Subgroups — C₂×#552×D₅₃ #28291076

Order 13568.

7934 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811315	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16811314	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811313	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811312	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811311	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811310	C₂	1	2	yes	maximal, complemented
7	C₂×#16811309	C₂	1	2	yes	maximal, complemented
8	C₂×#16811308	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16811307	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811306	C₂	1	2	yes	maximal, complemented
11	C₂×#16811305	C₂	1	2	yes	maximal, complemented
12	#552×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	2	yes	maximal, complemented
15	C₂×#125×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#123×D₅₃	C₂	1	2	yes	maximal
17	C₂×C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₄×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
21	C₂×#117×D₅₃	C₂	1	2	yes	maximal, complemented
22	C₂×#117×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂²×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
26	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
27	C₂³×C₄×D₅₃	C₂²	1	2	yes	—
28	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
29	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
30	#16811315	C₂²	1	16	yes	complemented
31	#16811314	C₂²	1	16	yes	complemented
32	#16811313	C₂²	1	16	yes	complemented
33	#16811312	C₂²	1	16	yes	complemented
34	#16811311	C₂²	1	16	yes	complemented
35	#16811310	C₂²	1	32	yes	complemented
36	#16811309	C₂²	1	32	yes	complemented
37	#16811308	C₂²	1	16	yes	complemented
38	#16811307	C₂²	1	16	yes	complemented
39	#16811306	C₂²	1	32	yes	complemented
40	#16811305	C₂²	1	32	yes	complemented
41	C₂×#13133212	C₂²	1	2	yes	complemented
42	C₂×#13133212	C₂²	1	2	yes	complemented
43	C₂×#13133212	C₂²	1	2	yes	complemented
44	C₂×#13133211	C₂²	1	2	yes	complemented
45	C₂×#13133210	C₂²	1	2	yes	complemented
46	C₂×#13133210	C₂²	1	2	yes	complemented
47	C₂×#13133210	C₂²	1	2	yes	complemented
48	#126×D₅₃	C₂²	1	32	yes	complemented
49	C₂×#13133209	C₂²	1	2	yes	complemented
50	C₂×#13133209	C₂²	1	1	yes	characteristic, complemented
51	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
52	C₂×#13133208	C₂²	1	2	yes	complemented
53	C₂×#13133208	C₂²	1	2	yes	complemented
54	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
55	C₂×#13133207	C₂²	1	2	yes	complemented
56	C₂×#13133207	C₂²	1	2	yes	complemented
57	C₂×#13133207	C₂²	1	2	yes	complemented
58	C₂×#13133207	C₂²	1	2	yes	complemented
59	C₂×#13133207	C₂²	1	2	yes	complemented
60	C₂×#13133207	C₂²	1	2	yes	complemented
61	#125×D₅₃	C₂²	1	32	yes	complemented
62	#125×D₅₃	C₂²	1	16	yes	complemented
63	C₂×#13133202	C₂²	1	2	yes	—
64	C₂×#13133202	C₂²	1	2	yes	—
65	C₂×#13133201	C₂²	1	2	yes	—
66	C₂×#13133200	C₂²	1	2	yes	—
67	C₂×#13133199	C₂²	1	2	yes	—
68	C₂×#13133199	C₂²	1	2	yes	—
69	C₂×#13133198	C₂²	1	2	yes	—
70	#123×D₅₃	C₂²	1	32	yes	—
71	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
72	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
73	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
74	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
75	C₂×#13133195	C₂²	1	2	yes	complemented
76	C₂×#13133195	C₂²	1	2	yes	complemented
77	C₂×#13133194	C₂²	1	2	yes	complemented
78	C₂×#13133194	C₂²	1	2	yes	complemented
79	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
80	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
81	C₂²⋊Q₈×D₅₃	C₂²	1	16	yes	complemented
82	C₂²⋊Q₈×D₅₃	C₂²	1	16	yes	complemented
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	1	yes	characteristic
90	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
91	C₂×#13133179	C₂²	1	1	yes	characteristic
92	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
93	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
94	C₂×#13133177	C₂²	1	1	yes	characteristic
95	C₂×#13133177	C₂²	1	1	yes	characteristic
96	C₄×D₄×D₅₃	C₂²	1	16	yes	—
97	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
98	C₂×#13133176	C₂²	1	2	yes	complemented
99	C₂×#13133175	C₂²	1	2	yes	complemented
100	C₂×#13133175	C₂²	1	1	yes	characteristic, complemented
101	C₂×#13133175	C₂²	1	2	yes	complemented
102	C₂×#13133175	C₂²	1	1	yes	characteristic, complemented
103	C₂×#13133174	C₂²	1	2	yes	complemented
104	C₂×#13133174	C₂²	1	2	yes	complemented
105	C₂×#13133174	C₂²	1	2	yes	complemented
106	C₂×#13133173	C₂²	1	2	yes	complemented
107	C₂×#13133173	C₂²	1	2	yes	complemented
108	C₂×#13133173	C₂²	1	2	yes	complemented
109	#117×D₅₃	C₂²	1	32	yes	complemented
110	#117×D₅₃	C₂²	1	16	yes	complemented
111	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₂²×#11719919	C₂²	1	2	yes	complemented
113	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
114	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
115	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
116	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
117	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
118	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
119	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
120	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
121	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
122	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
123	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
124	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₄⋊C₄×D₅₃	C₂²	1	16	yes	complemented
127	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
129	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
130	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
132	C₂×C₄²×D₅₃	C₂²	1	2	yes	—
133	C₂×C₄²×D₅₃	C₂²	1	2	yes	—
134	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
135	C₅₃×#552	C₂²	1	16	yes	complemented
136	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
137	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
138	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂×#123×C₅₃	C₂²	1	2	yes	—
140	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
141	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
144	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
145	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
146	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
154	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
155	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
156	C₂×D₄×D₅₃	—	2	8	no	—
157	C₂×D₄×D₅₃	C₂³	1	8	yes	—
158	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
159	C₂³×Dic₅₃	C₂³	1	2	yes	—
160	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
161	C₂²×C₄×D₅₃	—	2	16	no	—
162	C₂²×C₄×D₅₃	—	2	8	no	—
163	C₂²×C₄×D₅₃	—	2	8	no	—
164	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
165	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
166	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
167	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
168	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
169	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
170	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
171	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
172	C₂²×C₄×D₅₃	C₂³	1	16	yes	—
173	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
174	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
175	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
176	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
178	C₂²×C₄×D₅₃	C₂³	1	8	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	1	yes	characteristic
182	#13133212	C₂³	1	16	yes	complemented
183	#13133212	C₂³	1	16	yes	complemented
184	#13133212	C₂³	1	16	yes	complemented
185	#13133211	C₂³	1	16	yes	complemented
186	#13133210	C₂³	1	16	yes	complemented
187	#13133210	C₂³	1	16	yes	complemented
188	#13133210	C₂³	1	16	yes	complemented
189	#13133209	C₂³	1	16	yes	complemented
190	#13133209	C₂³	1	8	yes	complemented
191	#13133208	C₂³	1	8	yes	complemented
192	#13133208	C₂³	1	16	yes	complemented
193	#13133208	C₂³	1	16	yes	complemented
194	#13133208	C₂³	1	8	yes	complemented
195	#13133207	C₂³	1	16	yes	complemented
196	#13133207	C₂³	1	16	yes	complemented
197	#13133207	C₂³	1	16	yes	complemented
198	#13133207	C₂³	1	16	yes	complemented
199	#13133207	C₂³	1	16	yes	complemented
200	#13133207	C₂³	1	16	yes	complemented
201	#13133202	C₂³	1	16	yes	—
202	#13133202	C₂³	1	16	yes	—
203	#13133201	C₂³	1	16	yes	—
204	#13133200	C₂³	1	16	yes	—
205	#13133199	C₂³	1	16	yes	—
206	#13133199	C₂³	1	16	yes	—
207	#13133198	C₂³	1	16	yes	—
208	#13133197	C₂³	1	8	yes	complemented
209	#13133197	C₂³	1	8	yes	complemented
210	#13133196	C₂³	1	8	yes	complemented
211	#13133196	C₂³	1	8	yes	complemented
212	#13133195	C₂³	1	16	yes	complemented
213	#13133195	C₂³	1	16	yes	complemented
214	#13133194	C₂³	1	16	yes	complemented
215	#13133194	C₂³	1	16	yes	complemented
216	#13133193	C₂³	1	8	yes	complemented
217	#13133193	C₂³	1	8	yes	complemented
218	Q₈×Dic₅₃	C₂³	1	8	yes	complemented
219	C₄×Dic₁₀₆	C₂³	1	16	yes	complemented
220	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
221	#13133182	C₂³	1	16	yes	complemented
222	#13133182	C₂³	1	8	yes	complemented
223	C₄×D₂₁₂	C₂³	1	8	yes	—
224	D₄×Dic₅₃	C₂³	1	8	yes	—
225	#13133179	C₂³	1	8	yes	—
226	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
227	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
228	#13133177	C₂³	1	8	yes	—
229	#13133177	C₂³	1	8	yes	—
230	#13133176	C₂³	1	8	yes	complemented
231	#13133176	C₂³	1	16	yes	complemented
232	#13133175	C₂³	1	16	yes	complemented
233	#13133175	C₂³	1	8	yes	complemented
234	#13133175	C₂³	1	16	yes	complemented
235	#13133175	C₂³	1	8	yes	complemented
236	#13133174	C₂³	1	16	yes	complemented
237	#13133174	C₂³	1	16	yes	complemented
238	#13133174	C₂³	1	16	yes	complemented
239	#13133173	C₂³	1	16	yes	complemented
240	#13133173	C₂³	1	16	yes	complemented
241	#13133173	C₂³	1	16	yes	complemented
242	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
245	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
247	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
248	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
250	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
251	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
252	C₂×C₄⋊Dic₅₃	C₂³	1	8	yes	complemented
253	C₂×#11719919	C₂³	1	2	yes	—
254	C₂×#11719919	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	1	yes	characteristic
263	C₂×#11719919	C₂³	1	1	yes	characteristic
264	C₂×#11719919	C₂³	1	2	yes	—
265	C₂×#11719919	C₂³	1	2	yes	—
266	C₂×#11719919	C₂³	1	2	yes	—
267	C₂×#11719919	C₂³	1	2	yes	—
268	C₂×#11719919	C₂³	1	2	yes	—
269	C₂×#11719919	C₂³	1	2	yes	—
270	C₂×#11719919	C₂³	1	16	yes	complemented
271	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
272	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
273	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
274	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
275	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
276	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
277	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
278	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
279	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
280	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
281	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
282	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
283	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
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×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
289	C₂×#11719921	C₂³	1	1	yes	characteristic
290	C₂×#11719921	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
296	C₂×#11719921	C₂³	1	1	yes	characteristic
297	C₂×#11719921	C₂³	1	2	yes	—
298	C₂×#11719921	C₂³	1	2	yes	—
299	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
300	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
301	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
302	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
303	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
304	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
305	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
306	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
307	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
308	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
309	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
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	C₄²×D₅₃	C₂³	1	16	yes	—
314	C₄²×D₅₃	C₂³	1	16	yes	—
315	C₄²×D₅₃	C₂³	1	8	yes	—
316	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
319	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
321	#126×C₅₃	C₂³	1	16	yes	complemented
322	#125×C₅₃	C₂³	1	16	yes	complemented
323	#125×C₅₃	C₂³	1	8	yes	complemented
324	#123×C₅₃	C₂³	1	16	yes	—
325	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
326	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
327	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
328	C₄×D₄×C₅₃	C₂³	1	8	yes	—
329	#117×C₅₃	C₂³	1	16	yes	complemented
330	#117×C₅₃	C₂³	1	8	yes	complemented
331	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
334	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
335	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₅₃	C₂³	1	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	2	yes	—
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
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	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
347	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
348	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
349	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
350	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂³×D₅₃	—	2	4	no	—
353	C₂³×D₅₃	—	2	4	no	—
354	C₂³×D₅₃	—	2	4	no	—
355	C₂³×D₅₃	—	2	4	no	—
356	C₂³×D₅₃	—	2	4	no	—
357	C₂³×D₅₃	#41	1	8	yes	—
358	C₂³×D₅₃	C₂⁴	1	4	yes	—
359	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
360	C₂³×D₅₃	C₂⁴	1	4	yes	—
361	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
362	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×Q₈×C₅₃	—	2	4	no	—
364	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
365	C₂×D₄×C₅₃	—	2	4	no	—
366	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
367	C₂²×C₄×C₅₃	—	2	8	no	—
368	C₂²×C₄×C₅₃	—	2	4	no	—
369	C₂²×C₄×C₅₃	—	2	4	no	—
370	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
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	8	yes	—
379	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
380	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₂²⋊D₅₃	—	2	4	no	—
383	C₂×C₂²⋊D₅₃	—	2	4	no	—
384	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
385	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
386	C₂²×Dic₅₃	—	2	8	no	—
387	C₂²×Dic₅₃	—	2	4	no	—
388	C₂²×Dic₅₃	—	2	4	no	—
389	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
392	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
393	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
394	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
397	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
398	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
399	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
400	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	Q₈×D₅₃	—	2	32	no	—
402	D₄×D₅₃	—	2	32	no	—
403	C₂×D₂₁₂	—	2	4	no	—
404	C₂×D₂₁₂	C₂⁴	1	4	yes	—
405	C₂×C₄×D₅₃	—	2	8	no	—
406	C₂×C₄×D₅₃	—	2	8	no	—
407	C₂×C₄×D₅₃	—	2	64	no	—
408	C₂×C₄×D₅₃	—	2	8	no	—
409	C₂×C₄×D₅₃	—	2	8	no	—
410	C₂×C₄×D₅₃	—	2	4	no	—
411	C₂×C₄×D₅₃	—	2	4	no	—
412	C₂×C₄×D₅₃	—	2	4	no	—
413	C₂×C₄×D₅₃	—	2	8	no	—
414	C₂×C₄×D₅₃	—	2	4	no	—
415	C₂×C₄×D₅₃	—	2	8	no	—
416	C₂×C₄×D₅₃	—	2	4	no	—
417	C₂×C₄×D₅₃	—	2	4	no	—
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	32	no	—
422	C₂×C₄×D₅₃	#41	1	8	yes	—
423	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
424	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
425	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
426	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
427	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
428	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
429	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
430	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
431	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
432	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
433	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
434	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
435	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
436	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
437	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
438	C₂×Dic₁₀₆	—	2	4	no	—
439	C₂×Dic₁₀₆	—	2	8	no	—
440	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
441	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
442	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
443	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
444	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
445	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
446	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
447	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
448	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
449	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
450	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
451	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
452	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
453	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
454	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
455	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
456	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
457	C₄²×C₅₃	C₂⁴	1	8	yes	—
458	C₄²×C₅₃	C₂⁴	1	8	yes	—
459	C₄²×C₅₃	C₂⁴	1	4	yes	—
460	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
461	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
462	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
463	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
464	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
465	#11719921	C₂⁴	1	4	yes	—
466	#11719921	C₂⁴	1	4	yes	—
467	#11719921	C₂⁴	1	8	yes	—
468	#11719921	C₂⁴	1	8	yes	—
469	#11719921	C₂⁴	1	8	yes	—
470	#11719921	C₂⁴	1	8	yes	—
471	#11719921	C₂⁴	1	4	yes	—
472	#11719921	C₂⁴	1	4	yes	—
473	#11719921	C₂⁴	1	8	yes	—
474	#11719921	C₂⁴	1	8	yes	—
475	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
476	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
477	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
478	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
479	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
480	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
481	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
482	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
483	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
484	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
485	#11719919	C₂⁴	1	8	yes	—
486	#11719919	C₂⁴	1	8	yes	—
487	#11719919	C₂⁴	1	8	yes	—
488	#11719919	C₂⁴	1	8	yes	—
489	#11719919	C₂⁴	1	8	yes	—
490	#11719919	C₂⁴	1	8	yes	—
491	#11719919	C₂⁴	1	8	yes	—
492	#11719919	C₂⁴	1	8	yes	—
493	#11719919	C₂⁴	1	8	yes	—
494	#11719919	C₂⁴	1	4	yes	—
495	#11719919	C₂⁴	1	4	yes	—
496	#11719919	C₂⁴	1	8	yes	—
497	#11719919	C₂⁴	1	8	yes	—
498	#11719919	C₂⁴	1	8	yes	—
499	#11719919	C₂⁴	1	8	yes	—
500	#11719919	C₂⁴	1	8	yes	—
501	#11719919	C₂⁴	1	8	yes	—
502	C₄×Dic₅₃	C₂⁴	1	8	yes	—
503	C₄×Dic₅₃	C₂⁴	1	8	yes	—
504	C₄×Dic₅₃	C₂⁴	1	8	yes	—
505	C₄×Dic₅₃	C₂⁴	1	8	yes	—
506	C₄×Dic₅₃	C₂⁴	1	8	yes	—
507	C₄×Dic₅₃	C₂⁴	1	8	yes	—
508	C₄×Dic₅₃	C₂⁴	1	4	yes	—
509	C₄×Dic₅₃	C₂⁴	1	4	yes	—
510	C₄×Dic₅₃	C₂⁴	1	4	yes	—
511	C₂³×C₅₃	—	2	2	no	—
512	C₂³×C₅₃	—	2	2	no	—
513	C₂³×C₅₃	—	2	2	no	—
514	C₂³×C₅₃	—	2	2	no	—
515	C₂³×C₅₃	—	2	2	no	—
516	C₂³×C₅₃	C₂×#41	1	4	yes	—
517	C₂³×C₅₃	C₂⁵	1	2	yes	—
518	C₂³×C₅₃	C₂⁵	1	2	yes	—
519	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
520	C₂²×D₅₃	—	2	2	no	—
521	C₂²×D₅₃	—	2	2	no	—
522	C₂²×D₅₃	—	2	32	no	—
523	C₂²×D₅₃	—	2	8	no	—
524	C₂²×D₅₃	—	2	8	no	—
525	C₂²×D₅₃	—	2	2	no	—
526	C₂²×D₅₃	—	2	2	no	—
527	C₂²×D₅₃	—	2	2	no	—
528	C₂²×D₅₃	—	2	8	no	—
529	C₂²×D₅₃	—	2	8	no	—
530	C₂²×D₅₃	—	2	8	no	—
531	C₂²×D₅₃	—	4	16	no	—
532	C₂²×D₅₃	C₂×#41	1	4	yes	—
533	C₂²×D₅₃	C₂×#41	1	16	yes	—
534	C₂²×D₅₃	C₂×#41	1	4	yes	—
535	C₂²×D₅₃	C₂×#41	1	4	yes	—
536	C₂²×D₅₃	2₋¹⁺⁴	1	4	yes	—
537	C₂²×D₅₃	C₂⁵	1	2	yes	—
538	C₂²×D₅₃	C₂⁵	1	2	yes	—
539	C₂²×D₅₃	C₂⁵	1	2	yes	—
540	Q₈×C₅₃	—	2	8	no	—
541	D₄×C₅₃	—	2	8	no	—
542	C₂×C₄×C₅₃	—	2	4	no	—
543	C₂×C₄×C₅₃	—	2	16	no	—
544	C₂×C₄×C₅₃	—	2	4	no	—
545	C₂×C₄×C₅₃	—	2	4	no	—
546	C₂×C₄×C₅₃	—	2	2	no	—
547	C₂×C₄×C₅₃	—	2	2	no	—
548	C₂×C₄×C₅₃	—	2	2	no	—
549	C₂×C₄×C₅₃	—	2	2	no	—
550	C₂×C₄×C₅₃	—	2	4	no	—
551	C₂×C₄×C₅₃	—	2	8	no	—
552	C₂×C₄×C₅₃	—	2	8	no	—
553	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
554	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
555	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
556	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
557	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
558	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
559	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
560	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
561	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
562	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
563	C₂²⋊D₅₃	—	2	8	no	—
564	C₂²⋊D₅₃	—	2	8	no	—
565	C₂×Dic₅₃	—	2	4	no	—
566	C₂×Dic₅₃	—	2	16	no	—
567	C₂×Dic₅₃	—	2	4	no	—
568	C₂×Dic₅₃	—	2	4	no	—
569	C₂×Dic₅₃	—	2	2	no	—
570	C₂×Dic₅₃	—	2	2	no	—
571	C₂×Dic₅₃	—	2	2	no	—
572	C₂×Dic₅₃	—	2	2	no	—
573	C₂×Dic₅₃	—	2	4	no	—
574	C₂×Dic₅₃	—	2	8	no	—
575	C₂×Dic₅₃	—	2	8	no	—
576	C₂×Dic₅₃	C₂×#41	1	4	yes	—
577	C₂×Dic₅₃	C₂⁵	1	4	yes	—
578	C₂×Dic₅₃	C₂⁵	1	4	yes	—
579	C₂×Dic₅₃	C₂⁵	1	2	yes	—
580	C₂×Dic₅₃	C₂⁵	1	4	yes	—
581	C₂×Dic₅₃	C₂⁵	1	2	yes	—
582	C₂×Dic₅₃	C₂⁵	1	2	yes	—
583	C₂×Dic₅₃	C₂⁵	1	2	yes	—
584	C₂×Dic₅₃	C₂⁵	1	4	yes	—
585	C₂×Dic₅₃	C₂⁵	1	2	yes	—
586	D₂₁₂	—	2	8	no	—
587	C₄×D₅₃	—	2	16	no	—
588	C₄×D₅₃	—	2	16	no	—
589	C₄×D₅₃	—	2	16	no	—
590	C₄×D₅₃	—	2	16	no	—
591	C₄×D₅₃	—	2	8	no	—
592	C₄×D₅₃	—	2	8	no	—
593	C₄×D₅₃	—	2	8	no	—
594	C₄×D₅₃	—	2	16	no	—
595	C₄×D₅₃	—	2	8	no	—
596	C₄×D₅₃	—	2	16	no	—
597	C₄×D₅₃	—	2	8	no	—
598	C₄×D₅₃	—	2	8	no	—
599	C₄×D₅₃	—	2	8	no	—
600	C₄×D₅₃	—	2	8	no	—
601	C₄×D₅₃	C₂×#41	1	16	yes	—
602	Dic₁₀₆	—	2	8	no	—
603	Dic₁₀₆	—	2	16	no	—
604	C₂²×#552	—	53	1	no	maximal, Sylow
605	C₂²×C₅₃	—	2	2	no	—
606	C₂²×C₅₃	—	2	2	no	—
607	C₂²×C₅₃	—	2	8	no	—
608	C₂²×C₅₃	—	2	2	no	—
609	C₂²×C₅₃	—	2	2	no	—
610	C₂²×C₅₃	—	2	2	no	—
611	C₂²×C₅₃	—	4	4	no	—
612	C₂²×C₅₃	C₂²×#41	1	4	yes	—
613	C₂²×C₅₃	C₂²×#41	1	2	yes	—
614	C₂²×C₅₃	C₂²×#41	1	2	yes	—
615	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
616	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
617	C₂×D₅₃	—	2	2	no	—
618	C₂×D₅₃	—	2	2	no	—
619	C₂×D₅₃	—	2	8	no	—
620	C₂×D₅₃	—	2	32	no	—
621	C₂×D₅₃	—	2	2	no	—
622	C₂×D₅₃	—	2	2	no	—
623	C₂×D₅₃	—	2	2	no	—
624	C₂×D₅₃	—	4	4	no	—
625	C₂×D₅₃	—	4	16	no	—
626	C₂×D₅₃	#552	1	16	yes	direct product factor
627	C₂×D₅₃	C₂²×#41	1	4	yes	—
628	C₂×D₅₃	C₂²×#41	1	4	yes	—
629	C₂×D₅₃	C₂²×#41	1	4	yes	—
630	C₂×D₅₃	C₂×2₋¹⁺⁴	1	4	yes	—
631	C₄×C₅₃	—	2	4	no	—
632	C₄×C₅₃	—	2	4	no	—
633	C₄×C₅₃	—	2	4	no	—
634	C₄×C₅₃	—	2	2	no	—
635	C₄×C₅₃	—	2	2	no	—
636	C₄×C₅₃	—	2	2	no	—
637	C₄×C₅₃	—	2	2	no	—
638	C₄×C₅₃	—	2	4	no	—
639	C₄×C₅₃	C₂²×#41	1	4	yes	—
640	Dic₅₃	—	2	4	no	—
641	Dic₅₃	—	2	4	no	—
642	Dic₅₃	—	2	4	no	—
643	Dic₅₃	—	2	2	no	—
644	Dic₅₃	—	2	2	no	—
645	Dic₅₃	—	2	2	no	—
646	Dic₅₃	—	2	2	no	—
647	Dic₅₃	—	2	4	no	—
648	Dic₅₃	C₂²×#41	1	4	yes	—
649	C₂×#552	—	53	32	no	—
650	C₂×#552	—	53	2	no	—
651	C₂×#552	—	53	2	no	—
652	C₂×#552	—	53	1	no	—
653	C₂×#552	—	53	2	no	—
654	C₂×#552	—	53	1	no	—
655	C₂×#552	—	53	1	no	—
656	C₂×#552	—	53	1	no	—
657	C₂×#552	—	53	1	no	—
658	C₂×#552	—	53	2	no	—
659	C₂×#552	—	53	1	no	—
660	C₂×#552	—	53	1	no	—
661	C₂×#552	D₅₃	1	1	yes	characteristic, direct product factor
662	C₂²×#126	—	53	2	no	—
663	C₂²×#125	—	53	1	no	—
664	C₂²×#125	—	53	2	no	—
665	C₂²×#123	—	53	2	no	—
666	C₂²×C₂²⋊Q₈	—	53	1	no	—
667	C₂²×C₂²⋊Q₈	—	53	1	no	—
668	C₂²×C₄×Q₈	—	53	1	no	—
669	C₂²×C₄×D₄	—	53	1	no	—
670	C₂²×#117	—	53	2	no	—
671	C₂²×#117	—	53	1	no	—
672	C₂³×C₄⋊C₄	—	53	1	no	—
673	C₂×C₅₃	—	2	4	no	—
674	C₂×C₅₃	—	4	2	no	—
675	C₂×C₅₃	C₂×#552	1	4	yes	complemented
676	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
677	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
678	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
679	D₅₃	—	2	4	no	—
680	D₅₃	—	4	2	no	—
681	D₅₃	C₂×#552	1	8	yes	direct product factor
682	C₂³×Q₈	—	53	1	no	—
683	C₂³×D₄	—	53	1	no	—
684	C₂⁴×C₄	—	53	2	no	—
685	C₂⁴×C₄	—	53	1	no	—
686	C₂⁴×C₄	—	53	1	no	—
687	#552	—	53	32	no	—
688	#552	—	53	32	no	—
689	#552	—	53	16	no	—
690	#552	—	53	32	no	—
691	#552	—	53	16	no	—
692	#552	—	53	16	no	—
693	#552	—	53	16	no	—
694	#552	—	53	16	no	—
695	#552	—	53	32	no	—
696	#552	—	53	16	no	—
697	#552	—	53	16	no	—
698	#552	C₂×D₅₃	1	16	yes	direct product factor
699	C₂×#126	—	53	32	no	—
700	C₂×#126	—	53	2	no	—
701	C₂×#126	—	53	2	no	—
702	C₂×#126	—	53	2	no	—
703	C₂×#126	—	53	2	no	—
704	C₂×#126	—	53	2	no	—
705	C₂×#126	—	53	2	no	—
706	C₂×#126	—	53	2	no	—
707	C₂×#126	C₂×D₅₃	1	2	yes	complemented
708	C₂×#125	—	53	32	no	—
709	C₂×#125	—	53	16	no	—
710	C₂×#125	—	53	2	no	—
711	C₂×#125	—	53	2	no	—
712	C₂×#125	—	53	2	no	—
713	C₂×#125	—	53	2	no	—
714	C₂×#125	—	53	2	no	—
715	C₂×#125	—	53	2	no	—
716	C₂×#125	—	53	2	no	—
717	C₂×#125	—	53	2	no	—
718	C₂×#125	—	53	1	no	—
719	C₂×#125	—	53	1	no	—
720	C₂×#125	—	53	2	no	—
721	C₂×#125	—	53	1	no	—
722	C₂×#125	C₂×D₅₃	1	2	yes	complemented
723	C₂×#125	C₂×D₅₃	1	1	yes	characteristic, complemented
724	C₂×#123	—	53	2	no	—
725	C₂×#123	—	53	2	no	—
726	C₂×#123	—	53	32	no	—
727	C₂×#123	—	53	2	no	—
728	C₂×#123	—	53	2	no	—
729	C₂×#123	—	53	2	no	—
730	C₂×#123	—	53	2	no	—
731	C₂×#123	—	53	2	no	—
732	C₂×#123	C₂×D₅₃	1	2	yes	—
733	C₂×C₂²⋊Q₈	—	53	1	no	—
734	C₂×C₂²⋊Q₈	—	53	1	no	—
735	C₂×C₂²⋊Q₈	—	53	1	no	—
736	C₂×C₂²⋊Q₈	—	53	1	no	—
737	C₂×C₂²⋊Q₈	—	53	16	no	—
738	C₂×C₂²⋊Q₈	—	53	16	no	—
739	C₂×C₂²⋊Q₈	—	53	2	no	—
740	C₂×C₂²⋊Q₈	—	53	2	no	—
741	C₂×C₂²⋊Q₈	—	53	1	no	—
742	C₂×C₂²⋊Q₈	—	53	1	no	—
743	C₂×C₂²⋊Q₈	—	53	2	no	—
744	C₂×C₂²⋊Q₈	—	53	2	no	—
745	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
746	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
747	C₂×C₄×Q₈	—	53	1	no	—
748	C₂×C₄×Q₈	—	53	16	no	—
749	C₂×C₄×Q₈	—	53	2	no	—
750	C₂×C₄×Q₈	—	53	1	no	—
751	C₂×C₄×Q₈	—	53	1	no	—
752	C₂×C₄×Q₈	—	53	2	no	—
753	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
754	C₂×C₄×D₄	—	53	1	no	—
755	C₂×C₄×D₄	—	53	1	no	—
756	C₂×C₄×D₄	—	53	1	no	—
757	C₂×C₄×D₄	—	53	16	no	—
758	C₂×C₄×D₄	—	53	1	no	—
759	C₂×C₄×D₄	—	53	1	no	—
760	C₂×C₄×D₄	—	53	1	no	—
761	C₂×C₄×D₄	—	53	1	no	—
762	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
763	C₂×#117	—	53	1	no	—
764	C₂×#117	—	53	2	no	—
765	C₂×#117	—	53	16	no	—
766	C₂×#117	—	53	32	no	—
767	C₂×#117	—	53	1	no	—
768	C₂×#117	—	53	1	no	—
769	C₂×#117	—	53	2	no	—
770	C₂×#117	—	53	2	no	—
771	C₂×#117	—	53	2	no	—
772	C₂×#117	—	53	2	no	—
773	C₂×#117	—	53	2	no	—
774	C₂×#117	—	53	2	no	—
775	C₂×#117	—	53	2	no	—
776	C₂×#117	—	53	2	no	—
777	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
778	C₂×#117	C₂×D₅₃	1	2	yes	complemented
779	C₂²×C₄⋊C₄	—	53	2	no	—
780	C₂²×C₄⋊C₄	—	53	1	no	—
781	C₂²×C₄⋊C₄	—	53	1	no	—
782	C₂²×C₄⋊C₄	—	53	1	no	—
783	C₂²×C₄⋊C₄	—	53	2	no	—
784	C₂²×C₄⋊C₄	—	53	1	no	—
785	C₂²×C₄⋊C₄	—	53	2	no	—
786	C₂²×C₄⋊C₄	—	53	2	no	—
787	C₂²×C₄⋊C₄	—	53	1	no	—
788	C₂²×C₄⋊C₄	—	53	2	no	—
789	C₂²×C₄⋊C₄	—	53	2	no	—
790	C₂²×C₄⋊C₄	—	53	2	no	—
791	C₂²×C₄⋊C₄	—	53	2	no	—
792	C₂²×C₄⋊C₄	—	53	1	no	—
793	C₂²×C₄⋊C₄	—	53	1	no	—
794	C₂²×C₄⋊C₄	—	53	16	no	—
795	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
796	C₂²×C₂²⋊C₄	—	53	1	no	—
797	C₂²×C₂²⋊C₄	—	53	2	no	—
798	C₂²×C₂²⋊C₄	—	53	2	no	—
799	C₂²×C₂²⋊C₄	—	53	1	no	—
800	C₂²×C₂²⋊C₄	—	53	2	no	—
801	C₂²×C₄²	—	53	2	no	—
802	C₂²×C₄²	—	53	2	no	—
803	C₂²×C₄²	—	53	1	no	—
804	C₅₃	C₂²×#552	1	1	yes	characteristic, complemented, Sylow
805	C₂⁵	—	53	1	no	—
806	C₂⁵	—	53	1	no	—
807	C₂²×Q₈	—	53	8	no	—
808	C₂²×Q₈	—	53	2	no	—
809	C₂²×Q₈	—	53	1	no	—
810	C₂²×Q₈	—	106	8	no	—
811	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
812	C₂²×D₄	—	53	1	no	—
813	C₂²×D₄	—	53	1	no	—
814	C₂²×D₄	—	53	8	no	—
815	C₂²×D₄	—	53	1	no	—
816	C₂²×D₄	—	106	8	no	—
817	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
818	C₂³×C₄	—	53	1	no	—
819	C₂³×C₄	—	53	2	no	—
820	C₂³×C₄	—	53	1	no	—
821	C₂³×C₄	—	53	1	no	—
822	C₂³×C₄	—	53	2	no	—
823	C₂³×C₄	—	53	2	no	—
824	C₂³×C₄	—	53	1	no	—
825	C₂³×C₄	—	53	1	no	—
826	C₂³×C₄	—	53	2	no	—
827	C₂³×C₄	—	53	1	no	—
828	C₂³×C₄	—	53	2	no	—
829	C₂³×C₄	—	53	1	no	—
830	C₂³×C₄	—	53	16	no	—
831	C₂³×C₄	—	53	2	no	—
832	C₂³×C₄	—	53	2	no	—
833	C₂³×C₄	—	53	1	no	—
834	C₂³×C₄	—	53	8	no	—
835	C₂³×C₄	—	53	1	no	—
836	C₂³×C₄	—	53	1	no	—
837	C₂³×C₄	—	53	8	no	—
838	C₂³×C₄	—	53	1	no	—
839	C₂³×C₄	—	106	8	no	—
840	C₂³×C₄	—	106	8	no	—
841	C₂³×C₄	—	106	16	no	—
842	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
843	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
844	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
845	#126	—	53	16	no	—
846	#126	—	53	16	no	—
847	#126	—	53	16	no	—
848	#126	—	53	16	no	—
849	#126	—	53	16	no	—
850	#126	—	53	16	no	—
851	#126	—	53	16	no	—
852	#126	C₂²×D₅₃	1	16	yes	complemented
853	#125	—	53	16	no	—
854	#125	—	53	16	no	—
855	#125	—	53	16	no	—
856	#125	—	53	16	no	—
857	#125	—	53	16	no	—
858	#125	—	53	16	no	—
859	#125	—	53	16	no	—
860	#125	—	53	16	no	—
861	#125	—	53	8	no	—
862	#125	—	53	8	no	—
863	#125	—	53	16	no	—
864	#125	—	53	8	no	—
865	#125	C₂²×D₅₃	1	16	yes	complemented
866	#125	C₂²×D₅₃	1	8	yes	complemented
867	#123	—	53	16	no	—
868	#123	—	53	16	no	—
869	#123	—	53	16	no	—
870	#123	—	53	16	no	—
871	#123	—	53	16	no	—
872	#123	—	53	16	no	—
873	#123	—	53	16	no	—
874	#123	C₂²×D₅₃	1	16	yes	—
875	C₂²⋊Q₈	—	53	8	no	—
876	C₂²⋊Q₈	—	53	8	no	—
877	C₂²⋊Q₈	—	53	8	no	—
878	C₂²⋊Q₈	—	53	8	no	—
879	C₂²⋊Q₈	—	53	16	no	—
880	C₂²⋊Q₈	—	53	16	no	—
881	C₂²⋊Q₈	—	53	8	no	—
882	C₂²⋊Q₈	—	53	8	no	—
883	C₂²⋊Q₈	—	53	16	no	—
884	C₂²⋊Q₈	—	53	16	no	—
885	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
886	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
887	C₄×Q₈	—	53	8	no	—
888	C₄×Q₈	—	53	16	no	—
889	C₄×Q₈	—	53	8	no	—
890	C₄×Q₈	—	53	8	no	—
891	C₄×Q₈	—	53	16	no	—
892	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
893	C₄×D₄	—	53	8	no	—
894	C₄×D₄	—	53	8	no	—
895	C₄×D₄	—	53	8	no	—
896	C₄×D₄	—	53	8	no	—
897	C₄×D₄	—	53	8	no	—
898	C₄×D₄	—	53	8	no	—
899	C₄×D₄	—	53	8	no	—
900	C₄×D₄	C₂²×D₅₃	1	8	yes	—
901	#117	—	53	8	no	—
902	#117	—	53	16	no	—
903	#117	—	53	8	no	—
904	#117	—	53	8	no	—
905	#117	—	53	16	no	—
906	#117	—	53	16	no	—
907	#117	—	53	16	no	—
908	#117	—	53	16	no	—
909	#117	—	53	16	no	—
910	#117	—	53	16	no	—
911	#117	—	53	16	no	—
912	#117	—	53	16	no	—
913	#117	C₂²×D₅₃	1	8	yes	complemented
914	#117	C₂²×D₅₃	1	16	yes	complemented
915	C₂×C₄⋊C₄	—	53	2	no	—
916	C₂×C₄⋊C₄	—	53	1	no	—
917	C₂×C₄⋊C₄	—	53	2	no	—
918	C₂×C₄⋊C₄	—	53	1	no	—
919	C₂×C₄⋊C₄	—	53	2	no	—
920	C₂×C₄⋊C₄	—	53	2	no	—
921	C₂×C₄⋊C₄	—	53	2	no	—
922	C₂×C₄⋊C₄	—	53	16	no	—
923	C₂×C₄⋊C₄	—	53	8	no	—
924	C₂×C₄⋊C₄	—	53	2	no	—
925	C₂×C₄⋊C₄	—	53	2	no	—
926	C₂×C₄⋊C₄	—	53	2	no	—
927	C₂×C₄⋊C₄	—	53	2	no	—
928	C₂×C₄⋊C₄	—	53	1	no	—
929	C₂×C₄⋊C₄	—	53	2	no	—
930	C₂×C₄⋊C₄	—	53	2	no	—
931	C₂×C₄⋊C₄	—	53	2	no	—
932	C₂×C₄⋊C₄	—	53	1	no	—
933	C₂×C₄⋊C₄	—	53	1	no	—
934	C₂×C₄⋊C₄	—	53	1	no	—
935	C₂×C₄⋊C₄	—	53	2	no	—
936	C₂×C₄⋊C₄	—	53	2	no	—
937	C₂×C₄⋊C₄	—	53	2	no	—
938	C₂×C₄⋊C₄	—	53	2	no	—
939	C₂×C₄⋊C₄	—	53	2	no	—
940	C₂×C₄⋊C₄	—	53	2	no	—
941	C₂×C₄⋊C₄	—	53	2	no	—
942	C₂×C₄⋊C₄	—	53	2	no	—
943	C₂×C₄⋊C₄	—	53	2	no	—
944	C₂×C₄⋊C₄	—	53	8	no	—
945	C₂×C₄⋊C₄	—	53	8	no	—
946	C₂×C₄⋊C₄	—	53	16	no	—
947	C₂×C₄⋊C₄	—	53	16	no	—
948	C₂×C₄⋊C₄	—	53	8	no	—
949	C₂×C₄⋊C₄	—	53	8	no	—
950	C₂×C₄⋊C₄	—	53	8	no	—
951	C₂×C₄⋊C₄	—	53	16	no	—
952	C₂×C₄⋊C₄	—	53	16	no	—
953	C₂×C₄⋊C₄	—	53	8	no	—
954	C₂×C₄⋊C₄	—	53	16	no	—
955	C₂×C₄⋊C₄	—	53	16	no	—
956	C₂×C₄⋊C₄	—	53	16	no	—
957	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
960	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
961	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
963	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	2	yes	—
967	C₂×C₄⋊C₄	C₂²×D₅₃	1	8	yes	complemented
968	C₂×C₂²⋊C₄	—	53	1	no	—
969	C₂×C₂²⋊C₄	—	53	2	no	—
970	C₂×C₂²⋊C₄	—	53	2	no	—
971	C₂×C₂²⋊C₄	—	53	1	no	—
972	C₂×C₂²⋊C₄	—	53	2	no	—
973	C₂×C₂²⋊C₄	—	53	1	no	—
974	C₂×C₂²⋊C₄	—	53	1	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	1	no	—
980	C₂×C₂²⋊C₄	—	53	1	no	—
981	C₂×C₂²⋊C₄	—	53	2	no	—
982	C₂×C₂²⋊C₄	—	53	2	no	—
983	C₂×C₂²⋊C₄	—	53	8	no	—
984	C₂×C₂²⋊C₄	—	53	16	no	—
985	C₂×C₂²⋊C₄	—	53	16	no	—
986	C₂×C₂²⋊C₄	—	53	8	no	—
987	C₂×C₂²⋊C₄	—	53	16	no	—
988	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
989	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
990	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
991	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
992	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
993	C₂×C₄²	—	53	2	no	—
994	C₂×C₄²	—	53	2	no	—
995	C₂×C₄²	—	53	2	no	—
996	C₂×C₄²	—	53	2	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	16	no	—
1003	C₂×C₄²	—	53	16	no	—
1004	C₂×C₄²	—	53	8	no	—
1005	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
1006	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
1007	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1008	C₂⁴	—	53	1	no	—
1009	C₂⁴	—	53	8	no	—
1010	C₂⁴	—	53	4	no	—
1011	C₂⁴	—	53	1	no	—
1012	C₂⁴	—	53	4	no	—
1013	C₂⁴	—	53	1	no	—
1014	C₂⁴	—	106	4	no	—
1015	C₂⁴	—	106	4	no	—
1016	C₂⁴	—	106	4	no	—
1017	C₂⁴	—	106	4	no	—
1018	C₂⁴	—	106	4	no	—
1019	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1020	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1021	C₂×Q₈	—	2	4	no	—
1022	C₂×Q₈	—	53	8	no	—
1023	C₂×Q₈	—	53	4	no	—
1024	C₂×Q₈	—	106	8	no	—
1025	C₂×Q₈	—	106	32	no	—
1026	C₂×Q₈	—	106	4	no	—
1027	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1028	C₂×D₄	—	2	4	no	—
1029	C₂×D₄	—	53	4	no	—
1030	C₂×D₄	—	53	4	no	—
1031	C₂×D₄	—	53	4	no	—
1032	C₂×D₄	—	106	4	no	—
1033	C₂×D₄	—	106	32	no	—
1034	C₂×D₄	—	106	4	no	—
1035	C₂×D₄	—	106	4	no	—
1036	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1037	C₂²×C₄	—	2	8	no	—
1038	C₂²×C₄	—	2	4	no	—
1039	C₂²×C₄	—	2	4	no	—
1040	C₂²×C₄	—	53	1	no	—
1041	C₂²×C₄	—	53	8	no	—
1042	C₂²×C₄	—	53	4	no	—
1043	C₂²×C₄	—	53	8	no	—
1044	C₂²×C₄	—	53	4	no	—
1045	C₂²×C₄	—	53	4	no	—
1046	C₂²×C₄	—	53	1	no	—
1047	C₂²×C₄	—	53	1	no	—
1048	C₂²×C₄	—	53	2	no	—
1049	C₂²×C₄	—	53	2	no	—
1050	C₂²×C₄	—	53	2	no	—
1051	C₂²×C₄	—	53	1	no	—
1052	C₂²×C₄	—	53	1	no	—
1053	C₂²×C₄	—	53	2	no	—
1054	C₂²×C₄	—	53	4	no	—
1055	C₂²×C₄	—	53	4	no	—
1056	C₂²×C₄	—	53	8	no	—
1057	C₂²×C₄	—	53	8	no	—
1058	C₂²×C₄	—	53	8	no	—
1059	C₂²×C₄	—	53	4	no	—
1060	C₂²×C₄	—	53	4	no	—
1061	C₂²×C₄	—	53	8	no	—
1062	C₂²×C₄	—	53	8	no	—
1063	C₂²×C₄	—	53	8	no	—
1064	C₂²×C₄	—	53	4	no	—
1065	C₂²×C₄	—	53	4	no	—
1066	C₂²×C₄	—	53	4	no	—
1067	C₂²×C₄	—	53	4	no	—
1068	C₂²×C₄	—	106	4	no	—
1069	C₂²×C₄	—	106	4	no	—
1070	C₂²×C₄	—	106	32	no	—
1071	C₂²×C₄	—	106	32	no	—
1072	C₂²×C₄	—	106	8	no	—
1073	C₂²×C₄	—	106	4	no	—
1074	C₂²×C₄	—	106	4	no	—
1075	C₂²×C₄	—	106	4	no	—
1076	C₂²×C₄	—	106	8	no	—
1077	C₂²×C₄	—	106	8	no	—
1078	C₂²×C₄	—	106	64	no	—
1079	C₂²×C₄	—	106	8	no	—
1080	C₂²×C₄	—	106	8	no	—
1081	C₂²×C₄	—	106	4	no	—
1082	C₂²×C₄	—	106	8	no	—
1083	C₂²×C₄	—	106	4	no	—
1084	C₂²×C₄	—	106	4	no	—
1085	C₂²×C₄	—	106	8	no	—
1086	C₂²×C₄	—	106	4	no	—
1087	C₂²×C₄	—	106	4	no	—
1088	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1089	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1090	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1091	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1092	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1093	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1094	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1095	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1096	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1097	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1098	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1099	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1100	C₄⋊C₄	—	53	8	no	—
1101	C₄⋊C₄	—	53	4	no	—
1102	C₄⋊C₄	—	53	8	no	—
1103	C₄⋊C₄	—	53	4	no	—
1104	C₄⋊C₄	—	53	8	no	—
1105	C₄⋊C₄	—	53	8	no	—
1106	C₄⋊C₄	—	53	8	no	—
1107	C₄⋊C₄	—	53	8	no	—
1108	C₄⋊C₄	—	53	8	no	—
1109	C₄⋊C₄	—	53	8	no	—
1110	C₄⋊C₄	—	53	8	no	—
1111	C₄⋊C₄	—	53	4	no	—
1112	C₄⋊C₄	—	53	8	no	—
1113	C₄⋊C₄	—	53	8	no	—
1114	C₄⋊C₄	—	53	8	no	—
1115	C₄⋊C₄	—	53	4	no	—
1116	C₄⋊C₄	—	53	4	no	—
1117	C₄⋊C₄	—	53	4	no	—
1118	C₄⋊C₄	—	53	8	no	—
1119	C₄⋊C₄	—	53	8	no	—
1120	C₄⋊C₄	—	53	8	no	—
1121	C₄⋊C₄	—	53	8	no	—
1122	C₄⋊C₄	—	53	8	no	—
1123	C₄⋊C₄	—	53	8	no	—
1124	C₄⋊C₄	—	53	8	no	—
1125	C₄⋊C₄	—	53	8	no	—
1126	C₄⋊C₄	—	53	8	no	—
1127	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1128	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1129	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1130	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1131	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1132	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1133	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1134	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1135	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1136	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1137	C₂²⋊C₄	—	53	4	no	—
1138	C₂²⋊C₄	—	53	8	no	—
1139	C₂²⋊C₄	—	53	8	no	—
1140	C₂²⋊C₄	—	53	4	no	—
1141	C₂²⋊C₄	—	53	8	no	—
1142	C₂²⋊C₄	—	53	4	no	—
1143	C₂²⋊C₄	—	53	4	no	—
1144	C₂²⋊C₄	—	53	8	no	—
1145	C₂²⋊C₄	—	53	8	no	—
1146	C₂²⋊C₄	—	53	8	no	—
1147	C₂²⋊C₄	—	53	8	no	—
1148	C₂²⋊C₄	—	53	4	no	—
1149	C₂²⋊C₄	—	53	4	no	—
1150	C₂²⋊C₄	—	53	8	no	—
1151	C₂²⋊C₄	—	53	8	no	—
1152	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1153	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1154	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1155	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1156	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1157	C₄²	—	53	8	no	—
1158	C₄²	—	53	8	no	—
1159	C₄²	—	53	8	no	—
1160	C₄²	—	53	8	no	—
1161	C₄²	—	53	8	no	—
1162	C₄²	—	53	8	no	—
1163	C₄²	—	53	4	no	—
1164	C₄²	—	53	4	no	—
1165	C₄²	—	53	4	no	—
1166	C₄²	C₂³×D₅₃	1	8	yes	—
1167	C₄²	C₂³×D₅₃	1	8	yes	—
1168	C₄²	C₂³×D₅₃	1	4	yes	—
1169	C₂³	—	2	2	no	—
1170	C₂³	—	2	2	no	—
1171	C₂³	—	2	2	no	—
1172	C₂³	—	2	2	no	—
1173	C₂³	—	2	2	no	—
1174	C₂³	—	53	4	no	—
1175	C₂³	—	53	4	no	—
1176	C₂³	—	53	4	no	—
1177	C₂³	—	53	2	no	—
1178	C₂³	—	53	16	no	—
1179	C₂³	—	53	4	no	—
1180	C₂³	—	53	2	no	—
1181	C₂³	—	53	2	no	—
1182	C₂³	—	106	8	no	—
1183	C₂³	—	106	32	no	—
1184	C₂³	—	106	8	no	—
1185	C₂³	—	106	8	no	—
1186	C₂³	—	106	8	no	—
1187	C₂³	—	106	8	no	—
1188	C₂³	—	106	2	no	—
1189	C₂³	—	106	2	no	—
1190	C₂³	—	106	2	no	—
1191	C₂³	—	106	2	no	—
1192	C₂³	—	106	2	no	—
1193	C₂³	—	212	16	no	—
1194	C₂³	#41×D₅₃	1	4	yes	—
1195	C₂³	C₂⁴×D₅₃	1	2	yes	—
1196	C₂³	C₂⁴×D₅₃	1	2	yes	—
1197	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1198	Q₈	—	2	8	no	—
1199	Q₈	—	106	16	no	—
1200	Q₈	—	106	8	no	—
1201	D₄	—	2	8	no	—
1202	D₄	—	106	8	no	—
1203	D₄	—	106	8	no	—
1204	D₄	—	106	8	no	—
1205	C₂×C₄	—	2	16	no	—
1206	C₂×C₄	—	2	4	no	—
1207	C₂×C₄	—	2	4	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	4	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	4	no	—
1214	C₂×C₄	—	2	8	no	—
1215	C₂×C₄	—	2	8	no	—
1216	C₂×C₄	—	53	4	no	—
1217	C₂×C₄	—	53	2	no	—
1218	C₂×C₄	—	53	16	no	—
1219	C₂×C₄	—	53	2	no	—
1220	C₂×C₄	—	53	2	no	—
1221	C₂×C₄	—	53	4	no	—
1222	C₂×C₄	—	53	4	no	—
1223	C₂×C₄	—	53	4	no	—
1224	C₂×C₄	—	53	2	no	—
1225	C₂×C₄	—	53	2	no	—
1226	C₂×C₄	—	53	4	no	—
1227	C₂×C₄	—	106	8	no	—
1228	C₂×C₄	—	106	8	no	—
1229	C₂×C₄	—	106	8	no	—
1230	C₂×C₄	—	106	16	no	—
1231	C₂×C₄	—	106	8	no	—
1232	C₂×C₄	—	106	8	no	—
1233	C₂×C₄	—	106	16	no	—
1234	C₂×C₄	—	106	16	no	—
1235	C₂×C₄	—	106	16	no	—
1236	C₂×C₄	—	106	16	no	—
1237	C₂×C₄	—	106	8	no	—
1238	C₂×C₄	—	106	16	no	—
1239	C₂×C₄	—	106	8	no	—
1240	C₂×C₄	—	106	8	no	—
1241	C₂×C₄	—	106	16	no	—
1242	C₂×C₄	—	106	4	no	—
1243	C₂×C₄	—	106	4	no	—
1244	C₂×C₄	—	106	2	no	—
1245	C₂×C₄	—	106	2	no	—
1246	C₂×C₄	—	106	2	no	—
1247	C₂×C₄	—	106	4	no	—
1248	C₂×C₄	—	106	2	no	—
1249	C₂×C₄	—	106	4	no	—
1250	C₂×C₄	—	106	8	no	—
1251	C₂×C₄	—	106	8	no	—
1252	C₂×C₄	#41×D₅₃	1	4	yes	—
1253	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1254	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1255	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1256	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1257	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1258	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1259	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1260	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1261	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1262	C₂²	—	2	8	no	—
1263	C₂²	—	2	2	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	2	no	—
1267	C₂²	—	2	2	no	—
1268	C₂²	—	4	4	no	—
1269	C₂²	—	53	16	no	—
1270	C₂²	—	53	4	no	—
1271	C₂²	—	53	4	no	—
1272	C₂²	—	53	4	no	—
1273	C₂²	—	53	4	no	—
1274	C₂²	—	106	32	no	—
1275	C₂²	—	106	8	no	—
1276	C₂²	—	106	2	no	—
1277	C₂²	—	106	2	no	—
1278	C₂²	—	106	2	no	—
1279	C₂²	—	106	2	no	—
1280	C₂²	—	106	2	no	—
1281	C₂²	—	212	16	no	—
1282	C₂²	—	212	4	no	—
1283	C₂²	C₂×#41×D₅₃	1	4	yes	—
1284	C₂²	C₂×#41×D₅₃	1	2	yes	—
1285	C₂²	C₂×#41×D₅₃	1	2	yes	—
1286	C₂²	2₋¹⁺⁴×D₅₃	1	2	yes	—
1287	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1288	C₄	—	2	4	no	—
1289	C₄	—	2	4	no	—
1290	C₄	—	2	2	no	—
1291	C₄	—	2	2	no	—
1292	C₄	—	2	2	no	—
1293	C₄	—	2	4	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	4	no	—
1296	C₄	—	53	4	no	—
1297	C₄	—	106	4	no	—
1298	C₄	—	106	4	no	—
1299	C₄	—	106	2	no	—
1300	C₄	—	106	2	no	—
1301	C₄	—	106	2	no	—
1302	C₄	—	106	4	no	—
1303	C₄	—	106	2	no	—
1304	C₄	—	106	4	no	—
1305	C₄	C₂×#41×D₅₃	1	4	yes	—
1306	C₂	—	2	4	no	—
1307	C₂	—	4	2	no	—
1308	C₂	—	53	8	no	—
1309	C₂	—	106	4	no	—
1310	C₂	—	212	2	no	—
1311	C₂	#552×D₅₃	1	4	yes	direct product factor
1312	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1313	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1314	C₂	C₂×2₋¹⁺⁴×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#552	C₂
socle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×D₄×D₅₃	C₂²
hypercenter	C₂×#552	D₅₃
hypocenter	C₅₃	C₂²×#552
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#552

Complements

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

N	H ≅ G/N	type
1. C₂×#16811315	C₂	semidirect
2. C₂×#16811314	C₂	semidirect
3. C₂×#16811313	C₂	semidirect
4. C₂×#16811312	C₂	semidirect
5. C₂×#16811311	C₂	semidirect
6. C₂×#16811310	C₂	semidirect
7. C₂×#16811309	C₂	semidirect
8. C₂×#16811308	C₂	semidirect
9. C₂×#16811307	C₂	semidirect
10. C₂×#16811306	C₂	semidirect
11. C₂×#16811305	C₂	semidirect
12. #552×D₅₃	C₂	direct (N × H)
13. C₂×#126×D₅₃	C₂	semidirect
14. C₂×#125×D₅₃	C₂	semidirect
15. C₂×#125×D₅₃	C₂	semidirect
17. C₂×C₂²⋊Q₈×D₅₃	C₂	semidirect
18. C₂×C₂²⋊Q₈×D₅₃	C₂	semidirect
19. C₂×C₄×Q₈×D₅₃	C₂	semidirect
21. C₂×#117×D₅₃	C₂	semidirect
22. C₂×#117×D₅₃	C₂	semidirect
23. C₂²×C₄⋊C₄×D₅₃	C₂	semidirect
24. C₂×C₅₃×#552	C₂	semidirect
30. #16811315	C₂²	semidirect
31. #16811314	C₂²	semidirect
32. #16811313	C₂²	semidirect
33. #16811312	C₂²	semidirect
34. #16811311	C₂²	semidirect
35. #16811310	C₂²	semidirect
36. #16811309	C₂²	semidirect
37. #16811308	C₂²	semidirect
38. #16811307	C₂²	semidirect
39. #16811306	C₂²	semidirect
40. #16811305	C₂²	semidirect
41. C₂×#13133212	C₂²	semidirect
42. C₂×#13133212	C₂²	semidirect
43. C₂×#13133212	C₂²	semidirect
44. C₂×#13133211	C₂²	semidirect
45. C₂×#13133210	C₂²	semidirect
46. C₂×#13133210	C₂²	semidirect
47. C₂×#13133210	C₂²	semidirect
48. #126×D₅₃	C₂²	semidirect
49. C₂×#13133209	C₂²	semidirect
50. C₂×#13133209	C₂²	semidirect
51. C₂×#13133208	C₂²	semidirect
52. C₂×#13133208	C₂²	semidirect
53. C₂×#13133208	C₂²	semidirect
54. C₂×#13133208	C₂²	semidirect
55. C₂×#13133207	C₂²	semidirect
56. C₂×#13133207	C₂²	semidirect
57. C₂×#13133207	C₂²	semidirect
58. C₂×#13133207	C₂²	semidirect
59. C₂×#13133207	C₂²	semidirect
60. C₂×#13133207	C₂²	semidirect
61. #125×D₅₃	C₂²	semidirect
62. #125×D₅₃	C₂²	semidirect
71. C₂×#13133197	C₂²	semidirect
72. C₂×#13133197	C₂²	semidirect
73. C₂×#13133196	C₂²	semidirect
74. C₂×#13133196	C₂²	semidirect
75. C₂×#13133195	C₂²	semidirect
76. C₂×#13133195	C₂²	semidirect
77. C₂×#13133194	C₂²	semidirect
78. C₂×#13133194	C₂²	semidirect
79. C₂×#13133193	C₂²	semidirect
80. C₂×#13133193	C₂²	semidirect
81. C₂²⋊Q₈×D₅₃	C₂²	semidirect
82. 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
97. C₂×#13133176	C₂²	semidirect
98. C₂×#13133176	C₂²	semidirect
99. C₂×#13133175	C₂²	semidirect
100. C₂×#13133175	C₂²	semidirect
101. C₂×#13133175	C₂²	semidirect
102. C₂×#13133175	C₂²	semidirect
103. C₂×#13133174	C₂²	semidirect
104. C₂×#13133174	C₂²	semidirect
105. C₂×#13133174	C₂²	semidirect
106. C₂×#13133173	C₂²	semidirect
107. C₂×#13133173	C₂²	semidirect
108. C₂×#13133173	C₂²	semidirect
109. #117×D₅₃	C₂²	semidirect
110. #117×D₅₃	C₂²	semidirect
111. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
112. C₂²×#11719919	C₂²	semidirect
123. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
124. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
125. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
126. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
135. C₅₃×#552	C₂²	semidirect
136. C₂×#126×C₅₃	C₂²	semidirect
137. C₂×#125×C₅₃	C₂²	semidirect
138. C₂×#125×C₅₃	C₂²	semidirect
140. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
142. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
144. C₂×#117×C₅₃	C₂²	semidirect
145. C₂×#117×C₅₃	C₂²	semidirect
146. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
182. #13133212	C₂³	semidirect
183. #13133212	C₂³	semidirect
184. #13133212	C₂³	semidirect
185. #13133211	C₂³	semidirect
186. #13133210	C₂³	semidirect
187. #13133210	C₂³	semidirect
188. #13133210	C₂³	semidirect
189. #13133209	C₂³	semidirect
190. #13133209	C₂³	semidirect
191. #13133208	C₂³	semidirect
192. #13133208	C₂³	semidirect
193. #13133208	C₂³	semidirect
194. #13133208	C₂³	semidirect
195. #13133207	C₂³	semidirect
196. #13133207	C₂³	semidirect
197. #13133207	C₂³	semidirect
198. #13133207	C₂³	semidirect
199. #13133207	C₂³	semidirect
200. #13133207	C₂³	semidirect
208. #13133197	C₂³	semidirect
209. #13133197	C₂³	semidirect
210. #13133196	C₂³	semidirect
211. #13133196	C₂³	semidirect
212. #13133195	C₂³	semidirect
213. #13133195	C₂³	semidirect
214. #13133194	C₂³	semidirect
215. #13133194	C₂³	semidirect
216. #13133193	C₂³	semidirect
217. #13133193	C₂³	semidirect
218. Q₈×Dic₅₃	C₂³	semidirect
219. C₄×Dic₁₀₆	C₂³	semidirect
220. C₄×Dic₁₀₆	C₂³	semidirect
221. #13133182	C₂³	semidirect
222. #13133182	C₂³	semidirect
230. #13133176	C₂³	semidirect
231. #13133176	C₂³	semidirect
232. #13133175	C₂³	semidirect
233. #13133175	C₂³	semidirect
234. #13133175	C₂³	semidirect
235. #13133175	C₂³	semidirect
236. #13133174	C₂³	semidirect
237. #13133174	C₂³	semidirect
238. #13133174	C₂³	semidirect
239. #13133173	C₂³	semidirect
240. #13133173	C₂³	semidirect
241. #13133173	C₂³	semidirect
252. C₂×C₄⋊Dic₅₃	C₂³	semidirect
270. C₂×#11719919	C₂³	semidirect
281. C₄⋊C₄×D₅₃	C₂³	semidirect
282. C₄⋊C₄×D₅₃	C₂³	semidirect
283. C₄⋊C₄×D₅₃	C₂³	semidirect
321. #126×C₅₃	C₂³	semidirect
322. #125×C₅₃	C₂³	semidirect
323. #125×C₅₃	C₂³	semidirect
325. C₂²⋊Q₈×C₅₃	C₂³	semidirect
326. C₂²⋊Q₈×C₅₃	C₂³	semidirect
327. C₄×Q₈×C₅₃	C₂³	semidirect
329. #117×C₅₃	C₂³	semidirect
330. #117×C₅₃	C₂³	semidirect
341. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
626. C₂×D₅₃	#552	direct (N × H)
661. C₂×#552	D₅₃	direct (N × H)
675. C₂×C₅₃	C₂×#552	semidirect
681. D₅₃	C₂×#552	direct (N × H)
698. #552	C₂×D₅₃	direct (N × H)
707. C₂×#126	C₂×D₅₃	semidirect
722. C₂×#125	C₂×D₅₃	semidirect
723. C₂×#125	C₂×D₅₃	semidirect
745. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
746. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
753. C₂×C₄×Q₈	C₂×D₅₃	semidirect
777. C₂×#117	C₂×D₅₃	semidirect
778. C₂×#117	C₂×D₅₃	semidirect
795. C₂²×C₄⋊C₄	C₂×D₅₃	semidirect
804. C₅₃	C₂²×#552	semidirect
852. #126	C₂²×D₅₃	semidirect
865. #125	C₂²×D₅₃	semidirect
866. #125	C₂²×D₅₃	semidirect
885. C₂²⋊Q₈	C₂²×D₅₃	semidirect
886. C₂²⋊Q₈	C₂²×D₅₃	semidirect
892. C₄×Q₈	C₂²×D₅₃	semidirect
913. #117	C₂²×D₅₃	semidirect
914. #117	C₂²×D₅₃	semidirect
967. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1311. C₂	#552×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×#16811315	2
C₂×#16811314	2
C₂×#16811313	2
C₂×#16811312	2
C₂×#16811311	2
C₂×#16811310	2
C₂×#16811309	2
C₂×#16811308	2
C₂×#16811307	2
C₂×#16811306	2
C₂×#16811305	2
#552×D₅₃	2
C₂×#126×D₅₃	2
C₂×#125×D₅₃	2
C₂×#123×D₅₃	2
C₂×C₂²⋊Q₈×D₅₃	2
C₂×C₄×Q₈×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₂×#117×D₅₃	2
C₂²×C₄⋊C₄×D₅₃	2
C₂×C₅₃×#552	2
C₂²×#552	53

Subgroups — C2×#552×D53 #28291076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#552×D₅₃ #28291076