Subgroups — D₅₃×#3489 #28292488

Order 13568.

11438 conjugacy classes of subgroups.

The subgroup lattice has 1658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×2₋¹⁺⁴×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288396	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288395	C₂	1	1	yes	maximal, characteristic, complemented
5	#20288394	C₂	1	2	yes	maximal, complemented
6	#20288393	C₂	1	3	yes	maximal, complemented
7	#20288392	C₂	1	2	yes	maximal, complemented
8	#20288391	C₂	1	3	yes	maximal, complemented
9	#20288390	C₂	1	3	yes	maximal, complemented
10	#20288389	C₂	1	6	yes	maximal, complemented
11	#20288388	C₂	1	1	yes	maximal, characteristic, complemented
12	#20288387	C₂	1	3	yes	maximal, complemented
13	#20288386	C₂	1	6	yes	maximal, complemented
14	D₄×Q₈×D₅₃	C₂	1	2	yes	maximal, complemented
15	#548×D₅₃	C₂	1	2	yes	maximal, complemented
16	#547×D₅₃	C₂	1	6	yes	maximal, complemented
17	#546×D₅₃	C₂	1	6	yes	maximal, complemented
18	#537×D₅₃	C₂	1	3	yes	maximal, complemented
19	#536×D₅₃	C₂	1	3	yes	maximal, complemented
20	#525×D₅₃	C₂	1	3	yes	maximal, complemented
21	C₂×C₂²⋊Q₈×D₅₃	C₂	1	3	yes	maximal, complemented
22	#520×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133265	C₂²	1	3	yes	complemented
25	C₂×#13133265	C₂²	1	2	yes	complemented
26	C₂×#13133264	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13133264	C₂²	1	6	yes	complemented
28	C₂×#13133264	C₂²	1	3	yes	complemented
29	2₋¹⁺⁴×D₅₃	—	2	16	no	—
30	C₂²×#11719949	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#11719945	C₂²	1	3	yes	complemented
32	C₂²×#11719947	C₂²	1	3	yes	complemented
33	C₂×#41×D₅₃	—	2	16	no	—
34	C₂×#41×D₅₃	C₂²	1	3	yes	—
35	C₂×#41×D₅₃	C₂²	1	3	yes	—
36	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
37	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
38	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
40	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
41	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
43	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
44	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×D₅₃	C₂²	1	3	yes	complemented
46	C₂²×Q₈×D₅₃	C₂²	1	2	yes	complemented
47	C₂²×D₄×D₅₃	C₂²	1	3	yes	—
48	C₂³×C₄×D₅₃	C₂²	1	3	yes	—
49	Q₈×D₂₁₂	C₂²	1	2	yes	complemented
50	D₄×Dic₁₀₆	C₂²	1	6	yes	complemented
51	#16811288	C₂²	1	6	yes	complemented
52	Q₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
53	Q₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
54	#16811286	C₂²	1	6	yes	complemented
55	#16811286	C₂²	1	6	yes	complemented
56	#16811285	C₂²	1	2	yes	complemented
57	#16811284	C₂²	1	2	yes	complemented
58	#16811283	C₂²	1	6	yes	complemented
59	#16811282	C₂²	1	6	yes	complemented
60	#16811281	C₂²	1	6	yes	complemented
61	#16811280	C₂²	1	2	yes	complemented
62	#16811279	C₂²	1	6	yes	complemented
63	#16811278	C₂²	1	6	yes	complemented
64	#16811277	C₂²	1	6	yes	complemented
65	#16811276	C₂²	1	6	yes	complemented
66	#16811275	C₂²	1	6	yes	complemented
67	#16811275	C₂²	1	6	yes	complemented
68	#16811274	C₂²	1	12	yes	complemented
69	#16811273	C₂²	1	12	yes	complemented
70	#16811272	C₂²	1	6	yes	complemented
71	#16811272	C₂²	1	6	yes	complemented
72	#16811271	C₂²	1	12	yes	complemented
73	#16811271	C₂²	1	12	yes	complemented
74	#16811270	C₂²	1	6	yes	complemented
75	#16811269	C₂²	1	6	yes	complemented
76	#16811268	C₂²	1	6	yes	complemented
77	#16811267	C₂²	1	6	yes	complemented
78	#16811266	C₂²	1	6	yes	complemented
79	#16811265	C₂²	1	12	yes	complemented
80	#16811264	C₂²	1	6	yes	complemented
81	#16811263	C₂²	1	12	yes	complemented
82	#16811262	C₂²	1	12	yes	complemented
83	#16811261	C₂²	1	6	yes	complemented
84	#16811260	C₂²	1	12	yes	complemented
85	#16811204	C₂²	1	3	yes	complemented
86	#16811203	C₂²	1	6	yes	complemented
87	#16811203	C₂²	1	6	yes	complemented
88	#16811202	C₂²	1	6	yes	complemented
89	#16811202	C₂²	1	6	yes	complemented
90	#16811201	C₂²	1	3	yes	complemented
91	#16811201	C₂²	1	3	yes	complemented
92	#16811200	C₂²	1	12	yes	complemented
93	#16811199	C₂²	1	3	yes	complemented
94	#16811198	C₂²	1	6	yes	complemented
95	#16811197	C₂²	1	3	yes	complemented
96	#16811196	C₂²	1	6	yes	complemented
97	#16811196	C₂²	1	6	yes	complemented
98	#16811195	C₂²	1	12	yes	complemented
99	#16811194	C₂²	1	3	yes	complemented
100	#16811193	C₂²	1	6	yes	complemented
101	C₄⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
102	#124×D₅₃	C₂²	1	6	yes	complemented
103	#16811136	C₂²	1	3	yes	complemented
104	#16811136	C₂²	1	3	yes	complemented
105	#16811135	C₂²	1	3	yes	complemented
106	#16811134	C₂²	1	3	yes	complemented
107	#16811133	C₂²	1	3	yes	complemented
108	#16811133	C₂²	1	3	yes	complemented
109	#16811132	C₂²	1	6	yes	complemented
110	#16811132	C₂²	1	6	yes	complemented
111	#16811131	C₂²	1	6	yes	complemented
112	#16811130	C₂²	1	3	yes	complemented
113	#16811129	C₂²	1	6	yes	complemented
114	#123×D₅₃	C₂²	1	12	yes	complemented
115	#123×D₅₃	C₂²	1	6	yes	complemented
116	C₂×#13133197	C₂²	1	3	yes	complemented
117	C₂×#13133196	C₂²	1	3	yes	complemented
118	C₂×#13133195	C₂²	1	6	yes	complemented
119	C₂×#13133194	C₂²	1	6	yes	complemented
120	C₂×#13133193	C₂²	1	3	yes	complemented
121	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	—
122	C₂²⋊Q₈×D₅₃	C₂²	1	3	yes	—
123	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
124	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
125	C₂²⋊Q₈×D₅₃	C₂²	1	3	yes	complemented
126	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
127	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
128	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
129	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
130	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
131	#121×D₅₃	C₂²	1	1	yes	characteristic
132	#121×D₅₃	C₂²	1	3	yes	complemented
133	#121×D₅₃	C₂²	1	12	yes	complemented
134	#121×D₅₃	C₂²	1	6	yes	complemented
135	#120×D₅₃	C₂²	1	6	yes	—
136	#16811106	C₂²	1	1	yes	characteristic, complemented
137	#16811105	C₂²	1	2	yes	complemented
138	#16811104	C₂²	1	3	yes	complemented
139	#16811103	C₂²	1	3	yes	complemented
140	#16811102	C₂²	1	6	yes	complemented
141	C₄×Q₈×D₅₃	C₂²	1	2	yes	complemented
142	C₄×D₄×D₅₃	C₂²	1	6	yes	—
143	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
144	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
145	#117×D₅₃	C₂²	1	3	yes	complemented
146	C₂×C₄⋊C₄×D₅₃	C₂²	1	3	yes	complemented
147	C₂×C₄⋊C₄×D₅₃	C₂²	1	6	yes	complemented
148	C₂×C₂²⋊C₄×D₅₃	C₂²	1	6	yes	—
149	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
150	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
151	D₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
152	C₅₃×#548	C₂²	1	2	yes	complemented
153	C₅₃×#547	C₂²	1	6	yes	complemented
154	C₅₃×#546	C₂²	1	6	yes	complemented
155	C₅₃×#537	C₂²	1	3	yes	complemented
156	C₅₃×#536	C₂²	1	3	yes	complemented
157	C₅₃×#525	C₂²	1	3	yes	complemented
158	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	3	yes	complemented
159	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
160	C₂⁴×D₅₃	C₂³	1	3	yes	—
161	#13133265	—	2	16	no	—
162	#13133265	—	2	24	no	—
163	#13133264	—	2	8	no	—
164	#13133264	—	2	48	no	—
165	#13133264	—	2	24	no	—
166	C₂×#11719949	—	2	8	no	—
167	C₂×#11719949	C₂³	1	3	yes	—
168	C₂×#11719949	C₂³	1	1	yes	characteristic
169	C₂×#11719949	C₂³	1	3	yes	—
170	C₂×#11719949	C₂³	1	1	yes	characteristic
171	C₂×#11719949	C₂³	1	6	yes	complemented
172	C₂×#11719949	C₂³	1	3	yes	complemented
173	C₂×#11719945	—	2	24	no	—
174	C₂×#11719945	C₂³	1	6	yes	—
175	C₂×#11719945	C₂³	1	3	yes	—
176	C₂×#11719945	C₂³	1	3	yes	—
177	C₂×#11719945	C₂³	1	6	yes	—
178	C₂×#11719945	C₂³	1	3	yes	—
179	C₂×#11719945	C₂³	1	3	yes	—
180	C₂×#11719945	C₂³	1	12	yes	complemented
181	C₂×#11719945	C₂³	1	6	yes	complemented
182	C₂×#11719945	C₂³	1	6	yes	complemented
183	C₂×#11719945	C₂³	1	3	yes	complemented
184	C₂×#11719947	—	2	24	no	—
185	C₂×#11719947	C₂³	1	6	yes	—
186	C₂×#11719947	C₂³	1	3	yes	—
187	C₂×#11719947	C₂³	1	3	yes	—
188	C₂×#11719947	C₂³	1	3	yes	—
189	C₂×#11719947	C₂³	1	6	yes	—
190	C₂×#11719947	C₂³	1	3	yes	—
191	C₂×#11719947	C₂³	1	6	yes	complemented
192	C₂×#11719947	C₂³	1	12	yes	complemented
193	C₂×#11719947	C₂³	1	6	yes	complemented
194	C₂×#11719947	C₂³	1	3	yes	complemented
195	#41×D₅₃	—	2	8	no	—
196	#41×D₅₃	—	2	8	no	—
197	#41×D₅₃	—	2	8	no	—
198	#41×D₅₃	—	2	24	no	—
199	#41×D₅₃	—	2	24	no	—
200	#41×D₅₃	—	2	48	no	—
201	#41×D₅₃	—	2	24	no	—
202	#41×D₅₃	—	2	24	no	—
203	#41×D₅₃	—	2	24	no	—
204	#41×D₅₃	D₄	1	16	yes	complemented
205	C₂²×Dic₁₀₆	C₂³	1	3	yes	—
206	C₂²×Dic₁₀₆	C₂³	1	6	yes	complemented
207	C₂²×Dic₁₀₆	C₂³	1	6	yes	complemented
208	C₂²×Dic₁₀₆	C₂³	1	3	yes	complemented
209	C₂×Q₈×D₅₃	—	2	8	no	—
210	C₂×Q₈×D₅₃	—	2	16	no	—
211	C₂×Q₈×D₅₃	—	2	24	no	—
212	C₂×Q₈×D₅₃	C₂³	1	3	yes	—
213	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
214	C₂×Q₈×D₅₃	C₂³	1	3	yes	—
215	C₂×Q₈×D₅₃	C₂³	1	6	yes	—
216	C₂×Q₈×D₅₃	C₂³	1	3	yes	—
217	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
218	C₂×Q₈×D₅₃	C₂³	1	2	yes	complemented
219	C₂×Q₈×D₅₃	C₂³	1	6	yes	complemented
220	C₂×Q₈×D₅₃	C₂³	1	6	yes	complemented
221	C₂×Q₈×D₅₃	C₂³	1	6	yes	complemented
222	C₂²×D₂₁₂	C₂³	1	3	yes	—
223	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	—
224	C₂×D₄×D₅₃	—	2	24	no	—
225	C₂×D₄×D₅₃	C₂³	1	6	yes	—
226	C₂×D₄×D₅₃	C₂³	1	3	yes	—
227	C₂×D₄×D₅₃	C₂³	1	3	yes	—
228	C₂×D₄×D₅₃	C₂³	1	2	yes	—
229	C₂×D₄×D₅₃	C₂³	1	6	yes	—
230	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
231	C₂×D₄×D₅₃	C₂³	1	6	yes	—
232	C₂×D₄×D₅₃	C₂³	1	3	yes	—
233	C₂×D₄×D₅₃	C₂³	1	6	yes	—
234	C₂×D₄×D₅₃	C₂³	1	3	yes	—
235	C₂³×Dic₅₃	C₂³	1	3	yes	—
236	C₂²×C₄×D₅₃	—	2	24	no	—
237	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
238	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
239	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
240	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
241	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
242	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
243	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
244	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
245	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
246	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
247	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
248	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
249	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
250	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
251	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
252	#13133217	C₂³	1	6	yes	complemented
253	#13133216	C₂³	1	12	yes	complemented
254	#13133216	C₂³	1	12	yes	complemented
255	#13133215	C₂³	1	6	yes	complemented
256	#13133215	C₂³	1	6	yes	complemented
257	#13133206	C₂³	1	6	yes	complemented
258	#13133205	C₂³	1	6	yes	complemented
259	#13133204	C₂³	1	6	yes	complemented
260	#13133203	C₂³	1	12	yes	complemented
261	#13133203	C₂³	1	12	yes	complemented
262	#13133202	C₂³	1	12	yes	complemented
263	#13133202	C₂³	1	12	yes	complemented
264	#13133202	C₂³	1	6	yes	complemented
265	#13133202	C₂³	1	6	yes	complemented
266	#13133201	C₂³	1	12	yes	complemented
267	#13133201	C₂³	1	6	yes	complemented
268	#13133200	C₂³	1	6	yes	complemented
269	#13133200	C₂³	1	12	yes	complemented
270	#13133199	C₂³	1	12	yes	complemented
271	#13133199	C₂³	1	12	yes	complemented
272	#13133199	C₂³	1	6	yes	complemented
273	#13133199	C₂³	1	6	yes	complemented
274	#13133198	C₂³	1	12	yes	complemented
275	#13133198	C₂³	1	6	yes	complemented
276	#13133197	C₂³	1	6	yes	—
277	#13133197	C₂³	1	3	yes	—
278	#13133197	C₂³	1	6	yes	complemented
279	#13133197	C₂³	1	6	yes	complemented
280	#13133197	C₂³	1	6	yes	complemented
281	#13133197	C₂³	1	3	yes	complemented
282	#13133196	C₂³	1	6	yes	—
283	#13133196	C₂³	1	3	yes	—
284	#13133196	C₂³	1	6	yes	complemented
285	#13133196	C₂³	1	6	yes	complemented
286	#13133196	C₂³	1	6	yes	complemented
287	#13133196	C₂³	1	3	yes	complemented
288	#13133195	C₂³	1	12	yes	—
289	#13133195	C₂³	1	6	yes	—
290	#13133195	C₂³	1	12	yes	complemented
291	#13133195	C₂³	1	12	yes	complemented
292	#13133195	C₂³	1	12	yes	complemented
293	#13133195	C₂³	1	6	yes	complemented
294	#13133194	C₂³	1	12	yes	—
295	#13133194	C₂³	1	6	yes	—
296	#13133194	C₂³	1	12	yes	complemented
297	#13133194	C₂³	1	12	yes	complemented
298	#13133194	C₂³	1	12	yes	complemented
299	#13133194	C₂³	1	6	yes	complemented
300	#13133193	C₂³	1	6	yes	—
301	#13133193	C₂³	1	3	yes	—
302	#13133193	C₂³	1	6	yes	complemented
303	#13133193	C₂³	1	6	yes	complemented
304	#13133193	C₂³	1	6	yes	complemented
305	#13133193	C₂³	1	3	yes	complemented
306	#13133192	C₂³	1	1	yes	characteristic
307	#13133192	C₂³	1	12	yes	complemented
308	#13133192	C₂³	1	6	yes	complemented
309	#13133192	C₂³	1	3	yes	complemented
310	#13133191	C₂³	1	1	yes	characteristic
311	#13133191	C₂³	1	12	yes	complemented
312	#13133191	C₂³	1	6	yes	complemented
313	#13133191	C₂³	1	3	yes	complemented
314	#13133190	C₂³	1	2	yes	—
315	#13133190	C₂³	1	12	yes	complemented
316	#13133190	C₂³	1	12	yes	complemented
317	#13133190	C₂³	1	12	yes	complemented
318	#13133190	C₂³	1	6	yes	complemented
319	#13133189	C₂³	1	2	yes	—
320	#13133189	C₂³	1	12	yes	complemented
321	#13133189	C₂³	1	12	yes	complemented
322	#13133189	C₂³	1	12	yes	complemented
323	#13133189	C₂³	1	6	yes	complemented
324	#13133188	C₂³	1	1	yes	characteristic
325	#13133188	C₂³	1	6	yes	complemented
326	#13133188	C₂³	1	12	yes	complemented
327	#13133188	C₂³	1	3	yes	complemented
328	#13133187	C₂³	1	6	yes	—
329	#13133187	C₂³	1	6	yes	—
330	#13133187	C₂³	1	6	yes	—
331	#13133186	C₂³	1	6	yes	—
332	#13133185	C₂³	1	6	yes	—
333	#13133185	C₂³	1	6	yes	—
334	#13133185	C₂³	1	6	yes	—
335	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
336	C₄×Dic₁₀₆	C₂³	1	6	yes	complemented
337	#13133182	C₂³	1	6	yes	complemented
338	C₄×D₂₁₂	C₂³	1	6	yes	—
339	C₄×D₂₁₂	C₂³	1	6	yes	complemented
340	C₄×D₂₁₂	C₂³	1	6	yes	complemented
341	D₄×Dic₅₃	C₂³	1	6	yes	—
342	D₄×Dic₅₃	C₂³	1	6	yes	complemented
343	D₄×Dic₅₃	C₂³	1	6	yes	complemented
344	#13133179	C₂³	1	6	yes	—
345	#13133179	C₂³	1	6	yes	complemented
346	#13133179	C₂³	1	6	yes	complemented
347	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	—
348	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	—
349	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
350	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
351	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
352	#13133177	C₂³	1	6	yes	—
353	#13133177	C₂³	1	6	yes	—
354	#13133177	C₂³	1	12	yes	complemented
355	#13133177	C₂³	1	6	yes	complemented
356	#13133177	C₂³	1	6	yes	complemented
357	#13133176	C₂³	1	3	yes	complemented
358	#13133175	C₂³	1	3	yes	complemented
359	#13133175	C₂³	1	3	yes	complemented
360	#13133174	C₂³	1	6	yes	complemented
361	#13133173	C₂³	1	6	yes	complemented
362	C₂×C₄⋊Dic₅₃	C₂³	1	6	yes	complemented
363	C₂×C₄⋊Dic₅₃	C₂³	1	3	yes	complemented
364	C₂×#11719919	C₂³	1	6	yes	complemented
365	C₂×#11719919	C₂³	1	6	yes	complemented
366	C₂×#11719919	C₂³	1	6	yes	complemented
367	C₄⋊C₄×D₅₃	C₂³	1	3	yes	—
368	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
369	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
370	C₄⋊C₄×D₅₃	C₂³	1	12	yes	—
371	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
372	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
373	C₄⋊C₄×D₅₃	C₂³	1	12	yes	complemented
374	C₄⋊C₄×D₅₃	C₂³	1	12	yes	complemented
375	C₄⋊C₄×D₅₃	C₂³	1	6	yes	complemented
376	C₄⋊C₄×D₅₃	C₂³	1	6	yes	complemented
377	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	—
378	C₂×#11719921	C₂³	1	6	yes	—
379	C₂×#11719921	C₂³	1	6	yes	—
380	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
381	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
382	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
383	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
384	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
385	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
386	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
387	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
388	C₄²×D₅₃	C₂³	1	6	yes	—
389	2₋¹⁺⁴×C₅₃	—	2	8	no	—
390	C₂×#41×C₅₃	—	2	8	no	—
391	C₂×#41×C₅₃	C₂³	1	3	yes	—
392	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
393	C₂×#41×C₅₃	C₂³	1	3	yes	—
394	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
395	C₂×#41×C₅₃	C₂³	1	6	yes	complemented
396	C₂×#41×C₅₃	C₂³	1	3	yes	complemented
397	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
398	C₂²×Q₈×C₅₃	C₂³	1	2	yes	complemented
399	C₂²×Q₈×C₅₃	C₂³	1	3	yes	complemented
400	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
401	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
402	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
403	#124×C₅₃	C₂³	1	6	yes	complemented
404	#123×C₅₃	C₂³	1	12	yes	complemented
405	#123×C₅₃	C₂³	1	6	yes	complemented
406	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
407	C₂²⋊Q₈×C₅₃	C₂³	1	3	yes	—
408	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
409	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
410	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
411	C₂²⋊Q₈×C₅₃	C₂³	1	3	yes	complemented
412	#121×C₅₃	C₂³	1	1	yes	characteristic
413	#121×C₅₃	C₂³	1	6	yes	complemented
414	#121×C₅₃	C₂³	1	12	yes	complemented
415	#121×C₅₃	C₂³	1	3	yes	complemented
416	#120×C₅₃	C₂³	1	6	yes	—
417	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
418	C₄×D₄×C₅₃	C₂³	1	6	yes	—
419	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
420	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
421	#117×C₅₃	C₂³	1	3	yes	complemented
422	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	complemented
423	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	complemented
424	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
425	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
426	C₂³×D₅₃	—	2	12	no	—
427	C₂³×D₅₃	—	2	12	no	—
428	C₂³×D₅₃	—	4	6	no	—
429	C₂³×D₅₃	C₂⁴	1	3	yes	—
430	C₂³×D₅₃	C₂⁴	1	2	yes	—
431	C₂³×D₅₃	C₂⁴	1	3	yes	—
432	C₂³×D₅₃	C₂⁴	1	3	yes	—
433	C₂³×D₅₃	C₂⁴	1	3	yes	—
434	C₂³×D₅₃	C₂⁴	1	3	yes	—
435	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
436	#41×C₅₃	—	2	4	no	—
437	#41×C₅₃	—	2	12	no	—
438	#41×C₅₃	—	2	24	no	—
439	#41×C₅₃	—	2	12	no	—
440	#41×C₅₃	—	2	12	no	—
441	#41×C₅₃	C₂×D₄	1	8	yes	complemented
442	C₂×Q₈×C₅₃	—	2	4	no	—
443	C₂×Q₈×C₅₃	—	2	8	no	—
444	C₂×Q₈×C₅₃	—	2	12	no	—
445	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
446	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
447	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
448	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
449	C₂×D₄×C₅₃	—	2	12	no	—
450	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
451	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
452	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
454	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
455	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
456	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
457	C₂²×C₄×C₅₃	—	2	12	no	—
458	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
459	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
460	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
461	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
462	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
463	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
465	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
466	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
467	C₂×C₂²⋊D₅₃	—	2	24	no	—
468	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
469	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
470	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
471	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
472	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
473	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
474	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
475	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
476	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
477	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
478	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
479	C₂²×Dic₅₃	—	2	12	no	—
480	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
481	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
482	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
483	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
484	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
485	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
486	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
487	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
488	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
489	#11719949	—	2	4	no	—
490	#11719949	—	2	12	no	—
491	#11719949	—	2	24	no	—
492	#11719949	—	2	12	no	—
493	#11719949	—	2	12	no	—
494	#11719949	C₂×D₄	1	8	yes	complemented
495	Q₈×D₅₃	—	2	4	no	—
496	Q₈×D₅₃	—	2	8	no	—
497	Q₈×D₅₃	—	2	12	no	—
498	Q₈×D₅₃	—	2	24	no	—
499	Q₈×D₅₃	—	2	12	no	—
500	Q₈×D₅₃	—	2	24	no	—
501	Q₈×D₅₃	—	2	24	no	—
502	Q₈×D₅₃	—	2	12	no	—
503	Q₈×D₅₃	—	2	24	no	—
504	Q₈×D₅₃	C₂×D₄	1	8	yes	—
505	#11719947	—	2	12	no	—
506	#11719947	—	2	24	no	—
507	#11719947	—	2	24	no	—
508	#11719947	—	2	48	no	—
509	#11719947	—	2	24	no	—
510	#11719947	—	2	24	no	—
511	#11719947	—	2	12	no	—
512	#11719947	—	2	12	no	—
513	#11719947	—	2	12	no	—
514	#11719947	C₂×D₄	1	24	yes	complemented
515	D₄×D₅₃	—	2	24	no	—
516	D₄×D₅₃	—	2	24	no	—
517	D₄×D₅₃	—	2	8	no	—
518	D₄×D₅₃	—	2	12	no	—
519	D₄×D₅₃	—	2	24	no	—
520	D₄×D₅₃	—	2	12	no	—
521	D₄×D₅₃	—	2	12	no	—
522	D₄×D₅₃	—	2	4	no	—
523	D₄×D₅₃	—	4	12	no	—
524	D₄×D₅₃	C₂×D₄	1	24	yes	—
525	#11719945	—	2	12	no	—
526	#11719945	—	2	12	no	—
527	#11719945	—	2	24	no	—
528	#11719945	—	2	48	no	—
529	#11719945	—	2	12	no	—
530	#11719945	—	2	24	no	—
531	#11719945	—	2	24	no	—
532	#11719945	—	2	24	no	—
533	#11719945	—	2	12	no	—
534	#11719945	C₂×D₄	1	24	yes	complemented
535	C₂×D₂₁₂	—	2	12	no	—
536	C₂×D₂₁₂	C₂⁴	1	2	yes	—
537	C₂×D₂₁₂	C₂⁴	1	6	yes	—
538	C₂×D₂₁₂	C₂⁴	1	6	yes	—
539	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
540	C₂×D₂₁₂	C₂⁴	1	3	yes	—
541	C₂×D₂₁₂	C₂⁴	1	6	yes	—
542	C₂×D₂₁₂	C₂⁴	1	3	yes	—
543	C₂×C₄×D₅₃	—	2	12	no	—
544	C₂×C₄×D₅₃	—	2	24	no	—
545	C₂×C₄×D₅₃	—	2	12	no	—
546	C₂×C₄×D₅₃	—	2	12	no	—
547	C₂×C₄×D₅₃	—	2	4	no	—
548	C₂×C₄×D₅₃	—	2	12	no	—
549	C₂×C₄×D₅₃	—	2	12	no	—
550	C₂×C₄×D₅₃	—	2	12	no	—
551	C₂×C₄×D₅₃	—	2	12	no	—
552	C₂×C₄×D₅₃	—	2	12	no	—
553	C₂×C₄×D₅₃	—	2	12	no	—
554	C₂×C₄×D₅₃	—	2	12	no	—
555	C₂×C₄×D₅₃	—	2	24	no	—
556	C₂×C₄×D₅₃	—	4	12	no	—
557	C₂×C₄×D₅₃	C₂×D₄	1	24	yes	—
558	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
559	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
560	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
561	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
562	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
563	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
564	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
565	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
566	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
567	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
568	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
569	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
570	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
571	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
572	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
573	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
574	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
575	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
576	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
577	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
578	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
579	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
580	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
581	C₂×Dic₁₀₆	—	2	12	no	—
582	C₂×Dic₁₀₆	—	2	24	no	—
583	C₂×Dic₁₀₆	—	2	12	no	—
584	C₂×Dic₁₀₆	—	2	24	no	—
585	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
586	C₂×Dic₁₀₆	C₂⁴	1	12	yes	—
587	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
588	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
589	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
590	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
591	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
592	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
593	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
594	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
595	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
596	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
597	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
598	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
599	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
600	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
601	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
602	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
603	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
604	C₄²×C₅₃	C₂⁴	1	6	yes	—
605	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
606	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
607	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
608	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
609	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
610	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
611	#11719921	C₂⁴	1	6	yes	—
612	#11719921	C₂⁴	1	6	yes	—
613	#11719921	C₂⁴	1	12	yes	—
614	#11719921	C₂⁴	1	12	yes	—
615	#11719921	C₂⁴	1	6	yes	—
616	#11719921	C₂⁴	1	6	yes	—
617	#11719921	C₂⁴	1	6	yes	—
618	#11719921	C₂⁴	1	2	yes	—
619	#11719921	C₂⁴	1	6	yes	—
620	#11719921	C₂⁴	1	6	yes	—
621	#11719921	C₂⁴	1	2	yes	—
622	#11719921	C₂⁴	1	6	yes	—
623	C₄⋊Dic₅₃	C₂⁴	1	3	yes	—
624	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
625	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
626	C₄⋊Dic₅₃	C₂⁴	1	12	yes	—
627	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
628	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
629	#11719919	C₂⁴	1	6	yes	—
630	#11719919	C₂⁴	1	6	yes	—
631	#11719919	C₂⁴	1	6	yes	—
632	#11719919	C₂⁴	1	12	yes	—
633	#11719919	C₂⁴	1	12	yes	—
634	#11719919	C₂⁴	1	12	yes	—
635	#11719919	C₂⁴	1	2	yes	—
636	#11719919	C₂⁴	1	6	yes	—
637	#11719919	C₂⁴	1	6	yes	—
638	C₄×Dic₅₃	C₂⁴	1	6	yes	—
639	C₄×Dic₅₃	C₂⁴	1	6	yes	—
640	C₄×Dic₅₃	C₂⁴	1	6	yes	—
641	C₂³×C₅₃	—	2	6	no	—
642	C₂³×C₅₃	—	2	6	no	—
643	C₂³×C₅₃	—	4	3	no	—
644	C₂³×C₅₃	C₂⁵	1	2	yes	—
645	C₂³×C₅₃	C₂⁵	1	3	yes	—
646	C₂³×C₅₃	C₂⁵	1	3	yes	—
647	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
648	C₂²×D₅₃	—	2	2	no	—
649	C₂²×D₅₃	—	2	6	no	—
650	C₂²×D₅₃	—	2	6	no	—
651	C₂²×D₅₃	—	2	2	no	—
652	C₂²×D₅₃	—	2	6	no	—
653	C₂²×D₅₃	—	2	6	no	—
654	C₂²×D₅₃	—	2	4	no	—
655	C₂²×D₅₃	—	2	6	no	—
656	C₂²×D₅₃	—	2	6	no	—
657	C₂²×D₅₃	—	2	6	no	—
658	C₂²×D₅₃	—	2	4	no	—
659	C₂²×D₅₃	—	2	6	no	—
660	C₂²×D₅₃	—	2	6	no	—
661	C₂²×D₅₃	—	2	6	no	—
662	C₂²×D₅₃	—	2	4	no	—
663	C₂²×D₅₃	—	2	6	no	—
664	C₂²×D₅₃	—	4	3	no	—
665	C₂²×D₅₃	—	4	3	no	—
666	C₂²×D₅₃	—	4	3	no	—
667	C₂²×D₅₃	—	4	48	no	—
668	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
669	C₂²×D₅₃	2₋¹⁺⁴	1	4	yes	complemented
670	C₂²×D₅₃	C₂⁵	1	2	yes	—
671	C₂²×D₅₃	C₂⁵	1	3	yes	—
672	C₂²×D₅₃	C₂⁵	1	3	yes	—
673	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
674	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
675	Q₈×C₅₃	—	2	12	no	—
676	Q₈×C₅₃	—	2	6	no	—
677	Q₈×C₅₃	—	2	6	no	—
678	Q₈×C₅₃	C₂²×D₄	1	4	yes	—
679	D₄×C₅₃	—	2	12	no	—
680	D₄×C₅₃	—	2	12	no	—
681	D₄×C₅₃	—	2	4	no	—
682	D₄×C₅₃	—	2	6	no	—
683	D₄×C₅₃	—	2	2	no	—
684	D₄×C₅₃	—	4	6	no	—
685	D₄×C₅₃	C₂²×D₄	1	12	yes	—
686	C₂×C₄×C₅₃	—	2	12	no	—
687	C₂×C₄×C₅₃	—	2	6	no	—
688	C₂×C₄×C₅₃	—	2	6	no	—
689	C₂×C₄×C₅₃	—	2	12	no	—
690	C₂×C₄×C₅₃	—	2	2	no	—
691	C₂×C₄×C₅₃	—	2	6	no	—
692	C₂×C₄×C₅₃	—	2	6	no	—
693	C₂×C₄×C₅₃	—	4	6	no	—
694	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
695	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
696	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
697	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
698	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
699	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
700	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
701	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
702	C₂²⋊D₅₃	—	2	12	no	—
703	C₂²⋊D₅₃	—	2	12	no	—
704	C₂²⋊D₅₃	—	2	4	no	—
705	C₂²⋊D₅₃	—	2	12	no	—
706	C₂²⋊D₅₃	—	2	12	no	—
707	C₂²⋊D₅₃	—	2	4	no	—
708	C₂²⋊D₅₃	—	2	4	no	—
709	C₂²⋊D₅₃	—	2	12	no	—
710	C₂²⋊D₅₃	—	4	6	no	—
711	C₂²⋊D₅₃	—	4	6	no	—
712	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	—
713	C₂×Dic₅₃	—	2	12	no	—
714	C₂×Dic₅₃	—	2	6	no	—
715	C₂×Dic₅₃	—	2	6	no	—
716	C₂×Dic₅₃	—	2	12	no	—
717	C₂×Dic₅₃	—	2	2	no	—
718	C₂×Dic₅₃	—	2	6	no	—
719	C₂×Dic₅₃	—	2	6	no	—
720	C₂×Dic₅₃	—	4	6	no	—
721	C₂×Dic₅₃	C₂²×D₄	1	12	yes	—
722	C₂×Dic₅₃	C₂⁵	1	6	yes	—
723	C₂×Dic₅₃	C₂⁵	1	3	yes	—
724	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
725	C₂×Dic₅₃	C₂⁵	1	6	yes	—
726	C₂×Dic₅₃	C₂⁵	1	2	yes	—
727	C₂×Dic₅₃	C₂⁵	1	3	yes	—
728	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
729	D₂₁₂	—	2	12	no	—
730	D₂₁₂	—	2	12	no	—
731	D₂₁₂	—	2	4	no	—
732	D₂₁₂	—	2	6	no	—
733	D₂₁₂	—	2	2	no	—
734	D₂₁₂	—	4	6	no	—
735	D₂₁₂	C₂²×D₄	1	12	yes	—
736	C₄×D₅₃	—	2	2	no	—
737	C₄×D₅₃	—	2	6	no	—
738	C₄×D₅₃	—	2	6	no	—
739	C₄×D₅₃	—	2	12	no	—
740	C₄×D₅₃	—	2	6	no	—
741	C₄×D₅₃	—	2	24	no	—
742	C₄×D₅₃	—	2	4	no	—
743	C₄×D₅₃	—	2	12	no	—
744	C₄×D₅₃	—	2	2	no	—
745	C₄×D₅₃	—	2	6	no	—
746	C₄×D₅₃	—	2	6	no	—
747	C₄×D₅₃	—	2	6	no	—
748	C₄×D₅₃	—	2	12	no	—
749	C₄×D₅₃	—	2	2	no	—
750	C₄×D₅₃	—	2	6	no	—
751	C₄×D₅₃	—	2	6	no	—
752	C₄×D₅₃	—	2	6	no	—
753	C₄×D₅₃	—	2	12	no	—
754	C₄×D₅₃	—	4	12	no	—
755	C₄×D₅₃	C₂²×D₄	1	4	yes	—
756	C₄×D₅₃	C₂²×D₄	1	12	yes	—
757	C₄×D₅₃	C₂²×D₄	1	12	yes	—
758	C₄×D₅₃	C₂²×D₄	1	12	yes	—
759	Dic₁₀₆	—	2	12	no	—
760	Dic₁₀₆	—	2	6	no	—
761	Dic₁₀₆	—	2	6	no	—
762	Dic₁₀₆	—	2	24	no	—
763	Dic₁₀₆	—	2	12	no	—
764	Dic₁₀₆	—	2	12	no	—
765	Dic₁₀₆	C₂²×D₄	1	12	yes	—
766	C₂×#3489	—	53	1	no	maximal, Sylow
767	C₂²×C₅₃	—	2	1	no	—
768	C₂²×C₅₃	—	2	3	no	—
769	C₂²×C₅₃	—	2	3	no	—
770	C₂²×C₅₃	—	2	1	no	—
771	C₂²×C₅₃	—	2	2	no	—
772	C₂²×C₅₃	—	2	3	no	—
773	C₂²×C₅₃	—	2	2	no	—
774	C₂²×C₅₃	—	2	3	no	—
775	C₂²×C₅₃	—	2	2	no	—
776	C₂²×C₅₃	—	2	3	no	—
777	C₂²×C₅₃	—	4	12	no	—
778	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
779	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	complemented
780	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
781	C₂×D₅₃	—	2	1	no	—
782	C₂×D₅₃	—	2	3	no	—
783	C₂×D₅₃	—	2	3	no	—
784	C₂×D₅₃	—	2	1	no	—
785	C₂×D₅₃	—	2	8	no	—
786	C₂×D₅₃	—	2	24	no	—
787	C₂×D₅₃	—	2	2	no	—
788	C₂×D₅₃	—	2	3	no	—
789	C₂×D₅₃	—	2	2	no	—
790	C₂×D₅₃	—	2	3	no	—
791	C₂×D₅₃	—	2	2	no	—
792	C₂×D₅₃	—	2	3	no	—
793	C₂×D₅₃	—	4	12	no	—
794	C₂×D₅₃	—	4	12	no	—
795	C₂×D₅₃	—	4	12	no	—
796	C₂×D₅₃	—	4	8	no	—
797	C₂×D₅₃	—	4	12	no	—
798	C₂×D₅₃	C₂³×D₄	1	6	yes	—
799	C₂×D₅₃	C₂³×D₄	1	2	yes	—
800	C₂×D₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
801	C₂×D₅₃	C₂×2₋¹⁺⁴	1	2	yes	complemented
802	C₂×D₅₃	#585	1	2	yes	—
803	C₄×C₅₃	—	2	6	no	—
804	C₄×C₅₃	—	2	3	no	—
805	C₄×C₅₃	—	2	1	no	—
806	C₄×C₅₃	—	2	2	no	—
807	C₄×C₅₃	—	2	6	no	—
808	C₄×C₅₃	C₂³×D₄	1	6	yes	—
809	C₄×C₅₃	C₂³×D₄	1	2	yes	—
810	Dic₅₃	—	2	6	no	—
811	Dic₅₃	—	2	3	no	—
812	Dic₅₃	—	2	1	no	—
813	Dic₅₃	—	2	2	no	—
814	Dic₅₃	—	2	6	no	—
815	Dic₅₃	C₂³×D₄	1	6	yes	—
816	Dic₅₃	C₂³×D₄	1	2	yes	—
817	C₂²×2₋¹⁺⁴	—	53	1	no	—
818	C₂³×#41	—	53	1	no	—
819	#3489	—	53	1	no	—
820	#3489	—	53	1	no	—
821	#3489	—	53	2	no	—
822	#3489	—	53	2	no	—
823	#3489	—	53	6	no	—
824	#3489	—	53	6	no	—
825	#3489	—	53	3	no	—
826	#3489	—	53	3	no	—
827	#3489	—	53	3	no	—
828	#3489	—	53	3	no	—
829	#3489	—	53	1	no	—
830	#3489	D₅₃	1	1	yes	characteristic, direct product factor
831	C₂×D₄×Q₈	—	53	2	no	—
832	C₂×#548	—	53	2	no	—
833	C₂×#547	—	53	6	no	—
834	C₂×#546	—	53	6	no	—
835	C₂×#537	—	53	3	no	—
836	C₂×#536	—	53	3	no	—
837	C₂×#525	—	53	3	no	—
838	C₂²×C₂²⋊Q₈	—	53	3	no	—
839	C₂×#520	—	53	1	no	—
840	C₂×C₅₃	—	2	2	no	—
841	C₂×C₅₃	—	2	6	no	—
842	C₂×C₅₃	—	4	3	no	—
843	C₂×C₅₃	—	4	2	no	—
844	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
845	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
846	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
847	D₅₃	—	2	2	no	—
848	D₅₃	—	2	6	no	—
849	D₅₃	—	4	2	no	—
850	D₅₃	—	4	3	no	—
851	D₅₃	#3489	1	4	yes	direct product factor
852	C₂×2₋¹⁺⁴	—	53	1	no	—
853	C₂×2₋¹⁺⁴	—	53	3	no	—
854	C₂×2₋¹⁺⁴	—	53	6	no	—
855	C₂×2₋¹⁺⁴	—	53	2	no	—
856	C₂×2₋¹⁺⁴	—	53	3	no	—
857	C₂×2₋¹⁺⁴	—	106	16	no	—
858	C₂×2₋¹⁺⁴	C₂×D₅₃	1	1	yes	characteristic, complemented
859	C₂²×#41	—	53	1	no	—
860	C₂²×#41	—	53	3	no	—
861	C₂²×#41	—	53	3	no	—
862	C₂²×#41	—	53	1	no	—
863	C₂²×#41	—	53	1	no	—
864	C₂²×#41	—	53	3	no	—
865	C₂²×#41	—	53	3	no	—
866	C₂²×#41	—	53	1	no	—
867	C₂²×#41	—	53	3	no	—
868	C₂²×#41	—	53	6	no	—
869	C₂²×#41	—	53	1	no	—
870	C₂²×#41	—	53	3	no	—
871	C₂²×#41	—	53	3	no	—
872	C₂²×#41	—	106	16	no	—
873	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
874	C₂³×Q₈	—	53	1	no	—
875	C₂³×Q₈	—	53	3	no	—
876	C₂³×Q₈	—	53	2	no	—
877	C₂³×D₄	—	53	3	no	—
878	C₂⁴×C₄	—	53	3	no	—
879	D₄×Q₈	—	53	2	no	—
880	D₄×Q₈	—	53	2	no	—
881	D₄×Q₈	—	53	6	no	—
882	D₄×Q₈	—	53	6	no	—
883	D₄×Q₈	—	53	6	no	—
884	D₄×Q₈	—	53	2	no	—
885	D₄×Q₈	—	53	6	no	—
886	D₄×Q₈	C₂×D₅₃	1	2	yes	complemented
887	#548	—	53	2	no	—
888	#548	—	53	2	no	—
889	#548	—	53	6	no	—
890	#548	—	53	6	no	—
891	#548	—	53	6	no	—
892	#548	—	53	2	no	—
893	#548	—	53	6	no	—
894	#548	C₂×D₅₃	1	2	yes	complemented
895	#547	—	53	6	no	—
896	#547	—	53	6	no	—
897	#547	—	53	6	no	—
898	#547	—	53	12	no	—
899	#547	—	53	12	no	—
900	#547	—	53	6	no	—
901	#547	—	53	6	no	—
902	#547	—	53	12	no	—
903	#547	—	53	6	no	—
904	#547	—	53	6	no	—
905	#547	—	53	12	no	—
906	#547	C₂×D₅₃	1	6	yes	complemented
907	#546	—	53	6	no	—
908	#546	—	53	6	no	—
909	#546	—	53	6	no	—
910	#546	—	53	12	no	—
911	#546	—	53	6	no	—
912	#546	—	53	6	no	—
913	#546	—	53	12	no	—
914	#546	—	53	12	no	—
915	#546	—	53	6	no	—
916	#546	—	53	6	no	—
917	#546	—	53	12	no	—
918	#546	C₂×D₅₃	1	6	yes	complemented
919	#537	—	53	3	no	—
920	#537	—	53	3	no	—
921	#537	—	53	6	no	—
922	#537	—	53	6	no	—
923	#537	—	53	12	no	—
924	#537	—	53	6	no	—
925	#537	—	53	6	no	—
926	#537	—	53	3	no	—
927	#537	C₂×D₅₃	1	3	yes	complemented
928	#536	—	53	3	no	—
929	#536	—	53	3	no	—
930	#536	—	53	6	no	—
931	#536	—	53	6	no	—
932	#536	—	53	12	no	—
933	#536	—	53	6	no	—
934	#536	—	53	6	no	—
935	#536	—	53	3	no	—
936	#536	C₂×D₅₃	1	3	yes	complemented
937	C₂×C₄⋊Q₈	—	53	6	no	—
938	C₂×#124	—	53	6	no	—
939	#525	—	53	3	no	—
940	#525	—	53	3	no	—
941	#525	—	53	6	no	—
942	#525	—	53	3	no	—
943	#525	—	53	3	no	—
944	#525	—	53	3	no	—
945	#525	—	53	3	no	—
946	#525	—	53	6	no	—
947	#525	—	53	6	no	—
948	#525	—	53	6	no	—
949	#525	—	53	3	no	—
950	#525	C₂×D₅₃	1	3	yes	complemented
951	C₂×#123	—	53	6	no	—
952	C₂×#123	—	53	12	no	—
953	C₂×C₂²⋊Q₈	—	53	3	no	—
954	C₂×C₂²⋊Q₈	—	53	3	no	—
955	C₂×C₂²⋊Q₈	—	53	3	no	—
956	C₂×C₂²⋊Q₈	—	53	6	no	—
957	C₂×C₂²⋊Q₈	—	53	6	no	—
958	C₂×C₂²⋊Q₈	—	53	6	no	—
959	C₂×C₂²⋊Q₈	—	53	6	no	—
960	C₂×C₂²⋊Q₈	—	53	6	no	—
961	C₂×C₂²⋊Q₈	—	53	6	no	—
962	C₂×C₂²⋊Q₈	—	53	6	no	—
963	C₂×C₂²⋊Q₈	—	53	3	no	—
964	C₂×C₂²⋊Q₈	—	53	6	no	—
965	C₂×C₂²⋊Q₈	—	53	6	no	—
966	C₂×C₂²⋊Q₈	—	53	3	no	—
967	C₂×C₂²⋊Q₈	—	53	6	no	—
968	C₂×C₂²⋊Q₈	C₂×D₅₃	1	3	yes	complemented
969	C₂×#121	—	53	1	no	—
970	C₂×#121	—	53	3	no	—
971	C₂×#121	—	53	12	no	—
972	C₂×#121	—	53	6	no	—
973	C₂×#120	—	53	6	no	—
974	#520	—	53	1	no	—
975	#520	—	53	2	no	—
976	#520	—	53	6	no	—
977	#520	—	53	3	no	—
978	#520	—	53	3	no	—
979	#520	C₂×D₅₃	1	1	yes	characteristic, complemented
980	C₂×C₄×Q₈	—	53	2	no	—
981	C₂×C₄×D₄	—	53	6	no	—
982	C₂×C₄×D₄	—	53	6	no	—
983	C₂×C₄×D₄	—	53	6	no	—
984	C₂×#117	—	53	3	no	—
985	C₂²×C₄⋊C₄	—	53	3	no	—
986	C₂²×C₄⋊C₄	—	53	6	no	—
987	C₂²×C₂²⋊C₄	—	53	6	no	—
988	C₅₃	C₂×#3489	1	1	yes	characteristic, complemented, Sylow
989	C₂⁵	—	53	3	no	—
990	2₋¹⁺⁴	—	2	8	no	—
991	2₋¹⁺⁴	—	106	16	no	—
992	2₋¹⁺⁴	—	106	24	no	—
993	2₋¹⁺⁴	—	106	48	no	—
994	2₋¹⁺⁴	—	106	24	no	—
995	2₋¹⁺⁴	—	106	8	no	—
996	C₂×#41	—	2	8	no	—
997	C₂×#41	—	53	16	no	—
998	C₂×#41	—	53	1	no	—
999	C₂×#41	—	53	3	no	—
1000	C₂×#41	—	53	3	no	—
1001	C₂×#41	—	53	6	no	—
1002	C₂×#41	—	53	3	no	—
1003	C₂×#41	—	53	1	no	—
1004	C₂×#41	—	53	3	no	—
1005	C₂×#41	—	53	6	no	—
1006	C₂×#41	—	53	3	no	—
1007	C₂×#41	—	53	6	no	—
1008	C₂×#41	—	53	3	no	—
1009	C₂×#41	—	53	6	no	—
1010	C₂×#41	—	53	12	no	—
1011	C₂×#41	—	53	3	no	—
1012	C₂×#41	—	53	6	no	—
1013	C₂×#41	—	53	3	no	—
1014	C₂×#41	—	53	3	no	—
1015	C₂×#41	—	53	6	no	—
1016	C₂×#41	—	53	3	no	—
1017	C₂×#41	—	53	6	no	—
1018	C₂×#41	—	53	3	no	—
1019	C₂×#41	—	53	6	no	—
1020	C₂×#41	—	53	12	no	—
1021	C₂×#41	—	53	3	no	—
1022	C₂×#41	—	53	6	no	—
1023	C₂×#41	—	53	3	no	—
1024	C₂×#41	—	106	24	no	—
1025	C₂×#41	—	106	24	no	—
1026	C₂×#41	—	106	24	no	—
1027	C₂×#41	—	106	24	no	—
1028	C₂×#41	—	106	24	no	—
1029	C₂×#41	—	106	48	no	—
1030	C₂×#41	—	106	8	no	—
1031	C₂×#41	—	106	8	no	—
1032	C₂×#41	—	106	8	no	—
1033	C₂×#41	—	106	24	no	—
1034	C₂×#41	—	106	24	no	—
1035	C₂×#41	—	106	8	no	—
1036	C₂×#41	C₂²×D₅₃	1	3	yes	—
1037	C₂×#41	C₂²×D₅₃	1	3	yes	—
1038	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1039	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1040	C₂×#41	C₂²×D₅₃	1	3	yes	complemented
1041	C₂×#41	C₂²×D₅₃	1	6	yes	complemented
1042	C₂²×Q₈	—	53	1	no	—
1043	C₂²×Q₈	—	53	3	no	—
1044	C₂²×Q₈	—	53	6	no	—
1045	C₂²×Q₈	—	53	3	no	—
1046	C₂²×Q₈	—	53	6	no	—
1047	C₂²×Q₈	—	53	6	no	—
1048	C₂²×Q₈	—	53	6	no	—
1049	C₂²×Q₈	—	53	2	no	—
1050	C₂²×Q₈	—	53	3	no	—
1051	C₂²×Q₈	—	53	1	no	—
1052	C₂²×Q₈	—	53	6	no	—
1053	C₂²×Q₈	—	53	3	no	—
1054	C₂²×Q₈	—	53	6	no	—
1055	C₂²×Q₈	—	53	3	no	—
1056	C₂²×Q₈	—	106	24	no	—
1057	C₂²×Q₈	—	106	8	no	—
1058	C₂²×Q₈	—	106	16	no	—
1059	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1060	C₂²×Q₈	C₂²×D₅₃	1	3	yes	complemented
1061	C₂²×Q₈	C₂²×D₅₃	1	2	yes	complemented
1062	C₂²×D₄	—	53	3	no	—
1063	C₂²×D₄	—	53	6	no	—
1064	C₂²×D₄	—	53	2	no	—
1065	C₂²×D₄	—	53	6	no	—
1066	C₂²×D₄	—	53	1	no	—
1067	C₂²×D₄	—	53	6	no	—
1068	C₂²×D₄	—	53	3	no	—
1069	C₂²×D₄	—	53	6	no	—
1070	C₂²×D₄	—	53	3	no	—
1071	C₂²×D₄	—	53	3	no	—
1072	C₂²×D₄	—	53	6	no	—
1073	C₂²×D₄	—	53	3	no	—
1074	C₂²×D₄	—	106	24	no	—
1075	C₂²×D₄	C₂²×D₅₃	1	3	yes	—
1076	C₂³×C₄	—	53	3	no	—
1077	C₂³×C₄	—	53	3	no	—
1078	C₂³×C₄	—	53	6	no	—
1079	C₂³×C₄	—	53	3	no	—
1080	C₂³×C₄	—	53	6	no	—
1081	C₂³×C₄	—	53	3	no	—
1082	C₂³×C₄	—	53	3	no	—
1083	C₂³×C₄	—	53	1	no	—
1084	C₂³×C₄	—	53	3	no	—
1085	C₂³×C₄	—	53	3	no	—
1086	C₂³×C₄	—	53	3	no	—
1087	C₂³×C₄	—	53	3	no	—
1088	C₂³×C₄	—	53	3	no	—
1089	C₂³×C₄	—	53	3	no	—
1090	C₂³×C₄	—	53	3	no	—
1091	C₂³×C₄	—	53	6	no	—
1092	C₂³×C₄	—	106	24	no	—
1093	C₂³×C₄	C₂²×D₅₃	1	3	yes	—
1094	C₄⋊Q₈	—	53	6	no	—
1095	C₄⋊Q₈	—	53	6	no	—
1096	C₄⋊Q₈	—	53	12	no	—
1097	C₄⋊Q₈	—	53	12	no	—
1098	C₄⋊Q₈	—	53	6	no	—
1099	C₄⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1100	#124	—	53	6	no	—
1101	#124	—	53	6	no	—
1102	#124	—	53	12	no	—
1103	#124	—	53	12	no	—
1104	#124	—	53	6	no	—
1105	#124	C₂²×D₅₃	1	6	yes	complemented
1106	#123	—	53	6	no	—
1107	#123	—	53	12	no	—
1108	#123	—	53	6	no	—
1109	#123	—	53	12	no	—
1110	#123	—	53	6	no	—
1111	#123	—	53	6	no	—
1112	#123	—	53	12	no	—
1113	#123	—	53	12	no	—
1114	#123	—	53	6	no	—
1115	#123	—	53	6	no	—
1116	#123	—	53	6	no	—
1117	#123	—	53	12	no	—
1118	#123	—	53	12	no	—
1119	#123	—	53	12	no	—
1120	#123	C₂²×D₅₃	1	6	yes	complemented
1121	#123	C₂²×D₅₃	1	12	yes	complemented
1122	C₂²⋊Q₈	—	53	3	no	—
1123	C₂²⋊Q₈	—	53	6	no	—
1124	C₂²⋊Q₈	—	53	6	no	—
1125	C₂²⋊Q₈	—	53	6	no	—
1126	C₂²⋊Q₈	—	53	3	no	—
1127	C₂²⋊Q₈	—	53	6	no	—
1128	C₂²⋊Q₈	—	53	3	no	—
1129	C₂²⋊Q₈	—	53	6	no	—
1130	C₂²⋊Q₈	—	53	6	no	—
1131	C₂²⋊Q₈	—	53	6	no	—
1132	C₂²⋊Q₈	—	53	3	no	—
1133	C₂²⋊Q₈	—	53	6	no	—
1134	C₂²⋊Q₈	—	53	6	no	—
1135	C₂²⋊Q₈	—	53	3	no	—
1136	C₂²⋊Q₈	—	53	12	no	—
1137	C₂²⋊Q₈	—	53	6	no	—
1138	C₂²⋊Q₈	—	53	12	no	—
1139	C₂²⋊Q₈	—	53	6	no	—
1140	C₂²⋊Q₈	—	53	12	no	—
1141	C₂²⋊Q₈	—	53	6	no	—
1142	C₂²⋊Q₈	—	53	6	no	—
1143	C₂²⋊Q₈	—	53	3	no	—
1144	C₂²⋊Q₈	—	53	12	no	—
1145	C₂²⋊Q₈	—	53	6	no	—
1146	C₂²⋊Q₈	—	53	6	no	—
1147	C₂²⋊Q₈	—	53	12	no	—
1148	C₂²⋊Q₈	—	53	12	no	—
1149	C₂²⋊Q₈	—	53	12	no	—
1150	C₂²⋊Q₈	—	53	6	no	—
1151	C₂²⋊Q₈	—	53	12	no	—
1152	C₂²⋊Q₈	C₂²×D₅₃	1	3	yes	—
1153	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	—
1154	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1155	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1156	C₂²⋊Q₈	C₂²×D₅₃	1	3	yes	complemented
1157	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1158	#121	—	53	1	no	—
1159	#121	—	53	2	no	—
1160	#121	—	53	3	no	—
1161	#121	—	53	6	no	—
1162	#121	—	53	12	no	—
1163	#121	—	53	12	no	—
1164	#121	—	53	12	no	—
1165	#121	—	53	6	no	—
1166	#121	—	53	12	no	—
1167	#121	—	53	1	no	—
1168	#121	—	53	3	no	—
1169	#121	—	53	12	no	—
1170	#121	—	53	6	no	—
1171	#121	—	53	1	no	—
1172	#121	—	53	3	no	—
1173	#121	—	53	12	no	—
1174	#121	—	53	6	no	—
1175	#121	—	53	2	no	—
1176	#121	—	53	6	no	—
1177	#121	—	53	12	no	—
1178	#121	—	53	12	no	—
1179	#121	—	53	12	no	—
1180	#121	C₂²×D₅₃	1	1	yes	characteristic
1181	#121	C₂²×D₅₃	1	3	yes	complemented
1182	#121	C₂²×D₅₃	1	12	yes	complemented
1183	#121	C₂²×D₅₃	1	6	yes	complemented
1184	#120	—	53	6	no	—
1185	#120	—	53	6	no	—
1186	#120	—	53	6	no	—
1187	#120	—	53	6	no	—
1188	#120	—	53	6	no	—
1189	#120	—	53	6	no	—
1190	#120	—	53	6	no	—
1191	#120	C₂²×D₅₃	1	6	yes	—
1192	C₄×Q₈	—	53	2	no	—
1193	C₄×Q₈	—	53	6	no	—
1194	C₄×Q₈	—	53	6	no	—
1195	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1196	C₄×D₄	—	53	6	no	—
1197	C₄×D₄	—	53	6	no	—
1198	C₄×D₄	—	53	6	no	—
1199	C₄×D₄	—	53	12	no	—
1200	C₄×D₄	—	53	6	no	—
1201	C₄×D₄	—	53	6	no	—
1202	C₄×D₄	—	53	6	no	—
1203	C₄×D₄	—	53	6	no	—
1204	C₄×D₄	—	53	6	no	—
1205	C₄×D₄	—	53	6	no	—
1206	C₄×D₄	—	53	6	no	—
1207	C₄×D₄	—	53	12	no	—
1208	C₄×D₄	—	53	6	no	—
1209	C₄×D₄	—	53	6	no	—
1210	C₄×D₄	—	53	6	no	—
1211	C₄×D₄	—	53	6	no	—
1212	C₄×D₄	—	53	6	no	—
1213	C₄×D₄	—	53	6	no	—
1214	C₄×D₄	—	53	6	no	—
1215	C₄×D₄	C₂²×D₅₃	1	6	yes	—
1216	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1217	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1218	#117	—	53	3	no	—
1219	#117	—	53	3	no	—
1220	#117	—	53	3	no	—
1221	#117	—	53	6	no	—
1222	#117	—	53	6	no	—
1223	#117	C₂²×D₅₃	1	3	yes	complemented
1224	C₂×C₄⋊C₄	—	53	6	no	—
1225	C₂×C₄⋊C₄	—	53	3	no	—
1226	C₂×C₄⋊C₄	—	53	6	no	—
1227	C₂×C₄⋊C₄	—	53	6	no	—
1228	C₂×C₄⋊C₄	—	53	6	no	—
1229	C₂×C₄⋊C₄	—	53	3	no	—
1230	C₂×C₄⋊C₄	—	53	6	no	—
1231	C₂×C₄⋊C₄	—	53	6	no	—
1232	C₂×C₄⋊C₄	—	53	6	no	—
1233	C₂×C₄⋊C₄	—	53	6	no	—
1234	C₂×C₄⋊C₄	—	53	12	no	—
1235	C₂×C₄⋊C₄	—	53	12	no	—
1236	C₂×C₄⋊C₄	—	53	12	no	—
1237	C₂×C₄⋊C₄	—	53	1	no	—
1238	C₂×C₄⋊C₄	—	53	6	no	—
1239	C₂×C₄⋊C₄	C₂²×D₅₃	1	3	yes	complemented
1240	C₂×C₄⋊C₄	C₂²×D₅₃	1	6	yes	complemented
1241	C₂×C₂²⋊C₄	—	53	6	no	—
1242	C₂×C₂²⋊C₄	—	53	6	no	—
1243	C₂×C₂²⋊C₄	—	53	6	no	—
1244	C₂×C₂²⋊C₄	—	53	6	no	—
1245	C₂×C₂²⋊C₄	—	53	12	no	—
1246	C₂×C₂²⋊C₄	—	53	12	no	—
1247	C₂×C₂²⋊C₄	—	53	12	no	—
1248	C₂×C₂²⋊C₄	—	53	6	no	—
1249	C₂×C₂²⋊C₄	—	53	2	no	—
1250	C₂×C₂²⋊C₄	—	53	6	no	—
1251	C₂×C₂²⋊C₄	—	53	6	no	—
1252	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	—
1253	C₂×C₄²	—	53	6	no	—
1254	C₂⁴	—	53	1	no	—
1255	C₂⁴	—	53	3	no	—
1256	C₂⁴	—	53	3	no	—
1257	C₂⁴	—	53	2	no	—
1258	C₂⁴	—	53	3	no	—
1259	C₂⁴	—	53	3	no	—
1260	C₂⁴	—	53	3	no	—
1261	C₂⁴	—	106	12	no	—
1262	C₂⁴	—	106	12	no	—
1263	C₂⁴	—	212	6	no	—
1264	C₂⁴	C₂³×D₅₃	1	3	yes	—
1265	#41	—	2	4	no	—
1266	#41	—	2	12	no	—
1267	#41	—	2	24	no	—
1268	#41	—	2	12	no	—
1269	#41	—	2	12	no	—
1270	#41	—	53	8	no	—
1271	#41	—	53	24	no	—
1272	#41	—	53	24	no	—
1273	#41	—	106	24	no	—
1274	#41	—	106	24	no	—
1275	#41	—	106	24	no	—
1276	#41	—	106	12	no	—
1277	#41	—	106	48	no	—
1278	#41	—	106	24	no	—
1279	#41	—	106	12	no	—
1280	#41	—	106	24	no	—
1281	#41	—	106	12	no	—
1282	#41	—	106	24	no	—
1283	#41	—	106	12	no	—
1284	#41	—	106	12	no	—
1285	#41	—	106	12	no	—
1286	#41	—	106	24	no	—
1287	#41	—	106	48	no	—
1288	#41	—	106	12	no	—
1289	#41	—	106	12	no	—
1290	#41	—	106	24	no	—
1291	#41	—	106	4	no	—
1292	#41	—	106	12	no	—
1293	#41	—	106	24	no	—
1294	#41	—	106	12	no	—
1295	#41	—	106	12	no	—
1296	#41	D₄×D₅₃	1	8	yes	complemented
1297	C₂×Q₈	—	2	4	no	—
1298	C₂×Q₈	—	2	8	no	—
1299	C₂×Q₈	—	2	12	no	—
1300	C₂×Q₈	—	53	8	no	—
1301	C₂×Q₈	—	53	3	no	—
1302	C₂×Q₈	—	53	6	no	—
1303	C₂×Q₈	—	53	3	no	—
1304	C₂×Q₈	—	53	12	no	—
1305	C₂×Q₈	—	53	6	no	—
1306	C₂×Q₈	—	53	6	no	—
1307	C₂×Q₈	—	53	3	no	—
1308	C₂×Q₈	—	106	24	no	—
1309	C₂×Q₈	—	106	12	no	—
1310	C₂×Q₈	—	106	24	no	—
1311	C₂×Q₈	—	106	12	no	—
1312	C₂×Q₈	—	106	24	no	—
1313	C₂×Q₈	—	106	12	no	—
1314	C₂×Q₈	—	106	24	no	—
1315	C₂×Q₈	—	106	24	no	—
1316	C₂×Q₈	—	106	12	no	—
1317	C₂×Q₈	—	106	24	no	—
1318	C₂×Q₈	—	106	4	no	—
1319	C₂×Q₈	—	106	8	no	—
1320	C₂×Q₈	—	106	12	no	—
1321	C₂×Q₈	C₂³×D₅₃	1	3	yes	—
1322	C₂×Q₈	C₂³×D₅₃	1	6	yes	—
1323	C₂×Q₈	C₂³×D₅₃	1	3	yes	—
1324	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1325	C₂×D₄	—	2	12	no	—
1326	C₂×D₄	—	53	6	no	—
1327	C₂×D₄	—	53	24	no	—
1328	C₂×D₄	—	53	2	no	—
1329	C₂×D₄	—	53	2	no	—
1330	C₂×D₄	—	53	6	no	—
1331	C₂×D₄	—	53	6	no	—
1332	C₂×D₄	—	53	2	no	—
1333	C₂×D₄	—	53	6	no	—
1334	C₂×D₄	—	53	6	no	—
1335	C₂×D₄	—	53	6	no	—
1336	C₂×D₄	—	53	6	no	—
1337	C₂×D₄	—	53	6	no	—
1338	C₂×D₄	—	53	3	no	—
1339	C₂×D₄	—	53	2	no	—
1340	C₂×D₄	—	53	6	no	—
1341	C₂×D₄	—	53	1	no	—
1342	C₂×D₄	—	53	6	no	—
1343	C₂×D₄	—	53	3	no	—
1344	C₂×D₄	—	53	6	no	—
1345	C₂×D₄	—	106	12	no	—
1346	C₂×D₄	—	106	12	no	—
1347	C₂×D₄	—	106	4	no	—
1348	C₂×D₄	—	106	24	no	—
1349	C₂×D₄	—	106	12	no	—
1350	C₂×D₄	—	106	8	no	—
1351	C₂×D₄	—	106	24	no	—
1352	C₂×D₄	—	106	24	no	—
1353	C₂×D₄	—	106	24	no	—
1354	C₂×D₄	—	106	12	no	—
1355	C₂×D₄	—	212	12	no	—
1356	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1357	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1358	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1359	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1360	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1361	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1362	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1363	C₂²×C₄	—	2	12	no	—
1364	C₂²×C₄	—	53	3	no	—
1365	C₂²×C₄	—	53	24	no	—
1366	C₂²×C₄	—	53	3	no	—
1367	C₂²×C₄	—	53	1	no	—
1368	C₂²×C₄	—	53	3	no	—
1369	C₂²×C₄	—	53	3	no	—
1370	C₂²×C₄	—	53	6	no	—
1371	C₂²×C₄	—	53	3	no	—
1372	C₂²×C₄	—	53	6	no	—
1373	C₂²×C₄	—	53	3	no	—
1374	C₂²×C₄	—	53	3	no	—
1375	C₂²×C₄	—	53	1	no	—
1376	C₂²×C₄	—	53	3	no	—
1377	C₂²×C₄	—	53	6	no	—
1378	C₂²×C₄	—	53	2	no	—
1379	C₂²×C₄	—	53	6	no	—
1380	C₂²×C₄	—	53	6	no	—
1381	C₂²×C₄	—	53	1	no	—
1382	C₂²×C₄	—	53	3	no	—
1383	C₂²×C₄	—	53	12	no	—
1384	C₂²×C₄	—	53	3	no	—
1385	C₂²×C₄	—	53	3	no	—
1386	C₂²×C₄	—	53	6	no	—
1387	C₂²×C₄	—	53	6	no	—
1388	C₂²×C₄	—	53	3	no	—
1389	C₂²×C₄	—	53	3	no	—
1390	C₂²×C₄	—	53	3	no	—
1391	C₂²×C₄	—	53	3	no	—
1392	C₂²×C₄	—	53	1	no	—
1393	C₂²×C₄	—	53	1	no	—
1394	C₂²×C₄	—	53	3	no	—
1395	C₂²×C₄	—	53	3	no	—
1396	C₂²×C₄	—	53	12	no	—
1397	C₂²×C₄	—	106	4	no	—
1398	C₂²×C₄	—	106	12	no	—
1399	C₂²×C₄	—	106	12	no	—
1400	C₂²×C₄	—	106	12	no	—
1401	C₂²×C₄	—	106	12	no	—
1402	C₂²×C₄	—	106	12	no	—
1403	C₂²×C₄	—	106	12	no	—
1404	C₂²×C₄	—	106	12	no	—
1405	C₂²×C₄	—	106	12	no	—
1406	C₂²×C₄	—	106	24	no	—
1407	C₂²×C₄	—	106	12	no	—
1408	C₂²×C₄	—	106	24	no	—
1409	C₂²×C₄	—	106	12	no	—
1410	C₂²×C₄	—	106	12	no	—
1411	C₂²×C₄	—	212	12	no	—
1412	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1413	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1414	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1415	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1416	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1417	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1418	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1419	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1420	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1421	C₄⋊C₄	—	53	6	no	—
1422	C₄⋊C₄	—	53	3	no	—
1423	C₄⋊C₄	—	53	6	no	—
1424	C₄⋊C₄	—	53	6	no	—
1425	C₄⋊C₄	—	53	6	no	—
1426	C₄⋊C₄	—	53	12	no	—
1427	C₄⋊C₄	—	53	6	no	—
1428	C₄⋊C₄	—	53	12	no	—
1429	C₄⋊C₄	—	53	12	no	—
1430	C₄⋊C₄	—	53	12	no	—
1431	C₄⋊C₄	—	53	2	no	—
1432	C₄⋊C₄	—	53	1	no	—
1433	C₄⋊C₄	—	53	6	no	—
1434	C₄⋊C₄	—	53	6	no	—
1435	C₄⋊C₄	—	53	6	no	—
1436	C₄⋊C₄	C₂³×D₅₃	1	3	yes	—
1437	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1438	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1439	C₄⋊C₄	C₂³×D₅₃	1	12	yes	—
1440	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1441	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1442	C₂²⋊C₄	—	53	6	no	—
1443	C₂²⋊C₄	—	53	12	no	—
1444	C₂²⋊C₄	—	53	6	no	—
1445	C₂²⋊C₄	—	53	2	no	—
1446	C₂²⋊C₄	—	53	6	no	—
1447	C₂²⋊C₄	—	53	6	no	—
1448	C₂²⋊C₄	—	53	6	no	—
1449	C₂²⋊C₄	—	53	6	no	—
1450	C₂²⋊C₄	—	53	12	no	—
1451	C₂²⋊C₄	—	53	12	no	—
1452	C₂²⋊C₄	—	53	6	no	—
1453	C₂²⋊C₄	—	53	6	no	—
1454	C₂²⋊C₄	—	53	2	no	—
1455	C₂²⋊C₄	—	53	2	no	—
1456	C₂²⋊C₄	—	53	6	no	—
1457	C₂²⋊C₄	—	53	6	no	—
1458	C₂²⋊C₄	—	53	6	no	—
1459	C₂²⋊C₄	—	53	6	no	—
1460	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1461	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
1462	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1463	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1464	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1465	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1466	C₄²	—	53	6	no	—
1467	C₄²	—	53	6	no	—
1468	C₄²	—	53	6	no	—
1469	C₄²	C₂³×D₅₃	1	6	yes	—
1470	C₂³	—	2	6	no	—
1471	C₂³	—	2	6	no	—
1472	C₂³	—	4	3	no	—
1473	C₂³	—	53	1	no	—
1474	C₂³	—	53	12	no	—
1475	C₂³	—	53	4	no	—
1476	C₂³	—	53	1	no	—
1477	C₂³	—	53	3	no	—
1478	C₂³	—	53	3	no	—
1479	C₂³	—	53	2	no	—
1480	C₂³	—	106	2	no	—
1481	C₂³	—	106	6	no	—
1482	C₂³	—	106	6	no	—
1483	C₂³	—	106	2	no	—
1484	C₂³	—	106	4	no	—
1485	C₂³	—	106	6	no	—
1486	C₂³	—	106	6	no	—
1487	C₂³	—	106	6	no	—
1488	C₂³	—	106	4	no	—
1489	C₂³	—	106	4	no	—
1490	C₂³	—	106	6	no	—
1491	C₂³	—	106	6	no	—
1492	C₂³	—	106	6	no	—
1493	C₂³	—	106	6	no	—
1494	C₂³	—	106	6	no	—
1495	C₂³	—	106	6	no	—
1496	C₂³	—	212	3	no	—
1497	C₂³	—	212	3	no	—
1498	C₂³	—	212	3	no	—
1499	C₂³	—	212	48	no	—
1500	C₂³	C₂⁴×D₅₃	1	3	yes	—
1501	C₂³	C₂⁴×D₅₃	1	2	yes	—
1502	C₂³	C₂⁴×D₅₃	1	3	yes	—
1503	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1504	Q₈	—	2	6	no	—
1505	Q₈	—	2	12	no	—
1506	Q₈	—	2	6	no	—
1507	Q₈	—	53	12	no	—
1508	Q₈	—	106	12	no	—
1509	Q₈	—	106	24	no	—
1510	Q₈	—	106	12	no	—
1511	Q₈	—	106	6	no	—
1512	Q₈	—	106	12	no	—
1513	Q₈	—	106	6	no	—
1514	Q₈	C₂×D₄×D₅₃	1	4	yes	—
1515	D₄	—	2	12	no	—
1516	D₄	—	2	12	no	—
1517	D₄	—	2	4	no	—
1518	D₄	—	2	6	no	—
1519	D₄	—	2	2	no	—
1520	D₄	—	4	6	no	—
1521	D₄	—	53	24	no	—
1522	D₄	—	53	12	no	—
1523	D₄	—	106	4	no	—
1524	D₄	—	106	12	no	—
1525	D₄	—	106	12	no	—
1526	D₄	—	106	12	no	—
1527	D₄	—	106	4	no	—
1528	D₄	—	106	4	no	—
1529	D₄	—	106	12	no	—
1530	D₄	—	106	12	no	—
1531	D₄	—	106	12	no	—
1532	D₄	—	106	12	no	—
1533	D₄	—	106	4	no	—
1534	D₄	—	106	6	no	—
1535	D₄	—	106	2	no	—
1536	D₄	—	212	6	no	—
1537	D₄	—	212	6	no	—
1538	D₄	—	212	6	no	—
1539	D₄	C₂×D₄×D₅₃	1	12	yes	—
1540	C₂×C₄	—	2	6	no	—
1541	C₂×C₄	—	2	12	no	—
1542	C₂×C₄	—	2	2	no	—
1543	C₂×C₄	—	2	6	no	—
1544	C₂×C₄	—	2	6	no	—
1545	C₂×C₄	—	2	6	no	—
1546	C₂×C₄	—	2	12	no	—
1547	C₂×C₄	—	4	6	no	—
1548	C₂×C₄	—	53	12	no	—
1549	C₂×C₄	—	53	3	no	—
1550	C₂×C₄	—	53	1	no	—
1551	C₂×C₄	—	53	4	no	—
1552	C₂×C₄	—	53	12	no	—
1553	C₂×C₄	—	53	12	no	—
1554	C₂×C₄	—	53	12	no	—
1555	C₂×C₄	—	53	2	no	—
1556	C₂×C₄	—	53	6	no	—
1557	C₂×C₄	—	53	6	no	—
1558	C₂×C₄	—	53	1	no	—
1559	C₂×C₄	—	53	3	no	—
1560	C₂×C₄	—	106	2	no	—
1561	C₂×C₄	—	106	6	no	—
1562	C₂×C₄	—	106	6	no	—
1563	C₂×C₄	—	106	6	no	—
1564	C₂×C₄	—	106	12	no	—
1565	C₂×C₄	—	106	2	no	—
1566	C₂×C₄	—	106	6	no	—
1567	C₂×C₄	—	106	12	no	—
1568	C₂×C₄	—	106	6	no	—
1569	C₂×C₄	—	106	6	no	—
1570	C₂×C₄	—	106	24	no	—
1571	C₂×C₄	—	106	12	no	—
1572	C₂×C₄	—	106	4	no	—
1573	C₂×C₄	—	106	2	no	—
1574	C₂×C₄	—	106	6	no	—
1575	C₂×C₄	—	106	6	no	—
1576	C₂×C₄	—	106	6	no	—
1577	C₂×C₄	—	106	12	no	—
1578	C₂×C₄	—	106	6	no	—
1579	C₂×C₄	—	106	12	no	—
1580	C₂×C₄	—	106	2	no	—
1581	C₂×C₄	—	106	6	no	—
1582	C₂×C₄	—	106	6	no	—
1583	C₂×C₄	—	106	6	no	—
1584	C₂×C₄	—	106	12	no	—
1585	C₂×C₄	—	212	12	no	—
1586	C₂×C₄	—	212	6	no	—
1587	C₂×C₄	C₂×D₄×D₅₃	1	12	yes	—
1588	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1589	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1590	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1591	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1592	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1593	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1594	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1595	C₂²	—	2	1	no	—
1596	C₂²	—	2	3	no	—
1597	C₂²	—	2	3	no	—
1598	C₂²	—	2	1	no	—
1599	C₂²	—	2	2	no	—
1600	C₂²	—	2	3	no	—
1601	C₂²	—	2	2	no	—
1602	C₂²	—	2	3	no	—
1603	C₂²	—	2	2	no	—
1604	C₂²	—	2	3	no	—
1605	C₂²	—	4	12	no	—
1606	C₂²	—	53	2	no	—
1607	C₂²	—	53	2	no	—
1608	C₂²	—	53	2	no	—
1609	C₂²	—	53	6	no	—
1610	C₂²	—	53	2	no	—
1611	C₂²	—	106	8	no	—
1612	C₂²	—	106	24	no	—
1613	C₂²	—	106	1	no	—
1614	C₂²	—	106	3	no	—
1615	C₂²	—	106	3	no	—
1616	C₂²	—	106	1	no	—
1617	C₂²	—	106	2	no	—
1618	C₂²	—	106	3	no	—
1619	C₂²	—	106	2	no	—
1620	C₂²	—	106	3	no	—
1621	C₂²	—	106	2	no	—
1622	C₂²	—	106	3	no	—
1623	C₂²	—	212	12	no	—
1624	C₂²	—	212	12	no	—
1625	C₂²	—	212	12	no	—
1626	C₂²	—	212	8	no	—
1627	C₂²	—	212	12	no	—
1628	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
1629	C₂²	2₋¹⁺⁴×D₅₃	1	2	yes	complemented
1630	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1631	C₄	—	2	1	no	—
1632	C₄	—	2	3	no	—
1633	C₄	—	2	6	no	—
1634	C₄	—	2	2	no	—
1635	C₄	—	2	6	no	—
1636	C₄	—	53	2	no	—
1637	C₄	—	53	6	no	—
1638	C₄	—	106	1	no	—
1639	C₄	—	106	3	no	—
1640	C₄	—	106	6	no	—
1641	C₄	—	106	2	no	—
1642	C₄	—	106	6	no	—
1643	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1644	C₄	C₂²×D₄×D₅₃	1	6	yes	—
1645	C₂	—	2	2	no	—
1646	C₂	—	2	6	no	—
1647	C₂	—	4	3	no	—
1648	C₂	—	4	2	no	—
1649	C₂	—	53	4	no	—
1650	C₂	—	106	2	no	—
1651	C₂	—	106	6	no	—
1652	C₂	—	212	3	no	—
1653	C₂	—	212	2	no	—
1654	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1655	C₂	C₂×2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1656	C₂	#585×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3489	C₂
hypercenter	#3489	D₅₃
hypocenter	C₅₃	C₂×#3489
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3489

Complements

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

N	H ≅ G/N	type
1. C₂×2₋¹⁺⁴×D₅₃	C₂	semidirect
2. C₂²×#41×D₅₃	C₂	semidirect
3. #20288396	C₂	semidirect
4. #20288395	C₂	semidirect
5. #20288394	C₂	semidirect
6. #20288393	C₂	semidirect
7. #20288392	C₂	semidirect
8. #20288391	C₂	semidirect
9. #20288390	C₂	semidirect
10. #20288389	C₂	semidirect
11. #20288388	C₂	semidirect
12. #20288387	C₂	semidirect
13. #20288386	C₂	semidirect
14. D₄×Q₈×D₅₃	C₂	semidirect
15. #548×D₅₃	C₂	semidirect
16. #547×D₅₃	C₂	semidirect
17. #546×D₅₃	C₂	semidirect
18. #537×D₅₃	C₂	semidirect
19. #536×D₅₃	C₂	semidirect
20. #525×D₅₃	C₂	semidirect
21. C₂×C₂²⋊Q₈×D₅₃	C₂	semidirect
22. #520×D₅₃	C₂	semidirect
23. C₅₃×#3489	C₂	semidirect
24. C₂×#13133265	C₂²	semidirect
25. C₂×#13133265	C₂²	semidirect
26. C₂×#13133264	C₂²	semidirect
27. C₂×#13133264	C₂²	semidirect
28. C₂×#13133264	C₂²	semidirect
30. C₂²×#11719949	C₂²	semidirect
31. C₂²×#11719945	C₂²	semidirect
32. C₂²×#11719947	C₂²	semidirect
38. C₂×#41×D₅₃	C₂²	semidirect
39. C₂×#41×D₅₃	C₂²	semidirect
40. C₂×#41×D₅₃	C₂²	semidirect
41. C₂×#41×D₅₃	C₂²	semidirect
42. C₂×#41×D₅₃	C₂²	semidirect
43. C₂×#41×D₅₃	C₂²	semidirect
45. C₂²×Q₈×D₅₃	C₂²	semidirect
46. C₂²×Q₈×D₅₃	C₂²	semidirect
49. Q₈×D₂₁₂	C₂²	semidirect
50. D₄×Dic₁₀₆	C₂²	semidirect
51. #16811288	C₂²	semidirect
52. Q₈×C₂²⋊D₅₃	C₂²	semidirect
53. Q₈×C₂²⋊D₅₃	C₂²	semidirect
54. #16811286	C₂²	semidirect
55. #16811286	C₂²	semidirect
56. #16811285	C₂²	semidirect
57. #16811284	C₂²	semidirect
58. #16811283	C₂²	semidirect
59. #16811282	C₂²	semidirect
60. #16811281	C₂²	semidirect
61. #16811280	C₂²	semidirect
62. #16811279	C₂²	semidirect
63. #16811278	C₂²	semidirect
64. #16811277	C₂²	semidirect
65. #16811276	C₂²	semidirect
66. #16811275	C₂²	semidirect
67. #16811275	C₂²	semidirect
68. #16811274	C₂²	semidirect
69. #16811273	C₂²	semidirect
70. #16811272	C₂²	semidirect
71. #16811272	C₂²	semidirect
72. #16811271	C₂²	semidirect
73. #16811271	C₂²	semidirect
74. #16811270	C₂²	semidirect
75. #16811269	C₂²	semidirect
76. #16811268	C₂²	semidirect
77. #16811267	C₂²	semidirect
78. #16811266	C₂²	semidirect
79. #16811265	C₂²	semidirect
80. #16811264	C₂²	semidirect
81. #16811263	C₂²	semidirect
82. #16811262	C₂²	semidirect
83. #16811261	C₂²	semidirect
84. #16811260	C₂²	semidirect
85. #16811204	C₂²	semidirect
86. #16811203	C₂²	semidirect
87. #16811203	C₂²	semidirect
88. #16811202	C₂²	semidirect
89. #16811202	C₂²	semidirect
90. #16811201	C₂²	semidirect
91. #16811201	C₂²	semidirect
92. #16811200	C₂²	semidirect
93. #16811199	C₂²	semidirect
94. #16811198	C₂²	semidirect
95. #16811197	C₂²	semidirect
96. #16811196	C₂²	semidirect
97. #16811196	C₂²	semidirect
98. #16811195	C₂²	semidirect
99. #16811194	C₂²	semidirect
100. #16811193	C₂²	semidirect
101. C₄⋊Q₈×D₅₃	C₂²	semidirect
102. #124×D₅₃	C₂²	semidirect
103. #16811136	C₂²	semidirect
104. #16811136	C₂²	semidirect
105. #16811135	C₂²	semidirect
106. #16811134	C₂²	semidirect
107. #16811133	C₂²	semidirect
108. #16811133	C₂²	semidirect
109. #16811132	C₂²	semidirect
110. #16811132	C₂²	semidirect
111. #16811131	C₂²	semidirect
112. #16811130	C₂²	semidirect
113. #16811129	C₂²	semidirect
114. #123×D₅₃	C₂²	semidirect
115. #123×D₅₃	C₂²	semidirect
116. C₂×#13133197	C₂²	semidirect
117. C₂×#13133196	C₂²	semidirect
118. C₂×#13133195	C₂²	semidirect
119. C₂×#13133194	C₂²	semidirect
120. C₂×#13133193	C₂²	semidirect
123. C₂²⋊Q₈×D₅₃	C₂²	semidirect
124. C₂²⋊Q₈×D₅₃	C₂²	semidirect
125. C₂²⋊Q₈×D₅₃	C₂²	semidirect
126. C₂²⋊Q₈×D₅₃	C₂²	semidirect
127. C₂²⋊Q₈×D₅₃	C₂²	semidirect
128. C₂²⋊Q₈×D₅₃	C₂²	semidirect
129. C₂²⋊Q₈×D₅₃	C₂²	semidirect
130. C₂²⋊Q₈×D₅₃	C₂²	semidirect
132. #121×D₅₃	C₂²	semidirect
133. #121×D₅₃	C₂²	semidirect
134. #121×D₅₃	C₂²	semidirect
136. #16811106	C₂²	semidirect
137. #16811105	C₂²	semidirect
138. #16811104	C₂²	semidirect
139. #16811103	C₂²	semidirect
140. #16811102	C₂²	semidirect
141. C₄×Q₈×D₅₃	C₂²	semidirect
143. C₄×D₄×D₅₃	C₂²	semidirect
144. C₄×D₄×D₅₃	C₂²	semidirect
145. #117×D₅₃	C₂²	semidirect
146. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
147. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
149. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
150. C₂²×#41×C₅₃	C₂²	semidirect
151. D₄×Q₈×C₅₃	C₂²	semidirect
152. C₅₃×#548	C₂²	semidirect
153. C₅₃×#547	C₂²	semidirect
154. C₅₃×#546	C₂²	semidirect
155. C₅₃×#537	C₂²	semidirect
156. C₅₃×#536	C₂²	semidirect
157. C₅₃×#525	C₂²	semidirect
158. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
159. C₅₃×#520	C₂²	semidirect
171. C₂×#11719949	C₂³	semidirect
172. C₂×#11719949	C₂³	semidirect
180. C₂×#11719945	C₂³	semidirect
181. C₂×#11719945	C₂³	semidirect
182. C₂×#11719945	C₂³	semidirect
183. C₂×#11719945	C₂³	semidirect
191. C₂×#11719947	C₂³	semidirect
192. C₂×#11719947	C₂³	semidirect
193. C₂×#11719947	C₂³	semidirect
194. C₂×#11719947	C₂³	semidirect
204. #41×D₅₃	D₄	semidirect
206. C₂²×Dic₁₀₆	C₂³	semidirect
207. C₂²×Dic₁₀₆	C₂³	semidirect
208. C₂²×Dic₁₀₆	C₂³	semidirect
218. C₂×Q₈×D₅₃	C₂³	semidirect
219. C₂×Q₈×D₅₃	C₂³	semidirect
220. C₂×Q₈×D₅₃	C₂³	semidirect
221. C₂×Q₈×D₅₃	C₂³	semidirect
252. #13133217	C₂³	semidirect
253. #13133216	C₂³	semidirect
254. #13133216	C₂³	semidirect
255. #13133215	C₂³	semidirect
256. #13133215	C₂³	semidirect
257. #13133206	C₂³	semidirect
258. #13133205	C₂³	semidirect
259. #13133204	C₂³	semidirect
260. #13133203	C₂³	semidirect
261. #13133203	C₂³	semidirect
262. #13133202	C₂³	semidirect
263. #13133202	C₂³	semidirect
264. #13133202	C₂³	semidirect
265. #13133202	C₂³	semidirect
266. #13133201	C₂³	semidirect
267. #13133201	C₂³	semidirect
268. #13133200	C₂³	semidirect
269. #13133200	C₂³	semidirect
270. #13133199	C₂³	semidirect
271. #13133199	C₂³	semidirect
272. #13133199	C₂³	semidirect
273. #13133199	C₂³	semidirect
274. #13133198	C₂³	semidirect
275. #13133198	C₂³	semidirect
278. #13133197	C₂³	semidirect
279. #13133197	C₂³	semidirect
280. #13133197	C₂³	semidirect
281. #13133197	C₂³	semidirect
284. #13133196	C₂³	semidirect
285. #13133196	C₂³	semidirect
286. #13133196	C₂³	semidirect
287. #13133196	C₂³	semidirect
290. #13133195	C₂³	semidirect
291. #13133195	C₂³	semidirect
292. #13133195	C₂³	semidirect
293. #13133195	C₂³	semidirect
296. #13133194	C₂³	semidirect
297. #13133194	C₂³	semidirect
298. #13133194	C₂³	semidirect
299. #13133194	C₂³	semidirect
302. #13133193	C₂³	semidirect
303. #13133193	C₂³	semidirect
304. #13133193	C₂³	semidirect
305. #13133193	C₂³	semidirect
307. #13133192	C₂³	semidirect
308. #13133192	C₂³	semidirect
309. #13133192	C₂³	semidirect
311. #13133191	C₂³	semidirect
312. #13133191	C₂³	semidirect
313. #13133191	C₂³	semidirect
315. #13133190	C₂³	semidirect
316. #13133190	C₂³	semidirect
317. #13133190	C₂³	semidirect
318. #13133190	C₂³	semidirect
320. #13133189	C₂³	semidirect
321. #13133189	C₂³	semidirect
322. #13133189	C₂³	semidirect
323. #13133189	C₂³	semidirect
325. #13133188	C₂³	semidirect
326. #13133188	C₂³	semidirect
327. #13133188	C₂³	semidirect
335. Q₈×Dic₅₃	C₂³	semidirect
336. C₄×Dic₁₀₆	C₂³	semidirect
337. #13133182	C₂³	semidirect
339. C₄×D₂₁₂	C₂³	semidirect
340. C₄×D₂₁₂	C₂³	semidirect
342. D₄×Dic₅₃	C₂³	semidirect
343. D₄×Dic₅₃	C₂³	semidirect
345. #13133179	C₂³	semidirect
346. #13133179	C₂³	semidirect
349. C₄×C₂²⋊D₅₃	C₂³	semidirect
350. C₄×C₂²⋊D₅₃	C₂³	semidirect
351. C₄×C₂²⋊D₅₃	C₂³	semidirect
354. #13133177	C₂³	semidirect
355. #13133177	C₂³	semidirect
356. #13133177	C₂³	semidirect
357. #13133176	C₂³	semidirect
358. #13133175	C₂³	semidirect
359. #13133175	C₂³	semidirect
360. #13133174	C₂³	semidirect
361. #13133173	C₂³	semidirect
362. C₂×C₄⋊Dic₅₃	C₂³	semidirect
363. C₂×C₄⋊Dic₅₃	C₂³	semidirect
364. C₂×#11719919	C₂³	semidirect
365. C₂×#11719919	C₂³	semidirect
366. C₂×#11719919	C₂³	semidirect
373. C₄⋊C₄×D₅₃	C₂³	semidirect
374. C₄⋊C₄×D₅₃	C₂³	semidirect
375. C₄⋊C₄×D₅₃	C₂³	semidirect
376. C₄⋊C₄×D₅₃	C₂³	semidirect
395. C₂×#41×C₅₃	C₂³	semidirect
396. C₂×#41×C₅₃	C₂³	semidirect
398. C₂²×Q₈×C₅₃	C₂³	semidirect
399. C₂²×Q₈×C₅₃	C₂³	semidirect
402. C₄⋊Q₈×C₅₃	C₂³	semidirect
403. #124×C₅₃	C₂³	semidirect
404. #123×C₅₃	C₂³	semidirect
405. #123×C₅₃	C₂³	semidirect
408. C₂²⋊Q₈×C₅₃	C₂³	semidirect
409. C₂²⋊Q₈×C₅₃	C₂³	semidirect
410. C₂²⋊Q₈×C₅₃	C₂³	semidirect
411. C₂²⋊Q₈×C₅₃	C₂³	semidirect
413. #121×C₅₃	C₂³	semidirect
414. #121×C₅₃	C₂³	semidirect
415. #121×C₅₃	C₂³	semidirect
417. C₄×Q₈×C₅₃	C₂³	semidirect
419. C₄×D₄×C₅₃	C₂³	semidirect
420. C₄×D₄×C₅₃	C₂³	semidirect
421. #117×C₅₃	C₂³	semidirect
422. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
423. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
441. #41×C₅₃	C₂×D₄	semidirect
494. #11719949	C₂×D₄	semidirect
514. #11719947	C₂×D₄	semidirect
534. #11719945	C₂×D₄	semidirect
669. C₂²×D₅₃	2₋¹⁺⁴	semidirect
779. C₂²×C₅₃	C₂×2₋¹⁺⁴	semidirect
801. C₂×D₅₃	C₂×2₋¹⁺⁴	semidirect
830. #3489	D₅₃	direct (N × H)
851. D₅₃	#3489	direct (N × H)
858. C₂×2₋¹⁺⁴	C₂×D₅₃	semidirect
873. C₂²×#41	C₂×D₅₃	semidirect
886. D₄×Q₈	C₂×D₅₃	semidirect
894. #548	C₂×D₅₃	semidirect
906. #547	C₂×D₅₃	semidirect
918. #546	C₂×D₅₃	semidirect
927. #537	C₂×D₅₃	semidirect
936. #536	C₂×D₅₃	semidirect
950. #525	C₂×D₅₃	semidirect
968. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
979. #520	C₂×D₅₃	semidirect
988. C₅₃	C₂×#3489	semidirect
1040. C₂×#41	C₂²×D₅₃	semidirect
1041. C₂×#41	C₂²×D₅₃	semidirect
1060. C₂²×Q₈	C₂²×D₅₃	semidirect
1061. C₂²×Q₈	C₂²×D₅₃	semidirect
1099. C₄⋊Q₈	C₂²×D₅₃	semidirect
1105. #124	C₂²×D₅₃	semidirect
1120. #123	C₂²×D₅₃	semidirect
1121. #123	C₂²×D₅₃	semidirect
1154. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1155. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1156. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1157. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1181. #121	C₂²×D₅₃	semidirect
1182. #121	C₂²×D₅₃	semidirect
1183. #121	C₂²×D₅₃	semidirect
1195. C₄×Q₈	C₂²×D₅₃	semidirect
1216. C₄×D₄	C₂²×D₅₃	semidirect
1217. C₄×D₄	C₂²×D₅₃	semidirect
1223. #117	C₂²×D₅₃	semidirect
1239. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1240. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1296. #41	D₄×D₅₃	semidirect
1629. C₂²	2₋¹⁺⁴×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×2₋¹⁺⁴×D₅₃	2
C₂²×#41×D₅₃	2
#20288396	2
#20288395	2
#20288394	2
#20288393	2
#20288392	2
#20288391	2
#20288390	2
#20288389	2
#20288388	2
#20288387	2
#20288386	2
D₄×Q₈×D₅₃	2
#548×D₅₃	2
#547×D₅₃	2
#546×D₅₃	2
#537×D₅₃	2
#536×D₅₃	2
#525×D₅₃	2
C₂×C₂²⋊Q₈×D₅₃	2
#520×D₅₃	2
C₅₃×#3489	2
C₂×#3489	53

Subgroups — D53×#3489 #28292488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3489 #28292488