Subgroups — #28248765

Order 13568.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288277	C₂	1	1	yes	maximal, characteristic
2	#20283735	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283731	C₂	1	1	yes	maximal, characteristic, complemented
4	#20283721	C₂	1	1	yes	maximal, characteristic, complemented
5	#20283713	C₂	1	1	yes	maximal, characteristic, complemented
6	#20283713	C₂	1	2	yes	maximal, complemented
7	#20283712	C₂	1	2	yes	maximal, complemented
8	#20283700	C₂	1	2	yes	maximal, complemented
9	#20283694	C₂	1	2	yes	maximal, complemented
10	#20283690	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283689	C₂	1	1	yes	maximal, characteristic, complemented
12	#20283678	C₂	1	1	yes	maximal, characteristic, complemented
13	#20283663	C₂	1	1	yes	maximal, characteristic, complemented
14	#20283646	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283451	C₂	1	1	yes	maximal, characteristic, complemented
16	#20283438	C₂	1	2	yes	maximal, complemented
17	#20283413	C₂	1	2	yes	maximal, complemented
18	#436×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#20283376	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283368	C₂	1	2	yes	maximal, complemented
21	C₄×#13133223	C₂	1	1	yes	maximal, characteristic, complemented
22	#20283132	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133223	C₂²	1	1	yes	characteristic
25	C₂×#13133223	C₂²	1	1	yes	characteristic
26	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
27	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
28	#16811345	C₄	1	1	yes	characteristic
29	#16811336	C₄	1	1	yes	characteristic
30	#16811332	C₄	1	1	yes	characteristic
31	#16811322	C₄	1	2	yes	—
32	#16811314	C₄	1	1	yes	characteristic
33	#16811312	C₄	1	1	yes	characteristic
34	#16811306	C₄	1	2	yes	—
35	#16811302	C₄	1	2	yes	—
36	#16811297	C₄	1	2	yes	—
37	#16811272	C₄	1	1	yes	characteristic
38	#16811268	C₄	1	1	yes	characteristic
39	#16811261	C₄	1	1	yes	characteristic
40	#16811177	C₂²	1	1	yes	characteristic
41	#16811160	C₂²	1	1	yes	characteristic
42	#16811157	C₂²	1	1	yes	characteristic
43	#16811157	C₂²	1	2	yes	—
44	#16811153	C₂²	1	2	yes	—
45	#16811132	C₂²	1	2	yes	—
46	C₄×#11719945	C₂²	1	1	yes	characteristic
47	C₄×#11719947	C₂²	1	1	yes	characteristic
48	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
49	C₂×#13133174	C₂²	1	2	yes	—
50	#16810753	C₂²	1	1	yes	characteristic, complemented
51	#16810751	C₂²	1	2	yes	complemented
52	#16810751	C₂²	1	2	yes	complemented
53	#16810750	C₂²	1	1	yes	characteristic, complemented
54	#16810750	C₂²	1	2	yes	complemented
55	Q₈×#88322	C₂²	1	1	yes	characteristic, complemented
56	Q₈×#88322	C₂²	1	1	yes	characteristic, complemented
57	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
58	#16810747	C₂²	1	2	yes	complemented
59	#16810747	C₂²	1	1	yes	characteristic, complemented
60	#16810702	C₂²	1	1	yes	characteristic
61	#16810701	C₂²	1	1	yes	characteristic
62	#16810701	C₂²	1	1	yes	characteristic
63	#16810701	C₂²	1	2	yes	complemented
64	#16810701	C₂²	1	2	yes	complemented
65	#16810700	C₂²	1	1	yes	characteristic
66	#16810700	C₂²	1	2	yes	complemented
67	#16810699	C₂²	1	2	yes	—
68	#16810699	C₂²	1	2	yes	complemented
69	#16810698	C₂²	1	2	yes	—
70	#16810698	C₂²	1	2	yes	complemented
71	#16810698	C₂²	1	2	yes	complemented
72	#16810697	C₂²	1	2	yes	—
73	#16810697	C₂²	1	2	yes	complemented
74	#16810697	C₂²	1	2	yes	complemented
75	#16810696	C₂²	1	2	yes	complemented
76	#16810696	C₂²	1	2	yes	complemented
77	#16810694	C₂²	1	2	yes	complemented
78	#16810692	C₂²	1	2	yes	—
79	#16810692	C₂²	1	2	yes	complemented
80	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
81	#16810688	C₂²	1	1	yes	characteristic
82	#16810688	C₂²	1	2	yes	complemented
83	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
84	#16810683	C₂²	1	2	yes	complemented
85	#16810683	C₂²	1	2	yes	complemented
86	#16810682	C₂²	1	2	yes	complemented
87	#16810682	C₂²	1	2	yes	complemented
88	#16810682	C₂²	1	2	yes	complemented
89	#16810681	C₂²	1	2	yes	complemented
90	#16810680	C₂²	1	1	yes	characteristic, complemented
91	#16810680	C₂²	1	2	yes	complemented
92	#16810679	C₂²	1	1	yes	characteristic, complemented
93	#16810677	C₂²	1	2	yes	complemented
94	#16810675	C₂²	1	1	yes	characteristic, complemented
95	#16810673	C₂²	1	2	yes	complemented
96	#16810648	C₂²	1	2	yes	—
97	#16810648	C₂²	1	2	yes	—
98	#16810645	C₂²	1	1	yes	characteristic
99	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
100	#16810588	C₂²	1	2	yes	—
101	#16810585	C₂²	1	2	yes	—
102	C₂²⋊C₈×D₅₃	C₂²	1	2	yes	—
103	#16810580	C₂²	1	2	yes	—
104	#16810580	C₂²	1	2	yes	—
105	#16810580	C₂²	1	2	yes	complemented
106	#16810580	C₂²	1	2	yes	complemented
107	#16810578	C₂²	1	1	yes	characteristic, complemented
108	#16810578	C₂²	1	1	yes	characteristic, complemented
109	#16810577	C₂²	1	1	yes	characteristic
110	#16810577	C₂²	1	2	yes	—
111	#16810577	C₂²	1	1	yes	characteristic
112	#16810577	C₂²	1	2	yes	complemented
113	#16810577	C₂²	1	1	yes	characteristic, complemented
114	#16810577	C₂²	1	2	yes	complemented
115	#16810577	C₂²	1	1	yes	characteristic, complemented
116	C₄×#11719917	C₂²	1	2	yes	complemented
117	C₄×#11719917	C₂²	1	1	yes	characteristic, complemented
118	M₁₆×Dic₅₃	C₂²	1	2	yes	complemented
119	M₁₆×Dic₅₃	C₂²	1	2	yes	complemented
120	C₄×#11719912	C₂²	1	1	yes	characteristic
121	C₄×#11719912	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
123	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
125	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#436	C₂²	1	1	yes	characteristic
128	C₅₃×#436	C₂²	1	1	yes	characteristic
129	C₅₃×#435	C₂²	1	2	yes	complemented
130	C₅₃×#435	C₂²	1	2	yes	complemented
131	C₅₃×#431	C₂²	1	2	yes	complemented
132	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆×C₅₃	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11719945	C₂³	1	1	yes	characteristic
136	C₂×#11719947	C₂×C₄	1	1	yes	characteristic
137	C₂×D₄×D₅₃	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
139	#13133223	—	2	4	no	—
140	#13133223	—	2	4	no	—
141	C₂×#11719917	C₂³	1	2	yes	—
142	C₂×#11719917	C₂³	1	2	yes	—
143	C₂×#11719917	C₂³	1	1	yes	characteristic
144	C₂×#11719917	C₂³	1	1	yes	characteristic
145	C₂×#11719912	C₂³	1	1	yes	characteristic
146	C₂×#11719912	C₂³	1	1	yes	characteristic
147	C₂×#11719912	C₂³	1	1	yes	characteristic
148	C₂×#11719912	C₂³	1	2	yes	—
149	C₂×#11719912	C₂³	1	2	yes	—
150	C₂×#11719912	C₂³	1	2	yes	—
151	C₂×#11719912	C₂³	1	1	yes	characteristic
152	M₁₆×D₅₃	—	2	8	no	—
153	M₁₆×D₅₃	—	2	8	no	—
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	2	yes	—
158	C₂×C₈×D₅₃	C₂³	1	2	yes	—
159	C₂×C₈×D₅₃	C₂³	1	2	yes	—
160	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
161	#13133216	C₂×C₄	1	1	yes	characteristic
162	#13133215	C₂×C₄	1	1	yes	characteristic
163	#13133212	C₂×C₄	1	2	yes	—
164	#13133212	C₂×C₄	1	2	yes	—
165	#13133211	C₂×C₄	1	2	yes	—
166	#13133211	C₂×C₄	1	2	yes	—
167	#13133211	C₂×C₄	1	2	yes	—
168	#13133210	C₂×C₄	1	2	yes	—
169	#13133209	C₂×C₄	1	2	yes	—
170	#13133209	C₂×C₄	1	1	yes	characteristic
171	#13133208	C₂×C₄	1	1	yes	characteristic
172	#13133207	C₂×C₄	1	2	yes	—
173	#13133207	C₂×C₄	1	2	yes	—
174	#13133206	C₂×C₄	1	1	yes	characteristic
175	#13133205	C₂×C₄	1	1	yes	characteristic
176	#13133205	C₂×C₄	1	2	yes	—
177	#13133203	C₂×C₄	1	2	yes	—
178	#13133202	C₂×C₄	1	2	yes	—
179	#13133202	C₂×C₄	1	2	yes	—
180	#13133201	C₂×C₄	1	2	yes	—
181	#13133200	C₂×C₄	1	2	yes	—
182	#13133200	C₂×C₄	1	2	yes	—
183	#13133200	C₂×C₄	1	2	yes	—
184	#13133199	C₂×C₄	1	2	yes	—
185	#13133198	C₂×C₄	1	2	yes	—
186	#13133197	C₂×C₄	1	1	yes	characteristic
187	#13133196	C₂×C₄	1	1	yes	characteristic
188	#13133196	C₂×C₄	1	2	yes	—
189	#13133195	C₂×C₄	1	2	yes	—
190	#13133195	C₂×C₄	1	2	yes	—
191	#13133194	C₂×C₄	1	2	yes	—
192	#13133194	C₂×C₄	1	2	yes	—
193	#13133193	C₂×C₄	1	1	yes	characteristic
194	#13133193	C₂×C₄	1	1	yes	characteristic
195	#13133192	C₂×C₄	1	1	yes	characteristic
196	#13133191	C₂×C₄	1	2	yes	—
197	#13133191	C₂×C₄	1	1	yes	characteristic
198	#13133190	C₂×C₄	1	2	yes	—
199	#13133189	C₂×C₄	1	2	yes	—
200	#13133189	C₂×C₄	1	2	yes	—
201	#13133187	C₂×C₄	1	2	yes	—
202	#13133185	C₂×C₄	1	2	yes	—
203	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
204	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
205	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
206	C₄×Dic₁₀₆	C₂³	1	2	yes	—
207	#13133182	C₂×C₄	1	1	yes	characteristic
208	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
209	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
210	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
211	C₄×D₂₁₂	C₂³	1	2	yes	—
212	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
213	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
214	#13133179	C₂×C₄	1	1	yes	characteristic
215	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
216	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
217	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
218	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
219	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
220	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
221	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
222	#13133177	C₂×C₄	1	2	yes	—
223	#13133177	C₂×C₄	1	2	yes	—
224	#13133176	C₂³	1	1	yes	characteristic
225	#13133175	C₂×C₄	1	1	yes	characteristic
226	#13133174	C₂×C₄	1	2	yes	—
227	#13133174	C₂×C₄	1	2	yes	—
228	#13133174	C₂×C₄	1	2	yes	—
229	#13133174	C₂×C₄	1	2	yes	—
230	#13133174	C₂³	1	1	yes	characteristic
231	#13133174	C₂³	1	2	yes	—
232	#13133174	C₂³	1	2	yes	—
233	#13133174	C₂³	1	2	yes	—
234	#13133174	C₂³	1	1	yes	characteristic
235	#13133173	C₂×C₄	1	2	yes	—
236	C₂×#11719919	C₂×C₄	1	2	yes	—
237	C₂×#11719919	C₂×C₄	1	2	yes	—
238	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
239	C₂×#11719921	C₂×C₄	1	2	yes	—
240	C₂×#11719921	C₂×C₄	1	2	yes	—
241	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
242	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
243	C₄²×D₅₃	C₂³	1	1	yes	characteristic
244	C₄²×D₅₃	C₂³	1	1	yes	characteristic
245	C₄⋊#88322	C₂³	1	1	yes	characteristic
246	C₄⋊#88322	C₂³	1	1	yes	characteristic
247	C₄⋊#88322	C₂³	1	2	yes	—
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	1	yes	characteristic
265	#13133128	C₂³	1	2	yes	—
266	#13133128	C₂³	1	1	yes	characteristic
267	#13133127	C₂³	1	2	yes	—
268	#13133127	C₂³	1	1	yes	characteristic
269	#13133127	C₂³	1	1	yes	characteristic
270	#13133127	C₂³	1	1	yes	characteristic
271	#13133127	C₂³	1	1	yes	characteristic
272	#13133127	C₂³	1	2	yes	—
273	#13133127	C₂³	1	2	yes	—
274	C₄×#88322	C₂³	1	1	yes	characteristic
275	C₄×#88322	C₂³	1	1	yes	characteristic
276	C₄×#88322	C₂³	1	2	yes	—
277	C₄×#88322	C₂³	1	2	yes	—
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	2	yes	—
283	C₈×Dic₅₃	C₂³	1	2	yes	—
284	C₈×Dic₅₃	C₂³	1	2	yes	—
285	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
286	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
287	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
288	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
291	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
293	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
294	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₅₃	C₂³	1	2	yes	—
296	#117×C₅₃	C₂×C₄	1	2	yes	—
297	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
298	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
299	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
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	#41×C₅₃	—	4	2	no	—
316	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
317	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
318	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
319	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
321	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
322	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
323	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
325	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
326	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
327	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
328	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
329	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
330	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
331	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
332	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
333	#11719947	—	4	2	no	—
334	D₄×D₅₃	—	4	2	no	—
335	#11719945	—	2	2	no	—
336	#11719945	—	2	2	no	—
337	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
338	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
339	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
340	C₂×C₄×D₅₃	—	2	4	no	—
341	C₂×C₄×D₅₃	—	2	4	no	—
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	2	yes	—
345	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
346	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
350	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
351	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
352	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
353	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
354	M₁₆×C₅₃	—	2	4	no	—
355	M₁₆×C₅₃	—	2	4	no	—
356	C₂×C₈×C₅₃	—	2	2	no	—
357	C₂×C₈×C₅₃	—	2	2	no	—
358	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
361	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
362	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
365	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
367	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
368	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
369	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
370	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
371	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
372	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
373	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
374	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
375	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₄²×C₅₃	C₂⁴	1	2	yes	—
378	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
379	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
380	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
381	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
382	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
383	#11719921	C₂²×C₄	1	2	yes	—
384	#11719921	C₂²×C₄	1	2	yes	—
385	#11719921	C₂²×C₄	1	1	yes	characteristic
386	#11719921	C₂²×C₄	1	1	yes	characteristic
387	#11719921	C₂²×C₄	1	2	yes	—
388	#11719921	C₂²×C₄	1	2	yes	—
389	#11719921	C₂²×C₄	1	2	yes	—
390	#11719921	C₂²×C₄	1	2	yes	—
391	#11719921	C₂²×C₄	1	2	yes	—
392	#11719921	C₂²×C₄	1	2	yes	—
393	#11719921	C₂²×C₄	1	1	yes	characteristic
394	#11719921	C₂²×C₄	1	1	yes	characteristic
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	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
403	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
404	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
405	#11719919	C₂²×C₄	1	2	yes	—
406	#11719919	C₂²×C₄	1	1	yes	characteristic
407	#11719919	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
417	#11719919	C₂²×C₄	1	1	yes	characteristic
418	#11719919	C₂²×C₄	1	2	yes	—
419	#11719919	C₂²×C₄	1	2	yes	—
420	#11719919	C₂²×C₄	1	2	yes	—
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	2	yes	—
426	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
427	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
428	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
429	C₄×Dic₅₃	C₂⁴	1	2	yes	—
430	#11719917	—	2	4	no	—
431	#11719917	—	2	4	no	—
432	#11719917	—	2	2	no	—
433	#11719917	—	2	2	no	—
434	C₂×#88322	C₂⁴	1	1	yes	characteristic
435	C₂×#88322	C₂⁴	1	1	yes	characteristic
436	C₂×#88322	C₂⁴	1	2	yes	—
437	C₂×#88322	C₂⁴	1	2	yes	—
438	C₂×#88322	C₂⁴	1	1	yes	characteristic
439	C₂×#88322	C₂⁴	1	1	yes	characteristic
440	#11719912	—	2	4	no	—
441	#11719912	—	2	2	no	—
442	#11719912	—	2	4	no	—
443	#11719912	—	2	2	no	—
444	#11719912	—	2	4	no	—
445	#11719912	—	2	2	no	—
446	#11719912	#41	1	4	yes	complemented
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	4	no	—
452	C₈×D₅₃	—	2	2	no	—
453	C₈×D₅₃	#41	1	4	yes	complemented
454	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
455	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
456	C₂²×D₅₃	—	2	4	no	—
457	C₂²×D₅₃	—	4	2	no	—
458	C₂²×D₅₃	—	4	2	no	—
459	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
460	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
461	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
462	Q₈×C₅₃	—	2	2	no	—
463	D₄×C₅₃	—	2	2	no	—
464	D₄×C₅₃	—	4	2	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	2	no	—
467	C₂×C₄×C₅₃	—	2	2	no	—
468	C₂×C₄×C₅₃	—	2	1	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	4	2	no	—
471	C₂×C₄×C₅₃	—	4	1	no	—
472	C₂×C₄×C₅₃	—	4	2	no	—
473	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
474	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₅₃	C₂³×C₄	1	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	2	yes	—
480	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
481	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
482	C₂²⋊D₅₃	—	2	2	no	—
483	C₂²⋊D₅₃	—	2	2	no	—
484	C₂²⋊D₅₃	—	4	2	no	—
485	C₂²⋊D₅₃	—	4	2	no	—
486	C₂²⋊D₅₃	—	4	2	no	—
487	C₂×Dic₅₃	—	2	4	no	—
488	C₂×Dic₅₃	—	4	2	no	—
489	C₂×Dic₅₃	—	4	2	no	—
490	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
491	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
492	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
493	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
494	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
495	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
496	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
497	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
498	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
499	D₂₁₂	—	2	2	no	—
500	D₂₁₂	—	2	2	no	—
501	D₂₁₂	—	4	2	no	—
502	C₄×D₅₃	—	2	4	no	—
503	C₄×D₅₃	—	2	2	no	—
504	C₄×D₅₃	—	2	2	no	—
505	C₄×D₅₃	—	2	2	no	—
506	C₄×D₅₃	—	2	2	no	—
507	C₄×D₅₃	—	2	1	no	—
508	C₄×D₅₃	—	2	1	no	—
509	C₄×D₅₃	—	2	4	no	—
510	C₄×D₅₃	—	4	1	no	—
511	C₄×D₅₃	—	4	1	no	—
512	C₄×D₅₃	C₂×#41	1	2	yes	—
513	C₄×D₅₃	C₂×#41	1	2	yes	—
514	Dic₁₀₆	—	2	2	no	—
515	Dic₁₀₆	—	2	2	no	—
516	Dic₁₀₆	—	4	2	no	—
517	C₈×C₅₃	—	2	1	no	—
518	C₈×C₅₃	—	2	2	no	—
519	C₈×C₅₃	—	2	2	no	—
520	C₈×C₅₃	—	2	1	no	—
521	C₈×C₅₃	C₂×#41	1	2	yes	—
522	C₈×C₅₃	C₂×#41	1	2	yes	—
523	#88322	—	2	2	no	—
524	#88322	—	2	1	no	—
525	#88322	—	2	2	no	—
526	#88322	—	2	1	no	—
527	#88322	C₂×#41	1	2	yes	—
528	#88322	C₂×#41	1	2	yes	—
529	#60217	—	53	1	no	maximal, Sylow
530	C₂²×C₅₃	—	2	2	no	—
531	C₂²×C₅₃	—	2	1	no	—
532	C₂²×C₅₃	—	2	2	no	—
533	C₂²×C₅₃	—	2	1	no	—
534	C₂²×C₅₃	—	2	2	no	—
535	C₂²×C₅₃	—	2	1	no	—
536	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
537	C₂×D₅₃	—	2	1	no	—
538	C₂×D₅₃	—	2	1	no	—
539	C₂×D₅₃	—	2	2	no	—
540	C₂×D₅₃	—	2	1	no	—
541	C₂×D₅₃	—	2	1	no	—
542	C₂×D₅₃	—	2	2	no	—
543	C₂×D₅₃	—	2	1	no	—
544	C₂×D₅₃	—	2	2	no	—
545	C₂×D₅₃	—	8	4	no	—
546	C₂×D₅₃	C₄×#41	1	2	yes	—
547	C₄×C₅₃	—	2	1	no	—
548	C₄×C₅₃	—	2	2	no	—
549	C₄×C₅₃	—	2	1	no	—
550	C₄×C₅₃	—	2	2	no	—
551	C₄×C₅₃	—	2	2	no	—
552	C₄×C₅₃	—	2	1	no	—
553	C₄×C₅₃	—	2	1	no	—
554	C₄×C₅₃	#568	1	2	yes	—
555	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
556	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
557	Dic₅₃	—	2	1	no	—
558	Dic₅₃	—	2	2	no	—
559	Dic₅₃	—	2	2	no	—
560	Dic₅₃	—	2	1	no	—
561	Dic₅₃	—	2	1	no	—
562	Dic₅₃	—	2	1	no	—
563	Dic₅₃	—	2	2	no	—
564	Dic₅₃	—	2	1	no	—
565	Dic₅₃	C₄×#41	1	2	yes	—
566	#3475	—	53	1	no	—
567	#2971	—	53	1	no	—
568	#2971	—	53	1	no	—
569	#2969	—	53	1	no	—
570	#2969	—	53	2	no	—
571	#2969	—	53	1	no	—
572	#2969	—	53	2	no	—
573	#2967	—	53	2	no	—
574	#2967	—	53	2	no	—
575	#2966	—	53	1	no	—
576	#2966	—	53	1	no	—
577	#2965	—	53	1	no	—
578	#2965	D₅₃	1	1	yes	characteristic, complemented
579	#2962	—	53	1	no	—
580	#2960	—	53	1	no	—
581	D₄×M₁₆	—	53	1	no	—
582	#2933	—	53	2	no	—
583	#2930	—	53	2	no	—
584	C₂×#436	—	53	1	no	—
585	#2925	—	53	1	no	—
586	#2924	—	53	2	no	—
587	C₄×#131	—	53	1	no	—
588	#2873	—	53	2	no	—
589	C₂×C₅₃	—	4	2	no	—
590	C₂×C₅₃	—	4	1	no	—
591	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
592	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
593	C₂×C₅₃	#3573	1	1	yes	characteristic
594	D₅₃	—	2	2	no	—
595	D₅₃	—	4	1	no	—
596	D₅₃	—	4	2	no	—
597	C₂×#131	—	53	1	no	—
598	C₂×#131	—	53	1	no	—
599	C₂²×M₁₆	—	53	2	no	—
600	C₂²×M₁₆	—	53	2	no	—
601	#556	—	53	1	no	—
602	#555	—	53	1	no	—
603	#554	—	53	1	no	—
604	#553	—	53	2	no	—
605	#552	—	53	1	no	—
606	#552	—	53	2	no	—
607	#552	—	53	1	no	—
608	#551	—	53	2	no	—
609	#551	—	53	2	no	—
610	#547	—	53	1	no	—
611	#546	—	53	1	no	—
612	#546	—	53	1	no	—
613	#533	—	53	1	no	—
614	#529	—	53	1	no	—
615	#529	—	53	2	no	—
616	#529	—	53	1	no	—
617	#529	—	53	2	no	—
618	#525	—	53	2	no	—
619	C₄×#41	—	53	1	no	—
620	C₄×#41	—	53	1	no	—
621	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
622	C₂×C₄×D₄	—	53	1	no	—
623	C₂×#117	—	53	2	no	—
624	#446	—	53	1	no	—
625	#446	—	53	2	no	—
626	#446	—	53	2	no	—
627	#446	—	53	2	no	—
628	#446	—	53	1	no	—
629	#446	C₂×D₅₃	1	1	yes	characteristic, complemented
630	#446	C₂×D₅₃	1	1	yes	characteristic, complemented
631	C₈×Q₈	—	53	1	no	—
632	C₈×Q₈	—	53	1	no	—
633	C₈×Q₈	—	53	2	no	—
634	C₈×Q₈	—	53	1	no	—
635	C₈×Q₈	—	53	1	no	—
636	#436	—	53	2	no	—
637	#436	—	53	2	no	—
638	#436	—	53	1	no	—
639	#436	—	53	2	no	—
640	#436	—	53	2	no	—
641	#436	—	53	1	no	—
642	#436	—	53	1	no	—
643	#436	—	53	2	no	—
644	#436	—	53	2	no	—
645	#436	—	53	2	no	—
646	#436	—	53	2	no	—
647	#436	—	53	1	no	—
648	#436	C₂×D₅₃	1	1	yes	characteristic
649	#436	C₂×D₅₃	1	1	yes	characteristic
650	#435	—	53	2	no	—
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	#435	C₂×D₅₃	1	2	yes	complemented
660	C₈×D₄	—	53	2	no	—
661	C₈×D₄	—	53	2	no	—
662	C₈×D₄	—	53	1	no	—
663	C₈×D₄	—	53	1	no	—
664	#433	—	53	2	no	—
665	#433	—	53	2	no	—
666	#433	—	53	2	no	—
667	#433	—	53	2	no	—
668	#433	—	53	2	no	—
669	#433	—	53	2	no	—
670	#432	—	53	2	no	—
671	#432	—	53	1	no	—
672	#432	—	53	1	no	—
673	#432	—	53	2	no	—
674	#431	—	53	1	no	—
675	#431	—	53	2	no	—
676	#431	C₂×D₅₃	1	2	yes	complemented
677	#431	C₂×D₅₃	1	1	yes	characteristic, complemented
678	#424	—	53	2	no	—
679	#424	—	53	2	no	—
680	#423	—	53	1	no	—
681	C₂×C₄⋊C₈	—	53	1	no	—
682	#408	—	53	2	no	—
683	#407	—	53	2	no	—
684	C₂×C₂²⋊C₈	—	53	2	no	—
685	#405	—	53	1	no	—
686	#405	—	53	1	no	—
687	#405	—	53	2	no	—
688	#405	—	53	2	no	—
689	#405	—	53	2	no	—
690	#405	—	53	2	no	—
691	#405	—	53	1	no	—
692	#405	—	53	2	no	—
693	#405	—	53	2	no	—
694	#405	—	53	2	no	—
695	#405	—	53	1	no	—
696	#405	—	53	1	no	—
697	#405	—	53	1	no	—
698	C₄×M₁₆	—	53	2	no	—
699	C₄×M₁₆	—	53	2	no	—
700	C₄×M₁₆	—	53	2	no	—
701	C₄×M₁₆	—	53	1	no	—
702	C₄×M₁₆	—	53	1	no	—
703	C₄×M₁₆	—	53	1	no	—
704	C₄×M₁₆	C₂×D₅₃	1	2	yes	complemented
705	C₂×C₄×C₈	—	53	1	no	—
706	C₂×C₄×C₈	—	53	1	no	—
707	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
708	C₅₃	#60217	1	1	yes	characteristic, complemented, Sylow
709	C₂×#41	—	53	1	no	—
710	C₂×#41	—	53	1	no	—
711	C₂×#41	C₄×D₅₃	1	1	yes	characteristic
712	C₂²×D₄	—	53	1	no	—
713	C₂³×C₄	—	53	2	no	—
714	#131	—	106	4	no	—
715	#131	—	106	4	no	—
716	C₂×M₁₆	—	53	2	no	—
717	C₂×M₁₆	—	53	2	no	—
718	C₂×M₁₆	—	53	1	no	—
719	C₂×M₁₆	—	53	1	no	—
720	C₂×M₁₆	—	53	1	no	—
721	C₂×M₁₆	—	53	2	no	—
722	C₂×M₁₆	—	53	2	no	—
723	C₂×M₁₆	—	53	2	no	—
724	C₂×M₁₆	—	53	1	no	—
725	C₂×M₁₆	—	53	1	no	—
726	C₂×M₁₆	—	53	1	no	—
727	C₂×M₁₆	—	106	8	no	—
728	C₂×M₁₆	—	106	8	no	—
729	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
730	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
731	C₂²×C₈	—	53	1	no	—
732	C₂²×C₈	—	53	2	no	—
733	C₂²×C₈	—	53	2	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	C₂²×D₅₃	1	1	yes	characteristic
739	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
740	C₄⋊Q₈	—	53	1	no	—
741	C₄⋊Q₈	—	53	1	no	—
742	#126	—	53	2	no	—
743	#126	—	53	2	no	—
744	#126	—	53	2	no	—
745	#126	—	53	2	no	—
746	#126	—	53	2	no	—
747	#126	—	53	2	no	—
748	#125	—	53	2	no	—
749	#125	—	53	1	no	—
750	#125	—	53	2	no	—
751	#125	—	53	2	no	—
752	#125	—	53	1	no	—
753	#124	—	53	1	no	—
754	#124	—	53	2	no	—
755	#124	—	53	1	no	—
756	#124	—	53	2	no	—
757	#123	—	53	2	no	—
758	#123	—	53	2	no	—
759	#123	—	53	2	no	—
760	#123	—	53	2	no	—
761	#123	—	53	2	no	—
762	#123	—	53	2	no	—
763	#123	—	53	2	no	—
764	#123	—	53	2	no	—
765	C₂²⋊Q₈	—	53	1	no	—
766	C₂²⋊Q₈	—	53	1	no	—
767	C₂²⋊Q₈	—	53	1	no	—
768	C₂²⋊Q₈	—	53	2	no	—
769	C₂²⋊Q₈	—	53	2	no	—
770	C₂²⋊Q₈	—	53	1	no	—
771	C₂²⋊Q₈	—	53	2	no	—
772	C₂²⋊Q₈	—	53	2	no	—
773	C₂²⋊Q₈	—	53	2	no	—
774	#121	—	53	2	no	—
775	#121	—	53	2	no	—
776	#121	—	53	2	no	—
777	#121	—	53	1	no	—
778	#121	—	53	1	no	—
779	#121	—	53	2	no	—
780	#120	—	53	2	no	—
781	#120	—	53	2	no	—
782	C₄×Q₈	—	53	1	no	—
783	C₄×Q₈	—	53	1	no	—
784	C₄×Q₈	—	53	1	no	—
785	C₄×Q₈	—	53	1	no	—
786	C₄×Q₈	—	53	2	no	—
787	C₄×Q₈	C₄×D₅₃	1	1	yes	characteristic
788	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
789	C₄×D₄	—	53	1	no	—
790	C₄×D₄	—	53	1	no	—
791	C₄×D₄	—	53	1	no	—
792	C₄×D₄	—	53	1	no	—
793	C₄×D₄	—	53	1	no	—
794	C₄×D₄	—	53	1	no	—
795	C₄×D₄	—	53	2	no	—
796	C₄×D₄	—	53	2	no	—
797	C₄×D₄	—	53	2	no	—
798	C₄×D₄	—	53	1	no	—
799	C₄×D₄	—	53	2	no	—
800	C₄×D₄	—	53	2	no	—
801	C₄×D₄	—	53	1	no	—
802	C₄×D₄	—	53	1	no	—
803	C₄×D₄	—	53	1	no	—
804	C₄×D₄	—	53	2	no	—
805	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
806	C₄×D₄	C₄×D₅₃	1	2	yes	—
807	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
808	C₄×D₄	C₂²×D₅₃	1	2	yes	—
809	#117	—	53	1	no	—
810	#117	—	53	1	no	—
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	1	no	—
817	#117	—	53	2	no	—
818	#117	—	53	2	no	—
819	#117	—	53	2	no	—
820	#117	—	53	1	no	—
821	#117	C₄×D₅₃	1	2	yes	—
822	#117	C₄×D₅₃	1	1	yes	characteristic
823	C₂×C₄⋊C₄	—	53	2	no	—
824	C₂×C₄⋊C₄	—	53	2	no	—
825	C₂×C₄⋊C₄	—	53	1	no	—
826	C₂×C₂²⋊C₄	—	53	2	no	—
827	C₂×C₂²⋊C₄	—	53	2	no	—
828	C₂×C₂²⋊C₄	—	53	2	no	—
829	C₂×C₄²	—	53	2	no	—
830	C₂×C₄²	—	53	1	no	—
831	C₂×C₄²	—	53	1	no	—
832	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
833	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
834	C₄⋊C₈	—	53	2	no	—
835	C₄⋊C₈	—	53	2	no	—
836	C₄⋊C₈	—	53	2	no	—
837	C₄⋊C₈	—	53	2	no	—
838	C₄⋊C₈	—	53	2	no	—
839	C₄⋊C₈	—	53	2	no	—
840	C₄⋊C₈	—	53	1	no	—
841	C₄⋊C₈	—	53	1	no	—
842	C₄⋊C₈	—	53	2	no	—
843	C₄⋊C₈	—	53	2	no	—
844	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
845	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
847	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
848	C₂²⋊C₈	—	53	2	no	—
849	C₂²⋊C₈	—	53	2	no	—
850	C₂²⋊C₈	—	53	2	no	—
851	C₂²⋊C₈	—	53	2	no	—
852	C₂²⋊C₈	—	53	2	no	—
853	C₂²⋊C₈	—	53	2	no	—
854	C₂²⋊C₈	—	53	2	no	—
855	C₂²⋊C₈	—	53	2	no	—
856	C₂²⋊C₈	—	53	2	no	—
857	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
858	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
859	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
860	#97	—	53	1	no	—
861	#97	—	53	2	no	—
862	#97	—	53	1	no	—
863	#97	—	53	2	no	—
864	#97	—	53	1	no	—
865	#97	—	53	2	no	—
866	#97	—	53	1	no	—
867	#97	—	53	1	no	—
868	#97	—	53	2	no	—
869	#97	—	53	1	no	—
870	#97	C₂²×D₅₃	1	2	yes	—
871	#97	C₂²×D₅₃	1	2	yes	—
872	C₄×C₈	—	53	1	no	—
873	C₄×C₈	—	53	1	no	—
874	C₄×C₈	—	53	1	no	—
875	C₄×C₈	—	53	1	no	—
876	C₄×C₈	—	53	2	no	—
877	C₄×C₈	—	53	2	no	—
878	C₄×C₈	—	53	2	no	—
879	C₄×C₈	—	53	1	no	—
880	C₄×C₈	—	53	1	no	—
881	C₄×C₈	—	53	2	no	—
882	C₄×C₈	—	53	2	no	—
883	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
884	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
885	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
886	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
887	C₄×C₈	C₂²×D₅₃	1	2	yes	—
888	C₂⁴	—	53	2	no	—
889	#41	—	4	2	no	—
890	#41	—	106	2	no	—
891	#41	—	106	2	no	—
892	#41	—	212	2	no	—
893	C₂×Q₈	—	53	1	no	—
894	C₂×Q₈	—	53	1	no	—
895	C₂×Q₈	—	53	2	no	—
896	C₂×Q₈	C₂×C₄×D₅₃	1	1	yes	characteristic
897	C₂×D₄	—	53	1	no	—
898	C₂×D₄	—	53	1	no	—
899	C₂×D₄	—	53	2	no	—
900	C₂×D₄	—	53	2	no	—
901	C₂×D₄	—	53	2	no	—
902	C₂×D₄	—	53	1	no	—
903	C₂×D₄	—	53	1	no	—
904	C₂×D₄	—	53	2	no	—
905	C₂×D₄	—	212	2	no	—
906	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
907	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
908	C₂²×C₄	—	53	1	no	—
909	C₂²×C₄	—	53	2	no	—
910	C₂²×C₄	—	53	2	no	—
911	C₂²×C₄	—	53	2	no	—
912	C₂²×C₄	—	53	1	no	—
913	C₂²×C₄	—	53	1	no	—
914	C₂²×C₄	—	53	2	no	—
915	C₂²×C₄	—	53	2	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	—	106	4	no	—
921	C₂²×C₄	—	106	4	no	—
922	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
923	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
924	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
925	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
926	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
927	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
928	M₁₆	—	2	4	no	—
929	M₁₆	—	2	4	no	—
930	M₁₆	—	53	4	no	—
931	M₁₆	—	106	4	no	—
932	M₁₆	—	106	2	no	—
933	M₁₆	—	106	4	no	—
934	M₁₆	—	106	2	no	—
935	M₁₆	—	106	4	no	—
936	M₁₆	—	106	4	no	—
937	M₁₆	—	106	2	no	—
938	M₁₆	—	106	2	no	—
939	M₁₆	—	106	4	no	—
940	M₁₆	—	106	2	no	—
941	C₂×C₈	—	2	2	no	—
942	C₂×C₈	—	2	2	no	—
943	C₂×C₈	—	53	1	no	—
944	C₂×C₈	—	53	1	no	—
945	C₂×C₈	—	53	4	no	—
946	C₂×C₈	—	53	1	no	—
947	C₂×C₈	—	53	1	no	—
948	C₂×C₈	—	53	2	no	—
949	C₂×C₈	—	53	2	no	—
950	C₂×C₈	—	106	4	no	—
951	C₂×C₈	—	106	2	no	—
952	C₂×C₈	—	106	4	no	—
953	C₂×C₈	—	106	2	no	—
954	C₂×C₈	—	106	4	no	—
955	C₂×C₈	—	106	2	no	—
956	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
957	C₂×C₈	C₂³×D₅₃	1	2	yes	—
958	C₂×C₈	C₂³×D₅₃	1	2	yes	—
959	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
960	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
961	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
962	C₄⋊C₄	—	53	1	no	—
963	C₄⋊C₄	—	53	1	no	—
964	C₄⋊C₄	—	53	2	no	—
965	C₄⋊C₄	—	53	2	no	—
966	C₄⋊C₄	—	53	2	no	—
967	C₄⋊C₄	—	53	2	no	—
968	C₄⋊C₄	—	53	2	no	—
969	C₄⋊C₄	—	53	2	no	—
970	C₄⋊C₄	—	53	1	no	—
971	C₄⋊C₄	—	53	2	no	—
972	C₄⋊C₄	—	53	1	no	—
973	C₄⋊C₄	—	53	1	no	—
974	C₄⋊C₄	—	53	1	no	—
975	C₄⋊C₄	—	53	2	no	—
976	C₄⋊C₄	—	53	2	no	—
977	C₄⋊C₄	—	53	1	no	—
978	C₄⋊C₄	—	53	1	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	C₂×C₄×D₅₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
987	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
988	C₂²⋊C₄	—	53	2	no	—
989	C₂²⋊C₄	—	53	2	no	—
990	C₂²⋊C₄	—	53	1	no	—
991	C₂²⋊C₄	—	53	1	no	—
992	C₂²⋊C₄	—	53	2	no	—
993	C₂²⋊C₄	—	53	1	no	—
994	C₂²⋊C₄	—	53	1	no	—
995	C₂²⋊C₄	—	53	2	no	—
996	C₂²⋊C₄	—	53	2	no	—
997	C₂²⋊C₄	—	53	2	no	—
998	C₂²⋊C₄	—	53	2	no	—
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	1	no	—
1004	C₂²⋊C₄	—	53	2	no	—
1005	C₂²⋊C₄	—	53	1	no	—
1006	C₂²⋊C₄	—	53	2	no	—
1007	C₂²⋊C₄	—	53	2	no	—
1008	C₂²⋊C₄	—	53	2	no	—
1009	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1010	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1011	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1012	C₄²	—	53	2	no	—
1013	C₄²	—	53	2	no	—
1014	C₄²	—	53	1	no	—
1015	C₄²	—	53	1	no	—
1016	C₄²	—	53	1	no	—
1017	C₄²	—	53	1	no	—
1018	C₄²	—	53	1	no	—
1019	C₄²	—	53	1	no	—
1020	C₄²	—	53	2	no	—
1021	C₄²	C₂×C₄×D₅₃	1	2	yes	—
1022	C₄²	C₂×C₄×D₅₃	1	2	yes	—
1023	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1024	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1025	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1026	C₄²	C₂³×D₅₃	1	2	yes	—
1027	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1028	C₂³	—	53	1	no	—
1029	C₂³	—	53	2	no	—
1030	C₂³	—	53	1	no	—
1031	C₂³	—	106	4	no	—
1032	C₂³	—	212	2	no	—
1033	C₂³	—	212	2	no	—
1034	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1035	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	106	2	no	—
1038	Q₈	—	106	2	no	—
1039	Q₈	—	212	2	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	106	2	no	—
1043	D₄	—	106	2	no	—
1044	D₄	—	106	2	no	—
1045	D₄	—	106	2	no	—
1046	D₄	—	212	2	no	—
1047	D₄	—	212	2	no	—
1048	D₄	—	212	2	no	—
1049	D₄	—	212	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	4	1	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	53	1	no	—
1059	C₂×C₄	—	53	2	no	—
1060	C₂×C₄	—	53	2	no	—
1061	C₂×C₄	—	53	1	no	—
1062	C₂×C₄	—	53	1	no	—
1063	C₂×C₄	—	53	1	no	—
1064	C₂×C₄	—	53	2	no	—
1065	C₂×C₄	—	53	2	no	—
1066	C₂×C₄	—	53	1	no	—
1067	C₂×C₄	—	53	1	no	—
1068	C₂×C₄	—	53	2	no	—
1069	C₂×C₄	—	106	4	no	—
1070	C₂×C₄	—	106	4	no	—
1071	C₂×C₄	—	106	4	no	—
1072	C₂×C₄	—	106	2	no	—
1073	C₂×C₄	—	106	2	no	—
1074	C₂×C₄	—	106	2	no	—
1075	C₂×C₄	—	106	1	no	—
1076	C₂×C₄	—	106	1	no	—
1077	C₂×C₄	—	106	2	no	—
1078	C₂×C₄	—	212	1	no	—
1079	C₂×C₄	—	212	1	no	—
1080	C₂×C₄	—	212	2	no	—
1081	C₂×C₄	—	212	2	no	—
1082	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1083	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1086	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1087	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1088	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1089	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1090	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1091	C₈	—	2	1	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	2	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	53	2	no	—
1096	C₈	—	53	2	no	—
1097	C₈	—	106	2	no	—
1098	C₈	—	106	1	no	—
1099	C₈	—	106	2	no	—
1100	C₈	—	106	1	no	—
1101	C₈	#41×D₅₃	1	2	yes	—
1102	C₈	#41×D₅₃	1	2	yes	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	53	2	no	—
1110	C₂²	—	106	1	no	—
1111	C₂²	—	106	1	no	—
1112	C₂²	—	106	1	no	—
1113	C₂²	—	106	2	no	—
1114	C₂²	—	106	1	no	—
1115	C₂²	—	106	2	no	—
1116	C₂²	—	106	2	no	—
1117	C₂²	—	106	1	no	—
1118	C₂²	—	424	4	no	—
1119	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	53	2	no	—
1128	C₄	—	106	1	no	—
1129	C₄	—	106	1	no	—
1130	C₄	—	106	2	no	—
1131	C₄	—	106	1	no	—
1132	C₄	—	106	2	no	—
1133	C₄	—	106	1	no	—
1134	C₄	—	106	2	no	—
1135	C₄	—	106	1	no	—
1136	C₄	#16811389	1	2	yes	—
1137	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1138	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1139	C₂	—	4	2	no	—
1140	C₂	—	4	1	no	—
1141	C₂	—	106	2	no	—
1142	C₂	—	212	2	no	—
1143	C₂	—	212	1	no	—
1144	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1145	C₂	C₂×#16811389	1	1	yes	characteristic
1146	C₂	#20289426	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2965	C₂
prime radical	#20288277	C₂
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	#2965	D₅₃
hypocenter	C₅₃	#60217
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #2965

Complements

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

N	H ≅ G/N	type
2. #20283735	C₂	semidirect
3. #20283731	C₂	semidirect
4. #20283721	C₂	semidirect
5. #20283713	C₂	semidirect
6. #20283713	C₂	semidirect
7. #20283712	C₂	semidirect
8. #20283700	C₂	semidirect
9. #20283694	C₂	semidirect
10. #20283690	C₂	semidirect
11. #20283689	C₂	semidirect
12. #20283678	C₂	semidirect
13. #20283663	C₂	semidirect
14. #20283646	C₂	semidirect
15. #20283451	C₂	semidirect
16. #20283438	C₂	semidirect
17. #20283413	C₂	semidirect
18. #436×D₅₃	C₂	semidirect
19. #20283376	C₂	semidirect
20. #20283368	C₂	semidirect
21. C₄×#13133223	C₂	semidirect
22. #20283132	C₂	semidirect
23. C₅₃×#2965	C₂	semidirect
50. #16810753	C₂²	semidirect
51. #16810751	C₂²	semidirect
52. #16810751	C₂²	semidirect
53. #16810750	C₂²	semidirect
54. #16810750	C₂²	semidirect
55. Q₈×#88322	C₂²	semidirect
56. Q₈×#88322	C₂²	semidirect
57. C₈×Dic₁₀₆	C₂²	semidirect
58. #16810747	C₂²	semidirect
59. #16810747	C₂²	semidirect
63. #16810701	C₂²	semidirect
64. #16810701	C₂²	semidirect
66. #16810700	C₂²	semidirect
68. #16810699	C₂²	semidirect
70. #16810698	C₂²	semidirect
71. #16810698	C₂²	semidirect
73. #16810697	C₂²	semidirect
74. #16810697	C₂²	semidirect
75. #16810696	C₂²	semidirect
76. #16810696	C₂²	semidirect
77. #16810694	C₂²	semidirect
79. #16810692	C₂²	semidirect
82. #16810688	C₂²	semidirect
83. C₈×C₂²⋊D₅₃	C₂²	semidirect
84. #16810683	C₂²	semidirect
85. #16810683	C₂²	semidirect
86. #16810682	C₂²	semidirect
87. #16810682	C₂²	semidirect
88. #16810682	C₂²	semidirect
89. #16810681	C₂²	semidirect
90. #16810680	C₂²	semidirect
91. #16810680	C₂²	semidirect
92. #16810679	C₂²	semidirect
93. #16810677	C₂²	semidirect
94. #16810675	C₂²	semidirect
95. #16810673	C₂²	semidirect
105. #16810580	C₂²	semidirect
106. #16810580	C₂²	semidirect
107. #16810578	C₂²	semidirect
108. #16810578	C₂²	semidirect
112. #16810577	C₂²	semidirect
113. #16810577	C₂²	semidirect
114. #16810577	C₂²	semidirect
115. #16810577	C₂²	semidirect
116. C₄×#11719917	C₂²	semidirect
117. C₄×#11719917	C₂²	semidirect
118. M₁₆×Dic₅₃	C₂²	semidirect
119. M₁₆×Dic₅₃	C₂²	semidirect
121. C₄×#11719912	C₂²	semidirect
123. C₄×C₈×D₅₃	C₂²	semidirect
125. C₅₃×#446	C₂²	semidirect
126. C₅₃×#446	C₂²	semidirect
129. C₅₃×#435	C₂²	semidirect
130. C₅₃×#435	C₂²	semidirect
131. C₅₃×#431	C₂²	semidirect
132. C₅₃×#431	C₂²	semidirect
133. C₄×M₁₆×C₅₃	C₂²	semidirect
134. C₂×C₄×C₈×C₅₃	C₂²	semidirect
446. #11719912	#41	semidirect
453. C₈×D₅₃	#41	semidirect
578. #2965	D₅₃	semidirect
629. #446	C₂×D₅₃	semidirect
630. #446	C₂×D₅₃	semidirect
658. #435	C₂×D₅₃	semidirect
659. #435	C₂×D₅₃	semidirect
676. #431	C₂×D₅₃	semidirect
677. #431	C₂×D₅₃	semidirect
704. C₄×M₁₆	C₂×D₅₃	semidirect
707. C₂×C₄×C₈	C₂×D₅₃	semidirect
708. C₅₃	#60217	semidirect

Maximal subgroups

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

subgroup	index
#20288277	2
#20283735	2
#20283731	2
#20283721	2
#20283713	2
#20283712	2
#20283700	2
#20283694	2
#20283690	2
#20283689	2
#20283678	2
#20283663	2
#20283646	2
#20283451	2
#20283438	2
#20283413	2
#436×D₅₃	2
#20283376	2
#20283368	2
C₄×#13133223	2
#20283132	2
C₅₃×#2965	2
#60217	53