Subgroups — #30680442

Order 16768.

910 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554066	C₂	1	1	yes	maximal, characteristic, complemented
2	#22554064	C₂	1	1	yes	maximal, characteristic, complemented
3	#22554063	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554061	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554042	C₂	1	1	yes	maximal, characteristic, complemented
6	#22554040	C₂	1	1	yes	maximal, characteristic, complemented
7	#22554039	C₂	1	1	yes	maximal, characteristic, complemented
8	#22554039	C₂	1	1	yes	maximal, characteristic, complemented
9	#22554034	C₂	1	1	yes	maximal, characteristic, complemented
10	#22554030	C₂	1	1	yes	maximal, characteristic, complemented
11	#22554029	C₂	1	1	yes	maximal, characteristic, complemented
12	#22554029	C₂	1	1	yes	maximal, characteristic, complemented
13	#22554029	C₂	1	1	yes	maximal, characteristic, complemented
14	#22554016	C₂	1	1	yes	maximal, characteristic, complemented
15	#22553995	C₂	1	1	yes	maximal, characteristic, complemented
16	#22553994	C₂	1	1	yes	maximal, characteristic, complemented
17	#22553942	C₂	1	1	yes	maximal, characteristic, complemented
18	#22553941	C₂	1	1	yes	maximal, characteristic, complemented
19	#22553932	C₂	1	1	yes	maximal, characteristic
20	#22553928	C₂	1	1	yes	maximal, characteristic
21	#22553921	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553921	C₂	1	1	yes	maximal, characteristic, complemented
23	#22553921	C₂	1	1	yes	maximal, characteristic, complemented
24	#22553921	C₂	1	1	yes	maximal, characteristic, complemented
25	#22553920	C₂	1	1	yes	maximal, characteristic, complemented
26	#22553919	C₂	1	1	yes	maximal, characteristic, complemented
27	#22553919	C₂	1	1	yes	maximal, characteristic, complemented
28	#22553868	C₂	1	1	yes	maximal, characteristic, complemented
29	#22553866	C₂	1	1	yes	maximal, characteristic, complemented
30	#22553845	C₂	1	1	yes	maximal, characteristic
31	#541×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
32	#16862246	C₂²	1	1	yes	characteristic
33	#16862245	C₂²	1	1	yes	characteristic
34	#16862245	C₂²	1	1	yes	characteristic
35	#16862245	C₂²	1	1	yes	characteristic
36	#16862245	C₂²	1	1	yes	characteristic
37	#16862245	C₂²	1	1	yes	characteristic
38	#16862245	C₂²	1	1	yes	characteristic
39	#16862245	C₂²	1	1	yes	characteristic
40	#16862245	C₂²	1	1	yes	characteristic
41	#16862245	C₂²	1	1	yes	characteristic
42	#16862245	C₂²	1	1	yes	characteristic
43	#16862245	C₂²	1	1	yes	characteristic
44	#16862244	C₂²	1	1	yes	characteristic
45	#16862244	C₂²	1	1	yes	characteristic
46	#16862244	C₂²	1	1	yes	characteristic
47	#16862244	C₂²	1	1	yes	characteristic
48	#16862244	C₂²	1	1	yes	characteristic
49	#16862241	C₂²	1	1	yes	characteristic
50	#16862241	C₂²	1	1	yes	characteristic
51	#16862241	C₂²	1	1	yes	characteristic
52	#16862241	C₂²	1	1	yes	characteristic
53	#16862241	C₂²	1	1	yes	characteristic
54	#16862241	C₂²	1	1	yes	characteristic
55	#16862241	C₂²	1	1	yes	characteristic
56	#16862241	C₂²	1	1	yes	characteristic
57	#16862241	C₂²	1	1	yes	characteristic
58	#16862241	C₂²	1	1	yes	characteristic
59	#16862241	C₂²	1	1	yes	characteristic
60	#16862241	C₂²	1	1	yes	characteristic
61	#16862240	C₂²	1	1	yes	characteristic
62	#16862240	C₂²	1	1	yes	characteristic
63	#16862240	C₂²	1	1	yes	characteristic
64	#16862240	C₂²	1	1	yes	characteristic
65	#16862240	C₂²	1	1	yes	characteristic
66	#16862239	C₂²	1	1	yes	characteristic
67	#16862239	C₂²	1	1	yes	characteristic
68	#16862239	C₂²	1	1	yes	characteristic
69	#16862239	C₂²	1	1	yes	characteristic
70	#16862239	C₂²	1	1	yes	characteristic
71	#16862238	C₂²	1	1	yes	characteristic
72	#16862238	C₂²	1	1	yes	characteristic
73	#16862238	C₂²	1	1	yes	characteristic
74	#16862237	C₂²	1	1	yes	characteristic
75	#16862237	C₂²	1	1	yes	characteristic
76	#16862237	C₂²	1	1	yes	characteristic
77	#16862237	C₂²	1	1	yes	characteristic
78	#16862236	C₂²	1	1	yes	characteristic
79	#16862236	C₂²	1	1	yes	characteristic
80	#16862236	C₂²	1	1	yes	characteristic
81	#16862236	C₂²	1	1	yes	characteristic
82	#16862236	C₂²	1	1	yes	characteristic
83	#16862236	C₂²	1	1	yes	characteristic
84	#16862236	C₂²	1	1	yes	characteristic
85	#16862236	C₂²	1	1	yes	characteristic
86	#16862236	C₂²	1	1	yes	characteristic
87	#16862236	C₂²	1	1	yes	characteristic
88	#16862236	C₂²	1	1	yes	characteristic
89	#16862236	C₂²	1	1	yes	characteristic
90	#16862236	C₂²	1	1	yes	characteristic
91	#16862236	C₂²	1	1	yes	characteristic
92	#16862236	C₂²	1	1	yes	characteristic
93	#16862236	C₂²	1	1	yes	characteristic
94	#16862236	C₂²	1	1	yes	characteristic
95	#16862235	C₂²	1	1	yes	characteristic
96	#16862234	C₂²	1	1	yes	characteristic
97	#16862232	C₂²	1	1	yes	characteristic
98	#16862232	C₂²	1	1	yes	characteristic
99	#16862232	C₂²	1	1	yes	characteristic
100	#16862232	C₂²	1	1	yes	characteristic
101	#16862232	C₂²	1	1	yes	characteristic
102	#16862231	C₂²	1	1	yes	characteristic
103	#16862231	C₂²	1	1	yes	characteristic
104	#16862231	C₂²	1	1	yes	characteristic
105	#16862230	C₂²	1	1	yes	characteristic
106	#16862229	C₂²	1	1	yes	characteristic
107	#16862228	C₂²	1	1	yes	characteristic
108	#16862226	C₂²	1	1	yes	characteristic
109	#16862226	C₂²	1	1	yes	characteristic
110	#16862226	C₂²	1	1	yes	characteristic
111	#16862225	C₂²	1	1	yes	characteristic
112	#16862224	C₂²	1	1	yes	characteristic
113	#16862224	C₂²	1	1	yes	characteristic
114	#16862224	C₂²	1	1	yes	characteristic
115	#16862224	C₂²	1	1	yes	characteristic
116	#16862224	C₂²	1	1	yes	characteristic
117	#16862224	C₂²	1	1	yes	characteristic
118	#16862224	C₂²	1	1	yes	characteristic
119	#16862224	C₂²	1	1	yes	characteristic
120	#16862224	C₂²	1	1	yes	characteristic
121	#16862224	C₂²	1	1	yes	characteristic
122	#16862224	C₂²	1	1	yes	characteristic
123	#16862224	C₂²	1	1	yes	characteristic
124	#16862223	C₂²	1	1	yes	characteristic
125	#16862223	C₂²	1	1	yes	characteristic
126	#16862223	C₂²	1	1	yes	characteristic
127	#16862223	C₂²	1	1	yes	characteristic
128	#16862223	C₂²	1	1	yes	characteristic
129	#16862222	C₂²	1	1	yes	characteristic
130	#16862222	C₂²	1	1	yes	characteristic
131	#16862219	C₂²	1	1	yes	characteristic
132	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
133	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
134	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
135	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
136	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
137	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
138	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
139	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
140	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
141	#16862211	C₂²	1	1	yes	characteristic
142	#16862211	C₂²	1	1	yes	characteristic
143	#16862211	C₂²	1	1	yes	characteristic
144	#16862211	C₂²	1	1	yes	characteristic
145	#16862211	C₂²	1	1	yes	characteristic
146	#16862211	C₂²	1	1	yes	characteristic
147	#16862211	C₂²	1	1	yes	characteristic
148	#16862211	C₂²	1	1	yes	characteristic
149	#16862211	C₂²	1	1	yes	characteristic
150	#16862211	C₂²	1	1	yes	characteristic
151	#16862211	C₂²	1	1	yes	characteristic
152	#16862211	C₂²	1	1	yes	characteristic
153	#16862208	C₂²	1	1	yes	characteristic
154	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
155	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
156	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
157	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
158	#16862204	C₂²	1	1	yes	characteristic
159	#16862204	C₂²	1	1	yes	characteristic
160	#16862204	C₂²	1	1	yes	characteristic
161	#16862204	C₂²	1	1	yes	characteristic
162	#16862203	C₂²	1	1	yes	characteristic
163	#16862203	C₂²	1	1	yes	characteristic
164	#16862203	C₂²	1	1	yes	characteristic
165	#16862203	C₂²	1	1	yes	characteristic
166	#16862202	C₂²	1	1	yes	characteristic
167	#16862202	C₂²	1	1	yes	characteristic
168	#16862202	C₂²	1	1	yes	characteristic
169	C₂×Dic₁₃₁⋊C₄	C₂²	1	1	yes	characteristic
170	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
171	C₄²×D₁₃₁	C₂²	1	1	yes	characteristic
172	C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
173	#126×C₁₃₁	C₂²	1	1	yes	characteristic
174	#126×C₁₃₁	C₂²	1	1	yes	characteristic
175	#126×C₁₃₁	C₂²	1	1	yes	characteristic
176	#126×C₁₃₁	C₂²	1	1	yes	characteristic
177	#125×C₁₃₁	C₂²	1	1	yes	characteristic
178	#125×C₁₃₁	C₂²	1	1	yes	characteristic
179	#125×C₁₃₁	C₂²	1	1	yes	characteristic
180	#125×C₁₃₁	C₂²	1	1	yes	characteristic
181	#125×C₁₃₁	C₂²	1	1	yes	characteristic
182	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
183	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
184	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
185	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
186	#117×C₁₃₁	C₂²	1	1	yes	characteristic
187	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
188	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
189	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
190	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
191	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
192	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
193	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
194	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
195	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
196	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
197	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
198	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
201	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
202	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
223	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
224	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
225	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
226	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
227	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
229	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
230	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
233	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
260	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
261	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
262	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
267	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
268	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
269	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
270	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
271	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
272	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
273	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
274	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
287	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
288	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
289	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
290	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
291	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
292	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
293	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
294	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
295	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
296	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
297	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
298	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
299	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
300	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
301	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
302	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
303	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
304	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
305	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
306	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
307	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
308	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
309	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
310	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
311	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
312	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
313	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
314	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
315	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
316	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
317	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
318	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
330	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
331	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
336	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
337	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
338	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
339	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
340	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
341	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
342	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
343	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
344	Dic₂₆₂	—	2	2	no	—
345	Dic₂₆₂	—	2	2	no	—
346	Dic₂₆₂	—	2	2	no	—
347	Dic₂₆₂	—	2	2	no	—
348	Dic₂₆₂	—	2	2	no	—
349	Dic₂₆₂	—	4	1	no	—
350	Dic₂₆₂	—	4	1	no	—
351	Dic₂₆₂	—	4	1	no	—
352	Dic₂₆₂	—	4	1	no	—
353	Dic₂₆₂	—	4	1	no	—
354	Dic₂₆₂	—	4	1	no	—
355	D₅₂₄	—	4	1	no	—
356	C₂²⋊D₁₃₁	—	2	2	no	—
357	C₂²⋊D₁₃₁	—	4	1	no	—
358	C₂×Dic₁₃₁	—	2	2	no	—
359	C₂×Dic₁₃₁	—	4	1	no	—
360	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
374	C₄×D₁₃₁	—	2	2	no	—
375	C₄×D₁₃₁	—	2	2	no	—
376	C₄×D₁₃₁	—	2	2	no	—
377	C₄×D₁₃₁	—	4	1	no	—
378	C₄×D₁₃₁	—	4	1	no	—
379	C₄×D₁₃₁	—	4	1	no	—
380	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
381	Q₈×C₁₃₁	—	4	1	no	—
382	Q₈×C₁₃₁	—	4	1	no	—
383	C₂×C₄×C₁₃₁	—	4	1	no	—
384	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
398	C₂²×C₁₃₁	—	2	1	no	—
399	C₂²×C₁₃₁	—	2	1	no	—
400	C₂²×C₁₃₁	—	2	1	no	—
401	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
402	C₂×D₁₃₁	—	2	1	no	—
403	C₂×D₁₃₁	—	2	1	no	—
404	C₂×D₁₃₁	—	2	1	no	—
405	C₂×D₁₃₁	—	2	1	no	—
406	C₂×D₁₃₁	—	2	1	no	—
407	C₂×D₁₃₁	—	2	1	no	—
408	C₄×C₁₃₁	—	2	1	no	—
409	C₄×C₁₃₁	—	2	1	no	—
410	C₄×C₁₃₁	—	2	1	no	—
411	C₄×C₁₃₁	—	2	1	no	—
412	C₄×C₁₃₁	—	2	1	no	—
413	C₄×C₁₃₁	—	2	1	no	—
414	C₄×C₁₃₁	—	2	1	no	—
415	C₄×C₁₃₁	—	2	1	no	—
416	C₄×C₁₃₁	—	2	1	no	—
417	C₄×C₁₃₁	—	2	1	no	—
418	C₄×C₁₃₁	—	2	1	no	—
419	C₄×C₁₃₁	—	2	1	no	—
420	C₄×C₁₃₁	—	2	1	no	—
421	C₄×C₁₃₁	—	2	1	no	—
422	Dic₁₃₁	—	2	1	no	—
423	Dic₁₃₁	—	2	1	no	—
424	Dic₁₃₁	—	2	1	no	—
425	Dic₁₃₁	—	2	1	no	—
426	Dic₁₃₁	—	2	1	no	—
427	Dic₁₃₁	—	2	1	no	—
428	Dic₁₃₁	—	2	1	no	—
429	Dic₁₃₁	—	2	1	no	—
430	Dic₁₃₁	—	2	1	no	—
431	Dic₁₃₁	—	2	1	no	—
432	Dic₁₃₁	—	2	1	no	—
433	Dic₁₃₁	—	2	1	no	—
434	Dic₁₃₁	2₋¹⁺⁴	1	2	yes	—
435	Dic₁₃₁	2₋¹⁺⁴	1	2	yes	—
436	C₂×C₁₃₁	—	4	1	no	—
437	C₂×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
438	C₂×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
439	C₂×C₁₃₁	#585	1	1	yes	characteristic
440	D₁₃₁	—	4	1	no	—
441	D₁₃₁	—	4	1	no	—
442	C₁₃₁	#3555	1	1	yes	characteristic, complemented, Sylow
443	#3555	—	131	1	no	maximal, Sylow
444	#563	—	131	1	no	—
445	#563	—	131	1	no	—
446	#563	—	131	1	no	—
447	#563	—	131	1	no	—
448	Q₈²	—	131	1	no	—
449	#557	—	131	1	no	—
450	#557	—	131	1	no	—
451	#557	—	131	1	no	—
452	#556	—	131	1	no	—
453	#556	—	131	1	no	—
454	#556	—	131	1	no	—
455	#556	—	131	1	no	—
456	#556	—	131	1	no	—
457	#554	—	131	1	no	—
458	#552	—	131	1	no	—
459	#552	—	131	1	no	—
460	#544	—	131	1	no	—
461	#544	—	131	1	no	—
462	#542	—	131	1	no	—
463	#542	—	131	1	no	—
464	#541	—	131	1	no	—
465	#541	—	131	1	no	—
466	#541	—	131	1	no	—
467	#541	—	131	1	no	—
468	#541	—	131	1	no	—
469	#541	—	131	1	no	—
470	#541	—	131	1	no	—
471	#541	D₁₃₁	1	1	yes	characteristic, complemented
472	#533	—	131	1	no	—
473	#533	—	131	1	no	—
474	#529	—	131	1	no	—
475	C₄⋊Q₈	—	131	1	no	—
476	C₄⋊Q₈	—	131	1	no	—
477	C₄⋊Q₈	—	131	1	no	—
478	C₄⋊Q₈	—	131	1	no	—
479	C₄⋊Q₈	—	131	1	no	—
480	C₄⋊Q₈	—	131	1	no	—
481	C₄⋊Q₈	—	131	1	no	—
482	C₄⋊Q₈	—	131	1	no	—
483	C₄⋊Q₈	—	131	1	no	—
484	C₄⋊Q₈	—	131	1	no	—
485	C₄⋊Q₈	—	131	1	no	—
486	C₄⋊Q₈	—	131	1	no	—
487	C₄⋊Q₈	—	131	1	no	—
488	C₄⋊Q₈	—	131	1	no	—
489	C₄⋊Q₈	—	131	1	no	—
490	C₄⋊Q₈	—	131	1	no	—
491	C₄⋊Q₈	—	131	1	no	—
492	C₄⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic
493	#126	—	131	1	no	—
494	#126	—	131	1	no	—
495	#126	—	131	1	no	—
496	#126	—	131	1	no	—
497	#126	—	131	1	no	—
498	#126	—	131	1	no	—
499	#126	—	131	1	no	—
500	#126	—	131	1	no	—
501	#126	—	131	1	no	—
502	#126	—	131	1	no	—
503	#126	—	131	1	no	—
504	#126	—	131	1	no	—
505	#126	—	131	1	no	—
506	#126	—	131	1	no	—
507	#126	—	131	1	no	—
508	#126	—	131	1	no	—
509	#126	—	131	1	no	—
510	#126	—	131	1	no	—
511	#126	—	131	1	no	—
512	#126	—	131	1	no	—
513	#126	—	131	1	no	—
514	#126	—	131	1	no	—
515	#126	C₂×D₁₃₁	1	1	yes	characteristic
516	#126	C₂×D₁₃₁	1	1	yes	characteristic
517	#126	C₂×D₁₃₁	1	1	yes	characteristic
518	#126	C₂×D₁₃₁	1	1	yes	characteristic
519	#125	—	131	1	no	—
520	#125	—	131	1	no	—
521	#125	—	131	1	no	—
522	#125	—	131	1	no	—
523	#125	—	131	1	no	—
524	#125	—	131	1	no	—
525	#125	—	131	1	no	—
526	#125	—	131	1	no	—
527	#125	—	131	1	no	—
528	#125	—	131	1	no	—
529	#125	—	131	1	no	—
530	#125	—	131	1	no	—
531	#125	—	131	1	no	—
532	#125	—	131	1	no	—
533	#125	—	131	1	no	—
534	#125	—	131	1	no	—
535	#125	—	131	1	no	—
536	#125	—	131	1	no	—
537	#125	—	131	1	no	—
538	#125	—	131	1	no	—
539	#125	—	131	1	no	—
540	#125	—	131	1	no	—
541	#125	—	131	1	no	—
542	#125	—	131	1	no	—
543	#125	C₂×D₁₃₁	1	1	yes	characteristic
544	#125	C₂×D₁₃₁	1	1	yes	characteristic
545	#125	C₂×D₁₃₁	1	1	yes	characteristic
546	#125	C₂×D₁₃₁	1	1	yes	characteristic
547	#125	C₂×D₁₃₁	1	1	yes	characteristic
548	#124	—	131	1	no	—
549	#124	—	131	1	no	—
550	#124	—	131	1	no	—
551	#124	—	131	1	no	—
552	#124	—	131	1	no	—
553	#124	—	131	1	no	—
554	#124	—	131	1	no	—
555	#123	—	131	1	no	—
556	#123	—	131	1	no	—
557	#123	—	131	1	no	—
558	#123	—	131	1	no	—
559	#123	—	131	1	no	—
560	#123	—	131	1	no	—
561	C₂²⋊Q₈	—	131	1	no	—
562	C₂²⋊Q₈	—	131	1	no	—
563	C₂²⋊Q₈	—	131	1	no	—
564	C₂²⋊Q₈	—	131	1	no	—
565	C₂²⋊Q₈	—	131	1	no	—
566	C₂²⋊Q₈	—	131	1	no	—
567	C₂²⋊Q₈	—	131	1	no	—
568	C₂²⋊Q₈	—	131	1	no	—
569	C₂²⋊Q₈	—	131	1	no	—
570	C₂²⋊Q₈	—	131	1	no	—
571	C₂²⋊Q₈	—	131	1	no	—
572	C₂²⋊Q₈	—	131	1	no	—
573	C₂²⋊Q₈	—	131	1	no	—
574	C₂²⋊Q₈	—	131	1	no	—
575	C₂²⋊Q₈	—	131	1	no	—
576	C₂²⋊Q₈	—	131	1	no	—
577	C₂²⋊Q₈	—	131	1	no	—
578	C₂²⋊Q₈	—	131	1	no	—
579	C₂²⋊Q₈	—	131	1	no	—
580	C₂²⋊Q₈	—	131	1	no	—
581	C₂²⋊Q₈	—	131	1	no	—
582	C₂²⋊Q₈	—	131	1	no	—
583	C₂²⋊Q₈	—	131	1	no	—
584	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic
585	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic
586	#121	—	131	1	no	—
587	C₄×Q₈	—	131	1	no	—
588	C₄×Q₈	—	131	1	no	—
589	C₄×Q₈	—	131	1	no	—
590	C₄×Q₈	—	131	1	no	—
591	C₄×Q₈	—	131	1	no	—
592	C₄×Q₈	—	131	1	no	—
593	C₄×Q₈	—	131	1	no	—
594	C₄×Q₈	—	131	1	no	—
595	C₄×Q₈	—	131	1	no	—
596	C₄×Q₈	—	131	1	no	—
597	C₄×Q₈	—	131	1	no	—
598	C₄×Q₈	—	131	1	no	—
599	C₄×Q₈	—	131	1	no	—
600	C₄×Q₈	—	131	1	no	—
601	C₄×Q₈	—	131	1	no	—
602	C₄×Q₈	—	131	1	no	—
603	C₄×Q₈	—	131	1	no	—
604	C₄×Q₈	—	131	1	no	—
605	C₄×Q₈	—	131	1	no	—
606	C₄×Q₈	—	131	1	no	—
607	C₄×Q₈	—	131	1	no	—
608	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic
609	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic
610	C₄×D₄	—	131	1	no	—
611	C₄×D₄	—	131	1	no	—
612	C₄×D₄	—	131	1	no	—
613	C₄×D₄	—	131	1	no	—
614	C₄×D₄	—	131	1	no	—
615	#117	—	131	1	no	—
616	#117	—	131	1	no	—
617	#117	—	131	1	no	—
618	#117	—	131	1	no	—
619	#117	—	131	1	no	—
620	#117	—	131	1	no	—
621	#117	—	131	1	no	—
622	#117	—	131	1	no	—
623	#117	—	131	1	no	—
624	#117	—	131	1	no	—
625	#117	—	131	1	no	—
626	#117	C₂×D₁₃₁	1	1	yes	characteristic
627	C₂×C₄⋊C₄	—	131	1	no	—
628	C₂×C₄⋊C₄	—	131	1	no	—
629	C₂×C₄²	—	131	1	no	—
630	C₂×Q₈	—	131	1	no	—
631	C₂×Q₈	—	131	1	no	—
632	C₂×Q₈	—	131	1	no	—
633	C₂×Q₈	—	131	1	no	—
634	C₂×Q₈	—	131	1	no	—
635	C₂×Q₈	—	131	1	no	—
636	C₂×Q₈	—	131	1	no	—
637	C₂×Q₈	—	131	1	no	—
638	C₂×Q₈	—	131	1	no	—
639	C₂×Q₈	—	131	1	no	—
640	C₂×Q₈	—	131	1	no	—
641	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
642	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
643	C₂×D₄	—	131	1	no	—
644	C₂×D₄	—	131	1	no	—
645	C₂×D₄	—	131	1	no	—
646	C₂²×C₄	—	131	1	no	—
647	C₂²×C₄	—	131	1	no	—
648	C₂²×C₄	—	131	1	no	—
649	C₂²×C₄	—	131	1	no	—
650	C₂²×C₄	—	131	1	no	—
651	C₂²×C₄	—	131	1	no	—
652	C₂²×C₄	—	131	1	no	—
653	C₂²×C₄	—	131	1	no	—
654	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
655	C₄⋊C₄	—	131	1	no	—
656	C₄⋊C₄	—	131	1	no	—
657	C₄⋊C₄	—	131	1	no	—
658	C₄⋊C₄	—	131	1	no	—
659	C₄⋊C₄	—	131	1	no	—
660	C₄⋊C₄	—	131	1	no	—
661	C₄⋊C₄	—	131	1	no	—
662	C₄⋊C₄	—	131	1	no	—
663	C₄⋊C₄	—	131	1	no	—
664	C₄⋊C₄	—	131	1	no	—
665	C₄⋊C₄	—	131	1	no	—
666	C₄⋊C₄	—	131	1	no	—
667	C₄⋊C₄	—	131	1	no	—
668	C₄⋊C₄	—	131	1	no	—
669	C₄⋊C₄	—	131	1	no	—
670	C₄⋊C₄	—	131	1	no	—
671	C₄⋊C₄	—	131	1	no	—
672	C₄⋊C₄	—	131	1	no	—
673	C₄⋊C₄	—	131	1	no	—
674	C₄⋊C₄	—	131	1	no	—
675	C₄⋊C₄	—	131	1	no	—
676	C₄⋊C₄	—	131	1	no	—
677	C₄⋊C₄	—	131	1	no	—
678	C₄⋊C₄	—	131	1	no	—
679	C₄⋊C₄	—	131	1	no	—
680	C₄⋊C₄	—	131	1	no	—
681	C₄⋊C₄	—	131	1	no	—
682	C₄⋊C₄	—	131	1	no	—
683	C₄⋊C₄	—	131	1	no	—
684	C₄⋊C₄	—	131	1	no	—
685	C₄⋊C₄	—	131	1	no	—
686	C₄⋊C₄	—	131	1	no	—
687	C₄⋊C₄	—	131	1	no	—
688	C₄⋊C₄	—	131	1	no	—
689	C₄⋊C₄	—	131	1	no	—
690	C₄⋊C₄	—	131	1	no	—
691	C₄⋊C₄	—	131	1	no	—
692	C₄⋊C₄	—	131	1	no	—
693	C₄⋊C₄	—	131	1	no	—
694	C₄⋊C₄	—	131	1	no	—
695	C₄⋊C₄	—	131	1	no	—
696	C₄⋊C₄	—	131	1	no	—
697	C₄⋊C₄	—	131	1	no	—
698	C₄⋊C₄	—	131	1	no	—
699	C₄⋊C₄	—	131	1	no	—
700	C₄⋊C₄	—	131	1	no	—
701	C₄⋊C₄	—	131	1	no	—
702	C₄⋊C₄	—	131	1	no	—
703	C₄⋊C₄	—	131	1	no	—
704	C₄⋊C₄	—	131	1	no	—
705	C₄⋊C₄	—	131	1	no	—
706	C₄⋊C₄	—	131	1	no	—
707	C₄⋊C₄	—	131	1	no	—
708	C₄⋊C₄	—	131	1	no	—
709	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
710	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
711	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
712	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
713	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
714	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
715	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
716	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
717	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
718	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
719	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
720	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
721	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
722	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
723	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
724	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
725	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
729	C₂²⋊C₄	—	131	1	no	—
730	C₂²⋊C₄	—	131	1	no	—
731	C₂²⋊C₄	—	131	1	no	—
732	C₂²⋊C₄	—	131	1	no	—
733	C₂²⋊C₄	—	131	1	no	—
734	C₂²⋊C₄	—	131	1	no	—
735	C₂²⋊C₄	—	131	1	no	—
736	C₂²⋊C₄	—	131	1	no	—
737	C₂²⋊C₄	—	131	1	no	—
738	C₂²⋊C₄	—	131	1	no	—
739	C₂²⋊C₄	—	131	1	no	—
740	C₂²⋊C₄	—	131	1	no	—
741	C₂²⋊C₄	—	131	1	no	—
742	C₂²⋊C₄	—	131	1	no	—
743	C₂²⋊C₄	—	131	1	no	—
744	C₂²⋊C₄	—	131	1	no	—
745	C₂²⋊C₄	—	131	1	no	—
746	C₂²⋊C₄	—	131	1	no	—
747	C₂²⋊C₄	—	131	1	no	—
748	C₂²⋊C₄	—	131	1	no	—
749	C₂²⋊C₄	—	131	1	no	—
750	C₂²⋊C₄	—	131	1	no	—
751	C₂²⋊C₄	—	131	1	no	—
752	C₂²⋊C₄	—	131	1	no	—
753	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
754	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
755	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
756	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
757	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
758	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
759	C₄²	—	131	1	no	—
760	C₄²	—	131	1	no	—
761	C₄²	—	131	1	no	—
762	C₄²	—	131	1	no	—
763	C₄²	—	131	1	no	—
764	C₄²	—	131	1	no	—
765	C₄²	—	131	1	no	—
766	C₄²	—	131	1	no	—
767	C₄²	—	131	1	no	—
768	C₄²	—	131	1	no	—
769	C₄²	—	131	1	no	—
770	C₄²	—	131	1	no	—
771	C₄²	—	131	1	no	—
772	C₄²	—	131	1	no	—
773	C₄²	—	131	1	no	—
774	C₄²	—	131	1	no	—
775	C₄²	—	131	1	no	—
776	C₄²	—	131	1	no	—
777	C₄²	—	131	1	no	—
778	C₄²	—	131	1	no	—
779	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
780	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
781	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
782	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
783	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
784	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
785	C₂³	—	131	1	no	—
786	C₂³	—	131	1	no	—
787	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
788	Q₈	—	4	1	no	—
789	Q₈	—	4	1	no	—
790	Q₈	—	262	2	no	—
791	Q₈	—	262	2	no	—
792	Q₈	—	262	2	no	—
793	Q₈	—	262	2	no	—
794	Q₈	—	262	2	no	—
795	Q₈	—	524	1	no	—
796	Q₈	—	524	1	no	—
797	Q₈	—	524	1	no	—
798	Q₈	—	524	1	no	—
799	Q₈	—	524	1	no	—
800	Q₈	—	524	1	no	—
801	D₄	—	262	2	no	—
802	D₄	—	524	1	no	—
803	D₄	—	524	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	262	2	no	—
806	C₂×C₄	—	262	2	no	—
807	C₂×C₄	—	262	2	no	—
808	C₂×C₄	—	262	2	no	—
809	C₂×C₄	—	524	1	no	—
810	C₂×C₄	—	524	1	no	—
811	C₂×C₄	—	524	1	no	—
812	C₂×C₄	—	524	1	no	—
813	C₂×C₄	—	131	1	no	—
814	C₂×C₄	—	131	1	no	—
815	C₂×C₄	—	131	1	no	—
816	C₂×C₄	—	131	1	no	—
817	C₂×C₄	—	131	1	no	—
818	C₂×C₄	—	131	1	no	—
819	C₂×C₄	—	131	1	no	—
820	C₂×C₄	—	131	1	no	—
821	C₂×C₄	—	131	1	no	—
822	C₂×C₄	—	131	1	no	—
823	C₂×C₄	—	131	1	no	—
824	C₂×C₄	—	131	1	no	—
825	C₂×C₄	—	131	1	no	—
826	C₂×C₄	—	131	1	no	—
827	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
828	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
829	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
830	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
831	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
832	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
833	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
834	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
835	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
836	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
837	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
838	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
839	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
840	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	262	1	no	—
845	C₂²	—	262	1	no	—
846	C₂²	—	262	1	no	—
847	C₂²	—	262	1	no	—
848	C₂²	—	262	1	no	—
849	C₂²	—	262	1	no	—
850	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	262	1	no	—
866	C₄	—	262	1	no	—
867	C₄	—	262	1	no	—
868	C₄	—	262	1	no	—
869	C₄	—	262	1	no	—
870	C₄	—	262	1	no	—
871	C₄	—	262	1	no	—
872	C₄	—	262	1	no	—
873	C₄	—	262	1	no	—
874	C₄	—	262	1	no	—
875	C₄	—	262	1	no	—
876	C₄	—	262	1	no	—
877	C₄	—	131	2	no	—
878	C₄	—	131	2	no	—
879	C₂	—	4	1	no	—
880	C₂	—	524	1	no	—
881	C₂	—	524	1	no	—
882	C₂	2₋¹⁺⁴×D₁₃₁	1	1	yes	characteristic
883	C₂	2₋¹⁺⁴×D₁₃₁	1	1	yes	characteristic
884	C₂	#22554148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#541×C₁₃₁	C₂
prime radical	#16862219	C₂²
hypercenter	#541	D₁₃₁
hypocenter	C₁₃₁	#3555
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #22554066	C₂	semidirect
2. #22554064	C₂	semidirect
3. #22554063	C₂	semidirect
4. #22554061	C₂	semidirect
5. #22554042	C₂	semidirect
6. #22554040	C₂	semidirect
7. #22554039	C₂	semidirect
8. #22554039	C₂	semidirect
9. #22554034	C₂	semidirect
10. #22554030	C₂	semidirect
11. #22554029	C₂	semidirect
12. #22554029	C₂	semidirect
13. #22554029	C₂	semidirect
14. #22554016	C₂	semidirect
15. #22553995	C₂	semidirect
16. #22553994	C₂	semidirect
17. #22553942	C₂	semidirect
18. #22553941	C₂	semidirect
21. #22553921	C₂	semidirect
22. #22553921	C₂	semidirect
23. #22553921	C₂	semidirect
24. #22553921	C₂	semidirect
25. #22553920	C₂	semidirect
26. #22553919	C₂	semidirect
27. #22553919	C₂	semidirect
28. #22553868	C₂	semidirect
29. #22553866	C₂	semidirect
31. #541×C₁₃₁	C₂	semidirect
442. C₁₃₁	#3555	semidirect
471. #541	D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#22554066	2
#22554064	2
#22554063	2
#22554061	2
#22554042	2
#22554040	2
#22554039	2
#22554034	2
#22554030	2
#22554029	2
#22554016	2
#22553995	2
#22553994	2
#22553942	2
#22553941	2
#22553932	2
#22553928	2
#22553921	2
#22553920	2
#22553919	2
#22553868	2
#22553866	2
#22553845	2
#541×C₁₃₁	2
#3555	131