Subgroups — D₅₃×#3510 #28292574

Order 13568.

7302 conjugacy classes of subgroups.

The subgroup lattice has 1676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288614	C₂	1	1	yes	maximal, characteristic, complemented
2	#20288613	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288612	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288611	C₂	1	1	yes	maximal, characteristic, complemented
5	#20288610	C₂	1	1	yes	maximal, characteristic, complemented
6	#20288609	C₂	1	1	yes	maximal, characteristic, complemented
7	#20288608	C₂	1	4	yes	maximal, complemented
8	#20288607	C₂	1	4	yes	maximal, complemented
9	#20288606	C₂	1	1	yes	maximal, characteristic, complemented
10	#20288605	C₂	1	4	yes	maximal, complemented
11	#20288604	C₂	1	4	yes	maximal, complemented
12	#20288603	C₂	1	8	yes	maximal, complemented
13	#559×D₅₃	C₂	1	4	yes	maximal, complemented
14	#556×D₅₃	C₂	1	4	yes	maximal, complemented
15	#551×D₅₃	C₂	1	8	yes	maximal, complemented
16	#542×D₅₃	C₂	1	4	yes	maximal, complemented
17	#536×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#535×D₅₃	C₂	1	1	yes	maximal, characteristic
19	#533×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#529×D₅₃	C₂	1	4	yes	maximal, complemented
21	C₂×#124×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#519×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#518×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
27	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
28	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
29	#16811359	C₂²	1	4	yes	complemented
30	#16811358	C₂²	1	4	yes	complemented
31	#16811358	C₂²	1	4	yes	complemented
32	#16811357	C₂²	1	8	yes	complemented
33	#16811357	C₂²	1	8	yes	complemented
34	#16811356	C₂²	1	4	yes	complemented
35	#16811356	C₂²	1	8	yes	complemented
36	#16811356	C₂²	1	4	yes	complemented
37	#16811355	C₂²	1	4	yes	complemented
38	#16811355	C₂²	1	8	yes	complemented
39	#16811355	C₂²	1	4	yes	complemented
40	#16811347	C₂²	1	4	yes	complemented
41	#16811346	C₂²	1	4	yes	complemented
42	#16811345	C₂²	1	4	yes	complemented
43	#16811345	C₂²	1	4	yes	complemented
44	#16811344	C₂²	1	8	yes	complemented
45	#16811343	C₂²	1	4	yes	complemented
46	#16811342	C₂²	1	4	yes	complemented
47	#16811342	C₂²	1	4	yes	complemented
48	#16811341	C₂²	1	8	yes	complemented
49	#16811340	C₂²	1	8	yes	complemented
50	#16811340	C₂²	1	8	yes	complemented
51	#16811304	C₂²	1	8	yes	complemented
52	#16811303	C₂²	1	8	yes	complemented
53	#16811302	C₂²	1	8	yes	complemented
54	#16811302	C₂²	1	8	yes	complemented
55	#16811301	C₂²	1	8	yes	complemented
56	#16811300	C₂²	1	8	yes	complemented
57	#16811300	C₂²	1	8	yes	complemented
58	#16811299	C₂²	1	8	yes	complemented
59	#16811299	C₂²	1	8	yes	complemented
60	#16811298	C₂²	1	8	yes	complemented
61	#16811298	C₂²	1	8	yes	complemented
62	#16811297	C₂²	1	8	yes	complemented
63	#16811297	C₂²	1	8	yes	complemented
64	#16811296	C₂²	1	8	yes	complemented
65	#16811296	C₂²	1	8	yes	complemented
66	#16811247	C₂²	1	4	yes	complemented
67	#16811246	C₂²	1	4	yes	complemented
68	#16811245	C₂²	1	4	yes	complemented
69	#16811244	C₂²	1	4	yes	complemented
70	#16811243	C₂²	1	8	yes	complemented
71	#16811242	C₂²	1	4	yes	complemented
72	#16811241	C₂²	1	8	yes	complemented
73	#16811240	C₂²	1	4	yes	complemented
74	#16811239	C₂²	1	8	yes	complemented
75	#16811238	C₂²	1	4	yes	complemented
76	#16811237	C₂²	1	8	yes	complemented
77	#16811199	C₂²	1	1	yes	characteristic, complemented
78	#16811198	C₂²	1	2	yes	complemented
79	#16811197	C₂²	1	1	yes	characteristic, complemented
80	#16811196	C₂²	1	4	yes	complemented
81	#16811195	C₂²	1	4	yes	complemented
82	#16811194	C₂²	1	1	yes	characteristic, complemented
83	#16811193	C₂²	1	2	yes	complemented
84	#16811192	C₂²	1	1	yes	characteristic
85	#16811191	C₂²	1	2	yes	—
86	#16811190	C₂²	1	1	yes	characteristic
87	#16811189	C₂²	1	4	yes	—
88	#16811188	C₂²	1	4	yes	—
89	#16811187	C₂²	1	1	yes	characteristic
90	#16811186	C₂²	1	2	yes	—
91	#16811180	C₂²	1	1	yes	characteristic, complemented
92	#16811179	C₂²	1	2	yes	complemented
93	#16811178	C₂²	1	2	yes	complemented
94	#16811177	C₂²	1	4	yes	complemented
95	#16811176	C₂²	1	1	yes	characteristic, complemented
96	#16811176	C₂²	1	1	yes	characteristic, complemented
97	#16811175	C₂²	1	4	yes	complemented
98	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	complemented
99	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	complemented
100	#127×D₅₃	C₂²	1	2	yes	—
101	#16811160	C₂²	1	4	yes	complemented
102	#16811159	C₂²	1	4	yes	complemented
103	#16811158	C₂²	1	4	yes	complemented
104	#16811157	C₂²	1	4	yes	complemented
105	#16811156	C₂²	1	8	yes	complemented
106	#16811155	C₂²	1	4	yes	complemented
107	#16811154	C₂²	1	4	yes	complemented
108	#16811153	C₂²	1	8	yes	complemented
109	#16811152	C₂²	1	4	yes	complemented
110	#16811151	C₂²	1	8	yes	complemented
111	#16811150	C₂²	1	8	yes	complemented
112	#126×D₅₃	C₂²	1	8	yes	complemented
113	#126×D₅₃	C₂²	1	8	yes	complemented
114	#125×D₅₃	C₂²	1	2	yes	complemented
115	C₂×#13133206	C₂²	1	1	yes	characteristic, complemented
116	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
117	C₂×#13133204	C₂²	1	1	yes	characteristic, complemented
118	C₂×#13133203	C₂²	1	4	yes	complemented
119	#124×D₅₃	C₂²	1	2	yes	—
120	#124×D₅₃	C₂²	1	4	yes	—
121	#124×D₅₃	C₂²	1	2	yes	—
122	#124×D₅₃	C₂²	1	2	yes	—
123	#124×D₅₃	C₂²	1	2	yes	complemented
124	#124×D₅₃	C₂²	1	4	yes	complemented
125	#124×D₅₃	C₂²	1	2	yes	complemented
126	#124×D₅₃	C₂²	1	2	yes	complemented
127	#124×D₅₃	C₂²	1	8	yes	complemented
128	#123×D₅₃	C₂²	1	4	yes	—
129	#123×D₅₃	C₂²	1	8	yes	complemented
130	#123×D₅₃	C₂²	1	8	yes	complemented
131	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	—
132	C₂²⋊Q₈×D₅₃	C₂²	1	8	yes	complemented
133	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
134	#121×D₅₃	C₂²	1	4	yes	—
135	#120×D₅₃	C₂²	1	4	yes	—
136	#16811101	C₂²	1	1	yes	characteristic, complemented
137	#16811100	C₂²	1	4	yes	complemented
138	#16811100	C₂²	1	1	yes	characteristic, complemented
139	#16811100	C₂²	1	1	yes	characteristic, complemented
140	#16811099	C₂²	1	4	yes	complemented
141	#16811099	C₂²	1	4	yes	complemented
142	#16811098	C₂²	1	1	yes	characteristic, complemented
143	#16811097	C₂²	1	1	yes	characteristic, complemented
144	#16811097	C₂²	1	1	yes	characteristic, complemented
145	#16811096	C₂²	1	4	yes	complemented
146	#16811095	C₂²	1	4	yes	complemented
147	#16811095	C₂²	1	4	yes	complemented
148	#41×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
149	C₄×#11719949	C₂²	1	2	yes	complemented
150	C₄×#11719945	C₂²	1	1	yes	characteristic, complemented
151	C₄×#11719945	C₂²	1	2	yes	complemented
152	#16811091	C₂²	1	1	yes	characteristic, complemented
153	#16811091	C₂²	1	2	yes	complemented
154	C₄×#11719947	C₂²	1	4	yes	complemented
155	C₄×#11719947	C₂²	1	2	yes	complemented
156	C₄×Q₈×D₅₃	C₂²	1	4	yes	complemented
157	C₄×Q₈×D₅₃	C₂²	1	2	yes	complemented
158	C₄×Q₈×D₅₃	C₂²	1	4	yes	complemented
159	C₄×Q₈×D₅₃	C₂²	1	4	yes	complemented
160	C₄×D₄×D₅₃	C₂²	1	4	yes	—
161	C₄×D₄×D₅₃	C₂²	1	4	yes	—
162	C₄×D₄×D₅₃	C₂²	1	4	yes	—
163	C₄×D₄×D₅₃	C₂²	1	2	yes	complemented
164	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
165	#117×D₅₃	C₂²	1	1	yes	characteristic
166	#117×D₅₃	C₂²	1	1	yes	characteristic
167	#117×D₅₃	C₂²	1	1	yes	characteristic
168	#117×D₅₃	C₂²	1	4	yes	—
169	#117×D₅₃	C₂²	1	8	yes	complemented
170	#117×D₅₃	C₂²	1	2	yes	complemented
171	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
172	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
173	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
174	C₂×C₄²×D₅₃	C₂²	1	2	yes	complemented
175	C₅₃×#559	C₂²	1	4	yes	complemented
176	C₅₃×#556	C₂²	1	4	yes	complemented
177	C₅₃×#551	C₂²	1	8	yes	complemented
178	C₅₃×#542	C₂²	1	4	yes	complemented
179	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#535	C₂²	1	1	yes	characteristic
181	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#529	C₂²	1	4	yes	complemented
183	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
186	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₅₃	C₂³	1	2	yes	—
188	C₂×#11719949	C₂³	1	1	yes	characteristic
189	C₂×#11719945	C₂³	1	2	yes	—
190	C₂×#11719945	C₂³	1	1	yes	characteristic
191	C₂×#11719947	C₂³	1	1	yes	characteristic
192	C₂×#11719947	C₂³	1	2	yes	—
193	#41×D₅₃	—	2	8	no	—
194	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
195	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
196	C₂×Q₈×D₅₃	—	2	8	no	—
197	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
198	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
199	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
200	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
201	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
202	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
203	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
204	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
205	C₂×D₄×D₅₃	—	2	8	no	—
206	C₂×D₄×D₅₃	C₂³	1	2	yes	—
207	C₂×D₄×D₅₃	C₂³	1	2	yes	—
208	C₂×D₄×D₅₃	C₂³	1	2	yes	—
209	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
210	C₂×D₄×D₅₃	C₂³	1	2	yes	—
211	C₂×D₄×D₅₃	C₂³	1	2	yes	—
212	C₂×D₄×D₅₃	C₂³	1	8	yes	—
213	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
214	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
215	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
216	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
217	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
218	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
219	#13133217	C₂³	1	2	yes	complemented
220	#13133217	C₂³	1	2	yes	complemented
221	#13133216	C₂³	1	8	yes	complemented
222	#13133216	C₂³	1	4	yes	complemented
223	#13133216	C₂³	1	2	yes	complemented
224	#13133216	C₂³	1	2	yes	complemented
225	#13133215	C₂³	1	2	yes	complemented
226	#13133215	C₂³	1	2	yes	complemented
227	#13133215	C₂³	1	4	yes	complemented
228	#13133214	C₂³	1	2	yes	—
229	#13133213	C₂³	1	2	yes	—
230	#13133213	C₂³	1	2	yes	—
231	#13133213	C₂³	1	8	yes	—
232	#13133212	C₂³	1	8	yes	complemented
233	#13133212	C₂³	1	8	yes	complemented
234	#13133212	C₂³	1	8	yes	complemented
235	#13133212	C₂³	1	8	yes	complemented
236	#13133212	C₂³	1	8	yes	complemented
237	#13133212	C₂³	1	8	yes	complemented
238	#13133211	C₂³	1	8	yes	complemented
239	#13133211	C₂³	1	8	yes	complemented
240	#13133210	C₂³	1	8	yes	complemented
241	#13133210	C₂³	1	8	yes	complemented
242	#13133210	C₂³	1	8	yes	complemented
243	#13133210	C₂³	1	8	yes	complemented
244	#13133210	C₂³	1	8	yes	complemented
245	#13133210	C₂³	1	8	yes	complemented
246	#13133209	C₂³	1	2	yes	complemented
247	#13133208	C₂³	1	2	yes	complemented
248	#13133208	C₂³	1	2	yes	complemented
249	#13133207	C₂³	1	4	yes	complemented
250	#13133207	C₂³	1	4	yes	complemented
251	#13133206	C₂³	1	2	yes	—
252	#13133206	C₂³	1	4	yes	—
253	#13133206	C₂³	1	2	yes	—
254	#13133206	C₂³	1	2	yes	—
255	#13133206	C₂³	1	8	yes	complemented
256	#13133206	C₂³	1	2	yes	complemented
257	#13133205	C₂³	1	2	yes	—
258	#13133205	C₂³	1	4	yes	—
259	#13133205	C₂³	1	2	yes	—
260	#13133205	C₂³	1	2	yes	—
261	#13133205	C₂³	1	8	yes	complemented
262	#13133205	C₂³	1	2	yes	complemented
263	#13133204	C₂³	1	2	yes	—
264	#13133204	C₂³	1	4	yes	—
265	#13133204	C₂³	1	2	yes	—
266	#13133204	C₂³	1	2	yes	—
267	#13133204	C₂³	1	8	yes	complemented
268	#13133204	C₂³	1	2	yes	complemented
269	#13133203	C₂³	1	8	yes	—
270	#13133203	C₂³	1	8	yes	—
271	#13133203	C₂³	1	8	yes	—
272	#13133203	C₂³	1	8	yes	—
273	#13133203	C₂³	1	8	yes	—
274	#13133203	C₂³	1	8	yes	complemented
275	#13133203	C₂³	1	8	yes	complemented
276	#13133203	C₂³	1	8	yes	complemented
277	#13133203	C₂³	1	8	yes	complemented
278	#13133203	C₂³	1	8	yes	complemented
279	#13133202	C₂³	1	8	yes	—
280	#13133202	C₂³	1	8	yes	complemented
281	#13133202	C₂³	1	8	yes	complemented
282	#13133202	C₂³	1	8	yes	complemented
283	#13133202	C₂³	1	8	yes	complemented
284	#13133201	C₂³	1	4	yes	—
285	#13133201	C₂³	1	8	yes	complemented
286	#13133201	C₂³	1	8	yes	complemented
287	#13133200	C₂³	1	4	yes	—
288	#13133200	C₂³	1	8	yes	complemented
289	#13133200	C₂³	1	8	yes	complemented
290	#13133199	C₂³	1	8	yes	—
291	#13133199	C₂³	1	8	yes	complemented
292	#13133199	C₂³	1	8	yes	complemented
293	#13133199	C₂³	1	8	yes	complemented
294	#13133199	C₂³	1	8	yes	complemented
295	#13133198	C₂³	1	4	yes	—
296	#13133198	C₂³	1	8	yes	complemented
297	#13133198	C₂³	1	8	yes	complemented
298	#13133197	C₂³	1	4	yes	—
299	#13133197	C₂³	1	8	yes	complemented
300	#13133197	C₂³	1	4	yes	complemented
301	#13133196	C₂³	1	4	yes	—
302	#13133196	C₂³	1	8	yes	complemented
303	#13133196	C₂³	1	4	yes	complemented
304	#13133195	C₂³	1	4	yes	—
305	#13133195	C₂³	1	4	yes	—
306	#13133195	C₂³	1	8	yes	complemented
307	#13133195	C₂³	1	8	yes	complemented
308	#13133195	C₂³	1	8	yes	complemented
309	#13133194	C₂³	1	4	yes	—
310	#13133194	C₂³	1	4	yes	—
311	#13133194	C₂³	1	8	yes	complemented
312	#13133194	C₂³	1	8	yes	complemented
313	#13133194	C₂³	1	8	yes	complemented
314	#13133193	C₂³	1	4	yes	—
315	#13133193	C₂³	1	8	yes	complemented
316	#13133193	C₂³	1	4	yes	complemented
317	#13133192	C₂³	1	4	yes	—
318	#13133191	C₂³	1	4	yes	—
319	#13133190	C₂³	1	8	yes	—
320	#13133189	C₂³	1	8	yes	—
321	#13133188	C₂³	1	4	yes	—
322	#13133187	C₂³	1	4	yes	—
323	#13133187	C₂³	1	8	yes	—
324	#13133186	C₂³	1	4	yes	—
325	#13133185	C₂³	1	4	yes	—
326	#13133185	C₂³	1	8	yes	—
327	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
328	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
329	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
330	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
331	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
332	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
333	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
334	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
335	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
336	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
337	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
338	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
339	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
340	#13133182	C₂³	1	4	yes	complemented
341	#13133182	C₂³	1	4	yes	complemented
342	#13133182	C₂³	1	4	yes	complemented
343	#13133182	C₂³	1	8	yes	complemented
344	#13133182	C₂³	1	4	yes	complemented
345	#13133182	C₂³	1	2	yes	complemented
346	#13133182	C₂³	1	4	yes	complemented
347	#13133182	C₂³	1	8	yes	complemented
348	#13133182	C₂³	1	4	yes	complemented
349	C₄×D₂₁₂	C₂³	1	4	yes	—
350	C₄×D₂₁₂	C₂³	1	4	yes	—
351	C₄×D₂₁₂	C₂³	1	4	yes	—
352	C₄×D₂₁₂	C₂³	1	8	yes	complemented
353	C₄×D₂₁₂	C₂³	1	2	yes	complemented
354	D₄×Dic₅₃	C₂³	1	4	yes	—
355	D₄×Dic₅₃	C₂³	1	4	yes	—
356	D₄×Dic₅₃	C₂³	1	4	yes	—
357	D₄×Dic₅₃	C₂³	1	8	yes	complemented
358	D₄×Dic₅₃	C₂³	1	2	yes	complemented
359	#13133179	C₂³	1	4	yes	—
360	#13133179	C₂³	1	4	yes	—
361	#13133179	C₂³	1	4	yes	—
362	#13133179	C₂³	1	8	yes	complemented
363	#13133179	C₂³	1	2	yes	complemented
364	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
365	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
366	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
367	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
368	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
369	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
370	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
371	#13133177	C₂³	1	4	yes	—
372	#13133177	C₂³	1	4	yes	—
373	#13133177	C₂³	1	8	yes	—
374	#13133177	C₂³	1	8	yes	—
375	#13133177	C₂³	1	8	yes	complemented
376	#13133177	C₂³	1	8	yes	complemented
377	#13133177	C₂³	1	4	yes	complemented
378	#13133176	C₂³	1	4	yes	—
379	#13133176	C₂³	1	1	yes	characteristic
380	#13133176	C₂³	1	1	yes	characteristic
381	#13133176	C₂³	1	1	yes	characteristic
382	#13133176	C₂³	1	8	yes	complemented
383	#13133176	C₂³	1	2	yes	complemented
384	#13133175	C₂³	1	8	yes	—
385	#13133175	C₂³	1	2	yes	—
386	#13133175	C₂³	1	2	yes	—
387	#13133175	C₂³	1	2	yes	—
388	#13133175	C₂³	1	8	yes	complemented
389	#13133175	C₂³	1	8	yes	complemented
390	#13133175	C₂³	1	4	yes	complemented
391	#13133174	C₂³	1	8	yes	—
392	#13133174	C₂³	1	2	yes	—
393	#13133174	C₂³	1	2	yes	—
394	#13133174	C₂³	1	2	yes	—
395	#13133174	C₂³	1	8	yes	complemented
396	#13133174	C₂³	1	8	yes	complemented
397	#13133174	C₂³	1	2	yes	complemented
398	#13133174	C₂³	1	2	yes	complemented
399	#13133173	C₂³	1	4	yes	—
400	#13133173	C₂³	1	4	yes	—
401	#13133173	C₂³	1	2	yes	—
402	#13133173	C₂³	1	2	yes	—
403	#13133173	C₂³	1	2	yes	—
404	#13133173	C₂³	1	8	yes	complemented
405	#13133173	C₂³	1	8	yes	complemented
406	#13133173	C₂³	1	4	yes	complemented
407	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
408	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
409	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
410	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
411	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
412	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
413	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
414	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
415	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
416	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
417	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
418	C₂×#11719921	C₂³	1	4	yes	—
419	C₂×#11719921	C₂³	1	8	yes	—
420	C₂×#11719921	C₂³	1	4	yes	—
421	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
422	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
423	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
424	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
425	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
426	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
427	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
428	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
429	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
430	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
431	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
432	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
433	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
434	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
435	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
436	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
437	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
438	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
439	C₄²×D₅₃	C₂³	1	1	yes	characteristic
440	C₄²×D₅₃	C₂³	1	1	yes	characteristic
441	C₄²×D₅₃	C₂³	1	2	yes	—
442	C₄²×D₅₃	C₂³	1	2	yes	—
443	C₄²×D₅₃	C₂³	1	1	yes	characteristic
444	C₄²×D₅₃	C₂³	1	1	yes	characteristic
445	C₄²×D₅₃	C₂³	1	2	yes	—
446	C₄²×D₅₃	C₂³	1	4	yes	—
447	C₄²×D₅₃	C₂³	1	8	yes	—
448	C₄²×D₅₃	C₂³	1	2	yes	—
449	C₄²×D₅₃	C₂³	1	2	yes	—
450	C₄²×D₅₃	C₂³	1	4	yes	complemented
451	C₄²×D₅₃	C₂³	1	2	yes	complemented
452	C₄²×D₅₃	C₂³	1	2	yes	complemented
453	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
454	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
455	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
456	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
457	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
458	#127×C₅₃	C₂³	1	2	yes	—
459	#126×C₅₃	C₂³	1	8	yes	complemented
460	#126×C₅₃	C₂³	1	8	yes	complemented
461	#125×C₅₃	C₂³	1	2	yes	complemented
462	#124×C₅₃	C₂³	1	2	yes	—
463	#124×C₅₃	C₂³	1	2	yes	—
464	#124×C₅₃	C₂³	1	4	yes	—
465	#124×C₅₃	C₂³	1	2	yes	—
466	#124×C₅₃	C₂³	1	8	yes	complemented
467	#124×C₅₃	C₂³	1	2	yes	complemented
468	#123×C₅₃	C₂³	1	4	yes	—
469	#123×C₅₃	C₂³	1	8	yes	complemented
470	#123×C₅₃	C₂³	1	8	yes	complemented
471	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
472	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
473	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
474	#121×C₅₃	C₂³	1	4	yes	—
475	#120×C₅₃	C₂³	1	4	yes	—
476	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
477	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
478	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
479	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
480	C₄×D₄×C₅₃	C₂³	1	4	yes	—
481	C₄×D₄×C₅₃	C₂³	1	4	yes	—
482	C₄×D₄×C₅₃	C₂³	1	4	yes	—
483	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
484	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
485	#117×C₅₃	C₂³	1	1	yes	characteristic
486	#117×C₅₃	C₂³	1	1	yes	characteristic
487	#117×C₅₃	C₂³	1	4	yes	—
488	#117×C₅₃	C₂³	1	1	yes	characteristic
489	#117×C₅₃	C₂³	1	2	yes	complemented
490	#117×C₅₃	C₂³	1	8	yes	complemented
491	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
492	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
493	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
494	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
495	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
496	C₂³×D₅₃	—	2	8	no	—
497	C₂³×D₅₃	—	4	8	no	—
498	C₂³×D₅₃	C₂⁴	1	4	yes	—
499	C₂³×D₅₃	C₂⁴	1	2	yes	—
500	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
501	C₂³×D₅₃	C₂⁴	1	4	yes	—
502	C₂³×D₅₃	C₂⁴	1	2	yes	—
503	#41×C₅₃	—	2	4	no	—
504	C₂×Q₈×C₅₃	—	2	4	no	—
505	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
506	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
507	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
508	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
509	C₂×D₄×C₅₃	—	2	4	no	—
510	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
511	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
512	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
513	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
514	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
515	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
516	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
517	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
518	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
519	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
520	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
521	C₂×C₂²⋊D₅₃	—	2	8	no	—
522	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
523	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
524	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
525	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
526	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
527	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
528	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
529	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
530	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
531	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
532	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
533	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
534	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
535	#11719949	—	2	4	no	—
536	Q₈×D₅₃	—	2	8	no	—
537	Q₈×D₅₃	—	2	8	no	—
538	Q₈×D₅₃	—	2	8	no	—
539	Q₈×D₅₃	—	2	8	no	—
540	Q₈×D₅₃	—	2	4	no	—
541	Q₈×D₅₃	—	4	8	no	—
542	#11719947	—	2	8	no	—
543	#11719947	—	2	4	no	—
544	D₄×D₅₃	—	2	8	no	—
545	D₄×D₅₃	—	2	8	no	—
546	D₄×D₅₃	—	2	8	no	—
547	D₄×D₅₃	—	2	8	no	—
548	D₄×D₅₃	—	2	8	no	—
549	D₄×D₅₃	—	2	4	no	—
550	D₄×D₅₃	—	4	16	no	—
551	#11719945	—	2	4	no	—
552	#11719945	—	2	8	no	—
553	C₂×D₂₁₂	—	2	4	no	—
554	C₂×D₂₁₂	C₂⁴	1	2	yes	—
555	C₂×D₂₁₂	C₂⁴	1	2	yes	—
556	C₂×D₂₁₂	C₂⁴	1	2	yes	—
557	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
558	C₂×D₂₁₂	C₂⁴	1	8	yes	—
559	C₂×C₄×D₅₃	—	2	8	no	—
560	C₂×C₄×D₅₃	—	2	8	no	—
561	C₂×C₄×D₅₃	—	4	8	no	—
562	C₂×C₄×D₅₃	—	4	16	no	—
563	C₂×C₄×D₅₃	—	4	4	no	—
564	C₂×C₄×D₅₃	#41	1	8	yes	—
565	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
566	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
567	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
568	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
569	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
570	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
571	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
572	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
573	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
574	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
575	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
576	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
577	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
578	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
579	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
580	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
581	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
582	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
583	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
584	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
585	C₂×Dic₁₀₆	—	2	4	no	—
586	C₂×Dic₁₀₆	—	2	8	no	—
587	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
588	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
589	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
590	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
591	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
592	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
593	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
594	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
595	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
596	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
597	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
598	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
599	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
600	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
601	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
602	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
603	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
604	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
605	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
606	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
607	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
608	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
609	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
610	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
611	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
612	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
613	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
614	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
615	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
616	C₄²×C₅₃	C₂⁴	1	2	yes	—
617	C₄²×C₅₃	C₂⁴	1	2	yes	—
618	C₄²×C₅₃	C₂⁴	1	4	yes	—
619	C₄²×C₅₃	C₂⁴	1	8	yes	—
620	C₄²×C₅₃	C₂⁴	1	2	yes	—
621	C₄²×C₅₃	C₂⁴	1	2	yes	—
622	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
623	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
624	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
625	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
626	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
627	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
628	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
629	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
630	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
631	#11719921	C₂⁴	1	4	yes	—
632	#11719921	C₂⁴	1	4	yes	—
633	#11719921	C₂⁴	1	8	yes	—
634	#11719921	C₂⁴	1	8	yes	—
635	#11719921	C₂⁴	1	8	yes	—
636	#11719921	C₂⁴	1	8	yes	—
637	#11719921	C₂⁴	1	8	yes	—
638	#11719921	C₂⁴	1	8	yes	—
639	#11719921	C₂⁴	1	4	yes	—
640	#11719921	C₂⁴	1	4	yes	—
641	#11719921	C₂⁴	1	4	yes	—
642	#11719921	C₂⁴	1	8	yes	—
643	#11719921	C₂⁴	1	8	yes	—
644	#11719921	C₂⁴	1	8	yes	—
645	#11719921	C₂⁴	1	8	yes	—
646	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
647	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
648	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
649	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
650	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
651	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
652	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
653	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
654	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
655	#11719919	C₂⁴	1	4	yes	—
656	#11719919	C₂⁴	1	4	yes	—
657	#11719919	C₂⁴	1	4	yes	—
658	#11719919	C₂⁴	1	8	yes	—
659	#11719919	C₂⁴	1	8	yes	—
660	#11719919	C₂⁴	1	4	yes	—
661	#11719919	C₂⁴	1	4	yes	—
662	#11719919	C₂⁴	1	4	yes	—
663	#11719919	C₂⁴	1	4	yes	—
664	#11719919	C₂⁴	1	8	yes	—
665	#11719919	C₂⁴	1	8	yes	—
666	#11719919	C₂⁴	1	4	yes	—
667	#11719919	C₂⁴	1	4	yes	—
668	#11719919	C₂⁴	1	4	yes	—
669	#11719919	C₂⁴	1	4	yes	—
670	C₄×Dic₅₃	C₂⁴	1	2	yes	—
671	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
672	C₄×Dic₅₃	C₂⁴	1	2	yes	—
673	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
674	C₄×Dic₅₃	C₂⁴	1	2	yes	—
675	C₄×Dic₅₃	C₂⁴	1	2	yes	—
676	C₄×Dic₅₃	C₂⁴	1	2	yes	—
677	C₄×Dic₅₃	C₂⁴	1	4	yes	—
678	C₄×Dic₅₃	C₂⁴	1	4	yes	—
679	C₄×Dic₅₃	C₂⁴	1	4	yes	—
680	C₄×Dic₅₃	C₂⁴	1	2	yes	—
681	C₄×Dic₅₃	C₂⁴	1	4	yes	—
682	C₄×Dic₅₃	C₂⁴	1	8	yes	—
683	C₄×Dic₅₃	C₂⁴	1	8	yes	—
684	C₄×Dic₅₃	C₂⁴	1	4	yes	—
685	C₄×Dic₅₃	C₂⁴	1	4	yes	—
686	C₄×Dic₅₃	C₂⁴	1	8	yes	—
687	C₄×Dic₅₃	C₂⁴	1	2	yes	—
688	C₄×Dic₅₃	C₂⁴	1	2	yes	—
689	C₂³×C₅₃	—	2	4	no	—
690	C₂³×C₅₃	—	4	4	no	—
691	C₂³×C₅₃	C₂⁵	1	2	yes	—
692	C₂³×C₅₃	C₂⁵	1	4	yes	—
693	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
694	C₂²×D₅₃	—	2	4	no	—
695	C₂²×D₅₃	—	2	4	no	—
696	C₂²×D₅₃	—	2	4	no	—
697	C₂²×D₅₃	—	2	8	no	—
698	C₂²×D₅₃	—	2	8	no	—
699	C₂²×D₅₃	—	2	16	no	—
700	C₂²×D₅₃	—	2	8	no	—
701	C₂²×D₅₃	—	4	8	no	—
702	C₂²×D₅₃	—	4	4	no	—
703	C₂²×D₅₃	—	8	16	no	—
704	C₂²×D₅₃	C₂×#41	1	4	yes	—
705	C₂²×D₅₃	C₂⁵	1	2	yes	—
706	C₂²×D₅₃	C₂⁵	1	4	yes	—
707	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
708	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
709	Q₈×C₅₃	—	2	4	no	—
710	Q₈×C₅₃	—	2	4	no	—
711	Q₈×C₅₃	—	2	2	no	—
712	Q₈×C₅₃	—	4	4	no	—
713	D₄×C₅₃	—	2	4	no	—
714	D₄×C₅₃	—	2	4	no	—
715	D₄×C₅₃	—	2	4	no	—
716	D₄×C₅₃	—	2	2	no	—
717	D₄×C₅₃	—	4	8	no	—
718	C₂×C₄×C₅₃	—	2	4	no	—
719	C₂×C₄×C₅₃	—	2	4	no	—
720	C₂×C₄×C₅₃	—	4	2	no	—
721	C₂×C₄×C₅₃	—	4	8	no	—
722	C₂×C₄×C₅₃	—	4	4	no	—
723	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
724	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
725	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
726	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
727	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
728	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
729	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
730	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
731	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
732	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
733	C₂²⋊D₅₃	—	2	4	no	—
734	C₂²⋊D₅₃	—	2	4	no	—
735	C₂²⋊D₅₃	—	2	4	no	—
736	C₂²⋊D₅₃	—	2	8	no	—
737	C₂²⋊D₅₃	—	2	8	no	—
738	C₂²⋊D₅₃	—	4	8	no	—
739	C₂²⋊D₅₃	—	4	8	no	—
740	C₂×Dic₅₃	—	2	4	no	—
741	C₂×Dic₅₃	—	2	4	no	—
742	C₂×Dic₅₃	—	4	2	no	—
743	C₂×Dic₅₃	—	4	8	no	—
744	C₂×Dic₅₃	—	4	4	no	—
745	C₂×Dic₅₃	C₂×#41	1	4	yes	—
746	C₂×Dic₅₃	C₂⁵	1	4	yes	—
747	C₂×Dic₅₃	C₂⁵	1	2	yes	—
748	C₂×Dic₅₃	C₂⁵	1	4	yes	—
749	C₂×Dic₅₃	C₂⁵	1	2	yes	—
750	C₂×Dic₅₃	C₂⁵	1	4	yes	—
751	C₂×Dic₅₃	C₂⁵	1	2	yes	—
752	C₂×Dic₅₃	C₂⁵	1	4	yes	—
753	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
754	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
755	D₂₁₂	—	2	4	no	—
756	D₂₁₂	—	2	4	no	—
757	D₂₁₂	—	2	4	no	—
758	D₂₁₂	—	2	2	no	—
759	D₂₁₂	—	4	8	no	—
760	C₄×D₅₃	—	2	4	no	—
761	C₄×D₅₃	—	2	8	no	—
762	C₄×D₅₃	—	2	8	no	—
763	C₄×D₅₃	—	2	4	no	—
764	C₄×D₅₃	—	2	8	no	—
765	C₄×D₅₃	—	2	8	no	—
766	C₄×D₅₃	—	2	4	no	—
767	C₄×D₅₃	—	2	8	no	—
768	C₄×D₅₃	—	2	4	no	—
769	C₄×D₅₃	—	2	4	no	—
770	C₄×D₅₃	—	4	2	no	—
771	C₄×D₅₃	—	4	8	no	—
772	C₄×D₅₃	—	4	2	no	—
773	C₄×D₅₃	—	4	8	no	—
774	C₄×D₅₃	—	4	4	no	—
775	C₄×D₅₃	—	4	4	no	—
776	C₄×D₅₃	C₂×#41	1	4	yes	—
777	C₄×D₅₃	C₂×#41	1	4	yes	—
778	C₄×D₅₃	C₂×#41	1	4	yes	—
779	C₄×D₅₃	C₂×#41	1	4	yes	—
780	Dic₁₀₆	—	2	4	no	—
781	Dic₁₀₆	—	2	4	no	—
782	Dic₁₀₆	—	2	2	no	—
783	Dic₁₀₆	—	2	8	no	—
784	Dic₁₀₆	—	2	8	no	—
785	Dic₁₀₆	—	2	4	no	—
786	Dic₁₀₆	—	4	4	no	—
787	Dic₁₀₆	—	4	4	no	—
788	Dic₁₀₆	—	4	4	no	—
789	C₂×#3510	—	53	1	no	maximal, Sylow
790	C₂²×C₅₃	—	2	2	no	—
791	C₂²×C₅₃	—	2	2	no	—
792	C₂²×C₅₃	—	2	4	no	—
793	C₂²×C₅₃	—	2	4	no	—
794	C₂²×C₅₃	—	2	8	no	—
795	C₂²×C₅₃	—	8	4	no	—
796	C₂²×C₅₃	C₂²×#41	1	2	yes	—
797	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
798	C₂×D₅₃	—	2	2	no	—
799	C₂×D₅₃	—	2	8	no	—
800	C₂×D₅₃	—	2	2	no	—
801	C₂×D₅₃	—	2	4	no	—
802	C₂×D₅₃	—	2	4	no	—
803	C₂×D₅₃	—	2	8	no	—
804	C₂×D₅₃	—	4	8	no	—
805	C₂×D₅₃	—	4	16	no	—
806	C₂×D₅₃	—	8	8	no	—
807	C₂×D₅₃	—	8	4	no	—
808	C₂×D₅₃	C₂²×#41	1	2	yes	—
809	C₂×D₅₃	C₂²×#41	1	2	yes	—
810	C₂×D₅₃	#585	1	4	yes	—
811	C₄×C₅₃	—	2	4	no	—
812	C₄×C₅₃	—	2	2	no	—
813	C₄×C₅₃	—	2	2	no	—
814	C₄×C₅₃	—	2	4	no	—
815	C₄×C₅₃	—	2	4	no	—
816	C₄×C₅₃	—	2	2	no	—
817	C₄×C₅₃	—	2	4	no	—
818	C₄×C₅₃	C₂²×#41	1	2	yes	—
819	C₄×C₅₃	C₂²×#41	1	2	yes	—
820	Dic₅₃	—	2	4	no	—
821	Dic₅₃	—	2	2	no	—
822	Dic₅₃	—	2	2	no	—
823	Dic₅₃	—	2	4	no	—
824	Dic₅₃	—	2	4	no	—
825	Dic₅₃	—	2	2	no	—
826	Dic₅₃	—	2	4	no	—
827	Dic₅₃	C₂²×#41	1	2	yes	—
828	Dic₅₃	C₂²×#41	1	2	yes	—
829	#3510	—	53	4	no	—
830	#3510	—	53	4	no	—
831	#3510	—	53	8	no	—
832	#3510	—	53	4	no	—
833	#3510	—	53	1	no	—
834	#3510	—	53	1	no	—
835	#3510	—	53	1	no	—
836	#3510	—	53	4	no	—
837	#3510	—	53	1	no	—
838	#3510	—	53	1	no	—
839	#3510	—	53	1	no	—
840	#3510	—	53	1	no	—
841	#3510	D₅₃	1	1	yes	characteristic, direct product factor
842	C₂×#559	—	53	4	no	—
843	C₂×#556	—	53	4	no	—
844	C₂×#551	—	53	8	no	—
845	C₂×#542	—	53	4	no	—
846	C₂×#536	—	53	1	no	—
847	C₂×#535	—	53	1	no	—
848	C₂×#533	—	53	1	no	—
849	C₂×#529	—	53	4	no	—
850	C₂²×#124	—	53	1	no	—
851	C₂×#519	—	53	1	no	—
852	C₂×#518	—	53	1	no	—
853	C₂×C₄×#41	—	53	1	no	—
854	C₂×C₅₃	—	2	2	no	—
855	C₂×C₅₃	—	4	4	no	—
856	C₂×C₅₃	—	4	2	no	—
857	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
858	C₂×C₅₃	C₂×#585	1	2	yes	—
859	D₅₃	—	2	2	no	—
860	D₅₃	—	4	2	no	—
861	D₅₃	—	4	4	no	—
862	D₅₃	#3510	1	4	yes	direct product factor
863	C₂²×#41	—	53	1	no	—
864	C₂³×Q₈	—	53	1	no	—
865	C₂³×D₄	—	53	1	no	—
866	#559	—	53	4	no	—
867	#559	—	53	4	no	—
868	#559	—	53	4	no	—
869	#559	—	53	8	no	—
870	#559	—	53	8	no	—
871	#559	—	53	8	no	—
872	#559	—	53	4	no	—
873	#559	—	53	4	no	—
874	#559	—	53	4	no	—
875	#559	—	53	8	no	—
876	#559	—	53	4	no	—
877	#559	C₂×D₅₃	1	4	yes	complemented
878	#556	—	53	4	no	—
879	#556	—	53	8	no	—
880	#556	—	53	8	no	—
881	#556	—	53	4	no	—
882	#556	—	53	4	no	—
883	#556	—	53	8	no	—
884	#556	—	53	4	no	—
885	#556	—	53	4	no	—
886	#556	—	53	4	no	—
887	#556	—	53	4	no	—
888	#556	—	53	8	no	—
889	#556	C₂×D₅₃	1	4	yes	complemented
890	#551	—	53	8	no	—
891	#551	—	53	8	no	—
892	#551	—	53	8	no	—
893	#551	—	53	8	no	—
894	#551	—	53	8	no	—
895	#551	—	53	8	no	—
896	#551	—	53	8	no	—
897	#551	—	53	8	no	—
898	#551	—	53	8	no	—
899	#551	—	53	8	no	—
900	#551	—	53	8	no	—
901	#551	—	53	8	no	—
902	#551	—	53	8	no	—
903	#551	—	53	8	no	—
904	#551	—	53	8	no	—
905	#551	C₂×D₅₃	1	8	yes	complemented
906	#542	—	53	4	no	—
907	#542	—	53	8	no	—
908	#542	—	53	4	no	—
909	#542	—	53	8	no	—
910	#542	—	53	8	no	—
911	#542	—	53	8	no	—
912	#542	—	53	4	no	—
913	#542	—	53	4	no	—
914	#542	—	53	4	no	—
915	#542	—	53	4	no	—
916	#542	—	53	4	no	—
917	#542	C₂×D₅₃	1	4	yes	complemented
918	#536	—	53	1	no	—
919	#536	—	53	1	no	—
920	#536	—	53	2	no	—
921	#536	—	53	2	no	—
922	#536	—	53	4	no	—
923	#536	—	53	4	no	—
924	#536	—	53	1	no	—
925	#536	C₂×D₅₃	1	1	yes	characteristic, complemented
926	#535	—	53	1	no	—
927	#535	—	53	1	no	—
928	#535	—	53	2	no	—
929	#535	—	53	2	no	—
930	#535	—	53	4	no	—
931	#535	—	53	4	no	—
932	#535	—	53	1	no	—
933	#535	C₂×D₅₃	1	1	yes	characteristic
934	#533	—	53	2	no	—
935	#533	—	53	2	no	—
936	#533	—	53	4	no	—
937	#533	—	53	4	no	—
938	#533	—	53	1	no	—
939	#533	—	53	1	no	—
940	#533	—	53	1	no	—
941	#533	C₂×D₅₃	1	1	yes	characteristic, complemented
942	C₂×C₄⋊Q₈	—	53	2	no	—
943	C₂×C₄⋊Q₈	—	53	2	no	—
944	C₂×#127	—	53	2	no	—
945	#529	—	53	8	no	—
946	#529	—	53	4	no	—
947	#529	—	53	4	no	—
948	#529	—	53	8	no	—
949	#529	—	53	4	no	—
950	#529	—	53	4	no	—
951	#529	—	53	4	no	—
952	#529	—	53	4	no	—
953	#529	—	53	8	no	—
954	#529	—	53	8	no	—
955	#529	—	53	4	no	—
956	#529	C₂×D₅₃	1	4	yes	complemented
957	C₂×#126	—	53	8	no	—
958	C₂×#126	—	53	8	no	—
959	C₂×#125	—	53	2	no	—
960	C₂×#124	—	53	1	no	—
961	C₂×#124	—	53	1	no	—
962	C₂×#124	—	53	2	no	—
963	C₂×#124	—	53	2	no	—
964	C₂×#124	—	53	4	no	—
965	C₂×#124	—	53	2	no	—
966	C₂×#124	—	53	2	no	—
967	C₂×#124	—	53	4	no	—
968	C₂×#124	—	53	2	no	—
969	C₂×#124	—	53	2	no	—
970	C₂×#124	—	53	8	no	—
971	C₂×#124	—	53	4	no	—
972	C₂×#124	—	53	1	no	—
973	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
974	C₂×#123	—	53	4	no	—
975	C₂×#123	—	53	8	no	—
976	C₂×#123	—	53	8	no	—
977	C₂×C₂²⋊Q₈	—	53	4	no	—
978	C₂×C₂²⋊Q₈	—	53	4	no	—
979	C₂×C₂²⋊Q₈	—	53	8	no	—
980	C₂×#121	—	53	4	no	—
981	C₂×#120	—	53	4	no	—
982	#519	—	53	1	no	—
983	#519	—	53	4	no	—
984	#519	—	53	4	no	—
985	#519	—	53	1	no	—
986	#519	—	53	1	no	—
987	#519	—	53	4	no	—
988	#519	C₂×D₅₃	1	1	yes	characteristic, complemented
989	#518	—	53	1	no	—
990	#518	—	53	4	no	—
991	#518	—	53	4	no	—
992	#518	—	53	1	no	—
993	#518	—	53	1	no	—
994	#518	—	53	4	no	—
995	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
996	C₄×#41	—	53	1	no	—
997	C₄×#41	—	53	2	no	—
998	C₄×#41	—	53	4	no	—
999	C₄×#41	—	53	2	no	—
1000	C₄×#41	—	53	1	no	—
1001	C₄×#41	—	53	2	no	—
1002	C₄×#41	—	53	1	no	—
1003	C₄×#41	—	53	2	no	—
1004	C₄×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
1005	C₂×C₄×Q₈	—	53	2	no	—
1006	C₂×C₄×Q₈	—	53	4	no	—
1007	C₂×C₄×Q₈	—	53	4	no	—
1008	C₂×C₄×Q₈	—	53	4	no	—
1009	C₂×C₄×D₄	—	53	4	no	—
1010	C₂×C₄×D₄	—	53	4	no	—
1011	C₂×C₄×D₄	—	53	4	no	—
1012	C₂×C₄×D₄	—	53	2	no	—
1013	C₂×C₄×D₄	—	53	8	no	—
1014	C₂×#117	—	53	1	no	—
1015	C₂×#117	—	53	1	no	—
1016	C₂×#117	—	53	1	no	—
1017	C₂×#117	—	53	4	no	—
1018	C₂×#117	—	53	2	no	—
1019	C₂×#117	—	53	8	no	—
1020	C₂²×C₂²⋊C₄	—	53	4	no	—
1021	C₂²×C₂²⋊C₄	—	53	4	no	—
1022	C₂²×C₄²	—	53	1	no	—
1023	C₂²×C₄²	—	53	2	no	—
1024	C₅₃	C₂×#3510	1	1	yes	characteristic, complemented, Sylow
1025	C₂⁵	—	53	2	no	—
1026	C₂×#41	—	53	1	no	—
1027	C₂×#41	—	53	2	no	—
1028	C₂×#41	—	53	1	no	—
1029	C₂×#41	—	53	2	no	—
1030	C₂×#41	—	53	1	no	—
1031	C₂×#41	—	106	8	no	—
1032	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1033	C₂²×Q₈	—	53	2	no	—
1034	C₂²×Q₈	—	53	2	no	—
1035	C₂²×Q₈	—	53	1	no	—
1036	C₂²×Q₈	—	53	2	no	—
1037	C₂²×Q₈	—	53	2	no	—
1038	C₂²×Q₈	—	53	4	no	—
1039	C₂²×Q₈	—	53	2	no	—
1040	C₂²×Q₈	—	53	1	no	—
1041	C₂²×Q₈	—	106	8	no	—
1042	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1043	C₂²×D₄	—	53	2	no	—
1044	C₂²×D₄	—	53	2	no	—
1045	C₂²×D₄	—	53	2	no	—
1046	C₂²×D₄	—	53	2	no	—
1047	C₂²×D₄	—	53	1	no	—
1048	C₂²×D₄	—	53	2	no	—
1049	C₂²×D₄	—	53	2	no	—
1050	C₂²×D₄	—	53	8	no	—
1051	C₂²×D₄	—	53	1	no	—
1052	C₂²×D₄	—	106	8	no	—
1053	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1054	C₂³×C₄	—	53	1	no	—
1055	C₂³×C₄	—	53	2	no	—
1056	C₂³×C₄	—	53	2	no	—
1057	C₂³×C₄	—	53	2	no	—
1058	C₂³×C₄	—	53	8	no	—
1059	C₂³×C₄	—	53	4	no	—
1060	C₄⋊Q₈	—	53	4	no	—
1061	C₄⋊Q₈	—	53	2	no	—
1062	C₄⋊Q₈	—	53	2	no	—
1063	C₄⋊Q₈	—	53	4	no	—
1064	C₄⋊Q₈	—	53	2	no	—
1065	C₄⋊Q₈	—	53	2	no	—
1066	C₄⋊Q₈	—	53	8	no	—
1067	C₄⋊Q₈	—	53	2	no	—
1068	C₄⋊Q₈	—	53	2	no	—
1069	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
1070	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
1071	#127	—	53	8	no	—
1072	#127	—	53	2	no	—
1073	#127	—	53	2	no	—
1074	#127	—	53	2	no	—
1075	#127	C₂²×D₅₃	1	2	yes	—
1076	#126	—	53	8	no	—
1077	#126	—	53	8	no	—
1078	#126	—	53	8	no	—
1079	#126	—	53	8	no	—
1080	#126	—	53	8	no	—
1081	#126	—	53	8	no	—
1082	#126	—	53	8	no	—
1083	#126	—	53	8	no	—
1084	#126	—	53	8	no	—
1085	#126	—	53	8	no	—
1086	#126	—	53	8	no	—
1087	#126	—	53	8	no	—
1088	#126	—	53	8	no	—
1089	#126	—	53	8	no	—
1090	#126	C₂²×D₅₃	1	8	yes	complemented
1091	#126	C₂²×D₅₃	1	8	yes	complemented
1092	#125	—	53	4	no	—
1093	#125	—	53	4	no	—
1094	#125	—	53	2	no	—
1095	#125	—	53	2	no	—
1096	#125	—	53	2	no	—
1097	#125	C₂²×D₅₃	1	2	yes	complemented
1098	#124	—	53	2	no	—
1099	#124	—	53	2	no	—
1100	#124	—	53	4	no	—
1101	#124	—	53	2	no	—
1102	#124	—	53	2	no	—
1103	#124	—	53	8	no	—
1104	#124	—	53	2	no	—
1105	#124	—	53	2	no	—
1106	#124	—	53	4	no	—
1107	#124	—	53	2	no	—
1108	#124	—	53	2	no	—
1109	#124	—	53	8	no	—
1110	#124	—	53	8	no	—
1111	#124	—	53	8	no	—
1112	#124	—	53	8	no	—
1113	#124	—	53	8	no	—
1114	#124	—	53	8	no	—
1115	#124	—	53	8	no	—
1116	#124	—	53	8	no	—
1117	#124	—	53	8	no	—
1118	#124	—	53	8	no	—
1119	#124	—	53	8	no	—
1120	#124	—	53	2	no	—
1121	#124	—	53	2	no	—
1122	#124	—	53	4	no	—
1123	#124	—	53	2	no	—
1124	#124	—	53	2	no	—
1125	#124	—	53	8	no	—
1126	#124	C₂²×D₅₃	1	2	yes	—
1127	#124	C₂²×D₅₃	1	2	yes	—
1128	#124	C₂²×D₅₃	1	4	yes	—
1129	#124	C₂²×D₅₃	1	2	yes	—
1130	#124	C₂²×D₅₃	1	2	yes	complemented
1131	#124	C₂²×D₅₃	1	8	yes	complemented
1132	#123	—	53	8	no	—
1133	#123	—	53	4	no	—
1134	#123	—	53	8	no	—
1135	#123	—	53	8	no	—
1136	#123	—	53	4	no	—
1137	#123	—	53	8	no	—
1138	#123	—	53	8	no	—
1139	#123	—	53	8	no	—
1140	#123	—	53	8	no	—
1141	#123	—	53	8	no	—
1142	#123	—	53	8	no	—
1143	#123	—	53	8	no	—
1144	#123	—	53	8	no	—
1145	#123	—	53	8	no	—
1146	#123	—	53	8	no	—
1147	#123	—	53	4	no	—
1148	#123	—	53	8	no	—
1149	#123	—	53	8	no	—
1150	#123	—	53	8	no	—
1151	#123	C₂²×D₅₃	1	4	yes	—
1152	#123	C₂²×D₅₃	1	8	yes	complemented
1153	#123	C₂²×D₅₃	1	8	yes	complemented
1154	C₂²⋊Q₈	—	53	4	no	—
1155	C₂²⋊Q₈	—	53	4	no	—
1156	C₂²⋊Q₈	—	53	8	no	—
1157	C₂²⋊Q₈	—	53	4	no	—
1158	C₂²⋊Q₈	—	53	4	no	—
1159	C₂²⋊Q₈	—	53	8	no	—
1160	C₂²⋊Q₈	—	53	8	no	—
1161	C₂²⋊Q₈	—	53	4	no	—
1162	C₂²⋊Q₈	—	53	4	no	—
1163	C₂²⋊Q₈	—	53	4	no	—
1164	C₂²⋊Q₈	—	53	4	no	—
1165	C₂²⋊Q₈	—	53	8	no	—
1166	C₂²⋊Q₈	—	53	8	no	—
1167	C₂²⋊Q₈	—	53	8	no	—
1168	C₂²⋊Q₈	—	53	8	no	—
1169	C₂²⋊Q₈	—	53	4	no	—
1170	C₂²⋊Q₈	—	53	4	no	—
1171	C₂²⋊Q₈	—	53	8	no	—
1172	C₂²⋊Q₈	—	53	8	no	—
1173	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
1174	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1175	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
1176	#121	—	53	4	no	—
1177	#121	—	53	8	no	—
1178	#121	—	53	4	no	—
1179	#121	—	53	4	no	—
1180	#121	—	53	8	no	—
1181	#121	C₂²×D₅₃	1	4	yes	—
1182	#120	—	53	4	no	—
1183	#120	—	53	4	no	—
1184	#120	—	53	8	no	—
1185	#120	—	53	8	no	—
1186	#120	—	53	4	no	—
1187	#120	C₂²×D₅₃	1	4	yes	—
1188	C₄×Q₈	—	53	2	no	—
1189	C₄×Q₈	—	53	4	no	—
1190	C₄×Q₈	—	53	4	no	—
1191	C₄×Q₈	—	53	4	no	—
1192	C₄×Q₈	—	53	4	no	—
1193	C₄×Q₈	—	53	2	no	—
1194	C₄×Q₈	—	53	8	no	—
1195	C₄×Q₈	—	53	4	no	—
1196	C₄×Q₈	—	53	8	no	—
1197	C₄×Q₈	—	53	4	no	—
1198	C₄×Q₈	—	53	4	no	—
1199	C₄×Q₈	—	53	4	no	—
1200	C₄×Q₈	—	53	4	no	—
1201	C₄×Q₈	—	53	2	no	—
1202	C₄×Q₈	—	53	4	no	—
1203	C₄×Q₈	—	53	8	no	—
1204	C₄×Q₈	—	53	4	no	—
1205	C₄×Q₈	—	53	4	no	—
1206	C₄×Q₈	—	53	8	no	—
1207	C₄×Q₈	—	53	4	no	—
1208	C₄×Q₈	—	53	4	no	—
1209	C₄×Q₈	—	53	4	no	—
1210	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1211	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1212	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1213	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1214	C₄×D₄	—	53	4	no	—
1215	C₄×D₄	—	53	2	no	—
1216	C₄×D₄	—	53	4	no	—
1217	C₄×D₄	—	53	4	no	—
1218	C₄×D₄	—	53	8	no	—
1219	C₄×D₄	—	53	4	no	—
1220	C₄×D₄	—	53	4	no	—
1221	C₄×D₄	—	53	4	no	—
1222	C₄×D₄	—	53	8	no	—
1223	C₄×D₄	—	53	8	no	—
1224	C₄×D₄	—	53	8	no	—
1225	C₄×D₄	—	53	8	no	—
1226	C₄×D₄	—	53	4	no	—
1227	C₄×D₄	—	53	2	no	—
1228	C₄×D₄	—	53	4	no	—
1229	C₄×D₄	—	53	4	no	—
1230	C₄×D₄	—	53	8	no	—
1231	C₄×D₄	—	53	4	no	—
1232	C₄×D₄	—	53	4	no	—
1233	C₄×D₄	—	53	4	no	—
1234	C₄×D₄	—	53	8	no	—
1235	C₄×D₄	—	53	8	no	—
1236	C₄×D₄	—	53	8	no	—
1237	C₄×D₄	—	53	8	no	—
1238	C₄×D₄	—	53	4	no	—
1239	C₄×D₄	—	53	2	no	—
1240	C₄×D₄	—	53	4	no	—
1241	C₄×D₄	—	53	4	no	—
1242	C₄×D₄	—	53	8	no	—
1243	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1244	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1245	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1246	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1247	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1248	#117	—	53	1	no	—
1249	#117	—	53	2	no	—
1250	#117	—	53	1	no	—
1251	#117	—	53	1	no	—
1252	#117	—	53	4	no	—
1253	#117	—	53	8	no	—
1254	#117	—	53	2	no	—
1255	#117	—	53	4	no	—
1256	#117	—	53	2	no	—
1257	#117	—	53	2	no	—
1258	#117	—	53	8	no	—
1259	#117	—	53	8	no	—
1260	#117	—	53	8	no	—
1261	#117	—	53	2	no	—
1262	#117	—	53	4	no	—
1263	#117	—	53	2	no	—
1264	#117	—	53	2	no	—
1265	#117	—	53	4	no	—
1266	#117	—	53	4	no	—
1267	#117	—	53	8	no	—
1268	#117	—	53	8	no	—
1269	#117	—	53	2	no	—
1270	#117	—	53	2	no	—
1271	#117	—	53	2	no	—
1272	#117	—	53	2	no	—
1273	#117	—	53	2	no	—
1274	#117	—	53	8	no	—
1275	#117	—	53	8	no	—
1276	#117	—	53	8	no	—
1277	#117	C₂²×D₅₃	1	1	yes	characteristic
1278	#117	C₂²×D₅₃	1	1	yes	characteristic
1279	#117	C₂²×D₅₃	1	1	yes	characteristic
1280	#117	C₂²×D₅₃	1	4	yes	—
1281	#117	C₂²×D₅₃	1	2	yes	complemented
1282	#117	C₂²×D₅₃	1	8	yes	complemented
1283	C₂×C₄⋊C₄	—	53	4	no	—
1284	C₂×C₄⋊C₄	—	53	2	no	—
1285	C₂×C₄⋊C₄	—	53	2	no	—
1286	C₂×C₄⋊C₄	—	53	4	no	—
1287	C₂×C₄⋊C₄	—	53	2	no	—
1288	C₂×C₄⋊C₄	—	53	8	no	—
1289	C₂×C₄⋊C₄	—	53	8	no	—
1290	C₂×C₄⋊C₄	—	53	4	no	—
1291	C₂×C₄⋊C₄	—	53	4	no	—
1292	C₂×C₂²⋊C₄	—	53	4	no	—
1293	C₂×C₂²⋊C₄	—	53	4	no	—
1294	C₂×C₂²⋊C₄	—	53	8	no	—
1295	C₂×C₂²⋊C₄	—	53	4	no	—
1296	C₂×C₂²⋊C₄	—	53	4	no	—
1297	C₂×C₂²⋊C₄	—	53	2	no	—
1298	C₂×C₂²⋊C₄	—	53	2	no	—
1299	C₂×C₂²⋊C₄	—	53	8	no	—
1300	C₂×C₂²⋊C₄	—	53	8	no	—
1301	C₂×C₂²⋊C₄	—	53	4	no	—
1302	C₂×C₂²⋊C₄	—	53	4	no	—
1303	C₂×C₂²⋊C₄	—	53	8	no	—
1304	C₂×C₂²⋊C₄	—	53	8	no	—
1305	C₂×C₂²⋊C₄	—	53	8	no	—
1306	C₂×C₂²⋊C₄	—	53	8	no	—
1307	C₂×C₂²⋊C₄	—	53	2	no	—
1308	C₂×C₂²⋊C₄	—	53	4	no	—
1309	C₂×C₂²⋊C₄	—	53	8	no	—
1310	C₂×C₂²⋊C₄	—	53	8	no	—
1311	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
1312	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
1313	C₂×C₄²	—	53	2	no	—
1314	C₂×C₄²	—	53	1	no	—
1315	C₂×C₄²	—	53	4	no	—
1316	C₂×C₄²	—	53	2	no	—
1317	C₂×C₄²	—	53	2	no	—
1318	C₂×C₄²	—	53	8	no	—
1319	C₂×C₄²	—	53	4	no	—
1320	C₂×C₄²	—	53	1	no	—
1321	C₂×C₄²	—	53	2	no	—
1322	C₂×C₄²	—	53	2	no	—
1323	C₂×C₄²	—	53	2	no	—
1324	C₂×C₄²	—	53	2	no	—
1325	C₂×C₄²	—	53	1	no	—
1326	C₂×C₄²	—	53	1	no	—
1327	C₂×C₄²	—	53	4	no	—
1328	C₂×C₄²	—	53	2	no	—
1329	C₂×C₄²	—	53	2	no	—
1330	C₂×C₄²	—	53	1	no	—
1331	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1332	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
1333	C₂⁴	—	53	1	no	—
1334	C₂⁴	—	53	4	no	—
1335	C₂⁴	—	53	2	no	—
1336	C₂⁴	—	53	4	no	—
1337	C₂⁴	—	53	2	no	—
1338	C₂⁴	—	106	8	no	—
1339	C₂⁴	—	212	8	no	—
1340	C₂⁴	C₂³×D₅₃	1	2	yes	—
1341	#41	—	2	4	no	—
1342	#41	—	106	8	no	—
1343	#41	—	106	8	no	—
1344	#41	—	106	4	no	—
1345	#41	—	106	4	no	—
1346	#41	—	106	4	no	—
1347	C₂×Q₈	—	2	4	no	—
1348	C₂×Q₈	—	53	4	no	—
1349	C₂×Q₈	—	53	2	no	—
1350	C₂×Q₈	—	53	4	no	—
1351	C₂×Q₈	—	53	2	no	—
1352	C₂×Q₈	—	53	2	no	—
1353	C₂×Q₈	—	53	1	no	—
1354	C₂×Q₈	—	53	4	no	—
1355	C₂×Q₈	—	53	4	no	—
1356	C₂×Q₈	—	53	4	no	—
1357	C₂×Q₈	—	106	8	no	—
1358	C₂×Q₈	—	106	8	no	—
1359	C₂×Q₈	—	106	8	no	—
1360	C₂×Q₈	—	106	8	no	—
1361	C₂×Q₈	—	106	8	no	—
1362	C₂×Q₈	—	106	4	no	—
1363	C₂×Q₈	—	106	4	no	—
1364	C₂×Q₈	—	212	8	no	—
1365	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1366	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1367	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1368	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1369	C₂×D₄	—	2	4	no	—
1370	C₂×D₄	—	53	2	no	—
1371	C₂×D₄	—	53	2	no	—
1372	C₂×D₄	—	53	4	no	—
1373	C₂×D₄	—	53	4	no	—
1374	C₂×D₄	—	53	2	no	—
1375	C₂×D₄	—	53	8	no	—
1376	C₂×D₄	—	53	8	no	—
1377	C₂×D₄	—	53	2	no	—
1378	C₂×D₄	—	53	2	no	—
1379	C₂×D₄	—	53	2	no	—
1380	C₂×D₄	—	53	1	no	—
1381	C₂×D₄	—	53	8	no	—
1382	C₂×D₄	—	106	8	no	—
1383	C₂×D₄	—	106	8	no	—
1384	C₂×D₄	—	106	8	no	—
1385	C₂×D₄	—	106	8	no	—
1386	C₂×D₄	—	106	4	no	—
1387	C₂×D₄	—	106	8	no	—
1388	C₂×D₄	—	106	8	no	—
1389	C₂×D₄	—	106	4	no	—
1390	C₂×D₄	—	212	16	no	—
1391	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1392	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1393	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1394	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1395	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1396	C₂²×C₄	—	53	1	no	—
1397	C₂²×C₄	—	53	8	no	—
1398	C₂²×C₄	—	53	1	no	—
1399	C₂²×C₄	—	53	1	no	—
1400	C₂²×C₄	—	53	1	no	—
1401	C₂²×C₄	—	53	1	no	—
1402	C₂²×C₄	—	53	2	no	—
1403	C₂²×C₄	—	53	2	no	—
1404	C₂²×C₄	—	53	2	no	—
1405	C₂²×C₄	—	53	4	no	—
1406	C₂²×C₄	—	53	8	no	—
1407	C₂²×C₄	—	53	4	no	—
1408	C₂²×C₄	—	53	2	no	—
1409	C₂²×C₄	—	53	4	no	—
1410	C₂²×C₄	—	53	4	no	—
1411	C₂²×C₄	—	53	2	no	—
1412	C₂²×C₄	—	53	2	no	—
1413	C₂²×C₄	—	53	2	no	—
1414	C₂²×C₄	—	53	2	no	—
1415	C₂²×C₄	—	53	4	no	—
1416	C₂²×C₄	—	53	4	no	—
1417	C₂²×C₄	—	53	2	no	—
1418	C₂²×C₄	—	53	2	no	—
1419	C₂²×C₄	—	53	4	no	—
1420	C₂²×C₄	—	53	4	no	—
1421	C₂²×C₄	—	53	8	no	—
1422	C₂²×C₄	—	53	8	no	—
1423	C₂²×C₄	—	106	8	no	—
1424	C₂²×C₄	—	106	8	no	—
1425	C₂²×C₄	—	212	8	no	—
1426	C₂²×C₄	—	212	16	no	—
1427	C₂²×C₄	—	212	4	no	—
1428	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1429	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1430	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1431	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1432	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1433	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1434	C₄⋊C₄	—	53	4	no	—
1435	C₄⋊C₄	—	53	4	no	—
1436	C₄⋊C₄	—	53	4	no	—
1437	C₄⋊C₄	—	53	4	no	—
1438	C₄⋊C₄	—	53	2	no	—
1439	C₄⋊C₄	—	53	4	no	—
1440	C₄⋊C₄	—	53	2	no	—
1441	C₄⋊C₄	—	53	4	no	—
1442	C₄⋊C₄	—	53	4	no	—
1443	C₄⋊C₄	—	53	4	no	—
1444	C₄⋊C₄	—	53	4	no	—
1445	C₄⋊C₄	—	53	2	no	—
1446	C₄⋊C₄	—	53	8	no	—
1447	C₄⋊C₄	—	53	8	no	—
1448	C₄⋊C₄	—	53	8	no	—
1449	C₄⋊C₄	—	53	8	no	—
1450	C₄⋊C₄	—	53	8	no	—
1451	C₄⋊C₄	—	53	8	no	—
1452	C₄⋊C₄	—	53	4	no	—
1453	C₄⋊C₄	—	53	4	no	—
1454	C₄⋊C₄	—	53	4	no	—
1455	C₄⋊C₄	—	53	4	no	—
1456	C₄⋊C₄	—	53	4	no	—
1457	C₄⋊C₄	—	53	4	no	—
1458	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1459	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1460	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1461	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1462	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1463	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1464	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1465	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1466	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1467	C₂²⋊C₄	—	53	2	no	—
1468	C₂²⋊C₄	—	53	2	no	—
1469	C₂²⋊C₄	—	53	8	no	—
1470	C₂²⋊C₄	—	53	8	no	—
1471	C₂²⋊C₄	—	53	8	no	—
1472	C₂²⋊C₄	—	53	2	no	—
1473	C₂²⋊C₄	—	53	4	no	—
1474	C₂²⋊C₄	—	53	8	no	—
1475	C₂²⋊C₄	—	53	8	no	—
1476	C₂²⋊C₄	—	53	4	no	—
1477	C₂²⋊C₄	—	53	4	no	—
1478	C₂²⋊C₄	—	53	8	no	—
1479	C₂²⋊C₄	—	53	8	no	—
1480	C₂²⋊C₄	—	53	8	no	—
1481	C₂²⋊C₄	—	53	8	no	—
1482	C₂²⋊C₄	—	53	8	no	—
1483	C₂²⋊C₄	—	53	8	no	—
1484	C₂²⋊C₄	—	53	4	no	—
1485	C₂²⋊C₄	—	53	4	no	—
1486	C₂²⋊C₄	—	53	4	no	—
1487	C₂²⋊C₄	—	53	8	no	—
1488	C₂²⋊C₄	—	53	8	no	—
1489	C₂²⋊C₄	—	53	8	no	—
1490	C₂²⋊C₄	—	53	8	no	—
1491	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1492	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1493	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1494	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1495	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1496	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1497	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1498	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1499	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1500	C₄²	—	53	2	no	—
1501	C₄²	—	53	1	no	—
1502	C₄²	—	53	4	no	—
1503	C₄²	—	53	2	no	—
1504	C₄²	—	53	4	no	—
1505	C₄²	—	53	4	no	—
1506	C₄²	—	53	4	no	—
1507	C₄²	—	53	2	no	—
1508	C₄²	—	53	1	no	—
1509	C₄²	—	53	2	no	—
1510	C₄²	—	53	2	no	—
1511	C₄²	—	53	2	no	—
1512	C₄²	—	53	8	no	—
1513	C₄²	—	53	8	no	—
1514	C₄²	—	53	8	no	—
1515	C₄²	—	53	4	no	—
1516	C₄²	—	53	2	no	—
1517	C₄²	—	53	4	no	—
1518	C₄²	—	53	2	no	—
1519	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1520	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1521	C₄²	C₂³×D₅₃	1	2	yes	—
1522	C₄²	C₂³×D₅₃	1	2	yes	—
1523	C₄²	C₂³×D₅₃	1	4	yes	—
1524	C₄²	C₂³×D₅₃	1	8	yes	—
1525	C₄²	C₂³×D₅₃	1	2	yes	—
1526	C₄²	C₂³×D₅₃	1	2	yes	—
1527	C₂³	—	2	4	no	—
1528	C₂³	—	4	4	no	—
1529	C₂³	—	53	1	no	—
1530	C₂³	—	53	4	no	—
1531	C₂³	—	53	1	no	—
1532	C₂³	—	53	4	no	—
1533	C₂³	—	53	2	no	—
1534	C₂³	—	106	4	no	—
1535	C₂³	—	106	8	no	—
1536	C₂³	—	106	4	no	—
1537	C₂³	—	106	8	no	—
1538	C₂³	—	106	16	no	—
1539	C₂³	—	106	8	no	—
1540	C₂³	—	106	4	no	—
1541	C₂³	—	424	16	no	—
1542	C₂³	—	212	4	no	—
1543	C₂³	—	212	8	no	—
1544	C₂³	C₂⁴×D₅₃	1	4	yes	—
1545	C₂³	C₂⁴×D₅₃	1	2	yes	—
1546	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1547	Q₈	—	2	4	no	—
1548	Q₈	—	2	4	no	—
1549	Q₈	—	2	2	no	—
1550	Q₈	—	4	4	no	—
1551	Q₈	—	106	8	no	—
1552	Q₈	—	106	8	no	—
1553	Q₈	—	106	4	no	—
1554	Q₈	—	106	4	no	—
1555	Q₈	—	106	4	no	—
1556	Q₈	—	106	2	no	—
1557	Q₈	—	212	4	no	—
1558	Q₈	—	212	4	no	—
1559	Q₈	—	212	4	no	—
1560	D₄	—	2	4	no	—
1561	D₄	—	2	4	no	—
1562	D₄	—	2	4	no	—
1563	D₄	—	2	2	no	—
1564	D₄	—	4	8	no	—
1565	D₄	—	106	4	no	—
1566	D₄	—	106	8	no	—
1567	D₄	—	106	8	no	—
1568	D₄	—	106	4	no	—
1569	D₄	—	106	4	no	—
1570	D₄	—	106	4	no	—
1571	D₄	—	106	4	no	—
1572	D₄	—	106	4	no	—
1573	D₄	—	106	2	no	—
1574	D₄	—	212	8	no	—
1575	D₄	—	212	8	no	—
1576	D₄	—	212	8	no	—
1577	C₂×C₄	—	2	4	no	—
1578	C₂×C₄	—	2	4	no	—
1579	C₂×C₄	—	4	4	no	—
1580	C₂×C₄	—	4	8	no	—
1581	C₂×C₄	—	4	2	no	—
1582	C₂×C₄	—	53	4	no	—
1583	C₂×C₄	—	53	1	no	—
1584	C₂×C₄	—	53	1	no	—
1585	C₂×C₄	—	53	4	no	—
1586	C₂×C₄	—	53	4	no	—
1587	C₂×C₄	—	53	4	no	—
1588	C₂×C₄	—	53	4	no	—
1589	C₂×C₄	—	53	2	no	—
1590	C₂×C₄	—	53	4	no	—
1591	C₂×C₄	—	53	4	no	—
1592	C₂×C₄	—	53	4	no	—
1593	C₂×C₄	—	53	2	no	—
1594	C₂×C₄	—	53	2	no	—
1595	C₂×C₄	—	53	4	no	—
1596	C₂×C₄	—	106	4	no	—
1597	C₂×C₄	—	106	4	no	—
1598	C₂×C₄	—	106	8	no	—
1599	C₂×C₄	—	106	8	no	—
1600	C₂×C₄	—	106	8	no	—
1601	C₂×C₄	—	106	4	no	—
1602	C₂×C₄	—	106	8	no	—
1603	C₂×C₄	—	106	4	no	—
1604	C₂×C₄	—	106	8	no	—
1605	C₂×C₄	—	106	4	no	—
1606	C₂×C₄	—	106	4	no	—
1607	C₂×C₄	—	106	4	no	—
1608	C₂×C₄	—	212	4	no	—
1609	C₂×C₄	—	212	4	no	—
1610	C₂×C₄	—	212	8	no	—
1611	C₂×C₄	—	212	2	no	—
1612	C₂×C₄	—	212	8	no	—
1613	C₂×C₄	—	212	2	no	—
1614	C₂×C₄	—	212	4	no	—
1615	C₂×C₄	—	212	8	no	—
1616	C₂×C₄	—	212	2	no	—
1617	C₂×C₄	#41×D₅₃	1	4	yes	—
1618	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1619	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1620	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1621	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1622	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1623	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1624	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1625	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1626	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1627	C₂²	—	2	2	no	—
1628	C₂²	—	2	2	no	—
1629	C₂²	—	2	4	no	—
1630	C₂²	—	2	4	no	—
1631	C₂²	—	2	8	no	—
1632	C₂²	—	8	4	no	—
1633	C₂²	—	53	2	no	—
1634	C₂²	—	53	4	no	—
1635	C₂²	—	53	2	no	—
1636	C₂²	—	106	8	no	—
1637	C₂²	—	106	2	no	—
1638	C₂²	—	106	2	no	—
1639	C₂²	—	106	4	no	—
1640	C₂²	—	106	4	no	—
1641	C₂²	—	106	8	no	—
1642	C₂²	—	424	4	no	—
1643	C₂²	—	424	8	no	—
1644	C₂²	—	212	16	no	—
1645	C₂²	—	212	8	no	—
1646	C₂²	C₂×#41×D₅₃	1	2	yes	—
1647	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1648	C₄	—	2	2	no	—
1649	C₄	—	2	4	no	—
1650	C₄	—	2	2	no	—
1651	C₄	—	2	4	no	—
1652	C₄	—	2	4	no	—
1653	C₄	—	2	2	no	—
1654	C₄	—	2	4	no	—
1655	C₄	—	53	2	no	—
1656	C₄	—	53	2	no	—
1657	C₄	—	106	2	no	—
1658	C₄	—	106	4	no	—
1659	C₄	—	106	2	no	—
1660	C₄	—	106	4	no	—
1661	C₄	—	106	4	no	—
1662	C₄	—	106	2	no	—
1663	C₄	—	106	4	no	—
1664	C₄	C₂×#41×D₅₃	1	2	yes	—
1665	C₄	C₂×#41×D₅₃	1	2	yes	—
1666	C₂	—	2	2	no	—
1667	C₂	—	4	4	no	—
1668	C₂	—	4	2	no	—
1669	C₂	—	53	4	no	—
1670	C₂	—	106	2	no	—
1671	C₂	—	212	4	no	—
1672	C₂	—	212	2	no	—
1673	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1674	C₂	#585×D₅₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3510	C₂
prime radical	#535×D₅₃	C₂
hypercenter	#3510	D₅₃
hypocenter	C₅₃	C₂×#3510
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3510

Complements

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

N	H ≅ G/N	type
1. #20288614	C₂	semidirect
2. #20288613	C₂	semidirect
3. #20288612	C₂	semidirect
4. #20288611	C₂	semidirect
5. #20288610	C₂	semidirect
6. #20288609	C₂	semidirect
7. #20288608	C₂	semidirect
8. #20288607	C₂	semidirect
9. #20288606	C₂	semidirect
10. #20288605	C₂	semidirect
11. #20288604	C₂	semidirect
12. #20288603	C₂	semidirect
13. #559×D₅₃	C₂	semidirect
14. #556×D₅₃	C₂	semidirect
15. #551×D₅₃	C₂	semidirect
16. #542×D₅₃	C₂	semidirect
17. #536×D₅₃	C₂	semidirect
19. #533×D₅₃	C₂	semidirect
20. #529×D₅₃	C₂	semidirect
21. C₂×#124×D₅₃	C₂	semidirect
22. #519×D₅₃	C₂	semidirect
23. #518×D₅₃	C₂	semidirect
24. C₄×#41×D₅₃	C₂	semidirect
25. C₅₃×#3510	C₂	semidirect
29. #16811359	C₂²	semidirect
30. #16811358	C₂²	semidirect
31. #16811358	C₂²	semidirect
32. #16811357	C₂²	semidirect
33. #16811357	C₂²	semidirect
34. #16811356	C₂²	semidirect
35. #16811356	C₂²	semidirect
36. #16811356	C₂²	semidirect
37. #16811355	C₂²	semidirect
38. #16811355	C₂²	semidirect
39. #16811355	C₂²	semidirect
40. #16811347	C₂²	semidirect
41. #16811346	C₂²	semidirect
42. #16811345	C₂²	semidirect
43. #16811345	C₂²	semidirect
44. #16811344	C₂²	semidirect
45. #16811343	C₂²	semidirect
46. #16811342	C₂²	semidirect
47. #16811342	C₂²	semidirect
48. #16811341	C₂²	semidirect
49. #16811340	C₂²	semidirect
50. #16811340	C₂²	semidirect
51. #16811304	C₂²	semidirect
52. #16811303	C₂²	semidirect
53. #16811302	C₂²	semidirect
54. #16811302	C₂²	semidirect
55. #16811301	C₂²	semidirect
56. #16811300	C₂²	semidirect
57. #16811300	C₂²	semidirect
58. #16811299	C₂²	semidirect
59. #16811299	C₂²	semidirect
60. #16811298	C₂²	semidirect
61. #16811298	C₂²	semidirect
62. #16811297	C₂²	semidirect
63. #16811297	C₂²	semidirect
64. #16811296	C₂²	semidirect
65. #16811296	C₂²	semidirect
66. #16811247	C₂²	semidirect
67. #16811246	C₂²	semidirect
68. #16811245	C₂²	semidirect
69. #16811244	C₂²	semidirect
70. #16811243	C₂²	semidirect
71. #16811242	C₂²	semidirect
72. #16811241	C₂²	semidirect
73. #16811240	C₂²	semidirect
74. #16811239	C₂²	semidirect
75. #16811238	C₂²	semidirect
76. #16811237	C₂²	semidirect
77. #16811199	C₂²	semidirect
78. #16811198	C₂²	semidirect
79. #16811197	C₂²	semidirect
80. #16811196	C₂²	semidirect
81. #16811195	C₂²	semidirect
82. #16811194	C₂²	semidirect
83. #16811193	C₂²	semidirect
91. #16811180	C₂²	semidirect
92. #16811179	C₂²	semidirect
93. #16811178	C₂²	semidirect
94. #16811177	C₂²	semidirect
95. #16811176	C₂²	semidirect
96. #16811176	C₂²	semidirect
97. #16811175	C₂²	semidirect
98. C₄⋊Q₈×D₅₃	C₂²	semidirect
99. C₄⋊Q₈×D₅₃	C₂²	semidirect
101. #16811160	C₂²	semidirect
102. #16811159	C₂²	semidirect
103. #16811158	C₂²	semidirect
104. #16811157	C₂²	semidirect
105. #16811156	C₂²	semidirect
106. #16811155	C₂²	semidirect
107. #16811154	C₂²	semidirect
108. #16811153	C₂²	semidirect
109. #16811152	C₂²	semidirect
110. #16811151	C₂²	semidirect
111. #16811150	C₂²	semidirect
112. #126×D₅₃	C₂²	semidirect
113. #126×D₅₃	C₂²	semidirect
114. #125×D₅₃	C₂²	semidirect
115. C₂×#13133206	C₂²	semidirect
116. C₂×#13133205	C₂²	semidirect
117. C₂×#13133204	C₂²	semidirect
118. C₂×#13133203	C₂²	semidirect
123. #124×D₅₃	C₂²	semidirect
124. #124×D₅₃	C₂²	semidirect
125. #124×D₅₃	C₂²	semidirect
126. #124×D₅₃	C₂²	semidirect
127. #124×D₅₃	C₂²	semidirect
129. #123×D₅₃	C₂²	semidirect
130. #123×D₅₃	C₂²	semidirect
132. C₂²⋊Q₈×D₅₃	C₂²	semidirect
133. C₂²⋊Q₈×D₅₃	C₂²	semidirect
136. #16811101	C₂²	semidirect
137. #16811100	C₂²	semidirect
138. #16811100	C₂²	semidirect
139. #16811100	C₂²	semidirect
140. #16811099	C₂²	semidirect
141. #16811099	C₂²	semidirect
142. #16811098	C₂²	semidirect
143. #16811097	C₂²	semidirect
144. #16811097	C₂²	semidirect
145. #16811096	C₂²	semidirect
146. #16811095	C₂²	semidirect
147. #16811095	C₂²	semidirect
148. #41×Dic₅₃	C₂²	semidirect
149. C₄×#11719949	C₂²	semidirect
150. C₄×#11719945	C₂²	semidirect
151. C₄×#11719945	C₂²	semidirect
152. #16811091	C₂²	semidirect
153. #16811091	C₂²	semidirect
154. C₄×#11719947	C₂²	semidirect
155. C₄×#11719947	C₂²	semidirect
156. C₄×Q₈×D₅₃	C₂²	semidirect
157. C₄×Q₈×D₅₃	C₂²	semidirect
158. C₄×Q₈×D₅₃	C₂²	semidirect
159. C₄×Q₈×D₅₃	C₂²	semidirect
163. C₄×D₄×D₅₃	C₂²	semidirect
164. C₄×D₄×D₅₃	C₂²	semidirect
169. #117×D₅₃	C₂²	semidirect
170. #117×D₅₃	C₂²	semidirect
174. C₂×C₄²×D₅₃	C₂²	semidirect
175. C₅₃×#559	C₂²	semidirect
176. C₅₃×#556	C₂²	semidirect
177. C₅₃×#551	C₂²	semidirect
178. C₅₃×#542	C₂²	semidirect
179. C₅₃×#536	C₂²	semidirect
181. C₅₃×#533	C₂²	semidirect
182. C₅₃×#529	C₂²	semidirect
183. C₂×#124×C₅₃	C₂²	semidirect
184. C₅₃×#519	C₂²	semidirect
185. C₅₃×#518	C₂²	semidirect
186. C₄×#41×C₅₃	C₂²	semidirect
219. #13133217	C₂³	semidirect
220. #13133217	C₂³	semidirect
221. #13133216	C₂³	semidirect
222. #13133216	C₂³	semidirect
223. #13133216	C₂³	semidirect
224. #13133216	C₂³	semidirect
225. #13133215	C₂³	semidirect
226. #13133215	C₂³	semidirect
227. #13133215	C₂³	semidirect
232. #13133212	C₂³	semidirect
233. #13133212	C₂³	semidirect
234. #13133212	C₂³	semidirect
235. #13133212	C₂³	semidirect
236. #13133212	C₂³	semidirect
237. #13133212	C₂³	semidirect
238. #13133211	C₂³	semidirect
239. #13133211	C₂³	semidirect
240. #13133210	C₂³	semidirect
241. #13133210	C₂³	semidirect
242. #13133210	C₂³	semidirect
243. #13133210	C₂³	semidirect
244. #13133210	C₂³	semidirect
245. #13133210	C₂³	semidirect
246. #13133209	C₂³	semidirect
247. #13133208	C₂³	semidirect
248. #13133208	C₂³	semidirect
249. #13133207	C₂³	semidirect
250. #13133207	C₂³	semidirect
255. #13133206	C₂³	semidirect
256. #13133206	C₂³	semidirect
261. #13133205	C₂³	semidirect
262. #13133205	C₂³	semidirect
267. #13133204	C₂³	semidirect
268. #13133204	C₂³	semidirect
274. #13133203	C₂³	semidirect
275. #13133203	C₂³	semidirect
276. #13133203	C₂³	semidirect
277. #13133203	C₂³	semidirect
278. #13133203	C₂³	semidirect
280. #13133202	C₂³	semidirect
281. #13133202	C₂³	semidirect
282. #13133202	C₂³	semidirect
283. #13133202	C₂³	semidirect
285. #13133201	C₂³	semidirect
286. #13133201	C₂³	semidirect
288. #13133200	C₂³	semidirect
289. #13133200	C₂³	semidirect
291. #13133199	C₂³	semidirect
292. #13133199	C₂³	semidirect
293. #13133199	C₂³	semidirect
294. #13133199	C₂³	semidirect
296. #13133198	C₂³	semidirect
297. #13133198	C₂³	semidirect
299. #13133197	C₂³	semidirect
300. #13133197	C₂³	semidirect
302. #13133196	C₂³	semidirect
303. #13133196	C₂³	semidirect
306. #13133195	C₂³	semidirect
307. #13133195	C₂³	semidirect
308. #13133195	C₂³	semidirect
311. #13133194	C₂³	semidirect
312. #13133194	C₂³	semidirect
313. #13133194	C₂³	semidirect
315. #13133193	C₂³	semidirect
316. #13133193	C₂³	semidirect
327. Q₈×Dic₅₃	C₂³	semidirect
328. Q₈×Dic₅₃	C₂³	semidirect
329. Q₈×Dic₅₃	C₂³	semidirect
330. Q₈×Dic₅₃	C₂³	semidirect
331. C₄×Dic₁₀₆	C₂³	semidirect
332. C₄×Dic₁₀₆	C₂³	semidirect
333. C₄×Dic₁₀₆	C₂³	semidirect
334. C₄×Dic₁₀₆	C₂³	semidirect
335. C₄×Dic₁₀₆	C₂³	semidirect
336. C₄×Dic₁₀₆	C₂³	semidirect
337. C₄×Dic₁₀₆	C₂³	semidirect
338. C₄×Dic₁₀₆	C₂³	semidirect
339. C₄×Dic₁₀₆	C₂³	semidirect
340. #13133182	C₂³	semidirect
341. #13133182	C₂³	semidirect
342. #13133182	C₂³	semidirect
343. #13133182	C₂³	semidirect
344. #13133182	C₂³	semidirect
345. #13133182	C₂³	semidirect
346. #13133182	C₂³	semidirect
347. #13133182	C₂³	semidirect
348. #13133182	C₂³	semidirect
352. C₄×D₂₁₂	C₂³	semidirect
353. C₄×D₂₁₂	C₂³	semidirect
357. D₄×Dic₅₃	C₂³	semidirect
358. D₄×Dic₅₃	C₂³	semidirect
362. #13133179	C₂³	semidirect
363. #13133179	C₂³	semidirect
368. C₄×C₂²⋊D₅₃	C₂³	semidirect
369. C₄×C₂²⋊D₅₃	C₂³	semidirect
370. C₄×C₂²⋊D₅₃	C₂³	semidirect
375. #13133177	C₂³	semidirect
376. #13133177	C₂³	semidirect
377. #13133177	C₂³	semidirect
382. #13133176	C₂³	semidirect
383. #13133176	C₂³	semidirect
388. #13133175	C₂³	semidirect
389. #13133175	C₂³	semidirect
390. #13133175	C₂³	semidirect
395. #13133174	C₂³	semidirect
396. #13133174	C₂³	semidirect
397. #13133174	C₂³	semidirect
398. #13133174	C₂³	semidirect
404. #13133173	C₂³	semidirect
405. #13133173	C₂³	semidirect
406. #13133173	C₂³	semidirect
437. C₂×C₄×Dic₅₃	C₂³	semidirect
438. C₂×C₄×Dic₅₃	C₂³	semidirect
450. C₄²×D₅₃	C₂³	semidirect
451. C₄²×D₅₃	C₂³	semidirect
452. C₄²×D₅₃	C₂³	semidirect
456. C₄⋊Q₈×C₅₃	C₂³	semidirect
457. C₄⋊Q₈×C₅₃	C₂³	semidirect
459. #126×C₅₃	C₂³	semidirect
460. #126×C₅₃	C₂³	semidirect
461. #125×C₅₃	C₂³	semidirect
466. #124×C₅₃	C₂³	semidirect
467. #124×C₅₃	C₂³	semidirect
469. #123×C₅₃	C₂³	semidirect
470. #123×C₅₃	C₂³	semidirect
472. C₂²⋊Q₈×C₅₃	C₂³	semidirect
473. C₂²⋊Q₈×C₅₃	C₂³	semidirect
476. C₄×Q₈×C₅₃	C₂³	semidirect
477. C₄×Q₈×C₅₃	C₂³	semidirect
478. C₄×Q₈×C₅₃	C₂³	semidirect
479. C₄×Q₈×C₅₃	C₂³	semidirect
483. C₄×D₄×C₅₃	C₂³	semidirect
484. C₄×D₄×C₅₃	C₂³	semidirect
489. #117×C₅₃	C₂³	semidirect
490. #117×C₅₃	C₂³	semidirect
494. C₂×C₄²×C₅₃	C₂³	semidirect
841. #3510	D₅₃	direct (N × H)
862. D₅₃	#3510	direct (N × H)
877. #559	C₂×D₅₃	semidirect
889. #556	C₂×D₅₃	semidirect
905. #551	C₂×D₅₃	semidirect
917. #542	C₂×D₅₃	semidirect
925. #536	C₂×D₅₃	semidirect
941. #533	C₂×D₅₃	semidirect
956. #529	C₂×D₅₃	semidirect
973. C₂×#124	C₂×D₅₃	semidirect
988. #519	C₂×D₅₃	semidirect
995. #518	C₂×D₅₃	semidirect
1004. C₄×#41	C₂×D₅₃	semidirect
1024. C₅₃	C₂×#3510	semidirect
1069. C₄⋊Q₈	C₂²×D₅₃	semidirect
1070. C₄⋊Q₈	C₂²×D₅₃	semidirect
1090. #126	C₂²×D₅₃	semidirect
1091. #126	C₂²×D₅₃	semidirect
1097. #125	C₂²×D₅₃	semidirect
1130. #124	C₂²×D₅₃	semidirect
1131. #124	C₂²×D₅₃	semidirect
1152. #123	C₂²×D₅₃	semidirect
1153. #123	C₂²×D₅₃	semidirect
1174. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1175. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1210. C₄×Q₈	C₂²×D₅₃	semidirect
1211. C₄×Q₈	C₂²×D₅₃	semidirect
1212. C₄×Q₈	C₂²×D₅₃	semidirect
1213. C₄×Q₈	C₂²×D₅₃	semidirect
1246. C₄×D₄	C₂²×D₅₃	semidirect
1247. C₄×D₄	C₂²×D₅₃	semidirect
1281. #117	C₂²×D₅₃	semidirect
1282. #117	C₂²×D₅₃	semidirect
1332. C₂×C₄²	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288614	2
#20288613	2
#20288612	2
#20288611	2
#20288610	2
#20288609	2
#20288608	2
#20288607	2
#20288606	2
#20288605	2
#20288604	2
#20288603	2
#559×D₅₃	2
#556×D₅₃	2
#551×D₅₃	2
#542×D₅₃	2
#536×D₅₃	2
#535×D₅₃	2
#533×D₅₃	2
#529×D₅₃	2
C₂×#124×D₅₃	2
#519×D₅₃	2
#518×D₅₃	2
C₄×#41×D₅₃	2
C₅₃×#3510	2
C₂×#3510	53

Subgroups — D53×#3510 #28292574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3510 #28292574