Subgroups — C₁₃₁×#33737 #45719621

Order 33536.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3169×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3168×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2255×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2250×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2244×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2243×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2220×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2218×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	C₄×SD₃₂×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	C₄×D₁₆×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	C₄×M₃₂×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#532×C₁₃₁	—	2	1	no	—
13	#529×C₁₃₁	—	2	1	no	—
14	C₂×SD₃₂×C₁₃₁	C₂²	1	2	yes	—
15	C₂×D₁₆×C₁₃₁	C₂²	1	2	yes	—
16	C₂×M₃₂×C₁₃₁	C₂²	1	2	yes	—
17	#500×C₁₃₁	C₂²	1	1	yes	characteristic
18	#499×C₁₃₁	C₂²	1	1	yes	characteristic
19	#495×C₁₃₁	C₂²	1	1	yes	characteristic
20	#493×C₁₃₁	C₂²	1	1	yes	characteristic
21	#488×C₁₃₁	—	2	1	no	—
22	#486×C₁₃₁	—	2	1	no	—
23	#467×C₁₃₁	C₂²	1	1	yes	characteristic
24	#466×C₁₃₁	—	2	1	no	—
25	#466×C₁₃₁	C₂²	1	1	yes	characteristic
26	#466×C₁₃₁	C₂²	1	2	yes	—
27	#465×C₁₃₁	—	2	1	no	—
28	C₄×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₄×SD₁₆×C₁₃₁	—	2	1	no	—
30	C₄×D₈×C₁₃₁	—	2	1	no	—
31	C₄×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₁₃₁	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
34	#367×C₁₃₁	C₂²	1	2	yes	—
35	#366×C₁₃₁	C₂²	1	2	yes	—
36	#358×C₁₃₁	C₂²	1	2	yes	—
37	#357×C₁₃₁	C₂²	1	2	yes	—
38	#357×C₁₃₁	C₂²	1	2	yes	—
39	#357×C₁₃₁	C₂²	1	2	yes	—
40	#346×C₁₃₁	C₂²	1	1	yes	characteristic
41	#346×C₁₃₁	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₁₃₁	C₂²	1	2	yes	—
43	C₂×#41×C₁₃₁	—	4	1	no	—
44	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
46	C₂×D₈×C₁₃₁	—	2	1	no	—
47	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
48	C₂×D₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
52	#127×C₁₃₁	—	2	1	no	—
53	#126×C₁₃₁	—	4	1	no	—
54	#125×C₁₃₁	—	2	1	no	—
55	#124×C₁₃₁	—	2	1	no	—
56	#124×C₁₃₁	—	4	1	no	—
57	#123×C₁₃₁	—	4	1	no	—
58	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
59	#121×C₁₃₁	—	2	1	no	—
60	#121×C₁₃₁	—	2	2	no	—
61	#121×C₁₃₁	—	4	1	no	—
62	C₄×Q₈×C₁₃₁	—	2	1	no	—
63	C₄×D₄×C₁₃₁	—	2	2	no	—
64	C₄×D₄×C₁₃₁	—	2	1	no	—
65	C₄×D₄×C₁₃₁	—	4	1	no	—
66	C₄×D₄×C₁₃₁	—	4	1	no	—
67	#117×C₁₃₁	—	4	1	no	—
68	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
69	SD₃₂×C₁₃₁	—	2	4	no	—
70	D₁₆×C₁₃₁	—	2	4	no	—
71	M₃₂×C₁₃₁	—	2	4	no	—
72	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
73	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
74	#107×C₁₃₁	—	2	1	no	—
75	#107×C₁₃₁	C₂³	1	2	yes	—
76	#107×C₁₃₁	C₂³	1	1	yes	characteristic
77	#107×C₁₃₁	C₂³	1	1	yes	characteristic
78	#106×C₁₃₁	—	2	1	no	—
79	#103×C₁₃₁	—	2	1	no	—
80	#103×C₁₃₁	—	2	1	no	—
81	#102×C₁₃₁	—	2	2	no	—
82	#102×C₁₃₁	—	2	1	no	—
83	#102×C₁₃₁	—	2	2	no	—
84	#102×C₁₃₁	—	2	1	no	—
85	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
86	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
89	#41×C₁₃₁	—	8	4	no	—
90	C₂×Q₈×C₁₃₁	—	2	1	no	—
91	C₂×Q₈×C₁₃₁	—	4	1	no	—
92	C₂×D₄×C₁₃₁	—	2	1	no	—
93	C₂×D₄×C₁₃₁	—	2	2	no	—
94	C₂×D₄×C₁₃₁	—	4	1	no	—
95	C₂×D₄×C₁₃₁	—	4	2	no	—
96	C₂×D₄×C₁₃₁	—	4	1	no	—
97	C₂×D₄×C₁₃₁	—	4	1	no	—
98	C₂²×C₄×C₁₃₁	—	4	1	no	—
99	C₂²×C₄×C₁₃₁	—	4	2	no	—
100	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
103	Q₁₆×C₁₃₁	—	2	2	no	—
104	SD₁₆×C₁₃₁	—	4	2	no	—
105	D₈×C₁₃₁	—	2	2	no	—
106	D₈×C₁₃₁	—	2	2	no	—
107	D₈×C₁₃₁	—	2	2	no	—
108	D₈×C₁₃₁	—	4	2	no	—
109	C₂×C₈×C₁₃₁	—	2	2	no	—
110	C₂×C₈×C₁₃₁	—	2	2	no	—
111	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
119	C₄⋊C₄×C₁₃₁	—	4	1	no	—
120	C₄⋊C₄×C₁₃₁	—	4	1	no	—
121	C₄⋊C₄×C₁₃₁	—	4	1	no	—
122	C₄⋊C₄×C₁₃₁	—	4	1	no	—
123	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
124	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
125	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
126	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
127	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
128	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
129	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
130	C₄²×C₁₃₁	—	4	1	no	—
131	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
132	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
133	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
135	C₁₆×C₁₃₁	—	2	2	no	—
136	C₁₆×C₁₃₁	#41	1	4	yes	complemented
137	C₂³×C₁₃₁	—	4	1	no	—
138	C₂³×C₁₃₁	—	4	2	no	—
139	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
140	Q₈×C₁₃₁	—	4	1	no	—
141	Q₈×C₁₃₁	—	4	1	no	—
142	Q₈×C₁₃₁	—	8	2	no	—
143	D₄×C₁₃₁	—	4	1	no	—
144	D₄×C₁₃₁	—	4	2	no	—
145	D₄×C₁₃₁	—	4	2	no	—
146	D₄×C₁₃₁	—	4	1	no	—
147	D₄×C₁₃₁	—	8	2	no	—
148	D₄×C₁₃₁	—	8	2	no	—
149	D₄×C₁₃₁	—	8	2	no	—
150	D₄×C₁₃₁	—	8	4	no	—
151	C₂×C₄×C₁₃₁	—	2	1	no	—
152	C₂×C₄×C₁₃₁	—	2	1	no	—
153	C₂×C₄×C₁₃₁	—	2	2	no	—
154	C₂×C₄×C₁₃₁	—	4	1	no	—
155	C₂×C₄×C₁₃₁	—	4	1	no	—
156	C₂×C₄×C₁₃₁	—	4	1	no	—
157	C₂×C₄×C₁₃₁	—	4	1	no	—
158	C₂×C₄×C₁₃₁	—	4	2	no	—
159	C₂×C₄×C₁₃₁	—	8	2	no	—
160	C₂×C₄×C₁₃₁	—	8	4	no	—
161	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
167	C₈×C₁₃₁	—	2	1	no	—
168	C₈×C₁₃₁	—	2	1	no	—
169	C₈×C₁₃₁	#135	1	2	yes	—
170	C₈×C₁₃₁	C₂×#41	1	2	yes	—
171	C₂²×C₁₃₁	—	2	1	no	—
172	C₂²×C₁₃₁	—	2	1	no	—
173	C₂²×C₁₃₁	—	2	1	no	—
174	C₂²×C₁₃₁	—	8	2	no	—
175	C₂²×C₁₃₁	—	8	1	no	—
176	C₂²×C₁₃₁	—	8	2	no	—
177	C₂²×C₁₃₁	—	8	1	no	—
178	C₂²×C₁₃₁	—	8	2	no	—
179	C₂²×C₁₃₁	—	8	1	no	—
180	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
181	C₄×C₁₃₁	—	2	1	no	—
182	C₄×C₁₃₁	—	2	1	no	—
183	C₄×C₁₃₁	—	2	1	no	—
184	C₄×C₁₃₁	—	2	1	no	—
185	C₄×C₁₃₁	—	8	1	no	—
186	C₄×C₁₃₁	—	8	2	no	—
187	C₄×C₁₃₁	—	8	1	no	—
188	C₄×C₁₃₁	—	8	1	no	—
189	C₄×C₁₃₁	#509	1	2	yes	—
190	C₄×C₁₃₁	#532	1	1	yes	characteristic
191	C₄×C₁₃₁	C₂×#135	1	1	yes	characteristic
192	C₂×C₁₃₁	—	4	1	no	—
193	C₂×C₁₃₁	—	16	2	no	—
194	C₂×C₁₃₁	—	16	1	no	—
195	C₂×C₁₃₁	#3169	1	1	yes	characteristic
196	C₂×C₁₃₁	C₂×#509	1	1	yes	characteristic
197	C₂×C₁₃₁	#3414	1	1	yes	characteristic
198	#33737	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃₁	#33737	1	1	yes	characteristic, direct product factor, Sylow
200	#3169	C₂×C₁₃₁	1	1	yes	characteristic, complemented
201	#3168	C₂×C₁₃₁	1	1	yes	characteristic, complemented
202	#2255	C₂×C₁₃₁	1	1	yes	characteristic, complemented
203	#2250	C₂×C₁₃₁	1	1	yes	characteristic, complemented
204	#2244	C₂×C₁₃₁	1	1	yes	characteristic, complemented
205	#2243	C₂×C₁₃₁	1	1	yes	characteristic, complemented
206	#2220	C₂×C₁₃₁	1	2	yes	complemented
207	#2218	C₂×C₁₃₁	1	2	yes	complemented
208	C₄×SD₃₂	C₂×C₁₃₁	1	2	yes	complemented
209	C₄×D₁₆	C₂×C₁₃₁	1	2	yes	complemented
210	C₄×M₃₂	C₂×C₁₃₁	1	1	yes	characteristic, complemented
211	#532	—	2	1	no	—
212	#529	—	2	1	no	—
213	C₂×SD₃₂	C₂²×C₁₃₁	1	2	yes	—
214	C₂×D₁₆	C₂²×C₁₃₁	1	2	yes	—
215	C₂×M₃₂	C₂²×C₁₃₁	1	2	yes	—
216	#500	C₂²×C₁₃₁	1	1	yes	characteristic
217	#499	C₂²×C₁₃₁	1	1	yes	characteristic
218	#495	C₂²×C₁₃₁	1	1	yes	characteristic
219	#493	C₂²×C₁₃₁	1	1	yes	characteristic
220	#488	—	2	1	no	—
221	#486	—	2	1	no	—
222	#467	C₂²×C₁₃₁	1	1	yes	characteristic
223	#466	—	2	1	no	—
224	#466	C₂²×C₁₃₁	1	1	yes	characteristic
225	#466	C₂²×C₁₃₁	1	2	yes	—
226	#465	—	2	1	no	—
227	C₄×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
228	C₄×SD₁₆	—	2	1	no	—
229	C₄×D₈	—	2	1	no	—
230	C₄×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
231	C₄×D₈	C₂²×C₁₃₁	1	2	yes	—
232	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
233	#367	C₂²×C₁₃₁	1	2	yes	—
234	#366	C₂²×C₁₃₁	1	2	yes	—
235	#358	C₂²×C₁₃₁	1	2	yes	—
236	#357	C₂²×C₁₃₁	1	2	yes	—
237	#357	C₂²×C₁₃₁	1	2	yes	—
238	#357	C₂²×C₁₃₁	1	2	yes	—
239	#346	C₂²×C₁₃₁	1	1	yes	characteristic
240	#346	C₂²×C₁₃₁	1	1	yes	characteristic
241	C₄×C₁₆	C₂²×C₁₃₁	1	2	yes	—
242	C₂×#41	—	4	1	no	—
243	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
244	C₂×SD₁₆	—	2	1	no	—
245	C₂×D₈	—	2	1	no	—
246	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
247	C₂×D₈	C₂³×C₁₃₁	1	1	yes	characteristic
248	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
250	C₄⋊Q₈	—	2	1	no	—
251	#127	—	2	1	no	—
252	#126	—	4	1	no	—
253	#125	—	2	1	no	—
254	#124	—	2	1	no	—
255	#124	—	4	1	no	—
256	#123	—	4	1	no	—
257	C₂²⋊Q₈	—	2	1	no	—
258	#121	—	2	1	no	—
259	#121	—	2	2	no	—
260	#121	—	4	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	4	1	no	—
265	C₄×D₄	—	4	1	no	—
266	#117	—	4	1	no	—
267	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
268	SD₃₂	—	2	4	no	—
269	D₁₆	—	2	4	no	—
270	M₃₂	—	2	4	no	—
271	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
272	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
273	#107	—	2	1	no	—
274	#107	C₂³×C₁₃₁	1	1	yes	characteristic
275	#107	C₂³×C₁₃₁	1	1	yes	characteristic
276	#107	C₂³×C₁₃₁	1	2	yes	—
277	#106	—	2	1	no	—
278	#103	—	2	1	no	—
279	#103	—	2	1	no	—
280	#102	—	2	2	no	—
281	#102	—	2	1	no	—
282	#102	—	2	2	no	—
283	#102	—	2	1	no	—
284	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
285	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
288	#41	—	8	4	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
300	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
302	Q₁₆	—	2	2	no	—
303	SD₁₆	—	4	2	no	—
304	D₈	—	2	2	no	—
305	D₈	—	2	2	no	—
306	D₈	—	2	2	no	—
307	D₈	—	4	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
313	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
331	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
332	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
334	C₁₆	—	2	2	no	—
335	C₁₆	#41×C₁₃₁	1	4	yes	complemented
336	C₂³	—	4	1	no	—
337	C₂³	—	4	2	no	—
338	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
339	Q₈	—	4	1	no	—
340	Q₈	—	4	1	no	—
341	Q₈	—	8	2	no	—
342	D₄	—	4	1	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	1	no	—
346	D₄	—	8	2	no	—
347	D₄	—	8	2	no	—
348	D₄	—	8	4	no	—
349	D₄	—	8	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
361	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
363	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
364	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	#135×C₁₃₁	1	2	yes	—
369	C₈	C₂×#41×C₁₃₁	1	2	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	1	no	—
388	C₄	#509×C₁₃₁	1	2	yes	—
389	C₄	#532×C₁₃₁	1	1	yes	characteristic
390	C₄	C₂×#135×C₁₃₁	1	1	yes	characteristic
391	C₂	—	4	1	no	—
392	C₂	—	16	2	no	—
393	C₂	—	16	1	no	—
394	C₂	#3169×C₁₃₁	1	1	yes	characteristic
395	C₂	C₂×#509×C₁₃₁	1	1	yes	characteristic
396	C₂	#3414×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂²×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ C₂×C₄×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3169×C₁₃₁	C₂	semidirect
2. #3168×C₁₃₁	C₂	semidirect
3. #2255×C₁₃₁	C₂	semidirect
4. #2250×C₁₃₁	C₂	semidirect
5. #2244×C₁₃₁	C₂	semidirect
6. #2243×C₁₃₁	C₂	semidirect
7. #2220×C₁₃₁	C₂	semidirect
8. #2218×C₁₃₁	C₂	semidirect
9. C₄×SD₃₂×C₁₃₁	C₂	semidirect
10. C₄×D₁₆×C₁₃₁	C₂	semidirect
11. C₄×M₃₂×C₁₃₁	C₂	semidirect
136. C₁₆×C₁₃₁	#41	semidirect
198. #33737	C₁₃₁	direct (N × H)
199. C₁₃₁	#33737	direct (N × H)
200. #3169	C₂×C₁₃₁	semidirect
201. #3168	C₂×C₁₃₁	semidirect
202. #2255	C₂×C₁₃₁	semidirect
203. #2250	C₂×C₁₃₁	semidirect
204. #2244	C₂×C₁₃₁	semidirect
205. #2243	C₂×C₁₃₁	semidirect
206. #2220	C₂×C₁₃₁	semidirect
207. #2218	C₂×C₁₃₁	semidirect
208. C₄×SD₃₂	C₂×C₁₃₁	semidirect
209. C₄×D₁₆	C₂×C₁₃₁	semidirect
210. C₄×M₃₂	C₂×C₁₃₁	semidirect
335. C₁₆	#41×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3169×C₁₃₁	2
#3168×C₁₃₁	2
#2255×C₁₃₁	2
#2250×C₁₃₁	2
#2244×C₁₃₁	2
#2243×C₁₃₁	2
#2220×C₁₃₁	2
#2218×C₁₃₁	2
C₄×SD₃₂×C₁₃₁	2
C₄×D₁₆×C₁₃₁	2
C₄×M₃₂×C₁₃₁	2
#33737	131

Subgroups — C131×#33737 #45719621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33737 #45719621