Subgroups — C₄×#16811306 #27543994

Order 13568.

2376 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811306	C₂	1	1	yes	maximal, characteristic
2	#20277835	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277829	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277820	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277818	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277812	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277743	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277721	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277709	C₂	1	1	yes	maximal, characteristic
10	#20277707	C₂	1	1	yes	maximal, characteristic
11	#20277681	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277638	C₂	1	1	yes	maximal, characteristic
13	#20277601	C₂	1	1	yes	maximal, characteristic, complemented
14	#20277585	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277575	C₂	1	1	yes	maximal, characteristic, complemented
16	#20277569	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#13133209	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#13133207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13133207	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13133212	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13133211	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13133195	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#13133194	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#13133201	C₂	1	1	yes	maximal, characteristic
25	C₄×#13133200	C₂	1	1	yes	maximal, characteristic
26	C₄²×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×#13133177	C₂	1	1	yes	maximal, characteristic
28	C₄×#13133174	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#13133173	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₄×#11719919	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#117×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	#16811306	C₄	1	16	yes	direct product factor
33	C₂×#13133212	C₂²	1	1	yes	characteristic
34	C₂×#13133211	C₂²	1	1	yes	characteristic
35	C₂×#13133209	C₂²	1	1	yes	characteristic
36	C₂×#13133207	C₂²	1	1	yes	characteristic
37	C₂×#13133207	C₂²	1	1	yes	characteristic
38	C₂×#13133201	C₂²	1	1	yes	characteristic
39	C₂×#13133200	C₂²	1	1	yes	characteristic
40	C₂×#13133195	C₂²	1	1	yes	characteristic
41	C₂×#13133194	C₂²	1	1	yes	characteristic
42	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
43	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
44	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
46	C₂×#13133177	C₂²	1	1	yes	characteristic
47	C₂×#13133177	C₂²	1	1	yes	characteristic
48	C₂×#13133174	C₂²	1	1	yes	characteristic
49	C₂×#13133174	C₂²	1	1	yes	characteristic
50	C₂×#13133173	C₂²	1	1	yes	characteristic
51	C₂×#13133173	C₂²	1	1	yes	characteristic
52	C₂²×#11719919	C₂²	1	1	yes	characteristic
53	C₂²×#11719919	C₂²	1	1	yes	characteristic
54	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
55	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
57	#16810527	C₂²	1	1	yes	characteristic
58	#16810527	C₂²	1	1	yes	characteristic
59	#16810521	C₂²	1	1	yes	characteristic
60	#16810521	C₂²	1	1	yes	characteristic
61	#16810520	C₂²	1	1	yes	characteristic
62	#16810520	C₂²	1	1	yes	characteristic
63	#16810520	C₂²	1	1	yes	characteristic
64	#16810518	C₂²	1	1	yes	characteristic
65	#16810518	C₂²	1	1	yes	characteristic
66	#16810518	C₂²	1	1	yes	characteristic
67	#16810515	C₂²	1	1	yes	characteristic
68	#16810515	C₂²	1	1	yes	characteristic
69	#16810515	C₂²	1	1	yes	characteristic
70	#16810514	C₂²	1	1	yes	characteristic
71	#16810514	C₂²	1	1	yes	characteristic
72	#16810514	C₂²	1	1	yes	characteristic
73	#16810514	C₂²	1	1	yes	characteristic
74	#16810514	C₂²	1	1	yes	characteristic
75	#16810513	C₂²	1	1	yes	characteristic
76	#16810512	C₂²	1	1	yes	characteristic
77	#16810510	C₂²	1	1	yes	characteristic
78	#16810509	C₂²	1	1	yes	characteristic
79	#16810509	C₂²	1	1	yes	characteristic
80	#16810509	C₂²	1	1	yes	characteristic
81	#16810509	C₂²	1	1	yes	characteristic
82	#16810508	C₂²	1	1	yes	characteristic
83	#16810508	C₂²	1	1	yes	characteristic
84	#16810508	C₂²	1	1	yes	characteristic
85	#16810508	C₂²	1	1	yes	characteristic
86	#16810507	C₂²	1	1	yes	characteristic
87	#16810507	C₂²	1	1	yes	characteristic
88	#16810507	C₂²	1	1	yes	characteristic
89	#16810507	C₂²	1	1	yes	characteristic
90	#16810507	C₂²	1	1	yes	characteristic
91	#16810507	C₂²	1	1	yes	characteristic
92	#16810507	C₂²	1	1	yes	characteristic
93	#16810507	C₂²	1	1	yes	characteristic
94	#16810507	C₂²	1	1	yes	characteristic
95	#16810506	C₂²	1	1	yes	characteristic
96	#16810506	C₂²	1	1	yes	characteristic
97	#16810505	C₂²	1	1	yes	characteristic
98	#16810505	C₂²	1	1	yes	characteristic
99	#16810505	C₂²	1	1	yes	characteristic
100	#16810504	C₂²	1	1	yes	characteristic
101	#16810504	C₂²	1	1	yes	characteristic
102	#16810504	C₂²	1	1	yes	characteristic
103	#16810502	C₂²	1	1	yes	characteristic
104	#16810500	C₂²	1	1	yes	characteristic
105	#16810498	C₂²	1	1	yes	characteristic
106	#16810498	C₂²	1	1	yes	characteristic
107	#16810497	C₂²	1	1	yes	characteristic
108	#16810496	C₂²	1	1	yes	characteristic
109	#16810495	C₂²	1	1	yes	characteristic
110	#16810494	C₂²	1	1	yes	characteristic
111	#16810491	C₂²	1	1	yes	characteristic
112	#16810490	C₂²	1	1	yes	characteristic
113	#16810489	C₂²	1	1	yes	characteristic
114	#16810487	C₂²	1	1	yes	characteristic
115	#16810487	C₂²	1	1	yes	characteristic
116	#16810486	C₂²	1	1	yes	characteristic
117	#16810484	C₂²	1	1	yes	characteristic
118	#16810482	C₂²	1	1	yes	characteristic
119	#16810481	C₂²	1	1	yes	characteristic
120	C₄×#11719919	C₂²	1	1	yes	characteristic
121	C₄×#11719919	C₂²	1	1	yes	characteristic
122	C₄×#11719919	C₂²	1	1	yes	characteristic
123	C₄×#11719919	C₂²	1	1	yes	characteristic
124	C₄×#11719919	C₂²	1	1	yes	characteristic
125	C₄×#11719919	C₂²	1	1	yes	characteristic
126	C₄×#11719919	C₂²	1	1	yes	characteristic
127	C₄×#11719919	C₂²	1	1	yes	characteristic
128	C₄×#11719919	C₂²	1	1	yes	characteristic
129	C₄×#11719919	C₂²	1	1	yes	characteristic
130	C₄×#11719919	C₂²	1	1	yes	characteristic
131	C₄×#11719919	C₂²	1	1	yes	characteristic
132	C₄×#11719919	C₂²	1	1	yes	characteristic
133	C₄×#11719919	C₂²	1	1	yes	characteristic
134	C₄×#11719919	C₂²	1	1	yes	characteristic
135	C₄×#11719919	C₂²	1	1	yes	characteristic
136	C₄×#11719919	C₂²	1	1	yes	characteristic
137	C₄×#11719919	C₂²	1	1	yes	characteristic
138	C₄×#11719919	C₂²	1	1	yes	characteristic
139	C₄×#11719919	C₂²	1	1	yes	characteristic
140	C₄×#11719919	C₂²	1	1	yes	characteristic
141	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
142	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
143	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
144	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
145	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
146	#16810474	C₂²	1	1	yes	characteristic
147	#16810474	C₂²	1	1	yes	characteristic
148	#16810474	C₂²	1	1	yes	characteristic
149	#16810474	C₂²	1	1	yes	characteristic
150	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
151	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
152	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
153	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
154	C₄×#11719921	C₂²	1	1	yes	characteristic
155	C₄×#11719921	C₂²	1	1	yes	characteristic
156	C₄×#11719921	C₂²	1	1	yes	characteristic
157	C₄×#11719921	C₂²	1	1	yes	characteristic
158	C₄×#11719921	C₂²	1	1	yes	characteristic
159	C₄×#11719921	C₂²	1	1	yes	characteristic
160	C₄×#11719921	C₂²	1	1	yes	characteristic
161	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
162	#16810470	C₂²	1	1	yes	characteristic
163	#16810470	C₂²	1	1	yes	characteristic
164	#16810469	C₂²	1	1	yes	characteristic
165	#16810469	C₂²	1	1	yes	characteristic
166	#16810468	C₂²	1	1	yes	characteristic
167	#16810468	C₂²	1	1	yes	characteristic
168	C₂×#13133124	C₂²	1	1	yes	characteristic
169	C₂×#13133124	C₂²	1	1	yes	characteristic
170	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
171	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
172	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
173	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
174	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
175	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
176	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
178	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
179	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₅₃×#376	C₂²	1	1	yes	characteristic
185	C₅₃×#376	C₂²	1	1	yes	characteristic
186	C₄³×C₅₃	C₂²	1	1	yes	characteristic
187	C₄³×C₅₃	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
190	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
191	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
192	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
193	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
197	#13133212	C₂×C₄	1	8	yes	complemented
198	#13133211	C₂×C₄	1	8	yes	complemented
199	#13133209	C₂×C₄	1	8	yes	complemented
200	#13133207	C₂×C₄	1	8	yes	complemented
201	#13133207	C₂×C₄	1	8	yes	complemented
202	#13133201	C₂×C₄	1	8	yes	—
203	#13133200	C₂×C₄	1	8	yes	—
204	#13133195	C₂×C₄	1	8	yes	complemented
205	#13133194	C₂×C₄	1	8	yes	complemented
206	C₄×Dic₁₀₆	—	2	4	no	—
207	C₄×Dic₁₀₆	—	2	4	no	—
208	C₄×Dic₁₀₆	C₂×C₄	1	8	yes	complemented
209	C₄×C₂²⋊D₅₃	—	2	4	no	—
210	#13133177	—	2	4	no	—
211	#13133177	C₂×C₄	1	8	yes	—
212	#13133174	—	2	4	no	—
213	#13133174	C₂×C₄	1	8	yes	complemented
214	#13133173	—	2	4	no	—
215	#13133173	C₂×C₄	1	8	yes	complemented
216	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×#11719919	—	2	4	no	—
224	C₂×#11719919	C₂×C₄	1	8	yes	complemented
225	C₂×#11719919	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	C₂³	1	1	yes	characteristic
243	C₂×#11719919	C₂³	1	1	yes	characteristic
244	C₂×#11719919	C₂³	1	1	yes	characteristic
245	C₂×#11719919	C₂³	1	1	yes	characteristic
246	C₂×#11719919	C₂³	1	1	yes	characteristic
247	C₂×#11719919	C₂³	1	1	yes	characteristic
248	C₂×#11719919	C₂³	1	1	yes	characteristic
249	C₂×#11719919	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×#11719921	C₂³	1	1	yes	characteristic
254	C₂×#11719921	C₂³	1	1	yes	characteristic
255	C₂×#11719921	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	1	yes	characteristic
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	1	yes	characteristic
259	C₂×#11719921	C₂³	1	1	yes	characteristic
260	C₂×#11719921	C₂³	1	1	yes	characteristic
261	C₂×#11719921	C₂³	1	1	yes	characteristic
262	C₂×#11719921	C₂³	1	1	yes	characteristic
263	C₂×#11719921	C₂³	1	1	yes	characteristic
264	C₂×C₄×Dic₅₃	—	2	4	no	—
265	C₂×C₄×Dic₅₃	—	2	4	no	—
266	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
291	C₄²×D₅₃	—	2	4	no	—
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	#13133124	C₂³	1	1	yes	characteristic
327	#13133124	C₂³	1	1	yes	characteristic
328	#13133124	C₂³	1	1	yes	characteristic
329	#13133124	C₂³	1	1	yes	characteristic
330	#13133124	C₂³	1	1	yes	characteristic
331	#13133124	C₂³	1	1	yes	characteristic
332	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
335	#117×C₅₃	—	2	4	no	—
336	#117×C₅₃	C₂×C₄	1	8	yes	complemented
337	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₅₃	—	2	4	no	—
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	#95×C₅₃	C₂³	1	1	yes	characteristic
368	#95×C₅₃	C₂³	1	1	yes	characteristic
369	#95×C₅₃	C₂³	1	1	yes	characteristic
370	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	—	2	2	no	—
373	C₂²×C₄×C₅₃	—	2	2	no	—
374	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	2	2	no	—
376	C₂²×C₄×C₅₃	—	2	2	no	—
377	C₂²×C₄×C₅₃	—	2	2	no	—
378	C₂²×C₄×C₅₃	—	4	1	no	—
379	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
380	C₂²×C₄×C₅₃	#41	1	4	yes	—
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₂²⋊D₅₃	—	2	2	no	—
396	C₂×C₂²⋊D₅₃	—	2	2	no	—
397	C₂×C₂²⋊D₅₃	C₂²×C₄	1	4	yes	—
398	C₂²×Dic₅₃	—	2	2	no	—
399	C₂²×Dic₅₃	—	2	2	no	—
400	C₂²×Dic₅₃	—	2	2	no	—
401	C₂²×Dic₅₃	—	2	2	no	—
402	C₂²×Dic₅₃	—	2	2	no	—
403	C₂²×Dic₅₃	—	2	2	no	—
404	C₂²×Dic₅₃	—	2	2	no	—
405	C₂²×Dic₅₃	—	2	2	no	—
406	C₂²×Dic₅₃	—	4	1	no	—
407	C₂²×Dic₅₃	—	4	1	no	—
408	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	—
409	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	—
410	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₄×D₅₃	—	2	2	no	—
426	C₂×C₄×D₅₃	—	2	2	no	—
427	C₂×C₄×D₅₃	—	2	2	no	—
428	C₂×C₄×D₅₃	—	2	2	no	—
429	C₂×C₄×D₅₃	—	2	2	no	—
430	C₂×C₄×D₅₃	—	2	2	no	—
431	C₂×C₄×D₅₃	—	2	2	no	—
432	C₂×C₄×D₅₃	—	4	1	no	—
433	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
434	C₂×Dic₁₀₆	—	2	2	no	—
435	C₂×Dic₁₀₆	—	2	2	no	—
436	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
440	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
443	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
444	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
445	C₄²×C₅₃	—	2	2	no	—
446	C₄²×C₅₃	—	2	2	no	—
447	C₄²×C₅₃	—	2	2	no	—
448	C₄²×C₅₃	—	2	2	no	—
449	C₄²×C₅₃	—	2	2	no	—
450	C₄²×C₅₃	—	2	2	no	—
451	C₄²×C₅₃	—	2	2	no	—
452	C₄²×C₅₃	—	2	2	no	—
453	C₄²×C₅₃	—	2	2	no	—
454	C₄²×C₅₃	—	2	2	no	—
455	C₄²×C₅₃	—	2	2	no	—
456	C₄²×C₅₃	—	2	2	no	—
457	C₄²×C₅₃	—	4	1	no	—
458	C₄²×C₅₃	—	4	1	no	—
459	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
460	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
461	C₂²⋊Dic₅₃	—	2	2	no	—
462	C₂²⋊Dic₅₃	—	2	2	no	—
463	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
464	#11719921	—	2	2	no	—
465	#11719921	—	2	2	no	—
466	#11719921	—	2	2	no	—
467	#11719921	—	2	2	no	—
468	#11719921	—	4	1	no	—
469	#11719921	—	4	1	no	—
470	#11719921	C₂²×C₄	1	4	yes	—
471	#11719921	C₂²×C₄	1	4	yes	—
472	#11719921	C₂²×C₄	1	4	yes	—
473	#11719921	C₂²×C₄	1	4	yes	—
474	#11719921	C₂²×C₄	1	4	yes	—
475	C₄⋊Dic₅₃	—	2	2	no	—
476	C₄⋊Dic₅₃	—	2	2	no	—
477	C₄⋊Dic₅₃	—	4	1	no	—
478	C₄⋊Dic₅₃	—	4	1	no	—
479	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
480	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
481	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
482	#11719919	—	2	2	no	—
483	#11719919	—	2	2	no	—
484	#11719919	—	2	2	no	—
485	#11719919	—	2	2	no	—
486	#11719919	—	2	2	no	—
487	#11719919	—	2	2	no	—
488	#11719919	—	2	2	no	—
489	#11719919	—	2	2	no	—
490	#11719919	—	2	2	no	—
491	#11719919	—	2	2	no	—
492	#11719919	—	2	2	no	—
493	#11719919	—	4	1	no	—
494	#11719919	—	4	1	no	—
495	#11719919	C₂²×C₄	1	4	yes	—
496	#11719919	C₂²×C₄	1	4	yes	—
497	#11719919	C₂²×C₄	1	4	yes	—
498	#11719919	C₂²×C₄	1	4	yes	—
499	#11719919	C₂²×C₄	1	4	yes	—
500	#11719919	C₂²×C₄	1	4	yes	—
501	#11719919	C₂²×C₄	1	4	yes	—
502	#11719919	C₂²×C₄	1	4	yes	—
503	#11719919	C₂²×C₄	1	4	yes	—
504	#11719919	C₂²×C₄	1	4	yes	—
505	#11719919	C₂²×C₄	1	4	yes	—
506	#11719919	#41	1	4	yes	—
507	C₄×Dic₅₃	—	2	2	no	—
508	C₄×Dic₅₃	—	2	2	no	—
509	C₄×Dic₅₃	—	2	2	no	—
510	C₄×Dic₅₃	—	2	2	no	—
511	C₄×Dic₅₃	—	2	2	no	—
512	C₄×Dic₅₃	—	2	2	no	—
513	C₄×Dic₅₃	—	2	2	no	—
514	C₄×Dic₅₃	—	2	2	no	—
515	C₄×Dic₅₃	—	2	2	no	—
516	C₄×Dic₅₃	—	2	2	no	—
517	C₄×Dic₅₃	—	2	2	no	—
518	C₄×Dic₅₃	—	2	2	no	—
519	C₄×Dic₅₃	—	2	2	no	—
520	C₄×Dic₅₃	—	2	2	no	—
521	C₄×Dic₅₃	—	2	2	no	—
522	C₄×Dic₅₃	—	2	2	no	—
523	C₄×Dic₅₃	—	2	2	no	—
524	C₄×Dic₅₃	—	2	2	no	—
525	C₄×Dic₅₃	—	4	1	no	—
526	C₄×Dic₅₃	—	4	1	no	—
527	C₄×Dic₅₃	—	4	1	no	—
528	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
529	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
530	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
531	C₄×Dic₅₃	#41	1	4	yes	—
532	C₂³×C₅₃	—	2	1	no	—
533	C₂³×C₅₃	—	2	1	no	—
534	C₂³×C₅₃	—	2	1	no	—
535	C₂³×C₅₃	—	2	1	no	—
536	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
537	C₂³×C₅₃	C₂×#41	1	2	yes	—
538	C₂³×C₅₃	C₂×#41	1	2	yes	—
539	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
540	C₂²×D₅₃	—	2	1	no	—
541	C₂²×D₅₃	—	2	1	no	—
542	C₂²×D₅₃	—	2	1	no	—
543	C₂²×D₅₃	—	2	1	no	—
544	C₂²×D₅₃	—	2	1	no	—
545	C₂²×D₅₃	—	2	1	no	—
546	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
547	C₂×C₄×C₅₃	—	2	8	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	8	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	4	4	no	—
579	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
580	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
581	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
583	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
584	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
585	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
586	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
587	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
588	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
589	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
590	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
591	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
592	C₂²⋊D₅₃	—	2	8	no	—
593	C₂×Dic₅₃	—	2	8	no	—
594	C₂×Dic₅₃	—	2	1	no	—
595	C₂×Dic₅₃	—	2	1	no	—
596	C₂×Dic₅₃	—	2	1	no	—
597	C₂×Dic₅₃	—	2	1	no	—
598	C₂×Dic₅₃	—	2	1	no	—
599	C₂×Dic₅₃	—	2	1	no	—
600	C₂×Dic₅₃	—	2	1	no	—
601	C₂×Dic₅₃	—	2	1	no	—
602	C₂×Dic₅₃	—	2	1	no	—
603	C₂×Dic₅₃	—	2	1	no	—
604	C₂×Dic₅₃	—	2	1	no	—
605	C₂×Dic₅₃	—	2	1	no	—
606	C₂×Dic₅₃	—	2	1	no	—
607	C₂×Dic₅₃	—	2	1	no	—
608	C₂×Dic₅₃	—	2	1	no	—
609	C₂×Dic₅₃	—	2	1	no	—
610	C₂×Dic₅₃	—	2	8	no	—
611	C₂×Dic₅₃	—	2	1	no	—
612	C₂×Dic₅₃	—	2	1	no	—
613	C₂×Dic₅₃	—	2	1	no	—
614	C₂×Dic₅₃	—	2	1	no	—
615	C₂×Dic₅₃	—	2	1	no	—
616	C₂×Dic₅₃	—	2	1	no	—
617	C₂×Dic₅₃	—	2	1	no	—
618	C₂×Dic₅₃	—	2	1	no	—
619	C₂×Dic₅₃	—	2	1	no	—
620	C₂×Dic₅₃	—	2	1	no	—
621	C₂×Dic₅₃	—	2	1	no	—
622	C₂×Dic₅₃	—	2	1	no	—
623	C₂×Dic₅₃	—	2	1	no	—
624	C₂×Dic₅₃	—	2	1	no	—
625	C₂×Dic₅₃	—	2	1	no	—
626	C₂×Dic₅₃	—	2	1	no	—
627	C₂×Dic₅₃	—	2	1	no	—
628	C₂×Dic₅₃	—	2	1	no	—
629	C₂×Dic₅₃	—	4	4	no	—
630	C₂×Dic₅₃	—	4	4	no	—
631	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
632	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
633	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
634	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
635	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
636	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
637	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
638	C₂×Dic₅₃	C₂×#41	1	2	yes	—
639	C₂×Dic₅₃	C₂×#41	1	2	yes	—
640	C₂×Dic₅₃	C₂×#41	1	2	yes	—
641	C₂×Dic₅₃	C₂×#41	1	2	yes	—
642	C₄×D₅₃	—	2	8	no	—
643	C₄×D₅₃	—	4	4	no	—
644	C₄×D₅₃	—	4	4	no	—
645	Dic₁₀₆	—	2	8	no	—
646	C₄×#552	—	53	1	no	maximal, Sylow
647	C₂²×C₅₃	—	2	2	no	—
648	C₂²×C₅₃	—	2	2	no	—
649	C₂²×C₅₃	—	2	2	no	—
650	C₂²×C₅₃	—	2	2	no	—
651	C₂²×C₅₃	—	2	2	no	—
652	C₂²×C₅₃	—	2	2	no	—
653	C₂²×C₅₃	C₄×#41	1	4	yes	—
654	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
655	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
656	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
657	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
658	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
659	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
660	C₂²×C₅₃	#585	1	1	yes	characteristic
661	C₂×D₅₃	—	2	2	no	—
662	C₂×D₅₃	—	2	2	no	—
663	C₂×D₅₃	—	2	2	no	—
664	C₂×D₅₃	—	4	1	no	—
665	C₂×D₅₃	—	4	1	no	—
666	C₂×D₅₃	—	4	1	no	—
667	C₂×D₅₃	—	4	1	no	—
668	C₄×C₅₃	—	2	2	no	—
669	C₄×C₅₃	—	2	2	no	—
670	C₄×C₅₃	—	2	2	no	—
671	C₄×C₅₃	—	2	2	no	—
672	C₄×C₅₃	—	2	2	no	—
673	C₄×C₅₃	—	2	2	no	—
674	C₄×C₅₃	—	2	2	no	—
675	C₄×C₅₃	—	2	2	no	—
676	C₄×C₅₃	—	2	2	no	—
677	C₄×C₅₃	—	2	2	no	—
678	C₄×C₅₃	—	4	1	no	—
679	C₄×C₅₃	—	4	1	no	—
680	C₄×C₅₃	—	4	1	no	—
681	C₄×C₅₃	#552	1	4	yes	complemented
682	Dic₅₃	—	2	2	no	—
683	Dic₅₃	—	2	2	no	—
684	Dic₅₃	—	2	2	no	—
685	Dic₅₃	—	2	2	no	—
686	Dic₅₃	—	2	2	no	—
687	Dic₅₃	—	2	2	no	—
688	Dic₅₃	—	2	2	no	—
689	Dic₅₃	—	2	2	no	—
690	Dic₅₃	—	4	1	no	—
691	Dic₅₃	—	4	1	no	—
692	Dic₅₃	—	4	1	no	—
693	Dic₅₃	—	4	1	no	—
694	Dic₅₃	—	4	1	no	—
695	Dic₅₃	—	4	1	no	—
696	Dic₅₃	C₄×#41	1	4	yes	—
697	C₂×#552	—	53	1	no	—
698	#2373	—	53	1	no	—
699	#2373	—	53	1	no	—
700	#2371	—	53	1	no	—
701	#2371	—	53	1	no	—
702	#2370	—	53	1	no	—
703	#2362	—	53	1	no	—
704	#2360	—	53	1	no	—
705	#2359	—	53	1	no	—
706	#2359	—	53	1	no	—
707	#2356	—	53	1	no	—
708	#2352	—	53	1	no	—
709	#2346	—	53	1	no	—
710	#2344	—	53	1	no	—
711	#2343	—	53	1	no	—
712	#2343	—	53	1	no	—
713	C₄×#125	—	53	1	no	—
714	C₄×#125	—	53	1	no	—
715	C₄×#125	—	53	1	no	—
716	C₄×#126	—	53	1	no	—
717	C₄×#126	—	53	1	no	—
718	C₄×C₂²⋊Q₈	—	53	1	no	—
719	C₄×C₂²⋊Q₈	—	53	1	no	—
720	C₄×#123	—	53	1	no	—
721	C₄×#123	—	53	1	no	—
722	C₄²×Q₈	—	53	1	no	—
723	C₄²×D₄	—	53	1	no	—
724	C₄×#117	—	53	1	no	—
725	C₄×#117	—	53	1	no	—
726	C₄×#117	D₅₃	1	1	yes	characteristic, complemented
727	C₂×C₄×C₄⋊C₄	—	53	1	no	—
728	C₂×C₅₃	—	2	4	no	—
729	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
730	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
731	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
732	C₂×C₅₃	C₂×#552	1	1	yes	characteristic
733	C₂×C₅₃	#3475	1	1	yes	characteristic
734	C₂×C₅₃	#3475	1	1	yes	characteristic
735	C₂×C₅₃	#3482	1	1	yes	characteristic
736	D₅₃	—	4	2	no	—
737	#552	—	53	16	no	—
738	C₂×#126	—	53	1	no	—
739	C₂×#126	—	53	1	no	—
740	C₂×#125	—	53	1	no	—
741	C₂×#125	—	53	1	no	—
742	C₂×#125	—	53	1	no	—
743	C₂×#123	—	53	1	no	—
744	C₂×#123	—	53	1	no	—
745	C₂×C₂²⋊Q₈	—	53	1	no	—
746	C₂×C₂²⋊Q₈	—	53	1	no	—
747	C₂×C₄×Q₈	—	53	1	no	—
748	C₂×C₄×Q₈	—	53	1	no	—
749	C₂×C₄×Q₈	—	53	1	no	—
750	C₂×C₄×D₄	—	53	1	no	—
751	C₂×C₄×D₄	—	53	1	no	—
752	C₂×C₄×D₄	—	53	1	no	—
753	C₂×#117	—	53	1	no	—
754	C₂×#117	—	53	1	no	—
755	C₂×#117	—	53	1	no	—
756	C₂×#117	—	53	1	no	—
757	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
758	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
759	C₂²×C₄⋊C₄	—	53	1	no	—
760	C₂²×C₄⋊C₄	—	53	1	no	—
761	C₂²×C₄²	—	53	1	no	—
762	C₂²×C₄²	—	53	1	no	—
763	C₂²×C₄²	—	53	1	no	—
764	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
765	#391	—	53	1	no	—
766	#391	—	53	1	no	—
767	#389	—	53	1	no	—
768	#389	—	53	1	no	—
769	#389	—	53	1	no	—
770	#389	—	53	1	no	—
771	#389	—	53	1	no	—
772	#389	—	53	1	no	—
773	#389	—	53	1	no	—
774	#389	—	53	1	no	—
775	#388	—	53	1	no	—
776	#388	—	53	1	no	—
777	#388	—	53	1	no	—
778	#388	—	53	1	no	—
779	#388	—	53	1	no	—
780	#388	—	53	1	no	—
781	#388	—	53	1	no	—
782	#388	—	53	1	no	—
783	#388	—	53	1	no	—
784	#388	—	53	1	no	—
785	#387	—	53	1	no	—
786	#387	—	53	1	no	—
787	#387	—	53	1	no	—
788	#387	—	53	1	no	—
789	#387	—	53	1	no	—
790	#387	—	53	1	no	—
791	#387	—	53	1	no	—
792	#387	—	53	1	no	—
793	#387	—	53	1	no	—
794	#387	—	53	1	no	—
795	#387	—	53	1	no	—
796	#387	—	53	1	no	—
797	#387	—	53	1	no	—
798	#387	—	53	1	no	—
799	#387	—	53	1	no	—
800	#387	—	53	1	no	—
801	#387	—	53	1	no	—
802	#387	—	53	1	no	—
803	#387	—	53	1	no	—
804	#387	—	53	1	no	—
805	#387	—	53	1	no	—
806	#387	—	53	1	no	—
807	#387	—	53	1	no	—
808	#387	—	53	1	no	—
809	#387	—	53	1	no	—
810	#387	—	53	1	no	—
811	#386	—	53	1	no	—
812	#386	—	53	1	no	—
813	#385	—	53	1	no	—
814	#385	—	53	1	no	—
815	#385	—	53	1	no	—
816	#385	—	53	1	no	—
817	#385	—	53	1	no	—
818	#385	—	53	1	no	—
819	#383	—	53	1	no	—
820	#383	—	53	1	no	—
821	#382	—	53	1	no	—
822	#382	—	53	1	no	—
823	#382	—	53	1	no	—
824	#381	—	53	1	no	—
825	#381	—	53	1	no	—
826	#380	—	53	1	no	—
827	#380	—	53	1	no	—
828	C₄×C₄⋊C₄	—	53	1	no	—
829	C₄×C₄⋊C₄	—	53	1	no	—
830	C₄×C₄⋊C₄	—	53	1	no	—
831	C₄×C₄⋊C₄	—	53	1	no	—
832	C₄×C₄⋊C₄	—	53	1	no	—
833	C₄×C₄⋊C₄	—	53	1	no	—
834	C₄×C₄⋊C₄	—	53	1	no	—
835	C₄×C₄⋊C₄	—	53	1	no	—
836	C₄×C₄⋊C₄	—	53	1	no	—
837	C₄×C₄⋊C₄	—	53	1	no	—
838	C₄×C₄⋊C₄	—	53	1	no	—
839	C₄×C₄⋊C₄	—	53	1	no	—
840	C₄×C₄⋊C₄	—	53	1	no	—
841	C₄×C₄⋊C₄	—	53	1	no	—
842	C₄×C₄⋊C₄	—	53	1	no	—
843	C₄×C₄⋊C₄	—	53	1	no	—
844	C₄×C₄⋊C₄	—	53	1	no	—
845	C₄×C₄⋊C₄	—	53	1	no	—
846	C₄×C₄⋊C₄	—	53	1	no	—
847	C₄×C₄⋊C₄	—	53	1	no	—
848	C₄×C₄⋊C₄	—	53	1	no	—
849	C₄×C₄⋊C₄	—	53	1	no	—
850	C₄×C₄⋊C₄	—	53	1	no	—
851	C₄×C₄⋊C₄	—	53	1	no	—
852	C₄×C₄⋊C₄	—	53	1	no	—
853	C₄×C₄⋊C₄	—	53	1	no	—
854	C₄×C₄⋊C₄	—	53	1	no	—
855	C₄×C₄⋊C₄	—	53	1	no	—
856	C₄×C₄⋊C₄	—	53	1	no	—
857	C₄×C₄⋊C₄	—	53	1	no	—
858	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
859	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
860	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
861	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
862	C₄×C₂²⋊C₄	—	53	1	no	—
863	C₄×C₂²⋊C₄	—	53	1	no	—
864	C₄×C₂²⋊C₄	—	53	1	no	—
865	C₄×C₂²⋊C₄	—	53	1	no	—
866	C₄×C₂²⋊C₄	—	53	1	no	—
867	C₄×C₂²⋊C₄	—	53	1	no	—
868	C₄×C₂²⋊C₄	—	53	1	no	—
869	C₄×C₂²⋊C₄	—	53	1	no	—
870	C₄×C₂²⋊C₄	—	53	1	no	—
871	C₄×C₂²⋊C₄	—	53	1	no	—
872	C₄×C₂²⋊C₄	—	53	1	no	—
873	C₄×C₂²⋊C₄	—	53	1	no	—
874	C₄×C₂²⋊C₄	—	53	1	no	—
875	C₄×C₂²⋊C₄	—	53	1	no	—
876	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
877	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
878	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
879	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
880	#376	—	53	1	no	—
881	#376	—	53	1	no	—
882	#376	—	53	1	no	—
883	#376	—	53	1	no	—
884	#376	C₂×D₅₃	1	1	yes	characteristic
885	#376	C₂×D₅₃	1	1	yes	characteristic
886	C₂×#95	—	53	1	no	—
887	C₂×#95	—	53	1	no	—
888	C₄³	—	53	1	no	—
889	C₄³	—	53	1	no	—
890	C₄³	—	53	1	no	—
891	C₄³	C₂×D₅₃	1	1	yes	characteristic
892	C₄³	C₂×D₅₃	1	1	yes	characteristic
893	C₅₃	C₄×#552	1	1	yes	characteristic, complemented, Sylow
894	C₂²×Q₈	—	53	1	no	—
895	C₂²×D₄	—	53	1	no	—
896	C₂³×C₄	—	53	1	no	—
897	C₂³×C₄	—	53	1	no	—
898	C₂³×C₄	—	53	1	no	—
899	C₂³×C₄	—	53	1	no	—
900	C₂³×C₄	—	53	1	no	—
901	C₂³×C₄	—	53	1	no	—
902	C₂³×C₄	—	53	1	no	—
903	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
904	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
905	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
906	#126	—	53	8	no	—
907	#126	—	53	8	no	—
908	#125	—	53	8	no	—
909	#125	—	53	8	no	—
910	#125	—	53	8	no	—
911	#123	—	53	8	no	—
912	#123	—	53	8	no	—
913	C₂²⋊Q₈	—	53	8	no	—
914	C₂²⋊Q₈	—	53	8	no	—
915	C₄×Q₈	—	53	8	no	—
916	C₄×Q₈	—	106	4	no	—
917	C₄×Q₈	—	106	4	no	—
918	C₄×D₄	—	53	8	no	—
919	C₄×D₄	—	106	4	no	—
920	C₄×D₄	—	106	4	no	—
921	#117	—	2	4	no	—
922	#117	—	53	8	no	—
923	#117	—	53	8	no	—
924	#117	—	106	4	no	—
925	#117	—	106	4	no	—
926	#117	C₄×D₅₃	1	8	yes	complemented
927	C₂×C₄⋊C₄	—	53	8	no	—
928	C₂×C₄⋊C₄	—	53	1	no	—
929	C₂×C₄⋊C₄	—	53	1	no	—
930	C₂×C₄⋊C₄	—	53	1	no	—
931	C₂×C₄⋊C₄	—	53	1	no	—
932	C₂×C₄⋊C₄	—	53	1	no	—
933	C₂×C₄⋊C₄	—	53	1	no	—
934	C₂×C₄⋊C₄	—	53	1	no	—
935	C₂×C₄⋊C₄	—	53	1	no	—
936	C₂×C₄⋊C₄	—	53	1	no	—
937	C₂×C₄⋊C₄	—	53	1	no	—
938	C₂×C₄⋊C₄	—	53	1	no	—
939	C₂×C₄⋊C₄	—	53	1	no	—
940	C₂×C₄⋊C₄	—	53	1	no	—
941	C₂×C₄⋊C₄	—	53	1	no	—
942	C₂×C₄⋊C₄	—	53	1	no	—
943	C₂×C₄⋊C₄	—	53	1	no	—
944	C₂×C₄⋊C₄	—	53	1	no	—
945	C₂×C₄⋊C₄	—	53	1	no	—
946	C₂×C₄⋊C₄	—	53	1	no	—
947	C₂×C₄⋊C₄	—	53	1	no	—
948	C₂×C₄⋊C₄	—	53	1	no	—
949	C₂×C₄⋊C₄	—	53	1	no	—
950	C₂×C₄⋊C₄	—	53	1	no	—
951	C₂×C₄⋊C₄	—	53	1	no	—
952	C₂×C₄⋊C₄	—	53	1	no	—
953	C₂×C₄⋊C₄	—	53	1	no	—
954	C₂×C₄⋊C₄	—	53	1	no	—
955	C₂×C₄⋊C₄	—	53	1	no	—
956	C₂×C₄⋊C₄	—	53	1	no	—
957	C₂×C₄⋊C₄	—	53	1	no	—
958	C₂×C₄⋊C₄	—	53	1	no	—
959	C₂×C₄⋊C₄	—	53	1	no	—
960	C₂×C₄⋊C₄	—	106	4	no	—
961	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	—	53	1	no	—
966	C₂×C₂²⋊C₄	—	53	1	no	—
967	C₂×C₂²⋊C₄	—	53	1	no	—
968	C₂×C₂²⋊C₄	—	53	1	no	—
969	C₂×C₂²⋊C₄	—	53	1	no	—
970	C₂×C₂²⋊C₄	—	53	1	no	—
971	C₂×C₂²⋊C₄	—	53	1	no	—
972	C₂×C₂²⋊C₄	—	53	1	no	—
973	C₂×C₂²⋊C₄	—	53	1	no	—
974	C₂×C₂²⋊C₄	—	53	1	no	—
975	C₂×C₂²⋊C₄	—	53	1	no	—
976	C₂×C₂²⋊C₄	—	53	1	no	—
977	C₂×C₂²⋊C₄	—	53	1	no	—
978	C₂×C₂²⋊C₄	—	53	1	no	—
979	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
980	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
981	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
982	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
983	C₂×C₄²	—	2	4	no	—
984	C₂×C₄²	—	53	1	no	—
985	C₂×C₄²	—	53	1	no	—
986	C₂×C₄²	—	53	1	no	—
987	C₂×C₄²	—	53	1	no	—
988	C₂×C₄²	—	53	1	no	—
989	C₂×C₄²	—	53	1	no	—
990	C₂×C₄²	—	53	1	no	—
991	C₂×C₄²	—	53	1	no	—
992	C₂×C₄²	—	53	1	no	—
993	C₂×C₄²	—	53	1	no	—
994	C₂×C₄²	—	53	1	no	—
995	C₂×C₄²	—	53	1	no	—
996	C₂×C₄²	—	53	1	no	—
997	C₂×C₄²	—	53	1	no	—
998	C₂×C₄²	—	53	1	no	—
999	C₂×C₄²	—	53	1	no	—
1000	C₂×C₄²	—	53	1	no	—
1001	C₂×C₄²	—	53	1	no	—
1002	C₂×C₄²	—	53	1	no	—
1003	C₂×C₄²	—	53	1	no	—
1004	C₂×C₄²	—	53	1	no	—
1005	C₂×C₄²	—	53	1	no	—
1006	C₂×C₄²	—	53	1	no	—
1007	C₂×C₄²	—	53	1	no	—
1008	C₂×C₄²	—	53	1	no	—
1009	C₂×C₄²	—	106	4	no	—
1010	C₂×C₄²	—	106	4	no	—
1011	C₂×C₄²	—	106	4	no	—
1012	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1013	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1014	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1015	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1016	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1017	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1018	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1019	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1020	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1021	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1022	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1023	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1024	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1025	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1026	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1027	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1028	#95	—	53	1	no	—
1029	#95	—	53	1	no	—
1030	#95	—	53	1	no	—
1031	#95	—	53	1	no	—
1032	#95	—	53	1	no	—
1033	#95	—	53	1	no	—
1034	#95	—	53	1	no	—
1035	#95	—	53	1	no	—
1036	#95	—	53	1	no	—
1037	#95	—	53	1	no	—
1038	#95	—	53	1	no	—
1039	#95	—	53	1	no	—
1040	#95	—	53	1	no	—
1041	#95	—	53	1	no	—
1042	#95	—	53	1	no	—
1043	#95	—	53	1	no	—
1044	#95	—	53	1	no	—
1045	#95	—	53	1	no	—
1046	#95	—	53	1	no	—
1047	#95	—	53	1	no	—
1048	#95	—	53	1	no	—
1049	#95	—	53	1	no	—
1050	#95	—	53	1	no	—
1051	#95	—	53	1	no	—
1052	#95	—	53	1	no	—
1053	#95	—	53	1	no	—
1054	#95	—	53	1	no	—
1055	#95	—	53	1	no	—
1056	#95	—	53	1	no	—
1057	#95	—	53	1	no	—
1058	#95	—	53	1	no	—
1059	#95	—	53	1	no	—
1060	#95	—	53	1	no	—
1061	#95	—	53	1	no	—
1062	#95	—	53	1	no	—
1063	#95	—	53	1	no	—
1064	#95	—	53	1	no	—
1065	#95	—	53	1	no	—
1066	#95	—	53	1	no	—
1067	#95	—	53	1	no	—
1068	#95	C₂²×D₅₃	1	1	yes	characteristic
1069	#95	C₂²×D₅₃	1	1	yes	characteristic
1070	#95	C₂²×D₅₃	1	1	yes	characteristic
1071	#95	C₂²×D₅₃	1	1	yes	characteristic
1072	#95	C₂²×D₅₃	1	1	yes	characteristic
1073	#95	C₂²×D₅₃	1	1	yes	characteristic
1074	#95	C₂²×D₅₃	1	1	yes	characteristic
1075	#95	C₂²×D₅₃	1	1	yes	characteristic
1076	C₂⁴	—	53	1	no	—
1077	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1078	C₂×Q₈	—	53	4	no	—
1079	C₂×Q₈	—	106	2	no	—
1080	C₂×Q₈	—	106	2	no	—
1081	C₂×D₄	—	53	4	no	—
1082	C₂×D₄	—	106	2	no	—
1083	C₂×D₄	—	106	2	no	—
1084	C₂²×C₄	—	2	2	no	—
1085	C₂²×C₄	—	2	2	no	—
1086	C₂²×C₄	—	2	2	no	—
1087	C₂²×C₄	—	2	2	no	—
1088	C₂²×C₄	—	2	2	no	—
1089	C₂²×C₄	—	2	2	no	—
1090	C₂²×C₄	—	4	1	no	—
1091	C₂²×C₄	—	53	1	no	—
1092	C₂²×C₄	—	53	4	no	—
1093	C₂²×C₄	—	53	4	no	—
1094	C₂²×C₄	—	53	1	no	—
1095	C₂²×C₄	—	53	1	no	—
1096	C₂²×C₄	—	53	1	no	—
1097	C₂²×C₄	—	53	1	no	—
1098	C₂²×C₄	—	53	1	no	—
1099	C₂²×C₄	—	53	1	no	—
1100	C₂²×C₄	—	53	1	no	—
1101	C₂²×C₄	—	53	1	no	—
1102	C₂²×C₄	—	53	4	no	—
1103	C₂²×C₄	—	53	1	no	—
1104	C₂²×C₄	—	53	1	no	—
1105	C₂²×C₄	—	53	1	no	—
1106	C₂²×C₄	—	53	1	no	—
1107	C₂²×C₄	—	53	1	no	—
1108	C₂²×C₄	—	53	1	no	—
1109	C₂²×C₄	—	106	2	no	—
1110	C₂²×C₄	—	106	2	no	—
1111	C₂²×C₄	—	106	2	no	—
1112	C₂²×C₄	—	106	2	no	—
1113	C₂²×C₄	—	106	2	no	—
1114	C₂²×C₄	—	106	2	no	—
1115	C₂²×C₄	—	106	2	no	—
1116	C₂²×C₄	—	106	2	no	—
1117	C₂²×C₄	—	106	2	no	—
1118	C₂²×C₄	—	106	2	no	—
1119	C₂²×C₄	—	106	2	no	—
1120	C₂²×C₄	—	106	2	no	—
1121	C₂²×C₄	—	106	2	no	—
1122	C₂²×C₄	—	106	2	no	—
1123	C₂²×C₄	—	106	2	no	—
1124	C₂²×C₄	—	212	1	no	—
1125	C₂²×C₄	—	212	1	no	—
1126	C₂²×C₄	—	212	1	no	—
1127	C₂²×C₄	C₂×C₄×D₅₃	1	4	yes	—
1128	C₂²×C₄	#11719945	1	4	yes	—
1129	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1130	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1131	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1132	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1133	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1134	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1135	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1136	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1137	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1138	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1139	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1140	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1141	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1142	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1143	C₄⋊C₄	—	2	2	no	—
1144	C₄⋊C₄	—	2	2	no	—
1145	C₄⋊C₄	—	53	4	no	—
1146	C₄⋊C₄	—	53	4	no	—
1147	C₄⋊C₄	—	53	4	no	—
1148	C₄⋊C₄	—	53	4	no	—
1149	C₄⋊C₄	—	53	4	no	—
1150	C₄⋊C₄	—	53	4	no	—
1151	C₄⋊C₄	—	53	4	no	—
1152	C₄⋊C₄	—	53	4	no	—
1153	C₄⋊C₄	—	53	4	no	—
1154	C₄⋊C₄	—	53	4	no	—
1155	C₄⋊C₄	—	53	4	no	—
1156	C₄⋊C₄	—	53	4	no	—
1157	C₄⋊C₄	—	53	4	no	—
1158	C₄⋊C₄	—	53	4	no	—
1159	C₄⋊C₄	—	53	4	no	—
1160	C₄⋊C₄	—	106	2	no	—
1161	C₄⋊C₄	—	106	2	no	—
1162	C₄⋊C₄	—	106	2	no	—
1163	C₄⋊C₄	—	106	2	no	—
1164	C₄⋊C₄	—	106	2	no	—
1165	C₄⋊C₄	—	106	2	no	—
1166	C₄⋊C₄	—	106	2	no	—
1167	C₄⋊C₄	—	106	2	no	—
1168	C₄⋊C₄	—	106	2	no	—
1169	C₄⋊C₄	—	106	2	no	—
1170	C₄⋊C₄	—	106	2	no	—
1171	C₄⋊C₄	—	106	2	no	—
1172	C₄⋊C₄	—	106	2	no	—
1173	C₄⋊C₄	—	212	1	no	—
1174	C₄⋊C₄	—	212	1	no	—
1175	C₄⋊C₄	—	212	1	no	—
1176	C₄⋊C₄	—	212	1	no	—
1177	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1178	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1179	C₂²⋊C₄	—	2	2	no	—
1180	C₂²⋊C₄	—	53	4	no	—
1181	C₂²⋊C₄	—	53	4	no	—
1182	C₂²⋊C₄	—	53	4	no	—
1183	C₂²⋊C₄	—	53	4	no	—
1184	C₂²⋊C₄	—	53	4	no	—
1185	C₂²⋊C₄	—	53	4	no	—
1186	C₂²⋊C₄	—	106	2	no	—
1187	C₂²⋊C₄	—	106	2	no	—
1188	C₂²⋊C₄	—	106	2	no	—
1189	C₂²⋊C₄	—	106	2	no	—
1190	C₂²⋊C₄	—	106	2	no	—
1191	C₂²⋊C₄	—	106	2	no	—
1192	C₂²⋊C₄	—	212	1	no	—
1193	C₂²⋊C₄	—	212	1	no	—
1194	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1195	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1196	C₂²⋊C₄	#11719945	1	4	yes	—
1197	C₄²	—	2	2	no	—
1198	C₄²	—	2	2	no	—
1199	C₄²	—	2	2	no	—
1200	C₄²	—	2	2	no	—
1201	C₄²	—	2	2	no	—
1202	C₄²	—	2	2	no	—
1203	C₄²	—	2	2	no	—
1204	C₄²	—	2	2	no	—
1205	C₄²	—	2	2	no	—
1206	C₄²	—	2	2	no	—
1207	C₄²	—	2	2	no	—
1208	C₄²	—	2	2	no	—
1209	C₄²	—	4	1	no	—
1210	C₄²	—	4	1	no	—
1211	C₄²	—	53	4	no	—
1212	C₄²	—	53	4	no	—
1213	C₄²	—	53	4	no	—
1214	C₄²	—	53	4	no	—
1215	C₄²	—	106	2	no	—
1216	C₄²	—	106	2	no	—
1217	C₄²	—	106	2	no	—
1218	C₄²	—	106	2	no	—
1219	C₄²	—	106	2	no	—
1220	C₄²	—	106	2	no	—
1221	C₄²	—	106	2	no	—
1222	C₄²	—	106	2	no	—
1223	C₄²	—	106	2	no	—
1224	C₄²	—	106	2	no	—
1225	C₄²	—	106	2	no	—
1226	C₄²	—	106	2	no	—
1227	C₄²	—	106	2	no	—
1228	C₄²	—	106	2	no	—
1229	C₄²	—	106	2	no	—
1230	C₄²	—	106	2	no	—
1231	C₄²	—	106	2	no	—
1232	C₄²	—	106	2	no	—
1233	C₄²	—	212	1	no	—
1234	C₄²	—	212	1	no	—
1235	C₄²	—	212	1	no	—
1236	C₄²	C₂×C₄×D₅₃	1	4	yes	—
1237	C₄²	C₂×C₄×D₅₃	1	4	yes	—
1238	C₂³	—	2	1	no	—
1239	C₂³	—	2	1	no	—
1240	C₂³	—	2	1	no	—
1241	C₂³	—	2	1	no	—
1242	C₂³	—	53	2	no	—
1243	C₂³	—	106	1	no	—
1244	C₂³	—	106	1	no	—
1245	C₂³	—	106	1	no	—
1246	C₂³	—	106	1	no	—
1247	C₂³	—	106	1	no	—
1248	C₂³	—	106	1	no	—
1249	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1250	C₂³	C₂×#11719945	1	2	yes	—
1251	C₂³	C₂×#11719945	1	2	yes	—
1252	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1253	Q₈	—	106	8	no	—
1254	D₄	—	106	8	no	—
1255	C₂×C₄	—	2	8	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	2	1	no	—
1264	C₂×C₄	—	2	1	no	—
1265	C₂×C₄	—	2	1	no	—
1266	C₂×C₄	—	2	1	no	—
1267	C₂×C₄	—	2	1	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	2	1	no	—
1270	C₂×C₄	—	2	1	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	8	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	4	4	no	—
1287	C₂×C₄	—	53	2	no	—
1288	C₂×C₄	—	53	2	no	—
1289	C₂×C₄	—	53	2	no	—
1290	C₂×C₄	—	53	2	no	—
1291	C₂×C₄	—	53	2	no	—
1292	C₂×C₄	—	53	2	no	—
1293	C₂×C₄	—	53	2	no	—
1294	C₂×C₄	—	53	2	no	—
1295	C₂×C₄	—	53	2	no	—
1296	C₂×C₄	—	53	2	no	—
1297	C₂×C₄	—	53	2	no	—
1298	C₂×C₄	—	106	8	no	—
1299	C₂×C₄	—	106	8	no	—
1300	C₂×C₄	—	106	8	no	—
1301	C₂×C₄	—	106	1	no	—
1302	C₂×C₄	—	106	1	no	—
1303	C₂×C₄	—	106	1	no	—
1304	C₂×C₄	—	106	1	no	—
1305	C₂×C₄	—	106	1	no	—
1306	C₂×C₄	—	106	1	no	—
1307	C₂×C₄	—	106	1	no	—
1308	C₂×C₄	—	106	1	no	—
1309	C₂×C₄	—	106	1	no	—
1310	C₂×C₄	—	106	1	no	—
1311	C₂×C₄	—	106	1	no	—
1312	C₂×C₄	—	106	1	no	—
1313	C₂×C₄	—	106	1	no	—
1314	C₂×C₄	—	106	1	no	—
1315	C₂×C₄	—	106	1	no	—
1316	C₂×C₄	—	106	1	no	—
1317	C₂×C₄	—	106	1	no	—
1318	C₂×C₄	—	106	1	no	—
1319	C₂×C₄	—	106	1	no	—
1320	C₂×C₄	—	106	1	no	—
1321	C₂×C₄	—	106	1	no	—
1322	C₂×C₄	—	106	1	no	—
1323	C₂×C₄	—	106	1	no	—
1324	C₂×C₄	—	106	1	no	—
1325	C₂×C₄	—	106	1	no	—
1326	C₂×C₄	—	106	1	no	—
1327	C₂×C₄	—	106	1	no	—
1328	C₂×C₄	—	106	1	no	—
1329	C₂×C₄	—	106	1	no	—
1330	C₂×C₄	—	106	1	no	—
1331	C₂×C₄	—	106	1	no	—
1332	C₂×C₄	—	106	1	no	—
1333	C₂×C₄	—	106	1	no	—
1334	C₂×C₄	—	106	1	no	—
1335	C₂×C₄	—	212	4	no	—
1336	C₂×C₄	—	212	4	no	—
1337	C₂×C₄	—	212	4	no	—
1338	C₂×C₄	—	212	4	no	—
1339	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1340	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1341	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1342	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1343	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1344	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1345	C₂×C₄	#41×D₅₃	1	2	yes	—
1346	C₂×C₄	#41×D₅₃	1	2	yes	—
1347	C₂×C₄	C₂×#11719945	1	2	yes	—
1348	C₂×C₄	C₂×#11719945	1	2	yes	—
1349	C₂×C₄	C₂×#11719945	1	2	yes	—
1350	C₂×C₄	C₂×#11719945	1	2	yes	—
1351	C₂×C₄	#13133264	1	2	yes	—
1352	C₂²	—	2	2	no	—
1353	C₂²	—	2	2	no	—
1354	C₂²	—	2	2	no	—
1355	C₂²	—	2	2	no	—
1356	C₂²	—	2	2	no	—
1357	C₂²	—	2	2	no	—
1358	C₂²	—	106	2	no	—
1359	C₂²	—	106	2	no	—
1360	C₂²	—	106	2	no	—
1361	C₂²	—	212	1	no	—
1362	C₂²	—	212	1	no	—
1363	C₂²	—	212	1	no	—
1364	C₂²	—	212	1	no	—
1365	C₂²	C₄×#11719945	1	4	yes	—
1366	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1367	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1368	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1369	C₂²	C₂²×#11719945	1	1	yes	characteristic
1370	C₂²	C₂²×#11719945	1	1	yes	characteristic
1371	C₂²	C₂×#13133264	1	1	yes	characteristic
1372	C₂²	#16811459	1	1	yes	characteristic
1373	C₄	—	2	2	no	—
1374	C₄	—	2	2	no	—
1375	C₄	—	2	2	no	—
1376	C₄	—	2	2	no	—
1377	C₄	—	2	2	no	—
1378	C₄	—	2	2	no	—
1379	C₄	—	2	2	no	—
1380	C₄	—	2	2	no	—
1381	C₄	—	2	2	no	—
1382	C₄	—	2	2	no	—
1383	C₄	—	4	1	no	—
1384	C₄	—	4	1	no	—
1385	C₄	—	4	1	no	—
1386	C₄	—	53	4	no	—
1387	C₄	—	106	2	no	—
1388	C₄	—	106	2	no	—
1389	C₄	—	106	2	no	—
1390	C₄	—	106	2	no	—
1391	C₄	—	106	2	no	—
1392	C₄	—	106	2	no	—
1393	C₄	—	106	2	no	—
1394	C₄	—	106	2	no	—
1395	C₄	—	212	1	no	—
1396	C₄	—	212	1	no	—
1397	C₄	—	212	1	no	—
1398	C₄	—	212	1	no	—
1399	C₄	—	212	1	no	—
1400	C₄	—	212	1	no	—
1401	C₄	#16811306	1	4	yes	direct product factor
1402	C₂	—	2	4	no	—
1403	C₂	—	212	2	no	—
1404	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1405	C₂	C₂×C₄×#11719945	1	1	yes	characteristic
1406	C₂	C₄×#13133264	1	1	yes	characteristic
1407	C₂	C₂×#16811306	1	1	yes	characteristic
1408	C₂	#20288269	1	1	yes	characteristic
1409	C₂	#20288277	1	1	yes	characteristic
1410	C₂	#20288330	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₅₃
Fitting	C₄×#117×C₅₃	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×C₂²⋊D₅₃	C₂³
hypercenter	C₄×#117	D₅₃
hypocenter	C₅₃	C₄×#552
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
2. #20277835	C₂	semidirect
3. #20277829	C₂	semidirect
4. #20277820	C₂	semidirect
5. #20277818	C₂	semidirect
6. #20277812	C₂	semidirect
7. #20277743	C₂	semidirect
8. #20277721	C₂	semidirect
11. #20277681	C₂	semidirect
13. #20277601	C₂	semidirect
14. #20277585	C₂	semidirect
15. #20277575	C₂	semidirect
16. #20277569	C₂	semidirect
17. C₄×#13133209	C₂	semidirect
18. C₄×#13133207	C₂	semidirect
19. C₄×#13133207	C₂	semidirect
20. C₄×#13133212	C₂	semidirect
21. C₄×#13133211	C₂	semidirect
22. C₄×#13133195	C₂	semidirect
23. C₄×#13133194	C₂	semidirect
26. C₄²×Dic₁₀₆	C₂	semidirect
28. C₄×#13133174	C₂	semidirect
29. C₄×#13133173	C₂	semidirect
30. C₂×C₄×#11719919	C₂	semidirect
31. C₄×#117×C₅₃	C₂	semidirect
32. #16811306	C₄	direct (N × H)
197. #13133212	C₂×C₄	semidirect
198. #13133211	C₂×C₄	semidirect
199. #13133209	C₂×C₄	semidirect
200. #13133207	C₂×C₄	semidirect
201. #13133207	C₂×C₄	semidirect
204. #13133195	C₂×C₄	semidirect
205. #13133194	C₂×C₄	semidirect
208. C₄×Dic₁₀₆	C₂×C₄	semidirect
213. #13133174	C₂×C₄	semidirect
215. #13133173	C₂×C₄	semidirect
224. C₂×#11719919	C₂×C₄	semidirect
336. #117×C₅₃	C₂×C₄	semidirect
681. C₄×C₅₃	#552	semidirect
726. C₄×#117	D₅₃	semidirect
893. C₅₃	C₄×#552	semidirect
926. #117	C₄×D₅₃	semidirect
1401. C₄	#16811306	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16811306	2
#20277835	2
#20277829	2
#20277820	2
#20277818	2
#20277812	2
#20277743	2
#20277721	2
#20277709	2
#20277707	2
#20277681	2
#20277638	2
#20277601	2
#20277585	2
#20277575	2
#20277569	2
C₄×#13133209	2
C₄×#13133207	2
C₄×#13133212	2
C₄×#13133211	2
C₄×#13133195	2
C₄×#13133194	2
C₄×#13133201	2
C₄×#13133200	2
C₄²×Dic₁₀₆	2
C₄×#13133177	2
C₄×#13133174	2
C₄×#13133173	2
C₂×C₄×#11719919	2
C₄×#117×C₅₃	2
C₄×#552	53

Subgroups — C4×#16811306 #27543994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16811306 #27543994