Subgroups — D₅₃×#2373 #27543772

Order 13568.

2726 conjugacy classes of subgroups.

The subgroup lattice has 1512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#126×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20277842	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277841	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277840	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277839	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277838	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277837	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277836	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277835	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277834	C₂	1	1	yes	maximal, characteristic, complemented
11	#20277833	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277832	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277831	C₂	1	1	yes	maximal, characteristic, complemented
14	#20277830	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277829	C₂	1	1	yes	maximal, characteristic, complemented
16	#20277828	C₂	1	1	yes	maximal, characteristic, complemented
17	#389×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
19	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
20	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
21	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	#385×D₅₃	C₂	1	1	yes	maximal, characteristic
25	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic
29	C₄×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic
30	#376×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2373	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×#13133212	C₂²	1	1	yes	characteristic
34	C₂×#13133212	C₂²	1	1	yes	characteristic
35	C₂×#13133212	C₂²	1	1	yes	characteristic
36	C₂×#13133211	C₂²	1	1	yes	characteristic
37	C₂×#13133210	C₂²	1	1	yes	characteristic
38	C₂×#13133210	C₂²	1	1	yes	characteristic
39	C₂×#13133210	C₂²	1	1	yes	characteristic
40	#126×D₅₃	C₄	1	16	yes	complemented
41	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
60	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
61	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
62	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
63	#16810522	C₂²	1	1	yes	characteristic, complemented
64	#16810521	C₂²	1	1	yes	characteristic, complemented
65	#16810520	C₂²	1	1	yes	characteristic, complemented
66	#16810520	C₂²	1	1	yes	characteristic, complemented
67	#16810519	C₂²	1	1	yes	characteristic, complemented
68	#16810518	C₂²	1	1	yes	characteristic, complemented
69	#16810518	C₂²	1	1	yes	characteristic, complemented
70	#16810517	C₂²	1	1	yes	characteristic
71	#16810517	C₂²	1	1	yes	characteristic
72	#16810517	C₂²	1	1	yes	characteristic
73	#16810516	C₂²	1	1	yes	characteristic
74	#16810516	C₂²	1	1	yes	characteristic
75	#16810516	C₂²	1	1	yes	characteristic
76	#16810515	C₂²	1	1	yes	characteristic
77	#16810515	C₂²	1	1	yes	characteristic
78	#16810515	C₂²	1	1	yes	characteristic
79	#16810514	C₂²	1	1	yes	characteristic
80	#16810514	C₂²	1	1	yes	characteristic
81	#16810514	C₂²	1	1	yes	characteristic
82	#16810513	C₂²	1	1	yes	characteristic
83	#16810513	C₂²	1	1	yes	characteristic
84	#16810513	C₂²	1	1	yes	characteristic
85	#16810512	C₂²	1	1	yes	characteristic
86	#16810512	C₂²	1	1	yes	characteristic
87	#16810512	C₂²	1	1	yes	characteristic
88	#16810511	C₂²	1	1	yes	characteristic
89	#16810511	C₂²	1	1	yes	characteristic
90	#16810511	C₂²	1	1	yes	characteristic
91	#16810510	C₂²	1	1	yes	characteristic, complemented
92	#16810510	C₂²	1	1	yes	characteristic, complemented
93	#16810510	C₂²	1	1	yes	characteristic, complemented
94	#16810509	C₂²	1	1	yes	characteristic, complemented
95	#16810509	C₂²	1	1	yes	characteristic, complemented
96	#16810509	C₂²	1	1	yes	characteristic, complemented
97	#16810508	C₂²	1	1	yes	characteristic, complemented
98	#16810508	C₂²	1	1	yes	characteristic, complemented
99	#16810508	C₂²	1	1	yes	characteristic, complemented
100	#16810507	C₂²	1	1	yes	characteristic, complemented
101	#16810507	C₂²	1	1	yes	characteristic, complemented
102	#16810507	C₂²	1	1	yes	characteristic, complemented
103	#16810506	C₂²	1	1	yes	characteristic, complemented
104	#16810506	C₂²	1	1	yes	characteristic, complemented
105	#16810506	C₂²	1	1	yes	characteristic, complemented
106	#16810505	C₂²	1	1	yes	characteristic, complemented
107	#16810505	C₂²	1	1	yes	characteristic, complemented
108	#16810505	C₂²	1	1	yes	characteristic, complemented
109	#16810504	C₂²	1	1	yes	characteristic, complemented
110	#16810504	C₂²	1	1	yes	characteristic, complemented
111	#16810504	C₂²	1	1	yes	characteristic, complemented
112	#16810498	C₂²	1	1	yes	characteristic
113	#16810497	C₂²	1	1	yes	characteristic
114	#16810497	C₂²	1	1	yes	characteristic
115	#16810496	C₂²	1	1	yes	characteristic
116	#16810495	C₂²	1	1	yes	characteristic
117	#16810494	C₂²	1	1	yes	characteristic
118	#16810494	C₂²	1	1	yes	characteristic
119	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
126	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
127	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
128	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
129	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
130	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
131	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
133	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
134	#16810474	C₂²	1	1	yes	characteristic, complemented
135	#16810474	C₂²	1	1	yes	characteristic, complemented
136	#16810474	C₂²	1	1	yes	characteristic, complemented
137	#16810474	C₂²	1	1	yes	characteristic, complemented
138	#16810474	C₂²	1	1	yes	characteristic, complemented
139	#16810474	C₂²	1	1	yes	characteristic, complemented
140	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
141	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
142	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
143	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
144	C₄×#11719921	C₂²	1	1	yes	characteristic
145	C₄×#11719921	C₂²	1	1	yes	characteristic
146	C₄×#11719921	C₂²	1	1	yes	characteristic
147	C₄×#11719921	C₂²	1	1	yes	characteristic
148	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
150	#16810470	C₂²	1	1	yes	characteristic
151	#16810470	C₂²	1	1	yes	characteristic
152	#16810470	C₂²	1	1	yes	characteristic
153	#16810470	C₂²	1	1	yes	characteristic
154	#16810469	C₂²	1	1	yes	characteristic, complemented
155	#16810469	C₂²	1	1	yes	characteristic, complemented
156	#16810469	C₂²	1	1	yes	characteristic, complemented
157	#16810468	C₂²	1	1	yes	characteristic, complemented
158	#16810468	C₂²	1	1	yes	characteristic, complemented
159	#16810468	C₂²	1	1	yes	characteristic, complemented
160	#16810468	C₂²	1	1	yes	characteristic, complemented
161	#95×D₅₃	C₂²	1	1	yes	characteristic
162	#95×D₅₃	C₂²	1	1	yes	characteristic
163	#95×D₅₃	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	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
174	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#388	C₂²	1	1	yes	characteristic
176	C₅₃×#388	C₂²	1	1	yes	characteristic
177	C₅₃×#388	C₂²	1	1	yes	characteristic
178	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#385	C₂²	1	1	yes	characteristic
182	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₅₃×#376	C₂²	1	1	yes	characteristic, complemented
188	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
189	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₅₃	—	2	4	no	—
191	C₂²×C₄×D₅₃	—	2	4	no	—
192	C₂²×C₄×D₅₃	—	4	2	no	—
193	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
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	#13133212	C₂×C₄	1	8	yes	complemented
210	#13133212	C₂×C₄	1	8	yes	complemented
211	#13133212	C₂×C₄	1	8	yes	complemented
212	#13133211	C₂×C₄	1	8	yes	complemented
213	#13133210	C₂×C₄	1	8	yes	complemented
214	#13133210	C₂×C₄	1	8	yes	complemented
215	#13133210	C₂×C₄	1	8	yes	complemented
216	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
224	C₂×#11719919	C₂³	1	1	yes	characteristic
225	C₂×#11719919	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×D₅₃	—	2	4	no	—
241	C₄⋊C₄×D₅₃	—	2	4	no	—
242	C₄⋊C₄×D₅₃	—	2	4	no	—
243	C₄⋊C₄×D₅₃	—	2	4	no	—
244	C₄⋊C₄×D₅₃	—	4	2	no	—
245	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
246	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
247	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
248	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×#11719921	C₂³	1	1	yes	characteristic
255	C₂×#11719921	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	1	yes	characteristic
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	1	yes	characteristic
259	C₂×#11719921	C₂³	1	1	yes	characteristic
260	C₂×#11719921	C₂³	1	1	yes	characteristic
261	C₂×#11719921	C₂³	1	1	yes	characteristic
262	C₂×#11719921	C₂³	1	1	yes	characteristic
263	C₂×#11719921	C₂³	1	1	yes	characteristic
264	C₂×#11719921	C₂³	1	1	yes	characteristic
265	C₂×#11719921	C₂³	1	1	yes	characteristic
266	C₂²⋊C₄×D₅₃	—	2	4	no	—
267	C₂²⋊C₄×D₅₃	—	2	4	no	—
268	C₂²⋊C₄×D₅₃	—	4	2	no	—
269	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
270	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
271	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
296	C₄²×D₅₃	—	2	4	no	—
297	C₄²×D₅₃	—	2	4	no	—
298	C₄²×D₅₃	—	2	4	no	—
299	C₄²×D₅₃	—	2	4	no	—
300	C₄²×D₅₃	—	4	2	no	—
301	C₄²×D₅₃	—	4	2	no	—
302	C₄²×D₅₃	—	4	2	no	—
303	C₄²×D₅₃	C₂×C₄	1	8	yes	complemented
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
341	#126×C₅₃	C₂×C₄	1	8	yes	complemented
342	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
364	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	#95×C₅₃	C₂³	1	1	yes	characteristic
368	#95×C₅₃	C₂³	1	1	yes	characteristic
369	#95×C₅₃	C₂³	1	1	yes	characteristic
370	#95×C₅₃	C₂³	1	1	yes	characteristic
371	#95×C₅₃	C₂³	1	1	yes	characteristic
372	#95×C₅₃	C₂³	1	1	yes	characteristic
373	#95×C₅₃	C₂³	1	1	yes	characteristic
374	#95×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂³×D₅₃	—	2	2	no	—
378	C₂³×D₅₃	—	2	2	no	—
379	C₂³×D₅₃	—	2	2	no	—
380	C₂³×D₅₃	—	2	2	no	—
381	C₂³×D₅₃	—	2	2	no	—
382	C₂³×D₅₃	—	2	2	no	—
383	C₂³×D₅₃	C₂²×C₄	1	4	yes	—
384	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
385	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	—	2	2	no	—
387	C₂²×C₄×C₅₃	—	2	2	no	—
388	C₂²×C₄×C₅₃	—	4	1	no	—
389	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₅₃	—	2	2	no	—
404	C₂²×Dic₅₃	—	2	2	no	—
405	C₂²×Dic₅₃	—	4	1	no	—
406	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₄×D₅₃	—	2	2	no	—
421	C₂×C₄×D₅₃	—	2	2	no	—
422	C₂×C₄×D₅₃	—	2	2	no	—
423	C₂×C₄×D₅₃	—	2	2	no	—
424	C₂×C₄×D₅₃	—	2	2	no	—
425	C₂×C₄×D₅₃	—	2	2	no	—
426	C₂×C₄×D₅₃	—	2	2	no	—
427	C₂×C₄×D₅₃	—	2	2	no	—
428	C₂×C₄×D₅₃	—	2	2	no	—
429	C₂×C₄×D₅₃	—	2	2	no	—
430	C₂×C₄×D₅₃	—	2	2	no	—
431	C₂×C₄×D₅₃	—	2	2	no	—
432	C₂×C₄×D₅₃	—	2	2	no	—
433	C₂×C₄×D₅₃	—	2	2	no	—
434	C₂×C₄×D₅₃	—	2	2	no	—
435	C₂×C₄×D₅₃	—	2	2	no	—
436	C₂×C₄×D₅₃	—	2	2	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	—	4	16	no	—
457	C₂×C₄×D₅₃	—	4	1	no	—
458	C₂×C₄×D₅₃	—	4	1	no	—
459	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
460	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
461	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
462	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
463	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
464	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
465	C₂×C₄×D₅₃	#41	1	4	yes	—
466	C₂×C₄×D₅₃	#41	1	4	yes	—
467	C₂×C₄×D₅₃	#41	1	4	yes	—
468	C₂×C₄×D₅₃	#41	1	4	yes	—
469	C₄⋊C₄×C₅₃	—	2	2	no	—
470	C₄⋊C₄×C₅₃	—	2	2	no	—
471	C₄⋊C₄×C₅₃	—	2	2	no	—
472	C₄⋊C₄×C₅₃	—	2	2	no	—
473	C₄⋊C₄×C₅₃	—	4	1	no	—
474	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
475	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
476	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
477	C₂²⋊C₄×C₅₃	—	2	2	no	—
478	C₂²⋊C₄×C₅₃	—	2	2	no	—
479	C₂²⋊C₄×C₅₃	—	4	1	no	—
480	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
481	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
482	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
483	C₄²×C₅₃	—	2	2	no	—
484	C₄²×C₅₃	—	2	2	no	—
485	C₄²×C₅₃	—	2	2	no	—
486	C₄²×C₅₃	—	2	2	no	—
487	C₄²×C₅₃	—	4	1	no	—
488	C₄²×C₅₃	—	4	1	no	—
489	C₄²×C₅₃	—	4	1	no	—
490	C₄²×C₅₃	C₂²×C₄	1	4	yes	complemented
491	C₂²⋊Dic₅₃	—	2	2	no	—
492	C₂²⋊Dic₅₃	—	2	2	no	—
493	C₂²⋊Dic₅₃	—	4	1	no	—
494	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
495	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
496	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
497	#11719921	—	2	2	no	—
498	#11719921	—	2	2	no	—
499	#11719921	—	2	2	no	—
500	#11719921	—	2	2	no	—
501	#11719921	—	4	1	no	—
502	#11719921	—	4	1	no	—
503	#11719921	C₂²×C₄	1	4	yes	—
504	#11719921	C₂²×C₄	1	4	yes	—
505	#11719921	C₂²×C₄	1	4	yes	—
506	#11719921	C₂²×C₄	1	4	yes	—
507	#11719921	C₂²×C₄	1	4	yes	—
508	#11719921	C₂²×C₄	1	4	yes	—
509	C₄⋊Dic₅₃	—	2	2	no	—
510	C₄⋊Dic₅₃	—	2	2	no	—
511	C₄⋊Dic₅₃	—	2	2	no	—
512	C₄⋊Dic₅₃	—	2	2	no	—
513	C₄⋊Dic₅₃	—	4	1	no	—
514	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	complemented
515	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	complemented
516	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	complemented
517	#11719919	—	2	2	no	—
518	#11719919	—	2	2	no	—
519	#11719919	—	2	2	no	—
520	#11719919	—	2	2	no	—
521	#11719919	—	2	2	no	—
522	#11719919	—	2	2	no	—
523	#11719919	—	2	2	no	—
524	#11719919	—	2	2	no	—
525	#11719919	—	4	1	no	—
526	#11719919	—	4	1	no	—
527	#11719919	C₂²×C₄	1	4	yes	complemented
528	#11719919	C₂²×C₄	1	4	yes	complemented
529	#11719919	C₂²×C₄	1	4	yes	complemented
530	#11719919	C₂²×C₄	1	4	yes	complemented
531	#11719919	C₂²×C₄	1	4	yes	complemented
532	#11719919	C₂²×C₄	1	4	yes	complemented
533	C₄×Dic₅₃	—	2	2	no	—
534	C₄×Dic₅₃	—	2	2	no	—
535	C₄×Dic₅₃	—	2	2	no	—
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	—	4	1	no	—
546	C₄×Dic₅₃	—	4	1	no	—
547	C₄×Dic₅₃	—	4	1	no	—
548	C₄×Dic₅₃	—	4	1	no	—
549	C₄×Dic₅₃	—	4	1	no	—
550	C₄×Dic₅₃	—	4	1	no	—
551	C₄×Dic₅₃	—	4	1	no	—
552	C₄×Dic₅₃	—	4	1	no	—
553	C₄×Dic₅₃	—	4	1	no	—
554	C₄×Dic₅₃	C₂²×C₄	1	4	yes	complemented
555	C₄×Dic₅₃	C₂²×C₄	1	4	yes	complemented
556	C₄×Dic₅₃	C₂²×C₄	1	4	yes	complemented
557	C₂³×C₅₃	—	2	1	no	—
558	C₂³×C₅₃	—	2	1	no	—
559	C₂³×C₅₃	—	2	1	no	—
560	C₂³×C₅₃	—	2	1	no	—
561	C₂³×C₅₃	—	2	1	no	—
562	C₂³×C₅₃	—	2	1	no	—
563	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
564	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
565	C₂²×D₅₃	—	2	1	no	—
566	C₂²×D₅₃	—	2	1	no	—
567	C₂²×D₅₃	—	2	1	no	—
568	C₂²×D₅₃	—	2	1	no	—
569	C₂²×D₅₃	—	2	1	no	—
570	C₂²×D₅₃	—	2	1	no	—
571	C₂²×D₅₃	—	2	8	no	—
572	C₂²×D₅₃	—	2	8	no	—
573	C₂²×D₅₃	—	2	8	no	—
574	C₂²×D₅₃	—	4	4	no	—
575	C₂²×D₅₃	—	4	4	no	—
576	C₂²×D₅₃	—	4	4	no	—
577	C₂²×D₅₃	—	4	4	no	—
578	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
579	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
580	C₂²×D₅₃	C₂×#41	1	2	yes	—
581	C₂²×D₅₃	C₂×#41	1	2	yes	—
582	C₂²×D₅₃	C₂×#41	1	2	yes	—
583	C₂²×D₅₃	C₂×#41	1	2	yes	—
584	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
585	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	1	no	—
614	C₂×C₄×C₅₃	—	2	1	no	—
615	C₂×C₄×C₅₃	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	4	4	no	—
619	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
620	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
621	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
622	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
623	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
624	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
625	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
626	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
627	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
628	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
629	C₂×Dic₅₃	—	2	1	no	—
630	C₂×Dic₅₃	—	2	1	no	—
631	C₂×Dic₅₃	—	2	1	no	—
632	C₂×Dic₅₃	—	2	1	no	—
633	C₂×Dic₅₃	—	2	1	no	—
634	C₂×Dic₅₃	—	2	1	no	—
635	C₂×Dic₅₃	—	2	1	no	—
636	C₂×Dic₅₃	—	2	1	no	—
637	C₂×Dic₅₃	—	2	1	no	—
638	C₂×Dic₅₃	—	2	1	no	—
639	C₂×Dic₅₃	—	2	1	no	—
640	C₂×Dic₅₃	—	2	1	no	—
641	C₂×Dic₅₃	—	2	1	no	—
642	C₂×Dic₅₃	—	2	1	no	—
643	C₂×Dic₅₃	—	2	1	no	—
644	C₂×Dic₅₃	—	2	1	no	—
645	C₂×Dic₅₃	—	2	1	no	—
646	C₂×Dic₅₃	—	2	1	no	—
647	C₂×Dic₅₃	—	2	1	no	—
648	C₂×Dic₅₃	—	2	1	no	—
649	C₂×Dic₅₃	—	2	1	no	—
650	C₂×Dic₅₃	—	2	1	no	—
651	C₂×Dic₅₃	—	2	1	no	—
652	C₂×Dic₅₃	—	2	1	no	—
653	C₂×Dic₅₃	—	2	1	no	—
654	C₂×Dic₅₃	—	2	1	no	—
655	C₂×Dic₅₃	—	2	1	no	—
656	C₂×Dic₅₃	—	2	1	no	—
657	C₂×Dic₅₃	—	2	1	no	—
658	C₂×Dic₅₃	—	2	1	no	—
659	C₂×Dic₅₃	—	2	1	no	—
660	C₂×Dic₅₃	—	2	1	no	—
661	C₂×Dic₅₃	—	4	4	no	—
662	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
663	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
664	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
665	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
666	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
667	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
668	C₂×Dic₅₃	C₂×#41	1	2	yes	—
669	C₂×Dic₅₃	C₂×#41	1	2	yes	—
670	C₂×Dic₅₃	C₂×#41	1	2	yes	—
671	C₂×Dic₅₃	C₂×#41	1	2	yes	—
672	C₄×D₅₃	—	2	8	no	—
673	C₄×D₅₃	—	2	8	no	—
674	C₄×D₅₃	—	2	8	no	—
675	C₄×D₅₃	—	2	8	no	—
676	C₄×D₅₃	—	2	8	no	—
677	C₄×D₅₃	—	2	8	no	—
678	C₄×D₅₃	—	2	8	no	—
679	C₄×D₅₃	—	2	8	no	—
680	C₄×D₅₃	—	2	8	no	—
681	C₄×D₅₃	—	2	8	no	—
682	C₄×D₅₃	—	4	4	no	—
683	C₄×D₅₃	—	4	4	no	—
684	C₄×D₅₃	—	4	4	no	—
685	C₄×D₅₃	—	4	4	no	—
686	C₄×D₅₃	—	4	4	no	—
687	C₄×D₅₃	—	4	4	no	—
688	C₂×#2373	—	53	1	no	maximal, Sylow
689	C₂²×C₅₃	—	2	2	no	—
690	C₂²×C₅₃	—	2	2	no	—
691	C₂²×C₅₃	—	2	2	no	—
692	C₂²×C₅₃	—	4	1	no	—
693	C₂²×C₅₃	—	4	1	no	—
694	C₂²×C₅₃	—	4	1	no	—
695	C₂²×C₅₃	—	4	1	no	—
696	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
697	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
698	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
699	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
700	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
701	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
703	C₂×D₅₃	—	2	2	no	—
704	C₂×D₅₃	—	2	2	no	—
705	C₂×D₅₃	—	2	2	no	—
706	C₂×D₅₃	—	4	1	no	—
707	C₂×D₅₃	—	4	1	no	—
708	C₂×D₅₃	—	4	1	no	—
709	C₂×D₅₃	—	4	1	no	—
710	C₂×D₅₃	—	4	16	no	—
711	C₂×D₅₃	C₄×#41	1	4	yes	—
712	C₂×D₅₃	C₄×#41	1	4	yes	—
713	C₂×D₅₃	#520	1	4	yes	—
714	C₂×D₅₃	#551	1	4	yes	—
715	C₂×D₅₃	#552	1	4	yes	—
716	C₂×D₅₃	#553	1	4	yes	—
717	C₂×D₅₃	#556	1	4	yes	—
718	C₄×C₅₃	—	2	2	no	—
719	C₄×C₅₃	—	2	2	no	—
720	C₄×C₅₃	—	2	2	no	—
721	C₄×C₅₃	—	2	2	no	—
722	C₄×C₅₃	—	2	2	no	—
723	C₄×C₅₃	—	2	2	no	—
724	C₄×C₅₃	—	2	2	no	—
725	C₄×C₅₃	—	2	2	no	—
726	C₄×C₅₃	—	2	2	no	—
727	C₄×C₅₃	—	2	2	no	—
728	C₄×C₅₃	—	4	1	no	—
729	C₄×C₅₃	—	4	1	no	—
730	C₄×C₅₃	—	4	1	no	—
731	C₄×C₅₃	—	4	1	no	—
732	Dic₅₃	—	2	2	no	—
733	Dic₅₃	—	2	2	no	—
734	Dic₅₃	—	2	2	no	—
735	Dic₅₃	—	2	2	no	—
736	Dic₅₃	—	2	2	no	—
737	Dic₅₃	—	2	2	no	—
738	Dic₅₃	—	2	2	no	—
739	Dic₅₃	—	2	2	no	—
740	Dic₅₃	—	2	2	no	—
741	Dic₅₃	—	2	2	no	—
742	Dic₅₃	—	4	1	no	—
743	Dic₅₃	—	4	1	no	—
744	Dic₅₃	—	4	1	no	—
745	Dic₅₃	—	4	1	no	—
746	C₂²×#126	—	53	1	no	—
747	#2373	—	53	1	no	—
748	#2373	—	53	1	no	—
749	#2373	—	53	1	no	—
750	#2373	—	53	1	no	—
751	#2373	—	53	1	no	—
752	#2373	—	53	1	no	—
753	#2373	—	53	1	no	—
754	#2373	—	53	1	no	—
755	#2373	—	53	1	no	—
756	#2373	—	53	1	no	—
757	#2373	—	53	1	no	—
758	#2373	—	53	1	no	—
759	#2373	—	53	1	no	—
760	#2373	—	53	1	no	—
761	#2373	—	53	1	no	—
762	#2373	D₅₃	1	1	yes	characteristic, direct product factor
763	C₂×#389	—	53	1	no	—
764	C₂×#388	—	53	1	no	—
765	C₂×#388	—	53	1	no	—
766	C₂×#388	—	53	1	no	—
767	C₂×#387	—	53	1	no	—
768	C₂×#387	—	53	1	no	—
769	C₂×#387	—	53	1	no	—
770	C₂×#385	—	53	1	no	—
771	C₂×C₄×C₄⋊C₄	—	53	1	no	—
772	C₂×C₄×C₄⋊C₄	—	53	1	no	—
773	C₂×C₄×C₄⋊C₄	—	53	1	no	—
774	C₂×C₄×C₂²⋊C₄	—	53	1	no	—
775	C₂×C₄×C₂²⋊C₄	—	53	1	no	—
776	C₂×#376	—	53	1	no	—
777	C₂×C₅₃	—	4	2	no	—
778	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
779	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
780	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
781	C₂×C₅₃	C₂×#551	1	1	yes	characteristic
782	C₂×C₅₃	C₂×#552	1	1	yes	characteristic
783	C₂×C₅₃	C₂×#553	1	1	yes	characteristic
784	C₂×C₅₃	C₂×#556	1	1	yes	characteristic
785	D₅₃	—	4	2	no	—
786	D₅₃	#2373	1	8	yes	direct product factor
787	C₂⁴×C₄	—	53	1	no	—
788	C₂×#126	—	53	16	no	—
789	C₂×#126	—	53	1	no	—
790	C₂×#126	—	53	1	no	—
791	C₂×#126	—	53	1	no	—
792	C₂×#126	—	53	1	no	—
793	C₂×#126	—	53	1	no	—
794	C₂×#126	—	53	1	no	—
795	C₂×#126	—	53	1	no	—
796	C₂×#126	C₂×D₅₃	1	1	yes	characteristic
797	C₂²×C₄⋊C₄	—	53	1	no	—
798	C₂²×C₄⋊C₄	—	53	1	no	—
799	C₂²×C₄⋊C₄	—	53	1	no	—
800	C₂²×C₄⋊C₄	—	53	1	no	—
801	C₂²×C₄⋊C₄	—	53	1	no	—
802	C₂²×C₄⋊C₄	—	53	1	no	—
803	C₂²×C₄⋊C₄	—	53	1	no	—
804	C₂²×C₄⋊C₄	—	53	1	no	—
805	C₂²×C₂²⋊C₄	—	53	1	no	—
806	C₂²×C₂²⋊C₄	—	53	1	no	—
807	C₂²×C₂²⋊C₄	—	53	1	no	—
808	C₂²×C₂²⋊C₄	—	53	1	no	—
809	C₂²×C₂²⋊C₄	—	53	1	no	—
810	C₂²×C₂²⋊C₄	—	53	1	no	—
811	C₂²×C₄²	—	53	1	no	—
812	C₂²×C₄²	—	53	1	no	—
813	C₂²×C₄²	—	53	1	no	—
814	C₂²×C₄²	—	53	1	no	—
815	C₂²×C₄²	—	53	1	no	—
816	C₂²×C₄²	—	53	1	no	—
817	C₂²×C₄²	—	53	1	no	—
818	C₂²×C₄²	—	53	1	no	—
819	#389	—	53	1	no	—
820	#389	—	53	1	no	—
821	#389	—	53	1	no	—
822	#389	—	53	1	no	—
823	#389	—	53	1	no	—
824	#389	—	53	1	no	—
825	#389	—	53	1	no	—
826	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
827	#388	—	53	1	no	—
828	#388	—	53	1	no	—
829	#388	—	53	1	no	—
830	#388	—	53	1	no	—
831	#388	—	53	1	no	—
832	#388	—	53	1	no	—
833	#388	—	53	1	no	—
834	#388	—	53	1	no	—
835	#388	—	53	1	no	—
836	#388	—	53	1	no	—
837	#388	—	53	1	no	—
838	#388	—	53	1	no	—
839	#388	—	53	1	no	—
840	#388	—	53	1	no	—
841	#388	—	53	1	no	—
842	#388	—	53	1	no	—
843	#388	—	53	1	no	—
844	#388	—	53	1	no	—
845	#388	—	53	1	no	—
846	#388	—	53	1	no	—
847	#388	—	53	1	no	—
848	#388	C₂×D₅₃	1	1	yes	characteristic
849	#388	C₂×D₅₃	1	1	yes	characteristic
850	#388	C₂×D₅₃	1	1	yes	characteristic
851	#387	—	53	1	no	—
852	#387	—	53	1	no	—
853	#387	—	53	1	no	—
854	#387	—	53	1	no	—
855	#387	—	53	1	no	—
856	#387	—	53	1	no	—
857	#387	—	53	1	no	—
858	#387	—	53	1	no	—
859	#387	—	53	1	no	—
860	#387	—	53	1	no	—
861	#387	—	53	1	no	—
862	#387	—	53	1	no	—
863	#387	—	53	1	no	—
864	#387	—	53	1	no	—
865	#387	—	53	1	no	—
866	#387	—	53	1	no	—
867	#387	—	53	1	no	—
868	#387	—	53	1	no	—
869	#387	—	53	1	no	—
870	#387	—	53	1	no	—
871	#387	—	53	1	no	—
872	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
873	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
874	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
875	#385	—	53	1	no	—
876	#385	—	53	1	no	—
877	#385	—	53	1	no	—
878	#385	—	53	1	no	—
879	#385	—	53	1	no	—
880	#385	—	53	1	no	—
881	#385	—	53	1	no	—
882	#385	C₂×D₅₃	1	1	yes	characteristic
883	C₄×C₄⋊C₄	—	53	1	no	—
884	C₄×C₄⋊C₄	—	53	1	no	—
885	C₄×C₄⋊C₄	—	53	1	no	—
886	C₄×C₄⋊C₄	—	53	1	no	—
887	C₄×C₄⋊C₄	—	53	1	no	—
888	C₄×C₄⋊C₄	—	53	1	no	—
889	C₄×C₄⋊C₄	—	53	1	no	—
890	C₄×C₄⋊C₄	—	53	1	no	—
891	C₄×C₄⋊C₄	—	53	1	no	—
892	C₄×C₄⋊C₄	—	53	1	no	—
893	C₄×C₄⋊C₄	—	53	1	no	—
894	C₄×C₄⋊C₄	—	53	1	no	—
895	C₄×C₄⋊C₄	—	53	1	no	—
896	C₄×C₄⋊C₄	—	53	1	no	—
897	C₄×C₄⋊C₄	—	53	1	no	—
898	C₄×C₄⋊C₄	—	53	1	no	—
899	C₄×C₄⋊C₄	—	53	1	no	—
900	C₄×C₄⋊C₄	—	53	1	no	—
901	C₄×C₄⋊C₄	—	53	1	no	—
902	C₄×C₄⋊C₄	—	53	1	no	—
903	C₄×C₄⋊C₄	—	53	1	no	—
904	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
905	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
906	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
907	C₄×C₂²⋊C₄	—	53	1	no	—
908	C₄×C₂²⋊C₄	—	53	1	no	—
909	C₄×C₂²⋊C₄	—	53	1	no	—
910	C₄×C₂²⋊C₄	—	53	1	no	—
911	C₄×C₂²⋊C₄	—	53	1	no	—
912	C₄×C₂²⋊C₄	—	53	1	no	—
913	C₄×C₂²⋊C₄	—	53	1	no	—
914	C₄×C₂²⋊C₄	—	53	1	no	—
915	C₄×C₂²⋊C₄	—	53	1	no	—
916	C₄×C₂²⋊C₄	—	53	1	no	—
917	C₄×C₂²⋊C₄	—	53	1	no	—
918	C₄×C₂²⋊C₄	—	53	1	no	—
919	C₄×C₂²⋊C₄	—	53	1	no	—
920	C₄×C₂²⋊C₄	—	53	1	no	—
921	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
922	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
923	#376	—	53	1	no	—
924	#376	—	53	1	no	—
925	#376	—	53	1	no	—
926	#376	—	53	1	no	—
927	#376	—	53	1	no	—
928	#376	—	53	1	no	—
929	#376	—	53	1	no	—
930	#376	C₂×D₅₃	1	1	yes	characteristic, complemented
931	C₂×#95	—	53	1	no	—
932	C₂×#95	—	53	1	no	—
933	C₂×#95	—	53	1	no	—
934	C₂×#95	—	53	1	no	—
935	C₂×#95	—	53	1	no	—
936	C₂×#95	—	53	1	no	—
937	C₂×#95	—	53	1	no	—
938	C₂×#95	—	53	1	no	—
939	C₂×#95	—	53	1	no	—
940	C₂×#95	—	53	1	no	—
941	C₂×#95	—	53	1	no	—
942	C₂×#95	—	53	1	no	—
943	C₅₃	C₂×#2373	1	1	yes	characteristic, complemented, Sylow
944	C₂⁵	—	53	1	no	—
945	C₂³×C₄	—	53	1	no	—
946	C₂³×C₄	—	53	1	no	—
947	C₂³×C₄	—	53	1	no	—
948	C₂³×C₄	—	53	1	no	—
949	C₂³×C₄	—	53	1	no	—
950	C₂³×C₄	—	53	1	no	—
951	C₂³×C₄	—	53	1	no	—
952	C₂³×C₄	—	53	1	no	—
953	C₂³×C₄	—	53	1	no	—
954	C₂³×C₄	—	53	1	no	—
955	C₂³×C₄	—	53	1	no	—
956	C₂³×C₄	—	53	1	no	—
957	C₂³×C₄	—	53	1	no	—
958	C₂³×C₄	—	53	1	no	—
959	C₂³×C₄	—	53	1	no	—
960	C₂³×C₄	—	53	1	no	—
961	C₂³×C₄	—	53	1	no	—
962	C₂³×C₄	—	106	4	no	—
963	C₂³×C₄	—	106	4	no	—
964	C₂³×C₄	—	212	2	no	—
965	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
966	#126	—	53	8	no	—
967	#126	—	53	8	no	—
968	#126	—	53	8	no	—
969	#126	—	53	8	no	—
970	#126	—	53	8	no	—
971	#126	—	53	8	no	—
972	#126	—	53	8	no	—
973	#126	C₄×D₅₃	1	8	yes	complemented
974	C₂×C₄⋊C₄	—	53	1	no	—
975	C₂×C₄⋊C₄	—	53	1	no	—
976	C₂×C₄⋊C₄	—	53	1	no	—
977	C₂×C₄⋊C₄	—	53	1	no	—
978	C₂×C₄⋊C₄	—	53	1	no	—
979	C₂×C₄⋊C₄	—	53	1	no	—
980	C₂×C₄⋊C₄	—	53	1	no	—
981	C₂×C₄⋊C₄	—	53	1	no	—
982	C₂×C₄⋊C₄	—	53	1	no	—
983	C₂×C₄⋊C₄	—	53	8	no	—
984	C₂×C₄⋊C₄	—	53	8	no	—
985	C₂×C₄⋊C₄	—	53	8	no	—
986	C₂×C₄⋊C₄	—	53	1	no	—
987	C₂×C₄⋊C₄	—	53	1	no	—
988	C₂×C₄⋊C₄	—	53	1	no	—
989	C₂×C₄⋊C₄	—	53	1	no	—
990	C₂×C₄⋊C₄	—	53	1	no	—
991	C₂×C₄⋊C₄	—	53	1	no	—
992	C₂×C₄⋊C₄	—	53	1	no	—
993	C₂×C₄⋊C₄	—	53	1	no	—
994	C₂×C₄⋊C₄	—	53	1	no	—
995	C₂×C₄⋊C₄	—	53	1	no	—
996	C₂×C₄⋊C₄	—	53	1	no	—
997	C₂×C₄⋊C₄	—	53	1	no	—
998	C₂×C₄⋊C₄	—	53	1	no	—
999	C₂×C₄⋊C₄	—	53	1	no	—
1000	C₂×C₄⋊C₄	—	53	1	no	—
1001	C₂×C₄⋊C₄	—	106	4	no	—
1002	C₂×C₄⋊C₄	—	106	4	no	—
1003	C₂×C₄⋊C₄	—	106	4	no	—
1004	C₂×C₄⋊C₄	—	106	4	no	—
1005	C₂×C₄⋊C₄	—	212	2	no	—
1006	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1014	C₂×C₂²⋊C₄	—	53	1	no	—
1015	C₂×C₂²⋊C₄	—	53	1	no	—
1016	C₂×C₂²⋊C₄	—	53	1	no	—
1017	C₂×C₂²⋊C₄	—	53	1	no	—
1018	C₂×C₂²⋊C₄	—	53	1	no	—
1019	C₂×C₂²⋊C₄	—	53	1	no	—
1020	C₂×C₂²⋊C₄	—	53	1	no	—
1021	C₂×C₂²⋊C₄	—	53	1	no	—
1022	C₂×C₂²⋊C₄	—	53	1	no	—
1023	C₂×C₂²⋊C₄	—	53	8	no	—
1024	C₂×C₂²⋊C₄	—	53	8	no	—
1025	C₂×C₂²⋊C₄	—	53	8	no	—
1026	C₂×C₂²⋊C₄	—	53	1	no	—
1027	C₂×C₂²⋊C₄	—	53	1	no	—
1028	C₂×C₂²⋊C₄	—	53	1	no	—
1029	C₂×C₂²⋊C₄	—	53	1	no	—
1030	C₂×C₂²⋊C₄	—	53	1	no	—
1031	C₂×C₂²⋊C₄	—	53	1	no	—
1032	C₂×C₂²⋊C₄	—	53	1	no	—
1033	C₂×C₂²⋊C₄	—	53	1	no	—
1034	C₂×C₂²⋊C₄	—	53	1	no	—
1035	C₂×C₂²⋊C₄	—	106	4	no	—
1036	C₂×C₂²⋊C₄	—	106	4	no	—
1037	C₂×C₂²⋊C₄	—	212	2	no	—
1038	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1044	C₂×C₄²	—	53	1	no	—
1045	C₂×C₄²	—	53	1	no	—
1046	C₂×C₄²	—	53	1	no	—
1047	C₂×C₄²	—	53	8	no	—
1048	C₂×C₄²	—	53	1	no	—
1049	C₂×C₄²	—	53	1	no	—
1050	C₂×C₄²	—	53	1	no	—
1051	C₂×C₄²	—	53	1	no	—
1052	C₂×C₄²	—	53	1	no	—
1053	C₂×C₄²	—	53	1	no	—
1054	C₂×C₄²	—	53	1	no	—
1055	C₂×C₄²	—	53	1	no	—
1056	C₂×C₄²	—	53	1	no	—
1057	C₂×C₄²	—	53	1	no	—
1058	C₂×C₄²	—	53	1	no	—
1059	C₂×C₄²	—	53	1	no	—
1060	C₂×C₄²	—	53	1	no	—
1061	C₂×C₄²	—	53	1	no	—
1062	C₂×C₄²	—	53	1	no	—
1063	C₂×C₄²	—	53	1	no	—
1064	C₂×C₄²	—	53	1	no	—
1065	C₂×C₄²	—	53	1	no	—
1066	C₂×C₄²	—	53	1	no	—
1067	C₂×C₄²	—	53	1	no	—
1068	C₂×C₄²	—	53	1	no	—
1069	C₂×C₄²	—	106	4	no	—
1070	C₂×C₄²	—	106	4	no	—
1071	C₂×C₄²	—	106	4	no	—
1072	C₂×C₄²	—	106	4	no	—
1073	C₂×C₄²	—	212	2	no	—
1074	C₂×C₄²	—	212	2	no	—
1075	C₂×C₄²	—	212	2	no	—
1076	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1077	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1078	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1079	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1080	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1081	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1082	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1083	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1084	#95	—	53	1	no	—
1085	#95	—	53	1	no	—
1086	#95	—	53	1	no	—
1087	#95	—	53	1	no	—
1088	#95	—	53	1	no	—
1089	#95	—	53	1	no	—
1090	#95	—	53	1	no	—
1091	#95	—	53	1	no	—
1092	#95	—	53	1	no	—
1093	#95	—	53	1	no	—
1094	#95	—	53	1	no	—
1095	#95	—	53	1	no	—
1096	#95	—	53	1	no	—
1097	#95	—	53	1	no	—
1098	#95	—	53	1	no	—
1099	#95	—	53	1	no	—
1100	#95	—	53	1	no	—
1101	#95	—	53	1	no	—
1102	#95	—	53	1	no	—
1103	#95	—	53	1	no	—
1104	#95	—	53	1	no	—
1105	#95	—	53	1	no	—
1106	#95	—	53	1	no	—
1107	#95	—	53	1	no	—
1108	#95	—	53	1	no	—
1109	#95	—	53	1	no	—
1110	#95	—	53	1	no	—
1111	#95	—	53	1	no	—
1112	#95	—	53	1	no	—
1113	#95	—	53	1	no	—
1114	#95	—	53	1	no	—
1115	#95	—	53	1	no	—
1116	#95	—	53	1	no	—
1117	#95	—	53	1	no	—
1118	#95	—	53	1	no	—
1119	#95	—	53	1	no	—
1120	#95	C₂²×D₅₃	1	1	yes	characteristic
1121	#95	C₂²×D₅₃	1	1	yes	characteristic
1122	#95	C₂²×D₅₃	1	1	yes	characteristic
1123	#95	C₂²×D₅₃	1	1	yes	characteristic
1124	#95	C₂²×D₅₃	1	1	yes	characteristic
1125	#95	C₂²×D₅₃	1	1	yes	characteristic
1126	#95	C₂²×D₅₃	1	1	yes	characteristic
1127	#95	C₂²×D₅₃	1	1	yes	characteristic
1128	#95	C₂²×D₅₃	1	1	yes	characteristic
1129	#95	C₂²×D₅₃	1	1	yes	characteristic
1130	#95	C₂²×D₅₃	1	1	yes	characteristic
1131	#95	C₂²×D₅₃	1	1	yes	characteristic
1132	C₂⁴	—	53	1	no	—
1133	C₂⁴	—	53	4	no	—
1134	C₂⁴	—	53	1	no	—
1135	C₂⁴	—	106	2	no	—
1136	C₂⁴	—	106	2	no	—
1137	C₂⁴	—	106	2	no	—
1138	C₂⁴	—	106	2	no	—
1139	C₂⁴	—	106	2	no	—
1140	C₂⁴	—	106	2	no	—
1141	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1142	C₂²×C₄	—	2	2	no	—
1143	C₂²×C₄	—	2	2	no	—
1144	C₂²×C₄	—	4	1	no	—
1145	C₂²×C₄	—	53	1	no	—
1146	C₂²×C₄	—	53	1	no	—
1147	C₂²×C₄	—	53	1	no	—
1148	C₂²×C₄	—	53	1	no	—
1149	C₂²×C₄	—	53	1	no	—
1150	C₂²×C₄	—	53	1	no	—
1151	C₂²×C₄	—	53	1	no	—
1152	C₂²×C₄	—	53	1	no	—
1153	C₂²×C₄	—	53	1	no	—
1154	C₂²×C₄	—	53	1	no	—
1155	C₂²×C₄	—	53	4	no	—
1156	C₂²×C₄	—	53	4	no	—
1157	C₂²×C₄	—	53	4	no	—
1158	C₂²×C₄	—	53	4	no	—
1159	C₂²×C₄	—	53	4	no	—
1160	C₂²×C₄	—	53	4	no	—
1161	C₂²×C₄	—	53	4	no	—
1162	C₂²×C₄	—	53	4	no	—
1163	C₂²×C₄	—	53	4	no	—
1164	C₂²×C₄	—	53	4	no	—
1165	C₂²×C₄	—	53	1	no	—
1166	C₂²×C₄	—	53	1	no	—
1167	C₂²×C₄	—	53	1	no	—
1168	C₂²×C₄	—	53	1	no	—
1169	C₂²×C₄	—	106	2	no	—
1170	C₂²×C₄	—	106	2	no	—
1171	C₂²×C₄	—	106	2	no	—
1172	C₂²×C₄	—	106	2	no	—
1173	C₂²×C₄	—	106	2	no	—
1174	C₂²×C₄	—	106	2	no	—
1175	C₂²×C₄	—	106	2	no	—
1176	C₂²×C₄	—	106	2	no	—
1177	C₂²×C₄	—	106	2	no	—
1178	C₂²×C₄	—	106	2	no	—
1179	C₂²×C₄	—	106	2	no	—
1180	C₂²×C₄	—	106	2	no	—
1181	C₂²×C₄	—	106	2	no	—
1182	C₂²×C₄	—	106	2	no	—
1183	C₂²×C₄	—	106	2	no	—
1184	C₂²×C₄	—	106	2	no	—
1185	C₂²×C₄	—	106	2	no	—
1186	C₂²×C₄	—	106	2	no	—
1187	C₂²×C₄	—	106	2	no	—
1188	C₂²×C₄	—	106	2	no	—
1189	C₂²×C₄	—	106	2	no	—
1190	C₂²×C₄	—	106	2	no	—
1191	C₂²×C₄	—	106	2	no	—
1192	C₂²×C₄	—	106	2	no	—
1193	C₂²×C₄	—	106	2	no	—
1194	C₂²×C₄	—	106	2	no	—
1195	C₂²×C₄	—	106	2	no	—
1196	C₂²×C₄	—	106	2	no	—
1197	C₂²×C₄	—	106	2	no	—
1198	C₂²×C₄	—	106	2	no	—
1199	C₂²×C₄	—	106	2	no	—
1200	C₂²×C₄	—	106	2	no	—
1201	C₂²×C₄	—	106	2	no	—
1202	C₂²×C₄	—	106	2	no	—
1203	C₂²×C₄	—	106	2	no	—
1204	C₂²×C₄	—	106	2	no	—
1205	C₂²×C₄	—	106	2	no	—
1206	C₂²×C₄	—	106	2	no	—
1207	C₂²×C₄	—	212	1	no	—
1208	C₂²×C₄	—	212	1	no	—
1209	C₂²×C₄	—	212	16	no	—
1210	C₂²×C₄	—	212	1	no	—
1211	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1212	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1213	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1214	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1215	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1216	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1217	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1218	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1219	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1220	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1221	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1222	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1223	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1224	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1225	C₄⋊C₄	—	2	2	no	—
1226	C₄⋊C₄	—	2	2	no	—
1227	C₄⋊C₄	—	2	2	no	—
1228	C₄⋊C₄	—	2	2	no	—
1229	C₄⋊C₄	—	4	1	no	—
1230	C₄⋊C₄	—	53	4	no	—
1231	C₄⋊C₄	—	53	4	no	—
1232	C₄⋊C₄	—	53	4	no	—
1233	C₄⋊C₄	—	53	4	no	—
1234	C₄⋊C₄	—	53	4	no	—
1235	C₄⋊C₄	—	53	4	no	—
1236	C₄⋊C₄	—	53	4	no	—
1237	C₄⋊C₄	—	53	4	no	—
1238	C₄⋊C₄	—	53	4	no	—
1239	C₄⋊C₄	—	106	2	no	—
1240	C₄⋊C₄	—	106	2	no	—
1241	C₄⋊C₄	—	106	2	no	—
1242	C₄⋊C₄	—	106	2	no	—
1243	C₄⋊C₄	—	106	2	no	—
1244	C₄⋊C₄	—	106	2	no	—
1245	C₄⋊C₄	—	106	2	no	—
1246	C₄⋊C₄	—	106	2	no	—
1247	C₄⋊C₄	—	106	2	no	—
1248	C₄⋊C₄	—	106	2	no	—
1249	C₄⋊C₄	—	106	2	no	—
1250	C₄⋊C₄	—	106	2	no	—
1251	C₄⋊C₄	—	212	1	no	—
1252	C₄⋊C₄	—	212	1	no	—
1253	C₄⋊C₄	—	212	1	no	—
1254	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1255	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1256	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1257	C₂²⋊C₄	—	2	2	no	—
1258	C₂²⋊C₄	—	2	2	no	—
1259	C₂²⋊C₄	—	4	1	no	—
1260	C₂²⋊C₄	—	53	4	no	—
1261	C₂²⋊C₄	—	53	4	no	—
1262	C₂²⋊C₄	—	53	4	no	—
1263	C₂²⋊C₄	—	53	4	no	—
1264	C₂²⋊C₄	—	53	4	no	—
1265	C₂²⋊C₄	—	53	4	no	—
1266	C₂²⋊C₄	—	53	4	no	—
1267	C₂²⋊C₄	—	53	4	no	—
1268	C₂²⋊C₄	—	53	4	no	—
1269	C₂²⋊C₄	—	106	2	no	—
1270	C₂²⋊C₄	—	106	2	no	—
1271	C₂²⋊C₄	—	106	2	no	—
1272	C₂²⋊C₄	—	106	2	no	—
1273	C₂²⋊C₄	—	106	2	no	—
1274	C₂²⋊C₄	—	106	2	no	—
1275	C₂²⋊C₄	—	212	1	no	—
1276	C₂²⋊C₄	—	212	1	no	—
1277	C₂²⋊C₄	—	212	1	no	—
1278	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1279	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1280	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1281	C₄²	—	2	2	no	—
1282	C₄²	—	2	2	no	—
1283	C₄²	—	2	2	no	—
1284	C₄²	—	2	2	no	—
1285	C₄²	—	4	1	no	—
1286	C₄²	—	4	1	no	—
1287	C₄²	—	4	1	no	—
1288	C₄²	—	53	4	no	—
1289	C₄²	—	53	4	no	—
1290	C₄²	—	53	4	no	—
1291	C₄²	—	106	2	no	—
1292	C₄²	—	106	2	no	—
1293	C₄²	—	106	2	no	—
1294	C₄²	—	106	2	no	—
1295	C₄²	—	106	2	no	—
1296	C₄²	—	106	2	no	—
1297	C₄²	—	106	2	no	—
1298	C₄²	—	106	2	no	—
1299	C₄²	—	106	2	no	—
1300	C₄²	—	106	2	no	—
1301	C₄²	—	106	2	no	—
1302	C₄²	—	106	2	no	—
1303	C₄²	—	212	1	no	—
1304	C₄²	—	212	1	no	—
1305	C₄²	—	212	1	no	—
1306	C₄²	—	212	1	no	—
1307	C₄²	—	212	1	no	—
1308	C₄²	—	212	1	no	—
1309	C₄²	—	212	1	no	—
1310	C₄²	—	212	1	no	—
1311	C₄²	—	212	1	no	—
1312	C₄²	C₂×C₄×D₅₃	1	4	yes	complemented
1313	C₂³	—	2	1	no	—
1314	C₂³	—	2	1	no	—
1315	C₂³	—	2	1	no	—
1316	C₂³	—	2	1	no	—
1317	C₂³	—	2	1	no	—
1318	C₂³	—	2	1	no	—
1319	C₂³	—	53	2	no	—
1320	C₂³	—	53	2	no	—
1321	C₂³	—	53	2	no	—
1322	C₂³	—	53	2	no	—
1323	C₂³	—	53	2	no	—
1324	C₂³	—	53	2	no	—
1325	C₂³	—	53	2	no	—
1326	C₂³	—	53	2	no	—
1327	C₂³	—	106	8	no	—
1328	C₂³	—	106	8	no	—
1329	C₂³	—	106	8	no	—
1330	C₂³	—	106	1	no	—
1331	C₂³	—	106	1	no	—
1332	C₂³	—	106	1	no	—
1333	C₂³	—	106	1	no	—
1334	C₂³	—	106	1	no	—
1335	C₂³	—	106	1	no	—
1336	C₂³	—	212	4	no	—
1337	C₂³	—	212	4	no	—
1338	C₂³	—	212	4	no	—
1339	C₂³	—	212	4	no	—
1340	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1341	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	4	4	no	—
1375	C₂×C₄	—	53	2	no	—
1376	C₂×C₄	—	53	2	no	—
1377	C₂×C₄	—	53	2	no	—
1378	C₂×C₄	—	53	2	no	—
1379	C₂×C₄	—	53	2	no	—
1380	C₂×C₄	—	53	2	no	—
1381	C₂×C₄	—	53	2	no	—
1382	C₂×C₄	—	53	2	no	—
1383	C₂×C₄	—	53	2	no	—
1384	C₂×C₄	—	53	2	no	—
1385	C₂×C₄	—	106	8	no	—
1386	C₂×C₄	—	106	8	no	—
1387	C₂×C₄	—	106	8	no	—
1388	C₂×C₄	—	106	8	no	—
1389	C₂×C₄	—	106	8	no	—
1390	C₂×C₄	—	106	8	no	—
1391	C₂×C₄	—	106	8	no	—
1392	C₂×C₄	—	106	8	no	—
1393	C₂×C₄	—	106	8	no	—
1394	C₂×C₄	—	106	8	no	—
1395	C₂×C₄	—	106	1	no	—
1396	C₂×C₄	—	106	1	no	—
1397	C₂×C₄	—	106	1	no	—
1398	C₂×C₄	—	106	1	no	—
1399	C₂×C₄	—	106	1	no	—
1400	C₂×C₄	—	106	1	no	—
1401	C₂×C₄	—	106	1	no	—
1402	C₂×C₄	—	106	1	no	—
1403	C₂×C₄	—	106	1	no	—
1404	C₂×C₄	—	106	1	no	—
1405	C₂×C₄	—	106	1	no	—
1406	C₂×C₄	—	106	1	no	—
1407	C₂×C₄	—	106	1	no	—
1408	C₂×C₄	—	106	1	no	—
1409	C₂×C₄	—	106	1	no	—
1410	C₂×C₄	—	106	1	no	—
1411	C₂×C₄	—	106	1	no	—
1412	C₂×C₄	—	106	1	no	—
1413	C₂×C₄	—	106	1	no	—
1414	C₂×C₄	—	106	1	no	—
1415	C₂×C₄	—	106	1	no	—
1416	C₂×C₄	—	106	1	no	—
1417	C₂×C₄	—	106	1	no	—
1418	C₂×C₄	—	106	1	no	—
1419	C₂×C₄	—	106	1	no	—
1420	C₂×C₄	—	106	1	no	—
1421	C₂×C₄	—	106	1	no	—
1422	C₂×C₄	—	106	1	no	—
1423	C₂×C₄	—	106	1	no	—
1424	C₂×C₄	—	106	1	no	—
1425	C₂×C₄	—	106	1	no	—
1426	C₂×C₄	—	106	1	no	—
1427	C₂×C₄	—	212	4	no	—
1428	C₂×C₄	—	212	4	no	—
1429	C₂×C₄	—	212	4	no	—
1430	C₂×C₄	—	212	4	no	—
1431	C₂×C₄	—	212	4	no	—
1432	C₂×C₄	—	212	4	no	—
1433	C₂×C₄	—	212	4	no	—
1434	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1435	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1436	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1437	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1438	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1439	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1440	C₂×C₄	#41×D₅₃	1	2	yes	—
1441	C₂×C₄	#41×D₅₃	1	2	yes	—
1442	C₂×C₄	#41×D₅₃	1	2	yes	—
1443	C₂×C₄	#41×D₅₃	1	2	yes	—
1444	C₂²	—	2	2	no	—
1445	C₂²	—	2	2	no	—
1446	C₂²	—	2	2	no	—
1447	C₂²	—	4	1	no	—
1448	C₂²	—	4	1	no	—
1449	C₂²	—	4	1	no	—
1450	C₂²	—	4	1	no	—
1451	C₂²	—	53	4	no	—
1452	C₂²	—	53	4	no	—
1453	C₂²	—	53	4	no	—
1454	C₂²	—	53	4	no	—
1455	C₂²	—	53	4	no	—
1456	C₂²	—	53	4	no	—
1457	C₂²	—	53	4	no	—
1458	C₂²	—	106	2	no	—
1459	C₂²	—	106	2	no	—
1460	C₂²	—	106	2	no	—
1461	C₂²	—	212	16	no	—
1462	C₂²	—	212	1	no	—
1463	C₂²	—	212	1	no	—
1464	C₂²	—	212	1	no	—
1465	C₂²	—	212	1	no	—
1466	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1467	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1468	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1469	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1470	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1471	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1472	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1473	C₄	—	2	2	no	—
1474	C₄	—	2	2	no	—
1475	C₄	—	2	2	no	—
1476	C₄	—	2	2	no	—
1477	C₄	—	2	2	no	—
1478	C₄	—	2	2	no	—
1479	C₄	—	2	2	no	—
1480	C₄	—	2	2	no	—
1481	C₄	—	2	2	no	—
1482	C₄	—	2	2	no	—
1483	C₄	—	4	1	no	—
1484	C₄	—	4	1	no	—
1485	C₄	—	4	1	no	—
1486	C₄	—	4	1	no	—
1487	C₄	—	106	2	no	—
1488	C₄	—	106	2	no	—
1489	C₄	—	106	2	no	—
1490	C₄	—	106	2	no	—
1491	C₄	—	106	2	no	—
1492	C₄	—	106	2	no	—
1493	C₄	—	106	2	no	—
1494	C₄	—	106	2	no	—
1495	C₄	—	106	2	no	—
1496	C₄	—	106	2	no	—
1497	C₄	—	212	1	no	—
1498	C₄	—	212	1	no	—
1499	C₄	—	212	1	no	—
1500	C₄	—	212	1	no	—
1501	C₂	—	4	2	no	—
1502	C₂	—	53	8	no	—
1503	C₂	—	212	2	no	—
1504	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1505	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1506	C₂	#520×D₅₃	1	1	yes	characteristic
1507	C₂	#551×D₅₃	1	1	yes	characteristic
1508	C₂	#552×D₅₃	1	1	yes	characteristic
1509	C₂	#553×D₅₃	1	1	yes	characteristic
1510	C₂	#556×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2373	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	#2373	D₅₃
hypocenter	C₅₃	C₂×#2373
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2373

Complements

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

N	H ≅ G/N	type
2. #20277842	C₂	semidirect
3. #20277841	C₂	semidirect
4. #20277840	C₂	semidirect
5. #20277839	C₂	semidirect
6. #20277838	C₂	semidirect
7. #20277837	C₂	semidirect
8. #20277836	C₂	semidirect
9. #20277835	C₂	semidirect
10. #20277834	C₂	semidirect
11. #20277833	C₂	semidirect
12. #20277832	C₂	semidirect
13. #20277831	C₂	semidirect
14. #20277830	C₂	semidirect
15. #20277829	C₂	semidirect
16. #20277828	C₂	semidirect
17. #389×D₅₃	C₂	semidirect
21. #387×D₅₃	C₂	semidirect
22. #387×D₅₃	C₂	semidirect
23. #387×D₅₃	C₂	semidirect
25. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
26. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
27. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
30. #376×D₅₃	C₂	semidirect
31. C₅₃×#2373	C₂	semidirect
40. #126×D₅₃	C₄	semidirect
63. #16810522	C₂²	semidirect
64. #16810521	C₂²	semidirect
65. #16810520	C₂²	semidirect
66. #16810520	C₂²	semidirect
67. #16810519	C₂²	semidirect
68. #16810518	C₂²	semidirect
69. #16810518	C₂²	semidirect
91. #16810510	C₂²	semidirect
92. #16810510	C₂²	semidirect
93. #16810510	C₂²	semidirect
94. #16810509	C₂²	semidirect
95. #16810509	C₂²	semidirect
96. #16810509	C₂²	semidirect
97. #16810508	C₂²	semidirect
98. #16810508	C₂²	semidirect
99. #16810508	C₂²	semidirect
100. #16810507	C₂²	semidirect
101. #16810507	C₂²	semidirect
102. #16810507	C₂²	semidirect
103. #16810506	C₂²	semidirect
104. #16810506	C₂²	semidirect
105. #16810506	C₂²	semidirect
106. #16810505	C₂²	semidirect
107. #16810505	C₂²	semidirect
108. #16810505	C₂²	semidirect
109. #16810504	C₂²	semidirect
110. #16810504	C₂²	semidirect
111. #16810504	C₂²	semidirect
119. C₄⋊C₄×Dic₅₃	C₂²	semidirect
120. C₄⋊C₄×Dic₅₃	C₂²	semidirect
121. C₄⋊C₄×Dic₅₃	C₂²	semidirect
122. C₄⋊C₄×Dic₅₃	C₂²	semidirect
123. C₄⋊C₄×Dic₅₃	C₂²	semidirect
124. C₄⋊C₄×Dic₅₃	C₂²	semidirect
125. C₄×#11719919	C₂²	semidirect
126. C₄×#11719919	C₂²	semidirect
127. C₄×#11719919	C₂²	semidirect
128. C₄×#11719919	C₂²	semidirect
129. C₄×#11719919	C₂²	semidirect
130. C₄×#11719919	C₂²	semidirect
131. C₄×C₄⋊Dic₅₃	C₂²	semidirect
132. C₄×C₄⋊Dic₅₃	C₂²	semidirect
133. C₄×C₄⋊Dic₅₃	C₂²	semidirect
134. #16810474	C₂²	semidirect
135. #16810474	C₂²	semidirect
136. #16810474	C₂²	semidirect
137. #16810474	C₂²	semidirect
138. #16810474	C₂²	semidirect
139. #16810474	C₂²	semidirect
154. #16810469	C₂²	semidirect
155. #16810469	C₂²	semidirect
156. #16810469	C₂²	semidirect
157. #16810468	C₂²	semidirect
158. #16810468	C₂²	semidirect
159. #16810468	C₂²	semidirect
160. #16810468	C₂²	semidirect
174. C₅₃×#389	C₂²	semidirect
178. C₅₃×#387	C₂²	semidirect
179. C₅₃×#387	C₂²	semidirect
180. C₅₃×#387	C₂²	semidirect
182. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
183. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
184. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
187. C₅₃×#376	C₂²	semidirect
209. #13133212	C₂×C₄	semidirect
210. #13133212	C₂×C₄	semidirect
211. #13133212	C₂×C₄	semidirect
212. #13133211	C₂×C₄	semidirect
213. #13133210	C₂×C₄	semidirect
214. #13133210	C₂×C₄	semidirect
215. #13133210	C₂×C₄	semidirect
245. C₄⋊C₄×D₅₃	C₂×C₄	semidirect
246. C₄⋊C₄×D₅₃	C₂×C₄	semidirect
247. C₄⋊C₄×D₅₃	C₂×C₄	semidirect
303. C₄²×D₅₃	C₂×C₄	semidirect
341. #126×C₅₃	C₂×C₄	semidirect
474. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
475. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
476. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
490. C₄²×C₅₃	C₂²×C₄	semidirect
514. C₄⋊Dic₅₃	C₂²×C₄	semidirect
515. C₄⋊Dic₅₃	C₂²×C₄	semidirect
516. C₄⋊Dic₅₃	C₂²×C₄	semidirect
527. #11719919	C₂²×C₄	semidirect
528. #11719919	C₂²×C₄	semidirect
529. #11719919	C₂²×C₄	semidirect
530. #11719919	C₂²×C₄	semidirect
531. #11719919	C₂²×C₄	semidirect
532. #11719919	C₂²×C₄	semidirect
554. C₄×Dic₅₃	C₂²×C₄	semidirect
555. C₄×Dic₅₃	C₂²×C₄	semidirect
556. C₄×Dic₅₃	C₂²×C₄	semidirect
762. #2373	D₅₃	direct (N × H)
786. D₅₃	#2373	direct (N × H)
826. #389	C₂×D₅₃	semidirect
872. #387	C₂×D₅₃	semidirect
873. #387	C₂×D₅₃	semidirect
874. #387	C₂×D₅₃	semidirect
904. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
905. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
906. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
930. #376	C₂×D₅₃	semidirect
943. C₅₃	C₂×#2373	semidirect
973. #126	C₄×D₅₃	semidirect
1254. C₄⋊C₄	C₂×C₄×D₅₃	semidirect
1255. C₄⋊C₄	C₂×C₄×D₅₃	semidirect
1256. C₄⋊C₄	C₂×C₄×D₅₃	semidirect
1312. C₄²	C₂×C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#126×D₅₃	2
#20277842	2
#20277841	2
#20277840	2
#20277839	2
#20277838	2
#20277837	2
#20277836	2
#20277835	2
#20277834	2
#20277833	2
#20277832	2
#20277831	2
#20277830	2
#20277829	2
#20277828	2
#389×D₅₃	2
#388×D₅₃	2
#387×D₅₃	2
#385×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
C₄×C₂²⋊C₄×D₅₃	2
#376×D₅₃	2
C₅₃×#2373	2
C₂×#2373	53

Subgroups — D53×#2373 #27543772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2373 #27543772