Subgroups — C₁₃₁×#34397 #45720281

Order 33536.

2090 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2383×C₁₃₁	C₂	1	4	yes	maximal, complemented
3	#2370×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2367×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2357×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2356×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2351×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2349×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2346×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2343×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2335×C₁₃₁	C₂	1	4	yes	maximal, complemented
12	#2324×C₁₃₁	C₂	1	2	yes	maximal
13	#2323×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	#2319×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	#2318×C₁₃₁	C₂	1	2	yes	maximal, complemented
16	#2285×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#2283×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	#529×C₁₃₁	C₄	1	16	yes	complemented
19	C₂×#126×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
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	2	yes	—
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
31	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
33	#391×C₁₃₁	C₂²	1	2	yes	—
34	#390×C₁₃₁	C₂²	1	4	yes	—
35	#390×C₁₃₁	C₂²	1	2	yes	—
36	#389×C₁₃₁	C₂²	1	4	yes	—
37	#389×C₁₃₁	C₂²	1	4	yes	—
38	#389×C₁₃₁	C₂²	1	2	yes	—
39	#389×C₁₃₁	C₂²	1	2	yes	—
40	#389×C₁₃₁	C₂²	1	4	yes	—
41	#388×C₁₃₁	C₂²	1	4	yes	—
42	#388×C₁₃₁	C₂²	1	4	yes	—
43	#388×C₁₃₁	C₂²	1	4	yes	—
44	#388×C₁₃₁	C₂²	1	4	yes	—
45	#388×C₁₃₁	C₂²	1	4	yes	—
46	#388×C₁₃₁	C₂²	1	4	yes	—
47	#387×C₁₃₁	C₂²	1	4	yes	—
48	#387×C₁₃₁	C₂²	1	4	yes	—
49	#387×C₁₃₁	C₂²	1	4	yes	—
50	#387×C₁₃₁	C₂²	1	4	yes	—
51	#386×C₁₃₁	C₂²	1	4	yes	—
52	#385×C₁₃₁	C₂²	1	4	yes	—
53	#385×C₁₃₁	C₂²	1	4	yes	—
54	#385×C₁₃₁	C₂²	1	4	yes	—
55	#384×C₁₃₁	C₂²	1	2	yes	—
56	#383×C₁₃₁	C₂²	1	2	yes	—
57	#383×C₁₃₁	C₂²	1	2	yes	—
58	#382×C₁₃₁	C₂²	1	1	yes	characteristic
59	#382×C₁₃₁	C₂²	1	1	yes	characteristic
60	#382×C₁₃₁	C₂²	1	1	yes	characteristic
61	#382×C₁₃₁	C₂²	1	1	yes	characteristic
62	#382×C₁₃₁	C₂²	1	2	yes	—
63	#381×C₁₃₁	C₂²	1	2	yes	—
64	#381×C₁₃₁	C₂²	1	2	yes	—
65	#380×C₁₃₁	C₂²	1	2	yes	—
66	#380×C₁₃₁	C₂²	1	1	yes	characteristic
67	#380×C₁₃₁	C₂²	1	1	yes	characteristic
68	#380×C₁₃₁	C₂²	1	2	yes	—
69	#380×C₁₃₁	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
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	4	yes	—
78	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
81	#376×C₁₃₁	C₂²	1	2	yes	—
82	#376×C₁₃₁	C₂²	1	2	yes	—
83	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
84	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
89	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
92	#126×C₁₃₁	C₂×C₄	1	16	yes	complemented
93	#125×C₁₃₁	C₂×C₄	1	8	yes	complemented
94	#124×C₁₃₁	C₂×C₄	1	8	yes	—
95	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
96	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
97	#121×C₁₃₁	C₂×C₄	1	8	yes	—
98	C₄×Q₈×C₁₃₁	—	4	4	no	—
99	C₄×Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
100	C₄×D₄×C₁₃₁	—	4	4	no	—
101	C₄×D₄×C₁₃₁	C₂×C₄	1	8	yes	—
102	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
103	#117×C₁₃₁	—	4	4	no	—
104	#117×C₁₃₁	C₂×C₄	1	16	yes	complemented
105	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	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	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	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	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃₁	C₂×C₄	1	8	yes	complemented
134	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
138	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
145	#95×C₁₃₁	C₂³	1	4	yes	—
146	#95×C₁₃₁	C₂³	1	4	yes	—
147	#95×C₁₃₁	C₂³	1	2	yes	—
148	#95×C₁₃₁	C₂³	1	2	yes	—
149	#95×C₁₃₁	C₂³	1	4	yes	—
150	#95×C₁₃₁	C₂³	1	4	yes	—
151	#95×C₁₃₁	C₂³	1	4	yes	—
152	#95×C₁₃₁	C₂³	1	4	yes	—
153	#95×C₁₃₁	C₂³	1	4	yes	—
154	#95×C₁₃₁	C₂³	1	2	yes	—
155	#95×C₁₃₁	C₂³	1	1	yes	characteristic
156	#95×C₁₃₁	C₂³	1	2	yes	—
157	#95×C₁₃₁	C₂³	1	2	yes	—
158	#95×C₁₃₁	C₂³	1	1	yes	characteristic
159	#95×C₁₃₁	C₂³	1	1	yes	characteristic
160	#95×C₁₃₁	C₂³	1	2	yes	—
161	#95×C₁₃₁	C₂³	1	1	yes	characteristic
162	#95×C₁₃₁	C₂³	1	4	yes	—
163	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
165	C₂×Q₈×C₁₃₁	—	2	2	no	—
166	C₂×Q₈×C₁₃₁	—	2	2	no	—
167	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
168	C₂×D₄×C₁₃₁	—	2	2	no	—
169	C₂×D₄×C₁₃₁	—	2	2	no	—
170	C₂×D₄×C₁₃₁	—	4	4	no	—
171	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
172	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
173	C₂²×C₄×C₁₃₁	—	2	2	no	—
174	C₂²×C₄×C₁₃₁	—	2	2	no	—
175	C₂²×C₄×C₁₃₁	—	4	2	no	—
176	C₂²×C₄×C₁₃₁	—	4	4	no	—
177	C₂²×C₄×C₁₃₁	—	4	2	no	—
178	C₂²×C₄×C₁₃₁	—	4	4	no	—
179	C₂²×C₄×C₁₃₁	—	4	4	no	—
180	C₂²×C₄×C₁₃₁	—	4	4	no	—
181	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
185	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
196	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
200	C₄⋊C₄×C₁₃₁	—	2	4	no	—
201	C₄⋊C₄×C₁₃₁	—	2	4	no	—
202	C₄⋊C₄×C₁₃₁	—	4	4	no	—
203	C₄⋊C₄×C₁₃₁	—	4	4	no	—
204	C₄⋊C₄×C₁₃₁	—	4	2	no	—
205	C₄⋊C₄×C₁₃₁	—	4	2	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	C₂²×C₄	1	8	yes	—
212	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
213	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	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	8	yes	—
217	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
218	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
219	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
220	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
221	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
222	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
223	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
226	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
228	C₄²×C₁₃₁	—	2	4	no	—
229	C₄²×C₁₃₁	—	2	4	no	—
230	C₄²×C₁₃₁	—	4	4	no	—
231	C₄²×C₁₃₁	—	4	4	no	—
232	C₄²×C₁₃₁	—	4	4	no	—
233	C₄²×C₁₃₁	—	4	4	no	—
234	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
235	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
236	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
237	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
238	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	—
239	C₂³×C₁₃₁	—	2	1	no	—
240	C₂³×C₁₃₁	—	2	2	no	—
241	C₂³×C₁₃₁	—	2	1	no	—
242	C₂³×C₁₃₁	—	2	2	no	—
243	C₂³×C₁₃₁	—	2	2	no	—
244	C₂³×C₁₃₁	—	2	4	no	—
245	C₂³×C₁₃₁	—	2	4	no	—
246	C₂³×C₁₃₁	—	2	2	no	—
247	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
248	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
249	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
250	Q₈×C₁₃₁	—	2	8	no	—
251	D₄×C₁₃₁	—	2	8	no	—
252	D₄×C₁₃₁	—	4	8	no	—
253	C₂×C₄×C₁₃₁	—	2	2	no	—
254	C₂×C₄×C₁₃₁	—	2	1	no	—
255	C₂×C₄×C₁₃₁	—	2	1	no	—
256	C₂×C₄×C₁₃₁	—	2	2	no	—
257	C₂×C₄×C₁₃₁	—	2	2	no	—
258	C₂×C₄×C₁₃₁	—	2	4	no	—
259	C₂×C₄×C₁₃₁	—	2	4	no	—
260	C₂×C₄×C₁₃₁	—	2	2	no	—
261	C₂×C₄×C₁₃₁	—	2	2	no	—
262	C₂×C₄×C₁₃₁	—	2	2	no	—
263	C₂×C₄×C₁₃₁	—	2	8	no	—
264	C₂×C₄×C₁₃₁	—	2	2	no	—
265	C₂×C₄×C₁₃₁	—	2	2	no	—
266	C₂×C₄×C₁₃₁	—	2	2	no	—
267	C₂×C₄×C₁₃₁	—	2	2	no	—
268	C₂×C₄×C₁₃₁	—	2	4	no	—
269	C₂×C₄×C₁₃₁	—	2	4	no	—
270	C₂×C₄×C₁₃₁	—	2	4	no	—
271	C₂×C₄×C₁₃₁	—	2	2	no	—
272	C₂×C₄×C₁₃₁	—	2	2	no	—
273	C₂×C₄×C₁₃₁	—	2	4	no	—
274	C₂×C₄×C₁₃₁	—	2	4	no	—
275	C₂×C₄×C₁₃₁	—	2	2	no	—
276	C₂×C₄×C₁₃₁	—	2	2	no	—
277	C₂×C₄×C₁₃₁	—	2	4	no	—
278	C₂×C₄×C₁₃₁	—	2	2	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	—	4	4	no	—
283	C₂×C₄×C₁₃₁	—	4	8	no	—
284	C₂×C₄×C₁₃₁	—	4	4	no	—
285	C₂×C₄×C₁₃₁	—	8	8	no	—
286	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
287	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
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	2	yes	—
295	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
296	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
297	C₂²×C₁₃₁	—	2	2	no	—
298	C₂²×C₁₃₁	—	2	4	no	—
299	C₂²×C₁₃₁	—	2	2	no	—
300	C₂²×C₁₃₁	—	2	2	no	—
301	C₂²×C₁₃₁	—	2	4	no	—
302	C₂²×C₁₃₁	—	2	4	no	—
303	C₂²×C₁₃₁	—	4	4	no	—
304	C₂²×C₁₃₁	—	4	2	no	—
305	C₂²×C₁₃₁	—	4	2	no	—
306	C₂²×C₁₃₁	—	4	4	no	—
307	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
308	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₂²×C₁₃₁	#585	1	2	yes	—
311	C₂²×C₁₃₁	#585	1	2	yes	—
312	C₄×C₁₃₁	—	2	2	no	—
313	C₄×C₁₃₁	—	2	4	no	—
314	C₄×C₁₃₁	—	2	2	no	—
315	C₄×C₁₃₁	—	2	2	no	—
316	C₄×C₁₃₁	—	2	4	no	—
317	C₄×C₁₃₁	—	2	2	no	—
318	C₄×C₁₃₁	—	2	2	no	—
319	C₄×C₁₃₁	—	2	4	no	—
320	C₄×C₁₃₁	—	4	2	no	—
321	C₄×C₁₃₁	—	4	2	no	—
322	C₄×C₁₃₁	—	4	2	no	—
323	C₄×C₁₃₁	—	4	4	no	—
324	C₄×C₁₃₁	—	4	2	no	—
325	C₄×C₁₃₁	—	4	4	no	—
326	C₄×C₁₃₁	#520	1	4	yes	—
327	C₂×C₁₃₁	—	4	2	no	—
328	C₂×C₁₃₁	—	4	4	no	—
329	C₂×C₁₃₁	C₂×#520	1	1	yes	characteristic
330	C₂×C₁₃₁	#3428	1	1	yes	characteristic
331	C₂×C₁₃₁	#3428	1	1	yes	characteristic
332	C₂×C₁₃₁	#3551	1	2	yes	—
333	C₂×C₁₃₁	#3557	1	2	yes	—
334	#34397	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₁₃₁	#34397	1	1	yes	characteristic, direct product factor, Sylow
336	C₂×#529	C₂×C₁₃₁	1	1	yes	characteristic
337	#2383	C₂×C₁₃₁	1	4	yes	complemented
338	#2370	C₂×C₁₃₁	1	2	yes	complemented
339	#2367	C₂×C₁₃₁	1	2	yes	complemented
340	#2357	C₂×C₁₃₁	1	1	yes	characteristic, complemented
341	#2356	C₂×C₁₃₁	1	1	yes	characteristic, complemented
342	#2351	C₂×C₁₃₁	1	1	yes	characteristic, complemented
343	#2349	C₂×C₁₃₁	1	1	yes	characteristic, complemented
344	#2346	C₂×C₁₃₁	1	2	yes	complemented
345	#2343	C₂×C₁₃₁	1	2	yes	complemented
346	#2335	C₂×C₁₃₁	1	4	yes	complemented
347	#2324	C₂×C₁₃₁	1	2	yes	—
348	#2323	C₂×C₁₃₁	1	2	yes	complemented
349	#2319	C₂×C₁₃₁	1	2	yes	complemented
350	#2318	C₂×C₁₃₁	1	2	yes	complemented
351	#2285	C₂×C₁₃₁	1	1	yes	characteristic, complemented
352	#2283	C₂×C₁₃₁	1	1	yes	characteristic, complemented
353	#529	C₄×C₁₃₁	1	16	yes	complemented
354	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
355	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
356	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
357	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
358	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
359	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
361	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
363	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
365	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
366	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
367	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
368	#391	C₂²×C₁₃₁	1	2	yes	—
369	#390	C₂²×C₁₃₁	1	4	yes	—
370	#390	C₂²×C₁₃₁	1	2	yes	—
371	#389	C₂²×C₁₃₁	1	4	yes	—
372	#389	C₂²×C₁₃₁	1	4	yes	—
373	#389	C₂²×C₁₃₁	1	2	yes	—
374	#389	C₂²×C₁₃₁	1	2	yes	—
375	#389	C₂²×C₁₃₁	1	4	yes	—
376	#388	C₂²×C₁₃₁	1	4	yes	—
377	#388	C₂²×C₁₃₁	1	4	yes	—
378	#388	C₂²×C₁₃₁	1	4	yes	—
379	#388	C₂²×C₁₃₁	1	4	yes	—
380	#388	C₂²×C₁₃₁	1	4	yes	—
381	#388	C₂²×C₁₃₁	1	4	yes	—
382	#387	C₂²×C₁₃₁	1	4	yes	—
383	#387	C₂²×C₁₃₁	1	4	yes	—
384	#387	C₂²×C₁₃₁	1	4	yes	—
385	#387	C₂²×C₁₃₁	1	4	yes	—
386	#386	C₂²×C₁₃₁	1	4	yes	—
387	#385	C₂²×C₁₃₁	1	4	yes	—
388	#385	C₂²×C₁₃₁	1	4	yes	—
389	#385	C₂²×C₁₃₁	1	4	yes	—
390	#384	C₂²×C₁₃₁	1	2	yes	—
391	#383	C₂²×C₁₃₁	1	2	yes	—
392	#383	C₂²×C₁₃₁	1	2	yes	—
393	#382	C₂²×C₁₃₁	1	2	yes	—
394	#382	C₂²×C₁₃₁	1	1	yes	characteristic
395	#382	C₂²×C₁₃₁	1	1	yes	characteristic
396	#382	C₂²×C₁₃₁	1	1	yes	characteristic
397	#382	C₂²×C₁₃₁	1	1	yes	characteristic
398	#381	C₂²×C₁₃₁	1	2	yes	—
399	#381	C₂²×C₁₃₁	1	2	yes	—
400	#380	C₂²×C₁₃₁	1	1	yes	characteristic
401	#380	C₂²×C₁₃₁	1	1	yes	characteristic
402	#380	C₂²×C₁₃₁	1	2	yes	—
403	#380	C₂²×C₁₃₁	1	2	yes	—
404	#380	C₂²×C₁₃₁	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	—
409	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
415	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
416	#376	C₂²×C₁₃₁	1	2	yes	—
417	#376	C₂²×C₁₃₁	1	2	yes	—
418	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
419	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
421	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
422	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
424	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
425	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
427	#126	C₂×C₄×C₁₃₁	1	16	yes	complemented
428	#125	C₂×C₄×C₁₃₁	1	8	yes	complemented
429	#124	C₂×C₄×C₁₃₁	1	8	yes	—
430	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
431	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
432	#121	C₂×C₄×C₁₃₁	1	8	yes	—
433	C₄×Q₈	—	4	4	no	—
434	C₄×Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
435	C₄×D₄	—	4	4	no	—
436	C₄×D₄	C₂×C₄×C₁₃₁	1	8	yes	—
437	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
438	#117	—	4	4	no	—
439	#117	C₂×C₄×C₁₃₁	1	16	yes	complemented
440	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
463	C₂×C₂²⋊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	2	yes	—
468	C₂×C₄²	C₂×C₄×C₁₃₁	1	8	yes	complemented
469	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
470	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
471	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
472	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
473	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
474	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
475	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
477	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
480	#95	C₂³×C₁₃₁	1	1	yes	characteristic
481	#95	C₂³×C₁₃₁	1	2	yes	—
482	#95	C₂³×C₁₃₁	1	4	yes	—
483	#95	C₂³×C₁₃₁	1	2	yes	—
484	#95	C₂³×C₁₃₁	1	1	yes	characteristic
485	#95	C₂³×C₁₃₁	1	4	yes	—
486	#95	C₂³×C₁₃₁	1	4	yes	—
487	#95	C₂³×C₁₃₁	1	1	yes	characteristic
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	4	yes	—
492	#95	C₂³×C₁₃₁	1	1	yes	characteristic
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	4	yes	—
497	#95	C₂³×C₁₃₁	1	4	yes	—
498	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
499	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
507	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	4	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	4	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
517	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
518	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
519	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
520	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	4	4	no	—
538	C₄⋊C₄	—	4	4	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	4	no	—
546	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
547	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
548	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
549	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
550	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
551	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	4	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
559	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
560	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	4	4	no	—
566	C₄²	—	4	4	no	—
567	C₄²	—	4	4	no	—
568	C₄²	—	4	4	no	—
569	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
570	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
571	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
572	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
573	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	2	no	—
582	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
583	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
584	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
585	Q₈	—	2	8	no	—
586	D₄	—	2	8	no	—
587	D₄	—	4	8	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	8	8	no	—
621	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
622	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
624	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
625	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
626	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
627	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
628	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
629	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
630	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
631	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	4	no	—
642	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
643	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
644	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
645	C₂²	#585×C₁₃₁	1	2	yes	—
646	C₂²	#585×C₁₃₁	1	2	yes	—
647	C₄	—	2	2	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	4	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	4	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	4	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	4	no	—
661	C₄	#520×C₁₃₁	1	4	yes	—
662	C₂	—	4	2	no	—
663	C₂	—	4	4	no	—
664	C₂	C₂×#520×C₁₃₁	1	1	yes	characteristic
665	C₂	#3428×C₁₃₁	1	1	yes	characteristic
666	C₂	#3428×C₁₃₁	1	1	yes	characteristic
667	C₂	#3551×C₁₃₁	1	2	yes	—
668	C₂	#3557×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂×#121×C₁₃₁	C₂²
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. #2383×C₁₃₁	C₂	semidirect
3. #2370×C₁₃₁	C₂	semidirect
4. #2367×C₁₃₁	C₂	semidirect
5. #2357×C₁₃₁	C₂	semidirect
6. #2356×C₁₃₁	C₂	semidirect
7. #2351×C₁₃₁	C₂	semidirect
8. #2349×C₁₃₁	C₂	semidirect
9. #2346×C₁₃₁	C₂	semidirect
10. #2343×C₁₃₁	C₂	semidirect
11. #2335×C₁₃₁	C₂	semidirect
13. #2323×C₁₃₁	C₂	semidirect
14. #2319×C₁₃₁	C₂	semidirect
15. #2318×C₁₃₁	C₂	semidirect
16. #2285×C₁₃₁	C₂	semidirect
17. #2283×C₁₃₁	C₂	semidirect
18. #529×C₁₃₁	C₄	semidirect
92. #126×C₁₃₁	C₂×C₄	semidirect
93. #125×C₁₃₁	C₂×C₄	semidirect
95. #123×C₁₃₁	C₂×C₄	semidirect
96. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
99. C₄×Q₈×C₁₃₁	C₂×C₄	semidirect
102. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
104. #117×C₁₃₁	C₂×C₄	semidirect
133. C₂×C₄²×C₁₃₁	C₂×C₄	semidirect
334. #34397	C₁₃₁	direct (N × H)
335. C₁₃₁	#34397	direct (N × H)
337. #2383	C₂×C₁₃₁	semidirect
338. #2370	C₂×C₁₃₁	semidirect
339. #2367	C₂×C₁₃₁	semidirect
340. #2357	C₂×C₁₃₁	semidirect
341. #2356	C₂×C₁₃₁	semidirect
342. #2351	C₂×C₁₃₁	semidirect
343. #2349	C₂×C₁₃₁	semidirect
344. #2346	C₂×C₁₃₁	semidirect
345. #2343	C₂×C₁₃₁	semidirect
346. #2335	C₂×C₁₃₁	semidirect
348. #2323	C₂×C₁₃₁	semidirect
349. #2319	C₂×C₁₃₁	semidirect
350. #2318	C₂×C₁₃₁	semidirect
351. #2285	C₂×C₁₃₁	semidirect
352. #2283	C₂×C₁₃₁	semidirect
353. #529	C₄×C₁₃₁	semidirect
427. #126	C₂×C₄×C₁₃₁	semidirect
428. #125	C₂×C₄×C₁₃₁	semidirect
430. #123	C₂×C₄×C₁₃₁	semidirect
431. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
434. C₄×Q₈	C₂×C₄×C₁₃₁	semidirect
437. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
439. #117	C₂×C₄×C₁₃₁	semidirect
468. C₂×C₄²	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×#529×C₁₃₁	2
#2383×C₁₃₁	2
#2370×C₁₃₁	2
#2367×C₁₃₁	2
#2357×C₁₃₁	2
#2356×C₁₃₁	2
#2351×C₁₃₁	2
#2349×C₁₃₁	2
#2346×C₁₃₁	2
#2343×C₁₃₁	2
#2335×C₁₃₁	2
#2324×C₁₃₁	2
#2323×C₁₃₁	2
#2319×C₁₃₁	2
#2318×C₁₃₁	2
#2285×C₁₃₁	2
#2283×C₁₃₁	2
#34397	131

Subgroups — C131×#34397 #45720281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34397 #45720281