C₂²×Q₁₆	—	53	1	no	—
1092	C₂²×Q₁₆	—	53	1	no	—
1093	C₂²×SD₁₆	—	53	1	no	—
1094	C₂²×SD₁₆	—	53	1	no	—
1095	C₂²×SD₁₆	—	53	1	no	—
1096	C₂²×SD₁₆	—	53	1	no	—
1097	C₂²×SD₁₆	—	53	1	no	—
1098	C₂²×SD₁₆	—	53	1	no	—
1099	C₂²×SD₁₆	—	53	1	no	—
1100	C₂²×SD₁₆	—	53	1	no	—
1101	C₂²×SD₁₆	—	53	1	no	—
1102	C₂²×SD₁₆	—	53	1	no	—
1103	C₂²×SD₁₆	—	53	1	no	—
1104	C₂²×SD₁₆	—	53	1	no	—
1105	C₂²×SD₁₆	—	106	8	no	—
1106	C₂²×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
1107	C₂²×D₈	—	53	1	no	—
1108	C₂²×D₈	—	53	1	no	—
1109	C₂³×C₈	—	53	1	no	—
1110	C₂³×C₈	—	53	1	no	—
1111	#548	—	53	1	no	—
1112	#548	—	53	1	no	—
1113	#548	—	53	1	no	—
1114	#548	—	53	1	no	—
1115	#548	—	53	1	no	—
1116	#548	—	53	1	no	—
1117	#548	—	53	1	no	—
1118	#548	—	106	1	no	—
1119	#548	—	106	1	no	—
1120	#548	—	106	1	no	—
1121	#548	—	106	1	no	—
1122	#548	C₂×D₅₃	1	1	yes	characteristic, complemented
1123	#546	—	53	1	no	—
1124	#546	—	53	1	no	—
1125	#546	—	53	1	no	—
1126	#546	—	53	1	no	—
1127	#546	—	53	1	no	—
1128	#546	—	53	1	no	—
1129	#546	—	53	1	no	—
1130	#546	—	106	1	no	—
1131	#546	—	106	1	no	—
1132	#546	—	106	1	no	—
1133	#546	—	106	1	no	—
1134	#546	C₂×D₅₃	1	1	yes	characteristic, complemented
1135	C₂×#124	—	53	1	no	—
1136	C₂×#124	—	53	1	no	—
1137	C₂×#124	—	106	1	no	—
1138	C₂×#123	—	106	1	no	—
1139	C₂×C₂²⋊Q₈	—	53	1	no	—
1140	C₂×C₂²⋊Q₈	—	53	1	no	—
1141	C₂×C₂²⋊Q₈	—	106	1	no	—
1142	C₂×#121	—	53	1	no	—
1143	C₂×#121	—	53	1	no	—
1144	C₂×#121	—	106	1	no	—
1145	C₂×#121	—	106	1	no	—
1146	C₂×#120	—	106	1	no	—
1147	C₂×C₄×Q₈	—	53	1	no	—
1148	C₂×C₄×D₄	—	53	1	no	—
1149	C₂×C₄×D₄	—	53	1	no	—
1150	C₂×C₄×D₄	—	106	1	no	—
1151	C₂²×C₂²⋊C₄	—	106	1	no	—
1152	#495	—	53	1	no	—
1153	#495	—	53	1	no	—
1154	#495	—	53	1	no	—
1155	#495	—	53	1	no	—
1156	#495	—	53	1	no	—
1157	#495	—	53	1	no	—
1158	#495	—	53	1	no	—
1159	#495	C₂×D₅₃	1	1	yes	characteristic, complemented
1160	#465	—	53	1	no	—
1161	#465	—	53	1	no	—
1162	#465	—	53	1	no	—
1163	#465	—	53	1	no	—
1164	#465	—	53	1	no	—
1165	#465	—	53	1	no	—
1166	#465	—	53	1	no	—
1167	#465	—	53	1	no	—
1168	#465	—	53	1	no	—
1169	#465	—	53	1	no	—
1170	#465	—	53	1	no	—
1171	#465	—	53	1	no	—
1172	#465	—	53	1	no	—
1173	#465	—	53	1	no	—
1174	#465	C₂×D₅₃	1	1	yes	characteristic, complemented
1175	#465	C₂×D₅₃	1	1	yes	characteristic, complemented
1176	#464	—	53	1	no	—
1177	#464	—	53	1	no	—
1178	#464	—	53	1	no	—
1179	#464	—	53	1	no	—
1180	#464	—	53	1	no	—
1181	#464	—	53	1	no	—
1182	#464	—	53	1	no	—
1183	#464	C₂×D₅₃	1	1	yes	characteristic, complemented
1184	#463	—	53	1	no	—
1185	#463	—	53	1	no	—
1186	#463	—	53	1	no	—
1187	#463	—	53	1	no	—
1188	#463	—	53	1	no	—
1189	#463	—	53	1	no	—
1190	#463	—	53	1	no	—
1191	#463	C₂×D₅₃	1	1	yes	characteristic, complemented
1192	#452	—	53	1	no	—
1193	#452	—	53	1	no	—
1194	#452	—	53	1	no	—
1195	#452	—	53	1	no	—
1196	#452	—	53	1	no	—
1197	#452	—	53	1	no	—
1198	#452	—	53	1	no	—
1199	#452	C₂×D₅₃	1	1	yes	characteristic, complemented
1200	#451	—	53	1	no	—
1201	#451	—	53	1	no	—
1202	#451	—	53	1	no	—
1203	#451	—	53	1	no	—
1204	#451	—	53	1	no	—
1205	#451	—	53	1	no	—
1206	#451	—	53	1	no	—
1207	#451	C₂×D₅₃	1	1	yes	characteristic, complemented
1208	#449	—	53	1	no	—
1209	#449	—	53	1	no	—
1210	#449	—	53	1	no	—
1211	#449	—	53	1	no	—
1212	#449	—	53	1	no	—
1213	#449	—	53	1	no	—
1214	#449	—	53	1	no	—
1215	#449	C₂×D₅₃	1	1	yes	characteristic, complemented
1216	#447	—	53	1	no	—
1217	#447	—	53	1	no	—
1218	#447	—	53	1	no	—
1219	#447	—	53	1	no	—
1220	#447	—	53	1	no	—
1221	#447	—	53	1	no	—
1222	#447	—	53	1	no	—
1223	#447	C₂×D₅₃	1	1	yes	characteristic, complemented
1224	C₄×SD₁₆	—	53	1	no	—
1225	C₄×SD₁₆	—	53	1	no	—
1226	C₄×SD₁₆	—	53	1	no	—
1227	C₄×SD₁₆	—	53	1	no	—
1228	C₄×SD₁₆	—	53	1	no	—
1229	C₄×SD₁₆	—	53	1	no	—
1230	C₄×SD₁₆	—	53	1	no	—
1231	C₄×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
1232	C₈×D₄	—	53	1	no	—
1233	C₈×D₄	—	53	1	no	—
1234	C₈×D₄	—	53	1	no	—
1235	C₈×D₄	—	53	1	no	—
1236	C₈×D₄	—	53	1	no	—
1237	C₈×D₄	—	53	1	no	—
1238	C₈×D₄	—	53	1	no	—
1239	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
1240	C₂×#106	—	53	1	no	—
1241	C₂×C₄⋊C₈	—	53	1	no	—
1242	C₂×#103	—	53	1	no	—
1243	C₂×#103	—	53	1	no	—
1244	C₂×#103	—	53	1	no	—
1245	C₂×#102	—	53	1	no	—
1246	C₂×#102	—	53	1	no	—
1247	C₂×#102	—	53	1	no	—
1248	C₂×C₂²⋊C₈	—	53	1	no	—
1249	C₂×C₂²⋊C₈	—	53	1	no	—
1250	C₂×C₄×C₈	—	53	1	no	—
1251	C₅₃	C₂×#3282	1	1	yes	characteristic, complemented, Sylow
1252	C₂⁵	—	106	1	no	—
1253	C₂×#41	—	53	1	no	—
1254	C₂×#41	—	53	1	no	—
1255	C₂×#41	—	53	1	no	—
1256	C₂×#41	—	53	1	no	—
1257	C₂×#41	—	53	1	no	—
1258	C₂×#41	—	53	1	no	—
1259	C₂×#41	—	106	1	no	—
1260	C₂×#41	—	106	1	no	—
1261	C₂×#41	—	106	1	no	—
1262	C₂×#41	—	106	1	no	—
1263	C₂×#41	—	106	4	no	—
1264	C₂×#41	—	106	4	no	—
1265	C₂×#41	—	212	2	no	—
1266	C₂×#41	—	212	2	no	—
1267	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1268	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic, complemented
1269	C₂²×Q₈	—	53	1	no	—
1270	C₂²×Q₈	—	53	1	no	—
1271	C₂²×Q₈	—	53	1	no	—
1272	C₂²×Q₈	—	53	1	no	—
1273	C₂²×Q₈	—	53	1	no	—
1274	C₂²×Q₈	—	53	1	no	—
1275	C₂²×Q₈	—	106	1	no	—
1276	C₂²×Q₈	—	106	1	no	—
1277	C₂²×Q₈	—	106	1	no	—
1278	C₂²×Q₈	—	106	4	no	—
1279	C₂²×Q₈	—	212	2	no	—
1280	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1281	C₂²×D₄	—	53	1	no	—
1282	C₂²×D₄	—	53	1	no	—
1283	C₂²×D₄	—	53	1	no	—
1284	C₂²×D₄	—	53	1	no	—
1285	C₂²×D₄	—	53	1	no	—
1286	C₂²×D₄	—	53	1	no	—
1287	C₂²×D₄	—	53	1	no	—
1288	C₂²×D₄	—	106	1	no	—
1289	C₂²×D₄	—	106	1	no	—
1290	C₂²×D₄	—	106	1	no	—
1291	C₂²×D₄	—	106	4	no	—
1292	C₂²×D₄	—	106	1	no	—
1293	C₂²×D₄	—	106	1	no	—
1294	C₂²×D₄	—	106	1	no	—
1295	C₂²×D₄	—	106	1	no	—
1296	C₂²×D₄	—	212	2	no	—
1297	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1298	C₂³×C₄	—	53	1	no	—
1299	C₂³×C₄	—	53	1	no	—
1300	C₂³×C₄	—	106	1	no	—
1301	C₂³×C₄	—	106	1	no	—
1302	C₂³×C₄	—	106	1	no	—
1303	C₂³×C₄	—	106	1	no	—
1304	#135	—	2	4	no	—
1305	#135	—	106	4	no	—
1306	#135	—	106	4	no	—
1307	#135	—	106	4	no	—
1308	#135	—	106	4	no	—
1309	#135	—	106	4	no	—
1310	#135	—	106	4	no	—
1311	#135	—	106	4	no	—
1312	C₂×Q₁₆	—	53	1	no	—
1313	C₂×Q₁₆	—	53	1	no	—
1314	C₂×Q₁₆	—	53	1	no	—
1315	C₂×Q₁₆	—	53	1	no	—
1316	C₂×Q₁₆	—	53	1	no	—
1317	C₂×Q₁₆	—	53	1	no	—
1318	C₂×Q₁₆	—	106	4	no	—
1319	C₂×Q₁₆	—	212	2	no	—
1320	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1321	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1322	C₂×SD₁₆	—	2	4	no	—
1323	C₂×SD₁₆	—	53	1	no	—
1324	C₂×SD₁₆	—	53	1	no	—
1325	C₂×SD₁₆	—	53	8	no	—
1326	C₂×SD₁₆	—	53	1	no	—
1327	C₂×SD₁₆	—	53	1	no	—
1328	C₂×SD₁₆	—	53	1	no	—
1329	C₂×SD₁₆	—	53	1	no	—
1330	C₂×SD₁₆	—	53	1	no	—
1331	C₂×SD₁₆	—	53	1	no	—
1332	C₂×SD₁₆	—	53	1	no	—
1333	C₂×SD₁₆	—	53	1	no	—
1334	C₂×SD₁₆	—	53	1	no	—
1335	C₂×SD₁₆	—	53	1	no	—
1336	C₂×SD₁₆	—	53	1	no	—
1337	C₂×SD₁₆	—	53	1	no	—
1338	C₂×SD₁₆	—	53	1	no	—
1339	C₂×SD₁₆	—	106	4	no	—
1340	C₂×SD₁₆	—	106	4	no	—
1341	C₂×SD₁₆	—	106	4	no	—
1342	C₂×SD₁₆	—	106	4	no	—
1343	C₂×SD₁₆	—	106	4	no	—
1344	C₂×SD₁₆	—	106	4	no	—
1345	C₂×SD₁₆	—	106	4	no	—
1346	C₂×SD₁₆	—	106	4	no	—
1347	C₂×SD₁₆	—	106	4	no	—
1348	C₂×SD₁₆	—	106	4	no	—
1349	C₂×SD₁₆	—	106	4	no	—
1350	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1351	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1352	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1353	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1354	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1355	C₂×D₈	—	53	1	no	—
1356	C₂×D₈	—	53	1	no	—
1357	C₂×D₈	—	53	1	no	—
1358	C₂×D₈	—	53	1	no	—
1359	C₂×D₈	—	53	1	no	—
1360	C₂×D₈	—	53	1	no	—
1361	C₂×D₈	—	106	4	no	—
1362	C₂×D₈	—	212	2	no	—
1363	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1364	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1365	C₂²×C₈	—	53	1	no	—
1366	C₂²×C₈	—	53	1	no	—
1367	C₂²×C₈	—	53	1	no	—
1368	C₂²×C₈	—	53	1	no	—
1369	C₂²×C₈	—	53	1	no	—
1370	C₂²×C₈	—	53	1	no	—
1371	C₂²×C₈	—	53	1	no	—
1372	C₂²×C₈	—	53	1	no	—
1373	C₂²×C₈	—	53	1	no	—
1374	C₂²×C₈	—	53	1	no	—
1375	C₂²×C₈	—	106	4	no	—
1376	C₂²×C₈	—	106	4	no	—
1377	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
1378	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1379	#124	—	2	1	no	—
1380	#124	—	53	1	no	—
1381	#124	—	53	1	no	—
1382	#124	—	53	1	no	—
1383	#124	—	53	1	no	—
1384	#124	—	53	1	no	—
1385	#124	—	53	1	no	—
1386	#124	—	106	1	no	—
1387	#124	—	106	1	no	—
1388	#124	—	106	1	no	—
1389	#124	—	106	1	no	—
1390	#124	—	106	1	no	—
1391	#124	—	106	1	no	—
1392	#124	—	106	1	no	—
1393	#124	—	106	1	no	—
1394	#124	—	106	1	no	—
1395	#124	—	106	1	no	—
1396	#124	—	106	1	no	—
1397	#124	C₂²×D₅₃	1	1	yes	characteristic
1398	#124	C₂²×D₅₃	1	1	yes	characteristic, complemented
1399	#123	—	2	1	no	—
1400	#123	—	106	1	no	—
1401	#123	—	106	1	no	—
1402	#123	—	106	1	no	—
1403	#123	—	106	1	no	—
1404	#123	—	106	1	no	—
1405	#123	—	106	1	no	—
1406	#123	—	106	1	no	—
1407	C₂²⋊Q₈	—	2	1	no	—
1408	C₂²⋊Q₈	—	53	1	no	—
1409	C₂²⋊Q₈	—	53	1	no	—
1410	C₂²⋊Q₈	—	53	1	no	—
1411	C₂²⋊Q₈	—	53	1	no	—
1412	C₂²⋊Q₈	—	53	1	no	—
1413	C₂²⋊Q₈	—	53	1	no	—
1414	C₂²⋊Q₈	—	106	1	no	—
1415	C₂²⋊Q₈	—	106	1	no	—
1416	C₂²⋊Q₈	—	106	1	no	—
1417	C₂²⋊Q₈	—	106	1	no	—
1418	C₂²⋊Q₈	—	106	1	no	—
1419	C₂²⋊Q₈	—	106	1	no	—
1420	C₂²⋊Q₈	—	106	1	no	—
1421	C₂²⋊Q₈	—	106	1	no	—
1422	C₂²⋊Q₈	—	106	1	no	—
1423	C₂²⋊Q₈	—	106	1	no	—
1424	C₂²⋊Q₈	—	106	1	no	—
1425	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
1426	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1427	#121	—	2	1	no	—
1428	#121	—	2	1	no	—
1429	#121	—	53	1	no	—
1430	#121	—	53	1	no	—
1431	#121	—	53	1	no	—
1432	#121	—	53	1	no	—
1433	#121	—	53	1	no	—
1434	#121	—	53	1	no	—
1435	#121	—	106	1	no	—
1436	#121	—	106	1	no	—
1437	#121	—	106	1	no	—
1438	#121	—	106	1	no	—
1439	#121	—	106	1	no	—
1440	#121	—	106	1	no	—
1441	#121	—	106	1	no	—
1442	#121	—	106	1	no	—
1443	#121	—	106	1	no	—
1444	#121	—	106	1	no	—
1445	#121	—	106	1	no	—
1446	#121	—	106	1	no	—
1447	#121	—	106	1	no	—
1448	#121	—	106	1	no	—
1449	#121	—	106	1	no	—
1450	#121	—	106	1	no	—
1451	#121	—	106	1	no	—
1452	#121	—	106	1	no	—
1453	#121	C₂²×D₅₃	1	1	yes	characteristic
1454	#121	C₂²×D₅₃	1	1	yes	characteristic
1455	#120	—	2	1	no	—
1456	#120	—	106	1	no	—
1457	#120	—	106	1	no	—
1458	#120	—	106	1	no	—
1459	#120	—	106	1	no	—
1460	#120	—	106	1	no	—
1461	#120	—	106	1	no	—
1462	#120	—	106	1	no	—
1463	C₄×Q₈	—	53	1	no	—
1464	C₄×Q₈	—	53	1	no	—
1465	C₄×Q₈	—	53	1	no	—
1466	C₄×Q₈	—	106	1	no	—
1467	C₄×Q₈	—	106	1	no	—
1468	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1469	C₄×D₄	—	2	1	no	—
1470	C₄×D₄	—	53	1	no	—
1471	C₄×D₄	—	53	1	no	—
1472	C₄×D₄	—	53	1	no	—
1473	C₄×D₄	—	53	1	no	—
1474	C₄×D₄	—	53	1	no	—
1475	C₄×D₄	—	53	1	no	—
1476	C₄×D₄	—	53	1	no	—
1477	C₄×D₄	—	53	1	no	—
1478	C₄×D₄	—	53	1	no	—
1479	C₄×D₄	—	53	1	no	—
1480	C₄×D₄	—	106	1	no	—
1481	C₄×D₄	—	106	1	no	—
1482	C₄×D₄	—	106	1	no	—
1483	C₄×D₄	—	106	1	no	—
1484	C₄×D₄	—	106	1	no	—
1485	C₄×D₄	—	106	1	no	—
1486	C₄×D₄	—	106	1	no	—
1487	C₄×D₄	—	106	1	no	—
1488	C₄×D₄	—	106	1	no	—
1489	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1490	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1491	C₂×C₄⋊C₄	—	53	1	no	—
1492	C₂×C₄⋊C₄	—	53	1	no	—
1493	C₂×C₄⋊C₄	—	53	1	no	—
1494	C₂×C₄⋊C₄	—	106	1	no	—
1495	C₂×C₄⋊C₄	—	106	1	no	—
1496	C₂×C₄⋊C₄	—	106	1	no	—
1497	C₂×C₂²⋊C₄	—	2	1	no	—
1498	C₂×C₂²⋊C₄	—	53	1	no	—
1499	C₂×C₂²⋊C₄	—	53	1	no	—
1500	C₂×C₂²⋊C₄	—	106	1	no	—
1501	C₂×C₂²⋊C₄	—	106	1	no	—
1502	C₂×C₂²⋊C₄	—	106	1	no	—
1503	C₂×C₂²⋊C₄	—	106	1	no	—
1504	C₂×C₂²⋊C₄	—	106	1	no	—
1505	C₂×C₂²⋊C₄	—	106	1	no	—
1506	C₂×C₂²⋊C₄	—	106	1	no	—
1507	C₂×C₂²⋊C₄	—	106	1	no	—
1508	C₂×C₂²⋊C₄	—	106	1	no	—
1509	C₂×C₂²⋊C₄	—	106	1	no	—
1510	C₂×C₂²⋊C₄	—	106	1	no	—
1511	C₂×C₂²⋊C₄	—	106	1	no	—
1512	C₂×C₂²⋊C₄	—	106	1	no	—
1513	C₂×C₂²⋊C₄	—	106	1	no	—
1514	C₂×C₂²⋊C₄	—	106	1	no	—
1515	C₂×C₂²⋊C₄	—	106	1	no	—
1516	C₂×C₄²	—	53	1	no	—
1517	C₂×C₄²	—	106	1	no	—
1518	#106	—	53	1	no	—
1519	#106	—	53	1	no	—
1520	#106	—	53	1	no	—
1521	#106	C₂²×D₅₃	1	1	yes	characteristic, complemented
1522	C₄⋊C₈	—	53	1	no	—
1523	C₄⋊C₈	—	53	1	no	—
1524	C₄⋊C₈	—	53	1	no	—
1525	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1526	#103	—	53	1	no	—
1527	#103	—	53	1	no	—
1528	#103	—	53	1	no	—
1529	#103	—	53	1	no	—
1530	#103	—	53	1	no	—
1531	#103	—	53	1	no	—
1532	#103	—	53	1	no	—
1533	#103	—	53	1	no	—
1534	#103	—	53	1	no	—
1535	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
1536	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
1537	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
1538	#102	—	53	1	no	—
1539	#102	—	53	1	no	—
1540	#102	—	53	1	no	—
1541	#102	—	53	1	no	—
1542	#102	—	53	1	no	—
1543	#102	—	53	1	no	—
1544	#102	—	53	1	no	—
1545	#102	—	53	1	no	—
1546	#102	—	53	1	no	—
1547	#102	C₂²×D₅₃	1	1	yes	characteristic
1548	#102	C₂²×D₅₃	1	1	yes	characteristic
1549	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
1550	C₂²⋊C₈	—	53	1	no	—
1551	C₂²⋊C₈	—	53	1	no	—
1552	C₂²⋊C₈	—	53	1	no	—
1553	C₂²⋊C₈	—	53	1	no	—
1554	C₂²⋊C₈	—	53	1	no	—
1555	C₂²⋊C₈	—	53	1	no	—
1556	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1557	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1558	C₄×C₈	—	53	1	no	—
1559	C₄×C₈	—	53	1	no	—
1560	C₄×C₈	—	53	1	no	—
1561	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1562	C₂⁴	—	2	1	no	—
1563	C₂⁴	—	53	1	no	—
1564	C₂⁴	—	53	1	no	—
1565	C₂⁴	—	106	1	no	—
1566	C₂⁴	—	106	1	no	—
1567	C₂⁴	—	106	1	no	—
1568	C₂⁴	—	106	1	no	—
1569	C₂⁴	—	106	1	no	—
1570	C₂⁴	—	106	1	no	—
1571	C₂⁴	—	424	2	no	—
1572	C₂⁴	—	212	4	no	—
1573	C₂⁴	—	212	4	no	—
1574	#41	—	2	2	no	—
1575	#41	—	2	2	no	—
1576	#41	—	4	1	no	—
1577	#41	—	4	1	no	—
1578	#41	—	106	2	no	—
1579	#41	—	106	2	no	—
1580	#41	—	106	2	no	—
1581	#41	—	106	2	no	—
1582	#41	—	106	2	no	—
1583	#41	—	106	2	no	—
1584	#41	—	212	1	no	—
1585	#41	—	212	1	no	—
1586	#41	—	212	4	no	—
1587	#41	—	212	4	no	—
1588	#41	—	212	1	no	—
1589	#41	—	212	1	no	—
1590	#41	—	212	4	no	—
1591	#41	—	212	4	no	—
1592	#41	—	212	1	no	—
1593	#41	—	212	1	no	—
1594	C₂×Q₈	—	2	1	no	—
1595	C₂×Q₈	—	2	2	no	—
1596	C₂×Q₈	—	4	1	no	—
1597	C₂×Q₈	—	53	4	no	—
1598	C₂×Q₈	—	53	1	no	—
1599	C₂×Q₈	—	53	1	no	—
1600	C₂×Q₈	—	53	1	no	—
1601	C₂×Q₈	—	106	1	no	—
1602	C₂×Q₈	—	106	1	no	—
1603	C₂×Q₈	—	106	1	no	—
1604	C₂×Q₈	—	106	1	no	—
1605	C₂×Q₈	—	106	1	no	—
1606	C₂×Q₈	—	106	2	no	—
1607	C₂×Q₈	—	106	2	no	—
1608	C₂×Q₈	—	106	2	no	—
1609	C₂×Q₈	—	106	2	no	—
1610	C₂×Q₈	—	106	2	no	—
1611	C₂×Q₈	—	106	2	no	—
1612	C₂×Q₈	—	106	1	no	—
1613	C₂×Q₈	—	106	2	no	—
1614	C₂×Q₈	—	106	2	no	—
1615	C₂×Q₈	—	212	1	no	—
1616	C₂×Q₈	—	212	4	no	—
1617	C₂×Q₈	—	212	4	no	—
1618	C₂×Q₈	—	212	1	no	—
1619	C₂×Q₈	—	212	1	no	—
1620	C₂×Q₈	—	212	4	no	—
1621	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1622	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1623	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1624	C₂×D₄	—	2	2	no	—
1625	C₂×D₄	—	2	1	no	—
1626	C₂×D₄	—	2	1	no	—
1627	C₂×D₄	—	2	1	no	—
1628	C₂×D₄	—	2	1	no	—
1629	C₂×D₄	—	2	1	no	—
1630	C₂×D₄	—	4	1	no	—
1631	C₂×D₄	—	53	4	no	—
1632	C₂×D₄	—	53	1	no	—
1633	C₂×D₄	—	53	1	no	—
1634	C₂×D₄	—	53	1	no	—
1635	C₂×D₄	—	53	1	no	—
1636	C₂×D₄	—	53	1	no	—
1637	C₂×D₄	—	53	1	no	—
1638	C₂×D₄	—	106	2	no	—
1639	C₂×D₄	—	106	1	no	—
1640	C₂×D₄	—	106	1	no	—
1641	C₂×D₄	—	106	1	no	—
1642	C₂×D₄	—	106	1	no	—
1643	C₂×D₄	—	106	2	no	—
1644	C₂×D₄	—	106	2	no	—
1645	C₂×D₄	—	106	2	no	—
1646	C₂×D₄	—	106	2	no	—
1647	C₂×D₄	—	106	2	no	—
1648	C₂×D₄	—	106	1	no	—
1649	C₂×D₄	—	106	1	no	—
1650	C₂×D₄	—	106	1	no	—
1651	C₂×D₄	—	106	1	no	—
1652	C₂×D₄	—	106	1	no	—
1653	C₂×D₄	—	106	2	no	—
1654	C₂×D₄	—	106	4	no	—
1655	C₂×D₄	—	106	2	no	—
1656	C₂×D₄	—	106	1	no	—
1657	C₂×D₄	—	106	1	no	—
1658	C₂×D₄	—	106	1	no	—
1659	C₂×D₄	—	106	1	no	—
1660	C₂×D₄	—	106	1	no	—
1661	C₂×D₄	—	106	1	no	—
1662	C₂×D₄	—	106	1	no	—
1663	C₂×D₄	—	106	1	no	—
1664	C₂×D₄	—	106	1	no	—
1665	C₂×D₄	—	424	2	no	—
1666	C₂×D₄	—	212	1	no	—
1667	C₂×D₄	—	212	1	no	—
1668	C₂×D₄	—	212	1	no	—
1669	C₂×D₄	—	212	4	no	—
1670	C₂×D₄	—	212	4	no	—
1671	C₂×D₄	—	212	4	no	—
1672	C₂×D₄	—	212	4	no	—
1673	C₂×D₄	—	212	4	no	—
1674	C₂×D₄	—	212	4	no	—
1675	C₂×D₄	D₄×D₅₃	1	1	yes	characteristic
1676	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1677	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1678	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1679	C₂²×C₄	—	2	1	no	—
1680	C₂²×C₄	—	2	1	no	—
1681	C₂²×C₄	—	2	1	no	—
1682	C₂²×C₄	—	2	1	no	—
1683	C₂²×C₄	—	53	1	no	—
1684	C₂²×C₄	—	53	1	no	—
1685	C₂²×C₄	—	53	1	no	—
1686	C₂²×C₄	—	53	1	no	—
1687	C₂²×C₄	—	53	1	no	—
1688	C₂²×C₄	—	53	1	no	—
1689	C₂²×C₄	—	53	1	no	—
1690	C₂²×C₄	—	53	1	no	—
1691	C₂²×C₄	—	53	1	no	—
1692	C₂²×C₄	—	53	1	no	—
1693	C₂²×C₄	—	53	1	no	—
1694	C₂²×C₄	—	106	2	no	—
1695	C₂²×C₄	—	106	2	no	—
1696	C₂²×C₄	—	106	2	no	—
1697	C₂²×C₄	—	106	2	no	—
1698	C₂²×C₄	—	106	1	no	—
1699	C₂²×C₄	—	106	1	no	—
1700	C₂²×C₄	—	106	1	no	—
1701	C₂²×C₄	—	106	1	no	—
1702	C₂²×C₄	—	106	1	no	—
1703	C₂²×C₄	—	106	1	no	—
1704	C₂²×C₄	—	106	1	no	—
1705	C₂²×C₄	—	106	1	no	—
1706	C₂²×C₄	—	106	1	no	—
1707	C₂²×C₄	—	106	1	no	—
1708	C₂²×C₄	—	106	1	no	—
1709	C₂²×C₄	—	106	1	no	—
1710	C₂²×C₄	—	106	1	no	—
1711	C₂²×C₄	—	106	1	no	—
1712	C₂²×C₄	—	106	1	no	—
1713	C₂²×C₄	—	106	1	no	—
1714	C₂²×C₄	—	106	1	no	—
1715	C₂²×C₄	—	424	2	no	—
1716	C₂²×C₄	—	212	4	no	—
1717	C₂²×C₄	—	212	4	no	—
1718	C₂²×C₄	—	212	4	no	—
1719	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1720	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1721	Q₁₆	—	2	2	no	—
1722	Q₁₆	—	4	1	no	—
1723	Q₁₆	—	106	2	no	—
1724	Q₁₆	—	106	2	no	—
1725	Q₁₆	—	106	2	no	—
1726	Q₁₆	—	212	1	no	—
1727	Q₁₆	—	212	1	no	—
1728	Q₁₆	—	212	1	no	—
1729	SD₁₆	—	2	2	no	—
1730	SD₁₆	—	2	2	no	—
1731	SD₁₆	—	2	2	no	—
1732	SD₁₆	—	2	2	no	—
1733	SD₁₆	—	53	4	no	—
1734	SD₁₆	—	53	4	no	—
1735	SD₁₆	—	53	4	no	—
1736	SD₁₆	—	106	2	no	—
1737	SD₁₆	—	106	2	no	—
1738	SD₁₆	—	106	2	no	—
1739	SD₁₆	—	106	2	no	—
1740	SD₁₆	—	106	2	no	—
1741	SD₁₆	—	106	2	no	—
1742	SD₁₆	—	106	2	no	—
1743	SD₁₆	—	106	2	no	—
1744	SD₁₆	—	106	2	no	—
1745	SD₁₆	—	106	2	no	—
1746	SD₁₆	—	106	2	no	—
1747	SD₁₆	—	106	2	no	—
1748	SD₁₆	D₄×D₅₃	1	4	yes	complemented
1749	D₈	—	2	2	no	—
1750	D₈	—	4	1	no	—
1751	D₈	—	106	2	no	—
1752	D₈	—	106	2	no	—
1753	D₈	—	106	2	no	—
1754	D₈	—	212	1	no	—
1755	D₈	—	212	1	no	—
1756	D₈	—	212	1	no	—
1757	C₂×C₈	—	2	2	no	—
1758	C₂×C₈	—	2	2	no	—
1759	C₂×C₈	—	53	1	no	—
1760	C₂×C₈	—	53	4	no	—
1761	C₂×C₈	—	53	1	no	—
1762	C₂×C₈	—	53	1	no	—
1763	C₂×C₈	—	53	1	no	—
1764	C₂×C₈	—	106	2	no	—
1765	C₂×C₈	—	106	2	no	—
1766	C₂×C₈	—	106	2	no	—
1767	C₂×C₈	—	106	2	no	—
1768	C₂×C₈	—	106	2	no	—
1769	C₂×C₈	—	106	2	no	—
1770	C₂×C₈	—	106	2	no	—
1771	C₂×C₈	—	106	2	no	—
1772	C₂×C₈	—	106	2	no	—
1773	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1774	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1775	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1776	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1777	C₄⋊C₄	—	2	1	no	—
1778	C₄⋊C₄	—	2	1	no	—
1779	C₄⋊C₄	—	2	1	no	—
1780	C₄⋊C₄	—	53	1	no	—
1781	C₄⋊C₄	—	53	1	no	—
1782	C₄⋊C₄	—	53	1	no	—
1783	C₄⋊C₄	—	53	1	no	—
1784	C₄⋊C₄	—	53	1	no	—
1785	C₄⋊C₄	—	106	1	no	—
1786	C₄⋊C₄	—	106	1	no	—
1787	C₄⋊C₄	—	106	1	no	—
1788	C₄⋊C₄	—	106	1	no	—
1789	C₄⋊C₄	—	106	1	no	—
1790	C₄⋊C₄	—	106	1	no	—
1791	C₄⋊C₄	—	106	1	no	—
1792	C₄⋊C₄	—	106	1	no	—
1793	C₄⋊C₄	—	106	1	no	—
1794	C₄⋊C₄	—	106	1	no	—
1795	C₄⋊C₄	—	106	1	no	—
1796	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1797	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1798	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1799	C₂²⋊C₄	—	2	1	no	—
1800	C₂²⋊C₄	—	2	1	no	—
1801	C₂²⋊C₄	—	2	1	no	—
1802	C₂²⋊C₄	—	2	1	no	—
1803	C₂²⋊C₄	—	2	1	no	—
1804	C₂²⋊C₄	—	2	1	no	—
1805	C₂²⋊C₄	—	2	1	no	—
1806	C₂²⋊C₄	—	2	1	no	—
1807	C₂²⋊C₄	—	2	1	no	—
1808	C₂²⋊C₄	—	53	1	no	—
1809	C₂²⋊C₄	—	53	1	no	—
1810	C₂²⋊C₄	—	53	1	no	—
1811	C₂²⋊C₄	—	53	1	no	—
1812	C₂²⋊C₄	—	53	1	no	—
1813	C₂²⋊C₄	—	53	1	no	—
1814	C₂²⋊C₄	—	106	1	no	—
1815	C₂²⋊C₄	—	106	1	no	—
1816	C₂²⋊C₄	—	106	1	no	—
1817	C₂²⋊C₄	—	106	1	no	—
1818	C₂²⋊C₄	—	106	1	no	—
1819	C₂²⋊C₄	—	106	1	no	—
1820	C₂²⋊C₄	—	106	1	no	—
1821	C₂²⋊C₄	—	106	1	no	—
1822	C₂²⋊C₄	—	106	1	no	—
1823	C₂²⋊C₄	—	106	1	no	—
1824	C₂²⋊C₄	—	106	1	no	—
1825	C₂²⋊C₄	—	106	1	no	—
1826	C₂²⋊C₄	—	106	1	no	—
1827	C₂²⋊C₄	—	106	1	no	—
1828	C₂²⋊C₄	—	106	1	no	—
1829	C₂²⋊C₄	—	106	1	no	—
1830	C₂²⋊C₄	—	106	1	no	—
1831	C₂²⋊C₄	—	106	1	no	—
1832	C₂²⋊C₄	—	106	1	no	—
1833	C₂²⋊C₄	—	106	1	no	—
1834	C₂²⋊C₄	—	106	1	no	—
1835	C₂²⋊C₄	—	106	1	no	—
1836	C₂²⋊C₄	—	106	1	no	—
1837	C₂²⋊C₄	—	106	1	no	—
1838	C₂²⋊C₄	—	106	1	no	—
1839	C₂²⋊C₄	—	106	1	no	—
1840	C₂²⋊C₄	—	106	1	no	—
1841	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1842	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1843	C₄²	—	2	1	no	—
1844	C₄²	—	53	1	no	—
1845	C₄²	—	53	1	no	—
1846	C₄²	—	53	1	no	—
1847	C₄²	—	106	1	no	—
1848	C₄²	—	106	1	no	—
1849	C₄²	—	106	1	no	—
1850	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1851	C₂³	—	2	1	no	—
1852	C₂³	—	2	1	no	—
1853	C₂³	—	2	1	no	—
1854	C₂³	—	4	2	no	—
1855	C₂³	—	4	2	no	—
1856	C₂³	—	8	1	no	—
1857	C₂³	—	53	1	no	—
1858	C₂³	—	53	4	no	—
1859	C₂³	—	53	1	no	—
1860	C₂³	—	53	1	no	—
1861	C₂³	—	106	2	no	—
1862	C₂³	—	106	2	no	—
1863	C₂³	—	106	2	no	—
1864	C₂³	—	106	4	no	—
1865	C₂³	—	106	2	no	—
1866	C₂³	—	106	2	no	—
1867	C₂³	—	106	1	no	—
1868	C₂³	—	106	1	no	—
1869	C₂³	—	106	1	no	—
1870	C₂³	—	424	1	no	—
1871	C₂³	—	424	1	no	—
1872	C₂³	—	424	1	no	—
1873	C₂³	—	424	16	no	—
1874	C₂³	—	212	2	no	—
1875	C₂³	—	212	2	no	—
1876	C₂³	—	212	2	no	—
1877	C₂³	—	212	2	no	—
1878	C₂³	—	212	2	no	—
1879	C₂³	—	212	2	no	—
1880	C₂³	—	212	2	no	—
1881	C₂³	—	212	2	no	—
1882	C₂³	—	212	2	no	—
1883	C₂³	—	212	2	no	—
1884	C₂³	—	212	2	no	—
1885	C₂³	—	212	2	no	—
1886	C₂³	—	212	2	no	—
1887	C₂³	—	212	2	no	—
1888	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1889	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1890	Q₈	—	2	1	no	—
1891	Q₈	—	2	1	no	—
1892	Q₈	—	2	1	no	—
1893	Q₈	—	2	1	no	—
1894	Q₈	—	2	1	no	—
1895	Q₈	—	4	2	no	—
1896	Q₈	—	53	2	no	—
1897	Q₈	—	106	4	no	—
1898	Q₈	—	106	1	no	—
1899	Q₈	—	106	1	no	—
1900	Q₈	—	106	1	no	—
1901	Q₈	—	106	1	no	—
1902	Q₈	—	106	1	no	—
1903	Q₈	—	212	2	no	—
1904	Q₈	—	212	2	no	—
1905	Q₈	—	212	2	no	—
1906	Q₈	—	212	2	no	—
1907	Q₈	—	212	2	no	—
1908	Q₈	C₂×D₄×D₅₃	1	2	yes	—
1909	D₄	—	2	2	no	—
1910	D₄	—	2	1	no	—
1911	D₄	—	2	1	no	—
1912	D₄	—	2	1	no	—
1913	D₄	—	2	1	no	—
1914	D₄	—	2	1	no	—
1915	D₄	—	4	2	no	—
1916	D₄	—	4	2	no	—
1917	D₄	—	4	2	no	—
1918	D₄	—	4	2	no	—
1919	D₄	—	8	1	no	—
1920	D₄	—	53	2	no	—
1921	D₄	—	106	2	no	—
1922	D₄	—	106	4	no	—
1923	D₄	—	106	2	no	—
1924	D₄	—	106	2	no	—
1925	D₄	—	106	1	no	—
1926	D₄	—	106	1	no	—
1927	D₄	—	106	1	no	—
1928	D₄	—	106	1	no	—
1929	D₄	—	106	1	no	—
1930	D₄	—	424	1	no	—
1931	D₄	—	424	1	no	—
1932	D₄	—	424	1	no	—
1933	D₄	—	212	2	no	—
1934	D₄	—	212	2	no	—
1935	D₄	—	212	2	no	—
1936	D₄	—	212	2	no	—
1937	D₄	—	212	2	no	—
1938	D₄	—	212	2	no	—
1939	D₄	—	212	2	no	—
1940	D₄	—	212	2	no	—
1941	D₄	—	212	2	no	—
1942	D₄	—	212	2	no	—
1943	D₄	—	212	2	no	—
1944	D₄	—	212	2	no	—
1945	D₄	—	212	2	no	—
1946	D₄	—	212	2	no	—
1947	D₄	C₂×D₄×D₅₃	1	2	yes	—
1948	C₂×C₄	—	2	1	no	—
1949	C₂×C₄	—	2	1	no	—
1950	C₂×C₄	—	2	1	no	—
1951	C₂×C₄	—	2	1	no	—
1952	C₂×C₄	—	2	1	no	—
1953	C₂×C₄	—	2	1	no	—
1954	C₂×C₄	—	2	1	no	—
1955	C₂×C₄	—	2	1	no	—
1956	C₂×C₄	—	2	1	no	—
1957	C₂×C₄	—	4	2	no	—
1958	C₂×C₄	—	4	2	no	—
1959	C₂×C₄	—	4	2	no	—
1960	C₂×C₄	—	8	1	no	—
1961	C₂×C₄	—	53	1	no	—
1962	C₂×C₄	—	53	2	no	—
1963	C₂×C₄	—	53	2	no	—
1964	C₂×C₄	—	53	1	no	—
1965	C₂×C₄	—	53	1	no	—
1966	C₂×C₄	—	53	1	no	—
1967	C₂×C₄	—	53	1	no	—
1968	C₂×C₄	—	106	2	no	—
1969	C₂×C₄	—	106	2	no	—
1970	C₂×C₄	—	106	2	no	—
1971	C₂×C₄	—	106	2	no	—
1972	C₂×C₄	—	106	2	no	—
1973	C₂×C₄	—	106	2	no	—
1974	C₂×C₄	—	106	4	no	—
1975	C₂×C₄	—	106	2	no	—
1976	C₂×C₄	—	106	2	no	—
1977	C₂×C₄	—	106	1	no	—
1978	C₂×C₄	—	106	1	no	—
1979	C₂×C₄	—	106	1	no	—
1980	C₂×C₄	—	106	1	no	—
1981	C₂×C₄	—	106	1	no	—
1982	C₂×C₄	—	106	1	no	—
1983	C₂×C₄	—	106	1	no	—
1984	C₂×C₄	—	106	1	no	—
1985	C₂×C₄	—	106	1	no	—
1986	C₂×C₄	—	424	1	no	—
1987	C₂×C₄	—	424	1	no	—
1988	C₂×C₄	—	424	1	no	—
1989	C₂×C₄	—	212	2	no	—
1990	C₂×C₄	—	212	2	no	—
1991	C₂×C₄	—	212	2	no	—
1992	C₂×C₄	—	212	2	no	—
1993	C₂×C₄	—	212	2	no	—
1994	C₂×C₄	—	212	2	no	—
1995	C₂×C₄	—	212	2	no	—
1996	C₂×C₄	—	212	2	no	—
1997	C₂×C₄	—	212	2	no	—
1998	C₂×C₄	—	212	2	no	—
1999	C₂×C₄	—	212	2	no	—
2000	C₂×C₄	—	212	2	no	—
2001	C₂×C₄	—	212	2	no	—
2002	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2003	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2004	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2005	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2006	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
2007	C₈	—	2	1	no	—
2008	C₈	—	2	1	no	—
2009	C₈	—	2	1	no	—
2010	C₈	—	53	2	no	—
2011	C₈	—	106	1	no	—
2012	C₈	—	106	1	no	—
2013	C₈	—	106	1	no	—
2014	C₈	C₂×D₄×D₅₃	1	2	yes	—
2015	C₂²	—	2	1	no	—
2016	C₂²	—	2	1	no	—
2017	C₂²	—	2	1	no	—
2018	C₂²	—	2	2	no	—
2019	C₂²	—	2	1	no	—
2020	C₂²	—	2	1	no	—
2021	C₂²	—	4	1	no	—
2022	C₂²	—	4	1	no	—
2023	C₂²	—	4	1	no	—
2024	C₂²	—	4	1	no	—
2025	C₂²	—	4	1	no	—
2026	C₂²	—	4	1	no	—
2027	C₂²	—	4	1	no	—
2028	C₂²	—	4	1	no	—
2029	C₂²	—	8	4	no	—
2030	C₂²	—	53	2	no	—
2031	C₂²	—	53	2	no	—
2032	C₂²	—	53	2	no	—
2033	C₂²	—	53	2	no	—
2034	C₂²	—	106	8	no	—
2035	C₂²	—	106	1	no	—
2036	C₂²	—	106	1	no	—
2037	C₂²	—	106	1	no	—
2038	C₂²	—	106	2	no	—
2039	C₂²	—	106	1	no	—
2040	C₂²	—	106	1	no	—
2041	C₂²	—	424	4	no	—
2042	C₂²	—	424	4	no	—
2043	C₂²	—	424	4	no	—
2044	C₂²	—	424	4	no	—
2045	C₂²	—	424	4	no	—
2046	C₂²	—	212	4	no	—
2047	C₂²	—	212	8	no	—
2048	C₂²	—	212	1	no	—
2049	C₂²	—	212	1	no	—
2050	C₂²	—	212	1	no	—
2051	C₂²	—	212	1	no	—
2052	C₂²	—	212	1	no	—
2053	C₂²	—	212	1	no	—
2054	C₂²	—	212	1	no	—
2055	C₂²	—	212	1	no	—
2056	C₂²	#135×D₅₃	1	2	yes	complemented
2057	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
2058	C₄	—	2	1	no	—
2059	C₄	—	2	1	no	—
2060	C₄	—	2	2	no	—
2061	C₄	—	2	1	no	—
2062	C₄	—	2	1	no	—
2063	C₄	—	4	1	no	—
2064	C₄	—	4	1	no	—
2065	C₄	—	4	1	no	—
2066	C₄	—	4	1	no	—
2067	C₄	—	53	2	no	—
2068	C₄	—	106	1	no	—
2069	C₄	—	106	1	no	—
2070	C₄	—	106	2	no	—
2071	C₄	—	106	1	no	—
2072	C₄	—	106	1	no	—
2073	C₄	—	212	1	no	—
2074	C₄	—	212	1	no	—
2075	C₄	—	212	1	no	—
2076	C₄	—	212	1	no	—
2077	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
2078	C₄	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
2079	C₂	—	2	2	no	—
2080	C₂	—	4	1	no	—
2081	C₂	—	4	2	no	—
2082	C₂	—	8	1	no	—
2083	C₂	—	8	1	no	—
2084	C₂	—	53	4	no	—
2085	C₂	—	106	2	no	—
2086	C₂	—	424	1	no	—
2087	C₂	—	424	1	no	—
2088	C₂	—	212	1	no	—
2089	C₂	—	212	2	no	—
2090	C₂	D₄²×D₅₃	1	1	yes	characteristic
2091	C₂	C₂×#135×D₅₃	1	1	yes	characteristic
2092	C₂	#577×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3282	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	#3282	D₅₃
hypocenter	C₅₃	C₂×#3282
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3282

Complements

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

N	H ≅ G/N	type
1. C₂×#135×D₅₃	C₂	semidirect
2. C₂²×SD₁₆×D₅₃	C₂	semidirect
3. #548×D₅₃	C₂	semidirect
4. #546×D₅₃	C₂	semidirect
5. #20286429	C₂	semidirect
6. #20286428	C₂	semidirect
7. #20286427	C₂	semidirect
8. #20286426	C₂	semidirect
9. #20286425	C₂	semidirect
10. #20286424	C₂	semidirect
11. #20286423	C₂	semidirect
12. #20286422	C₂	semidirect
13. #20286421	C₂	semidirect
14. #20286420	C₂	semidirect
15. #20286419	C₂	semidirect
16. #20286418	C₂	semidirect
17. #20286417	C₂	semidirect
18. #20286416	C₂	semidirect
19. #20286415	C₂	semidirect
20. #495×D₅₃	C₂	semidirect
21. #465×D₅₃	C₂	semidirect
22. #465×D₅₃	C₂	semidirect
23. #464×D₅₃	C₂	semidirect
24. #463×D₅₃	C₂	semidirect
25. #452×D₅₃	C₂	semidirect
26. #449×D₅₃	C₂	semidirect
27. #451×D₅₃	C₂	semidirect
28. #447×D₅₃	C₂	semidirect
29. C₄×SD₁₆×D₅₃	C₂	semidirect
30. C₈×D₄×D₅₃	C₂	semidirect
31. C₅₃×#3282	C₂	semidirect
33. C₂×#41×D₅₃	C₂²	semidirect
36. C₂×#13133240	C₂²	semidirect
37. C₂×#13133239	C₂²	semidirect
38. C₂×#13133238	C₂²	semidirect
39. C₂×#13133238	C₂²	semidirect
40. C₂×#13133237	C₂²	semidirect
41. C₂×#13133237	C₂²	semidirect
42. C₂×#13133236	C₂²	semidirect
44. C₂×Q₁₆×D₅₃	C₂²	semidirect
45. C₂×Q₁₆×D₅₃	C₂²	semidirect
46. C₂²×#11719913	C₂²	semidirect
47. C₂²×#11719923	C₂²	semidirect
48. C₂²×#11719924	C₂²	semidirect
54. C₂×SD₁₆×D₅₃	C₂²	semidirect
55. C₂×SD₁₆×D₅₃	C₂²	semidirect
56. C₂×SD₁₆×D₅₃	C₂²	semidirect
57. C₂×SD₁₆×D₅₃	C₂²	semidirect
58. C₂×SD₁₆×D₅₃	C₂²	semidirect
62. C₂²×C₈×D₅₃	C₂²	semidirect
63. #16811285	C₂²	semidirect
64. #16811284	C₂²	semidirect
66. #16811283	C₂²	semidirect
68. #16811282	C₂²	semidirect
70. #16811281	C₂²	semidirect
71. #16811280	C₂²	semidirect
73. #16811279	C₂²	semidirect
74. #16811270	C₂²	semidirect
75. #16811269	C₂²	semidirect
76. #16811268	C₂²	semidirect
77. #16811267	C₂²	semidirect
78. #16811266	C₂²	semidirect
80. #16811264	C₂²	semidirect
83. #16811261	C₂²	semidirect
87. #124×D₅₃	C₂²	semidirect
91. C₂²⋊Q₈×D₅₃	C₂²	semidirect
97. C₄×Q₈×D₅₃	C₂²	semidirect
102. #16811008	C₂²	semidirect
103. #16811007	C₂²	semidirect
104. #16811006	C₂²	semidirect
105. #16811005	C₂²	semidirect
106. #16811005	C₂²	semidirect
107. #16811004	C₂²	semidirect
108. #16811004	C₂²	semidirect
109. #16810855	C₂²	semidirect
110. #16810855	C₂²	semidirect
111. #16810854	C₂²	semidirect
112. #16810854	C₂²	semidirect
113. #16810853	C₂²	semidirect
114. #16810853	C₂²	semidirect
115. #16810852	C₂²	semidirect
116. #16810852	C₂²	semidirect
117. #16810851	C₂²	semidirect
118. #16810851	C₂²	semidirect
119. #16810850	C₂²	semidirect
120. #16810850	C₂²	semidirect
121. #16810849	C₂²	semidirect
122. #16810849	C₂²	semidirect
123. #16810848	C₂²	semidirect
124. #16810847	C₂²	semidirect
125. #16810846	C₂²	semidirect
126. #16810845	C₂²	semidirect
127. #16810844	C₂²	semidirect
128. #16810843	C₂²	semidirect
129. #16810842	C₂²	semidirect
130. #16810841	C₂²	semidirect
131. #16810840	C₂²	semidirect
132. #16810839	C₂²	semidirect
133. #16810838	C₂²	semidirect
134. #16810837	C₂²	semidirect
135. #16810836	C₂²	semidirect
136. #16810835	C₂²	semidirect
137. #16810788	C₂²	semidirect
138. #16810787	C₂²	semidirect
139. #16810786	C₂²	semidirect
140. #16810785	C₂²	semidirect
141. #16810784	C₂²	semidirect
142. #16810783	C₂²	semidirect
143. #16810782	C₂²	semidirect
144. #16810781	C₂²	semidirect
145. #16810780	C₂²	semidirect
146. #16810780	C₂²	semidirect
147. #16810779	C₂²	semidirect
148. #16810778	C₂²	semidirect
149. #16810777	C₂²	semidirect
150. #16810777	C₂²	semidirect
151. #16810771	C₂²	semidirect
152. #16810770	C₂²	semidirect
153. #16810769	C₂²	semidirect
154. #16810768	C₂²	semidirect
155. #16810767	C₂²	semidirect
156. #16810766	C₂²	semidirect
157. #16810765	C₂²	semidirect
158. #16810759	C₂²	semidirect
159. #16810758	C₂²	semidirect
160. #16810758	C₂²	semidirect
161. #16810757	C₂²	semidirect
162. #16810756	C₂²	semidirect
163. #16810755	C₂²	semidirect
164. #16810755	C₂²	semidirect
165. #16810714	C₂²	semidirect
166. C₄×#11719913	C₂²	semidirect
167. SD₁₆×Dic₅₃	C₂²	semidirect
168. C₄×#11719924	C₂²	semidirect
169. #16810710	C₂²	semidirect
170. C₄×#11719923	C₂²	semidirect
171. #16810708	C₂²	semidirect
172. C₈×D₂₁₂	C₂²	semidirect
173. D₄×#88322	C₂²	semidirect
174. #16810688	C₂²	semidirect
175. C₈×C₂²⋊D₅₃	C₂²	semidirect
176. C₈×C₂²⋊D₅₃	C₂²	semidirect
177. #16810686	C₂²	semidirect
178. #16810686	C₂²	semidirect
179. #106×D₅₃	C₂²	semidirect
180. C₄⋊C₈×D₅₃	C₂²	semidirect
181. #103×D₅₃	C₂²	semidirect
182. #103×D₅₃	C₂²	semidirect
183. #103×D₅₃	C₂²	semidirect
186. #102×D₅₃	C₂²	semidirect
188. C₂²⋊C₈×D₅₃	C₂²	semidirect
189. C₄×C₈×D₅₃	C₂²	semidirect
190. C₂×#135×C₅₃	C₂²	semidirect
191. C₂²×SD₁₆×C₅₃	C₂²	semidirect
192. C₅₃×#548	C₂²	semidirect
193. C₅₃×#546	C₂²	semidirect
194. C₅₃×#495	C₂²	semidirect
195. C₅₃×#465	C₂²	semidirect
196. C₅₃×#465	C₂²	semidirect
197. C₅₃×#464	C₂²	semidirect
198. C₅₃×#463	C₂²	semidirect
199. C₅₃×#452	C₂²	semidirect
200. C₅₃×#451	C₂²	semidirect
201. C₅₃×#449	C₂²	semidirect
202. C₅₃×#447	C₂²	semidirect
203. C₄×SD₁₆×C₅₃	C₂²	semidirect
204. C₈×D₄×C₅₃	C₂²	semidirect
207. C₂×#11719949	C₂³	semidirect
211. C₂×#11719945	C₂³	semidirect
215. C₂×#11719947	C₂³	semidirect
260. C₂×Dic₂₁₂	C₂³	semidirect
261. C₂×Dic₂₁₂	C₂³	semidirect
262. C₂×#11719925	C₂³	semidirect
263. C₂×#11719925	C₂³	semidirect
264. C₂×#11719925	C₂³	semidirect
265. C₂×#11719925	C₂³	semidirect
273. C₂×#11719913	C₂³	semidirect
279. C₂×#11719923	C₂³	semidirect
285. C₂×#11719924	C₂³	semidirect
294. SD₁₆×D₅₃	D₄	semidirect
304. C₂²×#88322	C₂³	semidirect
313. C₂×C₈×D₅₃	C₂³	semidirect
314. C₂×C₈×D₅₃	C₂³	semidirect
317. #13133206	C₂³	semidirect
320. #13133205	C₂³	semidirect
323. #13133204	C₂³	semidirect
341. #13133197	C₂³	semidirect
344. #13133196	C₂³	semidirect
355. #13133193	C₂³	semidirect
387. Q₈×Dic₅₃	C₂³	semidirect
389. C₄×Dic₁₀₆	C₂³	semidirect
391. #13133182	C₂³	semidirect
437. #13133149	C₂³	semidirect
438. #13133148	C₂³	semidirect
439. #13133148	C₂³	semidirect
440. C₄⋊#88322	C₂³	semidirect
441. #13133146	C₂³	semidirect
442. #13133146	C₂³	semidirect
443. #13133142	C₂³	semidirect
444. #13133142	C₂³	semidirect
445. #13133142	C₂³	semidirect
446. #13133141	C₂³	semidirect
447. #13133141	C₂³	semidirect
448. #13133141	C₂³	semidirect
449. #13133140	C₂³	semidirect
450. #13133140	C₂³	semidirect
451. #13133140	C₂³	semidirect
454. #13133139	C₂³	semidirect
457. #13133138	C₂³	semidirect
460. #13133137	C₂³	semidirect
462. C₂²⋊#88322	C₂³	semidirect
465. #13133129	C₂³	semidirect
466. #13133129	C₂³	semidirect
467. C₄×#88322	C₂³	semidirect
468. C₈×Dic₅₃	C₂³	semidirect
469. C₈×Dic₅₃	C₂³	semidirect
471. C₂×#41×C₅₃	C₂³	semidirect
475. C₂×Q₁₆×C₅₃	C₂³	semidirect
476. C₂×Q₁₆×C₅₃	C₂³	semidirect
482. C₂×SD₁₆×C₅₃	C₂³	semidirect
486. C₂²×C₈×C₅₃	C₂³	semidirect
489. #124×C₅₃	C₂³	semidirect
493. C₂²⋊Q₈×C₅₃	C₂³	semidirect
499. C₄×Q₈×C₅₃	C₂³	semidirect
504. #106×C₅₃	C₂³	semidirect
505. C₄⋊C₈×C₅₃	C₂³	semidirect
506. #103×C₅₃	C₂³	semidirect
507. #103×C₅₃	C₂³	semidirect
508. #103×C₅₃	C₂³	semidirect
511. #102×C₅₃	C₂³	semidirect
513. C₂²⋊C₈×C₅₃	C₂³	semidirect
514. C₄×C₈×C₅₃	C₂³	semidirect
680. SD₁₆×C₅₃	C₂×D₄	semidirect
727. #11719924	C₂×D₄	semidirect
732. #11719923	C₂×D₄	semidirect
795. #11719913	C₂×D₄	semidirect
839. C₂²×D₅₃	#135	semidirect
984. C₂²×C₅₃	C₂×#135	semidirect
1010. C₂×D₅₃	C₂×#135	semidirect
1052. #3282	D₅₃	direct (N × H)
1077. D₅₃	#3282	direct (N × H)
1090. C₂×#135	C₂×D₅₃	semidirect
1106. C₂²×SD₁₆	C₂×D₅₃	semidirect
1122. #548	C₂×D₅₃	semidirect
1134. #546	C₂×D₅₃	semidirect
1159. #495	C₂×D₅₃	semidirect
1174. #465	C₂×D₅₃	semidirect
1175. #465	C₂×D₅₃	semidirect
1183. #464	C₂×D₅₃	semidirect
1191. #463	C₂×D₅₃	semidirect
1199. #452	C₂×D₅₃	semidirect
1207. #451	C₂×D₅₃	semidirect
1215. #449	C₂×D₅₃	semidirect
1223. #447	C₂×D₅₃	semidirect
1231. C₄×SD₁₆	C₂×D₅₃	semidirect
1239. C₈×D₄	C₂×D₅₃	semidirect
1251. C₅₃	C₂×#3282	semidirect
1268. C₂×#41	C₂²×D₅₃	semidirect
1320. C₂×Q₁₆	C₂²×D₅₃	semidirect
1321. C₂×Q₁₆	C₂²×D₅₃	semidirect
1354. C₂×SD₁₆	C₂²×D₅₃	semidirect
1378. C₂²×C₈	C₂²×D₅₃	semidirect
1398. #124	C₂²×D₅₃	semidirect
1426. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1468. C₄×Q₈	C₂²×D₅₃	semidirect
1521. #106	C₂²×D₅₃	semidirect
1525. C₄⋊C₈	C₂²×D₅₃	semidirect
1535. #103	C₂²×D₅₃	semidirect
1536. #103	C₂²×D₅₃	semidirect
1537. #103	C₂²×D₅₃	semidirect
1549. #102	C₂²×D₅₃	semidirect
1557. C₂²⋊C₈	C₂²×D₅₃	semidirect
1561. C₄×C₈	C₂²×D₅₃	semidirect
1748. SD₁₆	D₄×D₅₃	semidirect
2056. C₂²	#135×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#135×D₅₃	2
C₂²×SD₁₆×D₅₃	2
#548×D₅₃	2
#546×D₅₃	2
#20286429	2
#20286428	2
#20286427	2
#20286426	2
#20286425	2
#20286424	2
#20286423	2
#20286422	2
#20286421	2
#20286420	2
#20286419	2
#20286418	2
#20286417	2
#20286416	2
#20286415	2
#495×D₅₃	2
#465×D₅₃	2
#464×D₅₃	2
#463×D₅₃	2
#452×D₅₃	2
#449×D₅₃	2
#451×D₅₃	2
#447×D₅₃	2
C₄×SD₁₆×D₅₃	2
C₈×D₄×D₅₃	2
C₅₃×#3282	2
C₂×#3282	53

Subgroups — D53×#3282 #28259312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3282 #28259312