Subgroups — C₁₃₁×#33667 #45719551

Order 33536.

552 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	#3170×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#135×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2237×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2225×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2224×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2209×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2208×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2189×C₁₃₁	C₂	1	2	yes	maximal
9	C₄×Q₃₂×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	C₄×SD₃₂×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2162×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₁	C₂²	1	1	yes	characteristic
13	#533×C₁₃₁	—	2	1	no	—
14	C₄×#41×C₁₃₁	—	2	1	no	—
15	C₂×Q₃₂×C₁₃₁	C₂²	1	2	yes	—
16	C₂×SD₃₂×C₁₃₁	C₂²	1	2	yes	—
17	#500×C₁₃₁	C₂²	1	1	yes	characteristic
18	#494×C₁₃₁	C₂²	1	1	yes	characteristic
19	#487×C₁₃₁	—	2	1	no	—
20	#467×C₁₃₁	—	2	1	no	—
21	#467×C₁₃₁	C₂²	1	2	yes	—
22	C₄×Q₁₆×C₁₃₁	—	2	1	no	—
23	C₄×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₄×Q₁₆×C₁₃₁	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₄×SD₁₆×C₁₃₁	—	2	1	no	—
27	C₄×SD₁₆×C₁₃₁	—	2	1	no	—
28	C₄×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
30	#427×C₁₃₁	C₂²	1	1	yes	characteristic
31	#416×C₁₃₁	—	2	1	no	—
32	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
33	#367×C₁₃₁	C₂²	1	2	yes	—
34	#366×C₁₃₁	C₂²	1	2	yes	—
35	C₄⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₄⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
37	#358×C₁₃₁	C₂²	1	2	yes	—
38	#358×C₁₃₁	C₂²	1	2	yes	—
39	#358×C₁₃₁	C₂²	1	2	yes	—
40	#357×C₁₃₁	C₂²	1	2	yes	—
41	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
42	C₄×C₁₆×C₁₃₁	C₂²	1	2	yes	—
43	C₂×#41×C₁₃₁	—	2	1	no	—
44	#135×C₁₃₁	—	2	2	no	—
45	#135×C₁₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
47	C₂×Q₁₆×C₁₃₁	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
50	C₂×D₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
54	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
55	#125×C₁₃₁	—	4	1	no	—
56	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
57	C₂²⋊Q₈×C₁₃₁	—	4	1	no	—
58	C₄×Q₈×C₁₃₁	—	2	1	no	—
59	C₄×Q₈×C₁₃₁	—	2	1	no	—
60	C₄×Q₈×C₁₃₁	—	2	2	no	—
61	C₄×Q₈×C₁₃₁	—	4	1	no	—
62	C₄×D₄×C₁₃₁	—	2	1	no	—
63	C₄×D₄×C₁₃₁	—	2	1	no	—
64	C₄×D₄×C₁₃₁	—	4	1	no	—
65	C₄×D₄×C₁₃₁	—	4	1	no	—
66	#117×C₁₃₁	—	2	1	no	—
67	#117×C₁₃₁	—	4	1	no	—
68	#117×C₁₃₁	—	4	1	no	—
69	C₂×C₄²×C₁₃₁	—	4	1	no	—
70	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
71	Q₃₂×C₁₃₁	—	2	4	no	—
72	SD₃₂×C₁₃₁	—	2	4	no	—
73	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
74	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
75	#107×C₁₃₁	—	2	1	no	—
76	#107×C₁₃₁	C₂³	1	1	yes	characteristic
77	#107×C₁₃₁	C₂³	1	1	yes	characteristic
78	#107×C₁₃₁	C₂³	1	2	yes	—
79	#106×C₁₃₁	—	2	1	no	—
80	#103×C₁₃₁	—	2	1	no	—
81	#103×C₁₃₁	—	2	1	no	—
82	#103×C₁₃₁	—	2	2	no	—
83	#103×C₁₃₁	—	2	2	no	—
84	#102×C₁₃₁	—	2	1	no	—
85	#102×C₁₃₁	—	2	1	no	—
86	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
90	#41×C₁₃₁	—	2	4	no	—
91	#41×C₁₃₁	—	4	2	no	—
92	C₂×Q₈×C₁₃₁	—	2	1	no	—
93	C₂×Q₈×C₁₃₁	—	2	2	no	—
94	C₂×Q₈×C₁₃₁	—	4	1	no	—
95	C₂×D₄×C₁₃₁	—	2	1	no	—
96	C₂×D₄×C₁₃₁	—	4	1	no	—
97	C₂²×C₄×C₁₃₁	—	4	1	no	—
98	C₂²×C₄×C₁₃₁	—	4	1	no	—
99	C₂²×C₄×C₁₃₁	—	4	1	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	1	no	—
104	Q₁₆×C₁₃₁	—	2	2	no	—
105	Q₁₆×C₁₃₁	—	2	2	no	—
106	Q₁₆×C₁₃₁	—	4	2	no	—
107	Q₁₆×C₁₃₁	#41	1	2	yes	—
108	SD₁₆×C₁₃₁	—	2	4	no	—
109	D₈×C₁₃₁	—	2	1	no	—
110	D₈×C₁₃₁	#41	1	2	yes	—
111	C₂×C₈×C₁₃₁	—	2	1	no	—
112	C₂×C₈×C₁₃₁	—	2	1	no	—
113	C₂×C₈×C₁₃₁	—	4	1	no	—
114	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₁₃₁	—	2	1	no	—
119	C₄⋊C₄×C₁₃₁	—	2	1	no	—
120	C₄⋊C₄×C₁₃₁	—	2	2	no	—
121	C₄⋊C₄×C₁₃₁	—	4	1	no	—
122	C₄⋊C₄×C₁₃₁	—	4	1	no	—
123	C₄⋊C₄×C₁₃₁	—	4	1	no	—
124	C₄⋊C₄×C₁₃₁	—	4	1	no	—
125	C₄⋊C₄×C₁₃₁	—	4	2	no	—
126	C₄⋊C₄×C₁₃₁	—	4	2	no	—
127	C₄⋊C₄×C₁₃₁	—	4	1	no	—
128	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
129	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
131	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
132	C₄²×C₁₃₁	—	4	1	no	—
133	C₄²×C₁₃₁	—	4	1	no	—
134	C₄²×C₁₃₁	—	4	1	no	—
135	C₄²×C₁₃₁	—	4	2	no	—
136	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
137	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
138	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
140	C₁₆×C₁₃₁	—	2	2	no	—
141	C₁₆×C₁₃₁	—	2	2	no	—
142	C₂³×C₁₃₁	—	4	1	no	—
143	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
144	Q₈×C₁₃₁	—	2	2	no	—
145	Q₈×C₁₃₁	—	4	1	no	—
146	Q₈×C₁₃₁	—	4	2	no	—
147	Q₈×C₁₃₁	—	4	2	no	—
148	Q₈×C₁₃₁	—	8	2	no	—
149	D₄×C₁₃₁	—	2	2	no	—
150	D₄×C₁₃₁	—	4	4	no	—
151	D₄×C₁₃₁	—	4	1	no	—
152	C₂×C₄×C₁₃₁	—	2	1	no	—
153	C₂×C₄×C₁₃₁	—	2	1	no	—
154	C₂×C₄×C₁₃₁	—	2	2	no	—
155	C₂×C₄×C₁₃₁	—	2	2	no	—
156	C₂×C₄×C₁₃₁	—	4	4	no	—
157	C₂×C₄×C₁₃₁	—	4	1	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	—	8	2	no	—
163	C₂×C₄×C₁₃₁	—	8	2	no	—
164	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₁₃₁	—	2	1	no	—
171	C₈×C₁₃₁	—	2	1	no	—
172	C₈×C₁₃₁	—	2	1	no	—
173	C₈×C₁₃₁	C₂×#41	1	1	yes	characteristic
174	C₈×C₁₃₁	C₂×#41	1	1	yes	characteristic
175	C₂²×C₁₃₁	—	2	1	no	—
176	C₂²×C₁₃₁	—	2	1	no	—
177	C₂²×C₁₃₁	—	2	1	no	—
178	C₂²×C₁₃₁	—	4	2	no	—
179	C₂²×C₁₃₁	—	8	1	no	—
180	C₂²×C₁₃₁	—	8	1	no	—
181	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
182	C₄×C₁₃₁	—	2	1	no	—
183	C₄×C₁₃₁	—	2	1	no	—
184	C₄×C₁₃₁	—	2	1	no	—
185	C₄×C₁₃₁	—	4	2	no	—
186	C₄×C₁₃₁	—	8	2	no	—
187	C₄×C₁₃₁	—	8	1	no	—
188	C₄×C₁₃₁	—	8	2	no	—
189	C₄×C₁₃₁	—	8	1	no	—
190	C₄×C₁₃₁	#508	1	2	yes	—
191	C₄×C₁₃₁	#510	1	2	yes	—
192	C₄×C₁₃₁	#525	1	1	yes	characteristic
193	C₄×C₁₃₁	#575	1	1	yes	characteristic
194	C₂×C₁₃₁	—	4	1	no	—
195	C₂×C₁₃₁	—	8	2	no	—
196	C₂×C₁₃₁	#3100	1	1	yes	characteristic
197	C₂×C₁₃₁	C₂×#508	1	1	yes	characteristic
198	C₂×C₁₃₁	C₂×#510	1	1	yes	characteristic
199	#33667	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₁₃₁	#33667	1	1	yes	characteristic, direct product factor, Sylow
201	#3170	C₂×C₁₃₁	1	1	yes	characteristic, complemented
202	C₄×#135	C₂×C₁₃₁	1	1	yes	characteristic
203	#2237	C₂×C₁₃₁	1	2	yes	complemented
204	#2225	C₂×C₁₃₁	1	1	yes	characteristic, complemented
205	#2224	C₂×C₁₃₁	1	1	yes	characteristic, complemented
206	#2209	C₂×C₁₃₁	1	1	yes	characteristic, complemented
207	#2208	C₂×C₁₃₁	1	1	yes	characteristic, complemented
208	#2189	C₂×C₁₃₁	1	2	yes	—
209	C₄×Q₃₂	C₂×C₁₃₁	1	2	yes	complemented
210	C₄×SD₃₂	C₂×C₁₃₁	1	2	yes	complemented
211	#2162	C₂×C₁₃₁	1	1	yes	characteristic, complemented
212	C₂×#135	C₂²×C₁₃₁	1	1	yes	characteristic
213	#533	—	2	1	no	—
214	C₄×#41	—	2	1	no	—
215	C₂×Q₃₂	C₂²×C₁₃₁	1	2	yes	—
216	C₂×SD₃₂	C₂²×C₁₃₁	1	2	yes	—
217	#500	C₂²×C₁₃₁	1	1	yes	characteristic
218	#494	C₂²×C₁₃₁	1	1	yes	characteristic
219	#487	—	2	1	no	—
220	#467	—	2	1	no	—
221	#467	C₂²×C₁₃₁	1	2	yes	—
222	C₄×Q₁₆	—	2	1	no	—
223	C₄×Q₁₆	C₂²×C₁₃₁	1	2	yes	—
224	C₄×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
225	C₄×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
226	C₄×SD₁₆	—	2	1	no	—
227	C₄×SD₁₆	—	2	1	no	—
228	C₄×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
229	C₄×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
230	#427	C₂²×C₁₃₁	1	1	yes	characteristic
231	#416	—	2	1	no	—
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	C₄⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
236	C₄⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
237	#358	C₂²×C₁₃₁	1	2	yes	—
238	#358	C₂²×C₁₃₁	1	2	yes	—
239	#358	C₂²×C₁₃₁	1	2	yes	—
240	#357	C₂²×C₁₃₁	1	2	yes	—
241	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
242	C₄×C₁₆	C₂²×C₁₃₁	1	2	yes	—
243	C₂×#41	—	2	1	no	—
244	#135	—	2	2	no	—
245	#135	—	2	2	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×Q₁₆	C₂³×C₁₃₁	1	2	yes	—
248	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
249	C₂×SD₁₆	—	2	1	no	—
250	C₂×D₈	C₂³×C₁₃₁	1	1	yes	characteristic
251	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	#125	—	4	1	no	—
256	C₂²⋊Q₈	—	2	2	no	—
257	C₂²⋊Q₈	—	4	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	2	no	—
261	C₄×Q₈	—	4	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	4	1	no	—
265	C₄×D₄	—	4	1	no	—
266	#117	—	2	1	no	—
267	#117	—	4	1	no	—
268	#117	—	4	1	no	—
269	C₂×C₄²	—	4	1	no	—
270	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
271	Q₃₂	—	2	4	no	—
272	SD₃₂	—	2	4	no	—
273	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
274	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
275	#107	—	2	1	no	—
276	#107	C₂³×C₁₃₁	1	2	yes	—
277	#107	C₂³×C₁₃₁	1	1	yes	characteristic
278	#107	C₂³×C₁₃₁	1	1	yes	characteristic
279	#106	—	2	1	no	—
280	#103	—	2	1	no	—
281	#103	—	2	1	no	—
282	#103	—	2	2	no	—
283	#103	—	2	2	no	—
284	#102	—	2	1	no	—
285	#102	—	2	1	no	—
286	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
287	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
290	#41	—	2	4	no	—
291	#41	—	4	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
301	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
303	Q₁₆	—	2	1	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	—	2	2	no	—
306	Q₁₆	—	4	2	no	—
307	Q₁₆	#41×C₁₃₁	1	2	yes	—
308	SD₁₆	—	2	4	no	—
309	D₈	—	2	1	no	—
310	D₈	#41×C₁₃₁	1	2	yes	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
317	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	1	no	—
334	C₄²	—	4	1	no	—
335	C₄²	—	4	2	no	—
336	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
337	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
340	C₁₆	—	2	2	no	—
341	C₁₆	—	2	2	no	—
342	C₂³	—	4	1	no	—
343	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
344	Q₈	—	2	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	8	2	no	—
349	D₄	—	2	2	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
365	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
366	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
367	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
368	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	C₂×#41×C₁₃₁	1	1	yes	characteristic
374	C₈	C₂×#41×C₁₃₁	1	1	yes	characteristic
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	1	no	—
390	C₄	#508×C₁₃₁	1	2	yes	—
391	C₄	#510×C₁₃₁	1	2	yes	—
392	C₄	#525×C₁₃₁	1	1	yes	characteristic
393	C₄	#575×C₁₃₁	1	1	yes	characteristic
394	C₂	—	4	1	no	—
395	C₂	—	8	2	no	—
396	C₂	#3100×C₁₃₁	1	1	yes	characteristic
397	C₂	C₂×#508×C₁₃₁	1	1	yes	characteristic
398	C₂	C₂×#510×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
prime radical	C₂×#135×C₁₃₁	C₂²
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. #3170×C₁₃₁	C₂	semidirect
3. #2237×C₁₃₁	C₂	semidirect
4. #2225×C₁₃₁	C₂	semidirect
5. #2224×C₁₃₁	C₂	semidirect
6. #2209×C₁₃₁	C₂	semidirect
7. #2208×C₁₃₁	C₂	semidirect
9. C₄×Q₃₂×C₁₃₁	C₂	semidirect
10. C₄×SD₃₂×C₁₃₁	C₂	semidirect
11. #2162×C₁₃₁	C₂	semidirect
199. #33667	C₁₃₁	direct (N × H)
200. C₁₃₁	#33667	direct (N × H)
201. #3170	C₂×C₁₃₁	semidirect
203. #2237	C₂×C₁₃₁	semidirect
204. #2225	C₂×C₁₃₁	semidirect
205. #2224	C₂×C₁₃₁	semidirect
206. #2209	C₂×C₁₃₁	semidirect
207. #2208	C₂×C₁₃₁	semidirect
209. C₄×Q₃₂	C₂×C₁₃₁	semidirect
210. C₄×SD₃₂	C₂×C₁₃₁	semidirect
211. #2162	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3170×C₁₃₁	2
C₄×#135×C₁₃₁	2
#2237×C₁₃₁	2
#2225×C₁₃₁	2
#2224×C₁₃₁	2
#2209×C₁₃₁	2
#2208×C₁₃₁	2
#2189×C₁₃₁	2
C₄×Q₃₂×C₁₃₁	2
C₄×SD₃₂×C₁₃₁	2
#2162×C₁₃₁	2
#33667	131

Subgroups — C131×#33667 #45719551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33667 #45719551