Subgroups — C₁₃₁×#33674 #45719558

Order 33536.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3168×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2235×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2232×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2228×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2210×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2187×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2184×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#2177×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2175×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2163×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	#529×C₁₃₁	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃₁	—	2	1	no	—
15	C₂×SD₃₂×C₁₃₁	C₂²	1	2	yes	—
16	C₂×D₁₆×C₁₃₁	C₂²	1	2	yes	—
17	#499×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
18	#495×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
19	#488×C₁₃₁	—	2	1	no	—
20	#467×C₁₃₁	C₂²	1	1	yes	characteristic
21	#466×C₁₃₁	C₂²	1	1	yes	characteristic
22	#465×C₁₃₁	—	2	1	no	—
23	C₄×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₄×SD₁₆×C₁₃₁	—	2	1	no	—
25	C₄×D₈×C₁₃₁	—	2	1	no	—
26	C₄×D₈×C₁₃₁	—	2	1	no	—
27	C₄×D₈×C₁₃₁	C₂²	1	2	yes	—
28	C₄×D₈×C₁₃₁	C₂²	1	2	yes	—
29	C₄×D₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂×#102×C₁₃₁	—	2	1	no	—
32	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
33	#367×C₁₃₁	C₂²	1	2	yes	complemented
34	#366×C₁₃₁	C₂²	1	2	yes	complemented
35	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
36	#358×C₁₃₁	C₂²	1	2	yes	complemented
37	#357×C₁₃₁	C₂²	1	2	yes	—
38	#357×C₁₃₁	C₂²	1	2	yes	—
39	#357×C₁₃₁	C₂²	1	2	yes	complemented
40	C₂²⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂²⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
42	#346×C₁₃₁	C₂²	1	2	yes	complemented
43	C₂²×D₄×C₁₃₁	—	2	1	no	—
44	C₂³×C₄×C₁₃₁	—	4	1	no	—
45	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
47	C₂×D₈×C₁₃₁	—	2	4	no	—
48	C₂×D₈×C₁₃₁	—	2	1	no	—
49	C₂×D₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
53	#126×C₁₃₁	—	4	1	no	—
54	#125×C₁₃₁	—	2	1	no	—
55	#124×C₁₃₁	—	2	1	no	—
56	#123×C₁₃₁	—	4	1	no	—
57	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
58	#121×C₁₃₁	—	2	1	no	—
59	C₄×Q₈×C₁₃₁	—	2	1	no	—
60	C₄×D₄×C₁₃₁	—	2	2	no	—
61	C₄×D₄×C₁₃₁	—	2	2	no	—
62	C₄×D₄×C₁₃₁	—	2	1	no	—
63	C₄×D₄×C₁₃₁	—	4	1	no	—
64	C₄×D₄×C₁₃₁	—	4	1	no	—
65	C₄×D₄×C₁₃₁	—	4	1	no	—
66	#117×C₁₃₁	—	4	1	no	—
67	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₃₁	—	4	1	no	—
69	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
70	SD₃₂×C₁₃₁	—	2	4	no	—
71	D₁₆×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	2	no	—
83	#102×C₁₃₁	—	2	1	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	C₂⁴×C₁₃₁	—	4	1	no	—
90	C₂×Q₈×C₁₃₁	—	2	1	no	—
91	C₂×D₄×C₁₃₁	—	2	4	no	—
92	C₂×D₄×C₁₃₁	—	2	2	no	—
93	C₂×D₄×C₁₃₁	—	2	1	no	—
94	C₂×D₄×C₁₃₁	—	4	2	no	—
95	C₂×D₄×C₁₃₁	—	4	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	2	no	—
100	C₂²×C₄×C₁₃₁	—	4	2	no	—
101	C₂²×C₄×C₁₃₁	—	8	4	no	—
102	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
105	Q₁₆×C₁₃₁	—	2	2	no	—
106	SD₁₆×C₁₃₁	—	4	2	no	—
107	D₈×C₁₃₁	—	2	4	no	—
108	D₈×C₁₃₁	—	2	2	no	—
109	D₈×C₁₃₁	—	2	2	no	—
110	D₈×C₁₃₁	#41	1	4	yes	—
111	C₂×C₈×C₁₃₁	—	2	2	no	—
112	C₂×C₈×C₁₃₁	—	4	1	no	—
113	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₁₃₁	—	2	2	no	—
118	C₄⋊C₄×C₁₃₁	—	2	1	no	—
119	C₄⋊C₄×C₁₃₁	—	2	1	no	—
120	C₄⋊C₄×C₁₃₁	—	4	1	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	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
126	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
127	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
128	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
129	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
130	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
131	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
132	C₄²×C₁₃₁	—	4	1	no	—
133	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
134	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
135	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₁₃₁	—	2	2	no	—
138	C₁₆×C₁₃₁	—	2	2	no	—
139	C₂³×C₁₃₁	—	4	4	no	—
140	C₂³×C₁₃₁	—	4	2	no	—
141	C₂³×C₁₃₁	—	4	1	no	—
142	C₂³×C₁₃₁	—	8	2	no	—
143	C₂³×C₁₃₁	—	8	2	no	—
144	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
145	Q₈×C₁₃₁	—	4	1	no	—
146	Q₈×C₁₃₁	—	4	1	no	—
147	D₄×C₁₃₁	—	2	4	no	—
148	D₄×C₁₃₁	—	4	4	no	—
149	D₄×C₁₃₁	—	4	1	no	—
150	D₄×C₁₃₁	—	4	2	no	—
151	D₄×C₁₃₁	—	4	1	no	—
152	D₄×C₁₃₁	—	8	2	no	—
153	C₂×C₄×C₁₃₁	—	2	2	no	—
154	C₂×C₄×C₁₃₁	—	2	1	no	—
155	C₂×C₄×C₁₃₁	—	2	1	no	—
156	C₂×C₄×C₁₃₁	—	4	1	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	—	8	2	no	—
162	C₂×C₄×C₁₃₁	—	8	4	no	—
163	C₂×C₄×C₁₃₁	—	8	4	no	—
164	C₂×C₄×C₁₃₁	—	8	2	no	—
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	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₁₃₁	—	2	1	no	—
172	C₈×C₁₃₁	—	2	1	no	—
173	C₈×C₁₃₁	—	2	1	no	—
174	C₈×C₁₃₁	C₂×#41	1	2	yes	—
175	C₂²×C₁₃₁	—	2	1	no	—
176	C₂²×C₁₃₁	—	2	1	no	—
177	C₂²×C₁₃₁	—	4	4	no	—
178	C₂²×C₁₃₁	—	8	8	no	—
179	C₂²×C₁₃₁	—	8	2	no	—
180	C₂²×C₁₃₁	—	8	2	no	—
181	C₂²×C₁₃₁	—	8	1	no	—
182	C₂²×C₁₃₁	—	8	1	no	—
183	C₂²×C₁₃₁	—	8	1	no	—
184	C₂²×C₁₃₁	#509	1	2	yes	—
185	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
186	C₄×C₁₃₁	—	2	1	no	—
187	C₄×C₁₃₁	—	2	1	no	—
188	C₄×C₁₃₁	—	2	1	no	—
189	C₄×C₁₃₁	—	2	1	no	—
190	C₄×C₁₃₁	—	2	1	no	—
191	C₄×C₁₃₁	—	8	1	no	—
192	C₄×C₁₃₁	—	8	2	no	—
193	C₄×C₁₃₁	—	8	1	no	—
194	C₄×C₁₃₁	—	8	1	no	—
195	C₄×C₁₃₁	#525	1	1	yes	characteristic
196	C₄×C₁₃₁	#575	1	1	yes	characteristic
197	C₂×C₁₃₁	—	2	2	no	—
198	C₂×C₁₃₁	—	8	4	no	—
199	C₂×C₁₃₁	—	16	1	no	—
200	C₂×C₁₃₁	#3100	1	1	yes	characteristic
201	C₂×C₁₃₁	C₂×#509	1	1	yes	characteristic
202	C₂×C₁₃₁	#3414	1	1	yes	characteristic
203	#33674	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₁₃₁	#33674	1	1	yes	characteristic, direct product factor, Sylow
205	#3168	C₂×C₁₃₁	1	1	yes	characteristic, complemented
206	C₂×C₄×D₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
207	#2235	C₂×C₁₃₁	1	1	yes	characteristic, complemented
208	#2232	C₂×C₁₃₁	1	1	yes	characteristic, complemented
209	#2228	C₂×C₁₃₁	1	2	yes	complemented
210	#2210	C₂×C₁₃₁	1	2	yes	complemented
211	#2187	C₂×C₁₃₁	1	1	yes	characteristic, complemented
212	#2184	C₂×C₁₃₁	1	1	yes	characteristic
213	#2177	C₂×C₁₃₁	1	2	yes	complemented
214	#2175	C₂×C₁₃₁	1	2	yes	complemented
215	#2163	C₂×C₁₃₁	1	1	yes	characteristic, complemented
216	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
217	#529	—	2	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×SD₃₂	C₂²×C₁₃₁	1	2	yes	—
220	C₂×D₁₆	C₂²×C₁₃₁	1	2	yes	—
221	#499	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
222	#495	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
223	#488	—	2	1	no	—
224	#467	C₂²×C₁₃₁	1	1	yes	characteristic
225	#466	C₂²×C₁₃₁	1	1	yes	characteristic
226	#465	—	2	1	no	—
227	C₄×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
228	C₄×SD₁₆	—	2	1	no	—
229	C₄×D₈	—	2	1	no	—
230	C₄×D₈	—	2	1	no	—
231	C₄×D₈	C₂²×C₁₃₁	1	2	yes	—
232	C₄×D₈	C₂²×C₁₃₁	1	2	yes	—
233	C₄×D₈	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
234	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
235	C₂×#102	—	2	1	no	—
236	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
237	#367	C₂²×C₁₃₁	1	2	yes	complemented
238	#366	C₂²×C₁₃₁	1	2	yes	complemented
239	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
240	#358	C₂²×C₁₃₁	1	2	yes	complemented
241	#357	C₂²×C₁₃₁	1	2	yes	—
242	#357	C₂²×C₁₃₁	1	2	yes	—
243	#357	C₂²×C₁₃₁	1	2	yes	complemented
244	C₂²⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
245	C₂²⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
246	#346	C₂²×C₁₃₁	1	2	yes	complemented
247	C₂²×D₄	—	2	1	no	—
248	C₂³×C₄	—	4	1	no	—
249	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
250	C₂×SD₁₆	—	2	1	no	—
251	C₂×D₈	—	2	4	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	C₂³×C₁₃₁	1	1	yes	characteristic
254	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
255	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
257	#126	—	4	1	no	—
258	#125	—	2	1	no	—
259	#124	—	2	1	no	—
260	#123	—	4	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	#121	—	2	1	no	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	4	1	no	—
268	C₄×D₄	—	4	1	no	—
269	C₄×D₄	—	4	1	no	—
270	#117	—	4	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	4	1	no	—
273	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
274	SD₃₂	—	2	4	no	—
275	D₁₆	—	2	4	no	—
276	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
277	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
278	#107	—	2	1	no	—
279	#107	C₂³×C₁₃₁	1	1	yes	characteristic
280	#107	C₂³×C₁₃₁	1	1	yes	characteristic
281	#107	C₂³×C₁₃₁	1	2	yes	—
282	#106	—	2	1	no	—
283	#103	—	2	1	no	—
284	#103	—	2	1	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	1	no	—
288	#102	—	2	1	no	—
289	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
290	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
293	C₂⁴	—	4	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	8	4	no	—
306	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
307	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
309	Q₁₆	—	2	2	no	—
310	SD₁₆	—	4	2	no	—
311	D₈	—	2	4	no	—
312	D₈	—	2	2	no	—
313	D₈	—	2	2	no	—
314	D₈	#41×C₁₃₁	1	4	yes	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
320	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
338	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	2	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	8	2	no	—
347	C₂³	—	8	2	no	—
348	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	Q₈	—	4	1	no	—
351	D₄	—	2	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	1	no	—
356	D₄	—	8	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
370	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
373	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	C₂×#41×C₁₃₁	1	2	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	8	8	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	1	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	#509×C₁₃₁	1	2	yes	—
389	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	1	no	—
399	C₄	#525×C₁₃₁	1	1	yes	characteristic
400	C₄	#575×C₁₃₁	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	4	no	—
403	C₂	—	16	1	no	—
404	C₂	#3100×C₁₃₁	1	1	yes	characteristic
405	C₂	C₂×#509×C₁₃₁	1	1	yes	characteristic
406	C₂	#3414×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
prime radical	#2184×C₁₃₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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. #3168×C₁₃₁	C₂	semidirect
2. C₂×C₄×D₈×C₁₃₁	C₂	semidirect
3. #2235×C₁₃₁	C₂	semidirect
4. #2232×C₁₃₁	C₂	semidirect
5. #2228×C₁₃₁	C₂	semidirect
6. #2210×C₁₃₁	C₂	semidirect
7. #2187×C₁₃₁	C₂	semidirect
9. #2177×C₁₃₁	C₂	semidirect
10. #2175×C₁₃₁	C₂	semidirect
11. #2163×C₁₃₁	C₂	semidirect
17. #499×C₁₃₁	C₂²	semidirect
18. #495×C₁₃₁	C₂²	semidirect
23. C₄×Q₁₆×C₁₃₁	C₂²	semidirect
29. C₄×D₈×C₁₃₁	C₂²	semidirect
33. #367×C₁₃₁	C₂²	semidirect
34. #366×C₁₃₁	C₂²	semidirect
35. C₄⋊C₁₆×C₁₃₁	C₂²	semidirect
36. #358×C₁₃₁	C₂²	semidirect
39. #357×C₁₃₁	C₂²	semidirect
42. #346×C₁₃₁	C₂²	semidirect
203. #33674	C₁₃₁	direct (N × H)
204. C₁₃₁	#33674	direct (N × H)
205. #3168	C₂×C₁₃₁	semidirect
206. C₂×C₄×D₈	C₂×C₁₃₁	semidirect
207. #2235	C₂×C₁₃₁	semidirect
208. #2232	C₂×C₁₃₁	semidirect
209. #2228	C₂×C₁₃₁	semidirect
210. #2210	C₂×C₁₃₁	semidirect
211. #2187	C₂×C₁₃₁	semidirect
213. #2177	C₂×C₁₃₁	semidirect
214. #2175	C₂×C₁₃₁	semidirect
215. #2163	C₂×C₁₃₁	semidirect
221. #499	C₂²×C₁₃₁	semidirect
222. #495	C₂²×C₁₃₁	semidirect
227. C₄×Q₁₆	C₂²×C₁₃₁	semidirect
233. C₄×D₈	C₂²×C₁₃₁	semidirect
237. #367	C₂²×C₁₃₁	semidirect
238. #366	C₂²×C₁₃₁	semidirect
239. C₄⋊C₁₆	C₂²×C₁₃₁	semidirect
240. #358	C₂²×C₁₃₁	semidirect
243. #357	C₂²×C₁₃₁	semidirect
246. #346	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3168×C₁₃₁	2
C₂×C₄×D₈×C₁₃₁	2
#2235×C₁₃₁	2
#2232×C₁₃₁	2
#2228×C₁₃₁	2
#2210×C₁₃₁	2
#2187×C₁₃₁	2
#2184×C₁₃₁	2
#2177×C₁₃₁	2
#2175×C₁₃₁	2
#2163×C₁₃₁	2
#33674	131

Subgroups — C131×#33674 #45719558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33674 #45719558