Subgroups — #30680584

Order 16768.

936 conjugacy classes of subgroups.

The subgroup lattice has 920 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	#22554063	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554061	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554034	C₂	1	1	yes	maximal, characteristic, complemented
6	#22554033	C₂	1	1	yes	maximal, characteristic, complemented
7	#22554017	C₂	1	1	yes	maximal, characteristic, complemented
8	#22554004	C₂	1	1	yes	maximal, characteristic, complemented
9	#22554002	C₂	1	1	yes	maximal, characteristic, complemented
10	#22553997	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553994	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553991	C₂	1	1	yes	maximal, characteristic, complemented
13	#22553991	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553989	C₂	1	1	yes	maximal, characteristic, complemented
15	#22553989	C₂	1	1	yes	maximal, characteristic, complemented
16	#22553941	C₂	1	1	yes	maximal, characteristic, complemented
17	#22553937	C₂	1	1	yes	maximal, characteristic, complemented
18	#22553935	C₂	1	1	yes	maximal, characteristic, complemented
19	#22553932	C₂	1	1	yes	maximal, characteristic, complemented
20	#22553923	C₂	1	1	yes	maximal, characteristic, complemented
21	#22553921	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553921	C₂	1	1	yes	maximal, characteristic, complemented
23	#22553920	C₂	1	1	yes	maximal, characteristic, complemented
24	#22553909	C₂	1	1	yes	maximal, characteristic, complemented
25	#22553908	C₂	1	1	yes	maximal, characteristic, complemented
26	#22553904	C₂	1	1	yes	maximal, characteristic, complemented
27	#22553895	C₂	1	1	yes	maximal, characteristic
28	#22553864	C₂	1	1	yes	maximal, characteristic, complemented
29	#22553842	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16862241	C₂	1	1	yes	maximal, characteristic, complemented
31	#554×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
32	#16862245	C₂²	1	1	yes	characteristic, complemented
33	#16862245	C₂²	1	1	yes	characteristic, complemented
34	#16862245	C₂²	1	1	yes	characteristic, complemented
35	#16862245	C₂²	1	1	yes	characteristic, complemented
36	#16862244	C₂²	1	1	yes	characteristic, complemented
37	#16862244	C₂²	1	1	yes	characteristic, complemented
38	#16862244	C₂²	1	1	yes	characteristic, complemented
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
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
49	#16862241	C₂²	1	1	yes	characteristic
50	#16862241	C₂²	1	1	yes	characteristic
51	#16862241	C₂²	1	1	yes	characteristic
52	#16862241	C₂²	1	1	yes	characteristic
53	#16862241	C₂²	1	1	yes	characteristic
54	#16862241	C₂²	1	1	yes	characteristic, complemented
55	#16862241	C₂²	1	1	yes	characteristic, complemented
56	#16862241	C₂²	1	1	yes	characteristic, complemented
57	#16862240	C₂²	1	1	yes	characteristic
58	#16862240	C₂²	1	1	yes	characteristic
59	#16862240	C₂²	1	1	yes	characteristic
60	#16862240	C₂²	1	1	yes	characteristic, complemented
61	#16862239	C₂²	1	1	yes	characteristic, complemented
62	#16862239	C₂²	1	1	yes	characteristic, complemented
63	#16862239	C₂²	1	1	yes	characteristic, complemented
64	#16862239	C₂²	1	1	yes	characteristic, complemented
65	#16862238	C₂²	1	1	yes	characteristic, complemented
66	#16862238	C₂²	1	1	yes	characteristic, complemented
67	#16862237	C₂²	1	1	yes	characteristic, complemented
68	#16862237	C₂²	1	1	yes	characteristic, complemented
69	#16862237	C₂²	1	1	yes	characteristic, complemented
70	#16862236	C₂²	1	1	yes	characteristic, complemented
71	#16862236	C₂²	1	1	yes	characteristic, complemented
72	#16862236	C₂²	1	1	yes	characteristic, complemented
73	#16862236	C₂²	1	1	yes	characteristic, complemented
74	#16862236	C₂²	1	1	yes	characteristic, complemented
75	#16862236	C₂²	1	1	yes	characteristic, complemented
76	#16862236	C₂²	1	1	yes	characteristic, complemented
77	#16862236	C₂²	1	1	yes	characteristic, complemented
78	#16862236	C₂²	1	1	yes	characteristic, complemented
79	#16862236	C₂²	1	1	yes	characteristic, complemented
80	#16862236	C₂²	1	1	yes	characteristic, complemented
81	#16862236	C₂²	1	1	yes	characteristic, complemented
82	#16862235	C₂²	1	1	yes	characteristic
83	#16862235	C₂²	1	1	yes	characteristic
84	#16862234	C₂²	1	1	yes	characteristic
85	#16862232	C₂²	1	1	yes	characteristic
86	#16862232	C₂²	1	1	yes	characteristic
87	#16862232	C₂²	1	1	yes	characteristic
88	#16862232	C₂²	1	1	yes	characteristic, complemented
89	#16862231	C₂²	1	1	yes	characteristic
90	#16862231	C₂²	1	1	yes	characteristic
91	#16862231	C₂²	1	1	yes	characteristic
92	#16862231	C₂²	1	1	yes	characteristic
93	#16862231	C₂²	1	1	yes	characteristic
94	#16862230	C₂²	1	1	yes	characteristic
95	#16862230	C₂²	1	1	yes	characteristic
96	#16862229	C₂²	1	1	yes	characteristic
97	#16862229	C₂²	1	1	yes	characteristic
98	#16862229	C₂²	1	1	yes	characteristic
99	#16862229	C₂²	1	1	yes	characteristic, complemented
100	#16862228	C₂²	1	1	yes	characteristic
101	#16862228	C₂²	1	1	yes	characteristic
102	#16862228	C₂²	1	1	yes	characteristic, complemented
103	#16862227	C₂²	1	1	yes	characteristic
104	#16862227	C₂²	1	1	yes	characteristic
105	#16862226	C₂²	1	1	yes	characteristic
106	#16862226	C₂²	1	1	yes	characteristic
107	#16862226	C₂²	1	1	yes	characteristic, complemented
108	#16862225	C₂²	1	1	yes	characteristic
109	#16862225	C₂²	1	1	yes	characteristic
110	#16862225	C₂²	1	1	yes	characteristic
111	#16862225	C₂²	1	1	yes	characteristic, complemented
112	#16862225	C₂²	1	1	yes	characteristic, complemented
113	#16862224	C₂²	1	1	yes	characteristic
114	#16862224	C₂²	1	1	yes	characteristic
115	#16862224	C₂²	1	1	yes	characteristic
116	#16862224	C₂²	1	1	yes	characteristic
117	#16862224	C₂²	1	1	yes	characteristic
118	#16862224	C₂²	1	1	yes	characteristic
119	#16862224	C₂²	1	1	yes	characteristic, complemented
120	#16862224	C₂²	1	1	yes	characteristic, complemented
121	#16862224	C₂²	1	1	yes	characteristic, complemented
122	#16862223	C₂²	1	1	yes	characteristic
123	#16862223	C₂²	1	1	yes	characteristic
124	#16862223	C₂²	1	1	yes	characteristic
125	#16862222	C₂²	1	1	yes	characteristic
126	#16862222	C₂²	1	1	yes	characteristic
127	#16862222	C₂²	1	1	yes	characteristic
128	#16862222	C₂²	1	1	yes	characteristic
129	#16862222	C₂²	1	1	yes	characteristic, complemented
130	#16862220	C₂²	1	1	yes	characteristic
131	#16862219	C₂²	1	1	yes	characteristic
132	#16862218	C₂²	1	1	yes	characteristic
133	#16862216	C₂²	1	1	yes	characteristic
134	#16862214	C₂²	1	1	yes	characteristic
135	Q₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
136	Q₈×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
137	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
138	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
139	#16862211	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	#16862208	C₂²	1	1	yes	characteristic
144	#16862208	C₂²	1	1	yes	characteristic
145	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
146	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
147	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
148	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
150	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
151	#16862205	C₂²	1	1	yes	characteristic, complemented
152	#16862205	C₂²	1	1	yes	characteristic, complemented
153	#16862204	C₂²	1	1	yes	characteristic
154	#16862204	C₂²	1	1	yes	characteristic
155	#16862204	C₂²	1	1	yes	characteristic, complemented
156	#16862203	C₂²	1	1	yes	characteristic
157	#16862203	C₂²	1	1	yes	characteristic
158	#16862203	C₂²	1	1	yes	characteristic, complemented
159	#16862202	C₂²	1	1	yes	characteristic
160	#16862202	C₂²	1	1	yes	characteristic
161	#16862202	C₂²	1	1	yes	characteristic
162	#16862202	C₂²	1	1	yes	characteristic
163	C₂×C₄⋊Dic₁₃₁	C₂²	1	1	yes	characteristic
164	C₂×Dic₁₃₁⋊C₄	C₂²	1	1	yes	characteristic
165	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
166	C₂×(C₂×D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
167	C₂×(C₂×D₁₃₁)⋊C₄	C₂²	1	1	yes	characteristic
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
172	C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
173	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
174	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
175	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
176	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
177	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
178	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
179	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
181	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
183	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
186	C₂×C₄⋊C₄×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×Dic₂₆₂	C₂³	1	1	yes	characteristic
192	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
193	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
194	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
195	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
200	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
201	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
202	C₂²×Dic₁₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
209	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
224	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
225	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
226	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
227	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
229	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
230	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
233	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
256	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	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₁₃₁	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	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
293	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
294	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
295	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
296	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
297	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
298	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
299	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
300	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
301	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
302	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
303	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
304	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
305	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
306	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
307	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
308	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
309	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	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
315	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
316	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
317	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
318	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
330	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	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	—	2	2	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	Dic₂₆₂	—	4	1	no	—
349	Dic₂₆₂	—	4	1	no	—
350	Dic₂₆₂	—	4	1	no	—
351	Dic₂₆₂	—	4	1	no	—
352	Dic₂₆₂	—	4	1	no	—
353	Dic₂₆₂	—	4	1	no	—
354	D₅₂₄	—	4	1	no	—
355	D₅₂₄	—	4	1	no	—
356	C₂²⋊D₁₃₁	—	2	2	no	—
357	C₂²⋊D₁₃₁	—	4	1	no	—
358	C₂²⋊D₁₃₁	—	4	1	no	—
359	C₂²⋊D₁₃₁	—	4	1	no	—
360	C₂×Dic₁₃₁	—	2	2	no	—
361	C₂×Dic₁₃₁	—	2	2	no	—
362	C₂×Dic₁₃₁	—	4	1	no	—
363	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
376	C₄×D₁₃₁	—	4	1	no	—
377	C₄×D₁₃₁	—	4	1	no	—
378	C₄×D₁₃₁	—	4	1	no	—
379	C₄×D₁₃₁	—	4	1	no	—
380	C₄×D₁₃₁	—	4	1	no	—
381	C₄×D₁₃₁	—	4	1	no	—
382	C₄×D₁₃₁	—	4	1	no	—
383	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
384	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
385	Q₈×C₁₃₁	—	4	1	no	—
386	Q₈×C₁₃₁	—	4	1	no	—
387	Q₈×C₁₃₁	—	4	1	no	—
388	D₄×C₁₃₁	—	2	2	no	—
389	C₂×C₄×C₁₃₁	—	4	1	no	—
390	C₂×C₄×C₁₃₁	—	4	1	no	—
391	C₂×C₄×C₁₃₁	—	4	1	no	—
392	C₂×C₄×C₁₃₁	—	4	1	no	—
393	C₂×C₄×C₁₃₁	—	4	1	no	—
394	C₂×C₄×C₁₃₁	—	4	1	no	—
395	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
398	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
399	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
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	C₂²×C₁₃₁	—	2	1	no	—
409	C₂²×C₁₃₁	—	2	1	no	—
410	C₂²×C₁₃₁	—	2	1	no	—
411	C₂²×C₁₃₁	—	2	1	no	—
412	C₂²×C₁₃₁	—	2	1	no	—
413	C₂²×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
414	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
415	C₂×D₁₃₁	—	2	1	no	—
416	C₂×D₁₃₁	—	2	1	no	—
417	C₂×D₁₃₁	—	2	1	no	—
418	C₂×D₁₃₁	—	2	1	no	—
419	C₂×D₁₃₁	—	2	1	no	—
420	C₂×D₁₃₁	—	2	1	no	—
421	C₂×D₁₃₁	—	2	1	no	—
422	C₂×D₁₃₁	—	2	1	no	—
423	C₂×D₁₃₁	—	2	1	no	—
424	C₂×D₁₃₁	—	8	2	no	—
425	C₄×C₁₃₁	—	2	1	no	—
426	C₄×C₁₃₁	—	2	1	no	—
427	C₄×C₁₃₁	—	2	1	no	—
428	C₄×C₁₃₁	—	2	1	no	—
429	C₄×C₁₃₁	—	2	1	no	—
430	C₄×C₁₃₁	—	2	1	no	—
431	C₄×C₁₃₁	—	2	1	no	—
432	C₄×C₁₃₁	—	2	1	no	—
433	C₄×C₁₃₁	—	2	1	no	—
434	C₄×C₁₃₁	—	2	1	no	—
435	C₄×C₁₃₁	—	2	1	no	—
436	C₄×C₁₃₁	—	2	1	no	—
437	C₄×C₁₃₁	—	2	1	no	—
438	Dic₁₃₁	—	2	1	no	—
439	Dic₁₃₁	—	2	1	no	—
440	Dic₁₃₁	—	2	1	no	—
441	Dic₁₃₁	—	2	1	no	—
442	Dic₁₃₁	—	2	1	no	—
443	Dic₁₃₁	—	2	1	no	—
444	Dic₁₃₁	—	2	1	no	—
445	Dic₁₃₁	—	2	1	no	—
446	Dic₁₃₁	—	2	1	no	—
447	Dic₁₃₁	—	2	1	no	—
448	Dic₁₃₁	—	2	1	no	—
449	Dic₁₃₁	—	2	1	no	—
450	Dic₁₃₁	—	2	1	no	—
451	C₂×C₁₃₁	—	2	2	no	—
452	C₂×C₁₃₁	—	4	1	no	—
453	C₂×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂×C₁₃₁	#585	1	1	yes	characteristic
455	C₂×C₁₃₁	#585	1	1	yes	characteristic
456	D₁₃₁	—	4	1	no	—
457	D₁₃₁	—	4	1	no	—
458	D₁₃₁	—	4	1	no	—
459	C₁₃₁	#3564	1	1	yes	characteristic, complemented, Sylow
460	#3564	—	131	1	no	maximal, Sylow
461	#563	—	131	1	no	—
462	#563	—	131	1	no	—
463	#563	—	131	1	no	—
464	#563	—	131	1	no	—
465	#556	—	131	1	no	—
466	#556	—	131	1	no	—
467	#554	—	131	1	no	—
468	#554	D₁₃₁	1	1	yes	characteristic, complemented
469	#552	—	131	1	no	—
470	#552	—	131	1	no	—
471	#552	—	131	1	no	—
472	#552	—	131	1	no	—
473	#551	—	131	1	no	—
474	#551	—	131	1	no	—
475	#551	—	131	1	no	—
476	#551	—	131	1	no	—
477	#544	—	131	1	no	—
478	#543	—	131	1	no	—
479	#542	—	131	1	no	—
480	#542	—	131	1	no	—
481	#541	—	131	1	no	—
482	#541	—	131	1	no	—
483	#541	—	131	1	no	—
484	#541	—	131	1	no	—
485	#539	—	131	1	no	—
486	#539	—	131	1	no	—
487	#539	—	131	1	no	—
488	#538	—	131	1	no	—
489	#533	—	131	1	no	—
490	#529	—	131	1	no	—
491	C₂×#126	—	131	1	no	—
492	C₄⋊Q₈	—	131	1	no	—
493	C₄⋊Q₈	—	131	1	no	—
494	C₄⋊Q₈	—	131	1	no	—
495	C₄⋊Q₈	—	131	1	no	—
496	C₄⋊Q₈	—	131	1	no	—
497	C₄⋊Q₈	—	131	1	no	—
498	C₄⋊Q₈	—	131	1	no	—
499	C₄⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
500	#126	—	131	1	no	—
501	#126	—	131	1	no	—
502	#126	—	131	1	no	—
503	#126	—	131	1	no	—
504	#126	—	131	1	no	—
505	#126	—	131	1	no	—
506	#126	—	131	1	no	—
507	#126	—	131	1	no	—
508	#126	—	131	1	no	—
509	#126	—	131	1	no	—
510	#126	—	131	1	no	—
511	#126	—	131	1	no	—
512	#126	—	131	1	no	—
513	#126	—	131	1	no	—
514	#126	—	131	1	no	—
515	#126	—	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	#125	—	131	1	no	—
527	#125	—	131	1	no	—
528	#125	—	131	1	no	—
529	#125	—	131	1	no	—
530	#125	—	131	1	no	—
531	#125	—	131	1	no	—
532	#125	—	131	1	no	—
533	#125	—	131	1	no	—
534	#125	—	131	1	no	—
535	#125	—	131	1	no	—
536	#125	—	131	1	no	—
537	#125	—	131	1	no	—
538	#125	—	131	1	no	—
539	#125	—	131	1	no	—
540	#125	—	131	1	no	—
541	#125	—	131	1	no	—
542	#125	—	131	1	no	—
543	#125	C₂×D₁₃₁	1	1	yes	characteristic, complemented
544	#125	C₂×D₁₃₁	1	1	yes	characteristic, complemented
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	#123	—	131	1	no	—
553	#123	—	131	1	no	—
554	#123	—	131	1	no	—
555	#123	—	131	1	no	—
556	#123	—	131	1	no	—
557	#123	—	131	1	no	—
558	#123	—	131	1	no	—
559	#123	—	131	1	no	—
560	#123	—	131	1	no	—
561	#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	C₂²⋊Q₈	—	131	1	no	—
569	C₂²⋊Q₈	—	131	1	no	—
570	C₂²⋊Q₈	—	131	1	no	—
571	C₂²⋊Q₈	—	131	1	no	—
572	C₂²⋊Q₈	—	131	1	no	—
573	C₂²⋊Q₈	—	131	1	no	—
574	C₂²⋊Q₈	—	131	1	no	—
575	C₂²⋊Q₈	—	131	1	no	—
576	C₂²⋊Q₈	—	131	1	no	—
577	C₂²⋊Q₈	—	131	1	no	—
578	C₂²⋊Q₈	—	131	1	no	—
579	C₂²⋊Q₈	—	131	1	no	—
580	C₂²⋊Q₈	—	131	1	no	—
581	C₂²⋊Q₈	—	131	1	no	—
582	C₂²⋊Q₈	—	131	1	no	—
583	C₂²⋊Q₈	—	131	1	no	—
584	C₂²⋊Q₈	—	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	C₂×D₁₃₁	1	1	yes	characteristic
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	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
599	#121	—	131	1	no	—
600	#121	—	131	1	no	—
601	#121	—	131	1	no	—
602	#120	—	131	1	no	—
603	#120	—	131	1	no	—
604	C₄×Q₈	—	131	1	no	—
605	C₄×Q₈	—	131	1	no	—
606	C₄×Q₈	—	131	1	no	—
607	C₄×Q₈	—	131	1	no	—
608	C₄×Q₈	—	131	1	no	—
609	C₄×Q₈	—	131	1	no	—
610	C₄×Q₈	—	131	1	no	—
611	C₄×Q₈	—	131	1	no	—
612	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
613	C₄×D₄	—	131	1	no	—
614	C₄×D₄	—	131	1	no	—
615	C₄×D₄	—	131	1	no	—
616	C₄×D₄	—	131	1	no	—
617	C₄×D₄	—	131	1	no	—
618	C₄×D₄	—	131	1	no	—
619	C₄×D₄	—	131	1	no	—
620	C₄×D₄	—	131	1	no	—
621	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
622	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
623	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
624	#117	—	131	1	no	—
625	#117	—	131	1	no	—
626	#117	—	131	1	no	—
627	#117	—	131	1	no	—
628	#117	—	131	1	no	—
629	#117	—	131	1	no	—
630	#117	—	131	1	no	—
631	#117	—	131	1	no	—
632	#117	—	131	1	no	—
633	#117	—	131	1	no	—
634	#117	—	131	1	no	—
635	#117	—	131	1	no	—
636	C₂×C₄⋊C₄	—	131	1	no	—
637	C₂×C₄⋊C₄	—	131	1	no	—
638	C₂×C₄⋊C₄	—	131	1	no	—
639	C₂×C₄⋊C₄	C₂×D₁₃₁	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
641	C₂×C₂²⋊C₄	—	131	1	no	—
642	C₂×C₂²⋊C₄	—	131	1	no	—
643	C₂×C₂²⋊C₄	—	131	1	no	—
644	C₂×C₂²⋊C₄	—	131	1	no	—
645	C₂×C₂²⋊C₄	—	131	1	no	—
646	C₂×C₄²	—	131	1	no	—
647	C₂⁴	—	131	1	no	—
648	C₂×Q₈	—	131	1	no	—
649	C₂×Q₈	—	131	1	no	—
650	C₂×Q₈	—	131	1	no	—
651	C₂×Q₈	—	131	1	no	—
652	C₂×Q₈	—	131	1	no	—
653	C₂×Q₈	—	131	1	no	—
654	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
655	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
656	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
657	C₂×D₄	—	131	1	no	—
658	C₂×D₄	—	131	1	no	—
659	C₂×D₄	—	131	1	no	—
660	C₂×D₄	—	131	1	no	—
661	C₂×D₄	—	131	1	no	—
662	C₂×D₄	—	131	1	no	—
663	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
664	C₂²×C₄	—	131	1	no	—
665	C₂²×C₄	—	131	1	no	—
666	C₂²×C₄	—	131	1	no	—
667	C₂²×C₄	—	131	1	no	—
668	C₂²×C₄	—	131	1	no	—
669	C₂²×C₄	—	131	1	no	—
670	C₂²×C₄	—	131	1	no	—
671	C₂²×C₄	—	131	1	no	—
672	C₂²×C₄	—	131	1	no	—
673	C₂²×C₄	—	131	1	no	—
674	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
675	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
676	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
677	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
678	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
679	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
680	C₄⋊C₄	—	131	1	no	—
681	C₄⋊C₄	—	131	1	no	—
682	C₄⋊C₄	—	131	1	no	—
683	C₄⋊C₄	—	131	1	no	—
684	C₄⋊C₄	—	131	1	no	—
685	C₄⋊C₄	—	131	1	no	—
686	C₄⋊C₄	—	131	1	no	—
687	C₄⋊C₄	—	131	1	no	—
688	C₄⋊C₄	—	131	1	no	—
689	C₄⋊C₄	—	131	1	no	—
690	C₄⋊C₄	—	131	1	no	—
691	C₄⋊C₄	—	131	1	no	—
692	C₄⋊C₄	—	131	1	no	—
693	C₄⋊C₄	—	131	1	no	—
694	C₄⋊C₄	—	131	1	no	—
695	C₄⋊C₄	—	131	1	no	—
696	C₄⋊C₄	—	131	1	no	—
697	C₄⋊C₄	—	131	1	no	—
698	C₄⋊C₄	—	131	1	no	—
699	C₄⋊C₄	—	131	1	no	—
700	C₄⋊C₄	—	131	1	no	—
701	C₄⋊C₄	—	131	1	no	—
702	C₄⋊C₄	—	131	1	no	—
703	C₄⋊C₄	—	131	1	no	—
704	C₄⋊C₄	—	131	1	no	—
705	C₄⋊C₄	—	131	1	no	—
706	C₄⋊C₄	—	131	1	no	—
707	C₄⋊C₄	—	131	1	no	—
708	C₄⋊C₄	—	131	1	no	—
709	C₄⋊C₄	—	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	C₂²×D₁₃₁	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
731	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
732	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
733	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
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	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	—	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	C₂²×D₁₃₁	1	1	yes	characteristic
779	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
780	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
781	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
782	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
784	C₄²	—	131	1	no	—
785	C₄²	—	131	1	no	—
786	C₄²	—	131	1	no	—
787	C₄²	—	131	1	no	—
788	C₄²	—	131	1	no	—
789	C₄²	—	131	1	no	—
790	C₄²	—	131	1	no	—
791	C₄²	—	131	1	no	—
792	C₄²	—	131	1	no	—
793	C₄²	—	131	1	no	—
794	C₄²	—	131	1	no	—
795	C₄²	—	131	1	no	—
796	C₄²	—	131	1	no	—
797	C₄²	—	131	1	no	—
798	C₄²	—	131	1	no	—
799	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
800	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
801	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
802	C₂³	—	262	2	no	—
803	C₂³	—	524	1	no	—
804	C₂³	—	524	1	no	—
805	C₂³	—	131	1	no	—
806	C₂³	—	131	1	no	—
807	C₂³	—	131	1	no	—
808	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
809	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
810	Q₈	—	4	1	no	—
811	Q₈	—	4	1	no	—
812	Q₈	—	4	1	no	—
813	Q₈	—	524	1	no	—
814	Q₈	—	524	1	no	—
815	Q₈	—	524	1	no	—
816	Q₈	—	524	1	no	—
817	Q₈	—	524	1	no	—
818	Q₈	—	524	1	no	—
819	D₄	—	2	2	no	—
820	D₄	—	262	2	no	—
821	D₄	—	524	1	no	—
822	D₄	—	524	1	no	—
823	D₄	—	524	1	no	—
824	D₄	—	524	1	no	—
825	D₄	—	524	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	262	2	no	—
833	C₂×C₄	—	262	2	no	—
834	C₂×C₄	—	524	1	no	—
835	C₂×C₄	—	524	1	no	—
836	C₂×C₄	—	524	1	no	—
837	C₂×C₄	—	524	1	no	—
838	C₂×C₄	—	524	1	no	—
839	C₂×C₄	—	524	1	no	—
840	C₂×C₄	—	524	1	no	—
841	C₂×C₄	—	524	1	no	—
842	C₂×C₄	—	131	1	no	—
843	C₂×C₄	—	131	1	no	—
844	C₂×C₄	—	131	1	no	—
845	C₂×C₄	—	131	1	no	—
846	C₂×C₄	—	131	1	no	—
847	C₂×C₄	—	131	1	no	—
848	C₂×C₄	—	131	1	no	—
849	C₂×C₄	—	131	1	no	—
850	C₂×C₄	—	131	1	no	—
851	C₂×C₄	—	131	1	no	—
852	C₂×C₄	—	131	1	no	—
853	C₂×C₄	—	131	1	no	—
854	C₂×C₄	—	131	1	no	—
855	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
857	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
858	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
859	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
860	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
861	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
862	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
863	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
864	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
865	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
866	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
867	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	262	1	no	—
874	C₂²	—	262	1	no	—
875	C₂²	—	262	1	no	—
876	C₂²	—	262	1	no	—
877	C₂²	—	262	1	no	—
878	C₂²	—	262	1	no	—
879	C₂²	—	262	1	no	—
880	C₂²	—	262	1	no	—
881	C₂²	—	262	1	no	—
882	C₂²	—	1048	2	no	—
883	C₂²	#16862294	1	2	yes	—
884	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	262	1	no	—
899	C₄	—	262	1	no	—
900	C₄	—	262	1	no	—
901	C₄	—	262	1	no	—
902	C₄	—	262	1	no	—
903	C₄	—	262	1	no	—
904	C₄	—	262	1	no	—
905	C₄	—	262	1	no	—
906	C₄	—	262	1	no	—
907	C₄	—	262	1	no	—
908	C₄	—	262	1	no	—
909	C₄	—	262	1	no	—
910	C₄	—	262	1	no	—
911	C₂	—	2	2	no	—
912	C₂	—	4	1	no	—
913	C₂	—	524	1	no	—
914	C₂	—	524	1	no	—
915	C₂	—	524	1	no	—
916	C₂	C₂×#16862294	1	1	yes	characteristic
917	C₂	#22554147	1	1	yes	characteristic
918	C₂	#22554148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#554×C₁₃₁	C₂
prime radical	#22553895	C₂
hypercenter	#554	D₁₃₁
hypocenter	C₁₃₁	#3564
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #554

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. #22554063	C₂	semidirect
4. #22554061	C₂	semidirect
5. #22554034	C₂	semidirect
6. #22554033	C₂	semidirect
7. #22554017	C₂	semidirect
8. #22554004	C₂	semidirect
9. #22554002	C₂	semidirect
10. #22553997	C₂	semidirect
11. #22553994	C₂	semidirect
12. #22553991	C₂	semidirect
13. #22553991	C₂	semidirect
14. #22553989	C₂	semidirect
15. #22553989	C₂	semidirect
16. #22553941	C₂	semidirect
17. #22553937	C₂	semidirect
18. #22553935	C₂	semidirect
19. #22553932	C₂	semidirect
20. #22553923	C₂	semidirect
21. #22553921	C₂	semidirect
22. #22553921	C₂	semidirect
23. #22553920	C₂	semidirect
24. #22553909	C₂	semidirect
25. #22553908	C₂	semidirect
26. #22553904	C₂	semidirect
28. #22553864	C₂	semidirect
29. #22553842	C₂	semidirect
30. C₂×#16862241	C₂	semidirect
31. #554×C₁₃₁	C₂	semidirect
32. #16862245	C₂²	semidirect
33. #16862245	C₂²	semidirect
34. #16862245	C₂²	semidirect
35. #16862245	C₂²	semidirect
36. #16862244	C₂²	semidirect
37. #16862244	C₂²	semidirect
38. #16862244	C₂²	semidirect
54. #16862241	C₂²	semidirect
55. #16862241	C₂²	semidirect
56. #16862241	C₂²	semidirect
60. #16862240	C₂²	semidirect
61. #16862239	C₂²	semidirect
62. #16862239	C₂²	semidirect
63. #16862239	C₂²	semidirect
64. #16862239	C₂²	semidirect
65. #16862238	C₂²	semidirect
66. #16862238	C₂²	semidirect
67. #16862237	C₂²	semidirect
68. #16862237	C₂²	semidirect
69. #16862237	C₂²	semidirect
70. #16862236	C₂²	semidirect
71. #16862236	C₂²	semidirect
72. #16862236	C₂²	semidirect
73. #16862236	C₂²	semidirect
74. #16862236	C₂²	semidirect
75. #16862236	C₂²	semidirect
76. #16862236	C₂²	semidirect
77. #16862236	C₂²	semidirect
78. #16862236	C₂²	semidirect
79. #16862236	C₂²	semidirect
80. #16862236	C₂²	semidirect
81. #16862236	C₂²	semidirect
88. #16862232	C₂²	semidirect
99. #16862229	C₂²	semidirect
102. #16862228	C₂²	semidirect
107. #16862226	C₂²	semidirect
111. #16862225	C₂²	semidirect
112. #16862225	C₂²	semidirect
119. #16862224	C₂²	semidirect
120. #16862224	C₂²	semidirect
121. #16862224	C₂²	semidirect
129. #16862222	C₂²	semidirect
135. Q₈×Dic₁₃₁	C₂²	semidirect
136. Q₈×Dic₁₃₁	C₂²	semidirect
137. C₄×Dic₂₆₂	C₂²	semidirect
138. C₄×Dic₂₆₂	C₂²	semidirect
139. #16862211	C₂²	semidirect
140. #16862211	C₂²	semidirect
141. #16862211	C₂²	semidirect
142. #16862211	C₂²	semidirect
150. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
151. #16862205	C₂²	semidirect
152. #16862205	C₂²	semidirect
155. #16862204	C₂²	semidirect
158. #16862203	C₂²	semidirect
165. C₄⋊C₄×D₁₃₁	C₂²	semidirect
172. C₄⋊Q₈×C₁₃₁	C₂²	semidirect
173. #125×C₁₃₁	C₂²	semidirect
174. #125×C₁₃₁	C₂²	semidirect
178. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
179. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
180. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
181. C₄×Q₈×C₁₃₁	C₂²	semidirect
186. C₂×C₄⋊C₄×C₁₃₁	C₂²	semidirect
459. C₁₃₁	#3564	semidirect
468. #554	D₁₃₁	semidirect
499. C₄⋊Q₈	C₂×D₁₃₁	semidirect
543. #125	C₂×D₁₃₁	semidirect
544. #125	C₂×D₁₃₁	semidirect
596. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
597. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
598. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
612. C₄×Q₈	C₂×D₁₃₁	semidirect
640. 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
#22554061	2
#22554034	2
#22554033	2
#22554017	2
#22554004	2
#22554002	2
#22553997	2
#22553994	2
#22553991	2
#22553989	2
#22553941	2
#22553937	2
#22553935	2
#22553932	2
#22553923	2
#22553921	2
#22553920	2
#22553909	2
#22553908	2
#22553904	2
#22553895	2
#22553864	2
#22553842	2
C₂×#16862241	2
#554×C₁₃₁	2
#3564	131