Subgroups — #28292811

Order 13568.

7330 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289281	C₂	1	8	yes	maximal, complemented
2	#20289232	C₂	1	8	yes	maximal, complemented
3	#20289069	C₂	1	8	yes	maximal, complemented
4	#20288677	C₂	1	8	yes	maximal, complemented
5	#20288669	C₂	1	8	yes	maximal, complemented
6	#20288614	C₂	1	2	yes	maximal, complemented
7	#20288612	C₂	1	2	yes	maximal, complemented
8	#20288509	C₂	1	2	yes	maximal, complemented
9	#20288504	C₂	1	2	yes	maximal, complemented
10	#20288398	C₂	1	8	yes	maximal, complemented
11	#20288366	C₂	1	1	yes	maximal, characteristic, complemented
12	#20288348	C₂	1	2	yes	maximal, complemented
13	#20288007	C₂	1	2	yes	maximal, complemented
14	C₂²×#13133206	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13133265	C₂²	1	1	yes	characteristic, complemented
17	C₂×#13133263	C₂²	1	2	yes	complemented
18	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
19	#16811372	C₂²	1	8	yes	complemented
20	#16811369	C₂²	1	16	yes	complemented
21	#16811365	C₂²	1	8	yes	complemented
22	#16811358	C₂²	1	8	yes	complemented
23	#16811355	C₂²	1	8	yes	complemented
24	#16811347	C₂²	1	8	yes	complemented
25	#16811345	C₂²	1	8	yes	complemented
26	#16811339	C₂²	1	8	yes	complemented
27	#16811335	C₂²	1	8	yes	complemented
28	#16811302	C₂²	1	16	yes	complemented
29	#16811300	C₂²	1	16	yes	complemented
30	#16811300	C₂²	1	16	yes	complemented
31	#16811297	C₂²	1	16	yes	complemented
32	#16811296	C₂²	1	16	yes	complemented
33	Q₈×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
34	#16811284	C₂²	1	8	yes	complemented
35	#16811284	C₂²	1	8	yes	complemented
36	#16811283	C₂²	1	8	yes	complemented
37	#16811269	C₂²	1	8	yes	complemented
38	#16811268	C₂²	1	16	yes	complemented
39	#16811265	C₂²	1	16	yes	complemented
40	#16811264	C₂²	1	8	yes	complemented
41	#16811264	C₂²	1	8	yes	complemented
42	#16811262	C₂²	1	16	yes	complemented
43	#16811261	C₂²	1	16	yes	complemented
44	#16811261	C₂²	1	8	yes	complemented
45	D₄×D₂₁₂	C₂²	1	8	yes	complemented
46	#16811257	C₂²	1	8	yes	complemented
47	#16811248	C₂²	1	8	yes	complemented
48	#16811247	C₂²	1	16	yes	complemented
49	#16811246	C₂²	1	8	yes	complemented
50	#16811245	C₂²	1	8	yes	complemented
51	#16811243	C₂²	1	16	yes	complemented
52	#16811213	C₂²	1	8	yes	complemented
53	#16811213	C₂²	1	16	yes	complemented
54	#16811210	C₂²	1	8	yes	complemented
55	#16811207	C₂²	1	16	yes	complemented
56	#16811206	C₂²	1	16	yes	complemented
57	#16811198	C₂²	1	4	yes	complemented
58	#16811197	C₂²	1	4	yes	complemented
59	#16811197	C₂²	1	2	yes	complemented
60	#16811197	C₂²	1	4	yes	complemented
61	#16811192	C₂²	1	2	yes	—
62	#16811191	C₂²	1	4	yes	complemented
63	#16811187	C₂²	1	2	yes	—
64	#16811187	C₂²	1	4	yes	complemented
65	#16811184	C₂²	1	8	yes	complemented
66	#16811181	C₂²	1	8	yes	complemented
67	#16811176	C₂²	1	2	yes	complemented
68	#16811175	C₂²	1	4	yes	complemented
69	#16811174	C₂²	1	4	yes	complemented
70	#16811169	C₂²	1	2	yes	complemented
71	#16811169	C₂²	1	4	yes	complemented
72	#16811168	C₂²	1	4	yes	complemented
73	#16811160	C₂²	1	8	yes	complemented
74	#16811159	C₂²	1	4	yes	complemented
75	#16811159	C₂²	1	8	yes	complemented
76	#16811154	C₂²	1	4	yes	complemented
77	#16811153	C₂²	1	8	yes	complemented
78	#16811150	C₂²	1	8	yes	complemented
79	C₂×#13133206	C₂²	1	8	yes	complemented
80	C₂×#13133206	C₂²	1	4	yes	complemented
81	C₂×#13133206	C₂²	1	2	yes	complemented
82	C₂×#13133206	C₂²	1	2	yes	complemented
83	C₂×#13133206	C₂²	1	8	yes	complemented
84	C₂×#13133206	C₂²	1	4	yes	complemented
85	#124×D₅₃	C₂²	1	4	yes	complemented
86	#16811134	C₂²	1	2	yes	complemented
87	#16811134	C₂²	1	4	yes	complemented
88	#16811129	C₂²	1	8	yes	complemented
89	#120×D₅₃	C₂²	1	8	yes	complemented
90	#16811101	C₂²	1	1	yes	characteristic, complemented
91	#16811097	C₂²	1	2	yes	complemented
92	#16811095	C₂²	1	16	yes	complemented
93	#41×Dic₅₃	C₂²	1	2	yes	complemented
94	#16811091	C₂²	1	2	yes	complemented
95	C₄×#11719947	C₂²	1	8	yes	complemented
96	C₂²×#11719921	C₂²	1	4	yes	complemented
97	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
100	D₄×Q₈×C₅₃	C₂²	1	8	yes	complemented
101	C₅₃×#548	C₂²	1	8	yes	complemented
102	C₅₃×#536	C₂²	1	4	yes	complemented
103	C₅₃×#536	C₂²	1	2	yes	complemented
104	C₅₃×#525	C₂²	1	2	yes	complemented
105	C₅₃×#525	C₂²	1	4	yes	complemented
106	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×D₅₃	C₂³	1	2	yes	—
108	#13133265	—	4	4	no	—
109	#13133263	—	4	8	no	—
110	C₂×#11719949	C₂³	1	4	yes	—
111	C₂×#11719949	C₂³	1	4	yes	complemented
112	C₂×#11719945	C₂³	1	2	yes	—
113	C₂×#11719945	C₂³	1	4	yes	—
114	C₂×#11719945	C₂³	1	4	yes	—
115	C₂×#11719947	C₂³	1	8	yes	—
116	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
117	C₂²×D₂₁₂	—	4	4	no	—
118	C₂²×D₂₁₂	C₂³	1	2	yes	—
119	C₂²×D₂₁₂	C₂³	1	4	yes	—
120	C₂²×D₂₁₂	C₂³	1	8	yes	—
121	C₂²×D₂₁₂	C₂³	1	2	yes	—
122	C₂×D₄×D₅₃	C₂³	1	8	yes	—
123	C₂×D₄×D₅₃	C₂³	1	16	yes	—
124	C₂×D₄×D₅₃	C₂³	1	4	yes	—
125	C₂³×Dic₅₃	C₂³	1	2	yes	—
126	#13133216	C₂³	1	4	yes	complemented
127	#13133215	C₂³	1	8	yes	complemented
128	#13133215	C₂³	1	4	yes	complemented
129	#13133215	C₂³	1	2	yes	complemented
130	#13133214	C₂³	1	4	yes	—
131	#13133213	C₂³	1	4	yes	—
132	#13133213	C₂³	1	2	yes	complemented
133	#13133212	C₂³	1	16	yes	complemented
134	#13133212	C₂³	1	16	yes	complemented
135	#13133212	C₂³	1	16	yes	complemented
136	#13133212	C₂³	1	8	yes	complemented
137	#13133211	C₂³	1	16	yes	complemented
138	#13133210	C₂³	1	8	yes	complemented
139	#13133208	C₂³	1	4	yes	complemented
140	#13133207	C₂³	1	8	yes	complemented
141	#13133206	C₂³	1	4	yes	—
142	#13133206	C₂³	1	8	yes	—
143	#13133206	C₂³	1	8	yes	—
144	#13133206	C₂³	1	8	yes	—
145	#13133206	C₂³	1	8	yes	—
146	#13133206	C₂³	1	4	yes	—
147	#13133206	C₂³	1	4	yes	—
148	#13133206	C₂³	1	4	yes	—
149	#13133206	C₂³	1	4	yes	—
150	#13133206	C₂³	1	16	yes	—
151	#13133206	C₂³	1	8	yes	complemented
152	#13133206	C₂³	1	4	yes	complemented
153	#13133206	C₂³	1	16	yes	complemented
154	#13133206	C₂³	1	2	yes	complemented
155	#13133205	C₂³	1	4	yes	—
156	#13133205	C₂³	1	16	yes	complemented
157	#13133204	C₂³	1	2	yes	complemented
158	#13133203	C₂³	1	16	yes	complemented
159	#13133203	C₂³	1	16	yes	complemented
160	#13133203	C₂³	1	8	yes	complemented
161	#13133202	C₂³	1	16	yes	—
162	#13133202	C₂³	1	16	yes	complemented
163	#13133202	C₂³	1	16	yes	complemented
164	#13133202	C₂³	1	16	yes	complemented
165	#13133201	C₂³	1	8	yes	—
166	#13133201	C₂³	1	16	yes	complemented
167	#13133200	C₂³	1	8	yes	—
168	#13133200	C₂³	1	4	yes	—
169	#13133200	C₂³	1	16	yes	complemented
170	#13133199	C₂³	1	16	yes	complemented
171	#13133198	C₂³	1	8	yes	—
172	#13133197	C₂³	1	16	yes	complemented
173	#13133196	C₂³	1	4	yes	—
174	#13133196	C₂³	1	8	yes	—
175	#13133195	C₂³	1	16	yes	complemented
176	#13133195	C₂³	1	16	yes	complemented
177	#13133194	C₂³	1	8	yes	—
178	#13133194	C₂³	1	8	yes	—
179	#13133193	C₂³	1	8	yes	complemented
180	#13133193	C₂³	1	16	yes	complemented
181	#13133193	C₂³	1	16	yes	complemented
182	#13133192	C₂³	1	8	yes	—
183	#13133192	C₂³	1	16	yes	—
184	#13133192	C₂³	1	16	yes	complemented
185	#13133191	C₂³	1	8	yes	—
186	#13133191	C₂³	1	8	yes	—
187	#13133191	C₂³	1	4	yes	—
188	#13133191	C₂³	1	16	yes	complemented
189	#13133190	C₂³	1	16	yes	—
190	#13133190	C₂³	1	16	yes	complemented
191	#13133189	C₂³	1	8	yes	—
192	#13133189	C₂³	1	8	yes	—
193	#13133189	C₂³	1	16	yes	complemented
194	#13133187	C₂³	1	16	yes	—
195	#13133187	C₂³	1	8	yes	—
196	#13133187	C₂³	1	16	yes	—
197	#13133187	C₂³	1	16	yes	complemented
198	#13133186	C₂³	1	4	yes	—
199	#13133185	C₂³	1	16	yes	—
200	#13133185	C₂³	1	8	yes	—
201	#13133185	C₂³	1	16	yes	complemented
202	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
203	Q₈×Dic₅₃	C₂³	1	8	yes	complemented
204	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
205	#13133182	C₂³	1	4	yes	complemented
206	#13133182	C₂³	1	8	yes	complemented
207	C₄×D₂₁₂	C₂³	1	8	yes	—
208	C₄×D₂₁₂	C₂³	1	16	yes	complemented
209	D₄×Dic₅₃	C₂³	1	8	yes	—
210	D₄×Dic₅₃	C₂³	1	8	yes	—
211	D₄×Dic₅₃	C₂³	1	4	yes	complemented
212	#13133179	C₂³	1	8	yes	—
213	#13133179	C₂³	1	4	yes	complemented
214	#13133179	C₂³	1	16	yes	complemented
215	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
216	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	—
217	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
218	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
219	#13133177	C₂³	1	8	yes	—
220	#13133177	C₂³	1	8	yes	—
221	#13133177	C₂³	1	16	yes	complemented
222	#13133177	C₂³	1	8	yes	complemented
223	#13133176	C₂³	1	4	yes	—
224	#13133176	C₂³	1	2	yes	—
225	#13133176	C₂³	1	4	yes	complemented
226	#13133175	C₂³	1	16	yes	complemented
227	#13133175	C₂³	1	8	yes	complemented
228	#13133174	C₂³	1	16	yes	complemented
229	#13133174	C₂³	1	4	yes	complemented
230	#13133173	C₂³	1	8	yes	—
231	#13133173	C₂³	1	8	yes	complemented
232	C₂×#11719921	C₂³	1	8	yes	—
233	C₂×#11719921	C₂³	1	16	yes	—
234	C₂×#11719921	C₂³	1	8	yes	—
235	C₂×#11719921	C₂³	1	8	yes	—
236	C₂×#11719921	C₂³	1	8	yes	—
237	C₂×#11719921	C₂³	1	16	yes	complemented
238	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
239	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
240	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
241	C₂×C₄×Dic₅₃	C₂³	1	4	yes	—
242	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
243	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
244	C₂×C₄×Dic₅₃	C₂³	1	4	yes	—
245	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
246	C₄²×D₅₃	C₂³	1	4	yes	complemented
247	2₋¹⁺⁴×C₅₃	—	4	4	no	—
248	C₂×#41×C₅₃	C₂³	1	2	yes	—
249	C₂×#41×C₅₃	C₂³	1	4	yes	—
250	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
251	C₂²×Q₈×C₅₃	—	4	4	no	—
252	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
253	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
254	C₂²×Q₈×C₅₃	C₂³	1	8	yes	—
255	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
256	C₂²×Q₈×C₅₃	C₂³	1	4	yes	complemented
257	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
259	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
260	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
261	#124×C₅₃	C₂³	1	8	yes	complemented
262	#124×C₅₃	C₂³	1	4	yes	complemented
263	#123×C₅₃	C₂³	1	8	yes	—
264	#123×C₅₃	C₂³	1	4	yes	—
265	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
266	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
267	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
268	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
269	#121×C₅₃	C₂³	1	4	yes	—
270	#121×C₅₃	C₂³	1	8	yes	—
271	#120×C₅₃	C₂³	1	4	yes	—
272	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
273	C₄×D₄×C₅₃	C₂³	1	16	yes	—
274	C₄×D₄×C₅₃	C₂³	1	8	yes	—
275	#117×C₅₃	C₂³	1	4	yes	—
276	#117×C₅₃	C₂³	1	2	yes	—
277	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
278	C₂³×D₅₃	—	4	4	no	—
279	C₂³×D₅₃	—	4	8	no	—
280	C₂³×D₅₃	C₂⁴	1	4	yes	—
281	C₂³×D₅₃	C₂⁴	1	8	yes	—
282	C₂³×D₅₃	C₂⁴	1	8	yes	—
283	#41×C₅₃	—	2	8	no	—
284	#41×C₅₃	—	4	8	no	—
285	#41×C₅₃	—	4	8	no	—
286	C₂×Q₈×C₅₃	—	2	4	no	—
287	C₂×Q₈×C₅₃	—	2	4	no	—
288	C₂×Q₈×C₅₃	—	4	4	no	—
289	C₂×Q₈×C₅₃	—	4	16	no	—
290	C₂×Q₈×C₅₃	—	4	8	no	—
291	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
292	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
294	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
295	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
296	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
297	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
298	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
299	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₅₃	—	2	4	no	—
301	C₂²×C₄×C₅₃	—	4	4	no	—
302	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
308	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
309	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
310	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
311	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
312	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
313	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
314	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
315	C₂²×Dic₅₃	—	4	4	no	—
316	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
317	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
318	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
319	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
320	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
321	#11719949	—	4	8	no	—
322	#11719949	—	4	8	no	—
323	Q₈×D₅₃	—	4	8	no	—
324	#11719947	—	4	16	no	—
325	D₄×D₅₃	—	4	8	no	—
326	D₄×D₅₃	—	4	32	no	—
327	D₄×D₅₃	—	4	16	no	—
328	#11719945	—	2	8	no	—
329	#11719945	—	4	8	no	—
330	#11719945	—	4	8	no	—
331	C₂×D₂₁₂	—	2	8	no	—
332	C₂×D₂₁₂	—	4	16	no	—
333	C₂×D₂₁₂	—	4	8	no	—
334	C₂×D₂₁₂	—	4	4	no	—
335	C₂×D₂₁₂	C₂⁴	1	4	yes	—
336	C₂×D₂₁₂	C₂⁴	1	2	yes	—
337	C₂×D₂₁₂	C₂⁴	1	4	yes	—
338	C₂×D₂₁₂	C₂⁴	1	16	yes	—
339	C₂×D₂₁₂	C₂⁴	1	8	yes	—
340	C₂×D₂₁₂	C₂⁴	1	8	yes	—
341	C₂×D₂₁₂	C₂⁴	1	4	yes	—
342	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
343	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
344	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
345	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
346	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
347	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
348	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
349	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
350	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
351	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
352	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
353	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
354	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
355	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
356	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
357	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
358	C₄²×C₅₃	C₂⁴	1	4	yes	—
359	C₄²×C₅₃	C₂⁴	1	8	yes	—
360	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
361	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
362	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
363	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
364	#11719921	C₂⁴	1	16	yes	—
365	#11719921	C₂⁴	1	16	yes	—
366	#11719921	C₂⁴	1	16	yes	—
367	#11719921	C₂⁴	1	16	yes	—
368	#11719921	C₂⁴	1	16	yes	—
369	#11719921	C₂⁴	1	16	yes	—
370	#11719921	C₂⁴	1	16	yes	—
371	#11719921	C₂⁴	1	8	yes	—
372	#11719921	C₂⁴	1	16	yes	—
373	#11719921	C₂⁴	1	8	yes	—
374	#11719921	C₂⁴	1	8	yes	—
375	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
376	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
377	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
378	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
379	#11719919	C₂⁴	1	8	yes	—
380	#11719919	C₂⁴	1	8	yes	—
381	#11719919	C₂⁴	1	8	yes	—
382	#11719919	C₂⁴	1	8	yes	—
383	#11719919	C₂⁴	1	8	yes	—
384	#11719919	C₂⁴	1	16	yes	—
385	C₄×Dic₅₃	C₂⁴	1	2	yes	—
386	C₄×Dic₅₃	C₂⁴	1	8	yes	—
387	C₄×Dic₅₃	C₂⁴	1	2	yes	—
388	C₄×Dic₅₃	C₂⁴	1	2	yes	—
389	C₄×Dic₅₃	C₂⁴	1	4	yes	—
390	C₄×Dic₅₃	C₂⁴	1	4	yes	—
391	C₄×Dic₅₃	C₂⁴	1	2	yes	—
392	C₄×Dic₅₃	C₂⁴	1	8	yes	—
393	C₄×Dic₅₃	C₂⁴	1	4	yes	—
394	C₄×Dic₅₃	C₂⁴	1	8	yes	—
395	C₂³×C₅₃	—	2	2	no	—
396	C₂³×C₅₃	—	2	4	no	—
397	C₂³×C₅₃	C₂⁵	1	4	yes	—
398	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
399	C₂³×C₅₃	C₂⁵	1	2	yes	—
400	C₂²×D₅₃	—	2	8	no	—
401	C₂²×D₅₃	—	2	16	no	—
402	C₂²×D₅₃	—	4	8	no	—
403	C₂²×D₅₃	—	4	8	no	—
404	C₂²×D₅₃	—	4	8	no	—
405	C₂²×D₅₃	—	4	8	no	—
406	C₂²×D₅₃	—	4	16	no	—
407	C₂²×D₅₃	—	8	16	no	—
408	C₂²×D₅₃	C₂⁵	1	4	yes	—
409	C₂²×D₅₃	C₂⁵	1	8	yes	—
410	Q₈×C₅₃	—	2	8	no	—
411	Q₈×C₅₃	—	2	4	no	—
412	Q₈×C₅₃	—	2	8	no	—
413	Q₈×C₅₃	—	4	8	no	—
414	Q₈×C₅₃	—	4	4	no	—
415	D₄×C₅₃	—	2	8	no	—
416	D₄×C₅₃	—	2	16	no	—
417	D₄×C₅₃	—	2	4	no	—
418	D₄×C₅₃	—	4	4	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	4	no	—
421	C₂×C₄×C₅₃	—	2	4	no	—
422	C₂×C₄×C₅₃	—	2	8	no	—
423	C₂×C₄×C₅₃	—	2	8	no	—
424	C₂×C₄×C₅₃	—	4	8	no	—
425	C₂×C₄×C₅₃	—	4	8	no	—
426	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
427	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
428	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
429	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
430	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
431	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
432	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
433	C₂²⋊D₅₃	—	2	8	no	—
434	C₂²⋊D₅₃	—	2	16	no	—
435	C₂²⋊D₅₃	—	4	8	no	—
436	C₂²⋊D₅₃	—	4	16	no	—
437	C₂²⋊D₅₃	—	4	8	no	—
438	C₂×Dic₅₃	—	2	8	no	—
439	C₂×Dic₅₃	—	4	8	no	—
440	C₂×Dic₅₃	—	4	2	no	—
441	C₂×Dic₅₃	—	4	4	no	—
442	C₂×Dic₅₃	—	4	2	no	—
443	C₂×Dic₅₃	C₂⁵	1	4	yes	—
444	C₂×Dic₅₃	C₂⁵	1	4	yes	—
445	C₂×Dic₅₃	C₂⁵	1	8	yes	—
446	C₂×Dic₅₃	C₂⁵	1	4	yes	—
447	D₂₁₂	—	2	8	no	—
448	D₂₁₂	—	2	8	no	—
449	D₂₁₂	—	2	4	no	—
450	D₂₁₂	—	4	8	no	—
451	D₂₁₂	—	4	8	no	—
452	D₂₁₂	—	4	4	no	—
453	D₂₁₂	—	4	16	no	—
454	C₄×D₅₃	—	2	8	no	—
455	C₄×D₅₃	—	4	8	no	—
456	C₄×D₅₃	—	4	8	no	—
457	C₄×D₅₃	—	4	16	no	—
458	C₄×D₅₃	—	4	8	no	—
459	Dic₁₀₆	—	2	4	no	—
460	Dic₁₀₆	—	4	4	no	—
461	Dic₁₀₆	—	4	8	no	—
462	#62824	—	53	1	no	maximal, Sylow
463	C₂²×C₅₃	—	2	8	no	—
464	C₂²×C₅₃	—	2	2	no	—
465	C₂²×C₅₃	—	2	2	no	—
466	C₂²×C₅₃	—	2	2	no	—
467	C₂²×C₅₃	—	2	4	no	—
468	C₂²×C₅₃	—	2	8	no	—
469	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
470	C₂²×C₅₃	#585	1	4	yes	—
471	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
472	C₂×D₅₃	—	2	4	no	—
473	C₂×D₅₃	—	2	8	no	—
474	C₂×D₅₃	—	2	8	no	—
475	C₂×D₅₃	—	2	16	no	—
476	C₂×D₅₃	—	8	8	no	—
477	C₂×D₅₃	—	8	16	no	—
478	C₂×D₅₃	—	16	8	no	—
479	C₄×C₅₃	—	2	4	no	—
480	C₄×C₅₃	—	2	4	no	—
481	C₄×C₅₃	—	2	2	no	—
482	C₄×C₅₃	—	2	4	no	—
483	C₄×C₅₃	—	2	8	no	—
484	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
485	Dic₅₃	—	2	4	no	—
486	Dic₅₃	—	2	4	no	—
487	Dic₅₃	—	2	8	no	—
488	Dic₅₃	—	2	4	no	—
489	#3561	—	53	8	no	—
490	#3558	—	53	8	no	—
491	#3545	—	53	8	no	—
492	#3514	—	53	8	no	—
493	#3514	—	53	8	no	—
494	#3510	—	53	2	no	—
495	#3510	—	53	2	no	—
496	#3500	—	53	2	no	—
497	#3500	—	53	2	no	—
498	#3490	—	53	8	no	—
499	#3486	—	53	1	no	—
500	#3486	D₅₃	1	1	yes	characteristic, complemented
501	#3484	—	53	2	no	—
502	#3444	—	53	2	no	—
503	C₂²×#124	—	53	1	no	—
504	C₂×C₅₃	—	2	2	no	—
505	C₂×C₅₃	—	2	4	no	—
506	C₂×C₅₃	—	4	4	no	—
507	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂×C₅₃	C₂×#585	1	2	yes	—
509	D₅₃	—	4	8	no	—
510	D₅₃	—	4	4	no	—
511	C₂×2₋¹⁺⁴	—	53	1	no	—
512	C₂×2₋¹⁺⁴	C₂×D₅₃	1	1	yes	characteristic, complemented
513	C₂×H(5,𝔽₂)	—	53	2	no	—
514	C₂³×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
515	C₂³×D₄	—	53	1	no	—
516	#563	—	53	8	no	—
517	#562	—	53	16	no	—
518	H(3,𝔽₄)	—	53	8	no	—
519	#559	—	53	8	no	—
520	#559	—	53	8	no	—
521	#556	—	53	8	no	—
522	#556	—	53	8	no	—
523	#555	—	53	8	no	—
524	#555	—	53	8	no	—
525	#551	—	53	16	no	—
526	#551	—	53	16	no	—
527	#551	—	53	16	no	—
528	#551	—	53	16	no	—
529	#551	—	53	16	no	—
530	D₄×Q₈	—	53	8	no	—
531	D₄×Q₈	C₂×D₅₃	1	8	yes	complemented
532	#548	—	53	8	no	—
533	#548	—	53	8	no	—
534	#548	—	53	8	no	—
535	#548	C₂×D₅₃	1	8	yes	complemented
536	#546	—	53	16	no	—
537	#546	—	53	8	no	—
538	#546	—	53	16	no	—
539	#546	—	53	8	no	—
540	#546	—	53	8	no	—
541	#546	—	53	16	no	—
542	#546	—	53	16	no	—
543	#546	—	53	8	no	—
544	D₄²	—	53	8	no	—
545	D₄²	—	53	8	no	—
546	#543	—	53	8	no	—
547	#542	—	53	16	no	—
548	#542	—	53	8	no	—
549	#542	—	53	16	no	—
550	#542	—	53	8	no	—
551	#538	—	53	16	no	—
552	#538	—	53	8	no	—
553	#538	—	53	16	no	—
554	#538	—	53	8	no	—
555	#538	—	53	16	no	—
556	#536	—	53	2	no	—
557	#536	—	53	4	no	—
558	#536	—	53	4	no	—
559	#536	—	53	4	no	—
560	#536	C₂×D₅₃	1	2	yes	complemented
561	#536	C₂×D₅₃	1	4	yes	complemented
562	#535	—	53	2	no	—
563	#535	—	53	4	no	—
564	#535	—	53	4	no	—
565	#535	—	53	2	no	—
566	#534	—	53	8	no	—
567	#534	—	53	8	no	—
568	#533	—	53	4	no	—
569	#533	—	53	2	no	—
570	#532	—	53	2	no	—
571	#532	—	53	4	no	—
572	#532	—	53	4	no	—
573	#532	—	53	4	no	—
574	#529	—	53	8	no	—
575	#529	—	53	4	no	—
576	#529	—	53	8	no	—
577	#529	—	53	4	no	—
578	#529	—	53	8	no	—
579	#529	—	53	8	no	—
580	C₂×#124	—	53	2	no	—
581	C₂×#124	—	53	2	no	—
582	C₂×#124	—	53	8	no	—
583	C₂×#124	—	53	4	no	—
584	C₂×#124	—	53	8	no	—
585	C₂×#124	—	53	4	no	—
586	C₂×#124	—	53	4	no	—
587	#525	—	53	2	no	—
588	#525	—	53	4	no	—
589	#525	—	53	8	no	—
590	#525	C₂×D₅₃	1	2	yes	complemented
591	#525	C₂×D₅₃	1	4	yes	complemented
592	C₂×#120	—	53	8	no	—
593	#519	—	53	1	no	—
594	#519	C₂×D₅₃	1	1	yes	characteristic, complemented
595	#518	—	53	16	no	—
596	#518	—	53	2	no	—
597	C₄×#41	—	53	2	no	—
598	C₄×#41	—	53	8	no	—
599	C₄×#41	—	53	2	no	—
600	C₂²×C₂²⋊C₄	—	53	4	no	—
601	C₂²×C₄²	—	53	1	no	—
602	C₅₃	#62824	1	1	yes	characteristic, complemented, Sylow
603	C₂⁵	—	53	2	no	—
604	2₋¹⁺⁴	—	4	4	no	—
605	2₋¹⁺⁴	—	212	4	no	—
606	H(5,𝔽₂)	—	212	8	no	—
607	C₂×#41	—	53	4	no	—
608	C₂×#41	—	53	4	no	—
609	C₂×#41	—	53	8	no	—
610	C₂×#41	—	53	2	no	—
611	C₂×#41	—	53	4	no	—
612	C₂×#41	—	53	4	no	—
613	C₂×#41	C₂²×D₅₃	1	2	yes	—
614	C₂×#41	C₂²×D₅₃	1	4	yes	—
615	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
616	C₂²×Q₈	—	4	4	no	—
617	C₂²×Q₈	—	53	4	no	—
618	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
619	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
620	C₂²×Q₈	C₂²×D₅₃	1	2	yes	—
621	C₂²×Q₈	C₂²×D₅₃	1	8	yes	—
622	C₂²×Q₈	C₂²×D₅₃	1	4	yes	complemented
623	C₂²×D₄	—	53	16	no	—
624	C₂²×D₄	—	53	8	no	—
625	C₂²×D₄	—	53	4	no	—
626	C₂²×D₄	—	53	2	no	—
627	C₂²×D₄	—	53	2	no	—
628	C₂²×D₄	—	53	8	no	—
629	C₂²×D₄	—	53	4	no	—
630	C₂²×D₄	—	212	4	no	—
631	C₂³×C₄	—	53	2	no	—
632	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
633	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
634	C₄⋊Q₈	—	53	2	no	—
635	C₄⋊Q₈	—	53	4	no	—
636	C₄⋊Q₈	—	53	8	no	—
637	C₄⋊Q₈	—	53	4	no	—
638	C₄⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
639	C₄⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
640	#127	—	53	2	no	—
641	#127	—	53	4	no	—
642	#127	—	53	4	no	—
643	#126	—	53	8	no	—
644	#126	—	53	16	no	—
645	#126	—	53	16	no	—
646	#126	—	53	16	no	—
647	#126	—	53	8	no	—
648	#126	—	53	16	no	—
649	#125	—	53	4	no	—
650	#125	—	53	8	no	—
651	#124	—	53	4	no	—
652	#124	—	53	4	no	—
653	#124	—	53	4	no	—
654	#124	—	53	4	no	—
655	#124	—	53	16	no	—
656	#124	—	53	8	no	—
657	#124	—	53	8	no	—
658	#124	—	53	8	no	—
659	#124	—	53	8	no	—
660	#124	—	53	2	no	—
661	#124	—	53	4	no	—
662	#124	—	53	4	no	—
663	#124	—	53	16	no	—
664	#124	—	53	8	no	—
665	#124	—	53	2	no	—
666	#124	—	53	16	no	—
667	#124	—	53	8	no	—
668	#124	—	53	16	no	—
669	#124	—	53	4	no	—
670	#124	—	53	16	no	—
671	#124	C₂²×D₅₃	1	4	yes	complemented
672	#124	C₂²×D₅₃	1	8	yes	complemented
673	#123	—	53	8	no	—
674	#123	—	53	4	no	—
675	#123	—	53	8	no	—
676	#123	—	53	16	no	—
677	#123	—	53	16	no	—
678	#123	—	53	16	no	—
679	#123	—	53	16	no	—
680	#123	—	53	16	no	—
681	#123	—	53	8	no	—
682	#123	—	53	16	no	—
683	#123	—	53	16	no	—
684	#123	C₂²×D₅₃	1	4	yes	—
685	#123	C₂²×D₅₃	1	8	yes	—
686	C₂²⋊Q₈	—	53	8	no	—
687	C₂²⋊Q₈	—	53	16	no	—
688	C₂²⋊Q₈	—	53	16	no	—
689	C₂²⋊Q₈	—	53	4	no	—
690	C₂²⋊Q₈	—	53	8	no	—
691	C₂²⋊Q₈	—	53	16	no	—
692	C₂²⋊Q₈	—	53	16	no	—
693	C₂²⋊Q₈	—	53	16	no	—
694	C₂²⋊Q₈	—	53	8	no	—
695	C₂²⋊Q₈	—	53	8	no	—
696	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
697	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	—
698	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
699	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
700	#121	—	53	8	no	—
701	#121	—	53	8	no	—
702	#121	—	53	16	no	—
703	#121	—	53	4	no	—
704	#121	—	53	8	no	—
705	#121	—	53	8	no	—
706	#121	—	53	16	no	—
707	#121	—	53	8	no	—
708	#121	—	53	16	no	—
709	#121	—	53	16	no	—
710	#121	—	53	16	no	—
711	#121	—	53	16	no	—
712	#121	C₂²×D₅₃	1	4	yes	—
713	#121	C₂²×D₅₃	1	8	yes	—
714	#120	—	53	4	no	—
715	#120	—	53	8	no	—
716	#120	—	53	16	no	—
717	#120	—	53	16	no	—
718	#120	—	53	8	no	—
719	#120	—	53	16	no	—
720	#120	—	53	16	no	—
721	#120	—	53	16	no	—
722	#120	C₂²×D₅₃	1	4	yes	—
723	C₄×Q₈	—	53	4	no	—
724	C₄×Q₈	—	53	8	no	—
725	C₄×Q₈	—	53	8	no	—
726	C₄×Q₈	—	53	4	no	—
727	C₄×Q₈	—	53	8	no	—
728	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
729	C₄×D₄	—	53	8	no	—
730	C₄×D₄	—	53	8	no	—
731	C₄×D₄	—	53	4	no	—
732	C₄×D₄	—	53	8	no	—
733	C₄×D₄	—	53	8	no	—
734	C₄×D₄	—	53	16	no	—
735	C₄×D₄	—	53	16	no	—
736	C₄×D₄	—	53	4	no	—
737	C₄×D₄	—	53	8	no	—
738	C₄×D₄	—	53	16	no	—
739	C₄×D₄	—	53	8	no	—
740	C₄×D₄	—	53	8	no	—
741	C₄×D₄	—	53	8	no	—
742	C₄×D₄	—	53	16	no	—
743	C₄×D₄	—	53	16	no	—
744	C₄×D₄	—	53	8	no	—
745	C₄×D₄	C₂²×D₅₃	1	8	yes	—
746	C₄×D₄	C₂²×D₅₃	1	16	yes	—
747	#117	—	53	2	no	—
748	#117	—	53	4	no	—
749	#117	—	53	4	no	—
750	#117	—	53	8	no	—
751	#117	—	53	16	no	—
752	#117	—	53	8	no	—
753	#117	—	53	8	no	—
754	#117	—	53	4	no	—
755	#117	—	53	16	no	—
756	#117	C₂²×D₅₃	1	2	yes	—
757	#117	C₂²×D₅₃	1	4	yes	—
758	C₂×C₂²⋊C₄	—	53	8	no	—
759	C₂×C₂²⋊C₄	—	53	8	no	—
760	C₂×C₂²⋊C₄	—	53	16	no	—
761	C₂×C₂²⋊C₄	—	53	8	no	—
762	C₂×C₂²⋊C₄	—	53	8	no	—
763	C₂×C₂²⋊C₄	—	53	16	no	—
764	C₂×C₂²⋊C₄	—	53	8	no	—
765	C₂×C₂²⋊C₄	—	53	16	no	—
766	C₂×C₂²⋊C₄	—	53	16	no	—
767	C₂×C₄²	—	53	4	no	—
768	C₂×C₄²	—	53	4	no	—
769	C₂×C₄²	—	53	2	no	—
770	C₂×C₄²	—	53	2	no	—
771	C₂×C₄²	—	53	4	no	—
772	C₂×C₄²	—	53	4	no	—
773	C₂⁴	—	53	4	no	—
774	C₂⁴	—	53	8	no	—
775	C₂⁴	—	53	8	no	—
776	C₂⁴	—	212	4	no	—
777	C₂⁴	—	212	8	no	—
778	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
779	#41	—	2	8	no	—
780	#41	—	4	8	no	—
781	#41	—	4	8	no	—
782	#41	—	106	8	no	—
783	#41	—	212	8	no	—
784	#41	—	212	8	no	—
785	#41	—	212	16	no	—
786	#41	—	212	8	no	—
787	#41	—	212	8	no	—
788	C₂×Q₈	—	2	4	no	—
789	C₂×Q₈	—	2	4	no	—
790	C₂×Q₈	—	4	4	no	—
791	C₂×Q₈	—	4	16	no	—
792	C₂×Q₈	—	4	8	no	—
793	C₂×Q₈	—	53	2	no	—
794	C₂×Q₈	—	53	8	no	—
795	C₂×Q₈	—	53	4	no	—
796	C₂×Q₈	—	212	8	no	—
797	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
798	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
799	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
800	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
801	C₂×Q₈	C₂³×D₅₃	1	8	yes	—
802	C₂×D₄	—	53	8	no	—
803	C₂×D₄	—	53	4	no	—
804	C₂×D₄	—	53	8	no	—
805	C₂×D₄	—	53	16	no	—
806	C₂×D₄	—	53	8	no	—
807	C₂×D₄	—	53	4	no	—
808	C₂×D₄	—	53	4	no	—
809	C₂×D₄	—	53	2	no	—
810	C₂×D₄	—	53	16	no	—
811	C₂×D₄	—	53	4	no	—
812	C₂×D₄	—	53	8	no	—
813	C₂×D₄	—	53	8	no	—
814	C₂×D₄	—	106	8	no	—
815	C₂×D₄	—	212	16	no	—
816	C₂×D₄	—	212	8	no	—
817	C₂×D₄	—	212	4	no	—
818	C₂×D₄	—	212	8	no	—
819	C₂×D₄	—	212	32	no	—
820	C₂×D₄	—	212	16	no	—
821	C₂×D₄	C₂³×D₅₃	1	4	yes	—
822	C₂×D₄	C₂³×D₅₃	1	2	yes	—
823	C₂×D₄	C₂³×D₅₃	1	8	yes	—
824	C₂×D₄	C₂³×D₅₃	1	4	yes	—
825	C₂²×C₄	—	2	4	no	—
826	C₂²×C₄	—	4	4	no	—
827	C₂²×C₄	—	53	4	no	—
828	C₂²×C₄	—	53	2	no	—
829	C₂²×C₄	—	53	4	no	—
830	C₂²×C₄	—	53	2	no	—
831	C₂²×C₄	—	53	8	no	—
832	C₂²×C₄	—	53	4	no	—
833	C₂²×C₄	—	53	8	no	—
834	C₂²×C₄	—	53	16	no	—
835	C₂²×C₄	—	53	8	no	—
836	C₂²×C₄	—	53	8	no	—
837	C₂²×C₄	—	212	4	no	—
838	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
839	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
840	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
841	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
842	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
843	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
844	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
845	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
846	C₄⋊C₄	—	53	8	no	—
847	C₄⋊C₄	—	53	8	no	—
848	C₄⋊C₄	—	53	4	no	—
849	C₄⋊C₄	—	53	16	no	—
850	C₄⋊C₄	—	53	8	no	—
851	C₄⋊C₄	—	53	8	no	—
852	C₄⋊C₄	—	53	8	no	—
853	C₄⋊C₄	—	53	8	no	—
854	C₄⋊C₄	—	53	8	no	—
855	C₄⋊C₄	—	53	8	no	—
856	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
857	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
858	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
859	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
860	C₂²⋊C₄	—	53	4	no	—
861	C₂²⋊C₄	—	53	8	no	—
862	C₂²⋊C₄	—	53	8	no	—
863	C₂²⋊C₄	—	53	8	no	—
864	C₂²⋊C₄	—	53	16	no	—
865	C₂²⋊C₄	—	53	16	no	—
866	C₂²⋊C₄	—	53	16	no	—
867	C₂²⋊C₄	—	53	16	no	—
868	C₂²⋊C₄	—	53	8	no	—
869	C₂²⋊C₄	—	53	16	no	—
870	C₂²⋊C₄	—	53	16	no	—
871	C₂²⋊C₄	—	53	16	no	—
872	C₂²⋊C₄	—	53	16	no	—
873	C₂²⋊C₄	—	53	8	no	—
874	C₂²⋊C₄	—	53	8	no	—
875	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
876	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
877	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
878	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
879	C₄²	—	53	2	no	—
880	C₄²	—	53	2	no	—
881	C₄²	—	53	2	no	—
882	C₄²	—	53	4	no	—
883	C₄²	—	53	4	no	—
884	C₄²	—	53	2	no	—
885	C₄²	—	53	8	no	—
886	C₄²	—	53	8	no	—
887	C₄²	—	53	4	no	—
888	C₄²	—	53	8	no	—
889	C₄²	C₂³×D₅₃	1	4	yes	—
890	C₄²	C₂³×D₅₃	1	8	yes	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	4	no	—
893	C₂³	—	53	8	no	—
894	C₂³	—	53	4	no	—
895	C₂³	—	106	8	no	—
896	C₂³	—	106	16	no	—
897	C₂³	—	424	16	no	—
898	C₂³	—	212	8	no	—
899	C₂³	—	212	16	no	—
900	C₂³	—	212	8	no	—
901	C₂³	—	212	8	no	—
902	C₂³	—	212	8	no	—
903	C₂³	C₂⁴×D₅₃	1	4	yes	—
904	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
905	C₂³	C₂⁴×D₅₃	1	2	yes	—
906	Q₈	—	2	8	no	—
907	Q₈	—	2	8	no	—
908	Q₈	—	2	4	no	—
909	Q₈	—	4	8	no	—
910	Q₈	—	4	4	no	—
911	Q₈	—	106	4	no	—
912	Q₈	—	212	4	no	—
913	Q₈	—	212	8	no	—
914	D₄	—	2	8	no	—
915	D₄	—	2	16	no	—
916	D₄	—	2	4	no	—
917	D₄	—	4	4	no	—
918	D₄	—	106	8	no	—
919	D₄	—	106	16	no	—
920	D₄	—	106	8	no	—
921	D₄	—	106	8	no	—
922	D₄	—	106	4	no	—
923	D₄	—	212	16	no	—
924	D₄	—	212	8	no	—
925	D₄	—	212	8	no	—
926	D₄	—	212	4	no	—
927	D₄	—	212	16	no	—
928	D₄	—	212	8	no	—
929	D₄	—	212	8	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	4	no	—
932	C₂×C₄	—	2	4	no	—
933	C₂×C₄	—	2	8	no	—
934	C₂×C₄	—	2	8	no	—
935	C₂×C₄	—	4	8	no	—
936	C₂×C₄	—	4	8	no	—
937	C₂×C₄	—	53	4	no	—
938	C₂×C₄	—	53	4	no	—
939	C₂×C₄	—	53	8	no	—
940	C₂×C₄	—	53	4	no	—
941	C₂×C₄	—	106	8	no	—
942	C₂×C₄	—	106	8	no	—
943	C₂×C₄	—	212	16	no	—
944	C₂×C₄	—	212	8	no	—
945	C₂×C₄	—	212	8	no	—
946	C₂×C₄	—	212	8	no	—
947	C₂×C₄	—	212	2	no	—
948	C₂×C₄	—	212	4	no	—
949	C₂×C₄	—	212	2	no	—
950	C₂×C₄	—	212	8	no	—
951	C₂×C₄	#13133262	1	4	yes	—
952	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
953	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
954	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
955	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
956	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
957	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
958	C₂²	—	2	8	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	4	no	—
963	C₂²	—	2	8	no	—
964	C₂²	—	848	8	no	—
965	C₂²	—	106	4	no	—
966	C₂²	—	106	8	no	—
967	C₂²	—	106	8	no	—
968	C₂²	—	106	16	no	—
969	C₂²	—	424	8	no	—
970	C₂²	—	424	16	no	—
971	C₂²	C₂×#13133262	1	2	yes	—
972	C₂²	#16811460	1	4	yes	—
973	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
974	C₄	—	2	2	no	—
975	C₄	—	2	4	no	—
976	C₄	—	2	4	no	—
977	C₄	—	2	4	no	—
978	C₄	—	2	8	no	—
979	C₄	—	106	4	no	—
980	C₄	—	106	4	no	—
981	C₄	—	106	4	no	—
982	C₄	—	106	8	no	—
983	C₄	C₂×#13133262	1	4	yes	—
984	C₂	—	2	2	no	—
985	C₂	—	2	4	no	—
986	C₂	—	4	4	no	—
987	C₂	—	212	4	no	—
988	C₂	—	212	8	no	—
989	C₂	C₂²×#13133262	1	1	yes	characteristic
990	C₂	C₂×#16811460	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3486	C₂
hypercenter	#3486	D₅₃
hypocenter	C₅₃	#62824
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3486

Complements

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

N	H ≅ G/N	type
1. #20289281	C₂	semidirect
2. #20289232	C₂	semidirect
3. #20289069	C₂	semidirect
4. #20288677	C₂	semidirect
5. #20288669	C₂	semidirect
6. #20288614	C₂	semidirect
7. #20288612	C₂	semidirect
8. #20288509	C₂	semidirect
9. #20288504	C₂	semidirect
10. #20288398	C₂	semidirect
11. #20288366	C₂	semidirect
12. #20288348	C₂	semidirect
13. #20288007	C₂	semidirect
14. C₂²×#13133206	C₂	semidirect
15. C₅₃×#3486	C₂	semidirect
16. C₂×#13133265	C₂²	semidirect
17. C₂×#13133263	C₂²	semidirect
19. #16811372	C₂²	semidirect
20. #16811369	C₂²	semidirect
21. #16811365	C₂²	semidirect
22. #16811358	C₂²	semidirect
23. #16811355	C₂²	semidirect
24. #16811347	C₂²	semidirect
25. #16811345	C₂²	semidirect
26. #16811339	C₂²	semidirect
27. #16811335	C₂²	semidirect
28. #16811302	C₂²	semidirect
29. #16811300	C₂²	semidirect
30. #16811300	C₂²	semidirect
31. #16811297	C₂²	semidirect
32. #16811296	C₂²	semidirect
33. Q₈×C₂²⋊D₅₃	C₂²	semidirect
34. #16811284	C₂²	semidirect
35. #16811284	C₂²	semidirect
36. #16811283	C₂²	semidirect
37. #16811269	C₂²	semidirect
38. #16811268	C₂²	semidirect
39. #16811265	C₂²	semidirect
40. #16811264	C₂²	semidirect
41. #16811264	C₂²	semidirect
42. #16811262	C₂²	semidirect
43. #16811261	C₂²	semidirect
44. #16811261	C₂²	semidirect
45. D₄×D₂₁₂	C₂²	semidirect
46. #16811257	C₂²	semidirect
47. #16811248	C₂²	semidirect
48. #16811247	C₂²	semidirect
49. #16811246	C₂²	semidirect
50. #16811245	C₂²	semidirect
51. #16811243	C₂²	semidirect
52. #16811213	C₂²	semidirect
53. #16811213	C₂²	semidirect
54. #16811210	C₂²	semidirect
55. #16811207	C₂²	semidirect
56. #16811206	C₂²	semidirect
57. #16811198	C₂²	semidirect
58. #16811197	C₂²	semidirect
59. #16811197	C₂²	semidirect
60. #16811197	C₂²	semidirect
62. #16811191	C₂²	semidirect
64. #16811187	C₂²	semidirect
65. #16811184	C₂²	semidirect
66. #16811181	C₂²	semidirect
67. #16811176	C₂²	semidirect
68. #16811175	C₂²	semidirect
69. #16811174	C₂²	semidirect
70. #16811169	C₂²	semidirect
71. #16811169	C₂²	semidirect
72. #16811168	C₂²	semidirect
73. #16811160	C₂²	semidirect
74. #16811159	C₂²	semidirect
75. #16811159	C₂²	semidirect
76. #16811154	C₂²	semidirect
77. #16811153	C₂²	semidirect
78. #16811150	C₂²	semidirect
79. C₂×#13133206	C₂²	semidirect
80. C₂×#13133206	C₂²	semidirect
81. C₂×#13133206	C₂²	semidirect
82. C₂×#13133206	C₂²	semidirect
83. C₂×#13133206	C₂²	semidirect
84. C₂×#13133206	C₂²	semidirect
85. #124×D₅₃	C₂²	semidirect
86. #16811134	C₂²	semidirect
87. #16811134	C₂²	semidirect
88. #16811129	C₂²	semidirect
89. #120×D₅₃	C₂²	semidirect
90. #16811101	C₂²	semidirect
91. #16811097	C₂²	semidirect
92. #16811095	C₂²	semidirect
93. #41×Dic₅₃	C₂²	semidirect
94. #16811091	C₂²	semidirect
95. C₄×#11719947	C₂²	semidirect
96. C₂²×#11719921	C₂²	semidirect
97. C₂²×C₄×Dic₅₃	C₂²	semidirect
98. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
99. C₂³×Q₈×C₅₃	C₂²	semidirect
100. D₄×Q₈×C₅₃	C₂²	semidirect
101. C₅₃×#548	C₂²	semidirect
102. C₅₃×#536	C₂²	semidirect
103. C₅₃×#536	C₂²	semidirect
104. C₅₃×#525	C₂²	semidirect
105. C₅₃×#525	C₂²	semidirect
106. C₅₃×#519	C₂²	semidirect
111. C₂×#11719949	C₂³	semidirect
116. C₂×Q₈×D₅₃	C₂³	semidirect
126. #13133216	C₂³	semidirect
127. #13133215	C₂³	semidirect
128. #13133215	C₂³	semidirect
129. #13133215	C₂³	semidirect
132. #13133213	C₂³	semidirect
133. #13133212	C₂³	semidirect
134. #13133212	C₂³	semidirect
135. #13133212	C₂³	semidirect
136. #13133212	C₂³	semidirect
137. #13133211	C₂³	semidirect
138. #13133210	C₂³	semidirect
139. #13133208	C₂³	semidirect
140. #13133207	C₂³	semidirect
151. #13133206	C₂³	semidirect
152. #13133206	C₂³	semidirect
153. #13133206	C₂³	semidirect
154. #13133206	C₂³	semidirect
156. #13133205	C₂³	semidirect
157. #13133204	C₂³	semidirect
158. #13133203	C₂³	semidirect
159. #13133203	C₂³	semidirect
160. #13133203	C₂³	semidirect
162. #13133202	C₂³	semidirect
163. #13133202	C₂³	semidirect
164. #13133202	C₂³	semidirect
166. #13133201	C₂³	semidirect
169. #13133200	C₂³	semidirect
170. #13133199	C₂³	semidirect
172. #13133197	C₂³	semidirect
175. #13133195	C₂³	semidirect
176. #13133195	C₂³	semidirect
179. #13133193	C₂³	semidirect
180. #13133193	C₂³	semidirect
181. #13133193	C₂³	semidirect
184. #13133192	C₂³	semidirect
188. #13133191	C₂³	semidirect
190. #13133190	C₂³	semidirect
193. #13133189	C₂³	semidirect
197. #13133187	C₂³	semidirect
201. #13133185	C₂³	semidirect
202. Q₈×Dic₅₃	C₂³	semidirect
203. Q₈×Dic₅₃	C₂³	semidirect
204. C₄×Dic₁₀₆	C₂³	semidirect
205. #13133182	C₂³	semidirect
206. #13133182	C₂³	semidirect
208. C₄×D₂₁₂	C₂³	semidirect
211. D₄×Dic₅₃	C₂³	semidirect
213. #13133179	C₂³	semidirect
214. #13133179	C₂³	semidirect
217. C₄×C₂²⋊D₅₃	C₂³	semidirect
218. C₄×C₂²⋊D₅₃	C₂³	semidirect
221. #13133177	C₂³	semidirect
222. #13133177	C₂³	semidirect
225. #13133176	C₂³	semidirect
226. #13133175	C₂³	semidirect
227. #13133175	C₂³	semidirect
228. #13133174	C₂³	semidirect
229. #13133174	C₂³	semidirect
231. #13133173	C₂³	semidirect
237. C₂×#11719921	C₂³	semidirect
240. C₂²⋊C₄×D₅₃	C₂³	semidirect
245. C₂×C₄×Dic₅₃	C₂³	semidirect
246. C₄²×D₅₃	C₂³	semidirect
250. C₂×#41×C₅₃	C₂³	semidirect
256. C₂²×Q₈×C₅₃	C₂³	semidirect
259. C₄⋊Q₈×C₅₃	C₂³	semidirect
260. C₄⋊Q₈×C₅₃	C₂³	semidirect
261. #124×C₅₃	C₂³	semidirect
262. #124×C₅₃	C₂³	semidirect
267. C₂²⋊Q₈×C₅₃	C₂³	semidirect
268. C₂²⋊Q₈×C₅₃	C₂³	semidirect
272. C₄×Q₈×C₅₃	C₂³	semidirect
500. #3486	D₅₃	semidirect
512. C₂×2₋¹⁺⁴	C₂×D₅₃	semidirect
514. C₂³×Q₈	C₂×D₅₃	semidirect
531. D₄×Q₈	C₂×D₅₃	semidirect
535. #548	C₂×D₅₃	semidirect
560. #536	C₂×D₅₃	semidirect
561. #536	C₂×D₅₃	semidirect
590. #525	C₂×D₅₃	semidirect
591. #525	C₂×D₅₃	semidirect
594. #519	C₂×D₅₃	semidirect
602. C₅₃	#62824	semidirect
615. C₂×#41	C₂²×D₅₃	semidirect
622. C₂²×Q₈	C₂²×D₅₃	semidirect
638. C₄⋊Q₈	C₂²×D₅₃	semidirect
639. C₄⋊Q₈	C₂²×D₅₃	semidirect
671. #124	C₂²×D₅₃	semidirect
672. #124	C₂²×D₅₃	semidirect
698. C₂²⋊Q₈	C₂²×D₅₃	semidirect
699. C₂²⋊Q₈	C₂²×D₅₃	semidirect
728. C₄×Q₈	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20289281	2
#20289232	2
#20289069	2
#20288677	2
#20288669	2
#20288614	2
#20288612	2
#20288509	2
#20288504	2
#20288398	2
#20288366	2
#20288348	2
#20288007	2
C₂²×#13133206	2
C₅₃×#3486	2
#62824	53