Subgroups — C₁₃₁×#29494 #45715378

Order 33536.

782 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2860×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2084×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2071×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2043×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2013×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1968×C₁₃₁	C₂	1	2	yes	maximal
8	#1933×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1880×C₁₃₁	C₂	1	2	yes	maximal
10	#1865×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1744×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×#126×C₁₃₁	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
16	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
17	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
22	#391×C₁₃₁	C₂²	1	2	yes	—
23	#390×C₁₃₁	C₂²	1	1	yes	characteristic
24	#390×C₁₃₁	C₂²	1	1	yes	characteristic
25	#390×C₁₃₁	C₂²	1	1	yes	characteristic
26	#389×C₁₃₁	—	2	1	no	—
27	#389×C₁₃₁	—	2	1	no	—
28	#389×C₁₃₁	C₂²	1	1	yes	characteristic
29	#389×C₁₃₁	C₂²	1	1	yes	characteristic
30	#389×C₁₃₁	C₂²	1	1	yes	characteristic
31	#388×C₁₃₁	—	2	1	no	—
32	#388×C₁₃₁	—	2	1	no	—
33	#388×C₁₃₁	—	2	1	no	—
34	#384×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₃₁	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₃₁	—	2	1	no	—
37	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
38	#340×C₁₃₁	C₂²	1	2	yes	—
39	#340×C₁₃₁	C₂²	1	2	yes	—
40	#336×C₁₃₁	C₂²	1	1	yes	characteristic
41	#336×C₁₃₁	C₂²	1	1	yes	characteristic
42	#336×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
46	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
47	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
48	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
51	#126×C₁₃₁	—	4	4	no	—
52	C₄×Q₈×C₁₃₁	—	4	2	no	—
53	C₄×Q₈×C₁₃₁	—	4	2	no	—
54	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
72	C₂×C₄²×C₁₃₁	—	2	2	no	—
73	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
80	#106×C₁₃₁	—	4	2	no	—
81	#103×C₁₃₁	—	2	4	no	—
82	#103×C₁₃₁	—	2	4	no	—
83	#103×C₁₃₁	—	4	2	no	—
84	#102×C₁₃₁	—	4	2	no	—
85	C₄×C₈×C₁₃₁	—	2	4	no	—
86	#95×C₁₃₁	—	2	1	no	—
87	#95×C₁₃₁	—	2	1	no	—
88	#95×C₁₃₁	—	2	1	no	—
89	#95×C₁₃₁	—	2	2	no	—
90	#95×C₁₃₁	—	2	2	no	—
91	C₂⁴×C₁₃₁	—	2	1	no	—
92	C₂×Q₈×C₁₃₁	—	2	2	no	—
93	C₂×Q₈×C₁₃₁	—	2	2	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	#41	1	4	yes	—
98	C₂×D₄×C₁₃₁	—	2	2	no	—
99	C₂×D₄×C₁₃₁	—	2	2	no	—
100	C₂×D₄×C₁₃₁	—	2	1	no	—
101	C₂×D₄×C₁₃₁	—	2	1	no	—
102	C₂²×C₄×C₁₃₁	—	2	2	no	—
103	C₂²×C₄×C₁₃₁	—	2	2	no	—
104	C₂²×C₄×C₁₃₁	—	2	1	no	—
105	C₂²×C₄×C₁₃₁	—	2	1	no	—
106	C₂²×C₄×C₁₃₁	—	2	1	no	—
107	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
114	SD₁₆×C₁₃₁	—	4	8	no	—
115	C₂×C₈×C₁₃₁	—	2	2	no	—
116	C₂×C₈×C₁₃₁	—	2	2	no	—
117	C₂×C₈×C₁₃₁	—	2	2	no	—
118	C₂×C₈×C₁₃₁	—	2	2	no	—
119	C₂×C₈×C₁₃₁	—	2	2	no	—
120	C₂×C₈×C₁₃₁	#41	1	4	yes	—
121	C₄⋊C₄×C₁₃₁	—	2	4	no	—
122	C₄⋊C₄×C₁₃₁	—	2	4	no	—
123	C₄⋊C₄×C₁₃₁	—	2	2	no	—
124	C₄⋊C₄×C₁₃₁	—	2	2	no	—
125	C₄⋊C₄×C₁₃₁	—	2	2	no	—
126	C₄⋊C₄×C₁₃₁	—	2	1	no	—
127	C₄⋊C₄×C₁₃₁	—	2	1	no	—
128	C₄⋊C₄×C₁₃₁	—	2	2	no	—
129	C₄⋊C₄×C₁₃₁	—	4	2	no	—
130	C₄⋊C₄×C₁₃₁	—	4	4	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	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
136	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
137	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
138	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
139	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
140	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
141	C₄²×C₁₃₁	—	2	2	no	—
142	C₄²×C₁₃₁	—	2	2	no	—
143	C₄²×C₁₃₁	—	2	2	no	—
144	C₄²×C₁₃₁	—	2	2	no	—
145	C₄²×C₁₃₁	—	2	1	no	—
146	C₄²×C₁₃₁	—	2	1	no	—
147	C₄²×C₁₃₁	—	4	1	no	—
148	C₄²×C₁₃₁	—	4	4	no	—
149	C₄²×C₁₃₁	SD₁₆	1	4	yes	complemented
150	C₂³×C₁₃₁	—	4	1	no	—
151	C₂³×C₁₃₁	—	4	1	no	—
152	C₂³×C₁₃₁	—	4	1	no	—
153	C₂³×C₁₃₁	—	4	1	no	—
154	C₂³×C₁₃₁	—	4	1	no	—
155	C₂³×C₁₃₁	—	4	1	no	—
156	C₂³×C₁₃₁	—	4	1	no	—
157	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₃₁	—	2	4	no	—
159	Q₈×C₁₃₁	—	2	4	no	—
160	Q₈×C₁₃₁	—	4	2	no	—
161	Q₈×C₁₃₁	—	4	2	no	—
162	D₄×C₁₃₁	—	4	2	no	—
163	D₄×C₁₃₁	—	4	2	no	—
164	C₂×C₄×C₁₃₁	—	2	1	no	—
165	C₂×C₄×C₁₃₁	—	2	1	no	—
166	C₂×C₄×C₁₃₁	—	2	1	no	—
167	C₂×C₄×C₁₃₁	—	2	1	no	—
168	C₂×C₄×C₁₃₁	—	2	1	no	—
169	C₂×C₄×C₁₃₁	—	2	1	no	—
170	C₂×C₄×C₁₃₁	—	2	1	no	—
171	C₂×C₄×C₁₃₁	—	2	1	no	—
172	C₂×C₄×C₁₃₁	—	2	1	no	—
173	C₂×C₄×C₁₃₁	—	2	1	no	—
174	C₂×C₄×C₁₃₁	—	2	4	no	—
175	C₂×C₄×C₁₃₁	—	2	1	no	—
176	C₂×C₄×C₁₃₁	—	2	1	no	—
177	C₂×C₄×C₁₃₁	—	2	1	no	—
178	C₂×C₄×C₁₃₁	—	4	2	no	—
179	C₂×C₄×C₁₃₁	—	4	2	no	—
180	C₂×C₄×C₁₃₁	—	4	1	no	—
181	C₂×C₄×C₁₃₁	—	4	1	no	—
182	C₂×C₄×C₁₃₁	—	4	2	no	—
183	C₂×C₄×C₁₃₁	—	4	1	no	—
184	C₂×C₄×C₁₃₁	—	4	1	no	—
185	C₂×C₄×C₁₃₁	—	4	1	no	—
186	C₂×C₄×C₁₃₁	—	4	1	no	—
187	C₂×C₄×C₁₃₁	—	4	1	no	—
188	C₂×C₄×C₁₃₁	—	4	2	no	—
189	C₂×C₄×C₁₃₁	—	4	1	no	—
190	C₂×C₄×C₁₃₁	—	4	1	no	—
191	C₂×C₄×C₁₃₁	—	4	2	no	—
192	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	2	yes	—
193	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	2	yes	—
194	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	2	yes	—
195	C₂×C₄×C₁₃₁	#135	1	2	yes	—
196	C₂×C₄×C₁₃₁	#137	1	2	yes	—
197	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
199	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
201	C₈×C₁₃₁	—	2	4	no	—
202	C₈×C₁₃₁	—	4	2	no	—
203	C₂²×C₁₃₁	—	8	1	no	—
204	C₂²×C₁₃₁	—	8	1	no	—
205	C₂²×C₁₃₁	—	8	1	no	—
206	C₂²×C₁₃₁	—	8	1	no	—
207	C₂²×C₁₃₁	—	8	1	no	—
208	C₂²×C₁₃₁	—	8	1	no	—
209	C₂²×C₁₃₁	—	8	1	no	—
210	C₂²×C₁₃₁	#525	1	1	yes	characteristic
211	C₂²×C₁₃₁	#532	1	1	yes	characteristic
212	C₂²×C₁₃₁	#535	1	1	yes	characteristic
213	C₂²×C₁₃₁	C₂²×SD₁₆	1	1	yes	characteristic
214	C₂²×C₁₃₁	C₂×#135	1	1	yes	characteristic
215	C₂²×C₁₃₁	C₂×#137	1	1	yes	characteristic
216	C₂²×C₁₃₁	#575	1	1	yes	characteristic
217	C₄×C₁₃₁	—	2	2	no	—
218	C₄×C₁₃₁	—	2	2	no	—
219	C₄×C₁₃₁	—	2	2	no	—
220	C₄×C₁₃₁	—	2	2	no	—
221	C₄×C₁₃₁	—	2	2	no	—
222	C₄×C₁₃₁	—	4	4	no	—
223	C₄×C₁₃₁	—	4	1	no	—
224	C₄×C₁₃₁	—	8	1	no	—
225	C₄×C₁₃₁	—	8	1	no	—
226	C₄×C₁₃₁	—	8	1	no	—
227	C₄×C₁₃₁	—	8	2	no	—
228	C₄×C₁₃₁	#551	1	2	yes	—
229	C₄×C₁₃₁	#553	1	2	yes	—
230	C₂×C₁₃₁	—	16	1	no	—
231	C₂×C₁₃₁	#2603	1	1	yes	characteristic
232	C₂×C₁₃₁	#3103	1	1	yes	characteristic
233	C₂×C₁₃₁	#3108	1	1	yes	characteristic
234	C₂×C₁₃₁	#3167	1	1	yes	characteristic
235	C₂×C₁₃₁	#3181	1	1	yes	characteristic
236	C₂×C₁₃₁	#3206	1	1	yes	characteristic
237	C₂×C₁₃₁	#3212	1	1	yes	characteristic
238	#29494	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₁₃₁	#29494	1	1	yes	characteristic, direct product factor, Sylow
240	#2860	C₂×C₁₃₁	1	1	yes	characteristic
241	C₄×C₄⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
242	#2084	C₂×C₁₃₁	1	1	yes	characteristic, complemented
243	#2071	C₂×C₁₃₁	1	1	yes	characteristic
244	#2043	C₂×C₁₃₁	1	1	yes	characteristic, complemented
245	#2013	C₂×C₁₃₁	1	1	yes	characteristic
246	#1968	C₂×C₁₃₁	1	2	yes	—
247	#1933	C₂×C₁₃₁	1	2	yes	complemented
248	#1880	C₂×C₁₃₁	1	2	yes	—
249	#1865	C₂×C₁₃₁	1	2	yes	complemented
250	#1744	C₂×C₁₃₁	1	1	yes	characteristic, complemented
251	C₂²×SD₁₆	C₂²×C₁₃₁	1	2	yes	—
252	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
253	C₂×#126	—	2	1	no	—
254	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
255	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
256	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
257	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
258	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
259	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
260	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
261	#391	C₂²×C₁₃₁	1	2	yes	—
262	#390	C₂²×C₁₃₁	1	1	yes	characteristic
263	#390	C₂²×C₁₃₁	1	1	yes	characteristic
264	#390	C₂²×C₁₃₁	1	1	yes	characteristic
265	#389	—	2	1	no	—
266	#389	—	2	1	no	—
267	#389	C₂²×C₁₃₁	1	1	yes	characteristic
268	#389	C₂²×C₁₃₁	1	1	yes	characteristic
269	#389	C₂²×C₁₃₁	1	1	yes	characteristic
270	#388	—	2	1	no	—
271	#388	—	2	1	no	—
272	#388	—	2	1	no	—
273	#384	C₂²×C₁₃₁	1	1	yes	characteristic
274	C₄×C₄⋊C₄	—	2	1	no	—
275	C₄×C₄⋊C₄	—	2	1	no	—
276	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
277	#340	C₂²×C₁₃₁	1	2	yes	—
278	#340	C₂²×C₁₃₁	1	2	yes	—
279	#336	C₂²×C₁₃₁	1	1	yes	characteristic
280	#336	C₂²×C₁₃₁	1	1	yes	characteristic
281	#336	C₂²×C₁₃₁	1	2	yes	—
282	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
283	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
284	C₂×SD₁₆	—	2	4	no	—
285	C₂×SD₁₆	—	2	4	no	—
286	C₂×SD₁₆	—	4	2	no	—
287	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
289	C₄⋊Q₈	—	2	4	no	—
290	#126	—	4	4	no	—
291	C₄×Q₈	—	4	2	no	—
292	C₄×Q₈	—	4	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
313	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
314	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
315	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
319	#106	—	4	2	no	—
320	#103	—	2	4	no	—
321	#103	—	2	4	no	—
322	#103	—	4	2	no	—
323	#102	—	4	2	no	—
324	C₄×C₈	—	2	4	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	#95	—	2	1	no	—
330	C₂⁴	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	#41×C₁₃₁	1	4	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
353	SD₁₆	—	4	8	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	#41×C₁₃₁	1	4	yes	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	4	no	—
388	C₄²	SD₁₆×C₁₃₁	1	4	yes	complemented
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	2	yes	—
432	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	2	yes	—
433	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	2	yes	—
434	C₂×C₄	#135×C₁₃₁	1	2	yes	—
435	C₂×C₄	#137×C₁₃₁	1	2	yes	—
436	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
437	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
438	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
439	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
440	C₈	—	2	4	no	—
441	C₈	—	4	2	no	—
442	C₂²	—	8	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	#525×C₁₃₁	1	1	yes	characteristic
450	C₂²	#532×C₁₃₁	1	1	yes	characteristic
451	C₂²	#535×C₁₃₁	1	1	yes	characteristic
452	C₂²	C₂²×SD₁₆×C₁₃₁	1	1	yes	characteristic
453	C₂²	C₂×#135×C₁₃₁	1	1	yes	characteristic
454	C₂²	C₂×#137×C₁₃₁	1	1	yes	characteristic
455	C₂²	#575×C₁₃₁	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	1	no	—
463	C₄	—	8	1	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	2	no	—
467	C₄	#551×C₁₃₁	1	2	yes	—
468	C₄	#553×C₁₃₁	1	2	yes	—
469	C₂	—	16	1	no	—
470	C₂	#2603×C₁₃₁	1	1	yes	characteristic
471	C₂	#3103×C₁₃₁	1	1	yes	characteristic
472	C₂	#3108×C₁₃₁	1	1	yes	characteristic
473	C₂	#3167×C₁₃₁	1	1	yes	characteristic
474	C₂	#3181×C₁₃₁	1	1	yes	characteristic
475	C₂	#3206×C₁₃₁	1	1	yes	characteristic
476	C₂	#3212×C₁₃₁	1	1	yes	characteristic

	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 ◁ C₄³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊Q₈×C₁₃₁	C₂	semidirect
3. #2084×C₁₃₁	C₂	semidirect
5. #2043×C₁₃₁	C₂	semidirect
8. #1933×C₁₃₁	C₂	semidirect
10. #1865×C₁₃₁	C₂	semidirect
11. #1744×C₁₃₁	C₂	semidirect
149. C₄²×C₁₃₁	SD₁₆	semidirect
238. #29494	C₁₃₁	direct (N × H)
239. C₁₃₁	#29494	direct (N × H)
241. C₄×C₄⋊Q₈	C₂×C₁₃₁	semidirect
242. #2084	C₂×C₁₃₁	semidirect
244. #2043	C₂×C₁₃₁	semidirect
247. #1933	C₂×C₁₃₁	semidirect
249. #1865	C₂×C₁₃₁	semidirect
250. #1744	C₂×C₁₃₁	semidirect
388. C₄²	SD₁₆×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2860×C₁₃₁	2
C₄×C₄⋊Q₈×C₁₃₁	2
#2084×C₁₃₁	2
#2071×C₁₃₁	2
#2043×C₁₃₁	2
#2013×C₁₃₁	2
#1968×C₁₃₁	2
#1933×C₁₃₁	2
#1880×C₁₃₁	2
#1865×C₁₃₁	2
#1744×C₁₃₁	2
#29494	131

Subgroups — C131×#29494 #45715378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29494 #45715378