Subgroups — D₅₃×#2438 #27552730

Order 13568.

3006 conjugacy classes of subgroups.

The subgroup lattice has 1600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#117×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20278398	C₂	1	1	yes	maximal, characteristic, complemented
4	#20278397	C₂	1	1	yes	maximal, characteristic, complemented
5	#20278396	C₂	1	1	yes	maximal, characteristic, complemented
6	#20278395	C₂	1	1	yes	maximal, characteristic, complemented
7	#20278394	C₂	1	1	yes	maximal, characteristic, complemented
8	#20278393	C₂	1	1	yes	maximal, characteristic, complemented
9	#20278392	C₂	1	1	yes	maximal, characteristic, complemented
10	#20278391	C₂	1	1	yes	maximal, characteristic, complemented
11	#20278390	C₂	1	1	yes	maximal, characteristic, complemented
12	#20278389	C₂	1	1	yes	maximal, characteristic, complemented
13	#20278388	C₂	1	1	yes	maximal, characteristic, complemented
14	#20278387	C₂	1	1	yes	maximal, characteristic, complemented
15	#20278386	C₂	1	1	yes	maximal, characteristic, complemented
16	#20278385	C₂	1	1	yes	maximal, characteristic, complemented
17	#20278384	C₂	1	1	yes	maximal, characteristic, complemented
18	#400×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#398×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#398×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#395×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#391×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#389×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
26	#385×D₅₃	C₂	1	1	yes	maximal, characteristic
27	#385×D₅₃	C₂	1	1	yes	maximal, characteristic
28	#381×D₅₃	C₂	1	1	yes	maximal, characteristic
29	#380×D₅₃	C₂	1	1	yes	maximal, characteristic
30	C₂×#95×D₅₃	C₂	1	1	yes	maximal, characteristic
31	C₅₃×#2438	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
34	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
35	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
36	C₂×#13133197	C₂²	1	1	yes	characteristic
37	C₂×#13133196	C₂²	1	1	yes	characteristic
38	C₂×#13133195	C₂²	1	1	yes	characteristic
39	C₂×#13133195	C₂²	1	1	yes	characteristic
40	C₂×#13133194	C₂²	1	1	yes	characteristic
41	C₂×#13133194	C₂²	1	1	yes	characteristic
42	C₂×#13133193	C₂²	1	1	yes	characteristic
43	C₂²⋊Q₈×D₅₃	—	2	8	no	—
44	C₂×#13133176	C₂²	1	1	yes	characteristic
45	C₂×#13133175	C₂²	1	1	yes	characteristic
46	C₂×#13133175	C₂²	1	1	yes	characteristic
47	C₂×#13133174	C₂²	1	1	yes	characteristic
48	C₂×#13133174	C₂²	1	1	yes	characteristic
49	C₂×#13133173	C₂²	1	1	yes	characteristic
50	C₂×#13133173	C₂²	1	1	yes	characteristic
51	#117×D₅₃	—	2	8	no	—
52	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
60	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
68	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
69	#16810565	C₂²	1	1	yes	characteristic, complemented
70	#16810565	C₂²	1	1	yes	characteristic, complemented
71	#16810564	C₂²	1	1	yes	characteristic, complemented
72	#16810564	C₂²	1	1	yes	characteristic, complemented
73	#16810563	C₂²	1	1	yes	characteristic, complemented
74	#16810562	C₂²	1	1	yes	characteristic, complemented
75	#16810561	C₂²	1	1	yes	characteristic, complemented
76	#16810557	C₂²	1	1	yes	characteristic, complemented
77	#16810557	C₂²	1	1	yes	characteristic, complemented
78	#16810557	C₂²	1	1	yes	characteristic, complemented
79	#16810557	C₂²	1	1	yes	characteristic, complemented
80	#16810556	C₂²	1	1	yes	characteristic, complemented
81	#16810556	C₂²	1	1	yes	characteristic, complemented
82	#16810556	C₂²	1	1	yes	characteristic, complemented
83	#16810556	C₂²	1	1	yes	characteristic, complemented
84	#16810555	C₂²	1	1	yes	characteristic, complemented
85	#16810555	C₂²	1	1	yes	characteristic, complemented
86	#16810554	C₂²	1	1	yes	characteristic, complemented
87	#16810554	C₂²	1	1	yes	characteristic, complemented
88	#16810553	C₂²	1	1	yes	characteristic, complemented
89	#16810553	C₂²	1	1	yes	characteristic, complemented
90	#16810544	C₂²	1	1	yes	characteristic, complemented
91	#16810544	C₂²	1	1	yes	characteristic, complemented
92	#16810544	C₂²	1	1	yes	characteristic, complemented
93	#16810543	C₂²	1	1	yes	characteristic, complemented
94	#16810543	C₂²	1	1	yes	characteristic, complemented
95	#16810543	C₂²	1	1	yes	characteristic, complemented
96	#16810542	C₂²	1	1	yes	characteristic, complemented
97	#16810530	C₂²	1	1	yes	characteristic, complemented
98	#16810529	C₂²	1	1	yes	characteristic, complemented
99	#16810528	C₂²	1	1	yes	characteristic, complemented
100	#16810527	C₂²	1	1	yes	characteristic, complemented
101	#16810527	C₂²	1	1	yes	characteristic, complemented
102	#16810527	C₂²	1	1	yes	characteristic, complemented
103	#16810527	C₂²	1	1	yes	characteristic, complemented
104	#16810522	C₂²	1	1	yes	characteristic, complemented
105	#16810521	C₂²	1	1	yes	characteristic, complemented
106	#16810520	C₂²	1	1	yes	characteristic, complemented
107	#16810520	C₂²	1	1	yes	characteristic, complemented
108	#16810519	C₂²	1	1	yes	characteristic, complemented
109	#16810518	C₂²	1	1	yes	characteristic, complemented
110	#16810518	C₂²	1	1	yes	characteristic, complemented
111	#16810510	C₂²	1	1	yes	characteristic, complemented
112	#16810510	C₂²	1	1	yes	characteristic, complemented
113	#16810509	C₂²	1	1	yes	characteristic, complemented
114	#16810509	C₂²	1	1	yes	characteristic, complemented
115	#16810508	C₂²	1	1	yes	characteristic, complemented
116	#16810508	C₂²	1	1	yes	characteristic, complemented
117	#16810507	C₂²	1	1	yes	characteristic, complemented
118	#16810507	C₂²	1	1	yes	characteristic, complemented
119	#16810506	C₂²	1	1	yes	characteristic, complemented
120	#16810506	C₂²	1	1	yes	characteristic, complemented
121	#16810505	C₂²	1	1	yes	characteristic, complemented
122	#16810505	C₂²	1	1	yes	characteristic, complemented
123	#16810504	C₂²	1	1	yes	characteristic, complemented
124	#16810504	C₂²	1	1	yes	characteristic, complemented
125	#16810498	C₂²	1	1	yes	characteristic
126	#16810498	C₂²	1	1	yes	characteristic
127	#16810497	C₂²	1	1	yes	characteristic
128	#16810497	C₂²	1	1	yes	characteristic
129	#16810497	C₂²	1	1	yes	characteristic
130	#16810497	C₂²	1	1	yes	characteristic
131	#16810496	C₂²	1	1	yes	characteristic
132	#16810496	C₂²	1	1	yes	characteristic
133	#16810495	C₂²	1	1	yes	characteristic
134	#16810495	C₂²	1	1	yes	characteristic
135	#16810494	C₂²	1	1	yes	characteristic
136	#16810494	C₂²	1	1	yes	characteristic
137	#16810494	C₂²	1	1	yes	characteristic
138	#16810494	C₂²	1	1	yes	characteristic
139	#16810486	C₂²	1	1	yes	characteristic
140	#16810485	C₂²	1	1	yes	characteristic
141	#16810485	C₂²	1	1	yes	characteristic
142	#16810485	C₂²	1	1	yes	characteristic
143	#16810485	C₂²	1	1	yes	characteristic
144	#16810484	C₂²	1	1	yes	characteristic
145	#16810484	C₂²	1	1	yes	characteristic
146	#16810483	C₂²	1	1	yes	characteristic
147	#16810482	C₂²	1	1	yes	characteristic
148	#16810482	C₂²	1	1	yes	characteristic
149	#16810481	C₂²	1	1	yes	characteristic
150	#16810481	C₂²	1	1	yes	characteristic
151	#16810480	C₂²	1	1	yes	characteristic
152	#16810480	C₂²	1	1	yes	characteristic
153	C₂×#13133124	C₂²	1	1	yes	characteristic
154	C₂×#13133124	C₂²	1	1	yes	characteristic
155	C₂×#13133124	C₂²	1	1	yes	characteristic
156	#95×D₅₃	C₂²	1	1	yes	characteristic
157	#95×D₅₃	C₂²	1	1	yes	characteristic
158	#95×D₅₃	C₂²	1	1	yes	characteristic
159	#95×D₅₃	C₂²	1	1	yes	characteristic
160	#95×D₅₃	C₂²	1	1	yes	characteristic
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	#95×D₅₃	C₂²	1	1	yes	characteristic
174	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
175	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
176	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#385	C₂²	1	1	yes	characteristic
185	C₅₃×#385	C₂²	1	1	yes	characteristic
186	C₅₃×#381	C₂²	1	1	yes	characteristic
187	C₅₃×#380	C₂²	1	1	yes	characteristic
188	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
189	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
191	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
192	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
193	C₂×Q₈×D₅₃	—	2	4	no	—
194	C₂×Q₈×D₅₃	—	2	4	no	—
195	C₂×Q₈×D₅₃	—	4	2	no	—
196	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₅₃	—	2	4	no	—
200	C₂²×C₄×D₅₃	—	2	4	no	—
201	C₂²×C₄×D₅₃	—	2	4	no	—
202	C₂²×C₄×D₅₃	—	2	4	no	—
203	C₂²×C₄×D₅₃	—	2	4	no	—
204	C₂²×C₄×D₅₃	—	2	4	no	—
205	C₂²×C₄×D₅₃	—	4	2	no	—
206	C₂²×C₄×D₅₃	—	4	2	no	—
207	C₂²×C₄×D₅₃	Q₈	1	8	yes	complemented
208	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
211	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
214	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
215	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
216	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
217	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
218	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
219	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
220	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
221	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
222	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
223	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
224	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
225	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
226	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
227	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
228	#13133197	—	2	4	no	—
229	#13133196	—	2	4	no	—
230	#13133195	—	2	4	no	—
231	#13133195	—	2	4	no	—
232	#13133194	—	2	4	no	—
233	#13133194	—	2	4	no	—
234	#13133193	—	2	4	no	—
235	#13133176	—	2	4	no	—
236	#13133175	—	2	4	no	—
237	#13133175	—	2	4	no	—
238	#13133174	—	2	4	no	—
239	#13133174	—	2	4	no	—
240	#13133173	—	2	4	no	—
241	#13133173	—	2	4	no	—
242	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×#11719919	C₂³	1	1	yes	characteristic
254	C₂×#11719919	C₂³	1	1	yes	characteristic
255	C₂×#11719919	C₂³	1	1	yes	characteristic
256	C₂×#11719919	C₂³	1	1	yes	characteristic
257	C₂×#11719919	C₂³	1	1	yes	characteristic
258	C₂×#11719919	C₂³	1	1	yes	characteristic
259	C₂×#11719919	C₂³	1	1	yes	characteristic
260	C₂×#11719919	C₂³	1	1	yes	characteristic
261	C₂×#11719919	C₂³	1	1	yes	characteristic
262	C₂×#11719919	C₂³	1	1	yes	characteristic
263	C₂×#11719919	C₂³	1	1	yes	characteristic
264	C₂×#11719919	C₂³	1	1	yes	characteristic
265	C₂×#11719919	C₂³	1	1	yes	characteristic
266	C₂×#11719919	C₂³	1	1	yes	characteristic
267	C₂×#11719919	C₂³	1	1	yes	characteristic
268	C₂×#11719919	C₂³	1	1	yes	characteristic
269	C₂×#11719919	C₂³	1	1	yes	characteristic
270	C₂×#11719919	C₂³	1	1	yes	characteristic
271	C₂×#11719919	C₂³	1	1	yes	characteristic
272	C₂×#11719919	C₂³	1	1	yes	characteristic
273	C₂×#11719919	C₂³	1	1	yes	characteristic
274	C₂×#11719919	C₂³	1	1	yes	characteristic
275	C₄⋊C₄×D₅₃	—	2	4	no	—
276	C₄⋊C₄×D₅₃	—	2	4	no	—
277	C₄⋊C₄×D₅₃	—	2	4	no	—
278	C₄⋊C₄×D₅₃	—	2	4	no	—
279	C₄⋊C₄×D₅₃	—	2	4	no	—
280	C₄⋊C₄×D₅₃	—	2	4	no	—
281	C₄⋊C₄×D₅₃	—	2	4	no	—
282	C₄⋊C₄×D₅₃	—	2	4	no	—
283	C₄⋊C₄×D₅₃	—	4	2	no	—
284	C₄⋊C₄×D₅₃	—	4	2	no	—
285	C₄⋊C₄×D₅₃	—	4	2	no	—
286	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
290	C₂×#11719921	C₂³	1	1	yes	characteristic
291	C₂×#11719921	C₂³	1	1	yes	characteristic
292	C₂×#11719921	C₂³	1	1	yes	characteristic
293	C₂×#11719921	C₂³	1	1	yes	characteristic
294	C₂×#11719921	C₂³	1	1	yes	characteristic
295	C₂×#11719921	C₂³	1	1	yes	characteristic
296	C₂×#11719921	C₂³	1	1	yes	characteristic
297	C₂×#11719921	C₂³	1	1	yes	characteristic
298	C₂²⋊C₄×D₅₃	—	2	4	no	—
299	C₂²⋊C₄×D₅₃	—	2	4	no	—
300	C₂²⋊C₄×D₅₃	—	2	4	no	—
301	C₂²⋊C₄×D₅₃	D₄	1	8	yes	—
302	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
308	C₄²×D₅₃	—	2	4	no	—
309	C₄²×D₅₃	—	2	4	no	—
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	#13133124	C₂³	1	1	yes	characteristic
341	#13133124	C₂³	1	1	yes	characteristic
342	#13133124	C₂³	1	1	yes	characteristic
343	#13133124	C₂³	1	1	yes	characteristic
344	#13133124	C₂³	1	1	yes	characteristic
345	#13133124	C₂³	1	1	yes	characteristic
346	#13133124	C₂³	1	1	yes	characteristic
347	#13133124	C₂³	1	1	yes	characteristic
348	#13133124	C₂³	1	1	yes	characteristic
349	#13133124	C₂³	1	1	yes	characteristic
350	#13133124	C₂³	1	1	yes	characteristic
351	#13133124	C₂³	1	1	yes	characteristic
352	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
353	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂²⋊Q₈×C₅₃	—	2	4	no	—
357	#117×C₅₃	—	2	4	no	—
358	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
371	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
373	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
374	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	#95×C₅₃	C₂³	1	1	yes	characteristic
377	#95×C₅₃	C₂³	1	1	yes	characteristic
378	#95×C₅₃	C₂³	1	1	yes	characteristic
379	#95×C₅₃	C₂³	1	1	yes	characteristic
380	#95×C₅₃	C₂³	1	1	yes	characteristic
381	#95×C₅₃	C₂³	1	1	yes	characteristic
382	#95×C₅₃	C₂³	1	1	yes	characteristic
383	#95×C₅₃	C₂³	1	1	yes	characteristic
384	#95×C₅₃	C₂³	1	1	yes	characteristic
385	#95×C₅₃	C₂³	1	1	yes	characteristic
386	#95×C₅₃	C₂³	1	1	yes	characteristic
387	#95×C₅₃	C₂³	1	1	yes	characteristic
388	#95×C₅₃	C₂³	1	1	yes	characteristic
389	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂³×D₅₃	—	2	2	no	—
391	C₂³×D₅₃	—	2	2	no	—
392	C₂³×D₅₃	—	2	2	no	—
393	C₂³×D₅₃	—	2	2	no	—
394	C₂³×D₅₃	C₂×D₄	1	4	yes	—
395	C₂³×D₅₃	C₂×Q₈	1	4	yes	—
396	C₂³×D₅₃	#41	1	4	yes	—
397	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
398	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×Q₈×C₅₃	—	2	2	no	—
400	C₂×Q₈×C₅₃	—	2	2	no	—
401	C₂×Q₈×C₅₃	—	4	1	no	—
402	C₂²×C₄×C₅₃	—	2	2	no	—
403	C₂²×C₄×C₅₃	—	2	2	no	—
404	C₂²×C₄×C₅₃	—	2	2	no	—
405	C₂²×C₄×C₅₃	—	2	2	no	—
406	C₂²×C₄×C₅₃	—	2	2	no	—
407	C₂²×C₄×C₅₃	—	2	2	no	—
408	C₂²×C₄×C₅₃	—	4	1	no	—
409	C₂²×C₄×C₅₃	—	4	1	no	—
410	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×Dic₅₃	—	2	2	no	—
426	C₂²×Dic₅₃	—	2	2	no	—
427	C₂²×Dic₅₃	—	2	2	no	—
428	C₂²×Dic₅₃	—	2	2	no	—
429	C₂²×Dic₅₃	—	2	2	no	—
430	C₂²×Dic₅₃	—	2	2	no	—
431	C₂²×Dic₅₃	—	4	1	no	—
432	C₂²×Dic₅₃	—	4	1	no	—
433	C₂²×Dic₅₃	C₂×Q₈	1	4	yes	complemented
434	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
435	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
436	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
438	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
439	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
440	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
446	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
447	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
448	Q₈×D₅₃	—	4	16	no	—
449	C₂×C₄×D₅₃	—	2	32	no	—
450	C₂×C₄×D₅₃	—	2	2	no	—
451	C₂×C₄×D₅₃	—	2	2	no	—
452	C₂×C₄×D₅₃	—	2	2	no	—
453	C₂×C₄×D₅₃	—	2	2	no	—
454	C₂×C₄×D₅₃	—	2	2	no	—
455	C₂×C₄×D₅₃	—	2	2	no	—
456	C₂×C₄×D₅₃	—	2	2	no	—
457	C₂×C₄×D₅₃	—	2	2	no	—
458	C₂×C₄×D₅₃	—	2	2	no	—
459	C₂×C₄×D₅₃	—	2	2	no	—
460	C₂×C₄×D₅₃	—	2	2	no	—
461	C₂×C₄×D₅₃	—	2	2	no	—
462	C₂×C₄×D₅₃	—	2	2	no	—
463	C₂×C₄×D₅₃	—	2	2	no	—
464	C₂×C₄×D₅₃	—	2	2	no	—
465	C₂×C₄×D₅₃	—	2	2	no	—
466	C₂×C₄×D₅₃	—	2	2	no	—
467	C₂×C₄×D₅₃	—	2	2	no	—
468	C₂×C₄×D₅₃	—	2	2	no	—
469	C₂×C₄×D₅₃	—	2	2	no	—
470	C₂×C₄×D₅₃	—	2	2	no	—
471	C₂×C₄×D₅₃	—	2	2	no	—
472	C₂×C₄×D₅₃	—	2	2	no	—
473	C₂×C₄×D₅₃	—	2	2	no	—
474	C₂×C₄×D₅₃	—	2	2	no	—
475	C₂×C₄×D₅₃	—	2	2	no	—
476	C₂×C₄×D₅₃	—	2	2	no	—
477	C₂×C₄×D₅₃	—	2	2	no	—
478	C₂×C₄×D₅₃	—	2	2	no	—
479	C₂×C₄×D₅₃	—	2	2	no	—
480	C₂×C₄×D₅₃	—	2	2	no	—
481	C₂×C₄×D₅₃	—	2	2	no	—
482	C₂×C₄×D₅₃	—	2	2	no	—
483	C₂×C₄×D₅₃	—	2	2	no	—
484	C₂×C₄×D₅₃	—	2	2	no	—
485	C₂×C₄×D₅₃	—	2	2	no	—
486	C₂×C₄×D₅₃	—	2	2	no	—
487	C₂×C₄×D₅₃	—	2	2	no	—
488	C₂×C₄×D₅₃	—	2	2	no	—
489	C₂×C₄×D₅₃	—	2	2	no	—
490	C₂×C₄×D₅₃	—	2	2	no	—
491	C₂×C₄×D₅₃	—	2	2	no	—
492	C₂×C₄×D₅₃	—	2	2	no	—
493	C₂×C₄×D₅₃	—	2	2	no	—
494	C₂×C₄×D₅₃	—	2	2	no	—
495	C₂×C₄×D₅₃	—	2	2	no	—
496	C₂×C₄×D₅₃	—	2	2	no	—
497	C₂×C₄×D₅₃	—	2	2	no	—
498	C₂×C₄×D₅₃	—	4	16	no	—
499	C₂×C₄×D₅₃	—	4	16	no	—
500	C₂×C₄×D₅₃	—	4	1	no	—
501	C₂×C₄×D₅₃	—	4	1	no	—
502	C₂×C₄×D₅₃	—	4	1	no	—
503	C₂×C₄×D₅₃	—	4	1	no	—
504	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
505	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
506	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
507	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
508	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	complemented
509	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	complemented
510	C₂×C₄×D₅₃	#41	1	4	yes	—
511	C₂×C₄×D₅₃	#41	1	4	yes	—
512	C₂×Dic₁₀₆	—	2	2	no	—
513	C₂×Dic₁₀₆	—	2	2	no	—
514	C₂×Dic₁₀₆	—	2	2	no	—
515	C₂×Dic₁₀₆	—	2	2	no	—
516	C₂×Dic₁₀₆	—	2	2	no	—
517	C₂×Dic₁₀₆	—	2	2	no	—
518	C₂×Dic₁₀₆	—	4	1	no	—
519	C₂×Dic₁₀₆	—	4	1	no	—
520	C₂×Dic₁₀₆	—	4	1	no	—
521	C₄⋊C₄×C₅₃	—	2	2	no	—
522	C₄⋊C₄×C₅₃	—	2	2	no	—
523	C₄⋊C₄×C₅₃	—	2	2	no	—
524	C₄⋊C₄×C₅₃	—	2	2	no	—
525	C₄⋊C₄×C₅₃	—	2	2	no	—
526	C₄⋊C₄×C₅₃	—	2	2	no	—
527	C₄⋊C₄×C₅₃	—	2	2	no	—
528	C₄⋊C₄×C₅₃	—	2	2	no	—
529	C₄⋊C₄×C₅₃	—	4	1	no	—
530	C₄⋊C₄×C₅₃	—	4	1	no	—
531	C₄⋊C₄×C₅₃	—	4	1	no	—
532	C₂²⋊C₄×C₅₃	—	2	2	no	—
533	C₂²⋊C₄×C₅₃	—	2	2	no	—
534	C₂²⋊C₄×C₅₃	—	2	2	no	—
535	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
536	C₄²×C₅₃	—	2	2	no	—
537	C₄²×C₅₃	—	2	2	no	—
538	C₂²⋊Dic₅₃	—	2	2	no	—
539	C₂²⋊Dic₅₃	—	2	2	no	—
540	C₂²⋊Dic₅₃	—	2	2	no	—
541	C₂²⋊Dic₅₃	C₂×D₄	1	4	yes	—
542	#11719921	—	2	2	no	—
543	#11719921	—	2	2	no	—
544	#11719921	—	2	2	no	—
545	#11719921	—	2	2	no	—
546	#11719921	—	2	2	no	—
547	#11719921	—	2	2	no	—
548	#11719921	C₂×D₄	1	4	yes	—
549	#11719921	C₂×D₄	1	4	yes	—
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	—	2	2	no	—
558	C₄⋊Dic₅₃	—	4	1	no	—
559	C₄⋊Dic₅₃	—	4	1	no	—
560	C₄⋊Dic₅₃	—	4	1	no	—
561	#11719919	—	2	2	no	—
562	#11719919	—	2	2	no	—
563	#11719919	—	2	2	no	—
564	#11719919	—	2	2	no	—
565	#11719919	—	2	2	no	—
566	#11719919	—	2	2	no	—
567	#11719919	—	2	2	no	—
568	#11719919	—	2	2	no	—
569	#11719919	—	2	2	no	—
570	#11719919	—	2	2	no	—
571	#11719919	—	2	2	no	—
572	#11719919	—	2	2	no	—
573	#11719919	—	2	2	no	—
574	#11719919	—	2	2	no	—
575	#11719919	—	2	2	no	—
576	#11719919	—	2	2	no	—
577	#11719919	—	4	1	no	—
578	#11719919	—	4	1	no	—
579	#11719919	—	4	1	no	—
580	#11719919	—	4	1	no	—
581	#11719919	—	4	1	no	—
582	#11719919	—	4	1	no	—
583	C₄×Dic₅₃	—	2	2	no	—
584	C₄×Dic₅₃	—	2	2	no	—
585	C₄×Dic₅₃	—	2	2	no	—
586	C₄×Dic₅₃	—	2	2	no	—
587	C₄×Dic₅₃	—	2	2	no	—
588	C₄×Dic₅₃	—	2	2	no	—
589	C₂³×C₅₃	—	2	1	no	—
590	C₂³×C₅₃	—	2	1	no	—
591	C₂³×C₅₃	—	2	1	no	—
592	C₂³×C₅₃	—	2	1	no	—
593	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
594	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
595	C₂³×C₅₃	C₂×#41	1	2	yes	—
596	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
597	C₂²×D₅₃	—	2	1	no	—
598	C₂²×D₅₃	—	2	1	no	—
599	C₂²×D₅₃	—	2	1	no	—
600	C₂²×D₅₃	—	2	1	no	—
601	C₂²×D₅₃	—	2	8	no	—
602	C₂²×D₅₃	—	2	8	no	—
603	C₂²×D₅₃	—	2	8	no	—
604	C₂²×D₅₃	—	2	8	no	—
605	C₂²×D₅₃	—	2	8	no	—
606	C₂²×D₅₃	—	2	8	no	—
607	C₂²×D₅₃	C₂²⋊Q₈	1	16	yes	—
608	C₂²×D₅₃	C₂²×D₄	1	2	yes	—
609	C₂²×D₅₃	C₂²×D₄	1	2	yes	—
610	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
611	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
612	C₂²×D₅₃	C₂×#41	1	2	yes	—
613	C₂²×D₅₃	C₂×#41	1	2	yes	—
614	C₂²×D₅₃	C₂×#41	1	2	yes	—
615	C₂²×D₅₃	C₂×#41	1	2	yes	—
616	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
617	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
618	Q₈×C₅₃	—	4	4	no	—
619	C₂×C₄×C₅₃	—	2	8	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	2	1	no	—
639	C₂×C₄×C₅₃	—	2	1	no	—
640	C₂×C₄×C₅₃	—	2	1	no	—
641	C₂×C₄×C₅₃	—	2	1	no	—
642	C₂×C₄×C₅₃	—	2	1	no	—
643	C₂×C₄×C₅₃	—	2	1	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	2	1	no	—
646	C₂×C₄×C₅₃	—	2	1	no	—
647	C₂×C₄×C₅₃	—	2	1	no	—
648	C₂×C₄×C₅₃	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	2	1	no	—
652	C₂×C₄×C₅₃	—	2	1	no	—
653	C₂×C₄×C₅₃	—	2	1	no	—
654	C₂×C₄×C₅₃	—	2	1	no	—
655	C₂×C₄×C₅₃	—	2	1	no	—
656	C₂×C₄×C₅₃	—	4	4	no	—
657	C₂×C₄×C₅₃	—	4	4	no	—
658	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
659	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
660	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
661	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
662	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
663	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
664	C₂×Dic₅₃	—	2	8	no	—
665	C₂×Dic₅₃	—	2	1	no	—
666	C₂×Dic₅₃	—	2	1	no	—
667	C₂×Dic₅₃	—	2	1	no	—
668	C₂×Dic₅₃	—	2	1	no	—
669	C₂×Dic₅₃	—	2	1	no	—
670	C₂×Dic₅₃	—	2	1	no	—
671	C₂×Dic₅₃	—	2	1	no	—
672	C₂×Dic₅₃	—	2	1	no	—
673	C₂×Dic₅₃	—	2	1	no	—
674	C₂×Dic₅₃	—	2	1	no	—
675	C₂×Dic₅₃	—	2	1	no	—
676	C₂×Dic₅₃	—	2	1	no	—
677	C₂×Dic₅₃	—	2	1	no	—
678	C₂×Dic₅₃	—	2	1	no	—
679	C₂×Dic₅₃	—	2	1	no	—
680	C₂×Dic₅₃	—	2	1	no	—
681	C₂×Dic₅₃	—	2	1	no	—
682	C₂×Dic₅₃	—	2	1	no	—
683	C₂×Dic₅₃	—	2	1	no	—
684	C₂×Dic₅₃	—	2	1	no	—
685	C₂×Dic₅₃	—	2	1	no	—
686	C₂×Dic₅₃	—	2	1	no	—
687	C₂×Dic₅₃	—	2	1	no	—
688	C₂×Dic₅₃	—	2	1	no	—
689	C₂×Dic₅₃	—	2	1	no	—
690	C₂×Dic₅₃	—	2	1	no	—
691	C₂×Dic₅₃	—	2	1	no	—
692	C₂×Dic₅₃	—	2	1	no	—
693	C₂×Dic₅₃	—	2	1	no	—
694	C₂×Dic₅₃	—	2	1	no	—
695	C₂×Dic₅₃	—	2	1	no	—
696	C₂×Dic₅₃	—	2	1	no	—
697	C₂×Dic₅₃	—	2	1	no	—
698	C₂×Dic₅₃	—	2	1	no	—
699	C₂×Dic₅₃	—	2	1	no	—
700	C₂×Dic₅₃	—	2	1	no	—
701	C₂×Dic₅₃	—	4	4	no	—
702	C₂×Dic₅₃	—	4	4	no	—
703	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
704	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
705	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
706	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
707	C₂×Dic₅₃	C₂×#41	1	2	yes	—
708	C₂×Dic₅₃	C₂×#41	1	2	yes	—
709	C₄×D₅₃	—	2	8	no	—
710	C₄×D₅₃	—	2	8	no	—
711	C₄×D₅₃	—	2	8	no	—
712	C₄×D₅₃	—	2	8	no	—
713	C₄×D₅₃	—	2	8	no	—
714	C₄×D₅₃	—	2	8	no	—
715	C₄×D₅₃	—	2	8	no	—
716	C₄×D₅₃	—	2	8	no	—
717	C₄×D₅₃	—	4	4	no	—
718	C₄×D₅₃	—	4	4	no	—
719	C₄×D₅₃	—	4	4	no	—
720	C₄×D₅₃	—	4	4	no	—
721	C₄×D₅₃	—	4	4	no	—
722	C₄×D₅₃	—	4	4	no	—
723	C₄×D₅₃	—	4	4	no	—
724	C₄×D₅₃	—	4	4	no	—
725	C₄×D₅₃	—	4	4	no	—
726	C₄×D₅₃	—	4	4	no	—
727	C₄×D₅₃	—	4	4	no	—
728	C₄×D₅₃	—	4	4	no	—
729	Dic₁₀₆	—	4	4	no	—
730	Dic₁₀₆	—	4	4	no	—
731	Dic₁₀₆	—	4	4	no	—
732	C₂×#2438	—	53	1	no	maximal, Sylow
733	C₂²×C₅₃	—	2	2	no	—
734	C₂²×C₅₃	—	2	2	no	—
735	C₂²×C₅₃	—	2	2	no	—
736	C₂²×C₅₃	—	2	2	no	—
737	C₂²×C₅₃	—	2	2	no	—
738	C₂²×C₅₃	—	2	2	no	—
739	C₂²×C₅₃	C₂×C₂²⋊Q₈	1	4	yes	—
740	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
741	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
742	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
743	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
744	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
745	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
746	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
747	C₂×D₅₃	—	2	2	no	—
748	C₂×D₅₃	—	2	2	no	—
749	C₂×D₅₃	—	2	2	no	—
750	C₂×D₅₃	—	2	2	no	—
751	C₂×D₅₃	—	2	2	no	—
752	C₂×D₅₃	—	2	2	no	—
753	C₂×D₅₃	—	2	32	no	—
754	C₂×D₅₃	C₂×C₂²⋊Q₈	1	4	yes	—
755	C₂×D₅₃	C₂×C₂²⋊Q₈	1	4	yes	—
756	C₂×D₅₃	#533	1	4	yes	—
757	C₂×D₅₃	#544	1	4	yes	—
758	C₂×D₅₃	#546	1	4	yes	—
759	C₂×D₅₃	#547	1	4	yes	—
760	C₂×D₅₃	#551	1	4	yes	—
761	C₂×D₅₃	#552	1	4	yes	—
762	C₄×C₅₃	—	2	2	no	—
763	C₄×C₅₃	—	2	2	no	—
764	C₄×C₅₃	—	2	2	no	—
765	C₄×C₅₃	—	2	2	no	—
766	C₄×C₅₃	—	2	2	no	—
767	C₄×C₅₃	—	2	2	no	—
768	C₄×C₅₃	—	4	1	no	—
769	C₄×C₅₃	—	4	1	no	—
770	C₄×C₅₃	—	4	1	no	—
771	C₄×C₅₃	—	4	1	no	—
772	C₄×C₅₃	—	4	1	no	—
773	C₄×C₅₃	—	4	1	no	—
774	C₄×C₅₃	—	4	1	no	—
775	C₄×C₅₃	—	4	1	no	—
776	Dic₅₃	—	2	2	no	—
777	Dic₅₃	—	2	2	no	—
778	Dic₅₃	—	2	2	no	—
779	Dic₅₃	—	2	2	no	—
780	Dic₅₃	—	2	2	no	—
781	Dic₅₃	—	2	2	no	—
782	Dic₅₃	—	4	1	no	—
783	Dic₅₃	—	4	1	no	—
784	Dic₅₃	—	4	1	no	—
785	Dic₅₃	—	4	1	no	—
786	Dic₅₃	—	4	1	no	—
787	Dic₅₃	—	4	1	no	—
788	Dic₅₃	—	4	1	no	—
789	Dic₅₃	—	4	1	no	—
790	C₂²×C₂²⋊Q₈	—	53	1	no	—
791	C₂²×#117	—	53	1	no	—
792	#2438	—	53	1	no	—
793	#2438	—	53	1	no	—
794	#2438	—	53	1	no	—
795	#2438	—	53	1	no	—
796	#2438	—	53	1	no	—
797	#2438	—	53	1	no	—
798	#2438	—	53	1	no	—
799	#2438	—	53	1	no	—
800	#2438	—	53	1	no	—
801	#2438	—	53	1	no	—
802	#2438	—	53	1	no	—
803	#2438	—	53	1	no	—
804	#2438	—	53	1	no	—
805	#2438	—	53	1	no	—
806	#2438	—	53	1	no	—
807	#2438	D₅₃	1	1	yes	characteristic, direct product factor
808	C₂×#400	—	53	1	no	—
809	C₂×#398	—	53	1	no	—
810	C₂×#398	—	53	1	no	—
811	C₂×#395	—	53	1	no	—
812	C₂×#391	—	53	1	no	—
813	C₂×#389	—	53	1	no	—
814	C₂×#387	—	53	1	no	—
815	C₂×#387	—	53	1	no	—
816	C₂×#385	—	53	1	no	—
817	C₂×#385	—	53	1	no	—
818	C₂×#381	—	53	1	no	—
819	C₂×#380	—	53	1	no	—
820	C₂²×#95	—	53	1	no	—
821	C₂×C₅₃	—	2	4	no	—
822	C₂×C₅₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
823	C₂×C₅₃	C₂×#533	1	1	yes	characteristic
824	C₂×C₅₃	C₂×#544	1	1	yes	characteristic
825	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
826	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
827	C₂×C₅₃	C₂×#551	1	1	yes	characteristic
828	C₂×C₅₃	C₂×#552	1	1	yes	characteristic
829	D₅₃	—	2	4	no	—
830	D₅₃	#2438	1	8	yes	direct product factor
831	C₂³×Q₈	—	53	1	no	—
832	C₂⁴×C₄	—	53	1	no	—
833	C₂⁴×C₄	—	53	1	no	—
834	C₂⁴×C₄	—	53	1	no	—
835	C₂×C₂²⋊Q₈	—	53	1	no	—
836	C₂×C₂²⋊Q₈	—	53	1	no	—
837	C₂×C₂²⋊Q₈	—	53	1	no	—
838	C₂×C₂²⋊Q₈	—	53	1	no	—
839	C₂×C₂²⋊Q₈	—	53	1	no	—
840	C₂×C₂²⋊Q₈	—	53	1	no	—
841	C₂×C₂²⋊Q₈	—	53	1	no	—
842	C₂×C₂²⋊Q₈	—	106	8	no	—
843	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
844	C₂×#117	—	53	1	no	—
845	C₂×#117	—	53	1	no	—
846	C₂×#117	—	53	1	no	—
847	C₂×#117	—	53	1	no	—
848	C₂×#117	—	53	1	no	—
849	C₂×#117	—	53	1	no	—
850	C₂×#117	—	53	1	no	—
851	C₂×#117	—	106	8	no	—
852	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
853	C₂²×C₄⋊C₄	—	53	1	no	—
854	C₂²×C₄⋊C₄	—	53	1	no	—
855	C₂²×C₄⋊C₄	—	53	1	no	—
856	C₂²×C₄⋊C₄	—	53	1	no	—
857	C₂²×C₄⋊C₄	—	53	1	no	—
858	C₂²×C₄⋊C₄	—	53	1	no	—
859	C₂²×C₄⋊C₄	—	53	1	no	—
860	C₂²×C₄⋊C₄	—	53	1	no	—
861	C₂²×C₄⋊C₄	—	53	1	no	—
862	C₂²×C₄⋊C₄	—	53	1	no	—
863	C₂²×C₄⋊C₄	—	53	1	no	—
864	C₂²×C₂²⋊C₄	—	53	1	no	—
865	C₂²×C₂²⋊C₄	—	53	1	no	—
866	C₂²×C₂²⋊C₄	—	53	1	no	—
867	C₂²×C₂²⋊C₄	—	53	1	no	—
868	C₂²×C₄²	—	53	1	no	—
869	C₂²×C₄²	—	53	1	no	—
870	#400	—	53	1	no	—
871	#400	—	53	1	no	—
872	#400	—	53	1	no	—
873	#400	—	53	1	no	—
874	#400	—	53	1	no	—
875	#400	—	53	1	no	—
876	#400	—	53	1	no	—
877	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
878	#398	—	53	1	no	—
879	#398	—	53	1	no	—
880	#398	—	53	1	no	—
881	#398	—	53	1	no	—
882	#398	—	53	1	no	—
883	#398	—	53	1	no	—
884	#398	—	53	1	no	—
885	#398	—	53	1	no	—
886	#398	—	53	1	no	—
887	#398	—	53	1	no	—
888	#398	—	53	1	no	—
889	#398	—	53	1	no	—
890	#398	—	53	1	no	—
891	#398	—	53	1	no	—
892	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
893	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
894	#395	—	53	1	no	—
895	#395	—	53	1	no	—
896	#395	—	53	1	no	—
897	#395	—	53	1	no	—
898	#395	—	53	1	no	—
899	#395	—	53	1	no	—
900	#395	—	53	1	no	—
901	#395	C₂×D₅₃	1	1	yes	characteristic, complemented
902	#391	—	53	1	no	—
903	#391	—	53	1	no	—
904	#391	—	53	1	no	—
905	#391	—	53	1	no	—
906	#391	—	53	1	no	—
907	#391	—	53	1	no	—
908	#391	—	53	1	no	—
909	#391	C₂×D₅₃	1	1	yes	characteristic, complemented
910	#389	—	53	1	no	—
911	#389	—	53	1	no	—
912	#389	—	53	1	no	—
913	#389	—	53	1	no	—
914	#389	—	53	1	no	—
915	#389	—	53	1	no	—
916	#389	—	53	1	no	—
917	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
918	#387	—	53	1	no	—
919	#387	—	53	1	no	—
920	#387	—	53	1	no	—
921	#387	—	53	1	no	—
922	#387	—	53	1	no	—
923	#387	—	53	1	no	—
924	#387	—	53	1	no	—
925	#387	—	53	1	no	—
926	#387	—	53	1	no	—
927	#387	—	53	1	no	—
928	#387	—	53	1	no	—
929	#387	—	53	1	no	—
930	#387	—	53	1	no	—
931	#387	—	53	1	no	—
932	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
933	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
934	#385	—	53	1	no	—
935	#385	—	53	1	no	—
936	#385	—	53	1	no	—
937	#385	—	53	1	no	—
938	#385	—	53	1	no	—
939	#385	—	53	1	no	—
940	#385	—	53	1	no	—
941	#385	—	53	1	no	—
942	#385	—	53	1	no	—
943	#385	—	53	1	no	—
944	#385	—	53	1	no	—
945	#385	—	53	1	no	—
946	#385	—	53	1	no	—
947	#385	—	53	1	no	—
948	#385	C₂×D₅₃	1	1	yes	characteristic
949	#385	C₂×D₅₃	1	1	yes	characteristic
950	#381	—	53	1	no	—
951	#381	—	53	1	no	—
952	#381	—	53	1	no	—
953	#381	—	53	1	no	—
954	#381	—	53	1	no	—
955	#381	—	53	1	no	—
956	#381	—	53	1	no	—
957	#381	C₂×D₅₃	1	1	yes	characteristic
958	#380	—	53	1	no	—
959	#380	—	53	1	no	—
960	#380	—	53	1	no	—
961	#380	—	53	1	no	—
962	#380	—	53	1	no	—
963	#380	—	53	1	no	—
964	#380	—	53	1	no	—
965	#380	C₂×D₅₃	1	1	yes	characteristic
966	C₂×#95	—	53	1	no	—
967	C₂×#95	—	53	1	no	—
968	C₂×#95	—	53	1	no	—
969	C₂×#95	—	53	1	no	—
970	C₂×#95	—	53	1	no	—
971	C₂×#95	—	53	1	no	—
972	C₂×#95	—	53	1	no	—
973	C₂×#95	—	53	1	no	—
974	C₂×#95	—	53	1	no	—
975	C₂×#95	—	53	1	no	—
976	C₂×#95	—	53	1	no	—
977	C₂×#95	—	53	1	no	—
978	C₂×#95	—	53	1	no	—
979	C₂×#95	—	53	1	no	—
980	C₂×#95	—	53	1	no	—
981	C₂×#95	—	53	1	no	—
982	C₂×#95	—	53	1	no	—
983	C₂×#95	—	53	1	no	—
984	C₂×#95	—	53	1	no	—
985	C₂×#95	—	53	1	no	—
986	C₂×#95	—	53	1	no	—
987	C₂×#95	C₂×D₅₃	1	1	yes	characteristic
988	C₅₃	C₂×#2438	1	1	yes	characteristic, complemented, Sylow
989	C₂⁵	—	53	1	no	—
990	C₂²×Q₈	—	53	1	no	—
991	C₂²×Q₈	—	53	1	no	—
992	C₂²×Q₈	—	53	1	no	—
993	C₂²×Q₈	—	106	4	no	—
994	C₂²×Q₈	—	106	4	no	—
995	C₂²×Q₈	—	212	2	no	—
996	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
997	C₂³×C₄	—	53	1	no	—
998	C₂³×C₄	—	53	8	no	—
999	C₂³×C₄	—	53	1	no	—
1000	C₂³×C₄	—	53	1	no	—
1001	C₂³×C₄	—	53	1	no	—
1002	C₂³×C₄	—	53	1	no	—
1003	C₂³×C₄	—	53	1	no	—
1004	C₂³×C₄	—	53	1	no	—
1005	C₂³×C₄	—	53	1	no	—
1006	C₂³×C₄	—	53	1	no	—
1007	C₂³×C₄	—	53	1	no	—
1008	C₂³×C₄	—	53	1	no	—
1009	C₂³×C₄	—	53	1	no	—
1010	C₂³×C₄	—	53	1	no	—
1011	C₂³×C₄	—	53	1	no	—
1012	C₂³×C₄	—	53	1	no	—
1013	C₂³×C₄	—	53	1	no	—
1014	C₂³×C₄	—	53	1	no	—
1015	C₂³×C₄	—	53	1	no	—
1016	C₂³×C₄	—	53	1	no	—
1017	C₂³×C₄	—	53	1	no	—
1018	C₂³×C₄	—	53	1	no	—
1019	C₂³×C₄	—	53	1	no	—
1020	C₂³×C₄	—	53	1	no	—
1021	C₂³×C₄	—	106	4	no	—
1022	C₂³×C₄	—	106	4	no	—
1023	C₂³×C₄	—	106	4	no	—
1024	C₂³×C₄	—	106	4	no	—
1025	C₂³×C₄	—	106	4	no	—
1026	C₂³×C₄	—	106	4	no	—
1027	C₂³×C₄	—	212	2	no	—
1028	C₂³×C₄	—	212	2	no	—
1029	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1030	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1031	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1032	C₂²⋊Q₈	—	2	4	no	—
1033	C₂²⋊Q₈	—	106	4	no	—
1034	C₂²⋊Q₈	—	106	4	no	—
1035	C₂²⋊Q₈	—	106	4	no	—
1036	C₂²⋊Q₈	—	106	4	no	—
1037	C₂²⋊Q₈	—	106	4	no	—
1038	C₂²⋊Q₈	—	106	4	no	—
1039	C₂²⋊Q₈	—	106	4	no	—
1040	#117	—	2	4	no	—
1041	#117	—	106	4	no	—
1042	#117	—	106	4	no	—
1043	#117	—	106	4	no	—
1044	#117	—	106	4	no	—
1045	#117	—	106	4	no	—
1046	#117	—	106	4	no	—
1047	#117	—	106	4	no	—
1048	C₂×C₄⋊C₄	—	53	1	no	—
1049	C₂×C₄⋊C₄	—	53	1	no	—
1050	C₂×C₄⋊C₄	—	53	1	no	—
1051	C₂×C₄⋊C₄	—	53	1	no	—
1052	C₂×C₄⋊C₄	—	53	1	no	—
1053	C₂×C₄⋊C₄	—	53	1	no	—
1054	C₂×C₄⋊C₄	—	53	1	no	—
1055	C₂×C₄⋊C₄	—	53	1	no	—
1056	C₂×C₄⋊C₄	—	53	1	no	—
1057	C₂×C₄⋊C₄	—	53	1	no	—
1058	C₂×C₄⋊C₄	—	53	1	no	—
1059	C₂×C₄⋊C₄	—	53	1	no	—
1060	C₂×C₄⋊C₄	—	53	1	no	—
1061	C₂×C₄⋊C₄	—	53	1	no	—
1062	C₂×C₄⋊C₄	—	53	1	no	—
1063	C₂×C₄⋊C₄	—	53	1	no	—
1064	C₂×C₄⋊C₄	—	53	1	no	—
1065	C₂×C₄⋊C₄	—	53	1	no	—
1066	C₂×C₄⋊C₄	—	53	1	no	—
1067	C₂×C₄⋊C₄	—	53	1	no	—
1068	C₂×C₄⋊C₄	—	53	1	no	—
1069	C₂×C₄⋊C₄	—	53	1	no	—
1070	C₂×C₄⋊C₄	—	53	1	no	—
1071	C₂×C₄⋊C₄	—	53	1	no	—
1072	C₂×C₄⋊C₄	—	53	1	no	—
1073	C₂×C₄⋊C₄	—	53	1	no	—
1074	C₂×C₄⋊C₄	—	53	1	no	—
1075	C₂×C₄⋊C₄	—	53	1	no	—
1076	C₂×C₄⋊C₄	—	53	1	no	—
1077	C₂×C₄⋊C₄	—	53	1	no	—
1078	C₂×C₄⋊C₄	—	53	1	no	—
1079	C₂×C₄⋊C₄	—	53	1	no	—
1080	C₂×C₄⋊C₄	—	53	1	no	—
1081	C₂×C₄⋊C₄	—	106	4	no	—
1082	C₂×C₄⋊C₄	—	106	4	no	—
1083	C₂×C₄⋊C₄	—	106	4	no	—
1084	C₂×C₄⋊C₄	—	106	4	no	—
1085	C₂×C₄⋊C₄	—	106	4	no	—
1086	C₂×C₄⋊C₄	—	106	4	no	—
1087	C₂×C₄⋊C₄	—	106	4	no	—
1088	C₂×C₄⋊C₄	—	106	4	no	—
1089	C₂×C₄⋊C₄	—	212	2	no	—
1090	C₂×C₄⋊C₄	—	212	2	no	—
1091	C₂×C₄⋊C₄	—	212	2	no	—
1092	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1093	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1094	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1095	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1096	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1097	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1098	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1099	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1100	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1101	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1102	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1103	C₂×C₂²⋊C₄	—	53	1	no	—
1104	C₂×C₂²⋊C₄	—	53	1	no	—
1105	C₂×C₂²⋊C₄	—	53	1	no	—
1106	C₂×C₂²⋊C₄	—	53	8	no	—
1107	C₂×C₂²⋊C₄	—	53	1	no	—
1108	C₂×C₂²⋊C₄	—	53	1	no	—
1109	C₂×C₂²⋊C₄	—	53	1	no	—
1110	C₂×C₂²⋊C₄	—	53	1	no	—
1111	C₂×C₂²⋊C₄	—	53	1	no	—
1112	C₂×C₂²⋊C₄	—	53	1	no	—
1113	C₂×C₂²⋊C₄	—	53	1	no	—
1114	C₂×C₂²⋊C₄	—	53	1	no	—
1115	C₂×C₂²⋊C₄	—	53	1	no	—
1116	C₂×C₂²⋊C₄	—	106	4	no	—
1117	C₂×C₂²⋊C₄	—	106	4	no	—
1118	C₂×C₂²⋊C₄	—	106	4	no	—
1119	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1120	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1121	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1122	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1123	C₂×C₄²	—	53	1	no	—
1124	C₂×C₄²	—	53	1	no	—
1125	C₂×C₄²	—	53	1	no	—
1126	C₂×C₄²	—	53	1	no	—
1127	C₂×C₄²	—	53	1	no	—
1128	C₂×C₄²	—	53	1	no	—
1129	C₂×C₄²	—	106	4	no	—
1130	C₂×C₄²	—	106	4	no	—
1131	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1132	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1145	#95	—	53	1	no	—
1146	#95	—	53	1	no	—
1147	#95	—	53	1	no	—
1148	#95	—	53	1	no	—
1149	#95	—	53	1	no	—
1150	#95	—	53	1	no	—
1151	#95	—	53	1	no	—
1152	#95	—	53	1	no	—
1153	#95	—	53	1	no	—
1154	#95	—	53	1	no	—
1155	#95	—	53	1	no	—
1156	#95	—	53	1	no	—
1157	#95	—	53	1	no	—
1158	#95	—	53	1	no	—
1159	#95	—	53	1	no	—
1160	#95	—	53	1	no	—
1161	#95	—	53	1	no	—
1162	#95	—	53	1	no	—
1163	#95	—	53	1	no	—
1164	#95	—	53	1	no	—
1165	#95	—	53	1	no	—
1166	#95	—	53	1	no	—
1167	#95	—	53	1	no	—
1168	#95	—	53	1	no	—
1169	#95	—	53	1	no	—
1170	#95	—	53	1	no	—
1171	#95	—	53	1	no	—
1172	#95	—	53	1	no	—
1173	#95	—	53	1	no	—
1174	#95	—	53	1	no	—
1175	#95	C₂²×D₅₃	1	1	yes	characteristic
1176	#95	C₂²×D₅₃	1	1	yes	characteristic
1177	#95	C₂²×D₅₃	1	1	yes	characteristic
1178	#95	C₂²×D₅₃	1	1	yes	characteristic
1179	#95	C₂²×D₅₃	1	1	yes	characteristic
1180	#95	C₂²×D₅₃	1	1	yes	characteristic
1181	#95	C₂²×D₅₃	1	1	yes	characteristic
1182	#95	C₂²×D₅₃	1	1	yes	characteristic
1183	#95	C₂²×D₅₃	1	1	yes	characteristic
1184	#95	C₂²×D₅₃	1	1	yes	characteristic
1185	#95	C₂²×D₅₃	1	1	yes	characteristic
1186	#95	C₂²×D₅₃	1	1	yes	characteristic
1187	#95	C₂²×D₅₃	1	1	yes	characteristic
1188	#95	C₂²×D₅₃	1	1	yes	characteristic
1189	C₂⁴	—	53	1	no	—
1190	C₂⁴	—	53	4	no	—
1191	C₂⁴	—	53	4	no	—
1192	C₂⁴	—	53	4	no	—
1193	C₂⁴	—	53	1	no	—
1194	C₂⁴	—	106	2	no	—
1195	C₂⁴	—	106	2	no	—
1196	C₂⁴	—	106	2	no	—
1197	C₂⁴	—	106	2	no	—
1198	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1199	C₂×Q₈	—	2	2	no	—
1200	C₂×Q₈	—	2	2	no	—
1201	C₂×Q₈	—	4	1	no	—
1202	C₂×Q₈	—	106	2	no	—
1203	C₂×Q₈	—	106	2	no	—
1204	C₂×Q₈	—	106	2	no	—
1205	C₂×Q₈	—	106	2	no	—
1206	C₂×Q₈	—	106	2	no	—
1207	C₂×Q₈	—	106	2	no	—
1208	C₂×Q₈	—	212	1	no	—
1209	C₂×Q₈	—	212	1	no	—
1210	C₂×Q₈	—	212	1	no	—
1211	C₂×Q₈	—	212	16	no	—
1212	C₂²×C₄	—	2	2	no	—
1213	C₂²×C₄	—	2	2	no	—
1214	C₂²×C₄	—	2	2	no	—
1215	C₂²×C₄	—	2	2	no	—
1216	C₂²×C₄	—	2	2	no	—
1217	C₂²×C₄	—	2	2	no	—
1218	C₂²×C₄	—	4	1	no	—
1219	C₂²×C₄	—	4	1	no	—
1220	C₂²×C₄	—	53	4	no	—
1221	C₂²×C₄	—	53	1	no	—
1222	C₂²×C₄	—	53	1	no	—
1223	C₂²×C₄	—	53	1	no	—
1224	C₂²×C₄	—	53	1	no	—
1225	C₂²×C₄	—	53	1	no	—
1226	C₂²×C₄	—	53	1	no	—
1227	C₂²×C₄	—	53	4	no	—
1228	C₂²×C₄	—	53	4	no	—
1229	C₂²×C₄	—	53	4	no	—
1230	C₂²×C₄	—	53	4	no	—
1231	C₂²×C₄	—	53	4	no	—
1232	C₂²×C₄	—	53	4	no	—
1233	C₂²×C₄	—	53	4	no	—
1234	C₂²×C₄	—	53	4	no	—
1235	C₂²×C₄	—	53	1	no	—
1236	C₂²×C₄	—	53	1	no	—
1237	C₂²×C₄	—	53	1	no	—
1238	C₂²×C₄	—	53	1	no	—
1239	C₂²×C₄	—	53	1	no	—
1240	C₂²×C₄	—	53	1	no	—
1241	C₂²×C₄	—	53	1	no	—
1242	C₂²×C₄	—	53	1	no	—
1243	C₂²×C₄	—	106	2	no	—
1244	C₂²×C₄	—	106	2	no	—
1245	C₂²×C₄	—	106	2	no	—
1246	C₂²×C₄	—	106	2	no	—
1247	C₂²×C₄	—	106	2	no	—
1248	C₂²×C₄	—	106	2	no	—
1249	C₂²×C₄	—	106	2	no	—
1250	C₂²×C₄	—	106	2	no	—
1251	C₂²×C₄	—	106	2	no	—
1252	C₂²×C₄	—	106	2	no	—
1253	C₂²×C₄	—	106	2	no	—
1254	C₂²×C₄	—	106	32	no	—
1255	C₂²×C₄	—	106	2	no	—
1256	C₂²×C₄	—	106	2	no	—
1257	C₂²×C₄	—	106	2	no	—
1258	C₂²×C₄	—	106	2	no	—
1259	C₂²×C₄	—	106	2	no	—
1260	C₂²×C₄	—	106	2	no	—
1261	C₂²×C₄	—	106	2	no	—
1262	C₂²×C₄	—	106	2	no	—
1263	C₂²×C₄	—	106	2	no	—
1264	C₂²×C₄	—	106	2	no	—
1265	C₂²×C₄	—	106	2	no	—
1266	C₂²×C₄	—	106	2	no	—
1267	C₂²×C₄	—	106	2	no	—
1268	C₂²×C₄	—	106	2	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	—	106	2	no	—
1276	C₂²×C₄	—	106	2	no	—
1277	C₂²×C₄	—	106	2	no	—
1278	C₂²×C₄	—	106	2	no	—
1279	C₂²×C₄	—	106	2	no	—
1280	C₂²×C₄	—	106	2	no	—
1281	C₂²×C₄	—	106	2	no	—
1282	C₂²×C₄	—	106	2	no	—
1283	C₂²×C₄	—	106	2	no	—
1284	C₂²×C₄	—	106	2	no	—
1285	C₂²×C₄	—	106	2	no	—
1286	C₂²×C₄	—	106	2	no	—
1287	C₂²×C₄	—	106	2	no	—
1288	C₂²×C₄	—	106	2	no	—
1289	C₂²×C₄	—	106	2	no	—
1290	C₂²×C₄	—	106	2	no	—
1291	C₂²×C₄	—	106	2	no	—
1292	C₂²×C₄	—	106	2	no	—
1293	C₂²×C₄	—	106	2	no	—
1294	C₂²×C₄	—	106	2	no	—
1295	C₂²×C₄	—	106	2	no	—
1296	C₂²×C₄	—	106	2	no	—
1297	C₂²×C₄	—	106	2	no	—
1298	C₂²×C₄	—	212	1	no	—
1299	C₂²×C₄	—	212	1	no	—
1300	C₂²×C₄	—	212	1	no	—
1301	C₂²×C₄	—	212	1	no	—
1302	C₂²×C₄	—	212	16	no	—
1303	C₂²×C₄	—	212	16	no	—
1304	C₂²×C₄	—	212	1	no	—
1305	C₂²×C₄	—	212	1	no	—
1306	C₂²×C₄	Q₈×D₅₃	1	4	yes	complemented
1307	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1308	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1309	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1310	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1311	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1312	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1313	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1314	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1315	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1316	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1317	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1318	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1319	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1320	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1321	C₄⋊C₄	—	2	2	no	—
1322	C₄⋊C₄	—	2	2	no	—
1323	C₄⋊C₄	—	2	2	no	—
1324	C₄⋊C₄	—	2	2	no	—
1325	C₄⋊C₄	—	2	2	no	—
1326	C₄⋊C₄	—	2	2	no	—
1327	C₄⋊C₄	—	2	2	no	—
1328	C₄⋊C₄	—	2	2	no	—
1329	C₄⋊C₄	—	4	1	no	—
1330	C₄⋊C₄	—	4	1	no	—
1331	C₄⋊C₄	—	4	1	no	—
1332	C₄⋊C₄	—	106	2	no	—
1333	C₄⋊C₄	—	106	2	no	—
1334	C₄⋊C₄	—	106	2	no	—
1335	C₄⋊C₄	—	106	2	no	—
1336	C₄⋊C₄	—	106	2	no	—
1337	C₄⋊C₄	—	106	2	no	—
1338	C₄⋊C₄	—	106	2	no	—
1339	C₄⋊C₄	—	106	2	no	—
1340	C₄⋊C₄	—	106	2	no	—
1341	C₄⋊C₄	—	106	2	no	—
1342	C₄⋊C₄	—	106	2	no	—
1343	C₄⋊C₄	—	106	2	no	—
1344	C₄⋊C₄	—	106	2	no	—
1345	C₄⋊C₄	—	106	2	no	—
1346	C₄⋊C₄	—	106	2	no	—
1347	C₄⋊C₄	—	106	2	no	—
1348	C₄⋊C₄	—	106	2	no	—
1349	C₄⋊C₄	—	106	2	no	—
1350	C₄⋊C₄	—	106	2	no	—
1351	C₄⋊C₄	—	106	2	no	—
1352	C₄⋊C₄	—	106	2	no	—
1353	C₄⋊C₄	—	106	2	no	—
1354	C₄⋊C₄	—	106	2	no	—
1355	C₄⋊C₄	—	106	2	no	—
1356	C₄⋊C₄	—	212	1	no	—
1357	C₄⋊C₄	—	212	1	no	—
1358	C₄⋊C₄	—	212	1	no	—
1359	C₄⋊C₄	—	212	1	no	—
1360	C₄⋊C₄	—	212	1	no	—
1361	C₄⋊C₄	—	212	1	no	—
1362	C₄⋊C₄	—	212	1	no	—
1363	C₄⋊C₄	—	212	1	no	—
1364	C₄⋊C₄	—	212	1	no	—
1365	C₂²⋊C₄	—	2	2	no	—
1366	C₂²⋊C₄	—	2	2	no	—
1367	C₂²⋊C₄	—	2	2	no	—
1368	C₂²⋊C₄	—	53	4	no	—
1369	C₂²⋊C₄	—	53	4	no	—
1370	C₂²⋊C₄	—	53	4	no	—
1371	C₂²⋊C₄	—	106	2	no	—
1372	C₂²⋊C₄	—	106	2	no	—
1373	C₂²⋊C₄	—	106	2	no	—
1374	C₂²⋊C₄	—	106	2	no	—
1375	C₂²⋊C₄	—	106	2	no	—
1376	C₂²⋊C₄	—	106	2	no	—
1377	C₂²⋊C₄	—	106	2	no	—
1378	C₂²⋊C₄	—	106	2	no	—
1379	C₂²⋊C₄	—	106	2	no	—
1380	C₂²⋊C₄	D₄×D₅₃	1	4	yes	—
1381	C₄²	—	2	2	no	—
1382	C₄²	—	2	2	no	—
1383	C₄²	—	106	2	no	—
1384	C₄²	—	106	2	no	—
1385	C₄²	—	106	2	no	—
1386	C₄²	—	106	2	no	—
1387	C₄²	—	106	2	no	—
1388	C₄²	—	106	2	no	—
1389	C₂³	—	2	1	no	—
1390	C₂³	—	2	1	no	—
1391	C₂³	—	2	1	no	—
1392	C₂³	—	2	1	no	—
1393	C₂³	—	53	2	no	—
1394	C₂³	—	53	2	no	—
1395	C₂³	—	53	2	no	—
1396	C₂³	—	53	2	no	—
1397	C₂³	—	53	2	no	—
1398	C₂³	—	53	2	no	—
1399	C₂³	—	53	2	no	—
1400	C₂³	—	53	16	no	—
1401	C₂³	—	53	2	no	—
1402	C₂³	—	53	2	no	—
1403	C₂³	—	53	2	no	—
1404	C₂³	—	106	8	no	—
1405	C₂³	—	106	8	no	—
1406	C₂³	—	106	8	no	—
1407	C₂³	—	106	8	no	—
1408	C₂³	—	106	8	no	—
1409	C₂³	—	106	8	no	—
1410	C₂³	—	106	1	no	—
1411	C₂³	—	106	1	no	—
1412	C₂³	—	106	1	no	—
1413	C₂³	—	106	1	no	—
1414	C₂³	C₂×D₄×D₅₃	1	2	yes	—
1415	C₂³	C₂×Q₈×D₅₃	1	2	yes	—
1416	C₂³	#41×D₅₃	1	2	yes	—
1417	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1418	Q₈	—	4	4	no	—
1419	Q₈	—	212	4	no	—
1420	Q₈	—	212	4	no	—
1421	Q₈	—	212	4	no	—
1422	C₂×C₄	—	2	8	no	—
1423	C₂×C₄	—	2	1	no	—
1424	C₂×C₄	—	2	1	no	—
1425	C₂×C₄	—	2	1	no	—
1426	C₂×C₄	—	2	1	no	—
1427	C₂×C₄	—	2	1	no	—
1428	C₂×C₄	—	2	1	no	—
1429	C₂×C₄	—	2	1	no	—
1430	C₂×C₄	—	2	1	no	—
1431	C₂×C₄	—	2	1	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	2	1	no	—
1445	C₂×C₄	—	2	1	no	—
1446	C₂×C₄	—	2	1	no	—
1447	C₂×C₄	—	2	1	no	—
1448	C₂×C₄	—	2	1	no	—
1449	C₂×C₄	—	2	1	no	—
1450	C₂×C₄	—	2	1	no	—
1451	C₂×C₄	—	2	1	no	—
1452	C₂×C₄	—	2	1	no	—
1453	C₂×C₄	—	2	1	no	—
1454	C₂×C₄	—	2	1	no	—
1455	C₂×C₄	—	2	1	no	—
1456	C₂×C₄	—	2	1	no	—
1457	C₂×C₄	—	2	1	no	—
1458	C₂×C₄	—	2	1	no	—
1459	C₂×C₄	—	4	4	no	—
1460	C₂×C₄	—	4	4	no	—
1461	C₂×C₄	—	53	2	no	—
1462	C₂×C₄	—	53	2	no	—
1463	C₂×C₄	—	53	2	no	—
1464	C₂×C₄	—	53	2	no	—
1465	C₂×C₄	—	53	2	no	—
1466	C₂×C₄	—	53	2	no	—
1467	C₂×C₄	—	106	8	no	—
1468	C₂×C₄	—	106	8	no	—
1469	C₂×C₄	—	106	8	no	—
1470	C₂×C₄	—	106	8	no	—
1471	C₂×C₄	—	106	8	no	—
1472	C₂×C₄	—	106	8	no	—
1473	C₂×C₄	—	106	8	no	—
1474	C₂×C₄	—	106	8	no	—
1475	C₂×C₄	—	106	8	no	—
1476	C₂×C₄	—	106	1	no	—
1477	C₂×C₄	—	106	1	no	—
1478	C₂×C₄	—	106	1	no	—
1479	C₂×C₄	—	106	1	no	—
1480	C₂×C₄	—	106	1	no	—
1481	C₂×C₄	—	106	1	no	—
1482	C₂×C₄	—	106	1	no	—
1483	C₂×C₄	—	106	1	no	—
1484	C₂×C₄	—	106	1	no	—
1485	C₂×C₄	—	106	1	no	—
1486	C₂×C₄	—	106	1	no	—
1487	C₂×C₄	—	106	1	no	—
1488	C₂×C₄	—	106	1	no	—
1489	C₂×C₄	—	106	1	no	—
1490	C₂×C₄	—	106	1	no	—
1491	C₂×C₄	—	106	1	no	—
1492	C₂×C₄	—	106	1	no	—
1493	C₂×C₄	—	106	1	no	—
1494	C₂×C₄	—	106	1	no	—
1495	C₂×C₄	—	106	1	no	—
1496	C₂×C₄	—	106	1	no	—
1497	C₂×C₄	—	106	1	no	—
1498	C₂×C₄	—	106	1	no	—
1499	C₂×C₄	—	106	1	no	—
1500	C₂×C₄	—	106	1	no	—
1501	C₂×C₄	—	106	1	no	—
1502	C₂×C₄	—	106	1	no	—
1503	C₂×C₄	—	106	1	no	—
1504	C₂×C₄	—	106	1	no	—
1505	C₂×C₄	—	106	1	no	—
1506	C₂×C₄	—	106	1	no	—
1507	C₂×C₄	—	106	1	no	—
1508	C₂×C₄	—	106	1	no	—
1509	C₂×C₄	—	106	1	no	—
1510	C₂×C₄	—	106	1	no	—
1511	C₂×C₄	—	106	1	no	—
1512	C₂×C₄	—	212	4	no	—
1513	C₂×C₄	—	212	4	no	—
1514	C₂×C₄	—	212	4	no	—
1515	C₂×C₄	—	212	4	no	—
1516	C₂×C₄	—	212	4	no	—
1517	C₂×C₄	—	212	4	no	—
1518	C₂×C₄	—	212	4	no	—
1519	C₂×C₄	—	212	4	no	—
1520	C₂×C₄	—	212	4	no	—
1521	C₂×C₄	—	212	4	no	—
1522	C₂×C₄	—	212	4	no	—
1523	C₂×C₄	—	212	4	no	—
1524	C₂×C₄	—	212	4	no	—
1525	C₂×C₄	—	212	4	no	—
1526	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1527	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1528	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1529	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1530	C₂×C₄	#41×D₅₃	1	2	yes	—
1531	C₂×C₄	#41×D₅₃	1	2	yes	—
1532	C₂²	—	2	2	no	—
1533	C₂²	—	2	2	no	—
1534	C₂²	—	2	2	no	—
1535	C₂²	—	2	2	no	—
1536	C₂²	—	2	2	no	—
1537	C₂²	—	2	2	no	—
1538	C₂²	—	53	4	no	—
1539	C₂²	—	53	4	no	—
1540	C₂²	—	53	4	no	—
1541	C₂²	—	53	4	no	—
1542	C₂²	—	53	4	no	—
1543	C₂²	—	53	4	no	—
1544	C₂²	—	53	4	no	—
1545	C₂²	—	53	4	no	—
1546	C₂²	—	106	32	no	—
1547	C₂²	—	106	2	no	—
1548	C₂²	—	106	2	no	—
1549	C₂²	—	106	2	no	—
1550	C₂²	—	106	2	no	—
1551	C₂²	—	106	2	no	—
1552	C₂²	—	106	2	no	—
1553	C₂²	C₂²⋊Q₈×D₅₃	1	4	yes	—
1554	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1555	C₂²	C₂²×Q₈×D₅₃	1	1	yes	characteristic
1556	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1557	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1558	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1559	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1560	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1561	C₄	—	2	2	no	—
1562	C₄	—	2	2	no	—
1563	C₄	—	2	2	no	—
1564	C₄	—	2	2	no	—
1565	C₄	—	2	2	no	—
1566	C₄	—	2	2	no	—
1567	C₄	—	4	1	no	—
1568	C₄	—	4	1	no	—
1569	C₄	—	4	1	no	—
1570	C₄	—	4	1	no	—
1571	C₄	—	4	1	no	—
1572	C₄	—	4	1	no	—
1573	C₄	—	4	1	no	—
1574	C₄	—	4	1	no	—
1575	C₄	—	106	2	no	—
1576	C₄	—	106	2	no	—
1577	C₄	—	106	2	no	—
1578	C₄	—	106	2	no	—
1579	C₄	—	106	2	no	—
1580	C₄	—	106	2	no	—
1581	C₄	—	212	1	no	—
1582	C₄	—	212	1	no	—
1583	C₄	—	212	1	no	—
1584	C₄	—	212	1	no	—
1585	C₄	—	212	1	no	—
1586	C₄	—	212	1	no	—
1587	C₄	—	212	1	no	—
1588	C₄	—	212	1	no	—
1589	C₂	—	2	4	no	—
1590	C₂	—	53	8	no	—
1591	C₂	—	106	4	no	—
1592	C₂	C₂×C₂²⋊Q₈×D₅₃	1	1	yes	characteristic
1593	C₂	#533×D₅₃	1	1	yes	characteristic
1594	C₂	#544×D₅₃	1	1	yes	characteristic
1595	C₂	#546×D₅₃	1	1	yes	characteristic
1596	C₂	#547×D₅₃	1	1	yes	characteristic
1597	C₂	#551×D₅₃	1	1	yes	characteristic
1598	C₂	#552×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2438	C₂
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	#2438	D₅₃
hypocenter	C₅₃	C₂×#2438
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2438

Complements

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

N	H ≅ G/N	type
3. #20278398	C₂	semidirect
4. #20278397	C₂	semidirect
5. #20278396	C₂	semidirect
6. #20278395	C₂	semidirect
7. #20278394	C₂	semidirect
8. #20278393	C₂	semidirect
9. #20278392	C₂	semidirect
10. #20278391	C₂	semidirect
11. #20278390	C₂	semidirect
12. #20278389	C₂	semidirect
13. #20278388	C₂	semidirect
14. #20278387	C₂	semidirect
15. #20278386	C₂	semidirect
16. #20278385	C₂	semidirect
17. #20278384	C₂	semidirect
18. #400×D₅₃	C₂	semidirect
19. #398×D₅₃	C₂	semidirect
20. #398×D₅₃	C₂	semidirect
21. #395×D₅₃	C₂	semidirect
22. #391×D₅₃	C₂	semidirect
23. #389×D₅₃	C₂	semidirect
24. #387×D₅₃	C₂	semidirect
25. #387×D₅₃	C₂	semidirect
31. C₅₃×#2438	C₂	semidirect
69. #16810565	C₂²	semidirect
70. #16810565	C₂²	semidirect
71. #16810564	C₂²	semidirect
72. #16810564	C₂²	semidirect
73. #16810563	C₂²	semidirect
74. #16810562	C₂²	semidirect
75. #16810561	C₂²	semidirect
76. #16810557	C₂²	semidirect
77. #16810557	C₂²	semidirect
78. #16810557	C₂²	semidirect
79. #16810557	C₂²	semidirect
80. #16810556	C₂²	semidirect
81. #16810556	C₂²	semidirect
82. #16810556	C₂²	semidirect
83. #16810556	C₂²	semidirect
84. #16810555	C₂²	semidirect
85. #16810555	C₂²	semidirect
86. #16810554	C₂²	semidirect
87. #16810554	C₂²	semidirect
88. #16810553	C₂²	semidirect
89. #16810553	C₂²	semidirect
90. #16810544	C₂²	semidirect
91. #16810544	C₂²	semidirect
92. #16810544	C₂²	semidirect
93. #16810543	C₂²	semidirect
94. #16810543	C₂²	semidirect
95. #16810543	C₂²	semidirect
96. #16810542	C₂²	semidirect
97. #16810530	C₂²	semidirect
98. #16810529	C₂²	semidirect
99. #16810528	C₂²	semidirect
100. #16810527	C₂²	semidirect
101. #16810527	C₂²	semidirect
102. #16810527	C₂²	semidirect
103. #16810527	C₂²	semidirect
104. #16810522	C₂²	semidirect
105. #16810521	C₂²	semidirect
106. #16810520	C₂²	semidirect
107. #16810520	C₂²	semidirect
108. #16810519	C₂²	semidirect
109. #16810518	C₂²	semidirect
110. #16810518	C₂²	semidirect
111. #16810510	C₂²	semidirect
112. #16810510	C₂²	semidirect
113. #16810509	C₂²	semidirect
114. #16810509	C₂²	semidirect
115. #16810508	C₂²	semidirect
116. #16810508	C₂²	semidirect
117. #16810507	C₂²	semidirect
118. #16810507	C₂²	semidirect
119. #16810506	C₂²	semidirect
120. #16810506	C₂²	semidirect
121. #16810505	C₂²	semidirect
122. #16810505	C₂²	semidirect
123. #16810504	C₂²	semidirect
124. #16810504	C₂²	semidirect
176. C₅₃×#400	C₂²	semidirect
177. C₅₃×#398	C₂²	semidirect
178. C₅₃×#398	C₂²	semidirect
179. C₅₃×#395	C₂²	semidirect
180. C₅₃×#391	C₂²	semidirect
181. C₅₃×#389	C₂²	semidirect
182. C₅₃×#387	C₂²	semidirect
183. C₅₃×#387	C₂²	semidirect
207. C₂²×C₄×D₅₃	Q₈	semidirect
410. C₂²×C₄×C₅₃	C₂×Q₈	semidirect
433. C₂²×Dic₅₃	C₂×Q₈	semidirect
508. C₂×C₄×D₅₃	C₂×Q₈	semidirect
509. C₂×C₄×D₅₃	C₂×Q₈	semidirect
807. #2438	D₅₃	direct (N × H)
830. D₅₃	#2438	direct (N × H)
877. #400	C₂×D₅₃	semidirect
892. #398	C₂×D₅₃	semidirect
893. #398	C₂×D₅₃	semidirect
901. #395	C₂×D₅₃	semidirect
909. #391	C₂×D₅₃	semidirect
917. #389	C₂×D₅₃	semidirect
932. #387	C₂×D₅₃	semidirect
933. #387	C₂×D₅₃	semidirect
988. C₅₃	C₂×#2438	semidirect
1306. C₂²×C₄	Q₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊Q₈×D₅₃	2
C₂×#117×D₅₃	2
#20278398	2
#20278397	2
#20278396	2
#20278395	2
#20278394	2
#20278393	2
#20278392	2
#20278391	2
#20278390	2
#20278389	2
#20278388	2
#20278387	2
#20278386	2
#20278385	2
#20278384	2
#400×D₅₃	2
#398×D₅₃	2
#395×D₅₃	2
#391×D₅₃	2
#389×D₅₃	2
#387×D₅₃	2
#385×D₅₃	2
#381×D₅₃	2
#380×D₅₃	2
C₂×#95×D₅₃	2
C₅₃×#2438	2
C₂×#2438	53

Subgroups — D53×#2438 #27552730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2438 #27552730