Subgroups — #30680642

Order 16768.

954 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554058	C₂	1	1	yes	maximal, characteristic, complemented
2	#22554058	C₂	1	1	yes	maximal, characteristic, complemented
3	#22554052	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554044	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554036	C₂	1	1	yes	maximal, characteristic, complemented
6	#22554028	C₂	1	1	yes	maximal, characteristic, complemented
7	#22554015	C₂	1	1	yes	maximal, characteristic, complemented
8	#22554013	C₂	1	1	yes	maximal, characteristic, complemented
9	#22554013	C₂	1	1	yes	maximal, characteristic, complemented
10	#22554000	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553998	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553996	C₂	1	1	yes	maximal, characteristic, complemented
13	#22553989	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553987	C₂	1	1	yes	maximal, characteristic, complemented
15	#22553985	C₂	1	1	yes	maximal, characteristic, complemented
16	#22553936	C₂	1	1	yes	maximal, characteristic, complemented
17	#22553935	C₂	1	1	yes	maximal, characteristic, complemented
18	#22553928	C₂	1	1	yes	maximal, characteristic, complemented
19	#22553923	C₂	1	1	yes	maximal, characteristic, complemented
20	#22553921	C₂	1	1	yes	maximal, characteristic, complemented
21	#22553914	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553910	C₂	1	1	yes	maximal, characteristic, complemented
23	#22553903	C₂	1	1	yes	maximal, characteristic, complemented
24	#22553903	C₂	1	1	yes	maximal, characteristic, complemented
25	#22553902	C₂	1	1	yes	maximal, characteristic, complemented
26	#22553901	C₂	1	1	yes	maximal, characteristic, complemented
27	#22553896	C₂	1	1	yes	maximal, characteristic, complemented
28	#22553848	C₂	1	1	yes	maximal, characteristic, complemented
29	#22553848	C₂	1	1	yes	maximal, characteristic, complemented
30	#22553839	C₂	1	1	yes	maximal, characteristic, complemented
31	#563×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
32	#16862245	C₂²	1	1	yes	characteristic, complemented
33	#16862242	C₂²	1	1	yes	characteristic
34	#16862241	C₂²	1	1	yes	characteristic
35	#16862241	C₂²	1	1	yes	characteristic
36	#16862241	C₂²	1	1	yes	characteristic
37	#16862241	C₂²	1	1	yes	characteristic
38	#16862241	C₂²	1	1	yes	characteristic
39	#16862241	C₂²	1	1	yes	characteristic
40	#16862241	C₂²	1	1	yes	characteristic
41	#16862241	C₂²	1	1	yes	characteristic
42	#16862241	C₂²	1	1	yes	characteristic
43	#16862241	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	#16862240	C₂²	1	1	yes	characteristic
48	#16862239	C₂²	1	1	yes	characteristic
49	#16862239	C₂²	1	1	yes	characteristic
50	#16862238	C₂²	1	1	yes	characteristic, complemented
51	#16862237	C₂²	1	1	yes	characteristic, complemented
52	#16862237	C₂²	1	1	yes	characteristic, complemented
53	#16862237	C₂²	1	1	yes	characteristic, complemented
54	#16862236	C₂²	1	1	yes	characteristic, complemented
55	#16862236	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	#16862235	C₂²	1	1	yes	characteristic
61	#16862235	C₂²	1	1	yes	characteristic
62	#16862235	C₂²	1	1	yes	characteristic
63	#16862235	C₂²	1	1	yes	characteristic
64	#16862235	C₂²	1	1	yes	characteristic, complemented
65	#16862235	C₂²	1	1	yes	characteristic, complemented
66	#16862234	C₂²	1	1	yes	characteristic
67	#16862232	C₂²	1	1	yes	characteristic
68	#16862232	C₂²	1	1	yes	characteristic
69	#16862232	C₂²	1	1	yes	characteristic
70	#16862232	C₂²	1	1	yes	characteristic, complemented
71	#16862231	C₂²	1	1	yes	characteristic
72	#16862231	C₂²	1	1	yes	characteristic
73	#16862231	C₂²	1	1	yes	characteristic
74	#16862231	C₂²	1	1	yes	characteristic
75	#16862231	C₂²	1	1	yes	characteristic
76	#16862231	C₂²	1	1	yes	characteristic
77	#16862231	C₂²	1	1	yes	characteristic
78	#16862231	C₂²	1	1	yes	characteristic, complemented
79	#16862231	C₂²	1	1	yes	characteristic, complemented
80	#16862230	C₂²	1	1	yes	characteristic
81	#16862230	C₂²	1	1	yes	characteristic
82	#16862230	C₂²	1	1	yes	characteristic
83	#16862230	C₂²	1	1	yes	characteristic, complemented
84	#16862230	C₂²	1	1	yes	characteristic, complemented
85	#16862229	C₂²	1	1	yes	characteristic, complemented
86	#16862228	C₂²	1	1	yes	characteristic
87	#16862228	C₂²	1	1	yes	characteristic
88	#16862228	C₂²	1	1	yes	characteristic
89	#16862228	C₂²	1	1	yes	characteristic
90	#16862228	C₂²	1	1	yes	characteristic
91	#16862228	C₂²	1	1	yes	characteristic
92	#16862228	C₂²	1	1	yes	characteristic, complemented
93	#16862226	C₂²	1	1	yes	characteristic
94	#16862226	C₂²	1	1	yes	characteristic
95	#16862226	C₂²	1	1	yes	characteristic, complemented
96	#16862226	C₂²	1	1	yes	characteristic, complemented
97	#16862226	C₂²	1	1	yes	characteristic, complemented
98	#16862224	C₂²	1	1	yes	characteristic
99	#16862224	C₂²	1	1	yes	characteristic
100	#16862224	C₂²	1	1	yes	characteristic, complemented
101	#16862224	C₂²	1	1	yes	characteristic, complemented
102	#16862223	C₂²	1	1	yes	characteristic
103	#16862223	C₂²	1	1	yes	characteristic, complemented
104	#16862222	C₂²	1	1	yes	characteristic
105	#16862222	C₂²	1	1	yes	characteristic
106	#16862222	C₂²	1	1	yes	characteristic, complemented
107	#16862221	C₂²	1	1	yes	characteristic
108	#16862221	C₂²	1	1	yes	characteristic
109	#16862221	C₂²	1	1	yes	characteristic
110	#16862221	C₂²	1	1	yes	characteristic
111	#16862221	C₂²	1	1	yes	characteristic
112	#16862221	C₂²	1	1	yes	characteristic
113	#16862221	C₂²	1	1	yes	characteristic, complemented
114	#16862220	C₂²	1	1	yes	characteristic
115	#16862220	C₂²	1	1	yes	characteristic
116	#16862220	C₂²	1	1	yes	characteristic
117	#16862219	C₂²	1	1	yes	characteristic
118	#16862219	C₂²	1	1	yes	characteristic
119	#16862219	C₂²	1	1	yes	characteristic
120	#16862219	C₂²	1	1	yes	characteristic
121	#16862219	C₂²	1	1	yes	characteristic
122	#16862219	C₂²	1	1	yes	characteristic, complemented
123	#16862219	C₂²	1	1	yes	characteristic, complemented
124	#16862218	C₂²	1	1	yes	characteristic
125	#16862216	C₂²	1	1	yes	characteristic
126	#16862216	C₂²	1	1	yes	characteristic
127	#16862216	C₂²	1	1	yes	characteristic
128	#16862214	C₂²	1	1	yes	characteristic
129	Q₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
130	Q₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
131	Q₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
132	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
133	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
134	#16862211	C₂²	1	1	yes	characteristic, complemented
135	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
136	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
137	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
138	C₄×D₅₂₄	C₂²	1	1	yes	characteristic, complemented
139	C₄×D₅₂₄	C₂²	1	1	yes	characteristic, complemented
140	D₄×Dic₁₃₁	C₂²	1	1	yes	characteristic
141	#16862208	C₂²	1	1	yes	characteristic
142	#16862208	C₂²	1	1	yes	characteristic
143	#16862208	C₂²	1	1	yes	characteristic
144	#16862208	C₂²	1	1	yes	characteristic, complemented
145	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
146	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
147	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
148	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
149	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
150	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	#16862205	C₂²	1	1	yes	characteristic
154	#16862204	C₂²	1	1	yes	characteristic
155	#16862204	C₂²	1	1	yes	characteristic
156	#16862204	C₂²	1	1	yes	characteristic
157	#16862204	C₂²	1	1	yes	characteristic, complemented
158	#16862204	C₂²	1	1	yes	characteristic, complemented
159	#16862204	C₂²	1	1	yes	characteristic, complemented
160	#16862204	C₂²	1	1	yes	characteristic, complemented
161	#16862204	C₂²	1	1	yes	characteristic, complemented
162	#16862203	C₂²	1	1	yes	characteristic
163	#16862203	C₂²	1	1	yes	characteristic, complemented
164	#16862202	C₂²	1	1	yes	characteristic
165	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
166	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
167	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
168	C₂×(C₂×D₁₃₁)⋊C₄	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	C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
173	C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
174	#126×C₁₃₁	C₂²	1	1	yes	characteristic
175	#126×C₁₃₁	C₂²	1	1	yes	characteristic
176	#126×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
177	#126×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
178	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
179	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
180	#124×C₁₃₁	C₂²	1	1	yes	characteristic
181	#123×C₁₃₁	C₂²	1	1	yes	characteristic
182	#123×C₁₃₁	C₂²	1	1	yes	characteristic
183	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
184	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
185	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
186	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₃₁	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×D₅₂₄	C₂³	1	1	yes	characteristic
192	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
193	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
194	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
195	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
196	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
197	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
198	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
199	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
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	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
209	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
210	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₁₃₁	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	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
257	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
260	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
261	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
262	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
263	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
264	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
265	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
266	(C₂×D₁₃₁)⋊C₄	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	(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	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	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
310	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
311	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
312	C₂²×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	C₂²⋊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	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	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	—	4	1	no	—
343	C₂²×D₁₃₁	—	4	1	no	—
344	C₂²×D₁₃₁	—	4	1	no	—
345	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
346	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
347	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
348	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
349	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
350	Dic₂₆₂	—	4	1	no	—
351	Dic₂₆₂	—	4	1	no	—
352	Dic₂₆₂	—	4	1	no	—
353	D₅₂₄	—	4	1	no	—
354	D₅₂₄	—	4	1	no	—
355	D₅₂₄	—	4	1	no	—
356	D₅₂₄	—	4	1	no	—
357	D₅₂₄	—	4	1	no	—
358	D₅₂₄	—	4	1	no	—
359	D₅₂₄	—	4	1	no	—
360	D₅₂₄	—	4	1	no	—
361	D₅₂₄	—	4	1	no	—
362	C₂²⋊D₁₃₁	—	4	1	no	—
363	C₂²⋊D₁₃₁	—	4	1	no	—
364	C₂²⋊D₁₃₁	—	4	1	no	—
365	C₂²⋊D₁₃₁	—	4	1	no	—
366	C₂²⋊D₁₃₁	—	4	1	no	—
367	C₂²⋊D₁₃₁	—	4	1	no	—
368	C₂²⋊D₁₃₁	—	4	1	no	—
369	C₂²⋊D₁₃₁	—	4	1	no	—
370	C₂×Dic₁₃₁	—	4	1	no	—
371	C₂×Dic₁₃₁	—	4	1	no	—
372	C₂×Dic₁₃₁	—	4	1	no	—
373	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
384	C₄×D₁₃₁	—	4	1	no	—
385	C₄×D₁₃₁	—	4	1	no	—
386	C₄×D₁₃₁	—	4	1	no	—
387	C₄×D₁₃₁	—	4	1	no	—
388	C₄×D₁₃₁	—	4	1	no	—
389	C₄×D₁₃₁	—	4	1	no	—
390	C₄×D₁₃₁	—	4	1	no	—
391	C₄×D₁₃₁	—	4	1	no	—
392	C₄×D₁₃₁	—	4	1	no	—
393	C₄×D₁₃₁	—	4	1	no	—
394	C₄×D₁₃₁	—	4	1	no	—
395	C₄×D₁₃₁	—	4	1	no	—
396	C₄×D₁₃₁	—	4	1	no	—
397	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
398	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
399	Q₈×C₁₃₁	—	4	1	no	—
400	Q₈×C₁₃₁	—	4	1	no	—
401	Q₈×C₁₃₁	—	4	1	no	—
402	D₄×C₁₃₁	—	4	1	no	—
403	C₂×C₄×C₁₃₁	—	4	1	no	—
404	C₂×C₄×C₁₃₁	—	4	1	no	—
405	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
406	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
407	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
418	C₂²×C₁₃₁	—	2	1	no	—
419	C₂²×C₁₃₁	—	2	1	no	—
420	C₂²×C₁₃₁	—	2	1	no	—
421	C₂²×C₁₃₁	—	2	1	no	—
422	C₂²×C₁₃₁	—	2	1	no	—
423	C₂²×C₁₃₁	—	2	1	no	—
424	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
425	C₂×D₁₃₁	—	2	1	no	—
426	C₂×D₁₃₁	—	2	1	no	—
427	C₂×D₁₃₁	—	2	1	no	—
428	C₂×D₁₃₁	—	2	1	no	—
429	C₂×D₁₃₁	—	2	1	no	—
430	C₂×D₁₃₁	—	2	1	no	—
431	C₂×D₁₃₁	—	2	1	no	—
432	C₂×D₁₃₁	—	2	1	no	—
433	C₂×D₁₃₁	—	2	1	no	—
434	C₂×D₁₃₁	—	2	1	no	—
435	C₂×D₁₃₁	—	2	1	no	—
436	C₂×D₁₃₁	—	2	1	no	—
437	C₂×D₁₃₁	—	2	1	no	—
438	C₂×D₁₃₁	—	2	1	no	—
439	C₂×D₁₃₁	—	2	1	no	—
440	C₂×D₁₃₁	—	8	2	no	—
441	C₄×C₁₃₁	—	2	1	no	—
442	C₄×C₁₃₁	—	2	1	no	—
443	C₄×C₁₃₁	—	2	1	no	—
444	C₄×C₁₃₁	—	2	1	no	—
445	C₄×C₁₃₁	—	2	1	no	—
446	C₄×C₁₃₁	—	2	1	no	—
447	C₄×C₁₃₁	—	2	1	no	—
448	C₄×C₁₃₁	—	2	1	no	—
449	C₄×C₁₃₁	—	2	1	no	—
450	C₄×C₁₃₁	—	2	1	no	—
451	C₄×C₁₃₁	—	2	1	no	—
452	C₄×C₁₃₁	—	2	1	no	—
453	C₄×C₁₃₁	—	2	1	no	—
454	Dic₁₃₁	—	2	1	no	—
455	Dic₁₃₁	—	2	1	no	—
456	Dic₁₃₁	—	2	1	no	—
457	Dic₁₃₁	—	2	1	no	—
458	Dic₁₃₁	—	2	1	no	—
459	Dic₁₃₁	—	2	1	no	—
460	Dic₁₃₁	—	2	1	no	—
461	Dic₁₃₁	—	2	1	no	—
462	Dic₁₃₁	—	2	1	no	—
463	Dic₁₃₁	—	2	1	no	—
464	Dic₁₃₁	—	2	1	no	—
465	C₂×C₁₃₁	—	4	1	no	—
466	C₂×C₁₃₁	—	4	1	no	—
467	C₂×C₁₃₁	#585	1	1	yes	characteristic
468	C₂×C₁₃₁	#585	1	1	yes	characteristic
469	C₂×C₁₃₁	#585	1	1	yes	characteristic
470	D₁₃₁	—	4	1	no	—
471	D₁₃₁	—	4	1	no	—
472	D₁₃₁	—	4	1	no	—
473	D₁₃₁	—	4	1	no	—
474	D₁₃₁	—	4	1	no	—
475	C₁₃₁	#3566	1	1	yes	characteristic, complemented, Sylow
476	#3566	—	131	1	no	maximal, Sylow
477	#563	D₁₃₁	1	1	yes	characteristic, complemented
478	#562	—	131	1	no	—
479	#562	—	131	1	no	—
480	#560	—	131	1	no	—
481	#559	—	131	1	no	—
482	#556	—	131	1	no	—
483	#555	—	131	1	no	—
484	#553	—	131	1	no	—
485	#553	—	131	1	no	—
486	#553	—	131	1	no	—
487	#552	—	131	1	no	—
488	#552	—	131	1	no	—
489	#552	—	131	1	no	—
490	#551	—	131	1	no	—
491	#551	—	131	1	no	—
492	#551	—	131	1	no	—
493	#542	—	131	1	no	—
494	#542	—	131	1	no	—
495	#542	—	131	1	no	—
496	#541	—	131	1	no	—
497	#541	—	131	1	no	—
498	#540	—	131	1	no	—
499	#539	—	131	1	no	—
500	#539	—	131	1	no	—
501	#539	—	131	1	no	—
502	#538	—	131	1	no	—
503	#538	—	131	1	no	—
504	#538	—	131	1	no	—
505	#529	—	131	1	no	—
506	#529	—	131	1	no	—
507	#529	—	131	1	no	—
508	C₄⋊Q₈	—	131	1	no	—
509	C₄⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
510	C₄⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
511	#127	—	131	1	no	—
512	#126	—	131	1	no	—
513	#126	—	131	1	no	—
514	#126	—	131	1	no	—
515	#126	—	131	1	no	—
516	#126	—	131	1	no	—
517	#126	—	131	1	no	—
518	#126	—	131	1	no	—
519	#126	—	131	1	no	—
520	#126	—	131	1	no	—
521	#126	—	131	1	no	—
522	#126	—	131	1	no	—
523	#126	—	131	1	no	—
524	#126	—	131	1	no	—
525	#126	—	131	1	no	—
526	#126	—	131	1	no	—
527	#126	—	131	1	no	—
528	#126	C₂×D₁₃₁	1	1	yes	characteristic
529	#126	C₂×D₁₃₁	1	1	yes	characteristic
530	#126	C₂×D₁₃₁	1	1	yes	characteristic, complemented
531	#126	C₂×D₁₃₁	1	1	yes	characteristic, complemented
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	C₂×D₁₃₁	1	1	yes	characteristic, complemented
543	#125	C₂×D₁₃₁	1	1	yes	characteristic, complemented
544	#124	—	131	1	no	—
545	#124	—	131	1	no	—
546	#124	—	131	1	no	—
547	#124	—	131	1	no	—
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	#124	C₂×D₁₃₁	1	1	yes	characteristic
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	#123	—	131	1	no	—
562	#123	—	131	1	no	—
563	#123	—	131	1	no	—
564	#123	—	131	1	no	—
565	#123	—	131	1	no	—
566	#123	—	131	1	no	—
567	#123	—	131	1	no	—
568	#123	—	131	1	no	—
569	#123	—	131	1	no	—
570	#123	—	131	1	no	—
571	#123	—	131	1	no	—
572	#123	—	131	1	no	—
573	#123	—	131	1	no	—
574	#123	—	131	1	no	—
575	#123	—	131	1	no	—
576	#123	—	131	1	no	—
577	#123	—	131	1	no	—
578	#123	C₂×D₁₃₁	1	1	yes	characteristic
579	#123	C₂×D₁₃₁	1	1	yes	characteristic
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	—	131	1	no	—
585	C₂²⋊Q₈	—	131	1	no	—
586	C₂²⋊Q₈	—	131	1	no	—
587	C₂²⋊Q₈	—	131	1	no	—
588	C₂²⋊Q₈	—	131	1	no	—
589	C₂²⋊Q₈	—	131	1	no	—
590	C₂²⋊Q₈	—	131	1	no	—
591	C₂²⋊Q₈	—	131	1	no	—
592	C₂²⋊Q₈	—	131	1	no	—
593	C₂²⋊Q₈	—	131	1	no	—
594	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic
595	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic
596	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
597	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
598	#121	—	131	1	no	—
599	#121	—	131	1	no	—
600	#121	—	131	1	no	—
601	#121	—	131	1	no	—
602	#121	—	131	1	no	—
603	#121	—	131	1	no	—
604	#121	—	131	1	no	—
605	#121	—	131	1	no	—
606	#121	—	131	1	no	—
607	#121	—	131	1	no	—
608	#121	—	131	1	no	—
609	#121	—	131	1	no	—
610	#121	—	131	1	no	—
611	#121	—	131	1	no	—
612	#121	—	131	1	no	—
613	#121	—	131	1	no	—
614	#121	—	131	1	no	—
615	#121	—	131	1	no	—
616	#120	—	131	1	no	—
617	#120	—	131	1	no	—
618	#120	—	131	1	no	—
619	#120	—	131	1	no	—
620	C₄×Q₈	—	131	1	no	—
621	C₄×Q₈	—	131	1	no	—
622	C₄×Q₈	—	131	1	no	—
623	C₄×Q₈	—	131	1	no	—
624	C₄×Q₈	—	131	1	no	—
625	C₄×Q₈	—	131	1	no	—
626	C₄×D₄	—	131	1	no	—
627	C₄×D₄	—	131	1	no	—
628	C₄×D₄	—	131	1	no	—
629	C₄×D₄	—	131	1	no	—
630	C₄×D₄	—	131	1	no	—
631	C₄×D₄	—	131	1	no	—
632	C₄×D₄	—	131	1	no	—
633	C₄×D₄	—	131	1	no	—
634	C₄×D₄	—	131	1	no	—
635	C₄×D₄	—	131	1	no	—
636	C₄×D₄	—	131	1	no	—
637	C₄×D₄	—	131	1	no	—
638	C₄×D₄	—	131	1	no	—
639	C₄×D₄	—	131	1	no	—
640	C₄×D₄	—	131	1	no	—
641	C₄×D₄	—	131	1	no	—
642	C₄×D₄	—	131	1	no	—
643	C₄×D₄	—	131	1	no	—
644	#117	—	131	1	no	—
645	#117	—	131	1	no	—
646	#117	—	131	1	no	—
647	#117	—	131	1	no	—
648	#117	—	131	1	no	—
649	#117	—	131	1	no	—
650	#117	—	131	1	no	—
651	#117	—	131	1	no	—
652	#117	—	131	1	no	—
653	#117	—	131	1	no	—
654	#117	—	131	1	no	—
655	#117	—	131	1	no	—
656	C₂×C₄⋊C₄	—	131	1	no	—
657	C₂×C₄⋊C₄	—	131	1	no	—
658	C₂×C₄⋊C₄	—	131	1	no	—
659	C₂×C₂²⋊C₄	—	131	1	no	—
660	C₂×C₂²⋊C₄	—	131	1	no	—
661	C₂×C₂²⋊C₄	—	131	1	no	—
662	C₂×C₄²	—	131	1	no	—
663	C₂⁴	—	131	1	no	—
664	C₂×Q₈	—	131	1	no	—
665	C₂×Q₈	—	131	1	no	—
666	C₂×Q₈	—	131	1	no	—
667	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
668	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
669	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
670	C₂×D₄	—	131	1	no	—
671	C₂×D₄	—	131	1	no	—
672	C₂×D₄	—	131	1	no	—
673	C₂×D₄	—	131	1	no	—
674	C₂×D₄	—	131	1	no	—
675	C₂×D₄	—	131	1	no	—
676	C₂×D₄	—	131	1	no	—
677	C₂×D₄	—	131	1	no	—
678	C₂×D₄	—	131	1	no	—
679	C₂×D₄	—	131	1	no	—
680	C₂×D₄	—	131	1	no	—
681	C₂×D₄	—	131	1	no	—
682	C₂×D₄	—	131	1	no	—
683	C₂×D₄	—	131	1	no	—
684	C₂×D₄	—	131	1	no	—
685	C₂×D₄	—	131	1	no	—
686	C₂×D₄	—	131	1	no	—
687	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
688	C₂²×C₄	—	131	1	no	—
689	C₂²×C₄	—	131	1	no	—
690	C₂²×C₄	—	131	1	no	—
691	C₂²×C₄	—	131	1	no	—
692	C₂²×C₄	—	131	1	no	—
693	C₂²×C₄	—	131	1	no	—
694	C₂²×C₄	—	131	1	no	—
695	C₂²×C₄	—	131	1	no	—
696	C₂²×C₄	—	131	1	no	—
697	C₂²×C₄	—	131	1	no	—
698	C₂²×C₄	—	131	1	no	—
699	C₂²×C₄	—	131	1	no	—
700	C₂²×C₄	—	131	1	no	—
701	C₂²×C₄	—	131	1	no	—
702	C₂²×C₄	—	131	1	no	—
703	C₂²×C₄	—	131	1	no	—
704	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
705	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
706	C₄⋊C₄	—	131	1	no	—
707	C₄⋊C₄	—	131	1	no	—
708	C₄⋊C₄	—	131	1	no	—
709	C₄⋊C₄	—	131	1	no	—
710	C₄⋊C₄	—	131	1	no	—
711	C₄⋊C₄	—	131	1	no	—
712	C₄⋊C₄	—	131	1	no	—
713	C₄⋊C₄	—	131	1	no	—
714	C₄⋊C₄	—	131	1	no	—
715	C₄⋊C₄	—	131	1	no	—
716	C₄⋊C₄	—	131	1	no	—
717	C₄⋊C₄	—	131	1	no	—
718	C₄⋊C₄	—	131	1	no	—
719	C₄⋊C₄	—	131	1	no	—
720	C₄⋊C₄	—	131	1	no	—
721	C₄⋊C₄	—	131	1	no	—
722	C₄⋊C₄	—	131	1	no	—
723	C₄⋊C₄	—	131	1	no	—
724	C₄⋊C₄	—	131	1	no	—
725	C₄⋊C₄	—	131	1	no	—
726	C₄⋊C₄	—	131	1	no	—
727	C₄⋊C₄	—	131	1	no	—
728	C₄⋊C₄	—	131	1	no	—
729	C₄⋊C₄	—	131	1	no	—
730	C₄⋊C₄	—	131	1	no	—
731	C₄⋊C₄	—	131	1	no	—
732	C₄⋊C₄	—	131	1	no	—
733	C₄⋊C₄	—	131	1	no	—
734	C₄⋊C₄	—	131	1	no	—
735	C₄⋊C₄	—	131	1	no	—
736	C₄⋊C₄	—	131	1	no	—
737	C₄⋊C₄	—	131	1	no	—
738	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
746	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
747	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
748	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
751	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
752	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
754	C₂²⋊C₄	—	131	1	no	—
755	C₂²⋊C₄	—	131	1	no	—
756	C₂²⋊C₄	—	131	1	no	—
757	C₂²⋊C₄	—	131	1	no	—
758	C₂²⋊C₄	—	131	1	no	—
759	C₂²⋊C₄	—	131	1	no	—
760	C₂²⋊C₄	—	131	1	no	—
761	C₂²⋊C₄	—	131	1	no	—
762	C₂²⋊C₄	—	131	1	no	—
763	C₂²⋊C₄	—	131	1	no	—
764	C₂²⋊C₄	—	131	1	no	—
765	C₂²⋊C₄	—	131	1	no	—
766	C₂²⋊C₄	—	131	1	no	—
767	C₂²⋊C₄	—	131	1	no	—
768	C₂²⋊C₄	—	131	1	no	—
769	C₂²⋊C₄	—	131	1	no	—
770	C₂²⋊C₄	—	131	1	no	—
771	C₂²⋊C₄	—	131	1	no	—
772	C₂²⋊C₄	—	131	1	no	—
773	C₂²⋊C₄	—	131	1	no	—
774	C₂²⋊C₄	—	131	1	no	—
775	C₂²⋊C₄	—	131	1	no	—
776	C₂²⋊C₄	—	131	1	no	—
777	C₂²⋊C₄	—	131	1	no	—
778	C₂²⋊C₄	—	131	1	no	—
779	C₂²⋊C₄	—	131	1	no	—
780	C₂²⋊C₄	—	131	1	no	—
781	C₂²⋊C₄	—	131	1	no	—
782	C₂²⋊C₄	—	131	1	no	—
783	C₂²⋊C₄	—	131	1	no	—
784	C₂²⋊C₄	—	131	1	no	—
785	C₂²⋊C₄	—	131	1	no	—
786	C₂²⋊C₄	—	131	1	no	—
787	C₂²⋊C₄	—	131	1	no	—
788	C₂²⋊C₄	—	131	1	no	—
789	C₂²⋊C₄	—	131	1	no	—
790	C₂²⋊C₄	—	131	1	no	—
791	C₂²⋊C₄	—	131	1	no	—
792	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
802	C₄²	—	131	1	no	—
803	C₄²	—	131	1	no	—
804	C₄²	—	131	1	no	—
805	C₄²	—	131	1	no	—
806	C₄²	—	131	1	no	—
807	C₄²	—	131	1	no	—
808	C₄²	—	131	1	no	—
809	C₄²	—	131	1	no	—
810	C₄²	—	131	1	no	—
811	C₄²	—	131	1	no	—
812	C₄²	—	131	1	no	—
813	C₄²	—	131	1	no	—
814	C₄²	—	131	1	no	—
815	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
816	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
817	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
818	C₂³	—	524	1	no	—
819	C₂³	—	524	1	no	—
820	C₂³	—	524	1	no	—
821	C₂³	—	131	1	no	—
822	C₂³	—	131	1	no	—
823	C₂³	—	131	1	no	—
824	C₂³	—	131	1	no	—
825	C₂³	—	131	1	no	—
826	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
827	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
828	Q₈	—	4	1	no	—
829	Q₈	—	4	1	no	—
830	Q₈	—	4	1	no	—
831	Q₈	—	524	1	no	—
832	Q₈	—	524	1	no	—
833	Q₈	—	524	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	524	1	no	—
836	D₄	—	524	1	no	—
837	D₄	—	524	1	no	—
838	D₄	—	524	1	no	—
839	D₄	—	524	1	no	—
840	D₄	—	524	1	no	—
841	D₄	—	524	1	no	—
842	D₄	—	524	1	no	—
843	D₄	—	524	1	no	—
844	D₄	—	524	1	no	—
845	D₄	—	524	1	no	—
846	D₄	—	524	1	no	—
847	D₄	—	524	1	no	—
848	D₄	—	524	1	no	—
849	D₄	—	524	1	no	—
850	D₄	—	524	1	no	—
851	D₄	—	524	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	524	1	no	—
855	C₂×C₄	—	524	1	no	—
856	C₂×C₄	—	524	1	no	—
857	C₂×C₄	—	524	1	no	—
858	C₂×C₄	—	524	1	no	—
859	C₂×C₄	—	524	1	no	—
860	C₂×C₄	—	524	1	no	—
861	C₂×C₄	—	524	1	no	—
862	C₂×C₄	—	524	1	no	—
863	C₂×C₄	—	524	1	no	—
864	C₂×C₄	—	524	1	no	—
865	C₂×C₄	—	524	1	no	—
866	C₂×C₄	—	524	1	no	—
867	C₂×C₄	—	524	1	no	—
868	C₂×C₄	—	524	1	no	—
869	C₂×C₄	—	524	1	no	—
870	C₂×C₄	—	131	1	no	—
871	C₂×C₄	—	131	1	no	—
872	C₂×C₄	—	131	1	no	—
873	C₂×C₄	—	131	1	no	—
874	C₂×C₄	—	131	1	no	—
875	C₂×C₄	—	131	1	no	—
876	C₂×C₄	—	131	1	no	—
877	C₂×C₄	—	131	1	no	—
878	C₂×C₄	—	131	1	no	—
879	C₂×C₄	—	131	1	no	—
880	C₂×C₄	—	131	1	no	—
881	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
882	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
883	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
884	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
885	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	262	1	no	—
901	C₂²	—	262	1	no	—
902	C₂²	—	262	1	no	—
903	C₂²	—	262	1	no	—
904	C₂²	—	262	1	no	—
905	C₂²	—	262	1	no	—
906	C₂²	—	262	1	no	—
907	C₂²	—	262	1	no	—
908	C₂²	—	262	1	no	—
909	C₂²	—	262	1	no	—
910	C₂²	—	262	1	no	—
911	C₂²	—	262	1	no	—
912	C₂²	—	262	1	no	—
913	C₂²	—	262	1	no	—
914	C₂²	—	262	1	no	—
915	C₂²	—	1048	2	no	—
916	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	2	1	no	—
930	C₄	—	262	1	no	—
931	C₄	—	262	1	no	—
932	C₄	—	262	1	no	—
933	C₄	—	262	1	no	—
934	C₄	—	262	1	no	—
935	C₄	—	262	1	no	—
936	C₄	—	262	1	no	—
937	C₄	—	262	1	no	—
938	C₄	—	262	1	no	—
939	C₄	—	262	1	no	—
940	C₄	—	262	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	1	no	—
943	C₂	—	524	1	no	—
944	C₂	—	524	1	no	—
945	C₂	—	524	1	no	—
946	C₂	—	524	1	no	—
947	C₂	—	524	1	no	—
948	C₂	#22554147	1	1	yes	characteristic
949	C₂	#22554149	1	1	yes	characteristic
950	C₂	#22554149	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#563×C₁₃₁	C₂
hypercenter	#563	D₁₃₁
hypocenter	C₁₃₁	#3566
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #22554058	C₂	semidirect
2. #22554058	C₂	semidirect
3. #22554052	C₂	semidirect
4. #22554044	C₂	semidirect
5. #22554036	C₂	semidirect
6. #22554028	C₂	semidirect
7. #22554015	C₂	semidirect
8. #22554013	C₂	semidirect
9. #22554013	C₂	semidirect
10. #22554000	C₂	semidirect
11. #22553998	C₂	semidirect
12. #22553996	C₂	semidirect
13. #22553989	C₂	semidirect
14. #22553987	C₂	semidirect
15. #22553985	C₂	semidirect
16. #22553936	C₂	semidirect
17. #22553935	C₂	semidirect
18. #22553928	C₂	semidirect
19. #22553923	C₂	semidirect
20. #22553921	C₂	semidirect
21. #22553914	C₂	semidirect
22. #22553910	C₂	semidirect
23. #22553903	C₂	semidirect
24. #22553903	C₂	semidirect
25. #22553902	C₂	semidirect
26. #22553901	C₂	semidirect
27. #22553896	C₂	semidirect
28. #22553848	C₂	semidirect
29. #22553848	C₂	semidirect
30. #22553839	C₂	semidirect
31. #563×C₁₃₁	C₂	semidirect
32. #16862245	C₂²	semidirect
43. #16862241	C₂²	semidirect
44. #16862241	C₂²	semidirect
45. #16862241	C₂²	semidirect
46. #16862241	C₂²	semidirect
50. #16862238	C₂²	semidirect
51. #16862237	C₂²	semidirect
52. #16862237	C₂²	semidirect
53. #16862237	C₂²	semidirect
54. #16862236	C₂²	semidirect
55. #16862236	C₂²	semidirect
56. #16862236	C₂²	semidirect
57. #16862236	C₂²	semidirect
58. #16862236	C₂²	semidirect
59. #16862236	C₂²	semidirect
64. #16862235	C₂²	semidirect
65. #16862235	C₂²	semidirect
70. #16862232	C₂²	semidirect
78. #16862231	C₂²	semidirect
79. #16862231	C₂²	semidirect
83. #16862230	C₂²	semidirect
84. #16862230	C₂²	semidirect
85. #16862229	C₂²	semidirect
92. #16862228	C₂²	semidirect
95. #16862226	C₂²	semidirect
96. #16862226	C₂²	semidirect
97. #16862226	C₂²	semidirect
100. #16862224	C₂²	semidirect
101. #16862224	C₂²	semidirect
103. #16862223	C₂²	semidirect
106. #16862222	C₂²	semidirect
113. #16862221	C₂²	semidirect
122. #16862219	C₂²	semidirect
123. #16862219	C₂²	semidirect
129. Q₈×Dic₁₃₁	C₂²	semidirect
130. Q₈×Dic₁₃₁	C₂²	semidirect
131. Q₈×Dic₁₃₁	C₂²	semidirect
132. C₄×Dic₂₆₂	C₂²	semidirect
133. C₄×Dic₂₆₂	C₂²	semidirect
134. #16862211	C₂²	semidirect
138. C₄×D₅₂₄	C₂²	semidirect
139. C₄×D₅₂₄	C₂²	semidirect
144. #16862208	C₂²	semidirect
150. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
151. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
152. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
157. #16862204	C₂²	semidirect
158. #16862204	C₂²	semidirect
159. #16862204	C₂²	semidirect
160. #16862204	C₂²	semidirect
161. #16862204	C₂²	semidirect
163. #16862203	C₂²	semidirect
165. C₄⋊C₄×D₁₃₁	C₂²	semidirect
166. C₄⋊C₄×D₁₃₁	C₂²	semidirect
167. C₄⋊C₄×D₁₃₁	C₂²	semidirect
171. C₂×C₄×Dic₁₃₁	C₂²	semidirect
172. C₄⋊Q₈×C₁₃₁	C₂²	semidirect
173. C₄⋊Q₈×C₁₃₁	C₂²	semidirect
176. #126×C₁₃₁	C₂²	semidirect
177. #126×C₁₃₁	C₂²	semidirect
178. #125×C₁₃₁	C₂²	semidirect
179. #125×C₁₃₁	C₂²	semidirect
185. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
186. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
475. C₁₃₁	#3566	semidirect
477. #563	D₁₃₁	semidirect
509. C₄⋊Q₈	C₂×D₁₃₁	semidirect
510. C₄⋊Q₈	C₂×D₁₃₁	semidirect
530. #126	C₂×D₁₃₁	semidirect
531. #126	C₂×D₁₃₁	semidirect
542. #125	C₂×D₁₃₁	semidirect
543. #125	C₂×D₁₃₁	semidirect
596. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
597. C₂²⋊Q₈	C₂×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#22554058	2
#22554052	2
#22554044	2
#22554036	2
#22554028	2
#22554015	2
#22554013	2
#22554000	2
#22553998	2
#22553996	2
#22553989	2
#22553987	2
#22553985	2
#22553936	2
#22553935	2
#22553928	2
#22553923	2
#22553921	2
#22553914	2
#22553910	2
#22553903	2
#22553902	2
#22553901	2
#22553896	2
#22553848	2
#22553839	2
#563×C₁₃₁	2
#3566	131