Subgroups — #28248016

Order 13568.

2862 conjugacy classes of subgroups.

The subgroup lattice has 1716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811389	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811132	C₂	1	1	yes	maximal, characteristic
4	M₁₆×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×#11719917	C₂	1	1	yes	maximal, characteristic, complemented
6	#20283450	C₂	1	1	yes	maximal, characteristic, complemented
7	M₁₆×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	M₁₆×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#20283447	C₂	1	1	yes	maximal, characteristic, complemented
10	#20283447	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283444	C₂	1	2	yes	maximal, complemented
12	#20283441	C₂	1	2	yes	maximal, complemented
13	#20283438	C₂	1	2	yes	maximal, complemented
14	#20283435	C₂	1	2	yes	maximal, complemented
15	#20283415	C₂	1	2	yes	maximal, complemented
16	#20283413	C₂	1	2	yes	maximal, complemented
17	#20283406	C₂	1	2	yes	maximal, complemented
18	#20283404	C₂	1	2	yes	maximal, complemented
19	#20283277	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283158	C₂	1	1	yes	maximal, characteristic, complemented
21	#407×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#20283132	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#11719945	C₂²	1	1	yes	characteristic
25	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
26	#16811389	—	2	8	no	—
27	C₂×#13133225	C₂²	1	2	yes	complemented
28	C₂×#13133225	C₂²	1	2	yes	complemented
29	C₂×#13133223	C₂²	1	2	yes	complemented
30	C₂×#13133223	C₂²	1	2	yes	complemented
31	C₂²×#11719917	C₂²	1	1	yes	characteristic
32	C₂²×#11719917	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#11719912	C₂²	1	2	yes	complemented
34	C₂×M₁₆×D₅₃	—	2	8	no	—
35	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
36	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
37	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
38	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
39	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
40	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
41	C₂×M₁₆×D₅₃	C₂²	1	2	yes	complemented
42	C₂×M₁₆×D₅₃	C₂²	1	2	yes	complemented
43	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₈×D₅₃	C₂²	1	2	yes	complemented
46	#16811132	C₄	1	1	yes	characteristic
47	#16811132	C₄	1	1	yes	characteristic
48	#16811132	C₄	1	1	yes	characteristic
49	#16811132	C₄	1	1	yes	characteristic
50	#16811132	C₄	1	1	yes	characteristic
51	#16811132	C₄	1	1	yes	characteristic
52	#16811132	C₄	1	1	yes	characteristic
53	#16811132	C₄	1	1	yes	characteristic
54	#16811132	C₂²	1	1	yes	characteristic
55	#16811132	C₂²	1	1	yes	characteristic
56	#16811132	C₂²	1	1	yes	characteristic
57	#16811132	C₂²	1	1	yes	characteristic
58	#16811132	C₂²	1	1	yes	characteristic
59	#16811132	C₂²	1	1	yes	characteristic
60	#16811132	C₂²	1	1	yes	characteristic
61	#16811132	C₂²	1	1	yes	characteristic
62	C₂×#13133202	C₄	1	1	yes	characteristic
63	C₂×#13133199	C₄	1	1	yes	characteristic
64	C₂×#13133195	C₄	1	1	yes	characteristic
65	C₂×#13133194	C₄	1	1	yes	characteristic
66	C₂×#13133190	C₄	1	1	yes	characteristic
67	C₂×#13133189	C₄	1	1	yes	characteristic
68	C₂×#13133187	C₄	1	1	yes	characteristic
69	C₂×#13133185	C₄	1	1	yes	characteristic
70	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
71	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
72	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
73	C₂×#13133174	C₂²	1	1	yes	characteristic
74	#16810702	C₂²	1	2	yes	complemented
75	#16810701	C₂²	1	2	yes	complemented
76	#16810700	C₂²	1	2	yes	complemented
77	#16810699	C₂²	1	2	yes	complemented
78	#16810699	C₂²	1	2	yes	complemented
79	#16810698	C₂²	1	2	yes	complemented
80	#16810698	C₂²	1	2	yes	complemented
81	#16810697	C₂²	1	2	yes	complemented
82	#16810697	C₂²	1	2	yes	complemented
83	#16810696	C₂²	1	2	yes	complemented
84	#16810696	C₂²	1	2	yes	complemented
85	#16810695	C₂²	1	2	yes	complemented
86	#16810695	C₂²	1	2	yes	complemented
87	#16810694	C₂²	1	2	yes	complemented
88	#16810694	C₂²	1	2	yes	complemented
89	#16810693	C₂²	1	2	yes	complemented
90	#16810693	C₂²	1	2	yes	complemented
91	#16810692	C₂²	1	2	yes	complemented
92	#16810692	C₂²	1	2	yes	complemented
93	#16810691	C₂²	1	2	yes	complemented
94	#16810691	C₂²	1	2	yes	complemented
95	C₈×D₂₁₂	C₂²	1	2	yes	complemented
96	D₄×#88322	C₂²	1	2	yes	complemented
97	#16810688	C₂²	1	2	yes	complemented
98	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
99	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
100	#16810686	C₂²	1	2	yes	complemented
101	#16810686	C₂²	1	2	yes	complemented
102	#16810648	C₂²	1	2	yes	complemented
103	#16810648	C₂²	1	2	yes	complemented
104	#16810648	C₂²	1	2	yes	complemented
105	#16810648	C₂²	1	2	yes	complemented
106	#16810647	C₂²	1	1	yes	characteristic, complemented
107	#16810646	C₂²	1	1	yes	characteristic, complemented
108	#16810646	C₂²	1	1	yes	characteristic, complemented
109	#16810588	C₂²	1	2	yes	complemented
110	#16810588	C₂²	1	2	yes	complemented
111	#16810588	C₂²	1	2	yes	complemented
112	#16810588	C₂²	1	2	yes	complemented
113	#16810587	C₂²	1	1	yes	characteristic
114	#16810587	C₂²	1	1	yes	characteristic, complemented
115	#16810586	C₂²	1	1	yes	characteristic
116	#16810586	C₂²	1	1	yes	characteristic
117	#16810586	C₂²	1	1	yes	characteristic, complemented
118	#16810586	C₂²	1	1	yes	characteristic, complemented
119	#16810585	C₂²	1	2	yes	complemented
120	#16810585	C₂²	1	2	yes	complemented
121	C₂²⋊C₈×D₅₃	C₂²	1	2	yes	complemented
122	C₂²⋊C₈×D₅₃	C₂²	1	2	yes	complemented
123	#16810580	C₂²	1	2	yes	complemented
124	#16810580	C₂²	1	2	yes	complemented
125	#16810577	C₂²	1	2	yes	complemented
126	#16810577	C₂²	1	2	yes	complemented
127	C₄×#11719917	C₂²	1	1	yes	characteristic, complemented
128	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
129	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
131	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
133	C₅₃×#436	C₂²	1	2	yes	complemented
134	C₅₃×#435	C₂²	1	2	yes	complemented
135	C₅₃×#435	C₂²	1	2	yes	complemented
136	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
137	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#407	C₂²	1	1	yes	characteristic
139	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
140	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
141	C₂⁴×D₅₃	C₂×C₄	1	1	yes	characteristic
142	C₂×#11719945	—	2	4	no	—
143	C₂×#11719945	—	2	4	no	—
144	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
145	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
146	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
147	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
148	C₂×#11719945	C₂³	1	1	yes	characteristic
149	C₂×#11719945	C₂³	1	1	yes	characteristic
150	C₂×#11719945	C₂³	1	1	yes	characteristic
151	C₂×#11719945	C₂³	1	1	yes	characteristic
152	C₂²×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
153	C₂²×D₂₁₂	C₂×C₄	1	1	yes	characteristic
154	C₂²×D₂₁₂	C₂×C₄	1	1	yes	characteristic
155	C₂²×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
156	C₂²×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
157	C₂²×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
158	C₂²×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
159	C₂³×Dic₅₃	C₂×C₄	1	1	yes	characteristic
160	C₂²×C₄×D₅₃	—	2	4	no	—
161	C₂²×C₄×D₅₃	—	2	4	no	—
162	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
163	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
164	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
165	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
166	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
167	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
168	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
169	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
170	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
171	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
172	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
173	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
174	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
175	#13133225	—	2	8	no	—
176	#13133225	—	2	8	no	—
177	#13133223	—	2	8	no	—
178	#13133223	—	2	8	no	—
179	C₂×#11719917	—	2	4	no	—
180	C₂×#11719917	—	2	4	no	—
181	C₂×#11719917	C₂³	1	1	yes	characteristic
182	C₂×#11719917	C₂³	1	1	yes	characteristic
183	C₂×#11719917	C₂³	1	1	yes	characteristic
184	C₂×#11719917	C₂³	1	2	yes	—
185	C₂×#11719917	C₂³	1	1	yes	characteristic
186	C₂×#11719917	C₂³	1	2	yes	complemented
187	C₂×#11719912	—	2	8	no	—
188	C₂×#11719912	C₂³	1	2	yes	—
189	C₂×#11719912	C₂³	1	2	yes	—
190	C₂×#11719912	C₂³	1	2	yes	—
191	C₂×#11719912	C₂³	1	2	yes	—
192	C₂×#11719912	C₂³	1	2	yes	—
193	C₂×#11719912	C₂³	1	2	yes	—
194	C₂×#11719912	C₂³	1	2	yes	complemented
195	C₂×#11719912	C₂³	1	2	yes	complemented
196	M₁₆×D₅₃	—	2	4	no	—
197	M₁₆×D₅₃	—	2	4	no	—
198	M₁₆×D₅₃	—	2	4	no	—
199	M₁₆×D₅₃	—	2	4	no	—
200	M₁₆×D₅₃	—	2	8	no	—
201	M₁₆×D₅₃	—	2	8	no	—
202	M₁₆×D₅₃	—	2	4	no	—
203	M₁₆×D₅₃	—	2	4	no	—
204	M₁₆×D₅₃	—	2	4	no	—
205	M₁₆×D₅₃	D₄	1	8	yes	complemented
206	C₂²×#88322	C₂³	1	2	yes	—
207	C₂²×#88322	C₂³	1	2	yes	complemented
208	C₂×C₈×D₅₃	—	2	8	no	—
209	C₂×C₈×D₅₃	C₂³	1	2	yes	—
210	C₂×C₈×D₅₃	C₂³	1	2	yes	—
211	C₂×C₈×D₅₃	C₂³	1	2	yes	—
212	C₂×C₈×D₅₃	C₂³	1	2	yes	—
213	C₂×C₈×D₅₃	C₂³	1	2	yes	—
214	C₂×C₈×D₅₃	C₂³	1	2	yes	—
215	C₂×C₈×D₅₃	C₂³	1	2	yes	complemented
216	C₂×C₈×D₅₃	C₂³	1	2	yes	complemented
217	#13133202	C₂×C₄	1	1	yes	characteristic
218	#13133202	C₂×C₄	1	1	yes	characteristic
219	#13133202	C₂×C₄	1	1	yes	characteristic
220	#13133202	C₂×C₄	1	1	yes	characteristic
221	#13133202	C₂×C₄	1	1	yes	characteristic
222	#13133202	C₂×C₄	1	1	yes	characteristic
223	#13133202	C₂×C₄	1	1	yes	characteristic
224	#13133202	C₂×C₄	1	1	yes	characteristic
225	#13133199	C₂×C₄	1	1	yes	characteristic
226	#13133199	C₂×C₄	1	1	yes	characteristic
227	#13133199	C₂×C₄	1	1	yes	characteristic
228	#13133199	C₂×C₄	1	1	yes	characteristic
229	#13133199	C₂×C₄	1	1	yes	characteristic
230	#13133199	C₂×C₄	1	1	yes	characteristic
231	#13133199	C₂×C₄	1	1	yes	characteristic
232	#13133199	C₂×C₄	1	1	yes	characteristic
233	#13133195	C₂×C₄	1	1	yes	characteristic
234	#13133195	C₂×C₄	1	1	yes	characteristic
235	#13133195	C₂×C₄	1	1	yes	characteristic
236	#13133195	C₂×C₄	1	1	yes	characteristic
237	#13133195	C₂×C₄	1	1	yes	characteristic
238	#13133195	C₂×C₄	1	1	yes	characteristic
239	#13133195	C₂×C₄	1	1	yes	characteristic
240	#13133195	C₂×C₄	1	1	yes	characteristic
241	#13133194	C₂×C₄	1	1	yes	characteristic
242	#13133194	C₂×C₄	1	1	yes	characteristic
243	#13133194	C₂×C₄	1	1	yes	characteristic
244	#13133194	C₂×C₄	1	1	yes	characteristic
245	#13133194	C₂×C₄	1	1	yes	characteristic
246	#13133194	C₂×C₄	1	1	yes	characteristic
247	#13133194	C₂×C₄	1	1	yes	characteristic
248	#13133194	C₂×C₄	1	1	yes	characteristic
249	#13133190	C₂×C₄	1	1	yes	characteristic
250	#13133190	C₂×C₄	1	1	yes	characteristic
251	#13133190	C₂×C₄	1	1	yes	characteristic
252	#13133190	C₂×C₄	1	1	yes	characteristic
253	#13133190	C₂×C₄	1	1	yes	characteristic
254	#13133190	C₂×C₄	1	1	yes	characteristic
255	#13133190	C₂×C₄	1	1	yes	characteristic
256	#13133190	C₂×C₄	1	1	yes	characteristic
257	#13133189	C₂×C₄	1	1	yes	characteristic
258	#13133189	C₂×C₄	1	1	yes	characteristic
259	#13133189	C₂×C₄	1	1	yes	characteristic
260	#13133189	C₂×C₄	1	1	yes	characteristic
261	#13133189	C₂×C₄	1	1	yes	characteristic
262	#13133189	C₂×C₄	1	1	yes	characteristic
263	#13133189	C₂×C₄	1	1	yes	characteristic
264	#13133189	C₂×C₄	1	1	yes	characteristic
265	#13133187	C₂×C₄	1	1	yes	characteristic
266	#13133187	C₂×C₄	1	1	yes	characteristic
267	#13133187	C₂×C₄	1	1	yes	characteristic
268	#13133187	C₂×C₄	1	1	yes	characteristic
269	#13133187	C₂×C₄	1	1	yes	characteristic
270	#13133187	C₂×C₄	1	1	yes	characteristic
271	#13133187	C₂×C₄	1	1	yes	characteristic
272	#13133187	C₂×C₄	1	1	yes	characteristic
273	#13133185	C₂×C₄	1	1	yes	characteristic
274	#13133185	C₂×C₄	1	1	yes	characteristic
275	#13133185	C₂×C₄	1	1	yes	characteristic
276	#13133185	C₂×C₄	1	1	yes	characteristic
277	#13133185	C₂×C₄	1	1	yes	characteristic
278	#13133185	C₂×C₄	1	1	yes	characteristic
279	#13133185	C₂×C₄	1	1	yes	characteristic
280	#13133185	C₂×C₄	1	1	yes	characteristic
281	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
282	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
283	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
284	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
285	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
286	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
287	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
288	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
289	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
290	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
291	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
292	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
293	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
294	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
295	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
296	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
297	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
298	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
299	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
300	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
301	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
302	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
303	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
304	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
305	#13133174	C₂×C₄	1	1	yes	characteristic
306	#13133174	C₂×C₄	1	1	yes	characteristic
307	#13133174	C₂×C₄	1	1	yes	characteristic
308	#13133174	C₂×C₄	1	1	yes	characteristic
309	#13133174	C₂³	1	1	yes	characteristic
310	#13133174	C₂³	1	1	yes	characteristic
311	#13133174	C₂³	1	1	yes	characteristic
312	#13133174	C₂³	1	1	yes	characteristic
313	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
314	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
315	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
316	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
317	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
318	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
319	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
320	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
321	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
322	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
323	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
324	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
325	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
326	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
327	C₄⋊#88322	C₂³	1	2	yes	complemented
328	C₄⋊#88322	C₂³	1	2	yes	complemented
329	#13133146	C₂³	1	2	yes	complemented
330	#13133146	C₂³	1	2	yes	complemented
331	#13133146	C₂³	1	2	yes	complemented
332	#13133146	C₂³	1	2	yes	complemented
333	C₂²⋊#88322	C₂³	1	2	yes	—
334	C₂²⋊#88322	C₂³	1	2	yes	—
335	C₂²⋊#88322	C₂³	1	2	yes	complemented
336	C₂²⋊#88322	C₂³	1	2	yes	complemented
337	#13133129	C₂³	1	2	yes	—
338	#13133129	C₂³	1	2	yes	—
339	#13133129	C₂³	1	2	yes	—
340	#13133129	C₂³	1	2	yes	—
341	#13133129	C₂³	1	2	yes	complemented
342	#13133129	C₂³	1	2	yes	complemented
343	#13133129	C₂³	1	2	yes	complemented
344	#13133129	C₂³	1	2	yes	complemented
345	#13133128	C₂³	1	2	yes	complemented
346	#13133127	C₂³	1	2	yes	complemented
347	#13133127	C₂³	1	2	yes	complemented
348	C₄×#88322	C₂³	1	2	yes	complemented
349	C₈×Dic₅₃	C₂³	1	2	yes	complemented
350	C₈×Dic₅₃	C₂³	1	2	yes	complemented
351	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
352	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×M₁₆×C₅₃	—	2	4	no	—
355	C₂×M₁₆×C₅₃	—	2	4	no	—
356	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
359	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×M₁₆×C₅₃	C₂³	1	2	yes	complemented
362	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
363	C₂²×C₈×C₅₃	C₂³	1	2	yes	complemented
364	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
365	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
366	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
367	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
368	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
373	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
374	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
375	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
376	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
377	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
378	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
379	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
380	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
381	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
382	#97×C₅₃	C₂³	1	2	yes	complemented
383	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
384	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
385	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
386	C₂³×D₅₃	—	2	4	no	—
387	C₂³×D₅₃	—	4	2	no	—
388	C₂³×D₅₃	—	4	2	no	—
389	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
390	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
391	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
392	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
393	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
394	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
395	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
396	C₂×D₄×C₅₃	—	4	2	no	—
397	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
398	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
399	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
400	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	—	2	2	no	—
402	C₂²×C₄×C₅₃	—	2	2	no	—
403	C₂²×C₄×C₅₃	—	2	2	no	—
404	C₂²×C₄×C₅₃	—	2	2	no	—
405	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₂²⋊D₅₃	—	2	4	no	—
419	C₂×C₂²⋊D₅₃	—	2	4	no	—
420	C₂×C₂²⋊D₅₃	—	4	2	no	—
421	C₂×C₂²⋊D₅₃	—	4	2	no	—
422	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
423	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
424	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
425	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
426	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
427	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
428	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
429	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
430	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
431	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
432	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
433	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
434	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
435	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
436	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
437	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
438	C₂²×Dic₅₃	—	2	4	no	—
439	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
440	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
441	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
442	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
443	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
444	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
445	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
446	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
447	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
448	#11719945	—	2	4	no	—
449	#11719945	—	2	4	no	—
450	#11719945	—	2	4	no	—
451	#11719945	—	2	4	no	—
452	#11719945	—	2	2	no	—
453	#11719945	—	2	2	no	—
454	#11719945	—	2	2	no	—
455	#11719945	—	2	2	no	—
456	#11719945	—	2	2	no	—
457	#11719945	—	2	2	no	—
458	#11719945	—	2	2	no	—
459	#11719945	—	2	2	no	—
460	C₂×D₂₁₂	—	2	4	no	—
461	C₂×D₂₁₂	—	4	2	no	—
462	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
463	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
464	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
465	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
466	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
467	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
468	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
469	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
470	C₂×C₄×D₅₃	—	2	4	no	—
471	C₂×C₄×D₅₃	—	2	2	no	—
472	C₂×C₄×D₅₃	—	2	2	no	—
473	C₂×C₄×D₅₃	—	2	2	no	—
474	C₂×C₄×D₅₃	—	2	2	no	—
475	C₂×C₄×D₅₃	—	2	4	no	—
476	C₂×C₄×D₅₃	—	2	4	no	—
477	C₂×C₄×D₅₃	—	2	4	no	—
478	C₂×C₄×D₅₃	—	2	4	no	—
479	C₂×C₄×D₅₃	—	2	4	no	—
480	C₂×C₄×D₅₃	—	2	2	no	—
481	C₂×C₄×D₅₃	—	2	2	no	—
482	C₂×C₄×D₅₃	—	2	2	no	—
483	C₂×C₄×D₅₃	—	2	2	no	—
484	C₂×C₄×D₅₃	—	2	2	no	—
485	C₂×C₄×D₅₃	—	2	2	no	—
486	C₂×C₄×D₅₃	—	2	2	no	—
487	C₂×C₄×D₅₃	—	2	2	no	—
488	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
489	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
490	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
491	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
492	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
493	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
494	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
495	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
496	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
497	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
498	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
499	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
500	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
501	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
502	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
503	C₂×C₄×D₅₃	#41	1	4	yes	—
504	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
505	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
506	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
507	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
508	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
509	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
510	C₂×Dic₁₀₆	—	2	4	no	—
511	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
512	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
513	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
514	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
515	M₁₆×C₅₃	—	2	2	no	—
516	M₁₆×C₅₃	—	2	2	no	—
517	M₁₆×C₅₃	—	2	2	no	—
518	M₁₆×C₅₃	—	2	4	no	—
519	M₁₆×C₅₃	—	2	4	no	—
520	M₁₆×C₅₃	C₂×D₄	1	4	yes	—
521	C₂×C₈×C₅₃	—	2	4	no	—
522	C₂×C₈×C₅₃	—	2	4	no	—
523	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
524	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
525	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
526	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
527	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
528	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
529	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
530	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
531	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
532	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
533	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
534	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
535	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
536	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
537	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
538	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
539	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
540	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
541	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
544	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
545	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
546	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
547	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
548	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
549	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
550	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
551	#11719921	C₂²×C₄	1	1	yes	characteristic
552	#11719921	C₂²×C₄	1	1	yes	characteristic
553	#11719921	C₂²×C₄	1	1	yes	characteristic
554	#11719921	C₂²×C₄	1	1	yes	characteristic
555	#11719921	C₂²×C₄	1	1	yes	characteristic
556	#11719921	C₂²×C₄	1	1	yes	characteristic
557	#11719921	C₂²×C₄	1	1	yes	characteristic
558	#11719921	C₂²×C₄	1	1	yes	characteristic
559	#11719921	C₂²×C₄	1	1	yes	characteristic
560	#11719921	C₂²×C₄	1	1	yes	characteristic
561	#11719921	C₂²×C₄	1	1	yes	characteristic
562	#11719921	C₂²×C₄	1	1	yes	characteristic
563	#11719921	C₂²×C₄	1	1	yes	characteristic
564	#11719921	C₂²×C₄	1	1	yes	characteristic
565	#11719921	C₂²×C₄	1	1	yes	characteristic
566	#11719921	C₂²×C₄	1	1	yes	characteristic
567	#11719921	C₂²×C₄	1	1	yes	characteristic
568	#11719921	C₂²×C₄	1	1	yes	characteristic
569	#11719921	C₂²×C₄	1	1	yes	characteristic
570	#11719921	C₂²×C₄	1	1	yes	characteristic
571	#11719921	C₂²×C₄	1	1	yes	characteristic
572	#11719921	C₂²×C₄	1	1	yes	characteristic
573	#11719921	C₂²×C₄	1	1	yes	characteristic
574	#11719921	C₂²×C₄	1	1	yes	characteristic
575	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
576	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
577	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
578	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
579	#11719919	C₂²×C₄	1	1	yes	characteristic
580	#11719919	C₂²×C₄	1	1	yes	characteristic
581	#11719919	C₂²×C₄	1	1	yes	characteristic
582	#11719919	C₂²×C₄	1	1	yes	characteristic
583	#11719919	C₂²×C₄	1	1	yes	characteristic
584	#11719919	C₂²×C₄	1	1	yes	characteristic
585	#11719919	C₂²×C₄	1	1	yes	characteristic
586	#11719919	C₂²×C₄	1	1	yes	characteristic
587	#11719919	C₂²×C₄	1	1	yes	characteristic
588	#11719919	C₂²×C₄	1	1	yes	characteristic
589	#11719919	C₂²×C₄	1	1	yes	characteristic
590	#11719919	C₂²×C₄	1	1	yes	characteristic
591	#11719919	C₂²×C₄	1	1	yes	characteristic
592	#11719919	C₂²×C₄	1	1	yes	characteristic
593	#11719919	C₂²×C₄	1	1	yes	characteristic
594	#11719919	C₂²×C₄	1	1	yes	characteristic
595	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
596	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
597	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
598	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
599	#11719917	—	2	2	no	—
600	#11719917	—	2	2	no	—
601	#11719917	—	2	2	no	—
602	#11719917	—	2	4	no	—
603	#11719917	—	2	4	no	—
604	#11719917	C₂×D₄	1	4	yes	—
605	C₂×#88322	—	2	4	no	—
606	C₂×#88322	—	2	4	no	—
607	C₂×#88322	C₂⁴	1	2	yes	—
608	C₂×#88322	C₂⁴	1	2	yes	—
609	C₂×#88322	C₂⁴	1	2	yes	—
610	C₂×#88322	C₂⁴	1	2	yes	—
611	#11719912	—	2	4	no	—
612	#11719912	—	2	4	no	—
613	#11719912	—	2	4	no	—
614	#11719912	—	2	4	no	—
615	#11719912	—	2	4	no	—
616	#11719912	—	2	4	no	—
617	#11719912	—	2	4	no	—
618	#11719912	C₂×D₄	1	8	yes	complemented
619	C₈×D₅₃	—	2	4	no	—
620	C₈×D₅₃	—	2	4	no	—
621	C₈×D₅₃	—	2	4	no	—
622	C₈×D₅₃	—	2	4	no	—
623	C₈×D₅₃	—	2	4	no	—
624	C₈×D₅₃	—	2	4	no	—
625	C₈×D₅₃	—	2	4	no	—
626	C₈×D₅₃	C₂×D₄	1	8	yes	complemented
627	C₂³×C₅₃	—	2	2	no	—
628	C₂³×C₅₃	—	2	2	no	—
629	C₂³×C₅₃	—	2	2	no	—
630	C₂³×C₅₃	—	4	1	no	—
631	C₂³×C₅₃	—	4	1	no	—
632	C₂³×C₅₃	—	4	1	no	—
633	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
634	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
635	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
636	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
637	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
638	C₂²×D₅₃	—	2	2	no	—
639	C₂²×D₅₃	—	2	2	no	—
640	C₂²×D₅₃	—	2	2	no	—
641	C₂²×D₅₃	—	2	2	no	—
642	C₂²×D₅₃	—	2	2	no	—
643	C₂²×D₅₃	—	2	2	no	—
644	C₂²×D₅₃	—	2	2	no	—
645	C₂²×D₅₃	—	2	2	no	—
646	C₂²×D₅₃	—	2	2	no	—
647	C₂²×D₅₃	—	2	2	no	—
648	C₂²×D₅₃	—	2	2	no	—
649	C₂²×D₅₃	—	4	1	no	—
650	C₂²×D₅₃	—	4	1	no	—
651	C₂²×D₅₃	—	4	1	no	—
652	C₂²×D₅₃	—	4	1	no	—
653	C₂²×D₅₃	—	4	1	no	—
654	C₂²×D₅₃	—	4	1	no	—
655	C₂²×D₅₃	—	4	1	no	—
656	C₂²×D₅₃	—	4	1	no	—
657	C₂²×D₅₃	—	4	1	no	—
658	C₂²×D₅₃	—	4	16	no	—
659	C₂²×D₅₃	C₄×D₄	1	4	yes	—
660	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
661	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
662	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
663	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
664	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
665	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
666	D₄×C₅₃	—	2	2	no	—
667	D₄×C₅₃	—	2	2	no	—
668	D₄×C₅₃	—	4	1	no	—
669	D₄×C₅₃	—	4	1	no	—
670	C₂×C₄×C₅₃	—	2	2	no	—
671	C₂×C₄×C₅₃	—	2	2	no	—
672	C₂×C₄×C₅₃	—	2	2	no	—
673	C₂×C₄×C₅₃	—	2	2	no	—
674	C₂×C₄×C₅₃	—	2	2	no	—
675	C₂×C₄×C₅₃	—	2	2	no	—
676	C₂×C₄×C₅₃	—	2	1	no	—
677	C₂×C₄×C₅₃	—	2	1	no	—
678	C₂×C₄×C₅₃	—	2	1	no	—
679	C₂×C₄×C₅₃	—	2	1	no	—
680	C₂×C₄×C₅₃	—	2	1	no	—
681	C₂×C₄×C₅₃	—	2	1	no	—
682	C₂×C₄×C₅₃	—	2	1	no	—
683	C₂×C₄×C₅₃	—	2	1	no	—
684	C₂×C₄×C₅₃	—	4	1	no	—
685	C₂×C₄×C₅₃	—	4	1	no	—
686	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
687	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
688	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
689	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
690	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
691	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
692	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
693	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
694	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
695	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
696	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
697	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
698	C₂²⋊D₅₃	—	2	2	no	—
699	C₂²⋊D₅₃	—	2	2	no	—
700	C₂²⋊D₅₃	—	2	2	no	—
701	C₂²⋊D₅₃	—	2	2	no	—
702	C₂²⋊D₅₃	—	2	2	no	—
703	C₂²⋊D₅₃	—	2	2	no	—
704	C₂²⋊D₅₃	—	2	2	no	—
705	C₂²⋊D₅₃	—	2	2	no	—
706	C₂²⋊D₅₃	—	2	2	no	—
707	C₂²⋊D₅₃	—	2	2	no	—
708	C₂²⋊D₅₃	—	2	2	no	—
709	C₂²⋊D₅₃	—	2	2	no	—
710	C₂²⋊D₅₃	—	4	1	no	—
711	C₂²⋊D₅₃	—	4	1	no	—
712	C₂²⋊D₅₃	—	4	1	no	—
713	C₂²⋊D₅₃	—	4	1	no	—
714	C₂×Dic₅₃	—	2	2	no	—
715	C₂×Dic₅₃	—	2	2	no	—
716	C₂×Dic₅₃	—	2	2	no	—
717	C₂×Dic₅₃	—	2	2	no	—
718	C₂×Dic₅₃	—	2	2	no	—
719	C₂×Dic₅₃	—	2	2	no	—
720	C₂×Dic₅₃	—	4	1	no	—
721	C₂×Dic₅₃	—	4	1	no	—
722	C₂×Dic₅₃	C₄×D₄	1	4	yes	—
723	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
724	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
725	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
726	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
727	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
728	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
729	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
730	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
731	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
732	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
733	D₂₁₂	—	2	2	no	—
734	D₂₁₂	—	2	2	no	—
735	D₂₁₂	—	2	2	no	—
736	D₂₁₂	—	2	2	no	—
737	D₂₁₂	—	2	2	no	—
738	D₂₁₂	—	2	2	no	—
739	D₂₁₂	—	4	1	no	—
740	D₂₁₂	—	4	1	no	—
741	C₄×D₅₃	—	2	2	no	—
742	C₄×D₅₃	—	2	2	no	—
743	C₄×D₅₃	—	2	2	no	—
744	C₄×D₅₃	—	2	2	no	—
745	C₄×D₅₃	—	2	2	no	—
746	C₄×D₅₃	—	2	2	no	—
747	C₄×D₅₃	—	2	2	no	—
748	C₄×D₅₃	—	2	2	no	—
749	C₄×D₅₃	—	2	1	no	—
750	C₄×D₅₃	—	2	1	no	—
751	C₄×D₅₃	—	2	1	no	—
752	C₄×D₅₃	—	2	1	no	—
753	C₄×D₅₃	—	2	1	no	—
754	C₄×D₅₃	—	2	1	no	—
755	C₄×D₅₃	—	2	1	no	—
756	C₄×D₅₃	—	2	1	no	—
757	C₄×D₅₃	—	2	2	no	—
758	C₄×D₅₃	—	2	2	no	—
759	C₄×D₅₃	—	2	2	no	—
760	C₄×D₅₃	—	2	2	no	—
761	C₄×D₅₃	C₄×D₄	1	4	yes	—
762	C₄×D₅₃	C₄×D₄	1	4	yes	—
763	C₄×D₅₃	C₂²×D₄	1	2	yes	—
764	C₄×D₅₃	C₂²×D₄	1	2	yes	—
765	C₄×D₅₃	C₂×#41	1	2	yes	—
766	C₄×D₅₃	C₂×#41	1	2	yes	—
767	Dic₁₀₆	—	2	2	no	—
768	Dic₁₀₆	—	2	2	no	—
769	Dic₁₀₆	—	2	2	no	—
770	Dic₁₀₆	—	2	2	no	—
771	C₈×C₅₃	—	2	2	no	—
772	C₈×C₅₃	—	2	2	no	—
773	C₈×C₅₃	—	2	2	no	—
774	C₈×C₅₃	C₂²×D₄	1	4	yes	—
775	#88322	—	2	2	no	—
776	#88322	—	2	2	no	—
777	#88322	—	2	2	no	—
778	#88322	C₂²×D₄	1	4	yes	—
779	#60141	—	53	1	no	maximal, Sylow
780	C₂²×C₅₃	—	2	1	no	—
781	C₂²×C₅₃	—	2	1	no	—
782	C₂²×C₅₃	—	2	1	no	—
783	C₂²×C₅₃	—	2	1	no	—
784	C₂²×C₅₃	—	2	1	no	—
785	C₂²×C₅₃	—	2	1	no	—
786	C₂²×C₅₃	—	2	1	no	—
787	C₂²×C₅₃	—	2	1	no	—
788	C₂²×C₅₃	—	2	1	no	—
789	C₂²×C₅₃	—	2	1	no	—
790	C₂²×C₅₃	—	2	1	no	—
791	C₂²×C₅₃	—	2	1	no	—
792	C₂²×C₅₃	—	2	1	no	—
793	C₂²×C₅₃	—	4	4	no	—
794	C₂²×C₅₃	—	8	2	no	—
795	C₂²×C₅₃	C₂×C₄×D₄	1	2	yes	—
796	C₂²×C₅₃	#568	1	2	yes	complemented
797	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
798	C₂×D₅₃	—	2	8	no	—
799	C₂×D₅₃	—	2	1	no	—
800	C₂×D₅₃	—	2	1	no	—
801	C₂×D₅₃	—	2	1	no	—
802	C₂×D₅₃	—	2	1	no	—
803	C₂×D₅₃	—	2	1	no	—
804	C₂×D₅₃	—	2	1	no	—
805	C₂×D₅₃	—	2	1	no	—
806	C₂×D₅₃	—	2	1	no	—
807	C₂×D₅₃	—	2	1	no	—
808	C₂×D₅₃	—	2	1	no	—
809	C₂×D₅₃	—	2	1	no	—
810	C₂×D₅₃	—	2	1	no	—
811	C₂×D₅₃	—	2	1	no	—
812	C₂×D₅₃	—	2	1	no	—
813	C₂×D₅₃	—	2	1	no	—
814	C₂×D₅₃	—	4	4	no	—
815	C₂×D₅₃	—	4	4	no	—
816	C₂×D₅₃	—	4	4	no	—
817	C₂×D₅₃	—	4	4	no	—
818	C₂×D₅₃	—	4	4	no	—
819	C₂×D₅₃	—	8	2	no	—
820	C₂×D₅₃	C₂×C₄×D₄	1	2	yes	—
821	C₂×D₅₃	C₂×C₄×D₄	1	2	yes	—
822	C₂×D₅₃	#568	1	2	yes	complemented
823	C₄×C₅₃	—	2	1	no	—
824	C₄×C₅₃	—	2	1	no	—
825	C₄×C₅₃	—	2	1	no	—
826	C₄×C₅₃	—	2	1	no	—
827	C₄×C₅₃	—	2	1	no	—
828	C₄×C₅₃	—	2	1	no	—
829	C₄×C₅₃	—	2	1	no	—
830	C₄×C₅₃	—	2	1	no	—
831	C₄×C₅₃	C₂×C₄×D₄	1	2	yes	—
832	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
833	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
834	Dic₅₃	—	2	1	no	—
835	Dic₅₃	—	2	1	no	—
836	Dic₅₃	—	2	1	no	—
837	Dic₅₃	—	2	1	no	—
838	Dic₅₃	—	2	1	no	—
839	Dic₅₃	—	2	1	no	—
840	Dic₅₃	—	2	1	no	—
841	Dic₅₃	—	2	1	no	—
842	Dic₅₃	C₂×C₄×D₄	1	2	yes	—
843	Dic₅₃	C₂×C₄×D₄	1	2	yes	—
844	C₂×#568	—	53	1	no	—
845	C₂³×M₁₆	—	53	1	no	—
846	C₂×#525	—	53	1	no	—
847	D₄×M₁₆	—	53	1	no	—
848	D₄×M₁₆	—	53	1	no	—
849	D₄×M₁₆	—	53	1	no	—
850	D₄×M₁₆	—	53	1	no	—
851	D₄×M₁₆	—	53	1	no	—
852	D₄×M₁₆	—	53	1	no	—
853	D₄×M₁₆	—	53	1	no	—
854	D₄×M₁₆	D₅₃	1	1	yes	characteristic, complemented
855	#2933	—	53	2	no	—
856	#2933	—	53	2	no	—
857	#2933	—	53	2	no	—
858	#2933	—	53	2	no	—
859	#2930	—	53	2	no	—
860	#2930	—	53	2	no	—
861	#2929	—	53	2	no	—
862	#2929	—	53	2	no	—
863	#2905	—	53	1	no	—
864	#2879	—	53	1	no	—
865	C₂×#407	—	53	1	no	—
866	#2873	—	53	1	no	—
867	C₂×C₅₃	—	2	2	no	—
868	C₂×C₅₃	—	2	2	no	—
869	C₂×C₅₃	—	4	1	no	—
870	C₂×C₅₃	—	4	1	no	—
871	C₂×C₅₃	—	4	1	no	—
872	C₂×C₅₃	C₂²×C₄×D₄	1	1	yes	characteristic
873	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
874	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
875	D₅₃	—	2	2	no	—
876	D₅₃	—	2	2	no	—
877	D₅₃	—	2	2	no	—
878	D₅₃	—	4	1	no	—
879	D₅₃	—	4	1	no	—
880	D₅₃	—	4	1	no	—
881	C₂²×#41	—	53	1	no	—
882	C₂⁴×C₄	—	53	1	no	—
883	#568	—	106	8	no	—
884	C₂×#131	—	53	2	no	—
885	C₂×#131	—	53	2	no	—
886	C₂×#131	—	53	2	no	—
887	C₂×#131	—	53	2	no	—
888	C₂²×M₁₆	—	53	1	no	—
889	C₂²×M₁₆	—	53	1	no	—
890	C₂²×M₁₆	—	53	1	no	—
891	C₂²×M₁₆	—	53	1	no	—
892	C₂²×M₁₆	—	53	1	no	—
893	C₂²×M₁₆	—	53	1	no	—
894	C₂²×M₁₆	—	53	2	no	—
895	C₂²×M₁₆	—	53	2	no	—
896	C₂²×M₁₆	—	53	1	no	—
897	C₂²×M₁₆	—	53	1	no	—
898	C₂²×M₁₆	—	53	1	no	—
899	C₂²×M₁₆	—	53	1	no	—
900	C₂²×M₁₆	—	53	2	no	—
901	C₂²×M₁₆	—	106	8	no	—
902	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic
903	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
904	C₂³×C₈	—	53	2	no	—
905	#525	—	53	1	no	—
906	#525	—	53	1	no	—
907	#525	—	53	1	no	—
908	#525	—	53	1	no	—
909	#525	—	53	1	no	—
910	#525	—	53	1	no	—
911	#525	—	53	1	no	—
912	#525	—	53	1	no	—
913	#525	—	53	1	no	—
914	#525	—	53	1	no	—
915	#525	—	53	1	no	—
916	#525	—	53	1	no	—
917	#525	—	53	1	no	—
918	#525	—	53	1	no	—
919	#525	—	53	1	no	—
920	#525	—	53	1	no	—
921	C₂×#123	—	53	1	no	—
922	C₂×#123	—	53	1	no	—
923	C₂×C₂²⋊Q₈	—	53	1	no	—
924	C₂×C₂²⋊Q₈	—	53	1	no	—
925	C₂×#121	—	53	1	no	—
926	C₂×#121	—	53	1	no	—
927	C₂×#120	—	53	1	no	—
928	C₂×#120	—	53	1	no	—
929	C₂×C₄×D₄	—	53	1	no	—
930	C₂×C₄×D₄	—	53	1	no	—
931	C₂×C₄×D₄	—	53	1	no	—
932	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
933	C₂×#117	—	53	1	no	—
934	#436	—	53	2	no	—
935	#436	—	53	2	no	—
936	#436	—	53	2	no	—
937	#436	—	53	2	no	—
938	#436	—	53	2	no	—
939	#436	—	53	2	no	—
940	#436	—	53	2	no	—
941	#436	C₂×D₅₃	1	2	yes	complemented
942	#435	—	53	2	no	—
943	#435	—	53	2	no	—
944	#435	—	53	2	no	—
945	#435	—	53	2	no	—
946	#435	—	53	2	no	—
947	#435	—	53	2	no	—
948	#435	—	53	2	no	—
949	#435	—	53	2	no	—
950	#435	—	53	2	no	—
951	#435	—	53	2	no	—
952	#435	—	53	2	no	—
953	#435	—	53	2	no	—
954	#435	—	53	2	no	—
955	#435	—	53	2	no	—
956	#435	C₂×D₅₃	1	2	yes	complemented
957	#435	C₂×D₅₃	1	2	yes	complemented
958	C₈×D₄	—	53	2	no	—
959	C₈×D₄	—	53	2	no	—
960	C₈×D₄	—	53	2	no	—
961	C₈×D₄	—	53	2	no	—
962	C₈×D₄	—	53	2	no	—
963	C₈×D₄	—	53	2	no	—
964	C₈×D₄	—	53	2	no	—
965	C₈×D₄	C₂×D₅₃	1	2	yes	complemented
966	#424	—	53	2	no	—
967	#424	—	53	2	no	—
968	#424	—	53	2	no	—
969	#424	—	53	2	no	—
970	#423	—	53	1	no	—
971	#423	—	53	1	no	—
972	#423	—	53	1	no	—
973	#423	C₂×D₅₃	1	1	yes	characteristic, complemented
974	#408	—	53	2	no	—
975	#408	—	53	2	no	—
976	#408	—	53	2	no	—
977	#408	—	53	2	no	—
978	#407	—	53	1	no	—
979	#407	—	53	1	no	—
980	#407	—	53	1	no	—
981	#407	—	53	1	no	—
982	#407	—	53	1	no	—
983	#407	—	53	1	no	—
984	#407	—	53	2	no	—
985	#407	—	53	2	no	—
986	#407	C₂×D₅₃	1	1	yes	characteristic
987	#407	C₂×D₅₃	1	1	yes	characteristic, complemented
988	C₂×C₂²⋊C₈	—	53	2	no	—
989	C₂×C₂²⋊C₈	—	53	2	no	—
990	#405	—	53	2	no	—
991	#405	—	53	2	no	—
992	#405	—	53	2	no	—
993	#405	—	53	2	no	—
994	C₄×M₁₆	—	53	1	no	—
995	C₄×M₁₆	—	53	1	no	—
996	C₄×M₁₆	—	53	1	no	—
997	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
998	C₅₃	#60141	1	1	yes	characteristic, complemented, Sylow
999	C₂⁵	—	53	1	no	—
1000	C₂×#41	—	53	1	no	—
1001	C₂×#41	—	53	1	no	—
1002	C₂×#41	—	53	1	no	—
1003	C₂×#41	—	53	1	no	—
1004	C₂×#41	—	53	1	no	—
1005	C₂×#41	—	53	1	no	—
1006	C₂×#41	—	53	1	no	—
1007	C₂×#41	—	53	1	no	—
1008	C₂×#41	—	106	4	no	—
1009	C₂×#41	—	106	4	no	—
1010	C₂²×Q₈	—	53	1	no	—
1011	C₂²×D₄	—	53	1	no	—
1012	C₂²×D₄	—	53	1	no	—
1013	C₂²×D₄	—	53	1	no	—
1014	C₂²×D₄	—	53	1	no	—
1015	C₂²×D₄	—	53	1	no	—
1016	C₂²×D₄	—	53	1	no	—
1017	C₂²×D₄	C₄×D₅₃	1	1	yes	characteristic
1018	C₂³×C₄	—	53	1	no	—
1019	C₂³×C₄	—	53	1	no	—
1020	C₂³×C₄	—	53	1	no	—
1021	C₂³×C₄	—	53	1	no	—
1022	C₂³×C₄	—	53	1	no	—
1023	C₂³×C₄	—	53	1	no	—
1024	C₂³×C₄	—	53	1	no	—
1025	C₂³×C₄	—	53	1	no	—
1026	C₂³×C₄	—	53	1	no	—
1027	C₂³×C₄	—	53	1	no	—
1028	C₂³×C₄	—	53	1	no	—
1029	C₂³×C₄	—	53	1	no	—
1030	C₂³×C₄	—	53	1	no	—
1031	C₂³×C₄	—	53	1	no	—
1032	C₂³×C₄	—	106	4	no	—
1033	C₂³×C₄	—	106	4	no	—
1034	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1035	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1036	#131	—	106	8	no	—
1037	#131	—	106	8	no	—
1038	#131	—	106	8	no	—
1039	#131	—	106	8	no	—
1040	C₂×M₁₆	—	2	4	no	—
1041	C₂×M₁₆	—	2	4	no	—
1042	C₂×M₁₆	—	53	1	no	—
1043	C₂×M₁₆	—	53	8	no	—
1044	C₂×M₁₆	—	53	1	no	—
1045	C₂×M₁₆	—	53	1	no	—
1046	C₂×M₁₆	—	53	2	no	—
1047	C₂×M₁₆	—	53	2	no	—
1048	C₂×M₁₆	—	53	1	no	—
1049	C₂×M₁₆	—	53	2	no	—
1050	C₂×M₁₆	—	53	2	no	—
1051	C₂×M₁₆	—	53	2	no	—
1052	C₂×M₁₆	—	53	2	no	—
1053	C₂×M₁₆	—	53	2	no	—
1054	C₂×M₁₆	—	53	2	no	—
1055	C₂×M₁₆	—	53	2	no	—
1056	C₂×M₁₆	—	53	2	no	—
1057	C₂×M₁₆	—	106	8	no	—
1058	C₂×M₁₆	—	106	8	no	—
1059	C₂×M₁₆	—	106	4	no	—
1060	C₂×M₁₆	—	106	8	no	—
1061	C₂×M₁₆	—	106	4	no	—
1062	C₂×M₁₆	—	106	4	no	—
1063	C₂×M₁₆	—	106	4	no	—
1064	C₂×M₁₆	—	106	4	no	—
1065	C₂×M₁₆	—	106	4	no	—
1066	C₂×M₁₆	—	106	4	no	—
1067	C₂×M₁₆	—	106	4	no	—
1068	C₂×M₁₆	—	106	4	no	—
1069	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
1070	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
1071	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
1072	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
1073	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
1074	C₂×M₁₆	C₂²×D₅₃	1	2	yes	complemented
1075	C₂²×C₈	—	53	2	no	—
1076	C₂²×C₈	—	53	2	no	—
1077	C₂²×C₈	—	53	2	no	—
1078	C₂²×C₈	—	53	2	no	—
1079	C₂²×C₈	—	53	2	no	—
1080	C₂²×C₈	—	53	2	no	—
1081	C₂²×C₈	—	53	2	no	—
1082	C₂²×C₈	—	53	2	no	—
1083	C₂²×C₈	—	53	2	no	—
1084	C₂²×C₈	—	53	2	no	—
1085	C₂²×C₈	—	106	8	no	—
1086	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
1087	C₂²×C₈	C₂²×D₅₃	1	2	yes	complemented
1088	#123	—	53	1	no	—
1089	#123	—	53	1	no	—
1090	#123	—	53	1	no	—
1091	#123	—	53	1	no	—
1092	#123	—	53	1	no	—
1093	#123	—	53	1	no	—
1094	#123	—	53	1	no	—
1095	#123	—	53	1	no	—
1096	#123	—	53	1	no	—
1097	#123	—	53	1	no	—
1098	#123	—	53	1	no	—
1099	#123	—	53	1	no	—
1100	#123	—	53	1	no	—
1101	#123	—	53	1	no	—
1102	#123	—	53	1	no	—
1103	#123	—	53	1	no	—
1104	C₂²⋊Q₈	—	53	1	no	—
1105	C₂²⋊Q₈	—	53	1	no	—
1106	C₂²⋊Q₈	—	53	1	no	—
1107	C₂²⋊Q₈	—	53	1	no	—
1108	C₂²⋊Q₈	—	53	1	no	—
1109	C₂²⋊Q₈	—	53	1	no	—
1110	C₂²⋊Q₈	—	53	1	no	—
1111	C₂²⋊Q₈	—	53	1	no	—
1112	C₂²⋊Q₈	—	53	1	no	—
1113	C₂²⋊Q₈	—	53	1	no	—
1114	C₂²⋊Q₈	—	53	1	no	—
1115	C₂²⋊Q₈	—	53	1	no	—
1116	C₂²⋊Q₈	—	53	1	no	—
1117	C₂²⋊Q₈	—	53	1	no	—
1118	C₂²⋊Q₈	—	53	1	no	—
1119	C₂²⋊Q₈	—	53	1	no	—
1120	#121	—	53	1	no	—
1121	#121	—	53	1	no	—
1122	#121	—	53	1	no	—
1123	#121	—	53	1	no	—
1124	#121	—	53	1	no	—
1125	#121	—	53	1	no	—
1126	#121	—	53	1	no	—
1127	#121	—	53	1	no	—
1128	#121	—	53	1	no	—
1129	#121	—	53	1	no	—
1130	#121	—	53	1	no	—
1131	#121	—	53	1	no	—
1132	#121	—	53	1	no	—
1133	#121	—	53	1	no	—
1134	#121	—	53	1	no	—
1135	#121	—	53	1	no	—
1136	#120	—	53	1	no	—
1137	#120	—	53	1	no	—
1138	#120	—	53	1	no	—
1139	#120	—	53	1	no	—
1140	#120	—	53	1	no	—
1141	#120	—	53	1	no	—
1142	#120	—	53	1	no	—
1143	#120	—	53	1	no	—
1144	#120	—	53	1	no	—
1145	#120	—	53	1	no	—
1146	#120	—	53	1	no	—
1147	#120	—	53	1	no	—
1148	#120	—	53	1	no	—
1149	#120	—	53	1	no	—
1150	#120	—	53	1	no	—
1151	#120	—	53	1	no	—
1152	C₄×D₄	—	53	1	no	—
1153	C₄×D₄	—	53	1	no	—
1154	C₄×D₄	—	53	1	no	—
1155	C₄×D₄	—	53	1	no	—
1156	C₄×D₄	—	53	1	no	—
1157	C₄×D₄	—	53	1	no	—
1158	C₄×D₄	—	53	1	no	—
1159	C₄×D₄	—	53	1	no	—
1160	C₄×D₄	—	53	1	no	—
1161	C₄×D₄	—	53	1	no	—
1162	C₄×D₄	—	53	1	no	—
1163	C₄×D₄	—	53	1	no	—
1164	C₄×D₄	—	53	1	no	—
1165	C₄×D₄	—	53	1	no	—
1166	C₄×D₄	—	53	1	no	—
1167	C₄×D₄	—	53	1	no	—
1168	C₄×D₄	—	53	1	no	—
1169	C₄×D₄	—	53	1	no	—
1170	C₄×D₄	—	53	1	no	—
1171	C₄×D₄	—	53	1	no	—
1172	C₄×D₄	—	53	1	no	—
1173	C₄×D₄	—	53	1	no	—
1174	C₄×D₄	—	53	1	no	—
1175	C₄×D₄	—	53	1	no	—
1176	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
1177	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
1178	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
1179	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
1180	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1181	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1182	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1183	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1184	#117	—	53	1	no	—
1185	#117	—	53	1	no	—
1186	#117	—	53	1	no	—
1187	#117	—	53	1	no	—
1188	#117	—	53	1	no	—
1189	#117	—	53	1	no	—
1190	#117	—	53	1	no	—
1191	#117	—	53	1	no	—
1192	C₂×C₄⋊C₄	—	53	1	no	—
1193	C₂×C₄⋊C₄	—	53	1	no	—
1194	C₂×C₄⋊C₄	—	53	1	no	—
1195	C₂×C₄⋊C₄	—	53	1	no	—
1196	C₂×C₄⋊C₄	—	53	1	no	—
1197	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
1198	C₂×C₂²⋊C₄	—	53	1	no	—
1199	C₂×C₂²⋊C₄	—	53	1	no	—
1200	C₂×C₂²⋊C₄	—	53	1	no	—
1201	C₂×C₂²⋊C₄	—	53	1	no	—
1202	C₂×C₂²⋊C₄	—	53	1	no	—
1203	C₂×C₂²⋊C₄	—	53	1	no	—
1204	C₂×C₂²⋊C₄	—	53	1	no	—
1205	C₂×C₂²⋊C₄	—	53	1	no	—
1206	C₂×C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
1207	C₂×C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
1208	C₂×C₄²	—	53	1	no	—
1209	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1210	C₄⋊C₈	—	53	2	no	—
1211	C₄⋊C₈	—	53	2	no	—
1212	C₄⋊C₈	—	53	2	no	—
1213	C₄⋊C₈	—	53	2	no	—
1214	C₄⋊C₈	—	53	2	no	—
1215	C₄⋊C₈	—	53	2	no	—
1216	C₄⋊C₈	C₂²×D₅₃	1	2	yes	complemented
1217	C₄⋊C₈	C₂²×D₅₃	1	2	yes	complemented
1218	C₂²⋊C₈	—	53	2	no	—
1219	C₂²⋊C₈	—	53	2	no	—
1220	C₂²⋊C₈	—	53	2	no	—
1221	C₂²⋊C₈	—	53	2	no	—
1222	C₂²⋊C₈	—	53	2	no	—
1223	C₂²⋊C₈	—	53	2	no	—
1224	C₂²⋊C₈	—	53	2	no	—
1225	C₂²⋊C₈	—	53	2	no	—
1226	C₂²⋊C₈	—	53	2	no	—
1227	C₂²⋊C₈	—	53	2	no	—
1228	C₂²⋊C₈	—	53	2	no	—
1229	C₂²⋊C₈	—	53	2	no	—
1230	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
1231	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
1232	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	complemented
1233	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	complemented
1234	#97	—	53	2	no	—
1235	#97	—	53	2	no	—
1236	#97	—	53	2	no	—
1237	#97	C₂²×D₅₃	1	2	yes	complemented
1238	C₄×C₈	—	53	2	no	—
1239	C₄×C₈	—	53	2	no	—
1240	C₄×C₈	—	53	2	no	—
1241	C₄×C₈	C₂²×D₅₃	1	2	yes	complemented
1242	C₂⁴	—	53	1	no	—
1243	C₂⁴	—	53	1	no	—
1244	C₂⁴	—	53	1	no	—
1245	C₂⁴	—	53	1	no	—
1246	C₂⁴	—	53	1	no	—
1247	C₂⁴	—	53	1	no	—
1248	C₂⁴	—	53	1	no	—
1249	C₂⁴	—	106	4	no	—
1250	C₂⁴	—	212	2	no	—
1251	C₂⁴	—	212	2	no	—
1252	C₂⁴	C₂×C₄×D₅₃	1	1	yes	characteristic
1253	C₂⁴	C₂×C₄×D₅₃	1	1	yes	characteristic
1254	#41	—	106	2	no	—
1255	#41	—	106	2	no	—
1256	#41	—	106	2	no	—
1257	#41	—	106	2	no	—
1258	#41	—	106	4	no	—
1259	#41	—	106	4	no	—
1260	#41	—	106	4	no	—
1261	#41	—	106	4	no	—
1262	#41	—	106	2	no	—
1263	#41	—	106	2	no	—
1264	#41	—	106	2	no	—
1265	#41	—	106	2	no	—
1266	C₂×Q₈	—	53	1	no	—
1267	C₂×Q₈	—	53	1	no	—
1268	C₂×Q₈	—	53	1	no	—
1269	C₂×Q₈	—	53	1	no	—
1270	C₂×Q₈	—	106	4	no	—
1271	C₂×D₄	—	4	2	no	—
1272	C₂×D₄	—	53	1	no	—
1273	C₂×D₄	—	53	1	no	—
1274	C₂×D₄	—	53	1	no	—
1275	C₂×D₄	—	53	1	no	—
1276	C₂×D₄	—	53	1	no	—
1277	C₂×D₄	—	53	1	no	—
1278	C₂×D₄	—	53	1	no	—
1279	C₂×D₄	—	53	1	no	—
1280	C₂×D₄	—	53	1	no	—
1281	C₂×D₄	—	53	1	no	—
1282	C₂×D₄	—	53	1	no	—
1283	C₂×D₄	—	53	1	no	—
1284	C₂×D₄	—	53	1	no	—
1285	C₂×D₄	—	53	1	no	—
1286	C₂×D₄	—	53	1	no	—
1287	C₂×D₄	—	53	1	no	—
1288	C₂×D₄	—	53	1	no	—
1289	C₂×D₄	—	53	1	no	—
1290	C₂×D₄	—	53	1	no	—
1291	C₂×D₄	—	53	1	no	—
1292	C₂×D₄	—	53	1	no	—
1293	C₂×D₄	—	53	1	no	—
1294	C₂×D₄	—	53	1	no	—
1295	C₂×D₄	—	53	1	no	—
1296	C₂×D₄	—	106	4	no	—
1297	C₂×D₄	—	106	4	no	—
1298	C₂×D₄	—	106	4	no	—
1299	C₂×D₄	—	212	2	no	—
1300	C₂×D₄	—	212	2	no	—
1301	C₂×D₄	—	212	2	no	—
1302	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1303	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1304	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1305	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1306	C₂²×C₄	—	2	2	no	—
1307	C₂²×C₄	—	2	2	no	—
1308	C₂²×C₄	—	2	2	no	—
1309	C₂²×C₄	—	2	2	no	—
1310	C₂²×C₄	—	53	1	no	—
1311	C₂²×C₄	—	53	1	no	—
1312	C₂²×C₄	—	53	1	no	—
1313	C₂²×C₄	—	53	4	no	—
1314	C₂²×C₄	—	53	4	no	—
1315	C₂²×C₄	—	53	1	no	—
1316	C₂²×C₄	—	53	1	no	—
1317	C₂²×C₄	—	53	1	no	—
1318	C₂²×C₄	—	53	1	no	—
1319	C₂²×C₄	—	53	1	no	—
1320	C₂²×C₄	—	53	1	no	—
1321	C₂²×C₄	—	53	1	no	—
1322	C₂²×C₄	—	53	1	no	—
1323	C₂²×C₄	—	53	1	no	—
1324	C₂²×C₄	—	53	1	no	—
1325	C₂²×C₄	—	53	1	no	—
1326	C₂²×C₄	—	53	1	no	—
1327	C₂²×C₄	—	53	1	no	—
1328	C₂²×C₄	—	53	1	no	—
1329	C₂²×C₄	—	53	1	no	—
1330	C₂²×C₄	—	53	1	no	—
1331	C₂²×C₄	—	53	1	no	—
1332	C₂²×C₄	—	53	1	no	—
1333	C₂²×C₄	—	53	1	no	—
1334	C₂²×C₄	—	53	1	no	—
1335	C₂²×C₄	—	53	1	no	—
1336	C₂²×C₄	—	53	1	no	—
1337	C₂²×C₄	—	53	1	no	—
1338	C₂²×C₄	—	53	1	no	—
1339	C₂²×C₄	—	53	1	no	—
1340	C₂²×C₄	—	53	1	no	—
1341	C₂²×C₄	—	106	2	no	—
1342	C₂²×C₄	—	106	2	no	—
1343	C₂²×C₄	—	106	2	no	—
1344	C₂²×C₄	—	106	2	no	—
1345	C₂²×C₄	—	106	4	no	—
1346	C₂²×C₄	—	106	4	no	—
1347	C₂²×C₄	—	106	4	no	—
1348	C₂²×C₄	—	106	4	no	—
1349	C₂²×C₄	—	106	4	no	—
1350	C₂²×C₄	—	106	2	no	—
1351	C₂²×C₄	—	106	2	no	—
1352	C₂²×C₄	—	106	2	no	—
1353	C₂²×C₄	—	106	2	no	—
1354	C₂²×C₄	—	106	4	no	—
1355	C₂²×C₄	—	106	4	no	—
1356	C₂²×C₄	—	106	2	no	—
1357	C₂²×C₄	—	106	2	no	—
1358	C₂²×C₄	—	106	2	no	—
1359	C₂²×C₄	—	106	2	no	—
1360	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1361	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1362	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1363	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1364	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1365	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1366	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1367	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1368	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1369	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1370	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1371	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1372	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1373	M₁₆	—	2	2	no	—
1374	M₁₆	—	2	2	no	—
1375	M₁₆	—	2	2	no	—
1376	M₁₆	—	2	4	no	—
1377	M₁₆	—	2	4	no	—
1378	M₁₆	—	53	4	no	—
1379	M₁₆	—	53	8	no	—
1380	M₁₆	—	106	4	no	—
1381	M₁₆	—	106	4	no	—
1382	M₁₆	—	106	4	no	—
1383	M₁₆	—	106	4	no	—
1384	M₁₆	—	106	4	no	—
1385	M₁₆	—	106	4	no	—
1386	M₁₆	—	106	4	no	—
1387	M₁₆	—	106	2	no	—
1388	M₁₆	—	106	2	no	—
1389	M₁₆	—	106	2	no	—
1390	M₁₆	—	106	4	no	—
1391	M₁₆	—	106	4	no	—
1392	M₁₆	D₄×D₅₃	1	4	yes	—
1393	C₂×C₈	—	2	4	no	—
1394	C₂×C₈	—	2	4	no	—
1395	C₂×C₈	—	53	2	no	—
1396	C₂×C₈	—	53	8	no	—
1397	C₂×C₈	—	53	2	no	—
1398	C₂×C₈	—	53	2	no	—
1399	C₂×C₈	—	53	2	no	—
1400	C₂×C₈	—	106	4	no	—
1401	C₂×C₈	—	106	4	no	—
1402	C₂×C₈	—	106	4	no	—
1403	C₂×C₈	—	106	4	no	—
1404	C₂×C₈	—	106	4	no	—
1405	C₂×C₈	—	106	4	no	—
1406	C₂×C₈	—	106	4	no	—
1407	C₂×C₈	—	106	4	no	—
1408	C₂×C₈	—	106	4	no	—
1409	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1410	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1411	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1412	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1413	C₄⋊C₄	—	53	1	no	—
1414	C₄⋊C₄	—	53	1	no	—
1415	C₄⋊C₄	—	53	1	no	—
1416	C₄⋊C₄	—	53	1	no	—
1417	C₄⋊C₄	—	53	1	no	—
1418	C₄⋊C₄	—	53	1	no	—
1419	C₄⋊C₄	—	53	1	no	—
1420	C₄⋊C₄	—	53	1	no	—
1421	C₄⋊C₄	—	53	1	no	—
1422	C₄⋊C₄	—	53	1	no	—
1423	C₄⋊C₄	—	53	1	no	—
1424	C₄⋊C₄	—	53	1	no	—
1425	C₄⋊C₄	—	53	1	no	—
1426	C₄⋊C₄	—	53	1	no	—
1427	C₄⋊C₄	—	53	1	no	—
1428	C₄⋊C₄	—	53	1	no	—
1429	C₄⋊C₄	—	53	1	no	—
1430	C₄⋊C₄	—	53	1	no	—
1431	C₄⋊C₄	—	53	1	no	—
1432	C₄⋊C₄	—	53	1	no	—
1433	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1434	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1435	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1436	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1437	C₂²⋊C₄	—	53	1	no	—
1438	C₂²⋊C₄	—	53	1	no	—
1439	C₂²⋊C₄	—	53	1	no	—
1440	C₂²⋊C₄	—	53	1	no	—
1441	C₂²⋊C₄	—	53	1	no	—
1442	C₂²⋊C₄	—	53	1	no	—
1443	C₂²⋊C₄	—	53	1	no	—
1444	C₂²⋊C₄	—	53	1	no	—
1445	C₂²⋊C₄	—	53	1	no	—
1446	C₂²⋊C₄	—	53	1	no	—
1447	C₂²⋊C₄	—	53	1	no	—
1448	C₂²⋊C₄	—	53	1	no	—
1449	C₂²⋊C₄	—	53	1	no	—
1450	C₂²⋊C₄	—	53	1	no	—
1451	C₂²⋊C₄	—	53	1	no	—
1452	C₂²⋊C₄	—	53	1	no	—
1453	C₂²⋊C₄	—	53	1	no	—
1454	C₂²⋊C₄	—	53	1	no	—
1455	C₂²⋊C₄	—	53	1	no	—
1456	C₂²⋊C₄	—	53	1	no	—
1457	C₂²⋊C₄	—	53	1	no	—
1458	C₂²⋊C₄	—	53	1	no	—
1459	C₂²⋊C₄	—	53	1	no	—
1460	C₂²⋊C₄	—	53	1	no	—
1461	C₂²⋊C₄	—	53	1	no	—
1462	C₂²⋊C₄	—	53	1	no	—
1463	C₂²⋊C₄	—	53	1	no	—
1464	C₂²⋊C₄	—	53	1	no	—
1465	C₂²⋊C₄	—	53	1	no	—
1466	C₂²⋊C₄	—	53	1	no	—
1467	C₂²⋊C₄	—	53	1	no	—
1468	C₂²⋊C₄	—	53	1	no	—
1469	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1470	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1471	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1472	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1473	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1474	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1475	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1476	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1477	C₄²	—	53	1	no	—
1478	C₄²	—	53	1	no	—
1479	C₄²	—	53	1	no	—
1480	C₄²	—	53	1	no	—
1481	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1482	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1483	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1484	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1485	C₂³	—	2	2	no	—
1486	C₂³	—	2	2	no	—
1487	C₂³	—	2	2	no	—
1488	C₂³	—	4	1	no	—
1489	C₂³	—	4	1	no	—
1490	C₂³	—	4	1	no	—
1491	C₂³	—	53	1	no	—
1492	C₂³	—	53	1	no	—
1493	C₂³	—	53	1	no	—
1494	C₂³	—	53	4	no	—
1495	C₂³	—	53	1	no	—
1496	C₂³	—	53	1	no	—
1497	C₂³	—	53	1	no	—
1498	C₂³	—	106	2	no	—
1499	C₂³	—	106	2	no	—
1500	C₂³	—	106	2	no	—
1501	C₂³	—	106	2	no	—
1502	C₂³	—	106	2	no	—
1503	C₂³	—	106	2	no	—
1504	C₂³	—	106	2	no	—
1505	C₂³	—	106	2	no	—
1506	C₂³	—	106	2	no	—
1507	C₂³	—	106	2	no	—
1508	C₂³	—	106	2	no	—
1509	C₂³	—	212	1	no	—
1510	C₂³	—	212	1	no	—
1511	C₂³	—	212	1	no	—
1512	C₂³	—	212	1	no	—
1513	C₂³	—	212	1	no	—
1514	C₂³	—	212	1	no	—
1515	C₂³	—	212	1	no	—
1516	C₂³	—	212	1	no	—
1517	C₂³	—	212	1	no	—
1518	C₂³	—	212	16	no	—
1519	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1520	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1521	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1522	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1523	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1524	Q₈	—	106	2	no	—
1525	Q₈	—	106	2	no	—
1526	Q₈	—	106	2	no	—
1527	Q₈	—	106	2	no	—
1528	D₄	—	2	2	no	—
1529	D₄	—	2	2	no	—
1530	D₄	—	4	1	no	—
1531	D₄	—	4	1	no	—
1532	D₄	—	106	2	no	—
1533	D₄	—	106	2	no	—
1534	D₄	—	106	2	no	—
1535	D₄	—	106	2	no	—
1536	D₄	—	106	2	no	—
1537	D₄	—	106	2	no	—
1538	D₄	—	106	2	no	—
1539	D₄	—	106	2	no	—
1540	D₄	—	106	2	no	—
1541	D₄	—	106	2	no	—
1542	D₄	—	106	2	no	—
1543	D₄	—	106	2	no	—
1544	D₄	—	106	2	no	—
1545	D₄	—	106	2	no	—
1546	D₄	—	106	2	no	—
1547	D₄	—	106	2	no	—
1548	D₄	—	106	2	no	—
1549	D₄	—	106	2	no	—
1550	D₄	—	212	1	no	—
1551	D₄	—	212	1	no	—
1552	D₄	—	212	1	no	—
1553	D₄	—	212	1	no	—
1554	D₄	—	212	1	no	—
1555	D₄	—	212	1	no	—
1556	C₂×C₄	—	2	2	no	—
1557	C₂×C₄	—	2	2	no	—
1558	C₂×C₄	—	2	2	no	—
1559	C₂×C₄	—	2	2	no	—
1560	C₂×C₄	—	2	2	no	—
1561	C₂×C₄	—	2	2	no	—
1562	C₂×C₄	—	2	1	no	—
1563	C₂×C₄	—	2	1	no	—
1564	C₂×C₄	—	2	1	no	—
1565	C₂×C₄	—	2	1	no	—
1566	C₂×C₄	—	2	1	no	—
1567	C₂×C₄	—	2	1	no	—
1568	C₂×C₄	—	2	1	no	—
1569	C₂×C₄	—	2	1	no	—
1570	C₂×C₄	—	4	1	no	—
1571	C₂×C₄	—	4	1	no	—
1572	C₂×C₄	—	53	4	no	—
1573	C₂×C₄	—	53	1	no	—
1574	C₂×C₄	—	53	1	no	—
1575	C₂×C₄	—	53	4	no	—
1576	C₂×C₄	—	53	4	no	—
1577	C₂×C₄	—	53	2	no	—
1578	C₂×C₄	—	53	2	no	—
1579	C₂×C₄	—	53	2	no	—
1580	C₂×C₄	—	53	2	no	—
1581	C₂×C₄	—	53	1	no	—
1582	C₂×C₄	—	53	1	no	—
1583	C₂×C₄	—	53	1	no	—
1584	C₂×C₄	—	53	1	no	—
1585	C₂×C₄	—	53	1	no	—
1586	C₂×C₄	—	53	1	no	—
1587	C₂×C₄	—	53	1	no	—
1588	C₂×C₄	—	53	1	no	—
1589	C₂×C₄	—	106	2	no	—
1590	C₂×C₄	—	106	2	no	—
1591	C₂×C₄	—	106	2	no	—
1592	C₂×C₄	—	106	2	no	—
1593	C₂×C₄	—	106	2	no	—
1594	C₂×C₄	—	106	2	no	—
1595	C₂×C₄	—	106	2	no	—
1596	C₂×C₄	—	106	2	no	—
1597	C₂×C₄	—	106	2	no	—
1598	C₂×C₄	—	106	2	no	—
1599	C₂×C₄	—	106	2	no	—
1600	C₂×C₄	—	106	2	no	—
1601	C₂×C₄	—	106	2	no	—
1602	C₂×C₄	—	106	2	no	—
1603	C₂×C₄	—	106	2	no	—
1604	C₂×C₄	—	106	2	no	—
1605	C₂×C₄	—	106	2	no	—
1606	C₂×C₄	—	106	2	no	—
1607	C₂×C₄	—	106	1	no	—
1608	C₂×C₄	—	106	1	no	—
1609	C₂×C₄	—	106	1	no	—
1610	C₂×C₄	—	106	1	no	—
1611	C₂×C₄	—	106	1	no	—
1612	C₂×C₄	—	106	1	no	—
1613	C₂×C₄	—	106	1	no	—
1614	C₂×C₄	—	106	1	no	—
1615	C₂×C₄	—	212	1	no	—
1616	C₂×C₄	—	212	1	no	—
1617	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1618	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1619	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1620	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1621	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1622	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1623	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1624	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1625	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1626	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1627	C₂×C₄	#41×D₅₃	1	2	yes	—
1628	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1629	C₈	—	2	2	no	—
1630	C₈	—	2	2	no	—
1631	C₈	—	2	2	no	—
1632	C₈	—	53	4	no	—
1633	C₈	—	106	2	no	—
1634	C₈	—	106	2	no	—
1635	C₈	—	106	2	no	—
1636	C₈	C₂×D₄×D₅₃	1	4	yes	—
1637	C₂²	—	2	1	no	—
1638	C₂²	—	2	1	no	—
1639	C₂²	—	2	1	no	—
1640	C₂²	—	2	1	no	—
1641	C₂²	—	2	1	no	—
1642	C₂²	—	2	1	no	—
1643	C₂²	—	2	1	no	—
1644	C₂²	—	2	1	no	—
1645	C₂²	—	2	1	no	—
1646	C₂²	—	2	1	no	—
1647	C₂²	—	2	1	no	—
1648	C₂²	—	2	1	no	—
1649	C₂²	—	2	1	no	—
1650	C₂²	—	4	4	no	—
1651	C₂²	—	8	2	no	—
1652	C₂²	—	53	2	no	—
1653	C₂²	—	53	2	no	—
1654	C₂²	—	53	2	no	—
1655	C₂²	—	106	8	no	—
1656	C₂²	—	106	1	no	—
1657	C₂²	—	106	1	no	—
1658	C₂²	—	106	1	no	—
1659	C₂²	—	106	1	no	—
1660	C₂²	—	106	1	no	—
1661	C₂²	—	106	1	no	—
1662	C₂²	—	106	1	no	—
1663	C₂²	—	106	1	no	—
1664	C₂²	—	106	1	no	—
1665	C₂²	—	106	1	no	—
1666	C₂²	—	106	1	no	—
1667	C₂²	—	106	1	no	—
1668	C₂²	—	106	1	no	—
1669	C₂²	—	106	1	no	—
1670	C₂²	—	106	1	no	—
1671	C₂²	—	424	2	no	—
1672	C₂²	—	212	4	no	—
1673	C₂²	—	212	4	no	—
1674	C₂²	—	212	4	no	—
1675	C₂²	—	212	4	no	—
1676	C₂²	—	212	4	no	—
1677	C₂²	C₄×D₄×D₅₃	1	2	yes	—
1678	C₂²	#16811389	1	2	yes	complemented
1679	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1680	C₄	—	2	1	no	—
1681	C₄	—	2	1	no	—
1682	C₄	—	2	1	no	—
1683	C₄	—	2	1	no	—
1684	C₄	—	2	1	no	—
1685	C₄	—	2	1	no	—
1686	C₄	—	2	1	no	—
1687	C₄	—	2	1	no	—
1688	C₄	—	53	2	no	—
1689	C₄	—	53	2	no	—
1690	C₄	—	106	1	no	—
1691	C₄	—	106	1	no	—
1692	C₄	—	106	1	no	—
1693	C₄	—	106	1	no	—
1694	C₄	—	106	1	no	—
1695	C₄	—	106	1	no	—
1696	C₄	—	106	1	no	—
1697	C₄	—	106	1	no	—
1698	C₄	C₄×D₄×D₅₃	1	2	yes	—
1699	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
1700	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1701	C₂	—	2	2	no	—
1702	C₂	—	2	2	no	—
1703	C₂	—	4	1	no	—
1704	C₂	—	4	1	no	—
1705	C₂	—	4	1	no	—
1706	C₂	—	106	2	no	—
1707	C₂	—	106	2	no	—
1708	C₂	—	106	2	no	—
1709	C₂	—	212	1	no	—
1710	C₂	—	212	1	no	—
1711	C₂	—	212	1	no	—
1712	C₂	C₂×C₄×D₄×D₅₃	1	1	yes	characteristic
1713	C₂	#568×D₅₃	1	1	yes	characteristic
1714	C₂	C₂×#16811389	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	D₄×M₁₆×C₅₃	C₂
prime radical	C₂×#16811132	C₂
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	D₄×M₁₆	D₅₃
hypocenter	C₅₃	#60141
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#16811389	C₂	semidirect
2. C₂²×M₁₆×D₅₃	C₂	semidirect
4. M₁₆×D₂₁₂	C₂	semidirect
5. D₄×#11719917	C₂	semidirect
6. #20283450	C₂	semidirect
7. M₁₆×C₂²⋊D₅₃	C₂	semidirect
8. M₁₆×C₂²⋊D₅₃	C₂	semidirect
9. #20283447	C₂	semidirect
10. #20283447	C₂	semidirect
11. #20283444	C₂	semidirect
12. #20283441	C₂	semidirect
13. #20283438	C₂	semidirect
14. #20283435	C₂	semidirect
15. #20283415	C₂	semidirect
16. #20283413	C₂	semidirect
17. #20283406	C₂	semidirect
18. #20283404	C₂	semidirect
19. #20283277	C₂	semidirect
20. #20283158	C₂	semidirect
21. #407×D₅₃	C₂	semidirect
22. #20283132	C₂	semidirect
23. D₄×M₁₆×C₅₃	C₂	semidirect
27. C₂×#13133225	C₂²	semidirect
28. C₂×#13133225	C₂²	semidirect
29. C₂×#13133223	C₂²	semidirect
30. C₂×#13133223	C₂²	semidirect
32. C₂²×#11719917	C₂²	semidirect
33. C₂²×#11719912	C₂²	semidirect
41. C₂×M₁₆×D₅₃	C₂²	semidirect
42. C₂×M₁₆×D₅₃	C₂²	semidirect
43. C₂×M₁₆×D₅₃	C₂²	semidirect
44. C₂×M₁₆×D₅₃	C₂²	semidirect
45. C₂²×C₈×D₅₃	C₂²	semidirect
74. #16810702	C₂²	semidirect
75. #16810701	C₂²	semidirect
76. #16810700	C₂²	semidirect
77. #16810699	C₂²	semidirect
78. #16810699	C₂²	semidirect
79. #16810698	C₂²	semidirect
80. #16810698	C₂²	semidirect
81. #16810697	C₂²	semidirect
82. #16810697	C₂²	semidirect
83. #16810696	C₂²	semidirect
84. #16810696	C₂²	semidirect
85. #16810695	C₂²	semidirect
86. #16810695	C₂²	semidirect
87. #16810694	C₂²	semidirect
88. #16810694	C₂²	semidirect
89. #16810693	C₂²	semidirect
90. #16810693	C₂²	semidirect
91. #16810692	C₂²	semidirect
92. #16810692	C₂²	semidirect
93. #16810691	C₂²	semidirect
94. #16810691	C₂²	semidirect
95. C₈×D₂₁₂	C₂²	semidirect
96. D₄×#88322	C₂²	semidirect
97. #16810688	C₂²	semidirect
98. C₈×C₂²⋊D₅₃	C₂²	semidirect
99. C₈×C₂²⋊D₅₃	C₂²	semidirect
100. #16810686	C₂²	semidirect
101. #16810686	C₂²	semidirect
102. #16810648	C₂²	semidirect
103. #16810648	C₂²	semidirect
104. #16810648	C₂²	semidirect
105. #16810648	C₂²	semidirect
106. #16810647	C₂²	semidirect
107. #16810646	C₂²	semidirect
108. #16810646	C₂²	semidirect
109. #16810588	C₂²	semidirect
110. #16810588	C₂²	semidirect
111. #16810588	C₂²	semidirect
112. #16810588	C₂²	semidirect
114. #16810587	C₂²	semidirect
117. #16810586	C₂²	semidirect
118. #16810586	C₂²	semidirect
119. #16810585	C₂²	semidirect
120. #16810585	C₂²	semidirect
121. C₂²⋊C₈×D₅₃	C₂²	semidirect
122. C₂²⋊C₈×D₅₃	C₂²	semidirect
123. #16810580	C₂²	semidirect
124. #16810580	C₂²	semidirect
125. #16810577	C₂²	semidirect
126. #16810577	C₂²	semidirect
127. C₄×#11719917	C₂²	semidirect
128. M₁₆×Dic₅₃	C₂²	semidirect
129. M₁₆×Dic₅₃	C₂²	semidirect
131. C₂²×M₁₆×C₅₃	C₂²	semidirect
133. C₅₃×#436	C₂²	semidirect
134. C₅₃×#435	C₂²	semidirect
135. C₅₃×#435	C₂²	semidirect
136. C₈×D₄×C₅₃	C₂²	semidirect
137. C₅₃×#423	C₂²	semidirect
139. C₅₃×#407	C₂²	semidirect
140. C₄×M₁₆×C₅₃	C₂²	semidirect
186. C₂×#11719917	C₂³	semidirect
194. C₂×#11719912	C₂³	semidirect
195. C₂×#11719912	C₂³	semidirect
205. M₁₆×D₅₃	D₄	semidirect
207. C₂²×#88322	C₂³	semidirect
215. C₂×C₈×D₅₃	C₂³	semidirect
216. C₂×C₈×D₅₃	C₂³	semidirect
327. C₄⋊#88322	C₂³	semidirect
328. C₄⋊#88322	C₂³	semidirect
329. #13133146	C₂³	semidirect
330. #13133146	C₂³	semidirect
331. #13133146	C₂³	semidirect
332. #13133146	C₂³	semidirect
335. C₂²⋊#88322	C₂³	semidirect
336. C₂²⋊#88322	C₂³	semidirect
341. #13133129	C₂³	semidirect
342. #13133129	C₂³	semidirect
343. #13133129	C₂³	semidirect
344. #13133129	C₂³	semidirect
345. #13133128	C₂³	semidirect
346. #13133127	C₂³	semidirect
347. #13133127	C₂³	semidirect
348. C₄×#88322	C₂³	semidirect
349. C₈×Dic₅₃	C₂³	semidirect
350. C₈×Dic₅₃	C₂³	semidirect
361. C₂×M₁₆×C₅₃	C₂³	semidirect
363. C₂²×C₈×C₅₃	C₂³	semidirect
376. C₄⋊C₈×C₅₃	C₂³	semidirect
377. C₄⋊C₈×C₅₃	C₂³	semidirect
380. C₂²⋊C₈×C₅₃	C₂³	semidirect
381. C₂²⋊C₈×C₅₃	C₂³	semidirect
382. #97×C₅₃	C₂³	semidirect
383. C₄×C₈×C₅₃	C₂³	semidirect
618. #11719912	C₂×D₄	semidirect
626. C₈×D₅₃	C₂×D₄	semidirect
796. C₂²×C₅₃	#568	semidirect
822. C₂×D₅₃	#568	semidirect
854. D₄×M₁₆	D₅₃	semidirect
903. C₂²×M₁₆	C₂×D₅₃	semidirect
941. #436	C₂×D₅₃	semidirect
956. #435	C₂×D₅₃	semidirect
957. #435	C₂×D₅₃	semidirect
965. C₈×D₄	C₂×D₅₃	semidirect
973. #423	C₂×D₅₃	semidirect
987. #407	C₂×D₅₃	semidirect
997. C₄×M₁₆	C₂×D₅₃	semidirect
998. C₅₃	#60141	semidirect
1074. C₂×M₁₆	C₂²×D₅₃	semidirect
1087. C₂²×C₈	C₂²×D₅₃	semidirect
1216. C₄⋊C₈	C₂²×D₅₃	semidirect
1217. C₄⋊C₈	C₂²×D₅₃	semidirect
1232. C₂²⋊C₈	C₂²×D₅₃	semidirect
1233. C₂²⋊C₈	C₂²×D₅₃	semidirect
1237. #97	C₂²×D₅₃	semidirect
1241. C₄×C₈	C₂²×D₅₃	semidirect
1678. C₂²	#16811389	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811389	2
C₂²×M₁₆×D₅₃	2
C₂×#16811132	2
M₁₆×D₂₁₂	2
D₄×#11719917	2
#20283450	2
M₁₆×C₂²⋊D₅₃	2
#20283447	2
#20283444	2
#20283441	2
#20283438	2
#20283435	2
#20283415	2
#20283413	2
#20283406	2
#20283404	2
#20283277	2
#20283158	2
#407×D₅₃	2
#20283132	2
D₄×M₁₆×C₅₃	2
#60141	53