Subgroups — C₂×#529×D₅₃ #28290765

Order 13568.

8670 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811160	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16811159	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811158	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811157	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811156	C₂	1	2	yes	maximal, complemented
6	C₂×#16811155	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16811154	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16811153	C₂	1	2	yes	maximal, complemented
9	C₂×#16811152	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811151	C₂	1	2	yes	maximal, complemented
11	C₂×#16811150	C₂	1	2	yes	maximal, complemented
12	#529×D₅₃	C₂	1	32	yes	maximal, direct product factor
13	C₂×#126×D₅₃	C₂	1	2	yes	maximal, complemented
14	C₂×#125×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#124×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#123×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₂×C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#121×D₅₃	C₂	1	1	yes	maximal, characteristic
19	C₂×C₄×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
21	C₂×C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#117×D₅₃	C₂	1	2	yes	maximal, complemented
23	C₂²×C₄²×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
26	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
27	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
28	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
29	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
30	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
31	C₂³×C₄×D₅₃	C₂²	1	2	yes	—
32	#16811160	C₂²	1	16	yes	complemented
33	#16811159	C₂²	1	16	yes	complemented
34	#16811158	C₂²	1	16	yes	complemented
35	#16811157	C₂²	1	16	yes	complemented
36	#16811156	C₂²	1	32	yes	complemented
37	#16811155	C₂²	1	16	yes	complemented
38	#16811154	C₂²	1	16	yes	complemented
39	#16811153	C₂²	1	32	yes	complemented
40	#16811152	C₂²	1	16	yes	complemented
41	#16811151	C₂²	1	32	yes	complemented
42	#16811150	C₂²	1	32	yes	complemented
43	C₂×#13133212	C₂²	1	2	yes	complemented
44	C₂×#13133212	C₂²	1	2	yes	complemented
45	C₂×#13133212	C₂²	1	2	yes	complemented
46	C₂×#13133211	C₂²	1	2	yes	complemented
47	C₂×#13133210	C₂²	1	2	yes	complemented
48	C₂×#13133210	C₂²	1	2	yes	complemented
49	C₂×#13133210	C₂²	1	2	yes	complemented
50	#126×D₅₃	C₂²	1	32	yes	complemented
51	C₂×#13133209	C₂²	1	1	yes	characteristic, complemented
52	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13133207	C₂²	1	2	yes	complemented
55	C₂×#13133207	C₂²	1	2	yes	complemented
56	#125×D₅₃	C₂²	1	16	yes	complemented
57	C₂×#13133206	C₂²	1	1	yes	characteristic, complemented
58	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
59	C₂×#13133204	C₂²	1	1	yes	characteristic, complemented
60	C₂×#13133203	C₂²	1	2	yes	complemented
61	C₂×#13133203	C₂²	1	2	yes	complemented
62	#124×D₅₃	C₂²	1	16	yes	complemented
63	C₂×#13133202	C₂²	1	2	yes	complemented
64	C₂×#13133202	C₂²	1	2	yes	complemented
65	C₂×#13133201	C₂²	1	2	yes	complemented
66	C₂×#13133200	C₂²	1	2	yes	complemented
67	C₂×#13133199	C₂²	1	2	yes	complemented
68	C₂×#13133199	C₂²	1	2	yes	complemented
69	C₂×#13133198	C₂²	1	2	yes	complemented
70	#123×D₅₃	C₂²	1	32	yes	complemented
71	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
72	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
73	C₂×#13133195	C₂²	1	2	yes	complemented
74	C₂×#13133194	C₂²	1	2	yes	complemented
75	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
76	C₂²⋊Q₈×D₅₃	C₂²	1	16	yes	complemented
77	C₂×#13133192	C₂²	1	1	yes	characteristic
78	C₂×#13133191	C₂²	1	1	yes	characteristic
79	C₂×#13133190	C₂²	1	2	yes	—
80	C₂×#13133189	C₂²	1	2	yes	—
81	C₂×#13133188	C₂²	1	1	yes	characteristic
82	#121×D₅₃	C₂²	1	16	yes	—
83	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
85	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
86	C₂×#13133182	C₂²	1	2	yes	complemented
87	C₂×#13133182	C₂²	1	1	yes	characteristic, complemented
88	C₄×Q₈×D₅₃	C₂²	1	16	yes	complemented
89	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
90	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
91	C₂×D₄×Dic₅₃	C₂²	1	2	yes	complemented
92	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×#13133179	C₂²	1	2	yes	complemented
94	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
96	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
97	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
98	C₂×#13133177	C₂²	1	2	yes	complemented
99	C₂×#13133177	C₂²	1	2	yes	complemented
100	C₂×#13133177	C₂²	1	2	yes	complemented
101	C₄×D₄×D₅₃	C₂²	1	32	yes	complemented
102	C₄×D₄×D₅₃	C₂²	1	16	yes	complemented
103	C₂×#13133176	C₂²	1	2	yes	complemented
104	C₂×#13133175	C₂²	1	2	yes	complemented
105	C₂×#13133175	C₂²	1	2	yes	complemented
106	C₂×#13133174	C₂²	1	2	yes	complemented
107	C₂×#13133174	C₂²	1	2	yes	complemented
108	C₂×#13133173	C₂²	1	2	yes	complemented
109	C₂×#13133173	C₂²	1	2	yes	complemented
110	#117×D₅₃	C₂²	1	32	yes	complemented
111	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
112	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
113	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
114	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
115	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
116	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
117	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
118	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
119	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
120	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
121	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
122	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
126	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
127	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
128	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
129	C₂×C₄²×D₅₃	C₂²	1	2	yes	—
130	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄²×D₅₃	C₂²	1	16	yes	complemented
135	C₅₃×#529	C₂²	1	16	yes	complemented
136	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
137	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
138	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
140	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
141	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
142	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
144	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
145	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
146	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₅₃	C₂³	1	2	yes	—
148	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
150	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
151	C₂×Q₈×D₅₃	—	2	8	no	—
152	C₂×Q₈×D₅₃	C₂³	1	8	yes	—
153	C₂²×D₂₁₂	C₂³	1	2	yes	—
154	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
155	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
156	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
157	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
158	C₂×D₄×D₅₃	—	2	16	no	—
159	C₂×D₄×D₅₃	—	2	8	no	—
160	C₂×D₄×D₅₃	C₂³	1	16	yes	—
161	C₂×D₄×D₅₃	C₂³	1	8	yes	—
162	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
163	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
164	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
165	C₂³×Dic₅₃	C₂³	1	2	yes	—
166	C₂²×C₄×D₅₃	—	2	8	no	—
167	C₂²×C₄×D₅₃	—	2	8	no	—
168	C₂²×C₄×D₅₃	—	2	16	no	—
169	C₂²×C₄×D₅₃	—	2	8	no	—
170	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
171	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
172	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
173	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
174	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
175	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
176	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
177	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
178	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
179	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
180	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
182	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
183	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
184	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
185	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
186	C₂²×C₄×D₅₃	C₂³	1	16	yes	—
187	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
188	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
189	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
191	#13133212	C₂³	1	16	yes	complemented
192	#13133212	C₂³	1	16	yes	complemented
193	#13133212	C₂³	1	16	yes	complemented
194	#13133211	C₂³	1	16	yes	complemented
195	#13133210	C₂³	1	16	yes	complemented
196	#13133210	C₂³	1	16	yes	complemented
197	#13133210	C₂³	1	16	yes	complemented
198	#13133209	C₂³	1	8	yes	complemented
199	#13133208	C₂³	1	8	yes	complemented
200	#13133208	C₂³	1	8	yes	complemented
201	#13133207	C₂³	1	16	yes	complemented
202	#13133207	C₂³	1	16	yes	complemented
203	#13133206	C₂³	1	8	yes	complemented
204	#13133205	C₂³	1	8	yes	complemented
205	#13133204	C₂³	1	8	yes	complemented
206	#13133203	C₂³	1	16	yes	complemented
207	#13133203	C₂³	1	16	yes	complemented
208	#13133202	C₂³	1	16	yes	complemented
209	#13133202	C₂³	1	16	yes	complemented
210	#13133201	C₂³	1	16	yes	complemented
211	#13133200	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	8	yes	complemented
216	#13133196	C₂³	1	8	yes	complemented
217	#13133195	C₂³	1	16	yes	complemented
218	#13133194	C₂³	1	16	yes	complemented
219	#13133193	C₂³	1	8	yes	complemented
220	#13133192	C₂³	1	8	yes	—
221	#13133191	C₂³	1	8	yes	—
222	#13133190	C₂³	1	16	yes	—
223	#13133189	C₂³	1	16	yes	—
224	#13133188	C₂³	1	8	yes	—
225	Q₈×Dic₅₃	C₂³	1	8	yes	complemented
226	C₄×Dic₁₀₆	C₂³	1	16	yes	complemented
227	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
228	#13133182	C₂³	1	16	yes	complemented
229	#13133182	C₂³	1	8	yes	complemented
230	C₄×D₂₁₂	C₂³	1	16	yes	complemented
231	C₄×D₂₁₂	C₂³	1	8	yes	complemented
232	D₄×Dic₅₃	C₂³	1	16	yes	complemented
233	D₄×Dic₅₃	C₂³	1	8	yes	complemented
234	#13133179	C₂³	1	16	yes	complemented
235	#13133179	C₂³	1	8	yes	complemented
236	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
237	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
238	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
239	#13133177	C₂³	1	16	yes	complemented
240	#13133177	C₂³	1	16	yes	complemented
241	#13133177	C₂³	1	16	yes	complemented
242	#13133176	C₂³	1	16	yes	complemented
243	#13133175	C₂³	1	16	yes	complemented
244	#13133175	C₂³	1	16	yes	complemented
245	#13133174	C₂³	1	16	yes	complemented
246	#13133174	C₂³	1	16	yes	complemented
247	#13133173	C₂³	1	16	yes	complemented
248	#13133173	C₂³	1	16	yes	complemented
249	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
250	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
251	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
253	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
255	C₂×#11719919	C₂³	1	2	yes	—
256	C₂×#11719919	C₂³	1	2	yes	—
257	C₂×#11719919	C₂³	1	2	yes	—
258	C₂×#11719919	C₂³	1	2	yes	—
259	C₂×#11719919	C₂³	1	2	yes	—
260	C₂×#11719919	C₂³	1	2	yes	—
261	C₂×#11719919	C₂³	1	2	yes	—
262	C₂×#11719919	C₂³	1	2	yes	—
263	C₂×#11719919	C₂³	1	2	yes	—
264	C₂×#11719919	C₂³	1	2	yes	—
265	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
266	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
267	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
268	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
269	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
270	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
271	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
272	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
273	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
274	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
275	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
276	C₂×#11719921	C₂³	1	2	yes	—
277	C₂×#11719921	C₂³	1	2	yes	—
278	C₂×#11719921	C₂³	1	2	yes	—
279	C₂×#11719921	C₂³	1	2	yes	—
280	C₂×#11719921	C₂³	1	2	yes	—
281	C₂×#11719921	C₂³	1	2	yes	—
282	C₂×#11719921	C₂³	1	2	yes	—
283	C₂×#11719921	C₂³	1	2	yes	—
284	C₂×#11719921	C₂³	1	2	yes	—
285	C₂×#11719921	C₂³	1	2	yes	—
286	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
287	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
288	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
289	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
290	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
291	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
304	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
305	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
306	C₂×C₄×Dic₅₃	C₂³	1	8	yes	complemented
307	C₂×C₄×Dic₅₃	C₂³	1	8	yes	complemented
308	C₂×C₄×Dic₅₃	C₂³	1	8	yes	complemented
309	C₄²×D₅₃	C₂³	1	8	yes	—
310	C₄²×D₅₃	C₂³	1	8	yes	—
311	C₄²×D₅₃	C₂³	1	8	yes	—
312	C₄²×D₅₃	C₂³	1	8	yes	—
313	C₄²×D₅₃	C₂³	1	16	yes	—
314	C₄²×D₅₃	C₂³	1	8	yes	complemented
315	C₄²×D₅₃	C₂³	1	8	yes	complemented
316	C₄²×D₅₃	C₂³	1	8	yes	complemented
317	C₄²×D₅₃	C₂³	1	8	yes	complemented
318	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
320	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
323	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
325	#126×C₅₃	C₂³	1	16	yes	complemented
326	#125×C₅₃	C₂³	1	8	yes	complemented
327	#124×C₅₃	C₂³	1	8	yes	complemented
328	#123×C₅₃	C₂³	1	16	yes	complemented
329	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
330	#121×C₅₃	C₂³	1	8	yes	—
331	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
332	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
333	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
334	#117×C₅₃	C₂³	1	16	yes	complemented
335	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
336	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
351	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
352	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
353	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂³×D₅₃	—	2	4	no	—
355	C₂³×D₅₃	—	2	4	no	—
356	C₂³×D₅₃	—	2	8	no	—
357	C₂³×D₅₃	—	2	8	no	—
358	C₂³×D₅₃	—	2	8	no	—
359	C₂³×D₅₃	#41	1	8	yes	—
360	C₂³×D₅₃	C₂⁴	1	8	yes	—
361	C₂³×D₅₃	C₂⁴	1	2	yes	—
362	C₂³×D₅₃	C₂⁴	1	4	yes	—
363	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
364	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×Q₈×C₅₃	—	2	4	no	—
366	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
367	C₂×D₄×C₅₃	—	2	8	no	—
368	C₂×D₄×C₅₃	—	2	4	no	—
369	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
370	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
371	C₂²×C₄×C₅₃	—	2	4	no	—
372	C₂²×C₄×C₅₃	—	2	4	no	—
373	C₂²×C₄×C₅₃	—	2	4	no	—
374	C₂²×C₄×C₅₃	—	2	8	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	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
380	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
382	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
383	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
384	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₂²⋊D₅₃	—	2	8	no	—
389	C₂×C₂²⋊D₅₃	—	2	8	no	—
390	C₂×C₂²⋊D₅₃	—	2	8	no	—
391	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
392	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
393	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
394	C₂²×Dic₅₃	—	2	4	no	—
395	C₂²×Dic₅₃	—	2	4	no	—
396	C₂²×Dic₅₃	—	2	4	no	—
397	C₂²×Dic₅₃	—	2	8	no	—
398	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
403	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
404	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
405	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
406	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
407	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
408	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
409	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
411	Q₈×D₅₃	—	2	32	no	—
412	D₄×D₅₃	—	2	64	no	—
413	D₄×D₅₃	—	2	32	no	—
414	C₂×D₂₁₂	—	2	8	no	—
415	C₂×D₂₁₂	—	2	4	no	—
416	C₂×D₂₁₂	C₂⁴	1	8	yes	—
417	C₂×D₂₁₂	C₂⁴	1	4	yes	—
418	C₂×C₄×D₅₃	—	2	4	no	—
419	C₂×C₄×D₅₃	—	2	4	no	—
420	C₂×C₄×D₅₃	—	2	32	no	—
421	C₂×C₄×D₅₃	—	2	4	no	—
422	C₂×C₄×D₅₃	—	2	4	no	—
423	C₂×C₄×D₅₃	—	2	4	no	—
424	C₂×C₄×D₅₃	—	2	4	no	—
425	C₂×C₄×D₅₃	—	2	8	no	—
426	C₂×C₄×D₅₃	—	2	8	no	—
427	C₂×C₄×D₅₃	—	2	8	no	—
428	C₂×C₄×D₅₃	—	2	4	no	—
429	C₂×C₄×D₅₃	—	2	4	no	—
430	C₂×C₄×D₅₃	—	2	8	no	—
431	C₂×C₄×D₅₃	—	2	4	no	—
432	C₂×C₄×D₅₃	—	2	4	no	—
433	C₂×C₄×D₅₃	—	2	8	no	—
434	C₂×C₄×D₅₃	—	2	32	no	—
435	C₂×C₄×D₅₃	—	2	64	no	—
436	C₂×C₄×D₅₃	—	2	32	no	—
437	C₂×C₄×D₅₃	#41	1	8	yes	—
438	C₂×C₄×D₅₃	#41	1	8	yes	—
439	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
440	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
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	4	yes	—
448	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
449	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
450	C₂×C₄×D₅₃	C₂⁴	1	4	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×C₄×D₅₃	C₂⁴	1	4	yes	—
455	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
456	C₂×Dic₁₀₆	—	2	4	no	—
457	C₂×Dic₁₀₆	—	2	8	no	—
458	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
459	C₂×Dic₁₀₆	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	4	yes	—
463	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
464	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
465	C₄⋊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	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
471	C₄²×C₅₃	C₂⁴	1	4	yes	—
472	C₄²×C₅₃	C₂⁴	1	4	yes	—
473	C₄²×C₅₃	C₂⁴	1	4	yes	—
474	C₄²×C₅₃	C₂⁴	1	4	yes	—
475	C₄²×C₅₃	C₂⁴	1	8	yes	—
476	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
477	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
478	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
479	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
480	C₂²⋊Dic₅₃	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	8	yes	—
489	#11719921	C₂⁴	1	8	yes	—
490	#11719921	C₂⁴	1	8	yes	—
491	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
492	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
493	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
494	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
495	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
496	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
497	#11719919	C₂⁴	1	8	yes	—
498	#11719919	C₂⁴	1	8	yes	—
499	#11719919	C₂⁴	1	8	yes	—
500	#11719919	C₂⁴	1	8	yes	—
501	#11719919	C₂⁴	1	8	yes	—
502	#11719919	C₂⁴	1	8	yes	—
503	#11719919	C₂⁴	1	8	yes	—
504	#11719919	C₂⁴	1	8	yes	—
505	#11719919	C₂⁴	1	8	yes	—
506	#11719919	C₂⁴	1	8	yes	—
507	C₄×Dic₅₃	C₂⁴	1	4	yes	—
508	C₄×Dic₅₃	C₂⁴	1	4	yes	—
509	C₄×Dic₅₃	C₂⁴	1	4	yes	—
510	C₄×Dic₅₃	C₂⁴	1	4	yes	—
511	C₄×Dic₅₃	C₂⁴	1	4	yes	—
512	C₄×Dic₅₃	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	4	yes	—
517	C₄×Dic₅₃	C₂⁴	1	4	yes	—
518	C₄×Dic₅₃	C₂⁴	1	4	yes	—
519	C₄×Dic₅₃	C₂⁴	1	8	yes	—
520	C₄×Dic₅₃	C₂⁴	1	8	yes	—
521	C₄×Dic₅₃	C₂⁴	1	8	yes	—
522	C₂³×C₅₃	—	2	2	no	—
523	C₂³×C₅₃	—	2	2	no	—
524	C₂³×C₅₃	—	2	4	no	—
525	C₂³×C₅₃	—	2	4	no	—
526	C₂³×C₅₃	—	2	4	no	—
527	C₂³×C₅₃	C₂×#41	1	4	yes	—
528	C₂³×C₅₃	C₂⁵	1	4	yes	—
529	C₂³×C₅₃	C₂⁵	1	2	yes	—
530	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
531	C₂²×D₅₃	—	2	2	no	—
532	C₂²×D₅₃	—	2	2	no	—
533	C₂²×D₅₃	—	2	32	no	—
534	C₂²×D₅₃	—	2	8	no	—
535	C₂²×D₅₃	—	2	8	no	—
536	C₂²×D₅₃	—	2	4	no	—
537	C₂²×D₅₃	—	2	4	no	—
538	C₂²×D₅₃	—	2	4	no	—
539	C₂²×D₅₃	—	2	16	no	—
540	C₂²×D₅₃	—	2	16	no	—
541	C₂²×D₅₃	—	2	16	no	—
542	C₂²×D₅₃	—	4	32	no	—
543	C₂²×D₅₃	C₂×#41	1	4	yes	—
544	C₂²×D₅₃	C₂×#41	1	16	yes	—
545	C₂²×D₅₃	C₂×#41	1	4	yes	—
546	C₂²×D₅₃	C₂×#41	1	4	yes	—
547	C₂²×D₅₃	C₂×#41	1	4	yes	—
548	C₂²×D₅₃	C₂⁵	1	4	yes	—
549	C₂²×D₅₃	C₂⁵	1	2	yes	—
550	C₂²×D₅₃	C₂⁵	1	2	yes	—
551	Q₈×C₅₃	—	2	8	no	—
552	D₄×C₅₃	—	2	16	no	—
553	D₄×C₅₃	—	2	8	no	—
554	C₂×C₄×C₅₃	—	2	4	no	—
555	C₂×C₄×C₅₃	—	2	8	no	—
556	C₂×C₄×C₅₃	—	2	2	no	—
557	C₂×C₄×C₅₃	—	2	2	no	—
558	C₂×C₄×C₅₃	—	2	2	no	—
559	C₂×C₄×C₅₃	—	2	2	no	—
560	C₂×C₄×C₅₃	—	2	4	no	—
561	C₂×C₄×C₅₃	—	2	4	no	—
562	C₂×C₄×C₅₃	—	2	8	no	—
563	C₂×C₄×C₅₃	—	2	8	no	—
564	C₂×C₄×C₅₃	—	2	16	no	—
565	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
566	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
567	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
568	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
569	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
570	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
571	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
572	C₂×C₄×C₅₃	C₂⁵	1	4	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	16	no	—
578	C₂²⋊D₅₃	—	2	16	no	—
579	C₂×Dic₅₃	—	2	4	no	—
580	C₂×Dic₅₃	—	2	8	no	—
581	C₂×Dic₅₃	—	2	2	no	—
582	C₂×Dic₅₃	—	2	2	no	—
583	C₂×Dic₅₃	—	2	2	no	—
584	C₂×Dic₅₃	—	2	2	no	—
585	C₂×Dic₅₃	—	2	4	no	—
586	C₂×Dic₅₃	—	2	4	no	—
587	C₂×Dic₅₃	—	2	8	no	—
588	C₂×Dic₅₃	—	2	8	no	—
589	C₂×Dic₅₃	—	2	16	no	—
590	C₂×Dic₅₃	C₂×#41	1	4	yes	—
591	C₂×Dic₅₃	C₂×#41	1	4	yes	—
592	C₂×Dic₅₃	C₂⁵	1	4	yes	—
593	C₂×Dic₅₃	C₂⁵	1	2	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	4	yes	—
599	C₂×Dic₅₃	C₂⁵	1	2	yes	—
600	C₂×Dic₅₃	C₂⁵	1	2	yes	—
601	D₂₁₂	—	2	16	no	—
602	D₂₁₂	—	2	8	no	—
603	C₄×D₅₃	—	2	8	no	—
604	C₄×D₅₃	—	2	8	no	—
605	C₄×D₅₃	—	2	8	no	—
606	C₄×D₅₃	—	2	8	no	—
607	C₄×D₅₃	—	2	8	no	—
608	C₄×D₅₃	—	2	8	no	—
609	C₄×D₅₃	—	2	16	no	—
610	C₄×D₅₃	—	2	16	no	—
611	C₄×D₅₃	—	2	16	no	—
612	C₄×D₅₃	—	2	8	no	—
613	C₄×D₅₃	—	2	8	no	—
614	C₄×D₅₃	—	2	16	no	—
615	C₄×D₅₃	—	2	8	no	—
616	C₄×D₅₃	—	2	8	no	—
617	C₄×D₅₃	—	2	16	no	—
618	C₄×D₅₃	C₂×#41	1	16	yes	—
619	C₄×D₅₃	C₂×#41	1	16	yes	—
620	Dic₁₀₆	—	2	8	no	—
621	Dic₁₀₆	—	2	16	no	—
622	C₂²×#529	—	53	1	no	maximal, Sylow
623	C₂²×C₅₃	—	2	2	no	—
624	C₂²×C₅₃	—	2	2	no	—
625	C₂²×C₅₃	—	2	8	no	—
626	C₂²×C₅₃	—	2	4	no	—
627	C₂²×C₅₃	—	2	4	no	—
628	C₂²×C₅₃	—	2	4	no	—
629	C₂²×C₅₃	—	4	8	no	—
630	C₂²×C₅₃	C₂²×#41	1	4	yes	—
631	C₂²×C₅₃	C₂²×#41	1	2	yes	—
632	C₂²×C₅₃	C₂²×#41	1	2	yes	—
633	C₂²×C₅₃	C₂²×#41	1	2	yes	—
634	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
635	C₂×D₅₃	—	2	2	no	—
636	C₂×D₅₃	—	2	2	no	—
637	C₂×D₅₃	—	2	8	no	—
638	C₂×D₅₃	—	2	32	no	—
639	C₂×D₅₃	—	2	4	no	—
640	C₂×D₅₃	—	2	4	no	—
641	C₂×D₅₃	—	2	4	no	—
642	C₂×D₅₃	—	4	8	no	—
643	C₂×D₅₃	—	4	32	no	—
644	C₂×D₅₃	#529	1	16	yes	direct product factor
645	C₂×D₅₃	C₂²×#41	1	4	yes	—
646	C₂×D₅₃	C₂²×#41	1	4	yes	—
647	C₂×D₅₃	C₂²×#41	1	4	yes	—
648	C₂×D₅₃	C₂²×#41	1	4	yes	—
649	C₄×C₅₃	—	2	4	no	—
650	C₄×C₅₃	—	2	2	no	—
651	C₄×C₅₃	—	2	2	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	C₂²×#41	1	4	yes	—
657	C₄×C₅₃	C₂²×#41	1	4	yes	—
658	Dic₅₃	—	2	4	no	—
659	Dic₅₃	—	2	2	no	—
660	Dic₅₃	—	2	2	no	—
661	Dic₅₃	—	2	2	no	—
662	Dic₅₃	—	2	2	no	—
663	Dic₅₃	—	2	4	no	—
664	Dic₅₃	—	2	4	no	—
665	Dic₅₃	C₂²×#41	1	4	yes	—
666	Dic₅₃	C₂²×#41	1	4	yes	—
667	C₂×#529	—	53	1	no	—
668	C₂×#529	—	53	32	no	—
669	C₂×#529	—	53	2	no	—
670	C₂×#529	—	53	1	no	—
671	C₂×#529	—	53	1	no	—
672	C₂×#529	—	53	2	no	—
673	C₂×#529	—	53	1	no	—
674	C₂×#529	—	53	1	no	—
675	C₂×#529	—	53	1	no	—
676	C₂×#529	—	53	2	no	—
677	C₂×#529	—	53	1	no	—
678	C₂×#529	—	53	2	no	—
679	C₂×#529	D₅₃	1	1	yes	characteristic, direct product factor
680	C₂²×#126	—	53	2	no	—
681	C₂²×#125	—	53	1	no	—
682	C₂²×#124	—	53	1	no	—
683	C₂²×#123	—	53	2	no	—
684	C₂²×C₂²⋊Q₈	—	53	1	no	—
685	C₂²×#121	—	53	1	no	—
686	C₂²×C₄×Q₈	—	53	1	no	—
687	C₂²×C₄×D₄	—	53	2	no	—
688	C₂²×C₄×D₄	—	53	1	no	—
689	C₂²×#117	—	53	2	no	—
690	C₂³×C₄²	—	53	1	no	—
691	C₂×C₅₃	—	2	4	no	—
692	C₂×C₅₃	—	4	4	no	—
693	C₂×C₅₃	C₂×#529	1	4	yes	complemented
694	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
695	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
696	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
697	D₅₃	—	2	4	no	—
698	D₅₃	—	4	4	no	—
699	D₅₃	C₂×#529	1	8	yes	direct product factor
700	C₂³×Q₈	—	53	1	no	—
701	C₂³×D₄	—	53	2	no	—
702	C₂³×D₄	—	53	1	no	—
703	C₂⁴×C₄	—	53	1	no	—
704	C₂⁴×C₄	—	53	1	no	—
705	C₂⁴×C₄	—	53	1	no	—
706	C₂⁴×C₄	—	53	2	no	—
707	#529	—	53	32	no	—
708	#529	—	53	16	no	—
709	#529	—	53	16	no	—
710	#529	—	53	32	no	—
711	#529	—	53	16	no	—
712	#529	—	53	16	no	—
713	#529	—	53	16	no	—
714	#529	—	53	32	no	—
715	#529	—	53	16	no	—
716	#529	—	53	32	no	—
717	#529	—	53	16	no	—
718	#529	C₂×D₅₃	1	16	yes	direct product factor
719	C₂×#126	—	53	32	no	—
720	C₂×#126	—	53	2	no	—
721	C₂×#126	—	53	2	no	—
722	C₂×#126	—	53	2	no	—
723	C₂×#126	—	53	2	no	—
724	C₂×#126	—	53	2	no	—
725	C₂×#126	—	53	2	no	—
726	C₂×#126	—	53	2	no	—
727	C₂×#126	C₂×D₅₃	1	2	yes	complemented
728	C₂×#125	—	53	16	no	—
729	C₂×#125	—	53	2	no	—
730	C₂×#125	—	53	2	no	—
731	C₂×#125	—	53	1	no	—
732	C₂×#125	—	53	1	no	—
733	C₂×#125	—	53	1	no	—
734	C₂×#125	C₂×D₅₃	1	1	yes	characteristic, complemented
735	C₂×#124	—	53	1	no	—
736	C₂×#124	—	53	1	no	—
737	C₂×#124	—	53	16	no	—
738	C₂×#124	—	53	2	no	—
739	C₂×#124	—	53	2	no	—
740	C₂×#124	—	53	1	no	—
741	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
742	C₂×#123	—	53	2	no	—
743	C₂×#123	—	53	2	no	—
744	C₂×#123	—	53	32	no	—
745	C₂×#123	—	53	2	no	—
746	C₂×#123	—	53	2	no	—
747	C₂×#123	—	53	2	no	—
748	C₂×#123	—	53	2	no	—
749	C₂×#123	—	53	2	no	—
750	C₂×#123	C₂×D₅₃	1	2	yes	complemented
751	C₂×C₂²⋊Q₈	—	53	1	no	—
752	C₂×C₂²⋊Q₈	—	53	1	no	—
753	C₂×C₂²⋊Q₈	—	53	16	no	—
754	C₂×C₂²⋊Q₈	—	53	2	no	—
755	C₂×C₂²⋊Q₈	—	53	1	no	—
756	C₂×C₂²⋊Q₈	—	53	2	no	—
757	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
758	C₂×#121	—	53	1	no	—
759	C₂×#121	—	53	2	no	—
760	C₂×#121	—	53	1	no	—
761	C₂×#121	—	53	16	no	—
762	C₂×#121	—	53	1	no	—
763	C₂×#121	—	53	2	no	—
764	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
765	C₂×C₄×Q₈	—	53	1	no	—
766	C₂×C₄×Q₈	—	53	16	no	—
767	C₂×C₄×Q₈	—	53	2	no	—
768	C₂×C₄×Q₈	—	53	1	no	—
769	C₂×C₄×Q₈	—	53	1	no	—
770	C₂×C₄×Q₈	—	53	2	no	—
771	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
772	C₂×C₄×D₄	—	53	2	no	—
773	C₂×C₄×D₄	—	53	1	no	—
774	C₂×C₄×D₄	—	53	2	no	—
775	C₂×C₄×D₄	—	53	2	no	—
776	C₂×C₄×D₄	—	53	2	no	—
777	C₂×C₄×D₄	—	53	32	no	—
778	C₂×C₄×D₄	—	53	16	no	—
779	C₂×C₄×D₄	—	53	2	no	—
780	C₂×C₄×D₄	—	53	1	no	—
781	C₂×C₄×D₄	—	53	2	no	—
782	C₂×C₄×D₄	—	53	2	no	—
783	C₂×C₄×D₄	—	53	2	no	—
784	C₂×C₄×D₄	—	53	2	no	—
785	C₂×C₄×D₄	—	53	1	no	—
786	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
787	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
788	C₂×#117	—	53	2	no	—
789	C₂×#117	—	53	32	no	—
790	C₂×#117	—	53	2	no	—
791	C₂×#117	—	53	2	no	—
792	C₂×#117	—	53	2	no	—
793	C₂×#117	—	53	2	no	—
794	C₂×#117	—	53	2	no	—
795	C₂×#117	—	53	2	no	—
796	C₂×#117	C₂×D₅₃	1	2	yes	complemented
797	C₂²×C₄⋊C₄	—	53	2	no	—
798	C₂²×C₄⋊C₄	—	53	2	no	—
799	C₂²×C₄⋊C₄	—	53	1	no	—
800	C₂²×C₄⋊C₄	—	53	2	no	—
801	C₂²×C₄⋊C₄	—	53	1	no	—
802	C₂²×C₄⋊C₄	—	53	2	no	—
803	C₂²×C₂²⋊C₄	—	53	2	no	—
804	C₂²×C₂²⋊C₄	—	53	2	no	—
805	C₂²×C₂²⋊C₄	—	53	2	no	—
806	C₂²×C₂²⋊C₄	—	53	2	no	—
807	C₂²×C₂²⋊C₄	—	53	2	no	—
808	C₂²×C₄²	—	53	1	no	—
809	C₂²×C₄²	—	53	1	no	—
810	C₂²×C₄²	—	53	1	no	—
811	C₂²×C₄²	—	53	1	no	—
812	C₂²×C₄²	—	53	1	no	—
813	C₂²×C₄²	—	53	1	no	—
814	C₂²×C₄²	—	53	1	no	—
815	C₂²×C₄²	—	53	2	no	—
816	C₂²×C₄²	—	53	1	no	—
817	C₂²×C₄²	—	53	1	no	—
818	C₂²×C₄²	—	53	1	no	—
819	C₂²×C₄²	—	53	1	no	—
820	C₂²×C₄²	—	53	16	no	—
821	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
822	C₅₃	C₂²×#529	1	1	yes	characteristic, complemented, Sylow
823	C₂⁵	—	53	1	no	—
824	C₂⁵	—	53	2	no	—
825	C₂²×Q₈	—	53	8	no	—
826	C₂²×Q₈	—	53	2	no	—
827	C₂²×Q₈	—	53	1	no	—
828	C₂²×Q₈	—	106	8	no	—
829	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
830	C₂²×D₄	—	53	2	no	—
831	C₂²×D₄	—	53	2	no	—
832	C₂²×D₄	—	53	2	no	—
833	C₂²×D₄	—	53	16	no	—
834	C₂²×D₄	—	53	8	no	—
835	C₂²×D₄	—	53	2	no	—
836	C₂²×D₄	—	53	1	no	—
837	C₂²×D₄	—	106	8	no	—
838	C₂²×D₄	—	106	16	no	—
839	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
840	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
841	C₂³×C₄	—	53	1	no	—
842	C₂³×C₄	—	53	1	no	—
843	C₂³×C₄	—	53	2	no	—
844	C₂³×C₄	—	53	1	no	—
845	C₂³×C₄	—	53	1	no	—
846	C₂³×C₄	—	53	1	no	—
847	C₂³×C₄	—	53	2	no	—
848	C₂³×C₄	—	53	2	no	—
849	C₂³×C₄	—	53	1	no	—
850	C₂³×C₄	—	53	1	no	—
851	C₂³×C₄	—	53	1	no	—
852	C₂³×C₄	—	53	1	no	—
853	C₂³×C₄	—	53	2	no	—
854	C₂³×C₄	—	53	2	no	—
855	C₂³×C₄	—	53	16	no	—
856	C₂³×C₄	—	53	1	no	—
857	C₂³×C₄	—	53	8	no	—
858	C₂³×C₄	—	53	1	no	—
859	C₂³×C₄	—	53	8	no	—
860	C₂³×C₄	—	53	1	no	—
861	C₂³×C₄	—	53	1	no	—
862	C₂³×C₄	—	53	1	no	—
863	C₂³×C₄	—	53	8	no	—
864	C₂³×C₄	—	53	2	no	—
865	C₂³×C₄	—	53	1	no	—
866	C₂³×C₄	—	106	8	no	—
867	C₂³×C₄	—	106	16	no	—
868	C₂³×C₄	—	106	8	no	—
869	C₂³×C₄	—	106	8	no	—
870	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
871	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
872	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
873	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
874	#126	—	53	16	no	—
875	#126	—	53	16	no	—
876	#126	—	53	16	no	—
877	#126	—	53	16	no	—
878	#126	—	53	16	no	—
879	#126	—	53	16	no	—
880	#126	—	53	16	no	—
881	#126	C₂²×D₅₃	1	16	yes	complemented
882	#125	—	53	16	no	—
883	#125	—	53	16	no	—
884	#125	—	53	8	no	—
885	#125	—	53	8	no	—
886	#125	—	53	8	no	—
887	#125	C₂²×D₅₃	1	8	yes	complemented
888	#124	—	53	8	no	—
889	#124	—	53	8	no	—
890	#124	—	53	16	no	—
891	#124	—	53	16	no	—
892	#124	—	53	8	no	—
893	#124	C₂²×D₅₃	1	8	yes	complemented
894	#123	—	53	16	no	—
895	#123	—	53	16	no	—
896	#123	—	53	16	no	—
897	#123	—	53	16	no	—
898	#123	—	53	16	no	—
899	#123	—	53	16	no	—
900	#123	—	53	16	no	—
901	#123	C₂²×D₅₃	1	16	yes	complemented
902	C₂²⋊Q₈	—	53	8	no	—
903	C₂²⋊Q₈	—	53	8	no	—
904	C₂²⋊Q₈	—	53	16	no	—
905	C₂²⋊Q₈	—	53	8	no	—
906	C₂²⋊Q₈	—	53	16	no	—
907	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
908	#121	—	53	8	no	—
909	#121	—	53	16	no	—
910	#121	—	53	8	no	—
911	#121	—	53	8	no	—
912	#121	—	53	16	no	—
913	#121	C₂²×D₅₃	1	8	yes	—
914	C₄×Q₈	—	53	8	no	—
915	C₄×Q₈	—	53	16	no	—
916	C₄×Q₈	—	53	8	no	—
917	C₄×Q₈	—	53	16	no	—
918	C₄×Q₈	—	53	8	no	—
919	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
920	C₄×D₄	—	53	8	no	—
921	C₄×D₄	—	53	16	no	—
922	C₄×D₄	—	53	16	no	—
923	C₄×D₄	—	53	16	no	—
924	C₄×D₄	—	53	16	no	—
925	C₄×D₄	—	53	8	no	—
926	C₄×D₄	—	53	16	no	—
927	C₄×D₄	—	53	16	no	—
928	C₄×D₄	—	53	16	no	—
929	C₄×D₄	—	53	16	no	—
930	C₄×D₄	—	53	8	no	—
931	C₄×D₄	—	53	16	no	—
932	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
933	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
934	#117	—	53	16	no	—
935	#117	—	53	16	no	—
936	#117	—	53	16	no	—
937	#117	—	53	16	no	—
938	#117	—	53	16	no	—
939	#117	—	53	16	no	—
940	#117	—	53	16	no	—
941	#117	C₂²×D₅₃	1	16	yes	complemented
942	C₂×C₄⋊C₄	—	53	2	no	—
943	C₂×C₄⋊C₄	—	53	2	no	—
944	C₂×C₄⋊C₄	—	53	2	no	—
945	C₂×C₄⋊C₄	—	53	2	no	—
946	C₂×C₄⋊C₄	—	53	2	no	—
947	C₂×C₄⋊C₄	—	53	2	no	—
948	C₂×C₄⋊C₄	—	53	2	no	—
949	C₂×C₄⋊C₄	—	53	1	no	—
950	C₂×C₄⋊C₄	—	53	2	no	—
951	C₂×C₄⋊C₄	—	53	2	no	—
952	C₂×C₄⋊C₄	—	53	2	no	—
953	C₂×C₄⋊C₄	—	53	2	no	—
954	C₂×C₄⋊C₄	—	53	1	no	—
955	C₂×C₄⋊C₄	—	53	2	no	—
956	C₂×C₄⋊C₄	—	53	2	no	—
957	C₂×C₄⋊C₄	—	53	2	no	—
958	C₂×C₄⋊C₄	—	53	16	no	—
959	C₂×C₄⋊C₄	—	53	16	no	—
960	C₂×C₄⋊C₄	—	53	8	no	—
961	C₂×C₄⋊C₄	—	53	16	no	—
962	C₂×C₄⋊C₄	—	53	8	no	—
963	C₂×C₄⋊C₄	—	53	16	no	—
964	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
965	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
966	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
968	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
970	C₂×C₂²⋊C₄	—	53	2	no	—
971	C₂×C₂²⋊C₄	—	53	2	no	—
972	C₂×C₂²⋊C₄	—	53	2	no	—
973	C₂×C₂²⋊C₄	—	53	2	no	—
974	C₂×C₂²⋊C₄	—	53	2	no	—
975	C₂×C₂²⋊C₄	—	53	2	no	—
976	C₂×C₂²⋊C₄	—	53	2	no	—
977	C₂×C₂²⋊C₄	—	53	2	no	—
978	C₂×C₂²⋊C₄	—	53	2	no	—
979	C₂×C₂²⋊C₄	—	53	2	no	—
980	C₂×C₂²⋊C₄	—	53	2	no	—
981	C₂×C₂²⋊C₄	—	53	2	no	—
982	C₂×C₂²⋊C₄	—	53	2	no	—
983	C₂×C₂²⋊C₄	—	53	2	no	—
984	C₂×C₂²⋊C₄	—	53	2	no	—
985	C₂×C₂²⋊C₄	—	53	16	no	—
986	C₂×C₂²⋊C₄	—	53	16	no	—
987	C₂×C₂²⋊C₄	—	53	16	no	—
988	C₂×C₂²⋊C₄	—	53	16	no	—
989	C₂×C₂²⋊C₄	—	53	16	no	—
990	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
991	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
992	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
993	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
994	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
995	C₂×C₄²	—	53	1	no	—
996	C₂×C₄²	—	53	1	no	—
997	C₂×C₄²	—	53	2	no	—
998	C₂×C₄²	—	53	2	no	—
999	C₂×C₄²	—	53	1	no	—
1000	C₂×C₄²	—	53	1	no	—
1001	C₂×C₄²	—	53	1	no	—
1002	C₂×C₄²	—	53	1	no	—
1003	C₂×C₄²	—	53	1	no	—
1004	C₂×C₄²	—	53	1	no	—
1005	C₂×C₄²	—	53	1	no	—
1006	C₂×C₄²	—	53	1	no	—
1007	C₂×C₄²	—	53	8	no	—
1008	C₂×C₄²	—	53	8	no	—
1009	C₂×C₄²	—	53	8	no	—
1010	C₂×C₄²	—	53	1	no	—
1011	C₂×C₄²	—	53	2	no	—
1012	C₂×C₄²	—	53	1	no	—
1013	C₂×C₄²	—	53	8	no	—
1014	C₂×C₄²	—	53	16	no	—
1015	C₂×C₄²	—	53	8	no	—
1016	C₂×C₄²	—	53	8	no	—
1017	C₂×C₄²	—	53	8	no	—
1018	C₂×C₄²	—	53	8	no	—
1019	C₂×C₄²	—	53	8	no	—
1020	C₂×C₄²	—	53	8	no	—
1021	C₂×C₄²	—	53	8	no	—
1022	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1023	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1024	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1025	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
1026	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1027	C₂×C₄²	C₂²×D₅₃	1	8	yes	complemented
1028	C₂⁴	—	53	1	no	—
1029	C₂⁴	—	53	8	no	—
1030	C₂⁴	—	53	4	no	—
1031	C₂⁴	—	53	1	no	—
1032	C₂⁴	—	53	8	no	—
1033	C₂⁴	—	53	2	no	—
1034	C₂⁴	—	106	4	no	—
1035	C₂⁴	—	106	4	no	—
1036	C₂⁴	—	106	8	no	—
1037	C₂⁴	—	106	8	no	—
1038	C₂⁴	—	106	8	no	—
1039	C₂⁴	C₂³×D₅₃	1	2	yes	—
1040	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1041	C₂×Q₈	—	2	4	no	—
1042	C₂×Q₈	—	53	8	no	—
1043	C₂×Q₈	—	53	4	no	—
1044	C₂×Q₈	—	106	8	no	—
1045	C₂×Q₈	—	106	32	no	—
1046	C₂×Q₈	—	106	4	no	—
1047	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1048	C₂×D₄	—	2	8	no	—
1049	C₂×D₄	—	2	4	no	—
1050	C₂×D₄	—	53	8	no	—
1051	C₂×D₄	—	53	8	no	—
1052	C₂×D₄	—	53	8	no	—
1053	C₂×D₄	—	53	8	no	—
1054	C₂×D₄	—	53	4	no	—
1055	C₂×D₄	—	106	8	no	—
1056	C₂×D₄	—	106	32	no	—
1057	C₂×D₄	—	106	8	no	—
1058	C₂×D₄	—	106	64	no	—
1059	C₂×D₄	—	106	8	no	—
1060	C₂×D₄	—	106	8	no	—
1061	C₂×D₄	—	106	4	no	—
1062	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1063	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1064	C₂²×C₄	—	2	4	no	—
1065	C₂²×C₄	—	2	4	no	—
1066	C₂²×C₄	—	2	8	no	—
1067	C₂²×C₄	—	2	4	no	—
1068	C₂²×C₄	—	53	1	no	—
1069	C₂²×C₄	—	53	1	no	—
1070	C₂²×C₄	—	53	8	no	—
1071	C₂²×C₄	—	53	8	no	—
1072	C₂²×C₄	—	53	4	no	—
1073	C₂²×C₄	—	53	4	no	—
1074	C₂²×C₄	—	53	1	no	—
1075	C₂²×C₄	—	53	1	no	—
1076	C₂²×C₄	—	53	1	no	—
1077	C₂²×C₄	—	53	1	no	—
1078	C₂²×C₄	—	53	4	no	—
1079	C₂²×C₄	—	53	4	no	—
1080	C₂²×C₄	—	53	4	no	—
1081	C₂²×C₄	—	53	2	no	—
1082	C₂²×C₄	—	53	2	no	—
1083	C₂²×C₄	—	53	2	no	—
1084	C₂²×C₄	—	53	8	no	—
1085	C₂²×C₄	—	53	4	no	—
1086	C₂²×C₄	—	53	4	no	—
1087	C₂²×C₄	—	53	4	no	—
1088	C₂²×C₄	—	53	4	no	—
1089	C₂²×C₄	—	53	4	no	—
1090	C₂²×C₄	—	53	4	no	—
1091	C₂²×C₄	—	53	4	no	—
1092	C₂²×C₄	—	53	4	no	—
1093	C₂²×C₄	—	53	4	no	—
1094	C₂²×C₄	—	53	4	no	—
1095	C₂²×C₄	—	53	8	no	—
1096	C₂²×C₄	—	53	8	no	—
1097	C₂²×C₄	—	53	8	no	—
1098	C₂²×C₄	—	53	8	no	—
1099	C₂²×C₄	—	53	8	no	—
1100	C₂²×C₄	—	106	4	no	—
1101	C₂²×C₄	—	106	8	no	—
1102	C₂²×C₄	—	106	4	no	—
1103	C₂²×C₄	—	106	32	no	—
1104	C₂²×C₄	—	106	64	no	—
1105	C₂²×C₄	—	106	32	no	—
1106	C₂²×C₄	—	106	8	no	—
1107	C₂²×C₄	—	106	4	no	—
1108	C₂²×C₄	—	106	4	no	—
1109	C₂²×C₄	—	106	4	no	—
1110	C₂²×C₄	—	106	4	no	—
1111	C₂²×C₄	—	106	32	no	—
1112	C₂²×C₄	—	106	4	no	—
1113	C₂²×C₄	—	106	4	no	—
1114	C₂²×C₄	—	106	8	no	—
1115	C₂²×C₄	—	106	8	no	—
1116	C₂²×C₄	—	106	4	no	—
1117	C₂²×C₄	—	106	8	no	—
1118	C₂²×C₄	—	106	4	no	—
1119	C₂²×C₄	—	106	4	no	—
1120	C₂²×C₄	—	106	4	no	—
1121	C₂²×C₄	—	106	8	no	—
1122	C₂²×C₄	—	106	4	no	—
1123	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1124	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1126	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1127	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1128	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1129	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1130	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1131	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1132	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1133	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1134	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1135	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1136	C₄⋊C₄	—	53	8	no	—
1137	C₄⋊C₄	—	53	8	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	8	no	—
1143	C₄⋊C₄	—	53	4	no	—
1144	C₄⋊C₄	—	53	8	no	—
1145	C₄⋊C₄	—	53	8	no	—
1146	C₄⋊C₄	—	53	8	no	—
1147	C₄⋊C₄	—	53	8	no	—
1148	C₄⋊C₄	—	53	4	no	—
1149	C₄⋊C₄	—	53	8	no	—
1150	C₄⋊C₄	—	53	8	no	—
1151	C₄⋊C₄	—	53	8	no	—
1152	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1153	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1154	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1155	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1156	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1157	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1158	C₂²⋊C₄	—	53	8	no	—
1159	C₂²⋊C₄	—	53	8	no	—
1160	C₂²⋊C₄	—	53	8	no	—
1161	C₂²⋊C₄	—	53	8	no	—
1162	C₂²⋊C₄	—	53	8	no	—
1163	C₂²⋊C₄	—	53	8	no	—
1164	C₂²⋊C₄	—	53	8	no	—
1165	C₂²⋊C₄	—	53	8	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	C₂³×D₅₃	1	8	yes	—
1174	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1175	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1176	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1177	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1178	C₄²	—	53	4	no	—
1179	C₄²	—	53	4	no	—
1180	C₄²	—	53	4	no	—
1181	C₄²	—	53	4	no	—
1182	C₄²	—	53	4	no	—
1183	C₄²	—	53	4	no	—
1184	C₄²	—	53	4	no	—
1185	C₄²	—	53	4	no	—
1186	C₄²	—	53	4	no	—
1187	C₄²	—	53	4	no	—
1188	C₄²	—	53	4	no	—
1189	C₄²	—	53	4	no	—
1190	C₄²	—	53	8	no	—
1191	C₄²	—	53	8	no	—
1192	C₄²	—	53	8	no	—
1193	C₄²	C₂³×D₅₃	1	4	yes	—
1194	C₄²	C₂³×D₅₃	1	4	yes	—
1195	C₄²	C₂³×D₅₃	1	4	yes	—
1196	C₄²	C₂³×D₅₃	1	4	yes	—
1197	C₄²	C₂³×D₅₃	1	8	yes	—
1198	C₂³	—	2	2	no	—
1199	C₂³	—	2	2	no	—
1200	C₂³	—	2	4	no	—
1201	C₂³	—	2	4	no	—
1202	C₂³	—	2	4	no	—
1203	C₂³	—	53	4	no	—
1204	C₂³	—	53	4	no	—
1205	C₂³	—	53	4	no	—
1206	C₂³	—	53	2	no	—
1207	C₂³	—	53	16	no	—
1208	C₂³	—	53	4	no	—
1209	C₂³	—	53	2	no	—
1210	C₂³	—	53	4	no	—
1211	C₂³	—	106	8	no	—
1212	C₂³	—	106	8	no	—
1213	C₂³	—	106	32	no	—
1214	C₂³	—	106	16	no	—
1215	C₂³	—	106	16	no	—
1216	C₂³	—	106	16	no	—
1217	C₂³	—	106	2	no	—
1218	C₂³	—	106	2	no	—
1219	C₂³	—	106	4	no	—
1220	C₂³	—	106	4	no	—
1221	C₂³	—	106	4	no	—
1222	C₂³	—	212	32	no	—
1223	C₂³	#41×D₅₃	1	4	yes	—
1224	C₂³	C₂⁴×D₅₃	1	4	yes	—
1225	C₂³	C₂⁴×D₅₃	1	2	yes	—
1226	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1227	Q₈	—	2	8	no	—
1228	Q₈	—	106	16	no	—
1229	Q₈	—	106	8	no	—
1230	D₄	—	2	16	no	—
1231	D₄	—	2	8	no	—
1232	D₄	—	106	16	no	—
1233	D₄	—	106	16	no	—
1234	D₄	—	106	16	no	—
1235	D₄	—	106	16	no	—
1236	D₄	—	106	8	no	—
1237	C₂×C₄	—	2	8	no	—
1238	C₂×C₄	—	2	2	no	—
1239	C₂×C₄	—	2	2	no	—
1240	C₂×C₄	—	2	2	no	—
1241	C₂×C₄	—	2	2	no	—
1242	C₂×C₄	—	2	4	no	—
1243	C₂×C₄	—	2	4	no	—
1244	C₂×C₄	—	2	4	no	—
1245	C₂×C₄	—	2	8	no	—
1246	C₂×C₄	—	2	16	no	—
1247	C₂×C₄	—	2	8	no	—
1248	C₂×C₄	—	53	4	no	—
1249	C₂×C₄	—	53	4	no	—
1250	C₂×C₄	—	53	2	no	—
1251	C₂×C₄	—	53	2	no	—
1252	C₂×C₄	—	53	16	no	—
1253	C₂×C₄	—	53	16	no	—
1254	C₂×C₄	—	53	2	no	—
1255	C₂×C₄	—	53	2	no	—
1256	C₂×C₄	—	53	2	no	—
1257	C₂×C₄	—	53	2	no	—
1258	C₂×C₄	—	53	4	no	—
1259	C₂×C₄	—	53	4	no	—
1260	C₂×C₄	—	53	4	no	—
1261	C₂×C₄	—	106	8	no	—
1262	C₂×C₄	—	106	16	no	—
1263	C₂×C₄	—	106	8	no	—
1264	C₂×C₄	—	106	8	no	—
1265	C₂×C₄	—	106	8	no	—
1266	C₂×C₄	—	106	16	no	—
1267	C₂×C₄	—	106	8	no	—
1268	C₂×C₄	—	106	8	no	—
1269	C₂×C₄	—	106	8	no	—
1270	C₂×C₄	—	106	8	no	—
1271	C₂×C₄	—	106	16	no	—
1272	C₂×C₄	—	106	16	no	—
1273	C₂×C₄	—	106	8	no	—
1274	C₂×C₄	—	106	16	no	—
1275	C₂×C₄	—	106	8	no	—
1276	C₂×C₄	—	106	8	no	—
1277	C₂×C₄	—	106	2	no	—
1278	C₂×C₄	—	106	2	no	—
1279	C₂×C₄	—	106	2	no	—
1280	C₂×C₄	—	106	2	no	—
1281	C₂×C₄	—	106	4	no	—
1282	C₂×C₄	—	106	4	no	—
1283	C₂×C₄	—	106	4	no	—
1284	C₂×C₄	—	106	8	no	—
1285	C₂×C₄	—	106	16	no	—
1286	C₂×C₄	—	106	8	no	—
1287	C₂×C₄	#41×D₅₃	1	4	yes	—
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	2	yes	—
1292	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1293	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1294	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1295	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1296	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1297	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1298	C₂²	—	2	8	no	—
1299	C₂²	—	2	2	no	—
1300	C₂²	—	2	2	no	—
1301	C₂²	—	2	4	no	—
1302	C₂²	—	2	4	no	—
1303	C₂²	—	2	4	no	—
1304	C₂²	—	4	8	no	—
1305	C₂²	—	53	16	no	—
1306	C₂²	—	53	4	no	—
1307	C₂²	—	53	4	no	—
1308	C₂²	—	53	4	no	—
1309	C₂²	—	53	4	no	—
1310	C₂²	—	106	32	no	—
1311	C₂²	—	106	8	no	—
1312	C₂²	—	106	2	no	—
1313	C₂²	—	106	2	no	—
1314	C₂²	—	106	4	no	—
1315	C₂²	—	106	4	no	—
1316	C₂²	—	106	4	no	—
1317	C₂²	—	212	32	no	—
1318	C₂²	—	212	8	no	—
1319	C₂²	C₂×#41×D₅₃	1	4	yes	—
1320	C₂²	C₂×#41×D₅₃	1	2	yes	—
1321	C₂²	C₂×#41×D₅₃	1	2	yes	—
1322	C₂²	C₂×#41×D₅₃	1	2	yes	—
1323	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1324	C₄	—	2	2	no	—
1325	C₄	—	2	2	no	—
1326	C₄	—	2	2	no	—
1327	C₄	—	2	2	no	—
1328	C₄	—	2	4	no	—
1329	C₄	—	2	4	no	—
1330	C₄	—	2	4	no	—
1331	C₄	—	53	4	no	—
1332	C₄	—	53	4	no	—
1333	C₄	—	106	2	no	—
1334	C₄	—	106	2	no	—
1335	C₄	—	106	2	no	—
1336	C₄	—	106	2	no	—
1337	C₄	—	106	4	no	—
1338	C₄	—	106	4	no	—
1339	C₄	—	106	4	no	—
1340	C₄	C₂×#41×D₅₃	1	4	yes	—
1341	C₄	C₂×#41×D₅₃	1	4	yes	—
1342	C₂	—	2	4	no	—
1343	C₂	—	4	4	no	—
1344	C₂	—	53	8	no	—
1345	C₂	—	106	4	no	—
1346	C₂	—	212	4	no	—
1347	C₂	#529×D₅₃	1	4	yes	direct product factor
1348	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1349	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1350	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#529	C₂
socle	C₂³×C₅₃	C₂⁵
prime radical	C₂×#121×D₅₃	C₂
hypercenter	C₂×#529	D₅₃
hypocenter	C₅₃	C₂²×#529
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. C₂×#16811160	C₂	semidirect
2. C₂×#16811159	C₂	semidirect
3. C₂×#16811158	C₂	semidirect
4. C₂×#16811157	C₂	semidirect
5. C₂×#16811156	C₂	semidirect
6. C₂×#16811155	C₂	semidirect
7. C₂×#16811154	C₂	semidirect
8. C₂×#16811153	C₂	semidirect
9. C₂×#16811152	C₂	semidirect
10. C₂×#16811151	C₂	semidirect
11. C₂×#16811150	C₂	semidirect
12. #529×D₅₃	C₂	direct (N × H)
13. C₂×#126×D₅₃	C₂	semidirect
14. C₂×#125×D₅₃	C₂	semidirect
15. C₂×#124×D₅₃	C₂	semidirect
16. C₂×#123×D₅₃	C₂	semidirect
17. C₂×C₂²⋊Q₈×D₅₃	C₂	semidirect
19. C₂×C₄×Q₈×D₅₃	C₂	semidirect
20. C₂×C₄×D₄×D₅₃	C₂	semidirect
21. C₂×C₄×D₄×D₅₃	C₂	semidirect
22. C₂×#117×D₅₃	C₂	semidirect
23. C₂²×C₄²×D₅₃	C₂	semidirect
24. C₂×C₅₃×#529	C₂	semidirect
32. #16811160	C₂²	semidirect
33. #16811159	C₂²	semidirect
34. #16811158	C₂²	semidirect
35. #16811157	C₂²	semidirect
36. #16811156	C₂²	semidirect
37. #16811155	C₂²	semidirect
38. #16811154	C₂²	semidirect
39. #16811153	C₂²	semidirect
40. #16811152	C₂²	semidirect
41. #16811151	C₂²	semidirect
42. #16811150	C₂²	semidirect
43. C₂×#13133212	C₂²	semidirect
44. C₂×#13133212	C₂²	semidirect
45. C₂×#13133212	C₂²	semidirect
46. C₂×#13133211	C₂²	semidirect
47. C₂×#13133210	C₂²	semidirect
48. C₂×#13133210	C₂²	semidirect
49. C₂×#13133210	C₂²	semidirect
50. #126×D₅₃	C₂²	semidirect
51. C₂×#13133209	C₂²	semidirect
52. C₂×#13133208	C₂²	semidirect
53. C₂×#13133208	C₂²	semidirect
54. C₂×#13133207	C₂²	semidirect
55. C₂×#13133207	C₂²	semidirect
56. #125×D₅₃	C₂²	semidirect
57. C₂×#13133206	C₂²	semidirect
58. C₂×#13133205	C₂²	semidirect
59. C₂×#13133204	C₂²	semidirect
60. C₂×#13133203	C₂²	semidirect
61. C₂×#13133203	C₂²	semidirect
62. #124×D₅₃	C₂²	semidirect
63. C₂×#13133202	C₂²	semidirect
64. C₂×#13133202	C₂²	semidirect
65. C₂×#13133201	C₂²	semidirect
66. C₂×#13133200	C₂²	semidirect
67. C₂×#13133199	C₂²	semidirect
68. C₂×#13133199	C₂²	semidirect
69. C₂×#13133198	C₂²	semidirect
70. #123×D₅₃	C₂²	semidirect
71. C₂×#13133197	C₂²	semidirect
72. C₂×#13133196	C₂²	semidirect
73. C₂×#13133195	C₂²	semidirect
74. C₂×#13133194	C₂²	semidirect
75. C₂×#13133193	C₂²	semidirect
76. C₂²⋊Q₈×D₅₃	C₂²	semidirect
83. C₂×Q₈×Dic₅₃	C₂²	semidirect
84. C₂×C₄×Dic₁₀₆	C₂²	semidirect
85. C₂×C₄×Dic₁₀₆	C₂²	semidirect
86. C₂×#13133182	C₂²	semidirect
87. C₂×#13133182	C₂²	semidirect
88. C₄×Q₈×D₅₃	C₂²	semidirect
89. C₂×C₄×D₂₁₂	C₂²	semidirect
90. C₂×C₄×D₂₁₂	C₂²	semidirect
91. C₂×D₄×Dic₅₃	C₂²	semidirect
92. C₂×D₄×Dic₅₃	C₂²	semidirect
93. C₂×#13133179	C₂²	semidirect
94. C₂×#13133179	C₂²	semidirect
95. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
96. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
97. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
98. C₂×#13133177	C₂²	semidirect
99. C₂×#13133177	C₂²	semidirect
100. C₂×#13133177	C₂²	semidirect
101. C₄×D₄×D₅₃	C₂²	semidirect
102. C₄×D₄×D₅₃	C₂²	semidirect
103. C₂×#13133176	C₂²	semidirect
104. C₂×#13133175	C₂²	semidirect
105. C₂×#13133175	C₂²	semidirect
106. C₂×#13133174	C₂²	semidirect
107. C₂×#13133174	C₂²	semidirect
108. C₂×#13133173	C₂²	semidirect
109. C₂×#13133173	C₂²	semidirect
110. #117×D₅₃	C₂²	semidirect
122. C₂²×C₄×Dic₅₃	C₂²	semidirect
123. C₂²×C₄×Dic₅₃	C₂²	semidirect
124. C₂²×C₄×Dic₅₃	C₂²	semidirect
130. C₂×C₄²×D₅₃	C₂²	semidirect
131. C₂×C₄²×D₅₃	C₂²	semidirect
132. C₂×C₄²×D₅₃	C₂²	semidirect
133. C₂×C₄²×D₅₃	C₂²	semidirect
134. C₂×C₄²×D₅₃	C₂²	semidirect
135. C₅₃×#529	C₂²	semidirect
136. C₂×#126×C₅₃	C₂²	semidirect
137. C₂×#125×C₅₃	C₂²	semidirect
138. C₂×#124×C₅₃	C₂²	semidirect
139. C₂×#123×C₅₃	C₂²	semidirect
140. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
142. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
143. C₂×C₄×D₄×C₅₃	C₂²	semidirect
144. C₂×C₄×D₄×C₅₃	C₂²	semidirect
145. C₂×#117×C₅₃	C₂²	semidirect
146. C₂²×C₄²×C₅₃	C₂²	semidirect
191. #13133212	C₂³	semidirect
192. #13133212	C₂³	semidirect
193. #13133212	C₂³	semidirect
194. #13133211	C₂³	semidirect
195. #13133210	C₂³	semidirect
196. #13133210	C₂³	semidirect
197. #13133210	C₂³	semidirect
198. #13133209	C₂³	semidirect
199. #13133208	C₂³	semidirect
200. #13133208	C₂³	semidirect
201. #13133207	C₂³	semidirect
202. #13133207	C₂³	semidirect
203. #13133206	C₂³	semidirect
204. #13133205	C₂³	semidirect
205. #13133204	C₂³	semidirect
206. #13133203	C₂³	semidirect
207. #13133203	C₂³	semidirect
208. #13133202	C₂³	semidirect
209. #13133202	C₂³	semidirect
210. #13133201	C₂³	semidirect
211. #13133200	C₂³	semidirect
212. #13133199	C₂³	semidirect
213. #13133199	C₂³	semidirect
214. #13133198	C₂³	semidirect
215. #13133197	C₂³	semidirect
216. #13133196	C₂³	semidirect
217. #13133195	C₂³	semidirect
218. #13133194	C₂³	semidirect
219. #13133193	C₂³	semidirect
225. Q₈×Dic₅₃	C₂³	semidirect
226. C₄×Dic₁₀₆	C₂³	semidirect
227. C₄×Dic₁₀₆	C₂³	semidirect
228. #13133182	C₂³	semidirect
229. #13133182	C₂³	semidirect
230. C₄×D₂₁₂	C₂³	semidirect
231. C₄×D₂₁₂	C₂³	semidirect
232. D₄×Dic₅₃	C₂³	semidirect
233. D₄×Dic₅₃	C₂³	semidirect
234. #13133179	C₂³	semidirect
235. #13133179	C₂³	semidirect
236. C₄×C₂²⋊D₅₃	C₂³	semidirect
237. C₄×C₂²⋊D₅₃	C₂³	semidirect
238. C₄×C₂²⋊D₅₃	C₂³	semidirect
239. #13133177	C₂³	semidirect
240. #13133177	C₂³	semidirect
241. #13133177	C₂³	semidirect
242. #13133176	C₂³	semidirect
243. #13133175	C₂³	semidirect
244. #13133175	C₂³	semidirect
245. #13133174	C₂³	semidirect
246. #13133174	C₂³	semidirect
247. #13133173	C₂³	semidirect
248. #13133173	C₂³	semidirect
306. C₂×C₄×Dic₅₃	C₂³	semidirect
307. C₂×C₄×Dic₅₃	C₂³	semidirect
308. C₂×C₄×Dic₅₃	C₂³	semidirect
314. C₄²×D₅₃	C₂³	semidirect
315. C₄²×D₅₃	C₂³	semidirect
316. C₄²×D₅₃	C₂³	semidirect
317. C₄²×D₅₃	C₂³	semidirect
325. #126×C₅₃	C₂³	semidirect
326. #125×C₅₃	C₂³	semidirect
327. #124×C₅₃	C₂³	semidirect
328. #123×C₅₃	C₂³	semidirect
329. C₂²⋊Q₈×C₅₃	C₂³	semidirect
331. C₄×Q₈×C₅₃	C₂³	semidirect
332. C₄×D₄×C₅₃	C₂³	semidirect
333. C₄×D₄×C₅₃	C₂³	semidirect
334. #117×C₅₃	C₂³	semidirect
351. C₂×C₄²×C₅₃	C₂³	semidirect
644. C₂×D₅₃	#529	direct (N × H)
679. C₂×#529	D₅₃	direct (N × H)
693. C₂×C₅₃	C₂×#529	semidirect
699. D₅₃	C₂×#529	direct (N × H)
718. #529	C₂×D₅₃	direct (N × H)
727. C₂×#126	C₂×D₅₃	semidirect
734. C₂×#125	C₂×D₅₃	semidirect
741. C₂×#124	C₂×D₅₃	semidirect
750. C₂×#123	C₂×D₅₃	semidirect
757. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
771. C₂×C₄×Q₈	C₂×D₅₃	semidirect
786. C₂×C₄×D₄	C₂×D₅₃	semidirect
787. C₂×C₄×D₄	C₂×D₅₃	semidirect
796. C₂×#117	C₂×D₅₃	semidirect
821. C₂²×C₄²	C₂×D₅₃	semidirect
822. C₅₃	C₂²×#529	semidirect
881. #126	C₂²×D₅₃	semidirect
887. #125	C₂²×D₅₃	semidirect
893. #124	C₂²×D₅₃	semidirect
901. #123	C₂²×D₅₃	semidirect
907. C₂²⋊Q₈	C₂²×D₅₃	semidirect
919. C₄×Q₈	C₂²×D₅₃	semidirect
932. C₄×D₄	C₂²×D₅₃	semidirect
933. C₄×D₄	C₂²×D₅₃	semidirect
941. #117	C₂²×D₅₃	semidirect
1027. C₂×C₄²	C₂²×D₅₃	semidirect
1347. C₂	#529×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16811160	2
C₂×#16811159	2
C₂×#16811158	2
C₂×#16811157	2
C₂×#16811156	2
C₂×#16811155	2
C₂×#16811154	2
C₂×#16811153	2
C₂×#16811152	2
C₂×#16811151	2
C₂×#16811150	2
#529×D₅₃	2
C₂×#126×D₅₃	2
C₂×#125×D₅₃	2
C₂×#124×D₅₃	2
C₂×#123×D₅₃	2
C₂×C₂²⋊Q₈×D₅₃	2
C₂×#121×D₅₃	2
C₂×C₄×Q₈×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₂×#117×D₅₃	2
C₂²×C₄²×D₅₃	2
C₂×C₅₃×#529	2
C₂²×#529	53

Subgroups — C2×#529×D53 #28290765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#529×D₅₃ #28290765