Subgroups — #28292626

Order 13568.

11534 conjugacy classes of subgroups.

The subgroup lattice has 1668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288393	C₂	1	3	yes	maximal, complemented
4	#20288391	C₂	1	3	yes	maximal, complemented
5	#20288388	C₂	1	1	yes	maximal, characteristic, complemented
6	#20288385	C₂	1	1	yes	maximal, characteristic, complemented
7	#20288384	C₂	1	1	yes	maximal, characteristic, complemented
8	#20288379	C₂	1	3	yes	maximal, complemented
9	#20288376	C₂	1	3	yes	maximal, complemented
10	#20288372	C₂	1	2	yes	maximal, complemented
11	#20288365	C₂	1	2	yes	maximal, complemented
12	#20288354	C₂	1	6	yes	maximal, complemented
13	#20288345	C₂	1	6	yes	maximal, complemented
14	D₄×#11719949	C₂	1	2	yes	maximal, complemented
15	#20288204	C₂	1	2	yes	maximal, complemented
16	#20288202	C₂	1	6	yes	maximal, complemented
17	#20288199	C₂	1	6	yes	maximal, complemented
18	#20288047	C₂	1	3	yes	maximal, complemented
19	#20288043	C₂	1	3	yes	maximal, complemented
20	C₂×#16811136	C₂	1	3	yes	maximal, complemented
21	#525×D₅₃	C₂	1	3	yes	maximal, complemented
22	#20287915	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811460	—	2	16	no	—
25	C₂×#13133265	C₂²	1	2	yes	complemented
26	C₂×#13133265	C₂²	1	3	yes	complemented
27	C₂×#13133263	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13133263	C₂²	1	6	yes	complemented
29	C₂×#13133263	C₂²	1	3	yes	complemented
30	C₂²×#11719949	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#11719949	C₂²	1	3	yes	complemented
32	C₂²×#11719949	C₂²	1	2	yes	complemented
33	C₂²×#11719945	C₂²	1	3	yes	complemented
34	C₂²×#11719947	C₂²	1	3	yes	complemented
35	C₂×#41×D₅₃	—	2	16	no	—
36	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
37	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
38	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
39	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
44	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
45	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
46	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×D₄×D₅₃	C₂²	1	3	yes	complemented
48	C₂³×C₄×D₅₃	C₂²	1	3	yes	complemented
49	#16811295	C₂²	1	2	yes	complemented
50	#16811294	C₂²	1	6	yes	complemented
51	#16811292	C₂²	1	2	yes	complemented
52	#16811291	C₂²	1	6	yes	complemented
53	#16811288	C₂²	1	6	yes	complemented
54	Q₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
55	#16811286	C₂²	1	6	yes	complemented
56	#16811285	C₂²	1	2	yes	complemented
57	#16811284	C₂²	1	2	yes	complemented
58	#16811284	C₂²	1	2	yes	complemented
59	#16811283	C₂²	1	6	yes	complemented
60	#16811283	C₂²	1	6	yes	complemented
61	#16811282	C₂²	1	6	yes	complemented
62	#16811281	C₂²	1	6	yes	complemented
63	#16811276	C₂²	1	6	yes	complemented
64	#16811275	C₂²	1	6	yes	complemented
65	#16811274	C₂²	1	12	yes	complemented
66	#16811272	C₂²	1	6	yes	complemented
67	#16811271	C₂²	1	12	yes	complemented
68	#16811269	C₂²	1	6	yes	complemented
69	#16811268	C₂²	1	6	yes	complemented
70	#16811266	C₂²	1	6	yes	complemented
71	#16811265	C₂²	1	12	yes	complemented
72	#16811265	C₂²	1	12	yes	complemented
73	#16811264	C₂²	1	6	yes	complemented
74	#16811264	C₂²	1	6	yes	complemented
75	#16811263	C₂²	1	12	yes	complemented
76	#16811262	C₂²	1	12	yes	complemented
77	#16811261	C₂²	1	6	yes	complemented
78	#16811261	C₂²	1	6	yes	complemented
79	D₄×D₂₁₂	C₂²	1	6	yes	complemented
80	D₄×D₂₁₂	C₂²	1	6	yes	complemented
81	#16811257	C₂²	1	6	yes	complemented
82	#16811257	C₂²	1	12	yes	complemented
83	D₄×C₂²⋊D₅₃	C₂²	1	6	yes	complemented
84	#16811255	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	#16811201	C₂²	1	3	yes	complemented
89	#16811201	C₂²	1	3	yes	complemented
90	#16811198	C₂²	1	6	yes	complemented
91	#16811197	C₂²	1	3	yes	complemented
92	#16811196	C₂²	1	6	yes	complemented
93	#16811196	C₂²	1	6	yes	complemented
94	#16811192	C₂²	1	3	yes	complemented
95	#16811191	C₂²	1	6	yes	complemented
96	#16811189	C₂²	1	6	yes	complemented
97	#16811189	C₂²	1	6	yes	complemented
98	#16811187	C₂²	1	3	yes	complemented
99	#16811184	C₂²	1	12	yes	complemented
100	#16811181	C₂²	1	12	yes	complemented
101	#16811174	C₂²	1	6	yes	complemented
102	#16811172	C₂²	1	6	yes	complemented
103	#16811168	C₂²	1	12	yes	complemented
104	#16811136	C₂²	1	6	yes	complemented
105	#16811136	C₂²	1	3	yes	complemented
106	#16811136	C₂²	1	6	yes	complemented
107	#16811136	C₂²	1	6	yes	complemented
108	#16811136	C₂²	1	6	yes	complemented
109	#16811136	C₂²	1	3	yes	complemented
110	#16811136	C₂²	1	6	yes	complemented
111	#16811136	C₂²	1	6	yes	complemented
112	#16811136	C₂²	1	6	yes	complemented
113	#16811136	C₂²	1	6	yes	complemented
114	#16811135	C₂²	1	3	yes	complemented
115	#16811134	C₂²	1	3	yes	complemented
116	#16811133	C₂²	1	1	yes	characteristic, complemented
117	#16811133	C₂²	1	3	yes	complemented
118	#16811133	C₂²	1	6	yes	complemented
119	#16811132	C₂²	1	6	yes	complemented
120	#16811132	C₂²	1	6	yes	complemented
121	#16811131	C₂²	1	6	yes	complemented
122	#16811131	C₂²	1	12	yes	complemented
123	#16811130	C₂²	1	3	yes	complemented
124	#16811129	C₂²	1	6	yes	complemented
125	C₂×#13133202	C₂²	1	6	yes	complemented
126	#123×D₅₃	C₂²	1	6	yes	complemented
127	C₂×#13133193	C₂²	1	3	yes	complemented
128	C₂²⋊Q₈×D₅₃	C₂²	1	3	yes	complemented
129	C₂²⋊Q₈×D₅₃	C₂²	1	3	yes	complemented
130	C₂×#13133192	C₂²	1	3	yes	complemented
131	C₂×#13133191	C₂²	1	3	yes	complemented
132	#121×D₅₃	C₂²	1	3	yes	complemented
133	#121×D₅₃	C₂²	1	3	yes	complemented
134	C₂×#13133187	C₂²	1	6	yes	complemented
135	#120×D₅₃	C₂²	1	6	yes	complemented
136	#16811106	C₂²	1	1	yes	characteristic, complemented
137	#16811104	C₂²	1	3	yes	complemented
138	#16811103	C₂²	1	3	yes	complemented
139	#16811099	C₂²	1	2	yes	complemented
140	#16811095	C₂²	1	6	yes	complemented
141	C₄×#11719949	C₂²	1	2	yes	complemented
142	C₄×#11719947	C₂²	1	6	yes	complemented
143	C₂×#13133179	C₂²	1	6	yes	complemented
144	C₂×#13133177	C₂²	1	6	yes	complemented
145	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
146	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
147	C₂×#13133175	C₂²	1	3	yes	complemented
148	#117×D₅₃	C₂²	1	3	yes	complemented
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	#13133263	—	2	8	no	—
164	#13133263	—	2	48	no	—
165	#13133263	—	2	24	no	—
166	C₂×#11719949	—	2	8	no	—
167	C₂×#11719949	—	2	16	no	—
168	C₂×#11719949	—	2	24	no	—
169	C₂×#11719949	C₂³	1	3	yes	—
170	C₂×#11719949	C₂³	1	1	yes	characteristic
171	C₂×#11719949	C₂³	1	3	yes	—
172	C₂×#11719949	C₂³	1	3	yes	—
173	C₂×#11719949	C₂³	1	6	yes	—
174	C₂×#11719949	C₂³	1	1	yes	characteristic
175	C₂×#11719949	C₂³	1	6	yes	complemented
176	C₂×#11719949	C₂³	1	2	yes	complemented
177	C₂×#11719949	C₂³	1	6	yes	complemented
178	C₂×#11719949	C₂³	1	6	yes	complemented
179	C₂×#11719945	—	2	24	no	—
180	C₂×#11719945	C₂³	1	6	yes	—
181	C₂×#11719945	C₂³	1	3	yes	—
182	C₂×#11719945	C₂³	1	3	yes	—
183	C₂×#11719945	C₂³	1	6	yes	—
184	C₂×#11719945	C₂³	1	6	yes	—
185	C₂×#11719945	C₂³	1	3	yes	—
186	C₂×#11719945	C₂³	1	3	yes	—
187	C₂×#11719945	C₂³	1	12	yes	complemented
188	C₂×#11719945	C₂³	1	6	yes	complemented
189	C₂×#11719945	C₂³	1	3	yes	complemented
190	C₂×#11719947	—	2	24	no	—
191	C₂×#11719947	C₂³	1	3	yes	—
192	C₂×#11719947	C₂³	1	6	yes	—
193	C₂×#11719947	C₂³	1	3	yes	—
194	C₂×#11719947	C₂³	1	6	yes	—
195	C₂×#11719947	C₂³	1	1	yes	characteristic
196	C₂×#11719947	C₂³	1	3	yes	—
197	C₂×#11719947	C₂³	1	3	yes	—
198	C₂×#11719947	C₂³	1	6	yes	complemented
199	#41×D₅₃	—	2	8	no	—
200	#41×D₅₃	—	2	8	no	—
201	#41×D₅₃	—	2	8	no	—
202	#41×D₅₃	—	2	24	no	—
203	#41×D₅₃	—	2	48	no	—
204	#41×D₅₃	—	2	24	no	—
205	#41×D₅₃	—	2	24	no	—
206	#41×D₅₃	—	2	24	no	—
207	#41×D₅₃	—	2	24	no	—
208	#41×D₅₃	D₄	1	16	yes	complemented
209	C₂²×Dic₁₀₆	C₂³	1	3	yes	—
210	C₂×Q₈×D₅₃	—	2	8	no	—
211	C₂×Q₈×D₅₃	C₂³	1	3	yes	—
212	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
213	C₂×Q₈×D₅₃	C₂³	1	3	yes	—
214	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
215	C₂×Q₈×D₅₃	C₂³	1	6	yes	complemented
216	C₂×Q₈×D₅₃	C₂³	1	3	yes	complemented
217	C₂²×D₂₁₂	C₂³	1	3	yes	—
218	C₂²×D₂₁₂	C₂³	1	6	yes	—
219	C₂²×D₂₁₂	C₂³	1	6	yes	—
220	C₂²×D₂₁₂	C₂³	1	6	yes	complemented
221	C₂²×D₂₁₂	C₂³	1	3	yes	complemented
222	C₂²×C₂²⋊D₅₃	C₂³	1	6	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	6	yes	—
228	C₂×D₄×D₅₃	C₂³	1	6	yes	—
229	C₂×D₄×D₅₃	C₂³	1	3	yes	—
230	C₂×D₄×D₅₃	C₂³	1	3	yes	—
231	C₂×D₄×D₅₃	C₂³	1	6	yes	—
232	C₂×D₄×D₅₃	C₂³	1	6	yes	—
233	C₂×D₄×D₅₃	C₂³	1	3	yes	—
234	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
235	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
236	C₂×D₄×D₅₃	C₂³	1	3	yes	complemented
237	C₂³×Dic₅₃	C₂³	1	3	yes	—
238	C₂²×C₄×D₅₃	—	2	24	no	—
239	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
240	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
241	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
242	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
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	1	yes	characteristic
249	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
250	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
251	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
252	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
253	#13133216	C₂³	1	12	yes	complemented
254	#13133215	C₂³	1	6	yes	complemented
255	#13133214	C₂³	1	6	yes	complemented
256	#13133213	C₂³	1	6	yes	complemented
257	#13133213	C₂³	1	12	yes	complemented
258	#13133206	C₂³	1	6	yes	complemented
259	#13133206	C₂³	1	6	yes	complemented
260	#13133205	C₂³	1	6	yes	complemented
261	#13133203	C₂³	1	12	yes	complemented
262	#13133203	C₂³	1	12	yes	complemented
263	#13133202	C₂³	1	6	yes	—
264	#13133202	C₂³	1	6	yes	—
265	#13133202	C₂³	1	12	yes	—
266	#13133202	C₂³	1	12	yes	complemented
267	#13133202	C₂³	1	12	yes	complemented
268	#13133202	C₂³	1	12	yes	complemented
269	#13133201	C₂³	1	6	yes	complemented
270	#13133200	C₂³	1	12	yes	complemented
271	#13133200	C₂³	1	6	yes	complemented
272	#13133199	C₂³	1	2	yes	—
273	#13133199	C₂³	1	6	yes	—
274	#13133199	C₂³	1	12	yes	complemented
275	#13133198	C₂³	1	6	yes	complemented
276	#13133197	C₂³	1	1	yes	characteristic
277	#13133197	C₂³	1	6	yes	complemented
278	#13133197	C₂³	1	3	yes	complemented
279	#13133196	C₂³	1	1	yes	characteristic
280	#13133196	C₂³	1	6	yes	complemented
281	#13133196	C₂³	1	3	yes	complemented
282	#13133195	C₂³	1	6	yes	—
283	#13133195	C₂³	1	12	yes	complemented
284	#13133195	C₂³	1	6	yes	complemented
285	#13133195	C₂³	1	12	yes	complemented
286	#13133194	C₂³	1	6	yes	—
287	#13133194	C₂³	1	6	yes	complemented
288	#13133193	C₂³	1	6	yes	—
289	#13133193	C₂³	1	3	yes	—
290	#13133193	C₂³	1	6	yes	complemented
291	#13133193	C₂³	1	6	yes	complemented
292	#13133193	C₂³	1	3	yes	complemented
293	#13133193	C₂³	1	6	yes	complemented
294	#13133192	C₂³	1	6	yes	—
295	#13133192	C₂³	1	3	yes	—
296	#13133192	C₂³	1	12	yes	complemented
297	#13133192	C₂³	1	6	yes	complemented
298	#13133192	C₂³	1	6	yes	complemented
299	#13133192	C₂³	1	12	yes	complemented
300	#13133192	C₂³	1	3	yes	complemented
301	#13133192	C₂³	1	6	yes	complemented
302	#13133191	C₂³	1	6	yes	—
303	#13133191	C₂³	1	3	yes	—
304	#13133191	C₂³	1	12	yes	complemented
305	#13133191	C₂³	1	6	yes	complemented
306	#13133191	C₂³	1	6	yes	complemented
307	#13133191	C₂³	1	3	yes	complemented
308	#13133191	C₂³	1	6	yes	complemented
309	#13133190	C₂³	1	6	yes	—
310	#13133190	C₂³	1	6	yes	complemented
311	#13133190	C₂³	1	12	yes	complemented
312	#13133190	C₂³	1	12	yes	complemented
313	#13133190	C₂³	1	12	yes	complemented
314	#13133190	C₂³	1	12	yes	complemented
315	#13133189	C₂³	1	6	yes	—
316	#13133189	C₂³	1	12	yes	complemented
317	#13133189	C₂³	1	12	yes	complemented
318	#13133189	C₂³	1	6	yes	complemented
319	#13133188	C₂³	1	1	yes	characteristic
320	#13133188	C₂³	1	6	yes	complemented
321	#13133188	C₂³	1	3	yes	complemented
322	#13133187	C₂³	1	12	yes	—
323	#13133187	C₂³	1	6	yes	—
324	#13133187	C₂³	1	12	yes	—
325	#13133187	C₂³	1	6	yes	—
326	#13133187	C₂³	1	6	yes	—
327	#13133187	C₂³	1	12	yes	—
328	#13133187	C₂³	1	12	yes	complemented
329	#13133187	C₂³	1	12	yes	complemented
330	#13133186	C₂³	1	6	yes	—
331	#13133185	C₂³	1	2	yes	—
332	#13133185	C₂³	1	6	yes	—
333	#13133185	C₂³	1	6	yes	—
334	#13133185	C₂³	1	12	yes	complemented
335	#13133185	C₂³	1	12	yes	complemented
336	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
337	C₄×Dic₁₀₆	C₂³	1	6	yes	complemented
338	#13133182	C₂³	1	6	yes	complemented
339	C₄×D₂₁₂	C₂³	1	6	yes	—
340	C₄×D₂₁₂	C₂³	1	6	yes	complemented
341	C₄×D₂₁₂	C₂³	1	6	yes	complemented
342	D₄×Dic₅₃	C₂³	1	2	yes	—
343	D₄×Dic₅₃	C₂³	1	6	yes	complemented
344	D₄×Dic₅₃	C₂³	1	6	yes	complemented
345	#13133179	C₂³	1	12	yes	—
346	#13133179	C₂³	1	6	yes	—
347	#13133179	C₂³	1	6	yes	complemented
348	#13133179	C₂³	1	12	yes	complemented
349	#13133179	C₂³	1	6	yes	complemented
350	#13133179	C₂³	1	12	yes	complemented
351	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	—
352	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	—
353	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
354	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
355	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
356	#13133177	C₂³	1	12	yes	—
357	#13133177	C₂³	1	2	yes	—
358	#13133177	C₂³	1	6	yes	—
359	#13133177	C₂³	1	12	yes	complemented
360	#13133177	C₂³	1	12	yes	complemented
361	#13133177	C₂³	1	6	yes	complemented
362	#13133177	C₂³	1	6	yes	complemented
363	#13133177	C₂³	1	12	yes	complemented
364	#13133176	C₂³	1	3	yes	complemented
365	#13133175	C₂³	1	1	yes	characteristic
366	#13133175	C₂³	1	3	yes	—
367	#13133175	C₂³	1	6	yes	—
368	#13133175	C₂³	1	6	yes	complemented
369	#13133175	C₂³	1	6	yes	complemented
370	#13133174	C₂³	1	6	yes	—
371	#13133173	C₂³	1	6	yes	complemented
372	C₂×C₄⋊Dic₅₃	C₂³	1	3	yes	complemented
373	C₂×#11719919	C₂³	1	6	yes	complemented
374	C₄⋊C₄×D₅₃	C₂³	1	6	yes	complemented
375	C₄⋊C₄×D₅₃	C₂³	1	6	yes	complemented
376	C₄⋊C₄×D₅₃	C₂³	1	3	yes	complemented
377	C₄⋊C₄×D₅₃	C₂³	1	3	yes	complemented
378	C₂×#11719921	C₂³	1	6	yes	—
379	C₂×#11719921	C₂³	1	6	yes	—
380	C₂×#11719921	C₂³	1	6	yes	complemented
381	C₂×#11719921	C₂³	1	6	yes	complemented
382	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
383	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
384	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
385	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
386	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
387	C₂×C₄×Dic₅₃	C₂³	1	6	yes	complemented
388	C₄²×D₅₃	C₂³	1	6	yes	complemented
389	2₋¹⁺⁴×C₅₃	—	2	8	no	—
390	C₂×#41×C₅₃	—	2	8	no	—
391	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
392	C₂×#41×C₅₃	C₂³	1	3	yes	—
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	6	yes	complemented
405	#123×C₅₃	C₂³	1	12	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	3	yes	complemented
415	#121×C₅₃	C₂³	1	12	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	—	4	6	no	—
428	C₂³×D₅₃	—	4	6	no	—
429	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
430	C₂³×D₅₃	C₂⁴	1	3	yes	—
431	C₂³×D₅₃	C₂⁴	1	3	yes	—
432	C₂³×D₅₃	C₂⁴	1	3	yes	—
433	C₂³×D₅₃	C₂⁴	1	6	yes	—
434	C₂³×D₅₃	C₂⁴	1	6	yes	—
435	C₂³×D₅₃	C₂⁴	1	3	yes	—
436	C₂³×D₅₃	C₂⁴	1	3	yes	—
437	#41×C₅₃	—	2	4	no	—
438	#41×C₅₃	—	2	12	no	—
439	#41×C₅₃	—	2	24	no	—
440	#41×C₅₃	—	2	12	no	—
441	#41×C₅₃	—	2	12	no	—
442	#41×C₅₃	C₂×D₄	1	8	yes	complemented
443	C₂×Q₈×C₅₃	—	2	4	no	—
444	C₂×Q₈×C₅₃	—	2	8	no	—
445	C₂×Q₈×C₅₃	—	2	12	no	—
446	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
447	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
448	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
449	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₂×D₄×C₅₃	—	2	12	no	—
451	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
452	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
453	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
455	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
456	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
457	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
458	C₂²×C₄×C₅₃	—	2	12	no	—
459	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
460	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
461	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
462	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
463	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
464	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
466	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
467	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
468	C₂×C₂²⋊D₅₃	—	2	24	no	—
469	C₂×C₂²⋊D₅₃	—	4	12	no	—
470	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
471	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
472	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
473	C₂×C₂²⋊D₅₃	C₂⁴	1	6	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	12	yes	—
479	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
480	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
481	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
482	C₂²×Dic₅₃	—	2	12	no	—
483	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
484	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
485	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
486	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
487	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
488	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
489	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
490	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
491	#11719949	—	2	4	no	—
492	#11719949	—	2	8	no	—
493	#11719949	—	2	12	no	—
494	#11719949	—	2	24	no	—
495	#11719949	—	2	12	no	—
496	#11719949	—	2	12	no	—
497	#11719949	—	2	24	no	—
498	#11719949	—	2	24	no	—
499	#11719949	—	2	24	no	—
500	#11719949	C₂×D₄	1	8	yes	complemented
501	Q₈×D₅₃	—	2	4	no	—
502	Q₈×D₅₃	—	2	12	no	—
503	Q₈×D₅₃	—	2	12	no	—
504	Q₈×D₅₃	—	2	12	no	—
505	Q₈×D₅₃	—	2	24	no	—
506	Q₈×D₅₃	C₂×D₄	1	8	yes	complemented
507	#11719947	—	2	12	no	—
508	#11719947	—	2	24	no	—
509	#11719947	—	2	24	no	—
510	#11719947	—	2	24	no	—
511	#11719947	—	2	4	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	12	no	—
518	D₄×D₅₃	—	2	24	no	—
519	D₄×D₅₃	—	2	24	no	—
520	D₄×D₅₃	—	2	48	no	—
521	D₄×D₅₃	—	2	12	no	—
522	D₄×D₅₃	—	2	12	no	—
523	D₄×D₅₃	—	2	12	no	—
524	D₄×D₅₃	—	4	12	no	—
525	D₄×D₅₃	—	4	12	no	—
526	D₄×D₅₃	C₂×D₄	1	24	yes	complemented
527	#11719945	—	2	12	no	—
528	#11719945	—	2	12	no	—
529	#11719945	—	2	24	no	—
530	#11719945	—	2	48	no	—
531	#11719945	—	2	12	no	—
532	#11719945	—	2	24	no	—
533	#11719945	—	2	24	no	—
534	#11719945	—	2	12	no	—
535	#11719945	—	2	24	no	—
536	#11719945	C₂×D₄	1	24	yes	complemented
537	C₂×D₂₁₂	—	2	24	no	—
538	C₂×D₂₁₂	—	2	12	no	—
539	C₂×D₂₁₂	—	2	12	no	—
540	C₂×D₂₁₂	—	2	24	no	—
541	C₂×D₂₁₂	—	4	12	no	—
542	C₂×D₂₁₂	C₂⁴	1	6	yes	—
543	C₂×D₂₁₂	C₂⁴	1	6	yes	—
544	C₂×D₂₁₂	C₂⁴	1	12	yes	—
545	C₂×D₂₁₂	C₂⁴	1	6	yes	—
546	C₂×D₂₁₂	C₂⁴	1	3	yes	—
547	C₂×D₂₁₂	C₂⁴	1	6	yes	—
548	C₂×D₂₁₂	C₂⁴	1	3	yes	—
549	C₂×D₂₁₂	C₂⁴	1	12	yes	—
550	C₂×D₂₁₂	C₂⁴	1	6	yes	—
551	C₂×D₂₁₂	C₂⁴	1	3	yes	—
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	—	2	4	no	—
557	C₂×C₄×D₅₃	—	2	12	no	—
558	C₂×C₄×D₅₃	—	2	12	no	—
559	C₂×C₄×D₅₃	—	2	12	no	—
560	C₂×C₄×D₅₃	—	2	12	no	—
561	C₂×C₄×D₅₃	—	2	12	no	—
562	C₂×C₄×D₅₃	—	2	12	no	—
563	C₂×C₄×D₅₃	—	2	12	no	—
564	C₂×C₄×D₅₃	—	2	24	no	—
565	C₂×C₄×D₅₃	C₂×D₄	1	24	yes	complemented
566	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
567	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
568	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
569	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
570	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
571	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
572	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
573	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
574	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
575	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
576	C₂×C₄×D₅₃	C₂⁴	1	3	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	1	yes	characteristic
581	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
582	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
583	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
584	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
585	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
586	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
587	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
588	C₂×Dic₁₀₆	—	2	12	no	—
589	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
590	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
591	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
592	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
593	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
594	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
595	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
596	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
597	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
598	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
599	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
600	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
601	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
602	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
603	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
604	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
605	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
606	C₄²×C₅₃	C₂⁴	1	6	yes	—
607	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
608	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
609	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
610	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
611	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
612	#11719921	C₂⁴	1	2	yes	—
613	#11719921	C₂⁴	1	2	yes	—
614	#11719921	C₂⁴	1	6	yes	—
615	#11719921	C₂⁴	1	6	yes	—
616	#11719921	C₂⁴	1	6	yes	—
617	#11719921	C₂⁴	1	6	yes	—
618	#11719921	C₂⁴	1	6	yes	—
619	#11719921	C₂⁴	1	6	yes	—
620	#11719921	C₂⁴	1	6	yes	—
621	#11719921	C₂⁴	1	6	yes	—
622	#11719921	C₂⁴	1	12	yes	—
623	#11719921	C₂⁴	1	12	yes	—
624	#11719921	C₂⁴	1	12	yes	—
625	#11719921	C₂⁴	1	12	yes	—
626	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
627	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
628	C₄⋊Dic₅₃	C₂⁴	1	3	yes	—
629	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
630	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
631	#11719919	C₂⁴	1	2	yes	—
632	#11719919	C₂⁴	1	6	yes	—
633	#11719919	C₂⁴	1	6	yes	—
634	#11719919	C₂⁴	1	6	yes	—
635	#11719919	C₂⁴	1	6	yes	—
636	#11719919	C₂⁴	1	6	yes	—
637	#11719919	C₂⁴	1	12	yes	—
638	C₄×Dic₅₃	C₂⁴	1	2	yes	—
639	C₄×Dic₅₃	C₂⁴	1	6	yes	—
640	C₄×Dic₅₃	C₂⁴	1	6	yes	—
641	C₄×Dic₅₃	C₂⁴	1	12	yes	—
642	C₂³×C₅₃	—	2	6	no	—
643	C₂³×C₅₃	—	2	6	no	—
644	C₂³×C₅₃	—	4	3	no	—
645	C₂³×C₅₃	C₂⁵	1	3	yes	—
646	C₂³×C₅₃	C₂⁵	1	2	yes	—
647	C₂³×C₅₃	C₂⁵	1	3	yes	—
648	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
649	C₂²×D₅₃	—	2	2	no	—
650	C₂²×D₅₃	—	2	2	no	—
651	C₂²×D₅₃	—	2	2	no	—
652	C₂²×D₅₃	—	2	6	no	—
653	C₂²×D₅₃	—	2	6	no	—
654	C₂²×D₅₃	—	2	12	no	—
655	C₂²×D₅₃	—	2	6	no	—
656	C₂²×D₅₃	—	2	6	no	—
657	C₂²×D₅₃	—	2	6	no	—
658	C₂²×D₅₃	—	2	6	no	—
659	C₂²×D₅₃	—	2	6	no	—
660	C₂²×D₅₃	—	2	12	no	—
661	C₂²×D₅₃	—	4	3	no	—
662	C₂²×D₅₃	—	4	3	no	—
663	C₂²×D₅₃	—	4	3	no	—
664	C₂²×D₅₃	—	4	3	no	—
665	C₂²×D₅₃	—	4	3	no	—
666	C₂²×D₅₃	—	4	3	no	—
667	C₂²×D₅₃	—	4	3	no	—
668	C₂²×D₅₃	—	4	6	no	—
669	C₂²×D₅₃	—	4	6	no	—
670	C₂²×D₅₃	—	4	6	no	—
671	C₂²×D₅₃	—	4	6	no	—
672	C₂²×D₅₃	—	4	48	no	—
673	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
674	C₂²×D₅₃	C₂⁵	1	6	yes	—
675	C₂²×D₅₃	C₂⁵	1	3	yes	—
676	C₂²×D₅₃	C₂⁵	1	3	yes	—
677	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
678	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
679	Q₈×C₅₃	—	2	6	no	—
680	Q₈×C₅₃	—	2	12	no	—
681	Q₈×C₅₃	—	2	6	no	—
682	Q₈×C₅₃	C₂²×D₄	1	4	yes	—
683	D₄×C₅₃	—	2	12	no	—
684	D₄×C₅₃	—	2	12	no	—
685	D₄×C₅₃	—	2	4	no	—
686	D₄×C₅₃	—	2	2	no	—
687	D₄×C₅₃	—	2	6	no	—
688	D₄×C₅₃	—	4	6	no	—
689	D₄×C₅₃	C₂²×D₄	1	12	yes	—
690	C₂×C₄×C₅₃	—	2	6	no	—
691	C₂×C₄×C₅₃	—	2	12	no	—
692	C₂×C₄×C₅₃	—	2	6	no	—
693	C₂×C₄×C₅₃	—	2	2	no	—
694	C₂×C₄×C₅₃	—	2	6	no	—
695	C₂×C₄×C₅₃	—	2	6	no	—
696	C₂×C₄×C₅₃	—	2	12	no	—
697	C₂×C₄×C₅₃	—	4	6	no	—
698	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
699	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
700	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
701	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
702	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
703	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
704	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
705	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
706	C₂²⋊D₅₃	—	2	12	no	—
707	C₂²⋊D₅₃	—	2	12	no	—
708	C₂²⋊D₅₃	—	2	12	no	—
709	C₂²⋊D₅₃	—	2	4	no	—
710	C₂²⋊D₅₃	—	2	12	no	—
711	C₂²⋊D₅₃	—	2	4	no	—
712	C₂²⋊D₅₃	—	2	12	no	—
713	C₂²⋊D₅₃	—	2	12	no	—
714	C₂²⋊D₅₃	—	4	6	no	—
715	C₂²⋊D₅₃	—	4	6	no	—
716	C₂²⋊D₅₃	—	4	12	no	—
717	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	—
718	C₂×Dic₅₃	—	2	6	no	—
719	C₂×Dic₅₃	—	2	6	no	—
720	C₂×Dic₅₃	—	2	2	no	—
721	C₂×Dic₅₃	—	2	4	no	—
722	C₂×Dic₅₃	—	2	6	no	—
723	C₂×Dic₅₃	—	2	6	no	—
724	C₂×Dic₅₃	—	4	6	no	—
725	C₂×Dic₅₃	C₂²×D₄	1	12	yes	—
726	C₂×Dic₅₃	C₂⁵	1	2	yes	—
727	C₂×Dic₅₃	C₂⁵	1	3	yes	—
728	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
729	C₂×Dic₅₃	C₂⁵	1	2	yes	—
730	C₂×Dic₅₃	C₂⁵	1	6	yes	—
731	C₂×Dic₅₃	C₂⁵	1	3	yes	—
732	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
733	D₂₁₂	—	2	12	no	—
734	D₂₁₂	—	2	24	no	—
735	D₂₁₂	—	2	12	no	—
736	D₂₁₂	—	2	12	no	—
737	D₂₁₂	—	2	12	no	—
738	D₂₁₂	—	2	6	no	—
739	D₂₁₂	—	2	6	no	—
740	D₂₁₂	—	4	12	no	—
741	D₂₁₂	—	4	6	no	—
742	D₂₁₂	C₂²×D₄	1	12	yes	—
743	C₄×D₅₃	—	2	2	no	—
744	C₄×D₅₃	—	2	6	no	—
745	C₄×D₅₃	—	2	6	no	—
746	C₄×D₅₃	—	2	6	no	—
747	C₄×D₅₃	—	2	12	no	—
748	C₄×D₅₃	—	2	2	no	—
749	C₄×D₅₃	—	2	6	no	—
750	C₄×D₅₃	—	2	6	no	—
751	C₄×D₅₃	—	2	6	no	—
752	C₄×D₅₃	—	2	12	no	—
753	C₄×D₅₃	—	2	2	no	—
754	C₄×D₅₃	—	2	6	no	—
755	C₄×D₅₃	—	2	6	no	—
756	C₄×D₅₃	—	2	6	no	—
757	C₄×D₅₃	—	2	12	no	—
758	C₄×D₅₃	—	2	24	no	—
759	C₄×D₅₃	—	4	6	no	—
760	C₄×D₅₃	—	4	6	no	—
761	C₄×D₅₃	C₂²×D₄	1	4	yes	—
762	C₄×D₅₃	C₂²×D₄	1	12	yes	—
763	C₄×D₅₃	C₂²×D₄	1	12	yes	—
764	C₄×D₅₃	C₂²×D₄	1	12	yes	—
765	Dic₁₀₆	—	2	6	no	—
766	Dic₁₀₆	—	2	2	no	—
767	Dic₁₀₆	—	2	12	no	—
768	Dic₁₀₆	—	2	12	no	—
769	Dic₁₀₆	C₂²×D₄	1	12	yes	—
770	#62811	—	53	1	no	maximal, Sylow
771	C₂²×C₅₃	—	2	1	no	—
772	C₂²×C₅₃	—	2	3	no	—
773	C₂²×C₅₃	—	2	3	no	—
774	C₂²×C₅₃	—	2	1	no	—
775	C₂²×C₅₃	—	2	3	no	—
776	C₂²×C₅₃	—	2	2	no	—
777	C₂²×C₅₃	—	2	2	no	—
778	C₂²×C₅₃	—	2	3	no	—
779	C₂²×C₅₃	—	2	2	no	—
780	C₂²×C₅₃	—	2	3	no	—
781	C₂²×C₅₃	—	4	12	no	—
782	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
783	C₂²×C₅₃	#585	1	2	yes	complemented
784	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
785	C₂×D₅₃	—	2	8	no	—
786	C₂×D₅₃	—	2	1	no	—
787	C₂×D₅₃	—	2	3	no	—
788	C₂×D₅₃	—	2	3	no	—
789	C₂×D₅₃	—	2	1	no	—
790	C₂×D₅₃	—	2	1	no	—
791	C₂×D₅₃	—	2	1	no	—
792	C₂×D₅₃	—	2	6	no	—
793	C₂×D₅₃	—	2	3	no	—
794	C₂×D₅₃	—	2	6	no	—
795	C₂×D₅₃	—	2	3	no	—
796	C₂×D₅₃	—	2	3	no	—
797	C₂×D₅₃	—	2	6	no	—
798	C₂×D₅₃	—	4	12	no	—
799	C₂×D₅₃	—	4	12	no	—
800	C₂×D₅₃	—	4	12	no	—
801	C₂×D₅₃	—	4	12	no	—
802	C₂×D₅₃	—	4	12	no	—
803	C₂×D₅₃	—	8	12	no	—
804	C₂×D₅₃	—	8	12	no	—
805	C₂×D₅₃	C₂³×D₄	1	2	yes	—
806	C₂×D₅₃	C₂³×D₄	1	6	yes	—
807	C₂×D₅₃	#585	1	2	yes	complemented
808	C₄×C₅₃	—	2	3	no	—
809	C₄×C₅₃	—	2	6	no	—
810	C₄×C₅₃	—	2	1	no	—
811	C₄×C₅₃	—	2	2	no	—
812	C₄×C₅₃	—	2	6	no	—
813	C₄×C₅₃	C₂³×D₄	1	6	yes	—
814	C₄×C₅₃	C₂³×D₄	1	2	yes	—
815	Dic₅₃	—	2	2	no	—
816	Dic₅₃	—	2	3	no	—
817	Dic₅₃	—	2	1	no	—
818	Dic₅₃	—	2	2	no	—
819	Dic₅₃	—	2	6	no	—
820	Dic₅₃	C₂³×D₄	1	6	yes	—
821	Dic₅₃	C₂³×D₄	1	2	yes	—
822	C₂×#585	—	53	1	no	—
823	C₂³×#41	—	53	1	no	—
824	#3489	—	53	1	no	—
825	#3489	—	53	3	no	—
826	#3489	—	53	3	no	—
827	#3489	D₅₃	1	1	yes	characteristic, complemented
828	#3488	—	53	1	no	—
829	#3488	—	53	3	no	—
830	#3488	—	53	3	no	—
831	#3488	—	53	1	no	—
832	#3487	—	53	2	no	—
833	#3486	—	53	2	no	—
834	#3485	—	53	6	no	—
835	#3484	—	53	6	no	—
836	D₄×#41	—	53	2	no	—
837	D₄×#41	—	53	2	no	—
838	D₄×#41	—	53	6	no	—
839	D₄×#41	—	53	6	no	—
840	#3449	—	53	3	no	—
841	#3449	—	53	3	no	—
842	C₂×#525	—	53	3	no	—
843	C₂×#525	—	53	3	no	—
844	#3428	—	53	1	no	—
845	C₂×C₅₃	—	2	2	no	—
846	C₂×C₅₃	—	2	6	no	—
847	C₂×C₅₃	—	4	3	no	—
848	C₂×C₅₃	—	4	2	no	—
849	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
850	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
851	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
852	D₅₃	—	2	2	no	—
853	D₅₃	—	2	2	no	—
854	D₅₃	—	2	6	no	—
855	D₅₃	—	4	3	no	—
856	D₅₃	—	4	6	no	—
857	#585	—	106	16	no	—
858	C₂×2₋¹⁺⁴	—	53	2	no	—
859	C₂×2₋¹⁺⁴	—	53	3	no	—
860	C₂×2₋¹⁺⁴	C₂×D₅₃	1	1	yes	characteristic, complemented
861	C₂×H(5,𝔽₂)	—	53	1	no	—
862	C₂×H(5,𝔽₂)	—	53	6	no	—
863	C₂×H(5,𝔽₂)	—	53	3	no	—
864	C₂²×#41	—	53	1	no	—
865	C₂²×#41	—	53	3	no	—
866	C₂²×#41	—	53	1	no	—
867	C₂²×#41	—	53	3	no	—
868	C₂²×#41	—	53	3	no	—
869	C₂²×#41	—	53	1	no	—
870	C₂²×#41	—	53	3	no	—
871	C₂²×#41	—	53	1	no	—
872	C₂²×#41	—	53	3	no	—
873	C₂²×#41	—	53	6	no	—
874	C₂²×#41	—	53	1	no	—
875	C₂²×#41	—	53	3	no	—
876	C₂²×#41	—	53	2	no	—
877	C₂²×#41	—	53	3	no	—
878	C₂²×#41	—	53	3	no	—
879	C₂²×#41	—	106	16	no	—
880	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
881	C₂³×Q₈	—	53	1	no	—
882	C₂³×D₄	—	53	3	no	—
883	C₂⁴×C₄	—	53	3	no	—
884	#550	—	53	2	no	—
885	#550	—	53	6	no	—
886	#550	—	53	2	no	—
887	#550	—	53	6	no	—
888	D₄×Q₈	—	53	2	no	—
889	D₄×Q₈	—	53	6	no	—
890	D₄×Q₈	—	53	6	no	—
891	D₄×Q₈	C₂×D₅₃	1	2	yes	complemented
892	#548	—	53	2	no	—
893	#548	—	53	2	no	—
894	#548	—	53	6	no	—
895	#548	—	53	6	no	—
896	#548	—	53	6	no	—
897	#548	—	53	2	no	—
898	#548	—	53	6	no	—
899	#548	C₂×D₅₃	1	2	yes	complemented
900	#547	—	53	6	no	—
901	#547	—	53	6	no	—
902	#547	—	53	12	no	—
903	#547	—	53	6	no	—
904	#547	—	53	12	no	—
905	#547	C₂×D₅₃	1	6	yes	complemented
906	#546	—	53	6	no	—
907	#546	—	53	6	no	—
908	#546	—	53	6	no	—
909	#546	—	53	12	no	—
910	#546	—	53	12	no	—
911	#546	—	53	6	no	—
912	#546	—	53	6	no	—
913	#546	—	53	12	no	—
914	#546	—	53	6	no	—
915	#546	—	53	6	no	—
916	#546	—	53	12	no	—
917	#546	C₂×D₅₃	1	6	yes	complemented
918	D₄²	—	53	6	no	—
919	D₄²	—	53	6	no	—
920	D₄²	—	53	12	no	—
921	D₄²	—	53	12	no	—
922	D₄²	—	53	6	no	—
923	D₄²	—	53	6	no	—
924	#537	—	53	3	no	—
925	#537	—	53	3	no	—
926	#537	—	53	6	no	—
927	#537	—	53	6	no	—
928	#537	—	53	3	no	—
929	#537	C₂×D₅₃	1	3	yes	complemented
930	#536	—	53	3	no	—
931	#536	—	53	6	no	—
932	#536	—	53	6	no	—
933	#536	—	53	6	no	—
934	#536	C₂×D₅₃	1	3	yes	complemented
935	#535	—	53	3	no	—
936	#535	—	53	6	no	—
937	#535	—	53	6	no	—
938	#535	—	53	6	no	—
939	#535	—	53	3	no	—
940	#534	—	53	12	no	—
941	#534	—	53	12	no	—
942	#532	—	53	6	no	—
943	#532	—	53	6	no	—
944	#532	—	53	12	no	—
945	#525	—	53	3	no	—
946	#525	—	53	3	no	—
947	#525	—	53	6	no	—
948	#525	—	53	12	no	—
949	#525	—	53	3	no	—
950	#525	—	53	6	no	—
951	#525	—	53	6	no	—
952	#525	—	53	6	no	—
953	#525	—	53	3	no	—
954	#525	—	53	6	no	—
955	#525	—	53	6	no	—
956	#525	—	53	6	no	—
957	#525	—	53	6	no	—
958	#525	—	53	6	no	—
959	#525	—	53	1	no	—
960	#525	—	53	3	no	—
961	#525	—	53	6	no	—
962	#525	—	53	6	no	—
963	#525	—	53	6	no	—
964	#525	—	53	6	no	—
965	#525	—	53	3	no	—
966	#525	C₂×D₅₃	1	3	yes	complemented
967	C₂×#123	—	53	6	no	—
968	C₂×#123	—	53	6	no	—
969	C₂×C₂²⋊Q₈	—	53	3	no	—
970	C₂×C₂²⋊Q₈	—	53	3	no	—
971	C₂×C₂²⋊Q₈	—	53	3	no	—
972	C₂×C₂²⋊Q₈	C₂×D₅₃	1	3	yes	complemented
973	C₂×#121	—	53	3	no	—
974	C₂×#121	—	53	3	no	—
975	C₂×#121	—	53	3	no	—
976	C₂×#121	—	53	3	no	—
977	C₂×#120	—	53	6	no	—
978	C₂×#120	—	53	6	no	—
979	#520	—	53	1	no	—
980	#520	—	53	3	no	—
981	#520	—	53	3	no	—
982	#520	C₂×D₅₃	1	1	yes	characteristic, complemented
983	#519	—	53	2	no	—
984	#518	—	53	6	no	—
985	C₄×#41	—	53	2	no	—
986	C₄×#41	—	53	6	no	—
987	C₂×C₄×D₄	—	53	6	no	—
988	C₂×C₄×D₄	—	53	6	no	—
989	C₂×C₄×D₄	—	53	6	no	—
990	C₂×C₄×D₄	—	53	6	no	—
991	C₂×#117	—	53	3	no	—
992	C₂×#117	—	53	3	no	—
993	C₅₃	#62811	1	1	yes	characteristic, complemented, Sylow
994	C₂⁵	—	53	3	no	—
995	2₋¹⁺⁴	—	2	8	no	—
996	2₋¹⁺⁴	—	106	16	no	—
997	2₋¹⁺⁴	—	106	24	no	—
998	H(5,𝔽₂)	—	106	48	no	—
999	H(5,𝔽₂)	—	106	24	no	—
1000	H(5,𝔽₂)	—	106	8	no	—
1001	C₂×#41	—	2	8	no	—
1002	C₂×#41	—	53	16	no	—
1003	C₂×#41	—	53	1	no	—
1004	C₂×#41	—	53	3	no	—
1005	C₂×#41	—	53	3	no	—
1006	C₂×#41	—	53	6	no	—
1007	C₂×#41	—	53	6	no	—
1008	C₂×#41	—	53	6	no	—
1009	C₂×#41	—	53	3	no	—
1010	C₂×#41	—	53	6	no	—
1011	C₂×#41	—	53	1	no	—
1012	C₂×#41	—	53	2	no	—
1013	C₂×#41	—	53	3	no	—
1014	C₂×#41	—	53	1	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	3	no	—
1021	C₂×#41	—	53	3	no	—
1022	C₂×#41	—	53	6	no	—
1023	C₂×#41	—	53	3	no	—
1024	C₂×#41	—	53	6	no	—
1025	C₂×#41	—	53	3	no	—
1026	C₂×#41	—	53	3	no	—
1027	C₂×#41	—	53	6	no	—
1028	C₂×#41	—	53	12	no	—
1029	C₂×#41	—	53	3	no	—
1030	C₂×#41	—	53	6	no	—
1031	C₂×#41	—	106	24	no	—
1032	C₂×#41	—	106	24	no	—
1033	C₂×#41	—	106	24	no	—
1034	C₂×#41	—	106	24	no	—
1035	C₂×#41	—	106	24	no	—
1036	C₂×#41	—	106	24	no	—
1037	C₂×#41	—	106	8	no	—
1038	C₂×#41	—	106	16	no	—
1039	C₂×#41	—	106	8	no	—
1040	C₂×#41	—	106	8	no	—
1041	C₂×#41	—	106	24	no	—
1042	C₂×#41	—	106	24	no	—
1043	C₂×#41	—	106	48	no	—
1044	C₂×#41	—	106	8	no	—
1045	C₂×#41	C₂²×D₅₃	1	3	yes	—
1046	C₂×#41	C₂²×D₅₃	1	3	yes	—
1047	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1048	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1049	C₂×#41	C₂²×D₅₃	1	3	yes	complemented
1050	C₂×#41	C₂²×D₅₃	1	6	yes	complemented
1051	C₂²×Q₈	—	53	1	no	—
1052	C₂²×Q₈	—	53	3	no	—
1053	C₂²×Q₈	—	53	3	no	—
1054	C₂²×Q₈	—	53	3	no	—
1055	C₂²×Q₈	—	53	1	no	—
1056	C₂²×Q₈	—	53	6	no	—
1057	C₂²×Q₈	—	53	3	no	—
1058	C₂²×Q₈	—	106	8	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	6	no	—
1065	C₂²×D₄	—	53	6	no	—
1066	C₂²×D₄	—	53	3	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	12	no	—
1073	C₂²×D₄	—	53	6	no	—
1074	C₂²×D₄	—	53	6	no	—
1075	C₂²×D₄	—	53	6	no	—
1076	C₂²×D₄	—	53	6	no	—
1077	C₂²×D₄	—	53	3	no	—
1078	C₂²×D₄	—	53	3	no	—
1079	C₂²×D₄	—	53	6	no	—
1080	C₂²×D₄	—	53	6	no	—
1081	C₂²×D₄	—	106	24	no	—
1082	C₂²×D₄	C₂²×D₅₃	1	3	yes	—
1083	C₂³×C₄	—	53	3	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	6	no	—
1089	C₂³×C₄	—	53	6	no	—
1090	C₂³×C₄	—	53	3	no	—
1091	C₂³×C₄	—	53	3	no	—
1092	C₂³×C₄	—	53	3	no	—
1093	C₂³×C₄	—	53	3	no	—
1094	C₂³×C₄	—	53	1	no	—
1095	C₂³×C₄	—	53	3	no	—
1096	C₂³×C₄	—	53	3	no	—
1097	C₂³×C₄	—	53	3	no	—
1098	C₂³×C₄	—	106	24	no	—
1099	C₂³×C₄	C₂²×D₅₃	1	3	yes	—
1100	C₄⋊Q₈	—	53	6	no	—
1101	C₄⋊Q₈	—	53	12	no	—
1102	C₄⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1103	#127	—	53	12	no	—
1104	#127	—	53	6	no	—
1105	#127	—	53	6	no	—
1106	#124	—	53	6	no	—
1107	#124	—	53	6	no	—
1108	#124	—	53	12	no	—
1109	#124	—	53	12	no	—
1110	#124	—	53	6	no	—
1111	#124	C₂²×D₅₃	1	6	yes	complemented
1112	#123	—	53	6	no	—
1113	#123	—	53	6	no	—
1114	#123	—	53	12	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	—	53	12	no	—
1121	#123	—	53	2	no	—
1122	#123	—	53	6	no	—
1123	#123	—	53	6	no	—
1124	#123	—	53	12	no	—
1125	#123	C₂²×D₅₃	1	6	yes	complemented
1126	#123	C₂²×D₅₃	1	12	yes	complemented
1127	C₂²⋊Q₈	—	53	3	no	—
1128	C₂²⋊Q₈	—	53	6	no	—
1129	C₂²⋊Q₈	—	53	3	no	—
1130	C₂²⋊Q₈	—	53	6	no	—
1131	C₂²⋊Q₈	—	53	6	no	—
1132	C₂²⋊Q₈	—	53	6	no	—
1133	C₂²⋊Q₈	—	53	1	no	—
1134	C₂²⋊Q₈	—	53	3	no	—
1135	C₂²⋊Q₈	—	53	6	no	—
1136	C₂²⋊Q₈	—	53	1	no	—
1137	C₂²⋊Q₈	—	53	3	no	—
1138	C₂²⋊Q₈	—	53	6	no	—
1139	C₂²⋊Q₈	—	53	6	no	—
1140	C₂²⋊Q₈	—	53	12	no	—
1141	C₂²⋊Q₈	—	53	12	no	—
1142	C₂²⋊Q₈	—	53	6	no	—
1143	C₂²⋊Q₈	—	53	6	no	—
1144	C₂²⋊Q₈	—	53	6	no	—
1145	C₂²⋊Q₈	C₂²×D₅₃	1	3	yes	—
1146	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	—
1147	C₂²⋊Q₈	C₂²×D₅₃	1	3	yes	complemented
1148	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1149	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1150	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1151	#121	—	53	1	no	—
1152	#121	—	53	3	no	—
1153	#121	—	53	6	no	—
1154	#121	—	53	6	no	—
1155	#121	—	53	6	no	—
1156	#121	—	53	12	no	—
1157	#121	—	53	12	no	—
1158	#121	—	53	3	no	—
1159	#121	—	53	6	no	—
1160	#121	—	53	3	no	—
1161	#121	—	53	6	no	—
1162	#121	—	53	6	no	—
1163	#121	—	53	6	no	—
1164	#121	—	53	12	no	—
1165	#121	—	53	3	no	—
1166	#121	—	53	3	no	—
1167	#121	—	53	6	no	—
1168	#121	—	53	6	no	—
1169	#121	—	53	6	no	—
1170	#121	—	53	6	no	—
1171	#121	—	53	12	no	—
1172	#121	—	53	12	no	—
1173	#121	—	53	6	no	—
1174	#121	—	53	6	no	—
1175	#121	—	53	12	no	—
1176	#121	—	53	12	no	—
1177	#121	—	53	12	no	—
1178	#121	—	53	12	no	—
1179	#121	C₂²×D₅₃	1	1	yes	characteristic
1180	#121	C₂²×D₅₃	1	3	yes	complemented
1181	#121	C₂²×D₅₃	1	6	yes	complemented
1182	#121	C₂²×D₅₃	1	12	yes	complemented
1183	#120	—	53	6	no	—
1184	#120	—	53	2	no	—
1185	#120	—	53	6	no	—
1186	#120	—	53	6	no	—
1187	#120	—	53	12	no	—
1188	#120	—	53	12	no	—
1189	#120	—	53	6	no	—
1190	#120	—	53	6	no	—
1191	#120	—	53	12	no	—
1192	#120	—	53	12	no	—
1193	#120	—	53	6	no	—
1194	#120	—	53	12	no	—
1195	#120	—	53	12	no	—
1196	#120	—	53	12	no	—
1197	#120	C₂²×D₅₃	1	6	yes	—
1198	C₄×Q₈	—	53	2	no	—
1199	C₄×Q₈	—	53	6	no	—
1200	C₄×Q₈	—	53	6	no	—
1201	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1202	C₄×D₄	—	53	2	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	6	no	—
1208	C₄×D₄	—	53	6	no	—
1209	C₄×D₄	—	53	12	no	—
1210	C₄×D₄	—	53	6	no	—
1211	C₄×D₄	—	53	6	no	—
1212	C₄×D₄	—	53	12	no	—
1213	C₄×D₄	—	53	12	no	—
1214	C₄×D₄	—	53	12	no	—
1215	C₄×D₄	—	53	6	no	—
1216	C₄×D₄	—	53	2	no	—
1217	C₄×D₄	—	53	6	no	—
1218	C₄×D₄	—	53	6	no	—
1219	C₄×D₄	—	53	6	no	—
1220	C₄×D₄	—	53	12	no	—
1221	C₄×D₄	—	53	12	no	—
1222	C₄×D₄	—	53	12	no	—
1223	C₄×D₄	—	53	12	no	—
1224	C₄×D₄	—	53	6	no	—
1225	C₄×D₄	—	53	6	no	—
1226	C₄×D₄	—	53	6	no	—
1227	C₄×D₄	C₂²×D₅₃	1	6	yes	—
1228	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1229	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1230	#117	—	53	3	no	—
1231	#117	—	53	1	no	—
1232	#117	—	53	3	no	—
1233	#117	—	53	6	no	—
1234	#117	—	53	6	no	—
1235	#117	—	53	6	no	—
1236	#117	—	53	6	no	—
1237	#117	—	53	6	no	—
1238	#117	C₂²×D₅₃	1	3	yes	complemented
1239	C₂×C₄⋊C₄	—	53	3	no	—
1240	C₂×C₄⋊C₄	—	53	6	no	—
1241	C₂×C₄⋊C₄	—	53	3	no	—
1242	C₂×C₄⋊C₄	—	53	3	no	—
1243	C₂×C₄⋊C₄	—	53	6	no	—
1244	C₂×C₄⋊C₄	—	53	6	no	—
1245	C₂×C₄⋊C₄	C₂²×D₅₃	1	3	yes	complemented
1246	C₂×C₄⋊C₄	C₂²×D₅₃	1	6	yes	complemented
1247	C₂×C₂²⋊C₄	—	53	6	no	—
1248	C₂×C₂²⋊C₄	—	53	6	no	—
1249	C₂×C₂²⋊C₄	—	53	6	no	—
1250	C₂×C₂²⋊C₄	—	53	6	no	—
1251	C₂×C₂²⋊C₄	—	53	6	no	—
1252	C₂×C₂²⋊C₄	—	53	6	no	—
1253	C₂×C₂²⋊C₄	—	53	6	no	—
1254	C₂×C₂²⋊C₄	—	53	6	no	—
1255	C₂×C₂²⋊C₄	—	53	6	no	—
1256	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	—
1257	C₂×C₄²	—	53	6	no	—
1258	C₂×C₄²	—	53	6	no	—
1259	C₂⁴	—	53	3	no	—
1260	C₂⁴	—	53	1	no	—
1261	C₂⁴	—	53	3	no	—
1262	C₂⁴	—	53	3	no	—
1263	C₂⁴	—	53	3	no	—
1264	C₂⁴	—	53	6	no	—
1265	C₂⁴	—	53	6	no	—
1266	C₂⁴	—	53	3	no	—
1267	C₂⁴	—	106	12	no	—
1268	C₂⁴	—	212	6	no	—
1269	C₂⁴	—	212	6	no	—
1270	C₂⁴	C₂³×D₅₃	1	3	yes	—
1271	#41	—	2	4	no	—
1272	#41	—	2	12	no	—
1273	#41	—	2	24	no	—
1274	#41	—	2	12	no	—
1275	#41	—	2	12	no	—
1276	#41	—	53	8	no	—
1277	#41	—	53	24	no	—
1278	#41	—	53	24	no	—
1279	#41	—	106	24	no	—
1280	#41	—	106	24	no	—
1281	#41	—	106	24	no	—
1282	#41	—	106	12	no	—
1283	#41	—	106	48	no	—
1284	#41	—	106	12	no	—
1285	#41	—	106	24	no	—
1286	#41	—	106	24	no	—
1287	#41	—	106	24	no	—
1288	#41	—	106	4	no	—
1289	#41	—	106	12	no	—
1290	#41	—	106	12	no	—
1291	#41	—	106	24	no	—
1292	#41	—	106	12	no	—
1293	#41	—	106	24	no	—
1294	#41	—	106	24	no	—
1295	#41	—	106	24	no	—
1296	#41	—	106	12	no	—
1297	#41	—	106	12	no	—
1298	#41	—	106	24	no	—
1299	#41	—	106	4	no	—
1300	#41	—	106	8	no	—
1301	#41	—	106	12	no	—
1302	#41	—	106	12	no	—
1303	#41	—	106	12	no	—
1304	#41	D₄×D₅₃	1	8	yes	complemented
1305	C₂×Q₈	—	2	4	no	—
1306	C₂×Q₈	—	2	8	no	—
1307	C₂×Q₈	—	2	12	no	—
1308	C₂×Q₈	—	53	8	no	—
1309	C₂×Q₈	—	53	3	no	—
1310	C₂×Q₈	—	53	1	no	—
1311	C₂×Q₈	—	53	6	no	—
1312	C₂×Q₈	—	53	6	no	—
1313	C₂×Q₈	—	53	3	no	—
1314	C₂×Q₈	—	106	12	no	—
1315	C₂×Q₈	—	106	12	no	—
1316	C₂×Q₈	—	106	12	no	—
1317	C₂×Q₈	—	106	12	no	—
1318	C₂×Q₈	—	106	24	no	—
1319	C₂×Q₈	—	106	4	no	—
1320	C₂×Q₈	C₂³×D₅₃	1	3	yes	—
1321	C₂×Q₈	C₂³×D₅₃	1	6	yes	—
1322	C₂×Q₈	C₂³×D₅₃	1	3	yes	—
1323	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1324	C₂×D₄	—	2	12	no	—
1325	C₂×D₄	—	53	6	no	—
1326	C₂×D₄	—	53	24	no	—
1327	C₂×D₄	—	53	2	no	—
1328	C₂×D₄	—	53	6	no	—
1329	C₂×D₄	—	53	2	no	—
1330	C₂×D₄	—	53	6	no	—
1331	C₂×D₄	—	53	6	no	—
1332	C₂×D₄	—	53	6	no	—
1333	C₂×D₄	—	53	6	no	—
1334	C₂×D₄	—	53	6	no	—
1335	C₂×D₄	—	53	6	no	—
1336	C₂×D₄	—	53	12	no	—
1337	C₂×D₄	—	53	6	no	—
1338	C₂×D₄	—	53	3	no	—
1339	C₂×D₄	—	53	6	no	—
1340	C₂×D₄	—	53	6	no	—
1341	C₂×D₄	—	53	6	no	—
1342	C₂×D₄	—	53	12	no	—
1343	C₂×D₄	—	53	3	no	—
1344	C₂×D₄	—	53	6	no	—
1345	C₂×D₄	—	53	3	no	—
1346	C₂×D₄	—	53	12	no	—
1347	C₂×D₄	—	53	6	no	—
1348	C₂×D₄	—	106	12	no	—
1349	C₂×D₄	—	106	24	no	—
1350	C₂×D₄	—	106	24	no	—
1351	C₂×D₄	—	106	12	no	—
1352	C₂×D₄	—	106	12	no	—
1353	C₂×D₄	—	106	24	no	—
1354	C₂×D₄	—	106	12	no	—
1355	C₂×D₄	—	106	48	no	—
1356	C₂×D₄	—	106	24	no	—
1357	C₂×D₄	—	106	24	no	—
1358	C₂×D₄	—	106	24	no	—
1359	C₂×D₄	—	106	12	no	—
1360	C₂×D₄	—	106	24	no	—
1361	C₂×D₄	—	106	12	no	—
1362	C₂×D₄	—	212	12	no	—
1363	C₂×D₄	—	212	12	no	—
1364	C₂×D₄	—	212	12	no	—
1365	C₂×D₄	—	212	12	no	—
1366	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1367	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1368	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1369	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1370	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1371	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1372	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1373	C₂²×C₄	—	2	12	no	—
1374	C₂²×C₄	—	53	3	no	—
1375	C₂²×C₄	—	53	24	no	—
1376	C₂²×C₄	—	53	3	no	—
1377	C₂²×C₄	—	53	3	no	—
1378	C₂²×C₄	—	53	1	no	—
1379	C₂²×C₄	—	53	3	no	—
1380	C₂²×C₄	—	53	3	no	—
1381	C₂²×C₄	—	53	1	no	—
1382	C₂²×C₄	—	53	2	no	—
1383	C₂²×C₄	—	53	3	no	—
1384	C₂²×C₄	—	53	3	no	—
1385	C₂²×C₄	—	53	3	no	—
1386	C₂²×C₄	—	53	6	no	—
1387	C₂²×C₄	—	53	3	no	—
1388	C₂²×C₄	—	53	3	no	—
1389	C₂²×C₄	—	53	6	no	—
1390	C₂²×C₄	—	53	1	no	—
1391	C₂²×C₄	—	53	3	no	—
1392	C₂²×C₄	—	53	6	no	—
1393	C₂²×C₄	—	53	3	no	—
1394	C₂²×C₄	—	53	3	no	—
1395	C₂²×C₄	—	53	3	no	—
1396	C₂²×C₄	—	53	3	no	—
1397	C₂²×C₄	—	53	12	no	—
1398	C₂²×C₄	—	53	6	no	—
1399	C₂²×C₄	—	53	1	no	—
1400	C₂²×C₄	—	53	3	no	—
1401	C₂²×C₄	—	53	1	no	—
1402	C₂²×C₄	—	53	3	no	—
1403	C₂²×C₄	—	53	6	no	—
1404	C₂²×C₄	—	53	6	no	—
1405	C₂²×C₄	—	106	4	no	—
1406	C₂²×C₄	—	106	12	no	—
1407	C₂²×C₄	—	106	12	no	—
1408	C₂²×C₄	—	106	12	no	—
1409	C₂²×C₄	—	106	12	no	—
1410	C₂²×C₄	—	106	12	no	—
1411	C₂²×C₄	—	106	12	no	—
1412	C₂²×C₄	—	106	12	no	—
1413	C₂²×C₄	—	106	12	no	—
1414	C₂²×C₄	—	106	24	no	—
1415	C₂²×C₄	—	106	24	no	—
1416	C₂²×C₄	—	106	12	no	—
1417	C₂²×C₄	—	106	12	no	—
1418	C₂²×C₄	—	106	12	no	—
1419	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1420	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1421	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1422	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1423	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1424	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1425	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1426	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1427	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1428	C₄⋊C₄	—	53	3	no	—
1429	C₄⋊C₄	—	53	1	no	—
1430	C₄⋊C₄	—	53	6	no	—
1431	C₄⋊C₄	—	53	2	no	—
1432	C₄⋊C₄	—	53	2	no	—
1433	C₄⋊C₄	—	53	6	no	—
1434	C₄⋊C₄	—	53	6	no	—
1435	C₄⋊C₄	—	53	6	no	—
1436	C₄⋊C₄	—	53	6	no	—
1437	C₄⋊C₄	—	53	12	no	—
1438	C₄⋊C₄	—	53	6	no	—
1439	C₄⋊C₄	—	53	6	no	—
1440	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1441	C₄⋊C₄	C₂³×D₅₃	1	3	yes	—
1442	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1443	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1444	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1445	C₄⋊C₄	C₂³×D₅₃	1	12	yes	—
1446	C₂²⋊C₄	—	53	2	no	—
1447	C₂²⋊C₄	—	53	2	no	—
1448	C₂²⋊C₄	—	53	6	no	—
1449	C₂²⋊C₄	—	53	6	no	—
1450	C₂²⋊C₄	—	53	6	no	—
1451	C₂²⋊C₄	—	53	6	no	—
1452	C₂²⋊C₄	—	53	2	no	—
1453	C₂²⋊C₄	—	53	6	no	—
1454	C₂²⋊C₄	—	53	2	no	—
1455	C₂²⋊C₄	—	53	6	no	—
1456	C₂²⋊C₄	—	53	6	no	—
1457	C₂²⋊C₄	—	53	12	no	—
1458	C₂²⋊C₄	—	53	12	no	—
1459	C₂²⋊C₄	—	53	6	no	—
1460	C₂²⋊C₄	—	53	12	no	—
1461	C₂²⋊C₄	—	53	6	no	—
1462	C₂²⋊C₄	—	53	12	no	—
1463	C₂²⋊C₄	—	53	6	no	—
1464	C₂²⋊C₄	—	53	6	no	—
1465	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1466	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1467	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1468	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1469	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1470	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
1471	C₄²	—	53	6	no	—
1472	C₄²	—	53	2	no	—
1473	C₄²	—	53	12	no	—
1474	C₄²	—	53	6	no	—
1475	C₄²	C₂³×D₅₃	1	6	yes	—
1476	C₂³	—	2	6	no	—
1477	C₂³	—	2	6	no	—
1478	C₂³	—	4	3	no	—
1479	C₂³	—	53	1	no	—
1480	C₂³	—	53	1	no	—
1481	C₂³	—	53	3	no	—
1482	C₂³	—	53	12	no	—
1483	C₂³	—	53	6	no	—
1484	C₂³	—	53	3	no	—
1485	C₂³	—	106	2	no	—
1486	C₂³	—	106	2	no	—
1487	C₂³	—	106	12	no	—
1488	C₂³	—	106	6	no	—
1489	C₂³	—	106	6	no	—
1490	C₂³	—	106	6	no	—
1491	C₂³	—	106	6	no	—
1492	C₂³	—	106	6	no	—
1493	C₂³	—	106	2	no	—
1494	C₂³	—	106	12	no	—
1495	C₂³	—	106	6	no	—
1496	C₂³	—	106	6	no	—
1497	C₂³	—	212	6	no	—
1498	C₂³	—	212	6	no	—
1499	C₂³	—	212	6	no	—
1500	C₂³	—	212	6	no	—
1501	C₂³	—	212	3	no	—
1502	C₂³	—	212	3	no	—
1503	C₂³	—	212	3	no	—
1504	C₂³	—	212	3	no	—
1505	C₂³	—	212	3	no	—
1506	C₂³	—	212	3	no	—
1507	C₂³	—	212	3	no	—
1508	C₂³	—	212	48	no	—
1509	C₂³	C₂⁴×D₅₃	1	2	yes	—
1510	C₂³	C₂⁴×D₅₃	1	3	yes	—
1511	C₂³	C₂⁴×D₅₃	1	3	yes	—
1512	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1513	Q₈	—	2	6	no	—
1514	Q₈	—	2	12	no	—
1515	Q₈	—	2	6	no	—
1516	Q₈	—	53	12	no	—
1517	Q₈	—	106	12	no	—
1518	Q₈	—	106	12	no	—
1519	Q₈	—	106	2	no	—
1520	Q₈	—	106	6	no	—
1521	Q₈	C₂×D₄×D₅₃	1	4	yes	—
1522	D₄	—	2	12	no	—
1523	D₄	—	2	12	no	—
1524	D₄	—	2	4	no	—
1525	D₄	—	2	6	no	—
1526	D₄	—	2	2	no	—
1527	D₄	—	4	6	no	—
1528	D₄	—	53	24	no	—
1529	D₄	—	53	12	no	—
1530	D₄	—	106	12	no	—
1531	D₄	—	106	12	no	—
1532	D₄	—	106	24	no	—
1533	D₄	—	106	12	no	—
1534	D₄	—	106	12	no	—
1535	D₄	—	106	12	no	—
1536	D₄	—	106	4	no	—
1537	D₄	—	106	12	no	—
1538	D₄	—	106	4	no	—
1539	D₄	—	106	12	no	—
1540	D₄	—	106	12	no	—
1541	D₄	—	106	12	no	—
1542	D₄	—	106	6	no	—
1543	D₄	—	106	12	no	—
1544	D₄	—	106	6	no	—
1545	D₄	—	212	12	no	—
1546	D₄	—	212	6	no	—
1547	D₄	—	212	6	no	—
1548	D₄	—	212	6	no	—
1549	D₄	—	212	12	no	—
1550	D₄	C₂×D₄×D₅₃	1	12	yes	—
1551	C₂×C₄	—	2	6	no	—
1552	C₂×C₄	—	2	12	no	—
1553	C₂×C₄	—	2	2	no	—
1554	C₂×C₄	—	2	6	no	—
1555	C₂×C₄	—	2	6	no	—
1556	C₂×C₄	—	2	6	no	—
1557	C₂×C₄	—	2	12	no	—
1558	C₂×C₄	—	4	6	no	—
1559	C₂×C₄	—	53	12	no	—
1560	C₂×C₄	—	53	1	no	—
1561	C₂×C₄	—	53	3	no	—
1562	C₂×C₄	—	53	4	no	—
1563	C₂×C₄	—	53	12	no	—
1564	C₂×C₄	—	53	12	no	—
1565	C₂×C₄	—	53	12	no	—
1566	C₂×C₄	—	53	2	no	—
1567	C₂×C₄	—	53	6	no	—
1568	C₂×C₄	—	53	1	no	—
1569	C₂×C₄	—	53	2	no	—
1570	C₂×C₄	—	53	3	no	—
1571	C₂×C₄	—	106	2	no	—
1572	C₂×C₄	—	106	6	no	—
1573	C₂×C₄	—	106	6	no	—
1574	C₂×C₄	—	106	6	no	—
1575	C₂×C₄	—	106	12	no	—
1576	C₂×C₄	—	106	24	no	—
1577	C₂×C₄	—	106	2	no	—
1578	C₂×C₄	—	106	6	no	—
1579	C₂×C₄	—	106	6	no	—
1580	C₂×C₄	—	106	6	no	—
1581	C₂×C₄	—	106	12	no	—
1582	C₂×C₄	—	106	2	no	—
1583	C₂×C₄	—	106	6	no	—
1584	C₂×C₄	—	106	4	no	—
1585	C₂×C₄	—	106	6	no	—
1586	C₂×C₄	—	106	6	no	—
1587	C₂×C₄	—	106	6	no	—
1588	C₂×C₄	—	106	2	no	—
1589	C₂×C₄	—	106	6	no	—
1590	C₂×C₄	—	106	6	no	—
1591	C₂×C₄	—	106	6	no	—
1592	C₂×C₄	—	106	12	no	—
1593	C₂×C₄	—	212	6	no	—
1594	C₂×C₄	—	212	6	no	—
1595	C₂×C₄	—	212	6	no	—
1596	C₂×C₄	C₂×D₄×D₅₃	1	12	yes	—
1597	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1598	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1599	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1600	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1601	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1602	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1603	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1604	C₂²	—	2	1	no	—
1605	C₂²	—	2	3	no	—
1606	C₂²	—	2	1	no	—
1607	C₂²	—	2	3	no	—
1608	C₂²	—	2	2	no	—
1609	C₂²	—	2	3	no	—
1610	C₂²	—	2	2	no	—
1611	C₂²	—	2	3	no	—
1612	C₂²	—	2	2	no	—
1613	C₂²	—	2	3	no	—
1614	C₂²	—	4	12	no	—
1615	C₂²	—	53	2	no	—
1616	C₂²	—	53	6	no	—
1617	C₂²	—	53	2	no	—
1618	C₂²	—	106	8	no	—
1619	C₂²	—	106	1	no	—
1620	C₂²	—	106	3	no	—
1621	C₂²	—	106	1	no	—
1622	C₂²	—	106	3	no	—
1623	C₂²	—	106	1	no	—
1624	C₂²	—	106	1	no	—
1625	C₂²	—	106	6	no	—
1626	C₂²	—	106	3	no	—
1627	C₂²	—	106	6	no	—
1628	C₂²	—	106	3	no	—
1629	C₂²	—	106	6	no	—
1630	C₂²	—	106	3	no	—
1631	C₂²	—	424	12	no	—
1632	C₂²	—	424	12	no	—
1633	C₂²	—	212	12	no	—
1634	C₂²	—	212	12	no	—
1635	C₂²	—	212	12	no	—
1636	C₂²	—	212	12	no	—
1637	C₂²	—	212	12	no	—
1638	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
1639	C₂²	#16811460	1	2	yes	complemented
1640	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1641	C₄	—	2	1	no	—
1642	C₄	—	2	3	no	—
1643	C₄	—	2	6	no	—
1644	C₄	—	2	6	no	—
1645	C₄	—	2	2	no	—
1646	C₄	—	53	2	no	—
1647	C₄	—	53	6	no	—
1648	C₄	—	106	1	no	—
1649	C₄	—	106	3	no	—
1650	C₄	—	106	2	no	—
1651	C₄	—	106	2	no	—
1652	C₄	—	106	6	no	—
1653	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1654	C₄	C₂²×D₄×D₅₃	1	6	yes	—
1655	C₂	—	2	2	no	—
1656	C₂	—	2	6	no	—
1657	C₂	—	4	3	no	—
1658	C₂	—	4	2	no	—
1659	C₂	—	106	2	no	—
1660	C₂	—	106	2	no	—
1661	C₂	—	106	6	no	—
1662	C₂	—	212	6	no	—
1663	C₂	—	212	3	no	—
1664	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1665	C₂	#585×D₅₃	1	1	yes	characteristic
1666	C₂	C₂×#16811460	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	#62811
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×#16811460	C₂	semidirect
2. C₂²×#41×D₅₃	C₂	semidirect
3. #20288393	C₂	semidirect
4. #20288391	C₂	semidirect
5. #20288388	C₂	semidirect
6. #20288385	C₂	semidirect
7. #20288384	C₂	semidirect
8. #20288379	C₂	semidirect
9. #20288376	C₂	semidirect
10. #20288372	C₂	semidirect
11. #20288365	C₂	semidirect
12. #20288354	C₂	semidirect
13. #20288345	C₂	semidirect
14. D₄×#11719949	C₂	semidirect
15. #20288204	C₂	semidirect
16. #20288202	C₂	semidirect
17. #20288199	C₂	semidirect
18. #20288047	C₂	semidirect
19. #20288043	C₂	semidirect
20. C₂×#16811136	C₂	semidirect
21. #525×D₅₃	C₂	semidirect
22. #20287915	C₂	semidirect
23. C₅₃×#3489	C₂	semidirect
25. C₂×#13133265	C₂²	semidirect
26. C₂×#13133265	C₂²	semidirect
27. C₂×#13133263	C₂²	semidirect
28. C₂×#13133263	C₂²	semidirect
29. C₂×#13133263	C₂²	semidirect
30. C₂²×#11719949	C₂²	semidirect
31. C₂²×#11719949	C₂²	semidirect
32. C₂²×#11719949	C₂²	semidirect
33. C₂²×#11719945	C₂²	semidirect
34. C₂²×#11719947	C₂²	semidirect
37. C₂×#41×D₅₃	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
44. C₂×#41×D₅₃	C₂²	semidirect
45. C₂×#41×D₅₃	C₂²	semidirect
46. C₂²×Q₈×D₅₃	C₂²	semidirect
47. C₂²×D₄×D₅₃	C₂²	semidirect
48. C₂³×C₄×D₅₃	C₂²	semidirect
49. #16811295	C₂²	semidirect
50. #16811294	C₂²	semidirect
51. #16811292	C₂²	semidirect
52. #16811291	C₂²	semidirect
53. #16811288	C₂²	semidirect
54. Q₈×C₂²⋊D₅₃	C₂²	semidirect
55. #16811286	C₂²	semidirect
56. #16811285	C₂²	semidirect
57. #16811284	C₂²	semidirect
58. #16811284	C₂²	semidirect
59. #16811283	C₂²	semidirect
60. #16811283	C₂²	semidirect
61. #16811282	C₂²	semidirect
62. #16811281	C₂²	semidirect
63. #16811276	C₂²	semidirect
64. #16811275	C₂²	semidirect
65. #16811274	C₂²	semidirect
66. #16811272	C₂²	semidirect
67. #16811271	C₂²	semidirect
68. #16811269	C₂²	semidirect
69. #16811268	C₂²	semidirect
70. #16811266	C₂²	semidirect
71. #16811265	C₂²	semidirect
72. #16811265	C₂²	semidirect
73. #16811264	C₂²	semidirect
74. #16811264	C₂²	semidirect
75. #16811263	C₂²	semidirect
76. #16811262	C₂²	semidirect
77. #16811261	C₂²	semidirect
78. #16811261	C₂²	semidirect
79. D₄×D₂₁₂	C₂²	semidirect
80. D₄×D₂₁₂	C₂²	semidirect
81. #16811257	C₂²	semidirect
82. #16811257	C₂²	semidirect
83. D₄×C₂²⋊D₅₃	C₂²	semidirect
84. #16811255	C₂²	semidirect
85. #16811204	C₂²	semidirect
86. #16811203	C₂²	semidirect
87. #16811203	C₂²	semidirect
88. #16811201	C₂²	semidirect
89. #16811201	C₂²	semidirect
90. #16811198	C₂²	semidirect
91. #16811197	C₂²	semidirect
92. #16811196	C₂²	semidirect
93. #16811196	C₂²	semidirect
94. #16811192	C₂²	semidirect
95. #16811191	C₂²	semidirect
96. #16811189	C₂²	semidirect
97. #16811189	C₂²	semidirect
98. #16811187	C₂²	semidirect
99. #16811184	C₂²	semidirect
100. #16811181	C₂²	semidirect
101. #16811174	C₂²	semidirect
102. #16811172	C₂²	semidirect
103. #16811168	C₂²	semidirect
104. #16811136	C₂²	semidirect
105. #16811136	C₂²	semidirect
106. #16811136	C₂²	semidirect
107. #16811136	C₂²	semidirect
108. #16811136	C₂²	semidirect
109. #16811136	C₂²	semidirect
110. #16811136	C₂²	semidirect
111. #16811136	C₂²	semidirect
112. #16811136	C₂²	semidirect
113. #16811136	C₂²	semidirect
114. #16811135	C₂²	semidirect
115. #16811134	C₂²	semidirect
116. #16811133	C₂²	semidirect
117. #16811133	C₂²	semidirect
118. #16811133	C₂²	semidirect
119. #16811132	C₂²	semidirect
120. #16811132	C₂²	semidirect
121. #16811131	C₂²	semidirect
122. #16811131	C₂²	semidirect
123. #16811130	C₂²	semidirect
124. #16811129	C₂²	semidirect
125. C₂×#13133202	C₂²	semidirect
126. #123×D₅₃	C₂²	semidirect
127. C₂×#13133193	C₂²	semidirect
128. C₂²⋊Q₈×D₅₃	C₂²	semidirect
129. C₂²⋊Q₈×D₅₃	C₂²	semidirect
130. C₂×#13133192	C₂²	semidirect
131. C₂×#13133191	C₂²	semidirect
132. #121×D₅₃	C₂²	semidirect
133. #121×D₅₃	C₂²	semidirect
134. C₂×#13133187	C₂²	semidirect
135. #120×D₅₃	C₂²	semidirect
136. #16811106	C₂²	semidirect
137. #16811104	C₂²	semidirect
138. #16811103	C₂²	semidirect
139. #16811099	C₂²	semidirect
140. #16811095	C₂²	semidirect
141. C₄×#11719949	C₂²	semidirect
142. C₄×#11719947	C₂²	semidirect
143. C₂×#13133179	C₂²	semidirect
144. C₂×#13133177	C₂²	semidirect
145. C₄×D₄×D₅₃	C₂²	semidirect
146. C₄×D₄×D₅₃	C₂²	semidirect
147. C₂×#13133175	C₂²	semidirect
148. #117×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
175. C₂×#11719949	C₂³	semidirect
176. C₂×#11719949	C₂³	semidirect
177. C₂×#11719949	C₂³	semidirect
178. C₂×#11719949	C₂³	semidirect
187. C₂×#11719945	C₂³	semidirect
188. C₂×#11719945	C₂³	semidirect
189. C₂×#11719945	C₂³	semidirect
198. C₂×#11719947	C₂³	semidirect
208. #41×D₅₃	D₄	semidirect
215. C₂×Q₈×D₅₃	C₂³	semidirect
216. C₂×Q₈×D₅₃	C₂³	semidirect
220. C₂²×D₂₁₂	C₂³	semidirect
221. C₂²×D₂₁₂	C₂³	semidirect
234. C₂×D₄×D₅₃	C₂³	semidirect
235. C₂×D₄×D₅₃	C₂³	semidirect
236. C₂×D₄×D₅₃	C₂³	semidirect
251. C₂²×C₄×D₅₃	C₂³	semidirect
252. C₂²×C₄×D₅₃	C₂³	semidirect
253. #13133216	C₂³	semidirect
254. #13133215	C₂³	semidirect
255. #13133214	C₂³	semidirect
256. #13133213	C₂³	semidirect
257. #13133213	C₂³	semidirect
258. #13133206	C₂³	semidirect
259. #13133206	C₂³	semidirect
260. #13133205	C₂³	semidirect
261. #13133203	C₂³	semidirect
262. #13133203	C₂³	semidirect
266. #13133202	C₂³	semidirect
267. #13133202	C₂³	semidirect
268. #13133202	C₂³	semidirect
269. #13133201	C₂³	semidirect
270. #13133200	C₂³	semidirect
271. #13133200	C₂³	semidirect
274. #13133199	C₂³	semidirect
275. #13133198	C₂³	semidirect
277. #13133197	C₂³	semidirect
278. #13133197	C₂³	semidirect
280. #13133196	C₂³	semidirect
281. #13133196	C₂³	semidirect
283. #13133195	C₂³	semidirect
284. #13133195	C₂³	semidirect
285. #13133195	C₂³	semidirect
287. #13133194	C₂³	semidirect
290. #13133193	C₂³	semidirect
291. #13133193	C₂³	semidirect
292. #13133193	C₂³	semidirect
293. #13133193	C₂³	semidirect
296. #13133192	C₂³	semidirect
297. #13133192	C₂³	semidirect
298. #13133192	C₂³	semidirect
299. #13133192	C₂³	semidirect
300. #13133192	C₂³	semidirect
301. #13133192	C₂³	semidirect
304. #13133191	C₂³	semidirect
305. #13133191	C₂³	semidirect
306. #13133191	C₂³	semidirect
307. #13133191	C₂³	semidirect
308. #13133191	C₂³	semidirect
310. #13133190	C₂³	semidirect
311. #13133190	C₂³	semidirect
312. #13133190	C₂³	semidirect
313. #13133190	C₂³	semidirect
314. #13133190	C₂³	semidirect
316. #13133189	C₂³	semidirect
317. #13133189	C₂³	semidirect
318. #13133189	C₂³	semidirect
320. #13133188	C₂³	semidirect
321. #13133188	C₂³	semidirect
328. #13133187	C₂³	semidirect
329. #13133187	C₂³	semidirect
334. #13133185	C₂³	semidirect
335. #13133185	C₂³	semidirect
336. Q₈×Dic₅₃	C₂³	semidirect
337. C₄×Dic₁₀₆	C₂³	semidirect
338. #13133182	C₂³	semidirect
340. C₄×D₂₁₂	C₂³	semidirect
341. C₄×D₂₁₂	C₂³	semidirect
343. D₄×Dic₅₃	C₂³	semidirect
344. D₄×Dic₅₃	C₂³	semidirect
347. #13133179	C₂³	semidirect
348. #13133179	C₂³	semidirect
349. #13133179	C₂³	semidirect
350. #13133179	C₂³	semidirect
353. C₄×C₂²⋊D₅₃	C₂³	semidirect
354. C₄×C₂²⋊D₅₃	C₂³	semidirect
355. C₄×C₂²⋊D₅₃	C₂³	semidirect
359. #13133177	C₂³	semidirect
360. #13133177	C₂³	semidirect
361. #13133177	C₂³	semidirect
362. #13133177	C₂³	semidirect
363. #13133177	C₂³	semidirect
364. #13133176	C₂³	semidirect
368. #13133175	C₂³	semidirect
369. #13133175	C₂³	semidirect
371. #13133173	C₂³	semidirect
372. C₂×C₄⋊Dic₅₃	C₂³	semidirect
373. C₂×#11719919	C₂³	semidirect
374. C₄⋊C₄×D₅₃	C₂³	semidirect
375. C₄⋊C₄×D₅₃	C₂³	semidirect
376. C₄⋊C₄×D₅₃	C₂³	semidirect
377. C₄⋊C₄×D₅₃	C₂³	semidirect
380. C₂×#11719921	C₂³	semidirect
381. C₂×#11719921	C₂³	semidirect
385. C₂²⋊C₄×D₅₃	C₂³	semidirect
386. C₂²⋊C₄×D₅₃	C₂³	semidirect
387. C₂×C₄×Dic₅₃	C₂³	semidirect
388. C₄²×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
442. #41×C₅₃	C₂×D₄	semidirect
500. #11719949	C₂×D₄	semidirect
506. Q₈×D₅₃	C₂×D₄	semidirect
514. #11719947	C₂×D₄	semidirect
526. D₄×D₅₃	C₂×D₄	semidirect
536. #11719945	C₂×D₄	semidirect
565. C₂×C₄×D₅₃	C₂×D₄	semidirect
783. C₂²×C₅₃	#585	semidirect
807. C₂×D₅₃	#585	semidirect
827. #3489	D₅₃	semidirect
860. C₂×2₋¹⁺⁴	C₂×D₅₃	semidirect
880. C₂²×#41	C₂×D₅₃	semidirect
891. D₄×Q₈	C₂×D₅₃	semidirect
899. #548	C₂×D₅₃	semidirect
905. #547	C₂×D₅₃	semidirect
917. #546	C₂×D₅₃	semidirect
929. #537	C₂×D₅₃	semidirect
934. #536	C₂×D₅₃	semidirect
966. #525	C₂×D₅₃	semidirect
972. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
982. #520	C₂×D₅₃	semidirect
993. C₅₃	#62811	semidirect
1049. C₂×#41	C₂²×D₅₃	semidirect
1050. C₂×#41	C₂²×D₅₃	semidirect
1060. C₂²×Q₈	C₂²×D₅₃	semidirect
1061. C₂²×Q₈	C₂²×D₅₃	semidirect
1102. C₄⋊Q₈	C₂²×D₅₃	semidirect
1111. #124	C₂²×D₅₃	semidirect
1125. #123	C₂²×D₅₃	semidirect
1126. #123	C₂²×D₅₃	semidirect
1147. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1148. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1149. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1150. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1180. #121	C₂²×D₅₃	semidirect
1181. #121	C₂²×D₅₃	semidirect
1182. #121	C₂²×D₅₃	semidirect
1201. C₄×Q₈	C₂²×D₅₃	semidirect
1228. C₄×D₄	C₂²×D₅₃	semidirect
1229. C₄×D₄	C₂²×D₅₃	semidirect
1238. #117	C₂²×D₅₃	semidirect
1245. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1246. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1304. #41	D₄×D₅₃	semidirect
1639. C₂²	#16811460	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811460	2
C₂²×#41×D₅₃	2
#20288393	2
#20288391	2
#20288388	2
#20288385	2
#20288384	2
#20288379	2
#20288376	2
#20288372	2
#20288365	2
#20288354	2
#20288345	2
D₄×#11719949	2
#20288204	2
#20288202	2
#20288199	2
#20288047	2
#20288043	2
C₂×#16811136	2
#525×D₅₃	2
#20287915	2
C₅₃×#3489	2
#62811	53