Subgroups — D₅₃×#2966 #28248536

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#529×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20283693	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283692	C₂	1	1	yes	maximal, characteristic, complemented
4	#20283691	C₂	1	1	yes	maximal, characteristic, complemented
5	#20283690	C₂	1	1	yes	maximal, characteristic, complemented
6	#20283689	C₂	1	1	yes	maximal, characteristic, complemented
7	#20283688	C₂	1	2	yes	maximal, complemented
8	#20283687	C₂	1	1	yes	maximal, characteristic, complemented
9	#20283686	C₂	1	2	yes	maximal, complemented
10	#20283685	C₂	1	2	yes	maximal, complemented
11	#20283684	C₂	1	1	yes	maximal, characteristic, complemented
12	#20283683	C₂	1	2	yes	maximal, complemented
13	#446×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#436×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#435×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
19	#433×D₅₃	C₂	1	2	yes	maximal, complemented
20	#432×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#405×D₅₃	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
25	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₅₃	C₂²	1	2	yes	—
28	#16811160	C₂²	1	1	yes	characteristic
29	#16811159	C₄	1	1	yes	characteristic
30	#16811158	C₄	1	1	yes	characteristic
31	#16811157	C₂²	1	1	yes	characteristic
32	#16811156	C₄	1	2	yes	—
33	#16811155	C₂²	1	1	yes	characteristic
34	#16811154	C₄	1	1	yes	characteristic
35	#16811153	C₂²	1	2	yes	—
36	#16811152	C₄	1	1	yes	characteristic
37	#16811151	C₂²	1	2	yes	—
38	#16811150	C₄	1	2	yes	—
39	#126×D₅₃	C₄	1	2	yes	—
40	#125×D₅₃	C₄	1	1	yes	characteristic
41	#124×D₅₃	C₄	1	1	yes	characteristic
42	#123×D₅₃	C₄	1	2	yes	—
43	C₂²⋊Q₈×D₅₃	C₄	1	1	yes	characteristic
44	#121×D₅₃	C₄	1	1	yes	characteristic
45	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic
46	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
47	C₄×D₄×D₅₃	C₂²	1	2	yes	—
48	#117×D₅₃	C₂²	1	2	yes	—
49	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
50	#16810754	C₂²	1	1	yes	characteristic, complemented
51	#16810753	C₂²	1	1	yes	characteristic, complemented
52	#16810752	C₂²	1	2	yes	complemented
53	#16810751	C₂²	1	2	yes	complemented
54	#16810750	C₂²	1	1	yes	characteristic, complemented
55	Q₈×#88322	C₂²	1	1	yes	characteristic, complemented
56	C₈×Dic₁₀₆	C₂²	1	2	yes	complemented
57	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
58	#16810747	C₂²	1	1	yes	characteristic, complemented
59	#16810747	C₂²	1	2	yes	complemented
60	#16810702	C₂²	1	1	yes	characteristic, complemented
61	#16810701	C₂²	1	1	yes	characteristic, complemented
62	#16810700	C₂²	1	1	yes	characteristic, complemented
63	#16810699	C₂²	1	2	yes	complemented
64	#16810698	C₂²	1	2	yes	complemented
65	#16810697	C₂²	1	2	yes	complemented
66	#16810696	C₂²	1	2	yes	complemented
67	#16810695	C₂²	1	2	yes	complemented
68	#16810694	C₂²	1	2	yes	complemented
69	#16810693	C₂²	1	2	yes	complemented
70	#16810692	C₂²	1	2	yes	complemented
71	#16810691	C₂²	1	2	yes	complemented
72	C₈×D₂₁₂	C₂²	1	2	yes	complemented
73	C₈×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
74	D₄×#88322	C₂²	1	2	yes	complemented
75	D₄×#88322	C₂²	1	1	yes	characteristic, complemented
76	#16810688	C₂²	1	1	yes	characteristic, complemented
77	#16810688	C₂²	1	2	yes	complemented
78	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
79	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
80	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
81	#16810686	C₂²	1	2	yes	complemented
82	#16810686	C₂²	1	2	yes	complemented
83	#16810686	C₂²	1	2	yes	complemented
84	#16810685	C₂²	1	2	yes	complemented
85	#16810684	C₂²	1	2	yes	complemented
86	#16810683	C₂²	1	2	yes	complemented
87	#16810683	C₂²	1	2	yes	complemented
88	#16810682	C₂²	1	2	yes	complemented
89	#16810681	C₂²	1	2	yes	complemented
90	#16810681	C₂²	1	2	yes	complemented
91	#16810680	C₂²	1	1	yes	characteristic, complemented
92	#16810679	C₂²	1	1	yes	characteristic, complemented
93	#16810679	C₂²	1	1	yes	characteristic, complemented
94	#16810678	C₂²	1	2	yes	complemented
95	#16810677	C₂²	1	2	yes	complemented
96	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
97	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
98	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
99	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
100	C₂²⋊C₈×D₅₃	C₂²	1	2	yes	—
101	C₂²⋊C₈×D₅₃	C₂²	1	2	yes	—
102	C₂²⋊C₈×D₅₃	C₂²	1	2	yes	—
103	#16810581	C₂²	1	2	yes	complemented
104	#16810580	C₂²	1	2	yes	complemented
105	#16810580	C₂²	1	2	yes	complemented
106	#16810579	C₂²	1	2	yes	complemented
107	#16810578	C₂²	1	2	yes	complemented
108	#16810577	C₂²	1	2	yes	complemented
109	#16810577	C₂²	1	2	yes	complemented
110	#97×D₅₃	C₂²	1	2	yes	—
111	#97×D₅₃	C₂²	1	2	yes	—
112	C₂×C₄×#88322	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
116	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
117	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
118	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₅₃	C₂²	1	2	yes	—
120	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#529	C₂²	1	1	yes	characteristic
125	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
126	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#435	C₂²	1	2	yes	complemented
129	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
130	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#433	C₂²	1	2	yes	complemented
132	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×Q₈×D₅₃	C₂×C₄	1	1	yes	characteristic
136	C₂×D₄×D₅₃	C₂×C₄	1	2	yes	—
137	C₂×D₄×D₅₃	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
139	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
140	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
142	C₂×#11719917	C₂³	1	2	yes	—
143	C₂×#11719912	C₂³	1	2	yes	—
144	C₂×#11719912	C₂³	1	2	yes	—
145	M₁₆×D₅₃	—	2	8	no	—
146	C₂²×#88322	C₂³	1	1	yes	characteristic
147	C₂²×#88322	C₂³	1	1	yes	characteristic
148	C₂²×#88322	C₂³	1	2	yes	—
149	C₂×C₈×D₅₃	—	2	4	no	—
150	C₂×C₈×D₅₃	—	2	8	no	—
151	C₂×C₈×D₅₃	—	2	4	no	—
152	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₅₃	C₂³	1	2	yes	—
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	C₂×C₈×D₅₃	C₂³	1	2	yes	—
160	C₂×C₈×D₅₃	C₂³	1	2	yes	—
161	C₂×C₈×D₅₃	C₂³	1	2	yes	—
162	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
163	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
164	#13133212	C₂×C₄	1	2	yes	—
165	#13133212	C₂×C₄	1	2	yes	—
166	#13133212	C₂×C₄	1	2	yes	—
167	#13133211	C₂×C₄	1	2	yes	—
168	#13133210	C₂×C₄	1	2	yes	—
169	#13133210	C₂×C₄	1	2	yes	—
170	#13133210	C₂×C₄	1	2	yes	—
171	#13133209	C₂×C₄	1	1	yes	characteristic
172	#13133208	C₂×C₄	1	1	yes	characteristic
173	#13133208	C₂×C₄	1	1	yes	characteristic
174	#13133207	C₂×C₄	1	2	yes	—
175	#13133207	C₂×C₄	1	2	yes	—
176	#13133206	C₂×C₄	1	1	yes	characteristic
177	#13133205	C₂×C₄	1	1	yes	characteristic
178	#13133204	C₂×C₄	1	1	yes	characteristic
179	#13133203	C₂×C₄	1	2	yes	—
180	#13133203	C₂×C₄	1	2	yes	—
181	#13133202	C₂×C₄	1	2	yes	—
182	#13133202	C₂×C₄	1	2	yes	—
183	#13133201	C₂×C₄	1	2	yes	—
184	#13133200	C₂×C₄	1	2	yes	—
185	#13133199	C₂×C₄	1	2	yes	—
186	#13133199	C₂×C₄	1	2	yes	—
187	#13133198	C₂×C₄	1	2	yes	—
188	#13133197	C₂×C₄	1	1	yes	characteristic
189	#13133196	C₂×C₄	1	1	yes	characteristic
190	#13133195	C₂×C₄	1	2	yes	—
191	#13133194	C₂×C₄	1	2	yes	—
192	#13133193	C₂×C₄	1	1	yes	characteristic
193	#13133192	C₂×C₄	1	1	yes	characteristic
194	#13133191	C₂×C₄	1	1	yes	characteristic
195	#13133190	C₂×C₄	1	2	yes	—
196	#13133189	C₂×C₄	1	2	yes	—
197	#13133188	C₂×C₄	1	1	yes	characteristic
198	Q₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
199	C₄×Dic₁₀₆	C₂³	1	2	yes	—
200	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
201	#13133182	C₂×C₄	1	2	yes	—
202	#13133182	C₂×C₄	1	1	yes	characteristic
203	C₄×D₂₁₂	C₂³	1	2	yes	—
204	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
205	D₄×Dic₅₃	C₂×C₄	1	2	yes	—
206	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
207	#13133179	C₂×C₄	1	2	yes	—
208	#13133179	C₂×C₄	1	1	yes	characteristic
209	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
210	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
211	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
212	#13133177	C₂×C₄	1	2	yes	—
213	#13133177	C₂×C₄	1	2	yes	—
214	#13133177	C₂×C₄	1	2	yes	—
215	#13133176	C₂³	1	2	yes	—
216	#13133175	C₂×C₄	1	2	yes	—
217	#13133175	C₂×C₄	1	2	yes	—
218	#13133174	C₂³	1	2	yes	—
219	#13133174	C₂³	1	2	yes	—
220	#13133173	C₂×C₄	1	2	yes	—
221	#13133173	C₂×C₄	1	2	yes	—
222	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
223	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
224	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
225	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
226	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
227	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
228	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
229	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
230	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
231	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
232	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
233	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
234	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
235	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
236	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
237	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
238	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
239	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
240	C₄²×D₅₃	C₂³	1	1	yes	characteristic
241	C₄²×D₅₃	C₂³	1	1	yes	characteristic
242	C₄²×D₅₃	C₂³	1	1	yes	characteristic
243	C₄²×D₅₃	C₂³	1	1	yes	characteristic
244	C₄²×D₅₃	C₂³	1	2	yes	—
245	C₄⋊#88322	C₂³	1	1	yes	characteristic
246	C₄⋊#88322	C₂³	1	2	yes	—
247	C₄⋊#88322	C₂³	1	1	yes	characteristic
248	C₄⋊#88322	C₂³	1	2	yes	—
249	#13133146	C₂³	1	2	yes	—
250	#13133146	C₂³	1	2	yes	—
251	#13133146	C₂³	1	2	yes	—
252	#13133146	C₂³	1	2	yes	—
253	#13133146	C₂³	1	2	yes	—
254	#13133146	C₂³	1	2	yes	—
255	C₂²⋊#88322	C₂³	1	2	yes	—
256	C₂²⋊#88322	C₂³	1	2	yes	—
257	C₂²⋊#88322	C₂³	1	2	yes	—
258	#13133129	C₂³	1	2	yes	—
259	#13133129	C₂³	1	2	yes	—
260	#13133129	C₂³	1	2	yes	—
261	#13133129	C₂³	1	2	yes	—
262	#13133129	C₂³	1	2	yes	—
263	#13133129	C₂³	1	2	yes	—
264	#13133128	C₂³	1	2	yes	—
265	#13133128	C₂³	1	2	yes	—
266	#13133127	C₂³	1	2	yes	—
267	#13133127	C₂³	1	2	yes	—
268	#13133127	C₂³	1	2	yes	—
269	#13133127	C₂³	1	2	yes	—
270	C₄×#88322	C₂³	1	1	yes	characteristic
271	C₄×#88322	C₂³	1	1	yes	characteristic
272	C₄×#88322	C₂³	1	1	yes	characteristic
273	C₄×#88322	C₂³	1	1	yes	characteristic
274	C₄×#88322	C₂³	1	2	yes	—
275	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₈×Dic₅₃	C₂³	1	2	yes	—
284	C₈×Dic₅₃	C₂³	1	2	yes	—
285	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
286	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
288	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
289	#126×C₅₃	C₂×C₄	1	2	yes	—
290	#125×C₅₃	C₂×C₄	1	1	yes	characteristic
291	#124×C₅₃	C₂×C₄	1	1	yes	characteristic
292	#123×C₅₃	C₂×C₄	1	2	yes	—
293	C₂²⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
294	#121×C₅₃	C₂×C₄	1	1	yes	characteristic
295	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₅₃	C₂³	1	2	yes	—
297	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
298	#117×C₅₃	C₂³	1	2	yes	—
299	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
301	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	#97×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	2	yes	—
314	C₂³×D₅₃	C₂²×C₄	1	2	yes	—
315	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
317	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
318	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
319	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
321	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
323	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
324	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
325	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
326	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
327	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
328	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
329	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
330	Q₈×D₅₃	—	2	4	no	—
331	D₄×D₅₃	—	2	8	no	—
332	D₄×D₅₃	—	2	4	no	—
333	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
334	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
335	C₂×C₄×D₅₃	—	2	4	no	—
336	C₂×C₄×D₅₃	—	2	4	no	—
337	C₂×C₄×D₅₃	—	2	2	no	—
338	C₂×C₄×D₅₃	—	2	2	no	—
339	C₂×C₄×D₅₃	—	2	4	no	—
340	C₂×C₄×D₅₃	—	2	4	no	—
341	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
343	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
346	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
351	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
352	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
353	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
354	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
355	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
357	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
359	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
360	M₁₆×C₅₃	—	2	4	no	—
361	C₂×C₈×C₅₃	—	2	2	no	—
362	C₂×C₈×C₅₃	—	2	4	no	—
363	C₂×C₈×C₅₃	—	2	2	no	—
364	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
367	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
368	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
373	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
375	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
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	2	yes	—
379	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
381	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
382	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
383	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₄²×C₅₃	C₂⁴	1	2	yes	—
386	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
387	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
388	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
389	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
390	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
391	#11719921	C₂²×C₄	1	2	yes	—
392	#11719921	C₂²×C₄	1	2	yes	—
393	#11719921	C₂²×C₄	1	2	yes	—
394	#11719921	C₂²×C₄	1	2	yes	—
395	#11719921	C₂²×C₄	1	2	yes	—
396	#11719921	C₂²×C₄	1	2	yes	—
397	#11719921	C₂²×C₄	1	2	yes	—
398	#11719921	C₂²×C₄	1	2	yes	—
399	#11719921	C₂²×C₄	1	2	yes	—
400	#11719921	C₂²×C₄	1	2	yes	—
401	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
402	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
403	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
404	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
405	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
406	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
407	#11719919	C₂²×C₄	1	2	yes	—
408	#11719919	C₂²×C₄	1	2	yes	—
409	#11719919	C₂²×C₄	1	2	yes	—
410	#11719919	C₂²×C₄	1	2	yes	—
411	#11719919	C₂²×C₄	1	2	yes	—
412	#11719919	C₂²×C₄	1	2	yes	—
413	#11719919	C₂²×C₄	1	2	yes	—
414	#11719919	C₂²×C₄	1	2	yes	—
415	#11719919	C₂²×C₄	1	2	yes	—
416	#11719919	C₂²×C₄	1	2	yes	—
417	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
418	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
419	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
420	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
421	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
422	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
423	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
424	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
425	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
426	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
427	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
428	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
429	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
430	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
431	C₄×Dic₅₃	C₂⁴	1	2	yes	—
432	#11719917	—	2	4	no	—
433	C₂×#88322	—	2	2	no	—
434	C₂×#88322	—	2	4	no	—
435	C₂×#88322	—	2	2	no	—
436	C₂×#88322	C₂⁴	1	1	yes	characteristic
437	C₂×#88322	C₂⁴	1	1	yes	characteristic
438	C₂×#88322	C₂⁴	1	2	yes	—
439	C₂×#88322	C₂⁴	1	2	yes	—
440	C₂×#88322	C₂⁴	1	1	yes	characteristic
441	C₂×#88322	C₂⁴	1	1	yes	characteristic
442	#11719912	—	2	4	no	—
443	#11719912	—	2	4	no	—
444	C₈×D₅₃	—	2	2	no	—
445	C₈×D₅₃	—	2	2	no	—
446	C₈×D₅₃	—	2	4	no	—
447	C₈×D₅₃	—	2	4	no	—
448	C₈×D₅₃	—	2	2	no	—
449	C₈×D₅₃	—	2	4	no	—
450	C₈×D₅₃	—	2	2	no	—
451	C₈×D₅₃	—	2	2	no	—
452	C₈×D₅₃	—	2	4	no	—
453	C₈×D₅₃	—	2	2	no	—
454	C₈×D₅₃	#41	1	4	yes	—
455	C₈×D₅₃	#41	1	4	yes	—
456	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
457	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
458	C₂²×D₅₃	—	2	2	no	—
459	C₂²×D₅₃	—	2	2	no	—
460	C₂²×D₅₃	—	2	4	no	—
461	C₂²×D₅₃	—	2	4	no	—
462	C₂²×D₅₃	—	2	4	no	—
463	C₂²×D₅₃	#131	1	4	yes	—
464	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
465	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
466	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
467	Q₈×C₅₃	—	2	2	no	—
468	D₄×C₅₃	—	2	4	no	—
469	D₄×C₅₃	—	2	2	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	1	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	2	no	—
476	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
477	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
478	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
479	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
480	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
485	C₂²⋊D₅₃	—	2	4	no	—
486	C₂²⋊D₅₃	—	2	4	no	—
487	C₂²⋊D₅₃	—	2	4	no	—
488	C₂×Dic₅₃	—	2	2	no	—
489	C₂×Dic₅₃	—	2	2	no	—
490	C₂×Dic₅₃	—	2	4	no	—
491	C₂×Dic₅₃	—	2	2	no	—
492	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
493	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
494	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
495	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
496	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
497	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
498	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
499	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
500	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
501	D₂₁₂	—	2	4	no	—
502	D₂₁₂	—	2	2	no	—
503	C₄×D₅₃	—	2	2	no	—
504	C₄×D₅₃	—	2	4	no	—
505	C₄×D₅₃	—	2	2	no	—
506	C₄×D₅₃	—	2	2	no	—
507	C₄×D₅₃	—	2	2	no	—
508	C₄×D₅₃	—	2	2	no	—
509	C₄×D₅₃	—	2	2	no	—
510	C₄×D₅₃	—	2	4	no	—
511	C₄×D₅₃	—	2	4	no	—
512	C₄×D₅₃	—	2	2	no	—
513	C₄×D₅₃	—	2	1	no	—
514	C₄×D₅₃	—	2	1	no	—
515	C₄×D₅₃	—	2	2	no	—
516	C₄×D₅₃	—	2	2	no	—
517	C₄×D₅₃	—	2	2	no	—
518	C₄×D₅₃	—	2	4	no	—
519	C₄×D₅₃	—	2	2	no	—
520	C₄×D₅₃	#131	1	4	yes	—
521	C₄×D₅₃	C₂×#41	1	2	yes	—
522	C₄×D₅₃	C₂×#41	1	2	yes	—
523	Dic₁₀₆	—	2	2	no	—
524	Dic₁₀₆	—	2	4	no	—
525	C₈×C₅₃	—	2	1	no	—
526	C₈×C₅₃	—	2	1	no	—
527	C₈×C₅₃	—	2	2	no	—
528	C₈×C₅₃	—	2	2	no	—
529	C₈×C₅₃	C₂×#41	1	2	yes	—
530	C₈×C₅₃	C₂×#41	1	2	yes	—
531	#88322	—	2	1	no	—
532	#88322	—	2	1	no	—
533	#88322	—	2	2	no	—
534	#88322	—	2	2	no	—
535	#88322	C₂×#41	1	2	yes	—
536	#88322	C₂×#41	1	2	yes	—
537	C₂×#2966	—	53	1	no	maximal, Sylow
538	C₂²×C₅₃	—	2	1	no	—
539	C₂²×C₅₃	—	2	1	no	—
540	C₂²×C₅₃	—	2	2	no	—
541	C₂²×C₅₃	—	2	2	no	—
542	C₂²×C₅₃	—	2	2	no	—
543	C₂²×C₅₃	C₂×#131	1	2	yes	—
544	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
545	C₂×D₅₃	—	2	1	no	—
546	C₂×D₅₃	—	2	1	no	—
547	C₂×D₅₃	—	2	8	no	—
548	C₂×D₅₃	—	2	2	no	—
549	C₂×D₅₃	—	2	2	no	—
550	C₂×D₅₃	—	2	2	no	—
551	C₂×D₅₃	—	4	8	no	—
552	C₂×D₅₃	C₄×#41	1	2	yes	—
553	C₂×D₅₃	C₂×#131	1	2	yes	—
554	C₂×D₅₃	C₂×#131	1	2	yes	—
555	C₂×D₅₃	C₂×#131	1	2	yes	—
556	C₄×C₅₃	—	2	1	no	—
557	C₄×C₅₃	—	2	2	no	—
558	C₄×C₅₃	—	2	2	no	—
559	C₄×C₅₃	—	2	1	no	—
560	C₄×C₅₃	—	2	1	no	—
561	C₄×C₅₃	—	2	1	no	—
562	C₄×C₅₃	—	2	2	no	—
563	C₄×C₅₃	C₂×#131	1	2	yes	—
564	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
565	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
566	Dic₅₃	—	2	1	no	—
567	Dic₅₃	—	2	2	no	—
568	Dic₅₃	—	2	2	no	—
569	Dic₅₃	—	2	1	no	—
570	Dic₅₃	—	2	1	no	—
571	Dic₅₃	—	2	1	no	—
572	Dic₅₃	—	2	2	no	—
573	Dic₅₃	C₄×#41	1	2	yes	—
574	Dic₅₃	C₂×#131	1	2	yes	—
575	C₂×#529	—	53	1	no	—
576	#2966	—	53	1	no	—
577	#2966	—	53	1	no	—
578	#2966	—	53	1	no	—
579	#2966	—	53	2	no	—
580	#2966	—	53	2	no	—
581	#2966	—	53	1	no	—
582	#2966	—	53	2	no	—
583	#2966	—	53	1	no	—
584	#2966	—	53	2	no	—
585	#2966	—	53	1	no	—
586	#2966	—	53	1	no	—
587	#2966	D₅₃	1	1	yes	characteristic, direct product factor
588	C₂×#446	—	53	1	no	—
589	C₂×C₈×Q₈	—	53	1	no	—
590	C₂×#436	—	53	1	no	—
591	C₂×#435	—	53	2	no	—
592	C₂×C₈×D₄	—	53	2	no	—
593	C₂×C₈×D₄	—	53	1	no	—
594	C₂×#433	—	53	2	no	—
595	C₂×#432	—	53	1	no	—
596	C₂×#405	—	53	2	no	—
597	C₂²×C₄×C₈	—	53	1	no	—
598	C₂×C₅₃	—	2	2	no	—
599	C₂×C₅₃	—	4	2	no	—
600	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
601	C₂×C₅₃	C₂²×#131	1	1	yes	characteristic
602	C₂×C₅₃	C₂²×#131	1	1	yes	characteristic
603	D₅₃	—	2	2	no	—
604	D₅₃	—	4	2	no	—
605	D₅₃	#2966	1	4	yes	direct product factor
606	C₂²×M₁₆	—	53	2	no	—
607	C₂³×C₈	—	53	1	no	—
608	C₂³×C₈	—	53	1	no	—
609	C₂³×C₈	—	53	2	no	—
610	#529	—	53	2	no	—
611	#529	—	53	1	no	—
612	#529	—	53	1	no	—
613	#529	—	53	2	no	—
614	#529	—	53	1	no	—
615	#529	—	53	1	no	—
616	#529	—	53	1	no	—
617	#529	—	53	2	no	—
618	#529	—	53	1	no	—
619	#529	—	53	2	no	—
620	#529	—	53	1	no	—
621	#529	C₂×D₅₃	1	1	yes	characteristic
622	C₂×#126	—	53	2	no	—
623	C₂×#125	—	53	1	no	—
624	C₂×#124	—	53	1	no	—
625	C₂×#123	—	53	2	no	—
626	C₂×C₂²⋊Q₈	—	53	1	no	—
627	C₂×#121	—	53	1	no	—
628	C₂×C₄×Q₈	—	53	1	no	—
629	C₂×C₄×D₄	—	53	2	no	—
630	C₂×C₄×D₄	—	53	1	no	—
631	C₂×#117	—	53	2	no	—
632	C₂²×C₄²	—	53	1	no	—
633	#446	—	53	1	no	—
634	#446	—	53	2	no	—
635	#446	—	53	1	no	—
636	#446	—	53	2	no	—
637	#446	—	53	1	no	—
638	#446	C₂×D₅₃	1	1	yes	characteristic, complemented
639	C₈×Q₈	—	53	1	no	—
640	C₈×Q₈	—	53	2	no	—
641	C₈×Q₈	—	53	1	no	—
642	C₈×Q₈	—	53	2	no	—
643	C₈×Q₈	—	53	1	no	—
644	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
645	#436	—	53	2	no	—
646	#436	—	53	1	no	—
647	#436	—	53	1	no	—
648	#436	—	53	2	no	—
649	#436	—	53	1	no	—
650	#436	C₂×D₅₃	1	1	yes	characteristic, complemented
651	#435	—	53	2	no	—
652	#435	—	53	2	no	—
653	#435	—	53	2	no	—
654	#435	—	53	2	no	—
655	#435	—	53	2	no	—
656	#435	—	53	2	no	—
657	#435	—	53	2	no	—
658	#435	C₂×D₅₃	1	2	yes	complemented
659	C₈×D₄	—	53	2	no	—
660	C₈×D₄	—	53	2	no	—
661	C₈×D₄	—	53	2	no	—
662	C₈×D₄	—	53	1	no	—
663	C₈×D₄	—	53	2	no	—
664	C₈×D₄	—	53	1	no	—
665	C₈×D₄	—	53	2	no	—
666	C₈×D₄	—	53	2	no	—
667	C₈×D₄	—	53	2	no	—
668	C₈×D₄	—	53	2	no	—
669	C₈×D₄	—	53	1	no	—
670	C₈×D₄	—	53	2	no	—
671	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
672	C₈×D₄	C₂×D₅₃	1	2	yes	complemented
673	#433	—	53	2	no	—
674	#433	—	53	2	no	—
675	#433	—	53	2	no	—
676	#433	—	53	2	no	—
677	#433	—	53	2	no	—
678	#433	—	53	2	no	—
679	#433	—	53	2	no	—
680	#433	C₂×D₅₃	1	2	yes	complemented
681	#432	—	53	1	no	—
682	#432	—	53	1	no	—
683	#432	—	53	1	no	—
684	#432	—	53	2	no	—
685	#432	—	53	2	no	—
686	#432	C₂×D₅₃	1	1	yes	characteristic, complemented
687	C₂×C₄⋊C₈	—	53	1	no	—
688	C₂×C₄⋊C₈	—	53	1	no	—
689	C₂×C₄⋊C₈	—	53	2	no	—
690	C₂×C₄⋊C₈	—	53	2	no	—
691	C₂×C₂²⋊C₈	—	53	2	no	—
692	C₂×C₂²⋊C₈	—	53	2	no	—
693	C₂×C₂²⋊C₈	—	53	2	no	—
694	#405	—	53	2	no	—
695	#405	—	53	2	no	—
696	#405	—	53	2	no	—
697	#405	—	53	2	no	—
698	#405	—	53	2	no	—
699	#405	—	53	2	no	—
700	#405	—	53	2	no	—
701	#405	C₂×D₅₃	1	2	yes	complemented
702	C₂×#97	—	53	2	no	—
703	C₂×#97	—	53	2	no	—
704	C₂×C₄×C₈	—	53	1	no	—
705	C₂×C₄×C₈	—	53	1	no	—
706	C₂×C₄×C₈	—	53	1	no	—
707	C₂×C₄×C₈	—	53	1	no	—
708	C₂×C₄×C₈	—	53	1	no	—
709	C₂×C₄×C₈	—	53	1	no	—
710	C₂×C₄×C₈	—	53	1	no	—
711	C₂×C₄×C₈	—	53	1	no	—
712	C₂×C₄×C₈	—	53	1	no	—
713	C₂×C₄×C₈	—	53	1	no	—
714	C₂×C₄×C₈	—	53	1	no	—
715	C₂×C₄×C₈	—	53	2	no	—
716	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
717	C₅₃	C₂×#2966	1	1	yes	characteristic, complemented, Sylow
718	C₂²×Q₈	—	53	1	no	—
719	C₂²×D₄	—	53	2	no	—
720	C₂²×D₄	—	53	1	no	—
721	C₂³×C₄	—	53	1	no	—
722	C₂³×C₄	—	53	1	no	—
723	C₂³×C₄	—	53	2	no	—
724	C₂³×C₄	—	53	1	no	—
725	C₂×M₁₆	—	53	2	no	—
726	C₂×M₁₆	—	53	2	no	—
727	C₂×M₁₆	—	53	2	no	—
728	C₂×M₁₆	—	106	8	no	—
729	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
730	C₂²×C₈	—	53	1	no	—
731	C₂²×C₈	—	53	1	no	—
732	C₂²×C₈	—	53	1	no	—
733	C₂²×C₈	—	53	1	no	—
734	C₂²×C₈	—	53	2	no	—
735	C₂²×C₈	—	53	1	no	—
736	C₂²×C₈	—	53	1	no	—
737	C₂²×C₈	—	53	1	no	—
738	C₂²×C₈	—	53	1	no	—
739	C₂²×C₈	—	53	1	no	—
740	C₂²×C₈	—	53	2	no	—
741	C₂²×C₈	—	53	2	no	—
742	C₂²×C₈	—	53	2	no	—
743	C₂²×C₈	—	53	1	no	—
744	C₂²×C₈	—	53	2	no	—
745	C₂²×C₈	—	106	4	no	—
746	C₂²×C₈	—	106	8	no	—
747	C₂²×C₈	—	106	4	no	—
748	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
749	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
750	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
751	#126	—	53	2	no	—
752	#126	—	53	2	no	—
753	#126	—	53	2	no	—
754	#126	—	53	2	no	—
755	#126	—	53	2	no	—
756	#126	—	53	2	no	—
757	#126	—	53	2	no	—
758	#126	C₄×D₅₃	1	2	yes	—
759	#125	—	53	2	no	—
760	#125	—	53	2	no	—
761	#125	—	53	1	no	—
762	#125	—	53	1	no	—
763	#125	—	53	1	no	—
764	#125	C₄×D₅₃	1	1	yes	characteristic
765	#124	—	53	1	no	—
766	#124	—	53	1	no	—
767	#124	—	53	2	no	—
768	#124	—	53	2	no	—
769	#124	—	53	1	no	—
770	#124	C₄×D₅₃	1	1	yes	characteristic
771	#123	—	53	2	no	—
772	#123	—	53	2	no	—
773	#123	—	53	2	no	—
774	#123	—	53	2	no	—
775	#123	—	53	2	no	—
776	#123	—	53	2	no	—
777	#123	—	53	2	no	—
778	#123	C₄×D₅₃	1	2	yes	—
779	C₂²⋊Q₈	—	53	1	no	—
780	C₂²⋊Q₈	—	53	1	no	—
781	C₂²⋊Q₈	—	53	2	no	—
782	C₂²⋊Q₈	—	53	1	no	—
783	C₂²⋊Q₈	—	53	2	no	—
784	C₂²⋊Q₈	C₄×D₅₃	1	1	yes	characteristic
785	#121	—	53	1	no	—
786	#121	—	53	2	no	—
787	#121	—	53	1	no	—
788	#121	—	53	1	no	—
789	#121	—	53	2	no	—
790	#121	C₄×D₅₃	1	1	yes	characteristic
791	C₄×Q₈	—	53	1	no	—
792	C₄×Q₈	—	53	2	no	—
793	C₄×Q₈	—	53	1	no	—
794	C₄×Q₈	—	53	2	no	—
795	C₄×Q₈	—	53	1	no	—
796	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
797	C₄×D₄	—	53	1	no	—
798	C₄×D₄	—	53	2	no	—
799	C₄×D₄	—	53	2	no	—
800	C₄×D₄	—	53	2	no	—
801	C₄×D₄	—	53	2	no	—
802	C₄×D₄	—	53	1	no	—
803	C₄×D₄	—	53	2	no	—
804	C₄×D₄	—	53	2	no	—
805	C₄×D₄	—	53	2	no	—
806	C₄×D₄	—	53	2	no	—
807	C₄×D₄	—	53	2	no	—
808	C₄×D₄	—	53	1	no	—
809	C₄×D₄	C₂²×D₅₃	1	2	yes	—
810	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
811	#117	—	53	2	no	—
812	#117	—	53	2	no	—
813	#117	—	53	2	no	—
814	#117	—	53	2	no	—
815	#117	—	53	2	no	—
816	#117	—	53	2	no	—
817	#117	—	53	2	no	—
818	#117	C₂²×D₅₃	1	2	yes	—
819	C₂×C₄⋊C₄	—	53	2	no	—
820	C₂×C₄⋊C₄	—	53	2	no	—
821	C₂×C₄⋊C₄	—	53	1	no	—
822	C₂×C₄⋊C₄	—	53	2	no	—
823	C₂×C₄⋊C₄	—	53	1	no	—
824	C₂×C₄⋊C₄	—	53	2	no	—
825	C₂×C₂²⋊C₄	—	53	2	no	—
826	C₂×C₂²⋊C₄	—	53	2	no	—
827	C₂×C₂²⋊C₄	—	53	2	no	—
828	C₂×C₂²⋊C₄	—	53	2	no	—
829	C₂×C₂²⋊C₄	—	53	2	no	—
830	C₂×C₄²	—	53	1	no	—
831	C₂×C₄²	—	53	1	no	—
832	C₂×C₄²	—	53	1	no	—
833	C₂×C₄²	—	53	1	no	—
834	C₂×C₄²	—	53	1	no	—
835	C₂×C₄²	—	53	1	no	—
836	C₂×C₄²	—	53	1	no	—
837	C₂×C₄²	—	53	1	no	—
838	C₂×C₄²	—	53	2	no	—
839	C₂×C₄²	—	53	1	no	—
840	C₂×C₄²	—	53	1	no	—
841	C₂×C₄²	—	53	1	no	—
842	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
843	C₄⋊C₈	—	53	2	no	—
844	C₄⋊C₈	—	53	2	no	—
845	C₄⋊C₈	—	53	2	no	—
846	C₄⋊C₈	—	53	2	no	—
847	C₄⋊C₈	—	53	2	no	—
848	C₄⋊C₈	—	53	2	no	—
849	C₄⋊C₈	—	53	1	no	—
850	C₄⋊C₈	—	53	1	no	—
851	C₄⋊C₈	—	53	2	no	—
852	C₄⋊C₈	—	53	2	no	—
853	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
854	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
856	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
857	C₂²⋊C₈	—	53	2	no	—
858	C₂²⋊C₈	—	53	2	no	—
859	C₂²⋊C₈	—	53	2	no	—
860	C₂²⋊C₈	—	53	2	no	—
861	C₂²⋊C₈	—	53	2	no	—
862	C₂²⋊C₈	—	53	2	no	—
863	C₂²⋊C₈	—	53	2	no	—
864	C₂²⋊C₈	—	53	2	no	—
865	C₂²⋊C₈	—	53	2	no	—
866	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
867	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
868	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
869	#97	—	53	2	no	—
870	#97	—	53	2	no	—
871	#97	—	53	2	no	—
872	#97	—	53	2	no	—
873	#97	—	53	2	no	—
874	#97	—	53	2	no	—
875	#97	C₂²×D₅₃	1	2	yes	—
876	#97	C₂²×D₅₃	1	2	yes	—
877	C₄×C₈	—	53	1	no	—
878	C₄×C₈	—	53	1	no	—
879	C₄×C₈	—	53	1	no	—
880	C₄×C₈	—	53	1	no	—
881	C₄×C₈	—	53	1	no	—
882	C₄×C₈	—	53	1	no	—
883	C₄×C₈	—	53	2	no	—
884	C₄×C₈	—	53	1	no	—
885	C₄×C₈	—	53	1	no	—
886	C₄×C₈	—	53	2	no	—
887	C₄×C₈	—	53	1	no	—
888	C₄×C₈	—	53	1	no	—
889	C₄×C₈	—	53	1	no	—
890	C₄×C₈	—	53	1	no	—
891	C₄×C₈	—	53	2	no	—
892	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
893	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
894	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
895	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
896	C₄×C₈	C₂²×D₅₃	1	2	yes	—
897	C₂⁴	—	53	1	no	—
898	C₂⁴	—	53	2	no	—
899	C₂×Q₈	—	53	2	no	—
900	C₂×Q₈	—	53	1	no	—
901	C₂×Q₈	—	106	4	no	—
902	C₂×Q₈	C₂×C₄×D₅₃	1	1	yes	characteristic
903	C₂×D₄	—	53	2	no	—
904	C₂×D₄	—	53	2	no	—
905	C₂×D₄	—	53	2	no	—
906	C₂×D₄	—	53	2	no	—
907	C₂×D₄	—	53	1	no	—
908	C₂×D₄	—	106	4	no	—
909	C₂×D₄	—	106	8	no	—
910	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
911	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
912	C₂²×C₄	—	53	1	no	—
913	C₂²×C₄	—	53	1	no	—
914	C₂²×C₄	—	53	1	no	—
915	C₂²×C₄	—	53	1	no	—
916	C₂²×C₄	—	53	1	no	—
917	C₂²×C₄	—	53	2	no	—
918	C₂²×C₄	—	53	1	no	—
919	C₂²×C₄	—	53	1	no	—
920	C₂²×C₄	—	53	1	no	—
921	C₂²×C₄	—	53	1	no	—
922	C₂²×C₄	—	53	1	no	—
923	C₂²×C₄	—	53	1	no	—
924	C₂²×C₄	—	53	1	no	—
925	C₂²×C₄	—	53	1	no	—
926	C₂²×C₄	—	53	1	no	—
927	C₂²×C₄	—	53	2	no	—
928	C₂²×C₄	—	53	2	no	—
929	C₂²×C₄	—	53	2	no	—
930	C₂²×C₄	—	53	2	no	—
931	C₂²×C₄	—	53	1	no	—
932	C₂²×C₄	—	53	2	no	—
933	C₂²×C₄	—	106	2	no	—
934	C₂²×C₄	—	106	2	no	—
935	C₂²×C₄	—	106	4	no	—
936	C₂²×C₄	—	106	4	no	—
937	C₂²×C₄	—	106	4	no	—
938	C₂²×C₄	—	106	4	no	—
939	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
940	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
941	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
942	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
943	M₁₆	—	2	4	no	—
944	M₁₆	—	106	4	no	—
945	M₁₆	—	106	4	no	—
946	M₁₆	—	106	4	no	—
947	C₂×C₈	—	2	2	no	—
948	C₂×C₈	—	2	4	no	—
949	C₂×C₈	—	2	2	no	—
950	C₂×C₈	—	53	1	no	—
951	C₂×C₈	—	53	1	no	—
952	C₂×C₈	—	53	4	no	—
953	C₂×C₈	—	53	4	no	—
954	C₂×C₈	—	53	1	no	—
955	C₂×C₈	—	53	1	no	—
956	C₂×C₈	—	53	2	no	—
957	C₂×C₈	—	53	2	no	—
958	C₂×C₈	—	106	2	no	—
959	C₂×C₈	—	106	4	no	—
960	C₂×C₈	—	106	2	no	—
961	C₂×C₈	—	106	2	no	—
962	C₂×C₈	—	106	2	no	—
963	C₂×C₈	—	106	4	no	—
964	C₂×C₈	—	106	4	no	—
965	C₂×C₈	—	106	2	no	—
966	C₂×C₈	—	106	4	no	—
967	C₂×C₈	—	106	2	no	—
968	C₂×C₈	—	106	2	no	—
969	C₂×C₈	—	106	4	no	—
970	C₂×C₈	—	106	2	no	—
971	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
972	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
973	C₂×C₈	C₂³×D₅₃	1	2	yes	—
974	C₂×C₈	C₂³×D₅₃	1	2	yes	—
975	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
976	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
977	C₄⋊C₄	—	53	2	no	—
978	C₄⋊C₄	—	53	2	no	—
979	C₄⋊C₄	—	53	2	no	—
980	C₄⋊C₄	—	53	2	no	—
981	C₄⋊C₄	—	53	2	no	—
982	C₄⋊C₄	—	53	2	no	—
983	C₄⋊C₄	—	53	2	no	—
984	C₄⋊C₄	—	53	1	no	—
985	C₄⋊C₄	—	53	2	no	—
986	C₄⋊C₄	—	53	2	no	—
987	C₄⋊C₄	—	53	2	no	—
988	C₄⋊C₄	—	53	2	no	—
989	C₄⋊C₄	—	53	1	no	—
990	C₄⋊C₄	—	53	2	no	—
991	C₄⋊C₄	—	53	2	no	—
992	C₄⋊C₄	—	53	2	no	—
993	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
994	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
995	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
997	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
998	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
999	C₂²⋊C₄	—	53	2	no	—
1000	C₂²⋊C₄	—	53	2	no	—
1001	C₂²⋊C₄	—	53	2	no	—
1002	C₂²⋊C₄	—	53	2	no	—
1003	C₂²⋊C₄	—	53	2	no	—
1004	C₂²⋊C₄	—	53	2	no	—
1005	C₂²⋊C₄	—	53	2	no	—
1006	C₂²⋊C₄	—	53	2	no	—
1007	C₂²⋊C₄	—	53	2	no	—
1008	C₂²⋊C₄	—	53	2	no	—
1009	C₂²⋊C₄	—	53	2	no	—
1010	C₂²⋊C₄	—	53	2	no	—
1011	C₂²⋊C₄	—	53	2	no	—
1012	C₂²⋊C₄	—	53	2	no	—
1013	C₂²⋊C₄	—	53	2	no	—
1014	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1015	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1016	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1017	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1018	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1019	C₄²	—	53	1	no	—
1020	C₄²	—	53	1	no	—
1021	C₄²	—	53	1	no	—
1022	C₄²	—	53	1	no	—
1023	C₄²	—	53	1	no	—
1024	C₄²	—	53	1	no	—
1025	C₄²	—	53	1	no	—
1026	C₄²	—	53	1	no	—
1027	C₄²	—	53	1	no	—
1028	C₄²	—	53	1	no	—
1029	C₄²	—	53	2	no	—
1030	C₄²	—	53	2	no	—
1031	C₄²	—	53	1	no	—
1032	C₄²	—	53	1	no	—
1033	C₄²	—	53	2	no	—
1034	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1035	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1036	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1037	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1038	C₄²	C₂³×D₅₃	1	2	yes	—
1039	C₂³	—	53	1	no	—
1040	C₂³	—	53	4	no	—
1041	C₂³	—	53	1	no	—
1042	C₂³	—	53	2	no	—
1043	C₂³	—	106	2	no	—
1044	C₂³	—	106	2	no	—
1045	C₂³	—	106	4	no	—
1046	C₂³	—	106	4	no	—
1047	C₂³	—	106	4	no	—
1048	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1049	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1050	Q₈	—	2	2	no	—
1051	Q₈	—	106	4	no	—
1052	Q₈	—	106	2	no	—
1053	D₄	—	2	4	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	106	4	no	—
1056	D₄	—	106	4	no	—
1057	D₄	—	106	4	no	—
1058	D₄	—	106	4	no	—
1059	D₄	—	106	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	53	1	no	—
1067	C₂×C₄	—	53	1	no	—
1068	C₂×C₄	—	53	4	no	—
1069	C₂×C₄	—	53	2	no	—
1070	C₂×C₄	—	53	2	no	—
1071	C₂×C₄	—	53	1	no	—
1072	C₂×C₄	—	53	1	no	—
1073	C₂×C₄	—	53	1	no	—
1074	C₂×C₄	—	53	1	no	—
1075	C₂×C₄	—	53	2	no	—
1076	C₂×C₄	—	53	2	no	—
1077	C₂×C₄	—	53	2	no	—
1078	C₂×C₄	—	106	2	no	—
1079	C₂×C₄	—	106	2	no	—
1080	C₂×C₄	—	106	4	no	—
1081	C₂×C₄	—	106	2	no	—
1082	C₂×C₄	—	106	2	no	—
1083	C₂×C₄	—	106	2	no	—
1084	C₂×C₄	—	106	2	no	—
1085	C₂×C₄	—	106	2	no	—
1086	C₂×C₄	—	106	2	no	—
1087	C₂×C₄	—	106	4	no	—
1088	C₂×C₄	—	106	4	no	—
1089	C₂×C₄	—	106	4	no	—
1090	C₂×C₄	—	106	2	no	—
1091	C₂×C₄	—	106	2	no	—
1092	C₂×C₄	—	106	4	no	—
1093	C₂×C₄	—	106	2	no	—
1094	C₂×C₄	—	106	2	no	—
1095	C₂×C₄	—	106	1	no	—
1096	C₂×C₄	—	106	1	no	—
1097	C₂×C₄	—	106	2	no	—
1098	C₂×C₄	—	106	2	no	—
1099	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1100	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1103	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1104	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1105	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1106	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1107	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	53	2	no	—
1113	C₈	—	53	2	no	—
1114	C₈	—	106	1	no	—
1115	C₈	—	106	1	no	—
1116	C₈	—	106	2	no	—
1117	C₈	—	106	2	no	—
1118	C₈	#41×D₅₃	1	2	yes	—
1119	C₈	#41×D₅₃	1	2	yes	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	53	2	no	—
1126	C₂²	—	53	2	no	—
1127	C₂²	—	53	2	no	—
1128	C₂²	—	53	2	no	—
1129	C₂²	—	106	8	no	—
1130	C₂²	—	106	1	no	—
1131	C₂²	—	106	1	no	—
1132	C₂²	—	106	2	no	—
1133	C₂²	—	106	2	no	—
1134	C₂²	—	106	2	no	—
1135	C₂²	—	212	8	no	—
1136	C₂²	#131×D₅₃	1	2	yes	—
1137	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1138	C₄	—	2	1	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	2	no	—
1145	C₄	—	53	2	no	—
1146	C₄	—	53	2	no	—
1147	C₄	—	106	1	no	—
1148	C₄	—	106	1	no	—
1149	C₄	—	106	1	no	—
1150	C₄	—	106	2	no	—
1151	C₄	—	106	2	no	—
1152	C₄	—	106	1	no	—
1153	C₄	—	106	2	no	—
1154	C₄	#131×D₅₃	1	2	yes	—
1155	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1156	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1157	C₂	—	2	2	no	—
1158	C₂	—	4	2	no	—
1159	C₂	—	53	4	no	—
1160	C₂	—	106	2	no	—
1161	C₂	—	212	2	no	—
1162	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1163	C₂	C₂×#131×D₅₃	1	1	yes	characteristic
1164	C₂	C₂×#131×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#2966	C₂
prime radical	#121×D₅₃	C₄
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	#2966	D₅₃
hypocenter	C₅₃	C₂×#2966
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
2. #20283693	C₂	semidirect
3. #20283692	C₂	semidirect
4. #20283691	C₂	semidirect
5. #20283690	C₂	semidirect
6. #20283689	C₂	semidirect
7. #20283688	C₂	semidirect
8. #20283687	C₂	semidirect
9. #20283686	C₂	semidirect
10. #20283685	C₂	semidirect
11. #20283684	C₂	semidirect
12. #20283683	C₂	semidirect
13. #446×D₅₃	C₂	semidirect
14. C₈×Q₈×D₅₃	C₂	semidirect
15. #436×D₅₃	C₂	semidirect
16. #435×D₅₃	C₂	semidirect
17. C₈×D₄×D₅₃	C₂	semidirect
18. C₈×D₄×D₅₃	C₂	semidirect
19. #433×D₅₃	C₂	semidirect
20. #432×D₅₃	C₂	semidirect
21. #405×D₅₃	C₂	semidirect
22. C₂×C₄×C₈×D₅₃	C₂	semidirect
23. C₅₃×#2966	C₂	semidirect
50. #16810754	C₂²	semidirect
51. #16810753	C₂²	semidirect
52. #16810752	C₂²	semidirect
53. #16810751	C₂²	semidirect
54. #16810750	C₂²	semidirect
55. Q₈×#88322	C₂²	semidirect
56. C₈×Dic₁₀₆	C₂²	semidirect
57. C₈×Dic₁₀₆	C₂²	semidirect
58. #16810747	C₂²	semidirect
59. #16810747	C₂²	semidirect
60. #16810702	C₂²	semidirect
61. #16810701	C₂²	semidirect
62. #16810700	C₂²	semidirect
63. #16810699	C₂²	semidirect
64. #16810698	C₂²	semidirect
65. #16810697	C₂²	semidirect
66. #16810696	C₂²	semidirect
67. #16810695	C₂²	semidirect
68. #16810694	C₂²	semidirect
69. #16810693	C₂²	semidirect
70. #16810692	C₂²	semidirect
71. #16810691	C₂²	semidirect
72. C₈×D₂₁₂	C₂²	semidirect
73. C₈×D₂₁₂	C₂²	semidirect
74. D₄×#88322	C₂²	semidirect
75. D₄×#88322	C₂²	semidirect
76. #16810688	C₂²	semidirect
77. #16810688	C₂²	semidirect
78. C₈×C₂²⋊D₅₃	C₂²	semidirect
79. C₈×C₂²⋊D₅₃	C₂²	semidirect
80. C₈×C₂²⋊D₅₃	C₂²	semidirect
81. #16810686	C₂²	semidirect
82. #16810686	C₂²	semidirect
83. #16810686	C₂²	semidirect
84. #16810685	C₂²	semidirect
85. #16810684	C₂²	semidirect
86. #16810683	C₂²	semidirect
87. #16810683	C₂²	semidirect
88. #16810682	C₂²	semidirect
89. #16810681	C₂²	semidirect
90. #16810681	C₂²	semidirect
91. #16810680	C₂²	semidirect
92. #16810679	C₂²	semidirect
93. #16810679	C₂²	semidirect
94. #16810678	C₂²	semidirect
95. #16810677	C₂²	semidirect
103. #16810581	C₂²	semidirect
104. #16810580	C₂²	semidirect
105. #16810580	C₂²	semidirect
106. #16810579	C₂²	semidirect
107. #16810578	C₂²	semidirect
108. #16810577	C₂²	semidirect
109. #16810577	C₂²	semidirect
112. C₂×C₄×#88322	C₂²	semidirect
113. C₂×C₈×Dic₅₃	C₂²	semidirect
114. C₂×C₈×Dic₅₃	C₂²	semidirect
120. C₄×C₈×D₅₃	C₂²	semidirect
121. C₄×C₈×D₅₃	C₂²	semidirect
122. C₄×C₈×D₅₃	C₂²	semidirect
123. C₄×C₈×D₅₃	C₂²	semidirect
125. C₅₃×#446	C₂²	semidirect
126. C₈×Q₈×C₅₃	C₂²	semidirect
127. C₅₃×#436	C₂²	semidirect
128. C₅₃×#435	C₂²	semidirect
129. C₈×D₄×C₅₃	C₂²	semidirect
130. C₈×D₄×C₅₃	C₂²	semidirect
131. C₅₃×#433	C₂²	semidirect
132. C₅₃×#432	C₂²	semidirect
133. C₅₃×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₅₃	C₂²	semidirect
587. #2966	D₅₃	direct (N × H)
605. D₅₃	#2966	direct (N × H)
638. #446	C₂×D₅₃	semidirect
644. C₈×Q₈	C₂×D₅₃	semidirect
650. #436	C₂×D₅₃	semidirect
658. #435	C₂×D₅₃	semidirect
671. C₈×D₄	C₂×D₅₃	semidirect
672. C₈×D₄	C₂×D₅₃	semidirect
680. #433	C₂×D₅₃	semidirect
686. #432	C₂×D₅₃	semidirect
701. #405	C₂×D₅₃	semidirect
716. C₂×C₄×C₈	C₂×D₅₃	semidirect
717. C₅₃	C₂×#2966	semidirect

Maximal subgroups

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

subgroup	index
#529×D₅₃	2
#20283693	2
#20283692	2
#20283691	2
#20283690	2
#20283689	2
#20283688	2
#20283687	2
#20283686	2
#20283685	2
#20283684	2
#20283683	2
#446×D₅₃	2
C₈×Q₈×D₅₃	2
#436×D₅₃	2
#435×D₅₃	2
C₈×D₄×D₅₃	2
#433×D₅₃	2
#432×D₅₃	2
#405×D₅₃	2
C₂×C₄×C₈×D₅₃	2
C₅₃×#2966	2
C₂×#2966	53

Subgroups — D53×#2966 #28248536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2966 #28248536