Subgroups — D₅₃×#3485 #28292128

Order 13568.

11686 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288360	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288359	C₂	1	1	yes	maximal, characteristic, complemented
5	#20288358	C₂	1	2	yes	maximal, 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	#20288354	C₂	1	8	yes	maximal, complemented
10	#20288353	C₂	1	4	yes	maximal, complemented
11	#20288352	C₂	1	8	yes	maximal, complemented
12	#547×D₅₃	C₂	1	8	yes	maximal, complemented
13	#546×D₅₃	C₂	1	8	yes	maximal, complemented
14	#536×D₅₃	C₂	1	2	yes	maximal, complemented
15	#534×D₅₃	C₂	1	4	yes	maximal, complemented
16	#525×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₂×#123×D₅₃	C₂	1	4	yes	maximal, complemented
18	#518×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3485	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	C₂²	1	4	yes	complemented
23	C₂×#13133262	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13133262	C₂²	1	4	yes	complemented
25	H(5,𝔽₂)×D₅₃	—	2	16	no	—
26	C₂²×#11719949	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#11719945	C₂²	1	2	yes	complemented
28	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#11719947	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#11719947	C₂²	1	2	yes	complemented
31	C₂×#41×D₅₃	—	2	16	no	—
32	C₂×#41×D₅₃	C₂²	1	2	yes	—
33	C₂×#41×D₅₃	C₂²	1	8	yes	complemented
34	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
35	C₂×#41×D₅₃	C₂²	1	8	yes	complemented
36	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₄×D₅₃	C₂²	1	4	yes	—
38	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
39	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
40	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
41	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
42	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
43	#16811278	C₂²	1	8	yes	complemented
44	#16811277	C₂²	1	8	yes	complemented
45	#16811276	C₂²	1	8	yes	complemented
46	#16811275	C₂²	1	8	yes	complemented
47	#16811275	C₂²	1	8	yes	complemented
48	#16811274	C₂²	1	16	yes	complemented
49	#16811273	C₂²	1	16	yes	complemented
50	#16811272	C₂²	1	8	yes	complemented
51	#16811272	C₂²	1	8	yes	complemented
52	#16811271	C₂²	1	16	yes	complemented
53	#16811271	C₂²	1	16	yes	complemented
54	#16811270	C₂²	1	8	yes	complemented
55	#16811269	C₂²	1	8	yes	complemented
56	#16811268	C₂²	1	8	yes	complemented
57	#16811267	C₂²	1	8	yes	complemented
58	#16811266	C₂²	1	8	yes	complemented
59	#16811265	C₂²	1	16	yes	complemented
60	#16811264	C₂²	1	8	yes	complemented
61	#16811263	C₂²	1	16	yes	complemented
62	#16811262	C₂²	1	16	yes	complemented
63	#16811261	C₂²	1	8	yes	complemented
64	#16811260	C₂²	1	16	yes	complemented
65	#16811199	C₂²	1	2	yes	complemented
66	#16811198	C₂²	1	4	yes	complemented
67	#16811197	C₂²	1	2	yes	complemented
68	#16811196	C₂²	1	8	yes	complemented
69	#16811195	C₂²	1	8	yes	complemented
70	#16811194	C₂²	1	2	yes	complemented
71	#16811193	C₂²	1	4	yes	complemented
72	#16811185	C₂²	1	4	yes	complemented
73	#16811184	C₂²	1	8	yes	complemented
74	#16811184	C₂²	1	8	yes	complemented
75	#16811183	C₂²	1	8	yes	complemented
76	#16811183	C₂²	1	8	yes	complemented
77	#16811182	C₂²	1	4	yes	complemented
78	#16811182	C₂²	1	4	yes	complemented
79	#16811181	C₂²	1	16	yes	complemented
80	C₄⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
81	#124×D₅₃	C₂²	1	4	yes	complemented
82	#16811136	C₂²	1	4	yes	complemented
83	#16811135	C₂²	1	2	yes	complemented
84	#16811134	C₂²	1	2	yes	complemented
85	#16811133	C₂²	1	4	yes	complemented
86	#16811132	C₂²	1	8	yes	complemented
87	#16811131	C₂²	1	4	yes	complemented
88	#16811130	C₂²	1	2	yes	complemented
89	#16811129	C₂²	1	4	yes	complemented
90	C₂×#13133202	C₂²	1	8	yes	complemented
91	C₂×#13133201	C₂²	1	4	yes	complemented
92	C₂×#13133200	C₂²	1	4	yes	complemented
93	C₂×#13133199	C₂²	1	8	yes	complemented
94	C₂×#13133198	C₂²	1	4	yes	complemented
95	#123×D₅₃	C₂²	1	8	yes	complemented
96	#123×D₅₃	C₂²	1	8	yes	complemented
97	#123×D₅₃	C₂²	1	16	yes	complemented
98	#123×D₅₃	C₂²	1	4	yes	complemented
99	#123×D₅₃	C₂²	1	16	yes	complemented
100	#123×D₅₃	C₂²	1	8	yes	complemented
101	#123×D₅₃	C₂²	1	8	yes	complemented
102	C₂²⋊Q₈×D₅₃	C₂²	1	8	yes	complemented
103	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
104	#121×D₅₃	C₂²	1	16	yes	complemented
105	#121×D₅₃	C₂²	1	4	yes	complemented
106	#120×D₅₃	C₂²	1	4	yes	complemented
107	#120×D₅₃	C₂²	1	8	yes	complemented
108	#16811098	C₂²	1	1	yes	characteristic, complemented
109	#16811097	C₂²	1	2	yes	complemented
110	#16811096	C₂²	1	4	yes	complemented
111	#16811095	C₂²	1	8	yes	complemented
112	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
113	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
114	#117×D₅₃	C₂²	1	2	yes	complemented
115	C₂×C₄⋊C₄×D₅₃	C₂²	1	8	yes	complemented
116	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
117	C₂×C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
118	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#547	C₂²	1	8	yes	complemented
121	C₅₃×#546	C₂²	1	8	yes	complemented
122	C₅₃×#536	C₂²	1	2	yes	complemented
123	C₅₃×#534	C₂²	1	4	yes	complemented
124	C₅₃×#525	C₂²	1	2	yes	complemented
125	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
126	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
127	C₂⁴×D₅₃	C₂³	1	4	yes	—
128	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
129	C₂⁴×D₅₃	C₂³	1	2	yes	—
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	C₂×#11719949	—	2	8	no	—
136	C₂×#11719949	C₂³	1	2	yes	—
137	C₂×#11719949	C₂³	1	8	yes	complemented
138	C₂×#11719949	C₂³	1	4	yes	complemented
139	C₂×#11719945	—	2	16	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	16	yes	complemented
144	C₂×#11719945	C₂³	1	8	yes	complemented
145	C₂×#11719945	C₂³	1	8	yes	complemented
146	C₂×#11719945	C₂³	1	4	yes	complemented
147	C₂×#11719947	—	2	8	no	—
148	C₂×#11719947	—	2	16	no	—
149	C₂×#11719947	C₂³	1	4	yes	—
150	C₂×#11719947	C₂³	1	2	yes	—
151	C₂×#11719947	C₂³	1	8	yes	complemented
152	C₂×#11719947	C₂³	1	8	yes	complemented
153	C₂×#11719947	C₂³	1	16	yes	complemented
154	C₂×#11719947	C₂³	1	4	yes	complemented
155	#41×D₅₃	—	2	64	no	—
156	#41×D₅₃	—	2	32	no	—
157	#41×D₅₃	—	2	64	no	—
158	#41×D₅₃	—	2	16	no	—
159	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
160	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
161	C₂×Q₈×D₅₃	—	2	8	no	—
162	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
163	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
164	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
165	C₂²×D₂₁₂	C₂³	1	4	yes	—
166	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
167	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
168	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
169	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
170	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
171	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
172	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
173	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
174	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
175	C₂×D₄×D₅₃	—	2	32	no	—
176	C₂×D₄×D₅₃	—	2	16	no	—
177	C₂×D₄×D₅₃	—	2	32	no	—
178	C₂×D₄×D₅₃	D₄	1	16	yes	complemented
179	C₂×D₄×D₅₃	C₂³	1	8	yes	—
180	C₂×D₄×D₅₃	C₂³	1	4	yes	—
181	C₂×D₄×D₅₃	C₂³	1	8	yes	—
182	C₂×D₄×D₅₃	C₂³	1	2	yes	—
183	C₂×D₄×D₅₃	C₂³	1	8	yes	—
184	C₂×D₄×D₅₃	C₂³	1	8	yes	—
185	C₂×D₄×D₅₃	C₂³	1	8	yes	—
186	C₂×D₄×D₅₃	C₂³	1	4	yes	—
187	C₂×D₄×D₅₃	C₂³	1	4	yes	—
188	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
189	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
190	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
191	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
192	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
193	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
194	C₂²×C₄×D₅₃	—	2	16	no	—
195	C₂²×C₄×D₅₃	—	2	8	no	—
196	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
197	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
198	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
199	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
200	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
202	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
203	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
205	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
206	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
207	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
208	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
209	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
210	#13133217	C₂³	1	4	yes	complemented
211	#13133216	C₂³	1	16	yes	complemented
212	#13133215	C₂³	1	4	yes	complemented
213	#13133215	C₂³	1	4	yes	complemented
214	#13133206	C₂³	1	4	yes	complemented
215	#13133205	C₂³	1	4	yes	complemented
216	#13133204	C₂³	1	4	yes	complemented
217	#13133203	C₂³	1	16	yes	complemented
218	#13133202	C₂³	1	16	yes	complemented
219	#13133202	C₂³	1	16	yes	complemented
220	#13133202	C₂³	1	16	yes	complemented
221	#13133202	C₂³	1	8	yes	complemented
222	#13133202	C₂³	1	16	yes	complemented
223	#13133201	C₂³	1	16	yes	complemented
224	#13133201	C₂³	1	8	yes	complemented
225	#13133201	C₂³	1	4	yes	complemented
226	#13133201	C₂³	1	8	yes	complemented
227	#13133200	C₂³	1	8	yes	complemented
228	#13133200	C₂³	1	16	yes	complemented
229	#13133200	C₂³	1	4	yes	complemented
230	#13133200	C₂³	1	8	yes	complemented
231	#13133199	C₂³	1	16	yes	complemented
232	#13133199	C₂³	1	16	yes	complemented
233	#13133199	C₂³	1	16	yes	complemented
234	#13133199	C₂³	1	8	yes	complemented
235	#13133199	C₂³	1	16	yes	complemented
236	#13133198	C₂³	1	16	yes	complemented
237	#13133198	C₂³	1	8	yes	complemented
238	#13133198	C₂³	1	4	yes	complemented
239	#13133198	C₂³	1	8	yes	complemented
240	#13133197	C₂³	1	8	yes	complemented
241	#13133197	C₂³	1	4	yes	complemented
242	#13133196	C₂³	1	8	yes	complemented
243	#13133196	C₂³	1	4	yes	complemented
244	#13133195	C₂³	1	16	yes	complemented
245	#13133195	C₂³	1	8	yes	complemented
246	#13133194	C₂³	1	8	yes	complemented
247	#13133194	C₂³	1	16	yes	complemented
248	#13133193	C₂³	1	8	yes	complemented
249	#13133193	C₂³	1	4	yes	complemented
250	#13133192	C₂³	1	4	yes	complemented
251	#13133192	C₂³	1	16	yes	complemented
252	#13133191	C₂³	1	16	yes	complemented
253	#13133191	C₂³	1	4	yes	complemented
254	#13133190	C₂³	1	8	yes	complemented
255	#13133190	C₂³	1	16	yes	complemented
256	#13133190	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	4	yes	complemented
261	#13133188	C₂³	1	16	yes	complemented
262	#13133187	C₂³	1	16	yes	complemented
263	#13133187	C₂³	1	8	yes	complemented
264	#13133187	C₂³	1	4	yes	complemented
265	#13133187	C₂³	1	8	yes	complemented
266	#13133186	C₂³	1	8	yes	complemented
267	#13133186	C₂³	1	4	yes	complemented
268	#13133185	C₂³	1	16	yes	complemented
269	#13133185	C₂³	1	4	yes	complemented
270	#13133185	C₂³	1	8	yes	complemented
271	#13133185	C₂³	1	8	yes	complemented
272	C₄×D₂₁₂	C₂³	1	8	yes	complemented
273	C₄×D₂₁₂	C₂³	1	8	yes	complemented
274	D₄×Dic₅₃	C₂³	1	8	yes	complemented
275	D₄×Dic₅₃	C₂³	1	8	yes	complemented
276	#13133179	C₂³	1	8	yes	complemented
277	#13133179	C₂³	1	8	yes	complemented
278	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
279	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
280	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
281	#13133177	C₂³	1	16	yes	complemented
282	#13133177	C₂³	1	8	yes	complemented
283	#13133177	C₂³	1	8	yes	complemented
284	#13133176	C₂³	1	2	yes	complemented
285	#13133175	C₂³	1	4	yes	complemented
286	#13133174	C₂³	1	4	yes	complemented
287	#13133173	C₂³	1	4	yes	complemented
288	C₂×C₄⋊Dic₅₃	C₂³	1	8	yes	complemented
289	C₂×#11719919	C₂³	1	8	yes	complemented
290	C₂×#11719919	C₂³	1	8	yes	complemented
291	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
292	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
293	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
294	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
295	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
296	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
297	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
298	C₂×#11719921	C₂³	1	8	yes	complemented
299	C₂×#11719921	C₂³	1	8	yes	complemented
300	C₂×#11719921	C₂³	1	8	yes	complemented
301	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
302	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
303	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
304	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
305	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
306	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
307	C₂²⋊C₄×D₅₃	C₂³	1	16	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	—
311	H(5,𝔽₂)×C₅₃	—	2	8	no	—
312	C₂×#41×C₅₃	—	2	8	no	—
313	C₂×#41×C₅₃	C₂³	1	2	yes	—
314	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
315	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
316	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
317	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
318	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
320	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
321	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
322	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
323	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
324	#124×C₅₃	C₂³	1	4	yes	complemented
325	#123×C₅₃	C₂³	1	16	yes	complemented
326	#123×C₅₃	C₂³	1	8	yes	complemented
327	#123×C₅₃	C₂³	1	4	yes	complemented
328	#123×C₅₃	C₂³	1	8	yes	complemented
329	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
330	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
331	#121×C₅₃	C₂³	1	4	yes	complemented
332	#121×C₅₃	C₂³	1	16	yes	complemented
333	#120×C₅₃	C₂³	1	4	yes	complemented
334	#120×C₅₃	C₂³	1	8	yes	complemented
335	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
336	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
337	#117×C₅₃	C₂³	1	2	yes	complemented
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	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	C₂⁴	1	4	yes	—
342	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
344	C₂³×D₅₃	—	2	4	no	—
345	C₂³×D₅₃	—	2	16	no	—
346	C₂³×D₅₃	—	4	8	no	—
347	C₂³×D₅₃	—	4	4	no	—
348	C₂³×D₅₃	—	4	16	no	—
349	C₂³×D₅₃	C₂×D₄	1	16	yes	—
350	C₂³×D₅₃	C₂⁴	1	4	yes	—
351	C₂³×D₅₃	C₂⁴	1	2	yes	—
352	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
353	C₂³×D₅₃	C₂⁴	1	4	yes	—
354	C₂³×D₅₃	C₂⁴	1	8	yes	—
355	C₂³×D₅₃	C₂⁴	1	4	yes	—
356	C₂³×D₅₃	C₂⁴	1	2	yes	—
357	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
358	C₂³×D₅₃	C₂⁴	1	2	yes	—
359	C₂³×D₅₃	C₂⁴	1	4	yes	—
360	#41×C₅₃	—	2	32	no	—
361	#41×C₅₃	—	2	16	no	—
362	#41×C₅₃	—	2	8	no	—
363	C₂×Q₈×C₅₃	—	2	4	no	—
364	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
365	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
366	C₂×D₄×C₅₃	—	2	16	no	—
367	C₂×D₄×C₅₃	—	2	8	no	—
368	C₂×D₄×C₅₃	—	2	16	no	—
369	C₂×D₄×C₅₃	C₂×D₄	1	8	yes	complemented
370	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
371	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
372	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
373	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
374	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
375	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
376	C₂²×C₄×C₅₃	—	2	8	no	—
377	C₂²×C₄×C₅₃	—	2	4	no	—
378	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
379	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
380	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₂²⋊D₅₃	—	2	16	no	—
387	C₂×C₂²⋊D₅₃	—	2	8	no	—
388	C₂×C₂²⋊D₅₃	—	2	16	no	—
389	C₂×C₂²⋊D₅₃	—	2	8	no	—
390	C₂×C₂²⋊D₅₃	—	2	32	no	—
391	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
392	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
393	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
394	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
395	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
396	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
397	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
398	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
399	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
400	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
401	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
402	C₂²×Dic₅₃	—	2	8	no	—
403	C₂²×Dic₅₃	—	2	4	no	—
404	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
405	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
406	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
407	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
408	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
410	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
411	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
412	#11719949	—	2	32	no	—
413	#11719949	—	2	16	no	—
414	#11719949	—	2	8	no	—
415	Q₈×D₅₃	—	2	16	no	—
416	Q₈×D₅₃	—	2	16	no	—
417	Q₈×D₅₃	—	2	8	no	—
418	#11719947	—	2	32	no	—
419	#11719947	—	2	16	no	—
420	#11719947	—	2	64	no	—
421	#11719947	—	2	32	no	—
422	#11719947	—	2	16	no	—
423	#11719947	—	2	8	no	—
424	D₄×D₅₃	—	2	16	no	—
425	D₄×D₅₃	—	2	32	no	—
426	D₄×D₅₃	—	2	32	no	—
427	D₄×D₅₃	—	2	32	no	—
428	D₄×D₅₃	—	2	32	no	—
429	D₄×D₅₃	—	2	32	no	—
430	D₄×D₅₃	—	2	16	no	—
431	D₄×D₅₃	—	2	32	no	—
432	D₄×D₅₃	—	2	16	no	—
433	D₄×D₅₃	—	2	8	no	—
434	D₄×D₅₃	—	4	16	no	—
435	D₄×D₅₃	C₂×D₄	1	32	yes	—
436	D₄×D₅₃	C₂×D₄	1	32	yes	complemented
437	#11719945	—	2	8	no	—
438	#11719945	—	2	64	no	—
439	#11719945	—	2	32	no	—
440	#11719945	—	2	32	no	—
441	#11719945	—	2	16	no	—
442	#11719945	—	2	16	no	—
443	C₂×D₂₁₂	—	2	16	no	—
444	C₂×D₂₁₂	—	2	8	no	—
445	C₂×D₂₁₂	—	2	16	no	—
446	C₂×D₂₁₂	C₂×D₄	1	8	yes	complemented
447	C₂×D₂₁₂	C₂⁴	1	8	yes	—
448	C₂×D₂₁₂	C₂⁴	1	4	yes	—
449	C₂×D₂₁₂	C₂⁴	1	8	yes	—
450	C₂×D₂₁₂	C₂⁴	1	2	yes	—
451	C₂×D₂₁₂	C₂⁴	1	8	yes	—
452	C₂×D₂₁₂	C₂⁴	1	4	yes	—
453	C₂×C₄×D₅₃	—	2	4	no	—
454	C₂×C₄×D₅₃	—	2	8	no	—
455	C₂×C₄×D₅₃	—	2	32	no	—
456	C₂×C₄×D₅₃	—	2	32	no	—
457	C₂×C₄×D₅₃	—	2	8	no	—
458	C₂×C₄×D₅₃	—	2	8	no	—
459	C₂×C₄×D₅₃	—	2	16	no	—
460	C₂×C₄×D₅₃	—	2	4	no	—
461	C₂×C₄×D₅₃	—	2	4	no	—
462	C₂×C₄×D₅₃	—	2	16	no	—
463	C₂×C₄×D₅₃	—	2	16	no	—
464	C₂×C₄×D₅₃	—	2	16	no	—
465	C₂×C₄×D₅₃	—	4	16	no	—
466	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	—
467	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
468	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
469	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
470	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
471	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
472	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
473	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
474	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
475	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
476	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
477	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
478	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
479	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
480	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
481	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
482	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
483	C₂×Dic₁₀₆	—	2	4	no	—
484	C₂×Dic₁₀₆	—	2	8	no	—
485	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
486	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
487	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
488	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
489	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
490	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
491	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
492	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
493	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
494	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
495	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
496	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
497	C₄²×C₅₃	C₂⁴	1	4	yes	—
498	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
499	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
500	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
501	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
502	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
503	#11719921	C₂⁴	1	8	yes	—
504	#11719921	C₂⁴	1	8	yes	—
505	#11719921	C₂⁴	1	8	yes	—
506	#11719921	C₂⁴	1	16	yes	—
507	#11719921	C₂⁴	1	16	yes	—
508	#11719921	C₂⁴	1	16	yes	—
509	#11719921	C₂⁴	1	8	yes	—
510	#11719921	C₂⁴	1	8	yes	—
511	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
512	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
513	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
514	#11719919	C₂⁴	1	8	yes	—
515	#11719919	C₂⁴	1	8	yes	—
516	#11719919	C₂⁴	1	16	yes	—
517	#11719919	C₂⁴	1	16	yes	—
518	#11719919	C₂⁴	1	8	yes	—
519	C₄×Dic₅₃	C₂⁴	1	8	yes	—
520	C₄×Dic₅₃	C₂⁴	1	4	yes	—
521	C₂³×C₅₃	—	2	2	no	—
522	C₂³×C₅₃	—	2	8	no	—
523	C₂³×C₅₃	—	4	4	no	—
524	C₂³×C₅₃	—	4	2	no	—
525	C₂³×C₅₃	—	4	8	no	—
526	C₂³×C₅₃	C₂²×D₄	1	8	yes	—
527	C₂³×C₅₃	C₂⁵	1	2	yes	—
528	C₂³×C₅₃	C₂⁵	1	4	yes	—
529	C₂³×C₅₃	C₂⁵	1	4	yes	—
530	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
531	C₂²×D₅₃	—	2	16	no	—
532	C₂²×D₅₃	—	2	4	no	—
533	C₂²×D₅₃	—	2	2	no	—
534	C₂²×D₅₃	—	2	8	no	—
535	C₂²×D₅₃	—	2	4	no	—
536	C₂²×D₅₃	—	2	4	no	—
537	C₂²×D₅₃	—	2	8	no	—
538	C₂²×D₅₃	—	2	8	no	—
539	C₂²×D₅₃	—	2	16	no	—
540	C₂²×D₅₃	—	2	16	no	—
541	C₂²×D₅₃	—	4	32	no	—
542	C₂²×D₅₃	—	4	4	no	—
543	C₂²×D₅₃	—	4	8	no	—
544	C₂²×D₅₃	—	4	4	no	—
545	C₂²×D₅₃	—	4	2	no	—
546	C₂²×D₅₃	—	4	16	no	—
547	C₂²×D₅₃	—	4	8	no	—
548	C₂²×D₅₃	—	4	16	no	—
549	C₂²×D₅₃	—	8	32	no	—
550	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
551	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
552	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
553	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
554	C₂²×D₅₃	C₂⁵	1	2	yes	—
555	C₂²×D₅₃	C₂⁵	1	4	yes	—
556	C₂²×D₅₃	C₂⁵	1	4	yes	—
557	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
558	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
559	Q₈×C₅₃	—	2	8	no	—
560	Q₈×C₅₃	—	2	4	no	—
561	D₄×C₅₃	—	2	8	no	—
562	D₄×C₅₃	—	2	16	no	—
563	D₄×C₅₃	—	2	16	no	—
564	D₄×C₅₃	—	2	4	no	—
565	D₄×C₅₃	—	4	8	no	—
566	D₄×C₅₃	C₂²×D₄	1	16	yes	—
567	C₂×C₄×C₅₃	—	2	4	no	—
568	C₂×C₄×C₅₃	—	2	2	no	—
569	C₂×C₄×C₅₃	—	2	16	no	—
570	C₂×C₄×C₅₃	—	2	8	no	—
571	C₂×C₄×C₅₃	—	2	8	no	—
572	C₂×C₄×C₅₃	—	2	8	no	—
573	C₂×C₄×C₅₃	—	4	8	no	—
574	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
575	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
576	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
577	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
578	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
579	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
580	C₂²⋊D₅₃	—	2	16	no	—
581	C₂²⋊D₅₃	—	2	8	no	—
582	C₂²⋊D₅₃	—	2	16	no	—
583	C₂²⋊D₅₃	—	2	16	no	—
584	C₂²⋊D₅₃	—	2	8	no	—
585	C₂²⋊D₅₃	—	2	16	no	—
586	C₂²⋊D₅₃	—	2	8	no	—
587	C₂²⋊D₅₃	—	4	8	no	—
588	C₂²⋊D₅₃	—	4	8	no	—
589	C₂²⋊D₅₃	C₂²×D₄	1	32	yes	—
590	C₂×Dic₅₃	—	2	4	no	—
591	C₂×Dic₅₃	—	2	2	no	—
592	C₂×Dic₅₃	—	2	16	no	—
593	C₂×Dic₅₃	—	2	8	no	—
594	C₂×Dic₅₃	—	2	8	no	—
595	C₂×Dic₅₃	—	2	8	no	—
596	C₂×Dic₅₃	—	4	8	no	—
597	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
598	C₂×Dic₅₃	C₂⁵	1	4	yes	—
599	C₂×Dic₅₃	C₂⁵	1	4	yes	—
600	C₂×Dic₅₃	C₂⁵	1	2	yes	—
601	C₂×Dic₅₃	C₂⁵	1	8	yes	—
602	C₂×Dic₅₃	C₂⁵	1	2	yes	—
603	D₂₁₂	—	2	8	no	—
604	D₂₁₂	—	2	16	no	—
605	D₂₁₂	—	2	16	no	—
606	D₂₁₂	—	2	4	no	—
607	D₂₁₂	—	4	8	no	—
608	D₂₁₂	C₂²×D₄	1	16	yes	—
609	C₄×D₅₃	—	2	4	no	—
610	C₄×D₅₃	—	2	4	no	—
611	C₄×D₅₃	—	2	16	no	—
612	C₄×D₅₃	—	2	8	no	—
613	C₄×D₅₃	—	2	8	no	—
614	C₄×D₅₃	—	2	8	no	—
615	C₄×D₅₃	—	2	16	no	—
616	C₄×D₅₃	—	2	16	no	—
617	C₄×D₅₃	—	2	16	no	—
618	C₄×D₅₃	—	2	8	no	—
619	C₄×D₅₃	—	2	8	no	—
620	C₄×D₅₃	—	2	8	no	—
621	C₄×D₅₃	—	2	8	no	—
622	C₄×D₅₃	—	4	16	no	—
623	C₄×D₅₃	C₂²×D₄	1	8	yes	—
624	C₄×D₅₃	C₂²×D₄	1	8	yes	—
625	Dic₁₀₆	—	2	8	no	—
626	Dic₁₀₆	—	2	4	no	—
627	Dic₁₀₆	—	2	16	no	—
628	Dic₁₀₆	—	2	8	no	—
629	C₂×#3485	—	53	1	no	maximal, Sylow
630	C₂²×C₅₃	—	2	8	no	—
631	C₂²×C₅₃	—	2	2	no	—
632	C₂²×C₅₃	—	2	2	no	—
633	C₂²×C₅₃	—	2	4	no	—
634	C₂²×C₅₃	—	2	4	no	—
635	C₂²×C₅₃	—	2	8	no	—
636	C₂²×C₅₃	—	4	8	no	—
637	C₂²×C₅₃	—	4	4	no	—
638	C₂²×C₅₃	—	8	8	no	—
639	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
640	C₂²×C₅₃	C₂³×D₄	1	8	yes	—
641	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
642	C₂×D₅₃	—	2	8	no	—
643	C₂×D₅₃	—	2	2	no	—
644	C₂×D₅₃	—	2	8	no	—
645	C₂×D₅₃	—	2	32	no	—
646	C₂×D₅₃	—	2	2	no	—
647	C₂×D₅₃	—	2	4	no	—
648	C₂×D₅₃	—	2	4	no	—
649	C₂×D₅₃	—	2	8	no	—
650	C₂×D₅₃	—	4	16	no	—
651	C₂×D₅₃	—	4	8	no	—
652	C₂×D₅₃	—	4	8	no	—
653	C₂×D₅₃	—	4	4	no	—
654	C₂×D₅₃	—	4	8	no	—
655	C₂×D₅₃	—	4	16	no	—
656	C₂×D₅₃	—	8	16	no	—
657	C₂×D₅₃	—	8	8	no	—
658	C₂×D₅₃	C₂³×D₄	1	2	yes	—
659	C₂×D₅₃	C₂³×D₄	1	8	yes	—
660	C₂×D₅₃	C₂³×D₄	1	2	yes	—
661	C₂×D₅₃	#585	1	4	yes	—
662	C₄×C₅₃	—	2	4	no	—
663	C₄×C₅₃	—	2	4	no	—
664	C₄×C₅₃	—	2	2	no	—
665	C₄×C₅₃	—	2	8	no	—
666	C₄×C₅₃	C₂³×D₄	1	4	yes	—
667	Dic₅₃	—	2	4	no	—
668	Dic₅₃	—	2	4	no	—
669	Dic₅₃	—	2	2	no	—
670	Dic₅₃	—	2	8	no	—
671	Dic₅₃	C₂³×D₄	1	4	yes	—
672	C₂²×H(5,𝔽₂)	—	53	1	no	—
673	C₂³×#41	—	53	1	no	—
674	#3485	—	53	1	no	—
675	#3485	—	53	1	no	—
676	#3485	—	53	8	no	—
677	#3485	—	53	8	no	—
678	#3485	—	53	2	no	—
679	#3485	—	53	4	no	—
680	#3485	—	53	2	no	—
681	#3485	—	53	4	no	—
682	#3485	—	53	1	no	—
683	#3485	D₅₃	1	1	yes	characteristic, direct product factor
684	C₂×#547	—	53	8	no	—
685	C₂×#546	—	53	8	no	—
686	C₂×#536	—	53	2	no	—
687	C₂×#534	—	53	4	no	—
688	C₂×#525	—	53	2	no	—
689	C₂²×#123	—	53	4	no	—
690	C₂×#518	—	53	1	no	—
691	C₂×C₅₃	—	2	2	no	—
692	C₂×C₅₃	—	2	8	no	—
693	C₂×C₅₃	—	4	2	no	—
694	C₂×C₅₃	—	4	4	no	—
695	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
696	C₂×C₅₃	C₂×#585	1	2	yes	—
697	D₅₃	—	2	2	no	—
698	D₅₃	—	2	8	no	—
699	D₅₃	—	4	2	no	—
700	D₅₃	—	4	4	no	—
701	D₅₃	#3485	1	4	yes	direct product factor
702	C₂×H(5,𝔽₂)	—	53	2	no	—
703	C₂×H(5,𝔽₂)	—	53	4	no	—
704	C₂×H(5,𝔽₂)	—	53	4	no	—
705	C₂×H(5,𝔽₂)	—	53	1	no	—
706	C₂×H(5,𝔽₂)	—	53	4	no	—
707	C₂×H(5,𝔽₂)	—	106	16	no	—
708	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
709	C₂²×#41	—	53	2	no	—
710	C₂²×#41	—	53	8	no	—
711	C₂²×#41	—	53	8	no	—
712	C₂²×#41	—	53	4	no	—
713	C₂²×#41	—	53	1	no	—
714	C₂²×#41	—	53	1	no	—
715	C₂²×#41	—	53	2	no	—
716	C₂²×#41	—	53	1	no	—
717	C₂²×#41	—	53	2	no	—
718	C₂²×#41	—	106	16	no	—
719	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
720	C₂³×Q₈	—	53	1	no	—
721	C₂³×D₄	—	53	1	no	—
722	C₂³×D₄	—	53	4	no	—
723	C₂³×D₄	—	53	2	no	—
724	C₂³×D₄	—	53	4	no	—
725	C₂⁴×C₄	—	53	2	no	—
726	C₂⁴×C₄	—	53	1	no	—
727	#547	—	53	8	no	—
728	#547	—	53	8	no	—
729	#547	—	53	8	no	—
730	#547	—	53	16	no	—
731	#547	—	53	16	no	—
732	#547	—	53	8	no	—
733	#547	—	53	8	no	—
734	#547	—	53	16	no	—
735	#547	—	53	8	no	—
736	#547	—	53	8	no	—
737	#547	—	53	16	no	—
738	#547	C₂×D₅₃	1	8	yes	complemented
739	#546	—	53	8	no	—
740	#546	—	53	8	no	—
741	#546	—	53	8	no	—
742	#546	—	53	16	no	—
743	#546	—	53	8	no	—
744	#546	—	53	8	no	—
745	#546	—	53	16	no	—
746	#546	—	53	16	no	—
747	#546	—	53	8	no	—
748	#546	—	53	8	no	—
749	#546	—	53	16	no	—
750	#546	C₂×D₅₃	1	8	yes	complemented
751	#536	—	53	2	no	—
752	#536	—	53	2	no	—
753	#536	—	53	4	no	—
754	#536	—	53	4	no	—
755	#536	—	53	8	no	—
756	#536	—	53	8	no	—
757	#536	—	53	2	no	—
758	#536	C₂×D₅₃	1	2	yes	complemented
759	#534	—	53	4	no	—
760	#534	—	53	4	no	—
761	#534	—	53	8	no	—
762	#534	—	53	8	no	—
763	#534	—	53	16	no	—
764	#534	—	53	8	no	—
765	#534	—	53	8	no	—
766	#534	—	53	4	no	—
767	#534	C₂×D₅₃	1	4	yes	complemented
768	C₂×C₄⋊Q₈	—	53	4	no	—
769	C₂×#124	—	53	4	no	—
770	#525	—	53	2	no	—
771	#525	—	53	2	no	—
772	#525	—	53	4	no	—
773	#525	—	53	4	no	—
774	#525	—	53	4	no	—
775	#525	—	53	4	no	—
776	#525	—	53	8	no	—
777	#525	—	53	2	no	—
778	#525	C₂×D₅₃	1	2	yes	complemented
779	C₂×#123	—	53	4	no	—
780	C₂×#123	—	53	4	no	—
781	C₂×#123	—	53	4	no	—
782	C₂×#123	—	53	8	no	—
783	C₂×#123	—	53	16	no	—
784	C₂×#123	—	53	8	no	—
785	C₂×#123	—	53	8	no	—
786	C₂×#123	—	53	16	no	—
787	C₂×#123	—	53	8	no	—
788	C₂×#123	—	53	8	no	—
789	C₂×#123	—	53	8	no	—
790	C₂×#123	—	53	4	no	—
791	C₂×#123	C₂×D₅₃	1	4	yes	complemented
792	C₂×C₂²⋊Q₈	—	53	4	no	—
793	C₂×C₂²⋊Q₈	—	53	8	no	—
794	C₂×#121	—	53	4	no	—
795	C₂×#121	—	53	16	no	—
796	C₂×#120	—	53	4	no	—
797	C₂×#120	—	53	8	no	—
798	#518	—	53	1	no	—
799	#518	—	53	8	no	—
800	#518	—	53	2	no	—
801	#518	—	53	4	no	—
802	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
803	C₂×C₄×D₄	—	53	8	no	—
804	C₂×C₄×D₄	—	53	8	no	—
805	C₂×#117	—	53	2	no	—
806	C₂²×C₄⋊C₄	—	53	8	no	—
807	C₂²×C₂²⋊C₄	—	53	4	no	—
808	C₂²×C₂²⋊C₄	—	53	8	no	—
809	C₅₃	C₂×#3485	1	1	yes	characteristic, complemented, Sylow
810	C₂⁵	—	53	2	no	—
811	C₂⁵	—	53	4	no	—
812	C₂⁵	—	53	1	no	—
813	H(5,𝔽₂)	—	2	8	no	—
814	H(5,𝔽₂)	—	106	32	no	—
815	H(5,𝔽₂)	—	106	32	no	—
816	H(5,𝔽₂)	—	106	32	no	—
817	H(5,𝔽₂)	—	106	16	no	—
818	H(5,𝔽₂)	—	106	8	no	—
819	C₂×#41	—	2	8	no	—
820	C₂×#41	—	53	2	no	—
821	C₂×#41	—	53	8	no	—
822	C₂×#41	—	53	4	no	—
823	C₂×#41	—	53	4	no	—
824	C₂×#41	—	53	2	no	—
825	C₂×#41	—	53	8	no	—
826	C₂×#41	—	53	16	no	—
827	C₂×#41	—	53	4	no	—
828	C₂×#41	—	53	8	no	—
829	C₂×#41	—	53	4	no	—
830	C₂×#41	—	53	2	no	—
831	C₂×#41	—	53	8	no	—
832	C₂×#41	—	53	16	no	—
833	C₂×#41	—	53	4	no	—
834	C₂×#41	—	53	8	no	—
835	C₂×#41	—	106	16	no	—
836	C₂×#41	—	106	8	no	—
837	C₂×#41	—	106	16	no	—
838	C₂×#41	—	106	16	no	—
839	C₂×#41	—	106	8	no	—
840	C₂×#41	—	106	64	no	—
841	C₂×#41	—	106	64	no	—
842	C₂×#41	—	106	32	no	—
843	C₂×#41	—	106	8	no	—
844	C₂×#41	C₂²×D₅₃	1	2	yes	—
845	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
846	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
847	C₂²×Q₈	—	53	4	no	—
848	C₂²×Q₈	—	53	2	no	—
849	C₂²×Q₈	—	53	4	no	—
850	C₂²×Q₈	—	53	2	no	—
851	C₂²×Q₈	—	53	1	no	—
852	C₂²×Q₈	—	106	8	no	—
853	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
854	C₂²×D₄	—	53	2	no	—
855	C₂²×D₄	—	53	16	no	—
856	C₂²×D₄	—	53	4	no	—
857	C₂²×D₄	—	53	4	no	—
858	C₂²×D₄	—	53	4	no	—
859	C₂²×D₄	—	53	4	no	—
860	C₂²×D₄	—	53	2	no	—
861	C₂²×D₄	—	53	2	no	—
862	C₂²×D₄	—	53	8	no	—
863	C₂²×D₄	—	53	8	no	—
864	C₂²×D₄	—	53	4	no	—
865	C₂²×D₄	—	53	8	no	—
866	C₂²×D₄	—	53	2	no	—
867	C₂²×D₄	—	53	8	no	—
868	C₂²×D₄	—	53	8	no	—
869	C₂²×D₄	—	53	8	no	—
870	C₂²×D₄	—	53	8	no	—
871	C₂²×D₄	—	53	4	no	—
872	C₂²×D₄	—	53	4	no	—
873	C₂²×D₄	—	53	8	no	—
874	C₂²×D₄	—	53	1	no	—
875	C₂²×D₄	—	53	4	no	—
876	C₂²×D₄	—	53	2	no	—
877	C₂²×D₄	—	53	4	no	—
878	C₂²×D₄	—	106	32	no	—
879	C₂²×D₄	—	106	16	no	—
880	C₂²×D₄	—	106	32	no	—
881	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
882	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
883	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
884	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
885	C₂³×C₄	—	53	1	no	—
886	C₂³×C₄	—	53	2	no	—
887	C₂³×C₄	—	53	1	no	—
888	C₂³×C₄	—	53	8	no	—
889	C₂³×C₄	—	53	4	no	—
890	C₂³×C₄	—	53	4	no	—
891	C₂³×C₄	—	53	4	no	—
892	C₂³×C₄	—	53	1	no	—
893	C₂³×C₄	—	53	2	no	—
894	C₂³×C₄	—	53	8	no	—
895	C₂³×C₄	—	53	2	no	—
896	C₂³×C₄	—	53	2	no	—
897	C₂³×C₄	—	53	1	no	—
898	C₂³×C₄	—	53	4	no	—
899	C₂³×C₄	—	53	1	no	—
900	C₂³×C₄	—	53	8	no	—
901	C₂³×C₄	—	106	8	no	—
902	C₂³×C₄	—	106	16	no	—
903	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
904	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
905	C₄⋊Q₈	—	53	4	no	—
906	C₄⋊Q₈	—	53	4	no	—
907	C₄⋊Q₈	—	53	16	no	—
908	C₄⋊Q₈	—	53	4	no	—
909	C₄⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
910	#124	—	53	4	no	—
911	#124	—	53	4	no	—
912	#124	—	53	16	no	—
913	#124	—	53	4	no	—
914	#124	C₂²×D₅₃	1	4	yes	complemented
915	#123	—	53	4	no	—
916	#123	—	53	8	no	—
917	#123	—	53	16	no	—
918	#123	—	53	8	no	—
919	#123	—	53	4	no	—
920	#123	—	53	8	no	—
921	#123	—	53	16	no	—
922	#123	—	53	8	no	—
923	#123	—	53	8	no	—
924	#123	—	53	16	no	—
925	#123	—	53	16	no	—
926	#123	—	53	16	no	—
927	#123	—	53	16	no	—
928	#123	—	53	8	no	—
929	#123	—	53	4	no	—
930	#123	—	53	16	no	—
931	#123	—	53	8	no	—
932	#123	—	53	16	no	—
933	#123	—	53	16	no	—
934	#123	—	53	16	no	—
935	#123	—	53	16	no	—
936	#123	—	53	8	no	—
937	#123	C₂²×D₅₃	1	4	yes	complemented
938	#123	C₂²×D₅₃	1	8	yes	complemented
939	#123	C₂²×D₅₃	1	16	yes	complemented
940	#123	C₂²×D₅₃	1	8	yes	complemented
941	C₂²⋊Q₈	—	53	4	no	—
942	C₂²⋊Q₈	—	53	8	no	—
943	C₂²⋊Q₈	—	53	4	no	—
944	C₂²⋊Q₈	—	53	8	no	—
945	C₂²⋊Q₈	—	53	8	no	—
946	C₂²⋊Q₈	—	53	4	no	—
947	C₂²⋊Q₈	—	53	16	no	—
948	C₂²⋊Q₈	—	53	8	no	—
949	C₂²⋊Q₈	—	53	8	no	—
950	C₂²⋊Q₈	—	53	16	no	—
951	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
952	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
953	#121	—	53	4	no	—
954	#121	—	53	8	no	—
955	#121	—	53	16	no	—
956	#121	—	53	16	no	—
957	#121	—	53	16	no	—
958	#121	—	53	4	no	—
959	#121	—	53	16	no	—
960	#121	—	53	4	no	—
961	#121	—	53	16	no	—
962	#121	—	53	8	no	—
963	#121	—	53	16	no	—
964	#121	—	53	16	no	—
965	#121	C₂²×D₅₃	1	4	yes	complemented
966	#121	C₂²×D₅₃	1	16	yes	complemented
967	#120	—	53	4	no	—
968	#120	—	53	8	no	—
969	#120	—	53	4	no	—
970	#120	—	53	8	no	—
971	#120	—	53	8	no	—
972	#120	—	53	16	no	—
973	#120	—	53	8	no	—
974	#120	—	53	4	no	—
975	#120	—	53	16	no	—
976	#120	—	53	8	no	—
977	#120	C₂²×D₅₃	1	4	yes	complemented
978	#120	C₂²×D₅₃	1	8	yes	complemented
979	C₄×D₄	—	53	8	no	—
980	C₄×D₄	—	53	8	no	—
981	C₄×D₄	—	53	16	no	—
982	C₄×D₄	—	53	8	no	—
983	C₄×D₄	—	53	8	no	—
984	C₄×D₄	—	53	8	no	—
985	C₄×D₄	—	53	8	no	—
986	C₄×D₄	—	53	16	no	—
987	C₄×D₄	—	53	8	no	—
988	C₄×D₄	—	53	8	no	—
989	C₄×D₄	—	53	8	no	—
990	C₄×D₄	—	53	8	no	—
991	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
992	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
993	#117	—	53	2	no	—
994	#117	—	53	4	no	—
995	#117	—	53	4	no	—
996	#117	—	53	4	no	—
997	#117	C₂²×D₅₃	1	2	yes	complemented
998	C₂×C₄⋊C₄	—	53	8	no	—
999	C₂×C₄⋊C₄	—	53	8	no	—
1000	C₂×C₄⋊C₄	—	53	8	no	—
1001	C₂×C₄⋊C₄	—	53	8	no	—
1002	C₂×C₄⋊C₄	—	53	16	no	—
1003	C₂×C₄⋊C₄	—	53	16	no	—
1004	C₂×C₄⋊C₄	—	53	16	no	—
1005	C₂×C₄⋊C₄	—	53	4	no	—
1006	C₂×C₄⋊C₄	C₂²×D₅₃	1	8	yes	complemented
1007	C₂×C₂²⋊C₄	—	53	4	no	—
1008	C₂×C₂²⋊C₄	—	53	8	no	—
1009	C₂×C₂²⋊C₄	—	53	8	no	—
1010	C₂×C₂²⋊C₄	—	53	8	no	—
1011	C₂×C₂²⋊C₄	—	53	8	no	—
1012	C₂×C₂²⋊C₄	—	53	4	no	—
1013	C₂×C₂²⋊C₄	—	53	8	no	—
1014	C₂×C₂²⋊C₄	—	53	8	no	—
1015	C₂×C₂²⋊C₄	—	53	8	no	—
1016	C₂×C₂²⋊C₄	—	53	8	no	—
1017	C₂×C₂²⋊C₄	—	53	16	no	—
1018	C₂×C₂²⋊C₄	—	53	16	no	—
1019	C₂×C₂²⋊C₄	—	53	16	no	—
1020	C₂×C₂²⋊C₄	—	53	8	no	—
1021	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1022	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
1023	C₂×C₄²	—	53	4	no	—
1024	C₂⁴	—	53	1	no	—
1025	C₂⁴	—	53	4	no	—
1026	C₂⁴	—	53	16	no	—
1027	C₂⁴	—	53	4	no	—
1028	C₂⁴	—	53	2	no	—
1029	C₂⁴	—	53	4	no	—
1030	C₂⁴	—	53	2	no	—
1031	C₂⁴	—	53	8	no	—
1032	C₂⁴	—	53	4	no	—
1033	C₂⁴	—	53	2	no	—
1034	C₂⁴	—	53	1	no	—
1035	C₂⁴	—	106	16	no	—
1036	C₂⁴	—	106	4	no	—
1037	C₂⁴	—	212	16	no	—
1038	C₂⁴	—	212	8	no	—
1039	C₂⁴	—	212	4	no	—
1040	C₂⁴	C₂³×D₅₃	1	4	yes	—
1041	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1042	C₂⁴	C₂³×D₅₃	1	2	yes	—
1043	#41	—	2	32	no	—
1044	#41	—	2	16	no	—
1045	#41	—	2	8	no	—
1046	#41	—	106	16	no	—
1047	#41	—	106	64	no	—
1048	#41	—	106	32	no	—
1049	#41	—	106	32	no	—
1050	#41	—	106	16	no	—
1051	#41	—	106	16	no	—
1052	#41	—	106	8	no	—
1053	#41	—	106	8	no	—
1054	#41	—	106	64	no	—
1055	#41	—	106	32	no	—
1056	#41	—	106	32	no	—
1057	#41	—	106	16	no	—
1058	#41	—	106	32	no	—
1059	#41	—	106	16	no	—
1060	#41	—	106	8	no	—
1061	C₂×Q₈	—	2	4	no	—
1062	C₂×Q₈	—	53	8	no	—
1063	C₂×Q₈	—	53	4	no	—
1064	C₂×Q₈	—	53	4	no	—
1065	C₂×Q₈	—	53	2	no	—
1066	C₂×Q₈	—	106	8	no	—
1067	C₂×Q₈	—	106	16	no	—
1068	C₂×Q₈	—	106	16	no	—
1069	C₂×Q₈	—	106	8	no	—
1070	C₂×Q₈	—	106	4	no	—
1071	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1072	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1073	C₂×D₄	—	2	16	no	—
1074	C₂×D₄	—	2	8	no	—
1075	C₂×D₄	—	2	16	no	—
1076	C₂×D₄	—	53	16	no	—
1077	C₂×D₄	—	53	8	no	—
1078	C₂×D₄	—	53	32	no	—
1079	C₂×D₄	—	53	32	no	—
1080	C₂×D₄	—	53	8	no	—
1081	C₂×D₄	—	53	8	no	—
1082	C₂×D₄	—	53	4	no	—
1083	C₂×D₄	—	53	4	no	—
1084	C₂×D₄	—	53	8	no	—
1085	C₂×D₄	—	53	8	no	—
1086	C₂×D₄	—	53	4	no	—
1087	C₂×D₄	—	53	8	no	—
1088	C₂×D₄	—	53	8	no	—
1089	C₂×D₄	—	53	8	no	—
1090	C₂×D₄	—	53	4	no	—
1091	C₂×D₄	—	53	8	no	—
1092	C₂×D₄	—	53	4	no	—
1093	C₂×D₄	—	53	8	no	—
1094	C₂×D₄	—	53	2	no	—
1095	C₂×D₄	—	53	8	no	—
1096	C₂×D₄	—	106	16	no	—
1097	C₂×D₄	—	106	8	no	—
1098	C₂×D₄	—	106	16	no	—
1099	C₂×D₄	—	106	8	no	—
1100	C₂×D₄	—	106	32	no	—
1101	C₂×D₄	—	106	16	no	—
1102	C₂×D₄	—	106	16	no	—
1103	C₂×D₄	—	106	32	no	—
1104	C₂×D₄	—	106	32	no	—
1105	C₂×D₄	—	106	32	no	—
1106	C₂×D₄	—	106	32	no	—
1107	C₂×D₄	—	106	32	no	—
1108	C₂×D₄	—	106	32	no	—
1109	C₂×D₄	—	106	8	no	—
1110	C₂×D₄	—	106	16	no	—
1111	C₂×D₄	—	106	8	no	—
1112	C₂×D₄	—	106	16	no	—
1113	C₂×D₄	—	106	16	no	—
1114	C₂×D₄	—	212	16	no	—
1115	C₂×D₄	D₄×D₅₃	1	8	yes	complemented
1116	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1117	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1118	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1119	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1120	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1121	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1122	C₂²×C₄	—	2	8	no	—
1123	C₂²×C₄	—	2	4	no	—
1124	C₂²×C₄	—	53	1	no	—
1125	C₂²×C₄	—	53	8	no	—
1126	C₂²×C₄	—	53	2	no	—
1127	C₂²×C₄	—	53	2	no	—
1128	C₂²×C₄	—	53	8	no	—
1129	C₂²×C₄	—	53	4	no	—
1130	C₂²×C₄	—	53	4	no	—
1131	C₂²×C₄	—	53	4	no	—
1132	C₂²×C₄	—	53	1	no	—
1133	C₂²×C₄	—	53	2	no	—
1134	C₂²×C₄	—	53	8	no	—
1135	C₂²×C₄	—	53	8	no	—
1136	C₂²×C₄	—	53	2	no	—
1137	C₂²×C₄	—	53	4	no	—
1138	C₂²×C₄	—	53	4	no	—
1139	C₂²×C₄	—	53	8	no	—
1140	C₂²×C₄	—	53	8	no	—
1141	C₂²×C₄	—	53	8	no	—
1142	C₂²×C₄	—	53	4	no	—
1143	C₂²×C₄	—	53	4	no	—
1144	C₂²×C₄	—	53	4	no	—
1145	C₂²×C₄	—	53	4	no	—
1146	C₂²×C₄	—	53	2	no	—
1147	C₂²×C₄	—	53	4	no	—
1148	C₂²×C₄	—	53	16	no	—
1149	C₂²×C₄	—	106	4	no	—
1150	C₂²×C₄	—	106	16	no	—
1151	C₂²×C₄	—	106	16	no	—
1152	C₂²×C₄	—	106	16	no	—
1153	C₂²×C₄	—	106	4	no	—
1154	C₂²×C₄	—	106	8	no	—
1155	C₂²×C₄	—	106	8	no	—
1156	C₂²×C₄	—	106	8	no	—
1157	C₂²×C₄	—	106	32	no	—
1158	C₂²×C₄	—	106	32	no	—
1159	C₂²×C₄	—	106	16	no	—
1160	C₂²×C₄	—	106	4	no	—
1161	C₂²×C₄	—	106	8	no	—
1162	C₂²×C₄	—	106	4	no	—
1163	C₂²×C₄	—	212	16	no	—
1164	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1165	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1166	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1167	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1168	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1169	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1170	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1171	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1172	C₄⋊C₄	—	53	8	no	—
1173	C₄⋊C₄	—	53	8	no	—
1174	C₄⋊C₄	—	53	8	no	—
1175	C₄⋊C₄	—	53	16	no	—
1176	C₄⋊C₄	—	53	16	no	—
1177	C₄⋊C₄	—	53	16	no	—
1178	C₄⋊C₄	—	53	8	no	—
1179	C₄⋊C₄	—	53	4	no	—
1180	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1181	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
1182	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1183	C₂²⋊C₄	—	53	4	no	—
1184	C₂²⋊C₄	—	53	8	no	—
1185	C₂²⋊C₄	—	53	8	no	—
1186	C₂²⋊C₄	—	53	16	no	—
1187	C₂²⋊C₄	—	53	8	no	—
1188	C₂²⋊C₄	—	53	8	no	—
1189	C₂²⋊C₄	—	53	8	no	—
1190	C₂²⋊C₄	—	53	8	no	—
1191	C₂²⋊C₄	—	53	16	no	—
1192	C₂²⋊C₄	—	53	16	no	—
1193	C₂²⋊C₄	—	53	16	no	—
1194	C₂²⋊C₄	—	53	8	no	—
1195	C₂²⋊C₄	—	53	8	no	—
1196	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1197	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1198	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1199	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1200	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1201	C₄²	—	53	8	no	—
1202	C₄²	—	53	4	no	—
1203	C₄²	C₂³×D₅₃	1	4	yes	—
1204	C₂³	—	2	2	no	—
1205	C₂³	—	2	8	no	—
1206	C₂³	—	4	4	no	—
1207	C₂³	—	4	2	no	—
1208	C₂³	—	4	8	no	—
1209	C₂³	—	53	1	no	—
1210	C₂³	—	53	4	no	—
1211	C₂³	—	53	16	no	—
1212	C₂³	—	53	1	no	—
1213	C₂³	—	53	4	no	—
1214	C₂³	—	53	16	no	—
1215	C₂³	—	53	8	no	—
1216	C₂³	—	53	4	no	—
1217	C₂³	—	53	2	no	—
1218	C₂³	—	106	16	no	—
1219	C₂³	—	106	4	no	—
1220	C₂³	—	106	16	no	—
1221	C₂³	—	106	4	no	—
1222	C₂³	—	106	4	no	—
1223	C₂³	—	106	8	no	—
1224	C₂³	—	106	8	no	—
1225	C₂³	—	106	16	no	—
1226	C₂³	—	106	8	no	—
1227	C₂³	—	106	2	no	—
1228	C₂³	—	424	32	no	—
1229	C₂³	—	212	8	no	—
1230	C₂³	—	212	16	no	—
1231	C₂³	—	212	8	no	—
1232	C₂³	—	212	4	no	—
1233	C₂³	—	212	2	no	—
1234	C₂³	—	212	4	no	—
1235	C₂³	—	212	32	no	—
1236	C₂³	—	212	16	no	—
1237	C₂³	C₂×D₄×D₅₃	1	8	yes	—
1238	C₂³	C₂⁴×D₅₃	1	4	yes	—
1239	C₂³	C₂⁴×D₅₃	1	2	yes	—
1240	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1241	C₂³	C₂⁴×D₅₃	1	4	yes	—
1242	Q₈	—	2	8	no	—
1243	Q₈	—	2	4	no	—
1244	Q₈	—	106	16	no	—
1245	Q₈	—	106	8	no	—
1246	Q₈	—	106	8	no	—
1247	Q₈	—	106	4	no	—
1248	D₄	—	2	8	no	—
1249	D₄	—	2	16	no	—
1250	D₄	—	2	16	no	—
1251	D₄	—	2	4	no	—
1252	D₄	—	4	8	no	—
1253	D₄	—	53	32	no	—
1254	D₄	—	53	16	no	—
1255	D₄	—	106	8	no	—
1256	D₄	—	106	16	no	—
1257	D₄	—	106	16	no	—
1258	D₄	—	106	8	no	—
1259	D₄	—	106	8	no	—
1260	D₄	—	106	16	no	—
1261	D₄	—	106	16	no	—
1262	D₄	—	106	8	no	—
1263	D₄	—	106	16	no	—
1264	D₄	—	106	16	no	—
1265	D₄	—	106	4	no	—
1266	D₄	—	212	8	no	—
1267	D₄	—	212	8	no	—
1268	D₄	—	212	8	no	—
1269	D₄	C₂×D₄×D₅₃	1	16	yes	—
1270	C₂×C₄	—	2	2	no	—
1271	C₂×C₄	—	2	4	no	—
1272	C₂×C₄	—	2	16	no	—
1273	C₂×C₄	—	2	8	no	—
1274	C₂×C₄	—	2	8	no	—
1275	C₂×C₄	—	2	8	no	—
1276	C₂×C₄	—	4	8	no	—
1277	C₂×C₄	—	53	4	no	—
1278	C₂×C₄	—	53	2	no	—
1279	C₂×C₄	—	53	8	no	—
1280	C₂×C₄	—	53	8	no	—
1281	C₂×C₄	—	53	8	no	—
1282	C₂×C₄	—	53	2	no	—
1283	C₂×C₄	—	53	4	no	—
1284	C₂×C₄	—	53	4	no	—
1285	C₂×C₄	—	106	8	no	—
1286	C₂×C₄	—	106	8	no	—
1287	C₂×C₄	—	106	4	no	—
1288	C₂×C₄	—	106	4	no	—
1289	C₂×C₄	—	106	8	no	—
1290	C₂×C₄	—	106	8	no	—
1291	C₂×C₄	—	106	8	no	—
1292	C₂×C₄	—	106	16	no	—
1293	C₂×C₄	—	106	16	no	—
1294	C₂×C₄	—	106	16	no	—
1295	C₂×C₄	—	106	16	no	—
1296	C₂×C₄	—	106	8	no	—
1297	C₂×C₄	—	106	8	no	—
1298	C₂×C₄	—	106	2	no	—
1299	C₂×C₄	—	106	4	no	—
1300	C₂×C₄	—	106	16	no	—
1301	C₂×C₄	—	106	8	no	—
1302	C₂×C₄	—	106	8	no	—
1303	C₂×C₄	—	106	8	no	—
1304	C₂×C₄	—	212	16	no	—
1305	C₂×C₄	—	212	8	no	—
1306	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1307	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1308	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1309	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1310	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1311	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1312	C₂²	—	2	8	no	—
1313	C₂²	—	2	2	no	—
1314	C₂²	—	2	2	no	—
1315	C₂²	—	2	4	no	—
1316	C₂²	—	2	4	no	—
1317	C₂²	—	2	8	no	—
1318	C₂²	—	4	8	no	—
1319	C₂²	—	4	4	no	—
1320	C₂²	—	8	8	no	—
1321	C₂²	—	53	2	no	—
1322	C₂²	—	53	4	no	—
1323	C₂²	—	53	2	no	—
1324	C₂²	—	53	8	no	—
1325	C₂²	—	106	32	no	—
1326	C₂²	—	106	8	no	—
1327	C₂²	—	106	8	no	—
1328	C₂²	—	106	2	no	—
1329	C₂²	—	106	2	no	—
1330	C₂²	—	106	4	no	—
1331	C₂²	—	106	4	no	—
1332	C₂²	—	106	8	no	—
1333	C₂²	—	424	8	no	—
1334	C₂²	—	424	16	no	—
1335	C₂²	—	212	8	no	—
1336	C₂²	—	212	16	no	—
1337	C₂²	—	212	4	no	—
1338	C₂²	—	212	16	no	—
1339	C₂²	—	212	8	no	—
1340	C₂²	—	212	8	no	—
1341	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1342	C₂²	C₂²×D₄×D₅₃	1	8	yes	—
1343	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1344	C₄	—	2	2	no	—
1345	C₄	—	2	4	no	—
1346	C₄	—	2	4	no	—
1347	C₄	—	2	8	no	—
1348	C₄	—	53	4	no	—
1349	C₄	—	106	2	no	—
1350	C₄	—	106	4	no	—
1351	C₄	—	106	4	no	—
1352	C₄	—	106	8	no	—
1353	C₄	C₂²×D₄×D₅₃	1	4	yes	—
1354	C₂	—	2	2	no	—
1355	C₂	—	2	8	no	—
1356	C₂	—	4	2	no	—
1357	C₂	—	4	4	no	—
1358	C₂	—	53	4	no	—
1359	C₂	—	106	8	no	—
1360	C₂	—	106	2	no	—
1361	C₂	—	212	4	no	—
1362	C₂	—	212	2	no	—
1363	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1364	C₂	#585×D₅₃	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×H(5,𝔽₂)×D₅₃	C₂	semidirect
2. C₂²×#41×D₅₃	C₂	semidirect
3. #20288360	C₂	semidirect
4. #20288359	C₂	semidirect
5. #20288358	C₂	semidirect
6. #20288357	C₂	semidirect
7. #20288356	C₂	semidirect
8. #20288355	C₂	semidirect
9. #20288354	C₂	semidirect
10. #20288353	C₂	semidirect
11. #20288352	C₂	semidirect
12. #547×D₅₃	C₂	semidirect
13. #546×D₅₃	C₂	semidirect
14. #536×D₅₃	C₂	semidirect
15. #534×D₅₃	C₂	semidirect
16. #525×D₅₃	C₂	semidirect
17. C₂×#123×D₅₃	C₂	semidirect
18. #518×D₅₃	C₂	semidirect
19. C₅₃×#3485	C₂	semidirect
20. C₂×#13133263	C₂²	semidirect
21. C₂×#13133263	C₂²	semidirect
22. C₂×#13133262	C₂²	semidirect
23. C₂×#13133262	C₂²	semidirect
24. C₂×#13133262	C₂²	semidirect
26. C₂²×#11719949	C₂²	semidirect
27. C₂²×#11719945	C₂²	semidirect
28. C₂²×#11719945	C₂²	semidirect
29. C₂²×#11719947	C₂²	semidirect
30. C₂²×#11719947	C₂²	semidirect
33. C₂×#41×D₅₃	C₂²	semidirect
34. C₂×#41×D₅₃	C₂²	semidirect
35. C₂×#41×D₅₃	C₂²	semidirect
36. C₂²×Q₈×D₅₃	C₂²	semidirect
39. C₂²×D₄×D₅₃	C₂²	semidirect
40. C₂²×D₄×D₅₃	C₂²	semidirect
41. C₂³×C₄×D₅₃	C₂²	semidirect
42. C₂³×C₄×D₅₃	C₂²	semidirect
43. #16811278	C₂²	semidirect
44. #16811277	C₂²	semidirect
45. #16811276	C₂²	semidirect
46. #16811275	C₂²	semidirect
47. #16811275	C₂²	semidirect
48. #16811274	C₂²	semidirect
49. #16811273	C₂²	semidirect
50. #16811272	C₂²	semidirect
51. #16811272	C₂²	semidirect
52. #16811271	C₂²	semidirect
53. #16811271	C₂²	semidirect
54. #16811270	C₂²	semidirect
55. #16811269	C₂²	semidirect
56. #16811268	C₂²	semidirect
57. #16811267	C₂²	semidirect
58. #16811266	C₂²	semidirect
59. #16811265	C₂²	semidirect
60. #16811264	C₂²	semidirect
61. #16811263	C₂²	semidirect
62. #16811262	C₂²	semidirect
63. #16811261	C₂²	semidirect
64. #16811260	C₂²	semidirect
65. #16811199	C₂²	semidirect
66. #16811198	C₂²	semidirect
67. #16811197	C₂²	semidirect
68. #16811196	C₂²	semidirect
69. #16811195	C₂²	semidirect
70. #16811194	C₂²	semidirect
71. #16811193	C₂²	semidirect
72. #16811185	C₂²	semidirect
73. #16811184	C₂²	semidirect
74. #16811184	C₂²	semidirect
75. #16811183	C₂²	semidirect
76. #16811183	C₂²	semidirect
77. #16811182	C₂²	semidirect
78. #16811182	C₂²	semidirect
79. #16811181	C₂²	semidirect
80. C₄⋊Q₈×D₅₃	C₂²	semidirect
81. #124×D₅₃	C₂²	semidirect
82. #16811136	C₂²	semidirect
83. #16811135	C₂²	semidirect
84. #16811134	C₂²	semidirect
85. #16811133	C₂²	semidirect
86. #16811132	C₂²	semidirect
87. #16811131	C₂²	semidirect
88. #16811130	C₂²	semidirect
89. #16811129	C₂²	semidirect
90. C₂×#13133202	C₂²	semidirect
91. C₂×#13133201	C₂²	semidirect
92. C₂×#13133200	C₂²	semidirect
93. C₂×#13133199	C₂²	semidirect
94. C₂×#13133198	C₂²	semidirect
95. #123×D₅₃	C₂²	semidirect
96. #123×D₅₃	C₂²	semidirect
97. #123×D₅₃	C₂²	semidirect
98. #123×D₅₃	C₂²	semidirect
99. #123×D₅₃	C₂²	semidirect
100. #123×D₅₃	C₂²	semidirect
101. #123×D₅₃	C₂²	semidirect
102. C₂²⋊Q₈×D₅₃	C₂²	semidirect
103. C₂²⋊Q₈×D₅₃	C₂²	semidirect
104. #121×D₅₃	C₂²	semidirect
105. #121×D₅₃	C₂²	semidirect
106. #120×D₅₃	C₂²	semidirect
107. #120×D₅₃	C₂²	semidirect
108. #16811098	C₂²	semidirect
109. #16811097	C₂²	semidirect
110. #16811096	C₂²	semidirect
111. #16811095	C₂²	semidirect
112. C₄×D₄×D₅₃	C₂²	semidirect
113. C₄×D₄×D₅₃	C₂²	semidirect
114. #117×D₅₃	C₂²	semidirect
115. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
116. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
117. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
118. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
119. C₂²×#41×C₅₃	C₂²	semidirect
120. C₅₃×#547	C₂²	semidirect
121. C₅₃×#546	C₂²	semidirect
122. C₅₃×#536	C₂²	semidirect
123. C₅₃×#534	C₂²	semidirect
124. C₅₃×#525	C₂²	semidirect
125. C₂×#123×C₅₃	C₂²	semidirect
126. C₅₃×#518	C₂²	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
151. C₂×#11719947	C₂³	semidirect
152. C₂×#11719947	C₂³	semidirect
153. C₂×#11719947	C₂³	semidirect
154. C₂×#11719947	C₂³	semidirect
159. C₂²×Dic₁₀₆	C₂³	semidirect
160. C₂²×Dic₁₀₆	C₂³	semidirect
164. C₂×Q₈×D₅₃	C₂³	semidirect
167. C₂²×D₂₁₂	C₂³	semidirect
168. C₂²×D₂₁₂	C₂³	semidirect
172. C₂²×C₂²⋊D₅₃	C₂³	semidirect
173. C₂²×C₂²⋊D₅₃	C₂³	semidirect
174. C₂²×C₂²⋊D₅₃	C₂³	semidirect
178. C₂×D₄×D₅₃	D₄	semidirect
188. C₂×D₄×D₅₃	C₂³	semidirect
189. C₂×D₄×D₅₃	C₂³	semidirect
190. C₂×D₄×D₅₃	C₂³	semidirect
191. C₂×D₄×D₅₃	C₂³	semidirect
192. C₂³×Dic₅₃	C₂³	semidirect
193. C₂³×Dic₅₃	C₂³	semidirect
204. C₂²×C₄×D₅₃	C₂³	semidirect
205. C₂²×C₄×D₅₃	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. #13133217	C₂³	semidirect
211. #13133216	C₂³	semidirect
212. #13133215	C₂³	semidirect
213. #13133215	C₂³	semidirect
214. #13133206	C₂³	semidirect
215. #13133205	C₂³	semidirect
216. #13133204	C₂³	semidirect
217. #13133203	C₂³	semidirect
218. #13133202	C₂³	semidirect
219. #13133202	C₂³	semidirect
220. #13133202	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. #13133200	C₂³	semidirect
230. #13133200	C₂³	semidirect
231. #13133199	C₂³	semidirect
232. #13133199	C₂³	semidirect
233. #13133199	C₂³	semidirect
234. #13133199	C₂³	semidirect
235. #13133199	C₂³	semidirect
236. #13133198	C₂³	semidirect
237. #13133198	C₂³	semidirect
238. #13133198	C₂³	semidirect
239. #13133198	C₂³	semidirect
240. #13133197	C₂³	semidirect
241. #13133197	C₂³	semidirect
242. #13133196	C₂³	semidirect
243. #13133196	C₂³	semidirect
244. #13133195	C₂³	semidirect
245. #13133195	C₂³	semidirect
246. #13133194	C₂³	semidirect
247. #13133194	C₂³	semidirect
248. #13133193	C₂³	semidirect
249. #13133193	C₂³	semidirect
250. #13133192	C₂³	semidirect
251. #13133192	C₂³	semidirect
252. #13133191	C₂³	semidirect
253. #13133191	C₂³	semidirect
254. #13133190	C₂³	semidirect
255. #13133190	C₂³	semidirect
256. #13133190	C₂³	semidirect
257. #13133189	C₂³	semidirect
258. #13133189	C₂³	semidirect
259. #13133189	C₂³	semidirect
260. #13133188	C₂³	semidirect
261. #13133188	C₂³	semidirect
262. #13133187	C₂³	semidirect
263. #13133187	C₂³	semidirect
264. #13133187	C₂³	semidirect
265. #13133187	C₂³	semidirect
266. #13133186	C₂³	semidirect
267. #13133186	C₂³	semidirect
268. #13133185	C₂³	semidirect
269. #13133185	C₂³	semidirect
270. #13133185	C₂³	semidirect
271. #13133185	C₂³	semidirect
272. C₄×D₂₁₂	C₂³	semidirect
273. C₄×D₂₁₂	C₂³	semidirect
274. D₄×Dic₅₃	C₂³	semidirect
275. D₄×Dic₅₃	C₂³	semidirect
276. #13133179	C₂³	semidirect
277. #13133179	C₂³	semidirect
278. C₄×C₂²⋊D₅₃	C₂³	semidirect
279. C₄×C₂²⋊D₅₃	C₂³	semidirect
280. C₄×C₂²⋊D₅₃	C₂³	semidirect
281. #13133177	C₂³	semidirect
282. #13133177	C₂³	semidirect
283. #13133177	C₂³	semidirect
284. #13133176	C₂³	semidirect
285. #13133175	C₂³	semidirect
286. #13133174	C₂³	semidirect
287. #13133173	C₂³	semidirect
288. C₂×C₄⋊Dic₅₃	C₂³	semidirect
289. C₂×#11719919	C₂³	semidirect
290. C₂×#11719919	C₂³	semidirect
294. C₄⋊C₄×D₅₃	C₂³	semidirect
295. C₄⋊C₄×D₅₃	C₂³	semidirect
296. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
297. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
298. C₂×#11719921	C₂³	semidirect
299. C₂×#11719921	C₂³	semidirect
300. C₂×#11719921	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
314. C₂×#41×C₅₃	C₂³	semidirect
315. C₂×#41×C₅₃	C₂³	semidirect
316. C₂²×Q₈×C₅₃	C₂³	semidirect
319. C₂²×D₄×C₅₃	C₂³	semidirect
320. C₂²×D₄×C₅₃	C₂³	semidirect
321. C₂³×C₄×C₅₃	C₂³	semidirect
322. C₂³×C₄×C₅₃	C₂³	semidirect
323. C₄⋊Q₈×C₅₃	C₂³	semidirect
324. #124×C₅₃	C₂³	semidirect
325. #123×C₅₃	C₂³	semidirect
326. #123×C₅₃	C₂³	semidirect
327. #123×C₅₃	C₂³	semidirect
328. #123×C₅₃	C₂³	semidirect
329. C₂²⋊Q₈×C₅₃	C₂³	semidirect
330. C₂²⋊Q₈×C₅₃	C₂³	semidirect
331. #121×C₅₃	C₂³	semidirect
332. #121×C₅₃	C₂³	semidirect
333. #120×C₅₃	C₂³	semidirect
334. #120×C₅₃	C₂³	semidirect
335. C₄×D₄×C₅₃	C₂³	semidirect
336. C₄×D₄×C₅₃	C₂³	semidirect
337. #117×C₅₃	C₂³	semidirect
338. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
339. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
340. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
369. C₂×D₄×C₅₃	C₂×D₄	semidirect
391. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
436. D₄×D₅₃	C₂×D₄	semidirect
446. C₂×D₂₁₂	C₂×D₄	semidirect
683. #3485	D₅₃	direct (N × H)
701. D₅₃	#3485	direct (N × H)
708. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
719. C₂²×#41	C₂×D₅₃	semidirect
738. #547	C₂×D₅₃	semidirect
750. #546	C₂×D₅₃	semidirect
758. #536	C₂×D₅₃	semidirect
767. #534	C₂×D₅₃	semidirect
778. #525	C₂×D₅₃	semidirect
791. C₂×#123	C₂×D₅₃	semidirect
802. #518	C₂×D₅₃	semidirect
809. C₅₃	C₂×#3485	semidirect
845. C₂×#41	C₂²×D₅₃	semidirect
846. C₂×#41	C₂²×D₅₃	semidirect
853. C₂²×Q₈	C₂²×D₅₃	semidirect
883. C₂²×D₄	C₂²×D₅₃	semidirect
884. C₂²×D₄	C₂²×D₅₃	semidirect
903. C₂³×C₄	C₂²×D₅₃	semidirect
904. C₂³×C₄	C₂²×D₅₃	semidirect
909. C₄⋊Q₈	C₂²×D₅₃	semidirect
914. #124	C₂²×D₅₃	semidirect
937. #123	C₂²×D₅₃	semidirect
938. #123	C₂²×D₅₃	semidirect
939. #123	C₂²×D₅₃	semidirect
940. #123	C₂²×D₅₃	semidirect
951. C₂²⋊Q₈	C₂²×D₅₃	semidirect
952. C₂²⋊Q₈	C₂²×D₅₃	semidirect
965. #121	C₂²×D₅₃	semidirect
966. #121	C₂²×D₅₃	semidirect
977. #120	C₂²×D₅₃	semidirect
978. #120	C₂²×D₅₃	semidirect
991. C₄×D₄	C₂²×D₅₃	semidirect
992. C₄×D₄	C₂²×D₅₃	semidirect
997. #117	C₂²×D₅₃	semidirect
1006. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1021. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1022. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1115. 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
C₂×H(5,𝔽₂)×D₅₃	2
C₂²×#41×D₅₃	2
#20288360	2
#20288359	2
#20288358	2
#20288357	2
#20288356	2
#20288355	2
#20288354	2
#20288353	2
#20288352	2
#547×D₅₃	2
#546×D₅₃	2
#536×D₅₃	2
#534×D₅₃	2
#525×D₅₃	2
C₂×#123×D₅₃	2
#518×D₅₃	2
C₅₃×#3485	2
C₂×#3485	53

Subgroups — D53×#3485 #28292128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3485 #28292128