Subgroups — #28293135

Order 13568.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288785	C₂	1	4	yes	maximal, complemented
2	#20288783	C₂	1	4	yes	maximal, complemented
3	#20288747	C₂	1	4	yes	maximal, complemented
4	#20288737	C₂	1	4	yes	maximal, complemented
5	#20288676	C₂	1	4	yes	maximal, complemented
6	#20288666	C₂	1	4	yes	maximal, complemented
7	#20288657	C₂	1	4	yes	maximal, complemented
8	#20288655	C₂	1	4	yes	maximal, complemented
9	#20288560	C₂	1	2	yes	maximal, complemented
10	#20288545	C₂	1	4	yes	maximal, complemented
11	#20288513	C₂	1	1	yes	maximal, characteristic, complemented
12	#20288474	C₂	1	1	yes	maximal, characteristic, complemented
13	#20288428	C₂	1	2	yes	maximal, complemented
14	#20288400	C₂	1	4	yes	maximal, complemented
15	#20288351	C₂	1	1	yes	maximal, characteristic, complemented
16	#20288346	C₂	1	1	yes	maximal, characteristic, complemented
17	#20288131	C₂	1	2	yes	maximal, complemented
18	#20288124	C₂	1	4	yes	maximal, complemented
19	#20288100	C₂	1	2	yes	maximal, complemented
20	C₂×#16811206	C₂	1	4	yes	maximal, complemented
21	C₄×#13133262	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16811095	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×H(5,𝔽₂)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133262	C₂²	1	1	yes	characteristic
25	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
26	#16811358	C₂²	1	4	yes	complemented
27	#16811356	C₂²	1	4	yes	complemented
28	#16811346	C₂²	1	4	yes	complemented
29	#16811345	C₂²	1	4	yes	complemented
30	#16811341	C₂²	1	4	yes	complemented
31	#16811338	C₂²	1	4	yes	complemented
32	#16811336	C₂²	1	4	yes	complemented
33	#16811336	C₂²	1	4	yes	complemented
34	#16811332	C₂²	1	4	yes	complemented
35	#16811332	C₂²	1	4	yes	complemented
36	#16811330	C₂²	1	4	yes	complemented
37	#16811323	C₂²	1	4	yes	complemented
38	#16811322	C₂²	1	8	yes	complemented
39	#16811322	C₂²	1	8	yes	complemented
40	#16811321	C₂²	1	4	yes	complemented
41	#16811321	C₂²	1	4	yes	complemented
42	#16811319	C₂²	1	8	yes	complemented
43	#16811317	C₂²	1	4	yes	complemented
44	#16811314	C₂²	1	4	yes	complemented
45	#16811308	C₂²	1	4	yes	complemented
46	#16811306	C₂²	1	8	yes	complemented
47	#16811302	C₂²	1	8	yes	complemented
48	#16811302	C₂²	1	8	yes	complemented
49	#16811299	C₂²	1	8	yes	complemented
50	#16811297	C₂²	1	8	yes	complemented
51	#16811297	C₂²	1	8	yes	complemented
52	#16811297	C₂²	1	8	yes	complemented
53	#16811294	C₂²	1	4	yes	complemented
54	D₄×Dic₁₀₆	C₂²	1	4	yes	complemented
55	#16811282	C₂²	1	8	yes	complemented
56	#16811274	C₂²	1	4	yes	complemented
57	#16811272	C₂²	1	4	yes	complemented
58	#16811269	C₂²	1	8	yes	complemented
59	#16811269	C₂²	1	8	yes	complemented
60	#16811268	C₂²	1	4	yes	complemented
61	#16811268	C₂²	1	4	yes	complemented
62	#16811267	C₂²	1	4	yes	complemented
63	#16811263	C₂²	1	8	yes	complemented
64	#16811263	C₂²	1	8	yes	complemented
65	#16811263	C₂²	1	8	yes	complemented
66	#16811261	C₂²	1	4	yes	complemented
67	#16811261	C₂²	1	4	yes	complemented
68	#16811261	C₂²	1	4	yes	complemented
69	D₄×D₂₁₂	C₂²	1	4	yes	complemented
70	D₄×D₂₁₂	C₂²	1	4	yes	complemented
71	D₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
72	D₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
73	D₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
74	#16811251	C₂²	1	2	yes	complemented
75	#16811249	C₂²	1	4	yes	complemented
76	#16811245	C₂²	1	2	yes	complemented
77	#16811245	C₂²	1	2	yes	complemented
78	#16811245	C₂²	1	4	yes	complemented
79	#16811244	C₂²	1	4	yes	complemented
80	#16811238	C₂²	1	2	yes	complemented
81	#16811238	C₂²	1	2	yes	complemented
82	#16811231	C₂²	1	2	yes	complemented
83	#16811231	C₂²	1	2	yes	complemented
84	#16811228	C₂²	1	4	yes	complemented
85	#16811224	C₂²	1	2	yes	complemented
86	#16811224	C₂²	1	2	yes	complemented
87	#16811224	C₂²	1	4	yes	complemented
88	#16811220	C₂²	1	8	yes	complemented
89	#16811215	C₂²	1	4	yes	complemented
90	#16811215	C₂²	1	4	yes	complemented
91	#16811215	C₂²	1	8	yes	complemented
92	#16811211	C₂²	1	8	yes	complemented
93	#16811206	C₂²	1	4	yes	complemented
94	#16811206	C₂²	1	8	yes	complemented
95	#16811206	C₂²	1	4	yes	complemented
96	#16811206	C₂²	1	8	yes	complemented
97	#16811206	C₂²	1	8	yes	complemented
98	#16811206	C₂²	1	8	yes	complemented
99	#16811206	C₂²	1	8	yes	complemented
100	#16811206	C₂²	1	8	yes	complemented
101	#16811206	C₂²	1	8	yes	complemented
102	#16811206	C₂²	1	8	yes	complemented
103	#16811201	C₂²	1	2	yes	complemented
104	#16811192	C₂²	1	2	yes	complemented
105	#16811187	C₂²	1	2	yes	complemented
106	#16811185	C₂²	1	4	yes	complemented
107	#16811182	C₂²	1	4	yes	complemented
108	#16811182	C₂²	1	4	yes	complemented
109	#16811176	C₂²	1	2	yes	complemented
110	#16811173	C₂²	1	4	yes	complemented
111	#16811170	C₂²	1	4	yes	complemented
112	#16811169	C₂²	1	2	yes	complemented
113	#16811160	C₂²	1	4	yes	complemented
114	#16811157	C₂²	1	4	yes	complemented
115	#16811157	C₂²	1	4	yes	complemented
116	#16811157	C₂²	1	8	yes	complemented
117	#16811157	C₂²	1	4	yes	complemented
118	#16811153	C₂²	1	8	yes	complemented
119	#16811153	C₂²	1	8	yes	complemented
120	#16811151	C₂²	1	4	yes	complemented
121	#16811151	C₂²	1	4	yes	complemented
122	C₂×#13133212	C₂²	1	4	yes	complemented
123	C₂×#13133211	C₂²	1	4	yes	complemented
124	C₂×#13133205	C₂²	1	4	yes	complemented
125	C₂×#13133203	C₂²	1	4	yes	complemented
126	#16811135	C₂²	1	2	yes	complemented
127	#16811134	C₂²	1	8	yes	complemented
128	#16811132	C₂²	1	8	yes	complemented
129	#16811132	C₂²	1	8	yes	complemented
130	#16811132	C₂²	1	8	yes	complemented
131	#16811130	C₂²	1	2	yes	complemented
132	C₂×#13133202	C₂²	1	4	yes	complemented
133	C₂×#13133200	C₂²	1	4	yes	complemented
134	C₂×#13133194	C₂²	1	4	yes	complemented
135	C₂×#13133191	C₂²	1	4	yes	complemented
136	C₂×#13133190	C₂²	1	4	yes	complemented
137	C₂×#13133189	C₂²	1	4	yes	complemented
138	C₂×#13133187	C₂²	1	4	yes	complemented
139	C₂×#13133185	C₂²	1	4	yes	complemented
140	#16811104	C₂²	1	2	yes	complemented
141	#16811102	C₂²	1	4	yes	complemented
142	#16811098	C₂²	1	1	yes	characteristic
143	#16811096	C₂²	1	4	yes	complemented
144	#16811095	C₂²	1	4	yes	complemented
145	#16811095	C₂²	1	4	yes	complemented
146	#16811095	C₂²	1	4	yes	complemented
147	#16811095	C₂²	1	4	yes	complemented
148	#16811095	C₂²	1	4	yes	complemented
149	C₄×#11719945	C₂²	1	2	yes	complemented
150	C₄×#11719947	C₂²	1	4	yes	complemented
151	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
152	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
153	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
154	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
155	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
156	C₂×#13133177	C₂²	1	2	yes	complemented
157	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
158	C₂×#13133175	C₂²	1	1	yes	characteristic, complemented
159	C₂×#13133174	C₂²	1	1	yes	characteristic, complemented
160	C₂²×#11719921	C₂²	1	2	yes	complemented
161	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
162	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
163	C₅₃×#520	C₂²	1	2	yes	complemented
164	C₅₃×#520	C₂²	1	4	yes	complemented
165	C₅₃×#518	C₂²	1	1	yes	characteristic
166	C₅₃×#518	C₂²	1	4	yes	complemented
167	C₅₃×#518	C₂²	1	4	yes	complemented
168	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
169	C₄×#41×C₅₃	C₂²	1	4	yes	complemented
170	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
171	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
172	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
173	C₂⁴×D₅₃	C₂³	1	2	yes	—
174	#13133262	—	2	8	no	—
175	C₂×#11719945	C₂³	1	2	yes	—
176	C₂×#11719945	C₂³	1	8	yes	complemented
177	C₂×#11719945	C₂³	1	8	yes	complemented
178	C₂×#11719947	C₂³	1	4	yes	—
179	C₂²×Dic₁₀₆	C₂³	1	4	yes	complemented
180	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
181	C₂²×D₂₁₂	C₂³	1	4	yes	—
182	C₂²×D₂₁₂	C₂³	1	4	yes	—
183	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
184	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
185	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
186	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
187	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
188	C₂×D₄×D₅₃	—	2	8	no	—
189	C₂×D₄×D₅₃	C₂³	1	4	yes	—
190	C₂×D₄×D₅₃	C₂³	1	4	yes	—
191	C₂×D₄×D₅₃	C₂³	1	4	yes	—
192	C₂³×Dic₅₃	C₂³	1	2	yes	—
193	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
195	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
196	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
197	#13133217	C₂³	1	4	yes	complemented
198	#13133216	C₂³	1	2	yes	complemented
199	#13133216	C₂³	1	2	yes	complemented
200	#13133216	C₂³	1	4	yes	complemented
201	#13133215	C₂³	1	2	yes	complemented
202	#13133214	C₂³	1	4	yes	—
203	#13133213	C₂³	1	4	yes	—
204	#13133213	C₂³	1	2	yes	complemented
205	#13133212	C₂³	1	4	yes	—
206	#13133212	C₂³	1	8	yes	—
207	#13133212	C₂³	1	4	yes	—
208	#13133212	C₂³	1	8	yes	complemented
209	#13133212	C₂³	1	8	yes	complemented
210	#13133212	C₂³	1	8	yes	complemented
211	#13133211	C₂³	1	4	yes	—
212	#13133211	C₂³	1	8	yes	—
213	#13133211	C₂³	1	4	yes	—
214	#13133211	C₂³	1	4	yes	complemented
215	#13133211	C₂³	1	8	yes	complemented
216	#13133211	C₂³	1	8	yes	complemented
217	#13133211	C₂³	1	4	yes	complemented
218	#13133210	C₂³	1	4	yes	complemented
219	#13133210	C₂³	1	8	yes	complemented
220	#13133210	C₂³	1	4	yes	complemented
221	#13133209	C₂³	1	4	yes	complemented
222	#13133209	C₂³	1	4	yes	complemented
223	#13133209	C₂³	1	4	yes	complemented
224	#13133208	C₂³	1	4	yes	complemented
225	#13133208	C₂³	1	2	yes	complemented
226	#13133208	C₂³	1	2	yes	complemented
227	#13133207	C₂³	1	4	yes	complemented
228	#13133207	C₂³	1	8	yes	complemented
229	#13133207	C₂³	1	4	yes	complemented
230	#13133206	C₂³	1	4	yes	—
231	#13133206	C₂³	1	2	yes	complemented
232	#13133205	C₂³	1	4	yes	—
233	#13133205	C₂³	1	4	yes	—
234	#13133205	C₂³	1	8	yes	—
235	#13133205	C₂³	1	4	yes	—
236	#13133205	C₂³	1	8	yes	complemented
237	#13133205	C₂³	1	8	yes	complemented
238	#13133204	C₂³	1	2	yes	complemented
239	#13133203	C₂³	1	4	yes	—
240	#13133203	C₂³	1	8	yes	—
241	#13133203	C₂³	1	4	yes	—
242	#13133203	C₂³	1	8	yes	complemented
243	#13133203	C₂³	1	8	yes	complemented
244	#13133203	C₂³	1	8	yes	complemented
245	#13133202	C₂³	1	4	yes	—
246	#13133202	C₂³	1	8	yes	—
247	#13133202	C₂³	1	4	yes	—
248	#13133202	C₂³	1	8	yes	complemented
249	#13133202	C₂³	1	8	yes	complemented
250	#13133202	C₂³	1	8	yes	complemented
251	#13133202	C₂³	1	8	yes	complemented
252	#13133201	C₂³	1	8	yes	—
253	#13133201	C₂³	1	4	yes	—
254	#13133200	C₂³	1	8	yes	—
255	#13133200	C₂³	1	4	yes	—
256	#13133200	C₂³	1	8	yes	—
257	#13133200	C₂³	1	4	yes	—
258	#13133200	C₂³	1	8	yes	complemented
259	#13133200	C₂³	1	8	yes	complemented
260	#13133200	C₂³	1	4	yes	complemented
261	#13133200	C₂³	1	8	yes	complemented
262	#13133200	C₂³	1	4	yes	complemented
263	#13133199	C₂³	1	8	yes	complemented
264	#13133199	C₂³	1	8	yes	complemented
265	#13133199	C₂³	1	4	yes	complemented
266	#13133199	C₂³	1	4	yes	complemented
267	#13133198	C₂³	1	4	yes	—
268	#13133198	C₂³	1	8	yes	complemented
269	#13133197	C₂³	1	2	yes	—
270	#13133197	C₂³	1	2	yes	—
271	#13133196	C₂³	1	4	yes	complemented
272	#13133196	C₂³	1	8	yes	complemented
273	#13133196	C₂³	1	8	yes	complemented
274	#13133196	C₂³	1	4	yes	complemented
275	#13133196	C₂³	1	4	yes	complemented
276	#13133195	C₂³	1	8	yes	complemented
277	#13133195	C₂³	1	4	yes	complemented
278	#13133195	C₂³	1	8	yes	complemented
279	#13133195	C₂³	1	4	yes	complemented
280	#13133194	C₂³	1	4	yes	—
281	#13133194	C₂³	1	8	yes	—
282	#13133194	C₂³	1	4	yes	—
283	#13133194	C₂³	1	8	yes	complemented
284	#13133194	C₂³	1	8	yes	complemented
285	#13133194	C₂³	1	8	yes	complemented
286	#13133194	C₂³	1	8	yes	complemented
287	#13133193	C₂³	1	2	yes	—
288	#13133193	C₂³	1	2	yes	—
289	#13133193	C₂³	1	4	yes	complemented
290	#13133192	C₂³	1	4	yes	—
291	#13133192	C₂³	1	4	yes	—
292	#13133192	C₂³	1	2	yes	—
293	#13133192	C₂³	1	2	yes	—
294	#13133191	C₂³	1	8	yes	—
295	#13133191	C₂³	1	8	yes	—
296	#13133191	C₂³	1	4	yes	—
297	#13133191	C₂³	1	8	yes	—
298	#13133191	C₂³	1	4	yes	—
299	#13133191	C₂³	1	4	yes	—
300	#13133191	C₂³	1	4	yes	—
301	#13133191	C₂³	1	8	yes	complemented
302	#13133191	C₂³	1	4	yes	complemented
303	#13133191	C₂³	1	8	yes	complemented
304	#13133190	C₂³	1	4	yes	—
305	#13133190	C₂³	1	8	yes	—
306	#13133190	C₂³	1	4	yes	—
307	#13133190	C₂³	1	8	yes	complemented
308	#13133190	C₂³	1	8	yes	complemented
309	#13133190	C₂³	1	8	yes	complemented
310	#13133190	C₂³	1	8	yes	complemented
311	#13133189	C₂³	1	8	yes	—
312	#13133189	C₂³	1	8	yes	—
313	#13133189	C₂³	1	4	yes	—
314	#13133189	C₂³	1	8	yes	—
315	#13133189	C₂³	1	4	yes	—
316	#13133189	C₂³	1	8	yes	complemented
317	#13133189	C₂³	1	8	yes	complemented
318	#13133188	C₂³	1	2	yes	—
319	#13133188	C₂³	1	2	yes	—
320	#13133188	C₂³	1	4	yes	complemented
321	#13133187	C₂³	1	8	yes	—
322	#13133187	C₂³	1	8	yes	—
323	#13133187	C₂³	1	8	yes	—
324	#13133187	C₂³	1	4	yes	—
325	#13133187	C₂³	1	8	yes	—
326	#13133186	C₂³	1	8	yes	—
327	#13133186	C₂³	1	8	yes	complemented
328	#13133185	C₂³	1	8	yes	—
329	#13133185	C₂³	1	8	yes	—
330	#13133185	C₂³	1	4	yes	—
331	#13133185	C₂³	1	8	yes	—
332	#13133185	C₂³	1	8	yes	complemented
333	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
334	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
335	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
336	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
337	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
338	#13133182	C₂³	1	4	yes	complemented
339	C₄×D₂₁₂	C₂³	1	4	yes	—
340	C₄×D₂₁₂	C₂³	1	4	yes	—
341	C₄×D₂₁₂	C₂³	1	4	yes	—
342	C₄×D₂₁₂	C₂³	1	4	yes	—
343	C₄×D₂₁₂	C₂³	1	8	yes	complemented
344	C₄×D₂₁₂	C₂³	1	8	yes	complemented
345	C₄×D₂₁₂	C₂³	1	2	yes	complemented
346	C₄×D₂₁₂	C₂³	1	2	yes	complemented
347	D₄×Dic₅₃	C₂³	1	4	yes	—
348	D₄×Dic₅₃	C₂³	1	4	yes	—
349	D₄×Dic₅₃	C₂³	1	4	yes	—
350	D₄×Dic₅₃	C₂³	1	4	yes	—
351	#13133179	C₂³	1	4	yes	—
352	#13133179	C₂³	1	4	yes	—
353	#13133179	C₂³	1	4	yes	complemented
354	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
355	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
356	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
357	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
358	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
359	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
360	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
361	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
362	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
363	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
364	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
365	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
366	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
367	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
368	#13133177	C₂³	1	8	yes	—
369	#13133177	C₂³	1	8	yes	—
370	#13133177	C₂³	1	8	yes	complemented
371	#13133177	C₂³	1	8	yes	complemented
372	#13133176	C₂³	1	2	yes	—
373	#13133176	C₂³	1	8	yes	complemented
374	#13133175	C₂³	1	4	yes	—
375	#13133175	C₂³	1	4	yes	—
376	#13133175	C₂³	1	4	yes	complemented
377	#13133174	C₂³	1	2	yes	—
378	#13133174	C₂³	1	2	yes	—
379	#13133174	C₂³	1	2	yes	—
380	#13133174	C₂³	1	2	yes	—
381	#13133174	C₂³	1	8	yes	complemented
382	#13133174	C₂³	1	8	yes	complemented
383	#13133174	C₂³	1	8	yes	complemented
384	#13133174	C₂³	1	4	yes	complemented
385	#13133173	C₂³	1	8	yes	complemented
386	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
387	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
388	C₂×#11719919	C₂³	1	1	yes	characteristic
389	C₂×#11719919	C₂³	1	1	yes	characteristic
390	C₂×#11719919	C₂³	1	4	yes	complemented
391	C₂×#11719919	C₂³	1	4	yes	complemented
392	C₂×#11719919	C₂³	1	4	yes	complemented
393	C₂×#11719919	C₂³	1	4	yes	complemented
394	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
395	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
396	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
397	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
398	C₂×#11719921	C₂³	1	4	yes	—
399	C₂×#11719921	C₂³	1	4	yes	—
400	C₂×#11719921	C₂³	1	4	yes	—
401	C₂×#11719921	C₂³	1	4	yes	—
402	C₂×#11719921	C₂³	1	1	yes	characteristic
403	C₂×#11719921	C₂³	1	2	yes	—
404	C₂×#11719921	C₂³	1	1	yes	characteristic
405	C₂×#11719921	C₂³	1	2	yes	—
406	C₂×#11719921	C₂³	1	2	yes	—
407	C₂×#11719921	C₂³	1	4	yes	—
408	C₂×#11719921	C₂³	1	4	yes	—
409	C₂×#11719921	C₂³	1	4	yes	—
410	C₂×#11719921	C₂³	1	4	yes	—
411	C₂×#11719921	C₂³	1	4	yes	complemented
412	C₂×#11719921	C₂³	1	4	yes	complemented
413	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
414	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
415	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
416	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
417	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
418	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
419	C₄²×D₅₃	C₂³	1	4	yes	complemented
420	H(5,𝔽₂)×C₅₃	—	2	8	no	—
421	C₂×#41×C₅₃	C₂³	1	4	yes	—
422	C₂×#41×C₅₃	C₂³	1	2	yes	—
423	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
424	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
425	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
426	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
427	C₂³×C₄×C₅₃	C₂³	1	4	yes	complemented
428	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
429	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
430	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
431	C₄×D₄×C₅₃	C₂³	1	4	yes	—
432	C₄×D₄×C₅₃	C₂³	1	4	yes	—
433	C₄×D₄×C₅₃	C₂³	1	4	yes	—
434	C₄×D₄×C₅₃	C₂³	1	4	yes	—
435	C₄×D₄×C₅₃	C₂³	1	4	yes	—
436	C₄×D₄×C₅₃	C₂³	1	8	yes	—
437	C₄×D₄×C₅₃	C₂³	1	4	yes	—
438	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
439	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
440	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
441	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
442	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
443	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
444	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
445	#117×C₅₃	C₂³	1	2	yes	—
446	#117×C₅₃	C₂³	1	8	yes	complemented
447	#117×C₅₃	C₂³	1	4	yes	complemented
448	#117×C₅₃	C₂³	1	4	yes	complemented
449	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
450	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
451	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
452	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
453	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
454	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
455	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
456	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
457	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
458	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
459	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
460	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
461	C₂³×D₅₃	—	2	8	no	—
462	C₂³×D₅₃	—	8	2	no	—
463	C₂³×D₅₃	—	8	2	no	—
464	C₂³×D₅₃	C₂⁴	1	4	yes	—
465	C₂³×D₅₃	C₂⁴	1	4	yes	—
466	C₂³×D₅₃	C₂⁴	1	4	yes	—
467	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
468	C₂³×D₅₃	C₂⁴	1	2	yes	—
469	#41×C₅₃	—	2	16	no	—
470	#41×C₅₃	—	2	8	no	—
471	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
472	C₂×D₄×C₅₃	—	2	16	no	—
473	C₂×D₄×C₅₃	—	2	16	no	—
474	C₂×D₄×C₅₃	#41	1	8	yes	complemented
475	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
476	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
477	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
478	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
479	C₂²×C₄×C₅₃	—	8	2	no	—
480	C₂²×C₄×C₅₃	—	8	4	no	—
481	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
482	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
483	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
484	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
485	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
486	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
487	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
488	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
489	C₂²×C₄×C₅₃	C₂⁴	1	2	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	1	yes	characteristic
494	C₂×C₂²⋊D₅₃	—	2	8	no	—
495	C₂×C₂²⋊D₅₃	—	2	16	no	—
496	C₂×C₂²⋊D₅₃	—	8	4	no	—
497	C₂×C₂²⋊D₅₃	—	8	4	no	—
498	C₂×C₂²⋊D₅₃	—	8	4	no	—
499	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
500	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
501	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
502	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
503	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
504	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
505	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
506	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
507	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
508	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
509	C₂²×Dic₅₃	—	8	2	no	—
510	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
511	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
512	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
513	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
514	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
515	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
516	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
517	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
518	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
519	#11719947	—	2	16	no	—
520	D₄×D₅₃	—	2	16	no	—
521	D₄×D₅₃	—	2	16	no	—
522	D₄×D₅₃	—	2	16	no	—
523	#11719945	—	2	8	no	—
524	#11719945	—	8	8	no	—
525	#11719945	—	8	8	no	—
526	C₂×D₂₁₂	—	2	4	no	—
527	C₂×D₂₁₂	—	8	4	no	—
528	C₂×D₂₁₂	—	8	4	no	—
529	C₂×D₂₁₂	C₂⁴	1	4	yes	—
530	C₂×D₂₁₂	C₂⁴	1	2	yes	—
531	C₂×D₂₁₂	C₂⁴	1	4	yes	—
532	C₂×D₂₁₂	C₂⁴	1	4	yes	—
533	C₂×D₂₁₂	C₂⁴	1	8	yes	—
534	C₂×D₂₁₂	C₂⁴	1	8	yes	—
535	C₂×C₄×D₅₃	—	2	4	no	—
536	C₂×C₄×D₅₃	—	8	2	no	—
537	C₂×C₄×D₅₃	—	8	2	no	—
538	C₂×C₄×D₅₃	—	8	4	no	—
539	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
540	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
541	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
542	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
543	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
544	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
545	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
546	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
547	C₂×Dic₁₀₆	—	8	4	no	—
548	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
549	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
550	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
551	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
552	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
553	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
554	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
555	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
556	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
557	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
558	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
559	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
560	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
561	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
562	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
563	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
564	C₄²×C₅₃	C₂⁴	1	2	yes	—
565	C₄²×C₅₃	C₂⁴	1	2	yes	—
566	C₄²×C₅₃	C₂⁴	1	4	yes	—
567	C₄²×C₅₃	C₂⁴	1	4	yes	—
568	C₄²×C₅₃	C₂⁴	1	4	yes	—
569	C₄²×C₅₃	C₂⁴	1	8	yes	—
570	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
571	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
572	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
573	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
574	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
575	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
576	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
577	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
578	#11719921	C₂⁴	1	2	yes	—
579	#11719921	C₂⁴	1	2	yes	—
580	#11719921	C₂⁴	1	4	yes	—
581	#11719921	C₂⁴	1	4	yes	—
582	#11719921	C₂⁴	1	4	yes	—
583	#11719921	C₂⁴	1	8	yes	—
584	#11719921	C₂⁴	1	1	yes	characteristic
585	#11719921	C₂⁴	1	1	yes	characteristic
586	#11719921	C₂⁴	1	1	yes	characteristic
587	#11719921	C₂⁴	1	1	yes	characteristic
588	#11719921	C₂⁴	1	4	yes	—
589	#11719921	C₂⁴	1	4	yes	—
590	#11719921	C₂⁴	1	4	yes	—
591	#11719921	C₂⁴	1	4	yes	—
592	#11719921	C₂⁴	1	4	yes	—
593	#11719921	C₂⁴	1	4	yes	—
594	#11719921	C₂⁴	1	4	yes	—
595	#11719921	C₂⁴	1	4	yes	—
596	#11719921	C₂⁴	1	8	yes	—
597	#11719921	C₂⁴	1	8	yes	—
598	#11719921	C₂⁴	1	8	yes	—
599	#11719921	C₂⁴	1	8	yes	—
600	#11719921	C₂⁴	1	4	yes	—
601	#11719921	C₂⁴	1	4	yes	—
602	#11719921	C₂⁴	1	8	yes	—
603	#11719921	C₂⁴	1	4	yes	—
604	#11719921	C₂⁴	1	4	yes	—
605	#11719921	C₂⁴	1	4	yes	—
606	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
607	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
608	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
609	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
610	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
611	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
612	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
613	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
614	#11719919	C₂⁴	1	8	yes	—
615	#11719919	C₂⁴	1	2	yes	—
616	#11719919	C₂⁴	1	2	yes	—
617	#11719919	C₂⁴	1	2	yes	—
618	#11719919	C₂⁴	1	2	yes	—
619	#11719919	C₂⁴	1	4	yes	—
620	#11719919	C₂⁴	1	4	yes	—
621	#11719919	C₂⁴	1	4	yes	—
622	#11719919	C₂⁴	1	4	yes	—
623	#11719919	C₂⁴	1	8	yes	—
624	#11719919	C₂⁴	1	8	yes	—
625	#11719919	C₂⁴	1	8	yes	—
626	#11719919	C₂⁴	1	4	yes	—
627	#11719919	C₂⁴	1	4	yes	—
628	#11719919	C₂⁴	1	4	yes	—
629	#11719919	C₂⁴	1	4	yes	—
630	#11719919	C₂⁴	1	4	yes	—
631	#11719919	C₂⁴	1	4	yes	—
632	C₄×Dic₅₃	C₂⁴	1	4	yes	—
633	C₄×Dic₅₃	C₂⁴	1	4	yes	—
634	C₄×Dic₅₃	C₂⁴	1	4	yes	—
635	C₄×Dic₅₃	C₂⁴	1	2	yes	—
636	C₄×Dic₅₃	C₂⁴	1	2	yes	—
637	C₄×Dic₅₃	C₂⁴	1	8	yes	—
638	C₄×Dic₅₃	C₂⁴	1	8	yes	—
639	C₂³×C₅₃	—	2	8	no	—
640	C₂³×C₅₃	—	4	2	no	—
641	C₂³×C₅₃	—	4	2	no	—
642	C₂³×C₅₃	—	4	4	no	—
643	C₂³×C₅₃	—	4	4	no	—
644	C₂³×C₅₃	C₂×#41	1	8	yes	—
645	C₂³×C₅₃	C₂⁵	1	4	yes	—
646	C₂³×C₅₃	C₂⁵	1	4	yes	—
647	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
648	C₂²×D₅₃	—	2	2	no	—
649	C₂²×D₅₃	—	2	4	no	—
650	C₂²×D₅₃	—	2	8	no	—
651	C₂²×D₅₃	—	2	8	no	—
652	C₂²×D₅₃	—	2	8	no	—
653	C₂²×D₅₃	—	4	2	no	—
654	C₂²×D₅₃	—	4	2	no	—
655	C₂²×D₅₃	—	4	1	no	—
656	C₂²×D₅₃	—	4	1	no	—
657	C₂²×D₅₃	—	4	4	no	—
658	C₂²×D₅₃	—	4	4	no	—
659	C₂²×D₅₃	—	4	4	no	—
660	C₂²×D₅₃	—	4	4	no	—
661	C₂²×D₅₃	—	4	4	no	—
662	C₂²×D₅₃	—	4	4	no	—
663	C₂²×D₅₃	—	8	16	no	—
664	C₂²×D₅₃	C₂⁵	1	4	yes	—
665	C₂²×D₅₃	C₂⁵	1	4	yes	—
666	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
667	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
668	Q₈×C₅₃	—	2	4	no	—
669	D₄×C₅₃	—	2	16	no	—
670	D₄×C₅₃	—	2	8	no	—
671	D₄×C₅₃	—	2	4	no	—
672	D₄×C₅₃	C₂×#41	1	16	yes	—
673	C₂×C₄×C₅₃	—	2	8	no	—
674	C₂×C₄×C₅₃	—	2	8	no	—
675	C₂×C₄×C₅₃	—	4	4	no	—
676	C₂×C₄×C₅₃	—	4	1	no	—
677	C₂×C₄×C₅₃	—	4	2	no	—
678	C₂×C₄×C₅₃	—	4	4	no	—
679	C₂×C₄×C₅₃	—	4	4	no	—
680	C₂×C₄×C₅₃	—	4	4	no	—
681	C₂×C₄×C₅₃	—	4	8	no	—
682	C₂×C₄×C₅₃	—	4	4	no	—
683	C₂×C₄×C₅₃	—	4	1	no	—
684	C₂×C₄×C₅₃	—	4	4	no	—
685	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
686	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
687	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
688	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
689	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
690	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
691	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
692	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
693	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
694	C₂²⋊D₅₃	—	2	8	no	—
695	C₂²⋊D₅₃	—	2	16	no	—
696	C₂²⋊D₅₃	—	2	16	no	—
697	C₂²⋊D₅₃	—	4	4	no	—
698	C₂²⋊D₅₃	—	4	8	no	—
699	C₂²⋊D₅₃	—	4	8	no	—
700	C₂²⋊D₅₃	—	4	8	no	—
701	C₂²⋊D₅₃	—	4	4	no	—
702	C₂²⋊D₅₃	—	4	4	no	—
703	C₂²⋊D₅₃	—	4	4	no	—
704	C₂×Dic₅₃	—	2	2	no	—
705	C₂×Dic₅₃	—	2	8	no	—
706	C₂×Dic₅₃	—	4	4	no	—
707	C₂×Dic₅₃	—	4	4	no	—
708	C₂×Dic₅₃	—	4	1	no	—
709	C₂×Dic₅₃	—	4	2	no	—
710	C₂×Dic₅₃	—	4	4	no	—
711	C₂×Dic₅₃	—	4	1	no	—
712	C₂×Dic₅₃	—	4	4	no	—
713	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
714	C₂×Dic₅₃	C₂⁵	1	4	yes	—
715	C₂×Dic₅₃	C₂⁵	1	2	yes	—
716	C₂×Dic₅₃	C₂⁵	1	4	yes	—
717	C₂×Dic₅₃	C₂⁵	1	4	yes	—
718	C₂×Dic₅₃	C₂⁵	1	4	yes	—
719	C₂×Dic₅₃	C₂⁵	1	2	yes	—
720	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
721	D₂₁₂	—	2	8	no	—
722	D₂₁₂	—	2	4	no	—
723	D₂₁₂	—	4	4	no	—
724	D₂₁₂	—	4	4	no	—
725	D₂₁₂	—	4	8	no	—
726	D₂₁₂	—	4	8	no	—
727	C₄×D₅₃	—	2	4	no	—
728	C₄×D₅₃	—	2	4	no	—
729	C₄×D₅₃	—	2	8	no	—
730	C₄×D₅₃	—	4	4	no	—
731	C₄×D₅₃	—	4	8	no	—
732	C₄×D₅₃	—	4	8	no	—
733	C₄×D₅₃	—	4	8	no	—
734	C₄×D₅₃	—	4	4	no	—
735	Dic₁₀₆	—	2	4	no	—
736	Dic₁₀₆	—	4	4	no	—
737	Dic₁₀₆	—	4	8	no	—
738	Dic₁₀₆	—	4	4	no	—
739	#62846	—	53	1	no	maximal, Sylow
740	C₂²×C₅₃	—	2	1	no	—
741	C₂²×C₅₃	—	2	4	no	—
742	C₂²×C₅₃	—	2	1	no	—
743	C₂²×C₅₃	—	2	4	no	—
744	C₂²×C₅₃	—	2	4	no	—
745	C₂²×C₅₃	—	2	4	no	—
746	C₂²×C₅₃	—	2	4	no	—
747	C₂²×C₅₃	—	4	8	no	—
748	C₂²×C₅₃	—	8	8	no	—
749	C₂²×C₅₃	C₂²×#41	1	8	yes	—
750	C₂²×C₅₃	C₂²×#41	1	2	yes	—
751	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
752	C₂×D₅₃	—	2	1	no	—
753	C₂×D₅₃	—	2	1	no	—
754	C₂×D₅₃	—	2	4	no	—
755	C₂×D₅₃	—	2	4	no	—
756	C₂×D₅₃	—	2	4	no	—
757	C₂×D₅₃	—	2	4	no	—
758	C₂×D₅₃	—	2	4	no	—
759	C₂×D₅₃	—	2	4	no	—
760	C₂×D₅₃	—	2	1	no	—
761	C₂×D₅₃	—	2	1	no	—
762	C₂×D₅₃	—	2	1	no	—
763	C₂×D₅₃	—	2	1	no	—
764	C₂×D₅₃	—	4	8	no	—
765	C₂×D₅₃	—	4	4	no	—
766	C₂×D₅₃	—	8	8	no	—
767	C₂×D₅₃	—	8	8	no	—
768	C₂×D₅₃	—	8	8	no	—
769	C₄×C₅₃	—	2	4	no	—
770	C₄×C₅₃	—	2	4	no	—
771	C₄×C₅₃	—	2	4	no	—
772	C₄×C₅₃	—	2	2	no	—
773	C₄×C₅₃	—	2	1	no	—
774	C₄×C₅₃	—	2	4	no	—
775	C₄×C₅₃	—	2	1	no	—
776	C₄×C₅₃	C₂²×#41	1	4	yes	—
777	Dic₅₃	—	2	4	no	—
778	Dic₅₃	—	2	2	no	—
779	Dic₅₃	—	2	1	no	—
780	Dic₅₃	—	2	4	no	—
781	Dic₅₃	—	2	2	no	—
782	Dic₅₃	—	2	4	no	—
783	Dic₅₃	—	2	4	no	—
784	Dic₅₃	—	2	1	no	—
785	#3521	—	53	4	no	—
786	#3521	—	53	4	no	—
787	#3519	—	53	4	no	—
788	#3519	—	53	4	no	—
789	#3514	—	53	4	no	—
790	#3514	—	53	4	no	—
791	#3513	—	53	4	no	—
792	#3513	—	53	4	no	—
793	#3506	—	53	2	no	—
794	#3505	—	53	4	no	—
795	#3501	—	53	1	no	—
796	#3496	—	53	1	no	—
797	#3493	—	53	2	no	—
798	#3490	—	53	4	no	—
799	#3484	—	53	1	no	—
800	#3484	—	53	1	no	—
801	#3460	—	53	2	no	—
802	#3459	—	53	4	no	—
803	#3455	—	53	2	no	—
804	C₂×#538	—	53	4	no	—
805	C₄×H(5,𝔽₂)	—	53	1	no	—
806	C₄×H(5,𝔽₂)	D₅₃	1	1	yes	characteristic, complemented
807	C₂×#518	—	53	1	no	—
808	C₂×C₅₃	—	2	2	no	—
809	C₂×C₅₃	—	2	8	no	—
810	C₂×C₅₃	—	4	4	no	—
811	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
812	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
813	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
814	D₅₃	—	4	4	no	—
815	D₅₃	—	4	1	no	—
816	D₅₃	—	4	1	no	—
817	D₅₃	—	4	4	no	—
818	C₂×H(5,𝔽₂)	—	53	1	no	—
819	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic
820	C₂³×D₄	—	53	1	no	—
821	#559	—	53	4	no	—
822	#559	—	53	4	no	—
823	#556	—	53	4	no	—
824	#556	—	53	4	no	—
825	#556	—	53	4	no	—
826	#555	—	53	4	no	—
827	#555	—	53	4	no	—
828	#555	—	53	4	no	—
829	#554	—	53	4	no	—
830	#554	—	53	4	no	—
831	#554	—	53	4	no	—
832	#553	—	53	8	no	—
833	#553	—	53	8	no	—
834	#553	—	53	8	no	—
835	#553	—	53	4	no	—
836	#553	—	53	4	no	—
837	#553	—	53	4	no	—
838	#553	—	53	4	no	—
839	#552	—	53	4	no	—
840	#552	—	53	8	no	—
841	#552	—	53	4	no	—
842	#551	—	53	8	no	—
843	#551	—	53	8	no	—
844	#551	—	53	8	no	—
845	#551	—	53	8	no	—
846	#551	—	53	8	no	—
847	#551	—	53	8	no	—
848	#550	—	53	4	no	—
849	D₄×Q₈	—	53	4	no	—
850	#548	—	53	8	no	—
851	#547	—	53	4	no	—
852	#547	—	53	4	no	—
853	#546	—	53	4	no	—
854	#546	—	53	4	no	—
855	#546	—	53	4	no	—
856	#546	—	53	4	no	—
857	#546	—	53	4	no	—
858	#546	—	53	4	no	—
859	#546	—	53	8	no	—
860	#546	—	53	8	no	—
861	#546	—	53	8	no	—
862	#546	—	53	8	no	—
863	#546	—	53	8	no	—
864	D₄²	—	53	4	no	—
865	D₄²	—	53	4	no	—
866	D₄²	—	53	4	no	—
867	D₄²	—	53	4	no	—
868	D₄²	—	53	4	no	—
869	#544	—	53	2	no	—
870	#543	—	53	4	no	—
871	#542	—	53	2	no	—
872	#542	—	53	2	no	—
873	#542	—	53	4	no	—
874	#542	—	53	2	no	—
875	#542	—	53	2	no	—
876	#542	—	53	4	no	—
877	#541	—	53	2	no	—
878	#541	—	53	2	no	—
879	#540	—	53	2	no	—
880	#540	—	53	2	no	—
881	#540	—	53	4	no	—
882	#540	—	53	4	no	—
883	#539	—	53	4	no	—
884	#539	—	53	4	no	—
885	#539	—	53	8	no	—
886	#539	—	53	8	no	—
887	#538	—	53	4	no	—
888	#538	—	53	8	no	—
889	#538	—	53	8	no	—
890	#538	—	53	8	no	—
891	#538	—	53	4	no	—
892	#538	—	53	8	no	—
893	#538	—	53	8	no	—
894	#538	—	53	8	no	—
895	#538	—	53	8	no	—
896	#538	—	53	8	no	—
897	#538	—	53	8	no	—
898	#537	—	53	2	no	—
899	#535	—	53	2	no	—
900	#535	—	53	2	no	—
901	#534	—	53	4	no	—
902	#534	—	53	4	no	—
903	#534	—	53	4	no	—
904	#533	—	53	2	no	—
905	#532	—	53	2	no	—
906	#532	—	53	4	no	—
907	#532	—	53	4	no	—
908	#529	—	53	4	no	—
909	#529	—	53	8	no	—
910	#529	—	53	8	no	—
911	#529	—	53	4	no	—
912	#529	—	53	4	no	—
913	#529	—	53	4	no	—
914	#529	—	53	4	no	—
915	#529	—	53	8	no	—
916	#529	—	53	4	no	—
917	C₂×#126	—	53	4	no	—
918	C₂×#126	—	53	4	no	—
919	C₂×#124	—	53	4	no	—
920	C₂×#124	—	53	4	no	—
921	#525	—	53	2	no	—
922	#525	—	53	8	no	—
923	#525	—	53	8	no	—
924	#525	—	53	8	no	—
925	#525	—	53	8	no	—
926	#525	—	53	2	no	—
927	C₂×#123	—	53	4	no	—
928	C₂×#123	—	53	4	no	—
929	C₂×C₂²⋊Q₈	—	53	4	no	—
930	C₂×#121	—	53	4	no	—
931	C₂×#121	—	53	4	no	—
932	C₂×#121	—	53	4	no	—
933	C₂×#120	—	53	4	no	—
934	C₂×#120	—	53	4	no	—
935	#520	—	53	4	no	—
936	#520	—	53	2	no	—
937	#520	C₂×D₅₃	1	2	yes	complemented
938	#520	C₂×D₅₃	1	4	yes	complemented
939	#518	—	53	1	no	—
940	#518	—	53	4	no	—
941	#518	—	53	4	no	—
942	#518	—	53	4	no	—
943	#518	—	53	4	no	—
944	#518	—	53	4	no	—
945	#518	—	53	4	no	—
946	#518	C₂×D₅₃	1	1	yes	characteristic
947	#518	C₂×D₅₃	1	4	yes	complemented
948	#518	C₂×D₅₃	1	4	yes	complemented
949	C₄×#41	—	53	4	no	—
950	C₄×#41	—	53	2	no	—
951	C₄×#41	C₂×D₅₃	1	2	yes	complemented
952	C₄×#41	C₂×D₅₃	1	4	yes	complemented
953	C₂×C₄×D₄	—	53	1	no	—
954	C₂×C₄×D₄	—	53	2	no	—
955	C₂×C₄×D₄	—	53	4	no	—
956	C₂×C₄×D₄	—	53	4	no	—
957	C₂×C₄×D₄	—	53	1	no	—
958	C₂×C₄×D₄	—	53	2	no	—
959	C₂×C₄×D₄	—	53	1	no	—
960	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
961	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
962	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
963	C₂×#117	—	53	1	no	—
964	C₂×#117	—	53	1	no	—
965	C₂²×C₂²⋊C₄	—	53	2	no	—
966	C₂²×C₂²⋊C₄	—	53	2	no	—
967	C₅₃	#62846	1	1	yes	characteristic, complemented, Sylow
968	C₂⁵	—	53	2	no	—
969	H(5,𝔽₂)	—	2	8	no	—
970	H(5,𝔽₂)	—	106	8	no	—
971	C₂×#41	—	53	4	no	—
972	C₂×#41	—	53	2	no	—
973	C₂×#41	—	53	8	no	—
974	C₂×#41	—	53	8	no	—
975	C₂×#41	C₂²×D₅₃	1	2	yes	—
976	C₂×#41	C₂²×D₅₃	1	4	yes	—
977	C₂²×Q₈	—	53	4	no	—
978	C₂²×D₄	—	53	2	no	—
979	C₂²×D₄	—	53	4	no	—
980	C₂²×D₄	—	53	4	no	—
981	C₂²×D₄	—	53	4	no	—
982	C₂²×D₄	—	53	4	no	—
983	C₂²×D₄	—	53	4	no	—
984	C₂²×D₄	—	53	4	no	—
985	C₂²×D₄	—	53	4	no	—
986	C₂²×D₄	—	53	1	no	—
987	C₂²×D₄	—	53	4	no	—
988	C₂²×D₄	—	53	4	no	—
989	C₂²×D₄	—	106	8	no	—
990	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
991	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
992	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
993	C₂³×C₄	—	53	2	no	—
994	C₂³×C₄	—	53	1	no	—
995	C₂³×C₄	—	53	2	no	—
996	C₂³×C₄	—	53	2	no	—
997	C₂³×C₄	—	53	4	no	—
998	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
999	C₂³×C₄	C₂²×D₅₃	1	4	yes	complemented
1000	C₄⋊Q₈	—	53	2	no	—
1001	C₄⋊Q₈	—	53	4	no	—
1002	C₄⋊Q₈	—	53	2	no	—
1003	C₄⋊Q₈	—	53	2	no	—
1004	C₄⋊Q₈	—	53	4	no	—
1005	#127	—	53	4	no	—
1006	#127	—	53	2	no	—
1007	#127	—	53	4	no	—
1008	#126	—	53	4	no	—
1009	#126	—	53	8	no	—
1010	#126	—	53	8	no	—
1011	#126	—	53	8	no	—
1012	#126	—	53	8	no	—
1013	#126	—	53	4	no	—
1014	#126	—	53	4	no	—
1015	#126	—	53	8	no	—
1016	#126	—	53	4	no	—
1017	#126	—	53	4	no	—
1018	#126	—	53	8	no	—
1019	#126	—	53	8	no	—
1020	#126	—	53	8	no	—
1021	#126	—	53	4	no	—
1022	#126	—	53	4	no	—
1023	#126	—	53	4	no	—
1024	#125	—	53	4	no	—
1025	#125	—	53	8	no	—
1026	#125	—	53	4	no	—
1027	#125	—	53	4	no	—
1028	#125	—	53	2	no	—
1029	#125	—	53	2	no	—
1030	#125	—	53	4	no	—
1031	#125	—	53	4	no	—
1032	#125	—	53	4	no	—
1033	#124	—	53	4	no	—
1034	#124	—	53	2	no	—
1035	#124	—	53	2	no	—
1036	#124	—	53	4	no	—
1037	#124	—	53	8	no	—
1038	#124	—	53	8	no	—
1039	#124	—	53	8	no	—
1040	#124	—	53	8	no	—
1041	#124	—	53	4	no	—
1042	#124	—	53	4	no	—
1043	#124	—	53	8	no	—
1044	#124	—	53	8	no	—
1045	#124	—	53	8	no	—
1046	#124	—	53	4	no	—
1047	#124	—	53	4	no	—
1048	#123	—	53	4	no	—
1049	#123	—	53	8	no	—
1050	#123	—	53	4	no	—
1051	#123	—	53	8	no	—
1052	#123	—	53	8	no	—
1053	#123	—	53	8	no	—
1054	#123	—	53	4	no	—
1055	#123	—	53	8	no	—
1056	#123	—	53	8	no	—
1057	#123	—	53	4	no	—
1058	#123	—	53	4	no	—
1059	#123	—	53	4	no	—
1060	#123	—	53	8	no	—
1061	#123	—	53	8	no	—
1062	#123	—	53	8	no	—
1063	#123	—	53	8	no	—
1064	#123	—	53	8	no	—
1065	#123	—	53	4	no	—
1066	#123	—	53	4	no	—
1067	#123	—	53	4	no	—
1068	#123	—	53	8	no	—
1069	#123	—	53	8	no	—
1070	#123	—	53	8	no	—
1071	#123	—	53	4	no	—
1072	C₂²⋊Q₈	—	53	2	no	—
1073	C₂²⋊Q₈	—	53	2	no	—
1074	C₂²⋊Q₈	—	53	4	no	—
1075	C₂²⋊Q₈	—	53	4	no	—
1076	C₂²⋊Q₈	—	53	8	no	—
1077	C₂²⋊Q₈	—	53	4	no	—
1078	C₂²⋊Q₈	—	53	8	no	—
1079	C₂²⋊Q₈	—	53	4	no	—
1080	C₂²⋊Q₈	—	53	4	no	—
1081	C₂²⋊Q₈	—	53	8	no	—
1082	C₂²⋊Q₈	—	53	2	no	—
1083	C₂²⋊Q₈	—	53	2	no	—
1084	C₂²⋊Q₈	—	53	8	no	—
1085	C₂²⋊Q₈	—	53	4	no	—
1086	C₂²⋊Q₈	—	53	4	no	—
1087	C₂²⋊Q₈	—	53	8	no	—
1088	C₂²⋊Q₈	—	53	8	no	—
1089	C₂²⋊Q₈	—	53	8	no	—
1090	C₂²⋊Q₈	—	53	4	no	—
1091	C₂²⋊Q₈	—	53	8	no	—
1092	C₂²⋊Q₈	—	53	8	no	—
1093	#121	—	53	4	no	—
1094	#121	—	53	8	no	—
1095	#121	—	53	8	no	—
1096	#121	—	53	8	no	—
1097	#121	—	53	4	no	—
1098	#121	—	53	8	no	—
1099	#121	—	53	2	no	—
1100	#121	—	53	2	no	—
1101	#121	—	53	8	no	—
1102	#121	—	53	4	no	—
1103	#121	—	53	4	no	—
1104	#121	—	53	8	no	—
1105	#121	—	53	8	no	—
1106	#121	—	53	8	no	—
1107	#121	—	53	8	no	—
1108	#121	—	53	8	no	—
1109	#121	—	53	4	no	—
1110	#121	—	53	4	no	—
1111	#121	—	53	4	no	—
1112	#121	—	53	4	no	—
1113	#121	—	53	2	no	—
1114	#121	—	53	2	no	—
1115	#121	—	53	4	no	—
1116	#121	—	53	4	no	—
1117	#121	—	53	4	no	—
1118	#121	—	53	8	no	—
1119	#121	—	53	8	no	—
1120	#121	—	53	8	no	—
1121	#121	—	53	8	no	—
1122	#121	—	53	8	no	—
1123	#121	—	53	4	no	—
1124	#120	—	53	8	no	—
1125	#120	—	53	8	no	—
1126	#120	—	53	4	no	—
1127	#120	—	53	8	no	—
1128	#120	—	53	8	no	—
1129	#120	—	53	8	no	—
1130	#120	—	53	8	no	—
1131	#120	—	53	4	no	—
1132	#120	—	53	8	no	—
1133	#120	—	53	8	no	—
1134	#120	—	53	8	no	—
1135	#120	—	53	8	no	—
1136	C₄×Q₈	—	53	4	no	—
1137	C₄×Q₈	—	53	2	no	—
1138	C₄×Q₈	—	53	2	no	—
1139	C₄×Q₈	—	53	8	no	—
1140	C₄×Q₈	—	53	4	no	—
1141	C₄×Q₈	—	53	4	no	—
1142	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1143	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1144	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1145	C₄×D₄	—	53	4	no	—
1146	C₄×D₄	—	53	4	no	—
1147	C₄×D₄	—	53	4	no	—
1148	C₄×D₄	—	53	4	no	—
1149	C₄×D₄	—	53	4	no	—
1150	C₄×D₄	—	53	8	no	—
1151	C₄×D₄	—	53	8	no	—
1152	C₄×D₄	—	53	8	no	—
1153	C₄×D₄	—	53	8	no	—
1154	C₄×D₄	—	53	8	no	—
1155	C₄×D₄	—	53	4	no	—
1156	C₄×D₄	—	53	8	no	—
1157	C₄×D₄	—	53	8	no	—
1158	C₄×D₄	—	53	4	no	—
1159	C₄×D₄	—	53	4	no	—
1160	C₄×D₄	—	53	8	no	—
1161	C₄×D₄	—	53	4	no	—
1162	C₄×D₄	—	53	4	no	—
1163	C₄×D₄	—	53	4	no	—
1164	C₄×D₄	—	53	4	no	—
1165	C₄×D₄	—	53	4	no	—
1166	C₄×D₄	—	53	8	no	—
1167	C₄×D₄	—	53	8	no	—
1168	C₄×D₄	—	53	8	no	—
1169	C₄×D₄	—	53	8	no	—
1170	C₄×D₄	—	53	2	no	—
1171	C₄×D₄	—	53	4	no	—
1172	C₄×D₄	—	53	4	no	—
1173	C₄×D₄	—	53	2	no	—
1174	C₄×D₄	—	53	8	no	—
1175	C₄×D₄	—	53	4	no	—
1176	C₄×D₄	—	53	4	no	—
1177	C₄×D₄	—	53	8	no	—
1178	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1179	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1180	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1181	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1182	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1183	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1184	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1185	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1186	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1187	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1188	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1189	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1190	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1191	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1192	#117	—	53	2	no	—
1193	#117	—	53	8	no	—
1194	#117	—	53	4	no	—
1195	#117	—	53	4	no	—
1196	#117	—	53	4	no	—
1197	#117	—	53	8	no	—
1198	#117	—	53	2	no	—
1199	#117	—	53	2	no	—
1200	#117	—	53	2	no	—
1201	#117	—	53	2	no	—
1202	#117	—	53	4	no	—
1203	#117	—	53	8	no	—
1204	#117	—	53	8	no	—
1205	#117	—	53	8	no	—
1206	#117	C₂²×D₅₃	1	2	yes	—
1207	#117	C₂²×D₅₃	1	4	yes	complemented
1208	#117	C₂²×D₅₃	1	8	yes	complemented
1209	#117	C₂²×D₅₃	1	4	yes	complemented
1210	C₂×C₄⋊C₄	—	53	1	no	—
1211	C₂×C₄⋊C₄	—	53	1	no	—
1212	C₂×C₄⋊C₄	—	53	1	no	—
1213	C₂×C₄⋊C₄	—	53	4	no	—
1214	C₂×C₄⋊C₄	—	53	4	no	—
1215	C₂×C₄⋊C₄	—	53	4	no	—
1216	C₂×C₄⋊C₄	—	53	4	no	—
1217	C₂×C₄⋊C₄	—	53	4	no	—
1218	C₂×C₄⋊C₄	—	53	4	no	—
1219	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1220	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1221	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1222	C₂×C₂²⋊C₄	—	53	2	no	—
1223	C₂×C₂²⋊C₄	—	53	4	no	—
1224	C₂×C₂²⋊C₄	—	53	4	no	—
1225	C₂×C₂²⋊C₄	—	53	1	no	—
1226	C₂×C₂²⋊C₄	—	53	2	no	—
1227	C₂×C₂²⋊C₄	—	53	1	no	—
1228	C₂×C₂²⋊C₄	—	53	2	no	—
1229	C₂×C₂²⋊C₄	—	53	2	no	—
1230	C₂×C₂²⋊C₄	—	53	4	no	—
1231	C₂×C₂²⋊C₄	—	53	4	no	—
1232	C₂×C₂²⋊C₄	—	53	4	no	—
1233	C₂×C₂²⋊C₄	—	53	4	no	—
1234	C₂×C₂²⋊C₄	—	53	4	no	—
1235	C₂×C₂²⋊C₄	—	53	4	no	—
1236	C₂×C₂²⋊C₄	—	53	4	no	—
1237	C₂×C₂²⋊C₄	—	53	4	no	—
1238	C₂×C₂²⋊C₄	—	53	4	no	—
1239	C₂×C₂²⋊C₄	—	53	4	no	—
1240	C₂×C₂²⋊C₄	—	53	8	no	—
1241	C₂×C₂²⋊C₄	—	53	8	no	—
1242	C₂×C₂²⋊C₄	—	53	8	no	—
1243	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1244	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
1245	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1246	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
1247	C₂×C₄²	—	53	2	no	—
1248	C₂×C₄²	—	53	1	no	—
1249	C₂×C₄²	—	53	4	no	—
1250	C₂×C₄²	—	53	4	no	—
1251	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1252	C₂×C₄²	C₂²×D₅₃	1	4	yes	complemented
1253	C₂×C₄²	C₂²×D₅₃	1	4	yes	complemented
1254	C₂⁴	—	53	4	no	—
1255	C₂⁴	—	53	4	no	—
1256	C₂⁴	—	53	1	no	—
1257	C₂⁴	—	53	4	no	—
1258	C₂⁴	—	53	2	no	—
1259	C₂⁴	—	106	8	no	—
1260	C₂⁴	—	424	2	no	—
1261	C₂⁴	—	424	2	no	—
1262	C₂⁴	C₂³×D₅₃	1	4	yes	—
1263	C₂⁴	C₂³×D₅₃	1	2	yes	—
1264	#41	—	2	16	no	—
1265	#41	—	2	8	no	—
1266	#41	—	106	16	no	—
1267	#41	—	106	8	no	—
1268	#41	—	424	8	no	—
1269	#41	—	424	8	no	—
1270	C₂×Q₈	—	53	2	no	—
1271	C₂×Q₈	—	53	4	no	—
1272	C₂×Q₈	—	53	4	no	—
1273	C₂×Q₈	—	53	8	no	—
1274	C₂×Q₈	—	424	4	no	—
1275	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1276	C₂×D₄	—	2	16	no	—
1277	C₂×D₄	—	2	16	no	—
1278	C₂×D₄	—	53	8	no	—
1279	C₂×D₄	—	53	4	no	—
1280	C₂×D₄	—	53	8	no	—
1281	C₂×D₄	—	53	4	no	—
1282	C₂×D₄	—	53	4	no	—
1283	C₂×D₄	—	53	8	no	—
1284	C₂×D₄	—	53	4	no	—
1285	C₂×D₄	—	53	8	no	—
1286	C₂×D₄	—	53	8	no	—
1287	C₂×D₄	—	53	4	no	—
1288	C₂×D₄	—	53	4	no	—
1289	C₂×D₄	—	53	2	no	—
1290	C₂×D₄	—	53	4	no	—
1291	C₂×D₄	—	53	8	no	—
1292	C₂×D₄	—	53	4	no	—
1293	C₂×D₄	—	53	8	no	—
1294	C₂×D₄	—	106	8	no	—
1295	C₂×D₄	—	106	16	no	—
1296	C₂×D₄	—	106	16	no	—
1297	C₂×D₄	—	106	16	no	—
1298	C₂×D₄	—	106	16	no	—
1299	C₂×D₄	—	106	4	no	—
1300	C₂×D₄	—	424	4	no	—
1301	C₂×D₄	—	424	4	no	—
1302	C₂×D₄	—	424	4	no	—
1303	C₂×D₄	—	424	4	no	—
1304	C₂×D₄	—	424	4	no	—
1305	C₂×D₄	#11719945	1	8	yes	complemented
1306	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1307	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1308	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1309	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1310	C₂²×C₄	—	8	2	no	—
1311	C₂²×C₄	—	8	4	no	—
1312	C₂²×C₄	—	53	1	no	—
1313	C₂²×C₄	—	53	4	no	—
1314	C₂²×C₄	—	53	4	no	—
1315	C₂²×C₄	—	53	1	no	—
1316	C₂²×C₄	—	53	2	no	—
1317	C₂²×C₄	—	53	1	no	—
1318	C₂²×C₄	—	53	4	no	—
1319	C₂²×C₄	—	53	4	no	—
1320	C₂²×C₄	—	53	4	no	—
1321	C₂²×C₄	—	53	4	no	—
1322	C₂²×C₄	—	53	2	no	—
1323	C₂²×C₄	—	53	2	no	—
1324	C₂²×C₄	—	53	4	no	—
1325	C₂²×C₄	—	53	4	no	—
1326	C₂²×C₄	—	53	8	no	—
1327	C₂²×C₄	—	53	8	no	—
1328	C₂²×C₄	—	53	8	no	—
1329	C₂²×C₄	—	106	4	no	—
1330	C₂²×C₄	—	424	4	no	—
1331	C₂²×C₄	—	424	2	no	—
1332	C₂²×C₄	—	424	2	no	—
1333	C₂²×C₄	—	424	2	no	—
1334	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1335	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1336	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1337	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1338	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1339	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1340	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1341	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1342	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1343	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1344	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1345	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1346	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1347	C₄⋊C₄	—	53	2	no	—
1348	C₄⋊C₄	—	53	8	no	—
1349	C₄⋊C₄	—	53	4	no	—
1350	C₄⋊C₄	—	53	4	no	—
1351	C₄⋊C₄	—	53	4	no	—
1352	C₄⋊C₄	—	53	4	no	—
1353	C₄⋊C₄	—	53	4	no	—
1354	C₄⋊C₄	—	53	4	no	—
1355	C₄⋊C₄	—	53	2	no	—
1356	C₄⋊C₄	—	53	2	no	—
1357	C₄⋊C₄	—	53	2	no	—
1358	C₄⋊C₄	—	53	2	no	—
1359	C₄⋊C₄	—	53	8	no	—
1360	C₄⋊C₄	—	53	8	no	—
1361	C₄⋊C₄	—	53	8	no	—
1362	C₄⋊C₄	—	53	8	no	—
1363	C₄⋊C₄	—	53	2	no	—
1364	C₄⋊C₄	—	53	4	no	—
1365	C₄⋊C₄	—	53	4	no	—
1366	C₄⋊C₄	—	53	4	no	—
1367	C₄⋊C₄	—	53	4	no	—
1368	C₄⋊C₄	—	53	4	no	—
1369	C₄⋊C₄	—	53	4	no	—
1370	C₄⋊C₄	—	53	4	no	—
1371	C₄⋊C₄	—	53	4	no	—
1372	C₄⋊C₄	—	53	4	no	—
1373	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1374	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1375	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1376	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1377	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1378	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1379	C₂²⋊C₄	—	53	8	no	—
1380	C₂²⋊C₄	—	53	4	no	—
1381	C₂²⋊C₄	—	53	8	no	—
1382	C₂²⋊C₄	—	53	4	no	—
1383	C₂²⋊C₄	—	53	8	no	—
1384	C₂²⋊C₄	—	53	4	no	—
1385	C₂²⋊C₄	—	53	4	no	—
1386	C₂²⋊C₄	—	53	4	no	—
1387	C₂²⋊C₄	—	53	1	no	—
1388	C₂²⋊C₄	—	53	1	no	—
1389	C₂²⋊C₄	—	53	4	no	—
1390	C₂²⋊C₄	—	53	4	no	—
1391	C₂²⋊C₄	—	53	2	no	—
1392	C₂²⋊C₄	—	53	2	no	—
1393	C₂²⋊C₄	—	53	1	no	—
1394	C₂²⋊C₄	—	53	1	no	—
1395	C₂²⋊C₄	—	53	4	no	—
1396	C₂²⋊C₄	—	53	4	no	—
1397	C₂²⋊C₄	—	53	4	no	—
1398	C₂²⋊C₄	—	53	4	no	—
1399	C₂²⋊C₄	—	53	4	no	—
1400	C₂²⋊C₄	—	53	8	no	—
1401	C₂²⋊C₄	—	53	4	no	—
1402	C₂²⋊C₄	—	53	4	no	—
1403	C₂²⋊C₄	—	53	4	no	—
1404	C₂²⋊C₄	—	53	4	no	—
1405	C₂²⋊C₄	—	53	4	no	—
1406	C₂²⋊C₄	—	53	4	no	—
1407	C₂²⋊C₄	—	53	8	no	—
1408	C₂²⋊C₄	—	53	8	no	—
1409	C₂²⋊C₄	—	53	8	no	—
1410	C₂²⋊C₄	—	53	8	no	—
1411	C₂²⋊C₄	—	53	8	no	—
1412	C₂²⋊C₄	—	53	4	no	—
1413	C₂²⋊C₄	—	53	4	no	—
1414	C₂²⋊C₄	—	53	4	no	—
1415	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1416	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1417	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1418	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1419	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1420	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1421	C₄²	—	53	4	no	—
1422	C₄²	—	53	4	no	—
1423	C₄²	—	53	8	no	—
1424	C₄²	—	53	8	no	—
1425	C₄²	—	53	2	no	—
1426	C₄²	—	53	2	no	—
1427	C₄²	—	53	4	no	—
1428	C₄²	C₂³×D₅₃	1	2	yes	—
1429	C₄²	C₂³×D₅₃	1	2	yes	—
1430	C₄²	C₂³×D₅₃	1	4	yes	—
1431	C₄²	C₂³×D₅₃	1	4	yes	—
1432	C₄²	C₂³×D₅₃	1	8	yes	—
1433	C₄²	C₂³×D₅₃	1	4	yes	—
1434	C₂³	—	2	8	no	—
1435	C₂³	—	4	2	no	—
1436	C₂³	—	4	2	no	—
1437	C₂³	—	4	4	no	—
1438	C₂³	—	4	4	no	—
1439	C₂³	—	53	1	no	—
1440	C₂³	—	53	1	no	—
1441	C₂³	—	53	4	no	—
1442	C₂³	—	53	4	no	—
1443	C₂³	—	106	8	no	—
1444	C₂³	—	106	8	no	—
1445	C₂³	—	106	8	no	—
1446	C₂³	—	106	2	no	—
1447	C₂³	—	106	4	no	—
1448	C₂³	—	424	16	no	—
1449	C₂³	—	212	4	no	—
1450	C₂³	—	212	4	no	—
1451	C₂³	—	212	4	no	—
1452	C₂³	—	212	4	no	—
1453	C₂³	—	212	4	no	—
1454	C₂³	—	212	4	no	—
1455	C₂³	—	212	2	no	—
1456	C₂³	—	212	2	no	—
1457	C₂³	—	212	1	no	—
1458	C₂³	—	212	1	no	—
1459	C₂³	C₂×#11719945	1	8	yes	—
1460	C₂³	C₂⁴×D₅₃	1	4	yes	—
1461	C₂³	C₂⁴×D₅₃	1	4	yes	—
1462	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1463	Q₈	—	2	4	no	—
1464	Q₈	—	106	4	no	—
1465	Q₈	—	212	4	no	—
1466	Q₈	—	212	8	no	—
1467	Q₈	—	212	4	no	—
1468	D₄	—	2	16	no	—
1469	D₄	—	2	8	no	—
1470	D₄	—	2	4	no	—
1471	D₄	—	106	16	no	—
1472	D₄	—	106	16	no	—
1473	D₄	—	106	8	no	—
1474	D₄	—	106	8	no	—
1475	D₄	—	106	4	no	—
1476	D₄	—	212	4	no	—
1477	D₄	—	212	4	no	—
1478	D₄	—	212	8	no	—
1479	D₄	—	212	8	no	—
1480	D₄	—	212	4	no	—
1481	D₄	—	212	4	no	—
1482	D₄	—	212	4	no	—
1483	D₄	—	212	8	no	—
1484	D₄	—	212	8	no	—
1485	D₄	—	212	8	no	—
1486	D₄	—	212	4	no	—
1487	D₄	C₂×#11719945	1	16	yes	—
1488	C₂×C₄	—	2	8	no	—
1489	C₂×C₄	—	2	8	no	—
1490	C₂×C₄	—	4	1	no	—
1491	C₂×C₄	—	4	4	no	—
1492	C₂×C₄	—	4	4	no	—
1493	C₂×C₄	—	4	2	no	—
1494	C₂×C₄	—	4	4	no	—
1495	C₂×C₄	—	4	4	no	—
1496	C₂×C₄	—	4	8	no	—
1497	C₂×C₄	—	4	1	no	—
1498	C₂×C₄	—	4	4	no	—
1499	C₂×C₄	—	4	4	no	—
1500	C₂×C₄	—	53	4	no	—
1501	C₂×C₄	—	53	4	no	—
1502	C₂×C₄	—	53	2	no	—
1503	C₂×C₄	—	53	1	no	—
1504	C₂×C₄	—	53	2	no	—
1505	C₂×C₄	—	53	4	no	—
1506	C₂×C₄	—	53	4	no	—
1507	C₂×C₄	—	53	1	no	—
1508	C₂×C₄	—	106	2	no	—
1509	C₂×C₄	—	106	8	no	—
1510	C₂×C₄	—	106	4	no	—
1511	C₂×C₄	—	106	4	no	—
1512	C₂×C₄	—	106	8	no	—
1513	C₂×C₄	—	212	4	no	—
1514	C₂×C₄	—	212	8	no	—
1515	C₂×C₄	—	212	8	no	—
1516	C₂×C₄	—	212	8	no	—
1517	C₂×C₄	—	212	4	no	—
1518	C₂×C₄	—	212	1	no	—
1519	C₂×C₄	—	212	1	no	—
1520	C₂×C₄	—	212	2	no	—
1521	C₂×C₄	—	212	4	no	—
1522	C₂×C₄	—	212	4	no	—
1523	C₂×C₄	—	212	4	no	—
1524	C₂×C₄	—	212	4	no	—
1525	C₂×C₄	C₂×#11719945	1	4	yes	—
1526	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1527	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1528	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1529	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1530	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1531	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1532	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1533	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1534	C₂²	—	2	1	no	—
1535	C₂²	—	2	4	no	—
1536	C₂²	—	2	1	no	—
1537	C₂²	—	2	4	no	—
1538	C₂²	—	2	4	no	—
1539	C₂²	—	2	4	no	—
1540	C₂²	—	2	4	no	—
1541	C₂²	—	4	8	no	—
1542	C₂²	—	8	8	no	—
1543	C₂²	—	106	1	no	—
1544	C₂²	—	106	1	no	—
1545	C₂²	—	106	4	no	—
1546	C₂²	—	106	4	no	—
1547	C₂²	—	106	4	no	—
1548	C₂²	—	106	4	no	—
1549	C₂²	—	106	1	no	—
1550	C₂²	—	106	1	no	—
1551	C₂²	—	106	4	no	—
1552	C₂²	—	106	4	no	—
1553	C₂²	—	106	1	no	—
1554	C₂²	—	106	1	no	—
1555	C₂²	—	424	8	no	—
1556	C₂²	—	424	8	no	—
1557	C₂²	—	424	8	no	—
1558	C₂²	—	212	4	no	—
1559	C₂²	—	212	8	no	—
1560	C₂²	C₂²×#11719945	1	8	yes	—
1561	C₂²	C₂²×#11719945	1	2	yes	—
1562	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1563	C₄	—	2	4	no	—
1564	C₄	—	2	1	no	—
1565	C₄	—	2	1	no	—
1566	C₄	—	2	4	no	—
1567	C₄	—	2	4	no	—
1568	C₄	—	2	2	no	—
1569	C₄	—	2	4	no	—
1570	C₄	—	106	2	no	—
1571	C₄	—	106	4	no	—
1572	C₄	—	106	4	no	—
1573	C₄	—	106	2	no	—
1574	C₄	—	106	1	no	—
1575	C₄	—	106	4	no	—
1576	C₄	—	106	1	no	—
1577	C₄	—	106	4	no	—
1578	C₄	C₂²×#11719945	1	4	yes	—
1579	C₂	—	2	2	no	—
1580	C₂	—	2	8	no	—
1581	C₂	—	4	4	no	—
1582	C₂	—	212	1	no	—
1583	C₂	—	212	1	no	—
1584	C₂	—	212	4	no	—
1585	C₂	—	212	4	no	—
1586	C₂	C₂³×#11719945	1	1	yes	characteristic
1587	C₂	#20289525	1	1	yes	characteristic
1588	C₂	#20289526	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₄×H(5,𝔽₂)×C₅₃	C₂
hypercenter	C₄×H(5,𝔽₂)	D₅₃
hypocenter	C₅₃	#62846
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. #20288785	C₂	semidirect
2. #20288783	C₂	semidirect
3. #20288747	C₂	semidirect
4. #20288737	C₂	semidirect
5. #20288676	C₂	semidirect
6. #20288666	C₂	semidirect
7. #20288657	C₂	semidirect
8. #20288655	C₂	semidirect
9. #20288560	C₂	semidirect
10. #20288545	C₂	semidirect
11. #20288513	C₂	semidirect
12. #20288474	C₂	semidirect
13. #20288428	C₂	semidirect
14. #20288400	C₂	semidirect
15. #20288351	C₂	semidirect
16. #20288346	C₂	semidirect
17. #20288131	C₂	semidirect
18. #20288124	C₂	semidirect
19. #20288100	C₂	semidirect
20. C₂×#16811206	C₂	semidirect
21. C₄×#13133262	C₂	semidirect
22. C₂×#16811095	C₂	semidirect
23. C₄×H(5,𝔽₂)×C₅₃	C₂	semidirect
26. #16811358	C₂²	semidirect
27. #16811356	C₂²	semidirect
28. #16811346	C₂²	semidirect
29. #16811345	C₂²	semidirect
30. #16811341	C₂²	semidirect
31. #16811338	C₂²	semidirect
32. #16811336	C₂²	semidirect
33. #16811336	C₂²	semidirect
34. #16811332	C₂²	semidirect
35. #16811332	C₂²	semidirect
36. #16811330	C₂²	semidirect
37. #16811323	C₂²	semidirect
38. #16811322	C₂²	semidirect
39. #16811322	C₂²	semidirect
40. #16811321	C₂²	semidirect
41. #16811321	C₂²	semidirect
42. #16811319	C₂²	semidirect
43. #16811317	C₂²	semidirect
44. #16811314	C₂²	semidirect
45. #16811308	C₂²	semidirect
46. #16811306	C₂²	semidirect
47. #16811302	C₂²	semidirect
48. #16811302	C₂²	semidirect
49. #16811299	C₂²	semidirect
50. #16811297	C₂²	semidirect
51. #16811297	C₂²	semidirect
52. #16811297	C₂²	semidirect
53. #16811294	C₂²	semidirect
54. D₄×Dic₁₀₆	C₂²	semidirect
55. #16811282	C₂²	semidirect
56. #16811274	C₂²	semidirect
57. #16811272	C₂²	semidirect
58. #16811269	C₂²	semidirect
59. #16811269	C₂²	semidirect
60. #16811268	C₂²	semidirect
61. #16811268	C₂²	semidirect
62. #16811267	C₂²	semidirect
63. #16811263	C₂²	semidirect
64. #16811263	C₂²	semidirect
65. #16811263	C₂²	semidirect
66. #16811261	C₂²	semidirect
67. #16811261	C₂²	semidirect
68. #16811261	C₂²	semidirect
69. D₄×D₂₁₂	C₂²	semidirect
70. D₄×D₂₁₂	C₂²	semidirect
71. D₄×C₂²⋊D₅₃	C₂²	semidirect
72. D₄×C₂²⋊D₅₃	C₂²	semidirect
73. D₄×C₂²⋊D₅₃	C₂²	semidirect
74. #16811251	C₂²	semidirect
75. #16811249	C₂²	semidirect
76. #16811245	C₂²	semidirect
77. #16811245	C₂²	semidirect
78. #16811245	C₂²	semidirect
79. #16811244	C₂²	semidirect
80. #16811238	C₂²	semidirect
81. #16811238	C₂²	semidirect
82. #16811231	C₂²	semidirect
83. #16811231	C₂²	semidirect
84. #16811228	C₂²	semidirect
85. #16811224	C₂²	semidirect
86. #16811224	C₂²	semidirect
87. #16811224	C₂²	semidirect
88. #16811220	C₂²	semidirect
89. #16811215	C₂²	semidirect
90. #16811215	C₂²	semidirect
91. #16811215	C₂²	semidirect
92. #16811211	C₂²	semidirect
93. #16811206	C₂²	semidirect
94. #16811206	C₂²	semidirect
95. #16811206	C₂²	semidirect
96. #16811206	C₂²	semidirect
97. #16811206	C₂²	semidirect
98. #16811206	C₂²	semidirect
99. #16811206	C₂²	semidirect
100. #16811206	C₂²	semidirect
101. #16811206	C₂²	semidirect
102. #16811206	C₂²	semidirect
103. #16811201	C₂²	semidirect
104. #16811192	C₂²	semidirect
105. #16811187	C₂²	semidirect
106. #16811185	C₂²	semidirect
107. #16811182	C₂²	semidirect
108. #16811182	C₂²	semidirect
109. #16811176	C₂²	semidirect
110. #16811173	C₂²	semidirect
111. #16811170	C₂²	semidirect
112. #16811169	C₂²	semidirect
113. #16811160	C₂²	semidirect
114. #16811157	C₂²	semidirect
115. #16811157	C₂²	semidirect
116. #16811157	C₂²	semidirect
117. #16811157	C₂²	semidirect
118. #16811153	C₂²	semidirect
119. #16811153	C₂²	semidirect
120. #16811151	C₂²	semidirect
121. #16811151	C₂²	semidirect
122. C₂×#13133212	C₂²	semidirect
123. C₂×#13133211	C₂²	semidirect
124. C₂×#13133205	C₂²	semidirect
125. C₂×#13133203	C₂²	semidirect
126. #16811135	C₂²	semidirect
127. #16811134	C₂²	semidirect
128. #16811132	C₂²	semidirect
129. #16811132	C₂²	semidirect
130. #16811132	C₂²	semidirect
131. #16811130	C₂²	semidirect
132. C₂×#13133202	C₂²	semidirect
133. C₂×#13133200	C₂²	semidirect
134. C₂×#13133194	C₂²	semidirect
135. C₂×#13133191	C₂²	semidirect
136. C₂×#13133190	C₂²	semidirect
137. C₂×#13133189	C₂²	semidirect
138. C₂×#13133187	C₂²	semidirect
139. C₂×#13133185	C₂²	semidirect
140. #16811104	C₂²	semidirect
141. #16811102	C₂²	semidirect
143. #16811096	C₂²	semidirect
144. #16811095	C₂²	semidirect
145. #16811095	C₂²	semidirect
146. #16811095	C₂²	semidirect
147. #16811095	C₂²	semidirect
148. #16811095	C₂²	semidirect
149. C₄×#11719945	C₂²	semidirect
150. C₄×#11719947	C₂²	semidirect
151. C₂×C₄×D₂₁₂	C₂²	semidirect
153. C₂×#13133179	C₂²	semidirect
154. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
155. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
156. C₂×#13133177	C₂²	semidirect
157. C₄×D₄×D₅₃	C₂²	semidirect
158. C₂×#13133175	C₂²	semidirect
159. C₂×#13133174	C₂²	semidirect
160. C₂²×#11719921	C₂²	semidirect
161. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
163. C₅₃×#520	C₂²	semidirect
164. C₅₃×#520	C₂²	semidirect
166. C₅₃×#518	C₂²	semidirect
167. C₅₃×#518	C₂²	semidirect
168. C₄×#41×C₅₃	C₂²	semidirect
169. C₄×#41×C₅₃	C₂²	semidirect
171. C₂×C₄×D₄×C₅₃	C₂²	semidirect
172. C₂×C₄×D₄×C₅₃	C₂²	semidirect
176. C₂×#11719945	C₂³	semidirect
177. C₂×#11719945	C₂³	semidirect
179. C₂²×Dic₁₀₆	C₂³	semidirect
187. C₂²×C₂²⋊D₅₃	C₂³	semidirect
196. C₂²×C₄×D₅₃	C₂³	semidirect
197. #13133217	C₂³	semidirect
198. #13133216	C₂³	semidirect
199. #13133216	C₂³	semidirect
200. #13133216	C₂³	semidirect
201. #13133215	C₂³	semidirect
204. #13133213	C₂³	semidirect
208. #13133212	C₂³	semidirect
209. #13133212	C₂³	semidirect
210. #13133212	C₂³	semidirect
214. #13133211	C₂³	semidirect
215. #13133211	C₂³	semidirect
216. #13133211	C₂³	semidirect
217. #13133211	C₂³	semidirect
218. #13133210	C₂³	semidirect
219. #13133210	C₂³	semidirect
220. #13133210	C₂³	semidirect
221. #13133209	C₂³	semidirect
222. #13133209	C₂³	semidirect
223. #13133209	C₂³	semidirect
224. #13133208	C₂³	semidirect
225. #13133208	C₂³	semidirect
226. #13133208	C₂³	semidirect
227. #13133207	C₂³	semidirect
228. #13133207	C₂³	semidirect
229. #13133207	C₂³	semidirect
231. #13133206	C₂³	semidirect
236. #13133205	C₂³	semidirect
237. #13133205	C₂³	semidirect
238. #13133204	C₂³	semidirect
242. #13133203	C₂³	semidirect
243. #13133203	C₂³	semidirect
244. #13133203	C₂³	semidirect
248. #13133202	C₂³	semidirect
249. #13133202	C₂³	semidirect
250. #13133202	C₂³	semidirect
251. #13133202	C₂³	semidirect
258. #13133200	C₂³	semidirect
259. #13133200	C₂³	semidirect
260. #13133200	C₂³	semidirect
261. #13133200	C₂³	semidirect
262. #13133200	C₂³	semidirect
263. #13133199	C₂³	semidirect
264. #13133199	C₂³	semidirect
265. #13133199	C₂³	semidirect
266. #13133199	C₂³	semidirect
268. #13133198	C₂³	semidirect
271. #13133196	C₂³	semidirect
272. #13133196	C₂³	semidirect
273. #13133196	C₂³	semidirect
274. #13133196	C₂³	semidirect
275. #13133196	C₂³	semidirect
276. #13133195	C₂³	semidirect
277. #13133195	C₂³	semidirect
278. #13133195	C₂³	semidirect
279. #13133195	C₂³	semidirect
283. #13133194	C₂³	semidirect
284. #13133194	C₂³	semidirect
285. #13133194	C₂³	semidirect
286. #13133194	C₂³	semidirect
289. #13133193	C₂³	semidirect
301. #13133191	C₂³	semidirect
302. #13133191	C₂³	semidirect
303. #13133191	C₂³	semidirect
307. #13133190	C₂³	semidirect
308. #13133190	C₂³	semidirect
309. #13133190	C₂³	semidirect
310. #13133190	C₂³	semidirect
316. #13133189	C₂³	semidirect
317. #13133189	C₂³	semidirect
320. #13133188	C₂³	semidirect
327. #13133186	C₂³	semidirect
332. #13133185	C₂³	semidirect
333. C₄×Dic₁₀₆	C₂³	semidirect
334. C₄×Dic₁₀₆	C₂³	semidirect
335. C₄×Dic₁₀₆	C₂³	semidirect
336. C₄×Dic₁₀₆	C₂³	semidirect
337. C₄×Dic₁₀₆	C₂³	semidirect
338. #13133182	C₂³	semidirect
343. C₄×D₂₁₂	C₂³	semidirect
344. C₄×D₂₁₂	C₂³	semidirect
345. C₄×D₂₁₂	C₂³	semidirect
346. C₄×D₂₁₂	C₂³	semidirect
353. #13133179	C₂³	semidirect
361. C₄×C₂²⋊D₅₃	C₂³	semidirect
362. C₄×C₂²⋊D₅₃	C₂³	semidirect
363. C₄×C₂²⋊D₅₃	C₂³	semidirect
364. C₄×C₂²⋊D₅₃	C₂³	semidirect
365. C₄×C₂²⋊D₅₃	C₂³	semidirect
366. C₄×C₂²⋊D₅₃	C₂³	semidirect
367. C₄×C₂²⋊D₅₃	C₂³	semidirect
370. #13133177	C₂³	semidirect
371. #13133177	C₂³	semidirect
373. #13133176	C₂³	semidirect
376. #13133175	C₂³	semidirect
381. #13133174	C₂³	semidirect
382. #13133174	C₂³	semidirect
383. #13133174	C₂³	semidirect
384. #13133174	C₂³	semidirect
385. #13133173	C₂³	semidirect
387. C₂×C₄⋊Dic₅₃	C₂³	semidirect
390. C₂×#11719919	C₂³	semidirect
391. C₂×#11719919	C₂³	semidirect
392. C₂×#11719919	C₂³	semidirect
393. C₂×#11719919	C₂³	semidirect
394. C₄⋊C₄×D₅₃	C₂³	semidirect
397. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
411. C₂×#11719921	C₂³	semidirect
412. C₂×#11719921	C₂³	semidirect
415. C₂²⋊C₄×D₅₃	C₂³	semidirect
418. C₂×C₄×Dic₅₃	C₂³	semidirect
419. C₄²×D₅₃	C₂³	semidirect
427. C₂³×C₄×C₅₃	C₂³	semidirect
428. C₄×Q₈×C₅₃	C₂³	semidirect
429. C₄×Q₈×C₅₃	C₂³	semidirect
430. C₄×Q₈×C₅₃	C₂³	semidirect
438. C₄×D₄×C₅₃	C₂³	semidirect
439. C₄×D₄×C₅₃	C₂³	semidirect
440. C₄×D₄×C₅₃	C₂³	semidirect
441. C₄×D₄×C₅₃	C₂³	semidirect
442. C₄×D₄×C₅₃	C₂³	semidirect
443. C₄×D₄×C₅₃	C₂³	semidirect
444. C₄×D₄×C₅₃	C₂³	semidirect
446. #117×C₅₃	C₂³	semidirect
447. #117×C₅₃	C₂³	semidirect
448. #117×C₅₃	C₂³	semidirect
450. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
451. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
454. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
455. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
457. C₂×C₄²×C₅₃	C₂³	semidirect
458. C₂×C₄²×C₅₃	C₂³	semidirect
474. C₂×D₄×C₅₃	#41	semidirect
806. C₄×H(5,𝔽₂)	D₅₃	semidirect
937. #520	C₂×D₅₃	semidirect
938. #520	C₂×D₅₃	semidirect
947. #518	C₂×D₅₃	semidirect
948. #518	C₂×D₅₃	semidirect
951. C₄×#41	C₂×D₅₃	semidirect
952. C₄×#41	C₂×D₅₃	semidirect
961. C₂×C₄×D₄	C₂×D₅₃	semidirect
962. C₂×C₄×D₄	C₂×D₅₃	semidirect
967. C₅₃	#62846	semidirect
999. C₂³×C₄	C₂²×D₅₃	semidirect
1142. C₄×Q₈	C₂²×D₅₃	semidirect
1143. C₄×Q₈	C₂²×D₅₃	semidirect
1144. C₄×Q₈	C₂²×D₅₃	semidirect
1185. C₄×D₄	C₂²×D₅₃	semidirect
1186. C₄×D₄	C₂²×D₅₃	semidirect
1187. C₄×D₄	C₂²×D₅₃	semidirect
1188. C₄×D₄	C₂²×D₅₃	semidirect
1189. C₄×D₄	C₂²×D₅₃	semidirect
1190. C₄×D₄	C₂²×D₅₃	semidirect
1191. C₄×D₄	C₂²×D₅₃	semidirect
1207. #117	C₂²×D₅₃	semidirect
1208. #117	C₂²×D₅₃	semidirect
1209. #117	C₂²×D₅₃	semidirect
1220. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1221. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1245. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1246. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1252. C₂×C₄²	C₂²×D₅₃	semidirect
1253. C₂×C₄²	C₂²×D₅₃	semidirect
1305. C₂×D₄	#11719945	semidirect

Maximal subgroups

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

subgroup	index
#20288785	2
#20288783	2
#20288747	2
#20288737	2
#20288676	2
#20288666	2
#20288657	2
#20288655	2
#20288560	2
#20288545	2
#20288513	2
#20288474	2
#20288428	2
#20288400	2
#20288351	2
#20288346	2
#20288131	2
#20288124	2
#20288100	2
C₂×#16811206	2
C₄×#13133262	2
C₂×#16811095	2
C₄×H(5,𝔽₂)×C₅₃	2
#62846	53