Subgroups — #28292810

Order 13568.

7330 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289285	C₂	1	4	yes	maximal, complemented
2	#20289280	C₂	1	4	yes	maximal, complemented
3	#20289238	C₂	1	4	yes	maximal, complemented
4	#20289231	C₂	1	4	yes	maximal, complemented
5	#20289067	C₂	1	8	yes	maximal, complemented
6	#20288676	C₂	1	8	yes	maximal, complemented
7	#20288664	C₂	1	8	yes	maximal, complemented
8	#20288613	C₂	1	2	yes	maximal, complemented
9	#20288611	C₂	1	2	yes	maximal, complemented
10	#20288508	C₂	1	2	yes	maximal, complemented
11	#20288502	C₂	1	2	yes	maximal, complemented
12	#20288398	C₂	1	8	yes	maximal, complemented
13	#20288362	C₂	1	2	yes	maximal, complemented
14	#20288348	C₂	1	2	yes	maximal, complemented
15	#20288011	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#13133205	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13133264	C₂²	1	2	yes	complemented
19	C₂×#13133263	C₂²	1	2	yes	complemented
20	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
22	#16811377	C₂²	1	8	yes	complemented
23	#16811371	C₂²	1	8	yes	complemented
24	#16811367	C₂²	1	8	yes	complemented
25	#16811365	C₂²	1	8	yes	complemented
26	#16811358	C₂²	1	8	yes	complemented
27	#16811356	C₂²	1	8	yes	complemented
28	#16811346	C₂²	1	8	yes	complemented
29	#16811345	C₂²	1	8	yes	complemented
30	#16811336	C₂²	1	16	yes	complemented
31	#16811302	C₂²	1	16	yes	complemented
32	#16811300	C₂²	1	16	yes	complemented
33	#16811297	C₂²	1	16	yes	complemented
34	#16811297	C₂²	1	16	yes	complemented
35	#16811296	C₂²	1	16	yes	complemented
36	D₄×Dic₁₀₆	C₂²	1	8	yes	complemented
37	#16811286	C₂²	1	8	yes	complemented
38	#16811285	C₂²	1	8	yes	complemented
39	#16811282	C₂²	1	8	yes	complemented
40	#16811282	C₂²	1	8	yes	complemented
41	#16811279	C₂²	1	8	yes	complemented
42	#16811269	C₂²	1	8	yes	complemented
43	#16811269	C₂²	1	8	yes	complemented
44	#16811268	C₂²	1	16	yes	complemented
45	#16811268	C₂²	1	8	yes	complemented
46	#16811265	C₂²	1	16	yes	complemented
47	#16811264	C₂²	1	8	yes	complemented
48	#16811262	C₂²	1	16	yes	complemented
49	#16811261	C₂²	1	16	yes	complemented
50	D₄×D₂₁₂	C₂²	1	8	yes	complemented
51	#16811257	C₂²	1	8	yes	complemented
52	#16811248	C₂²	1	8	yes	complemented
53	#16811247	C₂²	1	8	yes	complemented
54	#16811245	C₂²	1	16	yes	complemented
55	#16811244	C₂²	1	8	yes	complemented
56	#16811239	C₂²	1	16	yes	complemented
57	#16811213	C₂²	1	8	yes	complemented
58	#16811212	C₂²	1	16	yes	complemented
59	#16811210	C₂²	1	8	yes	complemented
60	#16811206	C₂²	1	16	yes	complemented
61	#16811206	C₂²	1	16	yes	complemented
62	#16811199	C₂²	1	2	yes	complemented
63	#16811199	C₂²	1	4	yes	complemented
64	#16811198	C₂²	1	4	yes	complemented
65	#16811195	C₂²	1	8	yes	complemented
66	#16811194	C₂²	1	2	yes	complemented
67	#16811192	C₂²	1	2	yes	—
68	#16811192	C₂²	1	4	yes	complemented
69	#16811187	C₂²	1	2	yes	—
70	#16811186	C₂²	1	4	yes	complemented
71	#16811184	C₂²	1	8	yes	complemented
72	#16811181	C₂²	1	8	yes	complemented
73	#16811180	C₂²	1	2	yes	complemented
74	#16811180	C₂²	1	1	yes	characteristic, complemented
75	#16811173	C₂²	1	2	yes	complemented
76	#16811173	C₂²	1	1	yes	characteristic, complemented
77	#16811173	C₂²	1	4	yes	complemented
78	#16811172	C₂²	1	4	yes	complemented
79	#16811158	C₂²	1	8	yes	complemented
80	#16811157	C₂²	1	4	yes	complemented
81	#16811157	C₂²	1	4	yes	complemented
82	#16811157	C₂²	1	4	yes	complemented
83	#16811157	C₂²	1	8	yes	complemented
84	C₂×#13133205	C₂²	1	4	yes	complemented
85	C₂×#13133205	C₂²	1	4	yes	complemented
86	C₂×#13133205	C₂²	1	4	yes	complemented
87	C₂×#13133205	C₂²	1	2	yes	complemented
88	C₂×#13133205	C₂²	1	2	yes	complemented
89	C₂×#13133205	C₂²	1	4	yes	complemented
90	C₂×#13133205	C₂²	1	4	yes	complemented
91	C₂×#13133205	C₂²	1	4	yes	complemented
92	#124×D₅₃	C₂²	1	4	yes	complemented
93	#16811134	C₂²	1	2	yes	complemented
94	#16811134	C₂²	1	4	yes	complemented
95	#16811129	C₂²	1	8	yes	complemented
96	#120×D₅₃	C₂²	1	8	yes	complemented
97	#16811100	C₂²	1	2	yes	complemented
98	#16811097	C₂²	1	2	yes	complemented
99	#16811095	C₂²	1	16	yes	complemented
100	C₄×#11719945	C₂²	1	2	yes	complemented
101	C₄×#11719945	C₂²	1	4	yes	complemented
102	C₂²×#11719921	C₂²	1	4	yes	complemented
103	C₅₃×#533	C₂²	1	2	yes	complemented
104	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#532	C₂²	1	2	yes	complemented
106	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#529	C₂²	1	4	yes	complemented
108	C₅₃×#529	C₂²	1	4	yes	complemented
109	C₅₃×#529	C₂²	1	4	yes	complemented
110	C₅₃×#525	C₂²	1	2	yes	complemented
111	C₅₃×#525	C₂²	1	4	yes	complemented
112	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
113	C₄×#41×C₅₃	C₂²	1	4	yes	complemented
114	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₂⁴×D₅₃	C₂³	1	2	yes	—
116	#13133264	—	4	8	no	—
117	#13133263	—	4	8	no	—
118	C₂×#11719949	C₂³	1	4	yes	—
119	C₂×#11719945	C₂³	1	2	yes	—
120	C₂×#11719945	C₂³	1	4	yes	—
121	C₂×#11719945	C₂³	1	4	yes	—
122	C₂×#11719945	C₂³	1	4	yes	complemented
123	C₂×#11719947	C₂³	1	8	yes	—
124	C₂×#11719947	C₂³	1	4	yes	complemented
125	C₂²×Dic₁₀₆	—	4	4	no	—
126	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
127	C₂²×Dic₁₀₆	C₂³	1	4	yes	—
128	C₂²×Dic₁₀₆	C₂³	1	4	yes	—
129	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
130	C₂²×Dic₁₀₆	C₂³	1	4	yes	complemented
131	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
132	C₂²×D₂₁₂	—	4	4	no	—
133	C₂²×D₂₁₂	C₂³	1	2	yes	—
134	C₂²×D₂₁₂	C₂³	1	4	yes	—
135	C₂²×D₂₁₂	C₂³	1	4	yes	—
136	C₂²×D₂₁₂	C₂³	1	4	yes	—
137	C₂²×D₂₁₂	C₂³	1	2	yes	—
138	C₂×D₄×D₅₃	C₂³	1	16	yes	—
139	C₂×D₄×D₅₃	C₂³	1	8	yes	—
140	C₂×D₄×D₅₃	C₂³	1	4	yes	—
141	C₂³×Dic₅₃	C₂³	1	2	yes	—
142	#13133217	C₂³	1	4	yes	complemented
143	#13133217	C₂³	1	1	yes	characteristic, complemented
144	#13133217	C₂³	1	2	yes	complemented
145	#13133216	C₂³	1	16	yes	complemented
146	#13133215	C₂³	1	4	yes	complemented
147	#13133214	C₂³	1	4	yes	—
148	#13133214	C₂³	1	1	yes	characteristic, complemented
149	#13133213	C₂³	1	4	yes	—
150	#13133212	C₂³	1	16	yes	complemented
151	#13133212	C₂³	1	16	yes	complemented
152	#13133212	C₂³	1	16	yes	complemented
153	#13133211	C₂³	1	16	yes	complemented
154	#13133211	C₂³	1	8	yes	complemented
155	#13133209	C₂³	1	4	yes	complemented
156	#13133209	C₂³	1	2	yes	complemented
157	#13133206	C₂³	1	4	yes	—
158	#13133206	C₂³	1	16	yes	complemented
159	#13133205	C₂³	1	8	yes	—
160	#13133205	C₂³	1	4	yes	—
161	#13133205	C₂³	1	8	yes	—
162	#13133205	C₂³	1	8	yes	—
163	#13133205	C₂³	1	8	yes	—
164	#13133205	C₂³	1	4	yes	—
165	#13133205	C₂³	1	4	yes	—
166	#13133205	C₂³	1	4	yes	—
167	#13133205	C₂³	1	4	yes	—
168	#13133205	C₂³	1	8	yes	—
169	#13133205	C₂³	1	8	yes	—
170	#13133205	C₂³	1	16	yes	complemented
171	#13133205	C₂³	1	4	yes	complemented
172	#13133205	C₂³	1	4	yes	complemented
173	#13133205	C₂³	1	2	yes	complemented
174	#13133204	C₂³	1	4	yes	complemented
175	#13133203	C₂³	1	16	yes	complemented
176	#13133203	C₂³	1	16	yes	complemented
177	#13133203	C₂³	1	16	yes	complemented
178	#13133202	C₂³	1	16	yes	—
179	#13133202	C₂³	1	16	yes	complemented
180	#13133202	C₂³	1	16	yes	complemented
181	#13133202	C₂³	1	16	yes	complemented
182	#13133201	C₂³	1	8	yes	—
183	#13133201	C₂³	1	16	yes	complemented
184	#13133200	C₂³	1	8	yes	—
185	#13133200	C₂³	1	4	yes	—
186	#13133200	C₂³	1	16	yes	complemented
187	#13133199	C₂³	1	16	yes	complemented
188	#13133198	C₂³	1	8	yes	—
189	#13133197	C₂³	1	8	yes	complemented
190	#13133197	C₂³	1	16	yes	complemented
191	#13133196	C₂³	1	4	yes	—
192	#13133196	C₂³	1	4	yes	—
193	#13133196	C₂³	1	4	yes	—
194	#13133196	C₂³	1	8	yes	complemented
195	#13133195	C₂³	1	16	yes	complemented
196	#13133195	C₂³	1	16	yes	complemented
197	#13133195	C₂³	1	16	yes	complemented
198	#13133194	C₂³	1	16	yes	—
199	#13133194	C₂³	1	16	yes	complemented
200	#13133193	C₂³	1	16	yes	complemented
201	#13133192	C₂³	1	8	yes	—
202	#13133192	C₂³	1	16	yes	—
203	#13133192	C₂³	1	16	yes	complemented
204	#13133191	C₂³	1	4	yes	—
205	#13133191	C₂³	1	8	yes	—
206	#13133191	C₂³	1	4	yes	—
207	#13133191	C₂³	1	4	yes	—
208	#13133191	C₂³	1	16	yes	complemented
209	#13133190	C₂³	1	16	yes	—
210	#13133190	C₂³	1	16	yes	complemented
211	#13133189	C₂³	1	16	yes	—
212	#13133189	C₂³	1	16	yes	complemented
213	#13133187	C₂³	1	16	yes	—
214	#13133187	C₂³	1	8	yes	—
215	#13133187	C₂³	1	16	yes	—
216	#13133187	C₂³	1	16	yes	complemented
217	#13133186	C₂³	1	4	yes	—
218	#13133185	C₂³	1	16	yes	—
219	#13133185	C₂³	1	8	yes	—
220	#13133185	C₂³	1	16	yes	complemented
221	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
222	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
223	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
224	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
225	#13133182	C₂³	1	8	yes	complemented
226	C₄×D₂₁₂	C₂³	1	8	yes	—
227	C₄×D₂₁₂	C₂³	1	4	yes	complemented
228	C₄×D₂₁₂	C₂³	1	16	yes	complemented
229	C₄×D₂₁₂	C₂³	1	4	yes	complemented
230	C₄×D₂₁₂	C₂³	1	4	yes	complemented
231	D₄×Dic₅₃	C₂³	1	16	yes	—
232	#13133179	C₂³	1	8	yes	—
233	#13133179	C₂³	1	16	yes	complemented
234	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
235	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
236	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
237	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
238	#13133177	C₂³	1	16	yes	—
239	#13133177	C₂³	1	16	yes	complemented
240	#13133176	C₂³	1	4	yes	—
241	#13133176	C₂³	1	2	yes	—
242	#13133175	C₂³	1	16	yes	complemented
243	#13133174	C₂³	1	8	yes	complemented
244	#13133174	C₂³	1	16	yes	complemented
245	#13133174	C₂³	1	4	yes	complemented
246	#13133173	C₂³	1	8	yes	—
247	C₂×#11719921	C₂³	1	8	yes	—
248	C₂×#11719921	C₂³	1	8	yes	—
249	C₂×#11719921	C₂³	1	8	yes	—
250	C₂×#11719921	C₂³	1	8	yes	—
251	C₂×#11719921	C₂³	1	8	yes	—
252	C₂×#11719921	C₂³	1	8	yes	—
253	C₂×#11719921	C₂³	1	16	yes	complemented
254	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
255	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
256	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
257	C₄²×D₅₃	C₂³	1	4	yes	complemented
258	C₂×#41×C₅₃	C₂³	1	2	yes	—
259	C₂×#41×C₅₃	C₂³	1	4	yes	—
260	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
262	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
263	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
264	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
265	#126×C₅₃	C₂³	1	8	yes	complemented
266	#125×C₅₃	C₂³	1	4	yes	complemented
267	#125×C₅₃	C₂³	1	2	yes	complemented
268	#124×C₅₃	C₂³	1	4	yes	complemented
269	#124×C₅₃	C₂³	1	2	yes	complemented
270	#123×C₅₃	C₂³	1	8	yes	—
271	#123×C₅₃	C₂³	1	4	yes	—
272	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
273	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
274	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
275	#121×C₅₃	C₂³	1	4	yes	—
276	#121×C₅₃	C₂³	1	4	yes	—
277	#121×C₅₃	C₂³	1	4	yes	—
278	#120×C₅₃	C₂³	1	4	yes	—
279	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
280	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
281	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
282	C₄×D₄×C₅₃	C₂³	1	8	yes	—
283	C₄×D₄×C₅₃	C₂³	1	8	yes	—
284	C₄×D₄×C₅₃	C₂³	1	8	yes	—
285	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
286	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
287	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
288	#117×C₅₃	C₂³	1	4	yes	—
289	#117×C₅₃	C₂³	1	2	yes	—
290	#117×C₅₃	C₂³	1	8	yes	complemented
291	#117×C₅₃	C₂³	1	4	yes	complemented
292	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
293	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
295	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
296	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
297	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
299	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
300	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
301	C₂³×D₅₃	—	4	4	no	—
302	C₂³×D₅₃	—	4	8	no	—
303	C₂³×D₅₃	C₂⁴	1	4	yes	—
304	C₂³×D₅₃	C₂⁴	1	8	yes	—
305	C₂³×D₅₃	C₂⁴	1	8	yes	—
306	#41×C₅₃	—	2	8	no	—
307	#41×C₅₃	—	4	8	no	—
308	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
309	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
310	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
311	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
312	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
313	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
314	C₂²×C₄×C₅₃	—	2	4	no	—
315	C₂²×C₄×C₅₃	—	4	4	no	—
316	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
322	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
327	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
329	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
330	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
331	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
332	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
333	C₂²×Dic₅₃	—	4	4	no	—
334	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
335	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
336	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
337	#11719949	—	4	8	no	—
338	Q₈×D₅₃	—	4	8	no	—
339	#11719947	—	4	8	no	—
340	#11719947	—	4	16	no	—
341	D₄×D₅₃	—	4	8	no	—
342	D₄×D₅₃	—	4	32	no	—
343	D₄×D₅₃	—	4	16	no	—
344	#11719945	—	2	8	no	—
345	#11719945	—	4	8	no	—
346	#11719945	—	4	8	no	—
347	#11719945	—	4	8	no	—
348	C₂×D₂₁₂	—	2	8	no	—
349	C₂×D₂₁₂	—	4	8	no	—
350	C₂×D₂₁₂	—	4	8	no	—
351	C₂×D₂₁₂	—	4	8	no	—
352	C₂×D₂₁₂	—	4	4	no	—
353	C₂×D₂₁₂	C₂⁴	1	4	yes	—
354	C₂×D₂₁₂	C₂⁴	1	4	yes	—
355	C₂×D₂₁₂	C₂⁴	1	2	yes	—
356	C₂×D₂₁₂	C₂⁴	1	16	yes	—
357	C₂×D₂₁₂	C₂⁴	1	4	yes	—
358	C₂×D₂₁₂	C₂⁴	1	8	yes	—
359	C₂×D₂₁₂	C₂⁴	1	8	yes	—
360	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
361	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
362	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
363	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
364	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
365	C₂×Dic₁₀₆	—	2	8	no	—
366	C₂×Dic₁₀₆	—	4	8	no	—
367	C₂×Dic₁₀₆	—	4	8	no	—
368	C₂×Dic₁₀₆	—	4	8	no	—
369	C₂×Dic₁₀₆	—	4	4	no	—
370	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
371	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
372	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
373	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
374	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
375	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
376	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
377	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
378	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
379	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
380	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
381	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
382	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
383	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
384	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
385	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
386	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
387	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₄²×C₅₃	C₂⁴	1	2	yes	—
389	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₄²×C₅₃	C₂⁴	1	2	yes	—
391	C₄²×C₅₃	C₂⁴	1	2	yes	—
392	C₄²×C₅₃	C₂⁴	1	2	yes	—
393	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₄²×C₅₃	C₂⁴	1	2	yes	—
395	C₄²×C₅₃	C₂⁴	1	2	yes	—
396	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₄²×C₅₃	C₂⁴	1	8	yes	—
398	C₄²×C₅₃	C₂⁴	1	4	yes	—
399	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
400	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
401	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
402	#11719921	C₂⁴	1	16	yes	—
403	#11719921	C₂⁴	1	16	yes	—
404	#11719921	C₂⁴	1	16	yes	—
405	#11719921	C₂⁴	1	16	yes	—
406	#11719921	C₂⁴	1	16	yes	—
407	#11719921	C₂⁴	1	16	yes	—
408	#11719921	C₂⁴	1	16	yes	—
409	#11719921	C₂⁴	1	8	yes	—
410	#11719921	C₂⁴	1	16	yes	—
411	#11719921	C₂⁴	1	8	yes	—
412	#11719921	C₂⁴	1	8	yes	—
413	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
414	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
415	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
416	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
417	#11719919	C₂⁴	1	16	yes	—
418	#11719919	C₂⁴	1	8	yes	—
419	#11719919	C₂⁴	1	16	yes	—
420	#11719919	C₂⁴	1	8	yes	—
421	#11719919	C₂⁴	1	8	yes	—
422	C₄×Dic₅₃	C₂⁴	1	8	yes	—
423	C₄×Dic₅₃	C₂⁴	1	4	yes	—
424	C₄×Dic₅₃	C₂⁴	1	16	yes	—
425	C₂³×C₅₃	—	2	2	no	—
426	C₂³×C₅₃	—	2	4	no	—
427	C₂³×C₅₃	C₂⁵	1	4	yes	—
428	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
429	C₂³×C₅₃	C₂⁵	1	2	yes	—
430	C₂²×D₅₃	—	2	8	no	—
431	C₂²×D₅₃	—	2	16	no	—
432	C₂²×D₅₃	—	4	8	no	—
433	C₂²×D₅₃	—	4	8	no	—
434	C₂²×D₅₃	—	4	8	no	—
435	C₂²×D₅₃	—	4	8	no	—
436	C₂²×D₅₃	—	4	16	no	—
437	C₂²×D₅₃	—	8	16	no	—
438	C₂²×D₅₃	C₂⁵	1	4	yes	—
439	C₂²×D₅₃	C₂⁵	1	8	yes	—
440	Q₈×C₅₃	—	2	4	no	—
441	Q₈×C₅₃	—	4	4	no	—
442	D₄×C₅₃	—	2	8	no	—
443	D₄×C₅₃	—	2	16	no	—
444	D₄×C₅₃	—	2	4	no	—
445	D₄×C₅₃	—	4	4	no	—
446	C₂×C₄×C₅₃	—	2	2	no	—
447	C₂×C₄×C₅₃	—	2	4	no	—
448	C₂×C₄×C₅₃	—	2	4	no	—
449	C₂×C₄×C₅₃	—	2	4	no	—
450	C₂×C₄×C₅₃	—	2	4	no	—
451	C₂×C₄×C₅₃	—	2	8	no	—
452	C₂×C₄×C₅₃	—	4	2	no	—
453	C₂×C₄×C₅₃	—	4	2	no	—
454	C₂×C₄×C₅₃	—	4	2	no	—
455	C₂×C₄×C₅₃	—	4	2	no	—
456	C₂×C₄×C₅₃	—	4	8	no	—
457	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
458	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
459	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
460	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
461	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
462	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
463	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
464	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
465	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
466	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
467	C₂²⋊D₅₃	—	2	8	no	—
468	C₂²⋊D₅₃	—	2	16	no	—
469	C₂²⋊D₅₃	—	4	8	no	—
470	C₂²⋊D₅₃	—	4	8	no	—
471	C₂²⋊D₅₃	—	4	16	no	—
472	C₂×Dic₅₃	—	2	8	no	—
473	C₂×Dic₅₃	—	4	8	no	—
474	C₂×Dic₅₃	—	4	8	no	—
475	C₂×Dic₅₃	C₂⁵	1	8	yes	—
476	C₂×Dic₅₃	C₂⁵	1	4	yes	—
477	C₂×Dic₅₃	C₂⁵	1	8	yes	—
478	D₂₁₂	—	2	8	no	—
479	D₂₁₂	—	2	8	no	—
480	D₂₁₂	—	2	4	no	—
481	D₂₁₂	—	4	8	no	—
482	D₂₁₂	—	4	8	no	—
483	D₂₁₂	—	4	4	no	—
484	D₂₁₂	—	4	16	no	—
485	C₄×D₅₃	—	2	8	no	—
486	C₄×D₅₃	—	4	8	no	—
487	C₄×D₅₃	—	4	8	no	—
488	C₄×D₅₃	—	4	8	no	—
489	C₄×D₅₃	—	4	16	no	—
490	Dic₁₀₆	—	2	8	no	—
491	Dic₁₀₆	—	2	8	no	—
492	Dic₁₀₆	—	2	4	no	—
493	Dic₁₀₆	—	4	8	no	—
494	Dic₁₀₆	—	4	8	no	—
495	Dic₁₀₆	—	4	4	no	—
496	#62824	—	53	1	no	maximal, Sylow
497	C₂²×C₅₃	—	2	8	no	—
498	C₂²×C₅₃	—	2	2	no	—
499	C₂²×C₅₃	—	2	2	no	—
500	C₂²×C₅₃	—	2	2	no	—
501	C₂²×C₅₃	—	2	4	no	—
502	C₂²×C₅₃	—	2	8	no	—
503	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
504	C₂²×C₅₃	#585	1	4	yes	—
505	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
506	C₂×D₅₃	—	2	4	no	—
507	C₂×D₅₃	—	2	8	no	—
508	C₂×D₅₃	—	2	8	no	—
509	C₂×D₅₃	—	2	16	no	—
510	C₂×D₅₃	—	8	8	no	—
511	C₂×D₅₃	—	8	16	no	—
512	C₂×D₅₃	—	16	8	no	—
513	C₄×C₅₃	—	2	2	no	—
514	C₄×C₅₃	—	2	4	no	—
515	C₄×C₅₃	—	2	2	no	—
516	C₄×C₅₃	—	2	2	no	—
517	C₄×C₅₃	—	2	8	no	—
518	C₄×C₅₃	—	2	2	no	—
519	C₄×C₅₃	—	2	2	no	—
520	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
521	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
522	Dic₅₃	—	2	8	no	—
523	Dic₅₃	—	2	4	no	—
524	Dic₅₃	—	2	8	no	—
525	#3561	—	53	4	no	—
526	#3561	—	53	4	no	—
527	#3558	—	53	4	no	—
528	#3558	—	53	4	no	—
529	#3545	—	53	8	no	—
530	#3514	—	53	8	no	—
531	#3514	—	53	8	no	—
532	#3510	—	53	2	no	—
533	#3510	—	53	2	no	—
534	#3500	—	53	2	no	—
535	#3500	—	53	2	no	—
536	#3490	—	53	8	no	—
537	#3486	—	53	2	no	—
538	#3484	—	53	2	no	—
539	#3444	—	53	1	no	—
540	#3444	D₅₃	1	1	yes	characteristic, complemented
541	C₂²×#124	—	53	1	no	—
542	C₂×C₅₃	—	2	2	no	—
543	C₂×C₅₃	—	2	4	no	—
544	C₂×C₅₃	—	4	4	no	—
545	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂×C₅₃	C₂×#585	1	2	yes	—
547	D₅₃	—	4	8	no	—
548	D₅₃	—	4	4	no	—
549	C₂×2₋¹⁺⁴	—	53	2	no	—
550	C₂×H(5,𝔽₂)	—	53	2	no	—
551	C₂³×Q₈	—	53	1	no	—
552	C₂³×D₄	—	53	1	no	—
553	#563	—	53	8	no	—
554	#562	—	53	8	no	—
555	#562	—	53	8	no	—
556	H(3,𝔽₄)	—	53	8	no	—
557	#559	—	53	8	no	—
558	#559	—	53	8	no	—
559	#556	—	53	8	no	—
560	#556	—	53	8	no	—
561	#555	—	53	16	no	—
562	#551	—	53	16	no	—
563	#551	—	53	16	no	—
564	#551	—	53	16	no	—
565	#551	—	53	16	no	—
566	#551	—	53	16	no	—
567	D₄×Q₈	—	53	8	no	—
568	D₄×Q₈	—	53	8	no	—
569	#548	—	53	8	no	—
570	#548	—	53	8	no	—
571	#548	—	53	8	no	—
572	#548	—	53	8	no	—
573	#546	—	53	16	no	—
574	#546	—	53	16	no	—
575	#546	—	53	8	no	—
576	#546	—	53	16	no	—
577	#546	—	53	16	no	—
578	#546	—	53	8	no	—
579	#546	—	53	8	no	—
580	#546	—	53	8	no	—
581	D₄²	—	53	8	no	—
582	D₄²	—	53	8	no	—
583	#543	—	53	8	no	—
584	#542	—	53	8	no	—
585	#542	—	53	16	no	—
586	#542	—	53	16	no	—
587	#542	—	53	8	no	—
588	#538	—	53	16	no	—
589	#538	—	53	8	no	—
590	#538	—	53	8	no	—
591	#538	—	53	16	no	—
592	#538	—	53	16	no	—
593	#536	—	53	2	no	—
594	#536	—	53	4	no	—
595	#536	—	53	8	no	—
596	#536	—	53	2	no	—
597	#536	—	53	4	no	—
598	#535	—	53	2	no	—
599	#535	—	53	4	no	—
600	#535	—	53	2	no	—
601	#535	—	53	4	no	—
602	#534	—	53	8	no	—
603	#534	—	53	8	no	—
604	#533	—	53	1	no	—
605	#533	—	53	2	no	—
606	#533	C₂×D₅₃	1	1	yes	characteristic, complemented
607	#533	C₂×D₅₃	1	2	yes	complemented
608	#532	—	53	4	no	—
609	#532	—	53	1	no	—
610	#532	—	53	2	no	—
611	#532	—	53	4	no	—
612	#532	C₂×D₅₃	1	1	yes	characteristic, complemented
613	#532	C₂×D₅₃	1	2	yes	complemented
614	#529	—	53	8	no	—
615	#529	—	53	4	no	—
616	#529	—	53	4	no	—
617	#529	—	53	4	no	—
618	#529	—	53	8	no	—
619	#529	C₂×D₅₃	1	4	yes	complemented
620	#529	C₂×D₅₃	1	4	yes	complemented
621	#529	C₂×D₅₃	1	4	yes	complemented
622	C₂×#124	—	53	4	no	—
623	C₂×#124	—	53	2	no	—
624	C₂×#124	—	53	2	no	—
625	C₂×#124	—	53	4	no	—
626	C₂×#124	—	53	4	no	—
627	C₂×#124	—	53	4	no	—
628	C₂×#124	—	53	4	no	—
629	C₂×#124	—	53	4	no	—
630	C₂×#124	—	53	4	no	—
631	#525	—	53	2	no	—
632	#525	—	53	4	no	—
633	#525	—	53	8	no	—
634	#525	C₂×D₅₃	1	2	yes	complemented
635	#525	C₂×D₅₃	1	4	yes	complemented
636	C₂×#120	—	53	8	no	—
637	#519	—	53	2	no	—
638	#518	—	53	16	no	—
639	#518	—	53	2	no	—
640	C₄×#41	—	53	2	no	—
641	C₄×#41	—	53	4	no	—
642	C₄×#41	C₂×D₅₃	1	2	yes	complemented
643	C₄×#41	C₂×D₅₃	1	4	yes	complemented
644	C₂²×C₂²⋊C₄	—	53	4	no	—
645	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
646	C₅₃	#62824	1	1	yes	characteristic, complemented, Sylow
647	C₂⁵	—	53	2	no	—
648	2₋¹⁺⁴	—	212	8	no	—
649	H(5,𝔽₂)	—	212	8	no	—
650	C₂×#41	—	53	4	no	—
651	C₂×#41	—	53	8	no	—
652	C₂×#41	—	53	4	no	—
653	C₂×#41	—	53	2	no	—
654	C₂×#41	—	53	4	no	—
655	C₂×#41	—	53	4	no	—
656	C₂×#41	—	53	4	no	—
657	C₂×#41	C₂²×D₅₃	1	2	yes	—
658	C₂×#41	C₂²×D₅₃	1	4	yes	—
659	C₂²×Q₈	—	53	4	no	—
660	C₂²×Q₈	—	53	2	no	—
661	C₂²×Q₈	—	53	2	no	—
662	C₂²×Q₈	—	53	4	no	—
663	C₂²×Q₈	—	53	4	no	—
664	C₂²×Q₈	—	53	4	no	—
665	C₂²×Q₈	—	212	4	no	—
666	C₂²×D₄	—	53	16	no	—
667	C₂²×D₄	—	53	8	no	—
668	C₂²×D₄	—	53	4	no	—
669	C₂²×D₄	—	53	2	no	—
670	C₂²×D₄	—	53	2	no	—
671	C₂²×D₄	—	53	4	no	—
672	C₂²×D₄	—	53	4	no	—
673	C₂²×D₄	—	53	4	no	—
674	C₂²×D₄	—	212	4	no	—
675	C₂³×C₄	—	53	2	no	—
676	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
677	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
678	C₄⋊Q₈	—	53	4	no	—
679	C₄⋊Q₈	—	53	16	no	—
680	C₄⋊Q₈	—	53	1	no	—
681	C₄⋊Q₈	—	53	2	no	—
682	C₄⋊Q₈	—	53	4	no	—
683	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
684	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
685	#127	—	53	4	no	—
686	#127	—	53	1	no	—
687	#127	—	53	4	no	—
688	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
689	#126	—	53	16	no	—
690	#126	—	53	16	no	—
691	#126	—	53	16	no	—
692	#126	—	53	8	no	—
693	#126	—	53	16	no	—
694	#126	C₂²×D₅₃	1	8	yes	complemented
695	#125	—	53	2	no	—
696	#125	—	53	4	no	—
697	#125	C₂²×D₅₃	1	2	yes	complemented
698	#125	C₂²×D₅₃	1	4	yes	complemented
699	#124	—	53	4	no	—
700	#124	—	53	16	no	—
701	#124	—	53	4	no	—
702	#124	—	53	16	no	—
703	#124	—	53	16	no	—
704	#124	—	53	16	no	—
705	#124	—	53	4	no	—
706	#124	—	53	4	no	—
707	#124	—	53	4	no	—
708	#124	—	53	4	no	—
709	#124	—	53	8	no	—
710	#124	—	53	8	no	—
711	#124	—	53	8	no	—
712	#124	—	53	8	no	—
713	#124	—	53	8	no	—
714	#124	—	53	8	no	—
715	#124	—	53	2	no	—
716	#124	—	53	4	no	—
717	#124	—	53	4	no	—
718	#124	—	53	16	no	—
719	#124	—	53	4	no	—
720	#124	C₂²×D₅₃	1	2	yes	complemented
721	#124	C₂²×D₅₃	1	4	yes	complemented
722	#123	—	53	8	no	—
723	#123	—	53	4	no	—
724	#123	—	53	8	no	—
725	#123	—	53	16	no	—
726	#123	—	53	16	no	—
727	#123	—	53	16	no	—
728	#123	—	53	16	no	—
729	#123	—	53	16	no	—
730	#123	—	53	8	no	—
731	#123	—	53	16	no	—
732	#123	—	53	16	no	—
733	#123	C₂²×D₅₃	1	4	yes	—
734	#123	C₂²×D₅₃	1	8	yes	—
735	C₂²⋊Q₈	—	53	16	no	—
736	C₂²⋊Q₈	—	53	4	no	—
737	C₂²⋊Q₈	—	53	4	no	—
738	C₂²⋊Q₈	—	53	4	no	—
739	C₂²⋊Q₈	—	53	8	no	—
740	C₂²⋊Q₈	—	53	8	no	—
741	C₂²⋊Q₈	—	53	16	no	—
742	C₂²⋊Q₈	—	53	16	no	—
743	C₂²⋊Q₈	—	53	16	no	—
744	C₂²⋊Q₈	—	53	16	no	—
745	C₂²⋊Q₈	—	53	16	no	—
746	C₂²⋊Q₈	—	53	16	no	—
747	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
748	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
749	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
750	#121	—	53	16	no	—
751	#121	—	53	16	no	—
752	#121	—	53	4	no	—
753	#121	—	53	4	no	—
754	#121	—	53	4	no	—
755	#121	—	53	8	no	—
756	#121	—	53	16	no	—
757	#121	—	53	8	no	—
758	#121	—	53	16	no	—
759	#121	—	53	16	no	—
760	#121	—	53	16	no	—
761	#121	—	53	16	no	—
762	#121	C₂²×D₅₃	1	4	yes	—
763	#121	C₂²×D₅₃	1	4	yes	—
764	#121	C₂²×D₅₃	1	4	yes	—
765	#120	—	53	4	no	—
766	#120	—	53	8	no	—
767	#120	—	53	16	no	—
768	#120	—	53	16	no	—
769	#120	—	53	8	no	—
770	#120	—	53	16	no	—
771	#120	—	53	16	no	—
772	#120	—	53	16	no	—
773	#120	C₂²×D₅₃	1	4	yes	—
774	C₄×Q₈	—	53	8	no	—
775	C₄×Q₈	—	53	4	no	—
776	C₄×Q₈	—	53	4	no	—
777	C₄×Q₈	—	53	4	no	—
778	C₄×Q₈	—	53	8	no	—
779	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
780	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
781	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
782	C₄×D₄	—	53	16	no	—
783	C₄×D₄	—	53	8	no	—
784	C₄×D₄	—	53	8	no	—
785	C₄×D₄	—	53	8	no	—
786	C₄×D₄	—	53	16	no	—
787	C₄×D₄	—	53	16	no	—
788	C₄×D₄	—	53	8	no	—
789	C₄×D₄	—	53	16	no	—
790	C₄×D₄	—	53	16	no	—
791	C₄×D₄	—	53	4	no	—
792	C₄×D₄	—	53	4	no	—
793	C₄×D₄	—	53	4	no	—
794	C₄×D₄	—	53	8	no	—
795	C₄×D₄	—	53	16	no	—
796	C₄×D₄	C₂²×D₅₃	1	8	yes	—
797	C₄×D₄	C₂²×D₅₃	1	8	yes	—
798	C₄×D₄	C₂²×D₅₃	1	8	yes	—
799	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
800	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
801	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
802	#117	—	53	2	no	—
803	#117	—	53	4	no	—
804	#117	—	53	16	no	—
805	#117	—	53	8	no	—
806	#117	—	53	4	no	—
807	#117	—	53	8	no	—
808	#117	—	53	16	no	—
809	#117	C₂²×D₅₃	1	2	yes	—
810	#117	C₂²×D₅₃	1	4	yes	—
811	#117	C₂²×D₅₃	1	4	yes	complemented
812	#117	C₂²×D₅₃	1	8	yes	complemented
813	C₂×C₂²⋊C₄	—	53	8	no	—
814	C₂×C₂²⋊C₄	—	53	8	no	—
815	C₂×C₂²⋊C₄	—	53	8	no	—
816	C₂×C₂²⋊C₄	—	53	8	no	—
817	C₂×C₂²⋊C₄	—	53	8	no	—
818	C₂×C₂²⋊C₄	—	53	8	no	—
819	C₂×C₂²⋊C₄	—	53	16	no	—
820	C₂×C₂²⋊C₄	—	53	8	no	—
821	C₂×C₂²⋊C₄	—	53	16	no	—
822	C₂×C₂²⋊C₄	—	53	16	no	—
823	C₂×C₄²	—	53	4	no	—
824	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
825	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
826	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
827	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
828	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
829	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
830	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
831	C₂×C₄²	C₂²×D₅₃	1	4	yes	complemented
832	C₂⁴	—	53	4	no	—
833	C₂⁴	—	53	8	no	—
834	C₂⁴	—	53	8	no	—
835	C₂⁴	—	212	4	no	—
836	C₂⁴	—	212	8	no	—
837	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
838	#41	—	2	8	no	—
839	#41	—	4	8	no	—
840	#41	—	106	8	no	—
841	#41	—	212	8	no	—
842	#41	—	212	8	no	—
843	#41	—	212	8	no	—
844	#41	—	212	16	no	—
845	#41	—	212	8	no	—
846	#41	—	212	8	no	—
847	C₂×Q₈	—	53	4	no	—
848	C₂×Q₈	—	53	4	no	—
849	C₂×Q₈	—	53	2	no	—
850	C₂×Q₈	—	53	4	no	—
851	C₂×Q₈	—	53	8	no	—
852	C₂×Q₈	—	53	8	no	—
853	C₂×Q₈	—	106	8	no	—
854	C₂×Q₈	—	212	4	no	—
855	C₂×Q₈	—	212	8	no	—
856	C₂×Q₈	—	212	8	no	—
857	C₂×Q₈	—	212	8	no	—
858	C₂×Q₈	—	212	8	no	—
859	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
860	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
861	C₂×D₄	—	53	8	no	—
862	C₂×D₄	—	53	4	no	—
863	C₂×D₄	—	53	16	no	—
864	C₂×D₄	—	53	8	no	—
865	C₂×D₄	—	53	8	no	—
866	C₂×D₄	—	53	4	no	—
867	C₂×D₄	—	53	4	no	—
868	C₂×D₄	—	53	2	no	—
869	C₂×D₄	—	53	4	no	—
870	C₂×D₄	—	53	16	no	—
871	C₂×D₄	—	53	8	no	—
872	C₂×D₄	—	53	8	no	—
873	C₂×D₄	—	106	8	no	—
874	C₂×D₄	—	212	8	no	—
875	C₂×D₄	—	212	8	no	—
876	C₂×D₄	—	212	8	no	—
877	C₂×D₄	—	212	4	no	—
878	C₂×D₄	—	212	8	no	—
879	C₂×D₄	—	212	32	no	—
880	C₂×D₄	—	212	16	no	—
881	C₂×D₄	C₂³×D₅₃	1	8	yes	—
882	C₂×D₄	C₂³×D₅₃	1	4	yes	—
883	C₂×D₄	C₂³×D₅₃	1	2	yes	—
884	C₂×D₄	C₂³×D₅₃	1	4	yes	—
885	C₂²×C₄	—	2	4	no	—
886	C₂²×C₄	—	4	4	no	—
887	C₂²×C₄	—	53	4	no	—
888	C₂²×C₄	—	53	8	no	—
889	C₂²×C₄	—	53	8	no	—
890	C₂²×C₄	—	53	4	no	—
891	C₂²×C₄	—	53	8	no	—
892	C₂²×C₄	—	53	16	no	—
893	C₂²×C₄	—	53	8	no	—
894	C₂²×C₄	—	53	8	no	—
895	C₂²×C₄	—	212	4	no	—
896	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
897	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
898	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
899	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
900	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
901	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
902	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
903	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
904	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
905	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
906	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
907	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
908	C₄⋊C₄	—	53	8	no	—
909	C₄⋊C₄	—	53	4	no	—
910	C₄⋊C₄	—	53	16	no	—
911	C₄⋊C₄	—	53	16	no	—
912	C₄⋊C₄	—	53	8	no	—
913	C₄⋊C₄	—	53	8	no	—
914	C₄⋊C₄	—	53	4	no	—
915	C₄⋊C₄	—	53	4	no	—
916	C₄⋊C₄	—	53	16	no	—
917	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
918	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
919	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
920	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
921	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
922	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
923	C₂²⋊C₄	—	53	4	no	—
924	C₂²⋊C₄	—	53	8	no	—
925	C₂²⋊C₄	—	53	16	no	—
926	C₂²⋊C₄	—	53	16	no	—
927	C₂²⋊C₄	—	53	16	no	—
928	C₂²⋊C₄	—	53	16	no	—
929	C₂²⋊C₄	—	53	16	no	—
930	C₂²⋊C₄	—	53	8	no	—
931	C₂²⋊C₄	—	53	16	no	—
932	C₂²⋊C₄	—	53	16	no	—
933	C₂²⋊C₄	—	53	16	no	—
934	C₂²⋊C₄	—	53	16	no	—
935	C₂²⋊C₄	—	53	8	no	—
936	C₂²⋊C₄	—	53	8	no	—
937	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
938	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
939	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
940	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
941	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
942	C₄²	—	53	8	no	—
943	C₄²	—	53	4	no	—
944	C₄²	—	53	16	no	—
945	C₄²	C₂³×D₅₃	1	1	yes	characteristic
946	C₄²	C₂³×D₅₃	1	1	yes	characteristic
947	C₄²	C₂³×D₅₃	1	2	yes	—
948	C₄²	C₂³×D₅₃	1	1	yes	characteristic
949	C₄²	C₂³×D₅₃	1	1	yes	characteristic
950	C₄²	C₂³×D₅₃	1	2	yes	—
951	C₄²	C₂³×D₅₃	1	2	yes	—
952	C₄²	C₂³×D₅₃	1	2	yes	—
953	C₄²	C₂³×D₅₃	1	2	yes	—
954	C₄²	C₂³×D₅₃	1	2	yes	—
955	C₄²	C₂³×D₅₃	1	8	yes	—
956	C₄²	C₂³×D₅₃	1	4	yes	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	4	no	—
959	C₂³	—	53	8	no	—
960	C₂³	—	53	4	no	—
961	C₂³	—	106	8	no	—
962	C₂³	—	106	16	no	—
963	C₂³	—	424	16	no	—
964	C₂³	—	212	8	no	—
965	C₂³	—	212	16	no	—
966	C₂³	—	212	8	no	—
967	C₂³	—	212	8	no	—
968	C₂³	—	212	8	no	—
969	C₂³	C₂⁴×D₅₃	1	4	yes	—
970	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
971	C₂³	C₂⁴×D₅₃	1	2	yes	—
972	Q₈	—	2	4	no	—
973	Q₈	—	4	4	no	—
974	Q₈	—	106	8	no	—
975	Q₈	—	106	8	no	—
976	Q₈	—	106	4	no	—
977	Q₈	—	212	8	no	—
978	Q₈	—	212	8	no	—
979	Q₈	—	212	4	no	—
980	D₄	—	2	8	no	—
981	D₄	—	2	16	no	—
982	D₄	—	2	4	no	—
983	D₄	—	4	4	no	—
984	D₄	—	106	8	no	—
985	D₄	—	106	16	no	—
986	D₄	—	106	8	no	—
987	D₄	—	106	8	no	—
988	D₄	—	106	4	no	—
989	D₄	—	212	16	no	—
990	D₄	—	212	8	no	—
991	D₄	—	212	8	no	—
992	D₄	—	212	4	no	—
993	D₄	—	212	16	no	—
994	D₄	—	212	8	no	—
995	D₄	—	212	8	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	4	no	—
998	C₂×C₄	—	2	4	no	—
999	C₂×C₄	—	2	4	no	—
1000	C₂×C₄	—	2	4	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	4	2	no	—
1003	C₂×C₄	—	4	2	no	—
1004	C₂×C₄	—	4	2	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	8	no	—
1007	C₂×C₄	—	53	8	no	—
1008	C₂×C₄	—	53	8	no	—
1009	C₂×C₄	—	53	4	no	—
1010	C₂×C₄	—	106	8	no	—
1011	C₂×C₄	—	106	8	no	—
1012	C₂×C₄	—	212	16	no	—
1013	C₂×C₄	—	212	8	no	—
1014	C₂×C₄	—	212	8	no	—
1015	C₂×C₄	—	212	8	no	—
1016	C₂×C₄	—	212	8	no	—
1017	C₂×C₄	—	212	8	no	—
1018	C₂×C₄	#13133263	1	4	yes	—
1019	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1020	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1021	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1022	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1023	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1024	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1025	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1026	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1027	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1028	C₂²	—	2	8	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	8	no	—
1034	C₂²	—	848	8	no	—
1035	C₂²	—	106	4	no	—
1036	C₂²	—	106	8	no	—
1037	C₂²	—	106	8	no	—
1038	C₂²	—	106	16	no	—
1039	C₂²	—	424	8	no	—
1040	C₂²	—	424	16	no	—
1041	C₂²	C₂×#13133263	1	2	yes	—
1042	C₂²	#16811459	1	4	yes	—
1043	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1044	C₄	—	2	2	no	—
1045	C₄	—	2	4	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	8	no	—
1051	C₄	—	106	4	no	—
1052	C₄	—	106	8	no	—
1053	C₄	—	106	8	no	—
1054	C₄	C₂×#13133263	1	2	yes	—
1055	C₄	C₂×#13133263	1	2	yes	—
1056	C₂	—	2	2	no	—
1057	C₂	—	2	4	no	—
1058	C₂	—	4	4	no	—
1059	C₂	—	212	4	no	—
1060	C₂	—	212	8	no	—
1061	C₂	C₂²×#13133263	1	1	yes	characteristic
1062	C₂	C₂×#16811459	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3444	C₂
hypercenter	#3444	D₅₃
hypocenter	C₅₃	#62824
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. #20289285	C₂	semidirect
2. #20289280	C₂	semidirect
3. #20289238	C₂	semidirect
4. #20289231	C₂	semidirect
5. #20289067	C₂	semidirect
6. #20288676	C₂	semidirect
7. #20288664	C₂	semidirect
8. #20288613	C₂	semidirect
9. #20288611	C₂	semidirect
10. #20288508	C₂	semidirect
11. #20288502	C₂	semidirect
12. #20288398	C₂	semidirect
13. #20288362	C₂	semidirect
14. #20288348	C₂	semidirect
15. #20288011	C₂	semidirect
16. C₂²×#13133205	C₂	semidirect
17. C₅₃×#3444	C₂	semidirect
18. C₂×#13133264	C₂²	semidirect
19. C₂×#13133263	C₂²	semidirect
20. C₂³×Dic₁₀₆	C₂²	semidirect
22. #16811377	C₂²	semidirect
23. #16811371	C₂²	semidirect
24. #16811367	C₂²	semidirect
25. #16811365	C₂²	semidirect
26. #16811358	C₂²	semidirect
27. #16811356	C₂²	semidirect
28. #16811346	C₂²	semidirect
29. #16811345	C₂²	semidirect
30. #16811336	C₂²	semidirect
31. #16811302	C₂²	semidirect
32. #16811300	C₂²	semidirect
33. #16811297	C₂²	semidirect
34. #16811297	C₂²	semidirect
35. #16811296	C₂²	semidirect
36. D₄×Dic₁₀₆	C₂²	semidirect
37. #16811286	C₂²	semidirect
38. #16811285	C₂²	semidirect
39. #16811282	C₂²	semidirect
40. #16811282	C₂²	semidirect
41. #16811279	C₂²	semidirect
42. #16811269	C₂²	semidirect
43. #16811269	C₂²	semidirect
44. #16811268	C₂²	semidirect
45. #16811268	C₂²	semidirect
46. #16811265	C₂²	semidirect
47. #16811264	C₂²	semidirect
48. #16811262	C₂²	semidirect
49. #16811261	C₂²	semidirect
50. D₄×D₂₁₂	C₂²	semidirect
51. #16811257	C₂²	semidirect
52. #16811248	C₂²	semidirect
53. #16811247	C₂²	semidirect
54. #16811245	C₂²	semidirect
55. #16811244	C₂²	semidirect
56. #16811239	C₂²	semidirect
57. #16811213	C₂²	semidirect
58. #16811212	C₂²	semidirect
59. #16811210	C₂²	semidirect
60. #16811206	C₂²	semidirect
61. #16811206	C₂²	semidirect
62. #16811199	C₂²	semidirect
63. #16811199	C₂²	semidirect
64. #16811198	C₂²	semidirect
65. #16811195	C₂²	semidirect
66. #16811194	C₂²	semidirect
68. #16811192	C₂²	semidirect
70. #16811186	C₂²	semidirect
71. #16811184	C₂²	semidirect
72. #16811181	C₂²	semidirect
73. #16811180	C₂²	semidirect
74. #16811180	C₂²	semidirect
75. #16811173	C₂²	semidirect
76. #16811173	C₂²	semidirect
77. #16811173	C₂²	semidirect
78. #16811172	C₂²	semidirect
79. #16811158	C₂²	semidirect
80. #16811157	C₂²	semidirect
81. #16811157	C₂²	semidirect
82. #16811157	C₂²	semidirect
83. #16811157	C₂²	semidirect
84. C₂×#13133205	C₂²	semidirect
85. C₂×#13133205	C₂²	semidirect
86. C₂×#13133205	C₂²	semidirect
87. C₂×#13133205	C₂²	semidirect
88. C₂×#13133205	C₂²	semidirect
89. C₂×#13133205	C₂²	semidirect
90. C₂×#13133205	C₂²	semidirect
91. C₂×#13133205	C₂²	semidirect
92. #124×D₅₃	C₂²	semidirect
93. #16811134	C₂²	semidirect
94. #16811134	C₂²	semidirect
95. #16811129	C₂²	semidirect
96. #120×D₅₃	C₂²	semidirect
97. #16811100	C₂²	semidirect
98. #16811097	C₂²	semidirect
99. #16811095	C₂²	semidirect
100. C₄×#11719945	C₂²	semidirect
101. C₄×#11719945	C₂²	semidirect
102. C₂²×#11719921	C₂²	semidirect
103. C₅₃×#533	C₂²	semidirect
104. C₅₃×#533	C₂²	semidirect
105. C₅₃×#532	C₂²	semidirect
106. C₅₃×#532	C₂²	semidirect
107. C₅₃×#529	C₂²	semidirect
108. C₅₃×#529	C₂²	semidirect
109. C₅₃×#529	C₂²	semidirect
110. C₅₃×#525	C₂²	semidirect
111. C₅₃×#525	C₂²	semidirect
112. C₄×#41×C₅₃	C₂²	semidirect
113. C₄×#41×C₅₃	C₂²	semidirect
114. C₂²×C₄²×C₅₃	C₂²	semidirect
122. C₂×#11719945	C₂³	semidirect
124. C₂×#11719947	C₂³	semidirect
130. C₂²×Dic₁₀₆	C₂³	semidirect
131. C₂×Q₈×D₅₃	C₂³	semidirect
142. #13133217	C₂³	semidirect
143. #13133217	C₂³	semidirect
144. #13133217	C₂³	semidirect
145. #13133216	C₂³	semidirect
146. #13133215	C₂³	semidirect
148. #13133214	C₂³	semidirect
150. #13133212	C₂³	semidirect
151. #13133212	C₂³	semidirect
152. #13133212	C₂³	semidirect
153. #13133211	C₂³	semidirect
154. #13133211	C₂³	semidirect
155. #13133209	C₂³	semidirect
156. #13133209	C₂³	semidirect
158. #13133206	C₂³	semidirect
170. #13133205	C₂³	semidirect
171. #13133205	C₂³	semidirect
172. #13133205	C₂³	semidirect
173. #13133205	C₂³	semidirect
174. #13133204	C₂³	semidirect
175. #13133203	C₂³	semidirect
176. #13133203	C₂³	semidirect
177. #13133203	C₂³	semidirect
179. #13133202	C₂³	semidirect
180. #13133202	C₂³	semidirect
181. #13133202	C₂³	semidirect
183. #13133201	C₂³	semidirect
186. #13133200	C₂³	semidirect
187. #13133199	C₂³	semidirect
189. #13133197	C₂³	semidirect
190. #13133197	C₂³	semidirect
194. #13133196	C₂³	semidirect
195. #13133195	C₂³	semidirect
196. #13133195	C₂³	semidirect
197. #13133195	C₂³	semidirect
199. #13133194	C₂³	semidirect
200. #13133193	C₂³	semidirect
203. #13133192	C₂³	semidirect
208. #13133191	C₂³	semidirect
210. #13133190	C₂³	semidirect
212. #13133189	C₂³	semidirect
216. #13133187	C₂³	semidirect
220. #13133185	C₂³	semidirect
221. C₄×Dic₁₀₆	C₂³	semidirect
222. C₄×Dic₁₀₆	C₂³	semidirect
223. C₄×Dic₁₀₆	C₂³	semidirect
224. C₄×Dic₁₀₆	C₂³	semidirect
225. #13133182	C₂³	semidirect
227. C₄×D₂₁₂	C₂³	semidirect
228. C₄×D₂₁₂	C₂³	semidirect
229. C₄×D₂₁₂	C₂³	semidirect
230. C₄×D₂₁₂	C₂³	semidirect
233. #13133179	C₂³	semidirect
237. C₄×C₂²⋊D₅₃	C₂³	semidirect
239. #13133177	C₂³	semidirect
242. #13133175	C₂³	semidirect
243. #13133174	C₂³	semidirect
244. #13133174	C₂³	semidirect
245. #13133174	C₂³	semidirect
253. C₂×#11719921	C₂³	semidirect
256. C₂²⋊C₄×D₅₃	C₂³	semidirect
257. C₄²×D₅₃	C₂³	semidirect
262. C₄⋊Q₈×C₅₃	C₂³	semidirect
263. C₄⋊Q₈×C₅₃	C₂³	semidirect
264. #127×C₅₃	C₂³	semidirect
265. #126×C₅₃	C₂³	semidirect
266. #125×C₅₃	C₂³	semidirect
267. #125×C₅₃	C₂³	semidirect
268. #124×C₅₃	C₂³	semidirect
269. #124×C₅₃	C₂³	semidirect
279. C₄×Q₈×C₅₃	C₂³	semidirect
280. C₄×Q₈×C₅₃	C₂³	semidirect
281. C₄×Q₈×C₅₃	C₂³	semidirect
285. C₄×D₄×C₅₃	C₂³	semidirect
286. C₄×D₄×C₅₃	C₂³	semidirect
287. C₄×D₄×C₅₃	C₂³	semidirect
290. #117×C₅₃	C₂³	semidirect
291. #117×C₅₃	C₂³	semidirect
299. C₂×C₄²×C₅₃	C₂³	semidirect
540. #3444	D₅₃	semidirect
606. #533	C₂×D₅₃	semidirect
607. #533	C₂×D₅₃	semidirect
612. #532	C₂×D₅₃	semidirect
613. #532	C₂×D₅₃	semidirect
619. #529	C₂×D₅₃	semidirect
620. #529	C₂×D₅₃	semidirect
621. #529	C₂×D₅₃	semidirect
634. #525	C₂×D₅₃	semidirect
635. #525	C₂×D₅₃	semidirect
642. C₄×#41	C₂×D₅₃	semidirect
643. C₄×#41	C₂×D₅₃	semidirect
645. C₂²×C₄²	C₂×D₅₃	semidirect
646. C₅₃	#62824	semidirect
683. C₄⋊Q₈	C₂²×D₅₃	semidirect
684. C₄⋊Q₈	C₂²×D₅₃	semidirect
688. #127	C₂²×D₅₃	semidirect
694. #126	C₂²×D₅₃	semidirect
697. #125	C₂²×D₅₃	semidirect
698. #125	C₂²×D₅₃	semidirect
720. #124	C₂²×D₅₃	semidirect
721. #124	C₂²×D₅₃	semidirect
779. C₄×Q₈	C₂²×D₅₃	semidirect
780. C₄×Q₈	C₂²×D₅₃	semidirect
781. C₄×Q₈	C₂²×D₅₃	semidirect
799. C₄×D₄	C₂²×D₅₃	semidirect
800. C₄×D₄	C₂²×D₅₃	semidirect
801. C₄×D₄	C₂²×D₅₃	semidirect
811. #117	C₂²×D₅₃	semidirect
812. #117	C₂²×D₅₃	semidirect
831. 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
#20289285	2
#20289280	2
#20289238	2
#20289231	2
#20289067	2
#20288676	2
#20288664	2
#20288613	2
#20288611	2
#20288508	2
#20288502	2
#20288398	2
#20288362	2
#20288348	2
#20288011	2
C₂²×#13133205	2
C₅₃×#3444	2
#62824	53