Subgroups — D₅₃×#3336 #28262519

Order 13568.

1866 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	#552×D₅₃	C₂	1	2	yes	maximal
2	#20287086	C₂	1	1	yes	maximal, characteristic, complemented
3	#20287085	C₂	1	1	yes	maximal, characteristic, complemented
4	#20287084	C₂	1	1	yes	maximal, characteristic, complemented
5	#20287083	C₂	1	1	yes	maximal, characteristic, complemented
6	#20287082	C₂	1	1	yes	maximal, characteristic, complemented
7	#20287081	C₂	1	2	yes	maximal, complemented
8	#20287080	C₂	1	2	yes	maximal, complemented
9	#20287079	C₂	1	1	yes	maximal, characteristic, complemented
10	#20287078	C₂	1	1	yes	maximal, characteristic, complemented
11	#20287077	C₂	1	2	yes	maximal, complemented
12	#20287076	C₂	1	2	yes	maximal, complemented
13	#499×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#485×D₅₃	C₂	1	2	yes	maximal, complemented
15	#483×D₅₃	C₂	1	2	yes	maximal, complemented
16	#479×D₅₃	C₂	1	2	yes	maximal, complemented
17	#467×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#467×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×Q₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
21	#427×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#107×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3336	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₅₃	C₂²	1	1	yes	characteristic
25	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
27	#16811315	C₂²	1	2	yes	—
28	#16811314	C₂²	1	2	yes	—
29	#16811313	C₂²	1	2	yes	—
30	#16811312	C₂²	1	2	yes	—
31	#16811311	C₂²	1	2	yes	—
32	#16811310	—	2	2	no	—
33	#16811309	—	2	2	no	—
34	#16811308	C₂²	1	2	yes	—
35	#16811307	C₂²	1	2	yes	—
36	#16811306	—	2	2	no	—
37	#16811305	—	2	2	no	—
38	#126×D₅₃	—	2	2	no	—
39	#125×D₅₃	—	2	2	no	—
40	#125×D₅₃	C₂²	1	2	yes	—
41	#123×D₅₃	—	2	2	no	—
42	C₂²⋊Q₈×D₅₃	C₂²	1	2	yes	—
43	C₂²⋊Q₈×D₅₃	C₂²	1	2	yes	—
44	C₄×Q₈×D₅₃	C₂²	1	2	yes	—
45	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
46	#117×D₅₃	—	2	2	no	—
47	#117×D₅₃	C₂²	1	2	yes	—
48	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
49	#16811025	C₂²	1	1	yes	characteristic, complemented
50	#16811024	C₂²	1	1	yes	characteristic, complemented
51	#16811024	C₂²	1	1	yes	characteristic, complemented
52	#16811023	C₂²	1	2	yes	complemented
53	#16811022	C₂²	1	2	yes	complemented
54	#16810967	C₂²	1	2	yes	complemented
55	#16810966	C₂²	1	2	yes	complemented
56	#16810965	C₂²	1	2	yes	complemented
57	#16810964	C₂²	1	2	yes	complemented
58	#16810963	C₂²	1	2	yes	complemented
59	#16810962	C₂²	1	2	yes	complemented
60	#16810961	C₂²	1	2	yes	complemented
61	#16810955	C₂²	1	2	yes	complemented
62	#16810955	C₂²	1	2	yes	complemented
63	#16810954	C₂²	1	2	yes	complemented
64	#16810953	C₂²	1	2	yes	complemented
65	#16810952	C₂²	1	2	yes	complemented
66	#16810952	C₂²	1	2	yes	complemented
67	#16810951	C₂²	1	2	yes	complemented
68	#16810933	C₂²	1	2	yes	complemented
69	#16810932	C₂²	1	2	yes	complemented
70	#16810931	C₂²	1	2	yes	complemented
71	#16810930	C₂²	1	2	yes	complemented
72	#16810929	C₂²	1	2	yes	complemented
73	#16810928	C₂²	1	2	yes	complemented
74	#16810927	C₂²	1	2	yes	complemented
75	#16810865	C₂²	1	1	yes	characteristic, complemented
76	#16810865	C₂²	1	1	yes	characteristic, complemented
77	#16810864	C₂²	1	1	yes	characteristic, complemented
78	#16810864	C₂²	1	1	yes	characteristic, complemented
79	#16810863	C₂²	1	2	yes	complemented
80	#16810863	C₂²	1	2	yes	complemented
81	#16810862	C₂²	1	2	yes	complemented
82	#16810862	C₂²	1	2	yes	complemented
83	#16810861	C₂²	1	1	yes	characteristic, complemented
84	#16810861	C₂²	1	1	yes	characteristic, complemented
85	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic, complemented
86	Q₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
87	#16810717	C₂²	1	1	yes	characteristic, complemented
88	C₄×#11719925	C₂²	1	2	yes	complemented
89	#16810715	C₂²	1	2	yes	complemented
90	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
91	D₄×#88322	C₂²	1	1	yes	characteristic
92	#16810688	C₂²	1	1	yes	characteristic
93	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
94	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
95	#16810686	C₂²	1	1	yes	characteristic
96	#16810686	C₂²	1	1	yes	characteristic
97	#16810661	C₂²	1	1	yes	characteristic, complemented
98	#16810660	C₂²	1	1	yes	characteristic, complemented
99	#16810660	C₂²	1	1	yes	characteristic, complemented
100	#16810659	C₂²	1	2	yes	complemented
101	#16810658	C₂²	1	2	yes	complemented
102	C₂×#13133151	C₂²	1	1	yes	characteristic, complemented
103	C₂×#13133150	C₂²	1	2	yes	complemented
104	#107×D₅₃	C₂²	1	1	yes	characteristic
105	#107×D₅₃	C₂²	1	1	yes	characteristic
106	#107×D₅₃	C₂²	1	2	yes	—
107	#107×D₅₃	C₂²	1	1	yes	characteristic
108	#107×D₅₃	C₂²	1	2	yes	complemented
109	#107×D₅₃	C₂²	1	1	yes	characteristic, complemented
110	#107×D₅₃	C₂²	1	1	yes	characteristic, complemented
111	#106×D₅₃	C₂²	1	2	yes	—
112	#106×D₅₃	C₂²	1	2	yes	—
113	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
114	#103×D₅₃	C₂²	1	2	yes	—
115	#103×D₅₃	C₂²	1	2	yes	—
116	#103×D₅₃	C₂²	1	2	yes	—
117	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
118	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
120	C₅₃×#552	C₂²	1	2	yes	—
121	C₅₃×#499	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#485	C₂²	1	2	yes	complemented
123	C₅₃×#483	C₂²	1	2	yes	complemented
124	C₅₃×#479	C₂²	1	2	yes	complemented
125	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
127	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
129	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
130	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
132	C₂×D₄×D₅₃	D₄	1	1	yes	characteristic
133	C₂²×C₄×D₅₃	—	2	2	no	—
134	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
136	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic
137	C₂×#11719925	C₂³	1	2	yes	—
138	Q₁₆×D₅₃	—	2	4	no	—
139	C₂²×#88322	C₂³	1	1	yes	characteristic
140	C₂²×#88322	C₂³	1	1	yes	characteristic
141	C₂×C₈×D₅₃	—	2	4	no	—
142	C₂×C₈×D₅₃	—	2	4	no	—
143	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
145	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
146	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
151	#13133212	—	2	2	no	—
152	#13133212	—	2	2	no	—
153	#13133212	—	2	2	no	—
154	#13133211	—	2	2	no	—
155	#13133210	—	2	2	no	—
156	#13133210	—	2	2	no	—
157	#13133210	—	2	2	no	—
158	#13133209	—	2	2	no	—
159	#13133209	C₂³	1	2	yes	—
160	#13133208	—	2	2	no	—
161	#13133208	—	2	2	no	—
162	#13133208	C₂³	1	2	yes	—
163	#13133208	C₂³	1	2	yes	—
164	#13133207	—	2	2	no	—
165	#13133207	—	2	2	no	—
166	#13133207	—	2	2	no	—
167	#13133207	—	2	2	no	—
168	#13133207	—	2	2	no	—
169	#13133207	—	2	2	no	—
170	#13133202	—	2	2	no	—
171	#13133202	—	2	2	no	—
172	#13133201	—	2	2	no	—
173	#13133200	—	2	2	no	—
174	#13133199	—	2	2	no	—
175	#13133199	—	2	2	no	—
176	#13133198	—	2	2	no	—
177	#13133197	C₂³	1	2	yes	—
178	#13133197	C₂³	1	2	yes	—
179	#13133196	C₂³	1	2	yes	—
180	#13133196	C₂³	1	2	yes	—
181	#13133195	—	2	2	no	—
182	#13133195	—	2	2	no	—
183	#13133194	—	2	2	no	—
184	#13133194	—	2	2	no	—
185	#13133193	C₂³	1	2	yes	—
186	#13133193	C₂³	1	2	yes	—
187	Q₈×Dic₅₃	C₂³	1	2	yes	—
188	C₄×Dic₁₀₆	—	2	2	no	—
189	C₄×Dic₁₀₆	C₂³	1	2	yes	—
190	#13133182	—	2	2	no	—
191	#13133182	C₂³	1	2	yes	—
192	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
193	D₄×Dic₅₃	D₄	1	1	yes	characteristic
194	#13133179	D₄	1	1	yes	characteristic
195	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
196	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
197	#13133177	D₄	1	1	yes	characteristic
198	#13133177	D₄	1	1	yes	characteristic
199	#13133176	—	2	2	no	—
200	#13133176	C₂³	1	2	yes	—
201	#13133175	—	2	2	no	—
202	#13133175	—	2	2	no	—
203	#13133175	C₂³	1	2	yes	—
204	#13133175	C₂³	1	2	yes	—
205	#13133174	—	2	2	no	—
206	#13133174	—	2	2	no	—
207	#13133174	—	2	2	no	—
208	#13133173	—	2	2	no	—
209	#13133173	—	2	2	no	—
210	#13133173	—	2	2	no	—
211	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
212	C₂×#11719919	—	2	2	no	—
213	C₄⋊C₄×D₅₃	—	2	2	no	—
214	C₄⋊C₄×D₅₃	—	2	2	no	—
215	C₄⋊C₄×D₅₃	—	2	2	no	—
216	C₄⋊C₄×D₅₃	—	2	2	no	—
217	C₄⋊C₄×D₅₃	—	2	2	no	—
218	C₄⋊C₄×D₅₃	—	2	2	no	—
219	C₄⋊C₄×D₅₃	—	2	2	no	—
220	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
221	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
222	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
223	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
224	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
225	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×D₅₃	—	2	2	no	—
227	C₂²⋊C₄×D₅₃	—	2	2	no	—
228	C₂²⋊C₄×D₅₃	—	2	2	no	—
229	C₂²⋊C₄×D₅₃	D₄	1	1	yes	characteristic
230	C₂²⋊C₄×D₅₃	D₄	1	1	yes	characteristic
231	C₄²×D₅₃	—	2	2	no	—
232	C₄²×D₅₃	—	2	2	no	—
233	C₄²×D₅₃	C₂³	1	1	yes	characteristic
234	#13133151	C₂³	1	1	yes	characteristic
235	#13133151	C₂³	1	1	yes	characteristic
236	#13133151	C₂³	1	1	yes	characteristic
237	#13133151	C₂³	1	2	yes	—
238	#13133150	C₂³	1	2	yes	—
239	#13133150	C₂³	1	2	yes	—
240	#13133150	C₂³	1	2	yes	—
241	#13133150	C₂³	1	2	yes	—
242	#13133150	C₂³	1	2	yes	—
243	#13133149	C₂³	1	2	yes	—
244	#13133149	C₂³	1	2	yes	—
245	#13133148	C₂³	1	2	yes	—
246	#13133148	C₂³	1	2	yes	—
247	#13133148	C₂³	1	2	yes	—
248	#13133148	C₂³	1	2	yes	—
249	C₄⋊#88322	C₂³	1	1	yes	characteristic
250	#13133146	C₂³	1	1	yes	characteristic
251	#13133146	C₂³	1	1	yes	characteristic
252	#13133142	C₂³	1	2	yes	—
253	#13133142	C₂³	1	2	yes	—
254	#13133142	C₂³	1	2	yes	—
255	#13133141	C₂³	1	2	yes	—
256	#13133141	C₂³	1	2	yes	—
257	#13133141	C₂³	1	2	yes	—
258	#13133140	C₂³	1	2	yes	—
259	#13133140	C₂³	1	2	yes	—
260	#13133140	C₂³	1	2	yes	—
261	C₂²⋊#88322	C₂³	1	1	yes	characteristic
262	C₂²⋊#88322	C₂³	1	1	yes	characteristic
263	#13133129	C₂³	1	1	yes	characteristic
264	#13133129	C₂³	1	1	yes	characteristic
265	#13133129	C₂³	1	1	yes	characteristic
266	#13133129	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	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
273	#126×C₅₃	—	2	2	no	—
274	#125×C₅₃	—	2	2	no	—
275	#125×C₅₃	C₂³	1	2	yes	—
276	#123×C₅₃	—	2	2	no	—
277	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
278	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
280	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
281	#117×C₅₃	—	2	2	no	—
282	#117×C₅₃	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
284	#107×C₅₃	C₂³	1	2	yes	—
285	#107×C₅₃	C₂³	1	1	yes	characteristic
286	#107×C₅₃	C₂³	1	1	yes	characteristic
287	#107×C₅₃	C₂³	1	1	yes	characteristic
288	#106×C₅₃	C₂³	1	2	yes	—
289	#106×C₅₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
297	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
298	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
299	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
300	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₅₃	—	2	2	no	—
302	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
305	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×Dic₅₃	—	2	2	no	—
307	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
309	Q₈×D₅₃	—	2	4	no	—
310	Q₈×D₅₃	—	2	4	no	—
311	D₄×D₅₃	—	2	4	no	—
312	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
313	C₂×C₄×D₅₃	—	2	2	no	—
314	C₂×C₄×D₅₃	—	2	2	no	—
315	C₂×C₄×D₅₃	—	2	2	no	—
316	C₂×C₄×D₅₃	—	2	2	no	—
317	C₂×C₄×D₅₃	—	2	2	no	—
318	C₂×C₄×D₅₃	—	2	2	no	—
319	C₂×C₄×D₅₃	—	2	2	no	—
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	—	4	8	no	—
324	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
325	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
326	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
328	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
329	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
332	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
333	C₂×Dic₁₀₆	—	2	2	no	—
334	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
335	Q₁₆×C₅₃	—	2	2	no	—
336	C₂×C₈×C₅₃	—	2	2	no	—
337	C₂×C₈×C₅₃	—	2	2	no	—
338	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₄⋊C₄×C₅₃	—	2	2	no	—
343	C₄⋊C₄×C₅₃	—	2	2	no	—
344	C₄⋊C₄×C₅₃	—	2	2	no	—
345	C₄⋊C₄×C₅₃	—	2	2	no	—
346	C₄⋊C₄×C₅₃	—	2	2	no	—
347	C₄⋊C₄×C₅₃	—	2	2	no	—
348	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
350	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
351	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
352	C₂²⋊C₄×C₅₃	—	2	2	no	—
353	C₂²⋊C₄×C₅₃	—	2	2	no	—
354	C₂²⋊C₄×C₅₃	—	2	2	no	—
355	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
356	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₅₃	—	2	2	no	—
358	C₄²×C₅₃	—	2	2	no	—
359	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂²⋊Dic₅₃	—	2	2	no	—
361	C₂²⋊Dic₅₃	—	2	2	no	—
362	C₂²⋊Dic₅₃	—	2	2	no	—
363	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
364	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
365	#11719925	—	2	4	no	—
366	#11719921	—	2	2	no	—
367	#11719921	—	2	2	no	—
368	#11719921	—	2	2	no	—
369	#11719921	—	2	2	no	—
370	#11719921	—	2	2	no	—
371	#11719921	—	2	2	no	—
372	#11719921	C₂×D₄	1	1	yes	characteristic
373	#11719921	C₂×D₄	1	1	yes	characteristic
374	#11719921	C₂×D₄	1	1	yes	characteristic
375	#11719921	C₂×D₄	1	1	yes	characteristic
376	C₄⋊Dic₅₃	—	2	2	no	—
377	C₄⋊Dic₅₃	—	2	2	no	—
378	C₄⋊Dic₅₃	—	2	2	no	—
379	C₄⋊Dic₅₃	—	2	2	no	—
380	C₄⋊Dic₅₃	—	2	2	no	—
381	C₄⋊Dic₅₃	—	2	2	no	—
382	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
383	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
384	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
385	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
386	#11719919	—	2	2	no	—
387	#11719919	—	2	2	no	—
388	#11719919	—	2	2	no	—
389	#11719919	—	2	2	no	—
390	#11719919	—	2	2	no	—
391	#11719919	—	2	2	no	—
392	#11719919	—	2	2	no	—
393	#11719919	—	2	2	no	—
394	#11719919	—	2	2	no	—
395	#11719919	—	2	2	no	—
396	#11719919	—	2	2	no	—
397	#11719919	—	2	2	no	—
398	#11719919	—	2	2	no	—
399	#11719919	—	2	2	no	—
400	#11719919	—	2	2	no	—
401	#11719919	C₂×D₄	1	1	yes	characteristic
402	#11719919	C₂×D₄	1	1	yes	characteristic
403	C₄×Dic₅₃	—	2	2	no	—
404	C₄×Dic₅₃	—	2	2	no	—
405	C₄×Dic₅₃	—	2	2	no	—
406	C₄×Dic₅₃	—	2	2	no	—
407	C₄×Dic₅₃	—	2	2	no	—
408	C₄×Dic₅₃	—	2	2	no	—
409	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
410	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
412	C₂×#88322	—	2	2	no	—
413	C₂×#88322	—	2	2	no	—
414	C₂×#88322	C₂⁴	1	1	yes	characteristic
415	C₂×#88322	C₂⁴	1	1	yes	characteristic
416	C₂×#88322	C₂⁴	1	1	yes	characteristic
417	C₂×#88322	C₂⁴	1	1	yes	characteristic
418	Dic₂₁₂	—	2	2	no	—
419	C₈×D₅₃	—	2	2	no	—
420	C₈×D₅₃	—	2	2	no	—
421	C₈×D₅₃	—	2	2	no	—
422	C₈×D₅₃	—	2	2	no	—
423	C₈×D₅₃	—	2	2	no	—
424	C₈×D₅₃	—	2	2	no	—
425	C₈×D₅₃	—	2	2	no	—
426	C₈×D₅₃	#41	1	4	yes	—
427	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
428	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
429	C₂²×D₅₃	—	2	2	no	—
430	C₂²×D₅₃	—	2	2	no	—
431	C₂²×D₅₃	—	2	2	no	—
432	C₂²×D₅₃	—	2	2	no	—
433	C₂²×D₅₃	—	2	2	no	—
434	C₂²×D₅₃	#135	1	4	yes	—
435	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
436	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
437	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
438	Q₈×C₅₃	—	2	2	no	—
439	Q₈×C₅₃	—	2	2	no	—
440	D₄×C₅₃	—	2	2	no	—
441	C₂×C₄×C₅₃	—	2	1	no	—
442	C₂×C₄×C₅₃	—	2	1	no	—
443	C₂×C₄×C₅₃	—	2	1	no	—
444	C₂×C₄×C₅₃	—	2	1	no	—
445	C₂×C₄×C₅₃	—	2	2	no	—
446	C₂×C₄×C₅₃	—	2	2	no	—
447	C₂×C₄×C₅₃	—	2	2	no	—
448	C₂×C₄×C₅₃	—	2	2	no	—
449	C₂×C₄×C₅₃	—	4	4	no	—
450	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
455	C₂²⋊D₅₃	—	2	2	no	—
456	C₂²⋊D₅₃	—	2	2	no	—
457	C₂×Dic₅₃	—	2	2	no	—
458	C₂×Dic₅₃	—	2	2	no	—
459	C₂×Dic₅₃	—	2	2	no	—
460	C₂×Dic₅₃	—	2	2	no	—
461	C₂×Dic₅₃	—	2	2	no	—
462	C₂×Dic₅₃	—	2	2	no	—
463	C₂×Dic₅₃	—	4	4	no	—
464	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
469	D₂₁₂	—	2	2	no	—
470	C₄×D₅₃	—	2	2	no	—
471	C₄×D₅₃	—	2	2	no	—
472	C₄×D₅₃	—	2	2	no	—
473	C₄×D₅₃	—	2	2	no	—
474	C₄×D₅₃	—	2	1	no	—
475	C₄×D₅₃	—	2	1	no	—
476	C₄×D₅₃	—	2	1	no	—
477	C₄×D₅₃	—	2	1	no	—
478	C₄×D₅₃	—	2	2	no	—
479	C₄×D₅₃	—	2	2	no	—
480	C₄×D₅₃	—	4	4	no	—
481	C₄×D₅₃	—	4	4	no	—
482	C₄×D₅₃	—	4	4	no	—
483	C₄×D₅₃	—	4	4	no	—
484	C₄×D₅₃	—	4	4	no	—
485	C₄×D₅₃	—	4	4	no	—
486	C₄×D₅₃	C₂×#41	1	2	yes	—
487	C₄×D₅₃	2₋¹⁺⁴	1	2	yes	—
488	Dic₁₀₆	—	2	2	no	—
489	Dic₁₀₆	—	2	2	no	—
490	Dic₁₀₆	—	4	4	no	—
491	C₈×C₅₃	—	2	1	no	—
492	C₈×C₅₃	—	2	1	no	—
493	C₈×C₅₃	—	2	1	no	—
494	C₈×C₅₃	C₂×#41	1	2	yes	—
495	#88322	—	2	1	no	—
496	#88322	—	2	1	no	—
497	#88322	—	2	1	no	—
498	#88322	C₂×#41	1	2	yes	—
499	C₂×#3336	—	53	1	no	maximal, Sylow
500	C₂²×C₅₃	—	2	1	no	—
501	C₂²×C₅₃	—	2	1	no	—
502	C₂²×C₅₃	—	2	1	no	—
503	C₂²×C₅₃	—	2	1	no	—
504	C₂²×C₅₃	—	2	1	no	—
505	C₂²×C₅₃	C₂×#135	1	2	yes	—
506	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
507	C₂×D₅₃	—	2	1	no	—
508	C₂×D₅₃	—	2	1	no	—
509	C₂×D₅₃	—	2	8	no	—
510	C₂×D₅₃	—	2	1	no	—
511	C₂×D₅₃	—	2	1	no	—
512	C₂×D₅₃	—	2	1	no	—
513	C₂×D₅₃	—	4	4	no	—
514	C₂×D₅₃	#547	1	2	yes	—
515	C₂×D₅₃	C₂×#135	1	2	yes	—
516	C₂×D₅₃	C₂×#135	1	2	yes	—
517	C₂×D₅₃	#578	1	2	yes	—
518	C₄×C₅₃	—	2	1	no	—
519	C₄×C₅₃	—	2	1	no	—
520	C₄×C₅₃	—	2	1	no	—
521	C₄×C₅₃	—	2	1	no	—
522	C₄×C₅₃	—	4	2	no	—
523	C₄×C₅₃	—	4	2	no	—
524	C₄×C₅₃	—	4	2	no	—
525	C₄×C₅₃	—	4	2	no	—
526	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
527	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
528	Dic₅₃	—	2	1	no	—
529	Dic₅₃	—	2	1	no	—
530	Dic₅₃	—	2	1	no	—
531	Dic₅₃	—	2	1	no	—
532	Dic₅₃	—	4	2	no	—
533	Dic₅₃	—	4	2	no	—
534	Dic₅₃	—	4	2	no	—
535	Dic₅₃	—	4	2	no	—
536	Dic₅₃	#547	1	2	yes	—
537	C₂×#552	—	53	2	no	—
538	#3336	—	53	1	no	—
539	#3336	—	53	2	no	—
540	#3336	—	53	2	no	—
541	#3336	—	53	2	no	—
542	#3336	—	53	1	no	—
543	#3336	—	53	1	no	—
544	#3336	—	53	1	no	—
545	#3336	—	53	1	no	—
546	#3336	—	53	1	no	—
547	#3336	—	53	1	no	—
548	#3336	—	53	2	no	—
549	#3336	D₅₃	1	1	yes	characteristic, direct product factor
550	C₂×#499	—	53	1	no	—
551	C₂×#485	—	53	2	no	—
552	C₂×#483	—	53	2	no	—
553	C₂×#479	—	53	2	no	—
554	C₂×#467	—	53	1	no	—
555	C₂×#467	—	53	1	no	—
556	C₂×C₄×Q₁₆	—	53	1	no	—
557	C₂×C₈×D₄	—	53	1	no	—
558	C₂×#427	—	53	1	no	—
559	C₂²×#107	—	53	1	no	—
560	C₂×C₅₃	—	2	2	no	—
561	C₂×C₅₃	—	4	1	no	—
562	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
563	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
564	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
565	D₅₃	—	2	2	no	—
566	D₅₃	—	4	1	no	—
567	D₅₃	#3336	1	4	yes	direct product factor
568	C₂²×Q₁₆	—	53	1	no	—
569	C₂³×C₈	—	53	1	no	—
570	C₂³×C₈	—	53	1	no	—
571	#552	—	53	2	no	—
572	#552	—	53	2	no	—
573	#552	—	53	2	no	—
574	#552	—	53	2	no	—
575	#552	—	53	2	no	—
576	#552	—	53	2	no	—
577	#552	—	53	2	no	—
578	#552	—	106	2	no	—
579	#552	—	106	2	no	—
580	#552	—	106	2	no	—
581	#552	—	106	2	no	—
582	#552	C₂×D₅₃	1	2	yes	—
583	C₂×#126	—	106	2	no	—
584	C₂×#125	—	53	2	no	—
585	C₂×#125	—	106	2	no	—
586	C₂×#123	—	106	2	no	—
587	C₂×C₂²⋊Q₈	—	53	2	no	—
588	C₂×C₂²⋊Q₈	—	53	2	no	—
589	C₂×C₄×Q₈	—	53	2	no	—
590	C₂×C₄×D₄	—	53	1	no	—
591	C₂×#117	—	53	2	no	—
592	C₂×#117	—	106	2	no	—
593	C₂²×C₄⋊C₄	—	53	2	no	—
594	#499	—	53	2	no	—
595	#499	—	53	1	no	—
596	#499	—	53	1	no	—
597	#499	—	53	2	no	—
598	#499	—	53	1	no	—
599	#499	C₂×D₅₃	1	1	yes	characteristic, complemented
600	#485	—	53	2	no	—
601	#485	—	53	2	no	—
602	#485	—	53	2	no	—
603	#485	—	53	2	no	—
604	#485	—	53	2	no	—
605	#485	—	53	2	no	—
606	#485	—	53	2	no	—
607	#485	C₂×D₅₃	1	2	yes	complemented
608	#483	—	53	2	no	—
609	#483	—	53	2	no	—
610	#483	—	53	2	no	—
611	#483	—	53	2	no	—
612	#483	—	53	2	no	—
613	#483	—	53	2	no	—
614	#483	—	53	2	no	—
615	#483	C₂×D₅₃	1	2	yes	complemented
616	#479	—	53	2	no	—
617	#479	—	53	2	no	—
618	#479	—	53	2	no	—
619	#479	—	53	2	no	—
620	#479	—	53	2	no	—
621	#479	—	53	2	no	—
622	#479	—	53	2	no	—
623	#479	C₂×D₅₃	1	2	yes	complemented
624	#467	—	53	1	no	—
625	#467	—	53	1	no	—
626	#467	—	53	1	no	—
627	#467	—	53	1	no	—
628	#467	—	53	2	no	—
629	#467	—	53	2	no	—
630	#467	—	53	1	no	—
631	#467	—	53	1	no	—
632	#467	—	53	2	no	—
633	#467	—	53	2	no	—
634	#467	C₂×D₅₃	1	1	yes	characteristic, complemented
635	#467	C₂×D₅₃	1	1	yes	characteristic, complemented
636	C₄×Q₁₆	—	53	1	no	—
637	C₄×Q₁₆	—	53	2	no	—
638	C₄×Q₁₆	—	53	1	no	—
639	C₄×Q₁₆	—	53	2	no	—
640	C₄×Q₁₆	—	53	1	no	—
641	C₄×Q₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
642	C₈×D₄	—	53	1	no	—
643	C₈×D₄	—	53	1	no	—
644	C₈×D₄	—	53	1	no	—
645	C₈×D₄	—	53	1	no	—
646	C₈×D₄	—	53	1	no	—
647	C₈×D₄	—	53	1	no	—
648	C₈×D₄	—	53	1	no	—
649	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
650	#427	—	53	1	no	—
651	#427	—	53	2	no	—
652	#427	—	53	1	no	—
653	#427	—	53	1	no	—
654	#427	—	53	2	no	—
655	#427	C₂×D₅₃	1	1	yes	characteristic, complemented
656	C₂×#107	—	53	1	no	—
657	C₂×#107	—	53	2	no	—
658	C₂×#107	—	53	2	no	—
659	C₂×#107	—	53	1	no	—
660	C₂×#107	—	53	1	no	—
661	C₂×#107	—	53	2	no	—
662	C₂×#107	—	53	1	no	—
663	C₂×#107	—	53	1	no	—
664	C₂×#107	—	53	1	no	—
665	C₂×#107	C₂×D₅₃	1	1	yes	characteristic, complemented
666	C₂×#106	—	53	2	no	—
667	C₂×#106	—	53	2	no	—
668	C₂×C₄⋊C₈	—	53	1	no	—
669	C₂×#103	—	53	2	no	—
670	C₂×#103	—	53	2	no	—
671	C₂×#103	—	53	2	no	—
672	C₂×C₂²⋊C₈	—	53	1	no	—
673	C₂×C₂²⋊C₈	—	53	1	no	—
674	C₂×C₄×C₈	—	53	1	no	—
675	C₅₃	C₂×#3336	1	1	yes	characteristic, complemented, Sylow
676	C₂²×Q₈	—	53	2	no	—
677	C₂²×D₄	—	53	1	no	—
678	C₂³×C₄	—	53	1	no	—
679	C₂³×C₄	—	53	1	no	—
680	C₂³×C₄	—	106	2	no	—
681	C₂×Q₁₆	—	53	2	no	—
682	C₂×Q₁₆	—	53	1	no	—
683	C₂×Q₁₆	—	106	4	no	—
684	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic
685	C₂²×C₈	—	53	1	no	—
686	C₂²×C₈	—	53	1	no	—
687	C₂²×C₈	—	53	1	no	—
688	C₂²×C₈	—	53	1	no	—
689	C₂²×C₈	—	53	1	no	—
690	C₂²×C₈	—	53	1	no	—
691	C₂²×C₈	—	53	1	no	—
692	C₂²×C₈	—	53	1	no	—
693	C₂²×C₈	—	53	1	no	—
694	C₂²×C₈	—	53	1	no	—
695	C₂²×C₈	—	106	4	no	—
696	C₂²×C₈	—	106	4	no	—
697	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
698	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
699	#126	—	2	2	no	—
700	#126	—	106	2	no	—
701	#126	—	106	2	no	—
702	#126	—	106	2	no	—
703	#126	—	106	2	no	—
704	#126	—	106	2	no	—
705	#126	—	106	2	no	—
706	#126	—	106	2	no	—
707	#125	—	2	2	no	—
708	#125	—	53	2	no	—
709	#125	—	53	2	no	—
710	#125	—	53	2	no	—
711	#125	—	106	2	no	—
712	#125	—	106	2	no	—
713	#125	—	106	2	no	—
714	#125	—	106	2	no	—
715	#125	—	106	2	no	—
716	#125	—	106	2	no	—
717	#125	—	106	2	no	—
718	#125	—	106	2	no	—
719	#125	—	106	2	no	—
720	#125	C₂²×D₅₃	1	2	yes	—
721	#123	—	2	2	no	—
722	#123	—	106	2	no	—
723	#123	—	106	2	no	—
724	#123	—	106	2	no	—
725	#123	—	106	2	no	—
726	#123	—	106	2	no	—
727	#123	—	106	2	no	—
728	#123	—	106	2	no	—
729	C₂²⋊Q₈	—	53	2	no	—
730	C₂²⋊Q₈	—	53	2	no	—
731	C₂²⋊Q₈	—	53	2	no	—
732	C₂²⋊Q₈	—	53	2	no	—
733	C₂²⋊Q₈	—	53	2	no	—
734	C₂²⋊Q₈	—	53	2	no	—
735	C₂²⋊Q₈	—	106	2	no	—
736	C₂²⋊Q₈	—	106	2	no	—
737	C₂²⋊Q₈	—	106	2	no	—
738	C₂²⋊Q₈	—	106	2	no	—
739	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	—
740	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	—
741	C₄×Q₈	—	53	2	no	—
742	C₄×Q₈	—	53	2	no	—
743	C₄×Q₈	—	53	2	no	—
744	C₄×Q₈	—	106	2	no	—
745	C₄×Q₈	—	106	2	no	—
746	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
747	C₄×D₄	—	53	1	no	—
748	C₄×D₄	—	53	1	no	—
749	C₄×D₄	—	53	1	no	—
750	C₄×D₄	—	53	1	no	—
751	C₄×D₄	—	53	1	no	—
752	C₄×D₄	—	53	1	no	—
753	C₄×D₄	—	53	1	no	—
754	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
755	#117	—	2	2	no	—
756	#117	—	53	2	no	—
757	#117	—	53	2	no	—
758	#117	—	53	2	no	—
759	#117	—	106	2	no	—
760	#117	—	106	2	no	—
761	#117	—	106	2	no	—
762	#117	—	106	2	no	—
763	#117	—	106	2	no	—
764	#117	—	106	2	no	—
765	#117	—	106	2	no	—
766	#117	—	106	2	no	—
767	#117	—	106	2	no	—
768	#117	C₂²×D₅₃	1	2	yes	—
769	C₂×C₄⋊C₄	—	53	1	no	—
770	C₂×C₄⋊C₄	—	53	2	no	—
771	C₂×C₄⋊C₄	—	53	2	no	—
772	C₂×C₄⋊C₄	—	53	2	no	—
773	C₂×C₄⋊C₄	—	53	2	no	—
774	C₂×C₄⋊C₄	—	53	2	no	—
775	C₂×C₄⋊C₄	—	53	2	no	—
776	C₂×C₄⋊C₄	—	106	2	no	—
777	C₂×C₄⋊C₄	—	106	2	no	—
778	C₂×C₄⋊C₄	—	106	2	no	—
779	C₂×C₄⋊C₄	—	106	2	no	—
780	C₂×C₄⋊C₄	—	106	2	no	—
781	C₂×C₄⋊C₄	—	106	2	no	—
782	C₂×C₄⋊C₄	—	106	2	no	—
783	C₂×C₄⋊C₄	—	106	2	no	—
784	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
785	C₂×C₂²⋊C₄	—	53	1	no	—
786	C₂×C₂²⋊C₄	—	53	1	no	—
787	C₂×C₂²⋊C₄	—	106	2	no	—
788	C₂×C₂²⋊C₄	—	106	2	no	—
789	C₂×C₂²⋊C₄	—	106	2	no	—
790	C₂×C₄²	—	53	1	no	—
791	C₂×C₄²	—	106	2	no	—
792	C₂×C₄²	—	106	2	no	—
793	#107	—	53	1	no	—
794	#107	—	53	1	no	—
795	#107	—	53	2	no	—
796	#107	—	53	1	no	—
797	#107	—	53	2	no	—
798	#107	—	53	2	no	—
799	#107	—	53	2	no	—
800	#107	—	53	2	no	—
801	#107	—	53	2	no	—
802	#107	C₂²×D₅₃	1	1	yes	characteristic
803	#107	C₂²×D₅₃	1	1	yes	characteristic
804	#107	C₂²×D₅₃	1	2	yes	—
805	#107	C₂²×D₅₃	1	1	yes	characteristic
806	#106	—	53	2	no	—
807	#106	—	53	2	no	—
808	#106	—	53	2	no	—
809	#106	—	53	2	no	—
810	#106	—	53	2	no	—
811	#106	—	53	2	no	—
812	#106	C₂²×D₅₃	1	2	yes	—
813	#106	C₂²×D₅₃	1	2	yes	—
814	C₄⋊C₈	—	53	1	no	—
815	C₄⋊C₈	—	53	1	no	—
816	C₄⋊C₈	—	53	1	no	—
817	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
818	#103	—	53	2	no	—
819	#103	—	53	2	no	—
820	#103	—	53	2	no	—
821	#103	—	53	2	no	—
822	#103	—	53	2	no	—
823	#103	—	53	2	no	—
824	#103	—	53	2	no	—
825	#103	—	53	2	no	—
826	#103	—	53	2	no	—
827	#103	C₂²×D₅₃	1	2	yes	—
828	#103	C₂²×D₅₃	1	2	yes	—
829	#103	C₂²×D₅₃	1	2	yes	—
830	C₂²⋊C₈	—	53	1	no	—
831	C₂²⋊C₈	—	53	1	no	—
832	C₂²⋊C₈	—	53	1	no	—
833	C₂²⋊C₈	—	53	1	no	—
834	C₂²⋊C₈	—	53	1	no	—
835	C₂²⋊C₈	—	53	1	no	—
836	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
837	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
838	C₄×C₈	—	53	1	no	—
839	C₄×C₈	—	53	1	no	—
840	C₄×C₈	—	53	1	no	—
841	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
842	C₂⁴	—	53	1	no	—
843	C₂⁴	—	53	1	no	—
844	C₂×Q₈	—	53	2	no	—
845	C₂×Q₈	—	106	2	no	—
846	C₂×Q₈	—	106	4	no	—
847	C₂×Q₈	—	106	4	no	—
848	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
849	C₂×D₄	—	53	1	no	—
850	C₂×D₄	—	53	1	no	—
851	C₂×D₄	—	53	1	no	—
852	C₂×D₄	—	106	4	no	—
853	C₂×D₄	D₄×D₅₃	1	1	yes	characteristic
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	53	1	no	—
856	C₂²×C₄	—	53	1	no	—
857	C₂²×C₄	—	53	1	no	—
858	C₂²×C₄	—	53	1	no	—
859	C₂²×C₄	—	53	1	no	—
860	C₂²×C₄	—	53	1	no	—
861	C₂²×C₄	—	53	1	no	—
862	C₂²×C₄	—	53	1	no	—
863	C₂²×C₄	—	53	1	no	—
864	C₂²×C₄	—	53	1	no	—
865	C₂²×C₄	—	53	1	no	—
866	C₂²×C₄	—	106	2	no	—
867	C₂²×C₄	—	106	2	no	—
868	C₂²×C₄	—	106	2	no	—
869	C₂²×C₄	—	106	2	no	—
870	C₂²×C₄	—	106	2	no	—
871	C₂²×C₄	—	106	2	no	—
872	C₂²×C₄	—	106	2	no	—
873	C₂²×C₄	—	106	2	no	—
874	C₂²×C₄	—	106	2	no	—
875	C₂²×C₄	—	106	2	no	—
876	C₂²×C₄	—	106	2	no	—
877	C₂²×C₄	—	212	8	no	—
878	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
879	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
880	Q₁₆	—	2	2	no	—
881	Q₁₆	—	106	4	no	—
882	Q₁₆	—	106	2	no	—
883	C₂×C₈	—	2	2	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	53	1	no	—
886	C₂×C₈	—	53	4	no	—
887	C₂×C₈	—	53	1	no	—
888	C₂×C₈	—	53	1	no	—
889	C₂×C₈	—	53	1	no	—
890	C₂×C₈	—	106	2	no	—
891	C₂×C₈	—	106	2	no	—
892	C₂×C₈	—	106	2	no	—
893	C₂×C₈	—	106	2	no	—
894	C₂×C₈	—	106	2	no	—
895	C₂×C₈	—	106	2	no	—
896	C₂×C₈	—	106	2	no	—
897	C₂×C₈	—	106	2	no	—
898	C₂×C₈	—	106	2	no	—
899	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
900	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
901	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
902	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	53	1	no	—
910	C₄⋊C₄	—	53	1	no	—
911	C₄⋊C₄	—	53	1	no	—
912	C₄⋊C₄	—	53	2	no	—
913	C₄⋊C₄	—	53	2	no	—
914	C₄⋊C₄	—	53	2	no	—
915	C₄⋊C₄	—	106	2	no	—
916	C₄⋊C₄	—	106	2	no	—
917	C₄⋊C₄	—	106	2	no	—
918	C₄⋊C₄	—	106	2	no	—
919	C₄⋊C₄	—	106	2	no	—
920	C₄⋊C₄	—	106	2	no	—
921	C₄⋊C₄	—	106	2	no	—
922	C₄⋊C₄	—	106	2	no	—
923	C₄⋊C₄	—	106	2	no	—
924	C₄⋊C₄	—	106	2	no	—
925	C₄⋊C₄	—	106	2	no	—
926	C₄⋊C₄	—	106	2	no	—
927	C₄⋊C₄	—	106	2	no	—
928	C₄⋊C₄	—	106	2	no	—
929	C₄⋊C₄	—	106	2	no	—
930	C₄⋊C₄	—	106	2	no	—
931	C₄⋊C₄	—	106	2	no	—
932	C₄⋊C₄	—	106	2	no	—
933	C₄⋊C₄	—	106	2	no	—
934	C₄⋊C₄	—	106	2	no	—
935	C₄⋊C₄	—	106	2	no	—
936	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
938	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
939	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	53	1	no	—
944	C₂²⋊C₄	—	53	1	no	—
945	C₂²⋊C₄	—	53	1	no	—
946	C₂²⋊C₄	—	53	1	no	—
947	C₂²⋊C₄	—	53	1	no	—
948	C₂²⋊C₄	—	53	1	no	—
949	C₂²⋊C₄	—	106	2	no	—
950	C₂²⋊C₄	—	106	2	no	—
951	C₂²⋊C₄	—	106	2	no	—
952	C₂²⋊C₄	—	106	2	no	—
953	C₂²⋊C₄	—	106	2	no	—
954	C₂²⋊C₄	—	106	2	no	—
955	C₂²⋊C₄	—	106	2	no	—
956	C₂²⋊C₄	—	106	2	no	—
957	C₂²⋊C₄	—	106	2	no	—
958	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
959	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	53	1	no	—
963	C₄²	—	53	1	no	—
964	C₄²	—	53	1	no	—
965	C₄²	—	106	2	no	—
966	C₄²	—	106	2	no	—
967	C₄²	—	106	2	no	—
968	C₄²	—	106	2	no	—
969	C₄²	—	106	2	no	—
970	C₄²	—	106	2	no	—
971	C₄²	C₂³×D₅₃	1	1	yes	characteristic
972	C₂³	—	53	1	no	—
973	C₂³	—	53	4	no	—
974	C₂³	—	53	1	no	—
975	C₂³	—	53	1	no	—
976	C₂³	—	106	2	no	—
977	C₂³	—	106	2	no	—
978	C₂³	—	106	2	no	—
979	C₂³	—	106	2	no	—
980	C₂³	—	106	2	no	—
981	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
982	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
983	Q₈	—	2	2	no	—
984	Q₈	—	2	2	no	—
985	Q₈	—	106	2	no	—
986	Q₈	—	106	2	no	—
987	Q₈	—	212	4	no	—
988	D₄	—	2	2	no	—
989	D₄	—	106	2	no	—
990	D₄	—	106	2	no	—
991	D₄	—	106	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	4	4	no	—
1001	C₂×C₄	—	53	1	no	—
1002	C₂×C₄	—	53	2	no	—
1003	C₂×C₄	—	53	2	no	—
1004	C₂×C₄	—	53	1	no	—
1005	C₂×C₄	—	53	1	no	—
1006	C₂×C₄	—	53	1	no	—
1007	C₂×C₄	—	53	1	no	—
1008	C₂×C₄	—	106	2	no	—
1009	C₂×C₄	—	106	2	no	—
1010	C₂×C₄	—	106	2	no	—
1011	C₂×C₄	—	106	2	no	—
1012	C₂×C₄	—	106	2	no	—
1013	C₂×C₄	—	106	2	no	—
1014	C₂×C₄	—	106	2	no	—
1015	C₂×C₄	—	106	2	no	—
1016	C₂×C₄	—	106	1	no	—
1017	C₂×C₄	—	106	1	no	—
1018	C₂×C₄	—	106	1	no	—
1019	C₂×C₄	—	106	1	no	—
1020	C₂×C₄	—	106	2	no	—
1021	C₂×C₄	—	106	2	no	—
1022	C₂×C₄	—	106	2	no	—
1023	C₂×C₄	—	106	2	no	—
1024	C₂×C₄	—	212	4	no	—
1025	C₂×C₄	—	212	4	no	—
1026	C₂×C₄	—	212	4	no	—
1027	C₂×C₄	—	212	4	no	—
1028	C₂×C₄	—	212	4	no	—
1029	C₂×C₄	—	212	4	no	—
1030	C₂×C₄	—	212	4	no	—
1031	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1032	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1033	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1034	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1035	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1036	C₈	—	2	1	no	—
1037	C₈	—	2	1	no	—
1038	C₈	—	2	1	no	—
1039	C₈	—	53	2	no	—
1040	C₈	—	106	1	no	—
1041	C₈	—	106	1	no	—
1042	C₈	—	106	1	no	—
1043	C₈	#41×D₅₃	1	2	yes	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	1	no	—
1046	C₂²	—	2	1	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	53	2	no	—
1050	C₂²	—	53	2	no	—
1051	C₂²	—	53	2	no	—
1052	C₂²	—	53	2	no	—
1053	C₂²	—	106	8	no	—
1054	C₂²	—	106	1	no	—
1055	C₂²	—	106	1	no	—
1056	C₂²	—	106	1	no	—
1057	C₂²	—	106	1	no	—
1058	C₂²	—	106	1	no	—
1059	C₂²	—	212	4	no	—
1060	C₂²	#135×D₅₃	1	2	yes	—
1061	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	53	2	no	—
1071	C₄	—	106	1	no	—
1072	C₄	—	106	1	no	—
1073	C₄	—	106	1	no	—
1074	C₄	—	106	1	no	—
1075	C₄	—	212	2	no	—
1076	C₄	—	212	2	no	—
1077	C₄	—	212	2	no	—
1078	C₄	—	212	2	no	—
1079	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1080	C₄	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1081	C₂	—	2	2	no	—
1082	C₂	—	4	1	no	—
1083	C₂	—	53	4	no	—
1084	C₂	—	106	2	no	—
1085	C₂	—	212	1	no	—
1086	C₂	#547×D₅₃	1	1	yes	characteristic
1087	C₂	C₂×#135×D₅₃	1	1	yes	characteristic
1088	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×#3336	C₂
socle	C₂²×C₅₃	C₂³×D₄
prime radical	C₂×D₄×D₅₃	D₄
hypercenter	#3336	D₅₃
hypocenter	C₅₃	C₂×#3336
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3336

Complements

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

N	H ≅ G/N	type
2. #20287086	C₂	semidirect
3. #20287085	C₂	semidirect
4. #20287084	C₂	semidirect
5. #20287083	C₂	semidirect
6. #20287082	C₂	semidirect
7. #20287081	C₂	semidirect
8. #20287080	C₂	semidirect
9. #20287079	C₂	semidirect
10. #20287078	C₂	semidirect
11. #20287077	C₂	semidirect
12. #20287076	C₂	semidirect
13. #499×D₅₃	C₂	semidirect
14. #485×D₅₃	C₂	semidirect
15. #483×D₅₃	C₂	semidirect
16. #479×D₅₃	C₂	semidirect
17. #467×D₅₃	C₂	semidirect
18. #467×D₅₃	C₂	semidirect
19. C₄×Q₁₆×D₅₃	C₂	semidirect
21. #427×D₅₃	C₂	semidirect
22. C₂×#107×D₅₃	C₂	semidirect
23. C₅₃×#3336	C₂	semidirect
49. #16811025	C₂²	semidirect
50. #16811024	C₂²	semidirect
51. #16811024	C₂²	semidirect
52. #16811023	C₂²	semidirect
53. #16811022	C₂²	semidirect
54. #16810967	C₂²	semidirect
55. #16810966	C₂²	semidirect
56. #16810965	C₂²	semidirect
57. #16810964	C₂²	semidirect
58. #16810963	C₂²	semidirect
59. #16810962	C₂²	semidirect
60. #16810961	C₂²	semidirect
61. #16810955	C₂²	semidirect
62. #16810955	C₂²	semidirect
63. #16810954	C₂²	semidirect
64. #16810953	C₂²	semidirect
65. #16810952	C₂²	semidirect
66. #16810952	C₂²	semidirect
67. #16810951	C₂²	semidirect
68. #16810933	C₂²	semidirect
69. #16810932	C₂²	semidirect
70. #16810931	C₂²	semidirect
71. #16810930	C₂²	semidirect
72. #16810929	C₂²	semidirect
73. #16810928	C₂²	semidirect
74. #16810927	C₂²	semidirect
75. #16810865	C₂²	semidirect
76. #16810865	C₂²	semidirect
77. #16810864	C₂²	semidirect
78. #16810864	C₂²	semidirect
79. #16810863	C₂²	semidirect
80. #16810863	C₂²	semidirect
81. #16810862	C₂²	semidirect
82. #16810862	C₂²	semidirect
83. #16810861	C₂²	semidirect
84. #16810861	C₂²	semidirect
85. C₄×Dic₂₁₂	C₂²	semidirect
86. Q₁₆×Dic₅₃	C₂²	semidirect
87. #16810717	C₂²	semidirect
88. C₄×#11719925	C₂²	semidirect
89. #16810715	C₂²	semidirect
97. #16810661	C₂²	semidirect
98. #16810660	C₂²	semidirect
99. #16810660	C₂²	semidirect
100. #16810659	C₂²	semidirect
101. #16810658	C₂²	semidirect
102. C₂×#13133151	C₂²	semidirect
103. C₂×#13133150	C₂²	semidirect
108. #107×D₅₃	C₂²	semidirect
109. #107×D₅₃	C₂²	semidirect
110. #107×D₅₃	C₂²	semidirect
121. C₅₃×#499	C₂²	semidirect
122. C₅₃×#485	C₂²	semidirect
123. C₅₃×#483	C₂²	semidirect
124. C₅₃×#479	C₂²	semidirect
125. C₅₃×#467	C₂²	semidirect
126. C₅₃×#467	C₂²	semidirect
127. C₄×Q₁₆×C₅₃	C₂²	semidirect
129. C₅₃×#427	C₂²	semidirect
130. C₂×#107×C₅₃	C₂²	semidirect
549. #3336	D₅₃	direct (N × H)
567. D₅₃	#3336	direct (N × H)
599. #499	C₂×D₅₃	semidirect
607. #485	C₂×D₅₃	semidirect
615. #483	C₂×D₅₃	semidirect
623. #479	C₂×D₅₃	semidirect
634. #467	C₂×D₅₃	semidirect
635. #467	C₂×D₅₃	semidirect
641. C₄×Q₁₆	C₂×D₅₃	semidirect
655. #427	C₂×D₅₃	semidirect
665. C₂×#107	C₂×D₅₃	semidirect
675. C₅₃	C₂×#3336	semidirect

Maximal subgroups

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

subgroup	index
#552×D₅₃	2
#20287086	2
#20287085	2
#20287084	2
#20287083	2
#20287082	2
#20287081	2
#20287080	2
#20287079	2
#20287078	2
#20287077	2
#20287076	2
#499×D₅₃	2
#485×D₅₃	2
#483×D₅₃	2
#479×D₅₃	2
#467×D₅₃	2
C₄×Q₁₆×D₅₃	2
C₈×D₄×D₅₃	2
#427×D₅₃	2
C₂×#107×D₅₃	2
C₅₃×#3336	2
C₂×#3336	53

Subgroups — D53×#3336 #28262519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3336 #28262519