Subgroups — #28293330

Order 13568.

7498 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289069	C₂	1	4	yes	maximal, complemented
2	#20289042	C₂	1	4	yes	maximal, complemented
3	#20289032	C₂	1	8	yes	maximal, complemented
4	#20289016	C₂	1	8	yes	maximal, complemented
5	#20288909	C₂	1	4	yes	maximal, complemented
6	#20288899	C₂	1	4	yes	maximal, complemented
7	#20288885	C₂	1	8	yes	maximal, complemented
8	#20288864	C₂	1	8	yes	maximal, complemented
9	#20288411	C₂	1	2	yes	maximal, complemented
10	#20288403	C₂	1	2	yes	maximal, complemented
11	#20288400	C₂	1	2	yes	maximal, complemented
12	#20288359	C₂	1	1	yes	maximal, characteristic, complemented
13	#20288347	C₂	1	2	yes	maximal, complemented
14	#20288346	C₂	1	2	yes	maximal, complemented
15	C₂×#16811187	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16811184	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13133262	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
21	#16811372	C₂²	1	4	yes	complemented
22	#16811370	C₂²	1	8	yes	complemented
23	#16811369	C₂²	1	8	yes	complemented
24	#16811369	C₂²	1	8	yes	complemented
25	#16811365	C₂²	1	4	yes	complemented
26	#16811363	C₂²	1	8	yes	complemented
27	#16811363	C₂²	1	4	yes	complemented
28	#16811362	C₂²	1	4	yes	complemented
29	#16811361	C₂²	1	8	yes	complemented
30	#16811361	C₂²	1	8	yes	complemented
31	#16811357	C₂²	1	4	yes	complemented
32	#16811339	C₂²	1	4	yes	complemented
33	#16811335	C₂²	1	4	yes	complemented
34	#16811322	C₂²	1	8	yes	complemented
35	#16811321	C₂²	1	8	yes	complemented
36	#16811310	C₂²	1	8	yes	complemented
37	#16811308	C₂²	1	8	yes	complemented
38	#16811302	C₂²	1	8	yes	complemented
39	#16811300	C₂²	1	8	yes	complemented
40	#16811299	C₂²	1	8	yes	complemented
41	#16811297	C₂²	1	8	yes	complemented
42	#16811296	C₂²	1	8	yes	complemented
43	#16811296	C₂²	1	8	yes	complemented
44	#16811296	C₂²	1	8	yes	complemented
45	#16811291	C₂²	1	8	yes	complemented
46	#16811272	C₂²	1	8	yes	complemented
47	#16811269	C₂²	1	8	yes	complemented
48	#16811268	C₂²	1	8	yes	complemented
49	#16811265	C₂²	1	8	yes	complemented
50	#16811263	C₂²	1	8	yes	complemented
51	#16811263	C₂²	1	8	yes	complemented
52	#16811262	C₂²	1	8	yes	complemented
53	#16811261	C₂²	1	8	yes	complemented
54	#16811261	C₂²	1	8	yes	complemented
55	#16811261	C₂²	1	8	yes	complemented
56	#16811260	C₂²	1	8	yes	complemented
57	#16811260	C₂²	1	8	yes	complemented
58	#16811257	C₂²	1	8	yes	complemented
59	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
60	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
61	#16811255	C₂²	1	4	yes	complemented
62	#16811255	C₂²	1	8	yes	complemented
63	#16811249	C₂²	1	2	yes	complemented
64	#16811247	C₂²	1	8	yes	complemented
65	#16811243	C₂²	1	8	yes	complemented
66	#16811225	C₂²	1	8	yes	complemented
67	#16811225	C₂²	1	8	yes	complemented
68	#16811224	C₂²	1	8	yes	complemented
69	#16811223	C₂²	1	8	yes	complemented
70	#16811222	C₂²	1	4	yes	complemented
71	#16811220	C₂²	1	4	yes	complemented
72	#16811217	C₂²	1	8	yes	complemented
73	#16811213	C₂²	1	8	yes	complemented
74	#16811213	C₂²	1	4	yes	complemented
75	#16811211	C₂²	1	4	yes	complemented
76	#16811210	C₂²	1	8	yes	complemented
77	#16811209	C₂²	1	8	yes	complemented
78	#16811207	C₂²	1	8	yes	complemented
79	#16811206	C₂²	1	8	yes	complemented
80	#16811206	C₂²	1	8	yes	complemented
81	#16811204	C₂²	1	4	yes	complemented
82	#16811200	C₂²	1	4	yes	complemented
83	#16811197	C₂²	1	2	yes	complemented
84	#16811189	C₂²	1	8	yes	complemented
85	#16811188	C₂²	1	4	yes	complemented
86	#16811188	C₂²	1	8	yes	complemented
87	#16811187	C₂²	1	4	yes	complemented
88	#16811187	C₂²	1	8	yes	complemented
89	#16811187	C₂²	1	8	yes	complemented
90	#16811185	C₂²	1	4	yes	complemented
91	#16811184	C₂²	1	8	yes	complemented
92	#16811184	C₂²	1	8	yes	complemented
93	#16811184	C₂²	1	8	yes	complemented
94	#16811184	C₂²	1	8	yes	complemented
95	#16811184	C₂²	1	4	yes	complemented
96	#16811182	C₂²	1	2	yes	—
97	#16811182	C₂²	1	2	yes	complemented
98	#16811182	C₂²	1	4	yes	complemented
99	#16811182	C₂²	1	2	yes	complemented
100	#16811181	C₂²	1	4	yes	complemented
101	C₂×#13133213	C₂²	1	2	yes	complemented
102	#16811150	C₂²	1	8	yes	complemented
103	C₂×#13133206	C₂²	1	2	yes	complemented
104	#16811134	C₂²	1	2	yes	complemented
105	#16811133	C₂²	1	8	yes	complemented
106	#16811132	C₂²	1	8	yes	complemented
107	#16811131	C₂²	1	4	yes	complemented
108	#16811130	C₂²	1	4	yes	complemented
109	C₂×#13133202	C₂²	1	4	yes	complemented
110	C₂×#13133200	C₂²	1	2	yes	complemented
111	C₂×#13133200	C₂²	1	2	yes	complemented
112	C₂×#13133192	C₂²	1	4	yes	complemented
113	C₂×#13133191	C₂²	1	2	yes	complemented
114	C₂×#13133191	C₂²	1	2	yes	complemented
115	C₂×#13133190	C₂²	1	4	yes	complemented
116	C₂×#13133187	C₂²	1	2	yes	complemented
117	C₂×#13133187	C₂²	1	4	yes	complemented
118	C₂×#13133185	C₂²	1	2	yes	complemented
119	C₂×#13133185	C₂²	1	2	yes	complemented
120	C₂×#13133185	C₂²	1	2	yes	complemented
121	C₂×#13133185	C₂²	1	4	yes	complemented
122	#120×D₅₃	C₂²	1	4	yes	complemented
123	#16811098	C₂²	1	2	yes	complemented
124	#16811098	C₂²	1	1	yes	characteristic, complemented
125	#16811096	C₂²	1	2	yes	complemented
126	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
128	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#547	C₂²	1	8	yes	complemented
131	C₅₃×#546	C₂²	1	8	yes	complemented
132	C₅₃×#536	C₂²	1	2	yes	complemented
133	C₅₃×#534	C₂²	1	2	yes	complemented
134	C₅₃×#534	C₂²	1	2	yes	complemented
135	C₅₃×#525	C₂²	1	2	yes	complemented
136	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
137	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
138	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
139	C₂⁴×D₅₃	C₂³	1	2	yes	—
140	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
141	#13133262	—	4	4	no	—
142	C₂×#11719945	C₂³	1	2	yes	—
143	C₂×#11719945	C₂³	1	8	yes	complemented
144	C₂×#11719947	C₂³	1	4	yes	—
145	C₂×#11719947	C₂³	1	8	yes	complemented
146	C₂²×D₂₁₂	—	4	4	no	—
147	C₂²×D₂₁₂	C₂³	1	4	yes	—
148	C₂²×D₂₁₂	C₂³	1	4	yes	—
149	C₂²×D₂₁₂	C₂³	1	2	yes	—
150	C₂²×D₂₁₂	C₂³	1	2	yes	—
151	C₂²×D₂₁₂	C₂³	1	4	yes	—
152	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
153	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
154	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
155	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
156	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
157	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
158	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
159	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
160	C₂×D₄×D₅₃	—	4	8	no	—
161	C₂×D₄×D₅₃	C₂³	1	4	yes	—
162	C₂×D₄×D₅₃	C₂³	1	8	yes	—
163	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
164	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
165	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
166	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
167	#13133215	C₂³	1	4	yes	complemented
168	#13133213	C₂³	1	4	yes	—
169	#13133213	C₂³	1	4	yes	complemented
170	#13133213	C₂³	1	8	yes	complemented
171	#13133213	C₂³	1	8	yes	complemented
172	#13133213	C₂³	1	8	yes	complemented
173	#13133212	C₂³	1	8	yes	complemented
174	#13133212	C₂³	1	8	yes	complemented
175	#13133212	C₂³	1	8	yes	complemented
176	#13133212	C₂³	1	8	yes	complemented
177	#13133212	C₂³	1	8	yes	complemented
178	#13133211	C₂³	1	8	yes	complemented
179	#13133210	C₂³	1	8	yes	complemented
180	#13133210	C₂³	1	8	yes	complemented
181	#13133208	C₂³	1	8	yes	complemented
182	#13133207	C₂³	1	8	yes	complemented
183	#13133207	C₂³	1	8	yes	complemented
184	#13133206	C₂³	1	4	yes	—
185	#13133206	C₂³	1	4	yes	complemented
186	#13133206	C₂³	1	4	yes	complemented
187	#13133206	C₂³	1	8	yes	complemented
188	#13133206	C₂³	1	8	yes	complemented
189	#13133205	C₂³	1	8	yes	complemented
190	#13133203	C₂³	1	8	yes	complemented
191	#13133203	C₂³	1	8	yes	complemented
192	#13133203	C₂³	1	8	yes	complemented
193	#13133203	C₂³	1	8	yes	complemented
194	#13133203	C₂³	1	8	yes	complemented
195	#13133202	C₂³	1	8	yes	—
196	#13133202	C₂³	1	8	yes	—
197	#13133202	C₂³	1	8	yes	complemented
198	#13133202	C₂³	1	8	yes	complemented
199	#13133202	C₂³	1	8	yes	complemented
200	#13133202	C₂³	1	8	yes	complemented
201	#13133202	C₂³	1	8	yes	complemented
202	#13133201	C₂³	1	8	yes	complemented
203	#13133201	C₂³	1	8	yes	complemented
204	#13133201	C₂³	1	8	yes	complemented
205	#13133200	C₂³	1	8	yes	—
206	#13133200	C₂³	1	4	yes	—
207	#13133200	C₂³	1	8	yes	complemented
208	#13133200	C₂³	1	4	yes	complemented
209	#13133200	C₂³	1	8	yes	complemented
210	#13133200	C₂³	1	8	yes	complemented
211	#13133200	C₂³	1	4	yes	complemented
212	#13133200	C₂³	1	4	yes	complemented
213	#13133199	C₂³	1	8	yes	complemented
214	#13133199	C₂³	1	8	yes	complemented
215	#13133199	C₂³	1	8	yes	complemented
216	#13133199	C₂³	1	8	yes	complemented
217	#13133198	C₂³	1	4	yes	—
218	#13133198	C₂³	1	4	yes	complemented
219	#13133198	C₂³	1	4	yes	complemented
220	#13133197	C₂³	1	8	yes	complemented
221	#13133197	C₂³	1	8	yes	complemented
222	#13133196	C₂³	1	8	yes	complemented
223	#13133196	C₂³	1	4	yes	complemented
224	#13133195	C₂³	1	8	yes	complemented
225	#13133195	C₂³	1	8	yes	complemented
226	#13133194	C₂³	1	8	yes	complemented
227	#13133194	C₂³	1	8	yes	complemented
228	#13133194	C₂³	1	8	yes	complemented
229	#13133193	C₂³	1	8	yes	complemented
230	#13133193	C₂³	1	8	yes	complemented
231	#13133192	C₂³	1	8	yes	—
232	#13133192	C₂³	1	8	yes	—
233	#13133192	C₂³	1	8	yes	complemented
234	#13133192	C₂³	1	8	yes	complemented
235	#13133192	C₂³	1	8	yes	complemented
236	#13133191	C₂³	1	4	yes	—
237	#13133191	C₂³	1	4	yes	—
238	#13133191	C₂³	1	8	yes	complemented
239	#13133191	C₂³	1	8	yes	complemented
240	#13133191	C₂³	1	8	yes	complemented
241	#13133191	C₂³	1	8	yes	complemented
242	#13133191	C₂³	1	8	yes	complemented
243	#13133191	C₂³	1	4	yes	complemented
244	#13133191	C₂³	1	4	yes	complemented
245	#13133191	C₂³	1	4	yes	complemented
246	#13133190	C₂³	1	8	yes	—
247	#13133190	C₂³	1	8	yes	—
248	#13133190	C₂³	1	8	yes	complemented
249	#13133190	C₂³	1	8	yes	complemented
250	#13133190	C₂³	1	8	yes	complemented
251	#13133190	C₂³	1	8	yes	complemented
252	#13133190	C₂³	1	8	yes	complemented
253	#13133190	C₂³	1	8	yes	complemented
254	#13133190	C₂³	1	8	yes	complemented
255	#13133189	C₂³	1	8	yes	—
256	#13133189	C₂³	1	8	yes	—
257	#13133189	C₂³	1	8	yes	complemented
258	#13133189	C₂³	1	8	yes	complemented
259	#13133189	C₂³	1	8	yes	complemented
260	#13133189	C₂³	1	8	yes	complemented
261	#13133189	C₂³	1	8	yes	complemented
262	#13133189	C₂³	1	8	yes	complemented
263	#13133188	C₂³	1	8	yes	complemented
264	#13133188	C₂³	1	8	yes	complemented
265	#13133187	C₂³	1	8	yes	—
266	#13133187	C₂³	1	8	yes	—
267	#13133187	C₂³	1	4	yes	—
268	#13133187	C₂³	1	4	yes	—
269	#13133187	C₂³	1	8	yes	—
270	#13133187	C₂³	1	8	yes	complemented
271	#13133187	C₂³	1	8	yes	complemented
272	#13133187	C₂³	1	8	yes	complemented
273	#13133187	C₂³	1	8	yes	complemented
274	#13133186	C₂³	1	4	yes	—
275	#13133186	C₂³	1	8	yes	complemented
276	#13133186	C₂³	1	4	yes	complemented
277	#13133185	C₂³	1	8	yes	—
278	#13133185	C₂³	1	4	yes	—
279	#13133185	C₂³	1	8	yes	—
280	#13133185	C₂³	1	8	yes	—
281	#13133185	C₂³	1	4	yes	—
282	#13133185	C₂³	1	4	yes	—
283	#13133185	C₂³	1	4	yes	complemented
284	#13133185	C₂³	1	8	yes	complemented
285	#13133185	C₂³	1	8	yes	complemented
286	#13133185	C₂³	1	8	yes	complemented
287	#13133185	C₂³	1	4	yes	complemented
288	#13133185	C₂³	1	4	yes	complemented
289	#13133185	C₂³	1	4	yes	complemented
290	#13133185	C₂³	1	4	yes	complemented
291	#13133185	C₂³	1	4	yes	complemented
292	#13133182	C₂³	1	8	yes	complemented
293	C₄×D₂₁₂	C₂³	1	8	yes	complemented
294	D₄×Dic₅₃	C₂³	1	8	yes	—
295	D₄×Dic₅₃	C₂³	1	8	yes	complemented
296	D₄×Dic₅₃	C₂³	1	8	yes	complemented
297	#13133179	C₂³	1	8	yes	complemented
298	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
299	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
300	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
301	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
302	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
303	#13133177	C₂³	1	8	yes	complemented
304	#13133177	C₂³	1	8	yes	complemented
305	#13133177	C₂³	1	8	yes	complemented
306	#13133177	C₂³	1	8	yes	complemented
307	#13133177	C₂³	1	8	yes	complemented
308	#13133176	C₂³	1	2	yes	complemented
309	#13133176	C₂³	1	4	yes	complemented
310	#13133176	C₂³	1	8	yes	complemented
311	#13133175	C₂³	1	8	yes	complemented
312	#13133175	C₂³	1	8	yes	complemented
313	#13133174	C₂³	1	8	yes	complemented
314	#13133173	C₂³	1	8	yes	complemented
315	#13133173	C₂³	1	4	yes	complemented
316	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
317	C₂×#11719919	C₂³	1	4	yes	complemented
318	C₂×#11719919	C₂³	1	4	yes	complemented
319	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
320	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
321	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
322	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
323	C₂×#11719921	C₂³	1	4	yes	—
324	C₂×#11719921	C₂³	1	4	yes	—
325	C₂×#11719921	C₂³	1	4	yes	complemented
326	C₂×#11719921	C₂³	1	4	yes	complemented
327	C₂×#11719921	C₂³	1	8	yes	complemented
328	C₂×#11719921	C₂³	1	4	yes	complemented
329	C₂×#11719921	C₂³	1	4	yes	complemented
330	C₂×#11719921	C₂³	1	4	yes	complemented
331	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
332	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
333	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
334	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
335	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
336	H(5,𝔽₂)×C₅₃	—	4	4	no	—
337	C₂×#41×C₅₃	—	4	4	no	—
338	C₂×#41×C₅₃	C₂³	1	2	yes	—
339	C₂×#41×C₅₃	C₂³	1	4	yes	—
340	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
341	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
342	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
344	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
346	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
347	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
348	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
350	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
351	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
352	#124×C₅₃	C₂³	1	4	yes	complemented
353	#123×C₅₃	C₂³	1	8	yes	—
354	#123×C₅₃	C₂³	1	4	yes	complemented
355	#123×C₅₃	C₂³	1	4	yes	complemented
356	#123×C₅₃	C₂³	1	4	yes	complemented
357	#123×C₅₃	C₂³	1	4	yes	complemented
358	#123×C₅₃	C₂³	1	8	yes	complemented
359	#123×C₅₃	C₂³	1	4	yes	complemented
360	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
361	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
362	#121×C₅₃	C₂³	1	8	yes	—
363	#121×C₅₃	C₂³	1	8	yes	complemented
364	#121×C₅₃	C₂³	1	4	yes	complemented
365	#120×C₅₃	C₂³	1	4	yes	complemented
366	#120×C₅₃	C₂³	1	4	yes	complemented
367	#120×C₅₃	C₂³	1	4	yes	complemented
368	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
369	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
370	#117×C₅₃	C₂³	1	2	yes	complemented
371	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
372	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
373	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
374	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
375	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
376	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
377	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
378	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
381	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂³×D₅₃	—	2	8	no	—
383	C₂³×D₅₃	—	4	4	no	—
384	C₂³×D₅₃	—	8	4	no	—
385	C₂³×D₅₃	—	8	4	no	—
386	C₂³×D₅₃	C₂⁴	1	4	yes	—
387	C₂³×D₅₃	C₂⁴	1	2	yes	—
388	C₂³×D₅₃	C₂⁴	1	4	yes	—
389	C₂³×D₅₃	C₂⁴	1	2	yes	—
390	C₂³×D₅₃	C₂⁴	1	2	yes	—
391	C₂³×D₅₃	C₂⁴	1	8	yes	—
392	C₂³×D₅₃	C₂⁴	1	2	yes	—
393	#41×C₅₃	—	4	16	no	—
394	#41×C₅₃	—	4	8	no	—
395	#41×C₅₃	—	4	4	no	—
396	C₂×Q₈×C₅₃	—	4	2	no	—
397	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
398	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
399	C₂×D₄×C₅₃	—	2	4	no	—
400	C₂×D₄×C₅₃	—	2	4	no	—
401	C₂×D₄×C₅₃	—	2	8	no	—
402	C₂×D₄×C₅₃	—	4	2	no	—
403	C₂×D₄×C₅₃	—	4	4	no	—
404	C₂×D₄×C₅₃	—	4	8	no	—
405	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
406	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
407	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
408	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
409	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
410	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
411	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
412	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
413	C₂²×C₄×C₅₃	—	2	4	no	—
414	C₂²×C₄×C₅₃	—	4	2	no	—
415	C₂²×C₄×C₅₃	—	4	2	no	—
416	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
417	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
418	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
423	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
424	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
425	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
426	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
427	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
428	C₂×C₂²⋊D₅₃	—	2	8	no	—
429	C₂×C₂²⋊D₅₃	—	4	4	no	—
430	C₂×C₂²⋊D₅₃	—	4	4	no	—
431	C₂×C₂²⋊D₅₃	—	8	4	no	—
432	C₂×C₂²⋊D₅₃	—	8	8	no	—
433	C₂×C₂²⋊D₅₃	—	8	4	no	—
434	C₂×C₂²⋊D₅₃	—	8	4	no	—
435	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
436	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
437	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
438	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
439	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
440	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
441	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
442	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
443	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
444	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
445	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
446	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
447	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
448	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
449	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
450	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
451	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
452	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
453	#11719947	—	4	8	no	—
454	#11719947	—	8	8	no	—
455	D₄×D₅₃	—	4	16	no	—
456	D₄×D₅₃	—	4	16	no	—
457	D₄×D₅₃	—	4	8	no	—
458	D₄×D₅₃	—	8	8	no	—
459	#11719945	—	4	4	no	—
460	#11719945	—	8	8	no	—
461	C₂×D₂₁₂	—	4	4	no	—
462	C₂×D₂₁₂	—	4	4	no	—
463	C₂×D₂₁₂	—	4	4	no	—
464	C₂×D₂₁₂	—	4	8	no	—
465	C₂×D₂₁₂	—	4	8	no	—
466	C₂×D₂₁₂	—	8	4	no	—
467	C₂×D₂₁₂	C₂⁴	1	8	yes	—
468	C₂×D₂₁₂	C₂⁴	1	8	yes	—
469	C₂×D₂₁₂	C₂⁴	1	2	yes	—
470	C₂×D₂₁₂	C₂⁴	1	2	yes	—
471	C₂×D₂₁₂	C₂⁴	1	2	yes	—
472	C₂×D₂₁₂	C₂⁴	1	4	yes	—
473	C₂×D₂₁₂	C₂⁴	1	4	yes	—
474	C₂×D₂₁₂	C₂⁴	1	8	yes	—
475	C₂×D₂₁₂	C₂⁴	1	2	yes	—
476	C₂×D₂₁₂	C₂⁴	1	2	yes	—
477	C₂×C₄×D₅₃	—	4	4	no	—
478	C₂×C₄×D₅₃	—	8	4	no	—
479	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
480	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
481	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
482	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
483	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
484	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
485	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
486	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
487	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
488	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
489	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
490	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
491	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
492	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
493	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
494	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
495	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
496	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
497	C₄²×C₅₃	C₂⁴	1	4	yes	—
498	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
499	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
500	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
501	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
502	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
503	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
504	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
505	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
506	#11719921	C₂⁴	1	8	yes	—
507	#11719921	C₂⁴	1	8	yes	—
508	#11719921	C₂⁴	1	8	yes	—
509	#11719921	C₂⁴	1	8	yes	—
510	#11719921	C₂⁴	1	8	yes	—
511	#11719921	C₂⁴	1	8	yes	—
512	#11719921	C₂⁴	1	8	yes	—
513	#11719921	C₂⁴	1	8	yes	—
514	#11719921	C₂⁴	1	8	yes	—
515	#11719921	C₂⁴	1	8	yes	—
516	#11719921	C₂⁴	1	8	yes	—
517	#11719921	C₂⁴	1	8	yes	—
518	#11719921	C₂⁴	1	8	yes	—
519	#11719921	C₂⁴	1	8	yes	—
520	#11719921	C₂⁴	1	8	yes	—
521	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
522	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
523	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
524	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
525	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
526	#11719919	C₂⁴	1	8	yes	—
527	#11719919	C₂⁴	1	8	yes	—
528	#11719919	C₂⁴	1	8	yes	—
529	#11719919	C₂⁴	1	8	yes	—
530	#11719919	C₂⁴	1	8	yes	—
531	#11719919	C₂⁴	1	8	yes	—
532	#11719919	C₂⁴	1	8	yes	—
533	C₄×Dic₅₃	C₂⁴	1	4	yes	—
534	C₄×Dic₅₃	C₂⁴	1	4	yes	—
535	C₄×Dic₅₃	C₂⁴	1	8	yes	—
536	C₄×Dic₅₃	C₂⁴	1	4	yes	—
537	C₄×Dic₅₃	C₂⁴	1	8	yes	—
538	C₂³×C₅₃	—	2	2	no	—
539	C₂³×C₅₃	—	2	4	no	—
540	C₂³×C₅₃	—	2	2	no	—
541	C₂³×C₅₃	—	4	2	no	—
542	C₂³×C₅₃	—	4	2	no	—
543	C₂³×C₅₃	—	4	2	no	—
544	C₂³×C₅₃	—	4	4	no	—
545	C₂³×C₅₃	—	4	4	no	—
546	C₂³×C₅₃	—	4	2	no	—
547	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
548	C₂³×C₅₃	C₂⁵	1	2	yes	—
549	C₂³×C₅₃	C₂⁵	1	4	yes	—
550	C₂³×C₅₃	C₂⁵	1	2	yes	—
551	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
552	C₂³×C₅₃	C₂⁵	1	2	yes	—
553	C₂²×D₅₃	—	2	4	no	—
554	C₂²×D₅₃	—	2	4	no	—
555	C₂²×D₅₃	—	2	8	no	—
556	C₂²×D₅₃	—	2	8	no	—
557	C₂²×D₅₃	—	2	4	no	—
558	C₂²×D₅₃	—	4	4	no	—
559	C₂²×D₅₃	—	4	4	no	—
560	C₂²×D₅₃	—	4	4	no	—
561	C₂²×D₅₃	—	4	4	no	—
562	C₂²×D₅₃	—	4	8	no	—
563	C₂²×D₅₃	—	4	8	no	—
564	C₂²×D₅₃	—	4	4	no	—
565	C₂²×D₅₃	—	4	4	no	—
566	C₂²×D₅₃	—	4	4	no	—
567	C₂²×D₅₃	—	4	8	no	—
568	C₂²×D₅₃	—	4	2	no	—
569	C₂²×D₅₃	—	4	4	no	—
570	C₂²×D₅₃	—	8	16	no	—
571	C₂²×D₅₃	—	8	16	no	—
572	C₂²×D₅₃	C₂⁵	1	4	yes	—
573	C₂²×D₅₃	C₂⁵	1	4	yes	—
574	C₂²×D₅₃	C₂⁵	1	4	yes	—
575	Q₈×C₅₃	—	4	4	no	—
576	Q₈×C₅₃	—	4	2	no	—
577	D₄×C₅₃	—	2	8	no	—
578	D₄×C₅₃	—	2	8	no	—
579	D₄×C₅₃	—	2	8	no	—
580	D₄×C₅₃	—	2	8	no	—
581	D₄×C₅₃	—	4	8	no	—
582	D₄×C₅₃	—	4	4	no	—
583	D₄×C₅₃	—	4	2	no	—
584	D₄×C₅₃	—	4	4	no	—
585	C₂×C₄×C₅₃	—	2	4	no	—
586	C₂×C₄×C₅₃	—	2	2	no	—
587	C₂×C₄×C₅₃	—	2	2	no	—
588	C₂×C₄×C₅₃	—	2	8	no	—
589	C₂×C₄×C₅₃	—	2	2	no	—
590	C₂×C₄×C₅₃	—	2	2	no	—
591	C₂×C₄×C₅₃	—	4	4	no	—
592	C₂×C₄×C₅₃	—	4	4	no	—
593	C₂×C₄×C₅₃	—	4	4	no	—
594	C₂×C₄×C₅₃	—	4	4	no	—
595	C₂×C₄×C₅₃	—	4	2	no	—
596	C₂×C₄×C₅₃	—	4	4	no	—
597	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
598	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
599	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
600	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
601	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
602	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
603	C₂²⋊D₅₃	—	2	8	no	—
604	C₂²⋊D₅₃	—	2	8	no	—
605	C₂²⋊D₅₃	—	4	8	no	—
606	C₂²⋊D₅₃	—	4	8	no	—
607	C₂²⋊D₅₃	—	4	8	no	—
608	C₂²⋊D₅₃	—	4	4	no	—
609	C₂²⋊D₅₃	—	4	8	no	—
610	C₂²⋊D₅₃	—	4	8	no	—
611	C₂²⋊D₅₃	—	4	8	no	—
612	C₂²⋊D₅₃	—	4	8	no	—
613	C₂²⋊D₅₃	—	4	8	no	—
614	C₂²⋊D₅₃	—	4	8	no	—
615	C₂×Dic₅₃	—	2	4	no	—
616	C₂×Dic₅₃	—	4	4	no	—
617	C₂×Dic₅₃	—	4	2	no	—
618	C₂×Dic₅₃	—	4	4	no	—
619	C₂×Dic₅₃	—	4	8	no	—
620	C₂×Dic₅₃	—	4	4	no	—
621	C₂×Dic₅₃	C₂⁵	1	4	yes	—
622	C₂×Dic₅₃	C₂⁵	1	8	yes	—
623	C₂×Dic₅₃	C₂⁵	1	8	yes	—
624	D₂₁₂	—	4	2	no	—
625	D₂₁₂	—	4	4	no	—
626	D₂₁₂	—	4	2	no	—
627	D₂₁₂	—	4	2	no	—
628	D₂₁₂	—	4	4	no	—
629	D₂₁₂	—	4	2	no	—
630	D₂₁₂	—	4	8	no	—
631	D₂₁₂	—	4	8	no	—
632	D₂₁₂	—	4	8	no	—
633	D₂₁₂	—	4	2	no	—
634	C₄×D₅₃	—	4	8	no	—
635	C₄×D₅₃	—	4	8	no	—
636	C₄×D₅₃	—	4	8	no	—
637	C₄×D₅₃	—	4	4	no	—
638	C₄×D₅₃	—	4	8	no	—
639	Dic₁₀₆	—	4	2	no	—
640	Dic₁₀₆	—	4	8	no	—
641	#62862	—	53	1	no	maximal, Sylow
642	C₂²×C₅₃	—	2	2	no	—
643	C₂²×C₅₃	—	2	4	no	—
644	C₂²×C₅₃	—	2	2	no	—
645	C₂²×C₅₃	—	2	4	no	—
646	C₂²×C₅₃	—	2	2	no	—
647	C₂²×C₅₃	—	2	4	no	—
648	C₂²×C₅₃	—	2	8	no	—
649	C₂²×C₅₃	—	2	4	no	—
650	C₂²×C₅₃	—	4	4	no	—
651	C₂²×C₅₃	—	8	4	no	—
652	C₂²×C₅₃	—	8	2	no	—
653	C₂²×C₅₃	—	8	2	no	—
654	C₂²×C₅₃	—	16	2	no	—
655	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
656	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
657	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
658	C₂×D₅₃	—	2	4	no	—
659	C₂×D₅₃	—	2	4	no	—
660	C₂×D₅₃	—	2	4	no	—
661	C₂×D₅₃	—	2	4	no	—
662	C₂×D₅₃	—	2	4	no	—
663	C₂×D₅₃	—	2	8	no	—
664	C₂×D₅₃	—	2	4	no	—
665	C₂×D₅₃	—	2	4	no	—
666	C₂×D₅₃	—	4	8	no	—
667	C₂×D₅₃	—	4	8	no	—
668	C₂×D₅₃	—	8	8	no	—
669	C₂×D₅₃	—	8	8	no	—
670	C₂×D₅₃	—	8	4	no	—
671	C₂×D₅₃	—	8	16	no	—
672	C₂×D₅₃	—	16	2	no	—
673	C₄×C₅₃	—	2	2	no	—
674	C₄×C₅₃	—	2	4	no	—
675	C₄×C₅₃	—	2	2	no	—
676	C₄×C₅₃	—	2	2	no	—
677	C₄×C₅₃	—	2	2	no	—
678	C₄×C₅₃	—	2	8	no	—
679	Dic₅₃	—	2	4	no	—
680	Dic₅₃	—	2	8	no	—
681	Dic₅₃	—	2	8	no	—
682	#3545	—	53	4	no	—
683	#3543	—	53	4	no	—
684	#3542	—	53	8	no	—
685	#3542	—	53	8	no	—
686	#3534	—	53	4	no	—
687	#3534	—	53	4	no	—
688	#3533	—	53	8	no	—
689	#3532	—	53	8	no	—
690	#3491	—	53	2	no	—
691	#3490	—	53	2	no	—
692	#3490	—	53	2	no	—
693	#3485	—	53	1	no	—
694	#3485	D₅₃	1	1	yes	characteristic, complemented
695	#3484	—	53	2	no	—
696	#3484	—	53	2	no	—
697	C₂×#535	—	53	1	no	—
698	C₂×#534	—	53	2	no	—
699	C₂×C₅₃	—	2	4	no	—
700	C₂×C₅₃	—	2	2	no	—
701	C₂×C₅₃	—	4	4	no	—
702	C₂×C₅₃	—	4	2	no	—
703	C₂×C₅₃	—	4	2	no	—
704	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
706	D₅₃	—	4	4	no	—
707	D₅₃	—	4	4	no	—
708	D₅₃	—	4	4	no	—
709	C₂×H(5,𝔽₂)	—	53	1	no	—
710	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
711	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
712	C₂³×D₄	—	53	2	no	—
713	C₂³×D₄	—	53	1	no	—
714	#563	—	53	4	no	—
715	#562	—	53	8	no	—
716	#562	—	53	8	no	—
717	#562	—	53	8	no	—
718	H(3,𝔽₄)	—	53	4	no	—
719	#560	—	53	8	no	—
720	#560	—	53	4	no	—
721	#560	—	53	8	no	—
722	#560	—	53	8	no	—
723	#560	—	53	4	no	—
724	#559	—	53	4	no	—
725	#555	—	53	4	no	—
726	#555	—	53	4	no	—
727	#553	—	53	8	no	—
728	#553	—	53	8	no	—
729	#552	—	53	8	no	—
730	#552	—	53	8	no	—
731	#551	—	53	8	no	—
732	#551	—	53	8	no	—
733	#551	—	53	8	no	—
734	#551	—	53	8	no	—
735	#551	—	53	8	no	—
736	#551	—	53	8	no	—
737	#551	—	53	8	no	—
738	#550	—	53	8	no	—
739	#547	—	53	8	no	—
740	#547	C₂×D₅₃	1	8	yes	complemented
741	#546	—	53	8	no	—
742	#546	—	53	8	no	—
743	#546	—	53	8	no	—
744	#546	—	53	8	no	—
745	#546	—	53	8	no	—
746	#546	—	53	8	no	—
747	#546	—	53	8	no	—
748	#546	—	53	8	no	—
749	#546	—	53	8	no	—
750	#546	—	53	8	no	—
751	#546	—	53	8	no	—
752	#546	C₂×D₅₃	1	8	yes	complemented
753	D₄²	—	53	8	no	—
754	D₄²	—	53	8	no	—
755	D₄²	—	53	8	no	—
756	D₄²	—	53	8	no	—
757	D₄²	—	53	4	no	—
758	#543	—	53	2	no	—
759	#542	—	53	8	no	—
760	#542	—	53	8	no	—
761	#540	—	53	8	no	—
762	#540	—	53	8	no	—
763	#540	—	53	8	no	—
764	#540	—	53	8	no	—
765	#539	—	53	8	no	—
766	#539	—	53	4	no	—
767	#539	—	53	4	no	—
768	#538	—	53	8	no	—
769	#538	—	53	8	no	—
770	#538	—	53	8	no	—
771	#538	—	53	4	no	—
772	#538	—	53	8	no	—
773	#538	—	53	8	no	—
774	#538	—	53	8	no	—
775	#538	—	53	4	no	—
776	#537	—	53	4	no	—
777	#537	—	53	4	no	—
778	#536	—	53	2	no	—
779	#536	C₂×D₅₃	1	2	yes	complemented
780	#535	—	53	4	no	—
781	#535	—	53	8	no	—
782	#535	—	53	8	no	—
783	#535	—	53	8	no	—
784	#535	—	53	4	no	—
785	#535	—	53	8	no	—
786	#534	—	53	2	no	—
787	#534	—	53	2	no	—
788	#534	—	53	4	no	—
789	#534	—	53	2	no	—
790	#534	—	53	8	no	—
791	#534	—	53	8	no	—
792	#534	—	53	8	no	—
793	#534	—	53	8	no	—
794	#534	—	53	4	no	—
795	#534	—	53	4	no	—
796	#534	—	53	4	no	—
797	#534	C₂×D₅₃	1	2	yes	complemented
798	#534	C₂×D₅₃	1	2	yes	complemented
799	C₂×#127	—	53	2	no	—
800	#529	—	53	8	no	—
801	C₂×#124	—	53	2	no	—
802	#525	—	53	4	no	—
803	#525	—	53	2	no	—
804	#525	—	53	4	no	—
805	#525	—	53	8	no	—
806	#525	—	53	8	no	—
807	#525	C₂×D₅₃	1	2	yes	complemented
808	C₂×#123	—	53	2	no	—
809	C₂×#123	—	53	2	no	—
810	C₂×#123	—	53	4	no	—
811	C₂×#123	C₂×D₅₃	1	2	yes	complemented
812	C₂×#123	C₂×D₅₃	1	2	yes	complemented
813	C₂×#121	—	53	2	no	—
814	C₂×#121	—	53	2	no	—
815	C₂×#121	—	53	4	no	—
816	C₂×#121	—	53	4	no	—
817	C₂×#120	—	53	2	no	—
818	C₂×#120	—	53	2	no	—
819	C₂×#120	—	53	2	no	—
820	C₂×#120	—	53	4	no	—
821	C₂×#120	—	53	4	no	—
822	C₂×#120	—	53	2	no	—
823	C₂×#120	—	53	4	no	—
824	#518	—	53	2	no	—
825	#518	—	53	1	no	—
826	#518	—	53	2	no	—
827	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
828	C₂×#117	—	53	1	no	—
829	C₂²×C₂²⋊C₄	—	53	2	no	—
830	C₅₃	#62862	1	1	yes	characteristic, complemented, Sylow
831	C₂⁵	—	53	2	no	—
832	C₂⁵	—	53	2	no	—
833	H(5,𝔽₂)	—	4	4	no	—
834	H(5,𝔽₂)	—	212	4	no	—
835	C₂×#41	—	4	4	no	—
836	C₂×#41	—	53	8	no	—
837	C₂×#41	—	53	4	no	—
838	C₂×#41	—	53	8	no	—
839	C₂×#41	—	53	2	no	—
840	C₂×#41	C₂²×D₅₃	1	4	yes	—
841	C₂×#41	C₂²×D₅₃	1	2	yes	—
842	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
843	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
844	C₂²×D₄	—	53	2	no	—
845	C₂²×D₄	—	53	4	no	—
846	C₂²×D₄	—	53	4	no	—
847	C₂²×D₄	—	53	4	no	—
848	C₂²×D₄	—	53	8	no	—
849	C₂²×D₄	—	53	2	no	—
850	C₂²×D₄	—	53	2	no	—
851	C₂²×D₄	—	53	8	no	—
852	C₂²×D₄	—	53	4	no	—
853	C₂²×D₄	—	53	8	no	—
854	C₂²×D₄	—	53	8	no	—
855	C₂²×D₄	—	53	4	no	—
856	C₂²×D₄	—	53	4	no	—
857	C₂²×D₄	—	53	2	no	—
858	C₂²×D₄	—	53	4	no	—
859	C₂²×D₄	—	53	2	no	—
860	C₂²×D₄	—	53	2	no	—
861	C₂²×D₄	—	212	4	no	—
862	C₂²×D₄	—	212	8	no	—
863	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
864	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
865	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
866	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
867	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
868	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
869	C₂³×C₄	—	53	4	no	—
870	C₂³×C₄	—	53	2	no	—
871	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
872	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
873	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
874	C₄⋊Q₈	—	53	4	no	—
875	C₄⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
876	#127	—	53	8	no	—
877	#127	—	53	4	no	—
878	#127	—	53	4	no	—
879	#127	—	53	8	no	—
880	#127	—	53	8	no	—
881	#126	—	53	8	no	—
882	#126	—	53	8	no	—
883	#126	—	53	8	no	—
884	#126	—	53	8	no	—
885	#126	—	53	8	no	—
886	#126	—	53	8	no	—
887	#126	—	53	8	no	—
888	#126	—	53	8	no	—
889	#125	—	53	8	no	—
890	#125	—	53	8	no	—
891	#125	—	53	8	no	—
892	#124	—	53	8	no	—
893	#124	—	53	4	no	—
894	#124	—	53	4	no	—
895	#124	—	53	8	no	—
896	#124	—	53	4	no	—
897	#124	—	53	8	no	—
898	#124	—	53	8	no	—
899	#124	—	53	8	no	—
900	#124	—	53	8	no	—
901	#124	—	53	8	no	—
902	#124	—	53	8	no	—
903	#124	C₂²×D₅₃	1	4	yes	complemented
904	#123	—	53	4	no	—
905	#123	—	53	4	no	—
906	#123	—	53	4	no	—
907	#123	—	53	4	no	—
908	#123	—	53	4	no	—
909	#123	—	53	8	no	—
910	#123	—	53	4	no	—
911	#123	—	53	8	no	—
912	#123	—	53	4	no	—
913	#123	—	53	8	no	—
914	#123	—	53	8	no	—
915	#123	—	53	8	no	—
916	#123	—	53	8	no	—
917	#123	—	53	8	no	—
918	#123	—	53	8	no	—
919	#123	—	53	8	no	—
920	#123	—	53	8	no	—
921	#123	—	53	8	no	—
922	#123	—	53	8	no	—
923	#123	—	53	8	no	—
924	#123	—	53	8	no	—
925	#123	—	53	8	no	—
926	#123	—	53	8	no	—
927	#123	—	53	8	no	—
928	#123	—	53	8	no	—
929	#123	C₂²×D₅₃	1	8	yes	—
930	#123	C₂²×D₅₃	1	4	yes	complemented
931	#123	C₂²×D₅₃	1	4	yes	complemented
932	#123	C₂²×D₅₃	1	4	yes	complemented
933	#123	C₂²×D₅₃	1	8	yes	complemented
934	#123	C₂²×D₅₃	1	4	yes	complemented
935	#123	C₂²×D₅₃	1	4	yes	complemented
936	C₂²⋊Q₈	—	53	8	no	—
937	C₂²⋊Q₈	—	53	8	no	—
938	C₂²⋊Q₈	—	53	4	no	—
939	C₂²⋊Q₈	—	53	8	no	—
940	C₂²⋊Q₈	—	53	8	no	—
941	C₂²⋊Q₈	—	53	8	no	—
942	C₂²⋊Q₈	—	53	8	no	—
943	C₂²⋊Q₈	—	53	8	no	—
944	C₂²⋊Q₈	—	53	8	no	—
945	C₂²⋊Q₈	—	53	8	no	—
946	C₂²⋊Q₈	—	53	8	no	—
947	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
948	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
949	#121	—	53	8	no	—
950	#121	—	53	8	no	—
951	#121	—	53	8	no	—
952	#121	—	53	8	no	—
953	#121	—	53	8	no	—
954	#121	—	53	8	no	—
955	#121	—	53	8	no	—
956	#121	—	53	8	no	—
957	#121	—	53	8	no	—
958	#121	—	53	8	no	—
959	#121	—	53	4	no	—
960	#121	—	53	4	no	—
961	#121	—	53	4	no	—
962	#121	—	53	4	no	—
963	#121	—	53	8	no	—
964	#121	—	53	8	no	—
965	#121	—	53	4	no	—
966	#121	—	53	8	no	—
967	#121	—	53	8	no	—
968	#121	—	53	8	no	—
969	#121	—	53	8	no	—
970	#121	—	53	8	no	—
971	#121	—	53	8	no	—
972	#121	—	53	8	no	—
973	#121	—	53	8	no	—
974	#121	—	53	8	no	—
975	#121	—	53	8	no	—
976	#121	—	53	8	no	—
977	#121	—	53	8	no	—
978	#121	—	53	8	no	—
979	#121	—	53	8	no	—
980	#121	—	53	8	no	—
981	#121	—	53	8	no	—
982	#121	—	53	8	no	—
983	#121	C₂²×D₅₃	1	8	yes	—
984	#121	C₂²×D₅₃	1	4	yes	complemented
985	#121	C₂²×D₅₃	1	8	yes	complemented
986	#120	—	53	4	no	—
987	#120	—	53	4	no	—
988	#120	—	53	8	no	—
989	#120	—	53	4	no	—
990	#120	—	53	4	no	—
991	#120	—	53	4	no	—
992	#120	—	53	4	no	—
993	#120	—	53	4	no	—
994	#120	—	53	4	no	—
995	#120	—	53	8	no	—
996	#120	—	53	4	no	—
997	#120	—	53	4	no	—
998	#120	—	53	8	no	—
999	#120	—	53	8	no	—
1000	#120	—	53	8	no	—
1001	#120	—	53	8	no	—
1002	#120	—	53	8	no	—
1003	#120	—	53	4	no	—
1004	#120	—	53	4	no	—
1005	#120	—	53	4	no	—
1006	#120	—	53	8	no	—
1007	#120	—	53	8	no	—
1008	#120	—	53	8	no	—
1009	#120	—	53	8	no	—
1010	#120	—	53	8	no	—
1011	#120	—	53	8	no	—
1012	#120	—	53	8	no	—
1013	#120	C₂²×D₅₃	1	4	yes	complemented
1014	#120	C₂²×D₅₃	1	4	yes	complemented
1015	#120	C₂²×D₅₃	1	4	yes	complemented
1016	C₄×Q₈	—	53	8	no	—
1017	C₄×D₄	—	53	8	no	—
1018	C₄×D₄	—	53	8	no	—
1019	C₄×D₄	—	53	8	no	—
1020	C₄×D₄	—	53	8	no	—
1021	C₄×D₄	—	53	8	no	—
1022	C₄×D₄	—	53	8	no	—
1023	C₄×D₄	—	53	8	no	—
1024	C₄×D₄	—	53	8	no	—
1025	C₄×D₄	—	53	8	no	—
1026	C₄×D₄	—	53	8	no	—
1027	C₄×D₄	—	53	8	no	—
1028	C₄×D₄	—	53	8	no	—
1029	C₄×D₄	—	53	8	no	—
1030	C₄×D₄	—	53	8	no	—
1031	C₄×D₄	—	53	8	no	—
1032	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1033	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1034	#117	—	53	8	no	—
1035	#117	—	53	4	no	—
1036	#117	—	53	2	no	—
1037	#117	—	53	8	no	—
1038	#117	—	53	8	no	—
1039	#117	—	53	4	no	—
1040	#117	—	53	8	no	—
1041	#117	—	53	8	no	—
1042	#117	C₂²×D₅₃	1	2	yes	complemented
1043	C₂×C₄⋊C₄	—	53	2	no	—
1044	C₂×C₄⋊C₄	—	53	4	no	—
1045	C₂×C₄⋊C₄	—	53	4	no	—
1046	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1047	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1048	C₂×C₂²⋊C₄	—	53	2	no	—
1049	C₂×C₂²⋊C₄	—	53	2	no	—
1050	C₂×C₂²⋊C₄	—	53	4	no	—
1051	C₂×C₂²⋊C₄	—	53	2	no	—
1052	C₂×C₂²⋊C₄	—	53	4	no	—
1053	C₂×C₂²⋊C₄	—	53	4	no	—
1054	C₂×C₂²⋊C₄	—	53	4	no	—
1055	C₂×C₂²⋊C₄	—	53	4	no	—
1056	C₂×C₂²⋊C₄	—	53	4	no	—
1057	C₂×C₂²⋊C₄	—	53	4	no	—
1058	C₂×C₂²⋊C₄	—	53	8	no	—
1059	C₂×C₂²⋊C₄	—	53	4	no	—
1060	C₂×C₂²⋊C₄	—	53	8	no	—
1061	C₂×C₂²⋊C₄	—	53	8	no	—
1062	C₂×C₂²⋊C₄	—	53	4	no	—
1063	C₂×C₂²⋊C₄	—	53	8	no	—
1064	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1065	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1066	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1067	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1068	C₂×C₄²	—	53	2	no	—
1069	C₂⁴	—	53	4	no	—
1070	C₂⁴	—	53	4	no	—
1071	C₂⁴	—	53	2	no	—
1072	C₂⁴	—	53	2	no	—
1073	C₂⁴	—	53	2	no	—
1074	C₂⁴	—	53	8	no	—
1075	C₂⁴	—	53	2	no	—
1076	C₂⁴	—	106	8	no	—
1077	C₂⁴	—	424	4	no	—
1078	C₂⁴	—	424	4	no	—
1079	C₂⁴	—	212	4	no	—
1080	C₂⁴	C₂³×D₅₃	1	2	yes	—
1081	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1082	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1083	C₂⁴	C₂³×D₅₃	1	2	yes	—
1084	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1085	#41	—	4	16	no	—
1086	#41	—	4	4	no	—
1087	#41	—	4	8	no	—
1088	#41	—	424	8	no	—
1089	#41	—	424	8	no	—
1090	#41	—	212	4	no	—
1091	#41	—	212	8	no	—
1092	C₂×Q₈	—	4	2	no	—
1093	C₂×Q₈	—	53	8	no	—
1094	C₂×Q₈	—	53	2	no	—
1095	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1096	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1097	C₂×D₄	—	2	8	no	—
1098	C₂×D₄	—	2	4	no	—
1099	C₂×D₄	—	2	4	no	—
1100	C₂×D₄	—	4	2	no	—
1101	C₂×D₄	—	4	4	no	—
1102	C₂×D₄	—	4	8	no	—
1103	C₂×D₄	—	53	4	no	—
1104	C₂×D₄	—	53	4	no	—
1105	C₂×D₄	—	53	8	no	—
1106	C₂×D₄	—	53	8	no	—
1107	C₂×D₄	—	53	8	no	—
1108	C₂×D₄	—	53	8	no	—
1109	C₂×D₄	—	53	8	no	—
1110	C₂×D₄	—	53	8	no	—
1111	C₂×D₄	—	53	8	no	—
1112	C₂×D₄	—	53	8	no	—
1113	C₂×D₄	—	53	4	no	—
1114	C₂×D₄	—	53	8	no	—
1115	C₂×D₄	—	53	8	no	—
1116	C₂×D₄	—	53	8	no	—
1117	C₂×D₄	—	53	2	no	—
1118	C₂×D₄	—	53	2	no	—
1119	C₂×D₄	—	53	2	no	—
1120	C₂×D₄	—	53	4	no	—
1121	C₂×D₄	—	53	4	no	—
1122	C₂×D₄	—	53	8	no	—
1123	C₂×D₄	—	53	2	no	—
1124	C₂×D₄	—	53	2	no	—
1125	C₂×D₄	—	106	8	no	—
1126	C₂×D₄	—	424	4	no	—
1127	C₂×D₄	—	424	8	no	—
1128	C₂×D₄	—	424	4	no	—
1129	C₂×D₄	—	424	4	no	—
1130	C₂×D₄	—	424	4	no	—
1131	C₂×D₄	—	424	8	no	—
1132	C₂×D₄	—	212	4	no	—
1133	C₂×D₄	—	212	4	no	—
1134	C₂×D₄	—	212	8	no	—
1135	C₂×D₄	—	212	8	no	—
1136	C₂×D₄	—	212	4	no	—
1137	C₂×D₄	—	212	4	no	—
1138	C₂×D₄	—	212	16	no	—
1139	C₂×D₄	—	212	16	no	—
1140	C₂×D₄	—	212	8	no	—
1141	C₂×D₄	—	212	4	no	—
1142	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1143	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1144	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1145	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1146	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1147	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1148	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1149	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1150	C₂²×C₄	—	2	4	no	—
1151	C₂²×C₄	—	4	2	no	—
1152	C₂²×C₄	—	4	2	no	—
1153	C₂²×C₄	—	53	2	no	—
1154	C₂²×C₄	—	53	4	no	—
1155	C₂²×C₄	—	53	4	no	—
1156	C₂²×C₄	—	53	4	no	—
1157	C₂²×C₄	—	53	8	no	—
1158	C₂²×C₄	—	53	2	no	—
1159	C₂²×C₄	—	53	8	no	—
1160	C₂²×C₄	—	53	8	no	—
1161	C₂²×C₄	—	53	8	no	—
1162	C₂²×C₄	—	53	4	no	—
1163	C₂²×C₄	—	53	8	no	—
1164	C₂²×C₄	—	424	4	no	—
1165	C₂²×C₄	—	212	4	no	—
1166	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1167	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1168	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1169	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1170	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1171	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1172	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1173	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1174	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1175	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1176	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1177	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1178	C₄⋊C₄	—	53	8	no	—
1179	C₄⋊C₄	—	53	4	no	—
1180	C₄⋊C₄	—	53	4	no	—
1181	C₄⋊C₄	—	53	8	no	—
1182	C₄⋊C₄	—	53	8	no	—
1183	C₄⋊C₄	—	53	8	no	—
1184	C₄⋊C₄	—	53	8	no	—
1185	C₄⋊C₄	—	53	8	no	—
1186	C₄⋊C₄	—	53	8	no	—
1187	C₄⋊C₄	—	53	4	no	—
1188	C₄⋊C₄	—	53	8	no	—
1189	C₄⋊C₄	—	53	8	no	—
1190	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1191	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1192	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1193	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1194	C₂²⋊C₄	—	53	4	no	—
1195	C₂²⋊C₄	—	53	4	no	—
1196	C₂²⋊C₄	—	53	4	no	—
1197	C₂²⋊C₄	—	53	4	no	—
1198	C₂²⋊C₄	—	53	8	no	—
1199	C₂²⋊C₄	—	53	8	no	—
1200	C₂²⋊C₄	—	53	4	no	—
1201	C₂²⋊C₄	—	53	8	no	—
1202	C₂²⋊C₄	—	53	8	no	—
1203	C₂²⋊C₄	—	53	8	no	—
1204	C₂²⋊C₄	—	53	8	no	—
1205	C₂²⋊C₄	—	53	8	no	—
1206	C₂²⋊C₄	—	53	8	no	—
1207	C₂²⋊C₄	—	53	8	no	—
1208	C₂²⋊C₄	—	53	8	no	—
1209	C₂²⋊C₄	—	53	8	no	—
1210	C₂²⋊C₄	—	53	8	no	—
1211	C₂²⋊C₄	—	53	8	no	—
1212	C₂²⋊C₄	—	53	8	no	—
1213	C₂²⋊C₄	—	53	8	no	—
1214	C₂²⋊C₄	—	53	8	no	—
1215	C₂²⋊C₄	—	53	8	no	—
1216	C₂²⋊C₄	—	53	8	no	—
1217	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1218	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1219	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1220	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1221	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1222	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1223	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1224	C₄²	—	53	4	no	—
1225	C₄²	—	53	4	no	—
1226	C₄²	—	53	4	no	—
1227	C₄²	—	53	8	no	—
1228	C₄²	—	53	8	no	—
1229	C₄²	C₂³×D₅₃	1	4	yes	—
1230	C₂³	—	2	2	no	—
1231	C₂³	—	2	2	no	—
1232	C₂³	—	2	4	no	—
1233	C₂³	—	4	2	no	—
1234	C₂³	—	4	2	no	—
1235	C₂³	—	4	2	no	—
1236	C₂³	—	4	4	no	—
1237	C₂³	—	4	2	no	—
1238	C₂³	—	4	4	no	—
1239	C₂³	—	53	4	no	—
1240	C₂³	—	53	4	no	—
1241	C₂³	—	53	4	no	—
1242	C₂³	—	106	4	no	—
1243	C₂³	—	106	8	no	—
1244	C₂³	—	106	8	no	—
1245	C₂³	—	106	4	no	—
1246	C₂³	—	106	4	no	—
1247	C₂³	—	424	16	no	—
1248	C₂³	—	424	16	no	—
1249	C₂³	—	212	4	no	—
1250	C₂³	—	212	2	no	—
1251	C₂³	—	212	4	no	—
1252	C₂³	—	212	4	no	—
1253	C₂³	—	212	4	no	—
1254	C₂³	—	212	4	no	—
1255	C₂³	—	212	4	no	—
1256	C₂³	—	212	8	no	—
1257	C₂³	—	212	8	no	—
1258	C₂³	—	212	8	no	—
1259	C₂³	—	212	4	no	—
1260	C₂³	—	212	4	no	—
1261	C₂³	#13133262	1	4	yes	—
1262	C₂³	C₂⁴×D₅₃	1	4	yes	—
1263	C₂³	C₂⁴×D₅₃	1	2	yes	—
1264	C₂³	C₂⁴×D₅₃	1	2	yes	—
1265	C₂³	C₂⁴×D₅₃	1	2	yes	—
1266	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1267	Q₈	—	4	4	no	—
1268	Q₈	—	4	2	no	—
1269	Q₈	—	212	8	no	—
1270	Q₈	—	212	2	no	—
1271	D₄	—	2	8	no	—
1272	D₄	—	2	8	no	—
1273	D₄	—	2	8	no	—
1274	D₄	—	2	8	no	—
1275	D₄	—	4	2	no	—
1276	D₄	—	4	4	no	—
1277	D₄	—	4	4	no	—
1278	D₄	—	4	8	no	—
1279	D₄	—	106	8	no	—
1280	D₄	—	106	8	no	—
1281	D₄	—	212	8	no	—
1282	D₄	—	212	8	no	—
1283	D₄	—	212	2	no	—
1284	D₄	—	212	4	no	—
1285	D₄	—	212	2	no	—
1286	D₄	—	212	2	no	—
1287	D₄	—	212	4	no	—
1288	D₄	—	212	2	no	—
1289	D₄	—	212	8	no	—
1290	D₄	—	212	2	no	—
1291	D₄	—	212	8	no	—
1292	D₄	—	212	8	no	—
1293	D₄	—	212	8	no	—
1294	D₄	—	212	8	no	—
1295	D₄	—	212	8	no	—
1296	D₄	—	212	8	no	—
1297	D₄	—	212	8	no	—
1298	D₄	—	212	8	no	—
1299	D₄	—	212	8	no	—
1300	D₄	—	212	4	no	—
1301	C₂×C₄	—	2	2	no	—
1302	C₂×C₄	—	2	2	no	—
1303	C₂×C₄	—	2	8	no	—
1304	C₂×C₄	—	2	2	no	—
1305	C₂×C₄	—	2	2	no	—
1306	C₂×C₄	—	2	4	no	—
1307	C₂×C₄	—	4	4	no	—
1308	C₂×C₄	—	4	4	no	—
1309	C₂×C₄	—	4	4	no	—
1310	C₂×C₄	—	4	4	no	—
1311	C₂×C₄	—	4	2	no	—
1312	C₂×C₄	—	4	4	no	—
1313	C₂×C₄	—	53	8	no	—
1314	C₂×C₄	—	53	8	no	—
1315	C₂×C₄	—	53	4	no	—
1316	C₂×C₄	—	106	4	no	—
1317	C₂×C₄	—	212	8	no	—
1318	C₂×C₄	—	212	8	no	—
1319	C₂×C₄	—	212	8	no	—
1320	C₂×C₄	—	212	8	no	—
1321	C₂×C₄	—	212	4	no	—
1322	C₂×C₄	—	212	4	no	—
1323	C₂×C₄	—	212	4	no	—
1324	C₂×C₄	—	212	8	no	—
1325	C₂×C₄	—	212	2	no	—
1326	C₂×C₄	—	212	4	no	—
1327	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1328	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1329	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1330	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1331	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1332	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1333	C₂²	—	2	4	no	—
1334	C₂²	—	2	2	no	—
1335	C₂²	—	2	2	no	—
1336	C₂²	—	2	2	no	—
1337	C₂²	—	2	4	no	—
1338	C₂²	—	2	4	no	—
1339	C₂²	—	2	4	no	—
1340	C₂²	—	2	8	no	—
1341	C₂²	—	4	4	no	—
1342	C₂²	—	8	4	no	—
1343	C₂²	—	8	2	no	—
1344	C₂²	—	8	2	no	—
1345	C₂²	—	16	2	no	—
1346	C₂²	—	848	2	no	—
1347	C₂²	—	106	4	no	—
1348	C₂²	—	106	4	no	—
1349	C₂²	—	106	4	no	—
1350	C₂²	—	106	4	no	—
1351	C₂²	—	106	4	no	—
1352	C₂²	—	106	8	no	—
1353	C₂²	—	106	4	no	—
1354	C₂²	—	106	4	no	—
1355	C₂²	—	424	8	no	—
1356	C₂²	—	424	4	no	—
1357	C₂²	—	424	8	no	—
1358	C₂²	—	424	16	no	—
1359	C₂²	—	212	8	no	—
1360	C₂²	—	212	8	no	—
1361	C₂²	C₂×#13133262	1	2	yes	—
1362	C₂²	C₂×#13133262	1	4	yes	—
1363	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1364	C₄	—	2	2	no	—
1365	C₄	—	2	2	no	—
1366	C₄	—	2	2	no	—
1367	C₄	—	2	4	no	—
1368	C₄	—	2	2	no	—
1369	C₄	—	2	8	no	—
1370	C₄	—	106	4	no	—
1371	C₄	—	106	8	no	—
1372	C₄	—	106	8	no	—
1373	C₂	—	2	2	no	—
1374	C₂	—	2	4	no	—
1375	C₂	—	4	4	no	—
1376	C₂	—	4	2	no	—
1377	C₂	—	4	2	no	—
1378	C₂	—	212	4	no	—
1379	C₂	—	212	4	no	—
1380	C₂	—	212	4	no	—
1381	C₂	C₂²×#13133262	1	1	yes	characteristic
1382	C₂	#20289526	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3485	C₂
hypercenter	#3485	D₅₃
hypocenter	C₅₃	#62862
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3485

Complements

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

N	H ≅ G/N	type
1. #20289069	C₂	semidirect
2. #20289042	C₂	semidirect
3. #20289032	C₂	semidirect
4. #20289016	C₂	semidirect
5. #20288909	C₂	semidirect
6. #20288899	C₂	semidirect
7. #20288885	C₂	semidirect
8. #20288864	C₂	semidirect
9. #20288411	C₂	semidirect
10. #20288403	C₂	semidirect
11. #20288400	C₂	semidirect
12. #20288359	C₂	semidirect
13. #20288347	C₂	semidirect
14. #20288346	C₂	semidirect
15. C₂×#16811187	C₂	semidirect
16. C₂×#16811184	C₂	semidirect
17. C₅₃×#3485	C₂	semidirect
18. C₂×#13133262	C₂²	semidirect
19. C₂³×D₂₁₂	C₂²	semidirect
20. C₂²×D₄×D₅₃	C₂²	semidirect
21. #16811372	C₂²	semidirect
22. #16811370	C₂²	semidirect
23. #16811369	C₂²	semidirect
24. #16811369	C₂²	semidirect
25. #16811365	C₂²	semidirect
26. #16811363	C₂²	semidirect
27. #16811363	C₂²	semidirect
28. #16811362	C₂²	semidirect
29. #16811361	C₂²	semidirect
30. #16811361	C₂²	semidirect
31. #16811357	C₂²	semidirect
32. #16811339	C₂²	semidirect
33. #16811335	C₂²	semidirect
34. #16811322	C₂²	semidirect
35. #16811321	C₂²	semidirect
36. #16811310	C₂²	semidirect
37. #16811308	C₂²	semidirect
38. #16811302	C₂²	semidirect
39. #16811300	C₂²	semidirect
40. #16811299	C₂²	semidirect
41. #16811297	C₂²	semidirect
42. #16811296	C₂²	semidirect
43. #16811296	C₂²	semidirect
44. #16811296	C₂²	semidirect
45. #16811291	C₂²	semidirect
46. #16811272	C₂²	semidirect
47. #16811269	C₂²	semidirect
48. #16811268	C₂²	semidirect
49. #16811265	C₂²	semidirect
50. #16811263	C₂²	semidirect
51. #16811263	C₂²	semidirect
52. #16811262	C₂²	semidirect
53. #16811261	C₂²	semidirect
54. #16811261	C₂²	semidirect
55. #16811261	C₂²	semidirect
56. #16811260	C₂²	semidirect
57. #16811260	C₂²	semidirect
58. #16811257	C₂²	semidirect
59. D₄×C₂²⋊D₅₃	C₂²	semidirect
60. D₄×C₂²⋊D₅₃	C₂²	semidirect
61. #16811255	C₂²	semidirect
62. #16811255	C₂²	semidirect
63. #16811249	C₂²	semidirect
64. #16811247	C₂²	semidirect
65. #16811243	C₂²	semidirect
66. #16811225	C₂²	semidirect
67. #16811225	C₂²	semidirect
68. #16811224	C₂²	semidirect
69. #16811223	C₂²	semidirect
70. #16811222	C₂²	semidirect
71. #16811220	C₂²	semidirect
72. #16811217	C₂²	semidirect
73. #16811213	C₂²	semidirect
74. #16811213	C₂²	semidirect
75. #16811211	C₂²	semidirect
76. #16811210	C₂²	semidirect
77. #16811209	C₂²	semidirect
78. #16811207	C₂²	semidirect
79. #16811206	C₂²	semidirect
80. #16811206	C₂²	semidirect
81. #16811204	C₂²	semidirect
82. #16811200	C₂²	semidirect
83. #16811197	C₂²	semidirect
84. #16811189	C₂²	semidirect
85. #16811188	C₂²	semidirect
86. #16811188	C₂²	semidirect
87. #16811187	C₂²	semidirect
88. #16811187	C₂²	semidirect
89. #16811187	C₂²	semidirect
90. #16811185	C₂²	semidirect
91. #16811184	C₂²	semidirect
92. #16811184	C₂²	semidirect
93. #16811184	C₂²	semidirect
94. #16811184	C₂²	semidirect
95. #16811184	C₂²	semidirect
97. #16811182	C₂²	semidirect
98. #16811182	C₂²	semidirect
99. #16811182	C₂²	semidirect
100. #16811181	C₂²	semidirect
101. C₂×#13133213	C₂²	semidirect
102. #16811150	C₂²	semidirect
103. C₂×#13133206	C₂²	semidirect
104. #16811134	C₂²	semidirect
105. #16811133	C₂²	semidirect
106. #16811132	C₂²	semidirect
107. #16811131	C₂²	semidirect
108. #16811130	C₂²	semidirect
109. C₂×#13133202	C₂²	semidirect
110. C₂×#13133200	C₂²	semidirect
111. C₂×#13133200	C₂²	semidirect
112. C₂×#13133192	C₂²	semidirect
113. C₂×#13133191	C₂²	semidirect
114. C₂×#13133191	C₂²	semidirect
115. C₂×#13133190	C₂²	semidirect
116. C₂×#13133187	C₂²	semidirect
117. C₂×#13133187	C₂²	semidirect
118. C₂×#13133185	C₂²	semidirect
119. C₂×#13133185	C₂²	semidirect
120. C₂×#13133185	C₂²	semidirect
121. C₂×#13133185	C₂²	semidirect
122. #120×D₅₃	C₂²	semidirect
123. #16811098	C₂²	semidirect
124. #16811098	C₂²	semidirect
125. #16811096	C₂²	semidirect
126. C₂×#13133176	C₂²	semidirect
127. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
128. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
129. C₂²×#41×C₅₃	C₂²	semidirect
130. C₅₃×#547	C₂²	semidirect
131. C₅₃×#546	C₂²	semidirect
132. C₅₃×#536	C₂²	semidirect
133. C₅₃×#534	C₂²	semidirect
134. C₅₃×#534	C₂²	semidirect
135. C₅₃×#525	C₂²	semidirect
136. C₂×#123×C₅₃	C₂²	semidirect
137. C₂×#123×C₅₃	C₂²	semidirect
138. C₅₃×#518	C₂²	semidirect
140. C₂⁴×D₅₃	C₂³	semidirect
143. C₂×#11719945	C₂³	semidirect
145. C₂×#11719947	C₂³	semidirect
152. C₂²×D₂₁₂	C₂³	semidirect
156. C₂²×C₂²⋊D₅₃	C₂³	semidirect
157. C₂²×C₂²⋊D₅₃	C₂³	semidirect
158. C₂²×C₂²⋊D₅₃	C₂³	semidirect
159. C₂²×C₂²⋊D₅₃	C₂³	semidirect
163. C₂×D₄×D₅₃	C₂³	semidirect
164. C₂×D₄×D₅₃	C₂³	semidirect
165. C₂²×C₄×D₅₃	C₂³	semidirect
166. C₂²×C₄×D₅₃	C₂³	semidirect
167. #13133215	C₂³	semidirect
169. #13133213	C₂³	semidirect
170. #13133213	C₂³	semidirect
171. #13133213	C₂³	semidirect
172. #13133213	C₂³	semidirect
173. #13133212	C₂³	semidirect
174. #13133212	C₂³	semidirect
175. #13133212	C₂³	semidirect
176. #13133212	C₂³	semidirect
177. #13133212	C₂³	semidirect
178. #13133211	C₂³	semidirect
179. #13133210	C₂³	semidirect
180. #13133210	C₂³	semidirect
181. #13133208	C₂³	semidirect
182. #13133207	C₂³	semidirect
183. #13133207	C₂³	semidirect
185. #13133206	C₂³	semidirect
186. #13133206	C₂³	semidirect
187. #13133206	C₂³	semidirect
188. #13133206	C₂³	semidirect
189. #13133205	C₂³	semidirect
190. #13133203	C₂³	semidirect
191. #13133203	C₂³	semidirect
192. #13133203	C₂³	semidirect
193. #13133203	C₂³	semidirect
194. #13133203	C₂³	semidirect
197. #13133202	C₂³	semidirect
198. #13133202	C₂³	semidirect
199. #13133202	C₂³	semidirect
200. #13133202	C₂³	semidirect
201. #13133202	C₂³	semidirect
202. #13133201	C₂³	semidirect
203. #13133201	C₂³	semidirect
204. #13133201	C₂³	semidirect
207. #13133200	C₂³	semidirect
208. #13133200	C₂³	semidirect
209. #13133200	C₂³	semidirect
210. #13133200	C₂³	semidirect
211. #13133200	C₂³	semidirect
212. #13133200	C₂³	semidirect
213. #13133199	C₂³	semidirect
214. #13133199	C₂³	semidirect
215. #13133199	C₂³	semidirect
216. #13133199	C₂³	semidirect
218. #13133198	C₂³	semidirect
219. #13133198	C₂³	semidirect
220. #13133197	C₂³	semidirect
221. #13133197	C₂³	semidirect
222. #13133196	C₂³	semidirect
223. #13133196	C₂³	semidirect
224. #13133195	C₂³	semidirect
225. #13133195	C₂³	semidirect
226. #13133194	C₂³	semidirect
227. #13133194	C₂³	semidirect
228. #13133194	C₂³	semidirect
229. #13133193	C₂³	semidirect
230. #13133193	C₂³	semidirect
233. #13133192	C₂³	semidirect
234. #13133192	C₂³	semidirect
235. #13133192	C₂³	semidirect
238. #13133191	C₂³	semidirect
239. #13133191	C₂³	semidirect
240. #13133191	C₂³	semidirect
241. #13133191	C₂³	semidirect
242. #13133191	C₂³	semidirect
243. #13133191	C₂³	semidirect
244. #13133191	C₂³	semidirect
245. #13133191	C₂³	semidirect
248. #13133190	C₂³	semidirect
249. #13133190	C₂³	semidirect
250. #13133190	C₂³	semidirect
251. #13133190	C₂³	semidirect
252. #13133190	C₂³	semidirect
253. #13133190	C₂³	semidirect
254. #13133190	C₂³	semidirect
257. #13133189	C₂³	semidirect
258. #13133189	C₂³	semidirect
259. #13133189	C₂³	semidirect
260. #13133189	C₂³	semidirect
261. #13133189	C₂³	semidirect
262. #13133189	C₂³	semidirect
263. #13133188	C₂³	semidirect
264. #13133188	C₂³	semidirect
270. #13133187	C₂³	semidirect
271. #13133187	C₂³	semidirect
272. #13133187	C₂³	semidirect
273. #13133187	C₂³	semidirect
275. #13133186	C₂³	semidirect
276. #13133186	C₂³	semidirect
283. #13133185	C₂³	semidirect
284. #13133185	C₂³	semidirect
285. #13133185	C₂³	semidirect
286. #13133185	C₂³	semidirect
287. #13133185	C₂³	semidirect
288. #13133185	C₂³	semidirect
289. #13133185	C₂³	semidirect
290. #13133185	C₂³	semidirect
291. #13133185	C₂³	semidirect
292. #13133182	C₂³	semidirect
293. C₄×D₂₁₂	C₂³	semidirect
295. D₄×Dic₅₃	C₂³	semidirect
296. D₄×Dic₅₃	C₂³	semidirect
297. #13133179	C₂³	semidirect
299. C₄×C₂²⋊D₅₃	C₂³	semidirect
300. C₄×C₂²⋊D₅₃	C₂³	semidirect
301. C₄×C₂²⋊D₅₃	C₂³	semidirect
302. C₄×C₂²⋊D₅₃	C₂³	semidirect
303. #13133177	C₂³	semidirect
304. #13133177	C₂³	semidirect
305. #13133177	C₂³	semidirect
306. #13133177	C₂³	semidirect
307. #13133177	C₂³	semidirect
308. #13133176	C₂³	semidirect
309. #13133176	C₂³	semidirect
310. #13133176	C₂³	semidirect
311. #13133175	C₂³	semidirect
312. #13133175	C₂³	semidirect
313. #13133174	C₂³	semidirect
314. #13133173	C₂³	semidirect
315. #13133173	C₂³	semidirect
316. C₂×C₄⋊Dic₅₃	C₂³	semidirect
317. C₂×#11719919	C₂³	semidirect
318. C₂×#11719919	C₂³	semidirect
321. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
322. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
325. C₂×#11719921	C₂³	semidirect
326. C₂×#11719921	C₂³	semidirect
327. C₂×#11719921	C₂³	semidirect
328. C₂×#11719921	C₂³	semidirect
329. C₂×#11719921	C₂³	semidirect
330. C₂×#11719921	C₂³	semidirect
332. C₂²⋊C₄×D₅₃	C₂³	semidirect
333. C₂²⋊C₄×D₅₃	C₂³	semidirect
334. C₂²⋊C₄×D₅₃	C₂³	semidirect
335. C₂×C₄×Dic₅₃	C₂³	semidirect
340. C₂×#41×C₅₃	C₂³	semidirect
341. C₂²×Q₈×C₅₃	C₂³	semidirect
347. C₂²×D₄×C₅₃	C₂³	semidirect
349. C₂³×C₄×C₅₃	C₂³	semidirect
350. C₂³×C₄×C₅₃	C₂³	semidirect
351. C₄⋊Q₈×C₅₃	C₂³	semidirect
352. #124×C₅₃	C₂³	semidirect
354. #123×C₅₃	C₂³	semidirect
355. #123×C₅₃	C₂³	semidirect
356. #123×C₅₃	C₂³	semidirect
357. #123×C₅₃	C₂³	semidirect
358. #123×C₅₃	C₂³	semidirect
359. #123×C₅₃	C₂³	semidirect
360. C₂²⋊Q₈×C₅₃	C₂³	semidirect
361. C₂²⋊Q₈×C₅₃	C₂³	semidirect
363. #121×C₅₃	C₂³	semidirect
364. #121×C₅₃	C₂³	semidirect
365. #120×C₅₃	C₂³	semidirect
366. #120×C₅₃	C₂³	semidirect
367. #120×C₅₃	C₂³	semidirect
368. C₄×D₄×C₅₃	C₂³	semidirect
369. C₄×D₄×C₅₃	C₂³	semidirect
370. #117×C₅₃	C₂³	semidirect
371. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
372. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
374. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
375. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
376. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
694. #3485	D₅₃	semidirect
710. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
711. C₂²×#41	C₂×D₅₃	semidirect
740. #547	C₂×D₅₃	semidirect
752. #546	C₂×D₅₃	semidirect
779. #536	C₂×D₅₃	semidirect
797. #534	C₂×D₅₃	semidirect
798. #534	C₂×D₅₃	semidirect
807. #525	C₂×D₅₃	semidirect
811. C₂×#123	C₂×D₅₃	semidirect
812. C₂×#123	C₂×D₅₃	semidirect
827. #518	C₂×D₅₃	semidirect
830. C₅₃	#62862	semidirect
842. C₂×#41	C₂²×D₅₃	semidirect
843. C₂²×Q₈	C₂²×D₅₃	semidirect
868. C₂²×D₄	C₂²×D₅₃	semidirect
872. C₂³×C₄	C₂²×D₅₃	semidirect
873. C₂³×C₄	C₂²×D₅₃	semidirect
875. C₄⋊Q₈	C₂²×D₅₃	semidirect
903. #124	C₂²×D₅₃	semidirect
930. #123	C₂²×D₅₃	semidirect
931. #123	C₂²×D₅₃	semidirect
932. #123	C₂²×D₅₃	semidirect
933. #123	C₂²×D₅₃	semidirect
934. #123	C₂²×D₅₃	semidirect
935. #123	C₂²×D₅₃	semidirect
947. C₂²⋊Q₈	C₂²×D₅₃	semidirect
948. C₂²⋊Q₈	C₂²×D₅₃	semidirect
984. #121	C₂²×D₅₃	semidirect
985. #121	C₂²×D₅₃	semidirect
1013. #120	C₂²×D₅₃	semidirect
1014. #120	C₂²×D₅₃	semidirect
1015. #120	C₂²×D₅₃	semidirect
1032. C₄×D₄	C₂²×D₅₃	semidirect
1033. C₄×D₄	C₂²×D₅₃	semidirect
1042. #117	C₂²×D₅₃	semidirect
1046. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1047. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1065. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1066. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1067. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20289069	2
#20289042	2
#20289032	2
#20289016	2
#20288909	2
#20288899	2
#20288885	2
#20288864	2
#20288411	2
#20288403	2
#20288400	2
#20288359	2
#20288347	2
#20288346	2
C₂×#16811187	2
C₂×#16811184	2
C₅₃×#3485	2
#62862	53