Subgroups — D₅₃×#3175 #28253906

Order 13568.

1970 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#542×D₅₃	C₂	1	2	yes	maximal, complemented
2	#20285357	C₂	1	1	yes	maximal, characteristic, complemented
3	#20285356	C₂	1	1	yes	maximal, characteristic, complemented
4	#20285355	C₂	1	1	yes	maximal, characteristic, complemented
5	#20285354	C₂	1	1	yes	maximal, characteristic, complemented
6	#20285353	C₂	1	2	yes	maximal, complemented
7	#20285352	C₂	1	2	yes	maximal, complemented
8	#20285351	C₂	1	1	yes	maximal, characteristic, complemented
9	#20285350	C₂	1	1	yes	maximal, characteristic, complemented
10	#20285349	C₂	1	2	yes	maximal, complemented
11	#20285348	C₂	1	2	yes	maximal, complemented
12	#20285347	C₂	1	1	yes	maximal, characteristic, complemented
13	#500×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#495×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#489×D₅₃	C₂	1	2	yes	maximal, complemented
16	#468×D₅₃	C₂	1	2	yes	maximal, complemented
17	#467×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#466×D₅₃	C₂	1	1	yes	maximal, characteristic
19	#440×D₅₃	C₂	1	2	yes	maximal, complemented
20	C₄×Q₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#405×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3175	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₅₃	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×D₅₃	C₂²	1	2	yes	—
26	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
29	#16811247	C₂²	1	2	yes	complemented
30	#16811246	C₂²	1	2	yes	complemented
31	#16811245	C₂²	1	2	yes	complemented
32	#16811244	C₂²	1	2	yes	complemented
33	#16811243	—	2	2	no	—
34	#16811242	C₂²	1	2	yes	complemented
35	#16811241	—	2	2	no	—
36	#16811240	C₂²	1	2	yes	complemented
37	#16811239	—	2	2	no	—
38	#16811238	C₂²	1	2	yes	complemented
39	#16811237	—	2	2	no	—
40	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
41	#126×D₅₃	—	2	2	no	—
42	#124×D₅₃	—	2	2	no	—
43	#124×D₅₃	C₂²	1	2	yes	—
44	#123×D₅₃	—	2	2	no	—
45	C₂²⋊Q₈×D₅₃	—	2	2	no	—
46	C₂²⋊Q₈×D₅₃	C₂²	1	2	yes	—
47	#121×D₅₃	C₂²	1	2	yes	—
48	C₄×Q₈×D₅₃	C₂²	1	2	yes	—
49	C₄×D₄×D₅₃	C₂²	1	2	yes	—
50	#117×D₅₃	C₂²	1	1	yes	characteristic
51	#16811028	C₂²	1	1	yes	characteristic, complemented
52	#16811027	C₂²	1	1	yes	characteristic, complemented
53	#16811027	C₂²	1	2	yes	complemented
54	#16811027	C₂²	1	1	yes	characteristic, complemented
55	#16811026	C₂²	1	2	yes	complemented
56	#16811008	C₂²	1	1	yes	characteristic, complemented
57	#16811007	C₂²	1	1	yes	characteristic, complemented
58	#16811006	C₂²	1	1	yes	characteristic, complemented
59	#16811005	C₂²	1	2	yes	complemented
60	#16811004	C₂²	1	2	yes	complemented
61	#16810985	C₂²	1	2	yes	complemented
62	#16810984	C₂²	1	2	yes	complemented
63	#16810984	C₂²	1	2	yes	complemented
64	#16810983	C₂²	1	2	yes	complemented
65	#16810982	C₂²	1	2	yes	complemented
66	#16810981	C₂²	1	2	yes	complemented
67	#16810981	C₂²	1	2	yes	complemented
68	#16810872	C₂²	1	2	yes	complemented
69	#16810871	C₂²	1	2	yes	complemented
70	#16810870	C₂²	1	2	yes	complemented
71	#16810869	C₂²	1	2	yes	complemented
72	#16810868	C₂²	1	2	yes	complemented
73	#16810867	C₂²	1	2	yes	complemented
74	#16810866	C₂²	1	2	yes	complemented
75	#16810865	C₂²	1	1	yes	characteristic, complemented
76	#16810864	C₂²	1	1	yes	characteristic, complemented
77	#16810863	C₂²	1	2	yes	complemented
78	#16810862	C₂²	1	2	yes	complemented
79	#16810861	C₂²	1	1	yes	characteristic, complemented
80	#16810860	C₂²	1	1	yes	characteristic
81	#16810859	C₂²	1	1	yes	characteristic
82	#16810858	C₂²	1	2	yes	—
83	#16810857	C₂²	1	2	yes	—
84	#16810856	C₂²	1	1	yes	characteristic
85	#16810726	C₂²	1	2	yes	complemented
86	#16810725	C₂²	1	2	yes	complemented
87	#16810724	C₂²	1	2	yes	complemented
88	#16810723	C₂²	1	2	yes	complemented
89	#16810722	C₂²	1	2	yes	complemented
90	#16810721	C₂²	1	2	yes	complemented
91	#16810720	C₂²	1	2	yes	complemented
92	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic, complemented
93	Q₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
94	#16810717	C₂²	1	1	yes	characteristic, complemented
95	C₄×#11719925	C₂²	1	2	yes	complemented
96	#16810715	C₂²	1	2	yes	complemented
97	C₄×D₄₂₄	C₂²	1	1	yes	characteristic, complemented
98	D₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
99	#16810705	C₂²	1	1	yes	characteristic, complemented
100	C₄×#11719922	C₂²	1	2	yes	complemented
101	#16810703	C₂²	1	2	yes	complemented
102	#107×D₅₃	C₂²	1	1	yes	characteristic
103	#107×D₅₃	C₂²	1	1	yes	characteristic
104	#107×D₅₃	C₂²	1	2	yes	—
105	#103×D₅₃	C₂²	1	2	yes	—
106	#103×D₅₃	C₂²	1	2	yes	—
107	#102×D₅₃	C₂²	1	2	yes	—
108	#102×D₅₃	C₂²	1	2	yes	—
109	#16810581	C₂²	1	1	yes	characteristic, complemented
110	#16810580	C₂²	1	1	yes	characteristic, complemented
111	#16810580	C₂²	1	1	yes	characteristic, complemented
112	#16810579	C₂²	1	1	yes	characteristic, complemented
113	#16810578	C₂²	1	1	yes	characteristic, complemented
114	#16810577	C₂²	1	1	yes	characteristic, complemented
115	#16810577	C₂²	1	1	yes	characteristic, complemented
116	#97×D₅₃	C₂²	1	1	yes	characteristic
117	#97×D₅₃	C₂²	1	1	yes	characteristic
118	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
120	C₅₃×#542	C₂²	1	2	yes	complemented
121	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#489	C₂²	1	2	yes	complemented
124	C₅₃×#468	C₂²	1	2	yes	complemented
125	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#466	C₂²	1	1	yes	characteristic
127	C₅₃×#440	C₂²	1	2	yes	complemented
128	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×Q₈×D₅₃	—	2	2	no	—
132	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
133	C₂×D₄×D₅₃	—	2	2	no	—
134	C₂×D₄×D₅₃	C₂³	1	2	yes	—
135	C₂²×C₄×D₅₃	—	2	2	no	—
136	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
137	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic
138	C₂×#11719925	C₂³	1	2	yes	—
139	Q₁₆×D₅₃	—	2	4	no	—
140	C₂×#11719913	C₂³	1	2	yes	—
141	C₂×#11719923	C₂³	1	2	yes	—
142	C₂×#11719924	C₂³	1	2	yes	—
143	SD₁₆×D₅₃	—	2	8	no	—
144	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
145	C₂×#11719922	C₂³	1	2	yes	—
146	D₈×D₅₃	—	2	4	no	—
147	C₂×#11719917	C₂³	1	1	yes	characteristic
148	C₂×#11719912	C₂³	1	1	yes	characteristic
149	C₂×#11719912	C₂³	1	1	yes	characteristic
150	M₁₆×D₅₃	—	2	4	no	—
151	C₂²×#88322	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₅₃	—	2	4	no	—
153	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
159	#13133217	C₂³	1	2	yes	—
160	#13133216	—	2	2	no	—
161	#13133216	C₂³	1	2	yes	—
162	#13133216	C₂³	1	2	yes	—
163	#13133215	—	2	2	no	—
164	#13133212	—	2	2	no	—
165	#13133212	—	2	2	no	—
166	#13133212	—	2	2	no	—
167	#13133211	—	2	2	no	—
168	#13133210	—	2	2	no	—
169	#13133210	—	2	2	no	—
170	#13133210	—	2	2	no	—
171	#13133206	—	2	2	no	—
172	#13133206	C₂³	1	2	yes	—
173	#13133205	—	2	2	no	—
174	#13133205	C₂³	1	2	yes	—
175	#13133204	—	2	2	no	—
176	#13133204	C₂³	1	2	yes	—
177	#13133203	—	2	2	no	—
178	#13133203	—	2	2	no	—
179	#13133203	—	2	2	no	—
180	#13133203	—	2	2	no	—
181	#13133203	—	2	2	no	—
182	#13133203	—	2	2	no	—
183	#13133202	—	2	2	no	—
184	#13133202	—	2	2	no	—
185	#13133201	—	2	2	no	—
186	#13133200	—	2	2	no	—
187	#13133199	—	2	2	no	—
188	#13133199	—	2	2	no	—
189	#13133198	—	2	2	no	—
190	#13133197	—	2	2	no	—
191	#13133197	C₂³	1	2	yes	—
192	#13133196	—	2	2	no	—
193	#13133196	C₂³	1	2	yes	—
194	#13133195	—	2	2	no	—
195	#13133195	—	2	2	no	—
196	#13133195	—	2	2	no	—
197	#13133194	—	2	2	no	—
198	#13133194	—	2	2	no	—
199	#13133194	—	2	2	no	—
200	#13133193	—	2	2	no	—
201	#13133193	C₂³	1	2	yes	—
202	#13133192	C₂³	1	2	yes	—
203	#13133191	C₂³	1	2	yes	—
204	#13133190	—	2	2	no	—
205	#13133189	—	2	2	no	—
206	#13133188	C₂³	1	2	yes	—
207	Q₈×Dic₅₃	C₂³	1	2	yes	—
208	C₄×Dic₁₀₆	—	2	2	no	—
209	C₄×Dic₁₀₆	C₂³	1	2	yes	—
210	#13133182	—	2	2	no	—
211	#13133182	C₂³	1	2	yes	—
212	C₄×D₂₁₂	C₂³	1	2	yes	—
213	D₄×Dic₅₃	C₂³	1	2	yes	—
214	#13133179	C₂³	1	2	yes	—
215	C₄×C₂²⋊D₅₃	—	2	2	no	—
216	#13133177	—	2	2	no	—
217	#13133176	C₂³	1	1	yes	characteristic
218	#13133175	D₄	1	1	yes	characteristic
219	#13133175	D₄	1	1	yes	characteristic
220	#13133174	C₂³	1	1	yes	characteristic
221	#13133174	C₂³	1	1	yes	characteristic
222	#13133173	D₄	1	1	yes	characteristic
223	#13133173	D₄	1	1	yes	characteristic
224	C₄⋊C₄×D₅₃	—	2	2	no	—
225	C₄⋊C₄×D₅₃	—	2	2	no	—
226	C₄⋊C₄×D₅₃	—	2	2	no	—
227	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
228	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
229	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
230	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
231	C₂²⋊C₄×D₅₃	—	2	2	no	—
232	C₂²⋊C₄×D₅₃	—	2	2	no	—
233	C₂²⋊C₄×D₅₃	—	2	2	no	—
234	C₂²⋊C₄×D₅₃	—	2	2	no	—
235	C₂²⋊C₄×D₅₃	—	2	2	no	—
236	C₂²⋊C₄×D₅₃	D₄	1	1	yes	characteristic
237	C₂²⋊C₄×D₅₃	D₄	1	1	yes	characteristic
238	C₄²×D₅₃	—	2	2	no	—
239	C₄²×D₅₃	C₂³	1	1	yes	characteristic
240	C₄²×D₅₃	C₂³	1	1	yes	characteristic
241	#13133151	C₂³	1	1	yes	characteristic
242	#13133151	C₂³	1	1	yes	characteristic
243	#13133151	C₂³	1	2	yes	—
244	#13133150	C₂³	1	2	yes	—
245	#13133150	C₂³	1	2	yes	—
246	#13133150	C₂³	1	2	yes	—
247	#13133150	C₂³	1	2	yes	—
248	#13133142	C₂³	1	2	yes	—
249	#13133142	C₂³	1	2	yes	—
250	#13133141	C₂³	1	2	yes	—
251	#13133141	C₂³	1	2	yes	—
252	#13133140	C₂³	1	2	yes	—
253	#13133140	C₂³	1	2	yes	—
254	#13133139	C₂³	1	2	yes	—
255	#13133139	C₂³	1	2	yes	—
256	#13133138	C₂³	1	2	yes	—
257	#13133138	C₂³	1	2	yes	—
258	#13133137	C₂³	1	2	yes	—
259	#13133137	C₂³	1	2	yes	—
260	#13133128	C₂³	1	1	yes	characteristic
261	#13133128	C₂³	1	1	yes	characteristic
262	#13133127	C₂³	1	1	yes	characteristic
263	#13133127	C₂³	1	1	yes	characteristic
264	#13133127	C₂³	1	1	yes	characteristic
265	#13133127	C₂³	1	1	yes	characteristic
266	C₄×#88322	C₂³	1	1	yes	characteristic
267	C₄×#88322	C₂³	1	1	yes	characteristic
268	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
270	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
271	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
274	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
278	#126×C₅₃	—	2	2	no	—
279	#124×C₅₃	—	2	2	no	—
280	#124×C₅₃	C₂³	1	2	yes	—
281	#123×C₅₃	—	2	2	no	—
282	C₂²⋊Q₈×C₅₃	—	2	2	no	—
283	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
284	#121×C₅₃	C₂³	1	2	yes	—
285	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
286	C₄×D₄×C₅₃	C₂³	1	2	yes	—
287	#117×C₅₃	C₂³	1	1	yes	characteristic
288	#107×C₅₃	C₂³	1	1	yes	characteristic
289	#107×C₅₃	C₂³	1	1	yes	characteristic
290	#107×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	2	yes	—
295	#97×C₅₃	C₂³	1	1	yes	characteristic
296	#97×C₅₃	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
299	C₂³×D₅₃	—	2	2	no	—
300	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
301	C₂×Q₈×C₅₃	—	2	2	no	—
302	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
303	C₂×D₄×C₅₃	—	2	2	no	—
304	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₅₃	—	2	2	no	—
306	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
307	C₂×C₂²⋊D₅₃	—	2	2	no	—
308	C₂×C₂²⋊D₅₃	—	2	2	no	—
309	C₂×C₂²⋊D₅₃	—	2	2	no	—
310	C₂²×Dic₅₃	—	2	2	no	—
311	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
312	Q₈×D₅₃	—	2	4	no	—
313	Q₈×D₅₃	—	2	4	no	—
314	Q₈×D₅₃	—	8	4	no	—
315	D₄×D₅₃	—	2	4	no	—
316	D₄×D₅₃	—	2	4	no	—
317	D₄×D₅₃	—	8	4	no	—
318	C₂×D₂₁₂	—	2	2	no	—
319	C₂×D₂₁₂	C₂⁴	1	2	yes	—
320	C₂×C₄×D₅₃	—	2	2	no	—
321	C₂×C₄×D₅₃	—	2	2	no	—
322	C₂×C₄×D₅₃	—	2	2	no	—
323	C₂×C₄×D₅₃	—	2	2	no	—
324	C₂×C₄×D₅₃	—	2	2	no	—
325	C₂×C₄×D₅₃	—	2	2	no	—
326	C₂×C₄×D₅₃	—	2	2	no	—
327	C₂×C₄×D₅₃	—	8	4	no	—
328	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
329	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
331	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
332	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
333	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
334	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
336	C₂×Dic₁₀₆	—	2	2	no	—
337	C₂×Dic₁₀₆	—	2	2	no	—
338	C₂×Dic₁₀₆	—	2	2	no	—
339	C₂×Dic₁₀₆	—	2	2	no	—
340	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
341	Q₁₆×C₅₃	—	2	2	no	—
342	SD₁₆×C₅₃	—	2	4	no	—
343	D₈×C₅₃	—	2	2	no	—
344	M₁₆×C₅₃	—	2	2	no	—
345	C₂×C₈×C₅₃	—	2	2	no	—
346	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₄⋊C₄×C₅₃	—	2	2	no	—
351	C₄⋊C₄×C₅₃	—	2	2	no	—
352	C₄⋊C₄×C₅₃	—	2	2	no	—
353	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
357	C₂²⋊C₄×C₅₃	—	2	2	no	—
358	C₂²⋊C₄×C₅₃	—	2	2	no	—
359	C₂²⋊C₄×C₅₃	—	2	2	no	—
360	C₂²⋊C₄×C₅₃	—	2	2	no	—
361	C₂²⋊C₄×C₅₃	—	2	2	no	—
362	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
363	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₅₃	—	2	2	no	—
365	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²⋊Dic₅₃	—	2	2	no	—
368	C₂²⋊Dic₅₃	—	2	2	no	—
369	C₂²⋊Dic₅₃	—	2	2	no	—
370	C₂²⋊Dic₅₃	—	2	2	no	—
371	C₂²⋊Dic₅₃	—	2	2	no	—
372	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
373	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
374	#11719925	—	2	4	no	—
375	#11719924	—	2	4	no	—
376	#11719923	—	2	4	no	—
377	#11719922	—	2	4	no	—
378	#11719921	—	2	2	no	—
379	#11719921	—	2	2	no	—
380	#11719921	—	2	2	no	—
381	#11719921	—	2	2	no	—
382	#11719921	—	2	2	no	—
383	#11719921	—	2	2	no	—
384	#11719921	—	2	2	no	—
385	#11719921	—	2	2	no	—
386	#11719921	—	2	2	no	—
387	#11719921	—	2	2	no	—
388	#11719921	C₂×D₄	1	1	yes	characteristic
389	#11719921	C₂×D₄	1	1	yes	characteristic
390	#11719921	C₂×D₄	1	1	yes	characteristic
391	#11719921	C₂×D₄	1	1	yes	characteristic
392	C₄⋊Dic₅₃	—	2	2	no	—
393	C₄⋊Dic₅₃	—	2	2	no	—
394	C₄⋊Dic₅₃	—	2	2	no	—
395	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
397	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
398	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
399	#11719919	—	2	2	no	—
400	#11719919	—	2	2	no	—
401	#11719919	—	2	2	no	—
402	#11719919	—	2	2	no	—
403	#11719919	—	2	2	no	—
404	#11719919	—	2	2	no	—
405	#11719919	—	2	2	no	—
406	#11719919	—	2	2	no	—
407	#11719919	C₂×D₄	1	1	yes	characteristic
408	#11719919	C₂×D₄	1	1	yes	characteristic
409	#11719919	C₂×D₄	1	1	yes	characteristic
410	#11719919	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₅₃	—	2	2	no	—
412	C₄×Dic₅₃	—	2	2	no	—
413	C₄×Dic₅₃	—	2	2	no	—
414	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
417	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
418	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	#11719917	—	2	2	no	—
421	C₂×#88322	—	2	2	no	—
422	C₂×#88322	C₂⁴	1	1	yes	characteristic
423	C₂×#88322	C₂⁴	1	1	yes	characteristic
424	C₂×#88322	C₂⁴	1	1	yes	characteristic
425	C₂×#88322	C₂⁴	1	1	yes	characteristic
426	Dic₂₁₂	—	2	2	no	—
427	D₄₂₄	—	2	2	no	—
428	#11719913	—	2	4	no	—
429	#11719912	—	2	2	no	—
430	#11719912	—	2	2	no	—
431	C₈×D₅₃	—	2	2	no	—
432	C₈×D₅₃	—	2	2	no	—
433	C₈×D₅₃	—	2	2	no	—
434	C₈×D₅₃	—	2	2	no	—
435	C₈×D₅₃	#41	1	4	yes	—
436	C₈×D₅₃	#41	1	4	yes	—
437	C₂³×C₅₃	—	2	2	no	—
438	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
439	C₂²×D₅₃	—	2	2	no	—
440	C₂²×D₅₃	—	2	2	no	—
441	C₂²×D₅₃	—	2	2	no	—
442	C₂²×D₅₃	—	2	2	no	—
443	C₂²×D₅₃	—	4	4	no	—
444	C₂²×D₅₃	—	4	4	no	—
445	C₂²×D₅₃	—	4	4	no	—
446	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
447	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₅₃	—	2	2	no	—
449	Q₈×C₅₃	—	2	2	no	—
450	Q₈×C₅₃	—	8	2	no	—
451	D₄×C₅₃	—	2	2	no	—
452	D₄×C₅₃	—	2	2	no	—
453	D₄×C₅₃	—	8	2	no	—
454	C₂×C₄×C₅₃	—	2	1	no	—
455	C₂×C₄×C₅₃	—	2	1	no	—
456	C₂×C₄×C₅₃	—	2	2	no	—
457	C₂×C₄×C₅₃	—	2	2	no	—
458	C₂×C₄×C₅₃	—	2	2	no	—
459	C₂×C₄×C₅₃	—	8	2	no	—
460	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
466	C₂²⋊D₅₃	—	4	4	no	—
467	C₂²⋊D₅₃	—	8	2	no	—
468	C₂²⋊D₅₃	—	8	2	no	—
469	C₂×Dic₅₃	—	2	2	no	—
470	C₂×Dic₅₃	—	2	2	no	—
471	C₂×Dic₅₃	—	2	2	no	—
472	C₂×Dic₅₃	—	2	2	no	—
473	C₂×Dic₅₃	—	8	2	no	—
474	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
480	D₂₁₂	—	2	2	no	—
481	D₂₁₂	—	2	2	no	—
482	D₂₁₂	—	8	2	no	—
483	C₄×D₅₃	—	2	2	no	—
484	C₄×D₅₃	—	2	2	no	—
485	C₄×D₅₃	—	2	2	no	—
486	C₄×D₅₃	—	2	2	no	—
487	C₄×D₅₃	—	2	2	no	—
488	C₄×D₅₃	—	2	1	no	—
489	C₄×D₅₃	—	2	1	no	—
490	C₄×D₅₃	—	2	2	no	—
491	C₄×D₅₃	—	4	4	no	—
492	C₄×D₅₃	—	4	4	no	—
493	C₄×D₅₃	—	4	4	no	—
494	C₄×D₅₃	—	8	2	no	—
495	C₄×D₅₃	—	8	2	no	—
496	C₄×D₅₃	C₂×#41	1	2	yes	—
497	C₄×D₅₃	C₂×#41	1	2	yes	—
498	Dic₁₀₆	—	2	2	no	—
499	Dic₁₀₆	—	2	2	no	—
500	Dic₁₀₆	—	4	4	no	—
501	Dic₁₀₆	—	8	2	no	—
502	Dic₁₀₆	—	8	2	no	—
503	Dic₁₀₆	—	8	2	no	—
504	C₈×C₅₃	—	2	1	no	—
505	C₈×C₅₃	—	2	1	no	—
506	C₈×C₅₃	C₂×#41	1	2	yes	—
507	C₈×C₅₃	C₂×#41	1	2	yes	—
508	#88322	—	2	1	no	—
509	#88322	—	2	1	no	—
510	#88322	C₂×#41	1	2	yes	—
511	#88322	C₂×#41	1	2	yes	—
512	C₂×#3175	—	53	1	no	maximal, Sylow
513	C₂²×C₅₃	—	2	1	no	—
514	C₂²×C₅₃	—	2	1	no	—
515	C₂²×C₅₃	—	2	1	no	—
516	C₂²×C₅₃	—	4	2	no	—
517	C₂²×C₅₃	—	4	2	no	—
518	C₂²×C₅₃	—	4	2	no	—
519	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
520	C₂×D₅₃	—	2	1	no	—
521	C₂×D₅₃	—	2	1	no	—
522	C₂×D₅₃	—	2	1	no	—
523	C₂×D₅₃	—	4	4	no	—
524	C₂×D₅₃	—	4	2	no	—
525	C₂×D₅₃	—	4	2	no	—
526	C₂×D₅₃	—	4	2	no	—
527	C₂×D₅₃	—	8	8	no	—
528	C₂×D₅₃	#532	1	2	yes	—
529	C₂×D₅₃	#576	1	2	yes	—
530	C₂×D₅₃	#578	1	2	yes	—
531	C₄×C₅₃	—	2	1	no	—
532	C₄×C₅₃	—	2	1	no	—
533	C₄×C₅₃	—	2	1	no	—
534	C₄×C₅₃	—	2	1	no	—
535	C₄×C₅₃	—	2	1	no	—
536	C₄×C₅₃	—	4	2	no	—
537	C₄×C₅₃	—	4	2	no	—
538	C₄×C₅₃	—	4	2	no	—
539	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
540	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
541	Dic₅₃	—	2	1	no	—
542	Dic₅₃	—	2	1	no	—
543	Dic₅₃	—	2	1	no	—
544	Dic₅₃	—	2	1	no	—
545	Dic₅₃	—	2	1	no	—
546	Dic₅₃	—	4	2	no	—
547	Dic₅₃	—	4	2	no	—
548	Dic₅₃	—	4	2	no	—
549	Dic₅₃	#532	1	2	yes	—
550	C₂×#542	—	53	2	no	—
551	#3175	—	53	1	no	—
552	#3175	—	53	1	no	—
553	#3175	—	53	2	no	—
554	#3175	—	53	2	no	—
555	#3175	—	53	1	no	—
556	#3175	—	53	1	no	—
557	#3175	—	53	2	no	—
558	#3175	—	53	1	no	—
559	#3175	—	53	1	no	—
560	#3175	—	53	1	no	—
561	#3175	—	53	2	no	—
562	#3175	D₅₃	1	1	yes	characteristic, direct product factor
563	C₂×#500	—	53	1	no	—
564	C₂×#495	—	53	1	no	—
565	C₂×#489	—	53	2	no	—
566	C₂×#468	—	53	2	no	—
567	C₂×#467	—	53	1	no	—
568	C₂×#466	—	53	1	no	—
569	C₂×#440	—	53	2	no	—
570	C₂×C₄×Q₁₆	—	53	1	no	—
571	C₂×C₄×D₈	—	53	1	no	—
572	C₂×#405	—	53	1	no	—
573	C₂×C₅₃	—	4	1	no	—
574	C₂×C₅₃	—	8	2	no	—
575	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
576	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
577	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
578	D₅₃	—	4	1	no	—
579	D₅₃	—	8	2	no	—
580	D₅₃	#3175	1	4	yes	direct product factor
581	C₂²×Q₁₆	—	53	1	no	—
582	C₂²×SD₁₆	—	53	2	no	—
583	C₂²×D₈	—	53	1	no	—
584	C₂²×M₁₆	—	53	1	no	—
585	C₂³×C₈	—	53	1	no	—
586	#542	—	53	2	no	—
587	#542	—	53	2	no	—
588	#542	—	53	2	no	—
589	#542	—	53	2	no	—
590	#542	—	53	2	no	—
591	#542	—	53	2	no	—
592	#542	—	53	2	no	—
593	#542	—	106	2	no	—
594	#542	—	106	2	no	—
595	#542	—	106	2	no	—
596	#542	—	106	2	no	—
597	#542	C₂×D₅₃	1	2	yes	complemented
598	C₂×C₄⋊Q₈	—	53	2	no	—
599	C₂×#126	—	106	2	no	—
600	C₂×#124	—	53	2	no	—
601	C₂×#124	—	106	2	no	—
602	C₂×#123	—	106	2	no	—
603	C₂×C₂²⋊Q₈	—	53	2	no	—
604	C₂×C₂²⋊Q₈	—	106	2	no	—
605	C₂×#121	—	53	2	no	—
606	C₂×C₄×Q₈	—	53	2	no	—
607	C₂×C₄×D₄	—	53	2	no	—
608	C₂×#117	—	53	1	no	—
609	#500	—	53	2	no	—
610	#500	—	53	1	no	—
611	#500	—	53	1	no	—
612	#500	—	53	2	no	—
613	#500	—	53	1	no	—
614	#500	C₂×D₅₃	1	1	yes	characteristic, complemented
615	#495	—	53	1	no	—
616	#495	—	53	2	no	—
617	#495	—	53	1	no	—
618	#495	—	53	2	no	—
619	#495	—	53	1	no	—
620	#495	C₂×D₅₃	1	1	yes	characteristic, complemented
621	#489	—	53	2	no	—
622	#489	—	53	2	no	—
623	#489	—	53	2	no	—
624	#489	—	53	2	no	—
625	#489	—	53	2	no	—
626	#489	—	53	2	no	—
627	#489	—	53	2	no	—
628	#489	C₂×D₅₃	1	2	yes	complemented
629	#468	—	53	2	no	—
630	#468	—	53	2	no	—
631	#468	—	53	2	no	—
632	#468	—	53	2	no	—
633	#468	—	53	2	no	—
634	#468	—	53	2	no	—
635	#468	—	53	2	no	—
636	#468	C₂×D₅₃	1	2	yes	complemented
637	#467	—	53	1	no	—
638	#467	—	53	1	no	—
639	#467	—	53	2	no	—
640	#467	—	53	1	no	—
641	#467	—	53	2	no	—
642	#467	C₂×D₅₃	1	1	yes	characteristic, complemented
643	#466	—	53	1	no	—
644	#466	—	53	1	no	—
645	#466	—	53	2	no	—
646	#466	—	53	1	no	—
647	#466	—	53	2	no	—
648	#466	C₂×D₅₃	1	1	yes	characteristic
649	#440	—	53	2	no	—
650	#440	—	53	2	no	—
651	#440	—	53	2	no	—
652	#440	—	53	2	no	—
653	#440	—	53	2	no	—
654	#440	—	53	2	no	—
655	#440	—	53	2	no	—
656	#440	C₂×D₅₃	1	2	yes	complemented
657	C₄×Q₁₆	—	53	1	no	—
658	C₄×Q₁₆	—	53	2	no	—
659	C₄×Q₁₆	—	53	1	no	—
660	C₄×Q₁₆	—	53	2	no	—
661	C₄×Q₁₆	—	53	1	no	—
662	C₄×Q₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
663	C₄×D₈	—	53	1	no	—
664	C₄×D₈	—	53	2	no	—
665	C₄×D₈	—	53	1	no	—
666	C₄×D₈	—	53	2	no	—
667	C₄×D₈	—	53	1	no	—
668	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic, complemented
669	C₂×#107	—	53	1	no	—
670	C₂×#107	—	53	1	no	—
671	C₂×#107	—	53	2	no	—
672	C₂×#103	—	53	2	no	—
673	C₂×#103	—	53	2	no	—
674	C₂×#102	—	53	2	no	—
675	C₂×#102	—	53	2	no	—
676	#405	—	53	1	no	—
677	#405	—	53	1	no	—
678	#405	—	53	1	no	—
679	#405	—	53	1	no	—
680	#405	—	53	1	no	—
681	#405	—	53	1	no	—
682	#405	—	53	1	no	—
683	#405	C₂×D₅₃	1	1	yes	characteristic, complemented
684	C₂×#97	—	53	1	no	—
685	C₂×#97	—	53	1	no	—
686	C₂×C₄×C₈	—	53	1	no	—
687	C₂×C₄×C₈	—	53	1	no	—
688	C₅₃	C₂×#3175	1	1	yes	characteristic, complemented, Sylow
689	C₂²×Q₈	—	53	2	no	—
690	C₂²×Q₈	—	106	2	no	—
691	C₂²×D₄	—	53	2	no	—
692	C₂²×D₄	—	106	2	no	—
693	C₂³×C₄	—	53	1	no	—
694	C₂³×C₄	—	106	2	no	—
695	C₂×Q₁₆	—	53	2	no	—
696	C₂×Q₁₆	—	53	1	no	—
697	C₂×Q₁₆	—	106	4	no	—
698	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic
699	C₂×SD₁₆	—	53	2	no	—
700	C₂×SD₁₆	—	53	2	no	—
701	C₂×SD₁₆	—	53	2	no	—
702	C₂×SD₁₆	—	106	8	no	—
703	C₂×SD₁₆	C₂²×D₅₃	1	2	yes	—
704	C₂×D₈	—	53	2	no	—
705	C₂×D₈	—	53	1	no	—
706	C₂×D₈	—	106	4	no	—
707	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
708	C₂×M₁₆	—	53	1	no	—
709	C₂×M₁₆	—	53	1	no	—
710	C₂×M₁₆	—	53	1	no	—
711	C₂×M₁₆	—	106	4	no	—
712	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
713	C₂²×C₈	—	53	1	no	—
714	C₂²×C₈	—	53	1	no	—
715	C₂²×C₈	—	53	1	no	—
716	C₂²×C₈	—	53	1	no	—
717	C₂²×C₈	—	53	1	no	—
718	C₂²×C₈	—	53	1	no	—
719	C₂²×C₈	—	53	1	no	—
720	C₂²×C₈	—	106	4	no	—
721	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
722	C₄⋊Q₈	—	53	2	no	—
723	C₄⋊Q₈	—	53	2	no	—
724	C₄⋊Q₈	—	53	2	no	—
725	C₄⋊Q₈	—	106	2	no	—
726	C₄⋊Q₈	—	106	2	no	—
727	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
728	#126	—	2	2	no	—
729	#126	—	106	2	no	—
730	#126	—	106	2	no	—
731	#126	—	106	2	no	—
732	#126	—	106	2	no	—
733	#126	—	106	2	no	—
734	#126	—	106	2	no	—
735	#126	—	106	2	no	—
736	#124	—	2	2	no	—
737	#124	—	53	2	no	—
738	#124	—	53	2	no	—
739	#124	—	53	2	no	—
740	#124	—	106	2	no	—
741	#124	—	106	2	no	—
742	#124	—	106	2	no	—
743	#124	—	106	2	no	—
744	#124	—	106	2	no	—
745	#124	—	106	2	no	—
746	#124	—	106	2	no	—
747	#124	—	106	2	no	—
748	#124	—	106	2	no	—
749	#124	C₂²×D₅₃	1	2	yes	—
750	#123	—	2	2	no	—
751	#123	—	106	2	no	—
752	#123	—	106	2	no	—
753	#123	—	106	2	no	—
754	#123	—	106	2	no	—
755	#123	—	106	2	no	—
756	#123	—	106	2	no	—
757	#123	—	106	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	53	2	no	—
760	C₂²⋊Q₈	—	53	2	no	—
761	C₂²⋊Q₈	—	53	2	no	—
762	C₂²⋊Q₈	—	106	2	no	—
763	C₂²⋊Q₈	—	106	2	no	—
764	C₂²⋊Q₈	—	106	2	no	—
765	C₂²⋊Q₈	—	106	2	no	—
766	C₂²⋊Q₈	—	106	2	no	—
767	C₂²⋊Q₈	—	106	2	no	—
768	C₂²⋊Q₈	—	106	2	no	—
769	C₂²⋊Q₈	—	106	2	no	—
770	C₂²⋊Q₈	—	106	2	no	—
771	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	—
772	#121	—	53	2	no	—
773	#121	—	53	2	no	—
774	#121	—	53	2	no	—
775	#121	—	106	2	no	—
776	#121	—	106	2	no	—
777	#121	C₂²×D₅₃	1	2	yes	—
778	C₄×Q₈	—	53	2	no	—
779	C₄×Q₈	—	53	2	no	—
780	C₄×Q₈	—	53	2	no	—
781	C₄×Q₈	—	106	2	no	—
782	C₄×Q₈	—	106	2	no	—
783	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
784	C₄×D₄	—	53	2	no	—
785	C₄×D₄	—	53	2	no	—
786	C₄×D₄	—	53	2	no	—
787	C₄×D₄	—	106	2	no	—
788	C₄×D₄	—	106	2	no	—
789	C₄×D₄	C₂²×D₅₃	1	2	yes	—
790	#117	—	53	1	no	—
791	#117	—	53	1	no	—
792	#117	—	53	1	no	—
793	#117	—	53	1	no	—
794	#117	—	53	1	no	—
795	#117	—	53	1	no	—
796	#117	—	53	1	no	—
797	#117	C₂²×D₅₃	1	1	yes	characteristic
798	C₂×C₄⋊C₄	—	53	1	no	—
799	C₂×C₄⋊C₄	—	53	1	no	—
800	C₂×C₄⋊C₄	—	53	2	no	—
801	C₂×C₄⋊C₄	—	53	2	no	—
802	C₂×C₄⋊C₄	—	106	2	no	—
803	C₂×C₄⋊C₄	—	106	2	no	—
804	C₂×C₄⋊C₄	—	106	2	no	—
805	C₂×C₂²⋊C₄	—	53	1	no	—
806	C₂×C₂²⋊C₄	—	53	1	no	—
807	C₂×C₂²⋊C₄	—	106	2	no	—
808	C₂×C₂²⋊C₄	—	106	2	no	—
809	C₂×C₂²⋊C₄	—	106	2	no	—
810	C₂×C₂²⋊C₄	—	106	2	no	—
811	C₂×C₂²⋊C₄	—	106	2	no	—
812	C₂×C₄²	—	53	1	no	—
813	C₂×C₄²	—	53	1	no	—
814	C₂×C₄²	—	106	2	no	—
815	#107	—	53	1	no	—
816	#107	—	53	1	no	—
817	#107	—	53	2	no	—
818	#107	—	53	2	no	—
819	#107	—	53	2	no	—
820	#107	—	53	2	no	—
821	#107	—	53	2	no	—
822	#107	C₂²×D₅₃	1	1	yes	characteristic
823	#107	C₂²×D₅₃	1	1	yes	characteristic
824	#107	C₂²×D₅₃	1	2	yes	—
825	#103	—	53	2	no	—
826	#103	—	53	2	no	—
827	#103	—	53	2	no	—
828	#103	—	53	2	no	—
829	#103	—	53	2	no	—
830	#103	—	53	2	no	—
831	#103	C₂²×D₅₃	1	2	yes	—
832	#103	C₂²×D₅₃	1	2	yes	—
833	#102	—	53	2	no	—
834	#102	—	53	2	no	—
835	#102	—	53	2	no	—
836	#102	—	53	2	no	—
837	#102	—	53	2	no	—
838	#102	—	53	2	no	—
839	#102	C₂²×D₅₃	1	2	yes	—
840	#102	C₂²×D₅₃	1	2	yes	—
841	#97	—	53	1	no	—
842	#97	—	53	1	no	—
843	#97	—	53	1	no	—
844	#97	—	53	1	no	—
845	#97	—	53	1	no	—
846	#97	—	53	1	no	—
847	#97	C₂²×D₅₃	1	1	yes	characteristic
848	#97	C₂²×D₅₃	1	1	yes	characteristic
849	C₄×C₈	—	53	1	no	—
850	C₄×C₈	—	53	1	no	—
851	C₄×C₈	—	53	1	no	—
852	C₄×C₈	—	53	1	no	—
853	C₄×C₈	—	53	1	no	—
854	C₄×C₈	—	53	1	no	—
855	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
856	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
857	C₂⁴	—	53	1	no	—
858	C₂⁴	—	106	2	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	53	2	no	—
861	C₂×Q₈	—	106	2	no	—
862	C₂×Q₈	—	106	2	no	—
863	C₂×Q₈	—	106	2	no	—
864	C₂×Q₈	—	106	4	no	—
865	C₂×Q₈	—	106	4	no	—
866	C₂×Q₈	—	106	2	no	—
867	C₂×Q₈	—	424	4	no	—
868	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	53	2	no	—
871	C₂×D₄	—	106	2	no	—
872	C₂×D₄	—	106	4	no	—
873	C₂×D₄	—	106	4	no	—
874	C₂×D₄	—	106	2	no	—
875	C₂×D₄	—	106	2	no	—
876	C₂×D₄	—	106	2	no	—
877	C₂×D₄	—	424	4	no	—
878	C₂×D₄	C₂³×D₅₃	1	2	yes	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	53	1	no	—
881	C₂²×C₄	—	53	1	no	—
882	C₂²×C₄	—	53	1	no	—
883	C₂²×C₄	—	53	1	no	—
884	C₂²×C₄	—	53	1	no	—
885	C₂²×C₄	—	53	1	no	—
886	C₂²×C₄	—	53	1	no	—
887	C₂²×C₄	—	53	1	no	—
888	C₂²×C₄	—	53	1	no	—
889	C₂²×C₄	—	106	2	no	—
890	C₂²×C₄	—	106	2	no	—
891	C₂²×C₄	—	106	2	no	—
892	C₂²×C₄	—	106	2	no	—
893	C₂²×C₄	—	106	2	no	—
894	C₂²×C₄	—	106	2	no	—
895	C₂²×C₄	—	106	2	no	—
896	C₂²×C₄	—	106	2	no	—
897	C₂²×C₄	—	424	4	no	—
898	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
899	Q₁₆	—	2	2	no	—
900	Q₁₆	—	106	4	no	—
901	Q₁₆	—	106	2	no	—
902	SD₁₆	—	2	4	no	—
903	SD₁₆	—	106	4	no	—
904	SD₁₆	—	106	4	no	—
905	SD₁₆	—	106	4	no	—
906	D₈	—	2	2	no	—
907	D₈	—	106	4	no	—
908	D₈	—	106	2	no	—
909	M₁₆	—	2	2	no	—
910	M₁₆	—	106	2	no	—
911	M₁₆	—	106	2	no	—
912	M₁₆	—	106	2	no	—
913	C₂×C₈	—	2	2	no	—
914	C₂×C₈	—	53	1	no	—
915	C₂×C₈	—	53	1	no	—
916	C₂×C₈	—	53	4	no	—
917	C₂×C₈	—	53	4	no	—
918	C₂×C₈	—	53	1	no	—
919	C₂×C₈	—	53	1	no	—
920	C₂×C₈	—	106	2	no	—
921	C₂×C₈	—	106	2	no	—
922	C₂×C₈	—	106	2	no	—
923	C₂×C₈	—	106	2	no	—
924	C₂×C₈	—	106	2	no	—
925	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
926	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
927	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
928	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	53	1	no	—
933	C₄⋊C₄	—	53	1	no	—
934	C₄⋊C₄	—	53	1	no	—
935	C₄⋊C₄	—	53	1	no	—
936	C₄⋊C₄	—	53	1	no	—
937	C₄⋊C₄	—	53	1	no	—
938	C₄⋊C₄	—	53	2	no	—
939	C₄⋊C₄	—	53	2	no	—
940	C₄⋊C₄	—	106	2	no	—
941	C₄⋊C₄	—	106	2	no	—
942	C₄⋊C₄	—	106	2	no	—
943	C₄⋊C₄	—	106	2	no	—
944	C₄⋊C₄	—	106	2	no	—
945	C₄⋊C₄	—	106	2	no	—
946	C₄⋊C₄	—	106	2	no	—
947	C₄⋊C₄	—	106	2	no	—
948	C₄⋊C₄	—	106	2	no	—
949	C₄⋊C₄	—	106	2	no	—
950	C₄⋊C₄	—	106	2	no	—
951	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
952	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
953	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
954	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	53	1	no	—
961	C₂²⋊C₄	—	53	1	no	—
962	C₂²⋊C₄	—	53	1	no	—
963	C₂²⋊C₄	—	53	1	no	—
964	C₂²⋊C₄	—	53	1	no	—
965	C₂²⋊C₄	—	53	1	no	—
966	C₂²⋊C₄	—	106	2	no	—
967	C₂²⋊C₄	—	106	2	no	—
968	C₂²⋊C₄	—	106	2	no	—
969	C₂²⋊C₄	—	106	2	no	—
970	C₂²⋊C₄	—	106	2	no	—
971	C₂²⋊C₄	—	106	2	no	—
972	C₂²⋊C₄	—	106	2	no	—
973	C₂²⋊C₄	—	106	2	no	—
974	C₂²⋊C₄	—	106	2	no	—
975	C₂²⋊C₄	—	106	2	no	—
976	C₂²⋊C₄	—	106	2	no	—
977	C₂²⋊C₄	—	106	2	no	—
978	C₂²⋊C₄	—	106	2	no	—
979	C₂²⋊C₄	—	106	2	no	—
980	C₂²⋊C₄	—	106	2	no	—
981	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
982	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
983	C₄²	—	2	2	no	—
984	C₄²	—	53	1	no	—
985	C₄²	—	53	1	no	—
986	C₄²	—	53	1	no	—
987	C₄²	—	53	1	no	—
988	C₄²	—	53	1	no	—
989	C₄²	—	53	1	no	—
990	C₄²	—	106	2	no	—
991	C₄²	—	106	2	no	—
992	C₄²	—	106	2	no	—
993	C₄²	C₂³×D₅₃	1	1	yes	characteristic
994	C₄²	C₂³×D₅₃	1	1	yes	characteristic
995	C₂³	—	2	2	no	—
996	C₂³	—	53	1	no	—
997	C₂³	—	53	1	no	—
998	C₂³	—	106	2	no	—
999	C₂³	—	106	2	no	—
1000	C₂³	—	106	2	no	—
1001	C₂³	—	106	2	no	—
1002	C₂³	—	212	4	no	—
1003	C₂³	—	212	4	no	—
1004	C₂³	—	212	4	no	—
1005	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	8	2	no	—
1009	Q₈	—	106	2	no	—
1010	Q₈	—	106	2	no	—
1011	Q₈	—	424	2	no	—
1012	Q₈	—	424	2	no	—
1013	Q₈	—	424	2	no	—
1014	Q₈	—	212	4	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	8	2	no	—
1018	D₄	—	106	2	no	—
1019	D₄	—	106	2	no	—
1020	D₄	—	424	2	no	—
1021	D₄	—	424	2	no	—
1022	D₄	—	424	2	no	—
1023	D₄	—	212	4	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	53	1	no	—
1031	C₂×C₄	—	53	2	no	—
1032	C₂×C₄	—	53	2	no	—
1033	C₂×C₄	—	53	1	no	—
1034	C₂×C₄	—	53	1	no	—
1035	C₂×C₄	—	53	1	no	—
1036	C₂×C₄	—	53	1	no	—
1037	C₂×C₄	—	53	1	no	—
1038	C₂×C₄	—	106	2	no	—
1039	C₂×C₄	—	106	2	no	—
1040	C₂×C₄	—	106	2	no	—
1041	C₂×C₄	—	106	2	no	—
1042	C₂×C₄	—	106	2	no	—
1043	C₂×C₄	—	106	2	no	—
1044	C₂×C₄	—	106	2	no	—
1045	C₂×C₄	—	106	1	no	—
1046	C₂×C₄	—	106	1	no	—
1047	C₂×C₄	—	106	2	no	—
1048	C₂×C₄	—	106	2	no	—
1049	C₂×C₄	—	106	2	no	—
1050	C₂×C₄	—	424	2	no	—
1051	C₂×C₄	—	424	2	no	—
1052	C₂×C₄	—	424	2	no	—
1053	C₂×C₄	—	212	4	no	—
1054	C₂×C₄	—	212	4	no	—
1055	C₂×C₄	—	212	4	no	—
1056	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1057	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1058	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1059	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1060	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1061	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1062	C₈	—	2	1	no	—
1063	C₈	—	2	1	no	—
1064	C₈	—	53	2	no	—
1065	C₈	—	53	2	no	—
1066	C₈	—	106	1	no	—
1067	C₈	—	106	1	no	—
1068	C₈	#41×D₅₃	1	2	yes	—
1069	C₈	#41×D₅₃	1	2	yes	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	53	2	no	—
1077	C₂²	—	53	2	no	—
1078	C₂²	—	53	2	no	—
1079	C₂²	—	106	1	no	—
1080	C₂²	—	106	1	no	—
1081	C₂²	—	106	1	no	—
1082	C₂²	—	424	8	no	—
1083	C₂²	—	212	4	no	—
1084	C₂²	—	212	2	no	—
1085	C₂²	—	212	2	no	—
1086	C₂²	—	212	2	no	—
1087	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	53	2	no	—
1097	C₄	—	106	1	no	—
1098	C₄	—	106	1	no	—
1099	C₄	—	106	1	no	—
1100	C₄	—	106	1	no	—
1101	C₄	—	106	1	no	—
1102	C₄	—	212	2	no	—
1103	C₄	—	212	2	no	—
1104	C₄	—	212	2	no	—
1105	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1106	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1107	C₂	—	4	1	no	—
1108	C₂	—	8	2	no	—
1109	C₂	—	53	4	no	—
1110	C₂	—	424	2	no	—
1111	C₂	—	212	1	no	—
1112	C₂	#532×D₅₃	1	1	yes	characteristic
1113	C₂	#576×D₅₃	1	1	yes	characteristic
1114	C₂	#578×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3175	C₂
socle	C₂²×C₅₃	C₂³×D₄
prime radical	#466×D₅₃	C₂
hypercenter	#3175	D₅₃
hypocenter	C₅₃	C₂×#3175
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3175

Complements

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

N	H ≅ G/N	type
1. #542×D₅₃	C₂	semidirect
2. #20285357	C₂	semidirect
3. #20285356	C₂	semidirect
4. #20285355	C₂	semidirect
5. #20285354	C₂	semidirect
6. #20285353	C₂	semidirect
7. #20285352	C₂	semidirect
8. #20285351	C₂	semidirect
9. #20285350	C₂	semidirect
10. #20285349	C₂	semidirect
11. #20285348	C₂	semidirect
12. #20285347	C₂	semidirect
13. #500×D₅₃	C₂	semidirect
14. #495×D₅₃	C₂	semidirect
15. #489×D₅₃	C₂	semidirect
16. #468×D₅₃	C₂	semidirect
17. #467×D₅₃	C₂	semidirect
19. #440×D₅₃	C₂	semidirect
20. C₄×Q₁₆×D₅₃	C₂	semidirect
21. C₄×D₈×D₅₃	C₂	semidirect
22. #405×D₅₃	C₂	semidirect
23. C₅₃×#3175	C₂	semidirect
29. #16811247	C₂²	semidirect
30. #16811246	C₂²	semidirect
31. #16811245	C₂²	semidirect
32. #16811244	C₂²	semidirect
34. #16811242	C₂²	semidirect
36. #16811240	C₂²	semidirect
38. #16811238	C₂²	semidirect
51. #16811028	C₂²	semidirect
52. #16811027	C₂²	semidirect
53. #16811027	C₂²	semidirect
54. #16811027	C₂²	semidirect
55. #16811026	C₂²	semidirect
56. #16811008	C₂²	semidirect
57. #16811007	C₂²	semidirect
58. #16811006	C₂²	semidirect
59. #16811005	C₂²	semidirect
60. #16811004	C₂²	semidirect
61. #16810985	C₂²	semidirect
62. #16810984	C₂²	semidirect
63. #16810984	C₂²	semidirect
64. #16810983	C₂²	semidirect
65. #16810982	C₂²	semidirect
66. #16810981	C₂²	semidirect
67. #16810981	C₂²	semidirect
68. #16810872	C₂²	semidirect
69. #16810871	C₂²	semidirect
70. #16810870	C₂²	semidirect
71. #16810869	C₂²	semidirect
72. #16810868	C₂²	semidirect
73. #16810867	C₂²	semidirect
74. #16810866	C₂²	semidirect
75. #16810865	C₂²	semidirect
76. #16810864	C₂²	semidirect
77. #16810863	C₂²	semidirect
78. #16810862	C₂²	semidirect
79. #16810861	C₂²	semidirect
85. #16810726	C₂²	semidirect
86. #16810725	C₂²	semidirect
87. #16810724	C₂²	semidirect
88. #16810723	C₂²	semidirect
89. #16810722	C₂²	semidirect
90. #16810721	C₂²	semidirect
91. #16810720	C₂²	semidirect
92. C₄×Dic₂₁₂	C₂²	semidirect
93. Q₁₆×Dic₅₃	C₂²	semidirect
94. #16810717	C₂²	semidirect
95. C₄×#11719925	C₂²	semidirect
96. #16810715	C₂²	semidirect
97. C₄×D₄₂₄	C₂²	semidirect
98. D₈×Dic₅₃	C₂²	semidirect
99. #16810705	C₂²	semidirect
100. C₄×#11719922	C₂²	semidirect
101. #16810703	C₂²	semidirect
109. #16810581	C₂²	semidirect
110. #16810580	C₂²	semidirect
111. #16810580	C₂²	semidirect
112. #16810579	C₂²	semidirect
113. #16810578	C₂²	semidirect
114. #16810577	C₂²	semidirect
115. #16810577	C₂²	semidirect
120. C₅₃×#542	C₂²	semidirect
121. C₅₃×#500	C₂²	semidirect
122. C₅₃×#495	C₂²	semidirect
123. C₅₃×#489	C₂²	semidirect
124. C₅₃×#468	C₂²	semidirect
125. C₅₃×#467	C₂²	semidirect
127. C₅₃×#440	C₂²	semidirect
128. C₄×Q₁₆×C₅₃	C₂²	semidirect
129. C₄×D₈×C₅₃	C₂²	semidirect
130. C₅₃×#405	C₂²	semidirect
562. #3175	D₅₃	direct (N × H)
580. D₅₃	#3175	direct (N × H)
597. #542	C₂×D₅₃	semidirect
614. #500	C₂×D₅₃	semidirect
620. #495	C₂×D₅₃	semidirect
628. #489	C₂×D₅₃	semidirect
636. #468	C₂×D₅₃	semidirect
642. #467	C₂×D₅₃	semidirect
656. #440	C₂×D₅₃	semidirect
662. C₄×Q₁₆	C₂×D₅₃	semidirect
668. C₄×D₈	C₂×D₅₃	semidirect
683. #405	C₂×D₅₃	semidirect
688. C₅₃	C₂×#3175	semidirect

Maximal subgroups

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

subgroup	index
#542×D₅₃	2
#20285357	2
#20285356	2
#20285355	2
#20285354	2
#20285353	2
#20285352	2
#20285351	2
#20285350	2
#20285349	2
#20285348	2
#20285347	2
#500×D₅₃	2
#495×D₅₃	2
#489×D₅₃	2
#468×D₅₃	2
#467×D₅₃	2
#466×D₅₃	2
#440×D₅₃	2
C₄×Q₁₆×D₅₃	2
C₄×D₈×D₅₃	2
#405×D₅₃	2
C₅₃×#3175	2
C₂×#3175	53

Subgroups — D53×#3175 #28253906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3175 #28253906