Subgroups — C₁₃₁×#33284 #45719168

Order 33536.

718 conjugacy classes of subgroups.

The subgroup lattice has 400 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	#2641×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1992×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#1991×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1961×C₁₃₁	C₂	1	1	yes	maximal, characteristic
6	#1957×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1936×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1936×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1934×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#1934×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1726×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
15	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
16	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
17	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×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	#394×C₁₃₁	—	2	2	no	—
27	#394×C₁₃₁	—	2	2	no	—
28	#390×C₁₃₁	C₂²	1	2	yes	—
29	#390×C₁₃₁	C₂²	1	2	yes	—
30	#389×C₁₃₁	C₂²	1	2	yes	—
31	#389×C₁₃₁	C₂²	1	2	yes	—
32	#384×C₁₃₁	C₂²	1	1	yes	characteristic
33	#382×C₁₃₁	C₂²	1	1	yes	characteristic
34	#376×C₁₃₁	C₂²	1	1	yes	characteristic
35	#340×C₁₃₁	C₂²	1	2	yes	—
36	#340×C₁₃₁	C₂²	1	2	yes	—
37	#340×C₁₃₁	C₂²	1	2	yes	—
38	#340×C₁₃₁	C₂²	1	2	yes	—
39	C₂²×D₄×C₁₃₁	—	2	2	no	—
40	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
45	#127×C₁₃₁	—	2	2	no	—
46	#127×C₁₃₁	—	2	2	no	—
47	#125×C₁₃₁	—	2	2	no	—
48	#125×C₁₃₁	—	2	2	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	2	yes	—
56	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
60	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
63	#102×C₁₃₁	—	2	4	no	—
64	#102×C₁₃₁	—	2	4	no	—
65	#102×C₁₃₁	—	2	4	no	—
66	#102×C₁₃₁	—	2	4	no	—
67	#97×C₁₃₁	—	2	2	no	—
68	#97×C₁₃₁	—	2	2	no	—
69	#97×C₁₃₁	—	2	2	no	—
70	C₄×C₈×C₁₃₁	—	2	2	no	—
71	C₄×C₈×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	D₄	1	2	yes	—
77	#95×C₁₃₁	D₄	1	2	yes	—
78	C₂⁴×C₁₃₁	—	2	2	no	—
79	C₂×D₄×C₁₃₁	—	2	2	no	—
80	C₂×D₄×C₁₃₁	—	2	2	no	—
81	C₂×D₄×C₁₃₁	—	2	2	no	—
82	C₂×D₄×C₁₃₁	—	2	2	no	—
83	C₂×D₄×C₁₃₁	—	2	2	no	—
84	C₂×D₄×C₁₃₁	—	2	2	no	—
85	C₂×D₄×C₁₃₁	—	4	4	no	—
86	C₂×D₄×C₁₃₁	—	8	2	no	—
87	C₂×D₄×C₁₃₁	—	8	2	no	—
88	C₂²×C₄×C₁₃₁	—	2	2	no	—
89	C₂²×C₄×C₁₃₁	—	2	2	no	—
90	C₂²×C₄×C₁₃₁	—	2	2	no	—
91	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
95	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₁₃₁	—	2	1	no	—
97	C₂×C₈×C₁₃₁	—	2	1	no	—
98	C₂×C₈×C₁₃₁	—	2	1	no	—
99	C₂×C₈×C₁₃₁	—	2	1	no	—
100	C₂×C₈×C₁₃₁	—	2	1	no	—
101	C₂×C₈×C₁₃₁	—	2	1	no	—
102	C₂×C₈×C₁₃₁	—	2	1	no	—
103	C₂×C₈×C₁₃₁	—	2	1	no	—
104	C₂×C₈×C₁₃₁	#41	1	2	yes	—
105	C₂×C₈×C₁₃₁	#41	1	2	yes	—
106	C₂×C₈×C₁₃₁	#41	1	2	yes	—
107	C₂×C₈×C₁₃₁	#41	1	2	yes	—
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	—	2	2	no	—
113	C₄⋊C₄×C₁₃₁	—	2	2	no	—
114	C₄⋊C₄×C₁₃₁	—	4	4	no	—
115	C₄⋊C₄×C₁₃₁	—	8	2	no	—
116	C₄⋊C₄×C₁₃₁	—	8	2	no	—
117	C₄⋊C₄×C₁₃₁	—	8	2	no	—
118	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
119	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
120	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
121	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
122	C₄²×C₁₃₁	—	2	1	no	—
123	C₄²×C₁₃₁	—	2	1	no	—
124	C₄²×C₁₃₁	—	2	1	no	—
125	C₄²×C₁₃₁	—	2	1	no	—
126	C₄²×C₁₃₁	#41	1	2	yes	—
127	C₄²×C₁₃₁	#41	1	2	yes	—
128	C₂³×C₁₃₁	—	4	2	no	—
129	C₂³×C₁₃₁	—	4	2	no	—
130	C₂³×C₁₃₁	—	4	2	no	—
131	C₂³×C₁₃₁	—	4	2	no	—
132	C₂³×C₁₃₁	—	4	2	no	—
133	C₂³×C₁₃₁	—	4	2	no	—
134	C₂³×C₁₃₁	—	4	2	no	—
135	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₁₃₁	—	4	2	no	—
137	D₄×C₁₃₁	—	4	2	no	—
138	D₄×C₁₃₁	—	4	2	no	—
139	D₄×C₁₃₁	—	4	2	no	—
140	D₄×C₁₃₁	—	8	8	no	—
141	C₂×C₄×C₁₃₁	—	2	2	no	—
142	C₂×C₄×C₁₃₁	—	2	2	no	—
143	C₂×C₄×C₁₃₁	—	2	1	no	—
144	C₂×C₄×C₁₃₁	—	2	1	no	—
145	C₂×C₄×C₁₃₁	—	2	2	no	—
146	C₂×C₄×C₁₃₁	—	2	2	no	—
147	C₂×C₄×C₁₃₁	—	2	2	no	—
148	C₂×C₄×C₁₃₁	—	2	2	no	—
149	C₂×C₄×C₁₃₁	—	2	2	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	—	4	2	no	—
158	C₂×C₄×C₁₃₁	—	4	2	no	—
159	C₂×C₄×C₁₃₁	#124	1	4	yes	—
160	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
166	C₈×C₁₃₁	—	2	2	no	—
167	C₈×C₁₃₁	—	2	2	no	—
168	C₈×C₁₃₁	—	2	2	no	—
169	C₈×C₁₃₁	—	2	2	no	—
170	C₂²×C₁₃₁	—	8	2	no	—
171	C₂²×C₁₃₁	—	8	2	no	—
172	C₂²×C₁₃₁	—	8	2	no	—
173	C₂²×C₁₃₁	—	8	2	no	—
174	C₂²×C₁₃₁	—	8	2	no	—
175	C₂²×C₁₃₁	—	8	2	no	—
176	C₂²×C₁₃₁	—	8	2	no	—
177	C₂²×C₁₃₁	C₂×#124	1	1	yes	characteristic
178	C₂²×C₁₃₁	#532	1	1	yes	characteristic
179	C₂²×C₁₃₁	#532	1	1	yes	characteristic
180	C₂²×C₁₃₁	#576	1	2	yes	—
181	C₂²×C₁₃₁	#577	1	2	yes	—
182	C₄×C₁₃₁	—	2	4	no	—
183	C₄×C₁₃₁	—	4	1	no	—
184	C₄×C₁₃₁	—	4	1	no	—
185	C₄×C₁₃₁	—	4	2	no	—
186	C₄×C₁₃₁	—	8	2	no	—
187	C₄×C₁₃₁	—	8	2	no	—
188	C₄×C₁₃₁	—	8	2	no	—
189	C₄×C₁₃₁	#529	1	1	yes	characteristic
190	C₄×C₁₃₁	#529	1	1	yes	characteristic
191	C₄×C₁₃₁	#529	1	1	yes	characteristic
192	C₄×C₁₃₁	#529	1	1	yes	characteristic
193	C₂×C₁₃₁	—	16	2	no	—
194	C₂×C₁₃₁	#2861	1	1	yes	characteristic
195	C₂×C₁₃₁	#3136	1	2	yes	—
196	C₂×C₁₃₁	#3174	1	1	yes	characteristic
197	C₂×C₁₃₁	#3176	1	1	yes	characteristic
198	C₂×C₁₃₁	#3179	1	2	yes	—
199	#33284	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₁₃₁	#33284	1	1	yes	characteristic, direct product factor, Sylow
201	#2647	C₂×C₁₃₁	1	1	yes	characteristic, complemented
202	#2641	C₂×C₁₃₁	1	1	yes	characteristic
203	#1992	C₂×C₁₃₁	1	1	yes	characteristic, complemented
204	#1991	C₂×C₁₃₁	1	1	yes	characteristic, complemented
205	#1961	C₂×C₁₃₁	1	1	yes	characteristic
206	#1957	C₂×C₁₃₁	1	1	yes	characteristic
207	#1936	C₂×C₁₃₁	1	2	yes	complemented
208	#1936	C₂×C₁₃₁	1	2	yes	complemented
209	#1934	C₂×C₁₃₁	1	2	yes	complemented
210	#1934	C₂×C₁₃₁	1	2	yes	complemented
211	#1726	C₂×C₁₃₁	1	1	yes	characteristic, complemented
212	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
213	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
214	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
215	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
216	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
217	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
218	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
219	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
220	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
224	#400	—	2	2	no	—
225	#398	—	2	2	no	—
226	#394	—	2	2	no	—
227	#394	—	2	2	no	—
228	#390	C₂²×C₁₃₁	1	2	yes	—
229	#390	C₂²×C₁₃₁	1	2	yes	—
230	#389	C₂²×C₁₃₁	1	2	yes	—
231	#389	C₂²×C₁₃₁	1	2	yes	—
232	#384	C₂²×C₁₃₁	1	1	yes	characteristic
233	#382	C₂²×C₁₃₁	1	1	yes	characteristic
234	#376	C₂²×C₁₃₁	1	1	yes	characteristic
235	#340	C₂²×C₁₃₁	1	2	yes	—
236	#340	C₂²×C₁₃₁	1	2	yes	—
237	#340	C₂²×C₁₃₁	1	2	yes	—
238	#340	C₂²×C₁₃₁	1	2	yes	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
245	#127	—	2	2	no	—
246	#127	—	2	2	no	—
247	#125	—	2	2	no	—
248	#125	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
263	#102	—	2	4	no	—
264	#102	—	2	4	no	—
265	#102	—	2	4	no	—
266	#102	—	2	4	no	—
267	#97	—	2	2	no	—
268	#97	—	2	2	no	—
269	#97	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	D₄×C₁₃₁	1	2	yes	—
277	#95	D₄×C₁₃₁	1	2	yes	—
278	C₂⁴	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	4	4	no	—
286	C₂×D₄	—	8	2	no	—
287	C₂×D₄	—	8	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
295	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	#41×C₁₃₁	1	2	yes	—
305	C₂×C₈	#41×C₁₃₁	1	2	yes	—
306	C₂×C₈	#41×C₁₃₁	1	2	yes	—
307	C₂×C₈	#41×C₁₃₁	1	2	yes	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	8	2	no	—
316	C₄⋊C₄	—	8	2	no	—
317	C₄⋊C₄	—	8	2	no	—
318	C₂²⋊C₄	—	8	2	no	—
319	C₂²⋊C₄	—	8	2	no	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	#41×C₁₃₁	1	2	yes	—
327	C₄²	#41×C₁₃₁	1	2	yes	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	8	8	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	#124×C₁₃₁	1	4	yes	—
360	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
363	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
364	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
366	C₈	—	2	2	no	—
367	C₈	—	2	2	no	—
368	C₈	—	2	2	no	—
369	C₈	—	2	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	C₂×#124×C₁₃₁	1	1	yes	characteristic
378	C₂²	#532×C₁₃₁	1	1	yes	characteristic
379	C₂²	#532×C₁₃₁	1	1	yes	characteristic
380	C₂²	#576×C₁₃₁	1	2	yes	—
381	C₂²	#577×C₁₃₁	1	2	yes	—
382	C₄	—	2	4	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	2	no	—
389	C₄	#529×C₁₃₁	1	1	yes	characteristic
390	C₄	#529×C₁₃₁	1	1	yes	characteristic
391	C₄	#529×C₁₃₁	1	1	yes	characteristic
392	C₄	#529×C₁₃₁	1	1	yes	characteristic
393	C₂	—	16	2	no	—
394	C₂	#2861×C₁₃₁	1	1	yes	characteristic
395	C₂	#3136×C₁₃₁	1	2	yes	—
396	C₂	#3174×C₁₃₁	1	1	yes	characteristic
397	C₂	#3176×C₁₃₁	1	1	yes	characteristic
398	C₂	#3179×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#127×C₁₃₁	C₂²
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. #1992×C₁₃₁	C₂	semidirect
4. #1991×C₁₃₁	C₂	semidirect
7. #1936×C₁₃₁	C₂	semidirect
8. #1936×C₁₃₁	C₂	semidirect
9. #1934×C₁₃₁	C₂	semidirect
10. #1934×C₁₃₁	C₂	semidirect
11. #1726×C₁₃₁	C₂	semidirect
199. #33284	C₁₃₁	direct (N × H)
200. C₁₃₁	#33284	direct (N × H)
201. #2647	C₂×C₁₃₁	semidirect
203. #1992	C₂×C₁₃₁	semidirect
204. #1991	C₂×C₁₃₁	semidirect
207. #1936	C₂×C₁₃₁	semidirect
208. #1936	C₂×C₁₃₁	semidirect
209. #1934	C₂×C₁₃₁	semidirect
210. #1934	C₂×C₁₃₁	semidirect
211. #1726	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
#2641×C₁₃₁	2
#1992×C₁₃₁	2
#1991×C₁₃₁	2
#1961×C₁₃₁	2
#1957×C₁₃₁	2
#1936×C₁₃₁	2
#1934×C₁₃₁	2
#1726×C₁₃₁	2
#33284	131

Subgroups — C131×#33284 #45719168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33284 #45719168