Subgroups — C₁₃₁×#29865 #45715749

Order 33536.

774 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	C₂×#476×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#474×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2862×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2293×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2085×C₁₃₁	C₂	1	4	yes	maximal, complemented
6	#2073×C₁₃₁	C₂	1	4	yes	maximal
7	#1988×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1987×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1831×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₃₁	—	2	1	no	—
14	#476×C₁₃₁	—	2	4	no	—
15	#474×C₁₃₁	—	2	4	no	—
16	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
17	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
22	#391×C₁₃₁	—	2	1	no	—
23	#391×C₁₃₁	—	2	1	no	—
24	#391×C₁₃₁	—	2	2	no	—
25	#390×C₁₃₁	C₂²	1	2	yes	—
26	#389×C₁₃₁	C₂²	1	2	yes	—
27	#388×C₁₃₁	—	2	2	no	—
28	#382×C₁₃₁	C₂²	1	4	yes	—
29	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
31	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
32	#340×C₁₃₁	C₂²	1	4	yes	—
33	#340×C₁₃₁	C₂²	1	4	yes	—
34	#336×C₁₃₁	C₂²	1	4	yes	—
35	C₂²×Q₈×C₁₃₁	—	2	1	no	—
36	C₂²×Q₈×C₁₃₁	—	2	1	no	—
37	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₁	—	2	1	no	—
39	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
41	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
42	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
43	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
44	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
45	C₄×D₄×C₁₃₁	—	2	2	no	—
46	C₄×D₄×C₁₃₁	D₄	1	4	yes	—
47	#117×C₁₃₁	—	4	4	no	—
48	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
58	C₂×C₄²×C₁₃₁	—	2	1	no	—
59	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
64	#107×C₁₃₁	—	2	4	no	—
65	#106×C₁₃₁	—	2	4	no	—
66	C₄⋊C₈×C₁₃₁	—	2	2	no	—
67	C₄⋊C₈×C₁₃₁	—	2	2	no	—
68	#102×C₁₃₁	—	2	4	no	—
69	#102×C₁₃₁	—	2	4	no	—
70	#95×C₁₃₁	—	2	1	no	—
71	#95×C₁₃₁	—	2	2	no	—
72	#95×C₁₃₁	—	2	4	no	—
73	#95×C₁₃₁	—	2	4	no	—
74	C₂⁴×C₁₃₁	—	2	1	no	—
75	C₂×Q₈×C₁₃₁	—	4	4	no	—
76	C₂×Q₈×C₁₃₁	—	4	2	no	—
77	C₂×Q₈×C₁₃₁	—	4	2	no	—
78	C₂×Q₈×C₁₃₁	—	4	2	no	—
79	C₂×Q₈×C₁₃₁	—	4	2	no	—
80	C₂×D₄×C₁₃₁	—	2	1	no	—
81	C₂×D₄×C₁₃₁	—	2	2	no	—
82	C₂×D₄×C₁₃₁	—	2	2	no	—
83	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₃₁	—	2	1	no	—
85	C₂²×C₄×C₁₃₁	—	2	4	no	—
86	C₂²×C₄×C₁₃₁	—	2	2	no	—
87	C₂²×C₄×C₁₃₁	—	2	2	no	—
88	C₂²×C₄×C₁₃₁	—	2	2	no	—
89	C₂²×C₄×C₁₃₁	—	4	2	no	—
90	C₂²×C₄×C₁₃₁	—	4	2	no	—
91	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₁₃₁	—	2	2	no	—
97	C₂×C₈×C₁₃₁	—	2	2	no	—
98	C₂×C₈×C₁₃₁	—	2	4	no	—
99	C₂×C₈×C₁₃₁	—	2	4	no	—
100	C₄⋊C₄×C₁₃₁	—	2	1	no	—
101	C₄⋊C₄×C₁₃₁	—	2	2	no	—
102	C₄⋊C₄×C₁₃₁	—	2	2	no	—
103	C₄⋊C₄×C₁₃₁	—	2	2	no	—
104	C₄⋊C₄×C₁₃₁	—	2	2	no	—
105	C₄⋊C₄×C₁₃₁	—	2	2	no	—
106	C₄⋊C₄×C₁₃₁	—	2	2	no	—
107	C₄⋊C₄×C₁₃₁	—	4	4	no	—
108	C₄⋊C₄×C₁₃₁	—	4	2	no	—
109	C₄⋊C₄×C₁₃₁	—	4	2	no	—
110	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
111	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
112	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
113	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
114	C₄²×C₁₃₁	—	2	2	no	—
115	C₄²×C₁₃₁	—	2	2	no	—
116	C₄²×C₁₃₁	—	2	2	no	—
117	C₄²×C₁₃₁	—	2	2	no	—
118	C₄²×C₁₃₁	—	4	2	no	—
119	C₄²×C₁₃₁	—	4	2	no	—
120	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
121	C₄²×C₁₃₁	#41	1	2	yes	—
122	C₂³×C₁₃₁	—	2	2	no	—
123	C₂³×C₁₃₁	—	4	2	no	—
124	C₂³×C₁₃₁	—	4	1	no	—
125	C₂³×C₁₃₁	—	4	1	no	—
126	C₂³×C₁₃₁	—	4	2	no	—
127	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₁₃₁	—	8	4	no	—
129	Q₈×C₁₃₁	—	8	4	no	—
130	D₄×C₁₃₁	—	2	2	no	—
131	D₄×C₁₃₁	—	2	2	no	—
132	D₄×C₁₃₁	—	4	2	no	—
133	C₂×C₄×C₁₃₁	—	2	2	no	—
134	C₂×C₄×C₁₃₁	—	2	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	2	no	—
140	C₂×C₄×C₁₃₁	—	2	2	no	—
141	C₂×C₄×C₁₃₁	—	4	1	no	—
142	C₂×C₄×C₁₃₁	—	4	1	no	—
143	C₂×C₄×C₁₃₁	—	4	8	no	—
144	C₂×C₄×C₁₃₁	—	4	2	no	—
145	C₂×C₄×C₁₃₁	—	4	2	no	—
146	C₂×C₄×C₁₃₁	—	4	2	no	—
147	C₂×C₄×C₁₃₁	—	4	2	no	—
148	C₂×C₄×C₁₃₁	—	4	2	no	—
149	C₂×C₄×C₁₃₁	—	4	2	no	—
150	C₂×C₄×C₁₃₁	—	4	2	no	—
151	C₂×C₄×C₁₃₁	—	4	4	no	—
152	C₂×C₄×C₁₃₁	#121	1	2	yes	—
153	C₂×C₄×C₁₃₁	#121	1	2	yes	—
154	C₂×C₄×C₁₃₁	#135	1	2	yes	—
155	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
159	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
160	C₈×C₁₃₁	—	4	2	no	—
161	C₈×C₁₃₁	—	4	2	no	—
162	C₂²×C₁₃₁	—	4	2	no	—
163	C₂²×C₁₃₁	—	4	2	no	—
164	C₂²×C₁₃₁	—	4	2	no	—
165	C₂²×C₁₃₁	—	8	2	no	—
166	C₂²×C₁₃₁	—	8	2	no	—
167	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
168	C₂²×C₁₃₁	#536	1	2	yes	—
169	C₂²×C₁₃₁	C₂×#135	1	1	yes	characteristic
170	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂²×C₁₃₁	#575	1	2	yes	—
172	C₄×C₁₃₁	—	2	2	no	—
173	C₄×C₁₃₁	—	4	2	no	—
174	C₄×C₁₃₁	—	4	2	no	—
175	C₄×C₁₃₁	—	4	2	no	—
176	C₄×C₁₃₁	—	8	2	no	—
177	C₄×C₁₃₁	—	8	2	no	—
178	C₄×C₁₃₁	—	8	2	no	—
179	C₄×C₁₃₁	#463	1	4	yes	—
180	C₄×C₁₃₁	#536	1	1	yes	characteristic
181	C₄×C₁₃₁	#536	1	1	yes	characteristic
182	C₄×C₁₃₁	#541	1	2	yes	—
183	C₂×C₁₃₁	—	8	2	no	—
184	C₂×C₁₃₁	#2621	1	1	yes	characteristic
185	C₂×C₁₃₁	C₂×#463	1	1	yes	characteristic
186	C₂×C₁₃₁	#3040	1	1	yes	characteristic
187	C₂×C₁₃₁	#3233	1	2	yes	—
188	C₂×C₁₃₁	#3235	1	2	yes	—
189	#29865	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₁₃₁	#29865	1	1	yes	characteristic, direct product factor, Sylow
191	C₂×#476	C₂×C₁₃₁	1	1	yes	characteristic
192	C₂×#474	C₂×C₁₃₁	1	1	yes	characteristic
193	#2862	C₂×C₁₃₁	1	1	yes	characteristic, complemented
194	#2293	C₂×C₁₃₁	1	1	yes	characteristic
195	#2085	C₂×C₁₃₁	1	4	yes	complemented
196	#2073	C₂×C₁₃₁	1	4	yes	—
197	#1988	C₂×C₁₃₁	1	1	yes	characteristic, complemented
198	#1987	C₂×C₁₃₁	1	1	yes	characteristic, complemented
199	#1831	C₂×C₁₃₁	1	1	yes	characteristic, complemented
200	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
201	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
203	C₂×#117	—	2	1	no	—
204	#476	—	2	4	no	—
205	#474	—	2	4	no	—
206	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
207	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
208	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
210	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
211	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
212	#391	—	2	1	no	—
213	#391	—	2	1	no	—
214	#391	—	2	2	no	—
215	#390	C₂²×C₁₃₁	1	2	yes	—
216	#389	C₂²×C₁₃₁	1	2	yes	—
217	#388	—	2	2	no	—
218	#382	C₂²×C₁₃₁	1	4	yes	—
219	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
220	C₄×C₂²⋊C₄	—	2	1	no	—
221	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
222	#340	C₂²×C₁₃₁	1	4	yes	—
223	#340	C₂²×C₁₃₁	1	4	yes	—
224	#336	C₂²×C₁₃₁	1	4	yes	—
225	C₂²×Q₈	—	2	1	no	—
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	—	2	2	no	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	—	2	2	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	D₄×C₁₃₁	1	4	yes	—
237	#117	—	4	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	—	2	1	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
252	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
253	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
254	#107	—	2	4	no	—
255	#106	—	2	4	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	#102	—	2	4	no	—
259	#102	—	2	4	no	—
260	#95	—	2	2	no	—
261	#95	—	2	1	no	—
262	#95	—	2	4	no	—
263	#95	—	2	4	no	—
264	C₂⁴	—	2	1	no	—
265	C₂×Q₈	—	4	4	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	4	2	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₂²⋊C₄	—	4	4	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	4	2	no	—
309	C₄²	—	4	2	no	—
310	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
311	C₄²	#41×C₁₃₁	1	2	yes	—
312	C₂³	—	2	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
318	Q₈	—	8	4	no	—
319	Q₈	—	8	4	no	—
320	D₄	—	2	2	no	—
321	D₄	—	2	2	no	—
322	D₄	—	4	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	#121×C₁₃₁	1	2	yes	—
343	C₂×C₄	#121×C₁₃₁	1	2	yes	—
344	C₂×C₄	#135×C₁₃₁	1	2	yes	—
345	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
346	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
347	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
348	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
349	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
350	C₈	—	4	2	no	—
351	C₈	—	4	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
358	C₂²	#536×C₁₃₁	1	2	yes	—
359	C₂²	C₂×#135×C₁₃₁	1	1	yes	characteristic
360	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
361	C₂²	#575×C₁₃₁	1	2	yes	—
362	C₄	—	2	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	8	2	no	—
367	C₄	—	8	2	no	—
368	C₄	—	8	2	no	—
369	C₄	#463×C₁₃₁	1	4	yes	—
370	C₄	#536×C₁₃₁	1	1	yes	characteristic
371	C₄	#536×C₁₃₁	1	1	yes	characteristic
372	C₄	#541×C₁₃₁	1	2	yes	—
373	C₂	—	8	2	no	—
374	C₂	#2621×C₁₃₁	1	1	yes	characteristic
375	C₂	C₂×#463×C₁₃₁	1	1	yes	characteristic
376	C₂	#3040×C₁₃₁	1	1	yes	characteristic
377	C₂	#3233×C₁₃₁	1	2	yes	—
378	C₂	#3235×C₁₃₁	1	2	yes	—

	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 ◁ C₄³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2862×C₁₃₁	C₂	semidirect
5. #2085×C₁₃₁	C₂	semidirect
7. #1988×C₁₃₁	C₂	semidirect
8. #1987×C₁₃₁	C₂	semidirect
9. #1831×C₁₃₁	C₂	semidirect
189. #29865	C₁₃₁	direct (N × H)
190. C₁₃₁	#29865	direct (N × H)
193. #2862	C₂×C₁₃₁	semidirect
195. #2085	C₂×C₁₃₁	semidirect
197. #1988	C₂×C₁₃₁	semidirect
198. #1987	C₂×C₁₃₁	semidirect
199. #1831	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#476×C₁₃₁	2
C₂×#474×C₁₃₁	2
#2862×C₁₃₁	2
#2293×C₁₃₁	2
#2085×C₁₃₁	2
#2073×C₁₃₁	2
#1988×C₁₃₁	2
#1987×C₁₃₁	2
#1831×C₁₃₁	2
#29865	131

Subgroups — C131×#29865 #45715749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29865 #45715749