Subgroups — C₂×#20288661 #28292071

Order 13568.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288661	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811355	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811334	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811324	C₂	1	2	yes	maximal, complemented
5	C₂×#16811320	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811307	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16811303	C₂	1	2	yes	maximal, complemented
8	C₂×#16811298	C₂	1	2	yes	maximal, complemented
9	C₂×#16811276	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811266	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16811266	C₂	1	2	yes	maximal, complemented
12	C₂×#16811264	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16811257	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16811224	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16811219	C₂	1	2	yes	maximal, complemented
16	C₂×#16811209	C₂	1	2	yes	maximal, complemented
17	C₂×#16811160	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16811151	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16811136	C₂	1	2	yes	maximal, complemented
20	C₂×#123×D₅₃	C₂	1	2	yes	maximal, complemented
21	C₂×#16811105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16811097	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11719949	C₂²	1	1	yes	characteristic
26	C₂²×#11719949	C₂²	1	2	yes	complemented
27	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
28	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
29	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
30	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
31	#16811355	C₂²	1	16	yes	complemented
32	#16811334	C₂²	1	16	yes	complemented
33	#16811324	C₂²	1	32	yes	complemented
34	#16811320	C₂²	1	16	yes	complemented
35	#16811307	C₂²	1	16	yes	complemented
36	#16811303	C₂²	1	32	yes	complemented
37	#16811298	C₂²	1	32	yes	complemented
38	#16811276	C₂²	1	16	yes	complemented
39	#16811266	C₂²	1	16	yes	complemented
40	#16811266	C₂²	1	32	yes	complemented
41	#16811264	C₂²	1	16	yes	complemented
42	#16811257	C₂²	1	16	yes	complemented
43	#16811224	C₂²	1	16	yes	complemented
44	#16811219	C₂²	1	32	yes	complemented
45	#16811209	C₂²	1	32	yes	complemented
46	C₂×#13133213	C₂²	1	1	yes	characteristic
47	#16811160	C₂²	1	16	yes	complemented
48	#16811151	C₂²	1	16	yes	complemented
49	C₂×#13133212	C₂²	1	2	yes	complemented
50	C₂×#13133212	C₂²	1	1	yes	characteristic, complemented
51	C₂×#13133210	C₂²	1	2	yes	complemented
52	C₂×#13133210	C₂²	1	2	yes	complemented
53	C₂×#13133210	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
55	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
56	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
57	C₂×#13133207	C₂²	1	2	yes	complemented
58	C₂×#13133206	C₂²	1	1	yes	characteristic, complemented
59	C₂×#13133203	C₂²	1	2	yes	complemented
60	C₂×#13133203	C₂²	1	1	yes	characteristic, complemented
61	#16811136	C₂²	1	32	yes	complemented
62	C₂×#13133202	C₂²	1	2	yes	complemented
63	C₂×#13133202	C₂²	1	2	yes	complemented
64	C₂×#13133202	C₂²	1	2	yes	complemented
65	C₂×#13133202	C₂²	1	2	yes	complemented
66	C₂×#13133202	C₂²	1	1	yes	characteristic, complemented
67	C₂×#13133201	C₂²	1	2	yes	complemented
68	C₂×#13133200	C₂²	1	2	yes	complemented
69	C₂×#13133199	C₂²	1	2	yes	—
70	C₂×#13133199	C₂²	1	1	yes	characteristic
71	C₂×#13133199	C₂²	1	2	yes	complemented
72	C₂×#13133199	C₂²	1	2	yes	complemented
73	C₂×#13133199	C₂²	1	2	yes	complemented
74	C₂×#13133198	C₂²	1	2	yes	complemented
75	#123×D₅₃	C₂²	1	32	yes	complemented
76	C₂×#13133197	C₂²	1	2	yes	complemented
77	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
78	C₂×#13133193	C₂²	1	2	yes	complemented
79	C₂×#13133193	C₂²	1	2	yes	complemented
80	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
81	C₂×#13133193	C₂²	1	2	yes	complemented
82	C₂×#13133192	C₂²	1	1	yes	characteristic
83	C₂×#13133192	C₂²	1	1	yes	characteristic, complemented
84	C₂×#13133192	C₂²	1	2	yes	complemented
85	C₂×#13133191	C₂²	1	2	yes	complemented
86	C₂×#13133190	C₂²	1	2	yes	—
87	C₂×#13133190	C₂²	1	1	yes	characteristic
88	C₂×#13133190	C₂²	1	2	yes	complemented
89	C₂×#13133190	C₂²	1	2	yes	complemented
90	C₂×#13133188	C₂²	1	2	yes	complemented
91	C₂×#13133188	C₂²	1	1	yes	characteristic, complemented
92	C₂×#13133187	C₂²	1	2	yes	—
93	C₂×#13133187	C₂²	1	2	yes	complemented
94	C₂×#13133187	C₂²	1	2	yes	complemented
95	C₂×#13133185	C₂²	1	2	yes	—
96	#16811105	C₂²	1	16	yes	complemented
97	#16811097	C₂²	1	16	yes	complemented
98	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
101	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
102	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
105	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
107	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
108	C₂×#13133179	C₂²	1	1	yes	characteristic
109	C₂×#13133179	C₂²	1	1	yes	characteristic
110	C₂×#13133179	C₂²	1	2	yes	complemented
111	C₂×#13133179	C₂²	1	2	yes	complemented
112	C₂×#13133179	C₂²	1	2	yes	complemented
113	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
114	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
115	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₂×#13133177	C₂²	1	2	yes	complemented
117	C₂×#13133177	C₂²	1	2	yes	complemented
118	C₂×#13133177	C₂²	1	2	yes	complemented
119	C₄×D₄×D₅₃	C₂²	1	16	yes	complemented
120	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
121	C₂×#13133175	C₂²	1	2	yes	complemented
122	C₂×#13133174	C₂²	1	1	yes	characteristic, complemented
123	C₂×#13133174	C₂²	1	2	yes	complemented
124	C₂×#13133174	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
126	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
129	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
130	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
131	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
132	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
134	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#542	C₂²	1	16	yes	complemented
136	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
137	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
138	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
140	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
141	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
142	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
143	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
144	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
146	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₅₃	C₂³	1	2	yes	—
148	C₂⁴×D₅₃	C₂³	1	2	yes	—
149	C₂×#11719949	—	2	8	no	—
150	C₂×#11719949	—	4	8	no	—
151	C₂×#11719949	C₂³	1	8	yes	—
152	C₂×#11719949	C₂³	1	16	yes	complemented
153	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
154	C₂²×D₂₁₂	—	2	8	no	—
155	C₂²×D₂₁₂	C₂³	1	8	yes	—
156	C₂²×D₂₁₂	C₂³	1	2	yes	—
157	C₂²×D₂₁₂	C₂³	1	2	yes	—
158	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
159	C₂²×D₂₁₂	C₂³	1	2	yes	—
160	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
161	C₂²×D₂₁₂	C₂³	1	2	yes	—
162	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
163	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
164	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
165	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
166	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
167	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
168	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
169	C₂×D₄×D₅₃	—	2	8	no	—
170	C₂×D₄×D₅₃	—	4	8	no	—
171	C₂×D₄×D₅₃	C₂³	1	8	yes	—
172	C₂×D₄×D₅₃	C₂³	1	16	yes	—
173	C₂³×Dic₅₃	C₂³	1	2	yes	—
174	C₂²×C₄×D₅₃	—	4	8	no	—
175	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
176	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
178	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
179	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
180	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
182	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
183	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
184	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
185	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
186	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
187	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
188	C₂²×C₄×D₅₃	C₂³	1	16	yes	complemented
189	#13133213	C₂³	1	8	yes	—
190	#13133212	C₂³	1	8	yes	complemented
191	#13133212	C₂³	1	16	yes	complemented
192	#13133210	C₂³	1	16	yes	complemented
193	#13133210	C₂³	1	8	yes	complemented
194	#13133210	C₂³	1	16	yes	complemented
195	#13133208	C₂³	1	8	yes	complemented
196	#13133208	C₂³	1	8	yes	complemented
197	#13133207	C₂³	1	16	yes	complemented
198	#13133207	C₂³	1	8	yes	complemented
199	#13133206	C₂³	1	8	yes	complemented
200	#13133203	C₂³	1	16	yes	complemented
201	#13133203	C₂³	1	8	yes	complemented
202	#13133202	C₂³	1	16	yes	complemented
203	#13133202	C₂³	1	16	yes	complemented
204	#13133202	C₂³	1	16	yes	complemented
205	#13133202	C₂³	1	16	yes	complemented
206	#13133202	C₂³	1	8	yes	complemented
207	#13133201	C₂³	1	16	yes	complemented
208	#13133200	C₂³	1	16	yes	complemented
209	#13133199	C₂³	1	16	yes	—
210	#13133199	C₂³	1	8	yes	—
211	#13133199	C₂³	1	16	yes	complemented
212	#13133199	C₂³	1	16	yes	complemented
213	#13133199	C₂³	1	16	yes	complemented
214	#13133198	C₂³	1	16	yes	complemented
215	#13133197	C₂³	1	16	yes	complemented
216	#13133195	C₂³	1	8	yes	complemented
217	#13133193	C₂³	1	8	yes	complemented
218	#13133193	C₂³	1	16	yes	complemented
219	#13133193	C₂³	1	16	yes	complemented
220	#13133193	C₂³	1	16	yes	complemented
221	#13133192	C₂³	1	8	yes	—
222	#13133192	C₂³	1	8	yes	complemented
223	#13133192	C₂³	1	16	yes	complemented
224	#13133191	C₂³	1	16	yes	complemented
225	#13133190	C₂³	1	8	yes	—
226	#13133190	C₂³	1	16	yes	—
227	#13133190	C₂³	1	16	yes	complemented
228	#13133190	C₂³	1	16	yes	complemented
229	#13133188	C₂³	1	16	yes	complemented
230	#13133188	C₂³	1	8	yes	complemented
231	#13133187	C₂³	1	16	yes	—
232	#13133187	C₂³	1	16	yes	complemented
233	#13133187	C₂³	1	16	yes	complemented
234	#13133185	C₂³	1	16	yes	—
235	Q₈×Dic₅₃	C₂³	1	8	yes	complemented
236	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
237	C₄×D₂₁₂	C₂³	1	8	yes	—
238	C₄×D₂₁₂	C₂³	1	8	yes	—
239	C₄×D₂₁₂	C₂³	1	8	yes	complemented
240	C₄×D₂₁₂	C₂³	1	16	yes	complemented
241	C₄×D₂₁₂	C₂³	1	16	yes	complemented
242	C₄×D₂₁₂	C₂³	1	8	yes	complemented
243	C₄×D₂₁₂	C₂³	1	8	yes	complemented
244	D₄×Dic₅₃	C₂³	1	8	yes	complemented
245	#13133179	C₂³	1	8	yes	—
246	#13133179	C₂³	1	8	yes	—
247	#13133179	C₂³	1	16	yes	complemented
248	#13133179	C₂³	1	16	yes	complemented
249	#13133179	C₂³	1	16	yes	complemented
250	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
251	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
252	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
253	#13133177	C₂³	1	16	yes	complemented
254	#13133177	C₂³	1	16	yes	complemented
255	#13133177	C₂³	1	16	yes	complemented
256	#13133176	C₂³	1	8	yes	complemented
257	#13133175	C₂³	1	16	yes	complemented
258	#13133174	C₂³	1	16	yes	complemented
259	#13133174	C₂³	1	16	yes	complemented
260	#13133174	C₂³	1	8	yes	complemented
261	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
264	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
265	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
267	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂×#11719919	C₂³	1	2	yes	—
269	C₂×#11719919	C₂³	1	1	yes	characteristic
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	2	yes	—
275	C₂×#11719919	C₂³	1	1	yes	characteristic
276	C₂×#11719919	C₂³	1	1	yes	characteristic
277	C₂×#11719919	C₂³	1	1	yes	characteristic
278	C₂×#11719919	C₂³	1	1	yes	characteristic
279	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
280	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
281	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
282	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
283	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
284	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
286	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
287	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂×#11719921	C₂³	1	2	yes	—
289	C₂×#11719921	C₂³	1	1	yes	characteristic
290	C₂×#11719921	C₂³	1	2	yes	—
291	C₂×#11719921	C₂³	1	2	yes	—
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	2	yes	—
297	C₂×#11719921	C₂³	1	2	yes	—
298	C₂×#11719921	C₂³	1	1	yes	characteristic
299	C₂×#11719921	C₂³	1	1	yes	characteristic
300	C₂×#11719921	C₂³	1	2	yes	—
301	C₂×#11719921	C₂³	1	1	yes	characteristic
302	C₂×#11719921	C₂³	1	1	yes	characteristic
303	C₂×#11719921	C₂³	1	2	yes	—
304	C₂×#11719921	C₂³	1	1	yes	characteristic
305	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
306	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
307	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
308	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
309	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
310	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
314	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
316	C₄²×D₅₃	C₂³	1	8	yes	complemented
317	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
319	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
321	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
323	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
324	#126×C₅₃	C₂³	1	16	yes	complemented
325	#124×C₅₃	C₂³	1	16	yes	complemented
326	#124×C₅₃	C₂³	1	8	yes	complemented
327	#123×C₅₃	C₂³	1	16	yes	complemented
328	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
329	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
330	#121×C₅₃	C₂³	1	8	yes	—
331	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
332	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
333	#117×C₅₃	C₂³	1	8	yes	complemented
334	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
347	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
348	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
351	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
353	C₂³×D₅₃	—	2	8	no	—
354	C₂³×D₅₃	—	2	8	no	—
355	C₂³×D₅₃	—	2	8	no	—
356	C₂³×D₅₃	—	4	4	no	—
357	C₂³×D₅₃	—	4	4	no	—
358	C₂³×D₅₃	—	4	4	no	—
359	C₂³×D₅₃	C₂⁴	1	2	yes	—
360	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
361	C₂³×D₅₃	C₂⁴	1	8	yes	—
362	C₂³×D₅₃	C₂⁴	1	2	yes	—
363	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
364	C₂³×D₅₃	C₂⁴	1	8	yes	—
365	C₂×Q₈×C₅₃	—	2	4	no	—
366	C₂×Q₈×C₅₃	—	4	4	no	—
367	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
368	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
369	C₂×D₄×C₅₃	—	2	4	no	—
370	C₂×D₄×C₅₃	—	4	4	no	—
371	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
372	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
373	C₂²×C₄×C₅₃	—	2	4	no	—
374	C₂²×C₄×C₅₃	—	4	4	no	—
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
383	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
384	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₂²⋊D₅₃	—	2	8	no	—
387	C₂×C₂²⋊D₅₃	—	2	4	no	—
388	C₂×C₂²⋊D₅₃	—	4	4	no	—
389	C₂×C₂²⋊D₅₃	—	4	2	no	—
390	C₂×C₂²⋊D₅₃	—	4	4	no	—
391	C₂×C₂²⋊D₅₃	—	4	4	no	—
392	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
393	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
394	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
395	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
396	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
397	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
398	C₂²×Dic₅₃	—	4	4	no	—
399	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
404	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
405	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
408	#11719949	—	2	32	no	—
409	#11719949	—	4	32	no	—
410	D₄×D₅₃	—	2	32	no	—
411	D₄×D₅₃	—	4	32	no	—
412	C₂×D₂₁₂	—	2	8	no	—
413	C₂×D₂₁₂	—	2	8	no	—
414	C₂×D₂₁₂	—	2	8	no	—
415	C₂×D₂₁₂	—	2	4	no	—
416	C₂×D₂₁₂	—	2	4	no	—
417	C₂×D₂₁₂	—	2	32	no	—
418	C₂×D₂₁₂	—	4	4	no	—
419	C₂×D₂₁₂	#41	1	8	yes	complemented
420	C₂×D₂₁₂	C₂⁴	1	8	yes	—
421	C₂×D₂₁₂	C₂⁴	1	8	yes	—
422	C₂×D₂₁₂	C₂⁴	1	4	yes	—
423	C₂×D₂₁₂	C₂⁴	1	8	yes	—
424	C₂×D₂₁₂	C₂⁴	1	4	yes	—
425	C₂×D₂₁₂	C₂⁴	1	8	yes	—
426	C₂×D₂₁₂	C₂⁴	1	4	yes	—
427	C₂×C₄×D₅₃	—	2	8	no	—
428	C₂×C₄×D₅₃	—	2	4	no	—
429	C₂×C₄×D₅₃	—	2	8	no	—
430	C₂×C₄×D₅₃	—	2	4	no	—
431	C₂×C₄×D₅₃	—	2	4	no	—
432	C₂×C₄×D₅₃	—	4	32	no	—
433	C₂×C₄×D₅₃	—	4	4	no	—
434	C₂×C₄×D₅₃	—	4	4	no	—
435	C₂×C₄×D₅₃	—	4	2	no	—
436	C₂×C₄×D₅₃	—	4	4	no	—
437	C₂×C₄×D₅₃	—	4	4	no	—
438	C₂×C₄×D₅₃	—	4	4	no	—
439	C₂×C₄×D₅₃	—	4	4	no	—
440	C₂×C₄×D₅₃	—	4	4	no	—
441	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
442	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
443	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
444	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
445	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
446	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
447	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
448	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
449	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
450	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
451	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
452	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
453	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
454	C₂×Dic₁₀₆	—	4	2	no	—
455	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
456	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
457	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
458	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
459	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
460	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
461	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
462	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
463	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
464	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
465	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
466	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
467	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
468	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
469	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
470	C₄²×C₅₃	C₂⁴	1	4	yes	—
471	C₄²×C₅₃	C₂⁴	1	4	yes	—
472	C₄²×C₅₃	C₂⁴	1	8	yes	—
473	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
474	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
475	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
476	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
477	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
478	#11719921	C₂⁴	1	8	yes	—
479	#11719921	C₂⁴	1	4	yes	—
480	#11719921	C₂⁴	1	8	yes	—
481	#11719921	C₂⁴	1	8	yes	—
482	#11719921	C₂⁴	1	8	yes	—
483	#11719921	C₂⁴	1	8	yes	—
484	#11719921	C₂⁴	1	8	yes	—
485	#11719921	C₂⁴	1	8	yes	—
486	#11719921	C₂⁴	1	8	yes	—
487	#11719921	C₂⁴	1	8	yes	—
488	#11719921	C₂⁴	1	4	yes	—
489	#11719921	C₂⁴	1	4	yes	—
490	#11719921	C₂⁴	1	8	yes	—
491	#11719921	C₂⁴	1	4	yes	—
492	#11719921	C₂⁴	1	4	yes	—
493	#11719921	C₂⁴	1	8	yes	—
494	#11719921	C₂⁴	1	4	yes	—
495	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
496	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
497	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
498	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
499	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
500	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
501	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
502	#11719919	C₂⁴	1	8	yes	—
503	#11719919	C₂⁴	1	4	yes	—
504	#11719919	C₂⁴	1	8	yes	—
505	#11719919	C₂⁴	1	8	yes	—
506	#11719919	C₂⁴	1	8	yes	—
507	#11719919	C₂⁴	1	4	yes	—
508	#11719919	C₂⁴	1	8	yes	—
509	#11719919	C₂⁴	1	4	yes	—
510	#11719919	C₂⁴	1	4	yes	—
511	#11719919	C₂⁴	1	4	yes	—
512	#11719919	C₂⁴	1	4	yes	—
513	C₄×Dic₅₃	C₂⁴	1	4	yes	—
514	C₄×Dic₅₃	C₂⁴	1	4	yes	—
515	C₄×Dic₅₃	C₂⁴	1	4	yes	—
516	C₄×Dic₅₃	C₂⁴	1	8	yes	—
517	C₄×Dic₅₃	C₂⁴	1	4	yes	—
518	C₄×Dic₅₃	C₂⁴	1	8	yes	—
519	C₂³×C₅₃	—	2	4	no	—
520	C₂³×C₅₃	—	2	2	no	—
521	C₂³×C₅₃	—	2	4	no	—
522	C₂³×C₅₃	—	2	2	no	—
523	C₂³×C₅₃	—	2	4	no	—
524	C₂³×C₅₃	—	2	2	no	—
525	C₂³×C₅₃	C₂⁵	1	4	yes	—
526	C₂³×C₅₃	C₂⁵	1	2	yes	—
527	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
528	C₂²×D₅₃	—	2	2	no	—
529	C₂²×D₅₃	—	2	4	no	—
530	C₂²×D₅₃	—	2	2	no	—
531	C₂²×D₅₃	—	2	4	no	—
532	C₂²×D₅₃	—	2	2	no	—
533	C₂²×D₅₃	—	2	4	no	—
534	C₂²×D₅₃	—	2	2	no	—
535	C₂²×D₅₃	—	2	4	no	—
536	C₂²×D₅₃	—	2	4	no	—
537	C₂²×D₅₃	—	2	2	no	—
538	C₂²×D₅₃	—	2	16	no	—
539	C₂²×D₅₃	—	2	16	no	—
540	C₂²×D₅₃	—	2	16	no	—
541	C₂²×D₅₃	—	4	8	no	—
542	C₂²×D₅₃	—	4	32	no	—
543	C₂²×D₅₃	—	4	8	no	—
544	C₂²×D₅₃	—	4	8	no	—
545	C₂²×D₅₃	—	8	16	no	—
546	C₂²×D₅₃	C₂×#41	1	8	yes	—
547	C₂²×D₅₃	H(5,𝔽₂)	1	4	yes	—
548	C₂²×D₅₃	C₂⁵	1	2	yes	—
549	C₂²×D₅₃	C₂⁵	1	4	yes	—
550	C₂²×D₅₃	C₂⁵	1	4	yes	—
551	C₂²×D₅₃	C₂⁵	1	2	yes	—
552	Q₈×C₅₃	—	2	8	no	—
553	Q₈×C₅₃	—	4	8	no	—
554	D₄×C₅₃	—	2	8	no	—
555	D₄×C₅₃	—	4	8	no	—
556	C₂×C₄×C₅₃	—	2	4	no	—
557	C₂×C₄×C₅₃	—	2	2	no	—
558	C₂×C₄×C₅₃	—	2	2	no	—
559	C₂×C₄×C₅₃	—	2	4	no	—
560	C₂×C₄×C₅₃	—	2	4	no	—
561	C₂×C₄×C₅₃	—	2	2	no	—
562	C₂×C₄×C₅₃	—	2	2	no	—
563	C₂×C₄×C₅₃	—	2	2	no	—
564	C₂×C₄×C₅₃	—	2	8	no	—
565	C₂×C₄×C₅₃	—	4	8	no	—
566	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
567	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
568	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
569	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
570	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
571	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
572	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
573	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
574	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
575	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
576	C₂²⋊D₅₃	—	2	16	no	—
577	C₂²⋊D₅₃	—	2	8	no	—
578	C₂²⋊D₅₃	—	4	8	no	—
579	C₂²⋊D₅₃	—	4	4	no	—
580	C₂²⋊D₅₃	—	4	8	no	—
581	C₂²⋊D₅₃	—	4	8	no	—
582	C₂×Dic₅₃	—	2	2	no	—
583	C₂×Dic₅₃	—	2	2	no	—
584	C₂×Dic₅₃	—	2	4	no	—
585	C₂×Dic₅₃	—	2	2	no	—
586	C₂×Dic₅₃	—	2	2	no	—
587	C₂×Dic₅₃	—	2	2	no	—
588	C₂×Dic₅₃	—	2	2	no	—
589	C₂×Dic₅₃	—	2	4	no	—
590	C₂×Dic₅₃	—	4	8	no	—
591	C₂×Dic₅₃	C₂⁵	1	2	yes	—
592	C₂×Dic₅₃	C₂⁵	1	2	yes	—
593	C₂×Dic₅₃	C₂⁵	1	4	yes	—
594	C₂×Dic₅₃	C₂⁵	1	2	yes	—
595	C₂×Dic₅₃	C₂⁵	1	2	yes	—
596	C₂×Dic₅₃	C₂⁵	1	2	yes	—
597	C₂×Dic₅₃	C₂⁵	1	4	yes	—
598	C₂×Dic₅₃	C₂⁵	1	2	yes	—
599	D₂₁₂	—	2	16	no	—
600	D₂₁₂	—	2	16	no	—
601	D₂₁₂	—	2	16	no	—
602	D₂₁₂	—	2	8	no	—
603	D₂₁₂	—	2	8	no	—
604	D₂₁₂	—	4	8	no	—
605	D₂₁₂	C₂×#41	1	16	yes	complemented
606	C₄×D₅₃	—	2	16	no	—
607	C₄×D₅₃	—	2	8	no	—
608	C₄×D₅₃	—	2	16	no	—
609	C₄×D₅₃	—	2	8	no	—
610	C₄×D₅₃	—	2	8	no	—
611	C₄×D₅₃	—	4	8	no	—
612	C₄×D₅₃	—	4	8	no	—
613	C₄×D₅₃	—	4	4	no	—
614	C₄×D₅₃	—	4	8	no	—
615	C₄×D₅₃	—	4	8	no	—
616	C₄×D₅₃	—	4	8	no	—
617	C₄×D₅₃	—	4	8	no	—
618	C₄×D₅₃	—	4	8	no	—
619	Dic₁₀₆	—	4	4	no	—
620	C₂×#3513	—	53	1	no	maximal, Sylow
621	C₂²×C₅₃	—	2	4	no	—
622	C₂²×C₅₃	—	2	2	no	—
623	C₂²×C₅₃	—	2	4	no	—
624	C₂²×C₅₃	—	2	2	no	—
625	C₂²×C₅₃	—	2	4	no	—
626	C₂²×C₅₃	—	2	2	no	—
627	C₂²×C₅₃	—	4	8	no	—
628	C₂²×C₅₃	—	4	4	no	—
629	C₂²×C₅₃	C₂²×#41	1	2	yes	—
630	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
631	C₂²×C₅₃	#585	1	2	yes	—
632	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
633	C₂×D₅₃	—	2	2	no	—
634	C₂×D₅₃	—	2	4	no	—
635	C₂×D₅₃	—	2	2	no	—
636	C₂×D₅₃	—	2	4	no	—
637	C₂×D₅₃	—	2	8	no	—
638	C₂×D₅₃	—	2	16	no	—
639	C₂×D₅₃	—	2	2	no	—
640	C₂×D₅₃	—	2	4	no	—
641	C₂×D₅₃	—	2	2	no	—
642	C₂×D₅₃	—	2	4	no	—
643	C₂×D₅₃	—	2	4	no	—
644	C₂×D₅₃	—	2	2	no	—
645	C₂×D₅₃	—	4	32	no	—
646	C₂×D₅₃	—	4	4	no	—
647	C₂×D₅₃	—	4	8	no	—
648	C₂×D₅₃	—	8	16	no	—
649	C₂×D₅₃	C₂²×#41	1	8	yes	—
650	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
651	C₄×C₅₃	—	2	4	no	—
652	C₄×C₅₃	—	2	2	no	—
653	C₄×C₅₃	—	2	2	no	—
654	C₄×C₅₃	—	2	4	no	—
655	C₄×C₅₃	—	2	4	no	—
656	C₄×C₅₃	—	2	2	no	—
657	C₄×C₅₃	—	2	2	no	—
658	C₄×C₅₃	—	2	2	no	—
659	C₄×C₅₃	C₂²×#41	1	4	yes	—
660	Dic₅₃	—	2	2	no	—
661	Dic₅₃	—	2	2	no	—
662	Dic₅₃	—	2	4	no	—
663	Dic₅₃	—	2	2	no	—
664	Dic₅₃	—	2	2	no	—
665	Dic₅₃	—	2	2	no	—
666	Dic₅₃	—	2	2	no	—
667	Dic₅₃	—	2	4	no	—
668	#3513	—	53	32	no	—
669	C₂×#559	—	53	1	no	—
670	C₂×#554	—	53	1	no	—
671	C₂×#553	—	53	2	no	—
672	C₂×#553	—	53	1	no	—
673	C₂×#552	—	53	1	no	—
674	C₂×#551	—	53	2	no	—
675	C₂×#551	—	53	2	no	—
676	C₂×#547	—	53	1	no	—
677	C₂×#546	—	53	2	no	—
678	C₂×#546	—	53	1	no	—
679	C₂×#546	—	53	1	no	—
680	C₂×D₄²	—	53	1	no	—
681	C₂×#542	D₅₃	1	1	yes	characteristic, complemented
682	C₂×#540	—	53	1	no	—
683	C₂×#539	—	53	2	no	—
684	C₂×#538	—	53	2	no	—
685	C₂×#529	—	53	1	no	—
686	C₂×#529	—	53	1	no	—
687	C₂×#525	—	53	2	no	—
688	C₂²×#123	—	53	2	no	—
689	C₂×#520	—	53	1	no	—
690	C₂×#518	—	53	1	no	—
691	C₂²×C₄×D₄	—	53	1	no	—
692	C₂×C₅₃	—	4	4	no	—
693	C₂×C₅₃	—	4	2	no	—
694	C₂×C₅₃	#3513	1	4	yes	complemented
695	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
696	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
697	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
698	D₅₃	—	2	4	no	—
699	D₅₃	—	2	8	no	—
700	D₅₃	—	4	2	no	—
701	D₅₃	—	4	4	no	—
702	C₂²×#41	—	53	1	no	—
703	C₂²×#41	—	53	2	no	—
704	C₂³×D₄	—	53	1	no	—
705	C₂³×D₄	—	53	2	no	—
706	C₂³×D₄	—	53	1	no	—
707	C₂⁴×C₄	—	53	2	no	—
708	#559	—	53	16	no	—
709	#554	—	53	16	no	—
710	#553	—	53	32	no	—
711	#553	—	53	16	no	—
712	#552	—	53	16	no	—
713	#551	—	53	32	no	—
714	#551	—	53	32	no	—
715	#547	—	53	16	no	—
716	#546	—	53	32	no	—
717	#546	—	53	16	no	—
718	#546	—	53	16	no	—
719	D₄²	—	53	16	no	—
720	#542	C₂×D₅₃	1	16	yes	complemented
721	#540	—	53	16	no	—
722	#539	—	53	32	no	—
723	#538	—	53	32	no	—
724	C₂×C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
725	C₂×#127	—	53	1	no	—
726	#529	—	53	16	no	—
727	#529	—	53	16	no	—
728	C₂×#126	—	53	2	no	—
729	C₂×#126	—	53	1	no	—
730	C₂×#126	—	53	1	no	—
731	C₂×#126	—	53	2	no	—
732	C₂×#126	—	53	2	no	—
733	C₂×#126	C₂×D₅₃	1	2	yes	complemented
734	C₂×#125	—	53	1	no	—
735	C₂×#125	—	53	1	no	—
736	C₂×#125	—	53	2	no	—
737	C₂×#125	—	53	1	no	—
738	C₂×#124	—	53	1	no	—
739	C₂×#124	—	53	1	no	—
740	C₂×#124	—	53	2	no	—
741	C₂×#124	C₂×D₅₃	1	2	yes	complemented
742	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
743	#525	—	53	32	no	—
744	C₂×#123	—	53	2	no	—
745	C₂×#123	—	53	2	no	—
746	C₂×#123	—	53	32	no	—
747	C₂×#123	—	53	2	no	—
748	C₂×#123	—	53	2	no	—
749	C₂×#123	—	53	1	no	—
750	C₂×#123	—	53	2	no	—
751	C₂×#123	—	53	2	no	—
752	C₂×#123	—	53	1	no	—
753	C₂×#123	—	53	2	no	—
754	C₂×#123	—	53	2	no	—
755	C₂×#123	—	53	2	no	—
756	C₂×#123	—	53	2	no	—
757	C₂×#123	—	53	2	no	—
758	C₂×#123	C₂×D₅₃	1	2	yes	complemented
759	C₂×C₂²⋊Q₈	—	53	2	no	—
760	C₂×C₂²⋊Q₈	—	53	1	no	—
761	C₂×C₂²⋊Q₈	—	53	2	no	—
762	C₂×C₂²⋊Q₈	—	53	2	no	—
763	C₂×C₂²⋊Q₈	—	53	1	no	—
764	C₂×C₂²⋊Q₈	—	53	2	no	—
765	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
766	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
767	C₂×#121	—	53	2	no	—
768	C₂×#121	—	53	1	no	—
769	C₂×#121	—	53	2	no	—
770	C₂×#121	—	53	2	no	—
771	C₂×#121	—	53	1	no	—
772	C₂×#121	—	53	1	no	—
773	C₂×#121	—	53	1	no	—
774	C₂×#121	—	53	2	no	—
775	C₂×#121	—	53	2	no	—
776	C₂×#121	—	53	2	no	—
777	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
778	C₂×#120	—	53	2	no	—
779	C₂×#120	—	53	2	no	—
780	C₂×#120	—	53	2	no	—
781	C₂×#120	—	53	2	no	—
782	#520	—	53	16	no	—
783	#518	—	53	16	no	—
784	C₂×C₄×Q₈	—	53	1	no	—
785	C₂×C₄×Q₈	—	53	1	no	—
786	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
787	C₂×C₄×D₄	—	53	1	no	—
788	C₂×C₄×D₄	—	53	1	no	—
789	C₂×C₄×D₄	—	53	2	no	—
790	C₂×C₄×D₄	—	53	1	no	—
791	C₂×C₄×D₄	—	53	16	no	—
792	C₂×C₄×D₄	—	53	1	no	—
793	C₂×C₄×D₄	—	53	1	no	—
794	C₂×C₄×D₄	—	53	2	no	—
795	C₂×C₄×D₄	—	53	2	no	—
796	C₂×C₄×D₄	—	53	2	no	—
797	C₂×C₄×D₄	—	53	2	no	—
798	C₂×C₄×D₄	—	53	2	no	—
799	C₂×C₄×D₄	—	53	2	no	—
800	C₂×C₄×D₄	—	53	1	no	—
801	C₂×C₄×D₄	—	53	1	no	—
802	C₂×C₄×D₄	—	53	1	no	—
803	C₂×C₄×D₄	—	53	1	no	—
804	C₂×C₄×D₄	—	53	2	no	—
805	C₂×C₄×D₄	—	53	1	no	—
806	C₂×C₄×D₄	—	53	2	no	—
807	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
808	C₂×#117	—	53	1	no	—
809	C₂×#117	—	53	2	no	—
810	C₂×#117	—	53	1	no	—
811	C₂×#117	—	53	2	no	—
812	C₂×#117	—	53	2	no	—
813	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
814	C₂²×C₄⋊C₄	—	53	1	no	—
815	C₂²×C₄⋊C₄	—	53	2	no	—
816	C₂²×C₄⋊C₄	—	53	1	no	—
817	C₂²×C₄⋊C₄	—	53	2	no	—
818	C₂²×C₂²⋊C₄	—	53	2	no	—
819	C₂²×C₂²⋊C₄	—	53	2	no	—
820	C₂²×C₂²⋊C₄	—	53	2	no	—
821	C₂²×C₂²⋊C₄	—	53	2	no	—
822	C₂²×C₂²⋊C₄	—	53	2	no	—
823	C₂²×C₄²	—	53	1	no	—
824	C₅₃	C₂×#3513	1	1	yes	characteristic, complemented, Sylow
825	C₂⁵	—	53	2	no	—
826	C₂⁵	—	53	2	no	—
827	C₂×#41	—	53	8	no	—
828	C₂×#41	—	53	16	no	—
829	C₂×#41	—	106	8	no	—
830	C₂×#41	—	212	8	no	—
831	C₂²×Q₈	—	53	1	no	—
832	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
833	C₂²×Q₈	C₂²×D₅₃	1	2	yes	—
834	C₂²×D₄	—	53	2	no	—
835	C₂²×D₄	—	53	1	no	—
836	C₂²×D₄	—	53	1	no	—
837	C₂²×D₄	—	53	2	no	—
838	C₂²×D₄	—	53	2	no	—
839	C₂²×D₄	—	53	2	no	—
840	C₂²×D₄	—	53	8	no	—
841	C₂²×D₄	—	53	16	no	—
842	C₂²×D₄	—	53	1	no	—
843	C₂²×D₄	—	53	2	no	—
844	C₂²×D₄	—	53	2	no	—
845	C₂²×D₄	—	53	1	no	—
846	C₂²×D₄	—	53	1	no	—
847	C₂²×D₄	—	53	2	no	—
848	C₂²×D₄	—	53	8	no	—
849	C₂²×D₄	—	53	2	no	—
850	C₂²×D₄	—	106	8	no	—
851	C₂²×D₄	—	106	8	no	—
852	C₂²×D₄	—	212	8	no	—
853	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
854	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
855	C₂³×C₄	—	53	2	no	—
856	C₂³×C₄	—	53	2	no	—
857	C₂³×C₄	—	53	2	no	—
858	C₂³×C₄	—	53	1	no	—
859	C₂³×C₄	—	53	1	no	—
860	C₂³×C₄	—	53	1	no	—
861	C₂³×C₄	—	53	2	no	—
862	C₂³×C₄	—	53	1	no	—
863	C₂³×C₄	—	53	2	no	—
864	C₂³×C₄	—	53	2	no	—
865	C₂³×C₄	—	53	2	no	—
866	C₂³×C₄	—	53	2	no	—
867	C₂³×C₄	—	53	2	no	—
868	C₂³×C₄	—	53	2	no	—
869	C₂³×C₄	—	53	16	no	—
870	C₂³×C₄	—	212	8	no	—
871	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
872	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
873	C₄⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
874	#127	—	53	8	no	—
875	#126	—	53	16	no	—
876	#126	—	53	8	no	—
877	#126	—	53	8	no	—
878	#126	—	53	16	no	—
879	#126	—	53	16	no	—
880	#126	C₂²×D₅₃	1	16	yes	complemented
881	#125	—	53	8	no	—
882	#125	—	53	8	no	—
883	#125	—	53	16	no	—
884	#125	—	53	8	no	—
885	#124	—	53	8	no	—
886	#124	—	53	8	no	—
887	#124	—	53	16	no	—
888	#124	C₂²×D₅₃	1	16	yes	complemented
889	#124	C₂²×D₅₃	1	8	yes	complemented
890	#123	—	53	16	no	—
891	#123	—	53	16	no	—
892	#123	—	53	16	no	—
893	#123	—	53	16	no	—
894	#123	—	53	8	no	—
895	#123	—	53	16	no	—
896	#123	—	53	16	no	—
897	#123	—	53	8	no	—
898	#123	—	53	16	no	—
899	#123	—	53	16	no	—
900	#123	—	53	16	no	—
901	#123	—	53	16	no	—
902	#123	—	53	16	no	—
903	#123	C₂²×D₅₃	1	16	yes	complemented
904	C₂²⋊Q₈	—	53	16	no	—
905	C₂²⋊Q₈	—	53	8	no	—
906	C₂²⋊Q₈	—	53	16	no	—
907	C₂²⋊Q₈	—	53	16	no	—
908	C₂²⋊Q₈	—	53	8	no	—
909	C₂²⋊Q₈	—	53	16	no	—
910	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
911	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
912	#121	—	53	16	no	—
913	#121	—	53	8	no	—
914	#121	—	53	16	no	—
915	#121	—	53	16	no	—
916	#121	—	53	8	no	—
917	#121	—	53	8	no	—
918	#121	—	53	8	no	—
919	#121	—	53	16	no	—
920	#121	—	53	16	no	—
921	#121	—	53	16	no	—
922	#121	C₂²×D₅₃	1	8	yes	—
923	#120	—	53	16	no	—
924	#120	—	53	16	no	—
925	#120	—	53	16	no	—
926	#120	—	53	16	no	—
927	C₄×Q₈	—	53	8	no	—
928	C₄×Q₈	—	53	8	no	—
929	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
930	C₄×D₄	—	53	8	no	—
931	C₄×D₄	—	53	16	no	—
932	C₄×D₄	—	53	8	no	—
933	C₄×D₄	—	53	8	no	—
934	C₄×D₄	—	53	8	no	—
935	C₄×D₄	—	53	16	no	—
936	C₄×D₄	—	53	16	no	—
937	C₄×D₄	—	53	16	no	—
938	C₄×D₄	—	53	8	no	—
939	C₄×D₄	—	53	16	no	—
940	C₄×D₄	—	53	16	no	—
941	C₄×D₄	—	53	16	no	—
942	C₄×D₄	—	53	8	no	—
943	C₄×D₄	—	53	8	no	—
944	C₄×D₄	—	53	8	no	—
945	C₄×D₄	—	53	8	no	—
946	C₄×D₄	—	53	16	no	—
947	C₄×D₄	—	53	8	no	—
948	C₄×D₄	—	53	16	no	—
949	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
950	#117	—	53	8	no	—
951	#117	—	53	16	no	—
952	#117	—	53	8	no	—
953	#117	—	53	16	no	—
954	#117	—	53	16	no	—
955	#117	C₂²×D₅₃	1	8	yes	complemented
956	C₂×C₄⋊C₄	—	53	1	no	—
957	C₂×C₄⋊C₄	—	53	2	no	—
958	C₂×C₄⋊C₄	—	53	1	no	—
959	C₂×C₄⋊C₄	—	53	1	no	—
960	C₂×C₄⋊C₄	—	53	2	no	—
961	C₂×C₄⋊C₄	—	53	2	no	—
962	C₂×C₄⋊C₄	—	53	2	no	—
963	C₂×C₄⋊C₄	—	53	2	no	—
964	C₂×C₄⋊C₄	—	53	1	no	—
965	C₂×C₄⋊C₄	—	53	1	no	—
966	C₂×C₄⋊C₄	—	53	2	no	—
967	C₂×C₄⋊C₄	—	53	2	no	—
968	C₂×C₄⋊C₄	—	53	1	no	—
969	C₂×C₄⋊C₄	—	53	1	no	—
970	C₂×C₄⋊C₄	—	53	2	no	—
971	C₂×C₄⋊C₄	—	53	1	no	—
972	C₂×C₄⋊C₄	—	53	1	no	—
973	C₂×C₄⋊C₄	—	53	1	no	—
974	C₂×C₄⋊C₄	—	53	8	no	—
975	C₂×C₄⋊C₄	—	53	16	no	—
976	C₂×C₄⋊C₄	—	53	8	no	—
977	C₂×C₄⋊C₄	—	53	16	no	—
978	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
979	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
980	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
981	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
982	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
983	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
984	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
985	C₂×C₂²⋊C₄	—	53	2	no	—
986	C₂×C₂²⋊C₄	—	53	1	no	—
987	C₂×C₂²⋊C₄	—	53	2	no	—
988	C₂×C₂²⋊C₄	—	53	2	no	—
989	C₂×C₂²⋊C₄	—	53	1	no	—
990	C₂×C₂²⋊C₄	—	53	2	no	—
991	C₂×C₂²⋊C₄	—	53	1	no	—
992	C₂×C₂²⋊C₄	—	53	2	no	—
993	C₂×C₂²⋊C₄	—	53	2	no	—
994	C₂×C₂²⋊C₄	—	53	2	no	—
995	C₂×C₂²⋊C₄	—	53	2	no	—
996	C₂×C₂²⋊C₄	—	53	2	no	—
997	C₂×C₂²⋊C₄	—	53	2	no	—
998	C₂×C₂²⋊C₄	—	53	2	no	—
999	C₂×C₂²⋊C₄	—	53	1	no	—
1000	C₂×C₂²⋊C₄	—	53	2	no	—
1001	C₂×C₂²⋊C₄	—	53	1	no	—
1002	C₂×C₂²⋊C₄	—	53	1	no	—
1003	C₂×C₂²⋊C₄	—	53	2	no	—
1004	C₂×C₂²⋊C₄	—	53	1	no	—
1005	C₂×C₂²⋊C₄	—	53	2	no	—
1006	C₂×C₂²⋊C₄	—	53	1	no	—
1007	C₂×C₂²⋊C₄	—	53	16	no	—
1008	C₂×C₂²⋊C₄	—	53	16	no	—
1009	C₂×C₂²⋊C₄	—	53	16	no	—
1010	C₂×C₂²⋊C₄	—	53	16	no	—
1011	C₂×C₂²⋊C₄	—	53	16	no	—
1012	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1013	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1014	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1015	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1016	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1017	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1018	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1019	C₂×C₄²	—	53	2	no	—
1020	C₂×C₄²	—	53	2	no	—
1021	C₂×C₄²	—	53	1	no	—
1022	C₂×C₄²	—	53	1	no	—
1023	C₂×C₄²	—	53	1	no	—
1024	C₂×C₄²	—	53	1	no	—
1025	C₂×C₄²	—	53	8	no	—
1026	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
1027	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1028	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1029	C₂⁴	—	53	2	no	—
1030	C₂⁴	—	53	1	no	—
1031	C₂⁴	—	53	2	no	—
1032	C₂⁴	—	53	1	no	—
1033	C₂⁴	—	53	8	no	—
1034	C₂⁴	—	53	8	no	—
1035	C₂⁴	—	106	8	no	—
1036	C₂⁴	—	106	8	no	—
1037	C₂⁴	—	106	8	no	—
1038	C₂⁴	—	212	4	no	—
1039	C₂⁴	—	212	4	no	—
1040	C₂⁴	—	212	4	no	—
1041	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1042	C₂⁴	C₂³×D₅₃	1	2	yes	—
1043	#41	—	106	32	no	—
1044	#41	—	212	32	no	—
1045	C₂×Q₈	—	2	4	no	—
1046	C₂×Q₈	—	4	4	no	—
1047	C₂×Q₈	—	53	4	no	—
1048	C₂×Q₈	—	212	2	no	—
1049	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1050	C₂×Q₈	C₂³×D₅₃	1	8	yes	—
1051	C₂×D₄	—	2	4	no	—
1052	C₂×D₄	—	4	4	no	—
1053	C₂×D₄	—	53	8	no	—
1054	C₂×D₄	—	53	4	no	—
1055	C₂×D₄	—	53	4	no	—
1056	C₂×D₄	—	53	8	no	—
1057	C₂×D₄	—	53	8	no	—
1058	C₂×D₄	—	53	8	no	—
1059	C₂×D₄	—	53	8	no	—
1060	C₂×D₄	—	53	4	no	—
1061	C₂×D₄	—	53	8	no	—
1062	C₂×D₄	—	53	8	no	—
1063	C₂×D₄	—	53	4	no	—
1064	C₂×D₄	—	53	4	no	—
1065	C₂×D₄	—	53	8	no	—
1066	C₂×D₄	—	53	8	no	—
1067	C₂×D₄	—	106	32	no	—
1068	C₂×D₄	—	106	8	no	—
1069	C₂×D₄	—	106	8	no	—
1070	C₂×D₄	—	106	8	no	—
1071	C₂×D₄	—	106	4	no	—
1072	C₂×D₄	—	106	32	no	—
1073	C₂×D₄	—	106	8	no	—
1074	C₂×D₄	—	106	4	no	—
1075	C₂×D₄	—	106	4	no	—
1076	C₂×D₄	—	212	4	no	—
1077	C₂×D₄	—	212	4	no	—
1078	C₂×D₄	—	212	2	no	—
1079	C₂×D₄	—	212	4	no	—
1080	C₂×D₄	—	212	4	no	—
1081	C₂×D₄	—	212	32	no	—
1082	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1083	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1084	C₂²×C₄	—	2	4	no	—
1085	C₂²×C₄	—	4	4	no	—
1086	C₂²×C₄	—	53	1	no	—
1087	C₂²×C₄	—	53	1	no	—
1088	C₂²×C₄	—	53	1	no	—
1089	C₂²×C₄	—	53	1	no	—
1090	C₂²×C₄	—	53	2	no	—
1091	C₂²×C₄	—	53	2	no	—
1092	C₂²×C₄	—	53	1	no	—
1093	C₂²×C₄	—	53	1	no	—
1094	C₂²×C₄	—	53	8	no	—
1095	C₂²×C₄	—	53	4	no	—
1096	C₂²×C₄	—	53	4	no	—
1097	C₂²×C₄	—	53	8	no	—
1098	C₂²×C₄	—	53	8	no	—
1099	C₂²×C₄	—	53	4	no	—
1100	C₂²×C₄	—	53	4	no	—
1101	C₂²×C₄	—	53	8	no	—
1102	C₂²×C₄	—	53	8	no	—
1103	C₂²×C₄	—	53	8	no	—
1104	C₂²×C₄	—	53	8	no	—
1105	C₂²×C₄	—	53	8	no	—
1106	C₂²×C₄	—	53	8	no	—
1107	C₂²×C₄	—	53	8	no	—
1108	C₂²×C₄	—	106	4	no	—
1109	C₂²×C₄	—	106	8	no	—
1110	C₂²×C₄	—	106	8	no	—
1111	C₂²×C₄	—	106	4	no	—
1112	C₂²×C₄	—	106	4	no	—
1113	C₂²×C₄	—	212	4	no	—
1114	C₂²×C₄	—	212	2	no	—
1115	C₂²×C₄	—	212	4	no	—
1116	C₂²×C₄	—	212	4	no	—
1117	C₂²×C₄	—	212	4	no	—
1118	C₂²×C₄	—	212	4	no	—
1119	C₂²×C₄	—	212	4	no	—
1120	C₂²×C₄	—	212	4	no	—
1121	C₂²×C₄	—	212	32	no	—
1122	C₂²×C₄	—	212	4	no	—
1123	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1124	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1126	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1127	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1128	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1129	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1130	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1131	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1132	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1133	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1134	C₄⋊C₄	—	53	4	no	—
1135	C₄⋊C₄	—	53	8	no	—
1136	C₄⋊C₄	—	53	4	no	—
1137	C₄⋊C₄	—	53	4	no	—
1138	C₄⋊C₄	—	53	8	no	—
1139	C₄⋊C₄	—	53	8	no	—
1140	C₄⋊C₄	—	53	8	no	—
1141	C₄⋊C₄	—	53	8	no	—
1142	C₄⋊C₄	—	53	4	no	—
1143	C₄⋊C₄	—	53	4	no	—
1144	C₄⋊C₄	—	53	8	no	—
1145	C₄⋊C₄	—	53	8	no	—
1146	C₄⋊C₄	—	53	4	no	—
1147	C₄⋊C₄	—	53	4	no	—
1148	C₄⋊C₄	—	53	8	no	—
1149	C₄⋊C₄	—	53	4	no	—
1150	C₄⋊C₄	—	53	4	no	—
1151	C₄⋊C₄	—	53	4	no	—
1152	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1153	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1154	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1155	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1156	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1157	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1158	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1159	C₂²⋊C₄	—	53	8	no	—
1160	C₂²⋊C₄	—	53	4	no	—
1161	C₂²⋊C₄	—	53	8	no	—
1162	C₂²⋊C₄	—	53	8	no	—
1163	C₂²⋊C₄	—	53	4	no	—
1164	C₂²⋊C₄	—	53	8	no	—
1165	C₂²⋊C₄	—	53	4	no	—
1166	C₂²⋊C₄	—	53	8	no	—
1167	C₂²⋊C₄	—	53	8	no	—
1168	C₂²⋊C₄	—	53	8	no	—
1169	C₂²⋊C₄	—	53	8	no	—
1170	C₂²⋊C₄	—	53	8	no	—
1171	C₂²⋊C₄	—	53	8	no	—
1172	C₂²⋊C₄	—	53	8	no	—
1173	C₂²⋊C₄	—	53	4	no	—
1174	C₂²⋊C₄	—	53	8	no	—
1175	C₂²⋊C₄	—	53	4	no	—
1176	C₂²⋊C₄	—	53	4	no	—
1177	C₂²⋊C₄	—	53	8	no	—
1178	C₂²⋊C₄	—	53	4	no	—
1179	C₂²⋊C₄	—	53	8	no	—
1180	C₂²⋊C₄	—	53	4	no	—
1181	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1182	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1183	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1184	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1185	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1186	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1187	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1188	C₄²	—	53	4	no	—
1189	C₄²	—	53	4	no	—
1190	C₄²	—	53	4	no	—
1191	C₄²	—	53	8	no	—
1192	C₄²	—	53	8	no	—
1193	C₄²	—	53	4	no	—
1194	C₄²	C₂³×D₅₃	1	4	yes	—
1195	C₄²	C₂³×D₅₃	1	8	yes	—
1196	C₄²	C₂³×D₅₃	1	4	yes	—
1197	C₂³	—	2	2	no	—
1198	C₂³	—	2	4	no	—
1199	C₂³	—	2	4	no	—
1200	C₂³	—	2	2	no	—
1201	C₂³	—	2	4	no	—
1202	C₂³	—	2	2	no	—
1203	C₂³	—	53	8	no	—
1204	C₂³	—	53	4	no	—
1205	C₂³	—	53	4	no	—
1206	C₂³	—	53	2	no	—
1207	C₂³	—	53	4	no	—
1208	C₂³	—	53	2	no	—
1209	C₂³	—	106	16	no	—
1210	C₂³	—	106	16	no	—
1211	C₂³	—	106	16	no	—
1212	C₂³	—	106	2	no	—
1213	C₂³	—	106	4	no	—
1214	C₂³	—	106	4	no	—
1215	C₂³	—	106	2	no	—
1216	C₂³	—	106	2	no	—
1217	C₂³	—	106	4	no	—
1218	C₂³	—	106	2	no	—
1219	C₂³	—	106	4	no	—
1220	C₂³	—	106	4	no	—
1221	C₂³	—	106	2	no	—
1222	C₂³	—	424	16	no	—
1223	C₂³	—	212	8	no	—
1224	C₂³	—	212	8	no	—
1225	C₂³	—	212	8	no	—
1226	C₂³	—	212	32	no	—
1227	C₂³	C₂⁴×D₅₃	1	2	yes	—
1228	C₂³	C₂⁴×D₅₃	1	4	yes	—
1229	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1230	Q₈	—	2	8	no	—
1231	Q₈	—	4	8	no	—
1232	Q₈	—	212	4	no	—
1233	D₄	—	2	8	no	—
1234	D₄	—	4	8	no	—
1235	D₄	—	53	16	no	—
1236	D₄	—	106	16	no	—
1237	D₄	—	106	16	no	—
1238	D₄	—	106	16	no	—
1239	D₄	—	106	8	no	—
1240	D₄	—	106	16	no	—
1241	D₄	—	106	8	no	—
1242	D₄	—	106	8	no	—
1243	D₄	—	212	8	no	—
1244	D₄	—	212	8	no	—
1245	D₄	—	212	4	no	—
1246	D₄	—	212	8	no	—
1247	D₄	—	212	8	no	—
1248	C₂×C₄	—	2	2	no	—
1249	C₂×C₄	—	2	4	no	—
1250	C₂×C₄	—	2	2	no	—
1251	C₂×C₄	—	2	4	no	—
1252	C₂×C₄	—	2	4	no	—
1253	C₂×C₄	—	2	2	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	2	no	—
1256	C₂×C₄	—	2	8	no	—
1257	C₂×C₄	—	4	8	no	—
1258	C₂×C₄	—	53	2	no	—
1259	C₂×C₄	—	53	2	no	—
1260	C₂×C₄	—	53	2	no	—
1261	C₂×C₄	—	53	4	no	—
1262	C₂×C₄	—	53	2	no	—
1263	C₂×C₄	—	53	4	no	—
1264	C₂×C₄	—	53	2	no	—
1265	C₂×C₄	—	53	2	no	—
1266	C₂×C₄	—	106	8	no	—
1267	C₂×C₄	—	106	16	no	—
1268	C₂×C₄	—	106	16	no	—
1269	C₂×C₄	—	106	2	no	—
1270	C₂×C₄	—	106	2	no	—
1271	C₂×C₄	—	106	4	no	—
1272	C₂×C₄	—	106	2	no	—
1273	C₂×C₄	—	106	2	no	—
1274	C₂×C₄	—	106	4	no	—
1275	C₂×C₄	—	106	2	no	—
1276	C₂×C₄	—	106	2	no	—
1277	C₂×C₄	—	106	8	no	—
1278	C₂×C₄	—	106	8	no	—
1279	C₂×C₄	—	212	8	no	—
1280	C₂×C₄	—	212	4	no	—
1281	C₂×C₄	—	212	8	no	—
1282	C₂×C₄	—	212	8	no	—
1283	C₂×C₄	—	212	8	no	—
1284	C₂×C₄	—	212	8	no	—
1285	C₂×C₄	—	212	8	no	—
1286	C₂×C₄	—	212	8	no	—
1287	C₂×C₄	—	212	8	no	—
1288	C₂×C₄	#41×D₅₃	1	4	yes	—
1289	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1290	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1291	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1292	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1293	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1294	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1295	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1296	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1297	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1298	C₂²	—	2	2	no	—
1299	C₂²	—	2	4	no	—
1300	C₂²	—	2	4	no	—
1301	C₂²	—	2	2	no	—
1302	C₂²	—	2	4	no	—
1303	C₂²	—	2	2	no	—
1304	C₂²	—	4	4	no	—
1305	C₂²	—	4	8	no	—
1306	C₂²	—	53	8	no	—
1307	C₂²	—	53	4	no	—
1308	C₂²	—	106	16	no	—
1309	C₂²	—	106	8	no	—
1310	C₂²	—	106	2	no	—
1311	C₂²	—	106	4	no	—
1312	C₂²	—	106	4	no	—
1313	C₂²	—	106	2	no	—
1314	C₂²	—	106	2	no	—
1315	C₂²	—	106	4	no	—
1316	C₂²	—	106	2	no	—
1317	C₂²	—	106	4	no	—
1318	C₂²	—	106	4	no	—
1319	C₂²	—	106	2	no	—
1320	C₂²	—	424	16	no	—
1321	C₂²	—	212	32	no	—
1322	C₂²	—	212	8	no	—
1323	C₂²	—	212	4	no	—
1324	C₂²	C₂×#41×D₅₃	1	2	yes	—
1325	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	—
1326	C₂²	#16811460	1	2	yes	—
1327	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1328	C₄	—	2	2	no	—
1329	C₄	—	2	4	no	—
1330	C₄	—	2	2	no	—
1331	C₄	—	2	4	no	—
1332	C₄	—	2	4	no	—
1333	C₄	—	2	2	no	—
1334	C₄	—	2	2	no	—
1335	C₄	—	2	2	no	—
1336	C₄	—	106	2	no	—
1337	C₄	—	106	2	no	—
1338	C₄	—	106	2	no	—
1339	C₄	—	106	4	no	—
1340	C₄	—	106	2	no	—
1341	C₄	—	106	4	no	—
1342	C₄	—	106	2	no	—
1343	C₄	—	106	2	no	—
1344	C₄	C₂×#41×D₅₃	1	4	yes	—
1345	C₂	—	4	2	no	—
1346	C₂	—	4	4	no	—
1347	C₂	—	106	8	no	—
1348	C₂	—	106	4	no	—
1349	C₂	—	212	4	no	—
1350	C₂	—	212	2	no	—
1351	C₂	#20288661	1	4	yes	direct product factor
1352	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1353	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1354	C₂	C₂×#16811460	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#542	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#542	D₅₃
hypocenter	C₅₃	C₂×#3513
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

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

N	H ≅ G/N	type
1. #20288661	C₂	direct (N × H)
2. C₂×#16811355	C₂	semidirect
3. C₂×#16811334	C₂	semidirect
4. C₂×#16811324	C₂	semidirect
5. C₂×#16811320	C₂	semidirect
6. C₂×#16811307	C₂	semidirect
7. C₂×#16811303	C₂	semidirect
8. C₂×#16811298	C₂	semidirect
9. C₂×#16811276	C₂	semidirect
10. C₂×#16811266	C₂	semidirect
11. C₂×#16811266	C₂	semidirect
12. C₂×#16811264	C₂	semidirect
13. C₂×#16811257	C₂	semidirect
14. C₂×#16811224	C₂	semidirect
15. C₂×#16811219	C₂	semidirect
16. C₂×#16811209	C₂	semidirect
17. C₂×#16811160	C₂	semidirect
18. C₂×#16811151	C₂	semidirect
19. C₂×#16811136	C₂	semidirect
20. C₂×#123×D₅₃	C₂	semidirect
21. C₂×#16811105	C₂	semidirect
22. C₂×#16811097	C₂	semidirect
23. C₂×C₄×D₄×D₅₃	C₂	semidirect
24. C₂×C₅₃×#542	C₂	semidirect
26. C₂²×#11719949	C₂²	semidirect
30. C₂³×C₄×D₅₃	C₂²	semidirect
31. #16811355	C₂²	semidirect
32. #16811334	C₂²	semidirect
33. #16811324	C₂²	semidirect
34. #16811320	C₂²	semidirect
35. #16811307	C₂²	semidirect
36. #16811303	C₂²	semidirect
37. #16811298	C₂²	semidirect
38. #16811276	C₂²	semidirect
39. #16811266	C₂²	semidirect
40. #16811266	C₂²	semidirect
41. #16811264	C₂²	semidirect
42. #16811257	C₂²	semidirect
43. #16811224	C₂²	semidirect
44. #16811219	C₂²	semidirect
45. #16811209	C₂²	semidirect
47. #16811160	C₂²	semidirect
48. #16811151	C₂²	semidirect
49. C₂×#13133212	C₂²	semidirect
50. C₂×#13133212	C₂²	semidirect
51. C₂×#13133210	C₂²	semidirect
52. C₂×#13133210	C₂²	semidirect
53. C₂×#13133210	C₂²	semidirect
54. C₂×#13133208	C₂²	semidirect
55. C₂×#13133208	C₂²	semidirect
56. C₂×#13133207	C₂²	semidirect
57. C₂×#13133207	C₂²	semidirect
58. C₂×#13133206	C₂²	semidirect
59. C₂×#13133203	C₂²	semidirect
60. C₂×#13133203	C₂²	semidirect
61. #16811136	C₂²	semidirect
62. C₂×#13133202	C₂²	semidirect
63. C₂×#13133202	C₂²	semidirect
64. C₂×#13133202	C₂²	semidirect
65. C₂×#13133202	C₂²	semidirect
66. C₂×#13133202	C₂²	semidirect
67. C₂×#13133201	C₂²	semidirect
68. C₂×#13133200	C₂²	semidirect
71. C₂×#13133199	C₂²	semidirect
72. C₂×#13133199	C₂²	semidirect
73. C₂×#13133199	C₂²	semidirect
74. C₂×#13133198	C₂²	semidirect
75. #123×D₅₃	C₂²	semidirect
76. C₂×#13133197	C₂²	semidirect
77. C₂×#13133195	C₂²	semidirect
78. C₂×#13133193	C₂²	semidirect
79. C₂×#13133193	C₂²	semidirect
80. C₂×#13133193	C₂²	semidirect
81. C₂×#13133193	C₂²	semidirect
83. C₂×#13133192	C₂²	semidirect
84. C₂×#13133192	C₂²	semidirect
85. C₂×#13133191	C₂²	semidirect
88. C₂×#13133190	C₂²	semidirect
89. C₂×#13133190	C₂²	semidirect
90. C₂×#13133188	C₂²	semidirect
91. C₂×#13133188	C₂²	semidirect
93. C₂×#13133187	C₂²	semidirect
94. C₂×#13133187	C₂²	semidirect
96. #16811105	C₂²	semidirect
97. #16811097	C₂²	semidirect
98. C₂×Q₈×Dic₅₃	C₂²	semidirect
99. C₂×C₄×Dic₁₀₆	C₂²	semidirect
102. C₂×C₄×D₂₁₂	C₂²	semidirect
103. C₂×C₄×D₂₁₂	C₂²	semidirect
104. C₂×C₄×D₂₁₂	C₂²	semidirect
105. C₂×C₄×D₂₁₂	C₂²	semidirect
106. C₂×C₄×D₂₁₂	C₂²	semidirect
107. C₂×D₄×Dic₅₃	C₂²	semidirect
110. C₂×#13133179	C₂²	semidirect
111. C₂×#13133179	C₂²	semidirect
112. C₂×#13133179	C₂²	semidirect
114. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
115. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
116. C₂×#13133177	C₂²	semidirect
117. C₂×#13133177	C₂²	semidirect
118. C₂×#13133177	C₂²	semidirect
119. C₄×D₄×D₅₃	C₂²	semidirect
120. C₂×#13133176	C₂²	semidirect
121. C₂×#13133175	C₂²	semidirect
122. C₂×#13133174	C₂²	semidirect
123. C₂×#13133174	C₂²	semidirect
124. C₂×#13133174	C₂²	semidirect
125. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
126. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
127. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
128. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
129. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
130. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
131. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
132. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
133. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
134. C₂×C₄²×D₅₃	C₂²	semidirect
135. C₅₃×#542	C₂²	semidirect
136. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
137. C₂×#126×C₅₃	C₂²	semidirect
138. C₂×#124×C₅₃	C₂²	semidirect
139. C₂×#124×C₅₃	C₂²	semidirect
140. C₂×#123×C₅₃	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
142. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
144. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
145. C₂×C₄×D₄×C₅₃	C₂²	semidirect
146. C₂×#117×C₅₃	C₂²	semidirect
152. C₂×#11719949	C₂³	semidirect
188. C₂²×C₄×D₅₃	C₂³	semidirect
190. #13133212	C₂³	semidirect
191. #13133212	C₂³	semidirect
192. #13133210	C₂³	semidirect
193. #13133210	C₂³	semidirect
194. #13133210	C₂³	semidirect
195. #13133208	C₂³	semidirect
196. #13133208	C₂³	semidirect
197. #13133207	C₂³	semidirect
198. #13133207	C₂³	semidirect
199. #13133206	C₂³	semidirect
200. #13133203	C₂³	semidirect
201. #13133203	C₂³	semidirect
202. #13133202	C₂³	semidirect
203. #13133202	C₂³	semidirect
204. #13133202	C₂³	semidirect
205. #13133202	C₂³	semidirect
206. #13133202	C₂³	semidirect
207. #13133201	C₂³	semidirect
208. #13133200	C₂³	semidirect
211. #13133199	C₂³	semidirect
212. #13133199	C₂³	semidirect
213. #13133199	C₂³	semidirect
214. #13133198	C₂³	semidirect
215. #13133197	C₂³	semidirect
216. #13133195	C₂³	semidirect
217. #13133193	C₂³	semidirect
218. #13133193	C₂³	semidirect
219. #13133193	C₂³	semidirect
220. #13133193	C₂³	semidirect
222. #13133192	C₂³	semidirect
223. #13133192	C₂³	semidirect
224. #13133191	C₂³	semidirect
227. #13133190	C₂³	semidirect
228. #13133190	C₂³	semidirect
229. #13133188	C₂³	semidirect
230. #13133188	C₂³	semidirect
232. #13133187	C₂³	semidirect
233. #13133187	C₂³	semidirect
235. Q₈×Dic₅₃	C₂³	semidirect
236. C₄×Dic₁₀₆	C₂³	semidirect
239. C₄×D₂₁₂	C₂³	semidirect
240. C₄×D₂₁₂	C₂³	semidirect
241. C₄×D₂₁₂	C₂³	semidirect
242. C₄×D₂₁₂	C₂³	semidirect
243. C₄×D₂₁₂	C₂³	semidirect
244. D₄×Dic₅₃	C₂³	semidirect
247. #13133179	C₂³	semidirect
248. #13133179	C₂³	semidirect
249. #13133179	C₂³	semidirect
251. C₄×C₂²⋊D₅₃	C₂³	semidirect
252. C₄×C₂²⋊D₅₃	C₂³	semidirect
253. #13133177	C₂³	semidirect
254. #13133177	C₂³	semidirect
255. #13133177	C₂³	semidirect
256. #13133176	C₂³	semidirect
257. #13133175	C₂³	semidirect
258. #13133174	C₂³	semidirect
259. #13133174	C₂³	semidirect
260. #13133174	C₂³	semidirect
279. C₄⋊C₄×D₅₃	C₂³	semidirect
280. C₄⋊C₄×D₅₃	C₂³	semidirect
281. C₄⋊C₄×D₅₃	C₂³	semidirect
282. C₄⋊C₄×D₅₃	C₂³	semidirect
305. C₂²⋊C₄×D₅₃	C₂³	semidirect
306. C₂²⋊C₄×D₅₃	C₂³	semidirect
307. C₂²⋊C₄×D₅₃	C₂³	semidirect
308. C₂²⋊C₄×D₅₃	C₂³	semidirect
309. C₂²⋊C₄×D₅₃	C₂³	semidirect
316. C₄²×D₅₃	C₂³	semidirect
323. C₄⋊Q₈×C₅₃	C₂³	semidirect
324. #126×C₅₃	C₂³	semidirect
325. #124×C₅₃	C₂³	semidirect
326. #124×C₅₃	C₂³	semidirect
327. #123×C₅₃	C₂³	semidirect
328. C₂²⋊Q₈×C₅₃	C₂³	semidirect
329. C₂²⋊Q₈×C₅₃	C₂³	semidirect
331. C₄×Q₈×C₅₃	C₂³	semidirect
332. C₄×D₄×C₅₃	C₂³	semidirect
333. #117×C₅₃	C₂³	semidirect
419. C₂×D₂₁₂	#41	semidirect
605. D₂₁₂	C₂×#41	semidirect
681. C₂×#542	D₅₃	semidirect
694. C₂×C₅₃	#3513	semidirect
720. #542	C₂×D₅₃	semidirect
724. C₂×C₄⋊Q₈	C₂×D₅₃	semidirect
733. C₂×#126	C₂×D₅₃	semidirect
741. C₂×#124	C₂×D₅₃	semidirect
742. C₂×#124	C₂×D₅₃	semidirect
758. C₂×#123	C₂×D₅₃	semidirect
765. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
766. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
786. C₂×C₄×Q₈	C₂×D₅₃	semidirect
807. C₂×C₄×D₄	C₂×D₅₃	semidirect
813. C₂×#117	C₂×D₅₃	semidirect
824. C₅₃	C₂×#3513	semidirect
873. C₄⋊Q₈	C₂²×D₅₃	semidirect
880. #126	C₂²×D₅₃	semidirect
888. #124	C₂²×D₅₃	semidirect
889. #124	C₂²×D₅₃	semidirect
903. #123	C₂²×D₅₃	semidirect
910. C₂²⋊Q₈	C₂²×D₅₃	semidirect
911. C₂²⋊Q₈	C₂²×D₅₃	semidirect
929. C₄×Q₈	C₂²×D₅₃	semidirect
949. C₄×D₄	C₂²×D₅₃	semidirect
955. #117	C₂²×D₅₃	semidirect
1351. C₂	#20288661	direct (N × H)

Maximal subgroups

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

subgroup	index
#20288661	2
C₂×#16811355	2
C₂×#16811334	2
C₂×#16811324	2
C₂×#16811320	2
C₂×#16811307	2
C₂×#16811303	2
C₂×#16811298	2
C₂×#16811276	2
C₂×#16811266	2
C₂×#16811264	2
C₂×#16811257	2
C₂×#16811224	2
C₂×#16811219	2
C₂×#16811209	2
C₂×#16811160	2
C₂×#16811151	2
C₂×#16811136	2
C₂×#123×D₅₃	2
C₂×#16811105	2
C₂×#16811097	2
C₂×C₄×D₄×D₅₃	2
C₂×C₅₃×#542	2
C₂×#3513	53

Subgroups — C2×#20288661 #28292071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20288661 #28292071