Subgroups — C₁₃₁×#33789 #45719673

Order 33536.

562 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3177×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3156×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2251×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2247×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2245×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2242×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2211×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2209×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2189×C₁₃₁	C₂	1	2	yes	maximal
10	#2188×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2164×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₃₁	—	2	1	no	—
13	C₂×#135×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
15	#541×C₁₃₁	—	2	1	no	—
16	#536×C₁₃₁	—	2	1	no	—
17	C₂×Q₃₂×C₁₃₁	C₂²	1	2	yes	—
18	C₂×Q₃₂×C₁₃₁	C₂²	1	2	yes	—
19	C₂×Q₃₂×C₁₃₁	C₂²	1	2	yes	—
20	C₂×SD₃₂×C₁₃₁	C₂²	1	2	yes	—
21	#499×C₁₃₁	C₂²	1	1	yes	characteristic
22	#497×C₁₃₁	—	2	1	no	—
23	#497×C₁₃₁	—	2	1	no	—
24	#495×C₁₃₁	C₂²	1	1	yes	characteristic
25	#495×C₁₃₁	C₂²	1	1	yes	characteristic
26	#494×C₁₃₁	C₂²	1	1	yes	characteristic
27	#494×C₁₃₁	C₂²	1	1	yes	characteristic
28	#494×C₁₃₁	C₂²	1	1	yes	characteristic
29	#491×C₁₃₁	—	2	1	no	—
30	#470×C₁₃₁	—	2	1	no	—
31	#467×C₁₃₁	C₂²	1	2	yes	—
32	#441×C₁₃₁	—	2	1	no	—
33	C₄×Q₁₆×C₁₃₁	C₂²	1	2	yes	—
34	#405×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
36	#358×C₁₃₁	C₂²	1	2	yes	—
37	#358×C₁₃₁	C₂²	1	2	yes	—
38	#358×C₁₃₁	C₂²	1	2	yes	—
39	#357×C₁₃₁	C₂²	1	2	yes	—
40	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
41	#346×C₁₃₁	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
43	C₂×#41×C₁₃₁	—	2	1	no	—
44	C₂²×Q₈×C₁₃₁	—	2	1	no	—
45	#137×C₁₃₁	—	4	4	no	—
46	#135×C₁₃₁	—	4	2	no	—
47	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
49	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
50	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
51	C₂×Q₁₆×C₁₃₁	—	4	2	no	—
52	C₂×Q₁₆×C₁₃₁	C₂³	1	2	yes	—
53	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
55	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
57	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
58	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
59	C₂×D₈×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₁₃₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
63	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
64	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
65	#126×C₁₃₁	—	4	2	no	—
66	#125×C₁₃₁	—	2	1	no	—
67	#125×C₁₃₁	—	4	2	no	—
68	#124×C₁₃₁	—	2	1	no	—
69	#124×C₁₃₁	—	2	1	no	—
70	#123×C₁₃₁	—	4	2	no	—
71	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
72	C₂²⋊Q₈×C₁₃₁	—	4	2	no	—
73	C₄×Q₈×C₁₃₁	—	2	2	no	—
74	#117×C₁₃₁	D₄	1	1	yes	characteristic
75	Q₃₂×C₁₃₁	—	4	2	no	—
76	Q₃₂×C₁₃₁	—	4	2	no	—
77	Q₃₂×C₁₃₁	—	4	2	no	—
78	SD₃₂×C₁₃₁	—	4	2	no	—
79	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
80	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
81	#107×C₁₃₁	C₂³	1	2	yes	—
82	#106×C₁₃₁	—	2	1	no	—
83	#103×C₁₃₁	—	2	2	no	—
84	#103×C₁₃₁	—	2	2	no	—
85	#97×C₁₃₁	D₄	1	1	yes	characteristic
86	#97×C₁₃₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
89	#41×C₁₃₁	—	4	2	no	—
90	#41×C₁₃₁	—	4	2	no	—
91	C₂×Q₈×C₁₃₁	—	2	2	no	—
92	C₂×Q₈×C₁₃₁	—	2	1	no	—
93	C₂×Q₈×C₁₃₁	—	2	1	no	—
94	C₂×Q₈×C₁₃₁	—	2	1	no	—
95	C₂×Q₈×C₁₃₁	—	4	2	no	—
96	C₂×Q₈×C₁₃₁	—	4	2	no	—
97	C₂×Q₈×C₁₃₁	—	4	1	no	—
98	C₂×D₄×C₁₃₁	—	2	1	no	—
99	C₂×D₄×C₁₃₁	—	4	1	no	—
100	C₂²×C₄×C₁₃₁	—	4	1	no	—
101	C₂²×C₄×C₁₃₁	—	4	1	no	—
102	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
103	Q₁₆×C₁₃₁	—	2	2	no	—
104	Q₁₆×C₁₃₁	—	2	2	no	—
105	Q₁₆×C₁₃₁	—	2	2	no	—
106	Q₁₆×C₁₃₁	—	2	2	no	—
107	Q₁₆×C₁₃₁	—	2	2	no	—
108	Q₁₆×C₁₃₁	—	4	2	no	—
109	Q₁₆×C₁₃₁	—	4	2	no	—
110	Q₁₆×C₁₃₁	—	4	2	no	—
111	Q₁₆×C₁₃₁	—	4	2	no	—
112	SD₁₆×C₁₃₁	—	4	2	no	—
113	SD₁₆×C₁₃₁	—	4	2	no	—
114	SD₁₆×C₁₃₁	—	4	2	no	—
115	D₈×C₁₃₁	—	2	2	no	—
116	M₁₆×C₁₃₁	—	2	2	no	—
117	C₂×C₈×C₁₃₁	—	2	2	no	—
118	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
122	C₄⋊C₄×C₁₃₁	—	2	2	no	—
123	C₄⋊C₄×C₁₃₁	—	4	2	no	—
124	C₄⋊C₄×C₁₃₁	—	4	2	no	—
125	C₄⋊C₄×C₁₃₁	—	4	2	no	—
126	C₄⋊C₄×C₁₃₁	—	4	2	no	—
127	C₄⋊C₄×C₁₃₁	—	4	2	no	—
128	C₄⋊C₄×C₁₃₁	—	4	2	no	—
129	C₄⋊C₄×C₁₃₁	D₈	1	2	yes	—
130	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₁₃₁	D₈	1	2	yes	—
134	C₄²×C₁₃₁	—	4	2	no	—
135	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₁₃₁	—	2	2	no	—
138	C₁₆×C₁₃₁	—	2	2	no	—
139	C₂³×C₁₃₁	—	4	1	no	—
140	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
141	Q₈×C₁₃₁	—	4	1	no	—
142	Q₈×C₁₃₁	—	4	1	no	—
143	Q₈×C₁₃₁	—	4	1	no	—
144	Q₈×C₁₃₁	—	4	2	no	—
145	Q₈×C₁₃₁	—	4	1	no	—
146	Q₈×C₁₃₁	—	4	1	no	—
147	Q₈×C₁₃₁	—	4	1	no	—
148	Q₈×C₁₃₁	—	4	2	no	—
149	Q₈×C₁₃₁	—	8	2	no	—
150	D₄×C₁₃₁	—	4	1	no	—
151	D₄×C₁₃₁	—	4	1	no	—
152	D₄×C₁₃₁	—	8	2	no	—
153	C₂×C₄×C₁₃₁	—	2	1	no	—
154	C₂×C₄×C₁₃₁	—	2	1	no	—
155	C₂×C₄×C₁₃₁	—	4	2	no	—
156	C₂×C₄×C₁₃₁	—	4	2	no	—
157	C₂×C₄×C₁₃₁	—	4	1	no	—
158	C₂×C₄×C₁₃₁	—	4	1	no	—
159	C₂×C₄×C₁₃₁	—	4	1	no	—
160	C₂×C₄×C₁₃₁	—	8	2	no	—
161	C₂×C₄×C₁₃₁	—	8	2	no	—
162	C₂×C₄×C₁₃₁	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₁₃₁	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₁₃₁	—	2	1	no	—
167	C₈×C₁₃₁	—	2	1	no	—
168	C₈×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
169	C₈×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
170	C₂²×C₁₃₁	—	2	2	no	—
171	C₂²×C₁₃₁	—	2	1	no	—
172	C₂²×C₁₃₁	—	8	2	no	—
173	C₂²×C₁₃₁	—	8	1	no	—
174	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
175	C₄×C₁₃₁	—	2	2	no	—
176	C₄×C₁₃₁	—	2	2	no	—
177	C₄×C₁₃₁	—	2	1	no	—
178	C₄×C₁₃₁	—	8	2	no	—
179	C₄×C₁₃₁	—	8	1	no	—
180	C₄×C₁₃₁	—	8	1	no	—
181	C₄×C₁₃₁	—	8	1	no	—
182	C₄×C₁₃₁	—	8	2	no	—
183	C₄×C₁₃₁	#535	1	1	yes	characteristic
184	C₄×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₁₃₁	—	4	1	no	—
186	C₂×C₁₃₁	—	16	1	no	—
187	C₂×C₁₃₁	#3205	1	1	yes	characteristic
188	C₂×C₁₃₁	#3417	1	2	yes	—
189	#33789	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₁₃₁	#33789	1	1	yes	characteristic, direct product factor, Sylow
191	#3177	C₂×C₁₃₁	1	1	yes	characteristic, complemented
192	#3156	C₂×C₁₃₁	1	1	yes	characteristic
193	#2251	C₂×C₁₃₁	1	1	yes	characteristic, complemented
194	#2247	C₂×C₁₃₁	1	1	yes	characteristic, complemented
195	#2245	C₂×C₁₃₁	1	1	yes	characteristic, complemented
196	#2242	C₂×C₁₃₁	1	1	yes	characteristic, complemented
197	#2211	C₂×C₁₃₁	1	2	yes	complemented
198	#2209	C₂×C₁₃₁	1	2	yes	complemented
199	#2189	C₂×C₁₃₁	1	2	yes	—
200	#2188	C₂×C₁₃₁	1	2	yes	complemented
201	#2164	C₂×C₁₃₁	1	1	yes	characteristic, complemented
202	C₂×#137	—	2	1	no	—
203	C₂×#135	C₂²×C₁₃₁	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
205	#541	—	2	1	no	—
206	#536	—	2	1	no	—
207	C₂×Q₃₂	C₂²×C₁₃₁	1	2	yes	—
208	C₂×Q₃₂	C₂²×C₁₃₁	1	2	yes	—
209	C₂×Q₃₂	C₂²×C₁₃₁	1	2	yes	—
210	C₂×SD₃₂	C₂²×C₁₃₁	1	2	yes	—
211	#499	C₂²×C₁₃₁	1	1	yes	characteristic
212	#497	—	2	1	no	—
213	#497	—	2	1	no	—
214	#495	C₂²×C₁₃₁	1	1	yes	characteristic
215	#495	C₂²×C₁₃₁	1	1	yes	characteristic
216	#494	C₂²×C₁₃₁	1	1	yes	characteristic
217	#494	C₂²×C₁₃₁	1	1	yes	characteristic
218	#494	C₂²×C₁₃₁	1	1	yes	characteristic
219	#491	—	2	1	no	—
220	#470	—	2	1	no	—
221	#467	C₂²×C₁₃₁	1	2	yes	—
222	#441	—	2	1	no	—
223	C₄×Q₁₆	C₂²×C₁₃₁	1	2	yes	—
224	#405	C₂²×C₁₃₁	1	1	yes	characteristic
225	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
226	#358	C₂²×C₁₃₁	1	2	yes	—
227	#358	C₂²×C₁₃₁	1	2	yes	—
228	#358	C₂²×C₁₃₁	1	2	yes	—
229	#357	C₂²×C₁₃₁	1	2	yes	—
230	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
231	#346	C₂²×C₁₃₁	1	1	yes	characteristic
232	C₄×C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
233	C₂×#41	—	2	1	no	—
234	C₂²×Q₈	—	2	1	no	—
235	#137	—	4	4	no	—
236	#135	—	4	2	no	—
237	C₂×Q₁₆	—	2	1	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×Q₁₆	—	4	2	no	—
242	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
243	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
244	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
245	C₂×Q₁₆	C₂³×C₁₃₁	1	2	yes	—
246	C₂×SD₁₆	—	2	1	no	—
247	C₂×SD₁₆	—	2	1	no	—
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×D₈	C₂³×C₁₃₁	1	1	yes	characteristic
250	C₂×M₁₆	D₄×C₁₃₁	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	#126	—	4	2	no	—
256	#125	—	2	1	no	—
257	#125	—	4	2	no	—
258	#124	—	2	1	no	—
259	#124	—	2	1	no	—
260	#123	—	4	2	no	—
261	C₂²⋊Q₈	—	2	2	no	—
262	C₂²⋊Q₈	—	4	2	no	—
263	C₄×Q₈	—	2	2	no	—
264	#117	D₄×C₁₃₁	1	1	yes	characteristic
265	Q₃₂	—	4	2	no	—
266	Q₃₂	—	4	2	no	—
267	Q₃₂	—	4	2	no	—
268	SD₃₂	—	4	2	no	—
269	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
270	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
271	#107	C₂³×C₁₃₁	1	2	yes	—
272	#106	—	2	1	no	—
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#97	D₄×C₁₃₁	1	1	yes	characteristic
276	#97	D₄×C₁₃₁	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
293	Q₁₆	—	2	2	no	—
294	Q₁₆	—	2	2	no	—
295	Q₁₆	—	2	2	no	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	4	2	no	—
299	Q₁₆	—	4	2	no	—
300	Q₁₆	—	4	2	no	—
301	Q₁₆	—	4	2	no	—
302	SD₁₆	—	4	2	no	—
303	SD₁₆	—	4	2	no	—
304	SD₁₆	—	4	2	no	—
305	D₈	—	2	2	no	—
306	M₁₆	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
311	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	D₈×C₁₃₁	1	2	yes	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	D₈×C₁₃₁	1	2	yes	—
324	C₄²	—	4	2	no	—
325	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
327	C₁₆	—	2	2	no	—
328	C₁₆	—	2	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
331	Q₈	—	4	1	no	—
332	Q₈	—	4	1	no	—
333	Q₈	—	4	1	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	4	1	no	—
337	Q₈	—	4	1	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	8	2	no	—
340	D₄	—	4	1	no	—
341	D₄	—	4	1	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	C₂×D₈×C₁₃₁	1	2	yes	—
353	C₂×C₄	C₂×D₈×C₁₃₁	1	2	yes	—
354	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
359	C₈	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	8	2	no	—
363	C₂²	—	8	1	no	—
364	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	1	no	—
368	C₄	—	8	2	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	—	8	1	no	—
372	C₄	—	8	2	no	—
373	C₄	#535×C₁₃₁	1	1	yes	characteristic
374	C₄	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
375	C₂	—	4	1	no	—
376	C₂	—	16	1	no	—
377	C₂	#3205×C₁₃₁	1	1	yes	characteristic
378	C₂	#3417×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
prime radical	C₂×#135×C₁₃₁	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ #117×C₁₃₁ ◁ #405×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3177×C₁₃₁	C₂	semidirect
3. #2251×C₁₃₁	C₂	semidirect
4. #2247×C₁₃₁	C₂	semidirect
5. #2245×C₁₃₁	C₂	semidirect
6. #2242×C₁₃₁	C₂	semidirect
7. #2211×C₁₃₁	C₂	semidirect
8. #2209×C₁₃₁	C₂	semidirect
10. #2188×C₁₃₁	C₂	semidirect
11. #2164×C₁₃₁	C₂	semidirect
189. #33789	C₁₃₁	direct (N × H)
190. C₁₃₁	#33789	direct (N × H)
191. #3177	C₂×C₁₃₁	semidirect
193. #2251	C₂×C₁₃₁	semidirect
194. #2247	C₂×C₁₃₁	semidirect
195. #2245	C₂×C₁₃₁	semidirect
196. #2242	C₂×C₁₃₁	semidirect
197. #2211	C₂×C₁₃₁	semidirect
198. #2209	C₂×C₁₃₁	semidirect
200. #2188	C₂×C₁₃₁	semidirect
201. #2164	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3177×C₁₃₁	2
#3156×C₁₃₁	2
#2251×C₁₃₁	2
#2247×C₁₃₁	2
#2245×C₁₃₁	2
#2242×C₁₃₁	2
#2211×C₁₃₁	2
#2209×C₁₃₁	2
#2189×C₁₃₁	2
#2188×C₁₃₁	2
#2164×C₁₃₁	2
#33789	131

Subgroups — C131×#33789 #45719673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33789 #45719673