Subgroups — D₅₃×#2556 #27554181

Order 13568.

2726 conjugacy classes of subgroups.

The subgroup lattice has 1580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#125×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20279806	C₂	1	1	yes	maximal, characteristic, complemented
4	#20279805	C₂	1	1	yes	maximal, characteristic, complemented
5	#20279804	C₂	1	1	yes	maximal, characteristic, complemented
6	#20279803	C₂	1	1	yes	maximal, characteristic, complemented
7	#20279802	C₂	1	1	yes	maximal, characteristic, complemented
8	#20279801	C₂	1	1	yes	maximal, characteristic, complemented
9	#20279800	C₂	1	1	yes	maximal, characteristic, complemented
10	#20279799	C₂	1	1	yes	maximal, characteristic, complemented
11	#20279798	C₂	1	1	yes	maximal, characteristic, complemented
12	#20279797	C₂	1	1	yes	maximal, characteristic, complemented
13	#20279796	C₂	1	1	yes	maximal, characteristic, complemented
14	#20279795	C₂	1	1	yes	maximal, characteristic, complemented
15	#20279794	C₂	1	1	yes	maximal, characteristic, complemented
16	#20279793	C₂	1	1	yes	maximal, characteristic, complemented
17	#20279792	C₂	1	1	yes	maximal, characteristic, complemented
18	#399×D₅₃	C₂	1	1	yes	maximal, characteristic
19	#398×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#396×D₅₃	C₂	1	1	yes	maximal, characteristic
21	#395×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#391×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#389×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	#389×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
26	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
27	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	#385×D₅₃	C₂	1	1	yes	maximal, characteristic
29	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic
31	C₅₃×#2556	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
34	C₂×#13133209	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
41	#125×D₅₃	—	2	8	no	—
42	C₂×#13133197	C₂²	1	1	yes	characteristic
43	C₂×#13133196	C₂²	1	1	yes	characteristic
44	C₂×#13133195	C₂²	1	1	yes	characteristic
45	C₂×#13133195	C₂²	1	1	yes	characteristic
46	C₂×#13133194	C₂²	1	1	yes	characteristic
47	C₂×#13133194	C₂²	1	1	yes	characteristic
48	C₂×#13133193	C₂²	1	1	yes	characteristic
49	C₂²⋊Q₈×D₅₃	—	2	8	no	—
50	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
60	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
69	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
70	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
71	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
72	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
73	#16810560	C₂²	1	1	yes	characteristic
74	#16810559	C₂²	1	1	yes	characteristic
75	#16810559	C₂²	1	1	yes	characteristic
76	#16810559	C₂²	1	1	yes	characteristic
77	#16810558	C₂²	1	1	yes	characteristic
78	#16810558	C₂²	1	1	yes	characteristic
79	#16810558	C₂²	1	1	yes	characteristic
80	#16810557	C₂²	1	1	yes	characteristic, complemented
81	#16810557	C₂²	1	1	yes	characteristic, complemented
82	#16810556	C₂²	1	1	yes	characteristic, complemented
83	#16810556	C₂²	1	1	yes	characteristic, complemented
84	#16810555	C₂²	1	1	yes	characteristic, complemented
85	#16810554	C₂²	1	1	yes	characteristic, complemented
86	#16810553	C₂²	1	1	yes	characteristic, complemented
87	#16810547	C₂²	1	1	yes	characteristic
88	#16810546	C₂²	1	1	yes	characteristic
89	#16810546	C₂²	1	1	yes	characteristic
90	#16810546	C₂²	1	1	yes	characteristic
91	#16810545	C₂²	1	1	yes	characteristic
92	#16810545	C₂²	1	1	yes	characteristic
93	#16810545	C₂²	1	1	yes	characteristic
94	#16810544	C₂²	1	1	yes	characteristic, complemented
95	#16810544	C₂²	1	1	yes	characteristic, complemented
96	#16810544	C₂²	1	1	yes	characteristic, complemented
97	#16810543	C₂²	1	1	yes	characteristic, complemented
98	#16810543	C₂²	1	1	yes	characteristic, complemented
99	#16810543	C₂²	1	1	yes	characteristic, complemented
100	#16810542	C₂²	1	1	yes	characteristic, complemented
101	#16810530	C₂²	1	1	yes	characteristic, complemented
102	#16810529	C₂²	1	1	yes	characteristic, complemented
103	#16810528	C₂²	1	1	yes	characteristic, complemented
104	#16810527	C₂²	1	1	yes	characteristic, complemented
105	#16810527	C₂²	1	1	yes	characteristic, complemented
106	#16810527	C₂²	1	1	yes	characteristic, complemented
107	#16810527	C₂²	1	1	yes	characteristic, complemented
108	#16810522	C₂²	1	1	yes	characteristic, complemented
109	#16810522	C₂²	1	1	yes	characteristic, complemented
110	#16810521	C₂²	1	1	yes	characteristic, complemented
111	#16810521	C₂²	1	1	yes	characteristic, complemented
112	#16810520	C₂²	1	1	yes	characteristic, complemented
113	#16810520	C₂²	1	1	yes	characteristic, complemented
114	#16810520	C₂²	1	1	yes	characteristic, complemented
115	#16810520	C₂²	1	1	yes	characteristic, complemented
116	#16810519	C₂²	1	1	yes	characteristic, complemented
117	#16810519	C₂²	1	1	yes	characteristic, complemented
118	#16810518	C₂²	1	1	yes	characteristic, complemented
119	#16810518	C₂²	1	1	yes	characteristic, complemented
120	#16810518	C₂²	1	1	yes	characteristic, complemented
121	#16810518	C₂²	1	1	yes	characteristic, complemented
122	#16810517	C₂²	1	1	yes	characteristic
123	#16810517	C₂²	1	1	yes	characteristic
124	#16810516	C₂²	1	1	yes	characteristic
125	#16810516	C₂²	1	1	yes	characteristic
126	#16810515	C₂²	1	1	yes	characteristic
127	#16810515	C₂²	1	1	yes	characteristic
128	#16810514	C₂²	1	1	yes	characteristic
129	#16810514	C₂²	1	1	yes	characteristic
130	#16810513	C₂²	1	1	yes	characteristic
131	#16810513	C₂²	1	1	yes	characteristic
132	#16810512	C₂²	1	1	yes	characteristic
133	#16810512	C₂²	1	1	yes	characteristic
134	#16810511	C₂²	1	1	yes	characteristic
135	#16810511	C₂²	1	1	yes	characteristic
136	#16810510	C₂²	1	1	yes	characteristic, complemented
137	#16810509	C₂²	1	1	yes	characteristic, complemented
138	#16810508	C₂²	1	1	yes	characteristic, complemented
139	#16810507	C₂²	1	1	yes	characteristic, complemented
140	#16810506	C₂²	1	1	yes	characteristic, complemented
141	#16810505	C₂²	1	1	yes	characteristic, complemented
142	#16810504	C₂²	1	1	yes	characteristic, complemented
143	#16810498	C₂²	1	1	yes	characteristic
144	#16810497	C₂²	1	1	yes	characteristic
145	#16810497	C₂²	1	1	yes	characteristic
146	#16810496	C₂²	1	1	yes	characteristic
147	#16810495	C₂²	1	1	yes	characteristic
148	#16810494	C₂²	1	1	yes	characteristic
149	#16810494	C₂²	1	1	yes	characteristic
150	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
151	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
152	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
153	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
154	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
155	#16810474	C₂²	1	1	yes	characteristic, complemented
156	#16810474	C₂²	1	1	yes	characteristic, complemented
157	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
158	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
159	C₄×#11719921	C₂²	1	1	yes	characteristic
160	C₄×#11719921	C₂²	1	1	yes	characteristic
161	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
162	#16810470	C₂²	1	1	yes	characteristic
163	#16810470	C₂²	1	1	yes	characteristic
164	#95×D₅₃	C₂²	1	1	yes	characteristic
165	#95×D₅₃	C₂²	1	1	yes	characteristic
166	#95×D₅₃	C₂²	1	1	yes	characteristic
167	#95×D₅₃	C₂²	1	1	yes	characteristic
168	#95×D₅₃	C₂²	1	1	yes	characteristic
169	#95×D₅₃	C₂²	1	1	yes	characteristic
170	#95×D₅₃	C₂²	1	1	yes	characteristic
171	#95×D₅₃	C₂²	1	1	yes	characteristic
172	#95×D₅₃	C₂²	1	1	yes	characteristic
173	#95×D₅₃	C₂²	1	1	yes	characteristic
174	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
176	C₅₃×#399	C₂²	1	1	yes	characteristic
177	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#396	C₂²	1	1	yes	characteristic
179	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#388	C₂²	1	1	yes	characteristic
184	C₅₃×#388	C₂²	1	1	yes	characteristic
185	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#385	C₂²	1	1	yes	characteristic
187	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
189	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
191	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
192	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
193	C₂×Q₈×D₅₃	—	2	4	no	—
194	C₂×Q₈×D₅₃	—	2	4	no	—
195	C₂×Q₈×D₅₃	—	4	2	no	—
196	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅₃	—	2	4	no	—
198	C₂²×C₄×D₅₃	—	2	4	no	—
199	C₂²×C₄×D₅₃	—	4	2	no	—
200	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
202	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
211	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
214	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
215	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
216	#13133209	—	2	4	no	—
217	#13133208	—	2	4	no	—
218	#13133208	—	2	4	no	—
219	#13133207	—	2	4	no	—
220	#13133207	—	2	4	no	—
221	#13133207	—	2	4	no	—
222	#13133207	—	2	4	no	—
223	#13133197	—	2	4	no	—
224	#13133196	—	2	4	no	—
225	#13133195	—	2	4	no	—
226	#13133195	—	2	4	no	—
227	#13133194	—	2	4	no	—
228	#13133194	—	2	4	no	—
229	#13133193	—	2	4	no	—
230	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×#11719919	C₂³	1	1	yes	characteristic
244	C₂×#11719919	C₂³	1	1	yes	characteristic
245	C₂×#11719919	C₂³	1	1	yes	characteristic
246	C₂×#11719919	C₂³	1	1	yes	characteristic
247	C₂×#11719919	C₂³	1	1	yes	characteristic
248	C₂×#11719919	C₂³	1	1	yes	characteristic
249	C₂×#11719919	C₂³	1	1	yes	characteristic
250	C₂×#11719919	C₂³	1	1	yes	characteristic
251	C₂×#11719919	C₂³	1	1	yes	characteristic
252	C₂×#11719919	C₂³	1	1	yes	characteristic
253	C₂×#11719919	C₂³	1	1	yes	characteristic
254	C₂×#11719919	C₂³	1	1	yes	characteristic
255	C₂×#11719919	C₂³	1	1	yes	characteristic
256	C₂×#11719919	C₂³	1	1	yes	characteristic
257	C₂×#11719919	C₂³	1	1	yes	characteristic
258	C₂×#11719919	C₂³	1	1	yes	characteristic
259	C₂×#11719919	C₂³	1	1	yes	characteristic
260	C₂×#11719919	C₂³	1	1	yes	characteristic
261	C₂×#11719919	C₂³	1	1	yes	characteristic
262	C₂×#11719919	C₂³	1	1	yes	characteristic
263	C₂×#11719919	C₂³	1	1	yes	characteristic
264	C₂×#11719919	C₂³	1	1	yes	characteristic
265	C₂×#11719919	C₂³	1	1	yes	characteristic
266	C₂×#11719919	C₂³	1	1	yes	characteristic
267	C₂×#11719919	C₂³	1	1	yes	characteristic
268	C₂×#11719919	C₂³	1	1	yes	characteristic
269	C₄⋊C₄×D₅₃	—	2	4	no	—
270	C₄⋊C₄×D₅₃	—	2	4	no	—
271	C₄⋊C₄×D₅₃	—	2	4	no	—
272	C₄⋊C₄×D₅₃	—	2	4	no	—
273	C₄⋊C₄×D₅₃	—	2	4	no	—
274	C₄⋊C₄×D₅₃	—	2	4	no	—
275	C₄⋊C₄×D₅₃	—	2	4	no	—
276	C₄⋊C₄×D₅₃	—	2	4	no	—
277	C₄⋊C₄×D₅₃	—	2	4	no	—
278	C₄⋊C₄×D₅₃	—	2	4	no	—
279	C₄⋊C₄×D₅₃	—	2	4	no	—
280	C₄⋊C₄×D₅₃	—	4	2	no	—
281	C₄⋊C₄×D₅₃	D₄	1	8	yes	—
282	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂×#11719921	C₂³	1	1	yes	characteristic
289	C₂×#11719921	C₂³	1	1	yes	characteristic
290	C₂×#11719921	C₂³	1	1	yes	characteristic
291	C₂×#11719921	C₂³	1	1	yes	characteristic
292	C₂×#11719921	C₂³	1	1	yes	characteristic
293	C₂×#11719921	C₂³	1	1	yes	characteristic
294	C₂×#11719921	C₂³	1	1	yes	characteristic
295	C₂×#11719921	C₂³	1	1	yes	characteristic
296	C₂×#11719921	C₂³	1	1	yes	characteristic
297	C₂×#11719921	C₂³	1	1	yes	characteristic
298	C₂×#11719921	C₂³	1	1	yes	characteristic
299	C₂×#11719921	C₂³	1	1	yes	characteristic
300	C₂²⋊C₄×D₅₃	—	2	4	no	—
301	C₂²⋊C₄×D₅₃	—	2	4	no	—
302	C₂²⋊C₄×D₅₃	—	2	4	no	—
303	C₂²⋊C₄×D₅₃	—	2	4	no	—
304	C₂²⋊C₄×D₅₃	—	4	2	no	—
305	C₂²⋊C₄×D₅₃	Q₈	1	8	yes	complemented
306	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
318	C₄²×D₅₃	—	2	4	no	—
319	C₄²×D₅₃	—	2	4	no	—
320	C₄²×D₅₃	—	4	2	no	—
321	C₄²×D₅₃	—	4	2	no	—
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	#13133124	C₂³	1	1	yes	characteristic
327	#13133124	C₂³	1	1	yes	characteristic
328	#13133124	C₂³	1	1	yes	characteristic
329	#13133124	C₂³	1	1	yes	characteristic
330	#13133124	C₂³	1	1	yes	characteristic
331	#13133124	C₂³	1	1	yes	characteristic
332	#13133124	C₂³	1	1	yes	characteristic
333	#13133124	C₂³	1	1	yes	characteristic
334	#13133124	C₂³	1	1	yes	characteristic
335	#13133124	C₂³	1	1	yes	characteristic
336	#13133124	C₂³	1	1	yes	characteristic
337	#13133124	C₂³	1	1	yes	characteristic
338	#13133124	C₂³	1	1	yes	characteristic
339	#13133124	C₂³	1	1	yes	characteristic
340	#13133124	C₂³	1	1	yes	characteristic
341	#13133124	C₂³	1	1	yes	characteristic
342	#13133124	C₂³	1	1	yes	characteristic
343	#13133124	C₂³	1	1	yes	characteristic
344	#13133124	C₂³	1	1	yes	characteristic
345	#13133124	C₂³	1	1	yes	characteristic
346	#13133124	C₂³	1	1	yes	characteristic
347	#13133124	C₂³	1	1	yes	characteristic
348	#13133124	C₂³	1	1	yes	characteristic
349	#13133124	C₂³	1	1	yes	characteristic
350	#13133124	C₂³	1	1	yes	characteristic
351	#13133124	C₂³	1	1	yes	characteristic
352	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
353	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
354	#125×C₅₃	—	2	4	no	—
355	C₂²⋊Q₈×C₅₃	—	2	4	no	—
356	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
371	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
373	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
374	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
375	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
376	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
377	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
378	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
379	#95×C₅₃	C₂³	1	1	yes	characteristic
380	#95×C₅₃	C₂³	1	1	yes	characteristic
381	#95×C₅₃	C₂³	1	1	yes	characteristic
382	#95×C₅₃	C₂³	1	1	yes	characteristic
383	#95×C₅₃	C₂³	1	1	yes	characteristic
384	#95×C₅₃	C₂³	1	1	yes	characteristic
385	#95×C₅₃	C₂³	1	1	yes	characteristic
386	#95×C₅₃	C₂³	1	1	yes	characteristic
387	#95×C₅₃	C₂³	1	1	yes	characteristic
388	#95×C₅₃	C₂³	1	1	yes	characteristic
389	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂³×D₅₃	—	2	2	no	—
391	C₂³×D₅₃	—	2	2	no	—
392	C₂³×D₅₃	—	2	2	no	—
393	C₂³×D₅₃	—	2	2	no	—
394	C₂³×D₅₃	—	2	2	no	—
395	C₂³×D₅₃	—	2	2	no	—
396	C₂³×D₅₃	C₂×Q₈	1	4	yes	—
397	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
398	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×Q₈×C₅₃	—	2	2	no	—
400	C₂×Q₈×C₅₃	—	2	2	no	—
401	C₂×Q₈×C₅₃	—	4	1	no	—
402	C₂²×C₄×C₅₃	—	2	2	no	—
403	C₂²×C₄×C₅₃	—	2	2	no	—
404	C₂²×C₄×C₅₃	—	4	1	no	—
405	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×Dic₅₃	—	2	2	no	—
420	C₂²×Dic₅₃	—	2	2	no	—
421	C₂²×Dic₅₃	—	4	1	no	—
422	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
428	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
430	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
433	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
434	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
435	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
436	Q₈×D₅₃	—	4	16	no	—
437	C₂×C₄×D₅₃	—	2	2	no	—
438	C₂×C₄×D₅₃	—	2	2	no	—
439	C₂×C₄×D₅₃	—	2	2	no	—
440	C₂×C₄×D₅₃	—	2	2	no	—
441	C₂×C₄×D₅₃	—	2	2	no	—
442	C₂×C₄×D₅₃	—	2	2	no	—
443	C₂×C₄×D₅₃	—	2	2	no	—
444	C₂×C₄×D₅₃	—	2	2	no	—
445	C₂×C₄×D₅₃	—	2	2	no	—
446	C₂×C₄×D₅₃	—	2	2	no	—
447	C₂×C₄×D₅₃	—	2	2	no	—
448	C₂×C₄×D₅₃	—	2	2	no	—
449	C₂×C₄×D₅₃	—	2	2	no	—
450	C₂×C₄×D₅₃	—	2	2	no	—
451	C₂×C₄×D₅₃	—	2	2	no	—
452	C₂×C₄×D₅₃	—	2	2	no	—
453	C₂×C₄×D₅₃	—	2	2	no	—
454	C₂×C₄×D₅₃	—	2	2	no	—
455	C₂×C₄×D₅₃	—	2	2	no	—
456	C₂×C₄×D₅₃	—	2	2	no	—
457	C₂×C₄×D₅₃	—	2	2	no	—
458	C₂×C₄×D₅₃	—	2	2	no	—
459	C₂×C₄×D₅₃	—	2	2	no	—
460	C₂×C₄×D₅₃	—	2	2	no	—
461	C₂×C₄×D₅₃	—	2	2	no	—
462	C₂×C₄×D₅₃	—	2	2	no	—
463	C₂×C₄×D₅₃	—	2	2	no	—
464	C₂×C₄×D₅₃	—	2	2	no	—
465	C₂×C₄×D₅₃	—	2	2	no	—
466	C₂×C₄×D₅₃	—	2	2	no	—
467	C₂×C₄×D₅₃	—	2	2	no	—
468	C₂×C₄×D₅₃	—	2	2	no	—
469	C₂×C₄×D₅₃	—	2	2	no	—
470	C₂×C₄×D₅₃	—	2	2	no	—
471	C₂×C₄×D₅₃	—	2	2	no	—
472	C₂×C₄×D₅₃	—	2	2	no	—
473	C₂×C₄×D₅₃	—	2	2	no	—
474	C₂×C₄×D₅₃	—	2	2	no	—
475	C₂×C₄×D₅₃	—	4	16	no	—
476	C₂×C₄×D₅₃	—	4	1	no	—
477	C₂×C₄×D₅₃	—	4	1	no	—
478	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
479	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
480	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
481	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
482	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
483	C₂×C₄×D₅₃	#41	1	4	yes	—
484	C₂×C₄×D₅₃	#41	1	4	yes	—
485	C₂×C₄×D₅₃	#41	1	4	yes	—
486	C₂×Dic₁₀₆	—	2	2	no	—
487	C₂×Dic₁₀₆	—	2	2	no	—
488	C₂×Dic₁₀₆	—	2	2	no	—
489	C₂×Dic₁₀₆	—	2	2	no	—
490	C₂×Dic₁₀₆	—	2	2	no	—
491	C₂×Dic₁₀₆	—	2	2	no	—
492	C₂×Dic₁₀₆	—	4	1	no	—
493	C₂×Dic₁₀₆	—	4	1	no	—
494	C₂×Dic₁₀₆	—	4	1	no	—
495	C₄⋊C₄×C₅₃	—	2	2	no	—
496	C₄⋊C₄×C₅₃	—	2	2	no	—
497	C₄⋊C₄×C₅₃	—	2	2	no	—
498	C₄⋊C₄×C₅₃	—	2	2	no	—
499	C₄⋊C₄×C₅₃	—	2	2	no	—
500	C₄⋊C₄×C₅₃	—	2	2	no	—
501	C₄⋊C₄×C₅₃	—	2	2	no	—
502	C₄⋊C₄×C₅₃	—	2	2	no	—
503	C₄⋊C₄×C₅₃	—	2	2	no	—
504	C₄⋊C₄×C₅₃	—	2	2	no	—
505	C₄⋊C₄×C₅₃	—	2	2	no	—
506	C₄⋊C₄×C₅₃	—	4	1	no	—
507	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
508	C₂²⋊C₄×C₅₃	—	2	2	no	—
509	C₂²⋊C₄×C₅₃	—	2	2	no	—
510	C₂²⋊C₄×C₅₃	—	2	2	no	—
511	C₂²⋊C₄×C₅₃	—	2	2	no	—
512	C₂²⋊C₄×C₅₃	—	4	1	no	—
513	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
514	C₄²×C₅₃	—	2	2	no	—
515	C₄²×C₅₃	—	2	2	no	—
516	C₄²×C₅₃	—	4	1	no	—
517	C₄²×C₅₃	—	4	1	no	—
518	C₂²⋊Dic₅₃	—	2	2	no	—
519	C₂²⋊Dic₅₃	—	2	2	no	—
520	C₂²⋊Dic₅₃	—	2	2	no	—
521	C₂²⋊Dic₅₃	—	2	2	no	—
522	C₂²⋊Dic₅₃	—	4	1	no	—
523	C₂²⋊Dic₅₃	C₂×Q₈	1	4	yes	complemented
524	#11719921	—	2	2	no	—
525	#11719921	—	2	2	no	—
526	#11719921	—	2	2	no	—
527	#11719921	—	2	2	no	—
528	#11719921	—	2	2	no	—
529	#11719921	—	2	2	no	—
530	#11719921	—	2	2	no	—
531	#11719921	—	2	2	no	—
532	#11719921	—	4	1	no	—
533	#11719921	—	4	1	no	—
534	#11719921	C₂×Q₈	1	4	yes	complemented
535	#11719921	C₂×Q₈	1	4	yes	complemented
536	C₄⋊Dic₅₃	—	2	2	no	—
537	C₄⋊Dic₅₃	—	2	2	no	—
538	C₄⋊Dic₅₃	—	2	2	no	—
539	C₄⋊Dic₅₃	—	2	2	no	—
540	C₄⋊Dic₅₃	—	2	2	no	—
541	C₄⋊Dic₅₃	—	2	2	no	—
542	C₄⋊Dic₅₃	—	2	2	no	—
543	C₄⋊Dic₅₃	—	2	2	no	—
544	C₄⋊Dic₅₃	—	2	2	no	—
545	C₄⋊Dic₅₃	—	2	2	no	—
546	C₄⋊Dic₅₃	—	2	2	no	—
547	C₄⋊Dic₅₃	—	4	1	no	—
548	C₄⋊Dic₅₃	C₂×D₄	1	4	yes	—
549	#11719919	—	2	2	no	—
550	#11719919	—	2	2	no	—
551	#11719919	—	2	2	no	—
552	#11719919	—	2	2	no	—
553	#11719919	—	2	2	no	—
554	#11719919	—	2	2	no	—
555	#11719919	—	2	2	no	—
556	#11719919	—	2	2	no	—
557	#11719919	—	2	2	no	—
558	#11719919	—	2	2	no	—
559	#11719919	—	2	2	no	—
560	#11719919	—	2	2	no	—
561	#11719919	—	2	2	no	—
562	#11719919	—	2	2	no	—
563	#11719919	—	2	2	no	—
564	#11719919	—	2	2	no	—
565	#11719919	—	2	2	no	—
566	#11719919	—	2	2	no	—
567	#11719919	—	2	2	no	—
568	#11719919	—	2	2	no	—
569	#11719919	—	2	2	no	—
570	#11719919	—	2	2	no	—
571	#11719919	—	4	1	no	—
572	#11719919	—	4	1	no	—
573	#11719919	C₂×D₄	1	4	yes	—
574	#11719919	C₂×D₄	1	4	yes	—
575	C₄×Dic₅₃	—	2	2	no	—
576	C₄×Dic₅₃	—	2	2	no	—
577	C₄×Dic₅₃	—	2	2	no	—
578	C₄×Dic₅₃	—	2	2	no	—
579	C₄×Dic₅₃	—	2	2	no	—
580	C₄×Dic₅₃	—	2	2	no	—
581	C₄×Dic₅₃	—	4	1	no	—
582	C₄×Dic₅₃	—	4	1	no	—
583	C₄×Dic₅₃	—	4	1	no	—
584	C₄×Dic₅₃	—	4	1	no	—
585	C₄×Dic₅₃	—	4	1	no	—
586	C₄×Dic₅₃	—	4	1	no	—
587	C₂³×C₅₃	—	2	1	no	—
588	C₂³×C₅₃	—	2	1	no	—
589	C₂³×C₅₃	—	2	1	no	—
590	C₂³×C₅₃	—	2	1	no	—
591	C₂³×C₅₃	—	2	1	no	—
592	C₂³×C₅₃	—	2	1	no	—
593	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
594	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
595	C₂²×D₅₃	—	2	1	no	—
596	C₂²×D₅₃	—	2	1	no	—
597	C₂²×D₅₃	—	2	1	no	—
598	C₂²×D₅₃	—	2	1	no	—
599	C₂²×D₅₃	—	2	1	no	—
600	C₂²×D₅₃	—	2	1	no	—
601	C₂²×D₅₃	—	2	8	no	—
602	C₂²×D₅₃	—	2	8	no	—
603	C₂²×D₅₃	—	2	8	no	—
604	C₂²×D₅₃	—	4	4	no	—
605	C₂²×D₅₃	—	4	4	no	—
606	C₂²×D₅₃	—	4	4	no	—
607	C₂²×D₅₃	—	4	4	no	—
608	C₂²×D₅₃	C₂²×D₄	1	2	yes	—
609	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
610	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
611	C₂²×D₅₃	C₂×#41	1	2	yes	—
612	C₂²×D₅₃	C₂×#41	1	2	yes	—
613	C₂²×D₅₃	C₂×#41	1	2	yes	—
614	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
615	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
616	Q₈×C₅₃	—	4	4	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	2	1	no	—
639	C₂×C₄×C₅₃	—	2	1	no	—
640	C₂×C₄×C₅₃	—	2	1	no	—
641	C₂×C₄×C₅₃	—	2	1	no	—
642	C₂×C₄×C₅₃	—	2	1	no	—
643	C₂×C₄×C₅₃	—	2	1	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	2	1	no	—
646	C₂×C₄×C₅₃	—	2	1	no	—
647	C₂×C₄×C₅₃	—	2	1	no	—
648	C₂×C₄×C₅₃	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	4	4	no	—
652	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
653	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
654	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
655	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
656	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
657	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
658	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
659	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
660	C₂×Dic₅₃	—	2	1	no	—
661	C₂×Dic₅₃	—	2	1	no	—
662	C₂×Dic₅₃	—	2	1	no	—
663	C₂×Dic₅₃	—	2	1	no	—
664	C₂×Dic₅₃	—	2	1	no	—
665	C₂×Dic₅₃	—	2	1	no	—
666	C₂×Dic₅₃	—	2	1	no	—
667	C₂×Dic₅₃	—	2	1	no	—
668	C₂×Dic₅₃	—	2	1	no	—
669	C₂×Dic₅₃	—	2	1	no	—
670	C₂×Dic₅₃	—	2	1	no	—
671	C₂×Dic₅₃	—	2	1	no	—
672	C₂×Dic₅₃	—	2	1	no	—
673	C₂×Dic₅₃	—	2	1	no	—
674	C₂×Dic₅₃	—	2	1	no	—
675	C₂×Dic₅₃	—	2	1	no	—
676	C₂×Dic₅₃	—	2	1	no	—
677	C₂×Dic₅₃	—	2	1	no	—
678	C₂×Dic₅₃	—	2	1	no	—
679	C₂×Dic₅₃	—	2	1	no	—
680	C₂×Dic₅₃	—	2	1	no	—
681	C₂×Dic₅₃	—	2	1	no	—
682	C₂×Dic₅₃	—	2	1	no	—
683	C₂×Dic₅₃	—	2	1	no	—
684	C₂×Dic₅₃	—	2	1	no	—
685	C₂×Dic₅₃	—	2	1	no	—
686	C₂×Dic₅₃	—	2	1	no	—
687	C₂×Dic₅₃	—	2	1	no	—
688	C₂×Dic₅₃	—	2	1	no	—
689	C₂×Dic₅₃	—	2	1	no	—
690	C₂×Dic₅₃	—	2	1	no	—
691	C₂×Dic₅₃	—	2	1	no	—
692	C₂×Dic₅₃	—	2	1	no	—
693	C₂×Dic₅₃	—	2	1	no	—
694	C₂×Dic₅₃	—	4	4	no	—
695	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
696	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
697	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
698	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
699	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
700	C₂×Dic₅₃	C₂×#41	1	2	yes	—
701	C₂×Dic₅₃	C₂×#41	1	2	yes	—
702	C₂×Dic₅₃	C₂×#41	1	2	yes	—
703	C₄×D₅₃	—	2	8	no	—
704	C₄×D₅₃	—	2	8	no	—
705	C₄×D₅₃	—	2	8	no	—
706	C₄×D₅₃	—	2	8	no	—
707	C₄×D₅₃	—	2	8	no	—
708	C₄×D₅₃	—	2	8	no	—
709	C₄×D₅₃	—	2	8	no	—
710	C₄×D₅₃	—	2	8	no	—
711	C₄×D₅₃	—	4	4	no	—
712	C₄×D₅₃	—	4	4	no	—
713	C₄×D₅₃	—	4	4	no	—
714	C₄×D₅₃	—	4	4	no	—
715	C₄×D₅₃	—	4	4	no	—
716	C₄×D₅₃	—	4	4	no	—
717	C₄×D₅₃	—	4	4	no	—
718	C₄×D₅₃	—	4	4	no	—
719	Dic₁₀₆	—	4	4	no	—
720	Dic₁₀₆	—	4	4	no	—
721	Dic₁₀₆	—	4	4	no	—
722	C₂×#2556	—	53	1	no	maximal, Sylow
723	C₂²×C₅₃	—	2	2	no	—
724	C₂²×C₅₃	—	2	2	no	—
725	C₂²×C₅₃	—	2	2	no	—
726	C₂²×C₅₃	—	4	1	no	—
727	C₂²×C₅₃	—	4	1	no	—
728	C₂²×C₅₃	—	4	1	no	—
729	C₂²×C₅₃	—	4	1	no	—
730	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
731	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
732	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
733	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
734	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
735	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
736	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
737	C₂×D₅₃	—	2	2	no	—
738	C₂×D₅₃	—	2	2	no	—
739	C₂×D₅₃	—	2	2	no	—
740	C₂×D₅₃	—	4	1	no	—
741	C₂×D₅₃	—	4	1	no	—
742	C₂×D₅₃	—	4	1	no	—
743	C₂×D₅₃	—	4	1	no	—
744	C₂×D₅₃	—	4	16	no	—
745	C₂×D₅₃	#532	1	4	yes	—
746	C₂×D₅₃	#533	1	4	yes	—
747	C₂×D₅₃	#539	1	4	yes	—
748	C₂×D₅₃	#546	1	4	yes	—
749	C₂×D₅₃	D₄×Q₈	1	4	yes	—
750	C₂×D₅₃	#552	1	4	yes	—
751	C₂×D₅₃	#554	1	4	yes	—
752	C₄×C₅₃	—	2	2	no	—
753	C₄×C₅₃	—	2	2	no	—
754	C₄×C₅₃	—	2	2	no	—
755	C₄×C₅₃	—	2	2	no	—
756	C₄×C₅₃	—	2	2	no	—
757	C₄×C₅₃	—	2	2	no	—
758	C₄×C₅₃	—	2	2	no	—
759	C₄×C₅₃	—	2	2	no	—
760	C₄×C₅₃	—	4	1	no	—
761	C₄×C₅₃	—	4	1	no	—
762	C₄×C₅₃	—	4	1	no	—
763	C₄×C₅₃	—	4	1	no	—
764	C₄×C₅₃	—	4	1	no	—
765	C₄×C₅₃	—	4	1	no	—
766	Dic₅₃	—	2	2	no	—
767	Dic₅₃	—	2	2	no	—
768	Dic₅₃	—	2	2	no	—
769	Dic₅₃	—	2	2	no	—
770	Dic₅₃	—	2	2	no	—
771	Dic₅₃	—	2	2	no	—
772	Dic₅₃	—	2	2	no	—
773	Dic₅₃	—	2	2	no	—
774	Dic₅₃	—	4	1	no	—
775	Dic₅₃	—	4	1	no	—
776	Dic₅₃	—	4	1	no	—
777	Dic₅₃	—	4	1	no	—
778	Dic₅₃	—	4	1	no	—
779	Dic₅₃	—	4	1	no	—
780	C₂²×#125	—	53	1	no	—
781	C₂²×C₂²⋊Q₈	—	53	1	no	—
782	#2556	—	53	1	no	—
783	#2556	—	53	1	no	—
784	#2556	—	53	1	no	—
785	#2556	—	53	1	no	—
786	#2556	—	53	1	no	—
787	#2556	—	53	1	no	—
788	#2556	—	53	1	no	—
789	#2556	—	53	1	no	—
790	#2556	—	53	1	no	—
791	#2556	—	53	1	no	—
792	#2556	—	53	1	no	—
793	#2556	—	53	1	no	—
794	#2556	—	53	1	no	—
795	#2556	—	53	1	no	—
796	#2556	—	53	1	no	—
797	#2556	D₅₃	1	1	yes	characteristic, direct product factor
798	C₂×#399	—	53	1	no	—
799	C₂×#398	—	53	1	no	—
800	C₂×#396	—	53	1	no	—
801	C₂×#395	—	53	1	no	—
802	C₂×#391	—	53	1	no	—
803	C₂×#389	—	53	1	no	—
804	C₂×#389	—	53	1	no	—
805	C₂×#388	—	53	1	no	—
806	C₂×#388	—	53	1	no	—
807	C₂×#387	—	53	1	no	—
808	C₂×#385	—	53	1	no	—
809	C₂×C₄×C₄⋊C₄	—	53	1	no	—
810	C₂×C₄×C₂²⋊C₄	—	53	1	no	—
811	C₂×C₅₃	—	4	2	no	—
812	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
813	C₂×C₅₃	C₂×#533	1	1	yes	characteristic
814	C₂×C₅₃	C₂×#539	1	1	yes	characteristic
815	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
816	C₂×C₅₃	C₂×D₄×Q₈	1	1	yes	characteristic
817	C₂×C₅₃	C₂×#552	1	1	yes	characteristic
818	C₂×C₅₃	C₂×#554	1	1	yes	characteristic
819	D₅₃	—	4	2	no	—
820	D₅₃	#2556	1	8	yes	direct product factor
821	C₂³×Q₈	—	53	1	no	—
822	C₂⁴×C₄	—	53	1	no	—
823	C₂×#125	—	53	1	no	—
824	C₂×#125	—	53	1	no	—
825	C₂×#125	—	53	1	no	—
826	C₂×#125	—	53	1	no	—
827	C₂×#125	—	53	1	no	—
828	C₂×#125	—	53	1	no	—
829	C₂×#125	—	53	1	no	—
830	C₂×#125	—	106	8	no	—
831	C₂×#125	C₂×D₅₃	1	1	yes	characteristic, complemented
832	C₂×C₂²⋊Q₈	—	53	1	no	—
833	C₂×C₂²⋊Q₈	—	53	1	no	—
834	C₂×C₂²⋊Q₈	—	53	1	no	—
835	C₂×C₂²⋊Q₈	—	53	1	no	—
836	C₂×C₂²⋊Q₈	—	53	1	no	—
837	C₂×C₂²⋊Q₈	—	53	1	no	—
838	C₂×C₂²⋊Q₈	—	53	1	no	—
839	C₂×C₂²⋊Q₈	—	106	8	no	—
840	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
841	C₂²×C₄⋊C₄	—	53	1	no	—
842	C₂²×C₄⋊C₄	—	53	1	no	—
843	C₂²×C₄⋊C₄	—	53	1	no	—
844	C₂²×C₄⋊C₄	—	53	1	no	—
845	C₂²×C₄⋊C₄	—	53	1	no	—
846	C₂²×C₄⋊C₄	—	53	1	no	—
847	C₂²×C₄⋊C₄	—	53	1	no	—
848	C₂²×C₄⋊C₄	—	53	1	no	—
849	C₂²×C₄⋊C₄	—	53	1	no	—
850	C₂²×C₄⋊C₄	—	53	1	no	—
851	C₂²×C₄⋊C₄	—	53	1	no	—
852	C₂²×C₄⋊C₄	—	53	1	no	—
853	C₂²×C₄⋊C₄	—	53	1	no	—
854	C₂²×C₂²⋊C₄	—	53	1	no	—
855	C₂²×C₂²⋊C₄	—	53	1	no	—
856	C₂²×C₂²⋊C₄	—	53	1	no	—
857	C₂²×C₂²⋊C₄	—	53	1	no	—
858	C₂²×C₂²⋊C₄	—	53	1	no	—
859	C₂²×C₂²⋊C₄	—	53	1	no	—
860	C₂²×C₄²	—	53	1	no	—
861	C₂²×C₄²	—	53	1	no	—
862	C₂²×C₄²	—	53	1	no	—
863	C₂²×C₄²	—	53	1	no	—
864	#399	—	53	1	no	—
865	#399	—	53	1	no	—
866	#399	—	53	1	no	—
867	#399	—	53	1	no	—
868	#399	—	53	1	no	—
869	#399	—	53	1	no	—
870	#399	—	53	1	no	—
871	#399	C₂×D₅₃	1	1	yes	characteristic
872	#398	—	53	1	no	—
873	#398	—	53	1	no	—
874	#398	—	53	1	no	—
875	#398	—	53	1	no	—
876	#398	—	53	1	no	—
877	#398	—	53	1	no	—
878	#398	—	53	1	no	—
879	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
880	#396	—	53	1	no	—
881	#396	—	53	1	no	—
882	#396	—	53	1	no	—
883	#396	—	53	1	no	—
884	#396	—	53	1	no	—
885	#396	—	53	1	no	—
886	#396	—	53	1	no	—
887	#396	C₂×D₅₃	1	1	yes	characteristic
888	#395	—	53	1	no	—
889	#395	—	53	1	no	—
890	#395	—	53	1	no	—
891	#395	—	53	1	no	—
892	#395	—	53	1	no	—
893	#395	—	53	1	no	—
894	#395	—	53	1	no	—
895	#395	C₂×D₅₃	1	1	yes	characteristic, complemented
896	#391	—	53	1	no	—
897	#391	—	53	1	no	—
898	#391	—	53	1	no	—
899	#391	—	53	1	no	—
900	#391	—	53	1	no	—
901	#391	—	53	1	no	—
902	#391	—	53	1	no	—
903	#391	C₂×D₅₃	1	1	yes	characteristic, complemented
904	#389	—	53	1	no	—
905	#389	—	53	1	no	—
906	#389	—	53	1	no	—
907	#389	—	53	1	no	—
908	#389	—	53	1	no	—
909	#389	—	53	1	no	—
910	#389	—	53	1	no	—
911	#389	—	53	1	no	—
912	#389	—	53	1	no	—
913	#389	—	53	1	no	—
914	#389	—	53	1	no	—
915	#389	—	53	1	no	—
916	#389	—	53	1	no	—
917	#389	—	53	1	no	—
918	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
919	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
920	#388	—	53	1	no	—
921	#388	—	53	1	no	—
922	#388	—	53	1	no	—
923	#388	—	53	1	no	—
924	#388	—	53	1	no	—
925	#388	—	53	1	no	—
926	#388	—	53	1	no	—
927	#388	—	53	1	no	—
928	#388	—	53	1	no	—
929	#388	—	53	1	no	—
930	#388	—	53	1	no	—
931	#388	—	53	1	no	—
932	#388	—	53	1	no	—
933	#388	—	53	1	no	—
934	#388	C₂×D₅₃	1	1	yes	characteristic
935	#388	C₂×D₅₃	1	1	yes	characteristic
936	#387	—	53	1	no	—
937	#387	—	53	1	no	—
938	#387	—	53	1	no	—
939	#387	—	53	1	no	—
940	#387	—	53	1	no	—
941	#387	—	53	1	no	—
942	#387	—	53	1	no	—
943	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
944	#385	—	53	1	no	—
945	#385	—	53	1	no	—
946	#385	—	53	1	no	—
947	#385	—	53	1	no	—
948	#385	—	53	1	no	—
949	#385	—	53	1	no	—
950	#385	—	53	1	no	—
951	#385	C₂×D₅₃	1	1	yes	characteristic
952	C₄×C₄⋊C₄	—	53	1	no	—
953	C₄×C₄⋊C₄	—	53	1	no	—
954	C₄×C₄⋊C₄	—	53	1	no	—
955	C₄×C₄⋊C₄	—	53	1	no	—
956	C₄×C₄⋊C₄	—	53	1	no	—
957	C₄×C₄⋊C₄	—	53	1	no	—
958	C₄×C₄⋊C₄	—	53	1	no	—
959	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
960	C₄×C₂²⋊C₄	—	53	1	no	—
961	C₄×C₂²⋊C₄	—	53	1	no	—
962	C₄×C₂²⋊C₄	—	53	1	no	—
963	C₄×C₂²⋊C₄	—	53	1	no	—
964	C₄×C₂²⋊C₄	—	53	1	no	—
965	C₄×C₂²⋊C₄	—	53	1	no	—
966	C₄×C₂²⋊C₄	—	53	1	no	—
967	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
968	C₂×#95	—	53	1	no	—
969	C₂×#95	—	53	1	no	—
970	C₂×#95	—	53	1	no	—
971	C₂×#95	—	53	1	no	—
972	C₂×#95	—	53	1	no	—
973	C₂×#95	—	53	1	no	—
974	C₂×#95	—	53	1	no	—
975	C₂×#95	—	53	1	no	—
976	C₂×#95	—	53	1	no	—
977	C₂×#95	—	53	1	no	—
978	C₅₃	C₂×#2556	1	1	yes	characteristic, complemented, Sylow
979	C₂⁵	—	53	1	no	—
980	C₂²×Q₈	—	53	1	no	—
981	C₂²×Q₈	—	53	1	no	—
982	C₂²×Q₈	—	53	1	no	—
983	C₂²×Q₈	—	106	4	no	—
984	C₂²×Q₈	—	106	4	no	—
985	C₂²×Q₈	—	212	2	no	—
986	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
987	C₂³×C₄	—	53	1	no	—
988	C₂³×C₄	—	53	1	no	—
989	C₂³×C₄	—	53	1	no	—
990	C₂³×C₄	—	53	1	no	—
991	C₂³×C₄	—	53	1	no	—
992	C₂³×C₄	—	53	1	no	—
993	C₂³×C₄	—	53	1	no	—
994	C₂³×C₄	—	53	1	no	—
995	C₂³×C₄	—	53	1	no	—
996	C₂³×C₄	—	53	1	no	—
997	C₂³×C₄	—	53	1	no	—
998	C₂³×C₄	—	53	1	no	—
999	C₂³×C₄	—	53	1	no	—
1000	C₂³×C₄	—	53	1	no	—
1001	C₂³×C₄	—	53	1	no	—
1002	C₂³×C₄	—	53	1	no	—
1003	C₂³×C₄	—	53	1	no	—
1004	C₂³×C₄	—	106	4	no	—
1005	C₂³×C₄	—	106	4	no	—
1006	C₂³×C₄	—	212	2	no	—
1007	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1008	#125	—	2	4	no	—
1009	#125	—	106	4	no	—
1010	#125	—	106	4	no	—
1011	#125	—	106	4	no	—
1012	#125	—	106	4	no	—
1013	#125	—	106	4	no	—
1014	#125	—	106	4	no	—
1015	#125	—	106	4	no	—
1016	C₂²⋊Q₈	—	2	4	no	—
1017	C₂²⋊Q₈	—	106	4	no	—
1018	C₂²⋊Q₈	—	106	4	no	—
1019	C₂²⋊Q₈	—	106	4	no	—
1020	C₂²⋊Q₈	—	106	4	no	—
1021	C₂²⋊Q₈	—	106	4	no	—
1022	C₂²⋊Q₈	—	106	4	no	—
1023	C₂²⋊Q₈	—	106	4	no	—
1024	C₂×C₄⋊C₄	—	53	1	no	—
1025	C₂×C₄⋊C₄	—	53	1	no	—
1026	C₂×C₄⋊C₄	—	53	1	no	—
1027	C₂×C₄⋊C₄	—	53	8	no	—
1028	C₂×C₄⋊C₄	—	53	1	no	—
1029	C₂×C₄⋊C₄	—	53	1	no	—
1030	C₂×C₄⋊C₄	—	53	1	no	—
1031	C₂×C₄⋊C₄	—	53	1	no	—
1032	C₂×C₄⋊C₄	—	53	1	no	—
1033	C₂×C₄⋊C₄	—	53	1	no	—
1034	C₂×C₄⋊C₄	—	53	1	no	—
1035	C₂×C₄⋊C₄	—	53	1	no	—
1036	C₂×C₄⋊C₄	—	53	1	no	—
1037	C₂×C₄⋊C₄	—	53	1	no	—
1038	C₂×C₄⋊C₄	—	53	1	no	—
1039	C₂×C₄⋊C₄	—	53	1	no	—
1040	C₂×C₄⋊C₄	—	53	1	no	—
1041	C₂×C₄⋊C₄	—	53	1	no	—
1042	C₂×C₄⋊C₄	—	53	1	no	—
1043	C₂×C₄⋊C₄	—	53	1	no	—
1044	C₂×C₄⋊C₄	—	53	1	no	—
1045	C₂×C₄⋊C₄	—	53	1	no	—
1046	C₂×C₄⋊C₄	—	53	1	no	—
1047	C₂×C₄⋊C₄	—	53	1	no	—
1048	C₂×C₄⋊C₄	—	53	1	no	—
1049	C₂×C₄⋊C₄	—	53	1	no	—
1050	C₂×C₄⋊C₄	—	53	1	no	—
1051	C₂×C₄⋊C₄	—	53	1	no	—
1052	C₂×C₄⋊C₄	—	53	1	no	—
1053	C₂×C₄⋊C₄	—	53	1	no	—
1054	C₂×C₄⋊C₄	—	53	1	no	—
1055	C₂×C₄⋊C₄	—	53	1	no	—
1056	C₂×C₄⋊C₄	—	53	1	no	—
1057	C₂×C₄⋊C₄	—	53	1	no	—
1058	C₂×C₄⋊C₄	—	53	1	no	—
1059	C₂×C₄⋊C₄	—	53	1	no	—
1060	C₂×C₄⋊C₄	—	53	1	no	—
1061	C₂×C₄⋊C₄	—	53	1	no	—
1062	C₂×C₄⋊C₄	—	53	1	no	—
1063	C₂×C₄⋊C₄	—	53	1	no	—
1064	C₂×C₄⋊C₄	—	106	4	no	—
1065	C₂×C₄⋊C₄	—	106	4	no	—
1066	C₂×C₄⋊C₄	—	106	4	no	—
1067	C₂×C₄⋊C₄	—	106	4	no	—
1068	C₂×C₄⋊C₄	—	106	4	no	—
1069	C₂×C₄⋊C₄	—	106	4	no	—
1070	C₂×C₄⋊C₄	—	106	4	no	—
1071	C₂×C₄⋊C₄	—	106	4	no	—
1072	C₂×C₄⋊C₄	—	106	4	no	—
1073	C₂×C₄⋊C₄	—	106	4	no	—
1074	C₂×C₄⋊C₄	—	106	4	no	—
1075	C₂×C₄⋊C₄	—	212	2	no	—
1076	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1077	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1078	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1079	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1080	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1081	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1082	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1083	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1084	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1085	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1086	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1087	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1088	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1089	C₂×C₂²⋊C₄	—	53	1	no	—
1090	C₂×C₂²⋊C₄	—	53	1	no	—
1091	C₂×C₂²⋊C₄	—	53	1	no	—
1092	C₂×C₂²⋊C₄	—	53	8	no	—
1093	C₂×C₂²⋊C₄	—	53	1	no	—
1094	C₂×C₂²⋊C₄	—	53	1	no	—
1095	C₂×C₂²⋊C₄	—	53	1	no	—
1096	C₂×C₂²⋊C₄	—	53	1	no	—
1097	C₂×C₂²⋊C₄	—	53	1	no	—
1098	C₂×C₂²⋊C₄	—	53	1	no	—
1099	C₂×C₂²⋊C₄	—	53	1	no	—
1100	C₂×C₂²⋊C₄	—	53	1	no	—
1101	C₂×C₂²⋊C₄	—	53	1	no	—
1102	C₂×C₂²⋊C₄	—	53	1	no	—
1103	C₂×C₂²⋊C₄	—	53	1	no	—
1104	C₂×C₂²⋊C₄	—	53	1	no	—
1105	C₂×C₂²⋊C₄	—	53	1	no	—
1106	C₂×C₂²⋊C₄	—	53	1	no	—
1107	C₂×C₂²⋊C₄	—	53	1	no	—
1108	C₂×C₂²⋊C₄	—	106	4	no	—
1109	C₂×C₂²⋊C₄	—	106	4	no	—
1110	C₂×C₂²⋊C₄	—	106	4	no	—
1111	C₂×C₂²⋊C₄	—	106	4	no	—
1112	C₂×C₂²⋊C₄	—	212	2	no	—
1113	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1114	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1115	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1116	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1117	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1118	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1119	C₂×C₄²	—	53	1	no	—
1120	C₂×C₄²	—	53	1	no	—
1121	C₂×C₄²	—	53	1	no	—
1122	C₂×C₄²	—	53	1	no	—
1123	C₂×C₄²	—	53	1	no	—
1124	C₂×C₄²	—	53	1	no	—
1125	C₂×C₄²	—	53	1	no	—
1126	C₂×C₄²	—	53	1	no	—
1127	C₂×C₄²	—	53	1	no	—
1128	C₂×C₄²	—	53	1	no	—
1129	C₂×C₄²	—	53	1	no	—
1130	C₂×C₄²	—	53	1	no	—
1131	C₂×C₄²	—	106	4	no	—
1132	C₂×C₄²	—	106	4	no	—
1133	C₂×C₄²	—	212	2	no	—
1134	C₂×C₄²	—	212	2	no	—
1135	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1136	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1137	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1138	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1139	#95	—	53	1	no	—
1140	#95	—	53	1	no	—
1141	#95	—	53	1	no	—
1142	#95	—	53	1	no	—
1143	#95	—	53	1	no	—
1144	#95	—	53	1	no	—
1145	#95	—	53	1	no	—
1146	#95	—	53	1	no	—
1147	#95	—	53	1	no	—
1148	#95	—	53	1	no	—
1149	#95	—	53	1	no	—
1150	#95	—	53	1	no	—
1151	#95	—	53	1	no	—
1152	#95	—	53	1	no	—
1153	#95	—	53	1	no	—
1154	#95	—	53	1	no	—
1155	#95	—	53	1	no	—
1156	#95	—	53	1	no	—
1157	#95	—	53	1	no	—
1158	#95	—	53	1	no	—
1159	#95	—	53	1	no	—
1160	#95	—	53	1	no	—
1161	#95	—	53	1	no	—
1162	#95	—	53	1	no	—
1163	#95	—	53	1	no	—
1164	#95	—	53	1	no	—
1165	#95	—	53	1	no	—
1166	#95	—	53	1	no	—
1167	#95	—	53	1	no	—
1168	#95	—	53	1	no	—
1169	#95	C₂²×D₅₃	1	1	yes	characteristic
1170	#95	C₂²×D₅₃	1	1	yes	characteristic
1171	#95	C₂²×D₅₃	1	1	yes	characteristic
1172	#95	C₂²×D₅₃	1	1	yes	characteristic
1173	#95	C₂²×D₅₃	1	1	yes	characteristic
1174	#95	C₂²×D₅₃	1	1	yes	characteristic
1175	#95	C₂²×D₅₃	1	1	yes	characteristic
1176	#95	C₂²×D₅₃	1	1	yes	characteristic
1177	#95	C₂²×D₅₃	1	1	yes	characteristic
1178	#95	C₂²×D₅₃	1	1	yes	characteristic
1179	C₂⁴	—	53	1	no	—
1180	C₂⁴	—	53	4	no	—
1181	C₂⁴	—	53	1	no	—
1182	C₂⁴	—	106	2	no	—
1183	C₂⁴	—	106	2	no	—
1184	C₂⁴	—	106	2	no	—
1185	C₂⁴	—	106	2	no	—
1186	C₂⁴	—	106	2	no	—
1187	C₂⁴	—	106	2	no	—
1188	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1189	C₂×Q₈	—	2	2	no	—
1190	C₂×Q₈	—	2	2	no	—
1191	C₂×Q₈	—	4	1	no	—
1192	C₂×Q₈	—	106	2	no	—
1193	C₂×Q₈	—	106	2	no	—
1194	C₂×Q₈	—	106	2	no	—
1195	C₂×Q₈	—	106	2	no	—
1196	C₂×Q₈	—	106	2	no	—
1197	C₂×Q₈	—	106	2	no	—
1198	C₂×Q₈	—	212	1	no	—
1199	C₂×Q₈	—	212	1	no	—
1200	C₂×Q₈	—	212	1	no	—
1201	C₂×Q₈	—	212	16	no	—
1202	C₂²×C₄	—	2	2	no	—
1203	C₂²×C₄	—	2	2	no	—
1204	C₂²×C₄	—	4	1	no	—
1205	C₂²×C₄	—	53	1	no	—
1206	C₂²×C₄	—	53	1	no	—
1207	C₂²×C₄	—	53	1	no	—
1208	C₂²×C₄	—	53	1	no	—
1209	C₂²×C₄	—	53	1	no	—
1210	C₂²×C₄	—	53	1	no	—
1211	C₂²×C₄	—	53	1	no	—
1212	C₂²×C₄	—	53	1	no	—
1213	C₂²×C₄	—	53	4	no	—
1214	C₂²×C₄	—	53	4	no	—
1215	C₂²×C₄	—	53	4	no	—
1216	C₂²×C₄	—	53	4	no	—
1217	C₂²×C₄	—	53	4	no	—
1218	C₂²×C₄	—	53	4	no	—
1219	C₂²×C₄	—	53	4	no	—
1220	C₂²×C₄	—	53	4	no	—
1221	C₂²×C₄	—	53	1	no	—
1222	C₂²×C₄	—	53	1	no	—
1223	C₂²×C₄	—	53	1	no	—
1224	C₂²×C₄	—	53	1	no	—
1225	C₂²×C₄	—	53	1	no	—
1226	C₂²×C₄	—	53	1	no	—
1227	C₂²×C₄	—	106	2	no	—
1228	C₂²×C₄	—	106	2	no	—
1229	C₂²×C₄	—	106	2	no	—
1230	C₂²×C₄	—	106	2	no	—
1231	C₂²×C₄	—	106	2	no	—
1232	C₂²×C₄	—	106	2	no	—
1233	C₂²×C₄	—	106	2	no	—
1234	C₂²×C₄	—	106	2	no	—
1235	C₂²×C₄	—	106	2	no	—
1236	C₂²×C₄	—	106	2	no	—
1237	C₂²×C₄	—	106	2	no	—
1238	C₂²×C₄	—	106	2	no	—
1239	C₂²×C₄	—	106	2	no	—
1240	C₂²×C₄	—	106	2	no	—
1241	C₂²×C₄	—	106	2	no	—
1242	C₂²×C₄	—	106	2	no	—
1243	C₂²×C₄	—	106	2	no	—
1244	C₂²×C₄	—	106	2	no	—
1245	C₂²×C₄	—	106	2	no	—
1246	C₂²×C₄	—	106	2	no	—
1247	C₂²×C₄	—	106	2	no	—
1248	C₂²×C₄	—	106	2	no	—
1249	C₂²×C₄	—	106	2	no	—
1250	C₂²×C₄	—	106	2	no	—
1251	C₂²×C₄	—	106	2	no	—
1252	C₂²×C₄	—	106	2	no	—
1253	C₂²×C₄	—	106	2	no	—
1254	C₂²×C₄	—	106	2	no	—
1255	C₂²×C₄	—	106	2	no	—
1256	C₂²×C₄	—	106	2	no	—
1257	C₂²×C₄	—	106	2	no	—
1258	C₂²×C₄	—	106	2	no	—
1259	C₂²×C₄	—	106	2	no	—
1260	C₂²×C₄	—	106	2	no	—
1261	C₂²×C₄	—	106	2	no	—
1262	C₂²×C₄	—	106	2	no	—
1263	C₂²×C₄	—	106	2	no	—
1264	C₂²×C₄	—	106	2	no	—
1265	C₂²×C₄	—	106	2	no	—
1266	C₂²×C₄	—	106	2	no	—
1267	C₂²×C₄	—	212	1	no	—
1268	C₂²×C₄	—	212	1	no	—
1269	C₂²×C₄	—	212	16	no	—
1270	C₂²×C₄	—	212	1	no	—
1271	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1272	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1273	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1274	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1275	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1276	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1277	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1278	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1279	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1280	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1281	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1282	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1283	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1284	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1285	C₄⋊C₄	—	2	2	no	—
1286	C₄⋊C₄	—	2	2	no	—
1287	C₄⋊C₄	—	2	2	no	—
1288	C₄⋊C₄	—	2	2	no	—
1289	C₄⋊C₄	—	2	2	no	—
1290	C₄⋊C₄	—	2	2	no	—
1291	C₄⋊C₄	—	2	2	no	—
1292	C₄⋊C₄	—	2	2	no	—
1293	C₄⋊C₄	—	2	2	no	—
1294	C₄⋊C₄	—	2	2	no	—
1295	C₄⋊C₄	—	2	2	no	—
1296	C₄⋊C₄	—	4	1	no	—
1297	C₄⋊C₄	—	53	4	no	—
1298	C₄⋊C₄	—	53	4	no	—
1299	C₄⋊C₄	—	53	4	no	—
1300	C₄⋊C₄	—	106	2	no	—
1301	C₄⋊C₄	—	106	2	no	—
1302	C₄⋊C₄	—	106	2	no	—
1303	C₄⋊C₄	—	106	2	no	—
1304	C₄⋊C₄	—	106	2	no	—
1305	C₄⋊C₄	—	106	2	no	—
1306	C₄⋊C₄	—	106	2	no	—
1307	C₄⋊C₄	—	106	2	no	—
1308	C₄⋊C₄	—	106	2	no	—
1309	C₄⋊C₄	—	106	2	no	—
1310	C₄⋊C₄	—	106	2	no	—
1311	C₄⋊C₄	—	106	2	no	—
1312	C₄⋊C₄	—	106	2	no	—
1313	C₄⋊C₄	—	106	2	no	—
1314	C₄⋊C₄	—	106	2	no	—
1315	C₄⋊C₄	—	106	2	no	—
1316	C₄⋊C₄	—	106	2	no	—
1317	C₄⋊C₄	—	106	2	no	—
1318	C₄⋊C₄	—	106	2	no	—
1319	C₄⋊C₄	—	106	2	no	—
1320	C₄⋊C₄	—	106	2	no	—
1321	C₄⋊C₄	—	106	2	no	—
1322	C₄⋊C₄	—	106	2	no	—
1323	C₄⋊C₄	—	106	2	no	—
1324	C₄⋊C₄	—	106	2	no	—
1325	C₄⋊C₄	—	106	2	no	—
1326	C₄⋊C₄	—	106	2	no	—
1327	C₄⋊C₄	—	106	2	no	—
1328	C₄⋊C₄	—	106	2	no	—
1329	C₄⋊C₄	—	106	2	no	—
1330	C₄⋊C₄	—	106	2	no	—
1331	C₄⋊C₄	—	106	2	no	—
1332	C₄⋊C₄	—	106	2	no	—
1333	C₄⋊C₄	—	212	1	no	—
1334	C₄⋊C₄	—	212	1	no	—
1335	C₄⋊C₄	—	212	1	no	—
1336	C₄⋊C₄	D₄×D₅₃	1	4	yes	—
1337	C₂²⋊C₄	—	2	2	no	—
1338	C₂²⋊C₄	—	2	2	no	—
1339	C₂²⋊C₄	—	2	2	no	—
1340	C₂²⋊C₄	—	2	2	no	—
1341	C₂²⋊C₄	—	4	1	no	—
1342	C₂²⋊C₄	—	53	4	no	—
1343	C₂²⋊C₄	—	53	4	no	—
1344	C₂²⋊C₄	—	53	4	no	—
1345	C₂²⋊C₄	—	106	2	no	—
1346	C₂²⋊C₄	—	106	2	no	—
1347	C₂²⋊C₄	—	106	2	no	—
1348	C₂²⋊C₄	—	106	2	no	—
1349	C₂²⋊C₄	—	106	2	no	—
1350	C₂²⋊C₄	—	106	2	no	—
1351	C₂²⋊C₄	—	106	2	no	—
1352	C₂²⋊C₄	—	106	2	no	—
1353	C₂²⋊C₄	—	106	2	no	—
1354	C₂²⋊C₄	—	106	2	no	—
1355	C₂²⋊C₄	—	106	2	no	—
1356	C₂²⋊C₄	—	106	2	no	—
1357	C₂²⋊C₄	—	212	1	no	—
1358	C₂²⋊C₄	—	212	1	no	—
1359	C₂²⋊C₄	—	212	1	no	—
1360	C₂²⋊C₄	Q₈×D₅₃	1	4	yes	complemented
1361	C₄²	—	2	2	no	—
1362	C₄²	—	2	2	no	—
1363	C₄²	—	4	1	no	—
1364	C₄²	—	4	1	no	—
1365	C₄²	—	106	2	no	—
1366	C₄²	—	106	2	no	—
1367	C₄²	—	106	2	no	—
1368	C₄²	—	106	2	no	—
1369	C₄²	—	106	2	no	—
1370	C₄²	—	106	2	no	—
1371	C₄²	—	212	1	no	—
1372	C₄²	—	212	1	no	—
1373	C₄²	—	212	1	no	—
1374	C₄²	—	212	1	no	—
1375	C₄²	—	212	1	no	—
1376	C₄²	—	212	1	no	—
1377	C₂³	—	2	1	no	—
1378	C₂³	—	2	1	no	—
1379	C₂³	—	2	1	no	—
1380	C₂³	—	2	1	no	—
1381	C₂³	—	2	1	no	—
1382	C₂³	—	2	1	no	—
1383	C₂³	—	53	2	no	—
1384	C₂³	—	53	2	no	—
1385	C₂³	—	53	2	no	—
1386	C₂³	—	53	2	no	—
1387	C₂³	—	53	2	no	—
1388	C₂³	—	53	2	no	—
1389	C₂³	—	53	2	no	—
1390	C₂³	—	53	2	no	—
1391	C₂³	—	106	8	no	—
1392	C₂³	—	106	8	no	—
1393	C₂³	—	106	8	no	—
1394	C₂³	—	106	1	no	—
1395	C₂³	—	106	1	no	—
1396	C₂³	—	106	1	no	—
1397	C₂³	—	106	1	no	—
1398	C₂³	—	106	1	no	—
1399	C₂³	—	106	1	no	—
1400	C₂³	—	212	4	no	—
1401	C₂³	—	212	4	no	—
1402	C₂³	—	212	4	no	—
1403	C₂³	—	212	4	no	—
1404	C₂³	C₂×Q₈×D₅₃	1	2	yes	—
1405	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1406	Q₈	—	4	4	no	—
1407	Q₈	—	212	4	no	—
1408	Q₈	—	212	4	no	—
1409	Q₈	—	212	4	no	—
1410	C₂×C₄	—	2	1	no	—
1411	C₂×C₄	—	2	1	no	—
1412	C₂×C₄	—	2	1	no	—
1413	C₂×C₄	—	2	1	no	—
1414	C₂×C₄	—	2	1	no	—
1415	C₂×C₄	—	2	1	no	—
1416	C₂×C₄	—	2	1	no	—
1417	C₂×C₄	—	2	1	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	2	1	no	—
1422	C₂×C₄	—	2	1	no	—
1423	C₂×C₄	—	2	1	no	—
1424	C₂×C₄	—	2	1	no	—
1425	C₂×C₄	—	2	1	no	—
1426	C₂×C₄	—	2	1	no	—
1427	C₂×C₄	—	2	1	no	—
1428	C₂×C₄	—	2	1	no	—
1429	C₂×C₄	—	2	1	no	—
1430	C₂×C₄	—	2	1	no	—
1431	C₂×C₄	—	2	1	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	4	4	no	—
1445	C₂×C₄	—	53	2	no	—
1446	C₂×C₄	—	53	2	no	—
1447	C₂×C₄	—	53	2	no	—
1448	C₂×C₄	—	53	2	no	—
1449	C₂×C₄	—	53	2	no	—
1450	C₂×C₄	—	53	2	no	—
1451	C₂×C₄	—	53	2	no	—
1452	C₂×C₄	—	53	2	no	—
1453	C₂×C₄	—	106	8	no	—
1454	C₂×C₄	—	106	8	no	—
1455	C₂×C₄	—	106	8	no	—
1456	C₂×C₄	—	106	8	no	—
1457	C₂×C₄	—	106	8	no	—
1458	C₂×C₄	—	106	8	no	—
1459	C₂×C₄	—	106	8	no	—
1460	C₂×C₄	—	106	8	no	—
1461	C₂×C₄	—	106	1	no	—
1462	C₂×C₄	—	106	1	no	—
1463	C₂×C₄	—	106	1	no	—
1464	C₂×C₄	—	106	1	no	—
1465	C₂×C₄	—	106	1	no	—
1466	C₂×C₄	—	106	1	no	—
1467	C₂×C₄	—	106	1	no	—
1468	C₂×C₄	—	106	1	no	—
1469	C₂×C₄	—	106	1	no	—
1470	C₂×C₄	—	106	1	no	—
1471	C₂×C₄	—	106	1	no	—
1472	C₂×C₄	—	106	1	no	—
1473	C₂×C₄	—	106	1	no	—
1474	C₂×C₄	—	106	1	no	—
1475	C₂×C₄	—	106	1	no	—
1476	C₂×C₄	—	106	1	no	—
1477	C₂×C₄	—	106	1	no	—
1478	C₂×C₄	—	106	1	no	—
1479	C₂×C₄	—	106	1	no	—
1480	C₂×C₄	—	106	1	no	—
1481	C₂×C₄	—	106	1	no	—
1482	C₂×C₄	—	106	1	no	—
1483	C₂×C₄	—	106	1	no	—
1484	C₂×C₄	—	106	1	no	—
1485	C₂×C₄	—	106	1	no	—
1486	C₂×C₄	—	106	1	no	—
1487	C₂×C₄	—	106	1	no	—
1488	C₂×C₄	—	106	1	no	—
1489	C₂×C₄	—	106	1	no	—
1490	C₂×C₄	—	106	1	no	—
1491	C₂×C₄	—	106	1	no	—
1492	C₂×C₄	—	106	1	no	—
1493	C₂×C₄	—	106	1	no	—
1494	C₂×C₄	—	106	1	no	—
1495	C₂×C₄	—	212	4	no	—
1496	C₂×C₄	—	212	4	no	—
1497	C₂×C₄	—	212	4	no	—
1498	C₂×C₄	—	212	4	no	—
1499	C₂×C₄	—	212	4	no	—
1500	C₂×C₄	—	212	4	no	—
1501	C₂×C₄	—	212	4	no	—
1502	C₂×C₄	—	212	4	no	—
1503	C₂×C₄	—	212	4	no	—
1504	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1505	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1506	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1507	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1508	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1509	C₂×C₄	#41×D₅₃	1	2	yes	—
1510	C₂×C₄	#41×D₅₃	1	2	yes	—
1511	C₂×C₄	#41×D₅₃	1	2	yes	—
1512	C₂²	—	2	2	no	—
1513	C₂²	—	2	2	no	—
1514	C₂²	—	2	2	no	—
1515	C₂²	—	4	1	no	—
1516	C₂²	—	4	1	no	—
1517	C₂²	—	4	1	no	—
1518	C₂²	—	4	1	no	—
1519	C₂²	—	53	4	no	—
1520	C₂²	—	53	4	no	—
1521	C₂²	—	53	4	no	—
1522	C₂²	—	53	4	no	—
1523	C₂²	—	53	4	no	—
1524	C₂²	—	53	4	no	—
1525	C₂²	—	53	4	no	—
1526	C₂²	—	106	2	no	—
1527	C₂²	—	106	2	no	—
1528	C₂²	—	106	2	no	—
1529	C₂²	—	212	16	no	—
1530	C₂²	—	212	1	no	—
1531	C₂²	—	212	1	no	—
1532	C₂²	—	212	1	no	—
1533	C₂²	—	212	1	no	—
1534	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1535	C₂²	C₂²×Q₈×D₅₃	1	1	yes	characteristic
1536	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1537	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1538	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1539	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1540	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1541	C₄	—	2	2	no	—
1542	C₄	—	2	2	no	—
1543	C₄	—	2	2	no	—
1544	C₄	—	2	2	no	—
1545	C₄	—	2	2	no	—
1546	C₄	—	2	2	no	—
1547	C₄	—	2	2	no	—
1548	C₄	—	2	2	no	—
1549	C₄	—	4	1	no	—
1550	C₄	—	4	1	no	—
1551	C₄	—	4	1	no	—
1552	C₄	—	4	1	no	—
1553	C₄	—	4	1	no	—
1554	C₄	—	4	1	no	—
1555	C₄	—	106	2	no	—
1556	C₄	—	106	2	no	—
1557	C₄	—	106	2	no	—
1558	C₄	—	106	2	no	—
1559	C₄	—	106	2	no	—
1560	C₄	—	106	2	no	—
1561	C₄	—	106	2	no	—
1562	C₄	—	106	2	no	—
1563	C₄	—	212	1	no	—
1564	C₄	—	212	1	no	—
1565	C₄	—	212	1	no	—
1566	C₄	—	212	1	no	—
1567	C₄	—	212	1	no	—
1568	C₄	—	212	1	no	—
1569	C₂	—	4	2	no	—
1570	C₂	—	53	8	no	—
1571	C₂	—	212	2	no	—
1572	C₂	#532×D₅₃	1	1	yes	characteristic
1573	C₂	#533×D₅₃	1	1	yes	characteristic
1574	C₂	#539×D₅₃	1	1	yes	characteristic
1575	C₂	#546×D₅₃	1	1	yes	characteristic
1576	C₂	D₄×Q₈×D₅₃	1	1	yes	characteristic
1577	C₂	#552×D₅₃	1	1	yes	characteristic
1578	C₂	#554×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2556	C₂
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	#2556	D₅₃
hypocenter	C₅₃	C₂×#2556
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2556

Complements

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

N	H ≅ G/N	type
1. C₂×#125×D₅₃	C₂	semidirect
3. #20279806	C₂	semidirect
4. #20279805	C₂	semidirect
5. #20279804	C₂	semidirect
6. #20279803	C₂	semidirect
7. #20279802	C₂	semidirect
8. #20279801	C₂	semidirect
9. #20279800	C₂	semidirect
10. #20279799	C₂	semidirect
11. #20279798	C₂	semidirect
12. #20279797	C₂	semidirect
13. #20279796	C₂	semidirect
14. #20279795	C₂	semidirect
15. #20279794	C₂	semidirect
16. #20279793	C₂	semidirect
17. #20279792	C₂	semidirect
19. #398×D₅₃	C₂	semidirect
21. #395×D₅₃	C₂	semidirect
22. #391×D₅₃	C₂	semidirect
23. #389×D₅₃	C₂	semidirect
24. #389×D₅₃	C₂	semidirect
27. #387×D₅₃	C₂	semidirect
29. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
31. C₅₃×#2556	C₂	semidirect
34. C₂×#13133209	C₂²	semidirect
35. C₂×#13133208	C₂²	semidirect
36. C₂×#13133208	C₂²	semidirect
37. C₂×#13133207	C₂²	semidirect
38. C₂×#13133207	C₂²	semidirect
39. C₂×#13133207	C₂²	semidirect
40. C₂×#13133207	C₂²	semidirect
80. #16810557	C₂²	semidirect
81. #16810557	C₂²	semidirect
82. #16810556	C₂²	semidirect
83. #16810556	C₂²	semidirect
84. #16810555	C₂²	semidirect
85. #16810554	C₂²	semidirect
86. #16810553	C₂²	semidirect
94. #16810544	C₂²	semidirect
95. #16810544	C₂²	semidirect
96. #16810544	C₂²	semidirect
97. #16810543	C₂²	semidirect
98. #16810543	C₂²	semidirect
99. #16810543	C₂²	semidirect
100. #16810542	C₂²	semidirect
101. #16810530	C₂²	semidirect
102. #16810529	C₂²	semidirect
103. #16810528	C₂²	semidirect
104. #16810527	C₂²	semidirect
105. #16810527	C₂²	semidirect
106. #16810527	C₂²	semidirect
107. #16810527	C₂²	semidirect
108. #16810522	C₂²	semidirect
109. #16810522	C₂²	semidirect
110. #16810521	C₂²	semidirect
111. #16810521	C₂²	semidirect
112. #16810520	C₂²	semidirect
113. #16810520	C₂²	semidirect
114. #16810520	C₂²	semidirect
115. #16810520	C₂²	semidirect
116. #16810519	C₂²	semidirect
117. #16810519	C₂²	semidirect
118. #16810518	C₂²	semidirect
119. #16810518	C₂²	semidirect
120. #16810518	C₂²	semidirect
121. #16810518	C₂²	semidirect
136. #16810510	C₂²	semidirect
137. #16810509	C₂²	semidirect
138. #16810508	C₂²	semidirect
139. #16810507	C₂²	semidirect
140. #16810506	C₂²	semidirect
141. #16810505	C₂²	semidirect
142. #16810504	C₂²	semidirect
150. C₄⋊C₄×Dic₅₃	C₂²	semidirect
151. C₄⋊C₄×Dic₅₃	C₂²	semidirect
152. C₄×#11719919	C₂²	semidirect
153. C₄×#11719919	C₂²	semidirect
154. C₄×C₄⋊Dic₅₃	C₂²	semidirect
155. #16810474	C₂²	semidirect
156. #16810474	C₂²	semidirect
174. C₂×#125×C₅₃	C₂²	semidirect
177. C₅₃×#398	C₂²	semidirect
179. C₅₃×#395	C₂²	semidirect
180. C₅₃×#391	C₂²	semidirect
181. C₅₃×#389	C₂²	semidirect
182. C₅₃×#389	C₂²	semidirect
185. C₅₃×#387	C₂²	semidirect
187. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
305. C₂²⋊C₄×D₅₃	Q₈	semidirect
513. C₂²⋊C₄×C₅₃	C₂×Q₈	semidirect
523. C₂²⋊Dic₅₃	C₂×Q₈	semidirect
534. #11719921	C₂×Q₈	semidirect
535. #11719921	C₂×Q₈	semidirect
797. #2556	D₅₃	direct (N × H)
820. D₅₃	#2556	direct (N × H)
831. C₂×#125	C₂×D₅₃	semidirect
879. #398	C₂×D₅₃	semidirect
895. #395	C₂×D₅₃	semidirect
903. #391	C₂×D₅₃	semidirect
918. #389	C₂×D₅₃	semidirect
919. #389	C₂×D₅₃	semidirect
943. #387	C₂×D₅₃	semidirect
959. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
978. C₅₃	C₂×#2556	semidirect
1360. C₂²⋊C₄	Q₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#125×D₅₃	2
C₂×C₂²⋊Q₈×D₅₃	2
#20279806	2
#20279805	2
#20279804	2
#20279803	2
#20279802	2
#20279801	2
#20279800	2
#20279799	2
#20279798	2
#20279797	2
#20279796	2
#20279795	2
#20279794	2
#20279793	2
#20279792	2
#399×D₅₃	2
#398×D₅₃	2
#396×D₅₃	2
#395×D₅₃	2
#391×D₅₃	2
#389×D₅₃	2
#388×D₅₃	2
#387×D₅₃	2
#385×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
C₄×C₂²⋊C₄×D₅₃	2
C₅₃×#2556	2
C₂×#2556	53

Subgroups — D53×#2556 #27554181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2556 #27554181