Subgroups — C₁₃₁×#23129 #45709013

Order 33536.

866 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#467×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2362×C₁₃₁	C₂	1	2	yes	maximal
3	#1933×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#1918×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1878×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1873×C₁₃₁	C₂	1	2	yes	maximal
7	C₄×#103×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#1735×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
14	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
15	#467×C₁₃₁	C₄	1	8	yes	complemented
16	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
22	#391×C₁₃₁	C₂²	1	2	yes	—
23	#389×C₁₃₁	C₂²	1	2	yes	—
24	#388×C₁₃₁	—	2	2	no	—
25	#388×C₁₃₁	—	2	2	no	—
26	#387×C₁₃₁	—	2	2	no	—
27	C₄×C₄⋊C₄×C₁₃₁	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
30	#340×C₁₃₁	C₂²	1	1	yes	characteristic
31	#340×C₁₃₁	C₂²	1	2	yes	—
32	#340×C₁₃₁	C₂²	1	1	yes	characteristic
33	#340×C₁₃₁	C₂²	1	2	yes	—
34	#340×C₁₃₁	C₂²	1	2	yes	—
35	#336×C₁₃₁	C₂²	1	2	yes	—
36	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
38	C₂×Q₁₆×C₁₃₁	—	4	2	no	—
39	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₁₃₁	—	4	2	no	—
41	C₂²×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
42	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
46	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	—
47	C₄×Q₈×C₁₃₁	—	2	4	no	—
48	C₄×Q₈×C₁₃₁	—	4	2	no	—
49	#117×C₁₃₁	—	2	4	no	—
50	#117×C₁₃₁	—	4	2	no	—
51	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
60	C₂×C₄²×C₁₃₁	—	2	2	no	—
61	C₂×C₄²×C₁₃₁	—	2	2	no	—
62	C₂×C₄²×C₁₃₁	—	2	2	no	—
63	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
64	#107×C₁₃₁	C₂×C₄	1	4	yes	—
65	#103×C₁₃₁	—	2	4	no	—
66	#103×C₁₃₁	—	4	2	no	—
67	#103×C₁₃₁	C₂×C₄	1	8	yes	—
68	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
69	C₄×C₈×C₁₃₁	—	4	2	no	—
70	#95×C₁₃₁	—	2	2	no	—
71	#95×C₁₃₁	—	2	2	no	—
72	#95×C₁₃₁	—	2	2	no	—
73	#95×C₁₃₁	—	2	2	no	—
74	#95×C₁₃₁	D₄	1	1	yes	characteristic
75	#95×C₁₃₁	D₄	1	1	yes	characteristic
76	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₃₁	—	2	2	no	—
78	C₂×Q₈×C₁₃₁	—	2	2	no	—
79	C₂×Q₈×C₁₃₁	—	2	2	no	—
80	C₂×Q₈×C₁₃₁	—	2	2	no	—
81	C₂×Q₈×C₁₃₁	—	2	2	no	—
82	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₃₁	—	2	2	no	—
84	C₂²×C₄×C₁₃₁	—	2	2	no	—
85	C₂²×C₄×C₁₃₁	—	2	2	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	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
94	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
95	Q₁₆×C₁₃₁	—	4	4	no	—
96	C₂×C₈×C₁₃₁	—	2	2	no	—
97	C₂×C₈×C₁₃₁	—	2	2	no	—
98	C₂×C₈×C₁₃₁	—	2	2	no	—
99	C₂×C₈×C₁₃₁	—	2	2	no	—
100	C₂×C₈×C₁₃₁	—	2	2	no	—
101	C₂×C₈×C₁₃₁	—	4	4	no	—
102	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
104	C₄⋊C₄×C₁₃₁	—	2	8	no	—
105	C₄⋊C₄×C₁₃₁	—	2	2	no	—
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	—	4	4	no	—
110	C₄⋊C₄×C₁₃₁	—	4	4	no	—
111	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
112	C₄⋊C₄×C₁₃₁	#41	1	4	yes	—
113	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
114	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
115	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
116	C₄²×C₁₃₁	—	2	2	no	—
117	C₄²×C₁₃₁	—	2	2	no	—
118	C₄²×C₁₃₁	—	4	4	no	—
119	C₄²×C₁₃₁	—	4	4	no	—
120	C₄²×C₁₃₁	—	4	4	no	—
121	C₂³×C₁₃₁	—	2	2	no	—
122	C₂³×C₁₃₁	—	2	2	no	—
123	C₂³×C₁₃₁	—	2	1	no	—
124	C₂³×C₁₃₁	—	2	1	no	—
125	C₂³×C₁₃₁	C₄×D₄	1	2	yes	—
126	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₁₃₁	—	2	4	no	—
128	Q₈×C₁₃₁	—	2	4	no	—
129	Q₈×C₁₃₁	—	4	2	no	—
130	Q₈×C₁₃₁	—	4	2	no	—
131	C₂×C₄×C₁₃₁	—	2	2	no	—
132	C₂×C₄×C₁₃₁	—	2	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	4	no	—
137	C₂×C₄×C₁₃₁	—	2	4	no	—
138	C₂×C₄×C₁₃₁	—	2	4	no	—
139	C₂×C₄×C₁₃₁	—	2	2	no	—
140	C₂×C₄×C₁₃₁	—	2	4	no	—
141	C₂×C₄×C₁₃₁	—	2	2	no	—
142	C₂×C₄×C₁₃₁	—	2	2	no	—
143	C₂×C₄×C₁₃₁	—	4	2	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	2	no	—
152	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₃₁	#135	1	4	yes	—
154	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
156	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
158	C₈×C₁₃₁	—	2	2	no	—
159	C₈×C₁₃₁	—	2	2	no	—
160	C₈×C₁₃₁	—	4	2	no	—
161	C₂²×C₁₃₁	—	2	2	no	—
162	C₂²×C₁₃₁	—	2	2	no	—
163	C₂²×C₁₃₁	—	2	2	no	—
164	C₂²×C₁₃₁	—	4	2	no	—
165	C₂²×C₁₃₁	—	4	2	no	—
166	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
167	C₂²×C₁₃₁	#546	1	2	yes	—
168	C₂²×C₁₃₁	C₂×#135	1	2	yes	—
169	C₂²×C₁₃₁	#578	1	1	yes	characteristic
170	C₂²×C₁₃₁	#578	1	1	yes	characteristic
171	C₄×C₁₃₁	—	2	2	no	—
172	C₄×C₁₃₁	—	2	4	no	—
173	C₄×C₁₃₁	—	4	4	no	—
174	C₄×C₁₃₁	—	4	4	no	—
175	C₄×C₁₃₁	—	4	2	no	—
176	C₄×C₁₃₁	—	4	4	no	—
177	C₄×C₁₃₁	—	8	2	no	—
178	C₄×C₁₃₁	C₄×#41	1	1	yes	characteristic
179	C₄×C₁₃₁	#518	1	1	yes	characteristic
180	C₄×C₁₃₁	#553	1	2	yes	—
181	C₂×C₁₃₁	—	4	2	no	—
182	C₂×C₁₃₁	#2364	1	1	yes	characteristic
183	C₂×C₁₃₁	C₄×#135	1	1	yes	characteristic
184	C₂×C₁₃₁	#2950	1	1	yes	characteristic
185	C₂×C₁₃₁	#3300	1	2	yes	—
186	C₂×C₁₃₁	#3302	1	2	yes	—
187	#23129	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃₁	#23129	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#467	C₂×C₁₃₁	1	1	yes	characteristic
190	#2362	C₂×C₁₃₁	1	2	yes	—
191	#1933	C₂×C₁₃₁	1	2	yes	complemented
192	#1918	C₂×C₁₃₁	1	2	yes	complemented
193	#1878	C₂×C₁₃₁	1	2	yes	complemented
194	#1873	C₂×C₁₃₁	1	2	yes	—
195	C₄×#103	C₂×C₁₃₁	1	2	yes	complemented
196	C₈×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic
197	#1735	C₂×C₁₃₁	1	1	yes	characteristic
198	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
199	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
200	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
201	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
202	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
203	#467	C₄×C₁₃₁	1	8	yes	complemented
204	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
205	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
206	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
207	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
208	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
210	#391	C₂²×C₁₃₁	1	2	yes	—
211	#389	C₂²×C₁₃₁	1	2	yes	—
212	#388	—	2	2	no	—
213	#388	—	2	2	no	—
214	#387	—	2	2	no	—
215	C₄×C₄⋊C₄	—	2	2	no	—
216	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
217	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
218	#340	C₂²×C₁₃₁	1	2	yes	—
219	#340	C₂²×C₁₃₁	1	2	yes	—
220	#340	C₂²×C₁₃₁	1	2	yes	—
221	#340	C₂²×C₁₃₁	1	1	yes	characteristic
222	#340	C₂²×C₁₃₁	1	1	yes	characteristic
223	#336	C₂²×C₁₃₁	1	2	yes	—
224	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
225	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
226	C₂×Q₁₆	—	4	2	no	—
227	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
228	C₂²×C₈	—	4	2	no	—
229	C₂²×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
230	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
233	C₂²⋊Q₈	—	2	4	no	—
234	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	—
235	C₄×Q₈	—	2	4	no	—
236	C₄×Q₈	—	4	2	no	—
237	#117	—	2	4	no	—
238	#117	—	4	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
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	2	yes	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
252	#107	C₂×C₄×C₁₃₁	1	4	yes	—
253	#103	—	2	4	no	—
254	#103	—	4	2	no	—
255	#103	C₂×C₄×C₁₃₁	1	8	yes	—
256	C₂²⋊C₈	—	2	2	no	—
257	C₄×C₈	—	4	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	D₄×C₁₃₁	1	1	yes	characteristic
263	#95	D₄×C₁₃₁	1	1	yes	characteristic
264	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
281	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
282	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
283	Q₁₆	—	4	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
291	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
292	C₄⋊C₄	—	2	8	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	4	no	—
299	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
300	C₄⋊C₄	#41×C₁₃₁	1	4	yes	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	4	4	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	4	4	no	—
307	C₄²	—	4	4	no	—
308	C₄²	—	4	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	C₄×D₄×C₁₃₁	1	2	yes	—
314	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
315	Q₈	—	2	4	no	—
316	Q₈	—	2	4	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	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	C₄×D₄×C₁₃₁	1	2	yes	—
341	C₂×C₄	#135×C₁₃₁	1	4	yes	—
342	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
344	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
345	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
346	C₈	—	2	2	no	—
347	C₈	—	2	2	no	—
348	C₈	—	4	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
355	C₂²	#546×C₁₃₁	1	2	yes	—
356	C₂²	C₂×#135×C₁₃₁	1	2	yes	—
357	C₂²	#578×C₁₃₁	1	1	yes	characteristic
358	C₂²	#578×C₁₃₁	1	1	yes	characteristic
359	C₄	—	2	4	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	4	no	—
363	C₄	—	4	4	no	—
364	C₄	—	4	4	no	—
365	C₄	—	8	2	no	—
366	C₄	C₄×#41×C₁₃₁	1	1	yes	characteristic
367	C₄	#518×C₁₃₁	1	1	yes	characteristic
368	C₄	#553×C₁₃₁	1	2	yes	—
369	C₂	—	4	2	no	—
370	C₂	#2364×C₁₃₁	1	1	yes	characteristic
371	C₂	C₄×#135×C₁₃₁	1	1	yes	characteristic
372	C₂	#2950×C₁₃₁	1	1	yes	characteristic
373	C₂	#3300×C₁₃₁	1	2	yes	—
374	C₂	#3302×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	C₂⁴×C₁₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄×C₂²⋊C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1933×C₁₃₁	C₂	semidirect
4. #1918×C₁₃₁	C₂	semidirect
5. #1878×C₁₃₁	C₂	semidirect
7. C₄×#103×C₁₃₁	C₂	semidirect
15. #467×C₁₃₁	C₄	semidirect
187. #23129	C₁₃₁	direct (N × H)
188. C₁₃₁	#23129	direct (N × H)
191. #1933	C₂×C₁₃₁	semidirect
192. #1918	C₂×C₁₃₁	semidirect
193. #1878	C₂×C₁₃₁	semidirect
195. C₄×#103	C₂×C₁₃₁	semidirect
203. #467	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×#467×C₁₃₁	2
#2362×C₁₃₁	2
#1933×C₁₃₁	2
#1918×C₁₃₁	2
#1878×C₁₃₁	2
#1873×C₁₃₁	2
C₄×#103×C₁₃₁	2
C₈×C₂²⋊C₄×C₁₃₁	2
#1735×C₁₃₁	2
#23129	131

Subgroups — C131×#23129 #45709013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#23129 #45709013