Subgroups — D₅₃×#3290 #28260294

Order 13568.

2650 conjugacy classes of subgroups.

The subgroup lattice has 1638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#578×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#577×D₅₃	C₂	1	2	yes	maximal, complemented
3	#576×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#20286504	C₂	1	1	yes	maximal, characteristic, complemented
5	#20286503	C₂	1	1	yes	maximal, characteristic, complemented
6	#20286502	C₂	1	1	yes	maximal, characteristic, complemented
7	#20286501	C₂	1	1	yes	maximal, characteristic, complemented
8	#20286500	C₂	1	1	yes	maximal, characteristic, complemented
9	#20286499	C₂	1	2	yes	maximal, complemented
10	#20286498	C₂	1	2	yes	maximal, complemented
11	#20286497	C₂	1	1	yes	maximal, characteristic, complemented
12	#20286496	C₂	1	1	yes	maximal, characteristic, complemented
13	#20286495	C₂	1	2	yes	maximal, complemented
14	#20286494	C₂	1	2	yes	maximal, complemented
15	#495×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#473×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#472×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#471×D₅₃	C₂	1	2	yes	maximal, complemented
19	#454×D₅₃	C₂	1	2	yes	maximal, complemented
20	#455×D₅₃	C₂	1	2	yes	maximal, complemented
21	#443×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#443×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3290	C₂	1	1	yes	maximal, characteristic, complemented
24	2₋¹⁺⁴×D₅₃	C₂²	1	2	yes	complemented
25	H(5,𝔽₂)×D₅₃	C₂²	1	2	yes	—
26	#16811440	C₂²	1	1	yes	characteristic, complemented
27	#16811439	—	2	2	no	—
28	#16811439	C₂²	1	2	yes	complemented
29	#16811438	C₂²	1	2	yes	complemented
30	#16811437	—	2	1	no	—
31	#16811437	C₂²	1	1	yes	characteristic, complemented
32	#16811436	—	2	1	no	—
33	#16811436	C₂²	1	1	yes	characteristic, complemented
34	#16811435	C₂²	1	2	yes	complemented
35	#16811434	C₂²	1	2	yes	complemented
36	#16811433	—	2	2	no	—
37	#16811433	C₂²	1	2	yes	complemented
38	#16811432	—	2	2	no	—
39	#16811432	C₂²	1	2	yes	complemented
40	#16811431	C₂²	1	2	yes	complemented
41	#16811430	—	2	2	no	—
42	#16811430	C₂²	1	2	yes	complemented
43	#16811429	—	2	2	no	—
44	#16811429	C₂²	1	2	yes	complemented
45	#16811428	C₂²	1	1	yes	characteristic, complemented
46	#16811427	—	2	2	no	—
47	#16811427	C₂²	1	2	yes	complemented
48	#16811426	C₂²	1	2	yes	complemented
49	#16811425	—	2	1	no	—
50	#16811425	C₂²	1	1	yes	characteristic, complemented
51	#16811424	—	2	1	no	—
52	#16811424	C₂²	1	1	yes	characteristic, complemented
53	#137×D₅₃	—	2	2	no	—
54	#137×D₅₃	—	2	2	no	—
55	#137×D₅₃	C₂²	1	2	yes	—
56	#137×D₅₃	C₂²	1	2	yes	complemented
57	AGL(1,ℤ/8)×D₅₃	—	2	2	no	—
58	AGL(1,ℤ/8)×D₅₃	—	2	2	no	—
59	AGL(1,ℤ/8)×D₅₃	C₂²	1	2	yes	—
60	AGL(1,ℤ/8)×D₅₃	C₂²	1	2	yes	complemented
61	#135×D₅₃	—	2	1	no	—
62	#135×D₅₃	—	2	2	no	—
63	#135×D₅₃	—	2	1	no	—
64	#135×D₅₃	C₂²	1	1	yes	characteristic
65	#135×D₅₃	C₂²	1	1	yes	characteristic
66	C₂×Q₁₆×D₅₃	—	2	1	no	—
67	C₂×Q₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×SD₁₆×D₅₃	—	2	2	no	—
69	C₂×SD₁₆×D₅₃	C₂²	1	2	yes	complemented
70	C₂×D₈×D₅₃	—	2	1	no	—
71	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
72	#131×D₅₃	C₂²	1	1	yes	characteristic
73	#131×D₅₃	C₂²	1	1	yes	characteristic, complemented
74	#131×D₅₃	C₂²	1	2	yes	complemented
75	#124×D₅₃	C₂²	1	2	yes	complemented
76	#16811008	C₂²	1	1	yes	characteristic, complemented
77	#16811007	C₂²	1	1	yes	characteristic, complemented
78	#16811006	C₂²	1	1	yes	characteristic, complemented
79	#16811005	C₂²	1	2	yes	complemented
80	#16811004	C₂²	1	2	yes	complemented
81	#16810899	C₂²	1	1	yes	characteristic, complemented
82	#16810898	C₂²	1	1	yes	characteristic, complemented
83	#16810897	C₂²	1	2	yes	complemented
84	#16810896	C₂²	1	2	yes	complemented
85	#16810895	C₂²	1	1	yes	characteristic, complemented
86	#16810894	C₂²	1	1	yes	characteristic, complemented
87	#16810893	C₂²	1	1	yes	characteristic, complemented
88	#16810892	C₂²	1	2	yes	complemented
89	#16810891	C₂²	1	2	yes	complemented
90	#16810890	C₂²	1	1	yes	characteristic, complemented
91	#16810889	C₂²	1	2	yes	complemented
92	#16810888	C₂²	1	2	yes	complemented
93	#16810887	C₂²	1	2	yes	complemented
94	#16810886	C₂²	1	2	yes	complemented
95	#16810885	C₂²	1	2	yes	complemented
96	#16810884	C₂²	1	2	yes	complemented
97	#16810883	C₂²	1	2	yes	complemented
98	#16810803	C₂²	1	2	yes	complemented
99	#16810802	C₂²	1	2	yes	complemented
100	#16810802	C₂²	1	2	yes	complemented
101	#16810801	C₂²	1	2	yes	complemented
102	#16810800	C₂²	1	2	yes	complemented
103	#16810799	C₂²	1	2	yes	complemented
104	#16810799	C₂²	1	2	yes	complemented
105	#16810798	C₂²	1	2	yes	complemented
106	#16810797	C₂²	1	2	yes	complemented
107	#16810797	C₂²	1	2	yes	complemented
108	#16810796	C₂²	1	2	yes	complemented
109	#16810795	C₂²	1	2	yes	complemented
110	#16810794	C₂²	1	2	yes	complemented
111	#16810794	C₂²	1	2	yes	complemented
112	#16810741	C₂²	1	1	yes	characteristic, complemented
113	#16810741	C₂²	1	1	yes	characteristic, complemented
114	#16810740	C₂²	1	1	yes	characteristic, complemented
115	#16810740	C₂²	1	1	yes	characteristic, complemented
116	#16810739	C₂²	1	1	yes	characteristic, complemented
117	#16810739	C₂²	1	1	yes	characteristic, complemented
118	#16810738	C₂²	1	1	yes	characteristic, complemented
119	#16810738	C₂²	1	1	yes	characteristic, complemented
120	#16810738	C₂²	1	2	yes	complemented
121	#16810737	C₂²	1	1	yes	characteristic, complemented
122	#16810737	C₂²	1	1	yes	characteristic, complemented
123	#16810737	C₂²	1	2	yes	complemented
124	#108×D₅₃	C₂²	1	1	yes	characteristic, complemented
125	#108×D₅₃	C₂²	1	1	yes	characteristic, complemented
126	#104×D₅₃	C₂²	1	1	yes	characteristic
127	#104×D₅₃	C₂²	1	2	yes	complemented
128	#104×D₅₃	C₂²	1	1	yes	characteristic, complemented
129	#101×D₅₃	C₂²	1	2	yes	complemented
130	#100×D₅₃	C₂²	1	2	yes	complemented
131	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#578	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#577	C₂²	1	2	yes	complemented
134	C₅₃×#576	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#473	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#472	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#471	C₂²	1	2	yes	complemented
139	C₅₃×#455	C₂²	1	2	yes	complemented
140	C₅₃×#454	C₂²	1	2	yes	complemented
141	C₅₃×#443	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#443	C₂²	1	1	yes	characteristic, complemented
143	#13133265	—	2	2	no	—
144	#13133265	—	2	2	no	—
145	#13133265	C₂³	1	2	yes	complemented
146	#13133264	—	2	2	no	—
147	#13133264	—	2	2	no	—
148	#13133264	—	4	2	no	—
149	#13133264	C₂³	1	2	yes	complemented
150	#13133264	C₂³	1	2	yes	complemented
151	#13133263	—	2	2	no	—
152	#13133263	—	2	2	no	—
153	#13133263	C₂³	1	2	yes	—
154	#13133263	C₂³	1	2	yes	—
155	#13133262	—	2	2	no	—
156	#13133262	—	2	2	no	—
157	#13133262	—	4	2	no	—
158	#13133262	C₂³	1	2	yes	—
159	#41×D₅₃	—	2	2	no	—
160	#41×D₅₃	—	2	2	no	—
161	#41×D₅₃	—	2	2	no	—
162	#41×D₅₃	—	2	2	no	—
163	#41×D₅₃	—	4	2	no	—
164	#41×D₅₃	C₂³	1	1	yes	characteristic
165	#41×D₅₃	C₂³	1	2	yes	—
166	#41×D₅₃	C₂³	1	1	yes	characteristic
167	C₂×Q₈×D₅₃	—	2	2	no	—
168	C₂×Q₈×D₅₃	—	2	2	no	—
169	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
170	C₂×D₄×D₅₃	—	2	2	no	—
171	C₂×D₄×D₅₃	—	2	2	no	—
172	C₂×D₄×D₅₃	—	4	2	no	—
173	C₂×D₄×D₅₃	C₂³	1	2	yes	—
174	#13133250	—	2	2	no	—
175	#13133250	—	2	2	no	—
176	#13133250	C₂³	1	2	yes	—
177	#13133250	C₂³	1	2	yes	complemented
178	#13133249	—	2	2	no	—
179	#13133249	—	2	2	no	—
180	#13133249	—	2	2	no	—
181	#13133249	—	2	2	no	—
182	#13133249	—	2	2	no	—
183	#13133249	—	2	2	no	—
184	#13133248	—	2	2	no	—
185	#13133248	—	2	2	no	—
186	#13133248	C₂³	1	2	yes	—
187	#13133248	C₂³	1	2	yes	complemented
188	#13133247	—	2	2	no	—
189	#13133247	—	2	2	no	—
190	#13133247	C₂³	1	2	yes	—
191	#13133247	C₂³	1	2	yes	complemented
192	#13133246	—	2	2	no	—
193	#13133246	—	2	2	no	—
194	#13133246	—	2	2	no	—
195	#13133246	—	2	2	no	—
196	#13133246	—	2	2	no	—
197	#13133246	—	2	2	no	—
198	#13133245	—	2	2	no	—
199	#13133245	—	2	2	no	—
200	#13133245	C₂³	1	2	yes	—
201	#13133245	C₂³	1	2	yes	complemented
202	#13133244	—	2	2	no	—
203	#13133244	—	2	2	no	—
204	#13133244	—	2	2	no	—
205	#13133244	—	2	2	no	—
206	#13133244	—	2	2	no	—
207	#13133244	—	2	2	no	—
208	#13133243	—	2	2	no	—
209	#13133243	—	2	2	no	—
210	#13133243	C₂³	1	2	yes	—
211	#13133243	C₂³	1	2	yes	complemented
212	#13133242	—	2	2	no	—
213	#13133242	—	2	2	no	—
214	#13133242	C₂³	1	2	yes	—
215	#13133242	C₂³	1	2	yes	complemented
216	#13133241	—	2	2	no	—
217	#13133241	—	2	2	no	—
218	#13133241	—	2	2	no	—
219	#13133241	—	2	2	no	—
220	#13133241	—	2	2	no	—
221	#13133241	—	2	2	no	—
222	#13133240	—	2	1	no	—
223	#13133240	—	2	2	no	—
224	#13133240	—	2	1	no	—
225	#13133240	D₄	1	1	yes	characteristic
226	#13133240	D₄	1	1	yes	characteristic
227	#13133239	—	2	1	no	—
228	#13133239	—	2	1	no	—
229	#13133239	—	2	2	no	—
230	#13133239	C₂³	1	1	yes	characteristic
231	#13133239	C₂³	1	1	yes	characteristic
232	#13133238	—	2	2	no	—
233	#13133238	—	2	2	no	—
234	#13133238	—	2	2	no	—
235	#13133238	—	2	2	no	—
236	#13133238	D₄	1	2	yes	—
237	#13133238	D₄	1	1	yes	characteristic
238	#13133238	D₄	1	1	yes	characteristic
239	#13133237	—	2	2	no	—
240	#13133237	—	2	2	no	—
241	#13133237	—	2	2	no	—
242	#13133237	—	2	2	no	—
243	#13133237	C₂³	1	2	yes	—
244	#13133237	C₂³	1	1	yes	characteristic
245	#13133237	C₂³	1	1	yes	characteristic
246	#13133236	—	2	1	no	—
247	#13133236	—	2	2	no	—
248	#13133236	—	2	1	no	—
249	#13133236	D₄	1	1	yes	characteristic
250	#13133236	D₄	1	1	yes	characteristic
251	C₂×Dic₂₁₂	—	2	1	no	—
252	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic, complemented
253	C₂×#11719925	—	2	2	no	—
254	C₂×#11719925	C₂³	1	2	yes	complemented
255	Q₁₆×D₅₃	—	2	1	no	—
256	Q₁₆×D₅₃	—	2	2	no	—
257	Q₁₆×D₅₃	—	2	1	no	—
258	Q₁₆×D₅₃	—	2	1	no	—
259	Q₁₆×D₅₃	—	2	1	no	—
260	Q₁₆×D₅₃	—	2	1	no	—
261	Q₁₆×D₅₃	—	2	1	no	—
262	Q₁₆×D₅₃	—	2	2	no	—
263	Q₁₆×D₅₃	—	2	2	no	—
264	Q₁₆×D₅₃	D₄	1	1	yes	characteristic
265	Q₁₆×D₅₃	D₄	1	1	yes	characteristic
266	C₂×#11719913	—	2	2	no	—
267	C₂×#11719913	C₂³	1	2	yes	complemented
268	C₂×#11719923	—	2	2	no	—
269	C₂×#11719923	C₂³	1	2	yes	complemented
270	C₂×#11719924	—	2	2	no	—
271	C₂×#11719924	C₂³	1	2	yes	complemented
272	SD₁₆×D₅₃	—	2	2	no	—
273	SD₁₆×D₅₃	—	2	2	no	—
274	SD₁₆×D₅₃	—	2	2	no	—
275	SD₁₆×D₅₃	—	2	2	no	—
276	SD₁₆×D₅₃	—	2	2	no	—
277	SD₁₆×D₅₃	—	2	2	no	—
278	SD₁₆×D₅₃	—	2	2	no	—
279	SD₁₆×D₅₃	—	2	2	no	—
280	SD₁₆×D₅₃	—	2	2	no	—
281	SD₁₆×D₅₃	—	2	2	no	—
282	SD₁₆×D₅₃	—	2	2	no	—
283	SD₁₆×D₅₃	—	2	2	no	—
284	SD₁₆×D₅₃	D₄	1	1	yes	characteristic
285	SD₁₆×D₅₃	D₄	1	1	yes	characteristic
286	SD₁₆×D₅₃	D₄	1	2	yes	—
287	C₂×D₄₂₄	—	2	1	no	—
288	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
289	C₂×#11719922	—	2	2	no	—
290	C₂×#11719922	C₂³	1	2	yes	—
291	D₈×D₅₃	—	2	1	no	—
292	D₈×D₅₃	—	2	2	no	—
293	D₈×D₅₃	—	2	1	no	—
294	D₈×D₅₃	—	2	1	no	—
295	D₈×D₅₃	—	2	1	no	—
296	D₈×D₅₃	—	2	1	no	—
297	D₈×D₅₃	—	2	1	no	—
298	D₈×D₅₃	—	2	2	no	—
299	D₈×D₅₃	—	2	2	no	—
300	D₈×D₅₃	D₄	1	1	yes	characteristic
301	D₈×D₅₃	D₄	1	1	yes	characteristic
302	#13133225	—	2	1	no	—
303	#13133225	—	2	2	no	—
304	#13133225	—	2	1	no	—
305	#13133225	C₂³	1	1	yes	characteristic
306	#13133225	C₂³	1	2	yes	complemented
307	#13133225	C₂³	1	1	yes	characteristic, complemented
308	#13133224	C₂³	1	1	yes	characteristic
309	#13133224	C₂³	1	2	yes	complemented
310	#13133224	C₂³	1	1	yes	characteristic, complemented
311	#13133223	—	2	1	no	—
312	#13133223	—	2	2	no	—
313	#13133223	—	2	1	no	—
314	#13133223	C₂³	1	1	yes	characteristic
315	#13133223	C₂³	1	2	yes	complemented
316	#13133223	C₂³	1	1	yes	characteristic, complemented
317	M₁₆×D₅₃	—	2	1	no	—
318	M₁₆×D₅₃	—	2	2	no	—
319	M₁₆×D₅₃	—	2	1	no	—
320	M₁₆×D₅₃	C₂³	1	1	yes	characteristic
321	M₁₆×D₅₃	C₂³	1	2	yes	—
322	M₁₆×D₅₃	C₂³	1	1	yes	characteristic
323	C₂×C₈×D₅₃	—	2	1	no	—
324	C₂×C₈×D₅₃	—	2	2	no	—
325	C₂×C₈×D₅₃	—	2	1	no	—
326	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
328	#13133206	C₂³	1	2	yes	complemented
329	#13133205	C₂³	1	2	yes	complemented
330	#13133204	C₂³	1	2	yes	complemented
331	#13133203	—	4	2	no	—
332	C₂²⋊C₄×D₅₃	—	4	2	no	—
333	C₄²×D₅₃	C₂³	1	1	yes	characteristic
334	#13133153	C₂³	1	1	yes	characteristic, complemented
335	#13133153	C₂³	1	1	yes	characteristic, complemented
336	#13133152	C₂³	1	1	yes	characteristic, complemented
337	#13133152	C₂³	1	1	yes	characteristic, complemented
338	#13133152	C₂³	1	2	yes	complemented
339	#13133145	C₂³	1	1	yes	characteristic
340	#13133145	C₂³	1	1	yes	characteristic, complemented
341	#13133145	C₂³	1	2	yes	complemented
342	#13133144	C₂³	1	1	yes	characteristic
343	#13133144	C₂³	1	1	yes	characteristic, complemented
344	#13133144	C₂³	1	2	yes	complemented
345	#13133143	C₂³	1	1	yes	characteristic
346	#13133143	C₂³	1	1	yes	characteristic, complemented
347	#13133143	C₂³	1	2	yes	complemented
348	#13133136	C₂³	1	2	yes	complemented
349	#13133135	C₂³	1	2	yes	complemented
350	#13133135	C₂³	1	2	yes	complemented
351	#13133134	C₂³	1	2	yes	complemented
352	#13133133	C₂³	1	2	yes	complemented
353	#13133133	C₂³	1	2	yes	complemented
354	C₄×#88322	C₂³	1	1	yes	characteristic, complemented
355	C₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
356	C₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
357	2₋¹⁺⁴×C₅₃	C₂³	1	2	yes	complemented
358	H(5,𝔽₂)×C₅₃	C₂³	1	2	yes	—
359	#137×C₅₃	—	2	2	no	—
360	#137×C₅₃	—	2	2	no	—
361	#137×C₅₃	C₂³	1	2	yes	—
362	#137×C₅₃	C₂³	1	2	yes	complemented
363	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
364	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
365	AGL(1,ℤ/8)×C₅₃	C₂³	1	2	yes	—
366	AGL(1,ℤ/8)×C₅₃	C₂³	1	2	yes	complemented
367	#135×C₅₃	—	2	1	no	—
368	#135×C₅₃	—	2	2	no	—
369	#135×C₅₃	—	2	1	no	—
370	#135×C₅₃	C₂³	1	1	yes	characteristic
371	#135×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×Q₁₆×C₅₃	—	2	1	no	—
373	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
374	C₂×SD₁₆×C₅₃	—	2	2	no	—
375	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
376	C₂×D₈×C₅₃	—	2	1	no	—
377	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
378	#131×C₅₃	C₂³	1	1	yes	characteristic
379	#131×C₅₃	C₂³	1	2	yes	complemented
380	#131×C₅₃	C₂³	1	1	yes	characteristic, complemented
381	#124×C₅₃	C₂³	1	2	yes	complemented
382	#108×C₅₃	C₂³	1	1	yes	characteristic, complemented
383	#108×C₅₃	C₂³	1	1	yes	characteristic, complemented
384	#104×C₅₃	C₂³	1	1	yes	characteristic
385	#104×C₅₃	C₂³	1	1	yes	characteristic, complemented
386	#104×C₅₃	C₂³	1	2	yes	complemented
387	#101×C₅₃	C₂³	1	2	yes	complemented
388	#100×C₅₃	C₂³	1	2	yes	complemented
389	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
390	C₂³×D₅₃	—	2	2	no	—
391	C₂³×D₅₃	—	4	2	no	—
392	#41×C₅₃	—	2	2	no	—
393	#41×C₅₃	—	2	2	no	—
394	#41×C₅₃	—	2	2	no	—
395	#41×C₅₃	—	2	2	no	—
396	#41×C₅₃	—	4	2	no	—
397	#41×C₅₃	C₂⁴	1	1	yes	characteristic
398	#41×C₅₃	C₂⁴	1	2	yes	—
399	#41×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂×Q₈×C₅₃	—	2	2	no	—
401	C₂×Q₈×C₅₃	—	2	2	no	—
402	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
403	C₂×D₄×C₅₃	—	2	2	no	—
404	C₂×D₄×C₅₃	—	2	2	no	—
405	C₂×D₄×C₅₃	—	4	2	no	—
406	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
407	C₂×C₂²⋊D₅₃	—	2	2	no	—
408	C₂×C₂²⋊D₅₃	—	4	2	no	—
409	C₂×C₂²⋊D₅₃	—	4	2	no	—
410	C₂×C₂²⋊D₅₃	—	4	2	no	—
411	C₂×C₂²⋊D₅₃	—	4	2	no	—
412	#11719949	—	2	2	no	—
413	#11719949	—	2	2	no	—
414	#11719949	—	2	2	no	—
415	#11719949	—	2	2	no	—
416	#11719949	—	4	2	no	—
417	#11719949	C₂×D₄	1	1	yes	characteristic
418	#11719949	C₂×D₄	1	2	yes	—
419	#11719949	C₂×D₄	1	1	yes	characteristic
420	Q₈×D₅₃	—	2	2	no	—
421	Q₈×D₅₃	—	2	2	no	—
422	Q₈×D₅₃	—	2	2	no	—
423	Q₈×D₅₃	—	2	2	no	—
424	Q₈×D₅₃	—	2	2	no	—
425	Q₈×D₅₃	—	2	2	no	—
426	Q₈×D₅₃	—	2	2	no	—
427	Q₈×D₅₃	—	2	2	no	—
428	Q₈×D₅₃	—	4	2	no	—
429	Q₈×D₅₃	—	4	2	no	—
430	Q₈×D₅₃	—	4	2	no	—
431	Q₈×D₅₃	C₂×D₄	1	1	yes	characteristic
432	Q₈×D₅₃	C₂×D₄	1	2	yes	—
433	Q₈×D₅₃	C₂×D₄	1	1	yes	characteristic
434	#11719947	—	2	1	no	—
435	#11719947	—	2	2	no	—
436	#11719947	—	2	1	no	—
437	#11719947	—	2	2	no	—
438	#11719947	—	2	2	no	—
439	#11719947	—	2	2	no	—
440	#11719947	—	2	2	no	—
441	#11719947	—	4	2	no	—
442	#11719947	—	4	2	no	—
443	#11719947	—	4	2	no	—
444	#11719947	—	4	2	no	—
445	#11719947	—	4	2	no	—
446	#11719947	—	4	2	no	—
447	#11719947	—	4	2	no	—
448	#11719947	C₂×D₄	1	1	yes	characteristic
449	#11719947	C₂×D₄	1	2	yes	—
450	#11719947	C₂×D₄	1	1	yes	characteristic
451	D₄×D₅₃	—	2	1	no	—
452	D₄×D₅₃	—	2	2	no	—
453	D₄×D₅₃	—	2	1	no	—
454	D₄×D₅₃	—	2	2	no	—
455	D₄×D₅₃	—	2	2	no	—
456	D₄×D₅₃	—	2	2	no	—
457	D₄×D₅₃	—	2	2	no	—
458	D₄×D₅₃	—	2	2	no	—
459	D₄×D₅₃	—	2	2	no	—
460	D₄×D₅₃	—	2	2	no	—
461	D₄×D₅₃	—	2	2	no	—
462	D₄×D₅₃	—	4	2	no	—
463	D₄×D₅₃	—	4	2	no	—
464	D₄×D₅₃	—	4	2	no	—
465	D₄×D₅₃	—	4	2	no	—
466	D₄×D₅₃	—	4	2	no	—
467	D₄×D₅₃	—	4	2	no	—
468	D₄×D₅₃	—	4	2	no	—
469	D₄×D₅₃	—	4	2	no	—
470	D₄×D₅₃	—	4	2	no	—
471	D₄×D₅₃	C₂×D₄	1	1	yes	characteristic
472	D₄×D₅₃	C₂×D₄	1	2	yes	—
473	D₄×D₅₃	C₂×D₄	1	1	yes	characteristic
474	#11719945	—	2	1	no	—
475	#11719945	—	2	2	no	—
476	#11719945	—	2	1	no	—
477	#11719945	—	2	2	no	—
478	#11719945	—	2	2	no	—
479	#11719945	—	2	2	no	—
480	#11719945	—	2	2	no	—
481	#11719945	—	4	2	no	—
482	#11719945	—	4	2	no	—
483	#11719945	—	4	2	no	—
484	#11719945	—	4	2	no	—
485	#11719945	—	4	2	no	—
486	#11719945	—	4	2	no	—
487	#11719945	—	4	2	no	—
488	#11719945	C₂⁴	1	1	yes	characteristic
489	#11719945	C₂⁴	1	2	yes	—
490	#11719945	C₂⁴	1	1	yes	characteristic
491	C₂×D₂₁₂	—	2	2	no	—
492	C₂×D₂₁₂	—	2	2	no	—
493	C₂×D₂₁₂	—	4	2	no	—
494	C₂×D₂₁₂	C₂⁴	1	2	yes	—
495	C₂×C₄×D₅₃	—	2	1	no	—
496	C₂×C₄×D₅₃	—	2	2	no	—
497	C₂×C₄×D₅₃	—	2	1	no	—
498	C₂×C₄×D₅₃	—	2	1	no	—
499	C₂×C₄×D₅₃	—	2	2	no	—
500	C₂×C₄×D₅₃	—	4	2	no	—
501	C₂×C₄×D₅₃	—	4	2	no	—
502	C₂×C₄×D₅₃	—	4	2	no	—
503	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
504	C₂×Dic₁₀₆	—	2	2	no	—
505	C₂×Dic₁₀₆	—	2	2	no	—
506	C₂×Dic₁₀₆	—	2	2	no	—
507	C₂×Dic₁₀₆	—	4	2	no	—
508	C₂×Dic₁₀₆	—	4	2	no	—
509	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
510	Q₁₆×C₅₃	—	2	2	no	—
511	Q₁₆×C₅₃	—	2	2	no	—
512	Q₁₆×C₅₃	—	2	1	no	—
513	Q₁₆×C₅₃	—	2	1	no	—
514	Q₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
515	Q₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
516	SD₁₆×C₅₃	—	2	2	no	—
517	SD₁₆×C₅₃	—	2	2	no	—
518	SD₁₆×C₅₃	—	2	2	no	—
519	SD₁₆×C₅₃	—	2	2	no	—
520	SD₁₆×C₅₃	—	2	2	no	—
521	SD₁₆×C₅₃	—	2	2	no	—
522	SD₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
523	SD₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
524	SD₁₆×C₅₃	C₂×D₄	1	2	yes	—
525	D₈×C₅₃	—	2	2	no	—
526	D₈×C₅₃	—	2	2	no	—
527	D₈×C₅₃	—	2	1	no	—
528	D₈×C₅₃	—	2	1	no	—
529	D₈×C₅₃	C₂×D₄	1	1	yes	characteristic
530	D₈×C₅₃	C₂×D₄	1	1	yes	characteristic
531	M₁₆×C₅₃	—	2	1	no	—
532	M₁₆×C₅₃	—	2	2	no	—
533	M₁₆×C₅₃	—	2	1	no	—
534	M₁₆×C₅₃	C₂⁴	1	1	yes	characteristic
535	M₁₆×C₅₃	C₂⁴	1	2	yes	—
536	M₁₆×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂×C₈×C₅₃	—	2	1	no	—
538	C₂×C₈×C₅₃	—	2	2	no	—
539	C₂×C₈×C₅₃	—	2	1	no	—
540	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
541	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₂²⋊C₄×C₅₃	—	4	2	no	—
543	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
544	C₂²⋊Dic₅₃	—	4	2	no	—
545	#11719925	—	2	2	no	—
546	#11719925	—	2	2	no	—
547	#11719925	—	2	2	no	—
548	#11719925	—	2	2	no	—
549	#11719925	—	2	2	no	—
550	#11719925	—	2	2	no	—
551	#11719925	C₂×D₄	1	2	yes	—
552	#11719925	C₂×D₄	1	1	yes	characteristic
553	#11719925	C₂×D₄	1	1	yes	characteristic
554	#11719924	—	2	2	no	—
555	#11719924	—	2	2	no	—
556	#11719924	—	2	2	no	—
557	#11719924	—	2	2	no	—
558	#11719924	—	2	2	no	—
559	#11719924	—	2	2	no	—
560	#11719924	C₂×D₄	1	1	yes	characteristic
561	#11719924	C₂×D₄	1	1	yes	characteristic
562	#11719924	C₂×D₄	1	2	yes	—
563	#11719923	—	2	2	no	—
564	#11719923	—	2	2	no	—
565	#11719923	—	2	2	no	—
566	#11719923	—	2	2	no	—
567	#11719923	—	2	2	no	—
568	#11719923	—	2	2	no	—
569	#11719923	C₂×D₄	1	1	yes	characteristic
570	#11719923	C₂×D₄	1	1	yes	characteristic
571	#11719923	C₂×D₄	1	2	yes	—
572	#11719922	—	2	2	no	—
573	#11719922	—	2	2	no	—
574	#11719922	—	2	2	no	—
575	#11719922	—	2	2	no	—
576	#11719922	—	2	2	no	—
577	#11719922	—	2	2	no	—
578	#11719922	C₂×D₄	1	2	yes	—
579	#11719922	C₂×D₄	1	1	yes	characteristic
580	#11719922	C₂×D₄	1	1	yes	characteristic
581	#11719921	—	4	2	no	—
582	#11719921	—	4	2	no	—
583	C₄×Dic₅₃	—	2	1	no	—
584	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
585	#11719917	—	2	1	no	—
586	#11719917	—	2	2	no	—
587	#11719917	—	2	1	no	—
588	#11719917	C₂⁴	1	1	yes	characteristic
589	#11719917	C₂⁴	1	2	yes	—
590	#11719917	C₂⁴	1	1	yes	characteristic
591	C₂×#88322	—	2	1	no	—
592	C₂×#88322	—	2	2	no	—
593	C₂×#88322	—	2	1	no	—
594	C₂×#88322	C₂⁴	1	1	yes	characteristic
595	C₂×#88322	C₂⁴	1	1	yes	characteristic
596	Dic₂₁₂	—	2	2	no	—
597	Dic₂₁₂	—	2	2	no	—
598	Dic₂₁₂	—	2	1	no	—
599	Dic₂₁₂	—	2	1	no	—
600	Dic₂₁₂	C₂×D₄	1	1	yes	characteristic
601	Dic₂₁₂	C₂×D₄	1	1	yes	characteristic
602	D₄₂₄	—	2	2	no	—
603	D₄₂₄	—	2	2	no	—
604	D₄₂₄	—	2	1	no	—
605	D₄₂₄	—	2	1	no	—
606	D₄₂₄	C₂×D₄	1	1	yes	characteristic
607	D₄₂₄	C₂×D₄	1	1	yes	characteristic
608	#11719913	—	2	2	no	—
609	#11719913	—	2	2	no	—
610	#11719913	—	2	2	no	—
611	#11719913	—	2	2	no	—
612	#11719913	—	2	2	no	—
613	#11719913	—	2	2	no	—
614	#11719913	C₂×D₄	1	1	yes	characteristic
615	#11719913	C₂×D₄	1	1	yes	characteristic
616	#11719913	C₂×D₄	1	2	yes	—
617	#11719912	—	2	1	no	—
618	#11719912	—	2	2	no	—
619	#11719912	—	2	1	no	—
620	#11719912	—	2	1	no	—
621	#11719912	—	2	2	no	—
622	#11719912	—	2	1	no	—
623	#11719912	—	2	1	no	—
624	#11719912	—	2	2	no	—
625	#11719912	—	2	1	no	—
626	C₈×D₅₃	—	2	1	no	—
627	C₈×D₅₃	—	2	2	no	—
628	C₈×D₅₃	—	2	1	no	—
629	C₈×D₅₃	—	2	1	no	—
630	C₈×D₅₃	—	2	2	no	—
631	C₈×D₅₃	—	2	1	no	—
632	C₈×D₅₃	—	2	1	no	—
633	C₈×D₅₃	—	2	2	no	—
634	C₈×D₅₃	—	2	1	no	—
635	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
636	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
637	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
638	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
639	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
640	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
641	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
642	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
643	C₂³×C₅₃	—	2	2	no	—
644	C₂³×C₅₃	—	4	2	no	—
645	C₂²×D₅₃	—	2	1	no	—
646	C₂²×D₅₃	—	2	2	no	—
647	C₂²×D₅₃	—	2	1	no	—
648	C₂²×D₅₃	—	2	2	no	—
649	C₂²×D₅₃	—	4	2	no	—
650	C₂²×D₅₃	—	4	2	no	—
651	C₂²×D₅₃	—	4	2	no	—
652	C₂²×D₅₃	—	4	2	no	—
653	C₂²×D₅₃	—	4	2	no	—
654	C₂²×D₅₃	—	8	4	no	—
655	C₂²×D₅₃	—	16	4	no	—
656	C₂²×D₅₃	H(5,𝔽₂)	1	1	yes	characteristic
657	Q₈×C₅₃	—	2	2	no	—
658	Q₈×C₅₃	—	2	2	no	—
659	Q₈×C₅₃	—	4	2	no	—
660	Q₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
661	Q₈×C₅₃	C₂²×D₄	1	2	yes	—
662	Q₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
663	D₄×C₅₃	—	2	1	no	—
664	D₄×C₅₃	—	2	2	no	—
665	D₄×C₅₃	—	2	1	no	—
666	D₄×C₅₃	—	2	2	no	—
667	D₄×C₅₃	—	2	2	no	—
668	D₄×C₅₃	—	4	2	no	—
669	D₄×C₅₃	—	4	2	no	—
670	D₄×C₅₃	—	4	2	no	—
671	D₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
672	D₄×C₅₃	C₂²×D₄	1	2	yes	—
673	D₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
674	C₂×C₄×C₅₃	—	2	1	no	—
675	C₂×C₄×C₅₃	—	2	2	no	—
676	C₂×C₄×C₅₃	—	2	1	no	—
677	C₂×C₄×C₅₃	—	2	2	no	—
678	C₂×C₄×C₅₃	—	2	1	no	—
679	C₂×C₄×C₅₃	—	4	2	no	—
680	C₂×C₄×C₅₃	—	4	2	no	—
681	C₂×C₄×C₅₃	—	4	2	no	—
682	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
683	C₂²⋊D₅₃	—	2	1	no	—
684	C₂²⋊D₅₃	—	2	2	no	—
685	C₂²⋊D₅₃	—	2	1	no	—
686	C₂²⋊D₅₃	—	2	1	no	—
687	C₂²⋊D₅₃	—	2	2	no	—
688	C₂²⋊D₅₃	—	2	1	no	—
689	C₂²⋊D₅₃	—	2	1	no	—
690	C₂²⋊D₅₃	—	2	2	no	—
691	C₂²⋊D₅₃	—	2	1	no	—
692	C₂²⋊D₅₃	—	4	2	no	—
693	C₂²⋊D₅₃	—	4	2	no	—
694	C₂²⋊D₅₃	—	4	2	no	—
695	C₂²⋊D₅₃	—	4	2	no	—
696	C₂²⋊D₅₃	—	4	2	no	—
697	C₂²⋊D₅₃	—	4	2	no	—
698	C₂²⋊D₅₃	—	4	2	no	—
699	C₂²⋊D₅₃	—	4	2	no	—
700	C₂×Dic₅₃	—	2	1	no	—
701	C₂×Dic₅₃	—	2	2	no	—
702	C₂×Dic₅₃	—	2	1	no	—
703	C₂×Dic₅₃	—	2	2	no	—
704	C₂×Dic₅₃	—	2	1	no	—
705	C₂×Dic₅₃	—	4	2	no	—
706	C₂×Dic₅₃	—	4	2	no	—
707	C₂×Dic₅₃	—	4	2	no	—
708	C₂×Dic₅₃	H(5,𝔽₂)	1	1	yes	characteristic
709	D₂₁₂	—	2	1	no	—
710	D₂₁₂	—	2	2	no	—
711	D₂₁₂	—	2	1	no	—
712	D₂₁₂	—	2	2	no	—
713	D₂₁₂	—	2	2	no	—
714	D₂₁₂	—	4	2	no	—
715	D₂₁₂	—	4	2	no	—
716	D₂₁₂	—	4	2	no	—
717	D₂₁₂	C₂²×D₄	1	1	yes	characteristic
718	D₂₁₂	C₂²×D₄	1	2	yes	—
719	D₂₁₂	C₂²×D₄	1	1	yes	characteristic
720	C₄×D₅₃	—	2	1	no	—
721	C₄×D₅₃	—	2	2	no	—
722	C₄×D₅₃	—	2	1	no	—
723	C₄×D₅₃	—	2	1	no	—
724	C₄×D₅₃	—	2	2	no	—
725	C₄×D₅₃	—	2	1	no	—
726	C₄×D₅₃	—	2	1	no	—
727	C₄×D₅₃	—	2	2	no	—
728	C₄×D₅₃	—	2	1	no	—
729	C₄×D₅₃	—	4	2	no	—
730	C₄×D₅₃	—	4	2	no	—
731	C₄×D₅₃	—	4	2	no	—
732	C₄×D₅₃	—	4	2	no	—
733	C₄×D₅₃	—	4	2	no	—
734	C₄×D₅₃	—	4	2	no	—
735	C₄×D₅₃	—	4	2	no	—
736	C₄×D₅₃	—	4	2	no	—
737	C₄×D₅₃	—	4	2	no	—
738	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
739	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
740	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
741	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
742	Dic₁₀₆	—	2	1	no	—
743	Dic₁₀₆	—	2	2	no	—
744	Dic₁₀₆	—	2	1	no	—
745	Dic₁₀₆	—	2	2	no	—
746	Dic₁₀₆	—	2	2	no	—
747	Dic₁₀₆	—	4	2	no	—
748	Dic₁₀₆	—	4	2	no	—
749	Dic₁₀₆	—	4	2	no	—
750	Dic₁₀₆	—	4	2	no	—
751	Dic₁₀₆	—	4	2	no	—
752	Dic₁₀₆	C₂²×D₄	1	1	yes	characteristic
753	Dic₁₀₆	C₂²×D₄	1	2	yes	—
754	Dic₁₀₆	C₂²×D₄	1	1	yes	characteristic
755	C₈×C₅₃	—	2	1	no	—
756	C₈×C₅₃	—	2	2	no	—
757	C₈×C₅₃	—	2	1	no	—
758	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
759	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
760	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
761	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
762	#88322	—	2	1	no	—
763	#88322	—	2	2	no	—
764	#88322	—	2	1	no	—
765	#88322	C₂²×D₄	1	1	yes	characteristic
766	#88322	C₂²×D₄	1	1	yes	characteristic
767	#88322	C₂²×D₄	1	1	yes	characteristic
768	#88322	C₂²×D₄	1	1	yes	characteristic
769	C₂×#3290	—	53	1	no	maximal, Sylow
770	C₂²×C₅₃	—	2	1	no	—
771	C₂²×C₅₃	—	2	2	no	—
772	C₂²×C₅₃	—	2	1	no	—
773	C₂²×C₅₃	—	4	2	no	—
774	C₂²×C₅₃	—	8	2	no	—
775	C₂²×C₅₃	—	16	2	no	—
776	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
777	C₂×D₅₃	—	2	2	no	—
778	C₂×D₅₃	—	2	1	no	—
779	C₂×D₅₃	—	2	2	no	—
780	C₂×D₅₃	—	2	1	no	—
781	C₂×D₅₃	—	4	2	no	—
782	C₂×D₅₃	—	4	4	no	—
783	C₂×D₅₃	—	4	2	no	—
784	C₂×D₅₃	—	4	2	no	—
785	C₂×D₅₃	—	8	4	no	—
786	C₂×D₅₃	—	8	2	no	—
787	C₂×D₅₃	—	16	2	no	—
788	C₂×D₅₃	—	16	2	no	—
789	C₂×D₅₃	—	16	2	no	—
790	C₂×D₅₃	—	16	2	no	—
791	C₂×D₅₃	D₄²	1	1	yes	characteristic
792	C₂×D₅₃	D₄²	1	1	yes	characteristic
793	C₄×C₅₃	—	2	1	no	—
794	C₄×C₅₃	—	2	2	no	—
795	C₄×C₅₃	—	2	1	no	—
796	C₄×C₅₃	—	4	1	no	—
797	C₄×C₅₃	—	4	2	no	—
798	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
799	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
800	Dic₅₃	—	2	1	no	—
801	Dic₅₃	—	2	2	no	—
802	Dic₅₃	—	2	1	no	—
803	Dic₅₃	—	4	1	no	—
804	Dic₅₃	—	4	2	no	—
805	Dic₅₃	D₄²	1	1	yes	characteristic
806	Dic₅₃	D₄²	1	1	yes	characteristic
807	C₂×#578	—	53	1	no	—
808	C₂×#577	—	53	2	no	—
809	C₂×#576	—	53	1	no	—
810	#3290	—	53	1	no	—
811	#3290	—	53	1	no	—
812	#3290	—	53	1	no	—
813	#3290	—	53	2	no	—
814	#3290	—	53	2	no	—
815	#3290	—	53	2	no	—
816	#3290	—	53	1	no	—
817	#3290	—	53	1	no	—
818	#3290	—	53	1	no	—
819	#3290	—	53	2	no	—
820	#3290	—	53	1	no	—
821	#3290	D₅₃	1	1	yes	characteristic, direct product factor
822	C₂×#495	—	53	1	no	—
823	C₂×#473	—	53	1	no	—
824	C₂×#472	—	53	1	no	—
825	C₂×#471	—	53	2	no	—
826	C₂×#454	—	53	2	no	—
827	C₂×#455	—	53	2	no	—
828	C₂×#443	—	53	1	no	—
829	C₂×#443	—	53	1	no	—
830	C₂×C₅₃	—	2	1	no	—
831	C₂×C₅₃	—	4	1	no	—
832	C₂×C₅₃	—	4	2	no	—
833	C₂×C₅₃	—	4	1	no	—
834	C₂×C₅₃	—	8	2	no	—
835	C₂×C₅₃	C₂×D₄²	1	1	yes	characteristic
836	D₅₃	—	2	1	no	—
837	D₅₃	—	4	1	no	—
838	D₅₃	—	4	2	no	—
839	D₅₃	—	4	1	no	—
840	D₅₃	—	8	2	no	—
841	D₅₃	#3290	1	2	yes	direct product factor
842	C₂×2₋¹⁺⁴	—	53	2	no	—
843	C₂×H(5,𝔽₂)	—	53	2	no	—
844	#578	—	53	2	no	—
845	#578	—	53	2	no	—
846	#578	—	53	1	no	—
847	#578	—	53	1	no	—
848	#578	—	53	1	no	—
849	#578	—	106	1	no	—
850	#578	—	106	1	no	—
851	#578	—	106	2	no	—
852	#578	C₂×D₅₃	1	1	yes	characteristic, complemented
853	#577	—	53	2	no	—
854	#577	—	53	2	no	—
855	#577	—	53	2	no	—
856	#577	—	53	2	no	—
857	#577	—	53	2	no	—
858	#577	—	53	2	no	—
859	#577	—	53	2	no	—
860	#577	—	106	2	no	—
861	#577	—	106	2	no	—
862	#577	—	106	2	no	—
863	#577	—	106	2	no	—
864	#577	C₂×D₅₃	1	2	yes	complemented
865	#576	—	53	2	no	—
866	#576	—	53	2	no	—
867	#576	—	53	1	no	—
868	#576	—	53	1	no	—
869	#576	—	53	1	no	—
870	#576	—	106	1	no	—
871	#576	—	106	1	no	—
872	#576	—	106	2	no	—
873	#576	C₂×D₅₃	1	1	yes	characteristic, complemented
874	C₂×#137	—	53	2	no	—
875	C₂×#137	—	53	2	no	—
876	C₂×#137	—	106	2	no	—
877	C₂×#137	—	106	2	no	—
878	C₂×AGL(1,ℤ/8)	—	53	2	no	—
879	C₂×AGL(1,ℤ/8)	—	53	2	no	—
880	C₂×AGL(1,ℤ/8)	—	106	2	no	—
881	C₂×AGL(1,ℤ/8)	—	106	2	no	—
882	C₂×#135	—	53	1	no	—
883	C₂×#135	—	53	1	no	—
884	C₂×#135	—	106	1	no	—
885	C₂×#135	—	106	2	no	—
886	C₂×#135	—	106	1	no	—
887	C₂²×Q₁₆	—	53	1	no	—
888	C₂²×Q₁₆	—	106	1	no	—
889	C₂²×SD₁₆	—	53	2	no	—
890	C₂²×SD₁₆	—	106	2	no	—
891	C₂²×D₈	—	53	1	no	—
892	C₂²×D₈	—	106	1	no	—
893	C₂×#131	—	53	1	no	—
894	C₂×#131	—	53	2	no	—
895	C₂×#131	—	53	1	no	—
896	C₂×#124	—	53	2	no	—
897	#495	—	53	1	no	—
898	#495	—	53	2	no	—
899	#495	—	53	1	no	—
900	#495	—	53	2	no	—
901	#495	—	53	1	no	—
902	#495	C₂×D₅₃	1	1	yes	characteristic, complemented
903	#473	—	53	2	no	—
904	#473	—	53	1	no	—
905	#473	—	53	1	no	—
906	#473	—	53	1	no	—
907	#473	—	53	2	no	—
908	#473	C₂×D₅₃	1	1	yes	characteristic, complemented
909	#472	—	53	2	no	—
910	#472	—	53	1	no	—
911	#472	—	53	1	no	—
912	#472	—	53	1	no	—
913	#472	—	53	2	no	—
914	#472	C₂×D₅₃	1	1	yes	characteristic, complemented
915	#471	—	53	2	no	—
916	#471	—	53	2	no	—
917	#471	—	53	2	no	—
918	#471	—	53	2	no	—
919	#471	—	53	2	no	—
920	#471	—	53	2	no	—
921	#471	—	53	2	no	—
922	#471	C₂×D₅₃	1	2	yes	complemented
923	#455	—	53	2	no	—
924	#455	—	53	2	no	—
925	#455	—	53	2	no	—
926	#455	—	53	2	no	—
927	#455	—	53	2	no	—
928	#455	—	53	2	no	—
929	#455	—	53	2	no	—
930	#455	C₂×D₅₃	1	2	yes	complemented
931	#454	—	53	2	no	—
932	#454	—	53	2	no	—
933	#454	—	53	2	no	—
934	#454	—	53	2	no	—
935	#454	—	53	2	no	—
936	#454	—	53	2	no	—
937	#454	—	53	2	no	—
938	#454	C₂×D₅₃	1	2	yes	complemented
939	#443	—	53	1	no	—
940	#443	—	53	1	no	—
941	#443	—	53	1	no	—
942	#443	—	53	1	no	—
943	#443	—	53	2	no	—
944	#443	—	53	1	no	—
945	#443	—	53	1	no	—
946	#443	—	53	1	no	—
947	#443	—	53	1	no	—
948	#443	—	53	2	no	—
949	#443	—	53	1	no	—
950	#443	—	53	1	no	—
951	#443	C₂×D₅₃	1	1	yes	characteristic, complemented
952	#443	C₂×D₅₃	1	1	yes	characteristic, complemented
953	C₂×#108	—	53	1	no	—
954	C₂×#108	—	53	1	no	—
955	C₂×#104	—	53	1	no	—
956	C₂×#104	—	53	2	no	—
957	C₂×#104	—	53	1	no	—
958	C₂×#101	—	53	2	no	—
959	C₂×#100	—	53	2	no	—
960	C₂×C₄×C₈	—	53	1	no	—
961	C₅₃	C₂×#3290	1	1	yes	characteristic, complemented, Sylow
962	2₋¹⁺⁴	—	53	2	no	—
963	2₋¹⁺⁴	—	53	2	no	—
964	2₋¹⁺⁴	—	53	2	no	—
965	2₋¹⁺⁴	—	106	2	no	—
966	2₋¹⁺⁴	—	106	2	no	—
967	2₋¹⁺⁴	—	106	2	no	—
968	2₋¹⁺⁴	—	106	2	no	—
969	2₋¹⁺⁴	—	212	2	no	—
970	2₋¹⁺⁴	C₂²×D₅₃	1	2	yes	complemented
971	H(5,𝔽₂)	—	53	2	no	—
972	H(5,𝔽₂)	—	53	2	no	—
973	H(5,𝔽₂)	—	53	2	no	—
974	H(5,𝔽₂)	—	106	2	no	—
975	H(5,𝔽₂)	—	106	2	no	—
976	H(5,𝔽₂)	—	106	2	no	—
977	H(5,𝔽₂)	—	106	2	no	—
978	H(5,𝔽₂)	—	212	2	no	—
979	H(5,𝔽₂)	C₂²×D₅₃	1	2	yes	—
980	C₂×#41	—	53	1	no	—
981	C₂×#41	—	53	2	no	—
982	C₂×#41	—	53	1	no	—
983	C₂×#41	—	106	2	no	—
984	C₂×#41	—	106	2	no	—
985	C₂×#41	—	106	2	no	—
986	C₂×#41	—	106	2	no	—
987	C₂×#41	—	212	2	no	—
988	C₂²×Q₈	—	53	2	no	—
989	C₂²×Q₈	—	106	2	no	—
990	C₂²×Q₈	—	106	2	no	—
991	C₂²×D₄	—	53	2	no	—
992	C₂²×D₄	—	106	2	no	—
993	C₂²×D₄	—	106	2	no	—
994	C₂²×D₄	—	212	2	no	—
995	#137	—	2	2	no	—
996	#137	—	2	2	no	—
997	#137	—	53	2	no	—
998	#137	—	53	2	no	—
999	#137	—	53	2	no	—
1000	#137	—	53	2	no	—
1001	#137	—	53	2	no	—
1002	#137	—	53	2	no	—
1003	#137	—	106	2	no	—
1004	#137	—	106	2	no	—
1005	#137	—	106	2	no	—
1006	#137	—	106	2	no	—
1007	#137	—	106	2	no	—
1008	#137	—	106	2	no	—
1009	#137	—	106	2	no	—
1010	#137	—	106	2	no	—
1011	#137	—	106	2	no	—
1012	#137	—	106	2	no	—
1013	#137	—	106	2	no	—
1014	#137	—	106	2	no	—
1015	#137	—	106	2	no	—
1016	#137	—	106	2	no	—
1017	#137	—	106	2	no	—
1018	#137	—	106	2	no	—
1019	#137	—	106	2	no	—
1020	#137	—	106	2	no	—
1021	#137	C₂²×D₅₃	1	2	yes	—
1022	#137	C₂²×D₅₃	1	2	yes	complemented
1023	AGL(1,ℤ/8)	—	2	2	no	—
1024	AGL(1,ℤ/8)	—	2	2	no	—
1025	AGL(1,ℤ/8)	—	53	2	no	—
1026	AGL(1,ℤ/8)	—	53	2	no	—
1027	AGL(1,ℤ/8)	—	53	2	no	—
1028	AGL(1,ℤ/8)	—	53	2	no	—
1029	AGL(1,ℤ/8)	—	53	2	no	—
1030	AGL(1,ℤ/8)	—	53	2	no	—
1031	AGL(1,ℤ/8)	—	106	2	no	—
1032	AGL(1,ℤ/8)	—	106	2	no	—
1033	AGL(1,ℤ/8)	—	106	2	no	—
1034	AGL(1,ℤ/8)	—	106	2	no	—
1035	AGL(1,ℤ/8)	—	106	2	no	—
1036	AGL(1,ℤ/8)	—	106	2	no	—
1037	AGL(1,ℤ/8)	—	106	2	no	—
1038	AGL(1,ℤ/8)	—	106	2	no	—
1039	AGL(1,ℤ/8)	—	106	2	no	—
1040	AGL(1,ℤ/8)	—	106	2	no	—
1041	AGL(1,ℤ/8)	—	106	2	no	—
1042	AGL(1,ℤ/8)	—	106	2	no	—
1043	AGL(1,ℤ/8)	—	106	2	no	—
1044	AGL(1,ℤ/8)	—	106	2	no	—
1045	AGL(1,ℤ/8)	—	106	2	no	—
1046	AGL(1,ℤ/8)	—	106	2	no	—
1047	AGL(1,ℤ/8)	—	106	2	no	—
1048	AGL(1,ℤ/8)	—	106	2	no	—
1049	AGL(1,ℤ/8)	C₂²×D₅₃	1	2	yes	—
1050	AGL(1,ℤ/8)	C₂²×D₅₃	1	2	yes	complemented
1051	#135	—	2	1	no	—
1052	#135	—	2	2	no	—
1053	#135	—	2	1	no	—
1054	#135	—	53	2	no	—
1055	#135	—	53	1	no	—
1056	#135	—	53	1	no	—
1057	#135	—	53	1	no	—
1058	#135	—	53	1	no	—
1059	#135	—	53	2	no	—
1060	#135	—	53	1	no	—
1061	#135	—	53	1	no	—
1062	#135	—	53	1	no	—
1063	#135	—	53	1	no	—
1064	#135	—	53	1	no	—
1065	#135	—	53	1	no	—
1066	#135	—	106	1	no	—
1067	#135	—	106	2	no	—
1068	#135	—	106	1	no	—
1069	#135	—	106	2	no	—
1070	#135	—	106	1	no	—
1071	#135	—	106	2	no	—
1072	#135	—	106	1	no	—
1073	#135	—	106	2	no	—
1074	#135	—	106	2	no	—
1075	#135	—	106	2	no	—
1076	#135	—	106	2	no	—
1077	#135	—	106	2	no	—
1078	#135	—	106	2	no	—
1079	#135	—	106	2	no	—
1080	#135	—	106	1	no	—
1081	#135	—	106	2	no	—
1082	#135	—	106	1	no	—
1083	#135	C₂²×D₅₃	1	1	yes	characteristic
1084	#135	C₂²×D₅₃	1	1	yes	characteristic
1085	C₂×Q₁₆	—	2	1	no	—
1086	C₂×Q₁₆	—	53	1	no	—
1087	C₂×Q₁₆	—	53	1	no	—
1088	C₂×Q₁₆	—	53	2	no	—
1089	C₂×Q₁₆	—	53	1	no	—
1090	C₂×Q₁₆	—	106	1	no	—
1091	C₂×Q₁₆	—	106	1	no	—
1092	C₂×Q₁₆	—	106	1	no	—
1093	C₂×Q₁₆	—	106	1	no	—
1094	C₂×Q₁₆	—	106	1	no	—
1095	C₂×Q₁₆	—	106	2	no	—
1096	C₂×Q₁₆	—	106	1	no	—
1097	C₂×Q₁₆	—	106	2	no	—
1098	C₂×Q₁₆	—	106	2	no	—
1099	C₂×Q₁₆	—	106	2	no	—
1100	C₂×Q₁₆	—	106	1	no	—
1101	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1102	C₂×SD₁₆	—	2	2	no	—
1103	C₂×SD₁₆	—	53	1	no	—
1104	C₂×SD₁₆	—	53	1	no	—
1105	C₂×SD₁₆	—	53	2	no	—
1106	C₂×SD₁₆	—	53	2	no	—
1107	C₂×SD₁₆	—	53	2	no	—
1108	C₂×SD₁₆	—	53	2	no	—
1109	C₂×SD₁₆	—	106	2	no	—
1110	C₂×SD₁₆	—	106	2	no	—
1111	C₂×SD₁₆	—	106	2	no	—
1112	C₂×SD₁₆	—	106	2	no	—
1113	C₂×SD₁₆	—	106	2	no	—
1114	C₂×SD₁₆	—	106	2	no	—
1115	C₂×SD₁₆	—	106	2	no	—
1116	C₂×SD₁₆	—	106	2	no	—
1117	C₂×SD₁₆	—	106	2	no	—
1118	C₂×SD₁₆	—	106	2	no	—
1119	C₂×SD₁₆	—	106	2	no	—
1120	C₂×SD₁₆	—	106	2	no	—
1121	C₂×SD₁₆	—	106	2	no	—
1122	C₂×SD₁₆	—	106	2	no	—
1123	C₂×SD₁₆	—	106	2	no	—
1124	C₂×SD₁₆	C₂²×D₅₃	1	2	yes	complemented
1125	C₂×D₈	—	2	1	no	—
1126	C₂×D₈	—	53	1	no	—
1127	C₂×D₈	—	53	1	no	—
1128	C₂×D₈	—	53	2	no	—
1129	C₂×D₈	—	53	1	no	—
1130	C₂×D₈	—	106	1	no	—
1131	C₂×D₈	—	106	1	no	—
1132	C₂×D₈	—	106	1	no	—
1133	C₂×D₈	—	106	1	no	—
1134	C₂×D₈	—	106	1	no	—
1135	C₂×D₈	—	106	2	no	—
1136	C₂×D₈	—	106	1	no	—
1137	C₂×D₈	—	106	2	no	—
1138	C₂×D₈	—	106	2	no	—
1139	C₂×D₈	—	106	2	no	—
1140	C₂×D₈	—	106	1	no	—
1141	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1142	#131	—	53	1	no	—
1143	#131	—	53	2	no	—
1144	#131	—	53	1	no	—
1145	#131	—	53	1	no	—
1146	#131	—	53	2	no	—
1147	#131	—	53	1	no	—
1148	#131	—	53	1	no	—
1149	#131	—	53	2	no	—
1150	#131	—	53	1	no	—
1151	#131	—	106	1	no	—
1152	#131	—	106	2	no	—
1153	#131	—	106	1	no	—
1154	#131	—	106	1	no	—
1155	#131	—	106	2	no	—
1156	#131	—	106	1	no	—
1157	#131	C₂²×D₅₃	1	1	yes	characteristic
1158	#131	C₂²×D₅₃	1	2	yes	complemented
1159	#131	C₂²×D₅₃	1	1	yes	characteristic, complemented
1160	C₂×M₁₆	—	53	1	no	—
1161	C₂×M₁₆	—	53	2	no	—
1162	C₂×M₁₆	—	53	1	no	—
1163	C₂×M₁₆	—	106	1	no	—
1164	C₂×M₁₆	—	106	2	no	—
1165	C₂×M₁₆	—	106	1	no	—
1166	C₂²×C₈	—	53	1	no	—
1167	C₂²×C₈	—	53	1	no	—
1168	C₂²×C₈	—	106	1	no	—
1169	C₂²×C₈	—	106	2	no	—
1170	C₂²×C₈	—	106	1	no	—
1171	#124	—	53	2	no	—
1172	#124	—	53	2	no	—
1173	#124	—	53	2	no	—
1174	#124	—	212	2	no	—
1175	#124	C₂²×D₅₃	1	2	yes	complemented
1176	C₂×C₂²⋊C₄	—	212	2	no	—
1177	C₂×C₄²	—	53	1	no	—
1178	#108	—	53	1	no	—
1179	#108	—	53	1	no	—
1180	#108	—	53	2	no	—
1181	#108	—	53	1	no	—
1182	#108	—	53	1	no	—
1183	#108	C₂²×D₅₃	1	1	yes	characteristic, complemented
1184	#108	C₂²×D₅₃	1	1	yes	characteristic, complemented
1185	#104	—	53	1	no	—
1186	#104	—	53	1	no	—
1187	#104	—	53	2	no	—
1188	#104	—	53	1	no	—
1189	#104	—	53	1	no	—
1190	#104	—	53	2	no	—
1191	#104	—	53	1	no	—
1192	#104	—	53	1	no	—
1193	#104	—	53	2	no	—
1194	#104	C₂²×D₅₃	1	1	yes	characteristic
1195	#104	C₂²×D₅₃	1	1	yes	characteristic, complemented
1196	#104	C₂²×D₅₃	1	2	yes	complemented
1197	#101	—	53	2	no	—
1198	#101	—	53	2	no	—
1199	#101	—	53	2	no	—
1200	#101	C₂²×D₅₃	1	2	yes	complemented
1201	#100	—	53	2	no	—
1202	#100	—	53	2	no	—
1203	#100	—	53	2	no	—
1204	#100	C₂²×D₅₃	1	2	yes	complemented
1205	C₄×C₈	—	53	1	no	—
1206	C₄×C₈	—	53	1	no	—
1207	C₄×C₈	—	53	1	no	—
1208	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1209	C₂⁴	—	106	2	no	—
1210	C₂⁴	—	212	2	no	—
1211	#41	—	2	2	no	—
1212	#41	—	2	2	no	—
1213	#41	—	2	2	no	—
1214	#41	—	2	2	no	—
1215	#41	—	4	2	no	—
1216	#41	—	53	1	no	—
1217	#41	—	53	2	no	—
1218	#41	—	53	1	no	—
1219	#41	—	53	1	no	—
1220	#41	—	53	2	no	—
1221	#41	—	53	1	no	—
1222	#41	—	53	1	no	—
1223	#41	—	53	2	no	—
1224	#41	—	53	1	no	—
1225	#41	—	106	1	no	—
1226	#41	—	106	2	no	—
1227	#41	—	106	1	no	—
1228	#41	—	106	2	no	—
1229	#41	—	106	2	no	—
1230	#41	—	106	2	no	—
1231	#41	—	106	2	no	—
1232	#41	—	106	1	no	—
1233	#41	—	106	2	no	—
1234	#41	—	106	1	no	—
1235	#41	—	106	2	no	—
1236	#41	—	106	2	no	—
1237	#41	—	106	2	no	—
1238	#41	—	106	2	no	—
1239	#41	—	106	2	no	—
1240	#41	—	106	2	no	—
1241	#41	—	106	2	no	—
1242	#41	—	106	2	no	—
1243	#41	—	212	2	no	—
1244	#41	—	212	2	no	—
1245	#41	—	212	2	no	—
1246	#41	—	212	2	no	—
1247	#41	—	212	2	no	—
1248	#41	—	212	2	no	—
1249	#41	—	212	2	no	—
1250	#41	—	212	2	no	—
1251	#41	—	212	2	no	—
1252	#41	—	212	2	no	—
1253	#41	—	212	2	no	—
1254	#41	—	212	2	no	—
1255	#41	—	212	2	no	—
1256	#41	—	212	2	no	—
1257	#41	—	212	2	no	—
1258	#41	C₂³×D₅₃	1	1	yes	characteristic
1259	#41	C₂³×D₅₃	1	1	yes	characteristic
1260	#41	C₂³×D₅₃	1	2	yes	—
1261	C₂×Q₈	—	2	2	no	—
1262	C₂×Q₈	—	2	2	no	—
1263	C₂×Q₈	—	53	1	no	—
1264	C₂×Q₈	—	53	2	no	—
1265	C₂×Q₈	—	53	1	no	—
1266	C₂×Q₈	—	53	2	no	—
1267	C₂×Q₈	—	106	2	no	—
1268	C₂×Q₈	—	106	2	no	—
1269	C₂×Q₈	—	106	2	no	—
1270	C₂×Q₈	—	106	2	no	—
1271	C₂×Q₈	—	106	2	no	—
1272	C₂×Q₈	—	106	2	no	—
1273	C₂×Q₈	—	106	2	no	—
1274	C₂×Q₈	—	106	2	no	—
1275	C₂×Q₈	—	106	2	no	—
1276	C₂×Q₈	—	106	2	no	—
1277	C₂×Q₈	—	106	2	no	—
1278	C₂×Q₈	—	212	2	no	—
1279	C₂×Q₈	—	212	2	no	—
1280	C₂×Q₈	—	212	2	no	—
1281	C₂×Q₈	—	212	2	no	—
1282	C₂×Q₈	—	212	2	no	—
1283	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1284	C₂×D₄	—	2	2	no	—
1285	C₂×D₄	—	2	2	no	—
1286	C₂×D₄	—	4	2	no	—
1287	C₂×D₄	—	53	1	no	—
1288	C₂×D₄	—	53	2	no	—
1289	C₂×D₄	—	53	1	no	—
1290	C₂×D₄	—	53	2	no	—
1291	C₂×D₄	—	106	2	no	—
1292	C₂×D₄	—	106	2	no	—
1293	C₂×D₄	—	106	2	no	—
1294	C₂×D₄	—	106	2	no	—
1295	C₂×D₄	—	106	2	no	—
1296	C₂×D₄	—	106	2	no	—
1297	C₂×D₄	—	106	2	no	—
1298	C₂×D₄	—	106	2	no	—
1299	C₂×D₄	—	106	2	no	—
1300	C₂×D₄	—	106	1	no	—
1301	C₂×D₄	—	106	2	no	—
1302	C₂×D₄	—	106	1	no	—
1303	C₂×D₄	—	106	2	no	—
1304	C₂×D₄	—	106	2	no	—
1305	C₂×D₄	—	212	2	no	—
1306	C₂×D₄	—	212	2	no	—
1307	C₂×D₄	—	212	2	no	—
1308	C₂×D₄	—	212	2	no	—
1309	C₂×D₄	—	212	2	no	—
1310	C₂×D₄	—	212	2	no	—
1311	C₂×D₄	—	212	2	no	—
1312	C₂×D₄	—	212	2	no	—
1313	C₂×D₄	—	212	2	no	—
1314	C₂×D₄	—	212	2	no	—
1315	C₂×D₄	—	212	2	no	—
1316	C₂×D₄	—	212	2	no	—
1317	C₂×D₄	—	212	2	no	—
1318	C₂×D₄	—	212	2	no	—
1319	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1320	C₂²×C₄	—	53	1	no	—
1321	C₂²×C₄	—	106	1	no	—
1322	C₂²×C₄	—	106	2	no	—
1323	C₂²×C₄	—	106	1	no	—
1324	C₂²×C₄	—	106	1	no	—
1325	C₂²×C₄	—	106	2	no	—
1326	C₂²×C₄	—	212	2	no	—
1327	C₂²×C₄	—	212	2	no	—
1328	C₂²×C₄	—	212	2	no	—
1329	Q₁₆	—	2	2	no	—
1330	Q₁₆	—	2	2	no	—
1331	Q₁₆	—	2	1	no	—
1332	Q₁₆	—	2	1	no	—
1333	Q₁₆	—	53	2	no	—
1334	Q₁₆	—	53	1	no	—
1335	Q₁₆	—	53	1	no	—
1336	Q₁₆	—	53	1	no	—
1337	Q₁₆	—	53	1	no	—
1338	Q₁₆	—	106	2	no	—
1339	Q₁₆	—	106	2	no	—
1340	Q₁₆	—	106	2	no	—
1341	Q₁₆	—	106	2	no	—
1342	Q₁₆	—	106	2	no	—
1343	Q₁₆	—	106	2	no	—
1344	Q₁₆	—	106	2	no	—
1345	Q₁₆	—	106	2	no	—
1346	Q₁₆	—	106	1	no	—
1347	Q₁₆	—	106	1	no	—
1348	Q₁₆	D₄×D₅₃	1	1	yes	characteristic
1349	Q₁₆	D₄×D₅₃	1	1	yes	characteristic
1350	SD₁₆	—	2	2	no	—
1351	SD₁₆	—	2	2	no	—
1352	SD₁₆	—	2	2	no	—
1353	SD₁₆	—	2	2	no	—
1354	SD₁₆	—	2	2	no	—
1355	SD₁₆	—	2	2	no	—
1356	SD₁₆	—	53	1	no	—
1357	SD₁₆	—	53	1	no	—
1358	SD₁₆	—	53	2	no	—
1359	SD₁₆	—	53	1	no	—
1360	SD₁₆	—	53	1	no	—
1361	SD₁₆	—	53	2	no	—
1362	SD₁₆	—	53	1	no	—
1363	SD₁₆	—	53	1	no	—
1364	SD₁₆	—	53	2	no	—
1365	SD₁₆	—	106	2	no	—
1366	SD₁₆	—	106	2	no	—
1367	SD₁₆	—	106	2	no	—
1368	SD₁₆	—	106	2	no	—
1369	SD₁₆	—	106	2	no	—
1370	SD₁₆	—	106	2	no	—
1371	SD₁₆	—	106	2	no	—
1372	SD₁₆	—	106	2	no	—
1373	SD₁₆	—	106	2	no	—
1374	SD₁₆	—	106	2	no	—
1375	SD₁₆	—	106	2	no	—
1376	SD₁₆	—	106	2	no	—
1377	SD₁₆	—	106	2	no	—
1378	SD₁₆	—	106	2	no	—
1379	SD₁₆	—	106	2	no	—
1380	SD₁₆	—	106	2	no	—
1381	SD₁₆	—	106	2	no	—
1382	SD₁₆	—	106	2	no	—
1383	SD₁₆	D₄×D₅₃	1	1	yes	characteristic
1384	SD₁₆	D₄×D₅₃	1	1	yes	characteristic
1385	SD₁₆	D₄×D₅₃	1	2	yes	—
1386	D₈	—	2	2	no	—
1387	D₈	—	2	2	no	—
1388	D₈	—	2	1	no	—
1389	D₈	—	2	1	no	—
1390	D₈	—	53	2	no	—
1391	D₈	—	53	1	no	—
1392	D₈	—	53	1	no	—
1393	D₈	—	53	1	no	—
1394	D₈	—	53	1	no	—
1395	D₈	—	106	2	no	—
1396	D₈	—	106	2	no	—
1397	D₈	—	106	2	no	—
1398	D₈	—	106	2	no	—
1399	D₈	—	106	2	no	—
1400	D₈	—	106	2	no	—
1401	D₈	—	106	2	no	—
1402	D₈	—	106	2	no	—
1403	D₈	—	106	1	no	—
1404	D₈	—	106	1	no	—
1405	D₈	D₄×D₅₃	1	1	yes	characteristic
1406	D₈	D₄×D₅₃	1	1	yes	characteristic
1407	M₁₆	—	2	1	no	—
1408	M₁₆	—	2	2	no	—
1409	M₁₆	—	2	1	no	—
1410	M₁₆	—	53	1	no	—
1411	M₁₆	—	53	2	no	—
1412	M₁₆	—	53	1	no	—
1413	M₁₆	—	106	1	no	—
1414	M₁₆	—	106	2	no	—
1415	M₁₆	—	106	1	no	—
1416	M₁₆	—	106	1	no	—
1417	M₁₆	—	106	2	no	—
1418	M₁₆	—	106	1	no	—
1419	M₁₆	—	106	1	no	—
1420	M₁₆	—	106	2	no	—
1421	M₁₆	—	106	1	no	—
1422	M₁₆	—	106	1	no	—
1423	M₁₆	—	106	2	no	—
1424	M₁₆	—	106	1	no	—
1425	M₁₆	C₂³×D₅₃	1	1	yes	characteristic
1426	M₁₆	C₂³×D₅₃	1	2	yes	—
1427	M₁₆	C₂³×D₅₃	1	1	yes	characteristic
1428	C₂×C₈	—	2	1	no	—
1429	C₂×C₈	—	2	2	no	—
1430	C₂×C₈	—	2	1	no	—
1431	C₂×C₈	—	53	1	no	—
1432	C₂×C₈	—	53	1	no	—
1433	C₂×C₈	—	53	1	no	—
1434	C₂×C₈	—	53	1	no	—
1435	C₂×C₈	—	53	1	no	—
1436	C₂×C₈	—	53	1	no	—
1437	C₂×C₈	—	53	1	no	—
1438	C₂×C₈	—	53	1	no	—
1439	C₂×C₈	—	53	1	no	—
1440	C₂×C₈	—	53	1	no	—
1441	C₂×C₈	—	106	1	no	—
1442	C₂×C₈	—	106	2	no	—
1443	C₂×C₈	—	106	1	no	—
1444	C₂×C₈	—	106	1	no	—
1445	C₂×C₈	—	106	2	no	—
1446	C₂×C₈	—	106	1	no	—
1447	C₂×C₈	—	106	1	no	—
1448	C₂×C₈	—	106	2	no	—
1449	C₂×C₈	—	106	1	no	—
1450	C₂×C₈	—	106	1	no	—
1451	C₂×C₈	—	106	2	no	—
1452	C₂×C₈	—	106	1	no	—
1453	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1454	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1455	C₂²⋊C₄	—	4	2	no	—
1456	C₂²⋊C₄	—	212	2	no	—
1457	C₂²⋊C₄	—	212	2	no	—
1458	C₂²⋊C₄	—	212	2	no	—
1459	C₄²	—	53	1	no	—
1460	C₄²	—	106	1	no	—
1461	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1462	C₂³	—	2	2	no	—
1463	C₂³	—	4	2	no	—
1464	C₂³	—	53	1	no	—
1465	C₂³	—	848	4	no	—
1466	C₂³	—	106	1	no	—
1467	C₂³	—	106	2	no	—
1468	C₂³	—	106	1	no	—
1469	C₂³	—	106	2	no	—
1470	C₂³	—	424	4	no	—
1471	C₂³	—	212	2	no	—
1472	C₂³	—	212	2	no	—
1473	C₂³	—	212	2	no	—
1474	C₂³	—	212	2	no	—
1475	C₂³	—	212	2	no	—
1476	Q₈	—	2	2	no	—
1477	Q₈	—	2	2	no	—
1478	Q₈	—	4	2	no	—
1479	Q₈	—	53	1	no	—
1480	Q₈	—	53	2	no	—
1481	Q₈	—	53	1	no	—
1482	Q₈	—	106	1	no	—
1483	Q₈	—	106	2	no	—
1484	Q₈	—	106	1	no	—
1485	Q₈	—	106	2	no	—
1486	Q₈	—	106	2	no	—
1487	Q₈	—	212	2	no	—
1488	Q₈	—	212	2	no	—
1489	Q₈	—	212	2	no	—
1490	Q₈	—	212	2	no	—
1491	Q₈	—	212	2	no	—
1492	Q₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1493	Q₈	C₂×D₄×D₅₃	1	2	yes	—
1494	Q₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1495	D₄	—	2	1	no	—
1496	D₄	—	2	2	no	—
1497	D₄	—	2	1	no	—
1498	D₄	—	2	2	no	—
1499	D₄	—	2	2	no	—
1500	D₄	—	4	2	no	—
1501	D₄	—	4	2	no	—
1502	D₄	—	4	2	no	—
1503	D₄	—	53	1	no	—
1504	D₄	—	53	2	no	—
1505	D₄	—	53	1	no	—
1506	D₄	—	106	1	no	—
1507	D₄	—	106	2	no	—
1508	D₄	—	106	1	no	—
1509	D₄	—	106	1	no	—
1510	D₄	—	106	2	no	—
1511	D₄	—	106	1	no	—
1512	D₄	—	106	1	no	—
1513	D₄	—	106	2	no	—
1514	D₄	—	106	1	no	—
1515	D₄	—	106	1	no	—
1516	D₄	—	106	2	no	—
1517	D₄	—	106	1	no	—
1518	D₄	—	106	2	no	—
1519	D₄	—	106	2	no	—
1520	D₄	—	212	2	no	—
1521	D₄	—	212	2	no	—
1522	D₄	—	212	2	no	—
1523	D₄	—	212	2	no	—
1524	D₄	—	212	2	no	—
1525	D₄	—	212	2	no	—
1526	D₄	—	212	2	no	—
1527	D₄	—	212	2	no	—
1528	D₄	—	212	2	no	—
1529	D₄	—	212	2	no	—
1530	D₄	—	212	2	no	—
1531	D₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1532	D₄	C₂×D₄×D₅₃	1	2	yes	—
1533	D₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1534	C₂×C₄	—	2	1	no	—
1535	C₂×C₄	—	2	2	no	—
1536	C₂×C₄	—	2	1	no	—
1537	C₂×C₄	—	2	1	no	—
1538	C₂×C₄	—	2	2	no	—
1539	C₂×C₄	—	4	2	no	—
1540	C₂×C₄	—	4	2	no	—
1541	C₂×C₄	—	4	2	no	—
1542	C₂×C₄	—	53	1	no	—
1543	C₂×C₄	—	53	1	no	—
1544	C₂×C₄	—	53	1	no	—
1545	C₂×C₄	—	53	1	no	—
1546	C₂×C₄	—	53	1	no	—
1547	C₂×C₄	—	106	1	no	—
1548	C₂×C₄	—	106	2	no	—
1549	C₂×C₄	—	106	1	no	—
1550	C₂×C₄	—	106	1	no	—
1551	C₂×C₄	—	106	2	no	—
1552	C₂×C₄	—	106	1	no	—
1553	C₂×C₄	—	106	1	no	—
1554	C₂×C₄	—	106	2	no	—
1555	C₂×C₄	—	106	1	no	—
1556	C₂×C₄	—	106	1	no	—
1557	C₂×C₄	—	106	2	no	—
1558	C₂×C₄	—	106	1	no	—
1559	C₂×C₄	—	106	1	no	—
1560	C₂×C₄	—	106	2	no	—
1561	C₂×C₄	—	212	2	no	—
1562	C₂×C₄	—	212	2	no	—
1563	C₂×C₄	—	212	2	no	—
1564	C₂×C₄	—	212	2	no	—
1565	C₂×C₄	—	212	2	no	—
1566	C₂×C₄	—	212	2	no	—
1567	C₂×C₄	—	212	2	no	—
1568	C₂×C₄	—	212	2	no	—
1569	C₂×C₄	—	212	2	no	—
1570	C₂×C₄	—	212	2	no	—
1571	C₂×C₄	—	212	2	no	—
1572	C₂×C₄	—	212	2	no	—
1573	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1574	C₈	—	2	1	no	—
1575	C₈	—	2	2	no	—
1576	C₈	—	2	1	no	—
1577	C₈	—	53	1	no	—
1578	C₈	—	53	1	no	—
1579	C₈	—	53	1	no	—
1580	C₈	—	53	1	no	—
1581	C₈	—	106	1	no	—
1582	C₈	—	106	2	no	—
1583	C₈	—	106	1	no	—
1584	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1585	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1586	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1587	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1588	C₂²	—	2	1	no	—
1589	C₂²	—	2	2	no	—
1590	C₂²	—	2	1	no	—
1591	C₂²	—	4	2	no	—
1592	C₂²	—	8	2	no	—
1593	C₂²	—	16	2	no	—
1594	C₂²	—	53	1	no	—
1595	C₂²	—	53	1	no	—
1596	C₂²	—	848	2	no	—
1597	C₂²	—	848	2	no	—
1598	C₂²	—	848	2	no	—
1599	C₂²	—	848	2	no	—
1600	C₂²	—	106	2	no	—
1601	C₂²	—	106	1	no	—
1602	C₂²	—	106	2	no	—
1603	C₂²	—	106	1	no	—
1604	C₂²	—	424	2	no	—
1605	C₂²	—	424	4	no	—
1606	C₂²	—	212	2	no	—
1607	C₂²	—	212	4	no	—
1608	C₂²	—	212	2	no	—
1609	C₂²	—	212	2	no	—
1610	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1611	C₄	—	2	1	no	—
1612	C₄	—	2	2	no	—
1613	C₄	—	2	1	no	—
1614	C₄	—	4	1	no	—
1615	C₄	—	4	2	no	—
1616	C₄	—	53	1	no	—
1617	C₄	—	53	1	no	—
1618	C₄	—	106	1	no	—
1619	C₄	—	106	2	no	—
1620	C₄	—	106	1	no	—
1621	C₄	—	212	1	no	—
1622	C₄	—	212	2	no	—
1623	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
1624	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
1625	C₂	—	2	1	no	—
1626	C₂	—	4	1	no	—
1627	C₂	—	4	2	no	—
1628	C₂	—	4	1	no	—
1629	C₂	—	8	2	no	—
1630	C₂	—	53	2	no	—
1631	C₂	—	106	1	no	—
1632	C₂	—	424	2	no	—
1633	C₂	—	212	1	no	—
1634	C₂	—	212	2	no	—
1635	C₂	—	212	1	no	—
1636	C₂	D₄²×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄²×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3290	C₂
socle	C₂×C₅₃	C₂×D₄²
hypercenter	#3290	D₅₃
hypocenter	C₅₃	C₂×#3290
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #3290

Complements

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

N	H ≅ G/N	type
1. #578×D₅₃	C₂	semidirect
2. #577×D₅₃	C₂	semidirect
3. #576×D₅₃	C₂	semidirect
4. #20286504	C₂	semidirect
5. #20286503	C₂	semidirect
6. #20286502	C₂	semidirect
7. #20286501	C₂	semidirect
8. #20286500	C₂	semidirect
9. #20286499	C₂	semidirect
10. #20286498	C₂	semidirect
11. #20286497	C₂	semidirect
12. #20286496	C₂	semidirect
13. #20286495	C₂	semidirect
14. #20286494	C₂	semidirect
15. #495×D₅₃	C₂	semidirect
16. #473×D₅₃	C₂	semidirect
17. #472×D₅₃	C₂	semidirect
18. #471×D₅₃	C₂	semidirect
19. #454×D₅₃	C₂	semidirect
20. #455×D₅₃	C₂	semidirect
21. #443×D₅₃	C₂	semidirect
22. #443×D₅₃	C₂	semidirect
23. C₅₃×#3290	C₂	semidirect
24. 2₋¹⁺⁴×D₅₃	C₂²	semidirect
26. #16811440	C₂²	semidirect
28. #16811439	C₂²	semidirect
29. #16811438	C₂²	semidirect
31. #16811437	C₂²	semidirect
33. #16811436	C₂²	semidirect
34. #16811435	C₂²	semidirect
35. #16811434	C₂²	semidirect
37. #16811433	C₂²	semidirect
39. #16811432	C₂²	semidirect
40. #16811431	C₂²	semidirect
42. #16811430	C₂²	semidirect
44. #16811429	C₂²	semidirect
45. #16811428	C₂²	semidirect
47. #16811427	C₂²	semidirect
48. #16811426	C₂²	semidirect
50. #16811425	C₂²	semidirect
52. #16811424	C₂²	semidirect
56. #137×D₅₃	C₂²	semidirect
60. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
67. C₂×Q₁₆×D₅₃	C₂²	semidirect
69. C₂×SD₁₆×D₅₃	C₂²	semidirect
73. #131×D₅₃	C₂²	semidirect
74. #131×D₅₃	C₂²	semidirect
75. #124×D₅₃	C₂²	semidirect
76. #16811008	C₂²	semidirect
77. #16811007	C₂²	semidirect
78. #16811006	C₂²	semidirect
79. #16811005	C₂²	semidirect
80. #16811004	C₂²	semidirect
81. #16810899	C₂²	semidirect
82. #16810898	C₂²	semidirect
83. #16810897	C₂²	semidirect
84. #16810896	C₂²	semidirect
85. #16810895	C₂²	semidirect
86. #16810894	C₂²	semidirect
87. #16810893	C₂²	semidirect
88. #16810892	C₂²	semidirect
89. #16810891	C₂²	semidirect
90. #16810890	C₂²	semidirect
91. #16810889	C₂²	semidirect
92. #16810888	C₂²	semidirect
93. #16810887	C₂²	semidirect
94. #16810886	C₂²	semidirect
95. #16810885	C₂²	semidirect
96. #16810884	C₂²	semidirect
97. #16810883	C₂²	semidirect
98. #16810803	C₂²	semidirect
99. #16810802	C₂²	semidirect
100. #16810802	C₂²	semidirect
101. #16810801	C₂²	semidirect
102. #16810800	C₂²	semidirect
103. #16810799	C₂²	semidirect
104. #16810799	C₂²	semidirect
105. #16810798	C₂²	semidirect
106. #16810797	C₂²	semidirect
107. #16810797	C₂²	semidirect
108. #16810796	C₂²	semidirect
109. #16810795	C₂²	semidirect
110. #16810794	C₂²	semidirect
111. #16810794	C₂²	semidirect
112. #16810741	C₂²	semidirect
113. #16810741	C₂²	semidirect
114. #16810740	C₂²	semidirect
115. #16810740	C₂²	semidirect
116. #16810739	C₂²	semidirect
117. #16810739	C₂²	semidirect
118. #16810738	C₂²	semidirect
119. #16810738	C₂²	semidirect
120. #16810738	C₂²	semidirect
121. #16810737	C₂²	semidirect
122. #16810737	C₂²	semidirect
123. #16810737	C₂²	semidirect
124. #108×D₅₃	C₂²	semidirect
125. #108×D₅₃	C₂²	semidirect
127. #104×D₅₃	C₂²	semidirect
128. #104×D₅₃	C₂²	semidirect
129. #101×D₅₃	C₂²	semidirect
130. #100×D₅₃	C₂²	semidirect
131. C₄×C₈×D₅₃	C₂²	semidirect
132. C₅₃×#578	C₂²	semidirect
133. C₅₃×#577	C₂²	semidirect
134. C₅₃×#576	C₂²	semidirect
135. C₅₃×#495	C₂²	semidirect
136. C₅₃×#473	C₂²	semidirect
137. C₅₃×#472	C₂²	semidirect
138. C₅₃×#471	C₂²	semidirect
139. C₅₃×#455	C₂²	semidirect
140. C₅₃×#454	C₂²	semidirect
141. C₅₃×#443	C₂²	semidirect
142. C₅₃×#443	C₂²	semidirect
145. #13133265	C₂³	semidirect
149. #13133264	C₂³	semidirect
150. #13133264	C₂³	semidirect
177. #13133250	C₂³	semidirect
187. #13133248	C₂³	semidirect
191. #13133247	C₂³	semidirect
201. #13133245	C₂³	semidirect
211. #13133243	C₂³	semidirect
215. #13133242	C₂³	semidirect
252. C₂×Dic₂₁₂	C₂³	semidirect
254. C₂×#11719925	C₂³	semidirect
267. C₂×#11719913	C₂³	semidirect
269. C₂×#11719923	C₂³	semidirect
271. C₂×#11719924	C₂³	semidirect
306. #13133225	C₂³	semidirect
307. #13133225	C₂³	semidirect
309. #13133224	C₂³	semidirect
310. #13133224	C₂³	semidirect
315. #13133223	C₂³	semidirect
316. #13133223	C₂³	semidirect
328. #13133206	C₂³	semidirect
329. #13133205	C₂³	semidirect
330. #13133204	C₂³	semidirect
334. #13133153	C₂³	semidirect
335. #13133153	C₂³	semidirect
336. #13133152	C₂³	semidirect
337. #13133152	C₂³	semidirect
338. #13133152	C₂³	semidirect
340. #13133145	C₂³	semidirect
341. #13133145	C₂³	semidirect
343. #13133144	C₂³	semidirect
344. #13133144	C₂³	semidirect
346. #13133143	C₂³	semidirect
347. #13133143	C₂³	semidirect
348. #13133136	C₂³	semidirect
349. #13133135	C₂³	semidirect
350. #13133135	C₂³	semidirect
351. #13133134	C₂³	semidirect
352. #13133133	C₂³	semidirect
353. #13133133	C₂³	semidirect
354. C₄×#88322	C₂³	semidirect
355. C₈×Dic₅₃	C₂³	semidirect
356. C₈×Dic₅₃	C₂³	semidirect
357. 2₋¹⁺⁴×C₅₃	C₂³	semidirect
362. #137×C₅₃	C₂³	semidirect
366. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
373. C₂×Q₁₆×C₅₃	C₂³	semidirect
375. C₂×SD₁₆×C₅₃	C₂³	semidirect
379. #131×C₅₃	C₂³	semidirect
380. #131×C₅₃	C₂³	semidirect
381. #124×C₅₃	C₂³	semidirect
382. #108×C₅₃	C₂³	semidirect
383. #108×C₅₃	C₂³	semidirect
385. #104×C₅₃	C₂³	semidirect
386. #104×C₅₃	C₂³	semidirect
387. #101×C₅₃	C₂³	semidirect
388. #100×C₅₃	C₂³	semidirect
389. C₄×C₈×C₅₃	C₂³	semidirect
821. #3290	D₅₃	direct (N × H)
841. D₅₃	#3290	direct (N × H)
852. #578	C₂×D₅₃	semidirect
864. #577	C₂×D₅₃	semidirect
873. #576	C₂×D₅₃	semidirect
902. #495	C₂×D₅₃	semidirect
908. #473	C₂×D₅₃	semidirect
914. #472	C₂×D₅₃	semidirect
922. #471	C₂×D₅₃	semidirect
930. #455	C₂×D₅₃	semidirect
938. #454	C₂×D₅₃	semidirect
951. #443	C₂×D₅₃	semidirect
952. #443	C₂×D₅₃	semidirect
961. C₅₃	C₂×#3290	semidirect
970. 2₋¹⁺⁴	C₂²×D₅₃	semidirect
1022. #137	C₂²×D₅₃	semidirect
1050. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
1101. C₂×Q₁₆	C₂²×D₅₃	semidirect
1124. C₂×SD₁₆	C₂²×D₅₃	semidirect
1158. #131	C₂²×D₅₃	semidirect
1159. #131	C₂²×D₅₃	semidirect
1175. #124	C₂²×D₅₃	semidirect
1183. #108	C₂²×D₅₃	semidirect
1184. #108	C₂²×D₅₃	semidirect
1195. #104	C₂²×D₅₃	semidirect
1196. #104	C₂²×D₅₃	semidirect
1200. #101	C₂²×D₅₃	semidirect
1204. #100	C₂²×D₅₃	semidirect
1208. C₄×C₈	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#578×D₅₃	2
#577×D₅₃	2
#576×D₅₃	2
#20286504	2
#20286503	2
#20286502	2
#20286501	2
#20286500	2
#20286499	2
#20286498	2
#20286497	2
#20286496	2
#20286495	2
#20286494	2
#495×D₅₃	2
#473×D₅₃	2
#472×D₅₃	2
#471×D₅₃	2
#454×D₅₃	2
#455×D₅₃	2
#443×D₅₃	2
C₅₃×#3290	2
C₂×#3290	53

Subgroups — D53×#3290 #28260294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3290 #28260294