Subgroups — C₄×#16811298 #27543966

Order 13568.

2732 conjugacy classes of subgroups.

The subgroup lattice has 1560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811298	C₂	1	1	yes	maximal, characteristic
2	#20277843	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277842	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277839	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277822	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277797	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277792	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277714	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277700	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277693	C₂	1	1	yes	maximal, characteristic
11	#20277654	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277648	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277572	C₂	1	1	yes	maximal, characteristic, complemented
14	#20277570	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277563	C₂	1	1	yes	maximal, characteristic, complemented
16	#20277559	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#13133210	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#13133203	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13133197	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13133195	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13133202	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13133202	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#13133199	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#13133187	C₂	1	1	yes	maximal, characteristic
25	C₄²×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×#13133179	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×#13133174	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#13133175	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#126×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
33	#16811298	C₄	1	16	yes	direct product factor
34	C₂×#13133210	C₂²	1	1	yes	characteristic
35	C₂×#13133203	C₂²	1	1	yes	characteristic
36	C₂×#13133202	C₂²	1	1	yes	characteristic
37	C₂×#13133202	C₂²	1	1	yes	characteristic
38	C₂×#13133199	C₂²	1	1	yes	characteristic
39	C₂×#13133197	C₂²	1	1	yes	characteristic
40	C₂×#13133195	C₂²	1	1	yes	characteristic
41	C₂×#13133187	C₂²	1	1	yes	characteristic
42	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
47	C₂×#13133179	C₂²	1	1	yes	characteristic
48	C₂×#13133179	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
50	C₂×#13133175	C₂²	1	1	yes	characteristic
51	C₂×#13133175	C₂²	1	1	yes	characteristic
52	C₂×#13133174	C₂²	1	1	yes	characteristic
53	C₂×#13133174	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×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, complemented
63	#16810528	C₂²	1	1	yes	characteristic, complemented
64	#16810527	C₂²	1	1	yes	characteristic, complemented
65	#16810527	C₂²	1	1	yes	characteristic, complemented
66	#16810523	C₂²	1	1	yes	characteristic
67	#16810522	C₂²	1	1	yes	characteristic, complemented
68	#16810518	C₂²	1	1	yes	characteristic, complemented
69	#16810517	C₂²	1	1	yes	characteristic
70	#16810517	C₂²	1	1	yes	characteristic
71	#16810516	C₂²	1	1	yes	characteristic
72	#16810516	C₂²	1	1	yes	characteristic
73	#16810516	C₂²	1	1	yes	characteristic
74	#16810515	C₂²	1	1	yes	characteristic, complemented
75	#16810513	C₂²	1	1	yes	characteristic, complemented
76	#16810513	C₂²	1	1	yes	characteristic, complemented
77	#16810512	C₂²	1	1	yes	characteristic, complemented
78	#16810512	C₂²	1	1	yes	characteristic, complemented
79	#16810512	C₂²	1	1	yes	characteristic, complemented
80	#16810511	C₂²	1	1	yes	characteristic
81	#16810511	C₂²	1	1	yes	characteristic
82	#16810510	C₂²	1	1	yes	characteristic, complemented
83	#16810510	C₂²	1	1	yes	characteristic, complemented
84	#16810510	C₂²	1	1	yes	characteristic, complemented
85	#16810509	C₂²	1	1	yes	characteristic, complemented
86	#16810509	C₂²	1	1	yes	characteristic, complemented
87	#16810509	C₂²	1	1	yes	characteristic, complemented
88	#16810508	C₂²	1	1	yes	characteristic, complemented
89	#16810508	C₂²	1	1	yes	characteristic, complemented
90	#16810508	C₂²	1	1	yes	characteristic, complemented
91	#16810506	C₂²	1	1	yes	characteristic, complemented
92	#16810505	C₂²	1	1	yes	characteristic, complemented
93	#16810505	C₂²	1	1	yes	characteristic, complemented
94	#16810505	C₂²	1	1	yes	characteristic, complemented
95	#16810501	C₂²	1	1	yes	characteristic
96	#16810501	C₂²	1	1	yes	characteristic
97	#16810501	C₂²	1	1	yes	characteristic
98	#16810501	C₂²	1	1	yes	characteristic
99	#16810500	C₂²	1	1	yes	characteristic
100	#16810499	C₂²	1	1	yes	characteristic
101	#16810498	C₂²	1	1	yes	characteristic
102	#16810497	C₂²	1	1	yes	characteristic
103	#16810497	C₂²	1	1	yes	characteristic
104	#16810497	C₂²	1	1	yes	characteristic
105	#16810497	C₂²	1	1	yes	characteristic
106	#16810497	C₂²	1	1	yes	characteristic
107	#16810497	C₂²	1	1	yes	characteristic, complemented
108	#16810494	C₂²	1	1	yes	characteristic
109	#16810494	C₂²	1	1	yes	characteristic
110	#16810494	C₂²	1	1	yes	characteristic
111	#16810490	C₂²	1	1	yes	characteristic, complemented
112	#16810487	C₂²	1	1	yes	characteristic, complemented
113	#16810485	C₂²	1	1	yes	characteristic
114	#16810485	C₂²	1	1	yes	characteristic
115	#16810485	C₂²	1	1	yes	characteristic, complemented
116	#16810482	C₂²	1	1	yes	characteristic
117	#16810480	C₂²	1	1	yes	characteristic
118	#16810478	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×#11719919	C₂²	1	1	yes	characteristic, complemented
124	C₄×#11719919	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×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
133	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
134	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
135	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
136	C₄×#11719921	C₂²	1	1	yes	characteristic
137	C₄×#11719921	C₂²	1	1	yes	characteristic
138	C₄×#11719921	C₂²	1	1	yes	characteristic
139	C₄×#11719921	C₂²	1	1	yes	characteristic
140	C₄×#11719921	C₂²	1	1	yes	characteristic
141	C₄×#11719921	C₂²	1	1	yes	characteristic
142	C₄×#11719921	C₂²	1	1	yes	characteristic
143	C₄×#11719921	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, complemented
147	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
148	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
149	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
150	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
152	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
153	#16810470	C₂²	1	1	yes	characteristic
154	#16810470	C₂²	1	1	yes	characteristic
155	#16810470	C₂²	1	1	yes	characteristic
156	#16810470	C₂²	1	1	yes	characteristic
157	#16810470	C₂²	1	1	yes	characteristic
158	#16810470	C₂²	1	1	yes	characteristic
159	#16810470	C₂²	1	1	yes	characteristic
160	#16810470	C₂²	1	1	yes	characteristic
161	#16810470	C₂²	1	1	yes	characteristic, complemented
162	#16810470	C₂²	1	1	yes	characteristic, complemented
163	#16810469	C₂²	1	1	yes	characteristic, complemented
164	#16810469	C₂²	1	1	yes	characteristic, complemented
165	#16810468	C₂²	1	1	yes	characteristic, complemented
166	#16810468	C₂²	1	1	yes	characteristic, complemented
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	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
173	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
174	C₅₃×#388	C₂²	1	1	yes	characteristic
175	C₅₃×#388	C₂²	1	1	yes	characteristic
176	C₅₃×#388	C₂²	1	1	yes	characteristic
177	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
181	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₄³×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
191	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
192	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
193	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₅₃	—	2	4	no	—
195	C₂²×C₄×D₅₃	—	2	4	no	—
196	C₂²×C₄×D₅₃	—	4	2	no	—
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	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	#13133210	C₂×C₄	1	8	yes	complemented
213	#13133203	C₂×C₄	1	8	yes	complemented
214	#13133202	C₂×C₄	1	8	yes	complemented
215	#13133202	C₂×C₄	1	8	yes	complemented
216	#13133199	C₂×C₄	1	8	yes	complemented
217	#13133197	C₂×C₄	1	8	yes	complemented
218	#13133195	C₂×C₄	1	8	yes	complemented
219	#13133187	C₂×C₄	1	8	yes	—
220	C₄×Dic₁₀₆	—	4	2	no	—
221	C₄×D₂₁₂	—	2	4	no	—
222	C₄×D₂₁₂	—	2	4	no	—
223	C₄×D₂₁₂	—	2	4	no	—
224	C₄×D₂₁₂	C₂×C₄	1	8	yes	complemented
225	#13133179	—	2	4	no	—
226	#13133179	C₂×C₄	1	8	yes	complemented
227	C₄×C₂²⋊D₅₃	—	4	2	no	—
228	#13133175	—	2	4	no	—
229	#13133175	C₂×C₄	1	8	yes	complemented
230	#13133174	—	2	4	no	—
231	#13133174	C₂×C₄	1	8	yes	complemented
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×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	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×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×#11719921	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	C₂×#11719921	C₂³	1	1	yes	characteristic
267	C₂×#11719921	C₂³	1	1	yes	characteristic
268	C₂×#11719921	C₂³	1	1	yes	characteristic
269	C₂×#11719921	C₂³	1	1	yes	characteristic
270	C₂×#11719921	C₂³	1	1	yes	characteristic
271	C₂×#11719921	C₂³	1	1	yes	characteristic
272	C₂×#11719921	C₂³	1	1	yes	characteristic
273	C₂×#11719921	C₂³	1	1	yes	characteristic
274	C₂×#11719921	C₂³	1	1	yes	characteristic
275	C₂×#11719921	C₂³	1	1	yes	characteristic
276	C₂²⋊C₄×D₅₃	—	2	4	no	—
277	C₂²⋊C₄×D₅₃	—	2	4	no	—
278	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
279	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
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	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
303	C₄²×D₅₃	—	2	4	no	—
304	C₄²×D₅₃	—	2	4	no	—
305	C₄²×D₅₃	—	4	2	no	—
306	C₄²×D₅₃	—	4	2	no	—
307	C₄²×D₅₃	—	4	2	no	—
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊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×C₄²×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₄²×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	—	4	1	no	—
382	C₂³×D₅₃	—	4	1	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	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	—	2	2	no	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	2	no	—
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×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₂²⋊D₅₃	—	4	1	no	—
405	C₂×C₂²⋊D₅₃	—	4	1	no	—
406	C₂×C₂²⋊D₅₃	C₂²×C₄	1	4	yes	—
407	C₂²×Dic₅₃	—	2	2	no	—
408	C₂²×Dic₅₃	—	2	2	no	—
409	C₂²×Dic₅₃	—	4	1	no	—
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	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂×D₂₁₂	—	2	2	no	—
424	C₂×D₂₁₂	—	2	2	no	—
425	C₂×D₂₁₂	—	2	2	no	—
426	C₂×D₂₁₂	—	2	2	no	—
427	C₂×D₂₁₂	C₂²×C₄	1	4	yes	—
428	C₂×D₂₁₂	C₂²×C₄	1	4	yes	—
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	—	4	16	no	—
455	C₂×C₄×D₅₃	—	4	1	no	—
456	C₂×C₄×D₅₃	—	4	1	no	—
457	C₂×C₄×D₅₃	—	4	1	no	—
458	C₂×C₄×D₅₃	—	4	1	no	—
459	C₂×C₄×D₅₃	—	4	1	no	—
460	C₂×C₄×D₅₃	—	4	1	no	—
461	C₂×C₄×D₅₃	—	4	1	no	—
462	C₂×C₄×D₅₃	—	4	1	no	—
463	C₂×C₄×D₅₃	—	4	1	no	—
464	C₂×C₄×D₅₃	—	4	1	no	—
465	C₂×C₄×D₅₃	—	4	1	no	—
466	C₂×C₄×D₅₃	—	4	1	no	—
467	C₂×C₄×D₅₃	—	4	1	no	—
468	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
469	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
470	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
471	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
472	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	complemented
473	C₂×C₄×D₅₃	#41	1	4	yes	—
474	C₂×C₄×D₅₃	#41	1	4	yes	—
475	C₂×Dic₁₀₆	—	4	1	no	—
476	C₂×Dic₁₀₆	—	4	1	no	—
477	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	complemented
478	C₄⋊C₄×C₅₃	—	2	2	no	—
479	C₄⋊C₄×C₅₃	—	2	2	no	—
480	C₄⋊C₄×C₅₃	—	4	1	no	—
481	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
482	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
483	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
484	C₂²⋊C₄×C₅₃	—	2	2	no	—
485	C₂²⋊C₄×C₅₃	—	2	2	no	—
486	C₂²⋊C₄×C₅₃	—	4	1	no	—
487	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
488	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
489	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
490	C₄²×C₅₃	—	2	2	no	—
491	C₄²×C₅₃	—	2	2	no	—
492	C₄²×C₅₃	—	2	2	no	—
493	C₄²×C₅₃	—	2	2	no	—
494	C₄²×C₅₃	—	2	2	no	—
495	C₄²×C₅₃	—	2	2	no	—
496	C₄²×C₅₃	—	2	2	no	—
497	C₄²×C₅₃	—	2	2	no	—
498	C₄²×C₅₃	—	4	1	no	—
499	C₄²×C₅₃	C₂²×C₄	1	4	yes	complemented
500	C₂²⋊Dic₅₃	—	2	2	no	—
501	C₂²⋊Dic₅₃	—	2	2	no	—
502	C₂²⋊Dic₅₃	—	4	1	no	—
503	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
504	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
505	#11719921	—	2	2	no	—
506	#11719921	—	2	2	no	—
507	#11719921	—	2	2	no	—
508	#11719921	—	2	2	no	—
509	#11719921	—	2	2	no	—
510	#11719921	—	2	2	no	—
511	#11719921	—	2	2	no	—
512	#11719921	—	2	2	no	—
513	#11719921	—	2	2	no	—
514	#11719921	—	2	2	no	—
515	#11719921	—	4	1	no	—
516	#11719921	—	4	1	no	—
517	#11719921	C₂²×C₄	1	4	yes	—
518	#11719921	C₂²×C₄	1	4	yes	—
519	#11719921	C₂²×C₄	1	4	yes	—
520	#11719921	C₂²×C₄	1	4	yes	—
521	#11719921	C₂²×C₄	1	4	yes	—
522	#11719921	C₂²×C₄	1	4	yes	—
523	#11719921	C₂²×C₄	1	4	yes	complemented
524	#11719921	C₂²×C₄	1	4	yes	complemented
525	#11719921	C₂²×C₄	1	4	yes	complemented
526	#11719921	#41	1	4	yes	—
527	#11719921	#41	1	4	yes	—
528	C₄⋊Dic₅₃	—	2	2	no	—
529	C₄⋊Dic₅₃	—	2	2	no	—
530	C₄⋊Dic₅₃	—	2	2	no	—
531	C₄⋊Dic₅₃	—	2	2	no	—
532	C₄⋊Dic₅₃	—	4	1	no	—
533	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	complemented
534	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	complemented
535	#11719919	—	2	2	no	—
536	#11719919	—	2	2	no	—
537	#11719919	—	4	1	no	—
538	#11719919	—	4	1	no	—
539	#11719919	—	4	1	no	—
540	#11719919	—	4	1	no	—
541	#11719919	C₂²×C₄	1	4	yes	complemented
542	#11719919	C₂²×C₄	1	4	yes	complemented
543	#11719919	C₂²×C₄	1	4	yes	complemented
544	C₄×Dic₅₃	—	2	2	no	—
545	C₄×Dic₅₃	—	2	2	no	—
546	C₄×Dic₅₃	—	2	2	no	—
547	C₄×Dic₅₃	—	2	2	no	—
548	C₄×Dic₅₃	—	2	2	no	—
549	C₄×Dic₅₃	—	2	2	no	—
550	C₄×Dic₅₃	—	2	2	no	—
551	C₄×Dic₅₃	—	2	2	no	—
552	C₄×Dic₅₃	—	2	2	no	—
553	C₄×Dic₅₃	—	2	2	no	—
554	C₄×Dic₅₃	—	2	2	no	—
555	C₄×Dic₅₃	—	2	2	no	—
556	C₄×Dic₅₃	—	2	2	no	—
557	C₄×Dic₅₃	—	4	1	no	—
558	C₄×Dic₅₃	—	4	1	no	—
559	C₄×Dic₅₃	—	4	1	no	—
560	C₄×Dic₅₃	—	4	1	no	—
561	C₄×Dic₅₃	—	4	1	no	—
562	C₄×Dic₅₃	—	4	1	no	—
563	C₄×Dic₅₃	—	4	1	no	—
564	C₄×Dic₅₃	—	4	1	no	—
565	C₄×Dic₅₃	C₂²×C₄	1	4	yes	complemented
566	C₄×Dic₅₃	C₂²×C₄	1	4	yes	complemented
567	C₂³×C₅₃	—	2	1	no	—
568	C₂³×C₅₃	—	2	1	no	—
569	C₂³×C₅₃	—	2	1	no	—
570	C₂³×C₅₃	—	2	1	no	—
571	C₂³×C₅₃	—	2	1	no	—
572	C₂³×C₅₃	—	2	1	no	—
573	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
574	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
575	C₂²×D₅₃	—	2	1	no	—
576	C₂²×D₅₃	—	2	1	no	—
577	C₂²×D₅₃	—	2	1	no	—
578	C₂²×D₅₃	—	2	1	no	—
579	C₂²×D₅₃	—	2	1	no	—
580	C₂²×D₅₃	—	2	1	no	—
581	C₂²×D₅₃	—	2	1	no	—
582	C₂²×D₅₃	—	2	1	no	—
583	C₂²×D₅₃	—	2	1	no	—
584	C₂²×D₅₃	—	2	1	no	—
585	C₂²×D₅₃	—	2	1	no	—
586	C₂²×D₅₃	—	2	1	no	—
587	C₂²×D₅₃	—	2	1	no	—
588	C₂²×D₅₃	—	2	1	no	—
589	C₂²×D₅₃	—	2	8	no	—
590	C₂²×D₅₃	—	2	8	no	—
591	C₂²×D₅₃	—	4	4	no	—
592	C₂²×D₅₃	—	4	4	no	—
593	C₂²×D₅₃	—	4	4	no	—
594	C₂²×D₅₃	—	4	4	no	—
595	C₂²×D₅₃	—	4	4	no	—
596	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
597	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
598	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
599	C₂²×D₅₃	C₂×#41	1	2	yes	—
600	C₂²×D₅₃	C₂×#41	1	2	yes	—
601	C₂²×D₅₃	C₂×#41	1	2	yes	—
602	C₂²×D₅₃	C₂×#41	1	2	yes	—
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	—	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	—	4	4	no	—
635	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
636	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
637	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
638	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
639	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
640	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
641	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
642	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
643	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
644	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
645	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
646	C₂²⋊D₅₃	—	4	4	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	—	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	—	4	4	no	—
678	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
679	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
680	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
681	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
682	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
683	C₂×Dic₅₃	C₂×#41	1	2	yes	—
684	C₂×Dic₅₃	C₂×#41	1	2	yes	—
685	C₂×Dic₅₃	C₂×#41	1	2	yes	—
686	C₂×Dic₅₃	C₂×#41	1	2	yes	—
687	D₂₁₂	—	2	8	no	—
688	D₂₁₂	—	2	8	no	—
689	C₄×D₅₃	—	2	8	no	—
690	C₄×D₅₃	—	2	8	no	—
691	C₄×D₅₃	—	2	8	no	—
692	C₄×D₅₃	—	2	8	no	—
693	C₄×D₅₃	—	4	4	no	—
694	C₄×D₅₃	—	4	4	no	—
695	C₄×D₅₃	—	4	4	no	—
696	C₄×D₅₃	—	4	4	no	—
697	C₄×D₅₃	—	4	4	no	—
698	C₄×D₅₃	—	4	4	no	—
699	C₄×D₅₃	—	4	4	no	—
700	C₄×D₅₃	—	4	4	no	—
701	C₄×D₅₃	—	4	4	no	—
702	C₄×D₅₃	—	4	4	no	—
703	C₄×D₅₃	—	4	4	no	—
704	Dic₁₀₆	—	4	4	no	—
705	C₄×#551	—	53	1	no	maximal, Sylow
706	C₂²×C₅₃	—	2	2	no	—
707	C₂²×C₅₃	—	2	2	no	—
708	C₂²×C₅₃	—	2	2	no	—
709	C₂²×C₅₃	—	4	1	no	—
710	C₂²×C₅₃	—	4	1	no	—
711	C₂²×C₅₃	—	4	1	no	—
712	C₂²×C₅₃	—	4	1	no	—
713	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
714	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
715	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
716	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
717	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
718	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
719	C₂²×C₅₃	#585	1	1	yes	characteristic
720	C₂×D₅₃	—	2	2	no	—
721	C₂×D₅₃	—	2	2	no	—
722	C₂×D₅₃	—	2	2	no	—
723	C₂×D₅₃	—	2	2	no	—
724	C₂×D₅₃	—	2	2	no	—
725	C₂×D₅₃	—	2	2	no	—
726	C₂×D₅₃	—	2	2	no	—
727	C₂×D₅₃	—	2	2	no	—
728	C₂×D₅₃	—	2	2	no	—
729	C₂×D₅₃	—	2	2	no	—
730	C₂×D₅₃	—	2	2	no	—
731	C₂×D₅₃	—	2	2	no	—
732	C₂×D₅₃	—	2	2	no	—
733	C₂×D₅₃	—	2	2	no	—
734	C₂×D₅₃	—	2	2	no	—
735	C₂×D₅₃	—	4	16	no	—
736	C₂×D₅₃	—	4	1	no	—
737	C₂×D₅₃	—	4	1	no	—
738	C₂×D₅₃	—	4	1	no	—
739	C₂×D₅₃	—	4	1	no	—
740	C₂×D₅₃	C₄×#41	1	4	yes	—
741	C₂×D₅₃	C₄×#41	1	4	yes	—
742	C₄×C₅₃	—	2	2	no	—
743	C₄×C₅₃	—	2	2	no	—
744	C₄×C₅₃	—	2	2	no	—
745	C₄×C₅₃	—	2	2	no	—
746	C₄×C₅₃	—	2	2	no	—
747	C₄×C₅₃	—	2	2	no	—
748	C₄×C₅₃	—	2	2	no	—
749	C₄×C₅₃	—	2	2	no	—
750	C₄×C₅₃	—	4	1	no	—
751	C₄×C₅₃	—	4	1	no	—
752	C₄×C₅₃	—	4	1	no	—
753	C₄×C₅₃	—	4	1	no	—
754	C₄×C₅₃	—	4	1	no	—
755	C₄×C₅₃	#551	1	4	yes	complemented
756	Dic₅₃	—	2	2	no	—
757	Dic₅₃	—	2	2	no	—
758	Dic₅₃	—	2	2	no	—
759	Dic₅₃	—	2	2	no	—
760	Dic₅₃	—	2	2	no	—
761	Dic₅₃	—	2	2	no	—
762	Dic₅₃	—	2	2	no	—
763	Dic₅₃	—	2	2	no	—
764	Dic₅₃	—	2	2	no	—
765	Dic₅₃	—	4	1	no	—
766	Dic₅₃	—	4	1	no	—
767	Dic₅₃	—	4	1	no	—
768	Dic₅₃	—	4	1	no	—
769	C₂×#551	—	53	1	no	—
770	#2374	—	53	1	no	—
771	#2373	—	53	1	no	—
772	#2373	—	53	1	no	—
773	#2372	—	53	1	no	—
774	#2368	—	53	1	no	—
775	#2368	—	53	1	no	—
776	#2359	—	53	1	no	—
777	#2359	—	53	1	no	—
778	#2358	—	53	1	no	—
779	#2353	—	53	1	no	—
780	#2353	—	53	1	no	—
781	#2343	—	53	1	no	—
782	#2343	—	53	1	no	—
783	#2342	—	53	1	no	—
784	#2342	—	53	1	no	—
785	C₄×#126	—	53	1	no	—
786	C₄×#126	D₅₃	1	1	yes	characteristic, complemented
787	C₄×#124	—	53	1	no	—
788	C₄×C₂²⋊Q₈	—	53	1	no	—
789	C₄×C₂²⋊Q₈	—	53	1	no	—
790	C₄×#123	—	53	1	no	—
791	C₄×#123	—	53	1	no	—
792	C₄×#123	—	53	1	no	—
793	C₄×#120	—	53	1	no	—
794	C₄²×D₄	—	53	1	no	—
795	C₄²×D₄	—	53	1	no	—
796	C₄×#117	—	53	1	no	—
797	C₄×#117	—	53	1	no	—
798	C₂×C₄×C₂²⋊C₄	—	53	1	no	—
799	C₂×C₄×C₂²⋊C₄	—	53	1	no	—
800	C₂×C₅₃	—	4	2	no	—
801	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
802	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
803	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
804	C₂×C₅₃	C₂×#551	1	1	yes	characteristic
805	C₂×C₅₃	#3475	1	1	yes	characteristic
806	C₂×C₅₃	#3475	1	1	yes	characteristic
807	C₂×C₅₃	#3481	1	1	yes	characteristic
808	D₅₃	—	2	4	no	—
809	D₅₃	—	2	4	no	—
810	D₅₃	—	4	2	no	—
811	C₂⁴×C₄	—	53	1	no	—
812	#551	—	53	16	no	—
813	C₂×#126	—	53	1	no	—
814	C₂×#126	C₂×D₅₃	1	1	yes	characteristic
815	C₂×#124	—	53	1	no	—
816	C₂×#123	—	53	1	no	—
817	C₂×#123	—	53	1	no	—
818	C₂×#123	—	53	1	no	—
819	C₂×C₂²⋊Q₈	—	53	1	no	—
820	C₂×C₂²⋊Q₈	—	53	1	no	—
821	C₂×#120	—	53	1	no	—
822	C₂×C₄×Q₈	—	53	1	no	—
823	C₂×C₄×D₄	—	53	1	no	—
824	C₂×C₄×D₄	—	53	1	no	—
825	C₂×C₄×D₄	—	53	1	no	—
826	C₂×C₄×D₄	—	53	1	no	—
827	C₂×C₄×D₄	—	53	1	no	—
828	C₂×C₄×D₄	—	53	1	no	—
829	C₂×C₄×D₄	—	53	1	no	—
830	C₂×#117	—	53	1	no	—
831	C₂×#117	—	53	1	no	—
832	C₂×#117	—	53	1	no	—
833	C₂×#117	—	53	1	no	—
834	C₂²×C₂²⋊C₄	—	53	1	no	—
835	C₂²×C₂²⋊C₄	—	53	1	no	—
836	C₂²×C₂²⋊C₄	—	53	1	no	—
837	C₂²×C₂²⋊C₄	—	53	1	no	—
838	C₂²×C₄²	—	53	1	no	—
839	C₂²×C₄²	—	53	1	no	—
840	C₂²×C₄²	—	53	1	no	—
841	C₂²×C₄²	—	53	1	no	—
842	C₂²×C₄²	—	53	1	no	—
843	#391	—	53	1	no	—
844	#391	—	53	1	no	—
845	#391	—	53	1	no	—
846	#390	—	53	1	no	—
847	#389	—	53	1	no	—
848	#389	—	53	1	no	—
849	#388	—	53	1	no	—
850	#388	—	53	1	no	—
851	#388	—	53	1	no	—
852	#388	—	53	1	no	—
853	#388	—	53	1	no	—
854	#388	—	53	1	no	—
855	#388	—	53	1	no	—
856	#388	—	53	1	no	—
857	#388	—	53	1	no	—
858	#388	—	53	1	no	—
859	#388	—	53	1	no	—
860	#388	—	53	1	no	—
861	#388	—	53	1	no	—
862	#388	C₂×D₅₃	1	1	yes	characteristic
863	#388	C₂×D₅₃	1	1	yes	characteristic
864	#388	C₂×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
873	#387	—	53	1	no	—
874	#387	—	53	1	no	—
875	#387	—	53	1	no	—
876	#387	—	53	1	no	—
877	#387	—	53	1	no	—
878	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
879	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
880	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
881	#386	—	53	1	no	—
882	#386	—	53	1	no	—
883	#386	—	53	1	no	—
884	#386	—	53	1	no	—
885	#386	—	53	1	no	—
886	#386	—	53	1	no	—
887	#385	—	53	1	no	—
888	#385	—	53	1	no	—
889	#385	—	53	1	no	—
890	#385	—	53	1	no	—
891	#385	—	53	1	no	—
892	#385	—	53	1	no	—
893	#385	—	53	1	no	—
894	#385	—	53	1	no	—
895	#385	—	53	1	no	—
896	#385	—	53	1	no	—
897	#383	—	53	1	no	—
898	#383	C₂×D₅₃	1	1	yes	characteristic, complemented
899	#382	—	53	1	no	—
900	#381	—	53	1	no	—
901	#381	—	53	1	no	—
902	#381	—	53	1	no	—
903	#380	—	53	1	no	—
904	#380	—	53	1	no	—
905	#379	—	53	1	no	—
906	C₄×C₄⋊C₄	—	53	1	no	—
907	C₄×C₄⋊C₄	—	53	1	no	—
908	C₄×C₄⋊C₄	—	53	1	no	—
909	C₄×C₄⋊C₄	—	53	1	no	—
910	C₄×C₄⋊C₄	—	53	1	no	—
911	C₄×C₄⋊C₄	—	53	1	no	—
912	C₄×C₄⋊C₄	—	53	1	no	—
913	C₄×C₄⋊C₄	—	53	1	no	—
914	C₄×C₄⋊C₄	—	53	1	no	—
915	C₄×C₄⋊C₄	—	53	1	no	—
916	C₄×C₄⋊C₄	—	53	1	no	—
917	C₄×C₄⋊C₄	—	53	1	no	—
918	C₄×C₄⋊C₄	—	53	1	no	—
919	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
920	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
921	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
922	C₄×C₂²⋊C₄	—	53	1	no	—
923	C₄×C₂²⋊C₄	—	53	1	no	—
924	C₄×C₂²⋊C₄	—	53	1	no	—
925	C₄×C₂²⋊C₄	—	53	1	no	—
926	C₄×C₂²⋊C₄	—	53	1	no	—
927	C₄×C₂²⋊C₄	—	53	1	no	—
928	C₄×C₂²⋊C₄	—	53	1	no	—
929	C₄×C₂²⋊C₄	—	53	1	no	—
930	C₄×C₂²⋊C₄	—	53	1	no	—
931	C₄×C₂²⋊C₄	—	53	1	no	—
932	C₄×C₂²⋊C₄	—	53	1	no	—
933	C₄×C₂²⋊C₄	—	53	1	no	—
934	C₄×C₂²⋊C₄	—	53	1	no	—
935	C₄×C₂²⋊C₄	—	53	1	no	—
936	C₄×C₂²⋊C₄	—	53	1	no	—
937	C₄×C₂²⋊C₄	—	53	1	no	—
938	C₄×C₂²⋊C₄	—	53	1	no	—
939	C₄×C₂²⋊C₄	—	53	1	no	—
940	C₄×C₂²⋊C₄	—	53	1	no	—
941	C₄×C₂²⋊C₄	—	53	1	no	—
942	C₄×C₂²⋊C₄	—	53	1	no	—
943	C₄×C₂²⋊C₄	—	53	1	no	—
944	C₄×C₂²⋊C₄	—	53	1	no	—
945	C₄×C₂²⋊C₄	—	53	1	no	—
946	C₄×C₂²⋊C₄	—	53	1	no	—
947	C₄×C₂²⋊C₄	—	53	1	no	—
948	C₄×C₂²⋊C₄	—	53	1	no	—
949	C₄×C₂²⋊C₄	—	53	1	no	—
950	C₄×C₂²⋊C₄	—	53	1	no	—
951	C₄×C₂²⋊C₄	—	53	1	no	—
952	C₄×C₂²⋊C₄	—	53	1	no	—
953	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
954	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
955	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
956	#376	—	53	1	no	—
957	#376	—	53	1	no	—
958	#376	—	53	1	no	—
959	#376	—	53	1	no	—
960	C₂×#95	—	53	1	no	—
961	C₂×#95	—	53	1	no	—
962	C₂×#95	—	53	1	no	—
963	C₂×#95	—	53	1	no	—
964	C₄³	—	53	1	no	—
965	C₄³	—	53	1	no	—
966	C₄³	C₂×D₅₃	1	1	yes	characteristic, complemented
967	C₅₃	C₄×#551	1	1	yes	characteristic, complemented, Sylow
968	C₂⁵	—	53	1	no	—
969	C₂²×Q₈	—	53	1	no	—
970	C₂²×D₄	—	53	1	no	—
971	C₂²×D₄	—	53	1	no	—
972	C₂²×D₄	—	53	1	no	—
973	C₂³×C₄	—	53	1	no	—
974	C₂³×C₄	—	53	1	no	—
975	C₂³×C₄	—	53	1	no	—
976	C₂³×C₄	—	53	1	no	—
977	C₂³×C₄	—	53	1	no	—
978	C₂³×C₄	—	53	1	no	—
979	C₂³×C₄	—	53	1	no	—
980	C₂³×C₄	—	53	1	no	—
981	C₂³×C₄	—	53	1	no	—
982	C₂³×C₄	—	53	1	no	—
983	C₂³×C₄	—	53	1	no	—
984	C₂³×C₄	—	53	1	no	—
985	C₂³×C₄	—	53	1	no	—
986	C₂³×C₄	—	53	1	no	—
987	C₂³×C₄	—	53	1	no	—
988	C₂³×C₄	—	53	1	no	—
989	C₂³×C₄	—	106	4	no	—
990	C₂³×C₄	—	106	4	no	—
991	C₂³×C₄	—	212	2	no	—
992	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
993	#126	—	53	8	no	—
994	#126	C₄×D₅₃	1	8	yes	complemented
995	#124	—	53	8	no	—
996	#123	—	53	8	no	—
997	#123	—	53	8	no	—
998	#123	—	53	8	no	—
999	C₂²⋊Q₈	—	53	8	no	—
1000	C₂²⋊Q₈	—	53	8	no	—
1001	#120	—	53	8	no	—
1002	C₄×Q₈	—	212	2	no	—
1003	C₄×D₄	—	53	8	no	—
1004	C₄×D₄	—	53	8	no	—
1005	C₄×D₄	—	106	4	no	—
1006	C₄×D₄	—	106	4	no	—
1007	C₄×D₄	—	106	4	no	—
1008	C₄×D₄	—	106	4	no	—
1009	C₄×D₄	—	212	2	no	—
1010	#117	—	53	8	no	—
1011	#117	—	53	8	no	—
1012	#117	—	106	4	no	—
1013	#117	—	106	4	no	—
1014	C₂×C₄⋊C₄	—	53	1	no	—
1015	C₂×C₄⋊C₄	—	53	1	no	—
1016	C₂×C₄⋊C₄	—	53	1	no	—
1017	C₂×C₄⋊C₄	—	53	1	no	—
1018	C₂×C₄⋊C₄	—	53	1	no	—
1019	C₂×C₄⋊C₄	—	53	1	no	—
1020	C₂×C₄⋊C₄	—	53	1	no	—
1021	C₂×C₄⋊C₄	—	53	1	no	—
1022	C₂×C₄⋊C₄	—	53	1	no	—
1023	C₂×C₄⋊C₄	—	53	1	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	1	no	—
1028	C₂×C₄⋊C₄	—	53	1	no	—
1029	C₂×C₄⋊C₄	—	53	1	no	—
1030	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1031	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1032	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1033	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1034	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1035	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	—	53	1	no	—
1037	C₂×C₂²⋊C₄	—	53	1	no	—
1038	C₂×C₂²⋊C₄	—	53	1	no	—
1039	C₂×C₂²⋊C₄	—	53	1	no	—
1040	C₂×C₂²⋊C₄	—	53	1	no	—
1041	C₂×C₂²⋊C₄	—	53	1	no	—
1042	C₂×C₂²⋊C₄	—	53	1	no	—
1043	C₂×C₂²⋊C₄	—	53	1	no	—
1044	C₂×C₂²⋊C₄	—	53	1	no	—
1045	C₂×C₂²⋊C₄	—	53	1	no	—
1046	C₂×C₂²⋊C₄	—	53	1	no	—
1047	C₂×C₂²⋊C₄	—	53	1	no	—
1048	C₂×C₂²⋊C₄	—	53	1	no	—
1049	C₂×C₂²⋊C₄	—	53	8	no	—
1050	C₂×C₂²⋊C₄	—	53	8	no	—
1051	C₂×C₂²⋊C₄	—	53	1	no	—
1052	C₂×C₂²⋊C₄	—	53	1	no	—
1053	C₂×C₂²⋊C₄	—	53	1	no	—
1054	C₂×C₂²⋊C₄	—	53	1	no	—
1055	C₂×C₂²⋊C₄	—	53	1	no	—
1056	C₂×C₂²⋊C₄	—	53	1	no	—
1057	C₂×C₂²⋊C₄	—	53	1	no	—
1058	C₂×C₂²⋊C₄	—	53	1	no	—
1059	C₂×C₂²⋊C₄	—	53	1	no	—
1060	C₂×C₂²⋊C₄	—	53	1	no	—
1061	C₂×C₂²⋊C₄	—	53	1	no	—
1062	C₂×C₂²⋊C₄	—	53	1	no	—
1063	C₂×C₂²⋊C₄	—	53	1	no	—
1064	C₂×C₂²⋊C₄	—	53	1	no	—
1065	C₂×C₂²⋊C₄	—	53	1	no	—
1066	C₂×C₂²⋊C₄	—	106	4	no	—
1067	C₂×C₂²⋊C₄	—	106	4	no	—
1068	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1069	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1070	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1071	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1072	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1073	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1074	C₂×C₄²	—	53	1	no	—
1075	C₂×C₄²	—	53	1	no	—
1076	C₂×C₄²	—	53	1	no	—
1077	C₂×C₄²	—	53	1	no	—
1078	C₂×C₄²	—	53	1	no	—
1079	C₂×C₄²	—	53	1	no	—
1080	C₂×C₄²	—	53	1	no	—
1081	C₂×C₄²	—	53	1	no	—
1082	C₂×C₄²	—	53	1	no	—
1083	C₂×C₄²	—	53	1	no	—
1084	C₂×C₄²	—	53	1	no	—
1085	C₂×C₄²	—	53	1	no	—
1086	C₂×C₄²	—	53	1	no	—
1087	C₂×C₄²	—	53	1	no	—
1088	C₂×C₄²	—	53	1	no	—
1089	C₂×C₄²	—	53	1	no	—
1090	C₂×C₄²	—	53	1	no	—
1091	C₂×C₄²	—	53	1	no	—
1092	C₂×C₄²	—	53	1	no	—
1093	C₂×C₄²	—	53	1	no	—
1094	C₂×C₄²	—	53	1	no	—
1095	C₂×C₄²	—	53	1	no	—
1096	C₂×C₄²	—	53	1	no	—
1097	C₂×C₄²	—	106	4	no	—
1098	C₂×C₄²	—	106	4	no	—
1099	C₂×C₄²	—	212	2	no	—
1100	C₂×C₄²	—	212	2	no	—
1101	C₂×C₄²	—	212	2	no	—
1102	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1103	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1104	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1105	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1106	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1107	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1108	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1109	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1110	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1111	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1121	#95	—	53	1	no	—
1122	#95	—	53	1	no	—
1123	#95	—	53	1	no	—
1124	#95	—	53	1	no	—
1125	#95	—	53	1	no	—
1126	#95	—	53	1	no	—
1127	#95	—	53	1	no	—
1128	#95	—	53	1	no	—
1129	#95	—	53	1	no	—
1130	#95	—	53	1	no	—
1131	#95	—	53	1	no	—
1132	#95	—	53	1	no	—
1133	#95	—	53	1	no	—
1134	#95	—	53	1	no	—
1135	#95	—	53	1	no	—
1136	#95	—	53	1	no	—
1137	#95	—	53	1	no	—
1138	#95	—	53	1	no	—
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	C₂²×D₅₃	1	1	yes	characteristic
1145	#95	C₂²×D₅₃	1	1	yes	characteristic
1146	#95	C₂²×D₅₃	1	1	yes	characteristic
1147	#95	C₂²×D₅₃	1	1	yes	characteristic
1148	#95	C₂²×D₅₃	1	1	yes	characteristic
1149	#95	C₂²×D₅₃	1	1	yes	characteristic
1150	#95	C₂²×D₅₃	1	1	yes	characteristic
1151	#95	C₂²×D₅₃	1	1	yes	characteristic
1152	#95	C₂²×D₅₃	1	1	yes	characteristic
1153	#95	C₂²×D₅₃	1	1	yes	characteristic
1154	#95	C₂²×D₅₃	1	1	yes	characteristic
1155	#95	C₂²×D₅₃	1	1	yes	characteristic
1156	C₂⁴	—	53	1	no	—
1157	C₂⁴	—	53	1	no	—
1158	C₂⁴	—	53	1	no	—
1159	C₂⁴	—	53	4	no	—
1160	C₂⁴	—	106	2	no	—
1161	C₂⁴	—	106	2	no	—
1162	C₂⁴	—	106	2	no	—
1163	C₂⁴	—	106	2	no	—
1164	C₂⁴	—	212	1	no	—
1165	C₂⁴	—	212	1	no	—
1166	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1167	C₂×Q₈	—	53	4	no	—
1168	C₂×Q₈	—	212	1	no	—
1169	C₂×Q₈	—	212	1	no	—
1170	C₂×D₄	—	53	4	no	—
1171	C₂×D₄	—	53	4	no	—
1172	C₂×D₄	—	53	4	no	—
1173	C₂×D₄	—	106	2	no	—
1174	C₂×D₄	—	106	2	no	—
1175	C₂×D₄	—	106	2	no	—
1176	C₂×D₄	—	106	2	no	—
1177	C₂×D₄	—	212	1	no	—
1178	C₂×D₄	—	212	1	no	—
1179	C₂²×C₄	—	2	2	no	—
1180	C₂²×C₄	—	2	2	no	—
1181	C₂²×C₄	—	2	2	no	—
1182	C₂²×C₄	—	53	1	no	—
1183	C₂²×C₄	—	53	1	no	—
1184	C₂²×C₄	—	53	1	no	—
1185	C₂²×C₄	—	53	1	no	—
1186	C₂²×C₄	—	53	1	no	—
1187	C₂²×C₄	—	53	1	no	—
1188	C₂²×C₄	—	53	1	no	—
1189	C₂²×C₄	—	53	1	no	—
1190	C₂²×C₄	—	53	1	no	—
1191	C₂²×C₄	—	53	4	no	—
1192	C₂²×C₄	—	53	4	no	—
1193	C₂²×C₄	—	53	4	no	—
1194	C₂²×C₄	—	53	4	no	—
1195	C₂²×C₄	—	53	4	no	—
1196	C₂²×C₄	—	53	4	no	—
1197	C₂²×C₄	—	53	4	no	—
1198	C₂²×C₄	—	53	1	no	—
1199	C₂²×C₄	—	53	1	no	—
1200	C₂²×C₄	—	53	1	no	—
1201	C₂²×C₄	—	53	1	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	—	106	2	no	—
1208	C₂²×C₄	—	106	2	no	—
1209	C₂²×C₄	—	106	2	no	—
1210	C₂²×C₄	—	106	2	no	—
1211	C₂²×C₄	—	106	2	no	—
1212	C₂²×C₄	—	106	2	no	—
1213	C₂²×C₄	—	106	2	no	—
1214	C₂²×C₄	—	106	2	no	—
1215	C₂²×C₄	—	106	2	no	—
1216	C₂²×C₄	—	106	2	no	—
1217	C₂²×C₄	—	106	2	no	—
1218	C₂²×C₄	—	106	2	no	—
1219	C₂²×C₄	—	106	2	no	—
1220	C₂²×C₄	—	106	2	no	—
1221	C₂²×C₄	—	106	2	no	—
1222	C₂²×C₄	—	106	2	no	—
1223	C₂²×C₄	—	106	2	no	—
1224	C₂²×C₄	—	106	2	no	—
1225	C₂²×C₄	—	106	2	no	—
1226	C₂²×C₄	—	106	2	no	—
1227	C₂²×C₄	—	106	2	no	—
1228	C₂²×C₄	—	106	2	no	—
1229	C₂²×C₄	—	212	1	no	—
1230	C₂²×C₄	—	212	1	no	—
1231	C₂²×C₄	—	212	1	no	—
1232	C₂²×C₄	—	212	1	no	—
1233	C₂²×C₄	—	212	1	no	—
1234	C₂²×C₄	—	212	1	no	—
1235	C₂²×C₄	—	212	1	no	—
1236	C₂²×C₄	—	212	1	no	—
1237	C₂²×C₄	—	212	1	no	—
1238	C₂²×C₄	—	212	1	no	—
1239	C₂²×C₄	—	212	1	no	—
1240	C₂²×C₄	—	212	1	no	—
1241	C₂²×C₄	—	212	1	no	—
1242	C₂²×C₄	—	212	16	no	—
1243	C₂²×C₄	—	212	1	no	—
1244	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1245	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1246	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1247	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1248	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1249	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1250	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1251	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1252	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1253	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1254	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1255	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1256	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1257	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1258	C₄⋊C₄	—	2	2	no	—
1259	C₄⋊C₄	—	2	2	no	—
1260	C₄⋊C₄	—	4	1	no	—
1261	C₄⋊C₄	—	53	4	no	—
1262	C₄⋊C₄	—	53	4	no	—
1263	C₄⋊C₄	—	53	4	no	—
1264	C₄⋊C₄	—	53	4	no	—
1265	C₄⋊C₄	—	53	4	no	—
1266	C₄⋊C₄	—	106	2	no	—
1267	C₄⋊C₄	—	106	2	no	—
1268	C₄⋊C₄	—	106	2	no	—
1269	C₄⋊C₄	—	106	2	no	—
1270	C₄⋊C₄	—	106	2	no	—
1271	C₄⋊C₄	—	106	2	no	—
1272	C₄⋊C₄	—	212	1	no	—
1273	C₄⋊C₄	—	212	1	no	—
1274	C₄⋊C₄	—	212	1	no	—
1275	C₄⋊C₄	—	212	1	no	—
1276	C₄⋊C₄	—	212	1	no	—
1277	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1278	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1279	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	complemented
1280	C₂²⋊C₄	—	2	2	no	—
1281	C₂²⋊C₄	—	2	2	no	—
1282	C₂²⋊C₄	—	4	1	no	—
1283	C₂²⋊C₄	—	53	4	no	—
1284	C₂²⋊C₄	—	53	4	no	—
1285	C₂²⋊C₄	—	53	4	no	—
1286	C₂²⋊C₄	—	53	4	no	—
1287	C₂²⋊C₄	—	53	4	no	—
1288	C₂²⋊C₄	—	53	4	no	—
1289	C₂²⋊C₄	—	53	4	no	—
1290	C₂²⋊C₄	—	53	4	no	—
1291	C₂²⋊C₄	—	53	4	no	—
1292	C₂²⋊C₄	—	53	4	no	—
1293	C₂²⋊C₄	—	53	4	no	—
1294	C₂²⋊C₄	—	53	4	no	—
1295	C₂²⋊C₄	—	53	4	no	—
1296	C₂²⋊C₄	—	106	2	no	—
1297	C₂²⋊C₄	—	106	2	no	—
1298	C₂²⋊C₄	—	106	2	no	—
1299	C₂²⋊C₄	—	106	2	no	—
1300	C₂²⋊C₄	—	106	2	no	—
1301	C₂²⋊C₄	—	106	2	no	—
1302	C₂²⋊C₄	—	106	2	no	—
1303	C₂²⋊C₄	—	106	2	no	—
1304	C₂²⋊C₄	—	106	2	no	—
1305	C₂²⋊C₄	—	106	2	no	—
1306	C₂²⋊C₄	—	106	2	no	—
1307	C₂²⋊C₄	—	106	2	no	—
1308	C₂²⋊C₄	—	212	1	no	—
1309	C₂²⋊C₄	—	212	1	no	—
1310	C₂²⋊C₄	—	212	1	no	—
1311	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1312	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1313	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1314	C₄²	—	2	2	no	—
1315	C₄²	—	2	2	no	—
1316	C₄²	—	2	2	no	—
1317	C₄²	—	2	2	no	—
1318	C₄²	—	2	2	no	—
1319	C₄²	—	2	2	no	—
1320	C₄²	—	2	2	no	—
1321	C₄²	—	2	2	no	—
1322	C₄²	—	4	1	no	—
1323	C₄²	—	53	4	no	—
1324	C₄²	—	53	4	no	—
1325	C₄²	—	106	2	no	—
1326	C₄²	—	106	2	no	—
1327	C₄²	—	106	2	no	—
1328	C₄²	—	106	2	no	—
1329	C₄²	—	106	2	no	—
1330	C₄²	—	106	2	no	—
1331	C₄²	—	106	2	no	—
1332	C₄²	—	106	2	no	—
1333	C₄²	—	106	2	no	—
1334	C₄²	—	106	2	no	—
1335	C₄²	—	106	2	no	—
1336	C₄²	—	106	2	no	—
1337	C₄²	—	106	2	no	—
1338	C₄²	—	212	1	no	—
1339	C₄²	—	212	1	no	—
1340	C₄²	—	212	1	no	—
1341	C₄²	—	212	1	no	—
1342	C₄²	—	212	1	no	—
1343	C₄²	—	212	1	no	—
1344	C₄²	—	212	1	no	—
1345	C₄²	—	212	1	no	—
1346	C₄²	C₂×C₄×D₅₃	1	4	yes	complemented
1347	C₂³	—	2	1	no	—
1348	C₂³	—	2	1	no	—
1349	C₂³	—	2	1	no	—
1350	C₂³	—	2	1	no	—
1351	C₂³	—	2	1	no	—
1352	C₂³	—	2	1	no	—
1353	C₂³	—	53	2	no	—
1354	C₂³	—	53	2	no	—
1355	C₂³	—	53	2	no	—
1356	C₂³	—	53	2	no	—
1357	C₂³	—	53	2	no	—
1358	C₂³	—	53	2	no	—
1359	C₂³	—	53	2	no	—
1360	C₂³	—	106	8	no	—
1361	C₂³	—	106	8	no	—
1362	C₂³	—	106	1	no	—
1363	C₂³	—	106	1	no	—
1364	C₂³	—	106	1	no	—
1365	C₂³	—	106	1	no	—
1366	C₂³	—	106	1	no	—
1367	C₂³	—	106	1	no	—
1368	C₂³	—	106	1	no	—
1369	C₂³	—	106	1	no	—
1370	C₂³	—	106	1	no	—
1371	C₂³	—	106	1	no	—
1372	C₂³	—	106	1	no	—
1373	C₂³	—	106	1	no	—
1374	C₂³	—	106	1	no	—
1375	C₂³	—	106	1	no	—
1376	C₂³	—	212	4	no	—
1377	C₂³	—	212	4	no	—
1378	C₂³	—	212	4	no	—
1379	C₂³	—	212	4	no	—
1380	C₂³	—	212	4	no	—
1381	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1382	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1383	Q₈	—	212	4	no	—
1384	D₄	—	106	8	no	—
1385	D₄	—	106	8	no	—
1386	D₄	—	212	4	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	2	1	no	—
1409	C₂×C₄	—	2	1	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	—	4	4	no	—
1419	C₂×C₄	—	53	2	no	—
1420	C₂×C₄	—	53	2	no	—
1421	C₂×C₄	—	53	2	no	—
1422	C₂×C₄	—	53	2	no	—
1423	C₂×C₄	—	53	2	no	—
1424	C₂×C₄	—	53	2	no	—
1425	C₂×C₄	—	53	2	no	—
1426	C₂×C₄	—	53	2	no	—
1427	C₂×C₄	—	53	2	no	—
1428	C₂×C₄	—	106	8	no	—
1429	C₂×C₄	—	106	8	no	—
1430	C₂×C₄	—	106	1	no	—
1431	C₂×C₄	—	106	1	no	—
1432	C₂×C₄	—	106	1	no	—
1433	C₂×C₄	—	106	1	no	—
1434	C₂×C₄	—	106	1	no	—
1435	C₂×C₄	—	106	1	no	—
1436	C₂×C₄	—	106	1	no	—
1437	C₂×C₄	—	106	1	no	—
1438	C₂×C₄	—	106	1	no	—
1439	C₂×C₄	—	106	1	no	—
1440	C₂×C₄	—	106	1	no	—
1441	C₂×C₄	—	106	1	no	—
1442	C₂×C₄	—	106	1	no	—
1443	C₂×C₄	—	106	1	no	—
1444	C₂×C₄	—	106	1	no	—
1445	C₂×C₄	—	106	1	no	—
1446	C₂×C₄	—	106	1	no	—
1447	C₂×C₄	—	106	1	no	—
1448	C₂×C₄	—	106	8	no	—
1449	C₂×C₄	—	106	8	no	—
1450	C₂×C₄	—	106	1	no	—
1451	C₂×C₄	—	106	1	no	—
1452	C₂×C₄	—	106	1	no	—
1453	C₂×C₄	—	106	1	no	—
1454	C₂×C₄	—	106	1	no	—
1455	C₂×C₄	—	106	1	no	—
1456	C₂×C₄	—	106	1	no	—
1457	C₂×C₄	—	106	1	no	—
1458	C₂×C₄	—	106	1	no	—
1459	C₂×C₄	—	106	1	no	—
1460	C₂×C₄	—	106	1	no	—
1461	C₂×C₄	—	106	1	no	—
1462	C₂×C₄	—	212	4	no	—
1463	C₂×C₄	—	212	4	no	—
1464	C₂×C₄	—	212	4	no	—
1465	C₂×C₄	—	212	4	no	—
1466	C₂×C₄	—	212	4	no	—
1467	C₂×C₄	—	212	4	no	—
1468	C₂×C₄	—	212	4	no	—
1469	C₂×C₄	—	212	4	no	—
1470	C₂×C₄	—	212	4	no	—
1471	C₂×C₄	—	212	4	no	—
1472	C₂×C₄	—	212	4	no	—
1473	C₂×C₄	—	212	4	no	—
1474	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1475	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1476	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1477	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1478	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1479	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1480	C₂×C₄	#41×D₅₃	1	2	yes	—
1481	C₂×C₄	#41×D₅₃	1	2	yes	—
1482	C₂×C₄	#41×D₅₃	1	2	yes	—
1483	C₂×C₄	#41×D₅₃	1	2	yes	—
1484	C₂×C₄	#13133263	1	2	yes	—
1485	C₂²	—	2	2	no	—
1486	C₂²	—	2	2	no	—
1487	C₂²	—	2	2	no	—
1488	C₂²	—	4	1	no	—
1489	C₂²	—	4	1	no	—
1490	C₂²	—	4	1	no	—
1491	C₂²	—	4	1	no	—
1492	C₂²	—	53	4	no	—
1493	C₂²	—	53	4	no	—
1494	C₂²	—	106	2	no	—
1495	C₂²	—	106	2	no	—
1496	C₂²	—	106	2	no	—
1497	C₂²	—	106	2	no	—
1498	C₂²	—	106	2	no	—
1499	C₂²	—	106	2	no	—
1500	C₂²	—	106	2	no	—
1501	C₂²	—	106	2	no	—
1502	C₂²	—	106	2	no	—
1503	C₂²	—	106	2	no	—
1504	C₂²	—	106	2	no	—
1505	C₂²	—	106	2	no	—
1506	C₂²	—	106	2	no	—
1507	C₂²	—	106	2	no	—
1508	C₂²	—	106	2	no	—
1509	C₂²	—	212	16	no	—
1510	C₂²	—	212	1	no	—
1511	C₂²	—	212	1	no	—
1512	C₂²	—	212	1	no	—
1513	C₂²	—	212	1	no	—
1514	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1515	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1516	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1517	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1518	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1519	C₂²	C₂×#13133263	1	1	yes	characteristic
1520	C₂²	#16811459	1	1	yes	characteristic
1521	C₄	—	2	2	no	—
1522	C₄	—	2	2	no	—
1523	C₄	—	2	2	no	—
1524	C₄	—	2	2	no	—
1525	C₄	—	2	2	no	—
1526	C₄	—	2	2	no	—
1527	C₄	—	2	2	no	—
1528	C₄	—	2	2	no	—
1529	C₄	—	4	1	no	—
1530	C₄	—	4	1	no	—
1531	C₄	—	4	1	no	—
1532	C₄	—	4	1	no	—
1533	C₄	—	4	1	no	—
1534	C₄	—	106	2	no	—
1535	C₄	—	106	2	no	—
1536	C₄	—	106	2	no	—
1537	C₄	—	106	2	no	—
1538	C₄	—	106	2	no	—
1539	C₄	—	106	2	no	—
1540	C₄	—	106	2	no	—
1541	C₄	—	106	2	no	—
1542	C₄	—	106	2	no	—
1543	C₄	—	212	1	no	—
1544	C₄	—	212	1	no	—
1545	C₄	—	212	1	no	—
1546	C₄	—	212	1	no	—
1547	C₄	#16811298	1	4	yes	direct product factor
1548	C₂	—	4	2	no	—
1549	C₂	—	106	4	no	—
1550	C₂	—	106	4	no	—
1551	C₂	—	212	2	no	—
1552	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1553	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1554	C₂	C₄×#13133263	1	1	yes	characteristic
1555	C₂	C₂×#16811298	1	1	yes	characteristic
1556	C₂	#20288267	1	1	yes	characteristic
1557	C₂	#20288271	1	1	yes	characteristic
1558	C₂	#20288321	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₅₃
Fitting	C₄×#126×C₅₃	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂×#13133187	C₂²
hypercenter	C₄×#126	D₅₃
hypocenter	C₅₃	C₄×#551
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#126

Complements

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

N	H ≅ G/N	type
2. #20277843	C₂	semidirect
3. #20277842	C₂	semidirect
4. #20277839	C₂	semidirect
5. #20277822	C₂	semidirect
6. #20277797	C₂	semidirect
7. #20277792	C₂	semidirect
8. #20277714	C₂	semidirect
9. #20277700	C₂	semidirect
11. #20277654	C₂	semidirect
12. #20277648	C₂	semidirect
13. #20277572	C₂	semidirect
14. #20277570	C₂	semidirect
15. #20277563	C₂	semidirect
16. #20277559	C₂	semidirect
17. C₄×#13133210	C₂	semidirect
18. C₄×#13133203	C₂	semidirect
19. C₄×#13133197	C₂	semidirect
20. C₄×#13133195	C₂	semidirect
21. C₄×#13133202	C₂	semidirect
22. C₄×#13133202	C₂	semidirect
23. C₄×#13133199	C₂	semidirect
25. C₄²×D₂₁₂	C₂	semidirect
26. C₄×#13133179	C₂	semidirect
27. C₄×#13133174	C₂	semidirect
28. C₄×#13133175	C₂	semidirect
29. C₄×C₂²⋊C₄×D₅₃	C₂	semidirect
30. C₄×C₂²⋊C₄×D₅₃	C₂	semidirect
31. C₄×#126×C₅₃	C₂	semidirect
33. #16811298	C₄	direct (N × H)
42. C₂×C₄×Dic₁₀₆	C₂²	semidirect
62. C₂×C₄²×D₅₃	C₂²	semidirect
63. #16810528	C₂²	semidirect
64. #16810527	C₂²	semidirect
65. #16810527	C₂²	semidirect
67. #16810522	C₂²	semidirect
68. #16810518	C₂²	semidirect
74. #16810515	C₂²	semidirect
75. #16810513	C₂²	semidirect
76. #16810513	C₂²	semidirect
77. #16810512	C₂²	semidirect
78. #16810512	C₂²	semidirect
79. #16810512	C₂²	semidirect
82. #16810510	C₂²	semidirect
83. #16810510	C₂²	semidirect
84. #16810510	C₂²	semidirect
85. #16810509	C₂²	semidirect
86. #16810509	C₂²	semidirect
87. #16810509	C₂²	semidirect
88. #16810508	C₂²	semidirect
89. #16810508	C₂²	semidirect
90. #16810508	C₂²	semidirect
91. #16810506	C₂²	semidirect
92. #16810505	C₂²	semidirect
93. #16810505	C₂²	semidirect
94. #16810505	C₂²	semidirect
107. #16810497	C₂²	semidirect
111. #16810490	C₂²	semidirect
112. #16810487	C₂²	semidirect
115. #16810485	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×#11719919	C₂²	semidirect
124. C₄×#11719919	C₂²	semidirect
125. C₄×#11719919	C₂²	semidirect
126. C₄×#11719919	C₂²	semidirect
127. C₄×#11719919	C₂²	semidirect
128. C₄×C₄⋊Dic₅₃	C₂²	semidirect
129. C₄×C₄⋊Dic₅₃	C₂²	semidirect
130. C₄×C₄⋊Dic₅₃	C₂²	semidirect
131. C₄×C₄⋊Dic₅₃	C₂²	semidirect
146. C₄×#11719921	C₂²	semidirect
147. C₄×#11719921	C₂²	semidirect
148. C₄×#11719921	C₂²	semidirect
149. C₄×#11719921	C₂²	semidirect
150. C₄×#11719921	C₂²	semidirect
161. #16810470	C₂²	semidirect
162. #16810470	C₂²	semidirect
163. #16810469	C₂²	semidirect
164. #16810469	C₂²	semidirect
165. #16810468	C₂²	semidirect
166. #16810468	C₂²	semidirect
171. C₄²×Dic₅₃	C₂²	semidirect
172. C₄²×Dic₅₃	C₂²	semidirect
177. C₅₃×#387	C₂²	semidirect
178. C₅₃×#387	C₂²	semidirect
179. C₅₃×#387	C₂²	semidirect
180. C₅₃×#383	C₂²	semidirect
181. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
182. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
183. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
187. C₄³×C₅₃	C₂²	semidirect
212. #13133210	C₂×C₄	semidirect
213. #13133203	C₂×C₄	semidirect
214. #13133202	C₂×C₄	semidirect
215. #13133202	C₂×C₄	semidirect
216. #13133199	C₂×C₄	semidirect
217. #13133197	C₂×C₄	semidirect
218. #13133195	C₂×C₄	semidirect
224. C₄×D₂₁₂	C₂×C₄	semidirect
226. #13133179	C₂×C₄	semidirect
229. #13133175	C₂×C₄	semidirect
231. #13133174	C₂×C₄	semidirect
278. C₂²⋊C₄×D₅₃	C₂×C₄	semidirect
279. C₂²⋊C₄×D₅₃	C₂×C₄	semidirect
341. #126×C₅₃	C₂×C₄	semidirect
472. C₂×C₄×D₅₃	C₂²×C₄	semidirect
477. C₂×Dic₁₀₆	C₂²×C₄	semidirect
481. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
482. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
483. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
499. C₄²×C₅₃	C₂²×C₄	semidirect
523. #11719921	C₂²×C₄	semidirect
524. #11719921	C₂²×C₄	semidirect
525. #11719921	C₂²×C₄	semidirect
533. C₄⋊Dic₅₃	C₂²×C₄	semidirect
534. C₄⋊Dic₅₃	C₂²×C₄	semidirect
541. #11719919	C₂²×C₄	semidirect
542. #11719919	C₂²×C₄	semidirect
543. #11719919	C₂²×C₄	semidirect
565. C₄×Dic₅₃	C₂²×C₄	semidirect
566. C₄×Dic₅₃	C₂²×C₄	semidirect
755. C₄×C₅₃	#551	semidirect
786. C₄×#126	D₅₃	semidirect
878. #387	C₂×D₅₃	semidirect
879. #387	C₂×D₅₃	semidirect
880. #387	C₂×D₅₃	semidirect
898. #383	C₂×D₅₃	semidirect
919. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
920. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
921. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
966. C₄³	C₂×D₅₃	semidirect
967. C₅₃	C₄×#551	semidirect
994. #126	C₄×D₅₃	semidirect
1277. C₄⋊C₄	C₂×C₄×D₅₃	semidirect
1278. C₄⋊C₄	C₂×C₄×D₅₃	semidirect
1279. C₄⋊C₄	C₂×C₄×D₅₃	semidirect
1346. C₄²	C₂×C₄×D₅₃	semidirect
1547. C₄	#16811298	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16811298	2
#20277843	2
#20277842	2
#20277839	2
#20277822	2
#20277797	2
#20277792	2
#20277714	2
#20277700	2
#20277693	2
#20277654	2
#20277648	2
#20277572	2
#20277570	2
#20277563	2
#20277559	2
C₄×#13133210	2
C₄×#13133203	2
C₄×#13133197	2
C₄×#13133195	2
C₄×#13133202	2
C₄×#13133199	2
C₄×#13133187	2
C₄²×D₂₁₂	2
C₄×#13133179	2
C₄×#13133174	2
C₄×#13133175	2
C₄×C₂²⋊C₄×D₅₃	2
C₄×#126×C₅₃	2
C₄×#551	53

Subgroups — C4×#16811298 #27543966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16811298 #27543966