Subgroups — #28293326

Order 13568.

7498 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289067	C₂	1	4	yes	maximal, complemented
2	#20289045	C₂	1	4	yes	maximal, complemented
3	#20289025	C₂	1	8	yes	maximal, complemented
4	#20289024	C₂	1	8	yes	maximal, complemented
5	#20288903	C₂	1	8	yes	maximal, complemented
6	#20288881	C₂	1	8	yes	maximal, complemented
7	#20288871	C₂	1	8	yes	maximal, complemented
8	#20288413	C₂	1	1	yes	maximal, characteristic, complemented
9	#20288405	C₂	1	2	yes	maximal, complemented
10	#20288400	C₂	1	2	yes	maximal, complemented
11	#20288353	C₂	1	2	yes	maximal, complemented
12	#20288351	C₂	1	2	yes	maximal, complemented
13	#20288347	C₂	1	2	yes	maximal, complemented
14	C₂×#16811192	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16811184	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3491	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#13133262	C₂²	1	2	yes	complemented
18	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
21	#16811377	C₂²	1	4	yes	complemented
22	#16811371	C₂²	1	8	yes	complemented
23	#16811371	C₂²	1	4	yes	complemented
24	#16811369	C₂²	1	8	yes	complemented
25	#16811367	C₂²	1	4	yes	complemented
26	#16811365	C₂²	1	4	yes	complemented
27	#16811364	C₂²	1	8	yes	complemented
28	#16811364	C₂²	1	8	yes	complemented
29	#16811364	C₂²	1	8	yes	complemented
30	#16811363	C₂²	1	8	yes	complemented
31	#16811358	C₂²	1	4	yes	complemented
32	#16811336	C₂²	1	8	yes	complemented
33	#16811326	C₂²	1	8	yes	complemented
34	#16811324	C₂²	1	8	yes	complemented
35	#16811306	C₂²	1	8	yes	complemented
36	#16811302	C₂²	1	8	yes	complemented
37	#16811300	C₂²	1	8	yes	complemented
38	#16811300	C₂²	1	8	yes	complemented
39	#16811297	C₂²	1	8	yes	complemented
40	#16811297	C₂²	1	8	yes	complemented
41	#16811297	C₂²	1	8	yes	complemented
42	#16811295	C₂²	1	4	yes	complemented
43	#16811294	C₂²	1	4	yes	complemented
44	#16811274	C₂²	1	8	yes	complemented
45	#16811271	C₂²	1	8	yes	complemented
46	#16811269	C₂²	1	8	yes	complemented
47	#16811268	C₂²	1	8	yes	complemented
48	#16811268	C₂²	1	8	yes	complemented
49	#16811265	C₂²	1	8	yes	complemented
50	#16811265	C₂²	1	8	yes	complemented
51	#16811265	C₂²	1	8	yes	complemented
52	#16811264	C₂²	1	8	yes	complemented
53	#16811264	C₂²	1	8	yes	complemented
54	#16811264	C₂²	1	8	yes	complemented
55	#16811263	C₂²	1	8	yes	complemented
56	#16811263	C₂²	1	8	yes	complemented
57	#16811262	C₂²	1	8	yes	complemented
58	D₄×D₂₁₂	C₂²	1	8	yes	complemented
59	D₄×D₂₁₂	C₂²	1	4	yes	complemented
60	D₄×D₂₁₂	C₂²	1	8	yes	complemented
61	#16811257	C₂²	1	8	yes	complemented
62	#16811255	C₂²	1	8	yes	complemented
63	#16811249	C₂²	1	1	yes	characteristic, complemented
64	#16811245	C₂²	1	8	yes	complemented
65	#16811239	C₂²	1	8	yes	complemented
66	#16811229	C₂²	1	8	yes	complemented
67	#16811229	C₂²	1	8	yes	complemented
68	#16811228	C₂²	1	8	yes	complemented
69	#16811225	C₂²	1	8	yes	complemented
70	#16811221	C₂²	1	8	yes	complemented
71	#16811220	C₂²	1	4	yes	complemented
72	#16811213	C₂²	1	8	yes	complemented
73	#16811213	C₂²	1	8	yes	complemented
74	#16811212	C₂²	1	8	yes	complemented
75	#16811212	C₂²	1	8	yes	complemented
76	#16811212	C₂²	1	8	yes	complemented
77	#16811206	C₂²	1	8	yes	complemented
78	#16811206	C₂²	1	8	yes	complemented
79	#16811203	C₂²	1	8	yes	complemented
80	#16811195	C₂²	1	4	yes	complemented
81	#16811192	C₂²	1	8	yes	complemented
82	#16811192	C₂²	1	8	yes	complemented
83	#16811192	C₂²	1	4	yes	complemented
84	#16811192	C₂²	1	8	yes	complemented
85	#16811191	C₂²	1	8	yes	complemented
86	#16811188	C₂²	1	4	yes	complemented
87	#16811185	C₂²	1	1	yes	characteristic
88	#16811185	C₂²	1	2	yes	complemented
89	#16811185	C₂²	1	4	yes	complemented
90	#16811184	C₂²	1	8	yes	complemented
91	#16811184	C₂²	1	8	yes	complemented
92	#16811184	C₂²	1	4	yes	complemented
93	#16811184	C₂²	1	8	yes	complemented
94	#16811184	C₂²	1	8	yes	complemented
95	#16811184	C₂²	1	8	yes	complemented
96	#16811184	C₂²	1	4	yes	complemented
97	#16811182	C₂²	1	2	yes	complemented
98	C₂×#13133214	C₂²	1	2	yes	complemented
99	#16811157	C₂²	1	4	yes	complemented
100	C₂×#13133205	C₂²	1	2	yes	complemented
101	#16811136	C₂²	1	8	yes	complemented
102	#16811135	C₂²	1	4	yes	complemented
103	#16811132	C₂²	1	8	yes	complemented
104	#16811131	C₂²	1	4	yes	complemented
105	#16811131	C₂²	1	4	yes	complemented
106	C₂×#13133202	C₂²	1	4	yes	complemented
107	C₂×#13133200	C₂²	1	2	yes	complemented
108	#123×D₅₃	C₂²	1	4	yes	complemented
109	C₂×#13133192	C₂²	1	4	yes	complemented
110	C₂×#13133192	C₂²	1	4	yes	complemented
111	C₂×#13133190	C₂²	1	4	yes	complemented
112	C₂×#13133187	C₂²	1	2	yes	complemented
113	C₂×#13133187	C₂²	1	2	yes	complemented
114	C₂×#13133187	C₂²	1	2	yes	complemented
115	C₂×#13133187	C₂²	1	4	yes	complemented
116	C₂×#13133187	C₂²	1	4	yes	complemented
117	C₂×#13133185	C₂²	1	2	yes	complemented
118	#120×D₅₃	C₂²	1	4	yes	complemented
119	#16811096	C₂²	1	2	yes	complemented
120	#16811096	C₂²	1	2	yes	complemented
121	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
122	C₅₃×#552	C₂²	1	8	yes	complemented
123	C₅₃×#551	C₂²	1	8	yes	complemented
124	C₅₃×#543	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#539	C₂²	1	4	yes	complemented
126	C₅₃×#534	C₂²	1	1	yes	characteristic
127	C₅₃×#529	C₂²	1	4	yes	complemented
128	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
129	C₅₃×#518	C₂²	1	2	yes	complemented
130	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₂⁴×D₅₃	C₂³	1	2	yes	—
132	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
133	#13133262	—	4	8	no	—
134	C₂×#11719949	C₂³	1	8	yes	complemented
135	C₂×#11719945	—	4	4	no	—
136	C₂×#11719945	C₂³	1	4	yes	—
137	C₂×#11719945	C₂³	1	8	yes	complemented
138	C₂×#11719945	C₂³	1	8	yes	complemented
139	C₂×#11719947	C₂³	1	4	yes	—
140	C₂×#11719947	C₂³	1	4	yes	—
141	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
142	C₂²×D₂₁₂	—	4	4	no	—
143	C₂²×D₂₁₂	C₂³	1	4	yes	—
144	C₂²×D₂₁₂	C₂³	1	4	yes	—
145	C₂²×D₂₁₂	C₂³	1	2	yes	—
146	C₂²×D₂₁₂	C₂³	1	2	yes	—
147	C₂²×D₂₁₂	C₂³	1	4	yes	—
148	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
149	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
150	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
151	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
152	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
153	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
154	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
155	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
156	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
157	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
158	C₂×D₄×D₅₃	—	4	8	no	—
159	C₂×D₄×D₅₃	C₂³	1	4	yes	—
160	C₂×D₄×D₅₃	C₂³	1	8	yes	—
161	C₂×D₄×D₅₃	C₂³	1	4	yes	—
162	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
163	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
164	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
165	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
166	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
167	#13133216	C₂³	1	8	yes	complemented
168	#13133214	C₂³	1	4	yes	—
169	#13133214	C₂³	1	4	yes	complemented
170	#13133214	C₂³	1	8	yes	complemented
171	#13133214	C₂³	1	8	yes	complemented
172	#13133213	C₂³	1	8	yes	complemented
173	#13133212	C₂³	1	8	yes	complemented
174	#13133212	C₂³	1	8	yes	complemented
175	#13133212	C₂³	1	8	yes	complemented
176	#13133212	C₂³	1	8	yes	complemented
177	#13133211	C₂³	1	8	yes	complemented
178	#13133211	C₂³	1	8	yes	complemented
179	#13133209	C₂³	1	4	yes	complemented
180	#13133207	C₂³	1	8	yes	complemented
181	#13133206	C₂³	1	8	yes	complemented
182	#13133206	C₂³	1	8	yes	complemented
183	#13133205	C₂³	1	4	yes	—
184	#13133205	C₂³	1	8	yes	complemented
185	#13133205	C₂³	1	8	yes	complemented
186	#13133205	C₂³	1	4	yes	complemented
187	#13133205	C₂³	1	4	yes	complemented
188	#13133205	C₂³	1	8	yes	complemented
189	#13133203	C₂³	1	8	yes	complemented
190	#13133203	C₂³	1	8	yes	complemented
191	#13133203	C₂³	1	8	yes	complemented
192	#13133202	C₂³	1	8	yes	—
193	#13133202	C₂³	1	8	yes	—
194	#13133202	C₂³	1	8	yes	complemented
195	#13133202	C₂³	1	8	yes	complemented
196	#13133202	C₂³	1	8	yes	complemented
197	#13133202	C₂³	1	8	yes	complemented
198	#13133202	C₂³	1	8	yes	complemented
199	#13133202	C₂³	1	8	yes	complemented
200	#13133202	C₂³	1	8	yes	complemented
201	#13133202	C₂³	1	8	yes	complemented
202	#13133202	C₂³	1	8	yes	complemented
203	#13133202	C₂³	1	8	yes	complemented
204	#13133202	C₂³	1	8	yes	complemented
205	#13133202	C₂³	1	8	yes	complemented
206	#13133201	C₂³	1	4	yes	—
207	#13133201	C₂³	1	4	yes	complemented
208	#13133201	C₂³	1	8	yes	complemented
209	#13133201	C₂³	1	4	yes	complemented
210	#13133200	C₂³	1	8	yes	—
211	#13133200	C₂³	1	4	yes	complemented
212	#13133200	C₂³	1	8	yes	complemented
213	#13133200	C₂³	1	4	yes	complemented
214	#13133200	C₂³	1	4	yes	complemented
215	#13133199	C₂³	1	8	yes	complemented
216	#13133199	C₂³	1	8	yes	complemented
217	#13133198	C₂³	1	4	yes	complemented
218	#13133197	C₂³	1	8	yes	complemented
219	#13133196	C₂³	1	4	yes	complemented
220	#13133195	C₂³	1	8	yes	complemented
221	#13133195	C₂³	1	8	yes	complemented
222	#13133195	C₂³	1	8	yes	complemented
223	#13133195	C₂³	1	8	yes	complemented
224	#13133195	C₂³	1	8	yes	complemented
225	#13133194	C₂³	1	8	yes	complemented
226	#13133194	C₂³	1	8	yes	complemented
227	#13133193	C₂³	1	8	yes	complemented
228	#13133192	C₂³	1	8	yes	—
229	#13133192	C₂³	1	8	yes	—
230	#13133192	C₂³	1	8	yes	—
231	#13133192	C₂³	1	8	yes	complemented
232	#13133192	C₂³	1	8	yes	complemented
233	#13133192	C₂³	1	8	yes	complemented
234	#13133192	C₂³	1	8	yes	complemented
235	#13133192	C₂³	1	8	yes	complemented
236	#13133192	C₂³	1	8	yes	complemented
237	#13133192	C₂³	1	8	yes	complemented
238	#13133192	C₂³	1	8	yes	complemented
239	#13133192	C₂³	1	8	yes	complemented
240	#13133192	C₂³	1	8	yes	complemented
241	#13133192	C₂³	1	8	yes	complemented
242	#13133192	C₂³	1	8	yes	complemented
243	#13133192	C₂³	1	8	yes	complemented
244	#13133191	C₂³	1	4	yes	—
245	#13133191	C₂³	1	8	yes	—
246	#13133191	C₂³	1	8	yes	complemented
247	#13133191	C₂³	1	8	yes	complemented
248	#13133191	C₂³	1	8	yes	complemented
249	#13133190	C₂³	1	8	yes	—
250	#13133190	C₂³	1	8	yes	—
251	#13133190	C₂³	1	8	yes	complemented
252	#13133190	C₂³	1	8	yes	complemented
253	#13133190	C₂³	1	8	yes	complemented
254	#13133190	C₂³	1	8	yes	complemented
255	#13133190	C₂³	1	8	yes	complemented
256	#13133190	C₂³	1	8	yes	complemented
257	#13133190	C₂³	1	8	yes	complemented
258	#13133190	C₂³	1	8	yes	complemented
259	#13133190	C₂³	1	8	yes	complemented
260	#13133189	C₂³	1	8	yes	—
261	#13133189	C₂³	1	8	yes	complemented
262	#13133187	C₂³	1	8	yes	—
263	#13133187	C₂³	1	8	yes	—
264	#13133187	C₂³	1	8	yes	—
265	#13133187	C₂³	1	4	yes	—
266	#13133187	C₂³	1	8	yes	—
267	#13133187	C₂³	1	4	yes	—
268	#13133187	C₂³	1	4	yes	—
269	#13133187	C₂³	1	8	yes	—
270	#13133187	C₂³	1	4	yes	complemented
271	#13133187	C₂³	1	4	yes	complemented
272	#13133187	C₂³	1	8	yes	complemented
273	#13133187	C₂³	1	8	yes	complemented
274	#13133187	C₂³	1	8	yes	complemented
275	#13133187	C₂³	1	8	yes	complemented
276	#13133187	C₂³	1	8	yes	complemented
277	#13133187	C₂³	1	8	yes	complemented
278	#13133187	C₂³	1	8	yes	complemented
279	#13133187	C₂³	1	4	yes	complemented
280	#13133187	C₂³	1	4	yes	complemented
281	#13133187	C₂³	1	4	yes	complemented
282	#13133187	C₂³	1	4	yes	complemented
283	#13133187	C₂³	1	8	yes	complemented
284	#13133186	C₂³	1	4	yes	complemented
285	#13133185	C₂³	1	8	yes	—
286	#13133185	C₂³	1	4	yes	—
287	#13133185	C₂³	1	4	yes	—
288	#13133185	C₂³	1	4	yes	complemented
289	#13133185	C₂³	1	8	yes	complemented
290	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
291	C₄×D₂₁₂	C₂³	1	8	yes	complemented
292	C₄×D₂₁₂	C₂³	1	8	yes	complemented
293	C₄×D₂₁₂	C₂³	1	8	yes	complemented
294	C₄×D₂₁₂	C₂³	1	4	yes	complemented
295	#13133179	C₂³	1	8	yes	complemented
296	#13133179	C₂³	1	8	yes	complemented
297	#13133179	C₂³	1	8	yes	complemented
298	#13133179	C₂³	1	8	yes	complemented
299	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
300	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
301	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
302	#13133177	C₂³	1	8	yes	—
303	#13133177	C₂³	1	8	yes	complemented
304	#13133177	C₂³	1	8	yes	complemented
305	#13133177	C₂³	1	8	yes	complemented
306	#13133175	C₂³	1	8	yes	complemented
307	#13133174	C₂³	1	8	yes	complemented
308	#13133174	C₂³	1	8	yes	complemented
309	#13133173	C₂³	1	4	yes	complemented
310	#13133173	C₂³	1	4	yes	complemented
311	C₂×#11719919	C₂³	1	4	yes	complemented
312	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
313	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
314	C₂×#11719921	C₂³	1	4	yes	—
315	C₂×#11719921	C₂³	1	4	yes	—
316	C₂×#11719921	C₂³	1	4	yes	complemented
317	C₂×#11719921	C₂³	1	8	yes	complemented
318	C₂×#11719921	C₂³	1	4	yes	complemented
319	C₂×#11719921	C₂³	1	4	yes	complemented
320	C₂×#11719921	C₂³	1	4	yes	complemented
321	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
322	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
323	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
324	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
325	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
326	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
327	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
328	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
329	#126×C₅₃	C₂³	1	8	yes	complemented
330	#126×C₅₃	C₂³	1	8	yes	complemented
331	#125×C₅₃	C₂³	1	4	yes	complemented
332	#125×C₅₃	C₂³	1	8	yes	complemented
333	#124×C₅₃	C₂³	1	4	yes	complemented
334	#123×C₅₃	C₂³	1	4	yes	—
335	#123×C₅₃	C₂³	1	8	yes	—
336	#123×C₅₃	C₂³	1	8	yes	complemented
337	#123×C₅₃	C₂³	1	4	yes	complemented
338	#123×C₅₃	C₂³	1	4	yes	complemented
339	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
340	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
341	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
342	#121×C₅₃	C₂³	1	4	yes	—
343	#120×C₅₃	C₂³	1	4	yes	—
344	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
345	C₄×D₄×C₅₃	C₂³	1	8	yes	—
346	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
347	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
348	#117×C₅₃	C₂³	1	8	yes	complemented
349	#117×C₅₃	C₂³	1	4	yes	complemented
350	#117×C₅₃	C₂³	1	8	yes	complemented
351	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
352	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
353	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
356	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
357	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
358	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
359	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
360	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂³×D₅₃	—	2	8	no	—
362	C₂³×D₅₃	—	4	4	no	—
363	C₂³×D₅₃	—	8	4	no	—
364	C₂³×D₅₃	—	8	4	no	—
365	C₂³×D₅₃	C₂⁴	1	4	yes	—
366	C₂³×D₅₃	C₂⁴	1	4	yes	—
367	C₂³×D₅₃	C₂⁴	1	2	yes	—
368	C₂³×D₅₃	C₂⁴	1	2	yes	—
369	C₂³×D₅₃	C₂⁴	1	2	yes	—
370	C₂³×D₅₃	C₂⁴	1	2	yes	—
371	C₂³×D₅₃	C₂⁴	1	4	yes	—
372	C₂³×D₅₃	C₂⁴	1	8	yes	—
373	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
374	C₂×D₄×C₅₃	—	2	8	no	—
375	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
376	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
377	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
378	C₂²×C₄×C₅₃	—	2	4	no	—
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
386	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
387	C₂×C₂²⋊D₅₃	—	2	8	no	—
388	C₂×C₂²⋊D₅₃	—	2	8	no	—
389	C₂×C₂²⋊D₅₃	—	4	4	no	—
390	C₂×C₂²⋊D₅₃	—	4	8	no	—
391	C₂×C₂²⋊D₅₃	—	8	4	no	—
392	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
393	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
394	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
395	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
396	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
397	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
398	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
399	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
400	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
401	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
402	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
403	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
404	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
405	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
406	#11719949	—	8	8	no	—
407	#11719947	—	4	8	no	—
408	#11719947	—	4	8	no	—
409	D₄×D₅₃	—	4	16	no	—
410	D₄×D₅₃	—	4	16	no	—
411	D₄×D₅₃	—	4	8	no	—
412	D₄×D₅₃	—	4	8	no	—
413	D₄×D₅₃	—	8	8	no	—
414	#11719945	—	4	16	no	—
415	#11719945	—	4	8	no	—
416	#11719945	—	8	8	no	—
417	C₂×D₂₁₂	—	4	4	no	—
418	C₂×D₂₁₂	—	4	4	no	—
419	C₂×D₂₁₂	—	4	4	no	—
420	C₂×D₂₁₂	—	4	8	no	—
421	C₂×D₂₁₂	—	4	8	no	—
422	C₂×D₂₁₂	—	4	2	no	—
423	C₂×D₂₁₂	—	8	4	no	—
424	C₂×D₂₁₂	—	8	8	no	—
425	C₂×D₂₁₂	—	8	4	no	—
426	C₂×D₂₁₂	—	8	4	no	—
427	C₂×D₂₁₂	C₂⁴	1	8	yes	—
428	C₂×D₂₁₂	C₂⁴	1	8	yes	—
429	C₂×D₂₁₂	C₂⁴	1	8	yes	—
430	C₂×D₂₁₂	C₂⁴	1	8	yes	—
431	C₂×D₂₁₂	C₂⁴	1	8	yes	—
432	C₂×D₂₁₂	C₂⁴	1	4	yes	—
433	C₂×D₂₁₂	C₂⁴	1	8	yes	—
434	C₂×D₂₁₂	C₂⁴	1	8	yes	—
435	C₂×D₂₁₂	C₂⁴	1	2	yes	—
436	C₂×D₂₁₂	C₂⁴	1	2	yes	—
437	C₂×D₂₁₂	C₂⁴	1	4	yes	—
438	C₂×D₂₁₂	C₂⁴	1	4	yes	—
439	C₂×D₂₁₂	C₂⁴	1	4	yes	—
440	C₂×D₂₁₂	C₂⁴	1	4	yes	—
441	C₂×D₂₁₂	C₂⁴	1	8	yes	—
442	C₂×D₂₁₂	C₂⁴	1	2	yes	—
443	C₂×D₂₁₂	C₂⁴	1	2	yes	—
444	C₂×C₄×D₅₃	—	4	4	no	—
445	C₂×C₄×D₅₃	—	4	4	no	—
446	C₂×C₄×D₅₃	—	8	4	no	—
447	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
448	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
449	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
450	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
451	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
452	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
453	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
454	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
455	C₂×Dic₁₀₆	—	4	2	no	—
456	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
457	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
458	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
459	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
460	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
461	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
462	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
463	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
464	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
465	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
466	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
467	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
468	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
469	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
470	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
471	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
472	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
473	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
474	C₄²×C₅₃	C₂⁴	1	4	yes	—
475	C₄²×C₅₃	C₂⁴	1	4	yes	—
476	C₄²×C₅₃	C₂⁴	1	8	yes	—
477	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
478	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
479	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
480	#11719921	C₂⁴	1	8	yes	—
481	#11719921	C₂⁴	1	8	yes	—
482	#11719921	C₂⁴	1	8	yes	—
483	#11719921	C₂⁴	1	8	yes	—
484	#11719921	C₂⁴	1	8	yes	—
485	#11719921	C₂⁴	1	8	yes	—
486	#11719921	C₂⁴	1	8	yes	—
487	#11719921	C₂⁴	1	8	yes	—
488	#11719921	C₂⁴	1	8	yes	—
489	#11719921	C₂⁴	1	8	yes	—
490	#11719921	C₂⁴	1	8	yes	—
491	#11719921	C₂⁴	1	8	yes	—
492	#11719921	C₂⁴	1	8	yes	—
493	#11719921	C₂⁴	1	8	yes	—
494	#11719921	C₂⁴	1	8	yes	—
495	#11719921	C₂⁴	1	8	yes	—
496	#11719921	C₂⁴	1	8	yes	—
497	#11719921	C₂⁴	1	8	yes	—
498	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
499	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
500	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
501	#11719919	C₂⁴	1	8	yes	—
502	#11719919	C₂⁴	1	8	yes	—
503	#11719919	C₂⁴	1	8	yes	—
504	#11719919	C₂⁴	1	8	yes	—
505	#11719919	C₂⁴	1	8	yes	—
506	#11719919	C₂⁴	1	8	yes	—
507	C₄×Dic₅₃	C₂⁴	1	8	yes	—
508	C₄×Dic₅₃	C₂⁴	1	8	yes	—
509	C₂³×C₅₃	—	2	4	no	—
510	C₂³×C₅₃	—	4	2	no	—
511	C₂³×C₅₃	—	4	4	no	—
512	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
513	C₂³×C₅₃	C₂⁵	1	4	yes	—
514	C₂³×C₅₃	C₂⁵	1	2	yes	—
515	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
516	C₂²×D₅₃	—	2	4	no	—
517	C₂²×D₅₃	—	2	4	no	—
518	C₂²×D₅₃	—	2	4	no	—
519	C₂²×D₅₃	—	2	8	no	—
520	C₂²×D₅₃	—	2	8	no	—
521	C₂²×D₅₃	—	2	4	no	—
522	C₂²×D₅₃	—	4	4	no	—
523	C₂²×D₅₃	—	4	4	no	—
524	C₂²×D₅₃	—	4	4	no	—
525	C₂²×D₅₃	—	4	4	no	—
526	C₂²×D₅₃	—	4	4	no	—
527	C₂²×D₅₃	—	4	4	no	—
528	C₂²×D₅₃	—	4	4	no	—
529	C₂²×D₅₃	—	4	8	no	—
530	C₂²×D₅₃	—	4	8	no	—
531	C₂²×D₅₃	—	4	8	no	—
532	C₂²×D₅₃	—	4	4	no	—
533	C₂²×D₅₃	—	4	8	no	—
534	C₂²×D₅₃	—	4	4	no	—
535	C₂²×D₅₃	—	8	16	no	—
536	C₂²×D₅₃	—	8	16	no	—
537	C₂²×D₅₃	C₂⁵	1	4	yes	—
538	C₂²×D₅₃	C₂⁵	1	4	yes	—
539	C₂²×D₅₃	C₂⁵	1	4	yes	—
540	C₂²×D₅₃	C₂⁵	1	4	yes	—
541	Q₈×C₅₃	—	4	4	no	—
542	D₄×C₅₃	—	2	8	no	—
543	D₄×C₅₃	—	2	8	no	—
544	D₄×C₅₃	—	4	4	no	—
545	C₂×C₄×C₅₃	—	2	2	no	—
546	C₂×C₄×C₅₃	—	2	2	no	—
547	C₂×C₄×C₅₃	—	2	4	no	—
548	C₂×C₄×C₅₃	—	2	8	no	—
549	C₂×C₄×C₅₃	—	4	4	no	—
550	C₂×C₄×C₅₃	—	4	2	no	—
551	C₂×C₄×C₅₃	—	4	2	no	—
552	C₂×C₄×C₅₃	—	4	8	no	—
553	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
554	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
555	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
556	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
557	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
558	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
559	C₂²⋊D₅₃	—	2	8	no	—
560	C₂²⋊D₅₃	—	2	8	no	—
561	C₂²⋊D₅₃	—	2	8	no	—
562	C₂²⋊D₅₃	—	2	8	no	—
563	C₂²⋊D₅₃	—	4	8	no	—
564	C₂²⋊D₅₃	—	4	8	no	—
565	C₂²⋊D₅₃	—	4	8	no	—
566	C₂²⋊D₅₃	—	4	4	no	—
567	C₂²⋊D₅₃	—	4	4	no	—
568	C₂²⋊D₅₃	—	4	8	no	—
569	C₂×Dic₅₃	—	2	4	no	—
570	C₂×Dic₅₃	—	2	4	no	—
571	C₂×Dic₅₃	—	4	4	no	—
572	C₂×Dic₅₃	—	4	4	no	—
573	C₂×Dic₅₃	C₂⁵	1	4	yes	—
574	C₂×Dic₅₃	C₂⁵	1	8	yes	—
575	C₂×Dic₅₃	C₂⁵	1	4	yes	—
576	D₂₁₂	—	4	2	no	—
577	D₂₁₂	—	4	4	no	—
578	D₂₁₂	—	4	2	no	—
579	D₂₁₂	—	4	2	no	—
580	D₂₁₂	—	4	4	no	—
581	D₂₁₂	—	4	2	no	—
582	D₂₁₂	—	4	4	no	—
583	D₂₁₂	—	4	8	no	—
584	D₂₁₂	—	4	8	no	—
585	D₂₁₂	—	4	4	no	—
586	D₂₁₂	—	4	8	no	—
587	D₂₁₂	—	4	8	no	—
588	D₂₁₂	—	4	8	no	—
589	D₂₁₂	—	4	8	no	—
590	D₂₁₂	—	4	8	no	—
591	D₂₁₂	—	4	8	no	—
592	D₂₁₂	—	4	4	no	—
593	C₄×D₅₃	—	4	8	no	—
594	C₄×D₅₃	—	4	8	no	—
595	C₄×D₅₃	—	4	8	no	—
596	C₄×D₅₃	—	4	8	no	—
597	C₄×D₅₃	—	4	4	no	—
598	C₄×D₅₃	—	4	4	no	—
599	C₄×D₅₃	—	4	8	no	—
600	C₄×D₅₃	—	4	8	no	—
601	Dic₁₀₆	—	4	4	no	—
602	Dic₁₀₆	—	4	4	no	—
603	Dic₁₀₆	—	4	4	no	—
604	#62862	—	53	1	no	maximal, Sylow
605	C₂²×C₅₃	—	2	4	no	—
606	C₂²×C₅₃	—	2	2	no	—
607	C₂²×C₅₃	—	2	4	no	—
608	C₂²×C₅₃	—	2	8	no	—
609	C₂²×C₅₃	—	4	4	no	—
610	C₂²×C₅₃	—	8	4	no	—
611	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
612	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
613	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
614	C₂×D₅₃	—	2	4	no	—
615	C₂×D₅₃	—	2	4	no	—
616	C₂×D₅₃	—	2	4	no	—
617	C₂×D₅₃	—	2	4	no	—
618	C₂×D₅₃	—	2	4	no	—
619	C₂×D₅₃	—	2	4	no	—
620	C₂×D₅₃	—	2	8	no	—
621	C₂×D₅₃	—	2	8	no	—
622	C₂×D₅₃	—	2	4	no	—
623	C₂×D₅₃	—	2	4	no	—
624	C₂×D₅₃	—	4	8	no	—
625	C₂×D₅₃	—	4	8	no	—
626	C₂×D₅₃	—	8	4	no	—
627	C₂×D₅₃	—	8	8	no	—
628	C₂×D₅₃	—	8	8	no	—
629	C₂×D₅₃	—	8	4	no	—
630	C₂×D₅₃	—	8	16	no	—
631	C₂×D₅₃	—	16	4	no	—
632	C₄×C₅₃	—	2	2	no	—
633	C₄×C₅₃	—	2	4	no	—
634	C₄×C₅₃	—	2	2	no	—
635	C₄×C₅₃	—	2	4	no	—
636	C₄×C₅₃	—	2	8	no	—
637	C₄×C₅₃	—	2	4	no	—
638	Dic₅₃	—	2	4	no	—
639	Dic₅₃	—	2	4	no	—
640	Dic₅₃	—	2	8	no	—
641	#3545	—	53	4	no	—
642	#3543	—	53	4	no	—
643	#3542	—	53	8	no	—
644	#3542	—	53	8	no	—
645	#3534	—	53	8	no	—
646	#3533	—	53	8	no	—
647	#3532	—	53	8	no	—
648	#3491	—	53	1	no	—
649	#3491	D₅₃	1	1	yes	characteristic, complemented
650	#3490	—	53	2	no	—
651	#3490	—	53	2	no	—
652	#3485	—	53	2	no	—
653	#3484	—	53	2	no	—
654	#3484	—	53	2	no	—
655	C₂×#535	—	53	1	no	—
656	C₂×#534	—	53	2	no	—
657	C₂×C₅₃	—	2	4	no	—
658	C₂×C₅₃	—	2	2	no	—
659	C₂×C₅₃	—	4	4	no	—
660	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
662	D₅₃	—	4	4	no	—
663	D₅₃	—	4	4	no	—
664	D₅₃	—	4	4	no	—
665	D₅₃	—	4	4	no	—
666	C₂×H(5,𝔽₂)	—	53	2	no	—
667	C₂²×#41	—	53	1	no	—
668	C₂³×D₄	—	53	2	no	—
669	C₂³×D₄	—	53	1	no	—
670	#563	—	53	4	no	—
671	#562	—	53	8	no	—
672	#562	—	53	4	no	—
673	#562	—	53	4	no	—
674	#562	—	53	8	no	—
675	H(3,𝔽₄)	—	53	4	no	—
676	#560	—	53	8	no	—
677	#560	—	53	8	no	—
678	#560	—	53	8	no	—
679	#560	—	53	8	no	—
680	#559	—	53	4	no	—
681	#555	—	53	8	no	—
682	#553	—	53	8	no	—
683	#553	—	53	8	no	—
684	#552	—	53	8	no	—
685	#552	C₂×D₅₃	1	8	yes	complemented
686	#551	—	53	8	no	—
687	#551	—	53	8	no	—
688	#551	—	53	8	no	—
689	#551	—	53	8	no	—
690	#551	—	53	8	no	—
691	#551	—	53	8	no	—
692	#551	C₂×D₅₃	1	8	yes	complemented
693	#550	—	53	4	no	—
694	#550	—	53	4	no	—
695	#547	—	53	8	no	—
696	#547	—	53	8	no	—
697	#546	—	53	8	no	—
698	#546	—	53	8	no	—
699	#546	—	53	8	no	—
700	#546	—	53	8	no	—
701	#546	—	53	8	no	—
702	#546	—	53	8	no	—
703	#546	—	53	8	no	—
704	#546	—	53	8	no	—
705	#546	—	53	8	no	—
706	#546	—	53	8	no	—
707	#546	—	53	8	no	—
708	#546	—	53	8	no	—
709	D₄²	—	53	8	no	—
710	D₄²	—	53	8	no	—
711	D₄²	—	53	8	no	—
712	D₄²	—	53	8	no	—
713	D₄²	—	53	4	no	—
714	#543	—	53	1	no	—
715	#543	C₂×D₅₃	1	1	yes	characteristic, complemented
716	#542	—	53	8	no	—
717	#542	—	53	8	no	—
718	#540	—	53	8	no	—
719	#540	—	53	8	no	—
720	#540	—	53	8	no	—
721	#540	—	53	8	no	—
722	#539	—	53	8	no	—
723	#539	—	53	4	no	—
724	#539	C₂×D₅₃	1	4	yes	complemented
725	#538	—	53	8	no	—
726	#538	—	53	8	no	—
727	#538	—	53	8	no	—
728	#538	—	53	8	no	—
729	#538	—	53	8	no	—
730	#538	—	53	8	no	—
731	#538	—	53	8	no	—
732	#537	—	53	8	no	—
733	#536	—	53	4	no	—
734	#535	—	53	8	no	—
735	#535	—	53	4	no	—
736	#535	—	53	8	no	—
737	#535	—	53	8	no	—
738	#535	—	53	4	no	—
739	#535	—	53	8	no	—
740	#534	—	53	2	no	—
741	#534	—	53	8	no	—
742	#534	—	53	8	no	—
743	#534	—	53	4	no	—
744	#534	—	53	8	no	—
745	#534	—	53	8	no	—
746	#534	—	53	4	no	—
747	#534	—	53	8	no	—
748	#534	—	53	1	no	—
749	#534	—	53	2	no	—
750	#534	—	53	4	no	—
751	#534	C₂×D₅₃	1	1	yes	characteristic
752	C₂×#127	—	53	2	no	—
753	#529	—	53	4	no	—
754	#529	C₂×D₅₃	1	4	yes	complemented
755	C₂×#124	—	53	2	no	—
756	#525	—	53	4	no	—
757	#525	—	53	4	no	—
758	#525	—	53	8	no	—
759	#525	—	53	8	no	—
760	#525	—	53	4	no	—
761	C₂×#123	—	53	2	no	—
762	C₂×#123	—	53	4	no	—
763	C₂×#123	—	53	4	no	—
764	C₂×#123	C₂×D₅₃	1	2	yes	complemented
765	C₂×#121	—	53	4	no	—
766	C₂×#121	—	53	4	no	—
767	C₂×#121	—	53	4	no	—
768	C₂×#120	—	53	2	no	—
769	C₂×#120	—	53	4	no	—
770	C₂×#120	—	53	2	no	—
771	C₂×#120	—	53	2	no	—
772	C₂×#120	—	53	2	no	—
773	C₂×#120	—	53	4	no	—
774	C₂×#120	—	53	4	no	—
775	#518	—	53	2	no	—
776	#518	—	53	2	no	—
777	#518	C₂×D₅₃	1	2	yes	complemented
778	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
779	C₂²×C₂²⋊C₄	—	53	2	no	—
780	C₅₃	#62862	1	1	yes	characteristic, complemented, Sylow
781	C₂⁵	—	53	2	no	—
782	C₂⁵	—	53	2	no	—
783	H(5,𝔽₂)	—	212	8	no	—
784	C₂×#41	—	53	8	no	—
785	C₂×#41	—	53	4	no	—
786	C₂×#41	—	53	4	no	—
787	C₂×#41	—	53	8	no	—
788	C₂×#41	—	53	4	no	—
789	C₂×#41	—	53	8	no	—
790	C₂×#41	—	212	4	no	—
791	C₂²×Q₈	—	53	1	no	—
792	C₂²×D₄	—	53	2	no	—
793	C₂²×D₄	—	53	2	no	—
794	C₂²×D₄	—	53	4	no	—
795	C₂²×D₄	—	53	4	no	—
796	C₂²×D₄	—	53	2	no	—
797	C₂²×D₄	—	53	8	no	—
798	C₂²×D₄	—	53	4	no	—
799	C₂²×D₄	—	53	4	no	—
800	C₂²×D₄	—	53	8	no	—
801	C₂²×D₄	—	53	8	no	—
802	C₂²×D₄	—	53	4	no	—
803	C₂²×D₄	—	53	4	no	—
804	C₂²×D₄	—	53	4	no	—
805	C₂²×D₄	—	53	8	no	—
806	C₂²×D₄	—	53	4	no	—
807	C₂²×D₄	—	53	2	no	—
808	C₂²×D₄	—	53	4	no	—
809	C₂²×D₄	—	53	2	no	—
810	C₂²×D₄	—	53	2	no	—
811	C₂²×D₄	—	53	1	no	—
812	C₂²×D₄	—	212	4	no	—
813	C₂²×D₄	—	212	8	no	—
814	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
815	C₂³×C₄	—	53	4	no	—
816	C₂³×C₄	—	53	2	no	—
817	C₂³×C₄	—	53	2	no	—
818	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
819	C₄⋊Q₈	—	53	8	no	—
820	#127	—	53	8	no	—
821	#127	—	53	8	no	—
822	#127	—	53	4	no	—
823	#127	—	53	4	no	—
824	#127	—	53	8	no	—
825	#126	—	53	8	no	—
826	#126	—	53	8	no	—
827	#126	—	53	8	no	—
828	#126	—	53	8	no	—
829	#126	—	53	8	no	—
830	#126	—	53	8	no	—
831	#126	C₂²×D₅₃	1	8	yes	complemented
832	#126	C₂²×D₅₃	1	8	yes	complemented
833	#125	—	53	8	no	—
834	#125	—	53	4	no	—
835	#125	C₂²×D₅₃	1	4	yes	complemented
836	#125	C₂²×D₅₃	1	8	yes	complemented
837	#124	—	53	8	no	—
838	#124	—	53	8	no	—
839	#124	—	53	8	no	—
840	#124	—	53	8	no	—
841	#124	—	53	8	no	—
842	#124	—	53	8	no	—
843	#124	—	53	4	no	—
844	#124	—	53	4	no	—
845	#124	—	53	4	no	—
846	#124	—	53	8	no	—
847	#124	—	53	8	no	—
848	#124	C₂²×D₅₃	1	4	yes	complemented
849	#123	—	53	4	no	—
850	#123	—	53	4	no	—
851	#123	—	53	4	no	—
852	#123	—	53	8	no	—
853	#123	—	53	4	no	—
854	#123	—	53	8	no	—
855	#123	—	53	8	no	—
856	#123	—	53	8	no	—
857	#123	—	53	8	no	—
858	#123	—	53	8	no	—
859	#123	—	53	8	no	—
860	#123	—	53	8	no	—
861	#123	—	53	8	no	—
862	#123	—	53	8	no	—
863	#123	—	53	8	no	—
864	#123	—	53	8	no	—
865	#123	—	53	8	no	—
866	#123	—	53	8	no	—
867	#123	—	53	8	no	—
868	#123	—	53	8	no	—
869	#123	—	53	4	no	—
870	#123	—	53	8	no	—
871	#123	—	53	4	no	—
872	#123	—	53	4	no	—
873	#123	—	53	8	no	—
874	#123	—	53	8	no	—
875	#123	C₂²×D₅₃	1	8	yes	—
876	#123	C₂²×D₅₃	1	4	yes	—
877	#123	C₂²×D₅₃	1	4	yes	complemented
878	#123	C₂²×D₅₃	1	4	yes	complemented
879	#123	C₂²×D₅₃	1	8	yes	complemented
880	C₂²⋊Q₈	—	53	8	no	—
881	C₂²⋊Q₈	—	53	4	no	—
882	C₂²⋊Q₈	—	53	8	no	—
883	C₂²⋊Q₈	—	53	8	no	—
884	C₂²⋊Q₈	—	53	8	no	—
885	C₂²⋊Q₈	—	53	8	no	—
886	C₂²⋊Q₈	—	53	8	no	—
887	C₂²⋊Q₈	—	53	8	no	—
888	C₂²⋊Q₈	—	53	8	no	—
889	C₂²⋊Q₈	—	53	8	no	—
890	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
891	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
892	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
893	#121	—	53	8	no	—
894	#121	—	53	8	no	—
895	#121	—	53	8	no	—
896	#121	—	53	4	no	—
897	#121	—	53	8	no	—
898	#121	—	53	8	no	—
899	#121	—	53	8	no	—
900	#121	—	53	8	no	—
901	#121	—	53	8	no	—
902	#121	—	53	8	no	—
903	#121	—	53	8	no	—
904	#121	—	53	8	no	—
905	#121	—	53	8	no	—
906	#121	—	53	8	no	—
907	#121	—	53	8	no	—
908	#121	—	53	8	no	—
909	#121	—	53	8	no	—
910	#121	—	53	8	no	—
911	#121	—	53	8	no	—
912	#121	—	53	8	no	—
913	#121	—	53	8	no	—
914	#121	—	53	8	no	—
915	#121	—	53	8	no	—
916	#121	—	53	8	no	—
917	#121	—	53	8	no	—
918	#121	—	53	8	no	—
919	#121	—	53	8	no	—
920	#121	—	53	8	no	—
921	#121	—	53	8	no	—
922	#121	—	53	8	no	—
923	#121	—	53	8	no	—
924	#121	—	53	8	no	—
925	#121	—	53	8	no	—
926	#121	—	53	8	no	—
927	#121	C₂²×D₅₃	1	4	yes	—
928	#120	—	53	4	no	—
929	#120	—	53	4	no	—
930	#120	—	53	4	no	—
931	#120	—	53	8	no	—
932	#120	—	53	8	no	—
933	#120	—	53	4	no	—
934	#120	—	53	4	no	—
935	#120	—	53	4	no	—
936	#120	—	53	4	no	—
937	#120	—	53	4	no	—
938	#120	—	53	4	no	—
939	#120	—	53	4	no	—
940	#120	—	53	8	no	—
941	#120	—	53	8	no	—
942	#120	—	53	8	no	—
943	#120	—	53	8	no	—
944	#120	—	53	8	no	—
945	#120	—	53	4	no	—
946	#120	—	53	4	no	—
947	#120	—	53	8	no	—
948	#120	—	53	8	no	—
949	#120	—	53	8	no	—
950	#120	—	53	8	no	—
951	#120	—	53	8	no	—
952	#120	—	53	4	no	—
953	#120	—	53	8	no	—
954	#120	—	53	8	no	—
955	#120	—	53	8	no	—
956	#120	C₂²×D₅₃	1	4	yes	—
957	C₄×Q₈	—	53	4	no	—
958	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
959	C₄×D₄	—	53	8	no	—
960	C₄×D₄	—	53	8	no	—
961	C₄×D₄	—	53	8	no	—
962	C₄×D₄	—	53	8	no	—
963	C₄×D₄	—	53	8	no	—
964	C₄×D₄	—	53	8	no	—
965	C₄×D₄	—	53	8	no	—
966	C₄×D₄	—	53	8	no	—
967	C₄×D₄	—	53	8	no	—
968	C₄×D₄	—	53	8	no	—
969	C₄×D₄	—	53	8	no	—
970	C₄×D₄	—	53	8	no	—
971	C₄×D₄	—	53	8	no	—
972	C₄×D₄	—	53	8	no	—
973	C₄×D₄	—	53	4	no	—
974	C₄×D₄	C₂²×D₅₃	1	8	yes	—
975	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
976	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
977	#117	—	53	8	no	—
978	#117	—	53	4	no	—
979	#117	—	53	4	no	—
980	#117	—	53	8	no	—
981	#117	—	53	8	no	—
982	#117	C₂²×D₅₃	1	8	yes	complemented
983	#117	C₂²×D₅₃	1	4	yes	complemented
984	#117	C₂²×D₅₃	1	8	yes	complemented
985	C₂×C₄⋊C₄	—	53	4	no	—
986	C₂×C₄⋊C₄	—	53	8	no	—
987	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
988	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
989	C₂×C₂²⋊C₄	—	53	2	no	—
990	C₂×C₂²⋊C₄	—	53	4	no	—
991	C₂×C₂²⋊C₄	—	53	4	no	—
992	C₂×C₂²⋊C₄	—	53	4	no	—
993	C₂×C₂²⋊C₄	—	53	4	no	—
994	C₂×C₂²⋊C₄	—	53	4	no	—
995	C₂×C₂²⋊C₄	—	53	4	no	—
996	C₂×C₂²⋊C₄	—	53	8	no	—
997	C₂×C₂²⋊C₄	—	53	8	no	—
998	C₂×C₂²⋊C₄	—	53	8	no	—
999	C₂×C₂²⋊C₄	—	53	4	no	—
1000	C₂×C₂²⋊C₄	—	53	4	no	—
1001	C₂×C₂²⋊C₄	—	53	8	no	—
1002	C₂×C₂²⋊C₄	—	53	8	no	—
1003	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1004	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1005	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1006	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1007	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1008	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
1009	C₂⁴	—	53	4	no	—
1010	C₂⁴	—	53	4	no	—
1011	C₂⁴	—	53	2	no	—
1012	C₂⁴	—	53	2	no	—
1013	C₂⁴	—	53	2	no	—
1014	C₂⁴	—	53	2	no	—
1015	C₂⁴	—	53	8	no	—
1016	C₂⁴	—	53	4	no	—
1017	C₂⁴	—	106	8	no	—
1018	C₂⁴	—	424	4	no	—
1019	C₂⁴	—	424	4	no	—
1020	C₂⁴	—	212	4	no	—
1021	C₂⁴	C₂³×D₅₃	1	2	yes	—
1022	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1023	#41	—	424	8	no	—
1024	#41	—	424	8	no	—
1025	#41	—	212	16	no	—
1026	#41	—	212	8	no	—
1027	#41	—	212	8	no	—
1028	#41	—	212	8	no	—
1029	C₂×Q₈	—	53	4	no	—
1030	C₂×Q₈	—	53	4	no	—
1031	C₂×Q₈	—	53	4	no	—
1032	C₂×Q₈	—	212	2	no	—
1033	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1034	C₂×D₄	—	2	8	no	—
1035	C₂×D₄	—	53	4	no	—
1036	C₂×D₄	—	53	4	no	—
1037	C₂×D₄	—	53	4	no	—
1038	C₂×D₄	—	53	4	no	—
1039	C₂×D₄	—	53	8	no	—
1040	C₂×D₄	—	53	8	no	—
1041	C₂×D₄	—	53	8	no	—
1042	C₂×D₄	—	53	4	no	—
1043	C₂×D₄	—	53	4	no	—
1044	C₂×D₄	—	53	8	no	—
1045	C₂×D₄	—	53	8	no	—
1046	C₂×D₄	—	53	8	no	—
1047	C₂×D₄	—	53	8	no	—
1048	C₂×D₄	—	53	4	no	—
1049	C₂×D₄	—	53	8	no	—
1050	C₂×D₄	—	53	8	no	—
1051	C₂×D₄	—	53	8	no	—
1052	C₂×D₄	—	53	8	no	—
1053	C₂×D₄	—	53	2	no	—
1054	C₂×D₄	—	53	2	no	—
1055	C₂×D₄	—	53	4	no	—
1056	C₂×D₄	—	53	4	no	—
1057	C₂×D₄	—	53	4	no	—
1058	C₂×D₄	—	53	4	no	—
1059	C₂×D₄	—	53	8	no	—
1060	C₂×D₄	—	53	2	no	—
1061	C₂×D₄	—	53	2	no	—
1062	C₂×D₄	—	106	8	no	—
1063	C₂×D₄	—	106	8	no	—
1064	C₂×D₄	—	424	4	no	—
1065	C₂×D₄	—	424	4	no	—
1066	C₂×D₄	—	424	4	no	—
1067	C₂×D₄	—	424	8	no	—
1068	C₂×D₄	—	424	8	no	—
1069	C₂×D₄	—	424	4	no	—
1070	C₂×D₄	—	212	4	no	—
1071	C₂×D₄	—	212	4	no	—
1072	C₂×D₄	—	212	8	no	—
1073	C₂×D₄	—	212	8	no	—
1074	C₂×D₄	—	212	4	no	—
1075	C₂×D₄	—	212	2	no	—
1076	C₂×D₄	—	212	4	no	—
1077	C₂×D₄	—	212	16	no	—
1078	C₂×D₄	—	212	16	no	—
1079	C₂×D₄	—	212	8	no	—
1080	C₂×D₄	—	212	8	no	—
1081	C₂×D₄	—	212	8	no	—
1082	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1083	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1084	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1085	C₂²×C₄	—	2	4	no	—
1086	C₂²×C₄	—	53	2	no	—
1087	C₂²×C₄	—	53	2	no	—
1088	C₂²×C₄	—	53	4	no	—
1089	C₂²×C₄	—	53	4	no	—
1090	C₂²×C₄	—	53	8	no	—
1091	C₂²×C₄	—	53	8	no	—
1092	C₂²×C₄	—	53	8	no	—
1093	C₂²×C₄	—	53	8	no	—
1094	C₂²×C₄	—	53	4	no	—
1095	C₂²×C₄	—	53	8	no	—
1096	C₂²×C₄	—	53	4	no	—
1097	C₂²×C₄	—	53	8	no	—
1098	C₂²×C₄	—	424	4	no	—
1099	C₂²×C₄	—	212	4	no	—
1100	C₂²×C₄	—	212	4	no	—
1101	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1102	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1103	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1104	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1105	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1106	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1107	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1108	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1109	C₄⋊C₄	—	53	8	no	—
1110	C₄⋊C₄	—	53	8	no	—
1111	C₄⋊C₄	—	53	8	no	—
1112	C₄⋊C₄	—	53	8	no	—
1113	C₄⋊C₄	—	53	8	no	—
1114	C₄⋊C₄	—	53	8	no	—
1115	C₄⋊C₄	—	53	8	no	—
1116	C₄⋊C₄	—	53	4	no	—
1117	C₄⋊C₄	—	53	4	no	—
1118	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1119	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1120	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1121	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1122	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1123	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1124	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1125	C₂²⋊C₄	—	53	4	no	—
1126	C₂²⋊C₄	—	53	4	no	—
1127	C₂²⋊C₄	—	53	8	no	—
1128	C₂²⋊C₄	—	53	8	no	—
1129	C₂²⋊C₄	—	53	8	no	—
1130	C₂²⋊C₄	—	53	8	no	—
1131	C₂²⋊C₄	—	53	8	no	—
1132	C₂²⋊C₄	—	53	8	no	—
1133	C₂²⋊C₄	—	53	8	no	—
1134	C₂²⋊C₄	—	53	8	no	—
1135	C₂²⋊C₄	—	53	8	no	—
1136	C₂²⋊C₄	—	53	8	no	—
1137	C₂²⋊C₄	—	53	8	no	—
1138	C₂²⋊C₄	—	53	8	no	—
1139	C₂²⋊C₄	—	53	8	no	—
1140	C₂²⋊C₄	—	53	8	no	—
1141	C₂²⋊C₄	—	53	8	no	—
1142	C₂²⋊C₄	—	53	8	no	—
1143	C₂²⋊C₄	—	53	8	no	—
1144	C₂²⋊C₄	—	53	8	no	—
1145	C₂²⋊C₄	—	53	8	no	—
1146	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1147	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1148	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1149	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1150	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1151	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1152	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1153	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1154	C₄²	—	53	8	no	—
1155	C₄²	—	53	8	no	—
1156	C₄²	C₂³×D₅₃	1	4	yes	—
1157	C₄²	C₂³×D₅₃	1	4	yes	—
1158	C₄²	C₂³×D₅₃	1	8	yes	—
1159	C₂³	—	2	4	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	—	4	4	no	—
1162	C₂³	—	53	4	no	—
1163	C₂³	—	53	4	no	—
1164	C₂³	—	53	4	no	—
1165	C₂³	—	53	4	no	—
1166	C₂³	—	106	4	no	—
1167	C₂³	—	106	4	no	—
1168	C₂³	—	106	8	no	—
1169	C₂³	—	106	8	no	—
1170	C₂³	—	106	4	no	—
1171	C₂³	—	106	4	no	—
1172	C₂³	—	424	16	no	—
1173	C₂³	—	424	16	no	—
1174	C₂³	—	212	8	no	—
1175	C₂³	—	212	4	no	—
1176	C₂³	—	212	4	no	—
1177	C₂³	—	212	4	no	—
1178	C₂³	—	212	4	no	—
1179	C₂³	—	212	4	no	—
1180	C₂³	—	212	4	no	—
1181	C₂³	—	212	4	no	—
1182	C₂³	—	212	8	no	—
1183	C₂³	—	212	8	no	—
1184	C₂³	—	212	8	no	—
1185	C₂³	—	212	4	no	—
1186	C₂³	—	212	4	no	—
1187	C₂³	#13133263	1	4	yes	—
1188	C₂³	C₂⁴×D₅₃	1	4	yes	—
1189	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1190	C₂³	C₂⁴×D₅₃	1	2	yes	—
1191	Q₈	—	4	4	no	—
1192	Q₈	—	212	4	no	—
1193	Q₈	—	212	4	no	—
1194	Q₈	—	212	4	no	—
1195	D₄	—	2	8	no	—
1196	D₄	—	2	8	no	—
1197	D₄	—	4	4	no	—
1198	D₄	—	106	8	no	—
1199	D₄	—	106	8	no	—
1200	D₄	—	106	8	no	—
1201	D₄	—	106	8	no	—
1202	D₄	—	212	8	no	—
1203	D₄	—	212	4	no	—
1204	D₄	—	212	8	no	—
1205	D₄	—	212	8	no	—
1206	D₄	—	212	8	no	—
1207	D₄	—	212	8	no	—
1208	D₄	—	212	8	no	—
1209	D₄	—	212	8	no	—
1210	D₄	—	212	2	no	—
1211	D₄	—	212	4	no	—
1212	D₄	—	212	2	no	—
1213	D₄	—	212	2	no	—
1214	D₄	—	212	4	no	—
1215	D₄	—	212	2	no	—
1216	D₄	—	212	8	no	—
1217	D₄	—	212	4	no	—
1218	D₄	—	212	4	no	—
1219	D₄	—	212	8	no	—
1220	D₄	—	212	8	no	—
1221	D₄	—	212	8	no	—
1222	D₄	—	212	8	no	—
1223	D₄	—	212	4	no	—
1224	D₄	—	212	4	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	8	no	—
1228	C₂×C₄	—	2	4	no	—
1229	C₂×C₄	—	4	4	no	—
1230	C₂×C₄	—	4	2	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	8	no	—
1233	C₂×C₄	—	53	8	no	—
1234	C₂×C₄	—	53	4	no	—
1235	C₂×C₄	—	53	4	no	—
1236	C₂×C₄	—	106	4	no	—
1237	C₂×C₄	—	106	4	no	—
1238	C₂×C₄	—	212	8	no	—
1239	C₂×C₄	—	212	8	no	—
1240	C₂×C₄	—	212	8	no	—
1241	C₂×C₄	—	212	8	no	—
1242	C₂×C₄	—	212	8	no	—
1243	C₂×C₄	—	212	4	no	—
1244	C₂×C₄	—	212	4	no	—
1245	C₂×C₄	—	212	8	no	—
1246	C₂×C₄	—	212	4	no	—
1247	C₂×C₄	—	212	4	no	—
1248	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1249	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1250	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1251	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1252	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1253	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1254	C₂²	—	2	2	no	—
1255	C₂²	—	2	4	no	—
1256	C₂²	—	2	4	no	—
1257	C₂²	—	2	8	no	—
1258	C₂²	—	4	4	no	—
1259	C₂²	—	8	4	no	—
1260	C₂²	—	848	4	no	—
1261	C₂²	—	106	4	no	—
1262	C₂²	—	106	4	no	—
1263	C₂²	—	106	4	no	—
1264	C₂²	—	106	4	no	—
1265	C₂²	—	106	4	no	—
1266	C₂²	—	106	4	no	—
1267	C₂²	—	106	8	no	—
1268	C₂²	—	106	8	no	—
1269	C₂²	—	106	4	no	—
1270	C₂²	—	106	4	no	—
1271	C₂²	—	424	4	no	—
1272	C₂²	—	424	8	no	—
1273	C₂²	—	424	8	no	—
1274	C₂²	—	424	4	no	—
1275	C₂²	—	424	16	no	—
1276	C₂²	—	212	8	no	—
1277	C₂²	—	212	8	no	—
1278	C₂²	C₂×#13133263	1	4	yes	—
1279	C₂²	C₂×#13133263	1	2	yes	—
1280	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1281	C₄	—	2	2	no	—
1282	C₄	—	2	2	no	—
1283	C₄	—	2	4	no	—
1284	C₄	—	2	4	no	—
1285	C₄	—	2	8	no	—
1286	C₄	—	2	4	no	—
1287	C₄	—	106	4	no	—
1288	C₄	—	106	4	no	—
1289	C₄	—	106	8	no	—
1290	C₂	—	2	4	no	—
1291	C₂	—	2	2	no	—
1292	C₂	—	4	4	no	—
1293	C₂	—	212	4	no	—
1294	C₂	—	212	4	no	—
1295	C₂	—	212	4	no	—
1296	C₂	—	212	4	no	—
1297	C₂	C₂²×#13133263	1	1	yes	characteristic
1298	C₂	#20289526	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3491	C₂
hypercenter	#3491	D₅₃
hypocenter	C₅₃	#62862
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3491

Complements

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

N	H ≅ G/N	type
1. #20289067	C₂	semidirect
2. #20289045	C₂	semidirect
3. #20289025	C₂	semidirect
4. #20289024	C₂	semidirect
5. #20288903	C₂	semidirect
6. #20288881	C₂	semidirect
7. #20288871	C₂	semidirect
8. #20288413	C₂	semidirect
9. #20288405	C₂	semidirect
10. #20288400	C₂	semidirect
11. #20288353	C₂	semidirect
12. #20288351	C₂	semidirect
13. #20288347	C₂	semidirect
14. C₂×#16811192	C₂	semidirect
15. C₂×#16811184	C₂	semidirect
16. C₅₃×#3491	C₂	semidirect
17. C₂×#13133262	C₂²	semidirect
18. C₂²×#11719945	C₂²	semidirect
19. C₂³×D₂₁₂	C₂²	semidirect
20. C₂²×D₄×D₅₃	C₂²	semidirect
21. #16811377	C₂²	semidirect
22. #16811371	C₂²	semidirect
23. #16811371	C₂²	semidirect
24. #16811369	C₂²	semidirect
25. #16811367	C₂²	semidirect
26. #16811365	C₂²	semidirect
27. #16811364	C₂²	semidirect
28. #16811364	C₂²	semidirect
29. #16811364	C₂²	semidirect
30. #16811363	C₂²	semidirect
31. #16811358	C₂²	semidirect
32. #16811336	C₂²	semidirect
33. #16811326	C₂²	semidirect
34. #16811324	C₂²	semidirect
35. #16811306	C₂²	semidirect
36. #16811302	C₂²	semidirect
37. #16811300	C₂²	semidirect
38. #16811300	C₂²	semidirect
39. #16811297	C₂²	semidirect
40. #16811297	C₂²	semidirect
41. #16811297	C₂²	semidirect
42. #16811295	C₂²	semidirect
43. #16811294	C₂²	semidirect
44. #16811274	C₂²	semidirect
45. #16811271	C₂²	semidirect
46. #16811269	C₂²	semidirect
47. #16811268	C₂²	semidirect
48. #16811268	C₂²	semidirect
49. #16811265	C₂²	semidirect
50. #16811265	C₂²	semidirect
51. #16811265	C₂²	semidirect
52. #16811264	C₂²	semidirect
53. #16811264	C₂²	semidirect
54. #16811264	C₂²	semidirect
55. #16811263	C₂²	semidirect
56. #16811263	C₂²	semidirect
57. #16811262	C₂²	semidirect
58. D₄×D₂₁₂	C₂²	semidirect
59. D₄×D₂₁₂	C₂²	semidirect
60. D₄×D₂₁₂	C₂²	semidirect
61. #16811257	C₂²	semidirect
62. #16811255	C₂²	semidirect
63. #16811249	C₂²	semidirect
64. #16811245	C₂²	semidirect
65. #16811239	C₂²	semidirect
66. #16811229	C₂²	semidirect
67. #16811229	C₂²	semidirect
68. #16811228	C₂²	semidirect
69. #16811225	C₂²	semidirect
70. #16811221	C₂²	semidirect
71. #16811220	C₂²	semidirect
72. #16811213	C₂²	semidirect
73. #16811213	C₂²	semidirect
74. #16811212	C₂²	semidirect
75. #16811212	C₂²	semidirect
76. #16811212	C₂²	semidirect
77. #16811206	C₂²	semidirect
78. #16811206	C₂²	semidirect
79. #16811203	C₂²	semidirect
80. #16811195	C₂²	semidirect
81. #16811192	C₂²	semidirect
82. #16811192	C₂²	semidirect
83. #16811192	C₂²	semidirect
84. #16811192	C₂²	semidirect
85. #16811191	C₂²	semidirect
86. #16811188	C₂²	semidirect
88. #16811185	C₂²	semidirect
89. #16811185	C₂²	semidirect
90. #16811184	C₂²	semidirect
91. #16811184	C₂²	semidirect
92. #16811184	C₂²	semidirect
93. #16811184	C₂²	semidirect
94. #16811184	C₂²	semidirect
95. #16811184	C₂²	semidirect
96. #16811184	C₂²	semidirect
97. #16811182	C₂²	semidirect
98. C₂×#13133214	C₂²	semidirect
99. #16811157	C₂²	semidirect
100. C₂×#13133205	C₂²	semidirect
101. #16811136	C₂²	semidirect
102. #16811135	C₂²	semidirect
103. #16811132	C₂²	semidirect
104. #16811131	C₂²	semidirect
105. #16811131	C₂²	semidirect
106. C₂×#13133202	C₂²	semidirect
107. C₂×#13133200	C₂²	semidirect
108. #123×D₅₃	C₂²	semidirect
109. C₂×#13133192	C₂²	semidirect
110. C₂×#13133192	C₂²	semidirect
111. C₂×#13133190	C₂²	semidirect
112. C₂×#13133187	C₂²	semidirect
113. C₂×#13133187	C₂²	semidirect
114. C₂×#13133187	C₂²	semidirect
115. C₂×#13133187	C₂²	semidirect
116. C₂×#13133187	C₂²	semidirect
117. C₂×#13133185	C₂²	semidirect
118. #120×D₅₃	C₂²	semidirect
119. #16811096	C₂²	semidirect
120. #16811096	C₂²	semidirect
121. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
122. C₅₃×#552	C₂²	semidirect
123. C₅₃×#551	C₂²	semidirect
124. C₅₃×#543	C₂²	semidirect
125. C₅₃×#539	C₂²	semidirect
127. C₅₃×#529	C₂²	semidirect
128. C₂×#123×C₅₃	C₂²	semidirect
129. C₅₃×#518	C₂²	semidirect
130. C₂×#117×C₅₃	C₂²	semidirect
132. C₂⁴×D₅₃	C₂³	semidirect
134. C₂×#11719949	C₂³	semidirect
137. C₂×#11719945	C₂³	semidirect
138. C₂×#11719945	C₂³	semidirect
141. C₂²×Dic₁₀₆	C₂³	semidirect
148. C₂²×D₂₁₂	C₂³	semidirect
149. C₂²×D₂₁₂	C₂³	semidirect
150. C₂²×D₂₁₂	C₂³	semidirect
151. C₂²×D₂₁₂	C₂³	semidirect
152. C₂²×D₂₁₂	C₂³	semidirect
157. C₂²×C₂²⋊D₅₃	C₂³	semidirect
162. C₂×D₄×D₅₃	C₂³	semidirect
163. C₂×D₄×D₅₃	C₂³	semidirect
164. C₂²×C₄×D₅₃	C₂³	semidirect
165. C₂²×C₄×D₅₃	C₂³	semidirect
166. C₂²×C₄×D₅₃	C₂³	semidirect
167. #13133216	C₂³	semidirect
169. #13133214	C₂³	semidirect
170. #13133214	C₂³	semidirect
171. #13133214	C₂³	semidirect
172. #13133213	C₂³	semidirect
173. #13133212	C₂³	semidirect
174. #13133212	C₂³	semidirect
175. #13133212	C₂³	semidirect
176. #13133212	C₂³	semidirect
177. #13133211	C₂³	semidirect
178. #13133211	C₂³	semidirect
179. #13133209	C₂³	semidirect
180. #13133207	C₂³	semidirect
181. #13133206	C₂³	semidirect
182. #13133206	C₂³	semidirect
184. #13133205	C₂³	semidirect
185. #13133205	C₂³	semidirect
186. #13133205	C₂³	semidirect
187. #13133205	C₂³	semidirect
188. #13133205	C₂³	semidirect
189. #13133203	C₂³	semidirect
190. #13133203	C₂³	semidirect
191. #13133203	C₂³	semidirect
194. #13133202	C₂³	semidirect
195. #13133202	C₂³	semidirect
196. #13133202	C₂³	semidirect
197. #13133202	C₂³	semidirect
198. #13133202	C₂³	semidirect
199. #13133202	C₂³	semidirect
200. #13133202	C₂³	semidirect
201. #13133202	C₂³	semidirect
202. #13133202	C₂³	semidirect
203. #13133202	C₂³	semidirect
204. #13133202	C₂³	semidirect
205. #13133202	C₂³	semidirect
207. #13133201	C₂³	semidirect
208. #13133201	C₂³	semidirect
209. #13133201	C₂³	semidirect
211. #13133200	C₂³	semidirect
212. #13133200	C₂³	semidirect
213. #13133200	C₂³	semidirect
214. #13133200	C₂³	semidirect
215. #13133199	C₂³	semidirect
216. #13133199	C₂³	semidirect
217. #13133198	C₂³	semidirect
218. #13133197	C₂³	semidirect
219. #13133196	C₂³	semidirect
220. #13133195	C₂³	semidirect
221. #13133195	C₂³	semidirect
222. #13133195	C₂³	semidirect
223. #13133195	C₂³	semidirect
224. #13133195	C₂³	semidirect
225. #13133194	C₂³	semidirect
226. #13133194	C₂³	semidirect
227. #13133193	C₂³	semidirect
231. #13133192	C₂³	semidirect
232. #13133192	C₂³	semidirect
233. #13133192	C₂³	semidirect
234. #13133192	C₂³	semidirect
235. #13133192	C₂³	semidirect
236. #13133192	C₂³	semidirect
237. #13133192	C₂³	semidirect
238. #13133192	C₂³	semidirect
239. #13133192	C₂³	semidirect
240. #13133192	C₂³	semidirect
241. #13133192	C₂³	semidirect
242. #13133192	C₂³	semidirect
243. #13133192	C₂³	semidirect
246. #13133191	C₂³	semidirect
247. #13133191	C₂³	semidirect
248. #13133191	C₂³	semidirect
251. #13133190	C₂³	semidirect
252. #13133190	C₂³	semidirect
253. #13133190	C₂³	semidirect
254. #13133190	C₂³	semidirect
255. #13133190	C₂³	semidirect
256. #13133190	C₂³	semidirect
257. #13133190	C₂³	semidirect
258. #13133190	C₂³	semidirect
259. #13133190	C₂³	semidirect
261. #13133189	C₂³	semidirect
270. #13133187	C₂³	semidirect
271. #13133187	C₂³	semidirect
272. #13133187	C₂³	semidirect
273. #13133187	C₂³	semidirect
274. #13133187	C₂³	semidirect
275. #13133187	C₂³	semidirect
276. #13133187	C₂³	semidirect
277. #13133187	C₂³	semidirect
278. #13133187	C₂³	semidirect
279. #13133187	C₂³	semidirect
280. #13133187	C₂³	semidirect
281. #13133187	C₂³	semidirect
282. #13133187	C₂³	semidirect
283. #13133187	C₂³	semidirect
284. #13133186	C₂³	semidirect
288. #13133185	C₂³	semidirect
289. #13133185	C₂³	semidirect
290. C₄×Dic₁₀₆	C₂³	semidirect
291. C₄×D₂₁₂	C₂³	semidirect
292. C₄×D₂₁₂	C₂³	semidirect
293. C₄×D₂₁₂	C₂³	semidirect
294. C₄×D₂₁₂	C₂³	semidirect
295. #13133179	C₂³	semidirect
296. #13133179	C₂³	semidirect
297. #13133179	C₂³	semidirect
298. #13133179	C₂³	semidirect
299. C₄×C₂²⋊D₅₃	C₂³	semidirect
300. C₄×C₂²⋊D₅₃	C₂³	semidirect
301. C₄×C₂²⋊D₅₃	C₂³	semidirect
303. #13133177	C₂³	semidirect
304. #13133177	C₂³	semidirect
305. #13133177	C₂³	semidirect
306. #13133175	C₂³	semidirect
307. #13133174	C₂³	semidirect
308. #13133174	C₂³	semidirect
309. #13133173	C₂³	semidirect
310. #13133173	C₂³	semidirect
311. C₂×#11719919	C₂³	semidirect
312. C₄⋊C₄×D₅₃	C₂³	semidirect
316. C₂×#11719921	C₂³	semidirect
317. C₂×#11719921	C₂³	semidirect
318. C₂×#11719921	C₂³	semidirect
319. C₂×#11719921	C₂³	semidirect
320. C₂×#11719921	C₂³	semidirect
322. C₂²⋊C₄×D₅₃	C₂³	semidirect
323. C₂²⋊C₄×D₅₃	C₂³	semidirect
324. C₂²⋊C₄×D₅₃	C₂³	semidirect
325. C₂²⋊C₄×D₅₃	C₂³	semidirect
326. C₂²⋊C₄×D₅₃	C₂³	semidirect
329. #126×C₅₃	C₂³	semidirect
330. #126×C₅₃	C₂³	semidirect
331. #125×C₅₃	C₂³	semidirect
332. #125×C₅₃	C₂³	semidirect
333. #124×C₅₃	C₂³	semidirect
336. #123×C₅₃	C₂³	semidirect
337. #123×C₅₃	C₂³	semidirect
338. #123×C₅₃	C₂³	semidirect
339. C₂²⋊Q₈×C₅₃	C₂³	semidirect
340. C₂²⋊Q₈×C₅₃	C₂³	semidirect
341. C₂²⋊Q₈×C₅₃	C₂³	semidirect
344. C₄×Q₈×C₅₃	C₂³	semidirect
346. C₄×D₄×C₅₃	C₂³	semidirect
347. C₄×D₄×C₅₃	C₂³	semidirect
348. #117×C₅₃	C₂³	semidirect
349. #117×C₅₃	C₂³	semidirect
350. #117×C₅₃	C₂³	semidirect
351. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
352. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
356. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
357. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
358. C₂×C₄²×C₅₃	C₂³	semidirect
649. #3491	D₅₃	semidirect
685. #552	C₂×D₅₃	semidirect
692. #551	C₂×D₅₃	semidirect
715. #543	C₂×D₅₃	semidirect
724. #539	C₂×D₅₃	semidirect
754. #529	C₂×D₅₃	semidirect
764. C₂×#123	C₂×D₅₃	semidirect
777. #518	C₂×D₅₃	semidirect
778. C₂×#117	C₂×D₅₃	semidirect
780. C₅₃	#62862	semidirect
831. #126	C₂²×D₅₃	semidirect
832. #126	C₂²×D₅₃	semidirect
835. #125	C₂²×D₅₃	semidirect
836. #125	C₂²×D₅₃	semidirect
848. #124	C₂²×D₅₃	semidirect
877. #123	C₂²×D₅₃	semidirect
878. #123	C₂²×D₅₃	semidirect
879. #123	C₂²×D₅₃	semidirect
890. C₂²⋊Q₈	C₂²×D₅₃	semidirect
891. C₂²⋊Q₈	C₂²×D₅₃	semidirect
892. C₂²⋊Q₈	C₂²×D₅₃	semidirect
958. C₄×Q₈	C₂²×D₅₃	semidirect
975. C₄×D₄	C₂²×D₅₃	semidirect
976. C₄×D₄	C₂²×D₅₃	semidirect
982. #117	C₂²×D₅₃	semidirect
983. #117	C₂²×D₅₃	semidirect
984. #117	C₂²×D₅₃	semidirect
987. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
988. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1006. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1007. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1008. C₂×C₄²	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20289067	2
#20289045	2
#20289025	2
#20289024	2
#20288903	2
#20288881	2
#20288871	2
#20288413	2
#20288405	2
#20288400	2
#20288353	2
#20288351	2
#20288347	2
C₂×#16811192	2
C₂×#16811184	2
C₅₃×#3491	2
#62862	53