Subgroups — C₁₃₁×#29199 #45715083

Order 33536.

706 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2647×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#2326×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2066×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2065×C₁₃₁	C₂	1	2	yes	maximal
5	#1959×C₁₃₁	C₂	1	1	yes	maximal, characteristic
6	#1958×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1865×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1864×C₁₃₁	C₂	1	2	yes	maximal
9	#1844×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1836×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1768×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#124×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	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
16	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
24	#400×C₁₃₁	—	2	2	no	—
25	#398×C₁₃₁	—	2	2	no	—
26	#391×C₁₃₁	C₂²	1	1	yes	characteristic
27	#390×C₁₃₁	C₂²	1	1	yes	characteristic
28	#389×C₁₃₁	C₂²	1	2	yes	—
29	#389×C₁₃₁	C₂²	1	2	yes	—
30	#388×C₁₃₁	—	2	2	no	—
31	#385×C₁₃₁	—	2	2	no	—
32	#384×C₁₃₁	C₂²	1	1	yes	characteristic
33	#384×C₁₃₁	C₂²	1	1	yes	characteristic
34	#382×C₁₃₁	C₂²	1	1	yes	characteristic
35	#376×C₁₃₁	C₂²	1	1	yes	characteristic
36	#340×C₁₃₁	C₂²	1	2	yes	—
37	#340×C₁₃₁	C₂²	1	2	yes	—
38	#336×C₁₃₁	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃₁	—	2	1	no	—
42	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
44	#124×C₁₃₁	—	2	2	no	—
45	#124×C₁₃₁	Q₈	1	4	yes	—
46	C₄×Q₈×C₁₃₁	—	4	2	no	—
47	C₄×D₄×C₁₃₁	—	4	2	no	—
48	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
60	C₂×C₄²×C₁₃₁	—	2	1	no	—
61	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
64	#106×C₁₃₁	—	4	2	no	—
65	#106×C₁₃₁	—	4	2	no	—
66	C₄⋊C₈×C₁₃₁	—	2	4	no	—
67	#103×C₁₃₁	—	2	4	no	—
68	#103×C₁₃₁	—	4	2	no	—
69	#102×C₁₃₁	—	2	4	no	—
70	#102×C₁₃₁	—	4	2	no	—
71	#97×C₁₃₁	—	2	2	no	—
72	C₄×C₈×C₁₃₁	—	2	2	no	—
73	#95×C₁₃₁	—	2	2	no	—
74	#95×C₁₃₁	—	2	2	no	—
75	#95×C₁₃₁	—	2	2	no	—
76	#95×C₁₃₁	—	2	2	no	—
77	#95×C₁₃₁	D₄	1	2	yes	—
78	#95×C₁₃₁	D₄	1	2	yes	—
79	C₂⁴×C₁₃₁	—	2	1	no	—
80	C₂×Q₈×C₁₃₁	—	2	1	no	—
81	C₂×Q₈×C₁₃₁	—	2	2	no	—
82	C₂×Q₈×C₁₃₁	—	2	2	no	—
83	C₂×Q₈×C₁₃₁	C₂×Q₈	1	2	yes	—
84	C₂×D₄×C₁₃₁	—	2	2	no	—
85	C₂×D₄×C₁₃₁	—	2	1	no	—
86	C₂×D₄×C₁₃₁	—	2	2	no	—
87	C₂×D₄×C₁₃₁	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₁₃₁	—	2	1	no	—
89	C₂²×C₄×C₁₃₁	—	2	2	no	—
90	C₂²×C₄×C₁₃₁	—	2	1	no	—
91	C₂²×C₄×C₁₃₁	—	2	2	no	—
92	C₂²×C₄×C₁₃₁	—	2	1	no	—
93	C₂²×C₄×C₁₃₁	—	4	2	no	—
94	C₂²×C₄×C₁₃₁	—	8	2	no	—
95	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₁₃₁	—	2	2	no	—
101	C₂×C₈×C₁₃₁	—	2	2	no	—
102	C₂×C₈×C₁₃₁	—	2	2	no	—
103	C₂×C₈×C₁₃₁	—	2	2	no	—
104	C₂×C₈×C₁₃₁	—	2	2	no	—
105	C₂×C₈×C₁₃₁	#41	1	4	yes	—
106	C₄⋊C₄×C₁₃₁	—	2	2	no	—
107	C₄⋊C₄×C₁₃₁	—	2	2	no	—
108	C₄⋊C₄×C₁₃₁	—	2	2	no	—
109	C₄⋊C₄×C₁₃₁	—	2	2	no	—
110	C₄⋊C₄×C₁₃₁	—	2	2	no	—
111	C₄⋊C₄×C₁₃₁	—	2	2	no	—
112	C₄⋊C₄×C₁₃₁	—	4	2	no	—
113	C₄⋊C₄×C₁₃₁	—	8	2	no	—
114	C₄⋊C₄×C₁₃₁	—	8	2	no	—
115	C₄⋊C₄×C₁₃₁	—	8	2	no	—
116	C₄⋊C₄×C₁₃₁	—	8	2	no	—
117	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
118	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
119	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
120	C₄²×C₁₃₁	—	2	2	no	—
121	C₄²×C₁₃₁	—	2	2	no	—
122	C₄²×C₁₃₁	—	4	2	no	—
123	C₄²×C₁₃₁	C₂×Q₈	1	2	yes	—
124	C₄²×C₁₃₁	#41	1	2	yes	—
125	C₂³×C₁₃₁	—	2	2	no	—
126	C₂³×C₁₃₁	—	4	1	no	—
127	C₂³×C₁₃₁	—	4	1	no	—
128	C₂³×C₁₃₁	—	4	2	no	—
129	C₂³×C₁₃₁	—	4	2	no	—
130	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
131	Q₈×C₁₃₁	—	2	4	no	—
132	Q₈×C₁₃₁	—	4	2	no	—
133	D₄×C₁₃₁	—	2	4	no	—
134	D₄×C₁₃₁	—	4	2	no	—
135	C₂×C₄×C₁₃₁	—	2	2	no	—
136	C₂×C₄×C₁₃₁	—	2	2	no	—
137	C₂×C₄×C₁₃₁	—	2	2	no	—
138	C₂×C₄×C₁₃₁	—	2	2	no	—
139	C₂×C₄×C₁₃₁	—	2	1	no	—
140	C₂×C₄×C₁₃₁	—	2	1	no	—
141	C₂×C₄×C₁₃₁	—	2	2	no	—
142	C₂×C₄×C₁₃₁	—	2	2	no	—
143	C₂×C₄×C₁₃₁	—	2	2	no	—
144	C₂×C₄×C₁₃₁	—	2	2	no	—
145	C₂×C₄×C₁₃₁	—	4	1	no	—
146	C₂×C₄×C₁₃₁	—	4	1	no	—
147	C₂×C₄×C₁₃₁	—	4	2	no	—
148	C₂×C₄×C₁₃₁	—	4	1	no	—
149	C₂×C₄×C₁₃₁	—	4	1	no	—
150	C₂×C₄×C₁₃₁	—	4	2	no	—
151	C₂×C₄×C₁₃₁	—	4	2	no	—
152	C₂×C₄×C₁₃₁	—	4	2	no	—
153	C₂×C₄×C₁₃₁	—	4	2	no	—
154	C₂×C₄×C₁₃₁	—	4	2	no	—
155	C₂×C₄×C₁₃₁	—	4	2	no	—
156	C₂×C₄×C₁₃₁	—	4	2	no	—
157	C₂×C₄×C₁₃₁	—	8	4	no	—
158	C₂×C₄×C₁₃₁	C₂²⋊Q₈	1	4	yes	—
159	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
162	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
163	C₈×C₁₃₁	—	2	4	no	—
164	C₈×C₁₃₁	—	4	2	no	—
165	C₂²×C₁₃₁	—	4	2	no	—
166	C₂²×C₁₃₁	—	4	4	no	—
167	C₂²×C₁₃₁	—	8	2	no	—
168	C₂²×C₁₃₁	—	8	1	no	—
169	C₂²×C₁₃₁	—	8	1	no	—
170	C₂²×C₁₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
171	C₂²×C₁₃₁	#532	1	1	yes	characteristic
172	C₂²×C₁₃₁	#535	1	1	yes	characteristic
173	C₂²×C₁₃₁	#577	1	2	yes	—
174	C₂²×C₁₃₁	#577	1	2	yes	—
175	C₄×C₁₃₁	—	2	4	no	—
176	C₄×C₁₃₁	—	4	2	no	—
177	C₄×C₁₃₁	—	4	2	no	—
178	C₄×C₁₃₁	—	4	1	no	—
179	C₄×C₁₃₁	—	4	1	no	—
180	C₄×C₁₃₁	—	8	2	no	—
181	C₄×C₁₃₁	—	8	2	no	—
182	C₄×C₁₃₁	—	8	1	no	—
183	C₄×C₁₃₁	—	8	1	no	—
184	C₄×C₁₃₁	#553	1	2	yes	—
185	C₄×C₁₃₁	#554	1	2	yes	—
186	C₂×C₁₃₁	—	8	2	no	—
187	C₂×C₁₃₁	#2566	1	1	yes	characteristic
188	C₂×C₁₃₁	#3084	1	2	yes	—
189	C₂×C₁₃₁	#3173	1	2	yes	—
190	C₂×C₁₃₁	#3221	1	1	yes	characteristic
191	C₂×C₁₃₁	#3222	1	1	yes	characteristic
192	#29199	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₁₃₁	#29199	1	1	yes	characteristic, direct product factor, Sylow
194	#2647	C₂×C₁₃₁	1	1	yes	characteristic, complemented
195	#2326	C₂×C₁₃₁	1	1	yes	characteristic
196	#2066	C₂×C₁₃₁	1	2	yes	complemented
197	#2065	C₂×C₁₃₁	1	2	yes	—
198	#1959	C₂×C₁₃₁	1	1	yes	characteristic
199	#1958	C₂×C₁₃₁	1	1	yes	characteristic
200	#1865	C₂×C₁₃₁	1	2	yes	complemented
201	#1864	C₂×C₁₃₁	1	2	yes	—
202	#1844	C₂×C₁₃₁	1	1	yes	characteristic, complemented
203	#1836	C₂×C₁₃₁	1	1	yes	characteristic, complemented
204	#1768	C₂×C₁₃₁	1	1	yes	characteristic, complemented
205	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
207	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
208	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
209	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
211	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
212	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
213	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
214	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
215	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
217	#400	—	2	2	no	—
218	#398	—	2	2	no	—
219	#391	C₂²×C₁₃₁	1	1	yes	characteristic
220	#390	C₂²×C₁₃₁	1	1	yes	characteristic
221	#389	C₂²×C₁₃₁	1	2	yes	—
222	#389	C₂²×C₁₃₁	1	2	yes	—
223	#388	—	2	2	no	—
224	#385	—	2	2	no	—
225	#384	C₂²×C₁₃₁	1	1	yes	characteristic
226	#384	C₂²×C₁₃₁	1	1	yes	characteristic
227	#382	C₂²×C₁₃₁	1	1	yes	characteristic
228	#376	C₂²×C₁₃₁	1	1	yes	characteristic
229	#340	C₂²×C₁₃₁	1	2	yes	—
230	#340	C₂²×C₁₃₁	1	2	yes	—
231	#336	C₂²×C₁₃₁	1	2	yes	—
232	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
233	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
234	C₂³×C₄	—	2	1	no	—
235	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
236	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
237	#124	—	2	2	no	—
238	#124	Q₈×C₁₃₁	1	4	yes	—
239	C₄×Q₈	—	4	2	no	—
240	C₄×D₄	—	4	2	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
257	#106	—	4	2	no	—
258	#106	—	4	2	no	—
259	C₄⋊C₈	—	2	4	no	—
260	#103	—	2	4	no	—
261	#103	—	4	2	no	—
262	#102	—	2	4	no	—
263	#102	—	4	2	no	—
264	#97	—	2	2	no	—
265	C₄×C₈	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	D₄×C₁₃₁	1	2	yes	—
271	#95	D₄×C₁₃₁	1	2	yes	—
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	C₂×Q₈×C₁₃₁	1	2	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	C₂×Q₈×C₁₃₁	1	2	yes	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	8	2	no	—
288	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	#41×C₁₃₁	1	4	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	8	2	no	—
307	C₄⋊C₄	—	8	2	no	—
308	C₄⋊C₄	—	8	2	no	—
309	C₄⋊C₄	—	8	2	no	—
310	C₂²⋊C₄	—	2	8	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	8	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	4	2	no	—
316	C₄²	C₂×Q₈×C₁₃₁	1	2	yes	—
317	C₄²	#41×C₁₃₁	1	2	yes	—
318	C₂³	—	2	2	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	1	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
324	Q₈	—	2	4	no	—
325	Q₈	—	4	2	no	—
326	D₄	—	2	4	no	—
327	D₄	—	4	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	4	no	—
351	C₂×C₄	C₂²⋊Q₈×C₁₃₁	1	4	yes	—
352	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
353	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
354	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
355	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
356	C₈	—	2	4	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	8	1	no	—
363	C₂²	C₂×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
364	C₂²	#532×C₁₃₁	1	1	yes	characteristic
365	C₂²	#535×C₁₃₁	1	1	yes	characteristic
366	C₂²	#577×C₁₃₁	1	2	yes	—
367	C₂²	#577×C₁₃₁	1	2	yes	—
368	C₄	—	2	4	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	1	no	—
376	C₄	—	8	1	no	—
377	C₄	#553×C₁₃₁	1	2	yes	—
378	C₄	#554×C₁₃₁	1	2	yes	—
379	C₂	—	8	2	no	—
380	C₂	#2566×C₁₃₁	1	1	yes	characteristic
381	C₂	#3084×C₁₃₁	1	2	yes	—
382	C₂	#3173×C₁₃₁	1	2	yes	—
383	C₂	#3221×C₁₃₁	1	1	yes	characteristic
384	C₂	#3222×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	C₂³
LCS	G ▷ C₂²×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
1. #2647×C₁₃₁	C₂	semidirect
3. #2066×C₁₃₁	C₂	semidirect
7. #1865×C₁₃₁	C₂	semidirect
9. #1844×C₁₃₁	C₂	semidirect
10. #1836×C₁₃₁	C₂	semidirect
11. #1768×C₁₃₁	C₂	semidirect
192. #29199	C₁₃₁	direct (N × H)
193. C₁₃₁	#29199	direct (N × H)
194. #2647	C₂×C₁₃₁	semidirect
196. #2066	C₂×C₁₃₁	semidirect
200. #1865	C₂×C₁₃₁	semidirect
202. #1844	C₂×C₁₃₁	semidirect
203. #1836	C₂×C₁₃₁	semidirect
204. #1768	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2647×C₁₃₁	2
#2326×C₁₃₁	2
#2066×C₁₃₁	2
#2065×C₁₃₁	2
#1959×C₁₃₁	2
#1958×C₁₃₁	2
#1865×C₁₃₁	2
#1864×C₁₃₁	2
#1844×C₁₃₁	2
#1836×C₁₃₁	2
#1768×C₁₃₁	2
#29199	131

Subgroups — C131×#29199 #45715083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29199 #45715083