Subgroups — #28293100

Order 13568.

11770 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133262	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×H(5,𝔽₂)×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288475	C₂	1	8	yes	maximal, complemented
4	#20288471	C₂	1	8	yes	maximal, complemented
5	#20288360	C₂	1	1	yes	maximal, characteristic, complemented
6	#20288357	C₂	1	2	yes	maximal, complemented
7	#20288356	C₂	1	4	yes	maximal, complemented
8	#20288355	C₂	1	1	yes	maximal, characteristic, complemented
9	#20288352	C₂	1	8	yes	maximal, complemented
10	#20288350	C₂	1	1	yes	maximal, characteristic, complemented
11	#20288349	C₂	1	2	yes	maximal, complemented
12	#20288344	C₂	1	4	yes	maximal, complemented
13	#20288343	C₂	1	8	yes	maximal, complemented
14	#20288046	C₂	1	2	yes	maximal, complemented
15	#20288045	C₂	1	2	yes	maximal, complemented
16	C₂×#16811183	C₂	1	4	yes	maximal, complemented
17	#534×D₅₃	C₂	1	4	yes	maximal, complemented
18	#518×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13133263	C₂²	1	2	yes	complemented
21	C₂×#13133263	C₂²	1	4	yes	complemented
22	C₂×#13133262	—	2	16	no	—
23	C₂×#13133262	C₂²	1	4	yes	complemented
24	C₂×#13133262	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13133262	C₂²	1	8	yes	complemented
26	C₂×#13133262	C₂²	1	4	yes	complemented
27	C₂×#13133262	C₂²	1	8	yes	complemented
28	H(5,𝔽₂)×D₅₃	—	2	16	no	—
29	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#11719947	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#11719947	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#11719947	C₂²	1	2	yes	complemented
34	C₂×#41×D₅₃	C₂²	1	2	yes	complemented
35	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
36	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
37	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
38	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
39	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
40	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
41	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
42	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
43	#16811278	C₂²	1	8	yes	complemented
44	#16811277	C₂²	1	8	yes	complemented
45	#16811275	C₂²	1	8	yes	complemented
46	#16811273	C₂²	1	16	yes	complemented
47	#16811272	C₂²	1	8	yes	complemented
48	#16811271	C₂²	1	16	yes	complemented
49	#16811270	C₂²	1	8	yes	complemented
50	#16811270	C₂²	1	8	yes	complemented
51	#16811269	C₂²	1	8	yes	complemented
52	#16811268	C₂²	1	8	yes	complemented
53	#16811267	C₂²	1	8	yes	complemented
54	#16811267	C₂²	1	8	yes	complemented
55	#16811266	C₂²	1	8	yes	complemented
56	#16811263	C₂²	1	16	yes	complemented
57	#16811262	C₂²	1	16	yes	complemented
58	#16811260	C₂²	1	16	yes	complemented
59	#16811260	C₂²	1	16	yes	complemented
60	#16811258	C₂²	1	8	yes	complemented
61	#16811257	C₂²	1	8	yes	complemented
62	D₄×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
63	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
64	#16811255	C₂²	1	16	yes	complemented
65	#16811203	C₂²	1	4	yes	complemented
66	#16811202	C₂²	1	4	yes	complemented
67	#16811202	C₂²	1	8	yes	complemented
68	#16811199	C₂²	1	2	yes	complemented
69	#16811196	C₂²	1	4	yes	complemented
70	#16811195	C₂²	1	4	yes	complemented
71	#16811194	C₂²	1	2	yes	complemented
72	#16811193	C₂²	1	4	yes	complemented
73	#16811190	C₂²	1	2	yes	complemented
74	#16811189	C₂²	1	4	yes	complemented
75	#16811188	C₂²	1	4	yes	complemented
76	#16811186	C₂²	1	4	yes	complemented
77	#16811185	C₂²	1	4	yes	complemented
78	#16811184	C₂²	1	4	yes	complemented
79	#16811184	C₂²	1	8	yes	complemented
80	#16811183	C₂²	1	8	yes	complemented
81	#16811183	C₂²	1	4	yes	complemented
82	#16811183	C₂²	1	8	yes	complemented
83	#16811183	C₂²	1	8	yes	complemented
84	#16811183	C₂²	1	16	yes	complemented
85	#16811183	C₂²	1	8	yes	complemented
86	#16811183	C₂²	1	16	yes	complemented
87	#16811182	C₂²	1	4	yes	complemented
88	#16811182	C₂²	1	4	yes	complemented
89	#16811181	C₂²	1	16	yes	complemented
90	#16811172	C₂²	1	4	yes	complemented
91	#16811171	C₂²	1	4	yes	complemented
92	#16811170	C₂²	1	8	yes	complemented
93	#16811135	C₂²	1	2	yes	complemented
94	#16811134	C₂²	1	2	yes	complemented
95	#16811133	C₂²	1	8	yes	complemented
96	#16811132	C₂²	1	8	yes	complemented
97	#16811130	C₂²	1	2	yes	complemented
98	#16811129	C₂²	1	8	yes	complemented
99	C₂×#13133201	C₂²	1	4	yes	complemented
100	C₂×#13133199	C₂²	1	8	yes	complemented
101	C₂×#13133198	C₂²	1	4	yes	complemented
102	#123×D₅₃	C₂²	1	8	yes	complemented
103	#123×D₅₃	C₂²	1	8	yes	complemented
104	C₂×#13133190	C₂²	1	8	yes	complemented
105	C₂×#13133188	C₂²	1	8	yes	complemented
106	#121×D₅₃	C₂²	1	16	yes	complemented
107	C₂×#13133186	C₂²	1	4	yes	complemented
108	C₂×#13133185	C₂²	1	8	yes	complemented
109	#120×D₅₃	C₂²	1	8	yes	complemented
110	#120×D₅₃	C₂²	1	8	yes	complemented
111	#16811098	C₂²	1	1	yes	characteristic, complemented
112	#16811097	C₂²	1	2	yes	complemented
113	#16811096	C₂²	1	4	yes	complemented
114	#16811095	C₂²	1	8	yes	complemented
115	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
116	#117×D₅₃	C₂²	1	2	yes	complemented
117	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
118	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#546	C₂²	1	8	yes	complemented
121	D₄²×C₅₃	C₂²	1	8	yes	complemented
122	C₅₃×#535	C₂²	1	2	yes	complemented
123	C₅₃×#534	C₂²	1	4	yes	complemented
124	C₅₃×#525	C₂²	1	2	yes	complemented
125	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
126	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
127	C₂⁴×D₅₃	C₂³	1	2	yes	—
128	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
129	C₂⁴×D₅₃	C₂³	1	4	yes	complemented
130	#13133263	—	2	32	no	—
131	#13133263	—	2	16	no	—
132	#13133262	—	2	8	no	—
133	#13133262	—	2	32	no	—
134	#13133262	—	2	32	no	—
135	#13133262	—	2	64	no	—
136	#13133262	—	2	64	no	—
137	C₂×#11719949	C₂³	1	4	yes	complemented
138	C₂×#11719949	C₂³	1	2	yes	complemented
139	C₂×#11719945	—	2	8	no	—
140	C₂×#11719945	—	2	8	no	—
141	C₂×#11719945	C₂³	1	4	yes	—
142	C₂×#11719945	C₂³	1	2	yes	—
143	C₂×#11719945	C₂³	1	8	yes	complemented
144	C₂×#11719945	C₂³	1	4	yes	complemented
145	C₂×#11719945	C₂³	1	8	yes	complemented
146	C₂×#11719945	C₂³	1	4	yes	complemented
147	C₂×#11719945	C₂³	1	4	yes	complemented
148	C₂×#11719947	—	2	8	no	—
149	C₂×#11719947	—	2	16	no	—
150	C₂×#11719947	—	2	8	no	—
151	C₂×#11719947	C₂³	1	4	yes	—
152	C₂×#11719947	C₂³	1	4	yes	—
153	C₂×#11719947	C₂³	1	4	yes	complemented
154	C₂×#11719947	C₂³	1	8	yes	complemented
155	C₂×#11719947	C₂³	1	16	yes	complemented
156	C₂×#11719947	C₂³	1	8	yes	complemented
157	C₂×#11719947	C₂³	1	2	yes	complemented
158	C₂×#11719947	C₂³	1	4	yes	complemented
159	#41×D₅₃	—	2	32	no	—
160	#41×D₅₃	—	2	16	no	—
161	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
162	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
163	C₂×Q₈×D₅₃	C₂³	1	2	yes	complemented
164	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
165	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
166	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
167	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
168	C₂²×C₂²⋊D₅₃	—	2	16	no	—
169	C₂²×C₂²⋊D₅₃	—	2	16	no	—
170	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
171	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
172	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
173	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
174	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
175	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
176	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
177	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
178	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
179	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
180	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
181	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic, complemented
182	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
183	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
184	C₂×D₄×D₅₃	—	2	32	no	—
185	C₂×D₄×D₅₃	—	2	16	no	—
186	C₂×D₄×D₅₃	—	2	32	no	—
187	C₂×D₄×D₅₃	—	2	8	no	—
188	C₂×D₄×D₅₃	D₄	1	16	yes	complemented
189	C₂×D₄×D₅₃	C₂³	1	8	yes	—
190	C₂×D₄×D₅₃	C₂³	1	8	yes	—
191	C₂×D₄×D₅₃	C₂³	1	4	yes	—
192	C₂×D₄×D₅₃	C₂³	1	4	yes	—
193	C₂×D₄×D₅₃	C₂³	1	4	yes	—
194	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
195	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
196	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
197	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
198	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
199	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
200	C₂×D₄×D₅₃	C₂³	1	2	yes	complemented
201	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
202	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
203	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
204	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
207	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
208	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
209	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
210	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
211	#13133217	C₂³	1	4	yes	complemented
212	#13133216	C₂³	1	8	yes	complemented
213	#13133215	C₂³	1	4	yes	complemented
214	#13133213	C₂³	1	8	yes	complemented
215	#13133213	C₂³	1	4	yes	complemented
216	#13133205	C₂³	1	4	yes	complemented
217	#13133204	C₂³	1	4	yes	complemented
218	#13133204	C₂³	1	4	yes	complemented
219	#13133203	C₂³	1	8	yes	complemented
220	#13133203	C₂³	1	8	yes	complemented
221	#13133202	C₂³	1	16	yes	complemented
222	#13133202	C₂³	1	8	yes	complemented
223	#13133201	C₂³	1	16	yes	complemented
224	#13133201	C₂³	1	8	yes	complemented
225	#13133201	C₂³	1	8	yes	complemented
226	#13133201	C₂³	1	4	yes	complemented
227	#13133200	C₂³	1	8	yes	complemented
228	#13133200	C₂³	1	4	yes	complemented
229	#13133199	C₂³	1	16	yes	complemented
230	#13133199	C₂³	1	16	yes	complemented
231	#13133199	C₂³	1	16	yes	complemented
232	#13133199	C₂³	1	16	yes	complemented
233	#13133199	C₂³	1	8	yes	complemented
234	#13133198	C₂³	1	8	yes	complemented
235	#13133198	C₂³	1	16	yes	complemented
236	#13133198	C₂³	1	8	yes	complemented
237	#13133198	C₂³	1	4	yes	complemented
238	#13133197	C₂³	1	8	yes	complemented
239	#13133197	C₂³	1	4	yes	complemented
240	#13133196	C₂³	1	4	yes	complemented
241	#13133196	C₂³	1	8	yes	complemented
242	#13133195	C₂³	1	8	yes	complemented
243	#13133194	C₂³	1	16	yes	complemented
244	#13133194	C₂³	1	8	yes	complemented
245	#13133193	C₂³	1	4	yes	complemented
246	#13133192	C₂³	1	4	yes	complemented
247	#13133192	C₂³	1	8	yes	complemented
248	#13133191	C₂³	1	16	yes	complemented
249	#13133191	C₂³	1	4	yes	complemented
250	#13133190	C₂³	1	16	yes	complemented
251	#13133190	C₂³	1	16	yes	complemented
252	#13133190	C₂³	1	8	yes	complemented
253	#13133190	C₂³	1	16	yes	complemented
254	#13133190	C₂³	1	8	yes	complemented
255	#13133190	C₂³	1	8	yes	complemented
256	#13133189	C₂³	1	16	yes	complemented
257	#13133189	C₂³	1	16	yes	complemented
258	#13133189	C₂³	1	16	yes	complemented
259	#13133189	C₂³	1	8	yes	complemented
260	#13133188	C₂³	1	8	yes	complemented
261	#13133188	C₂³	1	4	yes	complemented
262	#13133188	C₂³	1	16	yes	complemented
263	#13133188	C₂³	1	16	yes	complemented
264	#13133188	C₂³	1	16	yes	complemented
265	#13133188	C₂³	1	8	yes	complemented
266	#13133187	C₂³	1	16	yes	complemented
267	#13133187	C₂³	1	8	yes	complemented
268	#13133187	C₂³	1	8	yes	complemented
269	#13133187	C₂³	1	4	yes	complemented
270	#13133186	C₂³	1	8	yes	complemented
271	#13133186	C₂³	1	16	yes	complemented
272	#13133186	C₂³	1	8	yes	complemented
273	#13133186	C₂³	1	4	yes	complemented
274	#13133185	C₂³	1	16	yes	complemented
275	#13133185	C₂³	1	16	yes	complemented
276	#13133185	C₂³	1	4	yes	complemented
277	#13133185	C₂³	1	16	yes	complemented
278	#13133185	C₂³	1	8	yes	complemented
279	#13133185	C₂³	1	8	yes	complemented
280	#13133185	C₂³	1	16	yes	complemented
281	C₄×D₂₁₂	C₂³	1	8	yes	complemented
282	C₄×D₂₁₂	C₂³	1	8	yes	complemented
283	D₄×Dic₅₃	C₂³	1	8	yes	complemented
284	D₄×Dic₅₃	C₂³	1	16	yes	complemented
285	#13133179	C₂³	1	8	yes	complemented
286	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
287	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
288	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
289	#13133177	C₂³	1	16	yes	complemented
290	#13133177	C₂³	1	16	yes	complemented
291	#13133176	C₂³	1	2	yes	complemented
292	#13133175	C₂³	1	4	yes	complemented
293	#13133174	C₂³	1	4	yes	complemented
294	#13133173	C₂³	1	4	yes	complemented
295	C₂×C₄⋊Dic₅₃	C₂³	1	8	yes	complemented
296	C₂×#11719919	C₂³	1	8	yes	complemented
297	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
298	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
299	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
300	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
301	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
302	C₂×#11719921	C₂³	1	8	yes	complemented
303	C₂×#11719921	C₂³	1	8	yes	complemented
304	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
305	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
306	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
307	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
308	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
309	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
310	C₄²×D₅₃	C₂³	1	4	yes	complemented
311	C₂⁵×C₅₃	C₂³	1	2	yes	complemented
312	H(5,𝔽₂)×C₅₃	—	2	8	no	—
313	C₂×#41×C₅₃	C₂³	1	2	yes	—
314	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
315	C₂²×D₄×C₅₃	—	2	8	no	—
316	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
317	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
319	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
320	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
321	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
322	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
323	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
324	#127×C₅₃	C₂³	1	4	yes	complemented
325	#124×C₅₃	C₂³	1	4	yes	complemented
326	#123×C₅₃	C₂³	1	8	yes	complemented
327	#123×C₅₃	C₂³	1	4	yes	complemented
328	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
329	#121×C₅₃	C₂³	1	4	yes	complemented
330	#121×C₅₃	C₂³	1	8	yes	complemented
331	#121×C₅₃	C₂³	1	16	yes	complemented
332	#120×C₅₃	C₂³	1	4	yes	complemented
333	#120×C₅₃	C₂³	1	8	yes	complemented
334	#120×C₅₃	C₂³	1	16	yes	complemented
335	#120×C₅₃	C₂³	1	8	yes	complemented
336	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
337	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
338	#117×C₅₃	C₂³	1	2	yes	complemented
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
341	C₂⁴×C₅₃	—	2	8	no	—
342	C₂⁴×C₅₃	—	8	4	no	—
343	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
344	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
346	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
347	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
348	C₂³×D₅₃	—	2	16	no	—
349	C₂³×D₅₃	—	2	8	no	—
350	C₂³×D₅₃	—	8	4	no	—
351	C₂³×D₅₃	—	8	8	no	—
352	C₂³×D₅₃	—	8	4	no	—
353	C₂³×D₅₃	C₂×D₄	1	16	yes	complemented
354	C₂³×D₅₃	C₂⁴	1	8	yes	—
355	C₂³×D₅₃	C₂⁴	1	8	yes	—
356	C₂³×D₅₃	C₂⁴	1	4	yes	—
357	C₂³×D₅₃	C₂⁴	1	4	yes	—
358	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
359	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
360	C₂³×D₅₃	C₂⁴	1	2	yes	—
361	C₂³×D₅₃	C₂⁴	1	4	yes	—
362	C₂³×D₅₃	C₂⁴	1	4	yes	—
363	#41×C₅₃	—	2	16	no	—
364	#41×C₅₃	—	2	8	no	—
365	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
366	C₂×D₄×C₅₃	—	2	8	no	—
367	C₂×D₄×C₅₃	—	2	16	no	—
368	C₂×D₄×C₅₃	—	2	32	no	—
369	C₂×D₄×C₅₃	—	2	16	no	—
370	C₂×D₄×C₅₃	—	2	4	no	—
371	C₂×D₄×C₅₃	—	8	8	no	—
372	C₂×D₄×C₅₃	C₂×D₄	1	8	yes	complemented
373	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
374	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
375	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
376	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
377	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
378	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
379	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
380	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₅₃	—	2	4	no	—
382	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
383	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
384	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₂²⋊D₅₃	—	2	8	no	—
389	C₂×C₂²⋊D₅₃	—	2	16	no	—
390	C₂×C₂²⋊D₅₃	—	2	8	no	—
391	C₂×C₂²⋊D₅₃	—	2	8	no	—
392	C₂×C₂²⋊D₅₃	—	2	16	no	—
393	C₂×C₂²⋊D₅₃	—	2	4	no	—
394	C₂×C₂²⋊D₅₃	—	2	8	no	—
395	C₂×C₂²⋊D₅₃	—	2	32	no	—
396	C₂×C₂²⋊D₅₃	—	2	32	no	—
397	C₂×C₂²⋊D₅₃	—	2	32	no	—
398	C₂×C₂²⋊D₅₃	—	2	64	no	—
399	C₂×C₂²⋊D₅₃	—	2	4	no	—
400	C₂×C₂²⋊D₅₃	—	8	8	no	—
401	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
402	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
403	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
404	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
405	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
406	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
407	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
408	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
409	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
410	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
411	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
412	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
413	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
414	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
415	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
416	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
417	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
418	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
419	C₂²×Dic₅₃	—	2	8	no	—
420	C₂²×Dic₅₃	—	2	8	no	—
421	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
422	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
423	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
424	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
425	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
426	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
428	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
429	#11719949	—	2	16	no	—
430	#11719949	—	2	8	no	—
431	Q₈×D₅₃	—	2	8	no	—
432	#11719947	—	2	16	no	—
433	#11719947	—	2	32	no	—
434	#11719947	—	2	32	no	—
435	#11719947	—	2	64	no	—
436	#11719947	—	2	16	no	—
437	#11719947	—	2	8	no	—
438	#11719947	—	2	16	no	—
439	#11719947	—	2	16	no	—
440	D₄×D₅₃	—	2	16	no	—
441	D₄×D₅₃	—	2	32	no	—
442	D₄×D₅₃	—	2	32	no	—
443	D₄×D₅₃	—	2	32	no	—
444	D₄×D₅₃	—	2	32	no	—
445	D₄×D₅₃	—	2	32	no	—
446	D₄×D₅₃	—	2	16	no	—
447	D₄×D₅₃	—	2	32	no	—
448	D₄×D₅₃	—	2	32	no	—
449	D₄×D₅₃	—	2	16	no	—
450	D₄×D₅₃	—	2	8	no	—
451	D₄×D₅₃	—	8	16	no	—
452	D₄×D₅₃	C₂×D₄	1	32	yes	complemented
453	D₄×D₅₃	C₂×D₄	1	32	yes	complemented
454	#11719945	—	2	8	no	—
455	#11719945	—	2	32	no	—
456	#11719945	—	2	16	no	—
457	#11719945	—	2	32	no	—
458	#11719945	—	2	16	no	—
459	#11719945	—	2	16	no	—
460	#11719945	—	2	16	no	—
461	C₂×D₂₁₂	—	2	4	no	—
462	C₂×D₂₁₂	—	2	16	no	—
463	C₂×D₂₁₂	—	2	16	no	—
464	C₂×D₂₁₂	C₂×D₄	1	8	yes	complemented
465	C₂×D₂₁₂	C₂⁴	1	2	yes	—
466	C₂×D₂₁₂	C₂⁴	1	8	yes	—
467	C₂×D₂₁₂	C₂⁴	1	4	yes	—
468	C₂×D₂₁₂	C₂⁴	1	2	yes	—
469	C₂×D₂₁₂	C₂⁴	1	2	yes	—
470	C₂×D₂₁₂	C₂⁴	1	8	yes	—
471	C₂×D₂₁₂	C₂⁴	1	4	yes	—
472	C₂×C₄×D₅₃	—	2	16	no	—
473	C₂×C₄×D₅₃	—	2	8	no	—
474	C₂×C₄×D₅₃	—	2	4	no	—
475	C₂×C₄×D₅₃	—	2	16	no	—
476	C₂×C₄×D₅₃	—	8	8	no	—
477	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	complemented
478	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
479	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
480	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
481	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
482	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
483	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
484	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
485	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
486	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
487	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
488	C₂×Dic₁₀₆	—	2	4	no	—
489	C₂×Dic₁₀₆	—	2	4	no	—
490	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
491	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
492	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
493	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
494	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
495	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
496	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
497	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
498	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
499	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
500	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
501	C₄²×C₅₃	C₂⁴	1	4	yes	—
502	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
503	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
504	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
505	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
506	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
507	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
508	#11719921	C₂⁴	1	8	yes	—
509	#11719921	C₂⁴	1	16	yes	—
510	#11719921	C₂⁴	1	8	yes	—
511	#11719921	C₂⁴	1	8	yes	—
512	#11719921	C₂⁴	1	8	yes	—
513	#11719921	C₂⁴	1	16	yes	—
514	#11719921	C₂⁴	1	8	yes	—
515	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
516	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
517	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
518	#11719919	C₂⁴	1	8	yes	—
519	#11719919	C₂⁴	1	16	yes	—
520	#11719919	C₂⁴	1	8	yes	—
521	#11719919	C₂⁴	1	8	yes	—
522	C₄×Dic₅₃	C₂⁴	1	8	yes	—
523	C₄×Dic₅₃	C₂⁴	1	4	yes	—
524	C₂³×C₅₃	—	2	4	no	—
525	C₂³×C₅₃	—	2	2	no	—
526	C₂³×C₅₃	—	2	16	no	—
527	C₂³×C₅₃	—	2	8	no	—
528	C₂³×C₅₃	—	4	4	no	—
529	C₂³×C₅₃	—	4	4	no	—
530	C₂³×C₅₃	—	4	2	no	—
531	C₂³×C₅₃	—	4	8	no	—
532	C₂³×C₅₃	—	4	8	no	—
533	C₂³×C₅₃	—	4	8	no	—
534	C₂³×C₅₃	—	8	16	no	—
535	C₂³×C₅₃	C₂²×D₄	1	8	yes	—
536	C₂³×C₅₃	C₂⁵	1	4	yes	—
537	C₂³×C₅₃	C₂⁵	1	4	yes	—
538	C₂³×C₅₃	C₂⁵	1	2	yes	—
539	C₂³×C₅₃	C₂⁵	1	4	yes	—
540	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
541	C₂²×D₅₃	—	2	2	no	—
542	C₂²×D₅₃	—	2	8	no	—
543	C₂²×D₅₃	—	2	8	no	—
544	C₂²×D₅₃	—	2	16	no	—
545	C₂²×D₅₃	—	2	16	no	—
546	C₂²×D₅₃	—	4	8	no	—
547	C₂²×D₅₃	—	4	2	no	—
548	C₂²×D₅₃	—	4	4	no	—
549	C₂²×D₅₃	—	4	8	no	—
550	C₂²×D₅₃	—	4	8	no	—
551	C₂²×D₅₃	—	4	2	no	—
552	C₂²×D₅₃	—	4	16	no	—
553	C₂²×D₅₃	—	4	16	no	—
554	C₂²×D₅₃	—	4	8	no	—
555	C₂²×D₅₃	—	8	16	no	—
556	C₂²×D₅₃	—	8	32	no	—
557	C₂²×D₅₃	—	8	16	no	—
558	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
559	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
560	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
561	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
562	C₂²×D₅₃	C₂⁵	1	4	yes	—
563	C₂²×D₅₃	C₂⁵	1	2	yes	—
564	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
565	C₂²×D₅₃	C₂⁵	1	4	yes	—
566	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
567	Q₈×C₅₃	—	2	4	no	—
568	D₄×C₅₃	—	2	8	no	—
569	D₄×C₅₃	—	2	16	no	—
570	D₄×C₅₃	—	2	16	no	—
571	D₄×C₅₃	—	2	4	no	—
572	D₄×C₅₃	—	2	8	no	—
573	D₄×C₅₃	—	4	16	no	—
574	D₄×C₅₃	—	4	8	no	—
575	D₄×C₅₃	C₂²×D₄	1	16	yes	—
576	C₂×C₄×C₅₃	—	2	2	no	—
577	C₂×C₄×C₅₃	—	2	8	no	—
578	C₂×C₄×C₅₃	—	2	8	no	—
579	C₂×C₄×C₅₃	—	2	8	no	—
580	C₂×C₄×C₅₃	—	4	8	no	—
581	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
582	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
583	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
584	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
585	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
586	C₂²⋊D₅₃	—	2	8	no	—
587	C₂²⋊D₅₃	—	2	16	no	—
588	C₂²⋊D₅₃	—	2	16	no	—
589	C₂²⋊D₅₃	—	2	4	no	—
590	C₂²⋊D₅₃	—	2	16	no	—
591	C₂²⋊D₅₃	—	2	4	no	—
592	C₂²⋊D₅₃	—	2	16	no	—
593	C₂²⋊D₅₃	—	2	8	no	—
594	C₂²⋊D₅₃	—	2	8	no	—
595	C₂²⋊D₅₃	—	2	16	no	—
596	C₂²⋊D₅₃	—	2	8	no	—
597	C₂²⋊D₅₃	—	2	8	no	—
598	C₂²⋊D₅₃	—	2	8	no	—
599	C₂²⋊D₅₃	—	4	8	no	—
600	C₂²⋊D₅₃	—	4	16	no	—
601	C₂²⋊D₅₃	—	4	8	no	—
602	C₂²⋊D₅₃	C₂²×D₄	1	32	yes	—
603	C₂×Dic₅₃	—	2	4	no	—
604	C₂×Dic₅₃	—	2	2	no	—
605	C₂×Dic₅₃	—	2	8	no	—
606	C₂×Dic₅₃	—	2	16	no	—
607	C₂×Dic₅₃	—	2	8	no	—
608	C₂×Dic₅₃	—	2	16	no	—
609	C₂×Dic₅₃	—	4	8	no	—
610	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
611	C₂×Dic₅₃	C₂⁵	1	4	yes	—
612	C₂×Dic₅₃	C₂⁵	1	2	yes	—
613	C₂×Dic₅₃	C₂⁵	1	4	yes	—
614	C₂×Dic₅₃	C₂⁵	1	8	yes	—
615	C₂×Dic₅₃	C₂⁵	1	2	yes	—
616	D₂₁₂	—	2	16	no	—
617	D₂₁₂	—	2	8	no	—
618	D₂₁₂	—	2	4	no	—
619	D₂₁₂	—	2	4	no	—
620	D₂₁₂	—	2	4	no	—
621	D₂₁₂	—	4	8	no	—
622	D₂₁₂	C₂²×D₄	1	16	yes	—
623	C₄×D₅₃	—	2	8	no	—
624	C₄×D₅₃	—	2	16	no	—
625	C₄×D₅₃	—	2	16	no	—
626	C₄×D₅₃	—	2	8	no	—
627	C₄×D₅₃	—	2	8	no	—
628	C₄×D₅₃	—	2	8	no	—
629	C₄×D₅₃	—	4	8	no	—
630	C₄×D₅₃	—	4	16	no	—
631	C₄×D₅₃	C₂²×D₄	1	8	yes	—
632	C₄×D₅₃	C₂²×D₄	1	8	yes	—
633	Dic₁₀₆	—	2	8	no	—
634	Dic₁₀₆	—	2	4	no	—
635	Dic₁₀₆	—	2	8	no	—
636	Dic₁₀₆	—	2	8	no	—
637	#62842	—	53	1	no	maximal, Sylow
638	C₂²×C₅₃	—	2	8	no	—
639	C₂²×C₅₃	—	2	2	no	—
640	C₂²×C₅₃	—	2	4	no	—
641	C₂²×C₅₃	—	2	4	no	—
642	C₂²×C₅₃	—	2	2	no	—
643	C₂²×C₅₃	—	2	2	no	—
644	C₂²×C₅₃	—	2	8	no	—
645	C₂²×C₅₃	—	2	8	no	—
646	C₂²×C₅₃	—	2	2	no	—
647	C₂²×C₅₃	—	4	8	no	—
648	C₂²×C₅₃	—	4	8	no	—
649	C₂²×C₅₃	—	4	4	no	—
650	C₂²×C₅₃	—	8	8	no	—
651	C₂²×C₅₃	—	8	16	no	—
652	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
653	C₂²×C₅₃	C₂³×D₄	1	8	yes	—
654	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
655	C₂×D₅₃	—	2	2	no	—
656	C₂×D₅₃	—	2	8	no	—
657	C₂×D₅₃	—	2	2	no	—
658	C₂×D₅₃	—	2	4	no	—
659	C₂×D₅₃	—	2	2	no	—
660	C₂×D₅₃	—	2	4	no	—
661	C₂×D₅₃	—	2	8	no	—
662	C₂×D₅₃	—	4	4	no	—
663	C₂×D₅₃	—	4	16	no	—
664	C₂×D₅₃	—	4	8	no	—
665	C₂×D₅₃	—	4	16	no	—
666	C₂×D₅₃	—	4	16	no	—
667	C₂×D₅₃	—	4	4	no	—
668	C₂×D₅₃	—	8	16	no	—
669	C₂×D₅₃	—	8	16	no	—
670	C₂×D₅₃	—	8	8	no	—
671	C₂×D₅₃	C₂³×D₄	1	2	yes	—
672	C₂×D₅₃	C₂³×D₄	1	8	yes	—
673	C₂×D₅₃	C₂³×D₄	1	2	yes	—
674	C₄×C₅₃	—	2	2	no	—
675	C₄×C₅₃	—	2	4	no	—
676	C₄×C₅₃	—	2	8	no	—
677	C₄×C₅₃	C₂³×D₄	1	4	yes	—
678	Dic₅₃	—	2	4	no	—
679	Dic₅₃	—	2	4	no	—
680	Dic₅₃	—	2	2	no	—
681	Dic₅₃	—	2	8	no	—
682	Dic₅₃	C₂³×D₄	1	4	yes	—
683	C₂²×H(5,𝔽₂)	—	53	1	no	—
684	C₂²×H(5,𝔽₂)	—	53	1	no	—
685	#3496	—	53	8	no	—
686	#3496	—	53	8	no	—
687	#3485	—	53	1	no	—
688	#3485	—	53	8	no	—
689	#3485	—	53	4	no	—
690	#3485	—	53	2	no	—
691	#3485	—	53	1	no	—
692	#3484	—	53	1	no	—
693	#3484	—	53	8	no	—
694	#3484	—	53	2	no	—
695	#3484	—	53	4	no	—
696	#3484	D₅₃	1	1	yes	characteristic, complemented
697	#3449	—	53	2	no	—
698	#3449	—	53	2	no	—
699	C₂×#534	—	53	4	no	—
700	C₂×#534	—	53	4	no	—
701	C₂×#518	—	53	1	no	—
702	C₂×C₅₃	—	2	2	no	—
703	C₂×C₅₃	—	2	8	no	—
704	C₂×C₅₃	—	4	4	no	—
705	C₂×C₅₃	—	4	4	no	—
706	C₂×C₅₃	—	4	2	no	—
707	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
708	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
709	D₅₃	—	2	2	no	—
710	D₅₃	—	2	2	no	—
711	D₅₃	—	2	8	no	—
712	D₅₃	—	4	4	no	—
713	D₅₃	—	4	2	no	—
714	C₂×H(5,𝔽₂)	—	53	2	no	—
715	C₂×H(5,𝔽₂)	—	53	4	no	—
716	C₂×H(5,𝔽₂)	—	53	4	no	—
717	C₂×H(5,𝔽₂)	—	53	1	no	—
718	C₂×H(5,𝔽₂)	—	53	8	no	—
719	C₂×H(5,𝔽₂)	—	53	8	no	—
720	C₂×H(5,𝔽₂)	—	53	4	no	—
721	C₂×H(5,𝔽₂)	—	106	16	no	—
722	C₂×H(5,𝔽₂)	—	106	16	no	—
723	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
724	C₂²×#41	—	53	2	no	—
725	C₂²×#41	—	53	4	no	—
726	C₂²×#41	—	53	1	no	—
727	C₂²×#41	—	53	1	no	—
728	C₂²×#41	—	53	2	no	—
729	C₂²×#41	—	53	1	no	—
730	C₂²×#41	—	53	1	no	—
731	C₂³×D₄	—	53	1	no	—
732	C₂³×D₄	—	53	2	no	—
733	C₂³×D₄	—	53	2	no	—
734	C₂³×D₄	—	53	4	no	—
735	C₂³×D₄	—	53	2	no	—
736	C₂³×D₄	—	53	4	no	—
737	C₂³×D₄	—	53	1	no	—
738	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
739	#547	—	53	8	no	—
740	#547	—	53	16	no	—
741	#547	—	53	8	no	—
742	#547	—	53	16	no	—
743	#547	—	53	8	no	—
744	#547	—	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	16	no	—
751	#546	—	53	16	no	—
752	#546	—	53	16	no	—
753	#546	—	53	8	no	—
754	#546	—	53	8	no	—
755	#546	—	53	16	no	—
756	#546	C₂×D₅₃	1	8	yes	complemented
757	D₄²	—	53	8	no	—
758	D₄²	—	53	16	no	—
759	D₄²	—	53	8	no	—
760	D₄²	—	53	8	no	—
761	D₄²	—	53	16	no	—
762	D₄²	C₂×D₅₃	1	8	yes	complemented
763	#537	—	53	4	no	—
764	#537	—	53	8	no	—
765	#537	—	53	4	no	—
766	#536	—	53	2	no	—
767	#536	—	53	4	no	—
768	#536	—	53	4	no	—
769	#536	—	53	4	no	—
770	#536	—	53	2	no	—
771	#535	—	53	2	no	—
772	#535	—	53	4	no	—
773	#535	—	53	4	no	—
774	#535	—	53	4	no	—
775	#535	C₂×D₅₃	1	2	yes	complemented
776	#534	—	53	4	no	—
777	#534	—	53	4	no	—
778	#534	—	53	4	no	—
779	#534	—	53	8	no	—
780	#534	—	53	16	no	—
781	#534	—	53	8	no	—
782	#534	—	53	4	no	—
783	#534	—	53	8	no	—
784	#534	—	53	8	no	—
785	#534	—	53	16	no	—
786	#534	—	53	8	no	—
787	#534	—	53	16	no	—
788	#534	—	53	4	no	—
789	#534	C₂×D₅₃	1	4	yes	complemented
790	#532	—	53	4	no	—
791	#532	—	53	4	no	—
792	#532	—	53	8	no	—
793	#525	—	53	2	no	—
794	#525	—	53	2	no	—
795	#525	—	53	8	no	—
796	#525	—	53	8	no	—
797	#525	—	53	8	no	—
798	#525	—	53	2	no	—
799	#525	C₂×D₅₃	1	2	yes	complemented
800	C₂×#123	—	53	4	no	—
801	C₂×#123	—	53	8	no	—
802	C₂×#123	—	53	8	no	—
803	C₂×#123	—	53	8	no	—
804	C₂×#123	—	53	4	no	—
805	C₂×#121	—	53	8	no	—
806	C₂×#121	—	53	16	no	—
807	C₂×#121	—	53	8	no	—
808	C₂×#120	—	53	4	no	—
809	C₂×#120	—	53	8	no	—
810	C₂×#120	—	53	8	no	—
811	C₂×#120	—	53	8	no	—
812	C₂×#120	C₂×D₅₃	1	4	yes	complemented
813	#518	—	53	1	no	—
814	#518	—	53	8	no	—
815	#518	—	53	2	no	—
816	#518	—	53	4	no	—
817	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
818	C₂×C₄×D₄	—	53	8	no	—
819	C₂×#117	—	53	2	no	—
820	C₂²×C₂²⋊C₄	—	53	4	no	—
821	C₅₃	#62842	1	1	yes	characteristic, complemented, Sylow
822	C₂⁵	—	53	2	no	—
823	C₂⁵	—	53	2	no	—
824	C₂⁵	—	53	4	no	—
825	C₂⁵	C₂²×D₅₃	1	2	yes	complemented
826	H(5,𝔽₂)	—	2	8	no	—
827	H(5,𝔽₂)	—	106	32	no	—
828	H(5,𝔽₂)	—	106	64	no	—
829	H(5,𝔽₂)	—	106	64	no	—
830	H(5,𝔽₂)	—	106	32	no	—
831	H(5,𝔽₂)	—	106	32	no	—
832	H(5,𝔽₂)	—	106	16	no	—
833	H(5,𝔽₂)	—	106	8	no	—
834	C₂×#41	—	53	2	no	—
835	C₂×#41	—	53	4	no	—
836	C₂×#41	—	53	4	no	—
837	C₂×#41	—	53	4	no	—
838	C₂×#41	—	53	2	no	—
839	C₂×#41	—	53	4	no	—
840	C₂×#41	—	53	4	no	—
841	C₂×#41	—	53	8	no	—
842	C₂×#41	—	53	16	no	—
843	C₂×#41	—	53	8	no	—
844	C₂×#41	—	53	4	no	—
845	C₂×#41	—	53	2	no	—
846	C₂×#41	—	53	4	no	—
847	C₂×#41	—	53	4	no	—
848	C₂×#41	—	53	8	no	—
849	C₂×#41	—	53	4	no	—
850	C₂×#41	—	53	8	no	—
851	C₂×#41	—	106	8	no	—
852	C₂×#41	—	106	8	no	—
853	C₂×#41	—	106	8	no	—
854	C₂×#41	—	106	16	no	—
855	C₂×#41	—	106	16	no	—
856	C₂×#41	—	106	32	no	—
857	C₂×#41	—	106	8	no	—
858	C₂×#41	C₂²×D₅₃	1	2	yes	—
859	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
860	C₂²×Q₈	—	53	2	no	—
861	C₂²×Q₈	—	53	1	no	—
862	C₂²×Q₈	—	53	1	no	—
863	C₂²×D₄	—	2	8	no	—
864	C₂²×D₄	—	53	2	no	—
865	C₂²×D₄	—	53	16	no	—
866	C₂²×D₄	—	53	4	no	—
867	C₂²×D₄	—	53	4	no	—
868	C₂²×D₄	—	53	8	no	—
869	C₂²×D₄	—	53	4	no	—
870	C₂²×D₄	—	53	4	no	—
871	C₂²×D₄	—	53	8	no	—
872	C₂²×D₄	—	53	2	no	—
873	C₂²×D₄	—	53	1	no	—
874	C₂²×D₄	—	53	2	no	—
875	C₂²×D₄	—	53	2	no	—
876	C₂²×D₄	—	53	2	no	—
877	C₂²×D₄	—	53	1	no	—
878	C₂²×D₄	—	53	8	no	—
879	C₂²×D₄	—	53	16	no	—
880	C₂²×D₄	—	53	8	no	—
881	C₂²×D₄	—	53	8	no	—
882	C₂²×D₄	—	53	8	no	—
883	C₂²×D₄	—	53	8	no	—
884	C₂²×D₄	—	53	8	no	—
885	C₂²×D₄	—	53	4	no	—
886	C₂²×D₄	—	53	8	no	—
887	C₂²×D₄	—	53	2	no	—
888	C₂²×D₄	—	53	8	no	—
889	C₂²×D₄	—	53	4	no	—
890	C₂²×D₄	—	53	8	no	—
891	C₂²×D₄	—	53	4	no	—
892	C₂²×D₄	—	53	16	no	—
893	C₂²×D₄	—	53	1	no	—
894	C₂²×D₄	—	53	4	no	—
895	C₂²×D₄	—	53	1	no	—
896	C₂²×D₄	—	53	4	no	—
897	C₂²×D₄	—	106	32	no	—
898	C₂²×D₄	—	106	8	no	—
899	C₂²×D₄	—	106	16	no	—
900	C₂²×D₄	—	106	32	no	—
901	C₂²×D₄	—	106	16	no	—
902	C₂²×D₄	—	106	16	no	—
903	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
904	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
905	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
906	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
907	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
908	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
909	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
910	C₂³×C₄	—	53	1	no	—
911	C₂³×C₄	—	53	2	no	—
912	C₂³×C₄	—	53	2	no	—
913	C₂³×C₄	—	53	4	no	—
914	C₂³×C₄	—	53	2	no	—
915	C₂³×C₄	—	53	4	no	—
916	C₂³×C₄	—	53	1	no	—
917	C₂³×C₄	—	53	8	no	—
918	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
919	C₄⋊Q₈	—	53	4	no	—
920	C₄⋊Q₈	—	53	8	no	—
921	C₄⋊Q₈	—	53	4	no	—
922	#127	—	53	8	no	—
923	#127	—	53	4	no	—
924	#127	C₂²×D₅₃	1	4	yes	complemented
925	#124	—	53	4	no	—
926	#124	—	53	4	no	—
927	#124	—	53	8	no	—
928	#124	—	53	8	no	—
929	#124	—	53	4	no	—
930	#124	C₂²×D₅₃	1	4	yes	complemented
931	#123	—	53	4	no	—
932	#123	—	53	8	no	—
933	#123	—	53	8	no	—
934	#123	—	53	16	no	—
935	#123	—	53	4	no	—
936	#123	—	53	8	no	—
937	#123	—	53	8	no	—
938	#123	—	53	16	no	—
939	#123	—	53	16	no	—
940	#123	—	53	8	no	—
941	#123	—	53	8	no	—
942	#123	—	53	4	no	—
943	#123	—	53	16	no	—
944	#123	—	53	16	no	—
945	#123	—	53	16	no	—
946	#123	—	53	8	no	—
947	#123	—	53	16	no	—
948	#123	C₂²×D₅₃	1	4	yes	complemented
949	#123	C₂²×D₅₃	1	8	yes	complemented
950	C₂²⋊Q₈	—	53	4	no	—
951	C₂²⋊Q₈	—	53	4	no	—
952	C₂²⋊Q₈	—	53	8	no	—
953	C₂²⋊Q₈	—	53	8	no	—
954	C₂²⋊Q₈	—	53	8	no	—
955	C₂²⋊Q₈	—	53	4	no	—
956	C₂²⋊Q₈	—	53	8	no	—
957	C₂²⋊Q₈	—	53	16	no	—
958	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
959	#121	—	53	16	no	—
960	#121	—	53	8	no	—
961	#121	—	53	16	no	—
962	#121	—	53	16	no	—
963	#121	—	53	16	no	—
964	#121	—	53	16	no	—
965	#121	—	53	4	no	—
966	#121	—	53	8	no	—
967	#121	—	53	16	no	—
968	#121	—	53	8	no	—
969	#121	—	53	16	no	—
970	#121	—	53	4	no	—
971	#121	—	53	8	no	—
972	#121	—	53	4	no	—
973	#121	—	53	8	no	—
974	#121	—	53	16	no	—
975	#121	—	53	8	no	—
976	#121	—	53	16	no	—
977	#121	—	53	16	no	—
978	#121	—	53	8	no	—
979	#121	C₂²×D₅₃	1	16	yes	complemented
980	#121	C₂²×D₅₃	1	8	yes	complemented
981	#121	C₂²×D₅₃	1	4	yes	complemented
982	#120	—	53	8	no	—
983	#120	—	53	4	no	—
984	#120	—	53	8	no	—
985	#120	—	53	16	no	—
986	#120	—	53	4	no	—
987	#120	—	53	16	no	—
988	#120	—	53	8	no	—
989	#120	—	53	8	no	—
990	#120	—	53	16	no	—
991	#120	—	53	16	no	—
992	#120	—	53	16	no	—
993	#120	—	53	8	no	—
994	#120	—	53	4	no	—
995	#120	—	53	16	no	—
996	#120	—	53	8	no	—
997	#120	C₂²×D₅₃	1	8	yes	complemented
998	#120	C₂²×D₅₃	1	8	yes	complemented
999	#120	C₂²×D₅₃	1	4	yes	complemented
1000	#120	C₂²×D₅₃	1	16	yes	complemented
1001	C₄×D₄	—	53	8	no	—
1002	C₄×D₄	—	53	16	no	—
1003	C₄×D₄	—	53	16	no	—
1004	C₄×D₄	—	53	8	no	—
1005	C₄×D₄	—	53	8	no	—
1006	C₄×D₄	—	53	8	no	—
1007	C₄×D₄	—	53	16	no	—
1008	C₄×D₄	—	53	16	no	—
1009	C₄×D₄	—	53	8	no	—
1010	C₄×D₄	—	53	8	no	—
1011	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1012	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1013	#117	—	53	2	no	—
1014	#117	—	53	4	no	—
1015	#117	—	53	4	no	—
1016	#117	—	53	4	no	—
1017	#117	C₂²×D₅₃	1	2	yes	complemented
1018	C₂×C₄⋊C₄	—	53	8	no	—
1019	C₂×C₄⋊C₄	—	53	8	no	—
1020	C₂×C₄⋊C₄	—	53	4	no	—
1021	C₂×C₄⋊C₄	—	53	16	no	—
1022	C₂×C₂²⋊C₄	—	53	4	no	—
1023	C₂×C₂²⋊C₄	—	53	8	no	—
1024	C₂×C₂²⋊C₄	—	53	8	no	—
1025	C₂×C₂²⋊C₄	—	53	8	no	—
1026	C₂×C₂²⋊C₄	—	53	8	no	—
1027	C₂×C₂²⋊C₄	—	53	4	no	—
1028	C₂×C₂²⋊C₄	—	53	8	no	—
1029	C₂×C₂²⋊C₄	—	53	8	no	—
1030	C₂×C₂²⋊C₄	—	53	8	no	—
1031	C₂×C₂²⋊C₄	—	53	16	no	—
1032	C₂×C₂²⋊C₄	—	53	16	no	—
1033	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1034	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
1035	C₂×C₄²	—	53	4	no	—
1036	C₂⁴	—	2	8	no	—
1037	C₂⁴	—	8	4	no	—
1038	C₂⁴	—	53	16	no	—
1039	C₂⁴	—	53	4	no	—
1040	C₂⁴	—	53	1	no	—
1041	C₂⁴	—	53	2	no	—
1042	C₂⁴	—	53	4	no	—
1043	C₂⁴	—	53	8	no	—
1044	C₂⁴	—	53	8	no	—
1045	C₂⁴	—	53	4	no	—
1046	C₂⁴	—	53	4	no	—
1047	C₂⁴	—	53	1	no	—
1048	C₂⁴	—	106	8	no	—
1049	C₂⁴	—	106	16	no	—
1050	C₂⁴	—	424	4	no	—
1051	C₂⁴	—	424	4	no	—
1052	C₂⁴	—	424	8	no	—
1053	C₂⁴	C₂³×D₅₃	1	4	yes	—
1054	C₂⁴	C₂³×D₅₃	1	8	yes	—
1055	C₂⁴	C₂³×D₅₃	1	2	yes	—
1056	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1057	C₂⁴	C₂³×D₅₃	1	2	yes	—
1058	#41	—	2	16	no	—
1059	#41	—	2	8	no	—
1060	#41	—	106	16	no	—
1061	#41	—	106	16	no	—
1062	#41	—	106	16	no	—
1063	#41	—	106	32	no	—
1064	#41	—	106	32	no	—
1065	#41	—	106	16	no	—
1066	#41	—	106	16	no	—
1067	#41	—	106	16	no	—
1068	#41	—	106	16	no	—
1069	#41	—	106	8	no	—
1070	#41	—	106	8	no	—
1071	#41	—	106	64	no	—
1072	#41	—	106	32	no	—
1073	#41	—	106	16	no	—
1074	#41	—	106	16	no	—
1075	#41	—	106	32	no	—
1076	#41	—	106	8	no	—
1077	C₂×Q₈	—	53	4	no	—
1078	C₂×Q₈	—	53	4	no	—
1079	C₂×Q₈	—	53	2	no	—
1080	C₂×Q₈	—	53	4	no	—
1081	C₂×Q₈	—	106	4	no	—
1082	C₂×Q₈	—	106	8	no	—
1083	C₂×Q₈	—	106	4	no	—
1084	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1085	C₂×D₄	—	2	8	no	—
1086	C₂×D₄	—	2	16	no	—
1087	C₂×D₄	—	2	32	no	—
1088	C₂×D₄	—	2	16	no	—
1089	C₂×D₄	—	2	4	no	—
1090	C₂×D₄	—	8	8	no	—
1091	C₂×D₄	—	53	16	no	—
1092	C₂×D₄	—	53	8	no	—
1093	C₂×D₄	—	53	32	no	—
1094	C₂×D₄	—	53	32	no	—
1095	C₂×D₄	—	53	4	no	—
1096	C₂×D₄	—	53	2	no	—
1097	C₂×D₄	—	53	4	no	—
1098	C₂×D₄	—	53	8	no	—
1099	C₂×D₄	—	53	8	no	—
1100	C₂×D₄	—	53	8	no	—
1101	C₂×D₄	—	53	8	no	—
1102	C₂×D₄	—	53	8	no	—
1103	C₂×D₄	—	53	4	no	—
1104	C₂×D₄	—	53	4	no	—
1105	C₂×D₄	—	53	2	no	—
1106	C₂×D₄	—	53	4	no	—
1107	C₂×D₄	—	53	4	no	—
1108	C₂×D₄	—	53	8	no	—
1109	C₂×D₄	—	53	16	no	—
1110	C₂×D₄	—	53	8	no	—
1111	C₂×D₄	—	53	8	no	—
1112	C₂×D₄	—	53	4	no	—
1113	C₂×D₄	—	53	2	no	—
1114	C₂×D₄	—	53	8	no	—
1115	C₂×D₄	—	53	2	no	—
1116	C₂×D₄	—	53	4	no	—
1117	C₂×D₄	—	53	2	no	—
1118	C₂×D₄	—	53	8	no	—
1119	C₂×D₄	—	106	16	no	—
1120	C₂×D₄	—	106	4	no	—
1121	C₂×D₄	—	106	16	no	—
1122	C₂×D₄	—	106	8	no	—
1123	C₂×D₄	—	106	4	no	—
1124	C₂×D₄	—	106	32	no	—
1125	C₂×D₄	—	106	32	no	—
1126	C₂×D₄	—	106	16	no	—
1127	C₂×D₄	—	106	16	no	—
1128	C₂×D₄	—	106	32	no	—
1129	C₂×D₄	—	106	32	no	—
1130	C₂×D₄	—	106	32	no	—
1131	C₂×D₄	—	106	32	no	—
1132	C₂×D₄	—	106	32	no	—
1133	C₂×D₄	—	106	32	no	—
1134	C₂×D₄	—	106	64	no	—
1135	C₂×D₄	—	106	4	no	—
1136	C₂×D₄	—	106	8	no	—
1137	C₂×D₄	—	106	8	no	—
1138	C₂×D₄	—	106	8	no	—
1139	C₂×D₄	—	106	16	no	—
1140	C₂×D₄	—	106	32	no	—
1141	C₂×D₄	—	106	32	no	—
1142	C₂×D₄	—	106	8	no	—
1143	C₂×D₄	—	106	16	no	—
1144	C₂×D₄	—	106	16	no	—
1145	C₂×D₄	—	424	16	no	—
1146	C₂×D₄	—	424	8	no	—
1147	C₂×D₄	D₄×D₅₃	1	8	yes	complemented
1148	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1149	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1150	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1151	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1152	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1153	C₂×D₄	C₂³×D₅₃	1	16	yes	—
1154	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1155	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1156	C₂²×C₄	—	2	4	no	—
1157	C₂²×C₄	—	53	1	no	—
1158	C₂²×C₄	—	53	8	no	—
1159	C₂²×C₄	—	53	2	no	—
1160	C₂²×C₄	—	53	2	no	—
1161	C₂²×C₄	—	53	8	no	—
1162	C₂²×C₄	—	53	4	no	—
1163	C₂²×C₄	—	53	4	no	—
1164	C₂²×C₄	—	53	8	no	—
1165	C₂²×C₄	—	53	1	no	—
1166	C₂²×C₄	—	53	2	no	—
1167	C₂²×C₄	—	53	8	no	—
1168	C₂²×C₄	—	53	8	no	—
1169	C₂²×C₄	—	53	8	no	—
1170	C₂²×C₄	—	53	4	no	—
1171	C₂²×C₄	—	53	4	no	—
1172	C₂²×C₄	—	53	4	no	—
1173	C₂²×C₄	—	53	4	no	—
1174	C₂²×C₄	—	53	8	no	—
1175	C₂²×C₄	—	53	16	no	—
1176	C₂²×C₄	—	106	16	no	—
1177	C₂²×C₄	—	106	8	no	—
1178	C₂²×C₄	—	106	16	no	—
1179	C₂²×C₄	—	106	8	no	—
1180	C₂²×C₄	—	106	8	no	—
1181	C₂²×C₄	—	106	4	no	—
1182	C₂²×C₄	—	424	8	no	—
1183	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1184	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1185	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1186	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1187	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1188	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1189	C₄⋊C₄	—	53	8	no	—
1190	C₄⋊C₄	—	53	8	no	—
1191	C₄⋊C₄	—	53	16	no	—
1192	C₄⋊C₄	—	53	8	no	—
1193	C₄⋊C₄	—	53	16	no	—
1194	C₄⋊C₄	—	53	8	no	—
1195	C₄⋊C₄	—	53	4	no	—
1196	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1197	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1198	C₂²⋊C₄	—	53	4	no	—
1199	C₂²⋊C₄	—	53	8	no	—
1200	C₂²⋊C₄	—	53	8	no	—
1201	C₂²⋊C₄	—	53	16	no	—
1202	C₂²⋊C₄	—	53	16	no	—
1203	C₂²⋊C₄	—	53	8	no	—
1204	C₂²⋊C₄	—	53	8	no	—
1205	C₂²⋊C₄	—	53	16	no	—
1206	C₂²⋊C₄	—	53	8	no	—
1207	C₂²⋊C₄	—	53	8	no	—
1208	C₂²⋊C₄	—	53	8	no	—
1209	C₂²⋊C₄	—	53	16	no	—
1210	C₂²⋊C₄	—	53	8	no	—
1211	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1212	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1213	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1214	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1215	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1216	C₄²	—	53	8	no	—
1217	C₄²	—	53	4	no	—
1218	C₄²	C₂³×D₅₃	1	4	yes	—
1219	C₂³	—	2	2	no	—
1220	C₂³	—	2	4	no	—
1221	C₂³	—	2	8	no	—
1222	C₂³	—	2	16	no	—
1223	C₂³	—	4	2	no	—
1224	C₂³	—	4	4	no	—
1225	C₂³	—	4	4	no	—
1226	C₂³	—	4	8	no	—
1227	C₂³	—	4	8	no	—
1228	C₂³	—	4	8	no	—
1229	C₂³	—	8	16	no	—
1230	C₂³	—	53	1	no	—
1231	C₂³	—	53	4	no	—
1232	C₂³	—	53	1	no	—
1233	C₂³	—	53	4	no	—
1234	C₂³	—	53	16	no	—
1235	C₂³	—	53	8	no	—
1236	C₂³	—	53	16	no	—
1237	C₂³	—	53	4	no	—
1238	C₂³	—	53	2	no	—
1239	C₂³	—	106	16	no	—
1240	C₂³	—	106	16	no	—
1241	C₂³	—	106	8	no	—
1242	C₂³	—	106	8	no	—
1243	C₂³	—	106	2	no	—
1244	C₂³	—	424	16	no	—
1245	C₂³	—	424	16	no	—
1246	C₂³	—	424	32	no	—
1247	C₂³	—	212	8	no	—
1248	C₂³	—	212	16	no	—
1249	C₂³	—	212	16	no	—
1250	C₂³	—	212	8	no	—
1251	C₂³	—	212	8	no	—
1252	C₂³	—	212	2	no	—
1253	C₂³	—	212	4	no	—
1254	C₂³	—	212	2	no	—
1255	C₂³	—	212	8	no	—
1256	C₂³	C₂×D₄×D₅₃	1	8	yes	—
1257	C₂³	C₂⁴×D₅₃	1	4	yes	—
1258	C₂³	C₂⁴×D₅₃	1	4	yes	—
1259	C₂³	C₂⁴×D₅₃	1	2	yes	—
1260	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1261	C₂³	C₂⁴×D₅₃	1	4	yes	—
1262	Q₈	—	2	4	no	—
1263	Q₈	—	106	8	no	—
1264	Q₈	—	106	8	no	—
1265	Q₈	—	106	8	no	—
1266	Q₈	—	106	4	no	—
1267	D₄	—	2	16	no	—
1268	D₄	—	2	8	no	—
1269	D₄	—	2	16	no	—
1270	D₄	—	2	8	no	—
1271	D₄	—	2	4	no	—
1272	D₄	—	4	8	no	—
1273	D₄	—	4	16	no	—
1274	D₄	—	53	32	no	—
1275	D₄	—	53	16	no	—
1276	D₄	—	106	4	no	—
1277	D₄	—	106	4	no	—
1278	D₄	—	106	8	no	—
1279	D₄	—	106	16	no	—
1280	D₄	—	106	8	no	—
1281	D₄	—	106	8	no	—
1282	D₄	—	106	4	no	—
1283	D₄	—	106	4	no	—
1284	D₄	—	106	16	no	—
1285	D₄	—	106	8	no	—
1286	D₄	—	106	16	no	—
1287	D₄	—	106	8	no	—
1288	D₄	—	106	8	no	—
1289	D₄	—	106	16	no	—
1290	D₄	—	106	8	no	—
1291	D₄	—	106	16	no	—
1292	D₄	—	106	16	no	—
1293	D₄	—	106	4	no	—
1294	D₄	—	212	8	no	—
1295	D₄	—	212	8	no	—
1296	D₄	—	212	16	no	—
1297	D₄	—	212	8	no	—
1298	D₄	C₂×D₄×D₅₃	1	16	yes	—
1299	C₂×C₄	—	2	2	no	—
1300	C₂×C₄	—	2	8	no	—
1301	C₂×C₄	—	2	8	no	—
1302	C₂×C₄	—	2	8	no	—
1303	C₂×C₄	—	4	8	no	—
1304	C₂×C₄	—	53	4	no	—
1305	C₂×C₄	—	53	2	no	—
1306	C₂×C₄	—	53	8	no	—
1307	C₂×C₄	—	53	8	no	—
1308	C₂×C₄	—	53	8	no	—
1309	C₂×C₄	—	53	4	no	—
1310	C₂×C₄	—	53	2	no	—
1311	C₂×C₄	—	53	4	no	—
1312	C₂×C₄	—	106	8	no	—
1313	C₂×C₄	—	106	8	no	—
1314	C₂×C₄	—	106	16	no	—
1315	C₂×C₄	—	106	16	no	—
1316	C₂×C₄	—	106	8	no	—
1317	C₂×C₄	—	106	16	no	—
1318	C₂×C₄	—	106	4	no	—
1319	C₂×C₄	—	106	2	no	—
1320	C₂×C₄	—	106	8	no	—
1321	C₂×C₄	—	106	16	no	—
1322	C₂×C₄	—	106	8	no	—
1323	C₂×C₄	—	106	8	no	—
1324	C₂×C₄	—	212	8	no	—
1325	C₂×C₄	—	212	16	no	—
1326	C₂×C₄	—	212	8	no	—
1327	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1328	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1329	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1330	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1331	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1332	C₂²	—	2	8	no	—
1333	C₂²	—	2	2	no	—
1334	C₂²	—	2	2	no	—
1335	C₂²	—	2	4	no	—
1336	C₂²	—	2	4	no	—
1337	C₂²	—	2	2	no	—
1338	C₂²	—	2	8	no	—
1339	C₂²	—	2	8	no	—
1340	C₂²	—	2	2	no	—
1341	C₂²	—	4	8	no	—
1342	C₂²	—	4	4	no	—
1343	C₂²	—	4	8	no	—
1344	C₂²	—	8	16	no	—
1345	C₂²	—	8	8	no	—
1346	C₂²	—	53	2	no	—
1347	C₂²	—	53	2	no	—
1348	C₂²	—	53	8	no	—
1349	C₂²	—	106	2	no	—
1350	C₂²	—	106	8	no	—
1351	C₂²	—	106	2	no	—
1352	C₂²	—	106	4	no	—
1353	C₂²	—	106	2	no	—
1354	C₂²	—	106	4	no	—
1355	C₂²	—	106	8	no	—
1356	C₂²	—	424	8	no	—
1357	C₂²	—	424	16	no	—
1358	C₂²	—	424	16	no	—
1359	C₂²	—	212	8	no	—
1360	C₂²	—	212	4	no	—
1361	C₂²	—	212	16	no	—
1362	C₂²	—	212	16	no	—
1363	C₂²	—	212	4	no	—
1364	C₂²	—	212	16	no	—
1365	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1366	C₂²	C₂²×D₄×D₅₃	1	8	yes	—
1367	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1368	C₄	—	2	2	no	—
1369	C₄	—	2	4	no	—
1370	C₄	—	2	8	no	—
1371	C₄	—	53	4	no	—
1372	C₄	—	106	4	no	—
1373	C₄	—	106	4	no	—
1374	C₄	—	106	2	no	—
1375	C₄	—	106	8	no	—
1376	C₄	C₂²×D₄×D₅₃	1	4	yes	—
1377	C₂	—	2	2	no	—
1378	C₂	—	2	8	no	—
1379	C₂	—	4	2	no	—
1380	C₂	—	4	4	no	—
1381	C₂	—	4	4	no	—
1382	C₂	—	106	8	no	—
1383	C₂	—	106	2	no	—
1384	C₂	—	106	2	no	—
1385	C₂	—	212	4	no	—
1386	C₂	—	212	2	no	—
1387	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1388	C₂	#20289525	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3484	C₂
hypercenter	#3484	D₅₃
hypocenter	C₅₃	#62842
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3484

Complements

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

N	H ≅ G/N	type
1. C₂²×#13133262	C₂	semidirect
2. C₂×H(5,𝔽₂)×D₅₃	C₂	semidirect
3. #20288475	C₂	semidirect
4. #20288471	C₂	semidirect
5. #20288360	C₂	semidirect
6. #20288357	C₂	semidirect
7. #20288356	C₂	semidirect
8. #20288355	C₂	semidirect
9. #20288352	C₂	semidirect
10. #20288350	C₂	semidirect
11. #20288349	C₂	semidirect
12. #20288344	C₂	semidirect
13. #20288343	C₂	semidirect
14. #20288046	C₂	semidirect
15. #20288045	C₂	semidirect
16. C₂×#16811183	C₂	semidirect
17. #534×D₅₃	C₂	semidirect
18. #518×D₅₃	C₂	semidirect
19. C₅₃×#3484	C₂	semidirect
20. C₂×#13133263	C₂²	semidirect
21. C₂×#13133263	C₂²	semidirect
23. C₂×#13133262	C₂²	semidirect
24. C₂×#13133262	C₂²	semidirect
25. C₂×#13133262	C₂²	semidirect
26. C₂×#13133262	C₂²	semidirect
27. C₂×#13133262	C₂²	semidirect
29. C₂²×#11719945	C₂²	semidirect
30. C₂²×#11719945	C₂²	semidirect
31. C₂²×#11719947	C₂²	semidirect
32. C₂²×#11719947	C₂²	semidirect
33. C₂²×#11719947	C₂²	semidirect
34. C₂×#41×D₅₃	C₂²	semidirect
35. C₂×#41×D₅₃	C₂²	semidirect
36. C₂³×C₂²⋊D₅₃	C₂²	semidirect
37. C₂³×C₂²⋊D₅₃	C₂²	semidirect
39. C₂²×D₄×D₅₃	C₂²	semidirect
40. C₂²×D₄×D₅₃	C₂²	semidirect
41. C₂²×D₄×D₅₃	C₂²	semidirect
42. C₂²×D₄×D₅₃	C₂²	semidirect
43. #16811278	C₂²	semidirect
44. #16811277	C₂²	semidirect
45. #16811275	C₂²	semidirect
46. #16811273	C₂²	semidirect
47. #16811272	C₂²	semidirect
48. #16811271	C₂²	semidirect
49. #16811270	C₂²	semidirect
50. #16811270	C₂²	semidirect
51. #16811269	C₂²	semidirect
52. #16811268	C₂²	semidirect
53. #16811267	C₂²	semidirect
54. #16811267	C₂²	semidirect
55. #16811266	C₂²	semidirect
56. #16811263	C₂²	semidirect
57. #16811262	C₂²	semidirect
58. #16811260	C₂²	semidirect
59. #16811260	C₂²	semidirect
60. #16811258	C₂²	semidirect
61. #16811257	C₂²	semidirect
62. D₄×C₂²⋊D₅₃	C₂²	semidirect
63. D₄×C₂²⋊D₅₃	C₂²	semidirect
64. #16811255	C₂²	semidirect
65. #16811203	C₂²	semidirect
66. #16811202	C₂²	semidirect
67. #16811202	C₂²	semidirect
68. #16811199	C₂²	semidirect
69. #16811196	C₂²	semidirect
70. #16811195	C₂²	semidirect
71. #16811194	C₂²	semidirect
72. #16811193	C₂²	semidirect
73. #16811190	C₂²	semidirect
74. #16811189	C₂²	semidirect
75. #16811188	C₂²	semidirect
76. #16811186	C₂²	semidirect
77. #16811185	C₂²	semidirect
78. #16811184	C₂²	semidirect
79. #16811184	C₂²	semidirect
80. #16811183	C₂²	semidirect
81. #16811183	C₂²	semidirect
82. #16811183	C₂²	semidirect
83. #16811183	C₂²	semidirect
84. #16811183	C₂²	semidirect
85. #16811183	C₂²	semidirect
86. #16811183	C₂²	semidirect
87. #16811182	C₂²	semidirect
88. #16811182	C₂²	semidirect
89. #16811181	C₂²	semidirect
90. #16811172	C₂²	semidirect
91. #16811171	C₂²	semidirect
92. #16811170	C₂²	semidirect
93. #16811135	C₂²	semidirect
94. #16811134	C₂²	semidirect
95. #16811133	C₂²	semidirect
96. #16811132	C₂²	semidirect
97. #16811130	C₂²	semidirect
98. #16811129	C₂²	semidirect
99. C₂×#13133201	C₂²	semidirect
100. C₂×#13133199	C₂²	semidirect
101. C₂×#13133198	C₂²	semidirect
102. #123×D₅₃	C₂²	semidirect
103. #123×D₅₃	C₂²	semidirect
104. C₂×#13133190	C₂²	semidirect
105. C₂×#13133188	C₂²	semidirect
106. #121×D₅₃	C₂²	semidirect
107. C₂×#13133186	C₂²	semidirect
108. C₂×#13133185	C₂²	semidirect
109. #120×D₅₃	C₂²	semidirect
110. #120×D₅₃	C₂²	semidirect
111. #16811098	C₂²	semidirect
112. #16811097	C₂²	semidirect
113. #16811096	C₂²	semidirect
114. #16811095	C₂²	semidirect
115. C₄×D₄×D₅₃	C₂²	semidirect
116. #117×D₅₃	C₂²	semidirect
117. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
118. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
119. C₂³×D₄×C₅₃	C₂²	semidirect
120. C₅₃×#546	C₂²	semidirect
121. D₄²×C₅₃	C₂²	semidirect
122. C₅₃×#535	C₂²	semidirect
123. C₅₃×#534	C₂²	semidirect
124. C₅₃×#525	C₂²	semidirect
125. C₂×#120×C₅₃	C₂²	semidirect
126. C₅₃×#518	C₂²	semidirect
128. C₂⁴×D₅₃	C₂³	semidirect
129. C₂⁴×D₅₃	C₂³	semidirect
137. C₂×#11719949	C₂³	semidirect
138. C₂×#11719949	C₂³	semidirect
143. C₂×#11719945	C₂³	semidirect
144. C₂×#11719945	C₂³	semidirect
145. C₂×#11719945	C₂³	semidirect
146. C₂×#11719945	C₂³	semidirect
147. C₂×#11719945	C₂³	semidirect
153. C₂×#11719947	C₂³	semidirect
154. C₂×#11719947	C₂³	semidirect
155. C₂×#11719947	C₂³	semidirect
156. C₂×#11719947	C₂³	semidirect
157. C₂×#11719947	C₂³	semidirect
158. C₂×#11719947	C₂³	semidirect
161. C₂²×Dic₁₀₆	C₂³	semidirect
162. C₂²×Dic₁₀₆	C₂³	semidirect
163. C₂×Q₈×D₅₃	C₂³	semidirect
166. C₂²×D₂₁₂	C₂³	semidirect
167. C₂²×D₂₁₂	C₂³	semidirect
175. C₂²×C₂²⋊D₅₃	C₂³	semidirect
176. C₂²×C₂²⋊D₅₃	C₂³	semidirect
177. C₂²×C₂²⋊D₅₃	C₂³	semidirect
178. C₂²×C₂²⋊D₅₃	C₂³	semidirect
179. C₂²×C₂²⋊D₅₃	C₂³	semidirect
180. C₂²×C₂²⋊D₅₃	C₂³	semidirect
181. C₂²×C₂²⋊D₅₃	C₂³	semidirect
182. C₂²×C₂²⋊D₅₃	C₂³	semidirect
183. C₂²×C₂²⋊D₅₃	C₂³	semidirect
188. C₂×D₄×D₅₃	D₄	semidirect
194. C₂×D₄×D₅₃	C₂³	semidirect
195. C₂×D₄×D₅₃	C₂³	semidirect
196. C₂×D₄×D₅₃	C₂³	semidirect
197. C₂×D₄×D₅₃	C₂³	semidirect
198. C₂×D₄×D₅₃	C₂³	semidirect
199. C₂×D₄×D₅₃	C₂³	semidirect
200. C₂×D₄×D₅₃	C₂³	semidirect
201. C₂×D₄×D₅₃	C₂³	semidirect
202. C₂×D₄×D₅₃	C₂³	semidirect
203. C₂³×Dic₅₃	C₂³	semidirect
204. C₂³×Dic₅₃	C₂³	semidirect
206. C₂²×C₄×D₅₃	C₂³	semidirect
207. C₂²×C₄×D₅₃	C₂³	semidirect
208. C₂²×C₄×D₅₃	C₂³	semidirect
209. C₂²×C₄×D₅₃	C₂³	semidirect
210. C₂²×C₄×D₅₃	C₂³	semidirect
211. #13133217	C₂³	semidirect
212. #13133216	C₂³	semidirect
213. #13133215	C₂³	semidirect
214. #13133213	C₂³	semidirect
215. #13133213	C₂³	semidirect
216. #13133205	C₂³	semidirect
217. #13133204	C₂³	semidirect
218. #13133204	C₂³	semidirect
219. #13133203	C₂³	semidirect
220. #13133203	C₂³	semidirect
221. #13133202	C₂³	semidirect
222. #13133202	C₂³	semidirect
223. #13133201	C₂³	semidirect
224. #13133201	C₂³	semidirect
225. #13133201	C₂³	semidirect
226. #13133201	C₂³	semidirect
227. #13133200	C₂³	semidirect
228. #13133200	C₂³	semidirect
229. #13133199	C₂³	semidirect
230. #13133199	C₂³	semidirect
231. #13133199	C₂³	semidirect
232. #13133199	C₂³	semidirect
233. #13133199	C₂³	semidirect
234. #13133198	C₂³	semidirect
235. #13133198	C₂³	semidirect
236. #13133198	C₂³	semidirect
237. #13133198	C₂³	semidirect
238. #13133197	C₂³	semidirect
239. #13133197	C₂³	semidirect
240. #13133196	C₂³	semidirect
241. #13133196	C₂³	semidirect
242. #13133195	C₂³	semidirect
243. #13133194	C₂³	semidirect
244. #13133194	C₂³	semidirect
245. #13133193	C₂³	semidirect
246. #13133192	C₂³	semidirect
247. #13133192	C₂³	semidirect
248. #13133191	C₂³	semidirect
249. #13133191	C₂³	semidirect
250. #13133190	C₂³	semidirect
251. #13133190	C₂³	semidirect
252. #13133190	C₂³	semidirect
253. #13133190	C₂³	semidirect
254. #13133190	C₂³	semidirect
255. #13133190	C₂³	semidirect
256. #13133189	C₂³	semidirect
257. #13133189	C₂³	semidirect
258. #13133189	C₂³	semidirect
259. #13133189	C₂³	semidirect
260. #13133188	C₂³	semidirect
261. #13133188	C₂³	semidirect
262. #13133188	C₂³	semidirect
263. #13133188	C₂³	semidirect
264. #13133188	C₂³	semidirect
265. #13133188	C₂³	semidirect
266. #13133187	C₂³	semidirect
267. #13133187	C₂³	semidirect
268. #13133187	C₂³	semidirect
269. #13133187	C₂³	semidirect
270. #13133186	C₂³	semidirect
271. #13133186	C₂³	semidirect
272. #13133186	C₂³	semidirect
273. #13133186	C₂³	semidirect
274. #13133185	C₂³	semidirect
275. #13133185	C₂³	semidirect
276. #13133185	C₂³	semidirect
277. #13133185	C₂³	semidirect
278. #13133185	C₂³	semidirect
279. #13133185	C₂³	semidirect
280. #13133185	C₂³	semidirect
281. C₄×D₂₁₂	C₂³	semidirect
282. C₄×D₂₁₂	C₂³	semidirect
283. D₄×Dic₅₃	C₂³	semidirect
284. D₄×Dic₅₃	C₂³	semidirect
285. #13133179	C₂³	semidirect
286. C₄×C₂²⋊D₅₃	C₂³	semidirect
287. C₄×C₂²⋊D₅₃	C₂³	semidirect
288. C₄×C₂²⋊D₅₃	C₂³	semidirect
289. #13133177	C₂³	semidirect
290. #13133177	C₂³	semidirect
291. #13133176	C₂³	semidirect
292. #13133175	C₂³	semidirect
293. #13133174	C₂³	semidirect
294. #13133173	C₂³	semidirect
295. C₂×C₄⋊Dic₅₃	C₂³	semidirect
296. C₂×#11719919	C₂³	semidirect
297. C₄⋊C₄×D₅₃	C₂³	semidirect
298. C₄⋊C₄×D₅₃	C₂³	semidirect
299. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
300. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
301. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
302. C₂×#11719921	C₂³	semidirect
303. C₂×#11719921	C₂³	semidirect
305. C₂²⋊C₄×D₅₃	C₂³	semidirect
306. C₂²⋊C₄×D₅₃	C₂³	semidirect
307. C₂²⋊C₄×D₅₃	C₂³	semidirect
308. C₂²⋊C₄×D₅₃	C₂³	semidirect
309. C₂²⋊C₄×D₅₃	C₂³	semidirect
310. C₄²×D₅₃	C₂³	semidirect
311. C₂⁵×C₅₃	C₂³	semidirect
314. C₂×#41×C₅₃	C₂³	semidirect
318. C₂²×D₄×C₅₃	C₂³	semidirect
319. C₂²×D₄×C₅₃	C₂³	semidirect
320. C₂²×D₄×C₅₃	C₂³	semidirect
321. C₂²×D₄×C₅₃	C₂³	semidirect
322. C₂²×D₄×C₅₃	C₂³	semidirect
323. C₂³×C₄×C₅₃	C₂³	semidirect
324. #127×C₅₃	C₂³	semidirect
325. #124×C₅₃	C₂³	semidirect
326. #123×C₅₃	C₂³	semidirect
327. #123×C₅₃	C₂³	semidirect
328. C₂²⋊Q₈×C₅₃	C₂³	semidirect
329. #121×C₅₃	C₂³	semidirect
330. #121×C₅₃	C₂³	semidirect
331. #121×C₅₃	C₂³	semidirect
332. #120×C₅₃	C₂³	semidirect
333. #120×C₅₃	C₂³	semidirect
334. #120×C₅₃	C₂³	semidirect
335. #120×C₅₃	C₂³	semidirect
336. C₄×D₄×C₅₃	C₂³	semidirect
337. C₄×D₄×C₅₃	C₂³	semidirect
338. #117×C₅₃	C₂³	semidirect
339. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
340. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
353. C₂³×D₅₃	C₂×D₄	semidirect
372. C₂×D₄×C₅₃	C₂×D₄	semidirect
401. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
452. D₄×D₅₃	C₂×D₄	semidirect
453. D₄×D₅₃	C₂×D₄	semidirect
464. C₂×D₂₁₂	C₂×D₄	semidirect
477. C₂×C₄×D₅₃	C₂×D₄	semidirect
696. #3484	D₅₃	semidirect
723. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
738. C₂³×D₄	C₂×D₅₃	semidirect
756. #546	C₂×D₅₃	semidirect
762. D₄²	C₂×D₅₃	semidirect
775. #535	C₂×D₅₃	semidirect
789. #534	C₂×D₅₃	semidirect
799. #525	C₂×D₅₃	semidirect
812. C₂×#120	C₂×D₅₃	semidirect
817. #518	C₂×D₅₃	semidirect
821. C₅₃	#62842	semidirect
825. C₂⁵	C₂²×D₅₃	semidirect
859. C₂×#41	C₂²×D₅₃	semidirect
905. C₂²×D₄	C₂²×D₅₃	semidirect
906. C₂²×D₄	C₂²×D₅₃	semidirect
907. C₂²×D₄	C₂²×D₅₃	semidirect
908. C₂²×D₄	C₂²×D₅₃	semidirect
909. C₂²×D₄	C₂²×D₅₃	semidirect
918. C₂³×C₄	C₂²×D₅₃	semidirect
924. #127	C₂²×D₅₃	semidirect
930. #124	C₂²×D₅₃	semidirect
948. #123	C₂²×D₅₃	semidirect
949. #123	C₂²×D₅₃	semidirect
958. C₂²⋊Q₈	C₂²×D₅₃	semidirect
979. #121	C₂²×D₅₃	semidirect
980. #121	C₂²×D₅₃	semidirect
981. #121	C₂²×D₅₃	semidirect
997. #120	C₂²×D₅₃	semidirect
998. #120	C₂²×D₅₃	semidirect
999. #120	C₂²×D₅₃	semidirect
1000. #120	C₂²×D₅₃	semidirect
1011. C₄×D₄	C₂²×D₅₃	semidirect
1012. C₄×D₄	C₂²×D₅₃	semidirect
1017. #117	C₂²×D₅₃	semidirect
1033. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1034. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1147. C₂×D₄	D₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13133262	2
C₂×H(5,𝔽₂)×D₅₃	2
#20288475	2
#20288471	2
#20288360	2
#20288357	2
#20288356	2
#20288355	2
#20288352	2
#20288350	2
#20288349	2
#20288344	2
#20288343	2
#20288046	2
#20288045	2
C₂×#16811183	2
#534×D₅₃	2
#518×D₅₃	2
C₅₃×#3484	2
#62842	53