Subgroups — C₂×#20288514 #28291993

Order 13568.

7738 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288514	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811333	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811329	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811329	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16811328	C₂	1	2	yes	maximal, complemented
8	C₂×#16811327	C₂	1	2	yes	maximal, complemented
9	C₂×#16811327	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16811288	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16811286	C₂	1	2	yes	maximal, complemented
13	C₂×#16811253	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16811250	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16811248	C₂	1	2	yes	maximal, complemented
16	C₂×#16811248	C₂	1	2	yes	maximal, complemented
17	C₂×#16811179	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16811177	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#13133195	C₂	1	2	yes	maximal, complemented
20	C₂×C₂²⋊Q₈×D₅₃	C₂	1	2	yes	maximal, complemented
21	C₂×#16811095	C₂	1	1	yes	maximal, characteristic
22	C₂×#16811095	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
24	C₂×C₅₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂³×Dic₁₀₆	C₂²	1	2	yes	complemented
26	C₂²×Q₈×D₅₃	C₂²	1	2	yes	complemented
27	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
28	C₂³×C₄×D₅₃	C₂²	1	2	yes	—
29	#16811333	C₂²	1	16	yes	complemented
30	#16811332	C₂²	1	16	yes	complemented
31	#16811332	C₂²	1	16	yes	complemented
32	#16811329	C₂²	1	16	yes	complemented
33	#16811329	C₂²	1	16	yes	complemented
34	#16811328	C₂²	1	32	yes	complemented
35	#16811327	C₂²	1	32	yes	complemented
36	#16811327	C₂²	1	32	yes	complemented
37	D₄×Dic₁₀₆	C₂²	1	16	yes	complemented
38	#16811288	C₂²	1	16	yes	complemented
39	#16811286	C₂²	1	32	yes	complemented
40	#16811253	C₂²	1	16	yes	complemented
41	#16811250	C₂²	1	16	yes	complemented
42	#16811248	C₂²	1	32	yes	complemented
43	#16811248	C₂²	1	32	yes	complemented
44	#16811179	C₂²	1	16	yes	complemented
45	#16811177	C₂²	1	16	yes	complemented
46	C₂×#13133217	C₂²	1	1	yes	characteristic, complemented
47	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
49	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
50	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
51	C₂×#13133216	C₂²	1	2	yes	complemented
52	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13133215	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13133215	C₂²	1	2	yes	complemented
55	C₂×#13133209	C₂²	1	1	yes	characteristic, complemented
56	C₂×#13133209	C₂²	1	1	yes	characteristic, complemented
57	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
58	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
59	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
60	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
61	C₂×#13133207	C₂²	1	2	yes	complemented
62	C₂×#13133207	C₂²	1	2	yes	complemented
63	C₂×#13133197	C₂²	1	1	yes	characteristic
64	C₂×#13133197	C₂²	1	2	yes	—
65	C₂×#13133197	C₂²	1	2	yes	complemented
66	C₂×#13133197	C₂²	1	2	yes	complemented
67	C₂×#13133196	C₂²	1	2	yes	complemented
68	C₂×#13133196	C₂²	1	2	yes	complemented
69	C₂×#13133196	C₂²	1	2	yes	complemented
70	C₂×#13133195	C₂²	1	1	yes	characteristic
71	C₂×#13133195	C₂²	1	1	yes	characteristic
72	C₂×#13133195	C₂²	1	2	yes	—
73	C₂×#13133195	C₂²	1	2	yes	—
74	C₂×#13133195	C₂²	1	2	yes	—
75	C₂×#13133195	C₂²	1	2	yes	—
76	C₂×#13133195	C₂²	1	2	yes	complemented
77	C₂×#13133195	C₂²	1	2	yes	complemented
78	C₂×#13133195	C₂²	1	2	yes	complemented
79	C₂×#13133195	C₂²	1	2	yes	complemented
80	C₂×#13133195	C₂²	1	2	yes	complemented
81	C₂×#13133195	C₂²	1	2	yes	complemented
82	C₂×#13133195	C₂²	1	2	yes	complemented
83	C₂×#13133195	C₂²	1	2	yes	complemented
84	C₂×#13133195	C₂²	1	32	yes	complemented
85	C₂×#13133194	C₂²	1	2	yes	complemented
86	C₂×#13133194	C₂²	1	2	yes	complemented
87	C₂×#13133194	C₂²	1	2	yes	complemented
88	C₂×#13133194	C₂²	1	2	yes	complemented
89	C₂×#13133194	C₂²	1	2	yes	complemented
90	C₂×#13133194	C₂²	1	2	yes	complemented
91	C₂×#13133193	C₂²	1	1	yes	characteristic
92	C₂×#13133193	C₂²	1	2	yes	—
93	C₂×#13133193	C₂²	1	2	yes	complemented
94	C₂×#13133193	C₂²	1	2	yes	complemented
95	C₂²⋊Q₈×D₅₃	C₂²	1	32	yes	complemented
96	#16811095	C₂²	1	16	yes	—
97	#16811095	C₂²	1	16	yes	—
98	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
101	C₂×#13133182	C₂²	1	2	yes	complemented
102	C₂×#13133182	C₂²	1	2	yes	complemented
103	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
104	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
105	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
106	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
107	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
108	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
109	C₂×#13133179	C₂²	1	1	yes	characteristic
110	C₂×#13133179	C₂²	1	1	yes	characteristic
111	C₂×#13133179	C₂²	1	1	yes	characteristic
112	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
113	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
114	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
115	C₂×#13133177	C₂²	1	2	yes	—
116	C₂×#13133177	C₂²	1	2	yes	—
117	C₂×#13133177	C₂²	1	2	yes	—
118	C₄×D₄×D₅₃	C₂²	1	16	yes	—
119	C₂×#13133175	C₂²	1	1	yes	characteristic
120	C₂×#13133175	C₂²	1	1	yes	characteristic
121	C₂×#13133174	C₂²	1	1	yes	characteristic
122	C₂×#13133174	C₂²	1	1	yes	characteristic
123	C₂²×#11719919	C₂²	1	2	yes	complemented
124	C₂²×#11719919	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
127	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
128	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
129	C₂²×#11719921	C₂²	1	2	yes	—
130	C₂²×#11719921	C₂²	1	2	yes	—
131	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
132	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
133	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
134	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
135	C₅₃×#554	C₂²	1	16	yes	complemented
136	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
137	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
138	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
140	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
141	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
142	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
144	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
145	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
146	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
147	C₂⁴×D₅₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₀₆	—	4	8	no	—
149	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
150	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
151	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
152	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
153	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
154	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
155	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
156	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
157	C₂²×Dic₁₀₆	C₂³	1	16	yes	complemented
158	C₂×Q₈×D₅₃	—	4	8	no	—
159	C₂×Q₈×D₅₃	C₂³	1	16	yes	complemented
160	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
161	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
162	C₂×D₄×D₅₃	Q₈	1	16	yes	complemented
163	C₂×D₄×D₅₃	C₂³	1	8	yes	—
164	C₂³×Dic₅₃	C₂³	1	2	yes	—
165	C₂³×Dic₅₃	C₂³	1	2	yes	—
166	C₂³×Dic₅₃	C₂³	1	2	yes	—
167	C₂²×C₄×D₅₃	—	4	8	no	—
168	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
169	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
170	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
171	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
172	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
173	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
174	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
175	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
176	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
177	C₂²×C₄×D₅₃	C₂³	1	16	yes	—
178	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
179	#13133217	C₂³	1	8	yes	complemented
180	#13133216	C₂³	1	8	yes	complemented
181	#13133216	C₂³	1	16	yes	complemented
182	#13133216	C₂³	1	8	yes	complemented
183	#13133216	C₂³	1	8	yes	complemented
184	#13133216	C₂³	1	8	yes	complemented
185	#13133216	C₂³	1	8	yes	complemented
186	#13133215	C₂³	1	16	yes	complemented
187	#13133215	C₂³	1	8	yes	complemented
188	#13133209	C₂³	1	8	yes	complemented
189	#13133209	C₂³	1	8	yes	complemented
190	#13133208	C₂³	1	8	yes	complemented
191	#13133208	C₂³	1	8	yes	complemented
192	#13133207	C₂³	1	8	yes	complemented
193	#13133207	C₂³	1	16	yes	complemented
194	#13133207	C₂³	1	16	yes	complemented
195	#13133207	C₂³	1	8	yes	complemented
196	#13133197	C₂³	1	16	yes	—
197	#13133197	C₂³	1	8	yes	—
198	#13133197	C₂³	1	16	yes	complemented
199	#13133197	C₂³	1	16	yes	complemented
200	#13133196	C₂³	1	16	yes	complemented
201	#13133196	C₂³	1	16	yes	complemented
202	#13133196	C₂³	1	16	yes	complemented
203	#13133195	C₂³	1	8	yes	—
204	#13133195	C₂³	1	16	yes	—
205	#13133195	C₂³	1	8	yes	—
206	#13133195	C₂³	1	16	yes	—
207	#13133195	C₂³	1	16	yes	—
208	#13133195	C₂³	1	16	yes	—
209	#13133195	C₂³	1	16	yes	complemented
210	#13133195	C₂³	1	16	yes	complemented
211	#13133195	C₂³	1	16	yes	complemented
212	#13133195	C₂³	1	16	yes	complemented
213	#13133195	C₂³	1	16	yes	complemented
214	#13133195	C₂³	1	16	yes	complemented
215	#13133195	C₂³	1	16	yes	complemented
216	#13133195	C₂³	1	16	yes	complemented
217	#13133194	C₂³	1	16	yes	complemented
218	#13133194	C₂³	1	16	yes	complemented
219	#13133194	C₂³	1	16	yes	complemented
220	#13133194	C₂³	1	16	yes	complemented
221	#13133194	C₂³	1	16	yes	complemented
222	#13133194	C₂³	1	16	yes	complemented
223	#13133193	C₂³	1	16	yes	—
224	#13133193	C₂³	1	8	yes	—
225	#13133193	C₂³	1	16	yes	complemented
226	#13133193	C₂³	1	16	yes	complemented
227	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
228	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
229	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
230	#13133182	C₂³	1	16	yes	complemented
231	#13133182	C₂³	1	16	yes	complemented
232	C₄×D₂₁₂	C₂³	1	8	yes	—
233	C₄×D₂₁₂	C₂³	1	8	yes	—
234	C₄×D₂₁₂	C₂³	1	8	yes	—
235	D₄×Dic₅₃	C₂³	1	8	yes	—
236	D₄×Dic₅₃	C₂³	1	8	yes	—
237	D₄×Dic₅₃	C₂³	1	8	yes	—
238	#13133179	C₂³	1	8	yes	—
239	#13133179	C₂³	1	8	yes	—
240	#13133179	C₂³	1	8	yes	—
241	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	—
242	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	—
243	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	—
244	#13133177	C₂³	1	16	yes	—
245	#13133177	C₂³	1	16	yes	—
246	#13133177	C₂³	1	16	yes	—
247	#13133175	C₂³	1	8	yes	—
248	#13133175	C₂³	1	8	yes	—
249	#13133174	C₂³	1	8	yes	—
250	#13133174	C₂³	1	8	yes	—
251	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
253	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
254	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
255	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
260	C₂×#11719919	C₂³	1	2	yes	—
261	C₂×#11719919	C₂³	1	1	yes	characteristic
262	C₂×#11719919	C₂³	1	1	yes	characteristic
263	C₂×#11719919	C₂³	1	2	yes	—
264	C₂×#11719919	C₂³	1	2	yes	—
265	C₂×#11719919	C₂³	1	2	yes	—
266	C₂×#11719919	C₂³	1	2	yes	—
267	C₂×#11719919	C₂³	1	1	yes	characteristic
268	C₂×#11719919	C₂³	1	1	yes	characteristic
269	C₂×#11719919	C₂³	1	2	yes	—
270	C₂×#11719919	C₂³	1	2	yes	—
271	C₂×#11719919	C₂³	1	2	yes	—
272	C₂×#11719919	C₂³	1	2	yes	—
273	C₂×#11719919	C₂³	1	1	yes	characteristic
274	C₂×#11719919	C₂³	1	1	yes	characteristic
275	C₂×#11719919	C₂³	1	1	yes	characteristic
276	C₂×#11719919	C₂³	1	1	yes	characteristic
277	C₂×#11719919	C₂³	1	2	yes	—
278	C₂×#11719919	C₂³	1	2	yes	—
279	C₂×#11719919	C₂³	1	1	yes	characteristic
280	C₂×#11719919	C₂³	1	1	yes	characteristic
281	C₂×#11719919	C₂³	1	16	yes	complemented
282	C₂×#11719919	C₂³	1	16	yes	complemented
283	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
284	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
285	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
286	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
287	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
288	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
289	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
290	C₂×#11719921	C₂³	1	1	yes	characteristic
291	C₂×#11719921	C₂³	1	1	yes	characteristic
292	C₂×#11719921	C₂³	1	2	yes	—
293	C₂×#11719921	C₂³	1	2	yes	—
294	C₂×#11719921	C₂³	1	2	yes	—
295	C₂×#11719921	C₂³	1	2	yes	—
296	C₂×#11719921	C₂³	1	1	yes	characteristic
297	C₂×#11719921	C₂³	1	1	yes	characteristic
298	C₂×#11719921	C₂³	1	2	yes	—
299	C₂×#11719921	C₂³	1	2	yes	—
300	C₂×#11719921	C₂³	1	2	yes	—
301	C₂×#11719921	C₂³	1	2	yes	—
302	C₂×#11719921	C₂³	1	16	yes	—
303	C₂×#11719921	C₂³	1	16	yes	—
304	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
305	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
306	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
307	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
313	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
314	C₄²×D₅₃	C₂³	1	8	yes	—
315	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
317	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
319	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
320	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
321	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
322	#125×C₅₃	C₂³	1	8	yes	complemented
323	#125×C₅₃	C₂³	1	8	yes	complemented
324	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
325	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
326	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
327	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
328	C₄×D₄×C₅₃	C₂³	1	8	yes	—
329	C₄×D₄×C₅₃	C₂³	1	8	yes	—
330	C₄×D₄×C₅₃	C₂³	1	8	yes	—
331	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
333	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
334	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
335	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
342	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	complemented
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
350	C₂³×D₅₃	—	4	4	no	—
351	C₂³×D₅₃	—	4	4	no	—
352	C₂³×D₅₃	C₂×Q₈	1	16	yes	complemented
353	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
354	C₂³×D₅₃	C₂⁴	1	2	yes	—
355	C₂³×D₅₃	C₂⁴	1	8	yes	—
356	C₂×Q₈×C₅₃	—	4	2	no	—
357	C₂×Q₈×C₅₃	—	4	4	no	—
358	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
359	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
360	C₂×D₄×C₅₃	C₂×Q₈	1	8	yes	complemented
361	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
362	C₂²×C₄×C₅₃	—	4	4	no	—
363	C₂²×C₄×C₅₃	—	4	4	no	—
364	C₂²×C₄×C₅₃	—	4	4	no	—
365	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
375	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
376	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₂²⋊D₅₃	C₂×Q₈	1	16	yes	complemented
379	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
380	C₂²×Dic₅₃	—	2	8	no	—
381	C₂²×Dic₅₃	—	4	4	no	—
382	C₂²×Dic₅₃	—	4	4	no	—
383	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
387	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
388	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
391	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
392	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
393	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
394	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
396	Q₈×D₅₃	—	4	32	no	—
397	D₄×D₅₃	C₂×Q₈	1	64	yes	complemented
398	C₂×D₂₁₂	C₂×Q₈	1	8	yes	complemented
399	C₂×D₂₁₂	C₂⁴	1	4	yes	—
400	C₂×C₄×D₅₃	—	2	4	no	—
401	C₂×C₄×D₅₃	—	2	8	no	—
402	C₂×C₄×D₅₃	—	4	32	no	—
403	C₂×C₄×D₅₃	—	4	4	no	—
404	C₂×C₄×D₅₃	—	4	4	no	—
405	C₂×C₄×D₅₃	—	4	2	no	—
406	C₂×C₄×D₅₃	—	4	4	no	—
407	C₂×C₄×D₅₃	—	4	4	no	—
408	C₂×C₄×D₅₃	—	4	4	no	—
409	C₂×C₄×D₅₃	—	4	4	no	—
410	C₂×C₄×D₅₃	C₂×Q₈	1	8	yes	complemented
411	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
412	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
413	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
414	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
415	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
416	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
417	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
418	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
419	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
420	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
421	C₂×Dic₁₀₆	—	2	4	no	—
422	C₂×Dic₁₀₆	—	2	8	no	—
423	C₂×Dic₁₀₆	—	2	4	no	—
424	C₂×Dic₁₀₆	—	4	32	no	—
425	C₂×Dic₁₀₆	—	4	4	no	—
426	C₂×Dic₁₀₆	—	4	4	no	—
427	C₂×Dic₁₀₆	—	4	4	no	—
428	C₂×Dic₁₀₆	—	4	4	no	—
429	C₂×Dic₁₀₆	—	4	2	no	—
430	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
431	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
432	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
433	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
434	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
435	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
436	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
437	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
438	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
439	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
440	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
441	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
442	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
443	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
444	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
445	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
446	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
447	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
448	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
449	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
451	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
452	C₄²×C₅₃	C₂⁴	1	4	yes	—
453	C₄²×C₅₃	C₂⁴	1	4	yes	—
454	C₄²×C₅₃	C₂⁴	1	4	yes	—
455	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
456	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
457	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
458	#11719921	C₂⁴	1	4	yes	—
459	#11719921	C₂⁴	1	4	yes	—
460	#11719921	C₂⁴	1	8	yes	—
461	#11719921	C₂⁴	1	8	yes	—
462	#11719921	C₂⁴	1	8	yes	—
463	#11719921	C₂⁴	1	8	yes	—
464	#11719921	C₂⁴	1	4	yes	—
465	#11719921	C₂⁴	1	4	yes	—
466	#11719921	C₂⁴	1	8	yes	—
467	#11719921	C₂⁴	1	8	yes	—
468	#11719921	C₂⁴	1	8	yes	—
469	#11719921	C₂⁴	1	8	yes	—
470	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
471	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
472	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
473	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
474	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
475	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
476	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
477	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
478	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
479	#11719919	C₂⁴	1	8	yes	—
480	#11719919	C₂⁴	1	4	yes	—
481	#11719919	C₂⁴	1	4	yes	—
482	#11719919	C₂⁴	1	8	yes	—
483	#11719919	C₂⁴	1	8	yes	—
484	#11719919	C₂⁴	1	8	yes	—
485	#11719919	C₂⁴	1	8	yes	—
486	#11719919	C₂⁴	1	4	yes	—
487	#11719919	C₂⁴	1	4	yes	—
488	#11719919	C₂⁴	1	8	yes	—
489	#11719919	C₂⁴	1	8	yes	—
490	#11719919	C₂⁴	1	8	yes	—
491	#11719919	C₂⁴	1	8	yes	—
492	#11719919	C₂⁴	1	4	yes	—
493	#11719919	C₂⁴	1	4	yes	—
494	#11719919	C₂⁴	1	4	yes	—
495	#11719919	C₂⁴	1	4	yes	—
496	#11719919	C₂⁴	1	8	yes	—
497	#11719919	C₂⁴	1	8	yes	—
498	#11719919	C₂⁴	1	4	yes	—
499	#11719919	C₂⁴	1	4	yes	—
500	C₄×Dic₅₃	C₂⁴	1	4	yes	—
501	C₄×Dic₅₃	C₂⁴	1	4	yes	—
502	C₄×Dic₅₃	C₂⁴	1	4	yes	—
503	C₄×Dic₅₃	C₂⁴	1	4	yes	—
504	C₄×Dic₅₃	C₂⁴	1	4	yes	—
505	C₄×Dic₅₃	C₂⁴	1	8	yes	—
506	C₄×Dic₅₃	C₂⁴	1	8	yes	—
507	C₂³×C₅₃	—	2	4	no	—
508	C₂³×C₅₃	—	2	4	no	—
509	C₂³×C₅₃	C₂²×Q₈	1	8	yes	—
510	C₂³×C₅₃	C₂⁵	1	4	yes	—
511	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
512	C₂²×D₅₃	—	2	4	no	—
513	C₂²×D₅₃	—	2	2	no	—
514	C₂²×D₅₃	—	2	4	no	—
515	C₂²×D₅₃	—	2	2	no	—
516	C₂²×D₅₃	—	4	8	no	—
517	C₂²×D₅₃	—	4	32	no	—
518	C₂²×D₅₃	—	4	8	no	—
519	C₂²×D₅₃	C₂²×Q₈	1	4	yes	—
520	C₂²×D₅₃	C₂²×Q₈	1	8	yes	—
521	C₂²×D₅₃	C₂²×Q₈	1	32	yes	complemented
522	C₂²×D₅₃	C₂⁵	1	4	yes	—
523	C₂²×D₅₃	C₂⁵	1	2	yes	—
524	Q₈×C₅₃	—	4	8	no	—
525	Q₈×C₅₃	—	4	4	no	—
526	D₄×C₅₃	C₂²×Q₈	1	16	yes	complemented
527	C₂×C₄×C₅₃	—	2	2	no	—
528	C₂×C₄×C₅₃	—	2	4	no	—
529	C₂×C₄×C₅₃	—	2	2	no	—
530	C₂×C₄×C₅₃	—	2	4	no	—
531	C₂×C₄×C₅₃	—	2	2	no	—
532	C₂×C₄×C₅₃	—	2	4	no	—
533	C₂×C₄×C₅₃	—	2	2	no	—
534	C₂×C₄×C₅₃	—	2	2	no	—
535	C₂×C₄×C₅₃	—	2	2	no	—
536	C₂×C₄×C₅₃	—	4	8	no	—
537	C₂×C₄×C₅₃	—	4	8	no	—
538	C₂×C₄×C₅₃	—	4	8	no	—
539	C₂×C₄×C₅₃	C₂²×Q₈	1	4	yes	—
540	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
541	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
542	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
543	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
544	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
545	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
546	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
547	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
548	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
549	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
550	C₂²⋊D₅₃	C₂²×Q₈	1	32	yes	complemented
551	C₂×Dic₅₃	—	2	2	no	—
552	C₂×Dic₅₃	—	2	4	no	—
553	C₂×Dic₅₃	—	2	2	no	—
554	C₂×Dic₅₃	—	2	4	no	—
555	C₂×Dic₅₃	—	2	2	no	—
556	C₂×Dic₅₃	—	2	2	no	—
557	C₂×Dic₅₃	—	2	4	no	—
558	C₂×Dic₅₃	—	2	2	no	—
559	C₂×Dic₅₃	—	2	16	no	—
560	C₂×Dic₅₃	—	4	8	no	—
561	C₂×Dic₅₃	—	4	8	no	—
562	C₂×Dic₅₃	C₂²×Q₈	1	4	yes	—
563	C₂×Dic₅₃	H(5,𝔽₂)	1	4	yes	—
564	C₂×Dic₅₃	C₂⁵	1	2	yes	—
565	C₂×Dic₅₃	C₂⁵	1	4	yes	—
566	C₂×Dic₅₃	C₂⁵	1	2	yes	—
567	C₂×Dic₅₃	C₂⁵	1	4	yes	—
568	C₂×Dic₅₃	C₂⁵	1	2	yes	—
569	C₂×Dic₅₃	C₂⁵	1	2	yes	—
570	C₂×Dic₅₃	C₂⁵	1	4	yes	—
571	C₂×Dic₅₃	C₂⁵	1	2	yes	—
572	C₂×Dic₅₃	C₂⁵	1	2	yes	—
573	C₂×Dic₅₃	C₂⁵	1	2	yes	—
574	D₂₁₂	C₂²×Q₈	1	16	yes	complemented
575	C₄×D₅₃	—	2	8	no	—
576	C₄×D₅₃	—	2	16	no	—
577	C₄×D₅₃	—	4	8	no	—
578	C₄×D₅₃	—	4	8	no	—
579	C₄×D₅₃	—	4	4	no	—
580	C₄×D₅₃	—	4	8	no	—
581	C₄×D₅₃	—	4	8	no	—
582	C₄×D₅₃	—	4	8	no	—
583	C₄×D₅₃	—	4	8	no	—
584	C₄×D₅₃	C₂²×Q₈	1	16	yes	complemented
585	Dic₁₀₆	—	2	8	no	—
586	Dic₁₀₆	—	2	16	no	—
587	Dic₁₀₆	—	2	8	no	—
588	Dic₁₀₆	—	4	8	no	—
589	Dic₁₀₆	—	4	8	no	—
590	Dic₁₀₆	—	4	8	no	—
591	Dic₁₀₆	—	4	4	no	—
592	Dic₁₀₆	—	4	8	no	—
593	C₂×#3501	—	53	1	no	maximal, Sylow
594	C₂²×C₅₃	—	2	4	no	—
595	C₂²×C₅₃	—	2	4	no	—
596	C₂²×C₅₃	—	2	16	no	—
597	C₂²×C₅₃	C₂³×Q₈	1	8	yes	—
598	C₂²×C₅₃	C₂³×Q₈	1	2	yes	—
599	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
600	C₂²×C₅₃	#585	1	2	yes	—
601	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
602	C₂×D₅₃	—	2	4	no	—
603	C₂×D₅₃	—	2	2	no	—
604	C₂×D₅₃	—	2	4	no	—
605	C₂×D₅₃	—	2	2	no	—
606	C₂×D₅₃	—	2	8	no	—
607	C₂×D₅₃	—	2	16	no	—
608	C₂×D₅₃	—	4	32	no	—
609	C₂×D₅₃	C₂³×Q₈	1	4	yes	—
610	C₂×D₅₃	C₂³×Q₈	1	8	yes	—
611	C₄×C₅₃	—	2	2	no	—
612	C₄×C₅₃	—	2	4	no	—
613	C₄×C₅₃	—	2	2	no	—
614	C₄×C₅₃	—	2	4	no	—
615	C₄×C₅₃	—	2	2	no	—
616	C₄×C₅₃	—	2	4	no	—
617	C₄×C₅₃	—	2	2	no	—
618	C₄×C₅₃	—	2	2	no	—
619	C₄×C₅₃	—	2	2	no	—
620	C₄×C₅₃	C₂³×Q₈	1	4	yes	—
621	Dic₅₃	—	2	2	no	—
622	Dic₅₃	—	2	4	no	—
623	Dic₅₃	—	2	2	no	—
624	Dic₅₃	—	2	4	no	—
625	Dic₅₃	—	2	2	no	—
626	Dic₅₃	—	2	2	no	—
627	Dic₅₃	—	2	4	no	—
628	Dic₅₃	—	2	2	no	—
629	Dic₅₃	C₂³×Q₈	1	4	yes	—
630	Dic₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
631	#3501	—	53	32	no	—
632	C₂×#554	—	53	1	no	—
633	C₂×#554	—	53	1	no	—
634	C₂×#554	—	53	2	no	—
635	C₂×#554	—	53	2	no	—
636	C₂×#554	—	53	1	no	—
637	C₂×#554	—	53	1	no	—
638	C₂×#554	—	53	1	no	—
639	C₂×#554	—	53	2	no	—
640	C₂×#554	D₅₃	1	1	yes	characteristic, complemented
641	C₂×D₄×Q₈	—	53	1	no	—
642	C₂×D₄×Q₈	—	53	2	no	—
643	C₂×D₄×Q₈	—	53	1	no	—
644	C₂×#544	—	53	1	no	—
645	C₂×#544	—	53	1	no	—
646	C₂×#543	—	53	2	no	—
647	C₂×#543	—	53	2	no	—
648	C₂×#533	—	53	1	no	—
649	C₂×#533	—	53	1	no	—
650	C₂²×C₂²⋊Q₈	—	53	2	no	—
651	C₂²×C₂²⋊Q₈	—	53	2	no	—
652	C₂×#518	—	53	1	no	—
653	C₂×#518	—	53	1	no	—
654	C₂²×C₄×D₄	—	53	1	no	—
655	C₂×C₅₃	—	2	8	no	—
656	C₂×C₅₃	#3501	1	4	yes	complemented
657	C₂×C₅₃	C₂⁴×Q₈	1	1	yes	characteristic
658	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
660	D₅₃	—	2	4	no	—
661	D₅₃	—	2	8	no	—
662	C₂³×Q₈	—	53	2	no	—
663	C₂³×Q₈	—	53	2	no	—
664	C₂³×D₄	—	53	1	no	—
665	C₂⁴×C₄	—	53	2	no	—
666	#554	—	53	16	no	—
667	#554	—	53	16	no	—
668	#554	—	53	32	no	—
669	#554	—	53	32	no	—
670	#554	—	53	16	no	—
671	#554	—	53	16	no	—
672	#554	—	53	16	no	—
673	#554	—	53	32	no	—
674	#554	C₂×D₅₃	1	16	yes	complemented
675	D₄×Q₈	—	53	16	no	—
676	D₄×Q₈	—	53	32	no	—
677	D₄×Q₈	—	53	16	no	—
678	#544	—	53	16	no	—
679	#544	—	53	16	no	—
680	#543	—	53	32	no	—
681	#543	—	53	32	no	—
682	#533	—	53	16	no	—
683	#533	—	53	16	no	—
684	C₂×C₄⋊Q₈	—	53	1	no	—
685	C₂×C₄⋊Q₈	—	53	2	no	—
686	C₂×C₄⋊Q₈	—	53	1	no	—
687	C₂×C₄⋊Q₈	—	53	1	no	—
688	C₂×C₄⋊Q₈	—	53	1	no	—
689	C₂×C₄⋊Q₈	—	53	2	no	—
690	C₂×C₄⋊Q₈	—	53	1	no	—
691	C₂×C₄⋊Q₈	—	53	1	no	—
692	C₂×C₄⋊Q₈	—	53	1	no	—
693	C₂×C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
694	C₂×#125	—	53	1	no	—
695	C₂×#125	—	53	1	no	—
696	C₂×#125	—	53	2	no	—
697	C₂×#125	—	53	2	no	—
698	C₂×#125	—	53	1	no	—
699	C₂×#125	—	53	1	no	—
700	C₂×#125	—	53	1	no	—
701	C₂×#125	—	53	1	no	—
702	C₂×#125	C₂×D₅₃	1	1	yes	characteristic, complemented
703	C₂×#125	C₂×D₅₃	1	1	yes	characteristic, complemented
704	C₂×C₂²⋊Q₈	—	53	2	no	—
705	C₂×C₂²⋊Q₈	—	53	1	no	—
706	C₂×C₂²⋊Q₈	—	53	2	no	—
707	C₂×C₂²⋊Q₈	—	53	2	no	—
708	C₂×C₂²⋊Q₈	—	53	2	no	—
709	C₂×C₂²⋊Q₈	—	53	2	no	—
710	C₂×C₂²⋊Q₈	—	53	2	no	—
711	C₂×C₂²⋊Q₈	—	53	32	no	—
712	C₂×C₂²⋊Q₈	—	53	1	no	—
713	C₂×C₂²⋊Q₈	—	53	2	no	—
714	C₂×C₂²⋊Q₈	—	53	1	no	—
715	C₂×C₂²⋊Q₈	—	53	2	no	—
716	C₂×C₂²⋊Q₈	—	53	2	no	—
717	C₂×C₂²⋊Q₈	—	53	2	no	—
718	C₂×C₂²⋊Q₈	—	53	2	no	—
719	C₂×C₂²⋊Q₈	—	53	2	no	—
720	C₂×C₂²⋊Q₈	—	53	2	no	—
721	C₂×C₂²⋊Q₈	—	53	2	no	—
722	C₂×C₂²⋊Q₈	—	53	2	no	—
723	C₂×C₂²⋊Q₈	—	53	2	no	—
724	C₂×C₂²⋊Q₈	—	53	2	no	—
725	C₂×C₂²⋊Q₈	—	53	2	no	—
726	C₂×C₂²⋊Q₈	—	53	2	no	—
727	C₂×C₂²⋊Q₈	—	53	1	no	—
728	C₂×C₂²⋊Q₈	—	53	2	no	—
729	C₂×C₂²⋊Q₈	—	53	2	no	—
730	C₂×C₂²⋊Q₈	—	53	32	no	—
731	C₂×C₂²⋊Q₈	—	53	2	no	—
732	C₂×C₂²⋊Q₈	—	53	2	no	—
733	C₂×C₂²⋊Q₈	—	53	2	no	—
734	C₂×C₂²⋊Q₈	—	53	2	no	—
735	C₂×C₂²⋊Q₈	—	53	2	no	—
736	C₂×C₂²⋊Q₈	—	53	2	no	—
737	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
738	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
739	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
740	#518	—	53	16	no	—
741	#518	—	53	16	no	—
742	C₂×C₄×Q₈	—	53	2	no	—
743	C₂×C₄×Q₈	—	53	2	no	—
744	C₂×C₄×Q₈	—	53	1	no	—
745	C₂×C₄×Q₈	—	53	1	no	—
746	C₂×C₄×Q₈	—	53	1	no	—
747	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
748	C₂×C₄×D₄	—	53	1	no	—
749	C₂×C₄×D₄	—	53	1	no	—
750	C₂×C₄×D₄	—	53	1	no	—
751	C₂×C₄×D₄	—	53	2	no	—
752	C₂×C₄×D₄	—	53	2	no	—
753	C₂×C₄×D₄	—	53	2	no	—
754	C₂×C₄×D₄	—	53	16	no	—
755	C₂×C₄×D₄	—	53	1	no	—
756	C₂×C₄×D₄	—	53	1	no	—
757	C₂×C₄×D₄	—	53	1	no	—
758	C₂×C₄×D₄	—	53	2	no	—
759	C₂×C₄×D₄	—	53	2	no	—
760	C₂×C₄×D₄	—	53	2	no	—
761	C₂×C₄×D₄	—	53	1	no	—
762	C₂×C₄×D₄	—	53	1	no	—
763	C₂×C₄×D₄	—	53	1	no	—
764	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
765	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
766	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
767	C₂×#117	—	53	1	no	—
768	C₂×#117	—	53	1	no	—
769	C₂×#117	—	53	1	no	—
770	C₂×#117	—	53	1	no	—
771	C₂²×C₄⋊C₄	—	53	2	no	—
772	C₂²×C₄⋊C₄	—	53	2	no	—
773	C₂²×C₄⋊C₄	—	53	1	no	—
774	C₂²×C₄⋊C₄	—	53	2	no	—
775	C₂²×C₄⋊C₄	—	53	2	no	—
776	C₂²×C₄⋊C₄	—	53	2	no	—
777	C₂²×C₄⋊C₄	C₂×D₅₃	1	2	yes	complemented
778	C₂²×C₂²⋊C₄	—	53	2	no	—
779	C₂²×C₂²⋊C₄	—	53	2	no	—
780	C₂²×C₂²⋊C₄	—	53	2	no	—
781	C₂²×C₂²⋊C₄	—	53	2	no	—
782	C₂²×C₂²⋊C₄	—	53	2	no	—
783	C₂²×C₄²	—	53	1	no	—
784	C₅₃	C₂×#3501	1	1	yes	characteristic, complemented, Sylow
785	C₂⁵	—	53	2	no	—
786	C₂²×Q₈	—	53	16	no	—
787	C₂²×Q₈	—	53	2	no	—
788	C₂²×Q₈	—	53	1	no	—
789	C₂²×Q₈	—	53	1	no	—
790	C₂²×Q₈	—	53	2	no	—
791	C₂²×Q₈	—	53	1	no	—
792	C₂²×Q₈	—	53	2	no	—
793	C₂²×Q₈	—	53	2	no	—
794	C₂²×Q₈	—	53	2	no	—
795	C₂²×Q₈	—	53	16	no	—
796	C₂²×Q₈	—	212	8	no	—
797	C₂²×Q₈	—	212	8	no	—
798	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
799	C₂²×Q₈	C₂²×D₅₃	1	2	yes	—
800	C₂²×D₄	—	53	2	no	—
801	C₂²×D₄	—	53	16	no	—
802	C₂²×D₄	—	53	8	no	—
803	C₂²×D₄	—	53	1	no	—
804	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
805	C₂³×C₄	—	53	1	no	—
806	C₂³×C₄	—	53	2	no	—
807	C₂³×C₄	—	53	2	no	—
808	C₂³×C₄	—	53	2	no	—
809	C₂³×C₄	—	53	2	no	—
810	C₂³×C₄	—	53	1	no	—
811	C₂³×C₄	—	53	1	no	—
812	C₂³×C₄	—	53	2	no	—
813	C₂³×C₄	—	53	2	no	—
814	C₂³×C₄	—	53	2	no	—
815	C₂³×C₄	—	53	2	no	—
816	C₂³×C₄	—	53	2	no	—
817	C₂³×C₄	—	53	2	no	—
818	C₂³×C₄	—	53	16	no	—
819	C₂³×C₄	—	212	8	no	—
820	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
821	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
822	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
823	C₄⋊Q₈	—	53	8	no	—
824	C₄⋊Q₈	—	53	16	no	—
825	C₄⋊Q₈	—	53	8	no	—
826	C₄⋊Q₈	—	53	8	no	—
827	C₄⋊Q₈	—	53	8	no	—
828	C₄⋊Q₈	—	53	16	no	—
829	C₄⋊Q₈	—	53	8	no	—
830	C₄⋊Q₈	—	53	8	no	—
831	C₄⋊Q₈	—	53	8	no	—
832	C₄⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
833	#125	—	53	8	no	—
834	#125	—	53	8	no	—
835	#125	—	53	16	no	—
836	#125	—	53	16	no	—
837	#125	—	53	8	no	—
838	#125	—	53	8	no	—
839	#125	—	53	8	no	—
840	#125	—	53	8	no	—
841	#125	C₂²×D₅₃	1	8	yes	complemented
842	#125	C₂²×D₅₃	1	8	yes	complemented
843	C₂²⋊Q₈	—	53	16	no	—
844	C₂²⋊Q₈	—	53	8	no	—
845	C₂²⋊Q₈	—	53	16	no	—
846	C₂²⋊Q₈	—	53	16	no	—
847	C₂²⋊Q₈	—	53	16	no	—
848	C₂²⋊Q₈	—	53	16	no	—
849	C₂²⋊Q₈	—	53	16	no	—
850	C₂²⋊Q₈	—	53	8	no	—
851	C₂²⋊Q₈	—	53	16	no	—
852	C₂²⋊Q₈	—	53	8	no	—
853	C₂²⋊Q₈	—	53	16	no	—
854	C₂²⋊Q₈	—	53	16	no	—
855	C₂²⋊Q₈	—	53	16	no	—
856	C₂²⋊Q₈	—	53	16	no	—
857	C₂²⋊Q₈	—	53	16	no	—
858	C₂²⋊Q₈	—	53	16	no	—
859	C₂²⋊Q₈	—	53	16	no	—
860	C₂²⋊Q₈	—	53	16	no	—
861	C₂²⋊Q₈	—	53	8	no	—
862	C₂²⋊Q₈	—	53	16	no	—
863	C₂²⋊Q₈	—	53	16	no	—
864	C₂²⋊Q₈	—	53	16	no	—
865	C₂²⋊Q₈	—	53	16	no	—
866	C₂²⋊Q₈	—	53	16	no	—
867	C₂²⋊Q₈	—	53	16	no	—
868	C₂²⋊Q₈	—	53	16	no	—
869	C₂²⋊Q₈	—	53	16	no	—
870	C₂²⋊Q₈	—	53	16	no	—
871	C₂²⋊Q₈	—	53	16	no	—
872	C₂²⋊Q₈	—	53	16	no	—
873	C₂²⋊Q₈	—	53	16	no	—
874	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
875	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
876	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
877	C₄×Q₈	—	53	16	no	—
878	C₄×Q₈	—	53	16	no	—
879	C₄×Q₈	—	53	8	no	—
880	C₄×Q₈	—	53	8	no	—
881	C₄×Q₈	—	53	8	no	—
882	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
883	C₄×D₄	—	53	8	no	—
884	C₄×D₄	—	53	8	no	—
885	C₄×D₄	—	53	8	no	—
886	C₄×D₄	—	53	16	no	—
887	C₄×D₄	—	53	16	no	—
888	C₄×D₄	—	53	16	no	—
889	C₄×D₄	—	53	8	no	—
890	C₄×D₄	—	53	8	no	—
891	C₄×D₄	—	53	8	no	—
892	C₄×D₄	—	53	16	no	—
893	C₄×D₄	—	53	16	no	—
894	C₄×D₄	—	53	16	no	—
895	C₄×D₄	—	53	8	no	—
896	C₄×D₄	—	53	8	no	—
897	C₄×D₄	—	53	8	no	—
898	C₄×D₄	C₂²×D₅₃	1	8	yes	—
899	C₄×D₄	C₂²×D₅₃	1	8	yes	—
900	C₄×D₄	C₂²×D₅₃	1	8	yes	—
901	#117	—	53	8	no	—
902	#117	—	53	8	no	—
903	#117	—	53	8	no	—
904	#117	—	53	8	no	—
905	C₂×C₄⋊C₄	—	53	1	no	—
906	C₂×C₄⋊C₄	—	53	2	no	—
907	C₂×C₄⋊C₄	—	53	1	no	—
908	C₂×C₄⋊C₄	—	53	2	no	—
909	C₂×C₄⋊C₄	—	53	1	no	—
910	C₂×C₄⋊C₄	—	53	1	no	—
911	C₂×C₄⋊C₄	—	53	2	no	—
912	C₂×C₄⋊C₄	—	53	1	no	—
913	C₂×C₄⋊C₄	—	53	2	no	—
914	C₂×C₄⋊C₄	—	53	2	no	—
915	C₂×C₄⋊C₄	—	53	2	no	—
916	C₂×C₄⋊C₄	—	53	2	no	—
917	C₂×C₄⋊C₄	—	53	2	no	—
918	C₂×C₄⋊C₄	—	53	2	no	—
919	C₂×C₄⋊C₄	—	53	2	no	—
920	C₂×C₄⋊C₄	—	53	2	no	—
921	C₂×C₄⋊C₄	—	53	2	no	—
922	C₂×C₄⋊C₄	—	53	16	no	—
923	C₂×C₄⋊C₄	—	53	16	no	—
924	C₂×C₄⋊C₄	—	53	1	no	—
925	C₂×C₄⋊C₄	—	53	1	no	—
926	C₂×C₄⋊C₄	—	53	1	no	—
927	C₂×C₄⋊C₄	—	53	1	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	2	no	—
933	C₂×C₄⋊C₄	—	53	1	no	—
934	C₂×C₄⋊C₄	—	53	1	no	—
935	C₂×C₄⋊C₄	—	53	2	no	—
936	C₂×C₄⋊C₄	—	53	1	no	—
937	C₂×C₄⋊C₄	—	53	8	no	—
938	C₂×C₄⋊C₄	—	53	16	no	—
939	C₂×C₄⋊C₄	—	53	16	no	—
940	C₂×C₄⋊C₄	—	53	16	no	—
941	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
943	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
945	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
947	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
948	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
951	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂²×D₅₃	1	16	yes	complemented
953	C₂×C₂²⋊C₄	—	53	2	no	—
954	C₂×C₂²⋊C₄	—	53	2	no	—
955	C₂×C₂²⋊C₄	—	53	2	no	—
956	C₂×C₂²⋊C₄	—	53	2	no	—
957	C₂×C₂²⋊C₄	—	53	1	no	—
958	C₂×C₂²⋊C₄	—	53	1	no	—
959	C₂×C₂²⋊C₄	—	53	2	no	—
960	C₂×C₂²⋊C₄	—	53	1	no	—
961	C₂×C₂²⋊C₄	—	53	1	no	—
962	C₂×C₂²⋊C₄	—	53	2	no	—
963	C₂×C₂²⋊C₄	—	53	2	no	—
964	C₂×C₂²⋊C₄	—	53	2	no	—
965	C₂×C₂²⋊C₄	—	53	2	no	—
966	C₂×C₂²⋊C₄	—	53	2	no	—
967	C₂×C₂²⋊C₄	—	53	2	no	—
968	C₂×C₂²⋊C₄	—	53	16	no	—
969	C₂×C₂²⋊C₄	—	53	16	no	—
970	C₂×C₂²⋊C₄	—	53	16	no	—
971	C₂×C₂²⋊C₄	—	53	16	no	—
972	C₂×C₂²⋊C₄	—	53	16	no	—
973	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
974	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
975	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
976	C₂×C₄²	—	53	2	no	—
977	C₂×C₄²	—	53	2	no	—
978	C₂×C₄²	—	53	1	no	—
979	C₂×C₄²	—	53	1	no	—
980	C₂×C₄²	—	53	1	no	—
981	C₂×C₄²	—	53	1	no	—
982	C₂×C₄²	—	53	1	no	—
983	C₂×C₄²	—	53	8	no	—
984	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
985	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
986	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
987	C₂⁴	—	53	1	no	—
988	C₂⁴	—	53	2	no	—
989	C₂⁴	—	53	16	no	—
990	C₂⁴	—	53	8	no	—
991	C₂⁴	—	212	4	no	—
992	C₂⁴	—	212	4	no	—
993	C₂⁴	C₂³×D₅₃	1	2	yes	—
994	C₂×Q₈	—	4	4	no	—
995	C₂×Q₈	—	4	2	no	—
996	C₂×Q₈	—	53	8	no	—
997	C₂×Q₈	—	53	4	no	—
998	C₂×Q₈	—	53	4	no	—
999	C₂×Q₈	—	53	8	no	—
1000	C₂×Q₈	—	53	4	no	—
1001	C₂×Q₈	—	53	8	no	—
1002	C₂×Q₈	—	53	8	no	—
1003	C₂×Q₈	—	53	8	no	—
1004	C₂×Q₈	—	106	4	no	—
1005	C₂×Q₈	—	106	8	no	—
1006	C₂×Q₈	—	106	4	no	—
1007	C₂×Q₈	—	212	4	no	—
1008	C₂×Q₈	—	212	2	no	—
1009	C₂×Q₈	—	212	4	no	—
1010	C₂×Q₈	—	212	4	no	—
1011	C₂×Q₈	—	212	4	no	—
1012	C₂×Q₈	—	212	32	no	—
1013	C₂×Q₈	—	212	32	no	—
1014	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1015	C₂×Q₈	C₂³×D₅₃	1	8	yes	—
1016	C₂×D₄	—	53	16	no	—
1017	C₂×D₄	—	53	8	no	—
1018	C₂×D₄	—	53	64	no	—
1019	C₂×D₄	—	53	8	no	—
1020	C₂×D₄	—	53	4	no	—
1021	C₂×D₄	Q₈×D₅₃	1	8	yes	complemented
1022	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1023	C₂²×C₄	—	4	4	no	—
1024	C₂²×C₄	—	4	4	no	—
1025	C₂²×C₄	—	4	4	no	—
1026	C₂²×C₄	—	53	1	no	—
1027	C₂²×C₄	—	53	1	no	—
1028	C₂²×C₄	—	53	8	no	—
1029	C₂²×C₄	—	53	4	no	—
1030	C₂²×C₄	—	53	8	no	—
1031	C₂²×C₄	—	53	1	no	—
1032	C₂²×C₄	—	53	1	no	—
1033	C₂²×C₄	—	53	2	no	—
1034	C₂²×C₄	—	53	1	no	—
1035	C₂²×C₄	—	53	1	no	—
1036	C₂²×C₄	—	53	2	no	—
1037	C₂²×C₄	—	53	1	no	—
1038	C₂²×C₄	—	53	2	no	—
1039	C₂²×C₄	—	53	8	no	—
1040	C₂²×C₄	—	53	8	no	—
1041	C₂²×C₄	—	53	4	no	—
1042	C₂²×C₄	—	53	8	no	—
1043	C₂²×C₄	—	53	4	no	—
1044	C₂²×C₄	—	53	8	no	—
1045	C₂²×C₄	—	53	8	no	—
1046	C₂²×C₄	—	53	8	no	—
1047	C₂²×C₄	—	53	8	no	—
1048	C₂²×C₄	—	53	8	no	—
1049	C₂²×C₄	—	53	8	no	—
1050	C₂²×C₄	—	106	4	no	—
1051	C₂²×C₄	—	106	8	no	—
1052	C₂²×C₄	—	106	8	no	—
1053	C₂²×C₄	—	212	4	no	—
1054	C₂²×C₄	—	212	4	no	—
1055	C₂²×C₄	—	212	2	no	—
1056	C₂²×C₄	—	212	4	no	—
1057	C₂²×C₄	—	212	4	no	—
1058	C₂²×C₄	—	212	4	no	—
1059	C₂²×C₄	—	212	4	no	—
1060	C₂²×C₄	—	212	32	no	—
1061	C₂²×C₄	—	212	4	no	—
1062	C₂²×C₄	—	212	4	no	—
1063	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1064	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1065	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1066	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1067	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1068	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1069	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1070	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1071	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1072	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1073	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1074	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1075	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1076	C₄⋊C₄	—	53	4	no	—
1077	C₄⋊C₄	—	53	8	no	—
1078	C₄⋊C₄	—	53	4	no	—
1079	C₄⋊C₄	—	53	8	no	—
1080	C₄⋊C₄	—	53	4	no	—
1081	C₄⋊C₄	—	53	4	no	—
1082	C₄⋊C₄	—	53	8	no	—
1083	C₄⋊C₄	—	53	4	no	—
1084	C₄⋊C₄	—	53	8	no	—
1085	C₄⋊C₄	—	53	8	no	—
1086	C₄⋊C₄	—	53	8	no	—
1087	C₄⋊C₄	—	53	8	no	—
1088	C₄⋊C₄	—	53	8	no	—
1089	C₄⋊C₄	—	53	8	no	—
1090	C₄⋊C₄	—	53	8	no	—
1091	C₄⋊C₄	—	53	8	no	—
1092	C₄⋊C₄	—	53	8	no	—
1093	C₄⋊C₄	—	53	4	no	—
1094	C₄⋊C₄	—	53	4	no	—
1095	C₄⋊C₄	—	53	4	no	—
1096	C₄⋊C₄	—	53	4	no	—
1097	C₄⋊C₄	—	53	4	no	—
1098	C₄⋊C₄	—	53	4	no	—
1099	C₄⋊C₄	—	53	4	no	—
1100	C₄⋊C₄	—	53	4	no	—
1101	C₄⋊C₄	—	53	8	no	—
1102	C₄⋊C₄	—	53	4	no	—
1103	C₄⋊C₄	—	53	4	no	—
1104	C₄⋊C₄	—	53	8	no	—
1105	C₄⋊C₄	—	53	4	no	—
1106	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1107	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1108	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1109	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1110	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1111	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1112	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1113	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1114	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1115	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1116	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1117	C₂²⋊C₄	—	53	8	no	—
1118	C₂²⋊C₄	—	53	8	no	—
1119	C₂²⋊C₄	—	53	8	no	—
1120	C₂²⋊C₄	—	53	8	no	—
1121	C₂²⋊C₄	—	53	4	no	—
1122	C₂²⋊C₄	—	53	4	no	—
1123	C₂²⋊C₄	—	53	8	no	—
1124	C₂²⋊C₄	—	53	4	no	—
1125	C₂²⋊C₄	—	53	4	no	—
1126	C₂²⋊C₄	—	53	8	no	—
1127	C₂²⋊C₄	—	53	8	no	—
1128	C₂²⋊C₄	—	53	8	no	—
1129	C₂²⋊C₄	—	53	8	no	—
1130	C₂²⋊C₄	—	53	8	no	—
1131	C₂²⋊C₄	—	53	8	no	—
1132	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1133	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1134	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1135	C₄²	—	53	4	no	—
1136	C₄²	—	53	4	no	—
1137	C₄²	—	53	4	no	—
1138	C₄²	—	53	8	no	—
1139	C₄²	—	53	8	no	—
1140	C₄²	—	53	4	no	—
1141	C₄²	—	53	4	no	—
1142	C₄²	C₂³×D₅₃	1	4	yes	—
1143	C₄²	C₂³×D₅₃	1	4	yes	—
1144	C₄²	C₂³×D₅₃	1	4	yes	—
1145	C₂³	—	2	4	no	—
1146	C₂³	—	2	4	no	—
1147	C₂³	—	53	4	no	—
1148	C₂³	—	53	8	no	—
1149	C₂³	—	53	2	no	—
1150	C₂³	—	53	4	no	—
1151	C₂³	—	53	32	no	—
1152	C₂³	—	106	4	no	—
1153	C₂³	—	106	2	no	—
1154	C₂³	—	106	4	no	—
1155	C₂³	—	106	2	no	—
1156	C₂³	—	212	8	no	—
1157	C₂³	—	212	32	no	—
1158	C₂³	—	212	8	no	—
1159	C₂³	C₂×Q₈×D₅₃	1	8	yes	—
1160	C₂³	C₂⁴×D₅₃	1	4	yes	—
1161	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1162	Q₈	—	4	8	no	—
1163	Q₈	—	4	4	no	—
1164	Q₈	—	106	8	no	—
1165	Q₈	—	106	16	no	—
1166	Q₈	—	106	8	no	—
1167	Q₈	—	212	8	no	—
1168	Q₈	—	212	4	no	—
1169	Q₈	—	212	8	no	—
1170	Q₈	—	212	8	no	—
1171	Q₈	—	212	8	no	—
1172	D₄	—	53	32	no	—
1173	D₄	—	53	16	no	—
1174	D₄	C₂×Q₈×D₅₃	1	16	yes	complemented
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	4	no	—
1178	C₂×C₄	—	2	4	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	4	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	4	8	no	—
1185	C₂×C₄	—	4	8	no	—
1186	C₂×C₄	—	4	8	no	—
1187	C₂×C₄	—	53	4	no	—
1188	C₂×C₄	—	53	4	no	—
1189	C₂×C₄	—	53	2	no	—
1190	C₂×C₄	—	53	2	no	—
1191	C₂×C₄	—	53	16	no	—
1192	C₂×C₄	—	53	2	no	—
1193	C₂×C₄	—	53	2	no	—
1194	C₂×C₄	—	53	4	no	—
1195	C₂×C₄	—	53	2	no	—
1196	C₂×C₄	—	53	2	no	—
1197	C₂×C₄	—	53	4	no	—
1198	C₂×C₄	—	53	2	no	—
1199	C₂×C₄	—	53	4	no	—
1200	C₂×C₄	—	106	8	no	—
1201	C₂×C₄	—	106	16	no	—
1202	C₂×C₄	—	106	16	no	—
1203	C₂×C₄	—	106	4	no	—
1204	C₂×C₄	—	106	2	no	—
1205	C₂×C₄	—	106	4	no	—
1206	C₂×C₄	—	106	2	no	—
1207	C₂×C₄	—	106	2	no	—
1208	C₂×C₄	—	106	4	no	—
1209	C₂×C₄	—	106	2	no	—
1210	C₂×C₄	—	106	2	no	—
1211	C₂×C₄	—	212	8	no	—
1212	C₂×C₄	—	212	8	no	—
1213	C₂×C₄	—	212	4	no	—
1214	C₂×C₄	—	212	8	no	—
1215	C₂×C₄	—	212	8	no	—
1216	C₂×C₄	—	212	8	no	—
1217	C₂×C₄	—	212	8	no	—
1218	C₂×C₄	—	212	8	no	—
1219	C₂×C₄	—	212	8	no	—
1220	C₂×C₄	C₂×Q₈×D₅₃	1	4	yes	—
1221	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1222	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1223	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1224	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1225	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1226	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1227	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1228	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1229	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1230	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1231	C₂²	—	2	16	no	—
1232	C₂²	—	2	4	no	—
1233	C₂²	—	2	4	no	—
1234	C₂²	—	53	4	no	—
1235	C₂²	—	53	8	no	—
1236	C₂²	—	106	8	no	—
1237	C₂²	—	106	16	no	—
1238	C₂²	—	106	4	no	—
1239	C₂²	—	106	2	no	—
1240	C₂²	—	106	4	no	—
1241	C₂²	—	106	2	no	—
1242	C₂²	—	212	32	no	—
1243	C₂²	C₂²×Q₈×D₅₃	1	8	yes	—
1244	C₂²	C₂²×Q₈×D₅₃	1	2	yes	—
1245	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	—
1246	C₂²	#16811459	1	2	yes	—
1247	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1248	C₄	—	2	2	no	—
1249	C₄	—	2	2	no	—
1250	C₄	—	2	4	no	—
1251	C₄	—	2	4	no	—
1252	C₄	—	2	2	no	—
1253	C₄	—	2	2	no	—
1254	C₄	—	2	4	no	—
1255	C₄	—	2	2	no	—
1256	C₄	—	2	2	no	—
1257	C₄	—	53	4	no	—
1258	C₄	—	53	4	no	—
1259	C₄	—	106	4	no	—
1260	C₄	—	106	2	no	—
1261	C₄	—	106	4	no	—
1262	C₄	—	106	2	no	—
1263	C₄	—	106	2	no	—
1264	C₄	—	106	4	no	—
1265	C₄	—	106	2	no	—
1266	C₄	—	106	2	no	—
1267	C₄	C₂²×Q₈×D₅₃	1	4	yes	—
1268	C₂	—	2	8	no	—
1269	C₂	—	106	4	no	—
1270	C₂	—	106	8	no	—
1271	C₂	#20288514	1	4	yes	direct product factor
1272	C₂	C₂³×Q₈×D₅₃	1	1	yes	characteristic
1273	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1274	C₂	C₂×#16811459	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#554	C₂
socle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×D₄×D₅₃	C₂²
hypercenter	C₂×#554	D₅₃
hypocenter	C₅₃	C₂×#3501
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#554

Complements

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

N	H ≅ G/N	type
1. #20288514	C₂	direct (N × H)
2. C₂×#16811333	C₂	semidirect
3. C₂×#16811332	C₂	semidirect
4. C₂×#16811332	C₂	semidirect
5. C₂×#16811329	C₂	semidirect
6. C₂×#16811329	C₂	semidirect
7. C₂×#16811328	C₂	semidirect
8. C₂×#16811327	C₂	semidirect
9. C₂×#16811327	C₂	semidirect
10. C₂×D₄×Dic₁₀₆	C₂	semidirect
11. C₂×#16811288	C₂	semidirect
12. C₂×#16811286	C₂	semidirect
13. C₂×#16811253	C₂	semidirect
14. C₂×#16811250	C₂	semidirect
15. C₂×#16811248	C₂	semidirect
16. C₂×#16811248	C₂	semidirect
17. C₂×#16811179	C₂	semidirect
18. C₂×#16811177	C₂	semidirect
19. C₂²×#13133195	C₂	semidirect
20. C₂×C₂²⋊Q₈×D₅₃	C₂	semidirect
24. C₂×C₅₃×#554	C₂	semidirect
25. C₂³×Dic₁₀₆	C₂²	semidirect
26. C₂²×Q₈×D₅₃	C₂²	semidirect
29. #16811333	C₂²	semidirect
30. #16811332	C₂²	semidirect
31. #16811332	C₂²	semidirect
32. #16811329	C₂²	semidirect
33. #16811329	C₂²	semidirect
34. #16811328	C₂²	semidirect
35. #16811327	C₂²	semidirect
36. #16811327	C₂²	semidirect
37. D₄×Dic₁₀₆	C₂²	semidirect
38. #16811288	C₂²	semidirect
39. #16811286	C₂²	semidirect
40. #16811253	C₂²	semidirect
41. #16811250	C₂²	semidirect
42. #16811248	C₂²	semidirect
43. #16811248	C₂²	semidirect
44. #16811179	C₂²	semidirect
45. #16811177	C₂²	semidirect
46. C₂×#13133217	C₂²	semidirect
47. C₂×#13133216	C₂²	semidirect
48. C₂×#13133216	C₂²	semidirect
49. C₂×#13133216	C₂²	semidirect
50. C₂×#13133216	C₂²	semidirect
51. C₂×#13133216	C₂²	semidirect
52. C₂×#13133216	C₂²	semidirect
53. C₂×#13133215	C₂²	semidirect
54. C₂×#13133215	C₂²	semidirect
55. C₂×#13133209	C₂²	semidirect
56. C₂×#13133209	C₂²	semidirect
57. C₂×#13133208	C₂²	semidirect
58. C₂×#13133208	C₂²	semidirect
59. C₂×#13133207	C₂²	semidirect
60. C₂×#13133207	C₂²	semidirect
61. C₂×#13133207	C₂²	semidirect
62. C₂×#13133207	C₂²	semidirect
65. C₂×#13133197	C₂²	semidirect
66. C₂×#13133197	C₂²	semidirect
67. C₂×#13133196	C₂²	semidirect
68. C₂×#13133196	C₂²	semidirect
69. C₂×#13133196	C₂²	semidirect
76. C₂×#13133195	C₂²	semidirect
77. C₂×#13133195	C₂²	semidirect
78. C₂×#13133195	C₂²	semidirect
79. C₂×#13133195	C₂²	semidirect
80. C₂×#13133195	C₂²	semidirect
81. C₂×#13133195	C₂²	semidirect
82. C₂×#13133195	C₂²	semidirect
83. C₂×#13133195	C₂²	semidirect
84. C₂×#13133195	C₂²	semidirect
85. C₂×#13133194	C₂²	semidirect
86. C₂×#13133194	C₂²	semidirect
87. C₂×#13133194	C₂²	semidirect
88. C₂×#13133194	C₂²	semidirect
89. C₂×#13133194	C₂²	semidirect
90. C₂×#13133194	C₂²	semidirect
93. C₂×#13133193	C₂²	semidirect
94. C₂×#13133193	C₂²	semidirect
95. C₂²⋊Q₈×D₅₃	C₂²	semidirect
98. C₂×C₄×Dic₁₀₆	C₂²	semidirect
99. C₂×C₄×Dic₁₀₆	C₂²	semidirect
100. C₂×C₄×Dic₁₀₆	C₂²	semidirect
101. C₂×#13133182	C₂²	semidirect
102. C₂×#13133182	C₂²	semidirect
123. C₂²×#11719919	C₂²	semidirect
124. C₂²×#11719919	C₂²	semidirect
126. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
127. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
128. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
135. C₅₃×#554	C₂²	semidirect
136. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
137. C₂×#125×C₅₃	C₂²	semidirect
138. C₂×#125×C₅₃	C₂²	semidirect
139. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
140. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
142. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
146. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
157. C₂²×Dic₁₀₆	C₂³	semidirect
159. C₂×Q₈×D₅₃	C₂³	semidirect
162. C₂×D₄×D₅₃	Q₈	semidirect
179. #13133217	C₂³	semidirect
180. #13133216	C₂³	semidirect
181. #13133216	C₂³	semidirect
182. #13133216	C₂³	semidirect
183. #13133216	C₂³	semidirect
184. #13133216	C₂³	semidirect
185. #13133216	C₂³	semidirect
186. #13133215	C₂³	semidirect
187. #13133215	C₂³	semidirect
188. #13133209	C₂³	semidirect
189. #13133209	C₂³	semidirect
190. #13133208	C₂³	semidirect
191. #13133208	C₂³	semidirect
192. #13133207	C₂³	semidirect
193. #13133207	C₂³	semidirect
194. #13133207	C₂³	semidirect
195. #13133207	C₂³	semidirect
198. #13133197	C₂³	semidirect
199. #13133197	C₂³	semidirect
200. #13133196	C₂³	semidirect
201. #13133196	C₂³	semidirect
202. #13133196	C₂³	semidirect
209. #13133195	C₂³	semidirect
210. #13133195	C₂³	semidirect
211. #13133195	C₂³	semidirect
212. #13133195	C₂³	semidirect
213. #13133195	C₂³	semidirect
214. #13133195	C₂³	semidirect
215. #13133195	C₂³	semidirect
216. #13133195	C₂³	semidirect
217. #13133194	C₂³	semidirect
218. #13133194	C₂³	semidirect
219. #13133194	C₂³	semidirect
220. #13133194	C₂³	semidirect
221. #13133194	C₂³	semidirect
222. #13133194	C₂³	semidirect
225. #13133193	C₂³	semidirect
226. #13133193	C₂³	semidirect
227. C₄×Dic₁₀₆	C₂³	semidirect
228. C₄×Dic₁₀₆	C₂³	semidirect
229. C₄×Dic₁₀₆	C₂³	semidirect
230. #13133182	C₂³	semidirect
231. #13133182	C₂³	semidirect
281. C₂×#11719919	C₂³	semidirect
282. C₂×#11719919	C₂³	semidirect
284. C₄⋊C₄×D₅₃	C₂³	semidirect
285. C₄⋊C₄×D₅₃	C₂³	semidirect
286. C₄⋊C₄×D₅₃	C₂³	semidirect
321. C₄⋊Q₈×C₅₃	C₂³	semidirect
322. #125×C₅₃	C₂³	semidirect
323. #125×C₅₃	C₂³	semidirect
324. C₂²⋊Q₈×C₅₃	C₂³	semidirect
325. C₂²⋊Q₈×C₅₃	C₂³	semidirect
326. C₂²⋊Q₈×C₅₃	C₂³	semidirect
327. C₄×Q₈×C₅₃	C₂³	semidirect
342. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
352. C₂³×D₅₃	C₂×Q₈	semidirect
360. C₂×D₄×C₅₃	C₂×Q₈	semidirect
378. C₂×C₂²⋊D₅₃	C₂×Q₈	semidirect
397. D₄×D₅₃	C₂×Q₈	semidirect
398. C₂×D₂₁₂	C₂×Q₈	semidirect
410. C₂×C₄×D₅₃	C₂×Q₈	semidirect
521. C₂²×D₅₃	C₂²×Q₈	semidirect
526. D₄×C₅₃	C₂²×Q₈	semidirect
550. C₂²⋊D₅₃	C₂²×Q₈	semidirect
574. D₂₁₂	C₂²×Q₈	semidirect
584. C₄×D₅₃	C₂²×Q₈	semidirect
640. C₂×#554	D₅₃	semidirect
656. C₂×C₅₃	#3501	semidirect
674. #554	C₂×D₅₃	semidirect
693. C₂×C₄⋊Q₈	C₂×D₅₃	semidirect
702. C₂×#125	C₂×D₅₃	semidirect
703. C₂×#125	C₂×D₅₃	semidirect
737. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
738. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
739. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
747. C₂×C₄×Q₈	C₂×D₅₃	semidirect
777. C₂²×C₄⋊C₄	C₂×D₅₃	semidirect
784. C₅₃	C₂×#3501	semidirect
832. C₄⋊Q₈	C₂²×D₅₃	semidirect
841. #125	C₂²×D₅₃	semidirect
842. #125	C₂²×D₅₃	semidirect
874. C₂²⋊Q₈	C₂²×D₅₃	semidirect
875. C₂²⋊Q₈	C₂²×D₅₃	semidirect
876. C₂²⋊Q₈	C₂²×D₅₃	semidirect
882. C₄×Q₈	C₂²×D₅₃	semidirect
952. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1021. C₂×D₄	Q₈×D₅₃	semidirect
1174. D₄	C₂×Q₈×D₅₃	semidirect
1271. C₂	#20288514	direct (N × H)

Maximal subgroups

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

subgroup	index
#20288514	2
C₂×#16811333	2
C₂×#16811332	2
C₂×#16811329	2
C₂×#16811328	2
C₂×#16811327	2
C₂×D₄×Dic₁₀₆	2
C₂×#16811288	2
C₂×#16811286	2
C₂×#16811253	2
C₂×#16811250	2
C₂×#16811248	2
C₂×#16811179	2
C₂×#16811177	2
C₂²×#13133195	2
C₂×C₂²⋊Q₈×D₅₃	2
C₂×#16811095	2
C₂×C₄×D₄×D₅₃	2
C₂×C₅₃×#554	2
C₂×#3501	53

Subgroups — C2×#20288514 #28291993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20288514 #28291993