Subgroups — #28250346

Order 13568.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283885	C₂	1	2	yes	maximal, complemented
2	#20283885	C₂	1	2	yes	maximal, complemented
3	#20283875	C₂	1	1	yes	maximal, characteristic, complemented
4	#20283864	C₂	1	2	yes	maximal, complemented
5	#20283864	C₂	1	1	yes	maximal, characteristic, complemented
6	#20283847	C₂	1	1	yes	maximal, characteristic, complemented
7	#20283832	C₂	1	1	yes	maximal, characteristic, complemented
8	#20283817	C₂	1	1	yes	maximal, characteristic, complemented
9	#20283810	C₂	1	2	yes	maximal, complemented
10	#20283810	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283804	C₂	1	1	yes	maximal, characteristic, complemented
12	#20283729	C₂	1	1	yes	maximal, characteristic, complemented
13	#20283720	C₂	1	1	yes	maximal, characteristic, complemented
14	#20283720	C₂	1	2	yes	maximal, complemented
15	#20283711	C₂	1	2	yes	maximal, complemented
16	#20283702	C₂	1	2	yes	maximal, complemented
17	#20283691	C₂	1	1	yes	maximal, characteristic, complemented
18	#20283682	C₂	1	1	yes	maximal, characteristic, complemented
19	Q₈×#11719917	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283664	C₂	1	1	yes	maximal, characteristic, complemented
21	#20283656	C₂	1	2	yes	maximal, complemented
22	#20283650	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3461	C₂	1	1	yes	maximal, characteristic
24	#16810754	C₂²	1	2	yes	—
25	#16810754	C₂²	1	1	yes	characteristic
26	#16810754	C₂²	1	1	yes	characteristic
27	#16810754	C₂²	1	1	yes	characteristic
28	#16810754	C₂²	1	2	yes	—
29	#16810754	C₂²	1	2	yes	—
30	#16810754	C₂²	1	2	yes	—
31	#16810754	C₂²	1	2	yes	—
32	#16810754	C₂²	1	2	yes	—
33	#16810754	C₂²	1	2	yes	—
34	#16810754	C₂²	1	1	yes	characteristic
35	#16810754	C₂²	1	2	yes	—
36	#16810754	C₂²	1	1	yes	characteristic
37	#16810754	C₂²	1	2	yes	—
38	#16810754	C₂²	1	1	yes	characteristic
39	#16810754	C₂²	1	1	yes	characteristic
40	#16810754	C₂²	1	2	yes	—
41	#16810754	C₂²	1	2	yes	—
42	#16810754	C₂²	1	1	yes	characteristic
43	Q₈×#88322	C₂²	1	1	yes	characteristic
44	Q₈×#88322	C₂²	1	2	yes	—
45	Q₈×#88322	C₂²	1	1	yes	characteristic
46	Q₈×#88322	C₂²	1	1	yes	characteristic
47	Q₈×#88322	C₂²	1	1	yes	characteristic
48	Q₈×#88322	C₂²	1	1	yes	characteristic
49	Q₈×#88322	C₂²	1	1	yes	characteristic
50	Q₈×#88322	C₂²	1	2	yes	—
51	#16810701	C₂²	1	1	yes	characteristic
52	#16810701	C₂²	1	1	yes	characteristic
53	#16810701	C₂²	1	1	yes	characteristic
54	#16810701	C₂²	1	2	yes	—
55	#16810701	C₂²	1	2	yes	—
56	#16810701	C₂²	1	1	yes	characteristic
57	#16810701	C₂²	1	2	yes	—
58	#16810701	C₂²	1	2	yes	—
59	#16810701	C₂²	1	2	yes	—
60	#16810695	C₂²	1	1	yes	characteristic
61	#16810695	C₂²	1	1	yes	characteristic
62	#16810695	C₂²	1	1	yes	characteristic
63	#16810695	C₂²	1	1	yes	characteristic
64	#16810695	C₂²	1	2	yes	—
65	#16810695	C₂²	1	2	yes	—
66	#16810695	C₂²	1	2	yes	—
67	#16810695	C₂²	1	2	yes	—
68	#16810695	C₂²	1	2	yes	—
69	#16810695	C₂²	1	2	yes	—
70	#16810695	C₂²	1	2	yes	—
71	#16810695	C₂²	1	2	yes	—
72	D₄×#88322	C₂²	1	2	yes	—
73	D₄×#88322	C₂²	1	1	yes	characteristic
74	D₄×#88322	C₂²	1	2	yes	—
75	D₄×#88322	C₂²	1	1	yes	characteristic
76	#16810684	C₂²	1	2	yes	—
77	#16810684	C₂²	1	2	yes	—
78	#16810684	C₂²	1	2	yes	—
79	#16810684	C₂²	1	2	yes	—
80	#16810684	C₂²	1	2	yes	—
81	#16810684	C₂²	1	2	yes	—
82	#16810684	C₂²	1	2	yes	—
83	#16810684	C₂²	1	2	yes	—
84	#16810680	C₂²	1	1	yes	characteristic
85	#16810680	C₂²	1	2	yes	—
86	#16810680	C₂²	1	1	yes	characteristic
87	#16810680	C₂²	1	2	yes	—
88	#16810676	C₂²	1	1	yes	characteristic
89	#16810676	C₂²	1	1	yes	characteristic
90	#16810676	C₂²	1	1	yes	characteristic
91	#16810676	C₂²	1	2	yes	—
92	#16810676	C₂²	1	2	yes	—
93	#16810676	C₂²	1	1	yes	characteristic
94	#16810650	C₂²	1	2	yes	—
95	#16810650	C₂²	1	2	yes	—
96	#16810650	C₂²	1	2	yes	—
97	#16810650	C₂²	1	2	yes	—
98	#16810647	C₂²	1	1	yes	characteristic
99	#16810647	C₂²	1	2	yes	—
100	#16810647	C₂²	1	1	yes	characteristic
101	#16810647	C₂²	1	2	yes	—
102	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
103	#16810579	C₂²	1	2	yes	—
104	#16810579	C₂²	1	2	yes	—
105	#16810579	C₂²	1	2	yes	—
106	#16810579	C₂²	1	2	yes	—
107	C₄×#11719917	C₂²	1	1	yes	characteristic
108	C₄×#11719917	C₂²	1	1	yes	characteristic
109	C₄×#11719917	C₂²	1	2	yes	—
110	C₂×#13133128	C₂²	1	2	yes	—
111	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
112	C₅₃×#544	C₄	1	1	yes	characteristic
113	C₅₃×#542	C₄	1	1	yes	characteristic
114	C₅₃×#542	C₄	1	1	yes	characteristic
115	C₅₃×#542	C₄	1	2	yes	—
116	C₅₃×#541	C₄	1	1	yes	characteristic
117	C₅₃×#541	C₄	1	1	yes	characteristic
118	C₅₃×#541	C₄	1	2	yes	—
119	C₅₃×#539	C₄	1	2	yes	—
120	C₅₃×#539	C₄	1	2	yes	—
121	C₅₃×#537	C₄	1	1	yes	characteristic
122	C₅₃×#536	C₄	1	1	yes	characteristic
123	C₅₃×#536	C₄	1	1	yes	characteristic
124	C₅₃×#533	C₂²	1	1	yes	characteristic
125	C₅₃×#533	C₂²	1	2	yes	—
126	C₅₃×#533	C₂²	1	1	yes	characteristic
127	C₅₃×#529	C₂²	1	1	yes	characteristic
128	C₅₃×#529	C₂²	1	2	yes	—
129	C₅₃×#529	C₂²	1	2	yes	—
130	C₅₃×#529	C₂²	1	1	yes	characteristic
131	C₅₃×#529	C₂²	1	2	yes	—
132	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
133	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
135	C₂×#11719917	C₂³	1	1	yes	characteristic
136	C₂×#11719917	C₂³	1	1	yes	characteristic
137	C₂×#11719917	C₂³	1	1	yes	characteristic
138	C₂×#11719917	C₂³	1	2	yes	—
139	C₂×#11719917	C₂³	1	1	yes	characteristic
140	C₂×#11719917	C₂³	1	2	yes	—
141	C₂×#11719917	C₂³	1	2	yes	—
142	C₂×#11719917	C₂³	1	2	yes	—
143	C₂²×#88322	C₂³	1	1	yes	characteristic
144	C₂²×#88322	C₂³	1	2	yes	—
145	C₂²×#88322	C₂³	1	1	yes	characteristic
146	C₂²×#88322	C₂³	1	2	yes	—
147	C₂²×#88322	C₂³	1	2	yes	—
148	C₄⋊#88322	C₂³	1	2	yes	—
149	C₄⋊#88322	C₂³	1	1	yes	characteristic
150	C₄⋊#88322	C₂³	1	2	yes	—
151	C₄⋊#88322	C₂³	1	2	yes	—
152	C₄⋊#88322	C₂³	1	1	yes	characteristic
153	C₄⋊#88322	C₂³	1	1	yes	characteristic
154	C₄⋊#88322	C₂³	1	2	yes	—
155	C₄⋊#88322	C₂³	1	1	yes	characteristic
156	C₄⋊#88322	C₂³	1	1	yes	characteristic
157	C₄⋊#88322	C₂³	1	1	yes	characteristic
158	C₄⋊#88322	C₂³	1	2	yes	—
159	C₄⋊#88322	C₂³	1	2	yes	—
160	C₄⋊#88322	C₂³	1	2	yes	—
161	C₄⋊#88322	C₂³	1	2	yes	—
162	C₄⋊#88322	C₂³	1	2	yes	—
163	C₄⋊#88322	C₂³	1	2	yes	—
164	C₄⋊#88322	C₂³	1	2	yes	—
165	C₄⋊#88322	C₂³	1	2	yes	—
166	C₄⋊#88322	C₂³	1	1	yes	characteristic
167	C₄⋊#88322	C₂³	1	2	yes	—
168	C₄⋊#88322	C₂³	1	2	yes	—
169	C₄⋊#88322	C₂³	1	2	yes	—
170	C₄⋊#88322	C₂³	1	1	yes	characteristic
171	C₄⋊#88322	C₂³	1	1	yes	characteristic
172	C₄⋊#88322	C₂³	1	1	yes	characteristic
173	C₂²⋊#88322	C₂³	1	1	yes	characteristic
174	C₂²⋊#88322	C₂³	1	2	yes	—
175	C₂²⋊#88322	C₂³	1	1	yes	characteristic
176	C₂²⋊#88322	C₂³	1	1	yes	characteristic
177	C₂²⋊#88322	C₂³	1	2	yes	—
178	C₂²⋊#88322	C₂³	1	1	yes	characteristic
179	C₂²⋊#88322	C₂³	1	1	yes	characteristic
180	C₂²⋊#88322	C₂³	1	2	yes	—
181	C₂²⋊#88322	C₂³	1	1	yes	characteristic
182	C₂²⋊#88322	C₂³	1	2	yes	—
183	C₂²⋊#88322	C₂³	1	2	yes	—
184	C₂²⋊#88322	C₂³	1	2	yes	—
185	C₂²⋊#88322	C₂³	1	2	yes	—
186	#13133128	C₂³	1	1	yes	characteristic
187	#13133128	C₂³	1	2	yes	—
188	#13133128	C₂³	1	2	yes	—
189	#13133128	C₂³	1	2	yes	—
190	#13133128	C₂³	1	2	yes	—
191	#13133128	C₂³	1	1	yes	characteristic
192	#13133128	C₂³	1	1	yes	characteristic
193	#13133128	C₂³	1	1	yes	characteristic
194	#13133128	C₂³	1	2	yes	—
195	#13133128	C₂³	1	2	yes	—
196	#13133128	C₂³	1	2	yes	—
197	#13133128	C₂³	1	2	yes	—
198	C₄×#88322	C₂³	1	1	yes	characteristic
199	C₄×#88322	C₂³	1	1	yes	characteristic
200	C₄×#88322	C₂³	1	2	yes	—
201	C₄×#88322	C₂³	1	1	yes	characteristic
202	C₄×#88322	C₂³	1	2	yes	—
203	C₄×#88322	C₂³	1	2	yes	—
204	C₄×#88322	C₂³	1	2	yes	—
205	C₄×#88322	C₂³	1	1	yes	characteristic
206	C₄×#88322	C₂³	1	1	yes	characteristic
207	C₄×#88322	C₂³	1	1	yes	characteristic
208	C₄×#88322	C₂³	1	2	yes	—
209	C₄×#88322	C₂³	1	2	yes	—
210	C₄×#88322	C₂³	1	2	yes	—
211	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
212	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
213	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
214	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
215	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
216	C₄⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
217	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
218	C₄⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
219	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
220	#126×C₅₃	C₂×C₄	1	2	yes	—
221	#126×C₅₃	C₂×C₄	1	2	yes	—
222	#126×C₅₃	C₂×C₄	1	2	yes	—
223	#126×C₅₃	C₂×C₄	1	2	yes	—
224	#126×C₅₃	C₂×C₄	1	2	yes	—
225	#126×C₅₃	C₂×C₄	1	2	yes	—
226	#126×C₅₃	C₂×C₄	1	2	yes	—
227	#126×C₅₃	C₂×C₄	1	2	yes	—
228	#125×C₅₃	C₂×C₄	1	2	yes	—
229	#125×C₅₃	C₂×C₄	1	2	yes	—
230	#125×C₅₃	C₂×C₄	1	1	yes	characteristic
231	#125×C₅₃	C₂×C₄	1	2	yes	—
232	#125×C₅₃	C₂×C₄	1	1	yes	characteristic
233	#125×C₅₃	C₂×C₄	1	2	yes	—
234	#125×C₅₃	C₂×C₄	1	2	yes	—
235	#125×C₅₃	C₂×C₄	1	2	yes	—
236	#125×C₅₃	C₂×C₄	1	2	yes	—
237	#124×C₅₃	C₂×C₄	1	1	yes	characteristic
238	#124×C₅₃	C₂×C₄	1	1	yes	characteristic
239	#124×C₅₃	C₂×C₄	1	2	yes	—
240	#124×C₅₃	C₂×C₄	1	2	yes	—
241	#124×C₅₃	C₂×C₄	1	2	yes	—
242	#123×C₅₃	C₂×C₄	1	2	yes	—
243	#123×C₅₃	C₂×C₄	1	2	yes	—
244	#123×C₅₃	C₂×C₄	1	2	yes	—
245	#123×C₅₃	C₂×C₄	1	2	yes	—
246	#123×C₅₃	C₂×C₄	1	2	yes	—
247	#123×C₅₃	C₂×C₄	1	2	yes	—
248	#123×C₅₃	C₂×C₄	1	2	yes	—
249	#123×C₅₃	C₂×C₄	1	2	yes	—
250	C₂²⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
251	C₂²⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
252	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
253	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
254	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
255	C₂²⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
256	C₂²⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
257	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
258	C₂²⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
259	C₂²⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
260	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
261	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
262	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
263	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
264	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
265	#121×C₅₃	C₂×C₄	1	2	yes	—
266	#121×C₅₃	C₂×C₄	1	2	yes	—
267	#121×C₅₃	C₂×C₄	1	1	yes	characteristic
268	#121×C₅₃	C₂×C₄	1	1	yes	characteristic
269	#121×C₅₃	C₂×C₄	1	2	yes	—
270	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
271	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
272	C₄×Q₈×C₅₃	C₂×C₄	1	2	yes	—
273	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
274	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
275	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
276	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
278	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
283	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
284	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
285	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
286	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
287	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₅₃	C₂³	1	2	yes	—
292	C₄×D₄×C₅₃	C₂³	1	2	yes	—
293	C₄×D₄×C₅₃	C₂³	1	2	yes	—
294	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
295	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
296	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
297	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
298	#117×C₅₃	C₂×C₄	1	2	yes	—
299	#117×C₅₃	C₂³	1	2	yes	—
300	#117×C₅₃	C₂³	1	2	yes	—
301	#117×C₅₃	C₂³	1	2	yes	—
302	#117×C₅₃	C₂³	1	2	yes	—
303	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
305	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
307	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
309	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
310	#41×C₅₃	—	4	2	no	—
311	#41×C₅₃	—	4	2	no	—
312	C₂×Q₈×C₅₃	—	4	2	no	—
313	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
314	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
315	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
317	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
319	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
320	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
321	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
322	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
324	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
325	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
326	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
327	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
328	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
329	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
331	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
332	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
333	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
334	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
336	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
337	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
342	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
343	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
344	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
345	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
346	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
347	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
348	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
349	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
350	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
351	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
352	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
353	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
354	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
355	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
356	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
357	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
358	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
359	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
360	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
362	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
364	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
365	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
368	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
369	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
373	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
374	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
375	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
376	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
379	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
380	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
381	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
382	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
383	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
384	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
385	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
386	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
387	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
388	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
389	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
390	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
391	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
392	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
393	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
394	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
395	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
396	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
397	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
398	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
399	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
400	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
401	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
402	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
403	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
404	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
405	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₄²×C₅₃	C₂⁴	1	2	yes	—
408	C₄²×C₅₃	C₂⁴	1	2	yes	—
409	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₄²×C₅₃	C₂⁴	1	2	yes	—
411	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
412	#11719917	—	2	2	no	—
413	#11719917	—	2	2	no	—
414	#11719917	—	4	1	no	—
415	#11719917	—	4	2	no	—
416	#11719917	—	4	2	no	—
417	#11719917	—	4	1	no	—
418	#11719917	—	4	2	no	—
419	#11719917	—	4	2	no	—
420	C₂×#88322	—	2	2	no	—
421	C₂×#88322	—	2	4	no	—
422	C₂×#88322	—	4	2	no	—
423	C₂×#88322	—	4	2	no	—
424	C₂×#88322	—	4	1	no	—
425	C₂×#88322	C₂⁴	1	1	yes	characteristic
426	C₂×#88322	C₂⁴	1	1	yes	characteristic
427	C₂×#88322	C₂⁴	1	1	yes	characteristic
428	C₂×#88322	C₂⁴	1	1	yes	characteristic
429	C₂×#88322	C₂⁴	1	2	yes	—
430	C₂×#88322	C₂⁴	1	2	yes	—
431	C₂×#88322	C₂⁴	1	1	yes	characteristic
432	C₂×#88322	C₂⁴	1	1	yes	characteristic
433	C₂×#88322	C₂⁴	1	2	yes	—
434	C₂×#88322	C₂⁴	1	1	yes	characteristic
435	C₂×#88322	C₂⁴	1	2	yes	—
436	C₂×#88322	C₂⁴	1	1	yes	characteristic
437	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
438	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
439	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
440	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
441	Q₈×C₅₃	—	2	2	no	—
442	Q₈×C₅₃	—	2	2	no	—
443	Q₈×C₅₃	—	2	2	no	—
444	Q₈×C₅₃	—	4	2	no	—
445	Q₈×C₅₃	—	4	2	no	—
446	Q₈×C₅₃	—	4	2	no	—
447	Q₈×C₅₃	—	4	1	no	—
448	D₄×C₅₃	—	2	2	no	—
449	D₄×C₅₃	—	4	2	no	—
450	D₄×C₅₃	—	4	2	no	—
451	D₄×C₅₃	—	4	1	no	—
452	D₄×C₅₃	—	4	1	no	—
453	D₄×C₅₃	—	4	1	no	—
454	D₄×C₅₃	—	4	2	no	—
455	C₂×C₄×C₅₃	—	2	2	no	—
456	C₂×C₄×C₅₃	—	2	2	no	—
457	C₂×C₄×C₅₃	—	2	2	no	—
458	C₂×C₄×C₅₃	—	2	1	no	—
459	C₂×C₄×C₅₃	—	2	2	no	—
460	C₂×C₄×C₅₃	—	2	1	no	—
461	C₂×C₄×C₅₃	—	2	1	no	—
462	C₂×C₄×C₅₃	—	2	1	no	—
463	C₂×C₄×C₅₃	—	2	1	no	—
464	C₂×C₄×C₅₃	—	2	2	no	—
465	C₂×C₄×C₅₃	—	2	1	no	—
466	C₂×C₄×C₅₃	—	4	1	no	—
467	C₂×C₄×C₅₃	—	4	1	no	—
468	C₂×C₄×C₅₃	—	4	2	no	—
469	C₂×C₄×C₅₃	—	4	1	no	—
470	C₂×C₄×C₅₃	—	4	2	no	—
471	C₂×C₄×C₅₃	—	4	2	no	—
472	C₂×C₄×C₅₃	—	4	2	no	—
473	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
477	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
478	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
479	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
480	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
481	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
482	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
483	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
484	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
485	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
486	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
487	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
488	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
489	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
492	#88322	—	2	1	no	—
493	#88322	—	2	2	no	—
494	#88322	—	2	1	no	—
495	#88322	—	2	1	no	—
496	#88322	—	2	1	no	—
497	#88322	—	2	2	no	—
498	#88322	—	2	2	no	—
499	#88322	—	2	1	no	—
500	#88322	—	2	1	no	—
501	#88322	—	2	1	no	—
502	#88322	—	2	2	no	—
503	#88322	2₋¹⁺⁴	1	2	yes	—
504	#60344	—	53	1	no	maximal, Sylow
505	C₂²×C₅₃	—	2	1	no	—
506	C₂²×C₅₃	—	2	2	no	—
507	C₂²×C₅₃	—	2	1	no	—
508	C₂²×C₅₃	—	2	1	no	—
509	C₂²×C₅₃	—	2	1	no	—
510	C₂²×C₅₃	—	2	1	no	—
511	C₂²×C₅₃	—	2	1	no	—
512	C₂²×C₅₃	—	2	2	no	—
513	C₂²×C₅₃	—	2	1	no	—
514	C₂²×C₅₃	—	2	1	no	—
515	C₂²×C₅₃	—	2	1	no	—
516	C₂²×C₅₃	—	2	2	no	—
517	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
518	C₄×C₅₃	—	2	1	no	—
519	C₄×C₅₃	—	2	2	no	—
520	C₄×C₅₃	—	2	1	no	—
521	C₄×C₅₃	—	2	1	no	—
522	C₄×C₅₃	—	2	1	no	—
523	C₄×C₅₃	—	2	1	no	—
524	C₄×C₅₃	—	2	1	no	—
525	C₄×C₅₃	—	2	2	no	—
526	C₄×C₅₃	—	2	2	no	—
527	C₄×C₅₃	—	2	2	no	—
528	C₄×C₅₃	—	2	1	no	—
529	C₄×C₅₃	—	2	1	no	—
530	C₄×C₅₃	—	2	2	no	—
531	C₄×C₅₃	—	2	2	no	—
532	C₄×C₅₃	—	2	1	no	—
533	C₄×C₅₃	—	2	2	no	—
534	C₄×C₅₃	—	2	1	no	—
535	C₄×C₅₃	#568	1	2	yes	—
536	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
537	C₄×C₅₃	#585	1	1	yes	characteristic
538	#3461	D₅₃	1	1	yes	characteristic
539	#2995	—	53	2	no	—
540	#2995	—	53	2	no	—
541	#2994	—	53	1	no	—
542	#2993	—	53	1	no	—
543	#2993	—	53	2	no	—
544	#2991	—	53	1	no	—
545	#2989	—	53	1	no	—
546	#2986	—	53	1	no	—
547	#2985	—	53	1	no	—
548	#2985	—	53	2	no	—
549	#2984	—	53	1	no	—
550	#2970	—	53	1	no	—
551	#2969	—	53	1	no	—
552	#2969	—	53	2	no	—
553	#2968	—	53	2	no	—
554	#2967	—	53	2	no	—
555	#2966	—	53	1	no	—
556	#2965	—	53	1	no	—
557	Q₈×M₁₆	—	53	1	no	—
558	#2962	—	53	1	no	—
559	#2961	—	53	2	no	—
560	#2960	—	53	1	no	—
561	C₂×C₅₃	—	4	1	no	—
562	C₂×C₅₃	—	4	1	no	—
563	C₂×C₅₃	—	4	1	no	—
564	C₂×C₅₃	—	4	2	no	—
565	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
566	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
567	C₂×C₅₃	#3573	1	1	yes	characteristic
568	#544	Dic₅₃	1	1	yes	characteristic
569	#542	Dic₅₃	1	1	yes	characteristic
570	#542	Dic₅₃	1	1	yes	characteristic
571	#542	Dic₅₃	1	2	yes	—
572	#541	Dic₅₃	1	1	yes	characteristic
573	#541	Dic₅₃	1	1	yes	characteristic
574	#541	Dic₅₃	1	2	yes	—
575	#539	Dic₅₃	1	2	yes	—
576	#539	Dic₅₃	1	2	yes	—
577	#537	Dic₅₃	1	1	yes	characteristic
578	#536	Dic₅₃	1	1	yes	characteristic
579	#536	Dic₅₃	1	1	yes	characteristic
580	#533	C₂×D₅₃	1	1	yes	characteristic
581	#533	C₂×D₅₃	1	2	yes	—
582	#533	C₂×D₅₃	1	1	yes	characteristic
583	#529	C₂×D₅₃	1	1	yes	characteristic
584	#529	C₂×D₅₃	1	2	yes	—
585	#529	C₂×D₅₃	1	2	yes	—
586	#529	C₂×D₅₃	1	1	yes	characteristic
587	#529	C₂×D₅₃	1	2	yes	—
588	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
589	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
590	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
591	#446	—	53	2	no	—
592	#446	—	53	1	no	—
593	#446	—	53	1	no	—
594	#446	—	53	1	no	—
595	#446	—	53	2	no	—
596	#446	—	53	2	no	—
597	#446	—	53	2	no	—
598	#446	—	53	2	no	—
599	#446	—	53	2	no	—
600	#446	—	53	2	no	—
601	#446	—	53	1	no	—
602	#446	—	53	2	no	—
603	#446	—	53	1	no	—
604	#446	—	53	2	no	—
605	#446	—	53	1	no	—
606	#446	—	53	1	no	—
607	#446	—	53	2	no	—
608	#446	—	53	2	no	—
609	#446	—	53	1	no	—
610	C₈×Q₈	—	53	1	no	—
611	C₈×Q₈	—	53	2	no	—
612	C₈×Q₈	—	53	1	no	—
613	C₈×Q₈	—	53	1	no	—
614	C₈×Q₈	—	53	1	no	—
615	C₈×Q₈	—	53	1	no	—
616	C₈×Q₈	—	53	1	no	—
617	C₈×Q₈	—	53	2	no	—
618	#436	—	53	1	no	—
619	#436	—	53	1	no	—
620	#436	—	53	1	no	—
621	#436	—	53	2	no	—
622	#436	—	53	2	no	—
623	#436	—	53	1	no	—
624	#436	—	53	2	no	—
625	#436	—	53	2	no	—
626	#436	—	53	2	no	—
627	#435	—	53	1	no	—
628	#435	—	53	1	no	—
629	#435	—	53	1	no	—
630	#435	—	53	1	no	—
631	#435	—	53	2	no	—
632	#435	—	53	2	no	—
633	#435	—	53	2	no	—
634	#435	—	53	2	no	—
635	#435	—	53	2	no	—
636	#435	—	53	2	no	—
637	#435	—	53	2	no	—
638	#435	—	53	2	no	—
639	C₈×D₄	—	53	2	no	—
640	C₈×D₄	—	53	1	no	—
641	C₈×D₄	—	53	2	no	—
642	C₈×D₄	—	53	1	no	—
643	#433	—	53	2	no	—
644	#433	—	53	2	no	—
645	#433	—	53	2	no	—
646	#433	—	53	2	no	—
647	#433	—	53	2	no	—
648	#433	—	53	2	no	—
649	#433	—	53	2	no	—
650	#433	—	53	2	no	—
651	#432	—	53	1	no	—
652	#432	—	53	2	no	—
653	#432	—	53	1	no	—
654	#432	—	53	2	no	—
655	#431	—	53	1	no	—
656	#431	—	53	1	no	—
657	#431	—	53	1	no	—
658	#431	—	53	2	no	—
659	#431	—	53	2	no	—
660	#431	—	53	1	no	—
661	#424	—	53	2	no	—
662	#424	—	53	2	no	—
663	#424	—	53	2	no	—
664	#424	—	53	2	no	—
665	#423	—	53	1	no	—
666	#423	—	53	2	no	—
667	#423	—	53	1	no	—
668	#423	—	53	2	no	—
669	C₂×C₄⋊C₈	—	53	1	no	—
670	#405	—	53	2	no	—
671	#405	—	53	2	no	—
672	#405	—	53	2	no	—
673	#405	—	53	2	no	—
674	C₄×M₁₆	—	53	1	no	—
675	C₄×M₁₆	—	53	1	no	—
676	C₄×M₁₆	—	53	2	no	—
677	C₂×#97	—	53	2	no	—
678	C₂×C₄×C₈	—	53	1	no	—
679	C₅₃	#60344	1	1	yes	characteristic, complemented, Sylow
680	C₂×#41	C₂×Dic₅₃	1	1	yes	characteristic
681	C₂×#41	C₂×Dic₅₃	1	1	yes	characteristic
682	C₂²×Q₈	C₂×Dic₅₃	1	1	yes	characteristic
683	C₂×M₁₆	—	53	1	no	—
684	C₂×M₁₆	—	53	1	no	—
685	C₂×M₁₆	—	53	1	no	—
686	C₂×M₁₆	—	53	2	no	—
687	C₂×M₁₆	—	53	1	no	—
688	C₂×M₁₆	—	53	2	no	—
689	C₂×M₁₆	—	53	2	no	—
690	C₂×M₁₆	—	53	2	no	—
691	C₂²×C₈	—	53	1	no	—
692	C₂²×C₈	—	53	2	no	—
693	C₂²×C₈	—	53	1	no	—
694	C₂²×C₈	—	53	2	no	—
695	C₂²×C₈	—	53	2	no	—
696	C₄⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂×Dic₅₃	1	2	yes	—
699	C₄⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
700	C₄⋊Q₈	C₂×Dic₅₃	1	2	yes	—
701	C₄⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
702	#126	C₂×Dic₅₃	1	2	yes	—
703	#126	C₂×Dic₅₃	1	2	yes	—
704	#126	C₂×Dic₅₃	1	2	yes	—
705	#126	C₂×Dic₅₃	1	2	yes	—
706	#126	C₂×Dic₅₃	1	2	yes	—
707	#126	C₂×Dic₅₃	1	2	yes	—
708	#126	C₂×Dic₅₃	1	2	yes	—
709	#126	C₂×Dic₅₃	1	2	yes	—
710	#125	C₂×Dic₅₃	1	2	yes	—
711	#125	C₂×Dic₅₃	1	2	yes	—
712	#125	C₂×Dic₅₃	1	1	yes	characteristic
713	#125	C₂×Dic₅₃	1	2	yes	—
714	#125	C₂×Dic₅₃	1	1	yes	characteristic
715	#125	C₂×Dic₅₃	1	2	yes	—
716	#125	C₂×Dic₅₃	1	2	yes	—
717	#125	C₂×Dic₅₃	1	2	yes	—
718	#125	C₂×Dic₅₃	1	2	yes	—
719	#124	C₂×Dic₅₃	1	1	yes	characteristic
720	#124	C₂×Dic₅₃	1	1	yes	characteristic
721	#124	C₂×Dic₅₃	1	2	yes	—
722	#124	C₂×Dic₅₃	1	2	yes	—
723	#124	C₂×Dic₅₃	1	2	yes	—
724	#123	C₂×Dic₅₃	1	2	yes	—
725	#123	C₂×Dic₅₃	1	2	yes	—
726	#123	C₂×Dic₅₃	1	2	yes	—
727	#123	C₂×Dic₅₃	1	2	yes	—
728	#123	C₂×Dic₅₃	1	2	yes	—
729	#123	C₂×Dic₅₃	1	2	yes	—
730	#123	C₂×Dic₅₃	1	2	yes	—
731	#123	C₂×Dic₅₃	1	2	yes	—
732	C₂²⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
733	C₂²⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
734	C₂²⋊Q₈	C₂×Dic₅₃	1	2	yes	—
735	C₂²⋊Q₈	C₂×Dic₅₃	1	2	yes	—
736	C₂²⋊Q₈	C₂×Dic₅₃	1	2	yes	—
737	C₂²⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
738	C₂²⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
739	C₂²⋊Q₈	C₂×Dic₅₃	1	2	yes	—
740	C₂²⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
741	C₂²⋊Q₈	C₂×Dic₅₃	1	1	yes	characteristic
742	C₂²⋊Q₈	C₂×Dic₅₃	1	2	yes	—
743	C₂²⋊Q₈	C₂×Dic₅₃	1	2	yes	—
744	C₂²⋊Q₈	C₂×Dic₅₃	1	2	yes	—
745	C₂²⋊Q₈	C₂×Dic₅₃	1	2	yes	—
746	C₂²⋊Q₈	C₂×Dic₅₃	1	2	yes	—
747	#121	C₂×Dic₅₃	1	2	yes	—
748	#121	C₂×Dic₅₃	1	2	yes	—
749	#121	C₂×Dic₅₃	1	1	yes	characteristic
750	#121	C₂×Dic₅₃	1	1	yes	characteristic
751	#121	C₂×Dic₅₃	1	2	yes	—
752	C₄×Q₈	C₂×Dic₅₃	1	1	yes	characteristic
753	C₄×Q₈	C₂×Dic₅₃	1	1	yes	characteristic
754	C₄×Q₈	C₂×Dic₅₃	1	2	yes	—
755	C₄×Q₈	C₂×Dic₅₃	1	1	yes	characteristic
756	C₄×Q₈	C₂×Dic₅₃	1	1	yes	characteristic
757	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
758	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
759	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
760	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
761	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
762	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
763	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
764	C₄×D₄	C₂×Dic₅₃	1	1	yes	characteristic
765	C₄×D₄	C₂×Dic₅₃	1	1	yes	characteristic
766	C₄×D₄	C₂×Dic₅₃	1	2	yes	—
767	C₄×D₄	C₂×Dic₅₃	1	1	yes	characteristic
768	C₄×D₄	C₂×Dic₅₃	1	1	yes	characteristic
769	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
770	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
771	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
772	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
773	C₄×D₄	C₂²×D₅₃	1	2	yes	—
774	C₄×D₄	C₂²×D₅₃	1	2	yes	—
775	C₄×D₄	C₂²×D₅₃	1	2	yes	—
776	#117	C₂×Dic₅₃	1	1	yes	characteristic
777	#117	C₂×Dic₅₃	1	1	yes	characteristic
778	#117	C₂×Dic₅₃	1	1	yes	characteristic
779	#117	C₂×Dic₅₃	1	1	yes	characteristic
780	#117	C₂×Dic₅₃	1	2	yes	—
781	#117	C₂²×D₅₃	1	2	yes	—
782	#117	C₂²×D₅₃	1	2	yes	—
783	#117	C₂²×D₅₃	1	2	yes	—
784	#117	C₂²×D₅₃	1	2	yes	—
785	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂×Dic₅₃	1	2	yes	—
787	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
788	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
789	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
790	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
791	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
792	C₄⋊C₈	—	53	1	no	—
793	C₄⋊C₈	—	53	1	no	—
794	C₄⋊C₈	—	53	2	no	—
795	C₄⋊C₈	—	53	1	no	—
796	C₄⋊C₈	—	53	2	no	—
797	C₄⋊C₈	—	53	1	no	—
798	C₄⋊C₈	—	53	2	no	—
799	C₄⋊C₈	—	53	2	no	—
800	C₄⋊C₈	—	53	2	no	—
801	C₄⋊C₈	—	53	2	no	—
802	C₄⋊C₈	—	53	2	no	—
803	C₄⋊C₈	—	53	2	no	—
804	C₄⋊C₈	—	53	2	no	—
805	C₄⋊C₈	—	53	1	no	—
806	C₄⋊C₈	—	53	1	no	—
807	C₄⋊C₈	—	53	2	no	—
808	C₄⋊C₈	—	53	2	no	—
809	C₄⋊C₈	—	53	2	no	—
810	C₄⋊C₈	—	53	1	no	—
811	C₄⋊C₈	—	53	1	no	—
812	C₄⋊C₈	—	53	2	no	—
813	C₄⋊C₈	—	53	1	no	—
814	C₄⋊C₈	—	53	1	no	—
815	C₄⋊C₈	—	53	2	no	—
816	C₄⋊C₈	—	53	2	no	—
817	C₂²⋊C₈	—	53	1	no	—
818	C₂²⋊C₈	—	53	2	no	—
819	C₂²⋊C₈	—	53	1	no	—
820	C₂²⋊C₈	—	53	1	no	—
821	C₂²⋊C₈	—	53	2	no	—
822	C₂²⋊C₈	—	53	1	no	—
823	C₂²⋊C₈	—	53	1	no	—
824	C₂²⋊C₈	—	53	2	no	—
825	C₂²⋊C₈	—	53	1	no	—
826	C₂²⋊C₈	—	53	2	no	—
827	C₂²⋊C₈	—	53	2	no	—
828	C₂²⋊C₈	—	53	2	no	—
829	C₂²⋊C₈	—	53	2	no	—
830	#97	—	53	1	no	—
831	#97	—	53	2	no	—
832	#97	—	53	2	no	—
833	#97	—	53	2	no	—
834	#97	—	53	1	no	—
835	#97	—	53	2	no	—
836	#97	—	53	1	no	—
837	#97	—	53	1	no	—
838	#97	—	53	2	no	—
839	#97	—	53	2	no	—
840	#97	—	53	2	no	—
841	#97	—	53	2	no	—
842	C₄×C₈	—	53	1	no	—
843	C₄×C₈	—	53	1	no	—
844	C₄×C₈	—	53	1	no	—
845	C₄×C₈	—	53	1	no	—
846	C₄×C₈	—	53	2	no	—
847	C₄×C₈	—	53	1	no	—
848	C₄×C₈	—	53	1	no	—
849	C₄×C₈	—	53	2	no	—
850	C₄×C₈	—	53	2	no	—
851	C₄×C₈	—	53	2	no	—
852	C₄×C₈	—	53	2	no	—
853	C₄×C₈	—	53	2	no	—
854	C₄×C₈	—	53	2	no	—
855	#41	—	4	2	no	—
856	#41	—	4	2	no	—
857	C₂×Q₈	—	4	2	no	—
858	C₂×Q₈	C₂²×Dic₅₃	1	1	yes	characteristic
859	C₂×Q₈	C₂²×Dic₅₃	1	1	yes	characteristic
860	C₂×Q₈	C₂²×Dic₅₃	1	1	yes	characteristic
861	C₂×Q₈	C₂²×Dic₅₃	1	2	yes	—
862	C₂×Q₈	C₂²×Dic₅₃	1	1	yes	characteristic
863	C₂×Q₈	C₂²×Dic₅₃	1	2	yes	—
864	C₂×Q₈	C₂²×Dic₅₃	1	2	yes	—
865	C₂×D₄	C₂²×Dic₅₃	1	1	yes	characteristic
866	C₂×D₄	C₂²×Dic₅₃	1	1	yes	characteristic
867	C₂×D₄	C₂²×Dic₅₃	1	1	yes	characteristic
868	C₂×D₄	C₂²×Dic₅₃	1	2	yes	—
869	C₂×D₄	C₂²×Dic₅₃	1	1	yes	characteristic
870	C₂×D₄	C₂²×Dic₅₃	1	2	yes	—
871	C₂×D₄	C₂²×Dic₅₃	1	2	yes	—
872	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
873	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
874	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
875	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
876	C₂²×C₄	C₂²×Dic₅₃	1	2	yes	—
877	C₂²×C₄	C₂²×Dic₅₃	1	2	yes	—
878	C₂²×C₄	C₂²×Dic₅₃	1	2	yes	—
879	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
880	C₂²×C₄	C₂²×Dic₅₃	1	2	yes	—
881	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
882	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
883	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
884	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
885	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
886	M₁₆	—	106	2	no	—
887	M₁₆	—	106	2	no	—
888	M₁₆	—	212	1	no	—
889	M₁₆	—	212	2	no	—
890	M₁₆	—	212	2	no	—
891	M₁₆	—	212	1	no	—
892	M₁₆	—	212	2	no	—
893	M₁₆	—	212	2	no	—
894	C₂×C₈	—	53	1	no	—
895	C₂×C₈	—	53	1	no	—
896	C₂×C₈	—	53	1	no	—
897	C₂×C₈	—	53	1	no	—
898	C₂×C₈	—	53	1	no	—
899	C₂×C₈	—	53	2	no	—
900	C₂×C₈	—	53	2	no	—
901	C₂×C₈	—	53	1	no	—
902	C₂×C₈	—	53	1	no	—
903	C₂×C₈	—	53	2	no	—
904	C₂×C₈	—	53	1	no	—
905	C₂×C₈	—	53	2	no	—
906	C₂×C₈	—	106	2	no	—
907	C₂×C₈	—	106	4	no	—
908	C₂×C₈	—	212	2	no	—
909	C₂×C₈	—	212	2	no	—
910	C₂×C₈	—	212	1	no	—
911	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
912	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
913	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
914	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
915	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
916	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
917	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
918	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
919	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
920	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
921	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
922	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
923	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
924	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
925	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
926	C₄⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
927	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
928	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
929	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
930	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
931	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
932	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
933	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
934	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
935	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
936	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
937	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
938	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
939	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
940	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
941	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
942	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
943	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
944	C₂²⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
945	C₂²⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
946	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
947	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
948	C₂²⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
949	C₂²⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
950	C₂²⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
951	C₂²⋊C₄	C₂²×Dic₅₃	1	1	yes	characteristic
952	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
953	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
954	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
955	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
956	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
957	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
958	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
959	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
960	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
961	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
962	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
963	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
964	C₂²⋊C₄	C₂²×Dic₅₃	1	2	yes	—
965	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
966	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
967	C₄²	C₂²×Dic₅₃	1	2	yes	—
968	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
969	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
970	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
971	C₄²	C₂²×Dic₅₃	1	2	yes	—
972	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
973	C₄²	C₂²×Dic₅₃	1	2	yes	—
974	C₄²	C₂²×Dic₅₃	1	2	yes	—
975	C₄²	C₂³×D₅₃	1	1	yes	characteristic
976	C₄²	C₂³×D₅₃	1	1	yes	characteristic
977	C₄²	C₂³×D₅₃	1	2	yes	—
978	C₄²	C₂³×D₅₃	1	2	yes	—
979	C₄²	C₂³×D₅₃	1	2	yes	—
980	C₄²	C₂³×D₅₃	1	1	yes	characteristic
981	C₄²	C₂³×D₅₃	1	1	yes	characteristic
982	C₂³	C₂³×Dic₅₃	1	1	yes	characteristic
983	C₂³	C₂³×Dic₅₃	1	1	yes	characteristic
984	C₂³	C₂³×Dic₅₃	1	2	yes	—
985	C₂³	C₂³×Dic₅₃	1	1	yes	characteristic
986	Q₈	—	2	2	no	—
987	Q₈	—	2	2	no	—
988	Q₈	—	2	2	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	4	2	no	—
991	Q₈	—	4	2	no	—
992	Q₈	—	4	1	no	—
993	D₄	—	2	2	no	—
994	D₄	—	4	2	no	—
995	D₄	—	4	2	no	—
996	D₄	—	4	1	no	—
997	D₄	—	4	1	no	—
998	D₄	—	4	1	no	—
999	D₄	—	4	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	1	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1019	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1020	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1021	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1022	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1023	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1024	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1025	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1026	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1027	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1028	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1029	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1030	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1031	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1032	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1033	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1034	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1035	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
1036	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1037	C₈	—	53	2	no	—
1038	C₈	—	106	1	no	—
1039	C₈	—	106	2	no	—
1040	C₈	—	106	1	no	—
1041	C₈	—	106	1	no	—
1042	C₈	—	106	1	no	—
1043	C₈	—	106	2	no	—
1044	C₈	—	106	1	no	—
1045	C₈	—	106	1	no	—
1046	C₈	—	106	2	no	—
1047	C₈	—	106	1	no	—
1048	C₈	—	106	2	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	1	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	C₂⁴×Dic₅₃	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	1	no	—
1079	C₄	#16811390	1	2	yes	—
1080	C₄	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1081	C₄	#16811460	1	1	yes	characteristic
1082	C₂	—	4	1	no	—
1083	C₂	—	4	1	no	—
1084	C₂	—	4	1	no	—
1085	C₂	—	4	2	no	—
1086	C₂	2₋¹⁺⁴×Dic₅₃	1	1	yes	characteristic
1087	C₂	C₂×#16811390	1	1	yes	characteristic
1088	C₂	#20289427	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#3461	C₂
prime radical	C₅₃×#537	C₄
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	#3461	D₅₃
hypocenter	C₅₃	#60344
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #3461

Complements

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

N	H ≅ G/N	type
1. #20283885	C₂	semidirect
2. #20283885	C₂	semidirect
3. #20283875	C₂	semidirect
4. #20283864	C₂	semidirect
5. #20283864	C₂	semidirect
6. #20283847	C₂	semidirect
7. #20283832	C₂	semidirect
8. #20283817	C₂	semidirect
9. #20283810	C₂	semidirect
10. #20283810	C₂	semidirect
11. #20283804	C₂	semidirect
12. #20283729	C₂	semidirect
13. #20283720	C₂	semidirect
14. #20283720	C₂	semidirect
15. #20283711	C₂	semidirect
16. #20283702	C₂	semidirect
17. #20283691	C₂	semidirect
18. #20283682	C₂	semidirect
19. Q₈×#11719917	C₂	semidirect
20. #20283664	C₂	semidirect
21. #20283656	C₂	semidirect
22. #20283650	C₂	semidirect
679. C₅₃	#60344	semidirect

Maximal subgroups

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

subgroup	index
#20283885	2
#20283875	2
#20283864	2
#20283847	2
#20283832	2
#20283817	2
#20283810	2
#20283804	2
#20283729	2
#20283720	2
#20283711	2
#20283702	2
#20283691	2
#20283682	2
Q₈×#11719917	2
#20283664	2
#20283656	2
#20283650	2
C₅₃×#3461	2
#60344	53