Subgroups — #27598867

Order 13568.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283105	C₂	1	1	yes	maximal, characteristic
2	#20283099	C₂	1	1	yes	maximal, characteristic, complemented
3	#20282704	C₂	1	1	yes	maximal, characteristic, complemented
4	#20282669	C₂	1	1	yes	maximal, characteristic, complemented
5	#20282467	C₂	1	1	yes	maximal, characteristic
6	#20282318	C₂	1	1	yes	maximal, characteristic
7	#20282279	C₂	1	1	yes	maximal, characteristic, complemented
8	#20282278	C₂	1	1	yes	maximal, characteristic, complemented
9	#20282273	C₂	1	1	yes	maximal, characteristic, complemented
10	#20282264	C₂	1	1	yes	maximal, characteristic
11	#20282232	C₂	1	1	yes	maximal, characteristic
12	#20282180	C₂	1	1	yes	maximal, characteristic, complemented
13	#20282126	C₂	1	1	yes	maximal, characteristic
14	#20282111	C₂	1	1	yes	maximal, characteristic, complemented
15	#20282088	C₂	1	1	yes	maximal, characteristic
16	#20282067	C₂	1	1	yes	maximal, characteristic, complemented
17	#20282007	C₂	1	1	yes	maximal, characteristic
18	#20281788	C₂	1	1	yes	maximal, characteristic
19	#20280810	C₂	1	1	yes	maximal, characteristic, complemented
20	#20280735	C₂	1	1	yes	maximal, characteristic
21	#20280423	C₂	1	1	yes	maximal, characteristic, complemented
22	#20280347	C₂	1	1	yes	maximal, characteristic
23	#20280347	C₂	1	1	yes	maximal, characteristic
24	#20280150	C₂	1	1	yes	maximal, characteristic, complemented
25	#20280003	C₂	1	1	yes	maximal, characteristic
26	#20279591	C₂	1	1	yes	maximal, characteristic, complemented
27	#20279546	C₂	1	1	yes	maximal, characteristic
28	#20277486	C₂	1	1	yes	maximal, characteristic
29	#20277366	C₂	1	1	yes	maximal, characteristic, complemented
30	#20277193	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133211	C₂²	1	1	yes	characteristic
33	C₅₃⋊#401	C₂²	1	1	yes	characteristic
34	#16810565	C₂²	1	1	yes	characteristic
35	#16810565	C₂²	1	1	yes	characteristic
36	#16810565	C₂²	1	1	yes	characteristic
37	#16810565	C₂²	1	1	yes	characteristic
38	#16810565	C₂²	1	1	yes	characteristic
39	#16810565	C₂²	1	1	yes	characteristic
40	#16810564	C₂²	1	1	yes	characteristic
41	#16810564	C₂²	1	1	yes	characteristic
42	#16810564	C₂²	1	1	yes	characteristic
43	#16810564	C₂²	1	1	yes	characteristic
44	#16810564	C₂²	1	1	yes	characteristic
45	#16810563	C₂²	1	1	yes	characteristic
46	#16810563	C₂²	1	1	yes	characteristic
47	#16810563	C₂²	1	1	yes	characteristic
48	#16810562	C₂²	1	1	yes	characteristic
49	#16810562	C₂²	1	1	yes	characteristic
50	#16810561	C₂²	1	1	yes	characteristic
51	#16810561	C₂²	1	1	yes	characteristic
52	#16810561	C₂²	1	1	yes	characteristic
53	#16810561	C₂²	1	1	yes	characteristic
54	#16810560	C₂²	1	1	yes	characteristic
55	#16810558	C₂²	1	1	yes	characteristic
56	#16810558	C₂²	1	1	yes	characteristic
57	#16810556	C₂²	1	1	yes	characteristic
58	#16810556	C₂²	1	1	yes	characteristic
59	#16810556	C₂²	1	1	yes	characteristic
60	#16810555	C₂²	1	1	yes	characteristic
61	#16810554	C₂²	1	1	yes	characteristic
62	#16810553	C₂²	1	1	yes	characteristic
63	#16810552	C₂²	1	1	yes	characteristic
64	#16810552	C₂²	1	1	yes	characteristic
65	#16810550	C₂²	1	1	yes	characteristic
66	#16810550	C₂²	1	1	yes	characteristic
67	#16810549	C₂²	1	1	yes	characteristic
68	#16810545	C₂²	1	1	yes	characteristic
69	#16810544	C₂²	1	1	yes	characteristic
70	#16810544	C₂²	1	1	yes	characteristic
71	#16810543	C₂²	1	1	yes	characteristic
72	#16810542	C₂²	1	1	yes	characteristic
73	#16810542	C₂²	1	1	yes	characteristic
74	#16810536	C₂²	1	1	yes	characteristic
75	#16810534	C₂²	1	1	yes	characteristic
76	#16810534	C₂²	1	1	yes	characteristic
77	#16810530	C₂²	1	1	yes	characteristic
78	#16810530	C₂²	1	1	yes	characteristic
79	#16810530	C₂²	1	1	yes	characteristic
80	#16810530	C₂²	1	1	yes	characteristic
81	#16810528	C₂²	1	1	yes	characteristic
82	#16810527	C₂²	1	1	yes	characteristic
83	#16810527	C₂²	1	1	yes	characteristic
84	#16810522	C₂²	1	1	yes	characteristic
85	#16810522	C₂²	1	1	yes	characteristic
86	#16810522	C₂²	1	1	yes	characteristic
87	#16810522	C₂²	1	1	yes	characteristic
88	#16810520	C₂²	1	1	yes	characteristic
89	#16810520	C₂²	1	1	yes	characteristic
90	#16810520	C₂²	1	1	yes	characteristic
91	#16810520	C₂²	1	1	yes	characteristic
92	#16810519	C₂²	1	1	yes	characteristic
93	#16810518	C₂²	1	1	yes	characteristic
94	#16810518	C₂²	1	1	yes	characteristic
95	#16810518	C₂²	1	1	yes	characteristic
96	#16810518	C₂²	1	1	yes	characteristic
97	#16810518	C₂²	1	1	yes	characteristic
98	#16810518	C₂²	1	1	yes	characteristic
99	#16810515	C₂²	1	1	yes	characteristic
100	#16810515	C₂²	1	1	yes	characteristic
101	#16810515	C₂²	1	1	yes	characteristic
102	#16810514	C₂²	1	1	yes	characteristic
103	#16810514	C₂²	1	1	yes	characteristic
104	#16810514	C₂²	1	1	yes	characteristic
105	#16810514	C₂²	1	1	yes	characteristic
106	#16810513	C₂²	1	1	yes	characteristic
107	#16810513	C₂²	1	1	yes	characteristic
108	#16810513	C₂²	1	1	yes	characteristic
109	#16810513	C₂²	1	1	yes	characteristic
110	#16810513	C₂²	1	1	yes	characteristic
111	#16810513	C₂²	1	1	yes	characteristic
112	#16810512	C₂²	1	1	yes	characteristic
113	#16810512	C₂²	1	1	yes	characteristic
114	#16810510	C₂²	1	1	yes	characteristic
115	#16810510	C₂²	1	1	yes	characteristic
116	#16810510	C₂²	1	1	yes	characteristic
117	#16810510	C₂²	1	1	yes	characteristic
118	#16810510	C₂²	1	1	yes	characteristic
119	#16810510	C₂²	1	1	yes	characteristic
120	#16810509	C₂²	1	1	yes	characteristic
121	#16810509	C₂²	1	1	yes	characteristic
122	#16810509	C₂²	1	1	yes	characteristic
123	#16810509	C₂²	1	1	yes	characteristic
124	#16810509	C₂²	1	1	yes	characteristic
125	#16810509	C₂²	1	1	yes	characteristic
126	#16810509	C₂²	1	1	yes	characteristic
127	#16810509	C₂²	1	1	yes	characteristic
128	#16810508	C₂²	1	1	yes	characteristic
129	#16810508	C₂²	1	1	yes	characteristic
130	#16810508	C₂²	1	1	yes	characteristic
131	#16810508	C₂²	1	1	yes	characteristic
132	#16810507	C₂²	1	1	yes	characteristic
133	#16810507	C₂²	1	1	yes	characteristic
134	#16810507	C₂²	1	1	yes	characteristic
135	#16810507	C₂²	1	1	yes	characteristic
136	#16810506	C₂²	1	1	yes	characteristic
137	#16810506	C₂²	1	1	yes	characteristic
138	#16810506	C₂²	1	1	yes	characteristic
139	#16810506	C₂²	1	1	yes	characteristic
140	#16810506	C₂²	1	1	yes	characteristic
141	#16810506	C₂²	1	1	yes	characteristic
142	#16810505	C₂²	1	1	yes	characteristic
143	#16810505	C₂²	1	1	yes	characteristic
144	#16810505	C₂²	1	1	yes	characteristic
145	#16810505	C₂²	1	1	yes	characteristic
146	#16810504	C₂²	1	1	yes	characteristic
147	#16810504	C₂²	1	1	yes	characteristic
148	#16810504	C₂²	1	1	yes	characteristic
149	#16810497	C₂²	1	1	yes	characteristic
150	#16810497	C₂²	1	1	yes	characteristic
151	#16810497	C₂²	1	1	yes	characteristic
152	#16810494	C₂²	1	1	yes	characteristic
153	#16810491	C₂²	1	1	yes	characteristic
154	#16810491	C₂²	1	1	yes	characteristic
155	#16810490	C₂²	1	1	yes	characteristic
156	#16810489	C₂²	1	1	yes	characteristic
157	#16810489	C₂²	1	1	yes	characteristic
158	#16810488	C₂²	1	1	yes	characteristic
159	#16810487	C₂²	1	1	yes	characteristic
160	#16810487	C₂²	1	1	yes	characteristic
161	#16810485	C₂²	1	1	yes	characteristic
162	#16810480	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
166	#16810474	C₂²	1	1	yes	characteristic
167	#16810470	C₂²	1	1	yes	characteristic
168	#16810469	C₂²	1	1	yes	characteristic
169	#16810469	C₂²	1	1	yes	characteristic
170	#16810469	C₂²	1	1	yes	characteristic
171	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
172	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
173	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
174	C₅₃×#400	C₂²	1	1	yes	characteristic
175	C₅₃×#400	C₂²	1	1	yes	characteristic
176	C₅₃×#395	C₂²	1	1	yes	characteristic
177	C₅₃×#395	C₂²	1	1	yes	characteristic
178	C₅₃×#391	C₂²	1	1	yes	characteristic
179	C₅₃×#391	C₂²	1	1	yes	characteristic
180	C₅₃×#389	C₂²	1	1	yes	characteristic
181	C₅₃×#389	C₂²	1	1	yes	characteristic
182	C₅₃×#387	C₂²	1	1	yes	characteristic
183	C₅₃×#387	C₂²	1	1	yes	characteristic
184	C₅₃×#387	C₂²	1	1	yes	characteristic
185	C₅₃×#387	C₂²	1	1	yes	characteristic
186	C₅₃×#382	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
188	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
189	#13133211	—	2	4	no	—
190	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
203	C₂×#11719919	C₂³	1	1	yes	characteristic
204	C₂×#11719919	C₂³	1	1	yes	characteristic
205	C₂×#11719919	C₂³	1	1	yes	characteristic
206	C₂×#11719919	C₂³	1	1	yes	characteristic
207	C₂×#11719919	C₂³	1	1	yes	characteristic
208	C₂×#11719919	C₂³	1	1	yes	characteristic
209	C₂×#11719919	C₂³	1	1	yes	characteristic
210	C₂×#11719919	C₂³	1	1	yes	characteristic
211	C₂×#11719919	C₂³	1	1	yes	characteristic
212	C₂×#11719919	C₂³	1	1	yes	characteristic
213	C₂×#11719919	C₂³	1	1	yes	characteristic
214	C₂×#11719919	C₂³	1	1	yes	characteristic
215	C₂×#11719919	C₂³	1	1	yes	characteristic
216	C₂×#11719919	C₂³	1	1	yes	characteristic
217	C₂×#11719919	C₂³	1	1	yes	characteristic
218	C₂×#11719919	C₂³	1	1	yes	characteristic
219	C₂×#11719919	C₂³	1	1	yes	characteristic
220	C₂×#11719919	C₂³	1	1	yes	characteristic
221	C₂×#11719919	C₂³	1	1	yes	characteristic
222	C₂×#11719919	C₂³	1	1	yes	characteristic
223	C₂×#11719921	C₂³	1	1	yes	characteristic
224	C₂×#11719921	C₂³	1	1	yes	characteristic
225	C₂×#11719921	C₂³	1	1	yes	characteristic
226	C₂×#11719921	C₂³	1	1	yes	characteristic
227	C₂×#11719921	C₂³	1	1	yes	characteristic
228	C₂×#11719921	C₂³	1	1	yes	characteristic
229	C₂×#11719921	C₂³	1	1	yes	characteristic
230	C₂×#11719921	C₂³	1	1	yes	characteristic
231	C₂×#11719921	C₂³	1	1	yes	characteristic
232	C₂×#11719921	C₂³	1	1	yes	characteristic
233	C₂×#11719921	C₂³	1	1	yes	characteristic
234	C₂×#11719921	C₂³	1	1	yes	characteristic
235	C₂×#11719921	C₂³	1	1	yes	characteristic
236	C₂×#11719921	C₂³	1	1	yes	characteristic
237	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×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	#13133124	C₂³	1	1	yes	characteristic
251	#13133124	C₂³	1	1	yes	characteristic
252	#13133124	C₂³	1	1	yes	characteristic
253	#13133124	C₂³	1	1	yes	characteristic
254	#13133124	C₂³	1	1	yes	characteristic
255	#13133124	C₂³	1	1	yes	characteristic
256	#13133124	C₂³	1	1	yes	characteristic
257	#13133124	C₂³	1	1	yes	characteristic
258	#13133124	C₂³	1	1	yes	characteristic
259	#13133124	C₂³	1	1	yes	characteristic
260	#13133124	C₂³	1	1	yes	characteristic
261	#13133124	C₂³	1	1	yes	characteristic
262	#13133124	C₂³	1	1	yes	characteristic
263	#13133124	C₂³	1	1	yes	characteristic
264	#13133124	C₂³	1	1	yes	characteristic
265	#13133124	C₂³	1	1	yes	characteristic
266	#13133124	C₂³	1	1	yes	characteristic
267	#13133124	C₂³	1	1	yes	characteristic
268	#13133124	C₂³	1	1	yes	characteristic
269	#13133124	C₂³	1	1	yes	characteristic
270	#13133124	C₂³	1	1	yes	characteristic
271	#13133124	C₂³	1	1	yes	characteristic
272	#13133124	C₂³	1	1	yes	characteristic
273	#13133124	C₂³	1	1	yes	characteristic
274	#13133124	C₂³	1	1	yes	characteristic
275	#13133124	C₂³	1	1	yes	characteristic
276	#13133124	C₂³	1	1	yes	characteristic
277	#13133124	C₂³	1	1	yes	characteristic
278	#13133124	C₂³	1	1	yes	characteristic
279	#13133124	C₂³	1	1	yes	characteristic
280	#13133124	C₂³	1	1	yes	characteristic
281	#13133124	C₂³	1	1	yes	characteristic
282	#13133124	C₂³	1	1	yes	characteristic
283	#13133124	C₂³	1	1	yes	characteristic
284	#13133124	C₂³	1	1	yes	characteristic
285	#13133124	C₂³	1	1	yes	characteristic
286	#13133124	C₂³	1	1	yes	characteristic
287	#13133124	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×Q₈×C₅₃	—	2	4	no	—
311	C₄×Q₈×C₅₃	—	2	4	no	—
312	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
323	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
326	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
329	#95×C₅₃	C₂³	1	1	yes	characteristic
330	#95×C₅₃	C₂³	1	1	yes	characteristic
331	#95×C₅₃	C₂³	1	1	yes	characteristic
332	#95×C₅₃	C₂³	1	1	yes	characteristic
333	#95×C₅₃	C₂³	1	1	yes	characteristic
334	#95×C₅₃	C₂³	1	1	yes	characteristic
335	#95×C₅₃	C₂³	1	1	yes	characteristic
336	#95×C₅₃	C₂³	1	1	yes	characteristic
337	#95×C₅₃	C₂³	1	1	yes	characteristic
338	#95×C₅₃	C₂³	1	1	yes	characteristic
339	#95×C₅₃	C₂³	1	1	yes	characteristic
340	#95×C₅₃	C₂³	1	1	yes	characteristic
341	#95×C₅₃	C₂³	1	1	yes	characteristic
342	#95×C₅₃	C₂³	1	1	yes	characteristic
343	#95×C₅₃	C₂³	1	1	yes	characteristic
344	#95×C₅₃	C₂³	1	1	yes	characteristic
345	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
346	C₂×Q₈×C₅₃	—	2	2	no	—
347	C₂×Q₈×C₅₃	—	2	2	no	—
348	C₂×Q₈×C₅₃	—	2	2	no	—
349	C₂×Q₈×C₅₃	—	4	1	no	—
350	C₂×Q₈×C₅₃	—	4	1	no	—
351	C₂×Q₈×C₅₃	—	4	1	no	—
352	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₄×D₅₃	—	4	1	no	—
383	C₂×C₄×D₅₃	—	4	1	no	—
384	C₂×C₄×D₅₃	—	4	1	no	—
385	C₂×Dic₁₀₆	—	4	1	no	—
386	C₂×Dic₁₀₆	—	4	1	no	—
387	C₂×Dic₁₀₆	—	4	1	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	—	2	2	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	4	1	no	—
395	C₄⋊C₄×C₅₃	—	4	1	no	—
396	C₄⋊C₄×C₅₃	—	4	1	no	—
397	C₄⋊C₄×C₅₃	—	4	1	no	—
398	C₄⋊C₄×C₅₃	—	4	1	no	—
399	C₄⋊C₄×C₅₃	—	4	1	no	—
400	C₄²×C₅₃	—	2	2	no	—
401	C₄²×C₅₃	—	2	2	no	—
402	C₄²×C₅₃	—	2	2	no	—
403	C₄²×C₅₃	—	2	2	no	—
404	C₄²×C₅₃	#41	1	4	yes	—
405	#11719921	—	2	2	no	—
406	#11719921	—	2	2	no	—
407	#11719921	—	2	2	no	—
408	#11719921	—	2	2	no	—
409	#11719921	—	2	2	no	—
410	#11719921	—	4	1	no	—
411	#11719921	—	4	1	no	—
412	#11719921	—	4	1	no	—
413	#11719921	—	4	1	no	—
414	#11719921	—	4	1	no	—
415	#11719921	—	4	1	no	—
416	#11719921	—	4	1	no	—
417	#11719921	—	4	1	no	—
418	#11719921	—	4	1	no	—
419	C₄⋊Dic₅₃	—	2	2	no	—
420	C₄⋊Dic₅₃	—	2	2	no	—
421	C₄⋊Dic₅₃	—	4	1	no	—
422	C₄⋊Dic₅₃	—	4	1	no	—
423	C₄⋊Dic₅₃	—	4	1	no	—
424	C₄⋊Dic₅₃	—	4	1	no	—
425	C₄⋊Dic₅₃	—	4	1	no	—
426	C₄⋊Dic₅₃	—	4	1	no	—
427	C₄⋊Dic₅₃	—	4	1	no	—
428	C₄⋊Dic₅₃	—	4	1	no	—
429	C₄⋊Dic₅₃	—	4	1	no	—
430	C₄⋊Dic₅₃	—	4	1	no	—
431	C₄⋊Dic₅₃	—	4	1	no	—
432	#11719919	—	2	2	no	—
433	#11719919	—	2	2	no	—
434	#11719919	—	2	2	no	—
435	#11719919	—	2	2	no	—
436	#11719919	—	2	2	no	—
437	#11719919	—	2	2	no	—
438	#11719919	—	4	1	no	—
439	#11719919	—	4	1	no	—
440	#11719919	—	4	1	no	—
441	#11719919	—	4	1	no	—
442	#11719919	—	4	1	no	—
443	#11719919	—	4	1	no	—
444	#11719919	—	4	1	no	—
445	#11719919	—	4	1	no	—
446	#11719919	—	4	1	no	—
447	#11719919	—	4	1	no	—
448	#11719919	—	4	1	no	—
449	#11719919	—	4	1	no	—
450	#11719919	—	4	1	no	—
451	#11719919	—	4	1	no	—
452	C₄×Dic₅₃	—	2	2	no	—
453	C₄×Dic₅₃	—	2	2	no	—
454	C₄×Dic₅₃	—	4	1	no	—
455	C₄×Dic₅₃	—	4	1	no	—
456	C₄×Dic₅₃	—	4	1	no	—
457	C₄×Dic₅₃	—	4	1	no	—
458	C₄×Dic₅₃	—	4	1	no	—
459	C₄×Dic₅₃	—	4	1	no	—
460	C₄×Dic₅₃	—	4	1	no	—
461	C₄×Dic₅₃	—	4	1	no	—
462	C₄×Dic₅₃	—	4	1	no	—
463	C₄×Dic₅₃	—	4	1	no	—
464	C₄×Dic₅₃	—	4	1	no	—
465	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
466	C₂²×D₅₃	—	2	1	no	—
467	C₂²×D₅₃	—	2	1	no	—
468	C₂²×D₅₃	—	2	1	no	—
469	C₂²×D₅₃	—	2	1	no	—
470	C₂²×D₅₃	—	2	1	no	—
471	C₂²×D₅₃	—	2	1	no	—
472	C₂²×D₅₃	—	2	1	no	—
473	Q₈×C₅₃	—	4	4	no	—
474	Q₈×C₅₃	—	4	4	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	1	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	1	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	1	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	1	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	2	1	no	—
490	C₂×C₄×C₅₃	—	2	1	no	—
491	C₂×C₄×C₅₃	—	2	1	no	—
492	C₂×C₄×C₅₃	—	2	1	no	—
493	C₂×C₄×C₅₃	—	2	1	no	—
494	C₂×C₄×C₅₃	—	2	1	no	—
495	C₂×C₄×C₅₃	—	2	1	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	1	no	—
498	C₂×C₄×C₅₃	—	2	1	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	2	1	no	—
502	C₂×C₄×C₅₃	—	2	1	no	—
503	C₂×C₄×C₅₃	—	2	1	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	1	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	1	no	—
512	C₂×C₄×C₅₃	—	2	1	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
517	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
518	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
519	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
520	C₂×Dic₅₃	—	2	1	no	—
521	C₂×Dic₅₃	—	2	1	no	—
522	C₂×Dic₅₃	—	2	1	no	—
523	C₂×Dic₅₃	—	2	1	no	—
524	C₂×Dic₅₃	—	2	1	no	—
525	C₂×Dic₅₃	—	2	1	no	—
526	C₂×Dic₅₃	—	2	1	no	—
527	C₂×Dic₅₃	—	2	1	no	—
528	C₂×Dic₅₃	—	2	1	no	—
529	C₂×Dic₅₃	—	2	1	no	—
530	C₂×Dic₅₃	—	2	1	no	—
531	C₂×Dic₅₃	—	2	1	no	—
532	C₂×Dic₅₃	—	2	1	no	—
533	C₂×Dic₅₃	—	2	1	no	—
534	C₂×Dic₅₃	—	2	1	no	—
535	C₂×Dic₅₃	—	2	1	no	—
536	C₂×Dic₅₃	—	2	1	no	—
537	C₂×Dic₅₃	—	2	1	no	—
538	C₂×Dic₅₃	—	2	1	no	—
539	C₂×Dic₅₃	—	2	1	no	—
540	C₂×Dic₅₃	—	2	1	no	—
541	C₂×Dic₅₃	—	2	1	no	—
542	C₂×Dic₅₃	—	2	1	no	—
543	C₂×Dic₅₃	—	2	1	no	—
544	C₂×Dic₅₃	—	2	1	no	—
545	C₂×Dic₅₃	—	2	1	no	—
546	C₂×Dic₅₃	—	2	1	no	—
547	C₂×Dic₅₃	—	2	1	no	—
548	C₂×Dic₅₃	—	2	1	no	—
549	C₂×Dic₅₃	—	2	1	no	—
550	C₂×Dic₅₃	—	2	1	no	—
551	C₂×Dic₅₃	—	2	1	no	—
552	C₂×Dic₅₃	—	2	1	no	—
553	C₂×Dic₅₃	—	2	1	no	—
554	C₂×Dic₅₃	—	2	1	no	—
555	C₂×Dic₅₃	—	2	1	no	—
556	C₂×Dic₅₃	—	2	1	no	—
557	C₂×Dic₅₃	—	2	1	no	—
558	C₂×Dic₅₃	—	2	1	no	—
559	C₂×Dic₅₃	—	2	1	no	—
560	C₂×Dic₅₃	—	2	1	no	—
561	C₂×Dic₅₃	—	2	1	no	—
562	C₂×Dic₅₃	—	2	1	no	—
563	C₂×Dic₅₃	—	2	1	no	—
564	C₂×Dic₅₃	2₋¹⁺⁴	1	2	yes	—
565	C₄×D₅₃	—	8	2	no	—
566	Dic₁₀₆	—	8	2	no	—
567	#37006	—	53	1	no	maximal, Sylow
568	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
569	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
570	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
571	C₂²×C₅₃	#585	1	1	yes	characteristic
572	C₂²×C₅₃	#585	1	1	yes	characteristic
573	C₂²×C₅₃	#585	1	1	yes	characteristic
574	C₂²×C₅₃	#585	1	1	yes	characteristic
575	C₂×D₅₃	—	4	1	no	—
576	C₂×D₅₃	—	4	1	no	—
577	C₂×D₅₃	—	4	1	no	—
578	C₂×D₅₃	—	4	1	no	—
579	C₂×D₅₃	—	4	1	no	—
580	C₂×D₅₃	—	4	1	no	—
581	C₂×D₅₃	—	4	1	no	—
582	C₄×C₅₃	—	2	2	no	—
583	C₄×C₅₃	—	2	2	no	—
584	C₄×C₅₃	—	2	2	no	—
585	C₄×C₅₃	—	2	2	no	—
586	C₄×C₅₃	—	4	1	no	—
587	C₄×C₅₃	—	4	1	no	—
588	C₄×C₅₃	—	4	1	no	—
589	C₄×C₅₃	—	4	1	no	—
590	C₄×C₅₃	—	4	1	no	—
591	C₄×C₅₃	—	4	1	no	—
592	C₄×C₅₃	—	4	1	no	—
593	C₄×C₅₃	—	4	1	no	—
594	C₄×C₅₃	—	4	1	no	—
595	C₄×C₅₃	—	4	1	no	—
596	C₄×C₅₃	—	4	1	no	—
597	Dic₅₃	—	2	2	no	—
598	Dic₅₃	—	4	1	no	—
599	Dic₅₃	—	4	1	no	—
600	Dic₅₃	—	4	1	no	—
601	Dic₅₃	—	4	1	no	—
602	Dic₅₃	—	4	1	no	—
603	Dic₅₃	—	4	1	no	—
604	Dic₅₃	—	4	1	no	—
605	Dic₅₃	—	4	1	no	—
606	Dic₅₃	—	4	1	no	—
607	Dic₅₃	—	4	1	no	—
608	Dic₅₃	—	4	1	no	—
609	Dic₅₃	—	4	1	no	—
610	Dic₅₃	—	4	1	no	—
611	Dic₅₃	—	4	1	no	—
612	#2865	—	53	1	no	—
613	#2864	—	53	1	no	—
614	#2810	—	53	1	no	—
615	#2805	—	53	1	no	—
616	#2788	—	53	1	no	—
617	#2777	—	53	1	no	—
618	#2774	—	53	1	no	—
619	#2774	—	53	1	no	—
620	#2774	—	53	1	no	—
621	#2773	—	53	1	no	—
622	#2771	—	53	1	no	—
623	#2767	—	53	1	no	—
624	#2763	—	53	1	no	—
625	#2762	—	53	1	no	—
626	#2759	—	53	1	no	—
627	#2758	—	53	1	no	—
628	#2754	—	53	1	no	—
629	#2738	—	53	1	no	—
630	#2655	—	53	1	no	—
631	#2650	—	53	1	no	—
632	#2612	—	53	1	no	—
633	#2604	—	53	1	no	—
634	#2604	—	53	1	no	—
635	#2588	—	53	1	no	—
636	#2581	D₅₃	1	1	yes	characteristic, complemented
637	#2575	—	53	1	no	—
638	#2533	—	53	1	no	—
639	#2530	—	53	1	no	—
640	#2334	—	53	1	no	—
641	#2320	—	53	1	no	—
642	#2295	—	53	1	no	—
643	C₂×C₅₃	#3455	1	1	yes	characteristic
644	C₂×C₅₃	#3495	1	1	yes	characteristic
645	C₂×C₅₃	#3507	1	1	yes	characteristic
646	C₂×C₅₃	#3557	1	1	yes	characteristic
647	C₂×C₅₃	#3563	1	1	yes	characteristic
648	C₂×C₅₃	#3565	1	1	yes	characteristic
649	C₂×C₅₃	#3568	1	1	yes	characteristic
650	D₅₃	—	8	1	no	—
651	C₂×#126	—	53	1	no	—
652	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
653	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
654	#401	—	53	1	no	—
655	#400	—	53	1	no	—
656	#400	—	53	1	no	—
657	#400	—	53	1	no	—
658	#400	—	53	1	no	—
659	#400	—	53	1	no	—
660	#400	—	53	1	no	—
661	#400	—	53	1	no	—
662	#400	—	53	1	no	—
663	#400	—	53	1	no	—
664	#400	—	53	1	no	—
665	#400	—	53	1	no	—
666	#400	—	53	1	no	—
667	#400	—	53	1	no	—
668	#400	—	53	1	no	—
669	#400	—	53	1	no	—
670	#400	—	53	1	no	—
671	#400	—	53	1	no	—
672	#400	—	53	1	no	—
673	#400	—	53	1	no	—
674	#400	—	53	1	no	—
675	#400	C₂×D₅₃	1	1	yes	characteristic
676	#400	C₂×D₅₃	1	1	yes	characteristic
677	#399	—	53	1	no	—
678	#399	—	53	1	no	—
679	#399	—	53	1	no	—
680	#398	—	53	1	no	—
681	#398	—	53	1	no	—
682	#398	—	53	1	no	—
683	#398	—	53	1	no	—
684	#398	—	53	1	no	—
685	#398	—	53	1	no	—
686	#397	—	53	1	no	—
687	#397	—	53	1	no	—
688	#397	—	53	1	no	—
689	#397	—	53	1	no	—
690	#397	—	53	1	no	—
691	#396	—	53	1	no	—
692	#395	—	53	1	no	—
693	#395	—	53	1	no	—
694	#395	—	53	1	no	—
695	#395	—	53	1	no	—
696	#395	—	53	1	no	—
697	#395	C₂×D₅₃	1	1	yes	characteristic
698	#395	C₂×D₅₃	1	1	yes	characteristic
699	#393	—	53	1	no	—
700	#393	—	53	1	no	—
701	#393	—	53	1	no	—
702	#391	—	53	1	no	—
703	#391	—	53	1	no	—
704	#391	—	53	1	no	—
705	#391	—	53	1	no	—
706	#391	—	53	1	no	—
707	#391	—	53	1	no	—
708	#391	—	53	1	no	—
709	#391	C₂×D₅₃	1	1	yes	characteristic
710	#391	C₂×D₅₃	1	1	yes	characteristic
711	#389	—	53	1	no	—
712	#389	—	53	1	no	—
713	#389	—	53	1	no	—
714	#389	—	53	1	no	—
715	#389	—	53	1	no	—
716	#389	—	53	1	no	—
717	#389	—	53	1	no	—
718	#389	—	53	1	no	—
719	#389	—	53	1	no	—
720	#389	—	53	1	no	—
721	#389	—	53	1	no	—
722	#389	—	53	1	no	—
723	#389	—	53	1	no	—
724	#389	—	53	1	no	—
725	#389	—	53	1	no	—
726	#389	C₂×D₅₃	1	1	yes	characteristic
727	#389	C₂×D₅₃	1	1	yes	characteristic
728	#388	—	53	1	no	—
729	#388	—	53	1	no	—
730	#388	—	53	1	no	—
731	#388	—	53	1	no	—
732	#388	—	53	1	no	—
733	#388	—	53	1	no	—
734	#388	—	53	1	no	—
735	#388	—	53	1	no	—
736	#388	—	53	1	no	—
737	#388	—	53	1	no	—
738	#388	—	53	1	no	—
739	#388	—	53	1	no	—
740	#388	—	53	1	no	—
741	#388	—	53	1	no	—
742	#388	—	53	1	no	—
743	#387	—	53	1	no	—
744	#387	—	53	1	no	—
745	#387	—	53	1	no	—
746	#387	—	53	1	no	—
747	#387	—	53	1	no	—
748	#387	—	53	1	no	—
749	#387	—	53	1	no	—
750	#387	—	53	1	no	—
751	#387	—	53	1	no	—
752	#387	—	53	1	no	—
753	#387	—	53	1	no	—
754	#387	—	53	1	no	—
755	#387	—	53	1	no	—
756	#387	—	53	1	no	—
757	#387	—	53	1	no	—
758	#387	—	53	1	no	—
759	#387	—	53	1	no	—
760	#387	—	53	1	no	—
761	#387	—	53	1	no	—
762	#387	—	53	1	no	—
763	#387	—	53	1	no	—
764	#387	—	53	1	no	—
765	#387	—	53	1	no	—
766	#387	—	53	1	no	—
767	#387	—	53	1	no	—
768	#387	—	53	1	no	—
769	#387	—	53	1	no	—
770	#387	—	53	1	no	—
771	#387	—	53	1	no	—
772	#387	—	53	1	no	—
773	#387	—	53	1	no	—
774	#387	—	53	1	no	—
775	#387	—	53	1	no	—
776	#387	—	53	1	no	—
777	#387	—	53	1	no	—
778	#387	C₂×D₅₃	1	1	yes	characteristic
779	#387	C₂×D₅₃	1	1	yes	characteristic
780	#387	C₂×D₅₃	1	1	yes	characteristic
781	#387	C₂×D₅₃	1	1	yes	characteristic
782	#385	—	53	1	no	—
783	#385	—	53	1	no	—
784	#385	—	53	1	no	—
785	#385	—	53	1	no	—
786	#383	—	53	1	no	—
787	#383	—	53	1	no	—
788	#383	—	53	1	no	—
789	#382	—	53	1	no	—
790	#382	—	53	1	no	—
791	#382	—	53	1	no	—
792	#382	—	53	1	no	—
793	#382	—	53	1	no	—
794	#382	C₂×D₅₃	1	1	yes	characteristic
795	#381	—	53	1	no	—
796	#380	—	53	1	no	—
797	C₄×C₄⋊C₄	—	53	1	no	—
798	C₄×C₄⋊C₄	—	53	1	no	—
799	C₄×C₄⋊C₄	—	53	1	no	—
800	C₄×C₄⋊C₄	—	53	1	no	—
801	C₄×C₂²⋊C₄	—	53	1	no	—
802	#376	—	53	1	no	—
803	#376	—	53	1	no	—
804	#376	—	53	1	no	—
805	C₄³	—	53	1	no	—
806	C₅₃	#37006	1	1	yes	characteristic, complemented, Sylow
807	C₂²×Q₈	—	53	1	no	—
808	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
809	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
810	C₂³×C₄	—	53	1	no	—
811	#126	—	106	4	no	—
812	C₄×Q₈	—	2	4	no	—
813	C₄×Q₈	—	2	4	no	—
814	C₂×C₄⋊C₄	—	53	1	no	—
815	C₂×C₄⋊C₄	—	53	1	no	—
816	C₂×C₄⋊C₄	—	53	1	no	—
817	C₂×C₄⋊C₄	—	53	1	no	—
818	C₂×C₄⋊C₄	—	53	1	no	—
819	C₂×C₄⋊C₄	—	53	1	no	—
820	C₂×C₄⋊C₄	—	53	1	no	—
821	C₂×C₄⋊C₄	—	53	1	no	—
822	C₂×C₄⋊C₄	—	53	1	no	—
823	C₂×C₄⋊C₄	—	53	1	no	—
824	C₂×C₄⋊C₄	—	53	1	no	—
825	C₂×C₄⋊C₄	—	53	1	no	—
826	C₂×C₄⋊C₄	—	53	1	no	—
827	C₂×C₄⋊C₄	—	53	1	no	—
828	C₂×C₄⋊C₄	—	53	1	no	—
829	C₂×C₄⋊C₄	—	53	1	no	—
830	C₂×C₄⋊C₄	—	53	1	no	—
831	C₂×C₄⋊C₄	—	53	1	no	—
832	C₂×C₄⋊C₄	—	53	1	no	—
833	C₂×C₄⋊C₄	—	53	1	no	—
834	C₂×C₄⋊C₄	—	53	1	no	—
835	C₂×C₄⋊C₄	—	53	1	no	—
836	C₂×C₄⋊C₄	—	53	1	no	—
837	C₂×C₄⋊C₄	—	53	1	no	—
838	C₂×C₄⋊C₄	—	53	1	no	—
839	C₂×C₄⋊C₄	—	53	1	no	—
840	C₂×C₄⋊C₄	—	53	1	no	—
841	C₂×C₄⋊C₄	—	53	1	no	—
842	C₂×C₄⋊C₄	—	53	1	no	—
843	C₂×C₄⋊C₄	—	53	1	no	—
844	C₂×C₄⋊C₄	—	53	1	no	—
845	C₂×C₄⋊C₄	—	53	1	no	—
846	C₂×C₄⋊C₄	—	53	1	no	—
847	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
848	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
850	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
853	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
854	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
855	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
856	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
857	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
858	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
859	C₂×C₂²⋊C₄	—	53	1	no	—
860	C₂×C₂²⋊C₄	—	53	1	no	—
861	C₂×C₂²⋊C₄	—	53	1	no	—
862	C₂×C₂²⋊C₄	—	53	1	no	—
863	C₂×C₂²⋊C₄	—	53	1	no	—
864	C₂×C₂²⋊C₄	—	53	1	no	—
865	C₂×C₂²⋊C₄	—	53	1	no	—
866	C₂×C₂²⋊C₄	—	53	1	no	—
867	C₂×C₂²⋊C₄	—	53	1	no	—
868	C₂×C₂²⋊C₄	—	53	1	no	—
869	C₂×C₂²⋊C₄	—	53	1	no	—
870	C₂×C₂²⋊C₄	—	53	1	no	—
871	C₂×C₂²⋊C₄	—	53	1	no	—
872	C₂×C₂²⋊C₄	—	53	1	no	—
873	C₂×C₄²	—	53	1	no	—
874	C₂×C₄²	—	53	1	no	—
875	C₂×C₄²	—	53	1	no	—
876	C₂×C₄²	—	53	1	no	—
877	C₂×C₄²	—	53	1	no	—
878	C₂×C₄²	—	53	1	no	—
879	C₂×C₄²	—	53	1	no	—
880	C₂×C₄²	—	53	1	no	—
881	C₂×C₄²	—	53	1	no	—
882	C₂×C₄²	—	53	1	no	—
883	C₂×C₄²	—	53	1	no	—
884	C₂×C₄²	—	53	1	no	—
885	C₂×C₄²	—	53	1	no	—
886	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
887	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
888	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
889	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
890	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
891	#95	—	53	1	no	—
892	#95	—	53	1	no	—
893	#95	—	53	1	no	—
894	#95	—	53	1	no	—
895	#95	—	53	1	no	—
896	#95	—	53	1	no	—
897	#95	—	53	1	no	—
898	#95	—	53	1	no	—
899	#95	—	53	1	no	—
900	#95	—	53	1	no	—
901	#95	—	53	1	no	—
902	#95	—	53	1	no	—
903	#95	—	53	1	no	—
904	#95	—	53	1	no	—
905	#95	—	53	1	no	—
906	#95	—	53	1	no	—
907	#95	—	53	1	no	—
908	#95	—	53	1	no	—
909	#95	—	53	1	no	—
910	#95	—	53	1	no	—
911	#95	—	53	1	no	—
912	#95	—	53	1	no	—
913	#95	—	53	1	no	—
914	#95	—	53	1	no	—
915	#95	—	53	1	no	—
916	#95	—	53	1	no	—
917	#95	—	53	1	no	—
918	#95	—	53	1	no	—
919	#95	—	53	1	no	—
920	#95	—	53	1	no	—
921	#95	—	53	1	no	—
922	#95	—	53	1	no	—
923	#95	—	53	1	no	—
924	#95	—	53	1	no	—
925	#95	—	53	1	no	—
926	#95	—	53	1	no	—
927	#95	—	53	1	no	—
928	#95	—	53	1	no	—
929	#95	—	53	1	no	—
930	#95	—	53	1	no	—
931	#95	—	53	1	no	—
932	#95	—	53	1	no	—
933	#95	—	53	1	no	—
934	#95	—	53	1	no	—
935	#95	—	53	1	no	—
936	#95	—	53	1	no	—
937	#95	—	53	1	no	—
938	#95	—	53	1	no	—
939	#95	—	53	1	no	—
940	#95	—	53	1	no	—
941	#95	—	53	1	no	—
942	#95	—	53	1	no	—
943	#95	—	53	1	no	—
944	#95	—	53	1	no	—
945	#95	—	53	1	no	—
946	#95	—	53	1	no	—
947	#95	—	53	1	no	—
948	#95	—	53	1	no	—
949	#95	C₂²×D₅₃	1	1	yes	characteristic
950	#95	C₂²×D₅₃	1	1	yes	characteristic
951	#95	C₂²×D₅₃	1	1	yes	characteristic
952	#95	C₂²×D₅₃	1	1	yes	characteristic
953	#95	C₂²×D₅₃	1	1	yes	characteristic
954	#95	C₂²×D₅₃	1	1	yes	characteristic
955	#95	C₂²×D₅₃	1	1	yes	characteristic
956	#95	C₂²×D₅₃	1	1	yes	characteristic
957	#95	C₂²×D₅₃	1	1	yes	characteristic
958	#95	C₂²×D₅₃	1	1	yes	characteristic
959	#95	C₂²×D₅₃	1	1	yes	characteristic
960	#95	C₂²×D₅₃	1	1	yes	characteristic
961	#95	C₂²×D₅₃	1	1	yes	characteristic
962	#95	C₂²×D₅₃	1	1	yes	characteristic
963	#95	C₂²×D₅₃	1	1	yes	characteristic
964	#95	C₂²×D₅₃	1	1	yes	characteristic
965	C₂⁴	—	53	1	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	2	2	no	—
969	C₂×Q₈	—	4	1	no	—
970	C₂×Q₈	—	4	1	no	—
971	C₂×Q₈	—	4	1	no	—
972	C₂×Q₈	—	212	1	no	—
973	C₂×Q₈	—	212	1	no	—
974	C₂×Q₈	—	212	1	no	—
975	C₂²×C₄	—	53	1	no	—
976	C₂²×C₄	—	53	1	no	—
977	C₂²×C₄	—	53	1	no	—
978	C₂²×C₄	—	53	1	no	—
979	C₂²×C₄	—	53	1	no	—
980	C₂²×C₄	—	53	1	no	—
981	C₂²×C₄	—	53	1	no	—
982	C₂²×C₄	—	53	1	no	—
983	C₂²×C₄	—	53	1	no	—
984	C₂²×C₄	—	53	1	no	—
985	C₂²×C₄	—	53	1	no	—
986	C₂²×C₄	—	53	1	no	—
987	C₂²×C₄	—	53	1	no	—
988	C₂²×C₄	—	53	1	no	—
989	C₂²×C₄	—	53	1	no	—
990	C₂²×C₄	—	212	1	no	—
991	C₂²×C₄	—	212	1	no	—
992	C₂²×C₄	—	212	1	no	—
993	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
994	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
995	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
996	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
997	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
998	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
999	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1000	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1001	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1002	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1003	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1004	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1005	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1006	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	4	1	no	—
1015	C₄⋊C₄	—	4	1	no	—
1016	C₄⋊C₄	—	4	1	no	—
1017	C₄⋊C₄	—	4	1	no	—
1018	C₄⋊C₄	—	4	1	no	—
1019	C₄⋊C₄	—	4	1	no	—
1020	C₄⋊C₄	—	106	2	no	—
1021	C₄⋊C₄	—	106	2	no	—
1022	C₄⋊C₄	—	106	2	no	—
1023	C₄⋊C₄	—	106	2	no	—
1024	C₄⋊C₄	—	106	2	no	—
1025	C₄⋊C₄	—	106	2	no	—
1026	C₄⋊C₄	—	106	2	no	—
1027	C₄⋊C₄	—	106	2	no	—
1028	C₄⋊C₄	—	212	1	no	—
1029	C₄⋊C₄	—	212	1	no	—
1030	C₄⋊C₄	—	212	1	no	—
1031	C₄⋊C₄	—	212	1	no	—
1032	C₄⋊C₄	—	212	1	no	—
1033	C₄⋊C₄	—	212	1	no	—
1034	C₄⋊C₄	—	212	1	no	—
1035	C₄⋊C₄	—	212	1	no	—
1036	C₄⋊C₄	—	212	1	no	—
1037	C₄⋊C₄	—	212	1	no	—
1038	C₄⋊C₄	—	212	1	no	—
1039	C₄⋊C₄	—	212	1	no	—
1040	C₄⋊C₄	—	212	1	no	—
1041	C₄⋊C₄	—	212	1	no	—
1042	C₄⋊C₄	—	212	1	no	—
1043	C₄⋊C₄	—	212	1	no	—
1044	C₄⋊C₄	—	212	1	no	—
1045	C₄⋊C₄	—	212	1	no	—
1046	C₄⋊C₄	—	212	1	no	—
1047	C₄⋊C₄	—	212	1	no	—
1048	C₄⋊C₄	—	212	1	no	—
1049	C₄⋊C₄	—	212	1	no	—
1050	C₄⋊C₄	—	212	1	no	—
1051	C₄⋊C₄	—	212	1	no	—
1052	C₄⋊C₄	—	212	1	no	—
1053	C₂²⋊C₄	—	106	2	no	—
1054	C₂²⋊C₄	—	106	2	no	—
1055	C₂²⋊C₄	—	106	2	no	—
1056	C₂²⋊C₄	—	106	2	no	—
1057	C₂²⋊C₄	—	106	2	no	—
1058	C₂²⋊C₄	—	212	1	no	—
1059	C₂²⋊C₄	—	212	1	no	—
1060	C₂²⋊C₄	—	212	1	no	—
1061	C₂²⋊C₄	—	212	1	no	—
1062	C₂²⋊C₄	—	212	1	no	—
1063	C₂²⋊C₄	—	212	1	no	—
1064	C₂²⋊C₄	—	212	1	no	—
1065	C₂²⋊C₄	—	212	1	no	—
1066	C₂²⋊C₄	—	212	1	no	—
1067	C₄²	—	2	2	no	—
1068	C₄²	—	2	2	no	—
1069	C₄²	—	2	2	no	—
1070	C₄²	—	2	2	no	—
1071	C₄²	—	106	2	no	—
1072	C₄²	—	106	2	no	—
1073	C₄²	—	212	1	no	—
1074	C₄²	—	212	1	no	—
1075	C₄²	—	212	1	no	—
1076	C₄²	—	212	1	no	—
1077	C₄²	—	212	1	no	—
1078	C₄²	—	212	1	no	—
1079	C₄²	—	212	1	no	—
1080	C₄²	—	212	1	no	—
1081	C₄²	—	212	1	no	—
1082	C₄²	—	212	1	no	—
1083	C₄²	—	212	1	no	—
1084	C₄²	#11719947	1	4	yes	—
1085	C₂³	—	106	1	no	—
1086	C₂³	—	106	1	no	—
1087	C₂³	—	106	1	no	—
1088	C₂³	—	106	1	no	—
1089	C₂³	—	106	1	no	—
1090	C₂³	—	106	1	no	—
1091	C₂³	—	106	1	no	—
1092	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1093	Q₈	—	4	4	no	—
1094	Q₈	—	4	4	no	—
1095	Q₈	—	424	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	53	2	no	—
1138	C₂×C₄	—	106	1	no	—
1139	C₂×C₄	—	106	1	no	—
1140	C₂×C₄	—	106	1	no	—
1141	C₂×C₄	—	106	1	no	—
1142	C₂×C₄	—	106	1	no	—
1143	C₂×C₄	—	106	1	no	—
1144	C₂×C₄	—	106	1	no	—
1145	C₂×C₄	—	106	1	no	—
1146	C₂×C₄	—	106	1	no	—
1147	C₂×C₄	—	106	1	no	—
1148	C₂×C₄	—	106	1	no	—
1149	C₂×C₄	—	106	1	no	—
1150	C₂×C₄	—	106	1	no	—
1151	C₂×C₄	—	106	1	no	—
1152	C₂×C₄	—	106	1	no	—
1153	C₂×C₄	—	106	1	no	—
1154	C₂×C₄	—	106	1	no	—
1155	C₂×C₄	—	106	1	no	—
1156	C₂×C₄	—	106	1	no	—
1157	C₂×C₄	—	106	1	no	—
1158	C₂×C₄	—	106	1	no	—
1159	C₂×C₄	—	106	1	no	—
1160	C₂×C₄	—	106	1	no	—
1161	C₂×C₄	—	106	1	no	—
1162	C₂×C₄	—	106	1	no	—
1163	C₂×C₄	—	106	1	no	—
1164	C₂×C₄	—	106	1	no	—
1165	C₂×C₄	—	106	1	no	—
1166	C₂×C₄	—	106	1	no	—
1167	C₂×C₄	—	106	1	no	—
1168	C₂×C₄	—	106	1	no	—
1169	C₂×C₄	—	106	1	no	—
1170	C₂×C₄	—	106	1	no	—
1171	C₂×C₄	—	106	1	no	—
1172	C₂×C₄	—	106	1	no	—
1173	C₂×C₄	—	106	1	no	—
1174	C₂×C₄	—	106	1	no	—
1175	C₂×C₄	—	106	1	no	—
1176	C₂×C₄	—	106	1	no	—
1177	C₂×C₄	—	106	1	no	—
1178	C₂×C₄	—	106	1	no	—
1179	C₂×C₄	—	106	1	no	—
1180	C₂×C₄	—	106	1	no	—
1181	C₂×C₄	—	106	1	no	—
1182	C₂×C₄	—	424	2	no	—
1183	C₂×C₄	C₂×#11719947	1	2	yes	—
1184	C₂×C₄	C₂×#11719947	1	2	yes	—
1185	C₂×C₄	C₂×#11719947	1	2	yes	—
1186	C₂×C₄	#13133265	1	2	yes	—
1187	C₂²	—	212	1	no	—
1188	C₂²	—	212	1	no	—
1189	C₂²	—	212	1	no	—
1190	C₂²	—	212	1	no	—
1191	C₂²	—	212	1	no	—
1192	C₂²	—	212	1	no	—
1193	C₂²	—	212	1	no	—
1194	C₂²	C₂²×#11719947	1	1	yes	characteristic
1195	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1196	C₂²	C₂×#13133265	1	1	yes	characteristic
1197	C₂²	#16811459	1	1	yes	characteristic
1198	C₂²	#16811459	1	1	yes	characteristic
1199	C₂²	#16811459	1	1	yes	characteristic
1200	C₂²	#16811460	1	1	yes	characteristic
1201	C₄	—	2	2	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	106	2	no	—
1217	C₄	—	212	1	no	—
1218	C₄	—	212	1	no	—
1219	C₄	—	212	1	no	—
1220	C₄	—	212	1	no	—
1221	C₄	—	212	1	no	—
1222	C₄	—	212	1	no	—
1223	C₄	—	212	1	no	—
1224	C₄	—	212	1	no	—
1225	C₄	—	212	1	no	—
1226	C₄	—	212	1	no	—
1227	C₄	—	212	1	no	—
1228	C₄	—	212	1	no	—
1229	C₄	—	212	1	no	—
1230	C₄	—	212	1	no	—
1231	C₂	—	424	1	no	—
1232	C₂	#20288103	1	1	yes	characteristic
1233	C₂	#20288461	1	1	yes	characteristic
1234	C₂	#20288579	1	1	yes	characteristic
1235	C₂	#20289222	1	1	yes	characteristic
1236	C₂	#20289311	1	1	yes	characteristic
1237	C₂	#20289353	1	1	yes	characteristic
1238	C₂	#20289410	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2581	C₂
prime radical	C₂³×D₅₃	C₂⁴
hypercenter	#2581	D₅₃
hypocenter	C₅₃	#37006
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2581

Complements

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

N	H ≅ G/N	type
2. #20283099	C₂	semidirect
3. #20282704	C₂	semidirect
4. #20282669	C₂	semidirect
7. #20282279	C₂	semidirect
8. #20282278	C₂	semidirect
9. #20282273	C₂	semidirect
12. #20282180	C₂	semidirect
14. #20282111	C₂	semidirect
16. #20282067	C₂	semidirect
19. #20280810	C₂	semidirect
21. #20280423	C₂	semidirect
24. #20280150	C₂	semidirect
26. #20279591	C₂	semidirect
29. #20277366	C₂	semidirect
30. #20277193	C₂	semidirect
31. C₅₃×#2581	C₂	semidirect
636. #2581	D₅₃	semidirect
806. C₅₃	#37006	semidirect

Maximal subgroups

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

subgroup	index
#20283105	2
#20283099	2
#20282704	2
#20282669	2
#20282467	2
#20282318	2
#20282279	2
#20282278	2
#20282273	2
#20282264	2
#20282232	2
#20282180	2
#20282126	2
#20282111	2
#20282088	2
#20282067	2
#20282007	2
#20281788	2
#20280810	2
#20280735	2
#20280423	2
#20280347	2
#20280150	2
#20280003	2
#20279591	2
#20279546	2
#20277486	2
#20277366	2
#20277193	2
C₅₃×#2581	2
#37006	53