Subgroups — C₁₃₁×#29836 #45715720

Order 33536.

760 conjugacy classes of subgroups.

The subgroup lattice has 438 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×#461×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2642×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2319×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2068×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2066×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2055×C₁₃₁	C₂	1	2	yes	maximal
8	#2055×C₁₃₁	C₂	1	2	yes	maximal
9	#1989×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1981×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1843×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₃₁	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
16	#478×C₁₃₁	—	2	4	no	—
17	#461×C₁₃₁	—	2	4	no	—
18	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
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×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
26	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
29	#400×C₁₃₁	—	2	2	no	—
30	#400×C₁₃₁	—	2	1	no	—
31	#400×C₁₃₁	—	2	1	no	—
32	#391×C₁₃₁	C₂²	1	2	yes	—
33	#391×C₁₃₁	C₂²	1	2	yes	—
34	#390×C₁₃₁	C₂²	1	2	yes	—
35	#389×C₁₃₁	C₂²	1	2	yes	—
36	#388×C₁₃₁	—	2	2	no	—
37	#381×C₁₃₁	—	2	1	no	—
38	#380×C₁₃₁	—	2	1	no	—
39	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
40	#376×C₁₃₁	C₂²	1	1	yes	characteristic
41	#340×C₁₃₁	C₂²	1	2	yes	—
42	#340×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₁	—	2	1	no	—
46	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
47	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
48	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
49	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
54	#125×C₁₃₁	—	2	2	no	—
55	#125×C₁₃₁	—	2	2	no	—
56	C₄×D₄×C₁₃₁	—	2	2	no	—
57	C₄×D₄×C₁₃₁	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
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×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
70	C₂×C₄²×C₁₃₁	—	2	1	no	—
71	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
73	#107×C₁₃₁	—	2	2	no	—
74	#106×C₁₃₁	—	2	2	no	—
75	C₄⋊C₈×C₁₃₁	—	2	2	no	—
76	C₄⋊C₈×C₁₃₁	—	2	2	no	—
77	C₄⋊C₈×C₁₃₁	—	4	2	no	—
78	C₄⋊C₈×C₁₃₁	—	4	2	no	—
79	#103×C₁₃₁	—	2	4	no	—
80	#103×C₁₃₁	—	4	2	no	—
81	#103×C₁₃₁	—	4	2	no	—
82	#102×C₁₃₁	—	2	2	no	—
83	#102×C₁₃₁	—	2	2	no	—
84	#95×C₁₃₁	—	2	2	no	—
85	#95×C₁₃₁	—	2	2	no	—
86	#95×C₁₃₁	—	2	2	no	—
87	#95×C₁₃₁	—	2	2	no	—
88	#95×C₁₃₁	—	2	2	no	—
89	#95×C₁₃₁	—	2	1	no	—
90	#95×C₁₃₁	D₄	1	2	yes	—
91	#95×C₁₃₁	D₄	1	1	yes	characteristic
92	#95×C₁₃₁	D₄	1	1	yes	characteristic
93	C₂⁴×C₁₃₁	—	2	1	no	—
94	C₂×Q₈×C₁₃₁	—	2	2	no	—
95	C₂×Q₈×C₁₃₁	—	2	2	no	—
96	C₂×Q₈×C₁₃₁	—	2	2	no	—
97	C₂×Q₈×C₁₃₁	—	2	2	no	—
98	C₂×Q₈×C₁₃₁	—	2	2	no	—
99	C₂×Q₈×C₁₃₁	—	2	2	no	—
100	C₂×D₄×C₁₃₁	—	2	1	no	—
101	C₂×D₄×C₁₃₁	—	2	2	no	—
102	C₂×D₄×C₁₃₁	—	2	2	no	—
103	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃₁	—	2	1	no	—
105	C₂²×C₄×C₁₃₁	—	2	4	no	—
106	C₂²×C₄×C₁₃₁	—	2	1	no	—
107	C₂²×C₄×C₁₃₁	—	2	1	no	—
108	C₂²×C₄×C₁₃₁	—	2	2	no	—
109	C₂²×C₄×C₁₃₁	—	2	2	no	—
110	C₂²×C₄×C₁₃₁	—	8	2	no	—
111	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
116	SD₁₆×C₁₃₁	—	4	8	no	—
117	C₂×C₈×C₁₃₁	—	2	1	no	—
118	C₂×C₈×C₁₃₁	—	2	1	no	—
119	C₂×C₈×C₁₃₁	—	2	2	no	—
120	C₂×C₈×C₁₃₁	—	2	2	no	—
121	C₂×C₈×C₁₃₁	—	2	2	no	—
122	C₂×C₈×C₁₃₁	—	2	2	no	—
123	C₂×C₈×C₁₃₁	—	2	2	no	—
124	C₄⋊C₄×C₁₃₁	—	2	1	no	—
125	C₄⋊C₄×C₁₃₁	—	2	1	no	—
126	C₄⋊C₄×C₁₃₁	—	2	1	no	—
127	C₄⋊C₄×C₁₃₁	—	2	1	no	—
128	C₄⋊C₄×C₁₃₁	—	2	1	no	—
129	C₄⋊C₄×C₁₃₁	—	2	2	no	—
130	C₄⋊C₄×C₁₃₁	—	2	2	no	—
131	C₄⋊C₄×C₁₃₁	—	4	2	no	—
132	C₄⋊C₄×C₁₃₁	—	4	2	no	—
133	C₄⋊C₄×C₁₃₁	—	4	2	no	—
134	C₄⋊C₄×C₁₃₁	—	4	2	no	—
135	C₄⋊C₄×C₁₃₁	—	8	2	no	—
136	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
138	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
139	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
140	C₄²×C₁₃₁	—	2	2	no	—
141	C₄²×C₁₃₁	—	2	2	no	—
142	C₄²×C₁₃₁	—	8	1	no	—
143	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
144	C₄²×C₁₃₁	#41	1	2	yes	—
145	C₂³×C₁₃₁	—	2	2	no	—
146	C₂³×C₁₃₁	—	4	2	no	—
147	C₂³×C₁₃₁	—	4	1	no	—
148	C₂³×C₁₃₁	—	4	2	no	—
149	C₂³×C₁₃₁	—	4	1	no	—
150	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₃₁	—	4	2	no	—
152	Q₈×C₁₃₁	—	4	2	no	—
153	Q₈×C₁₃₁	—	4	2	no	—
154	Q₈×C₁₃₁	—	4	2	no	—
155	D₄×C₁₃₁	—	2	2	no	—
156	D₄×C₁₃₁	—	2	2	no	—
157	D₄×C₁₃₁	—	4	2	no	—
158	C₂×C₄×C₁₃₁	—	2	1	no	—
159	C₂×C₄×C₁₃₁	—	2	2	no	—
160	C₂×C₄×C₁₃₁	—	2	1	no	—
161	C₂×C₄×C₁₃₁	—	2	2	no	—
162	C₂×C₄×C₁₃₁	—	2	2	no	—
163	C₂×C₄×C₁₃₁	—	2	2	no	—
164	C₂×C₄×C₁₃₁	—	2	2	no	—
165	C₂×C₄×C₁₃₁	—	2	2	no	—
166	C₂×C₄×C₁₃₁	—	2	2	no	—
167	C₂×C₄×C₁₃₁	—	2	2	no	—
168	C₂×C₄×C₁₃₁	—	4	2	no	—
169	C₂×C₄×C₁₃₁	—	4	1	no	—
170	C₂×C₄×C₁₃₁	—	4	1	no	—
171	C₂×C₄×C₁₃₁	—	4	2	no	—
172	C₂×C₄×C₁₃₁	—	4	2	no	—
173	C₂×C₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	4	2	no	—
175	C₂×C₄×C₁₃₁	—	4	2	no	—
176	C₂×C₄×C₁₃₁	—	4	2	no	—
177	C₂×C₄×C₁₃₁	—	4	2	no	—
178	C₂×C₄×C₁₃₁	—	4	1	no	—
179	C₂×C₄×C₁₃₁	—	4	1	no	—
180	C₂×C₄×C₁₃₁	—	8	4	no	—
181	C₂×C₄×C₁₃₁	#121	1	2	yes	—
182	C₂×C₄×C₁₃₁	#121	1	2	yes	—
183	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
186	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
187	C₈×C₁₃₁	—	4	1	no	—
188	C₈×C₁₃₁	—	4	1	no	—
189	C₈×C₁₃₁	—	4	2	no	—
190	C₂²×C₁₃₁	—	4	2	no	—
191	C₂²×C₁₃₁	—	4	2	no	—
192	C₂²×C₁₃₁	—	4	2	no	—
193	C₂²×C₁₃₁	—	8	2	no	—
194	C₂²×C₁₃₁	—	8	2	no	—
195	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
196	C₂²×C₁₃₁	#537	1	2	yes	—
197	C₂²×C₁₃₁	#577	1	2	yes	—
198	C₂²×C₁₃₁	#577	1	1	yes	characteristic
199	C₂²×C₁₃₁	#578	1	1	yes	characteristic
200	C₄×C₁₃₁	—	2	2	no	—
201	C₄×C₁₃₁	—	2	2	no	—
202	C₄×C₁₃₁	—	4	2	no	—
203	C₄×C₁₃₁	—	4	2	no	—
204	C₄×C₁₃₁	—	4	2	no	—
205	C₄×C₁₃₁	—	8	2	no	—
206	C₄×C₁₃₁	—	8	2	no	—
207	C₄×C₁₃₁	—	8	1	no	—
208	C₄×C₁₃₁	—	8	1	no	—
209	C₄×C₁₃₁	#535	1	1	yes	characteristic
210	C₄×C₁₃₁	#536	1	1	yes	characteristic
211	C₄×C₁₃₁	#542	1	2	yes	—
212	C₂×C₁₃₁	—	8	2	no	—
213	C₂×C₁₃₁	#2620	1	1	yes	characteristic
214	C₂×C₁₃₁	#3042	1	1	yes	characteristic
215	C₂×C₁₃₁	#3046	1	1	yes	characteristic
216	C₂×C₁₃₁	#3258	1	2	yes	—
217	C₂×C₁₃₁	#3260	1	2	yes	—
218	#29836	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₁₃₁	#29836	1	1	yes	characteristic, direct product factor, Sylow
220	C₂×#478	C₂×C₁₃₁	1	1	yes	characteristic
221	C₂×#461	C₂×C₁₃₁	1	1	yes	characteristic
222	#2642	C₂×C₁₃₁	1	1	yes	characteristic, complemented
223	#2319	C₂×C₁₃₁	1	1	yes	characteristic
224	#2068	C₂×C₁₃₁	1	2	yes	complemented
225	#2066	C₂×C₁₃₁	1	2	yes	complemented
226	#2055	C₂×C₁₃₁	1	2	yes	—
227	#2055	C₂×C₁₃₁	1	2	yes	—
228	#1989	C₂×C₁₃₁	1	1	yes	characteristic, complemented
229	#1981	C₂×C₁₃₁	1	1	yes	characteristic, complemented
230	#1843	C₂×C₁₃₁	1	1	yes	characteristic, complemented
231	C₂²×SD₁₆	C₂²×C₁₃₁	1	2	yes	—
232	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
233	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
235	#478	—	2	4	no	—
236	#461	—	2	4	no	—
237	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
238	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
243	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
244	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
245	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
246	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
247	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
248	#400	—	2	1	no	—
249	#400	—	2	1	no	—
250	#400	—	2	2	no	—
251	#391	C₂²×C₁₃₁	1	2	yes	—
252	#391	C₂²×C₁₃₁	1	2	yes	—
253	#390	C₂²×C₁₃₁	1	2	yes	—
254	#389	C₂²×C₁₃₁	1	2	yes	—
255	#388	—	2	2	no	—
256	#381	—	2	1	no	—
257	#380	—	2	1	no	—
258	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
259	#376	C₂²×C₁₃₁	1	1	yes	characteristic
260	#340	C₂²×C₁₃₁	1	2	yes	—
261	#340	C₂²×C₁₃₁	1	2	yes	—
262	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
263	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
264	C₂³×C₄	—	2	1	no	—
265	C₂×SD₁₆	—	2	4	no	—
266	C₂×SD₁₆	—	4	2	no	—
267	C₂×SD₁₆	—	4	2	no	—
268	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	2	2	no	—
273	#125	—	2	2	no	—
274	#125	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	D₄×C₁₃₁	1	4	yes	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#106	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	4	2	no	—
297	C₄⋊C₈	—	4	2	no	—
298	#103	—	2	4	no	—
299	#103	—	4	2	no	—
300	#103	—	4	2	no	—
301	#102	—	2	2	no	—
302	#102	—	2	2	no	—
303	#95	—	2	1	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	D₄×C₁₃₁	1	1	yes	characteristic
310	#95	D₄×C₁₃₁	1	1	yes	characteristic
311	#95	D₄×C₁₃₁	1	2	yes	—
312	C₂⁴	—	2	1	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	8	2	no	—
330	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
335	SD₁₆	—	4	8	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	8	2	no	—
355	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	8	2	no	—
358	C₂²⋊C₄	—	8	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	8	1	no	—
362	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
363	C₄²	#41×C₁₃₁	1	2	yes	—
364	C₂³	—	2	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	8	4	no	—
400	C₂×C₄	#121×C₁₃₁	1	2	yes	—
401	C₂×C₄	#121×C₁₃₁	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
404	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
405	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
406	C₈	—	4	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
415	C₂²	#537×C₁₃₁	1	2	yes	—
416	C₂²	#577×C₁₃₁	1	2	yes	—
417	C₂²	#577×C₁₃₁	1	1	yes	characteristic
418	C₂²	#578×C₁₃₁	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	8	2	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	#535×C₁₃₁	1	1	yes	characteristic
429	C₄	#536×C₁₃₁	1	1	yes	characteristic
430	C₄	#542×C₁₃₁	1	2	yes	—
431	C₂	—	8	2	no	—
432	C₂	#2620×C₁₃₁	1	1	yes	characteristic
433	C₂	#3042×C₁₃₁	1	1	yes	characteristic
434	C₂	#3046×C₁₃₁	1	1	yes	characteristic
435	C₂	#3258×C₁₃₁	1	2	yes	—
436	C₂	#3260×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. #2642×C₁₃₁	C₂	semidirect
5. #2068×C₁₃₁	C₂	semidirect
6. #2066×C₁₃₁	C₂	semidirect
9. #1989×C₁₃₁	C₂	semidirect
10. #1981×C₁₃₁	C₂	semidirect
11. #1843×C₁₃₁	C₂	semidirect
218. #29836	C₁₃₁	direct (N × H)
219. C₁₃₁	#29836	direct (N × H)
222. #2642	C₂×C₁₃₁	semidirect
224. #2068	C₂×C₁₃₁	semidirect
225. #2066	C₂×C₁₃₁	semidirect
228. #1989	C₂×C₁₃₁	semidirect
229. #1981	C₂×C₁₃₁	semidirect
230. #1843	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×#461×C₁₃₁	2
#2642×C₁₃₁	2
#2319×C₁₃₁	2
#2068×C₁₃₁	2
#2066×C₁₃₁	2
#2055×C₁₃₁	2
#1989×C₁₃₁	2
#1981×C₁₃₁	2
#1843×C₁₃₁	2
#29836	131

Subgroups — C131×#29836 #45715720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29836 #45715720