Subgroups — C₁₃₁×#34487 #45720371

Order 33536.

2244 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2378×C₁₃₁	C₂	1	4	yes	maximal, complemented
3	#2369×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2365×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2362×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2357×C₁₃₁	C₂	1	2	yes	maximal
7	#2355×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2354×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	Q₈×C₂²⋊C₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2332×C₁₃₁	C₂	1	4	yes	maximal, complemented
11	#2331×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#2323×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2319×C₁₃₁	C₂	1	2	yes	maximal
14	#2310×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#2295×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#2293×C₁₃₁	C₂	1	1	yes	maximal, characteristic
18	C₂³×Q₈×C₁₃₁	C₂²	1	2	yes	—
19	D₄×Q₈×C₁₃₁	C₄	1	16	yes	complemented
20	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
31	#391×C₁₃₁	C₂²	1	1	yes	characteristic
32	#391×C₁₃₁	C₂²	1	1	yes	characteristic
33	#391×C₁₃₁	C₂²	1	2	yes	—
34	#391×C₁₃₁	C₂²	1	4	yes	—
35	#391×C₁₃₁	C₂²	1	2	yes	—
36	#391×C₁₃₁	C₂²	1	2	yes	—
37	#391×C₁₃₁	C₂²	1	4	yes	—
38	#391×C₁₃₁	C₂²	1	4	yes	—
39	#391×C₁₃₁	C₂²	1	4	yes	—
40	#390×C₁₃₁	C₂²	1	1	yes	characteristic
41	#390×C₁₃₁	C₂²	1	1	yes	characteristic
42	#390×C₁₃₁	C₂²	1	2	yes	—
43	#389×C₁₃₁	C₂²	1	1	yes	characteristic
44	#389×C₁₃₁	C₂²	1	1	yes	characteristic
45	#389×C₁₃₁	C₂²	1	1	yes	characteristic
46	#389×C₁₃₁	C₂²	1	1	yes	characteristic
47	#389×C₁₃₁	C₂²	1	2	yes	—
48	#389×C₁₃₁	C₂²	1	2	yes	—
49	#389×C₁₃₁	C₂²	1	2	yes	—
50	#389×C₁₃₁	C₂²	1	4	yes	—
51	#388×C₁₃₁	C₂²	1	2	yes	—
52	#388×C₁₃₁	C₂²	1	2	yes	—
53	#388×C₁₃₁	C₂²	1	4	yes	—
54	#388×C₁₃₁	C₂²	1	4	yes	—
55	#388×C₁₃₁	C₂²	1	4	yes	—
56	#388×C₁₃₁	C₂²	1	4	yes	—
57	#388×C₁₃₁	C₂²	1	4	yes	—
58	#387×C₁₃₁	C₂²	1	2	yes	—
59	#387×C₁₃₁	C₂²	1	2	yes	—
60	#387×C₁₃₁	C₂²	1	4	yes	—
61	#387×C₁₃₁	C₂²	1	4	yes	—
62	#387×C₁₃₁	C₂²	1	4	yes	—
63	#387×C₁₃₁	C₂²	1	4	yes	—
64	#384×C₁₃₁	C₂²	1	1	yes	characteristic
65	#382×C₁₃₁	C₂²	1	2	yes	—
66	#381×C₁₃₁	C₂²	1	4	yes	—
67	#381×C₁₃₁	C₂²	1	4	yes	—
68	#380×C₁₃₁	C₂²	1	4	yes	—
69	#380×C₁₃₁	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	—
80	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
82	#376×C₁₃₁	C₂²	1	2	yes	—
83	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃₁	—	4	4	no	—
85	C₂²×Q₈×C₁₃₁	—	4	4	no	—
86	C₂²×Q₈×C₁₃₁	C₂×C₄	1	16	yes	—
87	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
89	C₂²×Q₈×C₁₃₁	C₂³	1	4	yes	—
90	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
93	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	—
94	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	16	yes	—
95	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	16	yes	—
96	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	32	yes	—
97	C₄×Q₈×C₁₃₁	—	4	4	no	—
98	C₄×Q₈×C₁₃₁	—	4	4	no	—
99	C₄×Q₈×C₁₃₁	C₂×C₄	1	8	yes	—
100	C₄×D₄×C₁₃₁	C₂×C₄	1	8	yes	—
101	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	—
102	#117×C₁₃₁	—	4	4	no	—
103	#117×C₁₃₁	—	4	4	no	—
104	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
145	#95×C₁₃₁	C₂³	1	2	yes	—
146	#95×C₁₃₁	C₂³	1	2	yes	—
147	#95×C₁₃₁	C₂³	1	4	yes	—
148	#95×C₁₃₁	C₂³	1	2	yes	—
149	#95×C₁₃₁	C₂³	1	2	yes	—
150	#95×C₁₃₁	C₂³	1	4	yes	—
151	#95×C₁₃₁	C₂³	1	2	yes	—
152	#95×C₁₃₁	C₂³	1	2	yes	—
153	#95×C₁₃₁	C₂³	1	4	yes	—
154	#95×C₁₃₁	C₂³	1	4	yes	—
155	#95×C₁₃₁	C₂³	1	4	yes	—
156	#95×C₁₃₁	C₂³	1	4	yes	—
157	#95×C₁₃₁	C₂³	1	2	yes	—
158	#95×C₁₃₁	C₂³	1	2	yes	—
159	#95×C₁₃₁	C₂³	1	2	yes	—
160	#95×C₁₃₁	C₂³	1	4	yes	—
161	#95×C₁₃₁	C₂³	1	4	yes	—
162	#95×C₁₃₁	C₂³	1	2	yes	—
163	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
164	C₂×Q₈×C₁₃₁	—	2	4	no	—
165	C₂×Q₈×C₁₃₁	—	2	4	no	—
166	C₂×Q₈×C₁₃₁	—	2	2	no	—
167	C₂×Q₈×C₁₃₁	—	2	2	no	—
168	C₂×Q₈×C₁₃₁	—	4	4	no	—
169	C₂×Q₈×C₁₃₁	—	4	4	no	—
170	C₂×Q₈×C₁₃₁	—	4	32	no	—
171	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
172	C₂×Q₈×C₁₃₁	C₂²×C₄	1	8	yes	—
173	C₂×Q₈×C₁₃₁	C₂²×C₄	1	16	yes	—
174	C₂×D₄×C₁₃₁	—	2	2	no	—
175	C₂×D₄×C₁₃₁	—	2	2	no	—
176	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₁₃₁	—	2	4	no	—
178	C₂²×C₄×C₁₃₁	—	2	4	no	—
179	C₂²×C₄×C₁₃₁	—	4	4	no	—
180	C₂²×C₄×C₁₃₁	—	4	4	no	—
181	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
182	C₂²×C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
183	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
199	C₄⋊C₄×C₁₃₁	—	2	2	no	—
200	C₄⋊C₄×C₁₃₁	—	2	4	no	—
201	C₄⋊C₄×C₁₃₁	—	2	2	no	—
202	C₄⋊C₄×C₁₃₁	—	2	4	no	—
203	C₄⋊C₄×C₁₃₁	—	2	2	no	—
204	C₄⋊C₄×C₁₃₁	—	2	2	no	—
205	C₄⋊C₄×C₁₃₁	—	2	4	no	—
206	C₄⋊C₄×C₁₃₁	—	4	2	no	—
207	C₄⋊C₄×C₁₃₁	—	4	2	no	—
208	C₄⋊C₄×C₁₃₁	—	4	2	no	—
209	C₄⋊C₄×C₁₃₁	—	4	2	no	—
210	C₄⋊C₄×C₁₃₁	—	4	4	no	—
211	C₄⋊C₄×C₁₃₁	—	4	4	no	—
212	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
213	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
214	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
215	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
217	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
218	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
219	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
220	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
221	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
222	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
223	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
224	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
226	C₄²×C₁₃₁	—	2	2	no	—
227	C₄²×C₁₃₁	—	2	4	no	—
228	C₄²×C₁₃₁	—	2	2	no	—
229	C₄²×C₁₃₁	—	2	2	no	—
230	C₄²×C₁₃₁	—	2	2	no	—
231	C₄²×C₁₃₁	—	2	4	no	—
232	C₄²×C₁₃₁	—	2	2	no	—
233	C₄²×C₁₃₁	—	4	4	no	—
234	C₄²×C₁₃₁	—	4	1	no	—
235	C₄²×C₁₃₁	—	4	4	no	—
236	C₄²×C₁₃₁	—	4	4	no	—
237	C₄²×C₁₃₁	—	4	4	no	—
238	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	—
239	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
240	C₂³×C₁₃₁	—	2	2	no	—
241	C₂³×C₁₃₁	—	2	2	no	—
242	C₂³×C₁₃₁	—	2	2	no	—
243	C₂³×C₁₃₁	—	2	2	no	—
244	C₂³×C₁₃₁	—	2	2	no	—
245	C₂³×C₁₃₁	—	2	2	no	—
246	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
247	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
248	Q₈×C₁₃₁	—	2	8	no	—
249	Q₈×C₁₃₁	—	2	16	no	—
250	Q₈×C₁₃₁	—	4	16	no	—
251	D₄×C₁₃₁	—	2	8	no	—
252	C₂×C₄×C₁₃₁	—	2	1	no	—
253	C₂×C₄×C₁₃₁	—	2	2	no	—
254	C₂×C₄×C₁₃₁	—	2	4	no	—
255	C₂×C₄×C₁₃₁	—	2	4	no	—
256	C₂×C₄×C₁₃₁	—	2	2	no	—
257	C₂×C₄×C₁₃₁	—	2	2	no	—
258	C₂×C₄×C₁₃₁	—	2	2	no	—
259	C₂×C₄×C₁₃₁	—	2	1	no	—
260	C₂×C₄×C₁₃₁	—	2	1	no	—
261	C₂×C₄×C₁₃₁	—	2	2	no	—
262	C₂×C₄×C₁₃₁	—	2	2	no	—
263	C₂×C₄×C₁₃₁	—	2	1	no	—
264	C₂×C₄×C₁₃₁	—	2	16	no	—
265	C₂×C₄×C₁₃₁	—	2	2	no	—
266	C₂×C₄×C₁₃₁	—	2	1	no	—
267	C₂×C₄×C₁₃₁	—	2	1	no	—
268	C₂×C₄×C₁₃₁	—	2	2	no	—
269	C₂×C₄×C₁₃₁	—	2	1	no	—
270	C₂×C₄×C₁₃₁	—	2	2	no	—
271	C₂×C₄×C₁₃₁	—	2	4	no	—
272	C₂×C₄×C₁₃₁	—	2	2	no	—
273	C₂×C₄×C₁₃₁	—	2	1	no	—
274	C₂×C₄×C₁₃₁	—	2	2	no	—
275	C₂×C₄×C₁₃₁	—	2	1	no	—
276	C₂×C₄×C₁₃₁	—	2	1	no	—
277	C₂×C₄×C₁₃₁	—	2	2	no	—
278	C₂×C₄×C₁₃₁	—	2	1	no	—
279	C₂×C₄×C₁₃₁	—	2	2	no	—
280	C₂×C₄×C₁₃₁	—	2	2	no	—
281	C₂×C₄×C₁₃₁	—	2	2	no	—
282	C₂×C₄×C₁₃₁	—	2	2	no	—
283	C₂×C₄×C₁₃₁	—	2	4	no	—
284	C₂×C₄×C₁₃₁	—	2	2	no	—
285	C₂×C₄×C₁₃₁	—	2	1	no	—
286	C₂×C₄×C₁₃₁	—	2	4	no	—
287	C₂×C₄×C₁₃₁	—	2	1	no	—
288	C₂×C₄×C₁₃₁	—	2	2	no	—
289	C₂×C₄×C₁₃₁	—	4	16	no	—
290	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
292	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₁₃₁	C₂³×C₄	1	8	yes	—
295	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
298	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
299	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
300	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
301	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
302	C₂²×C₁₃₁	—	2	4	no	—
303	C₂²×C₁₃₁	—	2	4	no	—
304	C₂²×C₁₃₁	—	2	4	no	—
305	C₂²×C₁₃₁	—	4	2	no	—
306	C₂²×C₁₃₁	—	4	2	no	—
307	C₂²×C₁₃₁	—	4	2	no	—
308	C₂²×C₁₃₁	—	4	2	no	—
309	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
310	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
311	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
313	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₂²×C₁₃₁	#585	1	1	yes	characteristic
316	C₄×C₁₃₁	—	2	4	no	—
317	C₄×C₁₃₁	—	2	4	no	—
318	C₄×C₁₃₁	—	2	8	no	—
319	C₄×C₁₃₁	—	2	2	no	—
320	C₄×C₁₃₁	—	2	4	no	—
321	C₄×C₁₃₁	—	2	2	no	—
322	C₄×C₁₃₁	—	4	1	no	—
323	C₄×C₁₃₁	—	4	2	no	—
324	C₄×C₁₃₁	—	4	2	no	—
325	C₄×C₁₃₁	—	4	2	no	—
326	C₄×C₁₃₁	—	4	1	no	—
327	C₄×C₁₃₁	—	4	2	no	—
328	C₄×C₁₃₁	—	4	1	no	—
329	C₄×C₁₃₁	—	4	4	no	—
330	C₄×C₁₃₁	#518	1	4	yes	—
331	C₄×C₁₃₁	#519	1	4	yes	—
332	C₂×C₁₃₁	—	4	4	no	—
333	C₂×C₁₃₁	C₂×#518	1	1	yes	characteristic
334	C₂×C₁₃₁	C₂×#519	1	1	yes	characteristic
335	C₂×C₁₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
336	C₂×C₁₃₁	#3547	1	1	yes	characteristic
337	C₂×C₁₃₁	#3550	1	1	yes	characteristic
338	C₂×C₁₃₁	#3552	1	1	yes	characteristic
339	C₂×C₁₃₁	#3554	1	1	yes	characteristic
340	#34487	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₁₃₁	#34487	1	1	yes	characteristic, direct product factor, Sylow
342	C₂×D₄×Q₈	C₂×C₁₃₁	1	1	yes	characteristic
343	#2378	C₂×C₁₃₁	1	4	yes	complemented
344	#2369	C₂×C₁₃₁	1	2	yes	complemented
345	#2365	C₂×C₁₃₁	1	1	yes	characteristic, complemented
346	#2362	C₂×C₁₃₁	1	2	yes	complemented
347	#2357	C₂×C₁₃₁	1	2	yes	—
348	#2355	C₂×C₁₃₁	1	1	yes	characteristic, complemented
349	#2354	C₂×C₁₃₁	1	1	yes	characteristic
350	Q₈×C₂²⋊C₄	C₂×C₁₃₁	1	2	yes	complemented
351	#2332	C₂×C₁₃₁	1	4	yes	complemented
352	#2331	C₂×C₁₃₁	1	2	yes	complemented
353	#2323	C₂×C₁₃₁	1	2	yes	complemented
354	#2319	C₂×C₁₃₁	1	2	yes	—
355	#2310	C₂×C₁₃₁	1	2	yes	complemented
356	C₄×C₄⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
357	#2295	C₂×C₁₃₁	1	1	yes	characteristic, complemented
358	#2293	C₂×C₁₃₁	1	1	yes	characteristic
359	C₂³×Q₈	C₂²×C₁₃₁	1	2	yes	—
360	D₄×Q₈	C₄×C₁₃₁	1	16	yes	complemented
361	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
362	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
364	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	4	yes	—
365	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
366	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
367	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
368	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
369	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
370	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
371	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
372	#391	C₂²×C₁₃₁	1	2	yes	—
373	#391	C₂²×C₁₃₁	1	1	yes	characteristic
374	#391	C₂²×C₁₃₁	1	4	yes	—
375	#391	C₂²×C₁₃₁	1	2	yes	—
376	#391	C₂²×C₁₃₁	1	2	yes	—
377	#391	C₂²×C₁₃₁	1	4	yes	—
378	#391	C₂²×C₁₃₁	1	4	yes	—
379	#391	C₂²×C₁₃₁	1	4	yes	—
380	#391	C₂²×C₁₃₁	1	1	yes	characteristic
381	#390	C₂²×C₁₃₁	1	1	yes	characteristic
382	#390	C₂²×C₁₃₁	1	2	yes	—
383	#390	C₂²×C₁₃₁	1	1	yes	characteristic
384	#389	C₂²×C₁₃₁	1	2	yes	—
385	#389	C₂²×C₁₃₁	1	2	yes	—
386	#389	C₂²×C₁₃₁	1	2	yes	—
387	#389	C₂²×C₁₃₁	1	1	yes	characteristic
388	#389	C₂²×C₁₃₁	1	4	yes	—
389	#389	C₂²×C₁₃₁	1	1	yes	characteristic
390	#389	C₂²×C₁₃₁	1	1	yes	characteristic
391	#389	C₂²×C₁₃₁	1	1	yes	characteristic
392	#388	C₂²×C₁₃₁	1	4	yes	—
393	#388	C₂²×C₁₃₁	1	4	yes	—
394	#388	C₂²×C₁₃₁	1	4	yes	—
395	#388	C₂²×C₁₃₁	1	2	yes	—
396	#388	C₂²×C₁₃₁	1	4	yes	—
397	#388	C₂²×C₁₃₁	1	4	yes	—
398	#388	C₂²×C₁₃₁	1	2	yes	—
399	#387	C₂²×C₁₃₁	1	4	yes	—
400	#387	C₂²×C₁₃₁	1	4	yes	—
401	#387	C₂²×C₁₃₁	1	2	yes	—
402	#387	C₂²×C₁₃₁	1	4	yes	—
403	#387	C₂²×C₁₃₁	1	4	yes	—
404	#387	C₂²×C₁₃₁	1	2	yes	—
405	#384	C₂²×C₁₃₁	1	1	yes	characteristic
406	#382	C₂²×C₁₃₁	1	2	yes	—
407	#381	C₂²×C₁₃₁	1	4	yes	—
408	#381	C₂²×C₁₃₁	1	4	yes	—
409	#380	C₂²×C₁₃₁	1	4	yes	—
410	#380	C₂²×C₁₃₁	1	2	yes	—
411	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
413	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
414	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
415	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
417	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	—
418	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
420	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
423	#376	C₂²×C₁₃₁	1	2	yes	—
424	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
425	C₂²×Q₈	—	4	4	no	—
426	C₂²×Q₈	—	4	4	no	—
427	C₂²×Q₈	C₂×C₄×C₁₃₁	1	16	yes	—
428	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
429	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₁₃₁	1	4	yes	—
431	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
433	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
434	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	—
435	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	16	yes	—
436	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	16	yes	—
437	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	32	yes	—
438	C₄×Q₈	—	4	4	no	—
439	C₄×Q₈	—	4	4	no	—
440	C₄×Q₈	C₂×C₄×C₁₃₁	1	8	yes	—
441	C₄×D₄	C₂×C₄×C₁₃₁	1	8	yes	—
442	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	—
443	#117	—	4	4	no	—
444	#117	—	4	4	no	—
445	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
472	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
474	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
479	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
480	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
481	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
482	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
484	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
486	#95	C₂³×C₁₃₁	1	2	yes	—
487	#95	C₂³×C₁₃₁	1	2	yes	—
488	#95	C₂³×C₁₃₁	1	2	yes	—
489	#95	C₂³×C₁₃₁	1	2	yes	—
490	#95	C₂³×C₁₃₁	1	2	yes	—
491	#95	C₂³×C₁₃₁	1	2	yes	—
492	#95	C₂³×C₁₃₁	1	4	yes	—
493	#95	C₂³×C₁₃₁	1	2	yes	—
494	#95	C₂³×C₁₃₁	1	4	yes	—
495	#95	C₂³×C₁₃₁	1	4	yes	—
496	#95	C₂³×C₁₃₁	1	2	yes	—
497	#95	C₂³×C₁₃₁	1	4	yes	—
498	#95	C₂³×C₁₃₁	1	4	yes	—
499	#95	C₂³×C₁₃₁	1	4	yes	—
500	#95	C₂³×C₁₃₁	1	4	yes	—
501	#95	C₂³×C₁₃₁	1	4	yes	—
502	#95	C₂³×C₁₃₁	1	2	yes	—
503	#95	C₂³×C₁₃₁	1	2	yes	—
504	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
505	C₂×Q₈	—	2	4	no	—
506	C₂×Q₈	—	2	4	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	—	4	4	no	—
510	C₂×Q₈	—	4	4	no	—
511	C₂×Q₈	—	4	32	no	—
512	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
513	C₂×Q₈	C₂²×C₄×C₁₃₁	1	8	yes	—
514	C₂×Q₈	C₂²×C₄×C₁₃₁	1	16	yes	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	—	4	4	no	—
522	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
523	C₂²×C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
524	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
555	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
556	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
557	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
558	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	4	no	—
565	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	2	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	2	no	—
574	C₄²	—	4	4	no	—
575	C₄²	—	4	1	no	—
576	C₄²	—	4	4	no	—
577	C₄²	—	4	4	no	—
578	C₄²	—	4	4	no	—
579	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	—
580	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
588	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
589	Q₈	—	2	8	no	—
590	Q₈	—	2	16	no	—
591	Q₈	—	4	16	no	—
592	D₄	—	2	8	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	16	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	16	no	—
631	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
632	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
633	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
634	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
635	C₂×C₄	C₂³×C₄×C₁₃₁	1	8	yes	—
636	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
637	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
638	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
639	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
640	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
641	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
642	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
643	C₂²	—	2	4	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
651	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
652	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
653	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
654	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
655	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
656	C₂²	#585×C₁₃₁	1	1	yes	characteristic
657	C₄	—	2	2	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	8	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	4	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	4	no	—
671	C₄	#518×C₁₃₁	1	4	yes	—
672	C₄	#519×C₁₃₁	1	4	yes	—
673	C₂	—	4	4	no	—
674	C₂	C₂×#518×C₁₃₁	1	1	yes	characteristic
675	C₂	C₂×#519×C₁₃₁	1	1	yes	characteristic
676	C₂	C₄×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
677	C₂	#3547×C₁₃₁	1	1	yes	characteristic
678	C₂	#3550×C₁₃₁	1	1	yes	characteristic
679	C₂	#3552×C₁₃₁	1	1	yes	characteristic
680	C₂	#3554×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	C₂²×D₄×C₁₃₁	C₂³
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. #2378×C₁₃₁	C₂	semidirect
3. #2369×C₁₃₁	C₂	semidirect
4. #2365×C₁₃₁	C₂	semidirect
5. #2362×C₁₃₁	C₂	semidirect
7. #2355×C₁₃₁	C₂	semidirect
9. Q₈×C₂²⋊C₄×C₁₃₁	C₂	semidirect
10. #2332×C₁₃₁	C₂	semidirect
11. #2331×C₁₃₁	C₂	semidirect
12. #2323×C₁₃₁	C₂	semidirect
14. #2310×C₁₃₁	C₂	semidirect
15. C₄×C₄⋊Q₈×C₁₃₁	C₂	semidirect
16. #2295×C₁₃₁	C₂	semidirect
19. D₄×Q₈×C₁₃₁	C₄	semidirect
340. #34487	C₁₃₁	direct (N × H)
341. C₁₃₁	#34487	direct (N × H)
343. #2378	C₂×C₁₃₁	semidirect
344. #2369	C₂×C₁₃₁	semidirect
345. #2365	C₂×C₁₃₁	semidirect
346. #2362	C₂×C₁₃₁	semidirect
348. #2355	C₂×C₁₃₁	semidirect
350. Q₈×C₂²⋊C₄	C₂×C₁₃₁	semidirect
351. #2332	C₂×C₁₃₁	semidirect
352. #2331	C₂×C₁₃₁	semidirect
353. #2323	C₂×C₁₃₁	semidirect
355. #2310	C₂×C₁₃₁	semidirect
356. C₄×C₄⋊Q₈	C₂×C₁₃₁	semidirect
357. #2295	C₂×C₁₃₁	semidirect
360. D₄×Q₈	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×D₄×Q₈×C₁₃₁	2
#2378×C₁₃₁	2
#2369×C₁₃₁	2
#2365×C₁₃₁	2
#2362×C₁₃₁	2
#2357×C₁₃₁	2
#2355×C₁₃₁	2
#2354×C₁₃₁	2
Q₈×C₂²⋊C₄×C₁₃₁	2
#2332×C₁₃₁	2
#2331×C₁₃₁	2
#2323×C₁₃₁	2
#2319×C₁₃₁	2
#2310×C₁₃₁	2
C₄×C₄⋊Q₈×C₁₃₁	2
#2295×C₁₃₁	2
#2293×C₁₃₁	2
#34487	131

Subgroups — C131×#34487 #45720371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34487 #45720371