Subgroups — C₁₃₁×#29841 #45715725

Order 33536.

754 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#475×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#464×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2640×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2320×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2066×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2065×C₁₃₁	C₂	1	2	yes	maximal
7	#2056×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2055×C₁₃₁	C₂	1	2	yes	maximal
9	#1987×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1983×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	#1843×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
17	#475×C₁₃₁	—	2	4	no	—
18	#464×C₁₃₁	—	2	4	no	—
19	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
29	#397×C₁₃₁	—	2	2	no	—
30	#393×C₁₃₁	—	2	1	no	—
31	#393×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	#387×C₁₃₁	—	2	2	no	—
37	#383×C₁₃₁	—	2	1	no	—
38	#382×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	—	2	1	no	—
44	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
48	C₂×Q₁₆×C₁₃₁	—	4	2	no	—
49	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
51	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
55	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
56	#124×C₁₃₁	—	2	2	no	—
57	#124×C₁₃₁	—	2	2	no	—
58	C₄×Q₈×C₁₃₁	—	2	2	no	—
59	C₄×Q₈×C₁₃₁	D₄	1	4	yes	—
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	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
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	—	2	1	no	—
72	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
74	#106×C₁₃₁	—	2	4	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	—	2	2	no	—
81	#103×C₁₃₁	—	4	2	no	—
82	#102×C₁₃₁	—	2	2	no	—
83	#102×C₁₃₁	—	4	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	1	yes	characteristic
91	#95×C₁₃₁	D₄	1	1	yes	characteristic
92	#95×C₁₃₁	D₄	1	2	yes	—
93	C₂⁴×C₁₃₁	—	2	1	no	—
94	C₂×Q₈×C₁₃₁	—	2	1	no	—
95	C₂×Q₈×C₁₃₁	—	2	1	no	—
96	C₂×Q₈×C₁₃₁	—	2	1	no	—
97	C₂×Q₈×C₁₃₁	—	2	2	no	—
98	C₂×Q₈×C₁₃₁	—	2	2	no	—
99	C₂×Q₈×C₁₃₁	—	2	2	no	—
100	C₂×Q₈×C₁₃₁	—	2	2	no	—
101	C₂×Q₈×C₁₃₁	—	4	2	no	—
102	C₂×Q₈×C₁₃₁	—	8	2	no	—
103	C₂×Q₈×C₁₃₁	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₁₃₁	—	2	1	no	—
105	C₂×D₄×C₁₃₁	—	2	1	no	—
106	C₂×D₄×C₁₃₁	—	2	2	no	—
107	C₂×D₄×C₁₃₁	—	2	2	no	—
108	C₂²×C₄×C₁₃₁	—	2	1	no	—
109	C₂²×C₄×C₁₃₁	—	2	1	no	—
110	C₂²×C₄×C₁₃₁	—	2	2	no	—
111	C₂²×C₄×C₁₃₁	—	2	1	no	—
112	C₂²×C₄×C₁₃₁	—	2	2	no	—
113	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₁₃₁	—	4	4	no	—
119	SD₁₆×C₁₃₁	—	4	4	no	—
120	C₂×C₈×C₁₃₁	—	2	1	no	—
121	C₂×C₈×C₁₃₁	—	2	2	no	—
122	C₂×C₈×C₁₃₁	—	2	1	no	—
123	C₂×C₈×C₁₃₁	—	2	2	no	—
124	C₂×C₈×C₁₃₁	—	2	2	no	—
125	C₂×C₈×C₁₃₁	—	2	2	no	—
126	C₂×C₈×C₁₃₁	—	2	2	no	—
127	C₄⋊C₄×C₁₃₁	—	2	4	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	—	2	2	no	—
132	C₄⋊C₄×C₁₃₁	—	2	2	no	—
133	C₄⋊C₄×C₁₃₁	—	4	2	no	—
134	C₄⋊C₄×C₁₃₁	—	8	2	no	—
135	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
136	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
137	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
138	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
139	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
140	C₄²×C₁₃₁	—	2	4	no	—
141	C₄²×C₁₃₁	—	2	2	no	—
142	C₄²×C₁₃₁	—	2	2	no	—
143	C₄²×C₁₃₁	—	8	1	no	—
144	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
145	C₄²×C₁₃₁	#41	1	2	yes	—
146	C₂³×C₁₃₁	—	4	1	no	—
147	C₂³×C₁₃₁	—	4	2	no	—
148	C₂³×C₁₃₁	—	4	2	no	—
149	C₂³×C₁₃₁	—	4	1	no	—
150	C₂³×C₁₃₁	—	4	1	no	—
151	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₁₃₁	—	2	2	no	—
153	Q₈×C₁₃₁	—	2	2	no	—
154	Q₈×C₁₃₁	—	4	2	no	—
155	Q₈×C₁₃₁	—	4	1	no	—
156	Q₈×C₁₃₁	—	4	1	no	—
157	Q₈×C₁₃₁	—	4	2	no	—
158	Q₈×C₁₃₁	—	8	4	no	—
159	D₄×C₁₃₁	—	4	1	no	—
160	D₄×C₁₃₁	—	4	1	no	—
161	D₄×C₁₃₁	—	4	2	no	—
162	C₂×C₄×C₁₃₁	—	2	1	no	—
163	C₂×C₄×C₁₃₁	—	2	2	no	—
164	C₂×C₄×C₁₃₁	—	2	1	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	—	2	2	no	—
169	C₂×C₄×C₁₃₁	—	2	2	no	—
170	C₂×C₄×C₁₃₁	—	2	2	no	—
171	C₂×C₄×C₁₃₁	—	2	2	no	—
172	C₂×C₄×C₁₃₁	—	2	2	no	—
173	C₂×C₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	4	1	no	—
175	C₂×C₄×C₁₃₁	—	4	1	no	—
176	C₂×C₄×C₁₃₁	—	4	1	no	—
177	C₂×C₄×C₁₃₁	—	4	2	no	—
178	C₂×C₄×C₁₃₁	—	4	2	no	—
179	C₂×C₄×C₁₃₁	—	4	2	no	—
180	C₂×C₄×C₁₃₁	—	4	2	no	—
181	C₂×C₄×C₁₃₁	—	4	2	no	—
182	C₂×C₄×C₁₃₁	—	4	2	no	—
183	C₂×C₄×C₁₃₁	—	4	2	no	—
184	C₂×C₄×C₁₃₁	#121	1	2	yes	—
185	C₂×C₄×C₁₃₁	#121	1	2	yes	—
186	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
189	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
190	C₈×C₁₃₁	—	4	2	no	—
191	C₈×C₁₃₁	—	4	1	no	—
192	C₈×C₁₃₁	—	4	1	no	—
193	C₂²×C₁₃₁	—	8	1	no	—
194	C₂²×C₁₃₁	—	8	2	no	—
195	C₂²×C₁₃₁	—	8	2	no	—
196	C₂²×C₁₃₁	—	8	1	no	—
197	C₂²×C₁₃₁	—	8	1	no	—
198	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
199	C₂²×C₁₃₁	#537	1	2	yes	—
200	C₂²×C₁₃₁	#577	1	2	yes	—
201	C₂²×C₁₃₁	#577	1	1	yes	characteristic
202	C₂²×C₁₃₁	#578	1	1	yes	characteristic
203	C₄×C₁₃₁	—	2	2	no	—
204	C₄×C₁₃₁	—	2	2	no	—
205	C₄×C₁₃₁	—	4	2	no	—
206	C₄×C₁₃₁	—	4	2	no	—
207	C₄×C₁₃₁	—	4	2	no	—
208	C₄×C₁₃₁	—	4	2	no	—
209	C₄×C₁₃₁	—	8	1	no	—
210	C₄×C₁₃₁	—	8	2	no	—
211	C₄×C₁₃₁	—	8	2	no	—
212	C₄×C₁₃₁	#535	1	1	yes	characteristic
213	C₄×C₁₃₁	#536	1	1	yes	characteristic
214	C₄×C₁₃₁	#542	1	2	yes	—
215	C₂×C₁₃₁	—	16	1	no	—
216	C₂×C₁₃₁	#2620	1	1	yes	characteristic
217	C₂×C₁₃₁	#3043	1	1	yes	characteristic
218	C₂×C₁₃₁	#3046	1	1	yes	characteristic
219	C₂×C₁₃₁	#3258	1	2	yes	—
220	C₂×C₁₃₁	#3263	1	2	yes	—
221	#29841	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₁₃₁	#29841	1	1	yes	characteristic, direct product factor, Sylow
223	C₂×#475	C₂×C₁₃₁	1	1	yes	characteristic, complemented
224	C₂×#464	C₂×C₁₃₁	1	1	yes	characteristic
225	#2640	C₂×C₁₃₁	1	1	yes	characteristic
226	#2320	C₂×C₁₃₁	1	1	yes	characteristic, complemented
227	#2066	C₂×C₁₃₁	1	2	yes	complemented
228	#2065	C₂×C₁₃₁	1	2	yes	—
229	#2056	C₂×C₁₃₁	1	2	yes	complemented
230	#2055	C₂×C₁₃₁	1	2	yes	—
231	#1987	C₂×C₁₃₁	1	1	yes	characteristic, complemented
232	#1983	C₂×C₁₃₁	1	1	yes	characteristic
233	#1843	C₂×C₁₃₁	1	1	yes	characteristic, complemented
234	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
235	C₂²×SD₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
237	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
239	#475	—	2	4	no	—
240	#464	—	2	4	no	—
241	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
246	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
247	C₂×#103	C₂²×C₁₃₁	1	1	yes	characteristic
248	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
249	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
250	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
251	#397	—	2	2	no	—
252	#393	—	2	1	no	—
253	#393	—	2	1	no	—
254	#391	C₂²×C₁₃₁	1	2	yes	—
255	#391	C₂²×C₁₃₁	1	2	yes	—
256	#390	C₂²×C₁₃₁	1	2	yes	—
257	#389	C₂²×C₁₃₁	1	2	yes	—
258	#387	—	2	2	no	—
259	#383	—	2	1	no	—
260	#382	—	2	1	no	—
261	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
262	#376	C₂²×C₁₃₁	1	1	yes	characteristic
263	#340	C₂²×C₁₃₁	1	2	yes	—
264	#340	C₂²×C₁₃₁	1	2	yes	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
267	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
268	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×Q₁₆	—	4	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	4	2	no	—
273	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	#124	—	2	2	no	—
279	#124	—	2	2	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	D₄×C₁₃₁	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
295	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
296	#106	—	2	4	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	4	2	no	—
300	C₄⋊C₈	—	4	2	no	—
301	#103	—	2	4	no	—
302	#103	—	2	2	no	—
303	#103	—	4	2	no	—
304	#102	—	2	2	no	—
305	#102	—	4	2	no	—
306	#95	—	2	1	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	D₄×C₁₃₁	1	1	yes	characteristic
313	#95	D₄×C₁₃₁	1	1	yes	characteristic
314	#95	D₄×C₁₃₁	1	2	yes	—
315	C₂⁴	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×Q₈	C₂×D₄×C₁₃₁	1	2	yes	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
340	Q₁₆	—	4	4	no	—
341	SD₁₆	—	4	4	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	8	2	no	—
357	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₂²⋊C₄	—	8	2	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	8	1	no	—
366	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
367	C₄²	#41×C₁₃₁	1	2	yes	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	8	4	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	1	no	—
383	D₄	—	4	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	#121×C₁₃₁	1	2	yes	—
407	C₂×C₄	#121×C₁₃₁	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
410	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
411	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
412	C₈	—	4	1	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
421	C₂²	#537×C₁₃₁	1	2	yes	—
422	C₂²	#577×C₁₃₁	1	2	yes	—
423	C₂²	#577×C₁₃₁	1	1	yes	characteristic
424	C₂²	#578×C₁₃₁	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	2	no	—
433	C₄	—	8	1	no	—
434	C₄	#535×C₁₃₁	1	1	yes	characteristic
435	C₄	#536×C₁₃₁	1	1	yes	characteristic
436	C₄	#542×C₁₃₁	1	2	yes	—
437	C₂	—	16	1	no	—
438	C₂	#2620×C₁₃₁	1	1	yes	characteristic
439	C₂	#3043×C₁₃₁	1	1	yes	characteristic
440	C₂	#3046×C₁₃₁	1	1	yes	characteristic
441	C₂	#3258×C₁₃₁	1	2	yes	—
442	C₂	#3263×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
1. C₂×#475×C₁₃₁	C₂	semidirect
4. #2320×C₁₃₁	C₂	semidirect
5. #2066×C₁₃₁	C₂	semidirect
7. #2056×C₁₃₁	C₂	semidirect
9. #1987×C₁₃₁	C₂	semidirect
11. #1843×C₁₃₁	C₂	semidirect
221. #29841	C₁₃₁	direct (N × H)
222. C₁₃₁	#29841	direct (N × H)
223. C₂×#475	C₂×C₁₃₁	semidirect
226. #2320	C₂×C₁₃₁	semidirect
227. #2066	C₂×C₁₃₁	semidirect
229. #2056	C₂×C₁₃₁	semidirect
231. #1987	C₂×C₁₃₁	semidirect
233. #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×#475×C₁₃₁	2
C₂×#464×C₁₃₁	2
#2640×C₁₃₁	2
#2320×C₁₃₁	2
#2066×C₁₃₁	2
#2065×C₁₃₁	2
#2056×C₁₃₁	2
#2055×C₁₃₁	2
#1987×C₁₃₁	2
#1983×C₁₃₁	2
#1843×C₁₃₁	2
#29841	131

Subgroups — C131×#29841 #45715725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29841 #45715725