Subgroups — #30680253

Order 16768.

1032 conjugacy classes of subgroups.

The subgroup lattice has 980 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	#22554063	C₂	1	1	yes	maximal, characteristic, complemented
3	#22554059	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554058	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554029	C₂	1	1	yes	maximal, characteristic, complemented
6	#22554018	C₂	1	1	yes	maximal, characteristic, complemented
7	#22554018	C₂	1	1	yes	maximal, characteristic, complemented
8	#22554017	C₂	1	1	yes	maximal, characteristic, complemented
9	#22554013	C₂	1	1	yes	maximal, characteristic, complemented
10	#22554012	C₂	1	1	yes	maximal, characteristic, complemented
11	#22554007	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553994	C₂	1	1	yes	maximal, characteristic, complemented
13	#22553975	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553972	C₂	1	1	yes	maximal, characteristic, complemented
15	#22553971	C₂	1	1	yes	maximal, characteristic, complemented
16	#22553963	C₂	1	1	yes	maximal, characteristic, complemented
17	#22553932	C₂	1	1	yes	maximal, characteristic, complemented
18	#22553930	C₂	1	1	yes	maximal, characteristic, complemented
19	#22553927	C₂	1	1	yes	maximal, characteristic, complemented
20	#22553919	C₂	1	1	yes	maximal, characteristic, complemented
21	#22553905	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553901	C₂	1	1	yes	maximal, characteristic, complemented
23	#22553898	C₂	1	1	yes	maximal, characteristic, complemented
24	#22553898	C₂	1	1	yes	maximal, characteristic, complemented
25	#22553894	C₂	1	1	yes	maximal, characteristic, complemented
26	#22553891	C₂	1	1	yes	maximal, characteristic, complemented
27	#22553884	C₂	1	1	yes	maximal, characteristic, complemented
28	#22553821	C₂	1	1	yes	maximal, characteristic, complemented
29	#22553820	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂²⋊Q₈×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
31	#539×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14523513	C₂²	1	1	yes	characteristic
33	C₂×#14523513	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14523512	C₂²	1	1	yes	characteristic
35	C₂²×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
36	C₂×Q₈×D₁₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₁₃₁	C₂²	1	1	yes	characteristic
38	#16862245	C₂²	1	1	yes	characteristic, complemented
39	#16862245	C₂²	1	1	yes	characteristic, complemented
40	#16862245	C₂²	1	1	yes	characteristic, complemented
41	#16862245	C₂²	1	1	yes	characteristic, complemented
42	#16862245	C₂²	1	1	yes	characteristic, complemented
43	#16862244	C₂²	1	1	yes	characteristic, complemented
44	#16862241	C₂²	1	1	yes	characteristic
45	#16862241	C₂²	1	1	yes	characteristic
46	#16862241	C₂²	1	1	yes	characteristic
47	#16862241	C₂²	1	1	yes	characteristic
48	#16862241	C₂²	1	1	yes	characteristic, complemented
49	#16862241	C₂²	1	1	yes	characteristic, complemented
50	#16862239	C₂²	1	1	yes	characteristic
51	#16862239	C₂²	1	1	yes	characteristic
52	#16862239	C₂²	1	1	yes	characteristic
53	#16862239	C₂²	1	1	yes	characteristic, complemented
54	#16862239	C₂²	1	1	yes	characteristic, complemented
55	#16862239	C₂²	1	1	yes	characteristic, complemented
56	#16862238	C₂²	1	1	yes	characteristic, complemented
57	#16862237	C₂²	1	1	yes	characteristic, complemented
58	#16862237	C₂²	1	1	yes	characteristic, complemented
59	#16862236	C₂²	1	1	yes	characteristic, complemented
60	#16862236	C₂²	1	1	yes	characteristic, complemented
61	#16862236	C₂²	1	1	yes	characteristic, complemented
62	#16862236	C₂²	1	1	yes	characteristic, complemented
63	#16862235	C₂²	1	1	yes	characteristic, complemented
64	#16862234	C₂²	1	1	yes	characteristic
65	#16862233	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
69	#16862232	C₂²	1	1	yes	characteristic
70	#16862232	C₂²	1	1	yes	characteristic
71	#16862232	C₂²	1	1	yes	characteristic
72	#16862232	C₂²	1	1	yes	characteristic, complemented
73	#16862232	C₂²	1	1	yes	characteristic, complemented
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	#16862230	C₂²	1	1	yes	characteristic, complemented
80	#16862229	C₂²	1	1	yes	characteristic
81	#16862229	C₂²	1	1	yes	characteristic
82	#16862229	C₂²	1	1	yes	characteristic, complemented
83	#16862229	C₂²	1	1	yes	characteristic, complemented
84	#16862228	C₂²	1	1	yes	characteristic
85	#16862228	C₂²	1	1	yes	characteristic
86	#16862228	C₂²	1	1	yes	characteristic, complemented
87	#16862227	C₂²	1	1	yes	characteristic
88	#16862226	C₂²	1	1	yes	characteristic
89	#16862226	C₂²	1	1	yes	characteristic
90	#16862226	C₂²	1	1	yes	characteristic
91	#16862226	C₂²	1	1	yes	characteristic, complemented
92	#16862226	C₂²	1	1	yes	characteristic, complemented
93	#16862225	C₂²	1	1	yes	characteristic
94	#16862225	C₂²	1	1	yes	characteristic, complemented
95	#16862225	C₂²	1	1	yes	characteristic, complemented
96	#16862225	C₂²	1	1	yes	characteristic, complemented
97	#16862224	C₂²	1	1	yes	characteristic
98	#16862224	C₂²	1	1	yes	characteristic
99	#16862224	C₂²	1	1	yes	characteristic
100	#16862224	C₂²	1	1	yes	characteristic
101	#16862224	C₂²	1	1	yes	characteristic
102	#16862224	C₂²	1	1	yes	characteristic
103	#16862224	C₂²	1	1	yes	characteristic
104	#16862224	C₂²	1	1	yes	characteristic, complemented
105	#16862224	C₂²	1	1	yes	characteristic, complemented
106	#16862224	C₂²	1	1	yes	characteristic, complemented
107	#16862224	C₂²	1	1	yes	characteristic, complemented
108	#16862224	C₂²	1	1	yes	characteristic, complemented
109	#16862224	C₂²	1	1	yes	characteristic, complemented
110	#16862223	C₂²	1	1	yes	characteristic
111	#16862223	C₂²	1	1	yes	characteristic
112	#16862223	C₂²	1	1	yes	characteristic
113	#16862223	C₂²	1	1	yes	characteristic, complemented
114	#16862223	C₂²	1	1	yes	characteristic, complemented
115	#16862222	C₂²	1	1	yes	characteristic
116	#16862221	C₂²	1	1	yes	characteristic
117	#16862221	C₂²	1	1	yes	characteristic
118	#16862220	C₂²	1	1	yes	characteristic
119	#16862220	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
123	#16862219	C₂²	1	1	yes	characteristic
124	#16862219	C₂²	1	1	yes	characteristic
125	#16862219	C₂²	1	1	yes	characteristic
126	#16862219	C₂²	1	1	yes	characteristic, complemented
127	#16862218	C₂²	1	1	yes	characteristic
128	#16862218	C₂²	1	1	yes	characteristic
129	#16862218	C₂²	1	1	yes	characteristic, complemented
130	#16862217	C₂²	1	1	yes	characteristic
131	#16862217	C₂²	1	1	yes	characteristic
132	#16862217	C₂²	1	1	yes	characteristic
133	#16862217	C₂²	1	1	yes	characteristic, complemented
134	#16862216	C₂²	1	1	yes	characteristic
135	#16862216	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	#16862211	C₂²	1	1	yes	characteristic, complemented
143	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
144	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
145	#16862208	C₂²	1	1	yes	characteristic
146	#16862208	C₂²	1	1	yes	characteristic
147	#16862208	C₂²	1	1	yes	characteristic
148	#16862208	C₂²	1	1	yes	characteristic
149	#16862208	C₂²	1	1	yes	characteristic
150	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
151	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
152	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
153	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
154	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
155	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
156	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
157	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
158	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
159	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	#16862204	C₂²	1	1	yes	characteristic, complemented
161	#16862203	C₂²	1	1	yes	characteristic
162	#16862203	C₂²	1	1	yes	characteristic, complemented
163	#16862202	C₂²	1	1	yes	characteristic
164	#16862202	C₂²	1	1	yes	characteristic, complemented
165	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
166	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
167	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
168	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
169	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
172	#126×C₁₃₁	C₂²	1	1	yes	characteristic
173	#126×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
174	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
175	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
176	#123×C₁₃₁	C₂²	1	1	yes	characteristic
177	#123×C₁₃₁	C₂²	1	1	yes	characteristic
178	#123×C₁₃₁	C₂²	1	1	yes	characteristic
179	#123×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
181	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
183	#121×C₁₃₁	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
185	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₃₁	C₂³	1	1	yes	characteristic
188	#14523513	—	4	2	no	—
189	#14523513	—	4	2	no	—
190	#14523512	—	4	2	no	—
191	C₂×Dic₂₆₂	—	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	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
198	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
199	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
200	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
201	Q₈×D₁₃₁	—	4	2	no	—
202	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
203	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
204	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
205	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
206	C₂×D₅₂₄	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	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
218	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
219	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₁₃₁	—	4	2	no	—
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	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₁₃₁	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	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₁₃₁	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	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	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	(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	(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	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
314	C₂×D₄×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	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
318	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
319	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
320	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
321	C₂²×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	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
335	C₄⋊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	—	2	2	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	Dic₂₆₂	—	4	1	no	—
361	Dic₂₆₂	—	4	1	no	—
362	Dic₂₆₂	—	4	1	no	—
363	Dic₂₆₂	—	4	1	no	—
364	D₅₂₄	—	2	2	no	—
365	D₅₂₄	—	2	2	no	—
366	D₅₂₄	—	4	1	no	—
367	D₅₂₄	—	4	1	no	—
368	D₅₂₄	—	4	1	no	—
369	C₂²⋊D₁₃₁	—	2	2	no	—
370	C₂²⋊D₁₃₁	—	2	2	no	—
371	C₂²⋊D₁₃₁	—	2	2	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	C₂×Dic₁₃₁	—	2	2	no	—
380	C₂×Dic₁₃₁	—	2	2	no	—
381	C₂×Dic₁₃₁	—	4	1	no	—
382	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
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	C₄×D₁₃₁	—	2	2	no	—
395	C₄×D₁₃₁	—	2	2	no	—
396	C₄×D₁₃₁	—	2	2	no	—
397	C₄×D₁₃₁	—	4	1	no	—
398	C₄×D₁₃₁	—	4	1	no	—
399	C₄×D₁₃₁	—	4	1	no	—
400	C₄×D₁₃₁	—	4	1	no	—
401	C₄×D₁₃₁	—	4	1	no	—
402	C₄×D₁₃₁	—	4	1	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	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
409	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
410	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
411	Q₈×C₁₃₁	—	4	1	no	—
412	D₄×C₁₃₁	—	4	1	no	—
413	D₄×C₁₃₁	—	4	1	no	—
414	D₄×C₁₃₁	—	4	1	no	—
415	C₂×C₄×C₁₃₁	—	4	1	no	—
416	C₂×C₄×C₁₃₁	—	4	1	no	—
417	C₂×C₄×C₁₃₁	—	4	1	no	—
418	C₂×C₄×C₁₃₁	—	4	1	no	—
419	C₂×C₄×C₁₃₁	—	4	1	no	—
420	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
421	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
423	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
424	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
425	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
426	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
427	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
428	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
429	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
430	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
431	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
432	C₂²×C₁₃₁	—	2	1	no	—
433	C₂²×C₁₃₁	—	2	1	no	—
434	C₂²×C₁₃₁	—	2	1	no	—
435	C₂²×C₁₃₁	—	2	1	no	—
436	C₂²×C₁₃₁	—	2	1	no	—
437	C₂²×C₁₃₁	—	2	1	no	—
438	C₂²×C₁₃₁	—	2	1	no	—
439	C₂²×C₁₃₁	—	2	1	no	—
440	C₂²×C₁₃₁	—	2	1	no	—
441	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
442	C₂×D₁₃₁	—	2	1	no	—
443	C₂×D₁₃₁	—	2	1	no	—
444	C₂×D₁₃₁	—	2	1	no	—
445	C₂×D₁₃₁	—	2	1	no	—
446	C₂×D₁₃₁	—	2	1	no	—
447	C₂×D₁₃₁	—	2	1	no	—
448	C₂×D₁₃₁	—	2	1	no	—
449	C₂×D₁₃₁	—	2	1	no	—
450	C₂×D₁₃₁	—	2	1	no	—
451	C₂×D₁₃₁	—	2	1	no	—
452	C₂×D₁₃₁	—	2	1	no	—
453	C₂×D₁₃₁	—	4	4	no	—
454	C₂×D₁₃₁	2₋¹⁺⁴	1	2	yes	—
455	C₄×C₁₃₁	—	2	1	no	—
456	C₄×C₁₃₁	—	2	1	no	—
457	C₄×C₁₃₁	—	2	1	no	—
458	C₄×C₁₃₁	—	2	1	no	—
459	C₄×C₁₃₁	—	2	1	no	—
460	C₄×C₁₃₁	—	2	1	no	—
461	C₄×C₁₃₁	—	2	1	no	—
462	C₄×C₁₃₁	—	2	1	no	—
463	C₄×C₁₃₁	—	2	1	no	—
464	C₄×C₁₃₁	—	2	1	no	—
465	C₄×C₁₃₁	—	2	1	no	—
466	C₄×C₁₃₁	—	2	1	no	—
467	Dic₁₃₁	—	2	1	no	—
468	Dic₁₃₁	—	2	1	no	—
469	Dic₁₃₁	—	2	1	no	—
470	Dic₁₃₁	—	2	1	no	—
471	Dic₁₃₁	—	2	1	no	—
472	Dic₁₃₁	—	2	1	no	—
473	Dic₁₃₁	—	2	1	no	—
474	Dic₁₃₁	—	2	1	no	—
475	Dic₁₃₁	—	2	1	no	—
476	Dic₁₃₁	—	2	1	no	—
477	Dic₁₃₁	—	2	1	no	—
478	Dic₁₃₁	H(5,𝔽₂)	1	2	yes	—
479	C₂×C₁₃₁	—	4	1	no	—
480	C₂×C₁₃₁	—	4	1	no	—
481	C₂×C₁₃₁	—	4	1	no	—
482	C₂×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂×C₁₃₁	#585	1	1	yes	characteristic
485	D₁₃₁	—	2	2	no	—
486	D₁₃₁	—	4	1	no	—
487	D₁₃₁	—	4	1	no	—
488	D₁₃₁	—	4	1	no	—
489	C₁₃₁	#3541	1	1	yes	characteristic, complemented, Sylow
490	#3541	—	131	1	no	maximal, Sylow
491	#563	—	131	1	no	—
492	#563	—	131	1	no	—
493	#562	—	131	1	no	—
494	#562	—	131	1	no	—
495	#556	—	131	1	no	—
496	#554	—	131	1	no	—
497	#554	—	131	1	no	—
498	#554	—	131	1	no	—
499	#553	—	131	1	no	—
500	#553	—	131	1	no	—
501	#553	—	131	1	no	—
502	#552	—	131	1	no	—
503	D₄×Q₈	—	131	1	no	—
504	#548	—	131	1	no	—
505	#548	—	131	1	no	—
506	#547	—	131	1	no	—
507	#542	—	131	1	no	—
508	#542	—	131	1	no	—
509	#542	—	131	1	no	—
510	#541	—	131	1	no	—
511	#539	—	131	1	no	—
512	#539	D₁₃₁	1	1	yes	characteristic, complemented
513	#538	—	131	1	no	—
514	#538	—	131	1	no	—
515	#538	—	131	1	no	—
516	#538	—	131	1	no	—
517	#537	—	131	1	no	—
518	#536	—	131	1	no	—
519	#525	—	131	1	no	—
520	#525	—	131	1	no	—
521	C₂×C₂²⋊Q₈	—	131	1	no	—
522	C₂×#41	—	131	1	no	—
523	C₂×#41	—	131	1	no	—
524	C₂×#41	—	131	1	no	—
525	C₂²×Q₈	—	131	1	no	—
526	C₂²×Q₈	—	131	1	no	—
527	C₂³×C₄	—	131	1	no	—
528	C₄⋊Q₈	—	131	1	no	—
529	C₄⋊Q₈	—	131	1	no	—
530	C₄⋊Q₈	—	131	1	no	—
531	C₄⋊Q₈	—	131	1	no	—
532	C₄⋊Q₈	—	131	1	no	—
533	C₄⋊Q₈	—	131	1	no	—
534	#126	—	131	1	no	—
535	#126	—	131	1	no	—
536	#126	—	131	1	no	—
537	#126	—	131	1	no	—
538	#126	—	131	1	no	—
539	#126	—	131	1	no	—
540	#126	—	131	1	no	—
541	#126	—	131	1	no	—
542	#126	—	131	1	no	—
543	#126	—	131	1	no	—
544	#126	—	131	1	no	—
545	#126	—	131	1	no	—
546	#126	C₂×D₁₃₁	1	1	yes	characteristic
547	#126	C₂×D₁₃₁	1	1	yes	characteristic, complemented
548	#125	—	131	1	no	—
549	#125	—	131	1	no	—
550	#125	—	131	1	no	—
551	#125	—	131	1	no	—
552	#125	—	131	1	no	—
553	#125	—	131	1	no	—
554	#125	—	131	1	no	—
555	#125	C₂×D₁₃₁	1	1	yes	characteristic, complemented
556	#125	C₂×D₁₃₁	1	1	yes	characteristic, complemented
557	#124	—	131	1	no	—
558	#124	—	131	1	no	—
559	#124	—	131	1	no	—
560	#124	—	131	1	no	—
561	#124	—	131	1	no	—
562	#124	—	131	1	no	—
563	#124	—	131	1	no	—
564	#124	—	131	1	no	—
565	#124	—	131	1	no	—
566	#124	—	131	1	no	—
567	#124	—	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	—	131	1	no	—
579	#123	—	131	1	no	—
580	#123	—	131	1	no	—
581	#123	—	131	1	no	—
582	#123	C₂×D₁₃₁	1	1	yes	characteristic
583	#123	C₂×D₁₃₁	1	1	yes	characteristic
584	#123	C₂×D₁₃₁	1	1	yes	characteristic
585	#123	C₂×D₁₃₁	1	1	yes	characteristic, complemented
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	—	131	1	no	—
595	C₂²⋊Q₈	—	131	1	no	—
596	C₂²⋊Q₈	—	131	1	no	—
597	C₂²⋊Q₈	—	131	1	no	—
598	C₂²⋊Q₈	—	131	1	no	—
599	C₂²⋊Q₈	—	131	1	no	—
600	C₂²⋊Q₈	—	131	1	no	—
601	C₂²⋊Q₈	—	131	1	no	—
602	C₂²⋊Q₈	—	131	1	no	—
603	C₂²⋊Q₈	—	131	1	no	—
604	C₂²⋊Q₈	—	131	1	no	—
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	C₂×D₁₃₁	1	1	yes	characteristic
615	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
616	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
617	#121	—	131	1	no	—
618	#121	—	131	1	no	—
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	C₂×D₁₃₁	1	1	yes	characteristic
636	#120	—	131	1	no	—
637	#120	—	131	1	no	—
638	#120	—	131	1	no	—
639	#120	—	131	1	no	—
640	C₄×Q₈	—	131	1	no	—
641	C₄×Q₈	—	131	1	no	—
642	C₄×Q₈	—	131	1	no	—
643	C₄×Q₈	—	131	1	no	—
644	C₄×Q₈	—	131	1	no	—
645	C₄×D₄	—	131	1	no	—
646	C₄×D₄	—	131	1	no	—
647	C₄×D₄	—	131	1	no	—
648	C₄×D₄	—	131	1	no	—
649	C₄×D₄	—	131	1	no	—
650	C₄×D₄	—	131	1	no	—
651	C₄×D₄	—	131	1	no	—
652	C₄×D₄	—	131	1	no	—
653	C₄×D₄	—	131	1	no	—
654	C₄×D₄	—	131	1	no	—
655	C₄×D₄	—	131	1	no	—
656	C₄×D₄	—	131	1	no	—
657	C₄×D₄	—	131	1	no	—
658	C₄×D₄	—	131	1	no	—
659	C₄×D₄	—	131	1	no	—
660	C₄×D₄	—	131	1	no	—
661	C₄×D₄	—	131	1	no	—
662	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
663	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
664	#117	—	131	1	no	—
665	#117	—	131	1	no	—
666	#117	—	131	1	no	—
667	#117	—	131	1	no	—
668	#117	—	131	1	no	—
669	C₂×C₄⋊C₄	—	131	1	no	—
670	C₂×C₄⋊C₄	—	131	1	no	—
671	C₂×C₄⋊C₄	—	131	1	no	—
672	C₂×C₄⋊C₄	—	131	1	no	—
673	C₂×C₄⋊C₄	—	131	1	no	—
674	C₂×C₄⋊C₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
675	C₂×C₂²⋊C₄	—	131	1	no	—
676	C₂×C₂²⋊C₄	—	131	1	no	—
677	C₂⁴	—	131	1	no	—
678	#41	—	524	2	no	—
679	#41	—	524	2	no	—
680	#41	—	524	2	no	—
681	C₂×Q₈	—	524	2	no	—
682	C₂×Q₈	—	524	2	no	—
683	C₂×Q₈	—	131	1	no	—
684	C₂×Q₈	—	131	1	no	—
685	C₂×Q₈	—	131	1	no	—
686	C₂×Q₈	—	131	1	no	—
687	C₂×Q₈	—	131	1	no	—
688	C₂×Q₈	—	131	1	no	—
689	C₂×Q₈	—	131	1	no	—
690	C₂×Q₈	—	131	1	no	—
691	C₂×Q₈	—	131	1	no	—
692	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
693	C₂×D₄	—	131	1	no	—
694	C₂×D₄	—	131	1	no	—
695	C₂×D₄	—	131	1	no	—
696	C₂×D₄	—	131	1	no	—
697	C₂×D₄	—	131	1	no	—
698	C₂×D₄	—	131	1	no	—
699	C₂×D₄	—	131	1	no	—
700	C₂×D₄	—	131	1	no	—
701	C₂×D₄	—	131	1	no	—
702	C₂×D₄	—	131	1	no	—
703	C₂×D₄	—	131	1	no	—
704	C₂×D₄	—	131	1	no	—
705	C₂×D₄	—	131	1	no	—
706	C₂×D₄	—	131	1	no	—
707	C₂×D₄	—	131	1	no	—
708	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
709	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
710	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
711	C₂²×C₄	—	524	2	no	—
712	C₂²×C₄	—	131	1	no	—
713	C₂²×C₄	—	131	1	no	—
714	C₂²×C₄	—	131	1	no	—
715	C₂²×C₄	—	131	1	no	—
716	C₂²×C₄	—	131	1	no	—
717	C₂²×C₄	—	131	1	no	—
718	C₂²×C₄	—	131	1	no	—
719	C₂²×C₄	—	131	1	no	—
720	C₂²×C₄	—	131	1	no	—
721	C₂²×C₄	—	131	1	no	—
722	C₂²×C₄	—	131	1	no	—
723	C₂²×C₄	—	131	1	no	—
724	C₂²×C₄	—	131	1	no	—
725	C₂²×C₄	—	131	1	no	—
726	C₂²×C₄	—	131	1	no	—
727	C₂²×C₄	—	131	1	no	—
728	C₂²×C₄	—	131	1	no	—
729	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
733	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
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	—	131	1	no	—
739	C₄⋊C₄	—	131	1	no	—
740	C₄⋊C₄	—	131	1	no	—
741	C₄⋊C₄	—	131	1	no	—
742	C₄⋊C₄	—	131	1	no	—
743	C₄⋊C₄	—	131	1	no	—
744	C₄⋊C₄	—	131	1	no	—
745	C₄⋊C₄	—	131	1	no	—
746	C₄⋊C₄	—	131	1	no	—
747	C₄⋊C₄	—	131	1	no	—
748	C₄⋊C₄	—	131	1	no	—
749	C₄⋊C₄	—	131	1	no	—
750	C₄⋊C₄	—	131	1	no	—
751	C₄⋊C₄	—	131	1	no	—
752	C₄⋊C₄	—	131	1	no	—
753	C₄⋊C₄	—	131	1	no	—
754	C₄⋊C₄	—	131	1	no	—
755	C₄⋊C₄	—	131	1	no	—
756	C₄⋊C₄	—	131	1	no	—
757	C₄⋊C₄	—	131	1	no	—
758	C₄⋊C₄	—	131	1	no	—
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	C₂²×D₁₃₁	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
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	—	131	1	no	—
793	C₂²⋊C₄	—	131	1	no	—
794	C₂²⋊C₄	—	131	1	no	—
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	C₂²×D₁₃₁	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
826	C₄²	—	131	1	no	—
827	C₄²	—	131	1	no	—
828	C₄²	—	131	1	no	—
829	C₄²	—	131	1	no	—
830	C₄²	—	131	1	no	—
831	C₄²	—	131	1	no	—
832	C₄²	—	131	1	no	—
833	C₄²	—	131	1	no	—
834	C₄²	—	131	1	no	—
835	C₄²	—	131	1	no	—
836	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
837	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
838	C₂³	—	262	2	no	—
839	C₂³	—	524	1	no	—
840	C₂³	—	524	1	no	—
841	C₂³	—	131	1	no	—
842	C₂³	—	131	1	no	—
843	C₂³	—	131	1	no	—
844	C₂³	—	131	1	no	—
845	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
846	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
847	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
848	Q₈	—	4	1	no	—
849	Q₈	—	262	2	no	—
850	Q₈	—	262	2	no	—
851	Q₈	—	262	2	no	—
852	Q₈	—	524	1	no	—
853	Q₈	—	524	1	no	—
854	Q₈	—	524	1	no	—
855	Q₈	—	524	1	no	—
856	Q₈	—	524	1	no	—
857	Q₈	—	524	1	no	—
858	D₄	—	4	1	no	—
859	D₄	—	4	1	no	—
860	D₄	—	4	1	no	—
861	D₄	—	262	2	no	—
862	D₄	—	262	2	no	—
863	D₄	—	262	2	no	—
864	D₄	—	262	2	no	—
865	D₄	—	262	2	no	—
866	D₄	—	524	1	no	—
867	D₄	—	524	1	no	—
868	D₄	—	524	1	no	—
869	D₄	—	524	1	no	—
870	D₄	—	524	1	no	—
871	D₄	—	524	1	no	—
872	D₄	—	524	1	no	—
873	D₄	—	524	1	no	—
874	D₄	—	524	1	no	—
875	D₄	—	524	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	262	2	no	—
882	C₂×C₄	—	262	2	no	—
883	C₂×C₄	—	262	2	no	—
884	C₂×C₄	—	262	2	no	—
885	C₂×C₄	—	262	2	no	—
886	C₂×C₄	—	524	1	no	—
887	C₂×C₄	—	524	1	no	—
888	C₂×C₄	—	524	1	no	—
889	C₂×C₄	—	524	1	no	—
890	C₂×C₄	—	524	1	no	—
891	C₂×C₄	—	524	1	no	—
892	C₂×C₄	—	524	1	no	—
893	C₂×C₄	—	524	1	no	—
894	C₂×C₄	—	524	1	no	—
895	C₂×C₄	—	524	1	no	—
896	C₂×C₄	—	524	1	no	—
897	C₂×C₄	—	524	1	no	—
898	C₂×C₄	—	131	1	no	—
899	C₂×C₄	—	131	1	no	—
900	C₂×C₄	—	131	1	no	—
901	C₂×C₄	—	131	1	no	—
902	C₂×C₄	—	131	1	no	—
903	C₂×C₄	—	131	1	no	—
904	C₂×C₄	—	131	1	no	—
905	C₂×C₄	—	131	1	no	—
906	C₂×C₄	—	131	1	no	—
907	C₂×C₄	—	131	1	no	—
908	C₂×C₄	—	131	1	no	—
909	C₂×C₄	—	131	1	no	—
910	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	262	1	no	—
932	C₂²	—	262	1	no	—
933	C₂²	—	262	1	no	—
934	C₂²	—	262	1	no	—
935	C₂²	—	262	1	no	—
936	C₂²	—	262	1	no	—
937	C₂²	—	262	1	no	—
938	C₂²	—	262	1	no	—
939	C₂²	—	262	1	no	—
940	C₂²	—	262	1	no	—
941	C₂²	—	262	1	no	—
942	C₂²	—	524	4	no	—
943	C₂²	—	131	2	no	—
944	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	262	1	no	—
958	C₄	—	262	1	no	—
959	C₄	—	262	1	no	—
960	C₄	—	262	1	no	—
961	C₄	—	262	1	no	—
962	C₄	—	262	1	no	—
963	C₄	—	262	1	no	—
964	C₄	—	262	1	no	—
965	C₄	—	262	1	no	—
966	C₄	—	262	1	no	—
967	C₄	—	262	1	no	—
968	C₄	—	131	2	no	—
969	C₂	—	4	1	no	—
970	C₂	—	4	1	no	—
971	C₂	—	4	1	no	—
972	C₂	—	262	2	no	—
973	C₂	—	524	1	no	—
974	C₂	—	524	1	no	—
975	C₂	—	524	1	no	—
976	C₂	H(5,𝔽₂)×D₁₃₁	1	1	yes	characteristic
977	C₂	2₋¹⁺⁴×D₁₃₁	1	1	yes	characteristic
978	C₂	#22554148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#539×C₁₃₁	C₂
hypercenter	#539	D₁₃₁
hypocenter	C₁₃₁	#3541
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #22554066	C₂	semidirect
2. #22554063	C₂	semidirect
3. #22554059	C₂	semidirect
4. #22554058	C₂	semidirect
5. #22554029	C₂	semidirect
6. #22554018	C₂	semidirect
7. #22554018	C₂	semidirect
8. #22554017	C₂	semidirect
9. #22554013	C₂	semidirect
10. #22554012	C₂	semidirect
11. #22554007	C₂	semidirect
12. #22553994	C₂	semidirect
13. #22553975	C₂	semidirect
14. #22553972	C₂	semidirect
15. #22553971	C₂	semidirect
16. #22553963	C₂	semidirect
17. #22553932	C₂	semidirect
18. #22553930	C₂	semidirect
19. #22553927	C₂	semidirect
20. #22553919	C₂	semidirect
21. #22553905	C₂	semidirect
22. #22553901	C₂	semidirect
23. #22553898	C₂	semidirect
24. #22553898	C₂	semidirect
25. #22553894	C₂	semidirect
26. #22553891	C₂	semidirect
27. #22553884	C₂	semidirect
28. #22553821	C₂	semidirect
29. #22553820	C₂	semidirect
30. C₂²⋊Q₈×D₁₃₁	C₂	semidirect
31. #539×C₁₃₁	C₂	semidirect
33. C₂×#14523513	C₂²	semidirect
35. C₂²×Dic₂₆₂	C₂²	semidirect
38. #16862245	C₂²	semidirect
39. #16862245	C₂²	semidirect
40. #16862245	C₂²	semidirect
41. #16862245	C₂²	semidirect
42. #16862245	C₂²	semidirect
43. #16862244	C₂²	semidirect
48. #16862241	C₂²	semidirect
49. #16862241	C₂²	semidirect
53. #16862239	C₂²	semidirect
54. #16862239	C₂²	semidirect
55. #16862239	C₂²	semidirect
56. #16862238	C₂²	semidirect
57. #16862237	C₂²	semidirect
58. #16862237	C₂²	semidirect
59. #16862236	C₂²	semidirect
60. #16862236	C₂²	semidirect
61. #16862236	C₂²	semidirect
62. #16862236	C₂²	semidirect
63. #16862235	C₂²	semidirect
72. #16862232	C₂²	semidirect
73. #16862232	C₂²	semidirect
78. #16862231	C₂²	semidirect
79. #16862230	C₂²	semidirect
82. #16862229	C₂²	semidirect
83. #16862229	C₂²	semidirect
86. #16862228	C₂²	semidirect
91. #16862226	C₂²	semidirect
92. #16862226	C₂²	semidirect
94. #16862225	C₂²	semidirect
95. #16862225	C₂²	semidirect
96. #16862225	C₂²	semidirect
104. #16862224	C₂²	semidirect
105. #16862224	C₂²	semidirect
106. #16862224	C₂²	semidirect
107. #16862224	C₂²	semidirect
108. #16862224	C₂²	semidirect
109. #16862224	C₂²	semidirect
113. #16862223	C₂²	semidirect
114. #16862223	C₂²	semidirect
126. #16862219	C₂²	semidirect
129. #16862218	C₂²	semidirect
133. #16862217	C₂²	semidirect
138. C₄×Dic₂₆₂	C₂²	semidirect
139. C₄×Dic₂₆₂	C₂²	semidirect
140. #16862211	C₂²	semidirect
141. #16862211	C₂²	semidirect
142. #16862211	C₂²	semidirect
155. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
159. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
160. #16862204	C₂²	semidirect
162. #16862203	C₂²	semidirect
164. #16862202	C₂²	semidirect
168. C₄⋊C₄×D₁₃₁	C₂²	semidirect
169. C₄⋊C₄×D₁₃₁	C₂²	semidirect
173. #126×C₁₃₁	C₂²	semidirect
174. #125×C₁₃₁	C₂²	semidirect
175. #125×C₁₃₁	C₂²	semidirect
179. #123×C₁₃₁	C₂²	semidirect
181. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
182. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
185. C₄×D₄×C₁₃₁	C₂²	semidirect
186. C₂×C₄⋊C₄×C₁₃₁	C₂²	semidirect
489. C₁₃₁	#3541	semidirect
512. #539	D₁₃₁	semidirect
547. #126	C₂×D₁₃₁	semidirect
555. #125	C₂×D₁₃₁	semidirect
556. #125	C₂×D₁₃₁	semidirect
585. #123	C₂×D₁₃₁	semidirect
615. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
616. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
663. C₄×D₄	C₂×D₁₃₁	semidirect
674. C₂×C₄⋊C₄	C₂×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
#22554063	2
#22554059	2
#22554058	2
#22554029	2
#22554018	2
#22554017	2
#22554013	2
#22554012	2
#22554007	2
#22553994	2
#22553975	2
#22553972	2
#22553971	2
#22553963	2
#22553932	2
#22553930	2
#22553927	2
#22553919	2
#22553905	2
#22553901	2
#22553898	2
#22553894	2
#22553891	2
#22553884	2
#22553821	2
#22553820	2
C₂²⋊Q₈×D₁₃₁	2
#539×C₁₃₁	2
#3541	131