Subgroups — C₁₃₁×#29131 #45715015

Order 33536.

742 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2859×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#124×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2101×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2042×C₁₃₁	C₂	1	2	yes	maximal
5	#1936×C₁₃₁	C₂	1	2	yes	maximal
6	#1935×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1803×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1803×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1802×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	#1802×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	#1767×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₁₃₁	—	2	1	no	—
13	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
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×#102×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
23	#391×C₁₃₁	C₂²	1	1	yes	characteristic
24	#390×C₁₃₁	C₂²	1	1	yes	characteristic
25	#389×C₁₃₁	—	2	1	no	—
26	#389×C₁₃₁	—	2	1	no	—
27	#389×C₁₃₁	C₂²	1	2	yes	—
28	#389×C₁₃₁	C₂²	1	2	yes	—
29	#388×C₁₃₁	—	2	1	no	—
30	#388×C₁₃₁	—	2	1	no	—
31	#384×C₁₃₁	C₂²	1	1	yes	characteristic
32	#384×C₁₃₁	C₂²	1	1	yes	characteristic
33	#382×C₁₃₁	—	2	1	no	—
34	#382×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
36	C₄×C₂²⋊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	#340×C₁₃₁	C₂²	1	2	yes	—
41	#340×C₁₃₁	C₂²	1	2	yes	—
42	#336×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₁	—	2	1	no	—
46	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
48	#125×C₁₃₁	—	4	4	no	—
49	#124×C₁₃₁	—	2	2	no	—
50	#124×C₁₃₁	—	2	2	no	—
51	C₄×Q₈×C₁₃₁	—	2	2	no	—
52	C₄×Q₈×C₁₃₁	—	2	2	no	—
53	C₄×D₄×C₁₃₁	—	2	2	no	—
54	C₄×D₄×C₁₃₁	—	2	2	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	2	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	2	yes	—
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×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×C₄²×C₁₃₁	—	2	1	no	—
72	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₁₃₁	—	2	2	no	—
80	C₄⋊C₈×C₁₃₁	—	2	2	no	—
81	#103×C₁₃₁	—	2	4	no	—
82	#103×C₁₃₁	—	4	2	no	—
83	#102×C₁₃₁	—	2	4	no	—
84	#102×C₁₃₁	—	4	2	no	—
85	#97×C₁₃₁	—	4	2	no	—
86	#95×C₁₃₁	—	2	1	no	—
87	#95×C₁₃₁	—	2	1	no	—
88	#95×C₁₃₁	—	2	1	no	—
89	#95×C₁₃₁	—	2	1	no	—
90	#95×C₁₃₁	—	2	2	no	—
91	#95×C₁₃₁	—	2	2	no	—
92	C₂⁴×C₁₃₁	—	2	1	no	—
93	C₂×Q₈×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	1	no	—
98	C₂×Q₈×C₁₃₁	#41	1	2	yes	—
99	C₂×D₄×C₁₃₁	—	2	1	no	—
100	C₂×D₄×C₁₃₁	—	2	1	no	—
101	C₂×D₄×C₁₃₁	—	2	1	no	—
102	C₂×D₄×C₁₃₁	—	2	1	no	—
103	C₂×D₄×C₁₃₁	—	2	1	no	—
104	C₂×D₄×C₁₃₁	#41	1	2	yes	—
105	C₂²×C₄×C₁₃₁	—	2	1	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	—	4	2	no	—
111	C₂²×C₄×C₁₃₁	—	4	2	no	—
112	C₂²×C₄×C₁₃₁	—	4	2	no	—
113	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₁₃₁	—	2	2	no	—
125	C₂×C₈×C₁₃₁	—	2	2	no	—
126	C₄⋊C₄×C₁₃₁	—	2	2	no	—
127	C₄⋊C₄×C₁₃₁	—	2	2	no	—
128	C₄⋊C₄×C₁₃₁	—	2	1	no	—
129	C₄⋊C₄×C₁₃₁	—	2	1	no	—
130	C₄⋊C₄×C₁₃₁	—	2	1	no	—
131	C₄⋊C₄×C₁₃₁	—	2	1	no	—
132	C₄⋊C₄×C₁₃₁	—	2	2	no	—
133	C₄⋊C₄×C₁₃₁	—	2	2	no	—
134	C₄⋊C₄×C₁₃₁	—	4	2	no	—
135	C₄⋊C₄×C₁₃₁	—	4	2	no	—
136	C₄⋊C₄×C₁₃₁	—	4	4	no	—
137	C₄⋊C₄×C₁₃₁	—	4	4	no	—
138	C₄⋊C₄×C₁₃₁	—	4	2	no	—
139	C₄⋊C₄×C₁₃₁	—	4	2	no	—
140	C₄⋊C₄×C₁₃₁	—	4	2	no	—
141	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
142	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
143	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
144	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
145	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
146	C₄²×C₁₃₁	—	2	2	no	—
147	C₄²×C₁₃₁	—	2	2	no	—
148	C₄²×C₁₃₁	—	2	1	no	—
149	C₄²×C₁₃₁	—	2	1	no	—
150	C₄²×C₁₃₁	—	2	1	no	—
151	C₄²×C₁₃₁	—	2	1	no	—
152	C₄²×C₁₃₁	—	4	1	no	—
153	C₄²×C₁₃₁	—	4	1	no	—
154	C₄²×C₁₃₁	—	4	2	no	—
155	C₄²×C₁₃₁	#41	1	2	yes	—
156	C₄²×C₁₃₁	#41	1	2	yes	—
157	C₂³×C₁₃₁	—	2	2	no	—
158	C₂³×C₁₃₁	—	4	1	no	—
159	C₂³×C₁₃₁	—	4	1	no	—
160	C₂³×C₁₃₁	—	4	1	no	—
161	C₂³×C₁₃₁	—	4	1	no	—
162	C₂³×C₁₃₁	—	4	1	no	—
163	C₂³×C₁₃₁	—	4	1	no	—
164	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃₁	—	2	2	no	—
166	Q₈×C₁₃₁	—	2	2	no	—
167	Q₈×C₁₃₁	—	4	1	no	—
168	Q₈×C₁₃₁	—	4	1	no	—
169	D₄×C₁₃₁	—	2	2	no	—
170	D₄×C₁₃₁	—	2	2	no	—
171	D₄×C₁₃₁	—	4	1	no	—
172	D₄×C₁₃₁	—	4	1	no	—
173	C₂×C₄×C₁₃₁	—	2	1	no	—
174	C₂×C₄×C₁₃₁	—	2	1	no	—
175	C₂×C₄×C₁₃₁	—	2	1	no	—
176	C₂×C₄×C₁₃₁	—	2	1	no	—
177	C₂×C₄×C₁₃₁	—	2	2	no	—
178	C₂×C₄×C₁₃₁	—	2	1	no	—
179	C₂×C₄×C₁₃₁	—	2	1	no	—
180	C₂×C₄×C₁₃₁	—	2	1	no	—
181	C₂×C₄×C₁₃₁	—	2	1	no	—
182	C₂×C₄×C₁₃₁	—	2	1	no	—
183	C₂×C₄×C₁₃₁	—	2	1	no	—
184	C₂×C₄×C₁₃₁	—	2	1	no	—
185	C₂×C₄×C₁₃₁	—	2	1	no	—
186	C₂×C₄×C₁₃₁	—	2	1	no	—
187	C₂×C₄×C₁₃₁	—	2	1	no	—
188	C₂×C₄×C₁₃₁	—	4	1	no	—
189	C₂×C₄×C₁₃₁	—	4	1	no	—
190	C₂×C₄×C₁₃₁	—	4	2	no	—
191	C₂×C₄×C₁₃₁	—	4	1	no	—
192	C₂×C₄×C₁₃₁	—	4	1	no	—
193	C₂×C₄×C₁₃₁	—	4	2	no	—
194	C₂×C₄×C₁₃₁	—	4	2	no	—
195	C₂×C₄×C₁₃₁	—	4	2	no	—
196	C₂×C₄×C₁₃₁	—	4	1	no	—
197	C₂×C₄×C₁₃₁	—	4	1	no	—
198	C₂×C₄×C₁₃₁	—	4	1	no	—
199	C₂×C₄×C₁₃₁	—	4	1	no	—
200	C₂×C₄×C₁₃₁	—	4	2	no	—
201	C₂×C₄×C₁₃₁	—	4	2	no	—
202	C₂×C₄×C₁₃₁	—	8	4	no	—
203	C₂×C₄×C₁₃₁	#124	1	2	yes	—
204	C₂×C₄×C₁₃₁	#124	1	2	yes	—
205	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₁₃₁	#137	1	2	yes	—
207	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
213	C₈×C₁₃₁	—	4	2	no	—
214	C₈×C₁₃₁	—	4	2	no	—
215	C₂²×C₁₃₁	—	4	2	no	—
216	C₂²×C₁₃₁	—	4	2	no	—
217	C₂²×C₁₃₁	—	4	2	no	—
218	C₂²×C₁₃₁	—	8	1	no	—
219	C₂²×C₁₃₁	—	8	1	no	—
220	C₂²×C₁₃₁	—	8	1	no	—
221	C₂²×C₁₃₁	—	8	1	no	—
222	C₂²×C₁₃₁	#525	1	1	yes	characteristic
223	C₂²×C₁₃₁	C₂×#124	1	1	yes	characteristic
224	C₂²×C₁₃₁	#537	1	1	yes	characteristic
225	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₂²×C₁₃₁	C₂×#137	1	1	yes	characteristic
227	C₂²×C₁₃₁	#575	1	1	yes	characteristic
228	C₂²×C₁₃₁	#575	1	1	yes	characteristic
229	C₄×C₁₃₁	—	2	2	no	—
230	C₄×C₁₃₁	—	4	2	no	—
231	C₄×C₁₃₁	—	4	1	no	—
232	C₄×C₁₃₁	—	4	1	no	—
233	C₄×C₁₃₁	—	4	1	no	—
234	C₄×C₁₃₁	—	4	1	no	—
235	C₄×C₁₃₁	—	8	2	no	—
236	C₄×C₁₃₁	—	8	1	no	—
237	C₄×C₁₃₁	—	8	1	no	—
238	C₄×C₁₃₁	—	8	2	no	—
239	C₄×C₁₃₁	#489	1	4	yes	—
240	C₄×C₁₃₁	#552	1	1	yes	characteristic
241	C₄×C₁₃₁	#552	1	1	yes	characteristic
242	C₄×C₁₃₁	#553	1	1	yes	characteristic
243	C₄×C₁₃₁	#553	1	1	yes	characteristic
244	C₂×C₁₃₁	—	8	2	no	—
245	C₂×C₁₃₁	#2562	1	1	yes	characteristic
246	C₂×C₁₃₁	#3115	1	1	yes	characteristic
247	C₂×C₁₃₁	#3116	1	1	yes	characteristic
248	C₂×C₁₃₁	C₂×#489	1	1	yes	characteristic
249	C₂×C₁₃₁	#3142	1	1	yes	characteristic
250	C₂×C₁₃₁	#3251	1	1	yes	characteristic
251	C₂×C₁₃₁	#3252	1	1	yes	characteristic
252	#29131	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₁₃₁	#29131	1	1	yes	characteristic, direct product factor, Sylow
254	#2859	C₂×C₁₃₁	1	1	yes	characteristic, complemented
255	C₄×#124	C₂×C₁₃₁	1	1	yes	characteristic
256	#2101	C₂×C₁₃₁	1	2	yes	complemented
257	#2042	C₂×C₁₃₁	1	2	yes	—
258	#1936	C₂×C₁₃₁	1	2	yes	—
259	#1935	C₂×C₁₃₁	1	2	yes	complemented
260	#1803	C₂×C₁₃₁	1	1	yes	characteristic, complemented
261	#1803	C₂×C₁₃₁	1	1	yes	characteristic, complemented
262	#1802	C₂×C₁₃₁	1	1	yes	characteristic
263	#1802	C₂×C₁₃₁	1	1	yes	characteristic
264	#1767	C₂×C₁₃₁	1	1	yes	characteristic, complemented
265	C₂×#125	—	2	1	no	—
266	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
271	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
272	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
273	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
274	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
275	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
276	#391	C₂²×C₁₃₁	1	1	yes	characteristic
277	#390	C₂²×C₁₃₁	1	1	yes	characteristic
278	#389	—	2	1	no	—
279	#389	—	2	1	no	—
280	#389	C₂²×C₁₃₁	1	2	yes	—
281	#389	C₂²×C₁₃₁	1	2	yes	—
282	#388	—	2	1	no	—
283	#388	—	2	1	no	—
284	#384	C₂²×C₁₃₁	1	1	yes	characteristic
285	#384	C₂²×C₁₃₁	1	1	yes	characteristic
286	#382	—	2	1	no	—
287	#382	C₂²×C₁₃₁	1	1	yes	characteristic
288	C₄×C₂²⋊C₄	—	2	1	no	—
289	C₄×C₂²⋊C₄	—	2	1	no	—
290	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
291	#340	C₂²×C₁₃₁	1	2	yes	—
292	#340	C₂²×C₁₃₁	1	2	yes	—
293	#340	C₂²×C₁₃₁	1	2	yes	—
294	#340	C₂²×C₁₃₁	1	2	yes	—
295	#336	C₂²×C₁₃₁	1	2	yes	—
296	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
297	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
300	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
301	#125	—	4	4	no	—
302	#124	—	2	2	no	—
303	#124	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
326	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
327	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
328	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	#103	—	2	4	no	—
335	#103	—	4	2	no	—
336	#102	—	2	4	no	—
337	#102	—	4	2	no	—
338	#97	—	4	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	C₂⁴	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	#41×C₁₃₁	1	2	yes	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	#41×C₁₃₁	1	2	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	4	1	no	—
406	C₄²	—	4	1	no	—
407	C₄²	—	4	2	no	—
408	C₄²	#41×C₁₃₁	1	2	yes	—
409	C₄²	#41×C₁₃₁	1	2	yes	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	8	4	no	—
456	C₂×C₄	#124×C₁₃₁	1	2	yes	—
457	C₂×C₄	#124×C₁₃₁	1	2	yes	—
458	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
459	C₂×C₄	#137×C₁₃₁	1	2	yes	—
460	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
464	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
465	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	#525×C₁₃₁	1	1	yes	characteristic
476	C₂²	C₂×#124×C₁₃₁	1	1	yes	characteristic
477	C₂²	#537×C₁₃₁	1	1	yes	characteristic
478	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
479	C₂²	C₂×#137×C₁₃₁	1	1	yes	characteristic
480	C₂²	#575×C₁₃₁	1	1	yes	characteristic
481	C₂²	#575×C₁₃₁	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	8	2	no	—
489	C₄	—	8	2	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	#489×C₁₃₁	1	4	yes	—
493	C₄	#552×C₁₃₁	1	1	yes	characteristic
494	C₄	#552×C₁₃₁	1	1	yes	characteristic
495	C₄	#553×C₁₃₁	1	1	yes	characteristic
496	C₄	#553×C₁₃₁	1	1	yes	characteristic
497	C₂	—	8	2	no	—
498	C₂	#2562×C₁₃₁	1	1	yes	characteristic
499	C₂	#3115×C₁₃₁	1	1	yes	characteristic
500	C₂	#3116×C₁₃₁	1	1	yes	characteristic
501	C₂	C₂×#489×C₁₃₁	1	1	yes	characteristic
502	C₂	#3142×C₁₃₁	1	1	yes	characteristic
503	C₂	#3251×C₁₃₁	1	1	yes	characteristic
504	C₂	#3252×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
1. #2859×C₁₃₁	C₂	semidirect
3. #2101×C₁₃₁	C₂	semidirect
6. #1935×C₁₃₁	C₂	semidirect
7. #1803×C₁₃₁	C₂	semidirect
8. #1803×C₁₃₁	C₂	semidirect
11. #1767×C₁₃₁	C₂	semidirect
252. #29131	C₁₃₁	direct (N × H)
253. C₁₃₁	#29131	direct (N × H)
254. #2859	C₂×C₁₃₁	semidirect
256. #2101	C₂×C₁₃₁	semidirect
259. #1935	C₂×C₁₃₁	semidirect
260. #1803	C₂×C₁₃₁	semidirect
261. #1803	C₂×C₁₃₁	semidirect
264. #1767	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2859×C₁₃₁	2
C₄×#124×C₁₃₁	2
#2101×C₁₃₁	2
#2042×C₁₃₁	2
#1936×C₁₃₁	2
#1935×C₁₃₁	2
#1803×C₁₃₁	2
#1802×C₁₃₁	2
#1767×C₁₃₁	2
#29131	131

Subgroups — C131×#29131 #45715015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29131 #45715015