Subgroups — C₁₃₁×#34467 #45720351

Order 33536.

2248 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2379×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2377×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2367×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2365×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2363×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2361×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2352×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2349×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#2347×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#2346×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#2343×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2337×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	#2331×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#2326×C₁₃₁	C₂	1	2	yes	maximal, complemented
16	#2325×C₁₃₁	C₂	1	2	yes	maximal, complemented
17	#2324×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	#2319×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
19	#2317×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#2314×C₁₃₁	C₂	1	2	yes	maximal, complemented
21	C₄×#121×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
22	#2296×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#2290×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	#555×C₁₃₁	C₄	1	16	yes	complemented
25	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
39	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
42	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
45	#391×C₁₃₁	C₂²	1	2	yes	—
46	#391×C₁₃₁	C₂²	1	2	yes	—
47	#391×C₁₃₁	C₂²	1	2	yes	—
48	#390×C₁₃₁	C₂²	1	1	yes	characteristic
49	#390×C₁₃₁	C₂²	1	1	yes	characteristic
50	#390×C₁₃₁	C₂²	1	2	yes	—
51	#390×C₁₃₁	C₂²	1	2	yes	—
52	#389×C₁₃₁	C₂²	1	1	yes	characteristic
53	#389×C₁₃₁	C₂²	1	1	yes	characteristic
54	#389×C₁₃₁	C₂²	1	1	yes	characteristic
55	#389×C₁₃₁	C₂²	1	1	yes	characteristic
56	#389×C₁₃₁	C₂²	1	1	yes	characteristic
57	#389×C₁₃₁	C₂²	1	1	yes	characteristic
58	#389×C₁₃₁	C₂²	1	1	yes	characteristic
59	#389×C₁₃₁	C₂²	1	1	yes	characteristic
60	#388×C₁₃₁	C₂²	1	1	yes	characteristic
61	#388×C₁₃₁	C₂²	1	1	yes	characteristic
62	#388×C₁₃₁	C₂²	1	2	yes	—
63	#388×C₁₃₁	C₂²	1	2	yes	—
64	#388×C₁₃₁	C₂²	1	2	yes	—
65	#388×C₁₃₁	C₂²	1	2	yes	—
66	#388×C₁₃₁	C₂²	1	2	yes	—
67	#388×C₁₃₁	C₂²	1	2	yes	—
68	#388×C₁₃₁	C₂²	1	2	yes	—
69	#388×C₁₃₁	C₂²	1	2	yes	—
70	#388×C₁₃₁	C₂²	1	2	yes	—
71	#388×C₁₃₁	C₂²	1	2	yes	—
72	#388×C₁₃₁	C₂²	1	2	yes	—
73	#387×C₁₃₁	C₂²	1	1	yes	characteristic
74	#387×C₁₃₁	C₂²	1	1	yes	characteristic
75	#387×C₁₃₁	C₂²	1	2	yes	—
76	#387×C₁₃₁	C₂²	1	2	yes	—
77	#387×C₁₃₁	C₂²	1	2	yes	—
78	#387×C₁₃₁	C₂²	1	2	yes	—
79	#387×C₁₃₁	C₂²	1	2	yes	—
80	#386×C₁₃₁	C₂²	1	1	yes	characteristic
81	#386×C₁₃₁	C₂²	1	1	yes	characteristic
82	#386×C₁₃₁	C₂²	1	2	yes	—
83	#386×C₁₃₁	C₂²	1	2	yes	—
84	#386×C₁₃₁	C₂²	1	2	yes	—
85	#386×C₁₃₁	C₂²	1	2	yes	—
86	#386×C₁₃₁	C₂²	1	2	yes	—
87	#385×C₁₃₁	C₂²	1	1	yes	characteristic
88	#385×C₁₃₁	C₂²	1	1	yes	characteristic
89	#385×C₁₃₁	C₂²	1	2	yes	—
90	#385×C₁₃₁	C₂²	1	2	yes	—
91	#385×C₁₃₁	C₂²	1	2	yes	—
92	#385×C₁₃₁	C₂²	1	2	yes	—
93	#385×C₁₃₁	C₂²	1	2	yes	—
94	#385×C₁₃₁	C₂²	1	2	yes	—
95	#385×C₁₃₁	C₂²	1	2	yes	—
96	#385×C₁₃₁	C₂²	1	2	yes	—
97	#384×C₁₃₁	C₂²	1	2	yes	—
98	#383×C₁₃₁	C₂²	1	2	yes	—
99	#382×C₁₃₁	C₂²	1	2	yes	—
100	#382×C₁₃₁	C₂²	1	2	yes	—
101	#382×C₁₃₁	C₂²	1	1	yes	characteristic
102	#381×C₁₃₁	C₂²	1	2	yes	—
103	#380×C₁₃₁	C₂²	1	1	yes	characteristic
104	#380×C₁₃₁	C₂²	1	2	yes	—
105	#380×C₁₃₁	C₂²	1	2	yes	—
106	#380×C₁₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
121	#376×C₁₃₁	C₂²	1	1	yes	characteristic
122	#376×C₁₃₁	C₂²	1	2	yes	—
123	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
124	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
138	#124×C₁₃₁	C₂×C₄	1	16	yes	complemented
139	#124×C₁₃₁	C₂×C₄	1	16	yes	complemented
140	#121×C₁₃₁	C₂×C₄	1	8	yes	complemented
141	#121×C₁₃₁	C₂×C₄	1	8	yes	complemented
142	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
143	C₄×Q₈×C₁₃₁	—	4	4	no	—
144	C₄×D₄×C₁₃₁	—	4	2	no	—
145	C₄×D₄×C₁₃₁	—	4	2	no	—
146	C₄×D₄×C₁₃₁	—	4	4	no	—
147	C₄×D₄×C₁₃₁	—	4	4	no	—
148	C₄×D₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
149	C₄×D₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
150	#117×C₁₃₁	—	4	2	no	—
151	#117×C₁₃₁	—	4	2	no	—
152	#117×C₁₃₁	C₂×C₄	1	8	yes	complemented
153	#117×C₁₃₁	C₂×C₄	1	8	yes	complemented
154	#117×C₁₃₁	C₂×C₄	1	16	yes	complemented
155	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
156	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃₁	—	4	2	no	—
201	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
209	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
210	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
213	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
214	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
215	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
216	#95×C₁₃₁	C₂³	1	2	yes	—
217	#95×C₁₃₁	C₂³	1	1	yes	characteristic
218	#95×C₁₃₁	C₂³	1	1	yes	characteristic
219	#95×C₁₃₁	C₂³	1	1	yes	characteristic
220	#95×C₁₃₁	C₂³	1	2	yes	—
221	#95×C₁₃₁	C₂³	1	2	yes	—
222	#95×C₁₃₁	C₂³	1	2	yes	—
223	#95×C₁₃₁	C₂³	1	1	yes	characteristic
224	#95×C₁₃₁	C₂³	1	2	yes	—
225	#95×C₁₃₁	C₂³	1	2	yes	—
226	#95×C₁₃₁	C₂³	1	2	yes	—
227	#95×C₁₃₁	C₂³	1	2	yes	—
228	#95×C₁₃₁	C₂³	1	2	yes	—
229	#95×C₁₃₁	C₂³	1	2	yes	—
230	#95×C₁₃₁	C₂³	1	2	yes	—
231	#95×C₁₃₁	C₂³	1	2	yes	—
232	#95×C₁₃₁	C₂³	1	1	yes	characteristic
233	#95×C₁₃₁	C₂³	1	2	yes	—
234	#95×C₁₃₁	C₂³	1	2	yes	—
235	#95×C₁₃₁	C₂³	1	2	yes	—
236	#95×C₁₃₁	C₂³	1	1	yes	characteristic
237	#95×C₁₃₁	C₂³	1	2	yes	—
238	#95×C₁₃₁	C₂³	1	1	yes	characteristic
239	#95×C₁₃₁	C₂³	1	1	yes	characteristic
240	#95×C₁₃₁	C₂³	1	1	yes	characteristic
241	#95×C₁₃₁	C₂³	1	1	yes	characteristic
242	#95×C₁₃₁	C₂³	1	2	yes	—
243	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₁₃₁	—	4	2	no	—
247	C₂×Q₈×C₁₃₁	—	4	2	no	—
248	C₂×Q₈×C₁₃₁	C₂²×C₄	1	8	yes	—
249	C₂×D₄×C₁₃₁	—	2	2	no	—
250	C₂×D₄×C₁₃₁	—	2	2	no	—
251	C₂×D₄×C₁₃₁	—	4	2	no	—
252	C₂×D₄×C₁₃₁	—	4	2	no	—
253	C₂×D₄×C₁₃₁	—	4	2	no	—
254	C₂×D₄×C₁₃₁	—	4	2	no	—
255	C₂×D₄×C₁₃₁	—	4	1	no	—
256	C₂×D₄×C₁₃₁	—	4	1	no	—
257	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
258	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
259	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
260	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
261	C₂²×C₄×C₁₃₁	—	2	2	no	—
262	C₂²×C₄×C₁₃₁	—	2	2	no	—
263	C₂²×C₄×C₁₃₁	—	2	2	no	—
264	C₂²×C₄×C₁₃₁	—	2	2	no	—
265	C₂²×C₄×C₁₃₁	—	2	2	no	—
266	C₂²×C₄×C₁₃₁	—	2	4	no	—
267	C₂²×C₄×C₁₃₁	—	4	1	no	—
268	C₂²×C₄×C₁₃₁	—	4	1	no	—
269	C₂²×C₄×C₁₃₁	—	4	2	no	—
270	C₂²×C₄×C₁₃₁	—	4	2	no	—
271	C₂²×C₄×C₁₃₁	—	4	1	no	—
272	C₂²×C₄×C₁₃₁	—	4	1	no	—
273	C₂²×C₄×C₁₃₁	—	4	1	no	—
274	C₂²×C₄×C₁₃₁	—	4	2	no	—
275	C₂²×C₄×C₁₃₁	—	4	2	no	—
276	C₂²×C₄×C₁₃₁	—	4	2	no	—
277	C₂²×C₄×C₁₃₁	—	4	2	no	—
278	C₂²×C₄×C₁₃₁	—	4	2	no	—
279	C₂²×C₄×C₁₃₁	—	4	2	no	—
280	C₂²×C₄×C₁₃₁	—	4	2	no	—
281	C₂²×C₄×C₁₃₁	—	4	2	no	—
282	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
283	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
284	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
285	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₁₃₁	—	2	2	no	—
306	C₄⋊C₄×C₁₃₁	—	2	2	no	—
307	C₄⋊C₄×C₁₃₁	—	2	2	no	—
308	C₄⋊C₄×C₁₃₁	—	2	4	no	—
309	C₄⋊C₄×C₁₃₁	—	2	2	no	—
310	C₄⋊C₄×C₁₃₁	—	2	2	no	—
311	C₄⋊C₄×C₁₃₁	—	4	2	no	—
312	C₄⋊C₄×C₁₃₁	—	4	2	no	—
313	C₄⋊C₄×C₁₃₁	—	4	2	no	—
314	C₄⋊C₄×C₁₃₁	—	4	2	no	—
315	C₄⋊C₄×C₁₃₁	—	4	2	no	—
316	C₄⋊C₄×C₁₃₁	—	4	2	no	—
317	C₄⋊C₄×C₁₃₁	—	4	1	no	—
318	C₄⋊C₄×C₁₃₁	—	4	1	no	—
319	C₄⋊C₄×C₁₃₁	—	4	1	no	—
320	C₄⋊C₄×C₁₃₁	—	4	2	no	—
321	C₄⋊C₄×C₁₃₁	—	4	2	no	—
322	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
323	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
324	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
325	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
326	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
327	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
328	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
329	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
330	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
331	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
332	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
333	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
334	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
335	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
336	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
337	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
338	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
339	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
340	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
341	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
342	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
343	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
344	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
345	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
346	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
347	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
348	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
349	C₄²×C₁₃₁	—	2	2	no	—
350	C₄²×C₁₃₁	—	2	2	no	—
351	C₄²×C₁₃₁	—	2	2	no	—
352	C₄²×C₁₃₁	—	2	4	no	—
353	C₄²×C₁₃₁	—	2	2	no	—
354	C₄²×C₁₃₁	—	4	1	no	—
355	C₄²×C₁₃₁	—	4	1	no	—
356	C₄²×C₁₃₁	—	4	2	no	—
357	C₄²×C₁₃₁	—	4	2	no	—
358	C₄²×C₁₃₁	—	4	2	no	—
359	C₄²×C₁₃₁	—	4	2	no	—
360	C₄²×C₁₃₁	—	4	2	no	—
361	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	—
362	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	—
363	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
364	C₂³×C₁₃₁	—	2	1	no	—
365	C₂³×C₁₃₁	—	2	1	no	—
366	C₂³×C₁₃₁	—	2	1	no	—
367	C₂³×C₁₃₁	—	2	1	no	—
368	C₂³×C₁₃₁	—	2	2	no	—
369	C₂³×C₁₃₁	—	2	2	no	—
370	C₂³×C₁₃₁	—	2	1	no	—
371	C₂³×C₁₃₁	—	2	1	no	—
372	C₂³×C₁₃₁	—	2	2	no	—
373	C₂³×C₁₃₁	—	2	1	no	—
374	C₂³×C₁₃₁	—	2	2	no	—
375	C₂³×C₁₃₁	—	2	2	no	—
376	C₂³×C₁₃₁	—	2	1	no	—
377	C₂³×C₁₃₁	—	2	1	no	—
378	C₂³×C₁₃₁	—	2	1	no	—
379	C₂³×C₁₃₁	—	2	1	no	—
380	C₂³×C₁₃₁	—	2	1	no	—
381	C₂³×C₁₃₁	—	2	2	no	—
382	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
383	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
384	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
385	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
386	Q₈×C₁₃₁	—	4	8	no	—
387	D₄×C₁₃₁	—	2	8	no	—
388	D₄×C₁₃₁	—	4	4	no	—
389	D₄×C₁₃₁	—	4	8	no	—
390	D₄×C₁₃₁	—	4	8	no	—
391	C₂×C₄×C₁₃₁	—	2	1	no	—
392	C₂×C₄×C₁₃₁	—	2	2	no	—
393	C₂×C₄×C₁₃₁	—	2	1	no	—
394	C₂×C₄×C₁₃₁	—	2	2	no	—
395	C₂×C₄×C₁₃₁	—	2	1	no	—
396	C₂×C₄×C₁₃₁	—	2	1	no	—
397	C₂×C₄×C₁₃₁	—	2	1	no	—
398	C₂×C₄×C₁₃₁	—	2	1	no	—
399	C₂×C₄×C₁₃₁	—	2	2	no	—
400	C₂×C₄×C₁₃₁	—	2	2	no	—
401	C₂×C₄×C₁₃₁	—	2	2	no	—
402	C₂×C₄×C₁₃₁	—	2	2	no	—
403	C₂×C₄×C₁₃₁	—	2	1	no	—
404	C₂×C₄×C₁₃₁	—	2	1	no	—
405	C₂×C₄×C₁₃₁	—	2	1	no	—
406	C₂×C₄×C₁₃₁	—	2	1	no	—
407	C₂×C₄×C₁₃₁	—	2	8	no	—
408	C₂×C₄×C₁₃₁	—	2	8	no	—
409	C₂×C₄×C₁₃₁	—	2	2	no	—
410	C₂×C₄×C₁₃₁	—	2	1	no	—
411	C₂×C₄×C₁₃₁	—	2	1	no	—
412	C₂×C₄×C₁₃₁	—	2	1	no	—
413	C₂×C₄×C₁₃₁	—	2	1	no	—
414	C₂×C₄×C₁₃₁	—	2	1	no	—
415	C₂×C₄×C₁₃₁	—	2	1	no	—
416	C₂×C₄×C₁₃₁	—	2	1	no	—
417	C₂×C₄×C₁₃₁	—	2	2	no	—
418	C₂×C₄×C₁₃₁	—	2	2	no	—
419	C₂×C₄×C₁₃₁	—	2	2	no	—
420	C₂×C₄×C₁₃₁	—	2	2	no	—
421	C₂×C₄×C₁₃₁	—	2	1	no	—
422	C₂×C₄×C₁₃₁	—	2	2	no	—
423	C₂×C₄×C₁₃₁	—	2	1	no	—
424	C₂×C₄×C₁₃₁	—	2	1	no	—
425	C₂×C₄×C₁₃₁	—	2	2	no	—
426	C₂×C₄×C₁₃₁	—	2	1	no	—
427	C₂×C₄×C₁₃₁	—	2	2	no	—
428	C₂×C₄×C₁₃₁	—	2	1	no	—
429	C₂×C₄×C₁₃₁	—	2	2	no	—
430	C₂×C₄×C₁₃₁	—	2	1	no	—
431	C₂×C₄×C₁₃₁	—	2	1	no	—
432	C₂×C₄×C₁₃₁	—	2	1	no	—
433	C₂×C₄×C₁₃₁	—	2	1	no	—
434	C₂×C₄×C₁₃₁	—	2	2	no	—
435	C₂×C₄×C₁₃₁	—	2	2	no	—
436	C₂×C₄×C₁₃₁	—	2	1	no	—
437	C₂×C₄×C₁₃₁	—	2	1	no	—
438	C₂×C₄×C₁₃₁	—	2	1	no	—
439	C₂×C₄×C₁₃₁	—	2	1	no	—
440	C₂×C₄×C₁₃₁	—	2	1	no	—
441	C₂×C₄×C₁₃₁	—	2	2	no	—
442	C₂×C₄×C₁₃₁	—	4	8	no	—
443	C₂×C₄×C₁₃₁	—	4	4	no	—
444	C₂×C₄×C₁₃₁	—	4	4	no	—
445	C₂×C₄×C₁₃₁	—	8	4	no	—
446	C₂×C₄×C₁₃₁	—	8	4	no	—
447	C₂×C₄×C₁₃₁	—	8	4	no	—
448	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
449	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
450	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
451	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
452	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
453	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
454	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
455	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
456	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
457	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
458	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
459	C₂²×C₁₃₁	—	2	2	no	—
460	C₂²×C₁₃₁	—	2	2	no	—
461	C₂²×C₁₃₁	—	2	4	no	—
462	C₂²×C₁₃₁	—	2	4	no	—
463	C₂²×C₁₃₁	—	2	2	no	—
464	C₂²×C₁₃₁	—	2	2	no	—
465	C₂²×C₁₃₁	—	2	2	no	—
466	C₂²×C₁₃₁	—	2	2	no	—
467	C₂²×C₁₃₁	—	2	4	no	—
468	C₂²×C₁₃₁	—	4	1	no	—
469	C₂²×C₁₃₁	—	4	2	no	—
470	C₂²×C₁₃₁	—	4	1	no	—
471	C₂²×C₁₃₁	—	4	1	no	—
472	C₂²×C₁₃₁	—	4	1	no	—
473	C₂²×C₁₃₁	—	4	2	no	—
474	C₂²×C₁₃₁	—	4	1	no	—
475	C₂²×C₁₃₁	—	4	1	no	—
476	C₂²×C₁₃₁	—	4	2	no	—
477	C₂²×C₁₃₁	—	4	1	no	—
478	C₂²×C₁₃₁	—	4	1	no	—
479	C₂²×C₁₃₁	—	4	2	no	—
480	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
481	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂²×C₁₃₁	#585	1	1	yes	characteristic
485	C₂²×C₁₃₁	#585	1	1	yes	characteristic
486	C₂²×C₁₃₁	#585	1	1	yes	characteristic
487	C₄×C₁₃₁	—	2	2	no	—
488	C₄×C₁₃₁	—	2	2	no	—
489	C₄×C₁₃₁	—	2	2	no	—
490	C₄×C₁₃₁	—	2	4	no	—
491	C₄×C₁₃₁	—	2	4	no	—
492	C₄×C₁₃₁	—	2	4	no	—
493	C₄×C₁₃₁	—	2	2	no	—
494	C₄×C₁₃₁	—	2	2	no	—
495	C₄×C₁₃₁	—	4	1	no	—
496	C₄×C₁₃₁	—	4	1	no	—
497	C₄×C₁₃₁	—	4	2	no	—
498	C₄×C₁₃₁	—	4	1	no	—
499	C₄×C₁₃₁	—	4	1	no	—
500	C₄×C₁₃₁	—	4	1	no	—
501	C₄×C₁₃₁	—	4	2	no	—
502	C₄×C₁₃₁	—	4	2	no	—
503	C₄×C₁₃₁	—	4	2	no	—
504	C₄×C₁₃₁	—	4	1	no	—
505	C₄×C₁₃₁	—	4	1	no	—
506	C₄×C₁₃₁	#520	1	4	yes	—
507	C₂×C₁₃₁	—	4	2	no	—
508	C₂×C₁₃₁	—	4	2	no	—
509	C₂×C₁₃₁	—	4	4	no	—
510	C₂×C₁₃₁	C₂×#520	1	1	yes	characteristic
511	C₂×C₁₃₁	#3428	1	1	yes	characteristic
512	C₂×C₁₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂×C₁₃₁	#3540	1	1	yes	characteristic
514	C₂×C₁₃₁	#3542	1	1	yes	characteristic
515	C₂×C₁₃₁	#3547	1	1	yes	characteristic
516	C₂×C₁₃₁	#3565	1	1	yes	characteristic
517	#34467	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
518	C₁₃₁	#34467	1	1	yes	characteristic, direct product factor, Sylow
519	C₂×#555	C₂×C₁₃₁	1	1	yes	characteristic
520	#2379	C₂×C₁₃₁	1	2	yes	complemented
521	#2377	C₂×C₁₃₁	1	2	yes	complemented
522	#2367	C₂×C₁₃₁	1	2	yes	complemented
523	#2365	C₂×C₁₃₁	1	1	yes	characteristic, complemented
524	#2363	C₂×C₁₃₁	1	1	yes	characteristic, complemented
525	#2361	C₂×C₁₃₁	1	1	yes	characteristic, complemented
526	#2352	C₂×C₁₃₁	1	1	yes	characteristic, complemented
527	#2349	C₂×C₁₃₁	1	1	yes	characteristic, complemented
528	#2347	C₂×C₁₃₁	1	1	yes	characteristic, complemented
529	#2346	C₂×C₁₃₁	1	1	yes	characteristic, complemented
530	#2343	C₂×C₁₃₁	1	2	yes	complemented
531	#2337	C₂×C₁₃₁	1	2	yes	complemented
532	#2331	C₂×C₁₃₁	1	1	yes	characteristic, complemented
533	#2326	C₂×C₁₃₁	1	2	yes	complemented
534	#2325	C₂×C₁₃₁	1	2	yes	complemented
535	#2324	C₂×C₁₃₁	1	1	yes	characteristic, complemented
536	#2319	C₂×C₁₃₁	1	1	yes	characteristic, complemented
537	#2317	C₂×C₁₃₁	1	1	yes	characteristic, complemented
538	#2314	C₂×C₁₃₁	1	2	yes	complemented
539	C₄×#121	C₂×C₁₃₁	1	1	yes	characteristic, complemented
540	#2296	C₂×C₁₃₁	1	1	yes	characteristic, complemented
541	#2290	C₂×C₁₃₁	1	1	yes	characteristic, complemented
542	#555	C₄×C₁₃₁	1	16	yes	complemented
543	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
544	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
545	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
546	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
547	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
548	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
549	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
550	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
552	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
553	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
554	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
555	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
556	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
557	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
558	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
559	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
560	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
561	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
562	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
563	#391	C₂²×C₁₃₁	1	2	yes	—
564	#391	C₂²×C₁₃₁	1	2	yes	—
565	#391	C₂²×C₁₃₁	1	2	yes	—
566	#390	C₂²×C₁₃₁	1	1	yes	characteristic
567	#390	C₂²×C₁₃₁	1	1	yes	characteristic
568	#390	C₂²×C₁₃₁	1	2	yes	—
569	#390	C₂²×C₁₃₁	1	2	yes	—
570	#389	C₂²×C₁₃₁	1	1	yes	characteristic
571	#389	C₂²×C₁₃₁	1	1	yes	characteristic
572	#389	C₂²×C₁₃₁	1	1	yes	characteristic
573	#389	C₂²×C₁₃₁	1	1	yes	characteristic
574	#389	C₂²×C₁₃₁	1	1	yes	characteristic
575	#389	C₂²×C₁₃₁	1	1	yes	characteristic
576	#389	C₂²×C₁₃₁	1	1	yes	characteristic
577	#389	C₂²×C₁₃₁	1	1	yes	characteristic
578	#388	C₂²×C₁₃₁	1	2	yes	—
579	#388	C₂²×C₁₃₁	1	2	yes	—
580	#388	C₂²×C₁₃₁	1	2	yes	—
581	#388	C₂²×C₁₃₁	1	2	yes	—
582	#388	C₂²×C₁₃₁	1	2	yes	—
583	#388	C₂²×C₁₃₁	1	2	yes	—
584	#388	C₂²×C₁₃₁	1	2	yes	—
585	#388	C₂²×C₁₃₁	1	2	yes	—
586	#388	C₂²×C₁₃₁	1	2	yes	—
587	#388	C₂²×C₁₃₁	1	2	yes	—
588	#388	C₂²×C₁₃₁	1	1	yes	characteristic
589	#388	C₂²×C₁₃₁	1	2	yes	—
590	#388	C₂²×C₁₃₁	1	1	yes	characteristic
591	#387	C₂²×C₁₃₁	1	1	yes	characteristic
592	#387	C₂²×C₁₃₁	1	2	yes	—
593	#387	C₂²×C₁₃₁	1	2	yes	—
594	#387	C₂²×C₁₃₁	1	2	yes	—
595	#387	C₂²×C₁₃₁	1	2	yes	—
596	#387	C₂²×C₁₃₁	1	2	yes	—
597	#387	C₂²×C₁₃₁	1	1	yes	characteristic
598	#386	C₂²×C₁₃₁	1	2	yes	—
599	#386	C₂²×C₁₃₁	1	1	yes	characteristic
600	#386	C₂²×C₁₃₁	1	2	yes	—
601	#386	C₂²×C₁₃₁	1	2	yes	—
602	#386	C₂²×C₁₃₁	1	2	yes	—
603	#386	C₂²×C₁₃₁	1	1	yes	characteristic
604	#386	C₂²×C₁₃₁	1	2	yes	—
605	#385	C₂²×C₁₃₁	1	2	yes	—
606	#385	C₂²×C₁₃₁	1	2	yes	—
607	#385	C₂²×C₁₃₁	1	2	yes	—
608	#385	C₂²×C₁₃₁	1	2	yes	—
609	#385	C₂²×C₁₃₁	1	1	yes	characteristic
610	#385	C₂²×C₁₃₁	1	2	yes	—
611	#385	C₂²×C₁₃₁	1	2	yes	—
612	#385	C₂²×C₁₃₁	1	2	yes	—
613	#385	C₂²×C₁₃₁	1	2	yes	—
614	#385	C₂²×C₁₃₁	1	1	yes	characteristic
615	#384	C₂²×C₁₃₁	1	2	yes	—
616	#383	C₂²×C₁₃₁	1	2	yes	—
617	#382	C₂²×C₁₃₁	1	2	yes	—
618	#382	C₂²×C₁₃₁	1	2	yes	—
619	#382	C₂²×C₁₃₁	1	1	yes	characteristic
620	#381	C₂²×C₁₃₁	1	2	yes	—
621	#380	C₂²×C₁₃₁	1	2	yes	—
622	#380	C₂²×C₁₃₁	1	2	yes	—
623	#380	C₂²×C₁₃₁	1	1	yes	characteristic
624	#380	C₂²×C₁₃₁	1	1	yes	characteristic
625	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
626	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
627	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
628	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
629	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
630	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
631	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
632	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
633	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
634	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
635	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
636	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
637	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
638	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
639	#376	C₂²×C₁₃₁	1	1	yes	characteristic
640	#376	C₂²×C₁₃₁	1	2	yes	—
641	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
642	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
643	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
645	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
646	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
647	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
648	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
649	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
650	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
652	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
653	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
655	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
656	#124	C₂×C₄×C₁₃₁	1	16	yes	complemented
657	#124	C₂×C₄×C₁₃₁	1	16	yes	complemented
658	#121	C₂×C₄×C₁₃₁	1	8	yes	complemented
659	#121	C₂×C₄×C₁₃₁	1	8	yes	complemented
660	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
661	C₄×Q₈	—	4	4	no	—
662	C₄×D₄	—	4	2	no	—
663	C₄×D₄	—	4	2	no	—
664	C₄×D₄	—	4	4	no	—
665	C₄×D₄	—	4	4	no	—
666	C₄×D₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
667	C₄×D₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
668	#117	—	4	2	no	—
669	#117	—	4	2	no	—
670	#117	C₂×C₄×C₁₃₁	1	8	yes	complemented
671	#117	C₂×C₄×C₁₃₁	1	8	yes	complemented
672	#117	C₂×C₄×C₁₃₁	1	16	yes	complemented
673	C₂×C₄⋊C₄	—	4	2	no	—
674	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
718	C₂×C₄²	—	4	2	no	—
719	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
722	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
725	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
726	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
727	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
728	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
729	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
732	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
733	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
734	#95	C₂³×C₁₃₁	1	1	yes	characteristic
735	#95	C₂³×C₁₃₁	1	2	yes	—
736	#95	C₂³×C₁₃₁	1	2	yes	—
737	#95	C₂³×C₁₃₁	1	2	yes	—
738	#95	C₂³×C₁₃₁	1	1	yes	characteristic
739	#95	C₂³×C₁₃₁	1	1	yes	characteristic
740	#95	C₂³×C₁₃₁	1	2	yes	—
741	#95	C₂³×C₁₃₁	1	1	yes	characteristic
742	#95	C₂³×C₁₃₁	1	2	yes	—
743	#95	C₂³×C₁₃₁	1	1	yes	characteristic
744	#95	C₂³×C₁₃₁	1	1	yes	characteristic
745	#95	C₂³×C₁₃₁	1	1	yes	characteristic
746	#95	C₂³×C₁₃₁	1	2	yes	—
747	#95	C₂³×C₁₃₁	1	1	yes	characteristic
748	#95	C₂³×C₁₃₁	1	1	yes	characteristic
749	#95	C₂³×C₁₃₁	1	2	yes	—
750	#95	C₂³×C₁₃₁	1	2	yes	—
751	#95	C₂³×C₁₃₁	1	2	yes	—
752	#95	C₂³×C₁₃₁	1	1	yes	characteristic
753	#95	C₂³×C₁₃₁	1	2	yes	—
754	#95	C₂³×C₁₃₁	1	2	yes	—
755	#95	C₂³×C₁₃₁	1	2	yes	—
756	#95	C₂³×C₁₃₁	1	2	yes	—
757	#95	C₂³×C₁₃₁	1	2	yes	—
758	#95	C₂³×C₁₃₁	1	2	yes	—
759	#95	C₂³×C₁₃₁	1	2	yes	—
760	#95	C₂³×C₁₃₁	1	2	yes	—
761	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
762	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
763	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
764	C₂×Q₈	—	4	2	no	—
765	C₂×Q₈	—	4	2	no	—
766	C₂×Q₈	C₂²×C₄×C₁₃₁	1	8	yes	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	2	no	—
771	C₂×D₄	—	4	2	no	—
772	C₂×D₄	—	4	2	no	—
773	C₂×D₄	—	4	1	no	—
774	C₂×D₄	—	4	1	no	—
775	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
776	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
777	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
778	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	4	no	—
785	C₂²×C₄	—	4	1	no	—
786	C₂²×C₄	—	4	1	no	—
787	C₂²×C₄	—	4	2	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	—	4	1	no	—
790	C₂²×C₄	—	4	1	no	—
791	C₂²×C₄	—	4	1	no	—
792	C₂²×C₄	—	4	2	no	—
793	C₂²×C₄	—	4	2	no	—
794	C₂²×C₄	—	4	2	no	—
795	C₂²×C₄	—	4	2	no	—
796	C₂²×C₄	—	4	2	no	—
797	C₂²×C₄	—	4	2	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	2	no	—
800	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
801	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
802	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
803	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
811	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
819	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	4	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	4	2	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₄⋊C₄	—	4	2	no	—
833	C₄⋊C₄	—	4	2	no	—
834	C₄⋊C₄	—	4	2	no	—
835	C₄⋊C₄	—	4	1	no	—
836	C₄⋊C₄	—	4	1	no	—
837	C₄⋊C₄	—	4	1	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
841	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
842	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
843	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
844	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	4	1	no	—
847	C₂²⋊C₄	—	4	1	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	—	4	2	no	—
851	C₂²⋊C₄	—	4	1	no	—
852	C₂²⋊C₄	—	4	1	no	—
853	C₂²⋊C₄	—	4	1	no	—
854	C₂²⋊C₄	—	4	2	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
861	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
862	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
863	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
864	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
865	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
866	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	4	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	4	1	no	—
873	C₄²	—	4	1	no	—
874	C₄²	—	4	2	no	—
875	C₄²	—	4	2	no	—
876	C₄²	—	4	2	no	—
877	C₄²	—	4	2	no	—
878	C₄²	—	4	2	no	—
879	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	—
880	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	—
881	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	2	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	2	no	—
900	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
901	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
902	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
903	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
904	Q₈	—	4	8	no	—
905	D₄	—	2	8	no	—
906	D₄	—	4	4	no	—
907	D₄	—	4	8	no	—
908	D₄	—	4	8	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	8	no	—
926	C₂×C₄	—	2	8	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	4	8	no	—
961	C₂×C₄	—	4	4	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	8	4	no	—
964	C₂×C₄	—	8	4	no	—
965	C₂×C₄	—	8	4	no	—
966	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
967	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
968	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
969	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
970	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
971	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
972	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
973	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
974	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
975	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
976	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
977	C₂²	—	2	2	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	2	4	no	—
980	C₂²	—	2	4	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	4	no	—
986	C₂²	—	4	1	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	2	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
999	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
1000	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
1001	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
1002	C₂²	#585×C₁₃₁	1	1	yes	characteristic
1003	C₂²	#585×C₁₃₁	1	1	yes	characteristic
1004	C₂²	#585×C₁₃₁	1	1	yes	characteristic
1005	C₄	—	2	2	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	4	no	—
1010	C₄	—	2	4	no	—
1011	C₄	—	2	4	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	1	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	1	no	—
1024	C₄	#520×C₁₃₁	1	4	yes	—
1025	C₂	—	4	2	no	—
1026	C₂	—	4	2	no	—
1027	C₂	—	4	4	no	—
1028	C₂	C₂×#520×C₁₃₁	1	1	yes	characteristic
1029	C₂	#3428×C₁₃₁	1	1	yes	characteristic
1030	C₂	C₄×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
1031	C₂	#3540×C₁₃₁	1	1	yes	characteristic
1032	C₂	#3542×C₁₃₁	1	1	yes	characteristic
1033	C₂	#3547×C₁₃₁	1	1	yes	characteristic
1034	C₂	#3565×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂×#555×C₁₃₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2379×C₁₃₁	C₂	semidirect
3. #2377×C₁₃₁	C₂	semidirect
4. #2367×C₁₃₁	C₂	semidirect
5. #2365×C₁₃₁	C₂	semidirect
6. #2363×C₁₃₁	C₂	semidirect
7. #2361×C₁₃₁	C₂	semidirect
8. #2352×C₁₃₁	C₂	semidirect
9. #2349×C₁₃₁	C₂	semidirect
10. #2347×C₁₃₁	C₂	semidirect
11. #2346×C₁₃₁	C₂	semidirect
12. #2343×C₁₃₁	C₂	semidirect
13. #2337×C₁₃₁	C₂	semidirect
14. #2331×C₁₃₁	C₂	semidirect
15. #2326×C₁₃₁	C₂	semidirect
16. #2325×C₁₃₁	C₂	semidirect
17. #2324×C₁₃₁	C₂	semidirect
18. #2319×C₁₃₁	C₂	semidirect
19. #2317×C₁₃₁	C₂	semidirect
20. #2314×C₁₃₁	C₂	semidirect
21. C₄×#121×C₁₃₁	C₂	semidirect
22. #2296×C₁₃₁	C₂	semidirect
23. #2290×C₁₃₁	C₂	semidirect
24. #555×C₁₃₁	C₄	semidirect
137. C₄⋊Q₈×C₁₃₁	C₂×C₄	semidirect
138. #124×C₁₃₁	C₂×C₄	semidirect
139. #124×C₁₃₁	C₂×C₄	semidirect
140. #121×C₁₃₁	C₂×C₄	semidirect
141. #121×C₁₃₁	C₂×C₄	semidirect
142. #121×C₁₃₁	C₂×C₄	semidirect
148. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
149. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
152. #117×C₁₃₁	C₂×C₄	semidirect
153. #117×C₁₃₁	C₂×C₄	semidirect
154. #117×C₁₃₁	C₂×C₄	semidirect
517. #34467	C₁₃₁	direct (N × H)
518. C₁₃₁	#34467	direct (N × H)
520. #2379	C₂×C₁₃₁	semidirect
521. #2377	C₂×C₁₃₁	semidirect
522. #2367	C₂×C₁₃₁	semidirect
523. #2365	C₂×C₁₃₁	semidirect
524. #2363	C₂×C₁₃₁	semidirect
525. #2361	C₂×C₁₃₁	semidirect
526. #2352	C₂×C₁₃₁	semidirect
527. #2349	C₂×C₁₃₁	semidirect
528. #2347	C₂×C₁₃₁	semidirect
529. #2346	C₂×C₁₃₁	semidirect
530. #2343	C₂×C₁₃₁	semidirect
531. #2337	C₂×C₁₃₁	semidirect
532. #2331	C₂×C₁₃₁	semidirect
533. #2326	C₂×C₁₃₁	semidirect
534. #2325	C₂×C₁₃₁	semidirect
535. #2324	C₂×C₁₃₁	semidirect
536. #2319	C₂×C₁₃₁	semidirect
537. #2317	C₂×C₁₃₁	semidirect
538. #2314	C₂×C₁₃₁	semidirect
539. C₄×#121	C₂×C₁₃₁	semidirect
540. #2296	C₂×C₁₃₁	semidirect
541. #2290	C₂×C₁₃₁	semidirect
542. #555	C₄×C₁₃₁	semidirect
655. C₄⋊Q₈	C₂×C₄×C₁₃₁	semidirect
656. #124	C₂×C₄×C₁₃₁	semidirect
657. #124	C₂×C₄×C₁₃₁	semidirect
658. #121	C₂×C₄×C₁₃₁	semidirect
659. #121	C₂×C₄×C₁₃₁	semidirect
660. #121	C₂×C₄×C₁₃₁	semidirect
666. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
667. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
670. #117	C₂×C₄×C₁₃₁	semidirect
671. #117	C₂×C₄×C₁₃₁	semidirect
672. #117	C₂×C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#555×C₁₃₁	2
#2379×C₁₃₁	2
#2377×C₁₃₁	2
#2367×C₁₃₁	2
#2365×C₁₃₁	2
#2363×C₁₃₁	2
#2361×C₁₃₁	2
#2352×C₁₃₁	2
#2349×C₁₃₁	2
#2347×C₁₃₁	2
#2346×C₁₃₁	2
#2343×C₁₃₁	2
#2337×C₁₃₁	2
#2331×C₁₃₁	2
#2326×C₁₃₁	2
#2325×C₁₃₁	2
#2324×C₁₃₁	2
#2319×C₁₃₁	2
#2317×C₁₃₁	2
#2314×C₁₃₁	2
C₄×#121×C₁₃₁	2
#2296×C₁₃₁	2
#2290×C₁₃₁	2
#34467	131

Subgroups — C131×#34467 #45720351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34467 #45720351