Subgroups — C₁₃₁×#29874 #45715758

Order 33536.

708 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#478×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#476×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2660×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2319×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2085×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2084×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2073×C₁₃₁	C₂	1	2	yes	maximal
8	#2071×C₁₃₁	C₂	1	2	yes	maximal
9	#1989×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1988×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1832×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
15	#478×C₁₃₁	—	2	4	no	—
16	#476×C₁₃₁	—	2	4	no	—
17	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
25	#398×C₁₃₁	—	2	1	no	—
26	#398×C₁₃₁	—	2	1	no	—
27	#395×C₁₃₁	—	2	2	no	—
28	#390×C₁₃₁	C₂²	1	2	yes	—
29	#389×C₁₃₁	C₂²	1	2	yes	—
30	#388×C₁₃₁	—	2	2	no	—
31	#384×C₁₃₁	C₂²	1	2	yes	—
32	#382×C₁₃₁	C₂²	1	2	yes	—
33	#381×C₁₃₁	—	2	1	no	—
34	#380×C₁₃₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
36	#376×C₁₃₁	C₂²	1	1	yes	characteristic
37	#340×C₁₃₁	C₂²	1	2	yes	—
38	#340×C₁₃₁	C₂²	1	2	yes	—
39	#340×C₁₃₁	C₂²	1	2	yes	—
40	#340×C₁₃₁	C₂²	1	2	yes	—
41	#336×C₁₃₁	C₂²	1	2	yes	—
42	#336×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₁	—	2	1	no	—
44	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₁	—	2	1	no	—
46	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
50	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
51	#125×C₁₃₁	—	2	2	no	—
52	#125×C₁₃₁	—	2	2	no	—
53	C₄×D₄×C₁₃₁	—	2	2	no	—
54	C₄×D₄×C₁₃₁	D₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
69	C₂×C₄²×C₁₃₁	—	2	1	no	—
70	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
72	#107×C₁₃₁	—	2	2	no	—
73	#106×C₁₃₁	—	2	4	no	—
74	#106×C₁₃₁	—	2	2	no	—
75	C₄⋊C₈×C₁₃₁	—	2	2	no	—
76	C₄⋊C₈×C₁₃₁	—	2	2	no	—
77	#102×C₁₃₁	—	2	4	no	—
78	#102×C₁₃₁	—	2	2	no	—
79	#102×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	D₄	1	2	yes	—
85	#95×C₁₃₁	D₄	1	1	yes	characteristic
86	#95×C₁₃₁	D₄	1	1	yes	characteristic
87	C₂⁴×C₁₃₁	—	2	1	no	—
88	C₂×Q₈×C₁₃₁	—	4	2	no	—
89	C₂×Q₈×C₁₃₁	—	8	1	no	—
90	C₂×Q₈×C₁₃₁	—	8	1	no	—
91	C₂×D₄×C₁₃₁	—	2	1	no	—
92	C₂×D₄×C₁₃₁	—	2	2	no	—
93	C₂×D₄×C₁₃₁	—	2	2	no	—
94	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₁	—	2	1	no	—
96	C₂²×C₄×C₁₃₁	—	2	4	no	—
97	C₂²×C₄×C₁₃₁	—	2	1	no	—
98	C₂²×C₄×C₁₃₁	—	2	2	no	—
99	C₂²×C₄×C₁₃₁	—	2	2	no	—
100	C₂²×C₄×C₁₃₁	—	2	1	no	—
101	C₂²×C₄×C₁₃₁	—	8	2	no	—
102	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₁₃₁	—	2	2	no	—
108	C₂×C₈×C₁₃₁	—	2	1	no	—
109	C₂×C₈×C₁₃₁	—	2	1	no	—
110	C₂×C₈×C₁₃₁	—	2	4	no	—
111	C₂×C₈×C₁₃₁	—	2	2	no	—
112	C₂×C₈×C₁₃₁	—	2	2	no	—
113	C₄⋊C₄×C₁₃₁	—	2	1	no	—
114	C₄⋊C₄×C₁₃₁	—	2	1	no	—
115	C₄⋊C₄×C₁₃₁	—	2	2	no	—
116	C₄⋊C₄×C₁₃₁	—	2	1	no	—
117	C₄⋊C₄×C₁₃₁	—	2	1	no	—
118	C₄⋊C₄×C₁₃₁	—	2	1	no	—
119	C₄⋊C₄×C₁₃₁	—	2	2	no	—
120	C₄⋊C₄×C₁₃₁	—	2	2	no	—
121	C₄⋊C₄×C₁₃₁	—	2	2	no	—
122	C₄⋊C₄×C₁₃₁	—	4	2	no	—
123	C₄⋊C₄×C₁₃₁	—	4	2	no	—
124	C₄⋊C₄×C₁₃₁	—	4	2	no	—
125	C₄⋊C₄×C₁₃₁	—	8	2	no	—
126	C₄⋊C₄×C₁₃₁	—	8	2	no	—
127	C₄⋊C₄×C₁₃₁	—	8	2	no	—
128	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
129	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
130	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
131	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
132	C₄²×C₁₃₁	—	2	2	no	—
133	C₄²×C₁₃₁	—	2	2	no	—
134	C₄²×C₁₃₁	—	8	1	no	—
135	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
136	C₄²×C₁₃₁	#41	1	2	yes	—
137	C₂³×C₁₃₁	—	2	2	no	—
138	C₂³×C₁₃₁	—	4	2	no	—
139	C₂³×C₁₃₁	—	4	1	no	—
140	C₂³×C₁₃₁	—	4	2	no	—
141	C₂³×C₁₃₁	—	4	1	no	—
142	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₁₃₁	—	8	4	no	—
144	D₄×C₁₃₁	—	2	2	no	—
145	D₄×C₁₃₁	—	2	2	no	—
146	D₄×C₁₃₁	—	4	2	no	—
147	C₂×C₄×C₁₃₁	—	2	1	no	—
148	C₂×C₄×C₁₃₁	—	2	2	no	—
149	C₂×C₄×C₁₃₁	—	2	1	no	—
150	C₂×C₄×C₁₃₁	—	2	2	no	—
151	C₂×C₄×C₁₃₁	—	2	2	no	—
152	C₂×C₄×C₁₃₁	—	2	2	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	—	4	2	no	—
158	C₂×C₄×C₁₃₁	—	4	1	no	—
159	C₂×C₄×C₁₃₁	—	4	1	no	—
160	C₂×C₄×C₁₃₁	—	4	2	no	—
161	C₂×C₄×C₁₃₁	—	4	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	2	no	—
166	C₂×C₄×C₁₃₁	—	4	1	no	—
167	C₂×C₄×C₁₃₁	—	4	2	no	—
168	C₂×C₄×C₁₃₁	—	4	2	no	—
169	C₂×C₄×C₁₃₁	—	8	4	no	—
170	C₂×C₄×C₁₃₁	#121	1	2	yes	—
171	C₂×C₄×C₁₃₁	#121	1	2	yes	—
172	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
175	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
176	C₈×C₁₃₁	—	4	2	no	—
177	C₈×C₁₃₁	—	4	1	no	—
178	C₈×C₁₃₁	—	4	1	no	—
179	C₂²×C₁₃₁	—	4	2	no	—
180	C₂²×C₁₃₁	—	4	2	no	—
181	C₂²×C₁₃₁	—	4	2	no	—
182	C₂²×C₁₃₁	—	8	2	no	—
183	C₂²×C₁₃₁	—	8	2	no	—
184	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
185	C₂²×C₁₃₁	#536	1	2	yes	—
186	C₂²×C₁₃₁	#576	1	1	yes	characteristic
187	C₂²×C₁₃₁	#577	1	2	yes	—
188	C₂²×C₁₃₁	#577	1	1	yes	characteristic
189	C₄×C₁₃₁	—	2	2	no	—
190	C₄×C₁₃₁	—	2	2	no	—
191	C₄×C₁₃₁	—	4	2	no	—
192	C₄×C₁₃₁	—	4	2	no	—
193	C₄×C₁₃₁	—	4	2	no	—
194	C₄×C₁₃₁	—	8	2	no	—
195	C₄×C₁₃₁	—	8	1	no	—
196	C₄×C₁₃₁	—	8	1	no	—
197	C₄×C₁₃₁	—	8	2	no	—
198	C₄×C₁₃₁	#536	1	1	yes	characteristic
199	C₄×C₁₃₁	#536	1	1	yes	characteristic
200	C₄×C₁₃₁	#541	1	2	yes	—
201	C₂×C₁₃₁	—	8	2	no	—
202	C₂×C₁₃₁	#2621	1	1	yes	characteristic
203	C₂×C₁₃₁	#3042	1	1	yes	characteristic
204	C₂×C₁₃₁	#3045	1	1	yes	characteristic
205	C₂×C₁₃₁	#3241	1	2	yes	—
206	C₂×C₁₃₁	#3244	1	2	yes	—
207	#29874	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₁₃₁	#29874	1	1	yes	characteristic, direct product factor, Sylow
209	C₂×#478	C₂×C₁₃₁	1	1	yes	characteristic
210	C₂×#476	C₂×C₁₃₁	1	1	yes	characteristic
211	#2660	C₂×C₁₃₁	1	1	yes	characteristic, complemented
212	#2319	C₂×C₁₃₁	1	1	yes	characteristic
213	#2085	C₂×C₁₃₁	1	2	yes	complemented
214	#2084	C₂×C₁₃₁	1	2	yes	complemented
215	#2073	C₂×C₁₃₁	1	2	yes	—
216	#2071	C₂×C₁₃₁	1	2	yes	—
217	#1989	C₂×C₁₃₁	1	1	yes	characteristic, complemented
218	#1988	C₂×C₁₃₁	1	1	yes	characteristic, complemented
219	#1832	C₂×C₁₃₁	1	1	yes	characteristic, complemented
220	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
221	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
223	#478	—	2	4	no	—
224	#476	—	2	4	no	—
225	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
226	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
227	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
228	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
230	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
231	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
232	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
233	#398	—	2	1	no	—
234	#398	—	2	1	no	—
235	#395	—	2	2	no	—
236	#390	C₂²×C₁₃₁	1	2	yes	—
237	#389	C₂²×C₁₃₁	1	2	yes	—
238	#388	—	2	2	no	—
239	#384	C₂²×C₁₃₁	1	2	yes	—
240	#382	C₂²×C₁₃₁	1	2	yes	—
241	#381	—	2	1	no	—
242	#380	—	2	1	no	—
243	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
244	#376	C₂²×C₁₃₁	1	1	yes	characteristic
245	#340	C₂²×C₁₃₁	1	2	yes	—
246	#340	C₂²×C₁₃₁	1	2	yes	—
247	#340	C₂²×C₁₃₁	1	2	yes	—
248	#340	C₂²×C₁₃₁	1	2	yes	—
249	#336	C₂²×C₁₃₁	1	2	yes	—
250	#336	C₂²×C₁₃₁	1	2	yes	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
253	C₂³×C₄	—	2	1	no	—
254	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
257	C₄⋊Q₈	—	2	2	no	—
258	C₄⋊Q₈	—	2	2	no	—
259	#125	—	2	2	no	—
260	#125	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	D₄×C₁₃₁	1	4	yes	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
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	—	2	2	no	—
269	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	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	2	no	—
281	#106	—	2	4	no	—
282	#106	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	#102	—	2	4	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	#95	—	2	1	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	D₄×C₁₃₁	1	1	yes	characteristic
293	#95	D₄×C₁₃₁	1	1	yes	characteristic
294	#95	D₄×C₁₃₁	1	2	yes	—
295	C₂⁴	—	2	1	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	8	1	no	—
298	C₂×Q₈	—	8	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₄⋊C₄	—	8	2	no	—
335	C₄⋊C₄	—	8	2	no	—
336	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	8	2	no	—
339	C₂²⋊C₄	—	8	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	8	1	no	—
343	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
344	C₄²	#41×C₁₃₁	1	2	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	1	no	—
350	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
351	Q₈	—	8	4	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	4	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	4	no	—
378	C₂×C₄	#121×C₁₃₁	1	2	yes	—
379	C₂×C₄	#121×C₁₃₁	1	2	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
382	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
383	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
384	C₈	—	4	2	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
393	C₂²	#536×C₁₃₁	1	2	yes	—
394	C₂²	#576×C₁₃₁	1	1	yes	characteristic
395	C₂²	#577×C₁₃₁	1	2	yes	—
396	C₂²	#577×C₁₃₁	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	8	2	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	1	no	—
406	C₄	#536×C₁₃₁	1	1	yes	characteristic
407	C₄	#536×C₁₃₁	1	1	yes	characteristic
408	C₄	#541×C₁₃₁	1	2	yes	—
409	C₂	—	8	2	no	—
410	C₂	#2621×C₁₃₁	1	1	yes	characteristic
411	C₂	#3042×C₁₃₁	1	1	yes	characteristic
412	C₂	#3045×C₁₃₁	1	1	yes	characteristic
413	C₂	#3241×C₁₃₁	1	2	yes	—
414	C₂	#3244×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 ◁ #376×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2660×C₁₃₁	C₂	semidirect
5. #2085×C₁₃₁	C₂	semidirect
6. #2084×C₁₃₁	C₂	semidirect
9. #1989×C₁₃₁	C₂	semidirect
10. #1988×C₁₃₁	C₂	semidirect
11. #1832×C₁₃₁	C₂	semidirect
207. #29874	C₁₃₁	direct (N × H)
208. C₁₃₁	#29874	direct (N × H)
211. #2660	C₂×C₁₃₁	semidirect
213. #2085	C₂×C₁₃₁	semidirect
214. #2084	C₂×C₁₃₁	semidirect
217. #1989	C₂×C₁₃₁	semidirect
218. #1988	C₂×C₁₃₁	semidirect
219. #1832	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×#478×C₁₃₁	2
C₂×#476×C₁₃₁	2
#2660×C₁₃₁	2
#2319×C₁₃₁	2
#2085×C₁₃₁	2
#2084×C₁₃₁	2
#2073×C₁₃₁	2
#2071×C₁₃₁	2
#1989×C₁₃₁	2
#1988×C₁₃₁	2
#1832×C₁₃₁	2
#29874	131

Subgroups — C131×#29874 #45715758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29874 #45715758