Subgroups — #30680548

Order 16768.

1050 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554057	C₂	1	1	yes	maximal, characteristic, complemented
2	#22554056	C₂	1	1	yes	maximal, characteristic, complemented
3	#22554051	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554050	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554045	C₂	1	1	yes	maximal, characteristic, complemented
6	#22554029	C₂	1	1	yes	maximal, characteristic, complemented
7	#22554013	C₂	1	1	yes	maximal, characteristic, complemented
8	#22554008	C₂	1	1	yes	maximal, characteristic, complemented
9	#22553992	C₂	1	1	yes	maximal, characteristic, complemented
10	#22553988	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553980	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553970	C₂	1	1	yes	maximal, characteristic, complemented
13	#22553970	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553962	C₂	1	1	yes	maximal, characteristic, complemented
15	#22553952	C₂	1	1	yes	maximal, characteristic, complemented
16	#22553949	C₂	1	1	yes	maximal, characteristic, complemented
17	#22553919	C₂	1	1	yes	maximal, characteristic, complemented
18	#22553914	C₂	1	1	yes	maximal, characteristic, complemented
19	#22553913	C₂	1	1	yes	maximal, characteristic, complemented
20	#22553912	C₂	1	1	yes	maximal, characteristic, complemented
21	#22553908	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553906	C₂	1	1	yes	maximal, characteristic, complemented
23	#22553901	C₂	1	1	yes	maximal, characteristic, complemented
24	#22553898	C₂	1	1	yes	maximal, characteristic, complemented
25	#22553897	C₂	1	1	yes	maximal, characteristic, complemented
26	#22553885	C₂	1	1	yes	maximal, characteristic, complemented
27	#22553877	C₂	1	1	yes	maximal, characteristic, complemented
28	#22553857	C₂	1	1	yes	maximal, characteristic, complemented
29	#22553842	C₂	1	1	yes	maximal, characteristic, complemented
30	#22553839	C₂	1	1	yes	maximal, characteristic, complemented
31	#538×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14523513	C₂²	1	1	yes	characteristic
33	C₂×#14523512	C₂²	1	1	yes	characteristic
34	C₂×#14523512	C₂²	1	1	yes	characteristic
35	C₂×#14523512	C₂²	1	1	yes	characteristic, complemented
36	C₂×Q₈×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
38	#16862245	C₂²	1	1	yes	characteristic, complemented
39	#16862245	C₂²	1	1	yes	characteristic, complemented
40	#16862242	C₂²	1	1	yes	characteristic
41	#16862242	C₂²	1	1	yes	characteristic
42	#16862242	C₂²	1	1	yes	characteristic, complemented
43	#16862242	C₂²	1	1	yes	characteristic, complemented
44	#16862241	C₂²	1	1	yes	characteristic, complemented
45	#16862241	C₂²	1	1	yes	characteristic, complemented
46	#16862241	C₂²	1	1	yes	characteristic, complemented
47	#16862241	C₂²	1	1	yes	characteristic, complemented
48	#16862239	C₂²	1	1	yes	characteristic
49	#16862239	C₂²	1	1	yes	characteristic
50	#16862239	C₂²	1	1	yes	characteristic
51	#16862239	C₂²	1	1	yes	characteristic
52	#16862239	C₂²	1	1	yes	characteristic, complemented
53	#16862239	C₂²	1	1	yes	characteristic, complemented
54	#16862238	C₂²	1	1	yes	characteristic, complemented
55	#16862237	C₂²	1	1	yes	characteristic, complemented
56	#16862236	C₂²	1	1	yes	characteristic, complemented
57	#16862236	C₂²	1	1	yes	characteristic, complemented
58	#16862236	C₂²	1	1	yes	characteristic, complemented
59	#16862236	C₂²	1	1	yes	characteristic, complemented
60	#16862234	C₂²	1	1	yes	characteristic, complemented
61	#16862233	C₂²	1	1	yes	characteristic, complemented
62	#16862232	C₂²	1	1	yes	characteristic
63	#16862232	C₂²	1	1	yes	characteristic
64	#16862232	C₂²	1	1	yes	characteristic
65	#16862232	C₂²	1	1	yes	characteristic
66	#16862232	C₂²	1	1	yes	characteristic
67	#16862232	C₂²	1	1	yes	characteristic
68	#16862232	C₂²	1	1	yes	characteristic, complemented
69	#16862232	C₂²	1	1	yes	characteristic, complemented
70	#16862231	C₂²	1	1	yes	characteristic, complemented
71	#16862231	C₂²	1	1	yes	characteristic, complemented
72	#16862231	C₂²	1	1	yes	characteristic, complemented
73	#16862230	C₂²	1	1	yes	characteristic
74	#16862230	C₂²	1	1	yes	characteristic, complemented
75	#16862230	C₂²	1	1	yes	characteristic, complemented
76	#16862229	C₂²	1	1	yes	characteristic
77	#16862229	C₂²	1	1	yes	characteristic, complemented
78	#16862229	C₂²	1	1	yes	characteristic, complemented
79	#16862229	C₂²	1	1	yes	characteristic, complemented
80	#16862228	C₂²	1	1	yes	characteristic
81	#16862228	C₂²	1	1	yes	characteristic
82	#16862228	C₂²	1	1	yes	characteristic
83	#16862228	C₂²	1	1	yes	characteristic, complemented
84	#16862228	C₂²	1	1	yes	characteristic, complemented
85	#16862228	C₂²	1	1	yes	characteristic, complemented
86	#16862228	C₂²	1	1	yes	characteristic, complemented
87	#16862228	C₂²	1	1	yes	characteristic, complemented
88	#16862228	C₂²	1	1	yes	characteristic, complemented
89	#16862227	C₂²	1	1	yes	characteristic
90	#16862227	C₂²	1	1	yes	characteristic, complemented
91	#16862227	C₂²	1	1	yes	characteristic, complemented
92	#16862226	C₂²	1	1	yes	characteristic, complemented
93	#16862225	C₂²	1	1	yes	characteristic, complemented
94	#16862224	C₂²	1	1	yes	characteristic, complemented
95	#16862223	C₂²	1	1	yes	characteristic
96	#16862223	C₂²	1	1	yes	characteristic
97	#16862223	C₂²	1	1	yes	characteristic, complemented
98	#16862223	C₂²	1	1	yes	characteristic, complemented
99	#16862223	C₂²	1	1	yes	characteristic, complemented
100	#16862223	C₂²	1	1	yes	characteristic, complemented
101	#16862223	C₂²	1	1	yes	characteristic, complemented
102	#16862222	C₂²	1	1	yes	characteristic, complemented
103	#16862222	C₂²	1	1	yes	characteristic, complemented
104	#16862222	C₂²	1	1	yes	characteristic, complemented
105	#16862221	C₂²	1	1	yes	characteristic, complemented
106	#16862221	C₂²	1	1	yes	characteristic, complemented
107	#16862220	C₂²	1	1	yes	characteristic
108	#16862220	C₂²	1	1	yes	characteristic, complemented
109	#16862220	C₂²	1	1	yes	characteristic, complemented
110	#16862219	C₂²	1	1	yes	characteristic
111	#16862219	C₂²	1	1	yes	characteristic
112	#16862219	C₂²	1	1	yes	characteristic
113	#16862219	C₂²	1	1	yes	characteristic
114	#16862219	C₂²	1	1	yes	characteristic
115	#16862219	C₂²	1	1	yes	characteristic, complemented
116	#16862219	C₂²	1	1	yes	characteristic, complemented
117	#16862219	C₂²	1	1	yes	characteristic, complemented
118	#16862219	C₂²	1	1	yes	characteristic, complemented
119	#16862218	C₂²	1	1	yes	characteristic
120	#16862218	C₂²	1	1	yes	characteristic
121	#16862218	C₂²	1	1	yes	characteristic
122	#16862218	C₂²	1	1	yes	characteristic
123	#16862218	C₂²	1	1	yes	characteristic
124	#16862218	C₂²	1	1	yes	characteristic, complemented
125	#16862218	C₂²	1	1	yes	characteristic, complemented
126	#16862218	C₂²	1	1	yes	characteristic, complemented
127	#16862218	C₂²	1	1	yes	characteristic, complemented
128	#16862217	C₂²	1	1	yes	characteristic
129	#16862217	C₂²	1	1	yes	characteristic
130	#16862217	C₂²	1	1	yes	characteristic
131	#16862217	C₂²	1	1	yes	characteristic, complemented
132	#16862216	C₂²	1	1	yes	characteristic
133	#16862216	C₂²	1	1	yes	characteristic
134	#16862215	C₂²	1	1	yes	characteristic
135	#16862215	C₂²	1	1	yes	characteristic
136	#16862214	C₂²	1	1	yes	characteristic
137	#16862214	C₂²	1	1	yes	characteristic
138	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
139	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
140	#16862211	C₂²	1	1	yes	characteristic, complemented
141	#16862211	C₂²	1	1	yes	characteristic, complemented
142	C₄×D₅₂₄	C₂²	1	1	yes	characteristic, complemented
143	C₄×D₅₂₄	C₂²	1	1	yes	characteristic, complemented
144	D₄×Dic₁₃₁	C₂²	1	1	yes	characteristic
145	D₄×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
146	#16862208	C₂²	1	1	yes	characteristic, complemented
147	#16862208	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
152	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
153	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
154	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
155	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
156	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	#16862205	C₂²	1	1	yes	characteristic, complemented
161	#16862204	C₂²	1	1	yes	characteristic, complemented
162	#16862203	C₂²	1	1	yes	characteristic, complemented
163	#16862203	C₂²	1	1	yes	characteristic, complemented
164	#16862202	C₂²	1	1	yes	characteristic
165	#16862202	C₂²	1	1	yes	characteristic, complemented
166	C₂×C₄⋊Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
167	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
168	C₂×C₂²⋊Dic₁₃₁	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
171	C₂×C₄×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
172	#126×C₁₃₁	C₂²	1	1	yes	characteristic
173	#126×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
174	#124×C₁₃₁	C₂²	1	1	yes	characteristic
175	#124×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
176	#123×C₁₃₁	C₂²	1	1	yes	characteristic
177	#123×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
179	#121×C₁₃₁	C₂²	1	1	yes	characteristic
180	#121×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
181	#121×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
182	#120×C₁₃₁	C₂²	1	1	yes	characteristic
183	#120×C₁₃₁	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
187	C₂³×D₁₃₁	C₂³	1	1	yes	characteristic
188	#14523513	—	4	2	no	—
189	#14523512	—	4	2	no	—
190	#14523512	—	4	2	no	—
191	#14523512	—	4	2	no	—
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	Q₈×D₁₃₁	—	4	2	no	—
198	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
199	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
200	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
201	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
202	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₃₁	—	4	2	no	—
204	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
222	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
223	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
224	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
225	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
226	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
227	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
228	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
245	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
246	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
248	C₄⋊Dic₁₃₁	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	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
264	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
265	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
266	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
267	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
268	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₁₃₁	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	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₁₃₁)⋊C₄	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	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
308	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
309	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
310	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
311	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
312	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
313	C₂⁴×C₁₃₁	C₂³	1	1	yes	characteristic
314	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
319	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
320	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
321	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
322	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
323	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
324	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
325	C₂²×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	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
331	C₄⋊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	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
346	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
347	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
348	C₂²×D₁₃₁	—	4	1	no	—
349	C₂²×D₁₃₁	—	4	1	no	—
350	C₂²×D₁₃₁	—	4	1	no	—
351	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
352	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
353	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
354	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
355	Dic₂₆₂	—	2	2	no	—
356	Dic₂₆₂	—	2	2	no	—
357	Dic₂₆₂	—	2	2	no	—
358	Dic₂₆₂	—	4	1	no	—
359	Dic₂₆₂	—	4	1	no	—
360	D₅₂₄	—	4	1	no	—
361	D₅₂₄	—	4	1	no	—
362	D₅₂₄	—	4	1	no	—
363	D₅₂₄	—	4	1	no	—
364	D₅₂₄	—	4	1	no	—
365	C₂²⋊D₁₃₁	—	2	2	no	—
366	C₂²⋊D₁₃₁	—	2	2	no	—
367	C₂²⋊D₁₃₁	—	2	2	no	—
368	C₂²⋊D₁₃₁	—	4	1	no	—
369	C₂²⋊D₁₃₁	—	4	1	no	—
370	C₂²⋊D₁₃₁	—	4	1	no	—
371	C₂²⋊D₁₃₁	—	4	1	no	—
372	C₂²⋊D₁₃₁	—	4	1	no	—
373	C₂²⋊D₁₃₁	—	4	1	no	—
374	C₂²⋊D₁₃₁	—	4	1	no	—
375	C₂²⋊D₁₃₁	—	4	1	no	—
376	C₂²⋊D₁₃₁	—	4	1	no	—
377	C₂²⋊D₁₃₁	—	4	1	no	—
378	C₂²⋊D₁₃₁	—	4	1	no	—
379	C₂²⋊D₁₃₁	—	4	1	no	—
380	C₂²⋊D₁₃₁	—	4	1	no	—
381	C₂²⋊D₁₃₁	—	4	1	no	—
382	C₂²⋊D₁₃₁	—	4	1	no	—
383	C₂×Dic₁₃₁	—	2	2	no	—
384	C₂×Dic₁₃₁	—	2	2	no	—
385	C₂×Dic₁₃₁	—	4	1	no	—
386	C₂×Dic₁₃₁	—	4	1	no	—
387	C₂×Dic₁₃₁	—	4	1	no	—
388	C₂×Dic₁₃₁	—	4	1	no	—
389	C₂×Dic₁₃₁	—	4	1	no	—
390	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
402	C₄×D₁₃₁	—	2	2	no	—
403	C₄×D₁₃₁	—	4	1	no	—
404	C₄×D₁₃₁	—	4	1	no	—
405	C₄×D₁₃₁	—	4	1	no	—
406	C₄×D₁₃₁	—	4	1	no	—
407	C₄×D₁₃₁	—	4	1	no	—
408	C₄×D₁₃₁	—	4	1	no	—
409	C₄×D₁₃₁	—	4	1	no	—
410	C₄×D₁₃₁	—	4	1	no	—
411	C₄×D₁₃₁	—	4	1	no	—
412	C₂³×C₁₃₁	—	4	1	no	—
413	C₂³×C₁₃₁	—	4	1	no	—
414	C₂³×C₁₃₁	—	4	1	no	—
415	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
416	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
417	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
418	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
419	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
420	Q₈×C₁₃₁	—	4	1	no	—
421	D₄×C₁₃₁	—	4	1	no	—
422	D₄×C₁₃₁	—	4	1	no	—
423	D₄×C₁₃₁	—	4	1	no	—
424	D₄×C₁₃₁	—	4	1	no	—
425	D₄×C₁₃₁	—	4	1	no	—
426	D₄×C₁₃₁	—	4	1	no	—
427	D₄×C₁₃₁	—	4	1	no	—
428	C₂×C₄×C₁₃₁	—	4	1	no	—
429	C₂×C₄×C₁₃₁	—	4	1	no	—
430	C₂×C₄×C₁₃₁	—	4	1	no	—
431	C₂×C₄×C₁₃₁	—	4	1	no	—
432	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
433	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
434	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
435	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
436	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
437	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
438	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
439	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
440	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
441	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
442	C₂²×C₁₃₁	—	2	1	no	—
443	C₂²×C₁₃₁	—	2	1	no	—
444	C₂²×C₁₃₁	—	2	1	no	—
445	C₂²×C₁₃₁	—	2	1	no	—
446	C₂²×C₁₃₁	—	2	1	no	—
447	C₂²×C₁₃₁	—	2	1	no	—
448	C₂²×C₁₃₁	—	2	1	no	—
449	C₂²×C₁₃₁	—	2	1	no	—
450	C₂²×C₁₃₁	—	2	1	no	—
451	C₂²×C₁₃₁	—	2	1	no	—
452	C₂²×C₁₃₁	—	2	1	no	—
453	C₂²×C₁₃₁	—	2	1	no	—
454	C₂²×C₁₃₁	—	2	1	no	—
455	C₂²×C₁₃₁	—	2	1	no	—
456	C₂²×C₁₃₁	—	2	1	no	—
457	C₂²×C₁₃₁	—	8	2	no	—
458	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
459	C₂×D₁₃₁	—	2	1	no	—
460	C₂×D₁₃₁	—	2	1	no	—
461	C₂×D₁₃₁	—	2	1	no	—
462	C₂×D₁₃₁	—	2	1	no	—
463	C₂×D₁₃₁	—	2	1	no	—
464	C₂×D₁₃₁	—	2	1	no	—
465	C₂×D₁₃₁	—	2	1	no	—
466	C₂×D₁₃₁	—	2	1	no	—
467	C₂×D₁₃₁	—	2	1	no	—
468	C₂×D₁₃₁	—	2	1	no	—
469	C₂×D₁₃₁	—	2	1	no	—
470	C₂×D₁₃₁	—	2	1	no	—
471	C₂×D₁₃₁	—	8	2	no	—
472	C₄×C₁₃₁	—	2	1	no	—
473	C₄×C₁₃₁	—	2	1	no	—
474	C₄×C₁₃₁	—	2	1	no	—
475	C₄×C₁₃₁	—	2	1	no	—
476	C₄×C₁₃₁	—	2	1	no	—
477	C₄×C₁₃₁	—	2	1	no	—
478	C₄×C₁₃₁	—	2	1	no	—
479	C₄×C₁₃₁	—	2	1	no	—
480	C₄×C₁₃₁	—	2	1	no	—
481	C₄×C₁₃₁	—	2	1	no	—
482	Dic₁₃₁	—	2	1	no	—
483	Dic₁₃₁	—	2	1	no	—
484	Dic₁₃₁	—	2	1	no	—
485	Dic₁₃₁	—	2	1	no	—
486	Dic₁₃₁	—	2	1	no	—
487	Dic₁₃₁	—	2	1	no	—
488	Dic₁₃₁	—	2	1	no	—
489	Dic₁₃₁	—	2	1	no	—
490	Dic₁₃₁	—	2	1	no	—
491	Dic₁₃₁	—	2	1	no	—
492	Dic₁₃₁	—	2	1	no	—
493	Dic₁₃₁	H(5,𝔽₂)	1	2	yes	—
494	C₂×C₁₃₁	—	4	1	no	—
495	C₂×C₁₃₁	—	4	1	no	—
496	C₂×C₁₃₁	—	4	1	no	—
497	C₂×C₁₃₁	—	4	1	no	—
498	C₂×C₁₃₁	—	4	1	no	—
499	C₂×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂×C₁₃₁	#585	1	1	yes	characteristic
501	C₂×C₁₃₁	#585	1	1	yes	characteristic
502	D₁₃₁	—	4	1	no	—
503	D₁₃₁	—	4	1	no	—
504	D₁₃₁	—	4	1	no	—
505	D₁₃₁	—	4	1	no	—
506	C₁₃₁	#3562	1	1	yes	characteristic, complemented, Sylow
507	#3562	—	131	1	no	maximal, Sylow
508	#562	—	131	1	no	—
509	#562	—	131	1	no	—
510	#560	—	131	1	no	—
511	#560	—	131	1	no	—
512	#559	—	131	1	no	—
513	#556	—	131	1	no	—
514	#553	—	131	1	no	—
515	#553	—	131	1	no	—
516	#551	—	131	1	no	—
517	#551	—	131	1	no	—
518	#550	—	131	1	no	—
519	#548	—	131	1	no	—
520	#548	—	131	1	no	—
521	#547	—	131	1	no	—
522	#546	—	131	1	no	—
523	#546	—	131	1	no	—
524	#541	—	131	1	no	—
525	#540	—	131	1	no	—
526	#540	—	131	1	no	—
527	#540	—	131	1	no	—
528	#539	—	131	1	no	—
529	#539	—	131	1	no	—
530	#538	—	131	1	no	—
531	#538	—	131	1	no	—
532	#538	—	131	1	no	—
533	#538	D₁₃₁	1	1	yes	characteristic, complemented
534	#536	—	131	1	no	—
535	#535	—	131	1	no	—
536	#532	—	131	1	no	—
537	#529	—	131	1	no	—
538	#529	—	131	1	no	—
539	C₂×#41	—	131	1	no	—
540	C₂×#41	—	131	1	no	—
541	C₂×#41	—	131	1	no	—
542	C₂×#41	—	131	1	no	—
543	C₂²×Q₈	—	131	1	no	—
544	C₂²×D₄	—	131	1	no	—
545	C₄⋊Q₈	—	131	1	no	—
546	C₄⋊Q₈	—	131	1	no	—
547	#127	—	131	1	no	—
548	#127	—	131	1	no	—
549	#127	—	131	1	no	—
550	#127	—	131	1	no	—
551	#126	—	131	1	no	—
552	#126	—	131	1	no	—
553	#126	—	131	1	no	—
554	#126	—	131	1	no	—
555	#126	—	131	1	no	—
556	#126	—	131	1	no	—
557	#126	—	131	1	no	—
558	#126	—	131	1	no	—
559	#126	—	131	1	no	—
560	#126	—	131	1	no	—
561	#126	C₂×D₁₃₁	1	1	yes	characteristic
562	#126	C₂×D₁₃₁	1	1	yes	characteristic, complemented
563	#125	—	131	1	no	—
564	#125	—	131	1	no	—
565	#125	—	131	1	no	—
566	#125	—	131	1	no	—
567	#125	—	131	1	no	—
568	#125	—	131	1	no	—
569	#124	—	131	1	no	—
570	#124	—	131	1	no	—
571	#124	—	131	1	no	—
572	#124	—	131	1	no	—
573	#124	—	131	1	no	—
574	#124	—	131	1	no	—
575	#124	—	131	1	no	—
576	#124	—	131	1	no	—
577	#124	—	131	1	no	—
578	#124	—	131	1	no	—
579	#124	C₂×D₁₃₁	1	1	yes	characteristic
580	#124	C₂×D₁₃₁	1	1	yes	characteristic, complemented
581	#123	—	131	1	no	—
582	#123	—	131	1	no	—
583	#123	—	131	1	no	—
584	#123	—	131	1	no	—
585	#123	—	131	1	no	—
586	#123	—	131	1	no	—
587	#123	—	131	1	no	—
588	#123	—	131	1	no	—
589	#123	—	131	1	no	—
590	#123	—	131	1	no	—
591	#123	—	131	1	no	—
592	#123	—	131	1	no	—
593	#123	—	131	1	no	—
594	#123	—	131	1	no	—
595	#123	—	131	1	no	—
596	#123	—	131	1	no	—
597	#123	—	131	1	no	—
598	#123	—	131	1	no	—
599	#123	—	131	1	no	—
600	#123	—	131	1	no	—
601	#123	—	131	1	no	—
602	#123	—	131	1	no	—
603	#123	C₂×D₁₃₁	1	1	yes	characteristic
604	#123	C₂×D₁₃₁	1	1	yes	characteristic, complemented
605	C₂²⋊Q₈	—	131	1	no	—
606	C₂²⋊Q₈	—	131	1	no	—
607	C₂²⋊Q₈	—	131	1	no	—
608	C₂²⋊Q₈	—	131	1	no	—
609	C₂²⋊Q₈	—	131	1	no	—
610	C₂²⋊Q₈	—	131	1	no	—
611	C₂²⋊Q₈	—	131	1	no	—
612	C₂²⋊Q₈	—	131	1	no	—
613	C₂²⋊Q₈	—	131	1	no	—
614	C₂²⋊Q₈	—	131	1	no	—
615	C₂²⋊Q₈	—	131	1	no	—
616	C₂²⋊Q₈	—	131	1	no	—
617	C₂²⋊Q₈	—	131	1	no	—
618	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
619	#121	—	131	1	no	—
620	#121	—	131	1	no	—
621	#121	—	131	1	no	—
622	#121	—	131	1	no	—
623	#121	—	131	1	no	—
624	#121	—	131	1	no	—
625	#121	—	131	1	no	—
626	#121	—	131	1	no	—
627	#121	—	131	1	no	—
628	#121	—	131	1	no	—
629	#121	—	131	1	no	—
630	#121	—	131	1	no	—
631	#121	—	131	1	no	—
632	#121	—	131	1	no	—
633	#121	—	131	1	no	—
634	#121	—	131	1	no	—
635	#121	—	131	1	no	—
636	#121	—	131	1	no	—
637	#121	—	131	1	no	—
638	#121	—	131	1	no	—
639	#121	—	131	1	no	—
640	#121	—	131	1	no	—
641	#121	—	131	1	no	—
642	#121	—	131	1	no	—
643	#121	—	131	1	no	—
644	#121	—	131	1	no	—
645	#121	—	131	1	no	—
646	#121	C₂×D₁₃₁	1	1	yes	characteristic
647	#121	C₂×D₁₃₁	1	1	yes	characteristic, complemented
648	#121	C₂×D₁₃₁	1	1	yes	characteristic, complemented
649	#120	—	131	1	no	—
650	#120	—	131	1	no	—
651	#120	—	131	1	no	—
652	#120	—	131	1	no	—
653	#120	—	131	1	no	—
654	#120	—	131	1	no	—
655	#120	C₂×D₁₃₁	1	1	yes	characteristic
656	#120	C₂×D₁₃₁	1	1	yes	characteristic
657	C₄×Q₈	—	131	1	no	—
658	C₄×Q₈	—	131	1	no	—
659	C₄×Q₈	—	131	1	no	—
660	C₄×Q₈	—	131	1	no	—
661	C₄×D₄	—	131	1	no	—
662	C₄×D₄	—	131	1	no	—
663	C₄×D₄	—	131	1	no	—
664	C₄×D₄	—	131	1	no	—
665	C₄×D₄	—	131	1	no	—
666	C₄×D₄	—	131	1	no	—
667	C₄×D₄	—	131	1	no	—
668	C₄×D₄	—	131	1	no	—
669	C₄×D₄	—	131	1	no	—
670	C₄×D₄	—	131	1	no	—
671	C₄×D₄	—	131	1	no	—
672	C₄×D₄	—	131	1	no	—
673	C₄×D₄	—	131	1	no	—
674	C₄×D₄	—	131	1	no	—
675	C₄×D₄	—	131	1	no	—
676	C₄×D₄	—	131	1	no	—
677	C₄×D₄	—	131	1	no	—
678	C₄×D₄	—	131	1	no	—
679	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
680	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
681	#117	—	131	1	no	—
682	#117	—	131	1	no	—
683	#117	—	131	1	no	—
684	#117	—	131	1	no	—
685	#117	—	131	1	no	—
686	#117	—	131	1	no	—
687	C₂×C₄⋊C₄	—	131	1	no	—
688	C₂×C₄⋊C₄	—	131	1	no	—
689	C₂×C₂²⋊C₄	—	131	1	no	—
690	C₂×C₂²⋊C₄	—	131	1	no	—
691	C₂×C₂²⋊C₄	—	131	1	no	—
692	C₂×C₂²⋊C₄	C₂×D₁₃₁	1	1	yes	characteristic
693	C₂×C₄²	—	131	1	no	—
694	C₂⁴	—	131	1	no	—
695	C₂⁴	C₂²×D₁₃₁	1	1	yes	characteristic
696	#41	—	524	2	no	—
697	#41	—	524	2	no	—
698	#41	—	524	2	no	—
699	#41	—	524	2	no	—
700	C₂×Q₈	—	524	2	no	—
701	C₂×Q₈	—	131	1	no	—
702	C₂×Q₈	—	131	1	no	—
703	C₂×Q₈	—	131	1	no	—
704	C₂×Q₈	—	131	1	no	—
705	C₂×Q₈	—	131	1	no	—
706	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
707	C₂×D₄	—	524	2	no	—
708	C₂×D₄	—	131	1	no	—
709	C₂×D₄	—	131	1	no	—
710	C₂×D₄	—	131	1	no	—
711	C₂×D₄	—	131	1	no	—
712	C₂×D₄	—	131	1	no	—
713	C₂×D₄	—	131	1	no	—
714	C₂×D₄	—	131	1	no	—
715	C₂×D₄	—	131	1	no	—
716	C₂×D₄	—	131	1	no	—
717	C₂×D₄	—	131	1	no	—
718	C₂×D₄	—	131	1	no	—
719	C₂×D₄	—	131	1	no	—
720	C₂×D₄	—	131	1	no	—
721	C₂×D₄	—	131	1	no	—
722	C₂×D₄	—	131	1	no	—
723	C₂×D₄	—	131	1	no	—
724	C₂×D₄	—	131	1	no	—
725	C₂×D₄	—	131	1	no	—
726	C₂×D₄	—	131	1	no	—
727	C₂×D₄	—	131	1	no	—
728	C₂×D₄	—	131	1	no	—
729	C₂×D₄	—	131	1	no	—
730	C₂×D₄	—	131	1	no	—
731	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
732	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
733	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
734	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
735	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
736	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
737	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
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	—	131	1	no	—
754	C₂²×C₄	—	131	1	no	—
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	C₄⋊C₄	—	131	1	no	—
760	C₄⋊C₄	—	131	1	no	—
761	C₄⋊C₄	—	131	1	no	—
762	C₄⋊C₄	—	131	1	no	—
763	C₄⋊C₄	—	131	1	no	—
764	C₄⋊C₄	—	131	1	no	—
765	C₄⋊C₄	—	131	1	no	—
766	C₄⋊C₄	—	131	1	no	—
767	C₄⋊C₄	—	131	1	no	—
768	C₄⋊C₄	—	131	1	no	—
769	C₄⋊C₄	—	131	1	no	—
770	C₄⋊C₄	—	131	1	no	—
771	C₄⋊C₄	—	131	1	no	—
772	C₄⋊C₄	—	131	1	no	—
773	C₄⋊C₄	—	131	1	no	—
774	C₄⋊C₄	—	131	1	no	—
775	C₄⋊C₄	—	131	1	no	—
776	C₄⋊C₄	—	131	1	no	—
777	C₄⋊C₄	—	131	1	no	—
778	C₄⋊C₄	—	131	1	no	—
779	C₄⋊C₄	—	131	1	no	—
780	C₄⋊C₄	—	131	1	no	—
781	C₄⋊C₄	—	131	1	no	—
782	C₄⋊C₄	—	131	1	no	—
783	C₄⋊C₄	—	131	1	no	—
784	C₄⋊C₄	—	131	1	no	—
785	C₄⋊C₄	—	131	1	no	—
786	C₄⋊C₄	—	131	1	no	—
787	C₄⋊C₄	—	131	1	no	—
788	C₄⋊C₄	—	131	1	no	—
789	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
795	C₂²⋊C₄	—	131	1	no	—
796	C₂²⋊C₄	—	131	1	no	—
797	C₂²⋊C₄	—	131	1	no	—
798	C₂²⋊C₄	—	131	1	no	—
799	C₂²⋊C₄	—	131	1	no	—
800	C₂²⋊C₄	—	131	1	no	—
801	C₂²⋊C₄	—	131	1	no	—
802	C₂²⋊C₄	—	131	1	no	—
803	C₂²⋊C₄	—	131	1	no	—
804	C₂²⋊C₄	—	131	1	no	—
805	C₂²⋊C₄	—	131	1	no	—
806	C₂²⋊C₄	—	131	1	no	—
807	C₂²⋊C₄	—	131	1	no	—
808	C₂²⋊C₄	—	131	1	no	—
809	C₂²⋊C₄	—	131	1	no	—
810	C₂²⋊C₄	—	131	1	no	—
811	C₂²⋊C₄	—	131	1	no	—
812	C₂²⋊C₄	—	131	1	no	—
813	C₂²⋊C₄	—	131	1	no	—
814	C₂²⋊C₄	—	131	1	no	—
815	C₂²⋊C₄	—	131	1	no	—
816	C₂²⋊C₄	—	131	1	no	—
817	C₂²⋊C₄	—	131	1	no	—
818	C₂²⋊C₄	—	131	1	no	—
819	C₂²⋊C₄	—	131	1	no	—
820	C₂²⋊C₄	—	131	1	no	—
821	C₂²⋊C₄	—	131	1	no	—
822	C₂²⋊C₄	—	131	1	no	—
823	C₂²⋊C₄	—	131	1	no	—
824	C₂²⋊C₄	—	131	1	no	—
825	C₂²⋊C₄	—	131	1	no	—
826	C₂²⋊C₄	—	131	1	no	—
827	C₂²⋊C₄	—	131	1	no	—
828	C₂²⋊C₄	—	131	1	no	—
829	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
830	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
832	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
834	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
843	C₄²	—	131	1	no	—
844	C₄²	—	131	1	no	—
845	C₄²	—	131	1	no	—
846	C₄²	—	131	1	no	—
847	C₄²	—	131	1	no	—
848	C₄²	—	131	1	no	—
849	C₄²	—	131	1	no	—
850	C₄²	—	131	1	no	—
851	C₄²	—	131	1	no	—
852	C₄²	—	131	1	no	—
853	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
854	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
855	C₂³	—	4	1	no	—
856	C₂³	—	4	1	no	—
857	C₂³	—	4	1	no	—
858	C₂³	—	524	1	no	—
859	C₂³	—	524	1	no	—
860	C₂³	—	524	1	no	—
861	C₂³	—	131	1	no	—
862	C₂³	—	131	1	no	—
863	C₂³	—	131	1	no	—
864	C₂³	—	131	1	no	—
865	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
866	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
867	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
868	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
869	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
870	Q₈	—	4	1	no	—
871	Q₈	—	262	2	no	—
872	Q₈	—	262	2	no	—
873	Q₈	—	262	2	no	—
874	Q₈	—	524	1	no	—
875	Q₈	—	524	1	no	—
876	D₄	—	4	1	no	—
877	D₄	—	4	1	no	—
878	D₄	—	4	1	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	1	no	—
881	D₄	—	4	1	no	—
882	D₄	—	4	1	no	—
883	D₄	—	262	2	no	—
884	D₄	—	262	2	no	—
885	D₄	—	262	2	no	—
886	D₄	—	524	1	no	—
887	D₄	—	524	1	no	—
888	D₄	—	524	1	no	—
889	D₄	—	524	1	no	—
890	D₄	—	524	1	no	—
891	D₄	—	524	1	no	—
892	D₄	—	524	1	no	—
893	D₄	—	524	1	no	—
894	D₄	—	524	1	no	—
895	D₄	—	524	1	no	—
896	D₄	—	524	1	no	—
897	D₄	—	524	1	no	—
898	D₄	—	524	1	no	—
899	D₄	—	524	1	no	—
900	D₄	—	524	1	no	—
901	D₄	—	524	1	no	—
902	D₄	—	524	1	no	—
903	D₄	—	524	1	no	—
904	D₄	—	524	1	no	—
905	D₄	—	524	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	262	2	no	—
911	C₂×C₄	—	262	2	no	—
912	C₂×C₄	—	262	2	no	—
913	C₂×C₄	—	524	1	no	—
914	C₂×C₄	—	524	1	no	—
915	C₂×C₄	—	524	1	no	—
916	C₂×C₄	—	524	1	no	—
917	C₂×C₄	—	524	1	no	—
918	C₂×C₄	—	524	1	no	—
919	C₂×C₄	—	524	1	no	—
920	C₂×C₄	—	524	1	no	—
921	C₂×C₄	—	524	1	no	—
922	C₂×C₄	—	524	1	no	—
923	C₂×C₄	—	524	1	no	—
924	C₂×C₄	—	524	1	no	—
925	C₂×C₄	—	524	1	no	—
926	C₂×C₄	—	524	1	no	—
927	C₂×C₄	—	131	1	no	—
928	C₂×C₄	—	131	1	no	—
929	C₂×C₄	—	131	1	no	—
930	C₂×C₄	—	131	1	no	—
931	C₂×C₄	—	131	1	no	—
932	C₂×C₄	—	131	1	no	—
933	C₂×C₄	—	131	1	no	—
934	C₂×C₄	—	131	1	no	—
935	C₂×C₄	—	131	1	no	—
936	C₂×C₄	—	131	1	no	—
937	C₂×C₄	—	131	1	no	—
938	C₂×C₄	—	131	1	no	—
939	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
949	C₂²	—	2	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	262	1	no	—
965	C₂²	—	262	1	no	—
966	C₂²	—	262	1	no	—
967	C₂²	—	262	1	no	—
968	C₂²	—	262	1	no	—
969	C₂²	—	262	1	no	—
970	C₂²	—	262	1	no	—
971	C₂²	—	262	1	no	—
972	C₂²	—	262	1	no	—
973	C₂²	—	262	1	no	—
974	C₂²	—	262	1	no	—
975	C₂²	—	262	1	no	—
976	C₂²	—	8	2	no	—
977	C₂²	—	1048	2	no	—
978	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	262	1	no	—
990	C₄	—	262	1	no	—
991	C₄	—	262	1	no	—
992	C₄	—	262	1	no	—
993	C₄	—	262	1	no	—
994	C₄	—	262	1	no	—
995	C₄	—	262	1	no	—
996	C₄	—	262	1	no	—
997	C₄	—	262	1	no	—
998	C₄	—	262	1	no	—
999	C₄	—	262	1	no	—
1000	C₄	—	131	2	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	4	1	no	—
1003	C₂	—	4	1	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	524	1	no	—
1007	C₂	—	524	1	no	—
1008	C₂	—	524	1	no	—
1009	C₂	—	524	1	no	—
1010	C₂	H(5,𝔽₂)×D₁₃₁	1	1	yes	characteristic
1011	C₂	#22554147	1	1	yes	characteristic
1012	C₂	#22554148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#538×C₁₃₁	C₂
hypercenter	#538	D₁₃₁
hypocenter	C₁₃₁	#3562
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #22554057	C₂	semidirect
2. #22554056	C₂	semidirect
3. #22554051	C₂	semidirect
4. #22554050	C₂	semidirect
5. #22554045	C₂	semidirect
6. #22554029	C₂	semidirect
7. #22554013	C₂	semidirect
8. #22554008	C₂	semidirect
9. #22553992	C₂	semidirect
10. #22553988	C₂	semidirect
11. #22553980	C₂	semidirect
12. #22553970	C₂	semidirect
13. #22553970	C₂	semidirect
14. #22553962	C₂	semidirect
15. #22553952	C₂	semidirect
16. #22553949	C₂	semidirect
17. #22553919	C₂	semidirect
18. #22553914	C₂	semidirect
19. #22553913	C₂	semidirect
20. #22553912	C₂	semidirect
21. #22553908	C₂	semidirect
22. #22553906	C₂	semidirect
23. #22553901	C₂	semidirect
24. #22553898	C₂	semidirect
25. #22553897	C₂	semidirect
26. #22553885	C₂	semidirect
27. #22553877	C₂	semidirect
28. #22553857	C₂	semidirect
29. #22553842	C₂	semidirect
30. #22553839	C₂	semidirect
31. #538×C₁₃₁	C₂	semidirect
35. C₂×#14523512	C₂²	semidirect
36. C₂×Q₈×D₁₃₁	C₂²	semidirect
38. #16862245	C₂²	semidirect
39. #16862245	C₂²	semidirect
42. #16862242	C₂²	semidirect
43. #16862242	C₂²	semidirect
44. #16862241	C₂²	semidirect
45. #16862241	C₂²	semidirect
46. #16862241	C₂²	semidirect
47. #16862241	C₂²	semidirect
52. #16862239	C₂²	semidirect
53. #16862239	C₂²	semidirect
54. #16862238	C₂²	semidirect
55. #16862237	C₂²	semidirect
56. #16862236	C₂²	semidirect
57. #16862236	C₂²	semidirect
58. #16862236	C₂²	semidirect
59. #16862236	C₂²	semidirect
60. #16862234	C₂²	semidirect
61. #16862233	C₂²	semidirect
68. #16862232	C₂²	semidirect
69. #16862232	C₂²	semidirect
70. #16862231	C₂²	semidirect
71. #16862231	C₂²	semidirect
72. #16862231	C₂²	semidirect
74. #16862230	C₂²	semidirect
75. #16862230	C₂²	semidirect
77. #16862229	C₂²	semidirect
78. #16862229	C₂²	semidirect
79. #16862229	C₂²	semidirect
83. #16862228	C₂²	semidirect
84. #16862228	C₂²	semidirect
85. #16862228	C₂²	semidirect
86. #16862228	C₂²	semidirect
87. #16862228	C₂²	semidirect
88. #16862228	C₂²	semidirect
90. #16862227	C₂²	semidirect
91. #16862227	C₂²	semidirect
92. #16862226	C₂²	semidirect
93. #16862225	C₂²	semidirect
94. #16862224	C₂²	semidirect
97. #16862223	C₂²	semidirect
98. #16862223	C₂²	semidirect
99. #16862223	C₂²	semidirect
100. #16862223	C₂²	semidirect
101. #16862223	C₂²	semidirect
102. #16862222	C₂²	semidirect
103. #16862222	C₂²	semidirect
104. #16862222	C₂²	semidirect
105. #16862221	C₂²	semidirect
106. #16862221	C₂²	semidirect
108. #16862220	C₂²	semidirect
109. #16862220	C₂²	semidirect
115. #16862219	C₂²	semidirect
116. #16862219	C₂²	semidirect
117. #16862219	C₂²	semidirect
118. #16862219	C₂²	semidirect
124. #16862218	C₂²	semidirect
125. #16862218	C₂²	semidirect
126. #16862218	C₂²	semidirect
127. #16862218	C₂²	semidirect
131. #16862217	C₂²	semidirect
138. C₄×Dic₂₆₂	C₂²	semidirect
139. C₄×Dic₂₆₂	C₂²	semidirect
140. #16862211	C₂²	semidirect
141. #16862211	C₂²	semidirect
142. C₄×D₅₂₄	C₂²	semidirect
143. C₄×D₅₂₄	C₂²	semidirect
145. D₄×Dic₁₃₁	C₂²	semidirect
146. #16862208	C₂²	semidirect
147. #16862208	C₂²	semidirect
149. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
150. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
151. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
154. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
155. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
156. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
157. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
158. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
159. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
160. #16862205	C₂²	semidirect
161. #16862204	C₂²	semidirect
162. #16862203	C₂²	semidirect
163. #16862203	C₂²	semidirect
165. #16862202	C₂²	semidirect
166. C₂×C₄⋊Dic₁₃₁	C₂²	semidirect
167. C₄⋊C₄×D₁₃₁	C₂²	semidirect
171. C₂×C₄×Dic₁₃₁	C₂²	semidirect
173. #126×C₁₃₁	C₂²	semidirect
175. #124×C₁₃₁	C₂²	semidirect
177. #123×C₁₃₁	C₂²	semidirect
178. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
180. #121×C₁₃₁	C₂²	semidirect
181. #121×C₁₃₁	C₂²	semidirect
184. C₄×D₄×C₁₃₁	C₂²	semidirect
185. C₄×D₄×C₁₃₁	C₂²	semidirect
506. C₁₃₁	#3562	semidirect
533. #538	D₁₃₁	semidirect
562. #126	C₂×D₁₃₁	semidirect
580. #124	C₂×D₁₃₁	semidirect
604. #123	C₂×D₁₃₁	semidirect
618. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
647. #121	C₂×D₁₃₁	semidirect
648. #121	C₂×D₁₃₁	semidirect
679. C₄×D₄	C₂×D₁₃₁	semidirect
680. C₄×D₄	C₂×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#22554057	2
#22554056	2
#22554051	2
#22554050	2
#22554045	2
#22554029	2
#22554013	2
#22554008	2
#22553992	2
#22553988	2
#22553980	2
#22553970	2
#22553962	2
#22553952	2
#22553949	2
#22553919	2
#22553914	2
#22553913	2
#22553912	2
#22553908	2
#22553906	2
#22553901	2
#22553898	2
#22553897	2
#22553885	2
#22553877	2
#22553857	2
#22553842	2
#22553839	2
#538×C₁₃₁	2
#3562	131