Subgroups — C₁₃₁×#21285 #45707169

Order 33536.

814 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×SD₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2320×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2319×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1973×C₁₃₁	C₂	1	2	yes	maximal
5	#1944×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1934×C₁₃₁	C₂	1	2	yes	maximal
7	#1933×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	C₄×#107×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1763×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1762×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	#1726×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₄×SD₁₆×C₁₃₁	C₄	1	8	yes	complemented
16	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
17	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#103×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	#391×C₁₃₁	C₂²	1	2	yes	—
27	#390×C₁₃₁	C₂²	1	2	yes	—
28	#389×C₁₃₁	C₂²	1	2	yes	—
29	#389×C₁₃₁	C₂²	1	2	yes	—
30	#388×C₁₃₁	—	2	2	no	—
31	#387×C₁₃₁	—	2	2	no	—
32	#383×C₁₃₁	—	2	1	no	—
33	#382×C₁₃₁	—	2	1	no	—
34	#381×C₁₃₁	—	2	1	no	—
35	#380×C₁₃₁	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
38	#376×C₁₃₁	C₂²	1	1	yes	characteristic
39	#340×C₁₃₁	C₂²	1	2	yes	—
40	#340×C₁₃₁	C₂²	1	2	yes	—
41	#340×C₁₃₁	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₁	—	2	1	no	—
45	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
46	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₁₃₁	—	2	2	no	—
51	C₄×Q₈×C₁₃₁	C₂×C₄	1	4	yes	—
52	C₄×D₄×C₁₃₁	—	2	2	no	—
53	C₄×D₄×C₁₃₁	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
64	C₂×C₄²×C₁₃₁	—	2	1	no	—
65	C₂×C₄²×C₁₃₁	—	2	1	no	—
66	C₂×C₄²×C₁₃₁	—	2	1	no	—
67	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
69	#107×C₁₃₁	—	2	4	no	—
70	#106×C₁₃₁	C₂×C₄	1	4	yes	—
71	#103×C₁₃₁	—	2	4	no	—
72	#103×C₁₃₁	C₂×C₄	1	4	yes	—
73	#102×C₁₃₁	—	2	4	no	—
74	#102×C₁₃₁	C₂×C₄	1	4	yes	—
75	#97×C₁₃₁	—	2	4	no	—
76	#97×C₁₃₁	—	2	2	no	—
77	C₄×C₈×C₁₃₁	—	2	4	no	—
78	C₄×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
79	#95×C₁₃₁	—	2	2	no	—
80	#95×C₁₃₁	—	2	2	no	—
81	#95×C₁₃₁	—	2	2	no	—
82	#95×C₁₃₁	—	2	2	no	—
83	#95×C₁₃₁	—	2	1	no	—
84	#95×C₁₃₁	—	2	1	no	—
85	#95×C₁₃₁	D₄	1	2	yes	—
86	#95×C₁₃₁	D₄	1	1	yes	characteristic
87	#95×C₁₃₁	D₄	1	1	yes	characteristic
88	C₂⁴×C₁₃₁	—	2	1	no	—
89	C₂×Q₈×C₁₃₁	—	2	1	no	—
90	C₂×Q₈×C₁₃₁	—	2	2	no	—
91	C₂×Q₈×C₁₃₁	—	2	2	no	—
92	C₂×Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
93	C₂×D₄×C₁₃₁	—	2	2	no	—
94	C₂×D₄×C₁₃₁	—	2	2	no	—
95	C₂×D₄×C₁₃₁	—	2	1	no	—
96	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₁	—	2	1	no	—
98	C₂²×C₄×C₁₃₁	—	2	1	no	—
99	C₂²×C₄×C₁₃₁	—	2	1	no	—
100	C₂²×C₄×C₁₃₁	—	2	4	no	—
101	C₂²×C₄×C₁₃₁	—	2	2	no	—
102	C₂²×C₄×C₁₃₁	—	2	2	no	—
103	C₂²×C₄×C₁₃₁	—	8	2	no	—
104	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
109	SD₁₆×C₁₃₁	—	2	8	no	—
110	C₂×C₈×C₁₃₁	—	2	2	no	—
111	C₂×C₈×C₁₃₁	—	2	2	no	—
112	C₂×C₈×C₁₃₁	—	2	2	no	—
113	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃₁	#41	1	4	yes	—
116	C₂×C₈×C₁₃₁	#41	1	4	yes	—
117	C₄⋊C₄×C₁₃₁	—	2	4	no	—
118	C₄⋊C₄×C₁₃₁	—	2	1	no	—
119	C₄⋊C₄×C₁₃₁	—	2	1	no	—
120	C₄⋊C₄×C₁₃₁	—	2	2	no	—
121	C₄⋊C₄×C₁₃₁	—	2	2	no	—
122	C₄⋊C₄×C₁₃₁	—	2	2	no	—
123	C₄⋊C₄×C₁₃₁	—	2	2	no	—
124	C₄⋊C₄×C₁₃₁	—	8	2	no	—
125	C₄⋊C₄×C₁₃₁	—	8	2	no	—
126	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
129	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
130	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
131	C₄²×C₁₃₁	—	2	4	no	—
132	C₄²×C₁₃₁	—	2	2	no	—
133	C₄²×C₁₃₁	—	2	2	no	—
134	C₄²×C₁₃₁	—	8	1	no	—
135	C₄²×C₁₃₁	—	8	1	no	—
136	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
137	C₄²×C₁₃₁	#41	1	2	yes	—
138	C₂³×C₁₃₁	—	2	2	no	—
139	C₂³×C₁₃₁	—	4	2	no	—
140	C₂³×C₁₃₁	—	4	1	no	—
141	C₂³×C₁₃₁	—	4	2	no	—
142	C₂³×C₁₃₁	—	4	1	no	—
143	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₁₃₁	—	2	2	no	—
145	Q₈×C₁₃₁	—	2	2	no	—
146	Q₈×C₁₃₁	—	4	2	no	—
147	D₄×C₁₃₁	—	2	2	no	—
148	D₄×C₁₃₁	—	2	2	no	—
149	D₄×C₁₃₁	—	4	2	no	—
150	C₂×C₄×C₁₃₁	—	2	1	no	—
151	C₂×C₄×C₁₃₁	—	2	2	no	—
152	C₂×C₄×C₁₃₁	—	2	1	no	—
153	C₂×C₄×C₁₃₁	—	2	2	no	—
154	C₂×C₄×C₁₃₁	—	2	2	no	—
155	C₂×C₄×C₁₃₁	—	2	2	no	—
156	C₂×C₄×C₁₃₁	—	2	2	no	—
157	C₂×C₄×C₁₃₁	—	2	2	no	—
158	C₂×C₄×C₁₃₁	—	2	2	no	—
159	C₂×C₄×C₁₃₁	—	2	2	no	—
160	C₂×C₄×C₁₃₁	—	2	2	no	—
161	C₂×C₄×C₁₃₁	—	2	2	no	—
162	C₂×C₄×C₁₃₁	—	4	2	no	—
163	C₂×C₄×C₁₃₁	—	4	1	no	—
164	C₂×C₄×C₁₃₁	—	4	2	no	—
165	C₂×C₄×C₁₃₁	—	4	1	no	—
166	C₂×C₄×C₁₃₁	—	4	2	no	—
167	C₂×C₄×C₁₃₁	—	4	2	no	—
168	C₂×C₄×C₁₃₁	—	4	2	no	—
169	C₂×C₄×C₁₃₁	—	4	2	no	—
170	C₂×C₄×C₁₃₁	—	4	2	no	—
171	C₂×C₄×C₁₃₁	—	4	2	no	—
172	C₂×C₄×C₁₃₁	—	8	4	no	—
173	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
177	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
178	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
179	C₈×C₁₃₁	—	2	2	no	—
180	C₈×C₁₃₁	—	2	4	no	—
181	C₈×C₁₃₁	#117	1	4	yes	—
182	C₂²×C₁₃₁	—	4	2	no	—
183	C₂²×C₁₃₁	—	4	2	no	—
184	C₂²×C₁₃₁	—	4	2	no	—
185	C₂²×C₁₃₁	—	8	2	no	—
186	C₂²×C₁₃₁	—	8	2	no	—
187	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₁₃₁	#532	1	2	yes	—
189	C₂²×C₁₃₁	#576	1	1	yes	characteristic
190	C₂²×C₁₃₁	#577	1	2	yes	—
191	C₂²×C₁₃₁	#578	1	1	yes	characteristic
192	C₄×C₁₃₁	—	2	2	no	—
193	C₄×C₁₃₁	—	2	2	no	—
194	C₄×C₁₃₁	—	4	2	no	—
195	C₄×C₁₃₁	—	4	2	no	—
196	C₄×C₁₃₁	—	4	2	no	—
197	C₄×C₁₃₁	—	4	2	no	—
198	C₄×C₁₃₁	—	4	2	no	—
199	C₄×C₁₃₁	—	8	2	no	—
200	C₄×C₁₃₁	—	8	2	no	—
201	C₄×C₁₃₁	C₂×#117	1	1	yes	characteristic
202	C₄×C₁₃₁	C₄×#41	1	1	yes	characteristic
203	C₄×C₁₃₁	#529	1	2	yes	—
204	C₂×C₁₃₁	—	8	2	no	—
205	C₂×C₁₃₁	#2293	1	1	yes	characteristic
206	C₂×C₁₃₁	#2949	1	1	yes	characteristic
207	C₂×C₁₃₁	#2951	1	1	yes	characteristic
208	C₂×C₁₃₁	#3178	1	2	yes	—
209	C₂×C₁₃₁	#3179	1	2	yes	—
210	#21285	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₁₃₁	#21285	1	1	yes	characteristic, direct product factor, Sylow
212	C₂×C₄×SD₁₆	C₂×C₁₃₁	1	1	yes	characteristic
213	#2320	C₂×C₁₃₁	1	1	yes	characteristic, complemented
214	#2319	C₂×C₁₃₁	1	1	yes	characteristic
215	#1973	C₂×C₁₃₁	1	2	yes	—
216	#1944	C₂×C₁₃₁	1	2	yes	complemented
217	#1934	C₂×C₁₃₁	1	2	yes	—
218	#1933	C₂×C₁₃₁	1	2	yes	complemented
219	C₄×#107	C₂×C₁₃₁	1	1	yes	characteristic, complemented
220	#1763	C₂×C₁₃₁	1	1	yes	characteristic, complemented
221	#1762	C₂×C₁₃₁	1	1	yes	characteristic
222	#1726	C₂×C₁₃₁	1	1	yes	characteristic, complemented
223	C₂²×SD₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
226	C₄×SD₁₆	C₄×C₁₃₁	1	8	yes	complemented
227	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
228	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
229	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
230	C₂×#103	C₂²×C₁₃₁	1	1	yes	characteristic
231	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
232	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
233	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
234	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
236	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
237	#391	C₂²×C₁₃₁	1	2	yes	—
238	#390	C₂²×C₁₃₁	1	2	yes	—
239	#389	C₂²×C₁₃₁	1	2	yes	—
240	#389	C₂²×C₁₃₁	1	2	yes	—
241	#388	—	2	2	no	—
242	#387	—	2	2	no	—
243	#383	—	2	1	no	—
244	#382	—	2	1	no	—
245	#381	—	2	1	no	—
246	#380	—	2	1	no	—
247	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
248	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
249	#376	C₂²×C₁₃₁	1	1	yes	characteristic
250	#340	C₂²×C₁₃₁	1	2	yes	—
251	#340	C₂²×C₁₃₁	1	2	yes	—
252	#340	C₂²×C₁₃₁	1	2	yes	—
253	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
254	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
255	C₂³×C₄	—	2	1	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
258	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
260	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	C₂×C₄×C₁₃₁	1	4	yes	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	C₂×C₄×C₁₃₁	1	4	yes	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
279	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
280	#107	—	2	4	no	—
281	#106	C₂×C₄×C₁₃₁	1	4	yes	—
282	#103	—	2	4	no	—
283	#103	C₂×C₄×C₁₃₁	1	4	yes	—
284	#102	—	2	4	no	—
285	#102	C₂×C₄×C₁₃₁	1	4	yes	—
286	#97	—	2	4	no	—
287	#97	—	2	2	no	—
288	C₄×C₈	—	2	4	no	—
289	C₄×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
290	#95	—	2	1	no	—
291	#95	—	2	1	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	D₄×C₁₃₁	1	1	yes	characteristic
297	#95	D₄×C₁₃₁	1	1	yes	characteristic
298	#95	D₄×C₁₃₁	1	2	yes	—
299	C₂⁴	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₂²×C₄×C₁₃₁	1	2	yes	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	8	2	no	—
315	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
319	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
320	SD₁₆	—	2	8	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
325	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
326	C₂×C₈	#41×C₁₃₁	1	4	yes	—
327	C₂×C₈	#41×C₁₃₁	1	4	yes	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	8	2	no	—
336	C₄⋊C₄	—	8	2	no	—
337	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
338	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	8	2	no	—
341	C₂²⋊C₄	—	8	2	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	8	1	no	—
346	C₄²	—	8	1	no	—
347	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
348	C₄²	#41×C₁₃₁	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	1	no	—
354	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
355	Q₈	—	2	2	no	—
356	Q₈	—	2	2	no	—
357	Q₈	—	4	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	4	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	4	no	—
384	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
385	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
386	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
388	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
389	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	2	4	no	—
392	C₈	#117×C₁₃₁	1	4	yes	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
399	C₂²	#532×C₁₃₁	1	2	yes	—
400	C₂²	#576×C₁₃₁	1	1	yes	characteristic
401	C₂²	#577×C₁₃₁	1	2	yes	—
402	C₂²	#578×C₁₃₁	1	1	yes	characteristic
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	2	no	—
412	C₄	C₂×#117×C₁₃₁	1	1	yes	characteristic
413	C₄	C₄×#41×C₁₃₁	1	1	yes	characteristic
414	C₄	#529×C₁₃₁	1	2	yes	—
415	C₂	—	8	2	no	—
416	C₂	#2293×C₁₃₁	1	1	yes	characteristic
417	C₂	#2949×C₁₃₁	1	1	yes	characteristic
418	C₂	#2951×C₁₃₁	1	1	yes	characteristic
419	C₂	#3178×C₁₃₁	1	2	yes	—
420	C₂	#3179×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ #376×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2320×C₁₃₁	C₂	semidirect
5. #1944×C₁₃₁	C₂	semidirect
7. #1933×C₁₃₁	C₂	semidirect
8. C₄×#107×C₁₃₁	C₂	semidirect
9. #1763×C₁₃₁	C₂	semidirect
11. #1726×C₁₃₁	C₂	semidirect
15. C₄×SD₁₆×C₁₃₁	C₄	semidirect
210. #21285	C₁₃₁	direct (N × H)
211. C₁₃₁	#21285	direct (N × H)
213. #2320	C₂×C₁₃₁	semidirect
216. #1944	C₂×C₁₃₁	semidirect
218. #1933	C₂×C₁₃₁	semidirect
219. C₄×#107	C₂×C₁₃₁	semidirect
220. #1763	C₂×C₁₃₁	semidirect
222. #1726	C₂×C₁₃₁	semidirect
226. C₄×SD₁₆	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×C₄×SD₁₆×C₁₃₁	2
#2320×C₁₃₁	2
#2319×C₁₃₁	2
#1973×C₁₃₁	2
#1944×C₁₃₁	2
#1934×C₁₃₁	2
#1933×C₁₃₁	2
C₄×#107×C₁₃₁	2
#1763×C₁₃₁	2
#1762×C₁₃₁	2
#1726×C₁₃₁	2
#21285	131

Subgroups — C131×#21285 #45707169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#21285 #45707169