Subgroups — #28297952

Order 13568.

10894 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289526	C₂	1	1	yes	maximal, characteristic, complemented
2	#20289525	C₂	1	1	yes	maximal, characteristic, complemented
3	#20289496	C₂	1	1	yes	maximal, characteristic, complemented
4	#20289493	C₂	1	8	yes	maximal, complemented
5	#20289492	C₂	1	6	yes	maximal, complemented
6	#20289491	C₂	1	6	yes	maximal, complemented
7	#20289490	C₂	1	8	yes	maximal, complemented
8	#20289488	C₂	1	6	yes	maximal, complemented
9	#20289487	C₂	1	8	yes	maximal, complemented
10	#20289486	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16811427	C₂	1	6	yes	maximal, complemented
12	C₂×#16811426	C₂	1	1	yes	maximal, characteristic, complemented
13	#576×D₅₃	C₂	1	8	yes	maximal, complemented
14	#20289428	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3585	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811460	—	2	2	no	—
17	#16811460	C₂²	1	8	yes	complemented
18	#16811459	—	2	2	no	—
19	#16811459	—	2	4	no	—
20	#16811459	C₂²	1	1	yes	characteristic
21	#16811459	C₂²	1	1	yes	characteristic, complemented
22	#16811459	C₂²	1	6	yes	complemented
23	#16811459	C₂²	1	6	yes	complemented
24	#16811458	—	2	4	no	—
25	#16811458	C₂²	1	8	yes	complemented
26	C₂×#13133263	—	2	4	no	—
27	C₂×#13133263	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13133263	C₂²	1	6	yes	complemented
29	C₂×#13133262	—	2	6	no	—
30	C₂×#13133262	C₂²	1	6	yes	complemented
31	H(5,𝔽₂)×D₅₃	—	2	4	no	—
32	H(5,𝔽₂)×D₅₃	—	2	6	no	—
33	H(5,𝔽₂)×D₅₃	C₂²	1	8	yes	complemented
34	H(5,𝔽₂)×D₅₃	C₂²	1	8	yes	complemented
35	#16811439	C₂²	1	12	yes	complemented
36	#16811439	C₂²	1	4	yes	complemented
37	#16811438	C₂²	1	4	yes	complemented
38	#16811435	C₂²	1	8	yes	complemented
39	#16811434	C₂²	1	4	yes	complemented
40	#16811433	C₂²	1	12	yes	complemented
41	#16811433	C₂²	1	12	yes	complemented
42	#16811432	C₂²	1	12	yes	complemented
43	#16811432	C₂²	1	12	yes	complemented
44	#16811431	C₂²	1	4	yes	complemented
45	#16811430	C₂²	1	24	yes	complemented
46	#16811429	C₂²	1	24	yes	complemented
47	#16811428	C₂²	1	8	yes	complemented
48	#16811427	C₂²	1	12	yes	complemented
49	#16811427	C₂²	1	24	yes	complemented
50	#16811427	C₂²	1	12	yes	complemented
51	#16811427	C₂²	1	24	yes	complemented
52	#16811427	C₂²	1	24	yes	complemented
53	#16811426	C₂²	1	4	yes	complemented
54	#16811426	C₂²	1	8	yes	complemented
55	#16811426	C₂²	1	8	yes	complemented
56	#16811425	C₂²	1	24	yes	complemented
57	#16811424	C₂²	1	24	yes	complemented
58	#16811423	C₂²	1	6	yes	complemented
59	#16811422	C₂²	1	24	yes	complemented
60	#16811421	C₂²	1	6	yes	complemented
61	#16811420	C₂²	1	24	yes	complemented
62	#16811419	C₂²	1	24	yes	complemented
63	C₂×#13133245	C₂²	1	6	yes	complemented
64	C₂×#13133244	C₂²	1	12	yes	complemented
65	C₂×#13133243	C₂²	1	3	yes	complemented
66	C₂×#13133242	C₂²	1	3	yes	complemented
67	C₂×#13133241	C₂²	1	12	yes	complemented
68	AGL(1,ℤ/8)×D₅₃	C₂²	1	24	yes	complemented
69	AGL(1,ℤ/8)×D₅₃	C₂²	1	24	yes	complemented
70	C₂×#13133238	C₂²	1	12	yes	complemented
71	C₂×#13133237	C₂²	1	3	yes	complemented
72	C₂×#13133237	C₂²	1	6	yes	complemented
73	#135×D₅₃	C₂²	1	24	yes	complemented
74	C₂²×#11719922	C₂²	1	3	yes	complemented
75	C₂×D₈×D₅₃	C₂²	1	12	yes	complemented
76	#16811389	C₂²	1	6	yes	complemented
77	#16811388	C₂²	1	8	yes	complemented
78	C₂×#13133225	C₂²	1	6	yes	complemented
79	C₂×#13133224	C₂²	1	1	yes	characteristic, complemented
80	#131×D₅₃	C₂²	1	8	yes	complemented
81	C₅₃×#585	C₂²	1	1	yes	characteristic, complemented
82	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#577	C₂²	1	8	yes	complemented
84	C₅₃×#576	C₂²	1	8	yes	complemented
85	C₅₃×#575	C₂²	1	6	yes	complemented
86	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	6	yes	complemented
87	C₅₃×#568	C₂²	1	1	yes	characteristic, complemented
88	#13133265	—	2	1	no	—
89	#13133265	—	2	8	no	—
90	#13133265	D₄	1	2	yes	—
91	#13133265	C₂³	1	12	yes	complemented
92	#13133265	C₂³	1	4	yes	complemented
93	#13133264	—	2	8	no	—
94	#13133264	—	2	6	no	—
95	#13133264	—	2	6	no	—
96	#13133264	D₄	1	4	yes	—
97	#13133264	C₂³	1	12	yes	complemented
98	#13133264	C₂³	1	4	yes	complemented
99	#13133264	C₂³	1	4	yes	complemented
100	#13133263	—	2	4	no	—
101	#13133263	—	2	8	no	—
102	#13133263	—	2	8	no	—
103	#13133263	—	2	24	no	—
104	#13133263	—	2	12	no	—
105	#13133263	—	2	12	no	—
106	#13133263	—	2	6	no	—
107	#13133263	—	2	6	no	—
108	#13133263	D₄	1	4	yes	—
109	#13133263	C₂³	1	12	yes	complemented
110	#13133263	C₂³	1	24	yes	complemented
111	#13133263	C₂³	1	12	yes	complemented
112	#13133263	C₂³	1	8	yes	complemented
113	#13133263	C₂³	1	4	yes	complemented
114	#13133262	—	2	3	no	—
115	#13133262	—	2	12	no	—
116	#13133262	—	2	12	no	—
117	#13133262	—	2	24	no	—
118	#13133262	—	2	24	no	—
119	#13133262	—	2	24	no	—
120	#13133262	—	2	12	no	—
121	#13133262	—	2	12	no	—
122	#13133262	D₄	1	6	yes	—
123	#13133262	C₂³	1	12	yes	complemented
124	#13133262	C₂³	1	24	yes	complemented
125	#13133262	C₂³	1	12	yes	complemented
126	C₂×#11719949	—	2	1	no	—
127	C₂×#11719949	—	2	8	no	—
128	C₂×#11719949	C₂³	1	12	yes	complemented
129	C₂×#11719945	—	2	12	no	—
130	C₂×#11719945	—	2	12	no	—
131	C₂×#11719945	—	2	6	no	—
132	C₂×#11719945	C₂³	1	6	yes	—
133	C₂×#11719945	C₂³	1	3	yes	complemented
134	C₂×#11719945	C₂³	1	6	yes	complemented
135	C₂×#11719947	—	2	24	no	—
136	C₂×#11719947	—	2	6	no	—
137	C₂×#11719947	C₂³	1	12	yes	complemented
138	#41×D₅₃	—	2	4	no	—
139	#41×D₅₃	—	2	8	no	—
140	#41×D₅₃	—	2	8	no	—
141	#41×D₅₃	—	2	8	no	—
142	#41×D₅₃	—	2	24	no	—
143	#41×D₅₃	—	2	12	no	—
144	#41×D₅₃	—	2	12	no	—
145	#41×D₅₃	C₂³	1	8	yes	—
146	#41×D₅₃	C₂³	1	24	yes	complemented
147	#41×D₅₃	C₂³	1	24	yes	complemented
148	C₂²×D₂₁₂	—	2	6	no	—
149	C₂²×D₂₁₂	C₂³	1	3	yes	complemented
150	C₂²×C₂²⋊D₅₃	—	2	12	no	—
151	C₂×D₄×D₅₃	—	2	3	no	—
152	C₂×D₄×D₅₃	—	2	12	no	—
153	C₂×D₄×D₅₃	—	2	24	no	—
154	C₂×D₄×D₅₃	—	2	24	no	—
155	C₂×D₄×D₅₃	—	2	6	no	—
156	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
157	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
158	#13133250	C₂³	1	12	yes	complemented
159	#13133250	C₂³	1	4	yes	complemented
160	#13133249	C₂³	1	8	yes	complemented
161	#13133249	C₂³	1	24	yes	complemented
162	#13133248	C₂³	1	12	yes	complemented
163	#13133247	C₂³	1	12	yes	complemented
164	#13133246	C₂³	1	24	yes	complemented
165	#13133246	C₂³	1	8	yes	complemented
166	#13133245	C₂³	1	12	yes	complemented
167	#13133245	C₂³	1	24	yes	complemented
168	#13133245	C₂³	1	12	yes	complemented
169	#13133244	C₂³	1	24	yes	complemented
170	#13133244	C₂³	1	48	yes	complemented
171	#13133244	C₂³	1	24	yes	complemented
172	#13133243	C₂³	1	12	yes	complemented
173	#13133243	C₂³	1	24	yes	complemented
174	#13133242	C₂³	1	12	yes	complemented
175	#13133242	C₂³	1	24	yes	complemented
176	#13133241	C₂³	1	24	yes	complemented
177	#13133241	C₂³	1	48	yes	complemented
178	#13133241	C₂³	1	24	yes	complemented
179	#13133240	C₂³	1	24	yes	complemented
180	#13133239	C₂³	1	24	yes	complemented
181	#13133238	C₂³	1	8	yes	complemented
182	#13133238	C₂³	1	24	yes	complemented
183	#13133238	C₂³	1	48	yes	complemented
184	#13133237	C₂³	1	12	yes	complemented
185	#13133237	C₂³	1	12	yes	complemented
186	#13133237	C₂³	1	4	yes	complemented
187	#13133237	C₂³	1	12	yes	complemented
188	#13133237	C₂³	1	12	yes	complemented
189	#13133237	C₂³	1	12	yes	complemented
190	#13133236	C₂³	1	24	yes	complemented
191	C₂×#11719925	C₂³	1	1	yes	characteristic, complemented
192	C₂×#11719925	C₂³	1	6	yes	complemented
193	Q₁₆×D₅₃	C₂³	1	8	yes	complemented
194	C₂×#11719913	C₂³	1	12	yes	complemented
195	C₂×#11719923	C₂³	1	6	yes	complemented
196	C₂×#11719923	C₂³	1	3	yes	complemented
197	C₂×#11719924	C₂³	1	3	yes	complemented
198	C₂×#11719924	C₂³	1	6	yes	complemented
199	SD₁₆×D₅₃	C₂³	1	24	yes	complemented
200	SD₁₆×D₅₃	C₂³	1	24	yes	complemented
201	C₂×D₄₂₄	C₂³	1	12	yes	complemented
202	C₂×#11719922	C₂³	1	6	yes	complemented
203	C₂×#11719922	C₂³	1	12	yes	complemented
204	C₂×#11719922	C₂³	1	3	yes	complemented
205	C₂×#11719922	C₂³	1	12	yes	complemented
206	C₂×#11719922	C₂³	1	6	yes	complemented
207	D₈×D₅₃	C₂³	1	24	yes	complemented
208	D₈×D₅₃	C₂³	1	48	yes	complemented
209	#13133225	C₂³	1	12	yes	complemented
210	#13133225	C₂³	1	4	yes	complemented
211	#13133225	C₂³	1	12	yes	complemented
212	#13133225	C₂³	1	12	yes	complemented
213	#13133224	C₂³	1	4	yes	complemented
214	#13133224	C₂³	1	4	yes	complemented
215	#13133223	C₂³	1	24	yes	complemented
216	C₂×#11719917	C₂³	1	3	yes	complemented
217	C₂×#11719912	C₂³	1	12	yes	complemented
218	M₁₆×D₅₃	C₂³	1	24	yes	complemented
219	C₂²×#88322	C₂³	1	3	yes	complemented
220	C₂×C₈×D₅₃	C₂³	1	12	yes	complemented
221	2₋¹⁺⁴×C₅₃	—	2	1	no	—
222	2₋¹⁺⁴×C₅₃	C₂³	1	4	yes	complemented
223	H(5,𝔽₂)×C₅₃	—	2	4	no	—
224	H(5,𝔽₂)×C₅₃	—	2	3	no	—
225	H(5,𝔽₂)×C₅₃	C₂³	1	4	yes	complemented
226	H(5,𝔽₂)×C₅₃	C₂³	1	8	yes	complemented
227	C₂×#41×C₅₃	—	2	4	no	—
228	C₂×#41×C₅₃	—	2	1	no	—
229	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×#41×C₅₃	C₂³	1	6	yes	complemented
231	C₂×#41×C₅₃	C₂³	1	3	yes	complemented
232	C₂²×D₄×C₅₃	—	2	3	no	—
233	C₂²×D₄×C₅₃	C₂³	1	3	yes	complemented
234	#137×C₅₃	C₂³	1	4	yes	complemented
235	#137×C₅₃	C₂³	1	12	yes	complemented
236	AGL(1,ℤ/8)×C₅₃	C₂³	1	12	yes	complemented
237	AGL(1,ℤ/8)×C₅₃	C₂³	1	24	yes	complemented
238	AGL(1,ℤ/8)×C₅₃	C₂³	1	12	yes	complemented
239	#135×C₅₃	C₂³	1	24	yes	complemented
240	C₂×SD₁₆×C₅₃	C₂³	1	12	yes	complemented
241	C₂×D₈×C₅₃	C₂³	1	12	yes	complemented
242	#131×C₅₃	C₂³	1	8	yes	complemented
243	C₂×M₁₆×C₅₃	C₂³	1	6	yes	complemented
244	C₂⁴×C₅₃	—	2	3	no	—
245	C₂³×D₅₃	—	2	3	no	—
246	C₂³×D₅₃	—	2	12	no	—
247	C₂³×D₅₃	—	2	12	no	—
248	#41×C₅₃	—	2	8	no	—
249	#41×C₅₃	—	2	4	no	—
250	#41×C₅₃	—	2	12	no	—
251	#41×C₅₃	—	2	6	no	—
252	#41×C₅₃	—	2	6	no	—
253	#41×C₅₃	—	2	6	no	—
254	#41×C₅₃	C₂×D₄	1	4	yes	—
255	#41×C₅₃	C₂⁴	1	12	yes	—
256	#41×C₅₃	C₂⁴	1	12	yes	—
257	#41×C₅₃	C₂⁴	1	4	yes	—
258	#41×C₅₃	C₂⁴	1	4	yes	—
259	C₂×Q₈×C₅₃	—	2	4	no	—
260	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
261	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
262	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₅₃	—	2	3	no	—
264	C₂×D₄×C₅₃	—	2	6	no	—
265	C₂×D₄×C₅₃	—	2	24	no	—
266	C₂×D₄×C₅₃	—	2	12	no	—
267	C₂×D₄×C₅₃	—	2	3	no	—
268	C₂×D₄×C₅₃	—	2	6	no	—
269	C₂×D₄×C₅₃	C₂×D₄	1	3	yes	—
270	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
271	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
272	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
273	C₂²×C₄×C₅₃	—	2	3	no	—
274	C₂²×C₄×C₅₃	—	2	6	no	—
275	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
276	C₂×C₂²⋊D₅₃	—	2	3	no	—
277	C₂×C₂²⋊D₅₃	—	2	6	no	—
278	C₂×C₂²⋊D₅₃	—	2	12	no	—
279	C₂×C₂²⋊D₅₃	—	2	24	no	—
280	C₂×C₂²⋊D₅₃	—	2	48	no	—
281	C₂×C₂²⋊D₅₃	—	2	24	no	—
282	C₂×C₂²⋊D₅₃	—	2	12	no	—
283	C₂×C₂²⋊D₅₃	—	2	12	no	—
284	C₂×C₂²⋊D₅₃	C₂×D₄	1	12	yes	—
285	C₂²×Dic₅₃	—	2	12	no	—
286	#11719949	—	2	4	no	—
287	#11719949	—	2	8	no	—
288	#11719949	—	2	4	no	—
289	#11719949	—	2	12	no	—
290	#11719949	—	2	24	no	—
291	#11719949	C₂×D₄	1	8	yes	—
292	#11719949	C₂⁴	1	24	yes	—
293	#11719949	C₂⁴	1	8	yes	—
294	Q₈×D₅₃	—	2	4	no	—
295	Q₈×D₅₃	—	2	4	no	—
296	Q₈×D₅₃	—	2	12	no	—
297	Q₈×D₅₃	C₂×D₄	1	8	yes	—
298	Q₈×D₅₃	C₂⁴	1	8	yes	—
299	Q₈×D₅₃	C₂⁴	1	8	yes	—
300	#11719947	—	2	12	no	—
301	#11719947	—	2	8	no	—
302	#11719947	—	2	24	no	—
303	#11719947	—	2	24	no	—
304	#11719947	—	2	24	no	—
305	#11719947	—	2	24	no	—
306	#11719947	—	2	12	no	—
307	#11719947	—	2	12	no	—
308	#11719947	—	2	24	no	—
309	#11719947	C₂×D₄	1	24	yes	—
310	#11719947	C₂⁴	1	8	yes	—
311	#11719947	C₂⁴	1	24	yes	—
312	D₄×D₅₃	—	2	24	no	—
313	D₄×D₅₃	—	2	24	no	—
314	D₄×D₅₃	—	2	12	no	—
315	D₄×D₅₃	—	2	24	no	—
316	D₄×D₅₃	—	2	24	no	—
317	D₄×D₅₃	—	2	24	no	—
318	D₄×D₅₃	—	2	48	no	—
319	D₄×D₅₃	—	2	12	no	—
320	D₄×D₅₃	—	2	24	no	—
321	D₄×D₅₃	—	2	12	no	—
322	D₄×D₅₃	—	2	24	no	—
323	D₄×D₅₃	—	2	24	no	—
324	D₄×D₅₃	C₂×D₄	1	24	yes	—
325	D₄×D₅₃	C₂⁴	1	24	yes	—
326	D₄×D₅₃	C₂⁴	1	24	yes	—
327	#11719945	—	2	6	no	—
328	#11719945	—	2	6	no	—
329	#11719945	—	2	6	no	—
330	#11719945	—	2	24	no	—
331	#11719945	—	2	8	no	—
332	#11719945	—	2	12	no	—
333	#11719945	—	2	4	no	—
334	#11719945	—	2	24	no	—
335	#11719945	—	2	24	no	—
336	#11719945	—	2	12	no	—
337	#11719945	—	2	24	no	—
338	#11719945	—	2	12	no	—
339	#11719945	C₂×D₄	1	12	yes	—
340	#11719945	C₂×D₄	1	12	yes	—
341	#11719945	C₂⁴	1	12	yes	—
342	#11719945	C₂⁴	1	4	yes	—
343	#11719945	C₂⁴	1	4	yes	—
344	#11719945	C₂⁴	1	12	yes	—
345	#11719945	C₂⁴	1	12	yes	—
346	C₂×D₂₁₂	—	2	12	no	—
347	C₂×D₂₁₂	—	2	3	no	—
348	C₂×D₂₁₂	—	2	6	no	—
349	C₂×D₂₁₂	—	2	12	no	—
350	C₂×D₂₁₂	—	2	24	no	—
351	C₂×D₂₁₂	—	2	12	no	—
352	C₂×D₂₁₂	C₂×D₄	1	6	yes	—
353	C₂×D₂₁₂	C₂⁴	1	3	yes	—
354	C₂×D₂₁₂	C₂⁴	1	12	yes	—
355	C₂×D₂₁₂	C₂⁴	1	6	yes	—
356	C₂×C₄×D₅₃	—	2	6	no	—
357	C₂×C₄×D₅₃	—	2	3	no	—
358	C₂×C₄×D₅₃	—	2	12	no	—
359	C₂×C₄×D₅₃	—	2	24	no	—
360	C₂×C₄×D₅₃	—	2	24	no	—
361	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
362	C₂×Dic₁₀₆	—	2	12	no	—
363	C₂×Dic₁₀₆	—	2	4	no	—
364	C₂×Dic₁₀₆	C₂×D₄	1	6	yes	—
365	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
366	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
367	Q₁₆×C₅₃	C₂⁴	1	8	yes	—
368	SD₁₆×C₅₃	C₂⁴	1	24	yes	—
369	SD₁₆×C₅₃	C₂⁴	1	8	yes	—
370	D₈×C₅₃	C₂⁴	1	24	yes	—
371	M₁₆×C₅₃	C₂⁴	1	4	yes	—
372	M₁₆×C₅₃	C₂⁴	1	12	yes	—
373	C₂×C₈×C₅₃	C₂⁴	1	12	yes	—
374	#11719925	C₂⁴	1	2	yes	—
375	#11719925	C₂⁴	1	4	yes	—
376	#11719925	C₂⁴	1	2	yes	—
377	#11719925	C₂⁴	1	12	yes	—
378	#11719924	C₂⁴	1	12	yes	—
379	#11719924	C₂⁴	1	12	yes	—
380	#11719924	C₂⁴	1	4	yes	—
381	#11719923	C₂⁴	1	12	yes	—
382	#11719923	C₂⁴	1	12	yes	—
383	#11719923	C₂⁴	1	4	yes	—
384	#11719922	C₂⁴	1	4	yes	—
385	#11719922	C₂⁴	1	6	yes	—
386	#11719922	C₂⁴	1	12	yes	—
387	#11719922	C₂⁴	1	24	yes	—
388	#11719922	C₂⁴	1	6	yes	—
389	#11719917	C₂⁴	1	12	yes	—
390	C₂×#88322	C₂⁴	1	6	yes	—
391	C₂×#88322	C₂⁴	1	1	yes	characteristic
392	C₂×#88322	C₂⁴	1	6	yes	—
393	C₂×#88322	C₂⁴	1	3	yes	—
394	Dic₂₁₂	C₂⁴	1	8	yes	—
395	D₄₂₄	C₂⁴	1	24	yes	—
396	#11719913	C₂⁴	1	8	yes	—
397	#11719913	C₂⁴	1	24	yes	—
398	#11719912	C₂⁴	1	24	yes	—
399	#11719912	C₂⁴	1	8	yes	—
400	C₈×D₅₃	C₂⁴	1	8	yes	—
401	C₈×D₅₃	C₂⁴	1	24	yes	—
402	C₂³×C₅₃	—	2	12	no	—
403	C₂³×C₅₃	—	2	3	no	—
404	C₂³×C₅₃	—	2	6	no	—
405	C₂³×C₅₃	—	16	3	no	—
406	C₂³×C₅₃	C₂²×D₄	1	3	yes	—
407	C₂²×D₅₃	—	2	12	no	—
408	C₂²×D₅₃	—	2	3	no	—
409	C₂²×D₅₃	—	2	6	no	—
410	C₂²×D₅₃	—	2	24	no	—
411	C₂²×D₅₃	—	2	24	no	—
412	C₂²×D₅₃	—	16	12	no	—
413	C₂²×D₅₃	—	16	12	no	—
414	C₂²×D₅₃	—	16	3	no	—
415	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
416	Q₈×C₅₃	—	2	1	no	—
417	Q₈×C₅₃	—	2	6	no	—
418	Q₈×C₅₃	C₂²×D₄	1	4	yes	—
419	Q₈×C₅₃	C₂⁵	1	2	yes	—
420	Q₈×C₅₃	C₂⁵	1	4	yes	—
421	D₄×C₅₃	—	2	12	no	—
422	D₄×C₅₃	—	2	4	no	—
423	D₄×C₅₃	—	2	12	no	—
424	D₄×C₅₃	—	2	6	no	—
425	D₄×C₅₃	—	2	3	no	—
426	D₄×C₅₃	—	2	12	no	—
427	D₄×C₅₃	C₂²×D₄	1	12	yes	—
428	D₄×C₅₃	C₂⁵	1	4	yes	—
429	D₄×C₅₃	C₂⁵	1	6	yes	—
430	C₂×C₄×C₅₃	—	2	6	no	—
431	C₂×C₄×C₅₃	—	2	1	no	—
432	C₂×C₄×C₅₃	—	2	12	no	—
433	C₂×C₄×C₅₃	—	2	4	no	—
434	C₂×C₄×C₅₃	—	2	12	no	—
435	C₂×C₄×C₅₃	C₂²×D₄	1	6	yes	—
436	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
437	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
438	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
439	C₂²⋊D₅₃	—	2	4	no	—
440	C₂²⋊D₅₃	—	2	12	no	—
441	C₂²⋊D₅₃	—	2	12	no	—
442	C₂²⋊D₅₃	—	2	8	no	—
443	C₂²⋊D₅₃	—	2	24	no	—
444	C₂²⋊D₅₃	—	2	24	no	—
445	C₂²⋊D₅₃	—	2	24	no	—
446	C₂²⋊D₅₃	C₂²×D₄	1	8	yes	—
447	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	—
448	C₂×Dic₅₃	—	2	1	no	—
449	C₂×Dic₅₃	—	2	6	no	—
450	C₂×Dic₅₃	—	2	8	no	—
451	C₂×Dic₅₃	—	2	24	no	—
452	C₂×Dic₅₃	C₂²×D₄	1	12	yes	—
453	D₂₁₂	—	2	24	no	—
454	D₂₁₂	—	2	8	no	—
455	D₂₁₂	—	2	3	no	—
456	D₂₁₂	—	2	12	no	—
457	D₂₁₂	—	2	6	no	—
458	D₂₁₂	C₂²×D₄	1	4	yes	—
459	D₂₁₂	C₂²×D₄	1	12	yes	—
460	D₂₁₂	C₂⁵	1	6	yes	—
461	D₂₁₂	C₂⁵	1	4	yes	—
462	C₄×D₅₃	—	2	8	no	—
463	C₄×D₅₃	—	2	8	no	—
464	C₄×D₅₃	—	2	4	no	—
465	C₄×D₅₃	—	2	12	no	—
466	C₄×D₅₃	—	2	12	no	—
467	C₄×D₅₃	—	2	8	no	—
468	C₄×D₅₃	—	2	24	no	—
469	C₄×D₅₃	C₂²×D₄	1	24	yes	—
470	C₄×D₅₃	C₂⁵	1	8	yes	—
471	Dic₁₀₆	—	2	1	no	—
472	Dic₁₀₆	—	2	6	no	—
473	Dic₁₀₆	—	2	8	no	—
474	Dic₁₀₆	—	2	8	no	—
475	Dic₁₀₆	C₂²×D₄	1	4	yes	—
476	Dic₁₀₆	C₂²×D₄	1	12	yes	—
477	Dic₁₀₆	C₂⁵	1	4	yes	—
478	Dic₁₀₆	C₂⁵	1	2	yes	—
479	C₈×C₅₃	C₂⁵	1	8	yes	—
480	#88322	C₂⁵	1	1	yes	characteristic
481	#88322	C₂⁵	1	6	yes	—
482	#88322	C₂⁵	1	1	yes	characteristic
483	#63091	—	53	1	no	maximal, Sylow
484	C₂²×C₅₃	—	2	6	no	—
485	C₂²×C₅₃	—	2	4	no	—
486	C₂²×C₅₃	—	4	3	no	—
487	C₂²×C₅₃	—	8	6	no	—
488	C₂²×C₅₃	—	8	12	no	—
489	C₂²×C₅₃	—	8	3	no	—
490	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
491	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
492	C₂×D₅₃	—	2	6	no	—
493	C₂×D₅₃	—	2	4	no	—
494	C₂×D₅₃	—	4	12	no	—
495	C₂×D₅₃	—	8	24	no	—
496	C₂×D₅₃	—	8	24	no	—
497	C₂×D₅₃	—	8	12	no	—
498	C₂×D₅₃	—	8	6	no	—
499	C₂×D₅₃	—	8	3	no	—
500	C₂×D₅₃	C₂³×D₄	1	8	yes	—
501	C₄×C₅₃	—	2	2	no	—
502	C₄×C₅₃	—	2	4	no	—
503	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₅₃	C₂³×D₄	1	6	yes	—
505	C₄×C₅₃	C₂⁶	1	1	yes	characteristic
506	Dic₅₃	—	2	2	no	—
507	Dic₅₃	—	2	4	no	—
508	Dic₅₃	C₂³×D₄	1	8	yes	—
509	H(7,𝔽₂)	—	53	1	no	—
510	H(7,𝔽₂)	—	53	1	no	—
511	#3585	—	53	8	no	—
512	#3585	—	53	8	no	—
513	#3585	—	53	6	no	—
514	#3585	—	53	6	no	—
515	#3585	—	53	1	no	—
516	#3585	D₅₃	1	1	yes	characteristic, complemented
517	#3584	—	53	1	no	—
518	#3584	—	53	8	no	—
519	#3584	—	53	6	no	—
520	C₂×#576	—	53	1	no	—
521	C₂×#576	—	53	8	no	—
522	C₂×#576	—	53	6	no	—
523	#3573	—	53	1	no	—
524	C₂×C₅₃	—	2	6	no	—
525	C₂×C₅₃	—	2	1	no	—
526	C₂×C₅₃	—	4	4	no	—
527	C₂×C₅₃	—	4	6	no	—
528	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
529	D₅₃	—	2	8	no	—
530	D₅₃	—	4	6	no	—
531	D₅₃	—	4	4	no	—
532	#585	—	53	1	no	—
533	#585	—	53	8	no	—
534	#585	—	53	8	no	—
535	#585	—	53	1	no	—
536	#585	—	53	6	no	—
537	#585	—	53	6	no	—
538	#585	—	106	4	no	—
539	#585	—	106	2	no	—
540	#585	—	106	4	no	—
541	#585	—	106	2	no	—
542	#585	C₂×D₅₃	1	1	yes	characteristic, complemented
543	C₂×H(5,𝔽₂)	—	53	8	no	—
544	C₂×H(5,𝔽₂)	—	53	8	no	—
545	C₂×H(5,𝔽₂)	—	53	1	no	—
546	C₂×H(5,𝔽₂)	—	53	6	no	—
547	C₂×H(5,𝔽₂)	—	53	6	no	—
548	C₂×H(5,𝔽₂)	—	106	6	no	—
549	C₂×H(5,𝔽₂)	—	106	4	no	—
550	C₂×H(5,𝔽₂)	—	106	4	no	—
551	C₂×H(5,𝔽₂)	—	106	6	no	—
552	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
553	#578	—	53	4	no	—
554	#578	—	53	12	no	—
555	#578	—	53	4	no	—
556	#577	—	53	4	no	—
557	#577	—	53	4	no	—
558	#577	—	53	12	no	—
559	#577	—	53	12	no	—
560	#577	—	53	12	no	—
561	#577	—	53	12	no	—
562	#577	—	53	24	no	—
563	#577	—	53	24	no	—
564	#577	—	53	8	no	—
565	#577	C₂×D₅₃	1	8	yes	complemented
566	#576	—	53	8	no	—
567	#576	—	53	4	no	—
568	#576	—	53	8	no	—
569	#576	—	53	12	no	—
570	#576	—	53	24	no	—
571	#576	—	53	12	no	—
572	#576	—	53	24	no	—
573	#576	—	53	24	no	—
574	#576	—	53	24	no	—
575	#576	—	53	24	no	—
576	#576	—	53	8	no	—
577	#576	C₂×D₅₃	1	8	yes	complemented
578	#575	—	53	6	no	—
579	#575	—	53	24	no	—
580	#575	—	53	24	no	—
581	#575	—	53	24	no	—
582	#575	—	53	6	no	—
583	#575	C₂×D₅₃	1	6	yes	complemented
584	C₂×AGL(1,ℤ/8)	—	53	3	no	—
585	C₂×AGL(1,ℤ/8)	—	53	3	no	—
586	C₂×AGL(1,ℤ/8)	—	53	24	no	—
587	C₂×AGL(1,ℤ/8)	—	53	24	no	—
588	C₂×AGL(1,ℤ/8)	—	53	12	no	—
589	C₂×AGL(1,ℤ/8)	—	53	12	no	—
590	C₂×AGL(1,ℤ/8)	—	53	6	no	—
591	C₂×AGL(1,ℤ/8)	C₂×D₅₃	1	6	yes	complemented
592	C₂×#135	—	53	3	no	—
593	C₂×#135	—	53	6	no	—
594	C₂×#135	—	53	24	no	—
595	C₂×#135	—	53	12	no	—
596	C₂²×D₈	—	53	3	no	—
597	C₂²×D₈	—	53	12	no	—
598	#568	—	53	8	no	—
599	#568	—	53	6	no	—
600	#568	C₂×D₅₃	1	1	yes	characteristic, complemented
601	C₂×#131	—	53	1	no	—
602	C₂×#131	—	53	8	no	—
603	C₂×#131	—	53	6	no	—
604	C₅₃	#63091	1	1	yes	characteristic, complemented, Sylow
605	2₋¹⁺⁴	—	2	1	no	—
606	2₋¹⁺⁴	—	53	4	no	—
607	2₋¹⁺⁴	—	53	2	no	—
608	2₋¹⁺⁴	—	53	4	no	—
609	2₋¹⁺⁴	—	53	12	no	—
610	2₋¹⁺⁴	—	53	4	no	—
611	2₋¹⁺⁴	—	53	4	no	—
612	2₋¹⁺⁴	—	53	12	no	—
613	2₋¹⁺⁴	—	106	8	no	—
614	2₋¹⁺⁴	—	106	8	no	—
615	2₋¹⁺⁴	—	106	6	no	—
616	2₋¹⁺⁴	—	106	6	no	—
617	2₋¹⁺⁴	—	106	1	no	—
618	2₋¹⁺⁴	C₂²×D₅₃	1	4	yes	complemented
619	H(5,𝔽₂)	—	2	4	no	—
620	H(5,𝔽₂)	—	2	3	no	—
621	H(5,𝔽₂)	—	53	4	no	—
622	H(5,𝔽₂)	—	53	6	no	—
623	H(5,𝔽₂)	—	53	12	no	—
624	H(5,𝔽₂)	—	53	12	no	—
625	H(5,𝔽₂)	—	53	24	no	—
626	H(5,𝔽₂)	—	53	8	no	—
627	H(5,𝔽₂)	—	53	4	no	—
628	H(5,𝔽₂)	—	53	12	no	—
629	H(5,𝔽₂)	—	53	24	no	—
630	H(5,𝔽₂)	—	53	12	no	—
631	H(5,𝔽₂)	—	106	12	no	—
632	H(5,𝔽₂)	—	106	12	no	—
633	H(5,𝔽₂)	—	106	24	no	—
634	H(5,𝔽₂)	—	106	24	no	—
635	H(5,𝔽₂)	—	106	24	no	—
636	H(5,𝔽₂)	—	106	12	no	—
637	H(5,𝔽₂)	—	106	12	no	—
638	H(5,𝔽₂)	—	106	24	no	—
639	H(5,𝔽₂)	—	106	6	no	—
640	H(5,𝔽₂)	—	106	6	no	—
641	H(5,𝔽₂)	—	106	8	no	—
642	H(5,𝔽₂)	—	106	8	no	—
643	H(5,𝔽₂)	—	106	12	no	—
644	H(5,𝔽₂)	—	106	12	no	—
645	H(5,𝔽₂)	—	106	4	no	—
646	H(5,𝔽₂)	—	106	3	no	—
647	H(5,𝔽₂)	C₂²×D₅₃	1	8	yes	complemented
648	H(5,𝔽₂)	C₂²×D₅₃	1	4	yes	complemented
649	C₂×#41	—	2	4	no	—
650	C₂×#41	—	2	1	no	—
651	C₂×#41	—	53	8	no	—
652	C₂×#41	—	53	6	no	—
653	C₂×#41	—	53	24	no	—
654	C₂×#41	—	53	24	no	—
655	C₂×#41	—	53	12	no	—
656	C₂×#41	—	53	12	no	—
657	C₂×#41	—	53	3	no	—
658	C₂×#41	—	53	6	no	—
659	C₂×#41	—	106	6	no	—
660	C₂×#41	—	106	12	no	—
661	C₂×#41	—	106	12	no	—
662	C₂×#41	—	106	6	no	—
663	C₂×#41	—	106	24	no	—
664	C₂×#41	—	106	8	no	—
665	C₂×#41	—	106	8	no	—
666	C₂×#41	—	106	8	no	—
667	C₂×#41	—	106	8	no	—
668	C₂×#41	—	106	24	no	—
669	C₂×#41	—	106	12	no	—
670	C₂×#41	—	106	12	no	—
671	C₂×#41	—	106	4	no	—
672	C₂×#41	—	106	1	no	—
673	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
674	C₂×#41	C₂²×D₅₃	1	3	yes	complemented
675	C₂×#41	C₂²×D₅₃	1	6	yes	complemented
676	C₂²×D₄	—	2	3	no	—
677	C₂²×D₄	—	53	12	no	—
678	C₂²×D₄	—	53	12	no	—
679	C₂²×D₄	—	53	3	no	—
680	C₂²×D₄	—	106	6	no	—
681	C₂²×D₄	—	106	12	no	—
682	C₂²×D₄	—	106	24	no	—
683	C₂²×D₄	—	106	24	no	—
684	C₂²×D₄	—	106	6	no	—
685	C₂²×D₄	—	106	12	no	—
686	C₂²×D₄	—	106	3	no	—
687	C₂²×D₄	C₂²×D₅₃	1	3	yes	complemented
688	#137	—	53	12	no	—
689	#137	—	53	12	no	—
690	#137	—	53	24	no	—
691	#137	—	53	8	no	—
692	#137	—	53	8	no	—
693	#137	—	53	24	no	—
694	#137	—	53	12	no	—
695	#137	—	53	4	no	—
696	#137	C₂²×D₅₃	1	12	yes	complemented
697	#137	C₂²×D₅₃	1	4	yes	complemented
698	AGL(1,ℤ/8)	—	53	24	no	—
699	AGL(1,ℤ/8)	—	53	12	no	—
700	AGL(1,ℤ/8)	—	53	24	no	—
701	AGL(1,ℤ/8)	—	53	12	no	—
702	AGL(1,ℤ/8)	—	53	24	no	—
703	AGL(1,ℤ/8)	—	53	48	no	—
704	AGL(1,ℤ/8)	—	53	24	no	—
705	AGL(1,ℤ/8)	—	53	24	no	—
706	AGL(1,ℤ/8)	—	53	48	no	—
707	AGL(1,ℤ/8)	—	53	24	no	—
708	AGL(1,ℤ/8)	—	53	12	no	—
709	AGL(1,ℤ/8)	—	53	24	no	—
710	AGL(1,ℤ/8)	—	53	12	no	—
711	AGL(1,ℤ/8)	C₂²×D₅₃	1	12	yes	complemented
712	AGL(1,ℤ/8)	C₂²×D₅₃	1	24	yes	complemented
713	AGL(1,ℤ/8)	C₂²×D₅₃	1	12	yes	complemented
714	#135	—	53	4	no	—
715	#135	—	53	12	no	—
716	#135	—	53	12	no	—
717	#135	—	53	12	no	—
718	#135	—	53	12	no	—
719	#135	—	53	12	no	—
720	#135	—	53	24	no	—
721	#135	—	53	8	no	—
722	#135	—	53	24	no	—
723	#135	—	53	48	no	—
724	#135	—	53	24	no	—
725	#135	—	53	24	no	—
726	#135	C₂²×D₅₃	1	24	yes	complemented
727	C₂×Q₁₆	—	53	1	no	—
728	C₂×Q₁₆	—	53	6	no	—
729	C₂×Q₁₆	—	53	8	no	—
730	C₂×SD₁₆	—	53	3	no	—
731	C₂×SD₁₆	—	53	6	no	—
732	C₂×SD₁₆	—	53	3	no	—
733	C₂×SD₁₆	—	53	6	no	—
734	C₂×SD₁₆	—	53	24	no	—
735	C₂×SD₁₆	—	53	24	no	—
736	C₂×SD₁₆	—	53	12	no	—
737	C₂×SD₁₆	C₂²×D₅₃	1	12	yes	complemented
738	C₂×D₈	—	53	3	no	—
739	C₂×D₈	—	53	12	no	—
740	C₂×D₈	—	53	6	no	—
741	C₂×D₈	—	53	6	no	—
742	C₂×D₈	—	53	12	no	—
743	C₂×D₈	—	53	24	no	—
744	C₂×D₈	—	53	48	no	—
745	C₂×D₈	—	53	12	no	—
746	C₂×D₈	C₂²×D₅₃	1	12	yes	complemented
747	#131	—	53	4	no	—
748	#131	—	53	4	no	—
749	#131	—	53	12	no	—
750	#131	—	53	4	no	—
751	#131	—	53	12	no	—
752	#131	—	53	12	no	—
753	#131	—	53	24	no	—
754	#131	C₂²×D₅₃	1	8	yes	complemented
755	C₂×M₁₆	—	53	3	no	—
756	C₂×M₁₆	—	53	24	no	—
757	C₂×M₁₆	—	53	12	no	—
758	C₂×M₁₆	C₂²×D₅₃	1	6	yes	complemented
759	C₂²×C₈	—	53	3	no	—
760	C₂²×C₈	—	53	12	no	—
761	C₂⁴	—	2	3	no	—
762	C₂⁴	—	106	12	no	—
763	C₂⁴	—	106	12	no	—
764	C₂⁴	—	106	3	no	—
765	#41	—	2	8	no	—
766	#41	—	2	4	no	—
767	#41	—	2	12	no	—
768	#41	—	2	6	no	—
769	#41	—	2	6	no	—
770	#41	—	2	6	no	—
771	#41	—	53	8	no	—
772	#41	—	53	24	no	—
773	#41	—	53	12	no	—
774	#41	—	53	12	no	—
775	#41	—	53	4	no	—
776	#41	—	53	12	no	—
777	#41	—	53	8	no	—
778	#41	—	53	24	no	—
779	#41	—	53	24	no	—
780	#41	—	53	8	no	—
781	#41	—	53	4	no	—
782	#41	—	53	12	no	—
783	#41	—	53	12	no	—
784	#41	—	106	24	no	—
785	#41	—	106	24	no	—
786	#41	—	106	8	no	—
787	#41	—	106	24	no	—
788	#41	—	106	4	no	—
789	#41	—	106	12	no	—
790	#41	—	106	12	no	—
791	#41	—	106	12	no	—
792	#41	—	106	24	no	—
793	#41	—	106	24	no	—
794	#41	—	106	24	no	—
795	#41	—	106	24	no	—
796	#41	—	106	24	no	—
797	#41	—	106	24	no	—
798	#41	—	106	8	no	—
799	#41	—	106	12	no	—
800	#41	—	106	24	no	—
801	#41	—	106	12	no	—
802	#41	—	106	12	no	—
803	#41	—	106	4	no	—
804	#41	—	106	4	no	—
805	#41	—	106	8	no	—
806	#41	—	106	12	no	—
807	#41	—	106	6	no	—
808	#41	—	106	6	no	—
809	#41	—	106	6	no	—
810	#41	D₄×D₅₃	1	4	yes	—
811	#41	C₂³×D₅₃	1	4	yes	—
812	#41	C₂³×D₅₃	1	12	yes	—
813	#41	C₂³×D₅₃	1	12	yes	—
814	#41	C₂³×D₅₃	1	4	yes	—
815	C₂×Q₈	—	2	4	no	—
816	C₂×Q₈	—	53	8	no	—
817	C₂×Q₈	—	53	6	no	—
818	C₂×Q₈	—	53	8	no	—
819	C₂×Q₈	—	53	8	no	—
820	C₂×Q₈	—	53	1	no	—
821	C₂×Q₈	—	53	6	no	—
822	C₂×Q₈	—	106	4	no	—
823	C₂×Q₈	—	106	12	no	—
824	C₂×Q₈	—	106	12	no	—
825	C₂×Q₈	—	106	4	no	—
826	C₂×Q₈	—	106	4	no	—
827	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
828	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
829	C₂×Q₈	C₂³×D₅₃	1	6	yes	—
830	C₂×D₄	—	2	3	no	—
831	C₂×D₄	—	2	6	no	—
832	C₂×D₄	—	2	24	no	—
833	C₂×D₄	—	2	12	no	—
834	C₂×D₄	—	2	3	no	—
835	C₂×D₄	—	2	6	no	—
836	C₂×D₄	—	53	12	no	—
837	C₂×D₄	—	53	24	no	—
838	C₂×D₄	—	53	24	no	—
839	C₂×D₄	—	53	24	no	—
840	C₂×D₄	—	53	6	no	—
841	C₂×D₄	—	53	3	no	—
842	C₂×D₄	—	53	12	no	—
843	C₂×D₄	—	53	6	no	—
844	C₂×D₄	—	106	12	no	—
845	C₂×D₄	—	106	12	no	—
846	C₂×D₄	—	106	24	no	—
847	C₂×D₄	—	106	12	no	—
848	C₂×D₄	—	106	24	no	—
849	C₂×D₄	—	106	24	no	—
850	C₂×D₄	—	106	12	no	—
851	C₂×D₄	—	106	12	no	—
852	C₂×D₄	—	106	24	no	—
853	C₂×D₄	—	106	24	no	—
854	C₂×D₄	—	106	48	no	—
855	C₂×D₄	—	106	24	no	—
856	C₂×D₄	—	106	12	no	—
857	C₂×D₄	—	106	12	no	—
858	C₂×D₄	—	106	24	no	—
859	C₂×D₄	—	106	24	no	—
860	C₂×D₄	—	106	24	no	—
861	C₂×D₄	—	106	24	no	—
862	C₂×D₄	—	106	48	no	—
863	C₂×D₄	—	106	12	no	—
864	C₂×D₄	—	106	3	no	—
865	C₂×D₄	—	106	6	no	—
866	C₂×D₄	—	106	12	no	—
867	C₂×D₄	—	106	24	no	—
868	C₂×D₄	—	106	6	no	—
869	C₂×D₄	—	106	3	no	—
870	C₂×D₄	D₄×D₅₃	1	3	yes	—
871	C₂×D₄	C₂³×D₅₃	1	3	yes	—
872	C₂×D₄	C₂³×D₅₃	1	12	yes	—
873	C₂×D₄	C₂³×D₅₃	1	6	yes	—
874	C₂²×C₄	—	2	3	no	—
875	C₂²×C₄	—	2	6	no	—
876	C₂²×C₄	—	53	12	no	—
877	C₂²×C₄	—	106	12	no	—
878	C₂²×C₄	—	106	24	no	—
879	C₂²×C₄	—	106	24	no	—
880	C₂²×C₄	—	106	12	no	—
881	C₂²×C₄	—	106	6	no	—
882	C₂²×C₄	—	106	3	no	—
883	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
884	Q₁₆	—	53	2	no	—
885	Q₁₆	—	53	4	no	—
886	Q₁₆	—	53	2	no	—
887	Q₁₆	—	53	12	no	—
888	Q₁₆	—	53	8	no	—
889	Q₁₆	C₂³×D₅₃	1	8	yes	—
890	SD₁₆	—	53	12	no	—
891	SD₁₆	—	53	4	no	—
892	SD₁₆	—	53	12	no	—
893	SD₁₆	—	53	12	no	—
894	SD₁₆	—	53	4	no	—
895	SD₁₆	—	53	12	no	—
896	SD₁₆	—	53	8	no	—
897	SD₁₆	—	53	24	no	—
898	SD₁₆	C₂³×D₅₃	1	8	yes	—
899	SD₁₆	C₂³×D₅₃	1	24	yes	—
900	D₈	—	53	6	no	—
901	D₈	—	53	4	no	—
902	D₈	—	53	6	no	—
903	D₈	—	53	24	no	—
904	D₈	—	53	12	no	—
905	D₈	—	53	24	no	—
906	D₈	C₂³×D₅₃	1	24	yes	—
907	M₁₆	—	53	12	no	—
908	M₁₆	—	53	24	no	—
909	M₁₆	—	53	8	no	—
910	M₁₆	C₂³×D₅₃	1	12	yes	—
911	M₁₆	C₂³×D₅₃	1	4	yes	—
912	C₂×C₈	—	53	1	no	—
913	C₂×C₈	—	53	6	no	—
914	C₂×C₈	—	53	3	no	—
915	C₂×C₈	—	53	6	no	—
916	C₂×C₈	—	53	8	no	—
917	C₂×C₈	—	53	24	no	—
918	C₂×C₈	C₂³×D₅₃	1	12	yes	—
919	C₂³	—	2	6	no	—
920	C₂³	—	2	3	no	—
921	C₂³	—	2	12	no	—
922	C₂³	—	16	3	no	—
923	C₂³	—	53	12	no	—
924	C₂³	—	848	3	no	—
925	C₂³	—	848	12	no	—
926	C₂³	—	848	12	no	—
927	C₂³	—	106	24	no	—
928	C₂³	—	106	24	no	—
929	C₂³	—	106	12	no	—
930	C₂³	—	106	6	no	—
931	C₂³	—	106	3	no	—
932	C₂³	C₂×D₄×D₅₃	1	3	yes	—
933	Q₈	—	2	6	no	—
934	Q₈	—	2	1	no	—
935	Q₈	—	53	12	no	—
936	Q₈	—	53	4	no	—
937	Q₈	—	53	4	no	—
938	Q₈	—	53	2	no	—
939	Q₈	—	106	8	no	—
940	Q₈	—	106	8	no	—
941	Q₈	—	106	6	no	—
942	Q₈	—	106	1	no	—
943	Q₈	C₂×D₄×D₅₃	1	4	yes	—
944	Q₈	C₂⁴×D₅₃	1	2	yes	—
945	Q₈	C₂⁴×D₅₃	1	4	yes	—
946	D₄	—	2	12	no	—
947	D₄	—	2	12	no	—
948	D₄	—	2	4	no	—
949	D₄	—	2	12	no	—
950	D₄	—	2	3	no	—
951	D₄	—	2	6	no	—
952	D₄	—	53	24	no	—
953	D₄	—	53	8	no	—
954	D₄	—	53	12	no	—
955	D₄	—	53	4	no	—
956	D₄	—	53	6	no	—
957	D₄	—	53	4	no	—
958	D₄	—	106	8	no	—
959	D₄	—	106	24	no	—
960	D₄	—	106	24	no	—
961	D₄	—	106	24	no	—
962	D₄	—	106	8	no	—
963	D₄	—	106	24	no	—
964	D₄	—	106	12	no	—
965	D₄	—	106	12	no	—
966	D₄	—	106	4	no	—
967	D₄	—	106	12	no	—
968	D₄	—	106	6	no	—
969	D₄	—	106	3	no	—
970	D₄	C₂×D₄×D₅₃	1	12	yes	—
971	D₄	C₂⁴×D₅₃	1	6	yes	—
972	D₄	C₂⁴×D₅₃	1	4	yes	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	6	no	—
975	C₂×C₄	—	2	4	no	—
976	C₂×C₄	—	2	12	no	—
977	C₂×C₄	—	2	12	no	—
978	C₂×C₄	—	53	12	no	—
979	C₂×C₄	—	53	24	no	—
980	C₂×C₄	—	53	8	no	—
981	C₂×C₄	—	106	8	no	—
982	C₂×C₄	—	106	24	no	—
983	C₂×C₄	—	106	8	no	—
984	C₂×C₄	—	106	8	no	—
985	C₂×C₄	—	106	8	no	—
986	C₂×C₄	—	106	24	no	—
987	C₂×C₄	—	106	6	no	—
988	C₂×C₄	—	106	1	no	—
989	C₂×C₄	—	106	12	no	—
990	C₂×C₄	—	106	12	no	—
991	C₂×C₄	—	106	4	no	—
992	C₂×C₄	C₂×D₄×D₅₃	1	6	yes	—
993	C₂×C₄	C₂×D₄×D₅₃	1	3	yes	—
994	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
995	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
996	C₈	—	53	1	no	—
997	C₈	—	53	6	no	—
998	C₈	—	53	1	no	—
999	C₈	C₂⁴×D₅₃	1	8	yes	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	6	no	—
1002	C₂²	—	4	3	no	—
1003	C₂²	—	8	3	no	—
1004	C₂²	—	8	12	no	—
1005	C₂²	—	8	6	no	—
1006	C₂²	—	53	8	no	—
1007	C₂²	—	106	6	no	—
1008	C₂²	—	106	4	no	—
1009	C₂²	—	424	3	no	—
1010	C₂²	—	424	12	no	—
1011	C₂²	—	424	6	no	—
1012	C₂²	—	424	24	no	—
1013	C₂²	—	424	24	no	—
1014	C₂²	—	212	12	no	—
1015	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
1016	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	4	no	—
1019	C₄	—	53	8	no	—
1020	C₄	—	106	2	no	—
1021	C₄	—	106	4	no	—
1022	C₄	C₂²×D₄×D₅₃	1	6	yes	—
1023	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
1024	C₄	C₂⁵×D₅₃	1	1	yes	characteristic
1025	C₂	—	2	1	no	—
1026	C₂	—	2	6	no	—
1027	C₂	—	4	6	no	—
1028	C₂	—	4	4	no	—
1029	C₂	—	106	8	no	—
1030	C₂	—	212	6	no	—
1031	C₂	—	212	4	no	—
1032	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₄×D₅₃
commutator, cosocle	C₄×C₅₃	C₂⁶
Frattini	C₄	C₂⁵×D₅₃
Fitting	C₅₃×#3585	C₂
socle	C₂×C₅₃	C₂⁴×D₄
hypercenter	#3585	D₅₃
hypocenter	C₅₃	#63091
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ #3585

Complements

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

N	H ≅ G/N	type
1. #20289526	C₂	semidirect
2. #20289525	C₂	semidirect
3. #20289496	C₂	semidirect
4. #20289493	C₂	semidirect
5. #20289492	C₂	semidirect
6. #20289491	C₂	semidirect
7. #20289490	C₂	semidirect
8. #20289488	C₂	semidirect
9. #20289487	C₂	semidirect
10. #20289486	C₂	semidirect
11. C₂×#16811427	C₂	semidirect
12. C₂×#16811426	C₂	semidirect
13. #576×D₅₃	C₂	semidirect
14. #20289428	C₂	semidirect
15. C₅₃×#3585	C₂	semidirect
17. #16811460	C₂²	semidirect
21. #16811459	C₂²	semidirect
22. #16811459	C₂²	semidirect
23. #16811459	C₂²	semidirect
25. #16811458	C₂²	semidirect
27. C₂×#13133263	C₂²	semidirect
28. C₂×#13133263	C₂²	semidirect
30. C₂×#13133262	C₂²	semidirect
33. H(5,𝔽₂)×D₅₃	C₂²	semidirect
34. H(5,𝔽₂)×D₅₃	C₂²	semidirect
35. #16811439	C₂²	semidirect
36. #16811439	C₂²	semidirect
37. #16811438	C₂²	semidirect
38. #16811435	C₂²	semidirect
39. #16811434	C₂²	semidirect
40. #16811433	C₂²	semidirect
41. #16811433	C₂²	semidirect
42. #16811432	C₂²	semidirect
43. #16811432	C₂²	semidirect
44. #16811431	C₂²	semidirect
45. #16811430	C₂²	semidirect
46. #16811429	C₂²	semidirect
47. #16811428	C₂²	semidirect
48. #16811427	C₂²	semidirect
49. #16811427	C₂²	semidirect
50. #16811427	C₂²	semidirect
51. #16811427	C₂²	semidirect
52. #16811427	C₂²	semidirect
53. #16811426	C₂²	semidirect
54. #16811426	C₂²	semidirect
55. #16811426	C₂²	semidirect
56. #16811425	C₂²	semidirect
57. #16811424	C₂²	semidirect
58. #16811423	C₂²	semidirect
59. #16811422	C₂²	semidirect
60. #16811421	C₂²	semidirect
61. #16811420	C₂²	semidirect
62. #16811419	C₂²	semidirect
63. C₂×#13133245	C₂²	semidirect
64. C₂×#13133244	C₂²	semidirect
65. C₂×#13133243	C₂²	semidirect
66. C₂×#13133242	C₂²	semidirect
67. C₂×#13133241	C₂²	semidirect
68. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
69. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
70. C₂×#13133238	C₂²	semidirect
71. C₂×#13133237	C₂²	semidirect
72. C₂×#13133237	C₂²	semidirect
73. #135×D₅₃	C₂²	semidirect
74. C₂²×#11719922	C₂²	semidirect
75. C₂×D₈×D₅₃	C₂²	semidirect
76. #16811389	C₂²	semidirect
77. #16811388	C₂²	semidirect
78. C₂×#13133225	C₂²	semidirect
79. C₂×#13133224	C₂²	semidirect
80. #131×D₅₃	C₂²	semidirect
81. C₅₃×#585	C₂²	semidirect
82. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
83. C₅₃×#577	C₂²	semidirect
84. C₅₃×#576	C₂²	semidirect
85. C₅₃×#575	C₂²	semidirect
86. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
87. C₅₃×#568	C₂²	semidirect
91. #13133265	C₂³	semidirect
92. #13133265	C₂³	semidirect
97. #13133264	C₂³	semidirect
98. #13133264	C₂³	semidirect
99. #13133264	C₂³	semidirect
109. #13133263	C₂³	semidirect
110. #13133263	C₂³	semidirect
111. #13133263	C₂³	semidirect
112. #13133263	C₂³	semidirect
113. #13133263	C₂³	semidirect
123. #13133262	C₂³	semidirect
124. #13133262	C₂³	semidirect
125. #13133262	C₂³	semidirect
128. C₂×#11719949	C₂³	semidirect
133. C₂×#11719945	C₂³	semidirect
134. C₂×#11719945	C₂³	semidirect
137. C₂×#11719947	C₂³	semidirect
146. #41×D₅₃	C₂³	semidirect
147. #41×D₅₃	C₂³	semidirect
149. C₂²×D₂₁₂	C₂³	semidirect
156. C₂×D₄×D₅₃	C₂³	semidirect
157. C₂×D₄×D₅₃	C₂³	semidirect
158. #13133250	C₂³	semidirect
159. #13133250	C₂³	semidirect
160. #13133249	C₂³	semidirect
161. #13133249	C₂³	semidirect
162. #13133248	C₂³	semidirect
163. #13133247	C₂³	semidirect
164. #13133246	C₂³	semidirect
165. #13133246	C₂³	semidirect
166. #13133245	C₂³	semidirect
167. #13133245	C₂³	semidirect
168. #13133245	C₂³	semidirect
169. #13133244	C₂³	semidirect
170. #13133244	C₂³	semidirect
171. #13133244	C₂³	semidirect
172. #13133243	C₂³	semidirect
173. #13133243	C₂³	semidirect
174. #13133242	C₂³	semidirect
175. #13133242	C₂³	semidirect
176. #13133241	C₂³	semidirect
177. #13133241	C₂³	semidirect
178. #13133241	C₂³	semidirect
179. #13133240	C₂³	semidirect
180. #13133239	C₂³	semidirect
181. #13133238	C₂³	semidirect
182. #13133238	C₂³	semidirect
183. #13133238	C₂³	semidirect
184. #13133237	C₂³	semidirect
185. #13133237	C₂³	semidirect
186. #13133237	C₂³	semidirect
187. #13133237	C₂³	semidirect
188. #13133237	C₂³	semidirect
189. #13133237	C₂³	semidirect
190. #13133236	C₂³	semidirect
191. C₂×#11719925	C₂³	semidirect
192. C₂×#11719925	C₂³	semidirect
193. Q₁₆×D₅₃	C₂³	semidirect
194. C₂×#11719913	C₂³	semidirect
195. C₂×#11719923	C₂³	semidirect
196. C₂×#11719923	C₂³	semidirect
197. C₂×#11719924	C₂³	semidirect
198. C₂×#11719924	C₂³	semidirect
199. SD₁₆×D₅₃	C₂³	semidirect
200. SD₁₆×D₅₃	C₂³	semidirect
201. C₂×D₄₂₄	C₂³	semidirect
202. C₂×#11719922	C₂³	semidirect
203. C₂×#11719922	C₂³	semidirect
204. C₂×#11719922	C₂³	semidirect
205. C₂×#11719922	C₂³	semidirect
206. C₂×#11719922	C₂³	semidirect
207. D₈×D₅₃	C₂³	semidirect
208. D₈×D₅₃	C₂³	semidirect
209. #13133225	C₂³	semidirect
210. #13133225	C₂³	semidirect
211. #13133225	C₂³	semidirect
212. #13133225	C₂³	semidirect
213. #13133224	C₂³	semidirect
214. #13133224	C₂³	semidirect
215. #13133223	C₂³	semidirect
216. C₂×#11719917	C₂³	semidirect
217. C₂×#11719912	C₂³	semidirect
218. M₁₆×D₅₃	C₂³	semidirect
219. C₂²×#88322	C₂³	semidirect
220. C₂×C₈×D₅₃	C₂³	semidirect
222. 2₋¹⁺⁴×C₅₃	C₂³	semidirect
225. H(5,𝔽₂)×C₅₃	C₂³	semidirect
226. H(5,𝔽₂)×C₅₃	C₂³	semidirect
230. C₂×#41×C₅₃	C₂³	semidirect
231. C₂×#41×C₅₃	C₂³	semidirect
233. C₂²×D₄×C₅₃	C₂³	semidirect
234. #137×C₅₃	C₂³	semidirect
235. #137×C₅₃	C₂³	semidirect
236. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
237. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
238. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
239. #135×C₅₃	C₂³	semidirect
240. C₂×SD₁₆×C₅₃	C₂³	semidirect
241. C₂×D₈×C₅₃	C₂³	semidirect
242. #131×C₅₃	C₂³	semidirect
243. C₂×M₁₆×C₅₃	C₂³	semidirect
516. #3585	D₅₃	semidirect
542. #585	C₂×D₅₃	semidirect
552. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
565. #577	C₂×D₅₃	semidirect
577. #576	C₂×D₅₃	semidirect
583. #575	C₂×D₅₃	semidirect
591. C₂×AGL(1,ℤ/8)	C₂×D₅₃	semidirect
600. #568	C₂×D₅₃	semidirect
604. C₅₃	#63091	semidirect
618. 2₋¹⁺⁴	C₂²×D₅₃	semidirect
647. H(5,𝔽₂)	C₂²×D₅₃	semidirect
648. H(5,𝔽₂)	C₂²×D₅₃	semidirect
674. C₂×#41	C₂²×D₅₃	semidirect
675. C₂×#41	C₂²×D₅₃	semidirect
687. C₂²×D₄	C₂²×D₅₃	semidirect
696. #137	C₂²×D₅₃	semidirect
697. #137	C₂²×D₅₃	semidirect
711. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
712. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
713. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
726. #135	C₂²×D₅₃	semidirect
737. C₂×SD₁₆	C₂²×D₅₃	semidirect
746. C₂×D₈	C₂²×D₅₃	semidirect
754. #131	C₂²×D₅₃	semidirect
758. C₂×M₁₆	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20289526	2
#20289525	2
#20289496	2
#20289493	2
#20289492	2
#20289491	2
#20289490	2
#20289488	2
#20289487	2
#20289486	2
C₂×#16811427	2
C₂×#16811426	2
#576×D₅₃	2
#20289428	2
C₅₃×#3585	2
#63091	53