Subgroups — C₁₃₁×#22562 #45708446

Order 33536.

1206 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#102×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2344×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1936×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1926×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1864×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1823×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1807×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1786×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	#1762×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1752×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
15	C₂×#117×C₁₃₁	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
18	C₂×#106×C₁₃₁	C₂²	1	2	yes	complemented
19	C₂×#102×C₁₃₁	C₄	1	8	yes	complemented
20	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×#97×C₁₃₁	C₂²	1	2	yes	complemented
28	#390×C₁₃₁	C₂²	1	2	yes	—
29	#389×C₁₃₁	C₂²	1	2	yes	complemented
30	#387×C₁₃₁	—	2	2	no	—
31	#386×C₁₃₁	—	2	2	no	—
32	#381×C₁₃₁	—	2	1	no	—
33	#380×C₁₃₁	C₂²	1	1	yes	characteristic
34	#380×C₁₃₁	C₂²	1	1	yes	characteristic
35	#379×C₁₃₁	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
37	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
38	#340×C₁₃₁	C₂²	1	2	yes	complemented
39	#340×C₁₃₁	C₂²	1	2	yes	complemented
40	#340×C₁₃₁	C₂²	1	2	yes	complemented
41	#336×C₁₃₁	C₂²	1	2	yes	complemented
42	C₂⁵×C₁₃₁	—	2	1	no	—
43	C₂²×D₄×C₁₃₁	—	2	4	no	—
44	C₂²×D₄×C₁₃₁	—	2	1	no	—
45	C₂²×D₄×C₁₃₁	—	2	2	no	—
46	C₂²×D₄×C₁₃₁	—	4	2	no	—
47	C₂²×D₄×C₁₃₁	C₂×C₄	1	4	yes	—
48	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₁	—	2	1	no	—
51	C₂³×C₄×C₁₃₁	—	2	2	no	—
52	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₁	—	4	2	no	—
54	C₂²×C₈×C₁₃₁	C₂×C₄	1	4	yes	complemented
55	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₃₁	—	2	4	no	—
59	C₄×D₄×C₁₃₁	—	4	2	no	—
60	#117×C₁₃₁	—	4	4	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	4	yes	complemented
65	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
75	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₁	—	2	2	no	—
78	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
79	#106×C₁₃₁	—	4	2	no	—
80	#102×C₁₃₁	—	2	4	no	—
81	#102×C₁₃₁	—	4	2	no	—
82	#102×C₁₃₁	C₂×C₄	1	4	yes	—
83	#102×C₁₃₁	C₂×C₄	1	4	yes	—
84	#102×C₁₃₁	C₂×C₄	1	4	yes	complemented
85	#102×C₁₃₁	C₂×C₄	1	4	yes	complemented
86	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
87	#97×C₁₃₁	—	4	2	no	—
88	#95×C₁₃₁	—	2	2	no	—
89	#95×C₁₃₁	—	2	2	no	—
90	#95×C₁₃₁	—	2	1	no	—
91	#95×C₁₃₁	—	2	1	no	—
92	#95×C₁₃₁	D₄	1	2	yes	—
93	C₂⁴×C₁₃₁	—	2	1	no	—
94	C₂⁴×C₁₃₁	—	2	1	no	—
95	C₂⁴×C₁₃₁	—	2	4	no	—
96	C₂⁴×C₁₃₁	—	4	4	no	—
97	C₂⁴×C₁₃₁	—	4	2	no	—
98	C₂⁴×C₁₃₁	—	4	2	no	—
99	C₂⁴×C₁₃₁	—	8	2	no	—
100	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₁₃₁	—	2	8	no	—
102	C₂×D₄×C₁₃₁	—	2	4	no	—
103	C₂×D₄×C₁₃₁	—	2	1	no	—
104	C₂×D₄×C₁₃₁	—	2	2	no	—
105	C₂×D₄×C₁₃₁	—	2	1	no	—
106	C₂×D₄×C₁₃₁	—	2	2	no	—
107	C₂×D₄×C₁₃₁	—	2	2	no	—
108	C₂×D₄×C₁₃₁	—	4	4	no	—
109	C₂×D₄×C₁₃₁	—	4	8	no	—
110	C₂×D₄×C₁₃₁	—	4	4	no	—
111	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
113	C₂×D₄×C₁₃₁	#41	1	4	yes	—
114	C₂²×C₄×C₁₃₁	—	2	2	no	—
115	C₂²×C₄×C₁₃₁	—	2	2	no	—
116	C₂²×C₄×C₁₃₁	—	2	4	no	—
117	C₂²×C₄×C₁₃₁	—	2	1	no	—
118	C₂²×C₄×C₁₃₁	—	2	1	no	—
119	C₂²×C₄×C₁₃₁	—	2	2	no	—
120	C₂²×C₄×C₁₃₁	—	2	2	no	—
121	C₂²×C₄×C₁₃₁	—	4	4	no	—
122	C₂²×C₄×C₁₃₁	—	4	4	no	—
123	C₂²×C₄×C₁₃₁	—	4	2	no	—
124	C₂²×C₄×C₁₃₁	—	4	2	no	—
125	C₂²×C₄×C₁₃₁	—	8	2	no	—
126	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
131	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₁₃₁	—	2	2	no	—
133	C₂×C₈×C₁₃₁	—	2	2	no	—
134	C₂×C₈×C₁₃₁	—	2	2	no	—
135	C₂×C₈×C₁₃₁	—	2	2	no	—
136	C₂×C₈×C₁₃₁	—	2	2	no	—
137	C₂×C₈×C₁₃₁	—	4	4	no	—
138	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
140	C₄⋊C₄×C₁₃₁	—	2	4	no	—
141	C₄⋊C₄×C₁₃₁	—	2	1	no	—
142	C₄⋊C₄×C₁₃₁	—	2	1	no	—
143	C₄⋊C₄×C₁₃₁	—	2	2	no	—
144	C₄⋊C₄×C₁₃₁	—	2	2	no	—
145	C₄⋊C₄×C₁₃₁	—	2	2	no	—
146	C₄⋊C₄×C₁₃₁	—	2	2	no	—
147	C₄⋊C₄×C₁₃₁	—	4	4	no	—
148	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
149	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
150	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
151	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
152	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
153	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
154	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
155	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
156	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
157	C₄²×C₁₃₁	—	2	2	no	—
158	C₄²×C₁₃₁	—	2	2	no	—
159	C₄²×C₁₃₁	—	4	4	no	—
160	C₂³×C₁₃₁	—	2	2	no	—
161	C₂³×C₁₃₁	—	2	2	no	—
162	C₂³×C₁₃₁	—	2	2	no	—
163	C₂³×C₁₃₁	—	2	4	no	—
164	C₂³×C₁₃₁	—	2	2	no	—
165	C₂³×C₁₃₁	—	4	8	no	—
166	C₂³×C₁₃₁	—	4	1	no	—
167	C₂³×C₁₃₁	—	4	1	no	—
168	C₂³×C₁₃₁	—	4	2	no	—
169	C₂³×C₁₃₁	—	4	2	no	—
170	C₂³×C₁₃₁	—	4	1	no	—
171	C₂³×C₁₃₁	—	4	1	no	—
172	C₂³×C₁₃₁	—	4	2	no	—
173	C₂³×C₁₃₁	—	4	8	no	—
174	C₂³×C₁₃₁	—	8	4	no	—
175	C₂³×C₁₃₁	—	8	8	no	—
176	C₂³×C₁₃₁	—	8	8	no	—
177	C₂³×C₁₃₁	C₄×D₄	1	2	yes	—
178	C₂³×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
179	C₂³×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
180	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
181	D₄×C₁₃₁	—	2	2	no	—
182	D₄×C₁₃₁	—	2	2	no	—
183	D₄×C₁₃₁	—	2	2	no	—
184	D₄×C₁₃₁	—	2	4	no	—
185	D₄×C₁₃₁	—	4	8	no	—
186	D₄×C₁₃₁	—	4	2	no	—
187	D₄×C₁₃₁	#117	1	4	yes	complemented
188	C₂×C₄×C₁₃₁	—	2	2	no	—
189	C₂×C₄×C₁₃₁	—	2	2	no	—
190	C₂×C₄×C₁₃₁	—	2	2	no	—
191	C₂×C₄×C₁₃₁	—	2	4	no	—
192	C₂×C₄×C₁₃₁	—	2	2	no	—
193	C₂×C₄×C₁₃₁	—	2	2	no	—
194	C₂×C₄×C₁₃₁	—	2	2	no	—
195	C₂×C₄×C₁₃₁	—	2	2	no	—
196	C₂×C₄×C₁₃₁	—	2	2	no	—
197	C₂×C₄×C₁₃₁	—	2	2	no	—
198	C₂×C₄×C₁₃₁	—	2	2	no	—
199	C₂×C₄×C₁₃₁	—	2	2	no	—
200	C₂×C₄×C₁₃₁	—	4	1	no	—
201	C₂×C₄×C₁₃₁	—	4	1	no	—
202	C₂×C₄×C₁₃₁	—	4	1	no	—
203	C₂×C₄×C₁₃₁	—	4	1	no	—
204	C₂×C₄×C₁₃₁	—	4	8	no	—
205	C₂×C₄×C₁₃₁	—	4	2	no	—
206	C₂×C₄×C₁₃₁	—	4	2	no	—
207	C₂×C₄×C₁₃₁	—	4	2	no	—
208	C₂×C₄×C₁₃₁	—	4	2	no	—
209	C₂×C₄×C₁₃₁	—	4	2	no	—
210	C₂×C₄×C₁₃₁	—	4	2	no	—
211	C₂×C₄×C₁₃₁	—	8	8	no	—
212	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
215	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
217	C₈×C₁₃₁	—	2	2	no	—
218	C₈×C₁₃₁	—	2	2	no	—
219	C₈×C₁₃₁	—	4	2	no	—
220	C₂²×C₁₃₁	—	2	2	no	—
221	C₂²×C₁₃₁	—	2	2	no	—
222	C₂²×C₁₃₁	—	2	4	no	—
223	C₂²×C₁₃₁	—	2	4	no	—
224	C₂²×C₁₃₁	—	2	4	no	—
225	C₂²×C₁₃₁	—	4	2	no	—
226	C₂²×C₁₃₁	—	4	2	no	—
227	C₂²×C₁₃₁	—	4	4	no	—
228	C₂²×C₁₃₁	—	4	4	no	—
229	C₂²×C₁₃₁	—	4	2	no	—
230	C₂²×C₁₃₁	—	4	2	no	—
231	C₂²×C₁₃₁	—	4	2	no	—
232	C₂²×C₁₃₁	—	8	16	no	—
233	C₂²×C₁₃₁	—	8	2	no	—
234	C₂²×C₁₃₁	—	8	2	no	—
235	C₂²×C₁₃₁	#442	1	4	yes	—
236	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
237	C₂²×C₁₃₁	#546	1	2	yes	—
238	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₂²×C₁₃₁	#577	1	2	yes	—
241	C₄×C₁₃₁	—	2	2	no	—
242	C₄×C₁₃₁	—	4	2	no	—
243	C₄×C₁₃₁	—	4	2	no	—
244	C₄×C₁₃₁	—	4	2	no	—
245	C₄×C₁₃₁	—	4	2	no	—
246	C₄×C₁₃₁	—	8	2	no	—
247	C₄×C₁₃₁	—	8	2	no	—
248	C₄×C₁₃₁	C₂×#117	1	1	yes	characteristic
249	C₄×C₁₃₁	#518	1	1	yes	characteristic
250	C₄×C₁₃₁	#551	1	2	yes	—
251	C₂×C₁₃₁	—	2	4	no	—
252	C₂×C₁₃₁	—	4	4	no	—
253	C₂×C₁₃₁	—	8	2	no	—
254	C₂×C₁₃₁	#2342	1	1	yes	characteristic
255	C₂×C₁₃₁	C₂×#442	1	1	yes	characteristic
256	C₂×C₁₃₁	#2949	1	1	yes	characteristic
257	C₂×C₁₃₁	#3306	1	2	yes	—
258	C₂×C₁₃₁	#3310	1	2	yes	—
259	#22562	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₁₃₁	#22562	1	1	yes	characteristic, direct product factor, Sylow
261	C₂²×#102	C₂×C₁₃₁	1	1	yes	characteristic
262	#2344	C₂×C₁₃₁	1	1	yes	characteristic, complemented
263	D₄×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic
264	#1936	C₂×C₁₃₁	1	2	yes	complemented
265	#1926	C₂×C₁₃₁	1	2	yes	complemented
266	#1864	C₂×C₁₃₁	1	2	yes	complemented
267	#1823	C₂×C₁₃₁	1	1	yes	characteristic, complemented
268	#1807	C₂×C₁₃₁	1	1	yes	characteristic, complemented
269	#1786	C₂×C₁₃₁	1	1	yes	characteristic
270	#1762	C₂×C₁₃₁	1	2	yes	complemented
271	#1752	C₂×C₁₃₁	1	1	yes	characteristic, complemented
272	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
273	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
275	C₂×#117	—	2	1	no	—
276	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	—	2	1	no	—
278	C₂×#106	C₂²×C₁₃₁	1	2	yes	complemented
279	C₂×#102	C₄×C₁₃₁	1	8	yes	complemented
280	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
281	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
282	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
283	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
284	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
285	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
287	C₂×#97	C₂²×C₁₃₁	1	2	yes	complemented
288	#390	C₂²×C₁₃₁	1	2	yes	—
289	#389	C₂²×C₁₃₁	1	2	yes	complemented
290	#387	—	2	2	no	—
291	#386	—	2	2	no	—
292	#381	—	2	1	no	—
293	#380	C₂²×C₁₃₁	1	1	yes	characteristic
294	#380	C₂²×C₁₃₁	1	1	yes	characteristic
295	#379	—	2	1	no	—
296	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
297	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
298	#340	C₂²×C₁₃₁	1	2	yes	complemented
299	#340	C₂²×C₁₃₁	1	2	yes	complemented
300	#340	C₂²×C₁₃₁	1	2	yes	complemented
301	#336	C₂²×C₁₃₁	1	2	yes	complemented
302	C₂⁵	—	2	1	no	—
303	C₂²×D₄	—	2	4	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	4	2	no	—
307	C₂²×D₄	C₂×C₄×C₁₃₁	1	4	yes	—
308	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
309	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	—	2	2	no	—
312	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
313	C₂²×C₈	—	4	2	no	—
314	C₂²×C₈	C₂×C₄×C₁₃₁	1	4	yes	complemented
315	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
316	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	4	2	no	—
320	#117	—	4	4	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	4	yes	complemented
325	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	4	4	no	—
335	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
339	#106	—	4	2	no	—
340	#102	—	2	4	no	—
341	#102	—	4	2	no	—
342	#102	C₂×C₄×C₁₃₁	1	4	yes	—
343	#102	C₂×C₄×C₁₃₁	1	4	yes	—
344	#102	C₂×C₄×C₁₃₁	1	4	yes	complemented
345	#102	C₂×C₄×C₁₃₁	1	4	yes	complemented
346	C₂²⋊C₈	—	2	2	no	—
347	#97	—	4	2	no	—
348	#95	—	2	2	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	#95	—	2	2	no	—
352	#95	D₄×C₁₃₁	1	2	yes	—
353	C₂⁴	—	2	1	no	—
354	C₂⁴	—	2	1	no	—
355	C₂⁴	—	2	4	no	—
356	C₂⁴	—	4	4	no	—
357	C₂⁴	—	4	2	no	—
358	C₂⁴	—	4	2	no	—
359	C₂⁴	—	8	2	no	—
360	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
372	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
373	C₂×D₄	#41×C₁₃₁	1	4	yes	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	4	4	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	8	2	no	—
386	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
390	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	4	4	no	—
398	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
399	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	4	no	—
408	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
409	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	4	4	no	—
413	C₂²⋊C₄	—	4	4	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	8	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	4	4	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	8	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	8	4	no	—
435	C₂³	—	8	8	no	—
436	C₂³	—	8	8	no	—
437	C₂³	C₄×D₄×C₁₃₁	1	2	yes	—
438	C₂³	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
439	C₂³	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
440	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	4	no	—
445	D₄	—	4	8	no	—
446	D₄	—	4	2	no	—
447	D₄	#117×C₁₃₁	1	4	yes	complemented
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	8	8	no	—
472	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
473	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
475	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
476	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
477	C₈	—	2	2	no	—
478	C₈	—	2	2	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	8	16	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	#442×C₁₃₁	1	4	yes	—
496	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
497	C₂²	#546×C₁₃₁	1	2	yes	—
498	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
499	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
500	C₂²	#577×C₁₃₁	1	2	yes	—
501	C₄	—	2	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	8	2	no	—
507	C₄	—	8	2	no	—
508	C₄	C₂×#117×C₁₃₁	1	1	yes	characteristic
509	C₄	#518×C₁₃₁	1	1	yes	characteristic
510	C₄	#551×C₁₃₁	1	2	yes	—
511	C₂	—	2	4	no	—
512	C₂	—	4	4	no	—
513	C₂	—	8	2	no	—
514	C₂	#2342×C₁₃₁	1	1	yes	characteristic
515	C₂	C₂×#442×C₁₃₁	1	1	yes	characteristic
516	C₂	#2949×C₁₃₁	1	1	yes	characteristic
517	C₂	#3306×C₁₃₁	1	2	yes	—
518	C₂	#3310×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂³×D₄×C₁₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄×C₂²⋊C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2344×C₁₃₁	C₂	semidirect
4. #1936×C₁₃₁	C₂	semidirect
5. #1926×C₁₃₁	C₂	semidirect
6. #1864×C₁₃₁	C₂	semidirect
7. #1823×C₁₃₁	C₂	semidirect
8. #1807×C₁₃₁	C₂	semidirect
10. #1762×C₁₃₁	C₂	semidirect
11. #1752×C₁₃₁	C₂	semidirect
18. C₂×#106×C₁₃₁	C₂²	semidirect
19. C₂×#102×C₁₃₁	C₄	semidirect
27. C₂×#97×C₁₃₁	C₂²	semidirect
29. #389×C₁₃₁	C₂²	semidirect
36. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
38. #340×C₁₃₁	C₂²	semidirect
39. #340×C₁₃₁	C₂²	semidirect
40. #340×C₁₃₁	C₂²	semidirect
41. #336×C₁₃₁	C₂²	semidirect
54. C₂²×C₈×C₁₃₁	C₂×C₄	semidirect
64. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
84. #102×C₁₃₁	C₂×C₄	semidirect
85. #102×C₁₃₁	C₂×C₄	semidirect
187. D₄×C₁₃₁	#117	semidirect
259. #22562	C₁₃₁	direct (N × H)
260. C₁₃₁	#22562	direct (N × H)
262. #2344	C₂×C₁₃₁	semidirect
264. #1936	C₂×C₁₃₁	semidirect
265. #1926	C₂×C₁₃₁	semidirect
266. #1864	C₂×C₁₃₁	semidirect
267. #1823	C₂×C₁₃₁	semidirect
268. #1807	C₂×C₁₃₁	semidirect
270. #1762	C₂×C₁₃₁	semidirect
271. #1752	C₂×C₁₃₁	semidirect
278. C₂×#106	C₂²×C₁₃₁	semidirect
279. C₂×#102	C₄×C₁₃₁	semidirect
287. C₂×#97	C₂²×C₁₃₁	semidirect
289. #389	C₂²×C₁₃₁	semidirect
296. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
298. #340	C₂²×C₁₃₁	semidirect
299. #340	C₂²×C₁₃₁	semidirect
300. #340	C₂²×C₁₃₁	semidirect
301. #336	C₂²×C₁₃₁	semidirect
314. C₂²×C₈	C₂×C₄×C₁₃₁	semidirect
324. C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	semidirect
344. #102	C₂×C₄×C₁₃₁	semidirect
345. #102	C₂×C₄×C₁₃₁	semidirect
447. D₄	#117×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#102×C₁₃₁	2
#2344×C₁₃₁	2
D₄×C₂²⋊C₄×C₁₃₁	2
#1936×C₁₃₁	2
#1926×C₁₃₁	2
#1864×C₁₃₁	2
#1823×C₁₃₁	2
#1807×C₁₃₁	2
#1786×C₁₃₁	2
#1762×C₁₃₁	2
#1752×C₁₃₁	2
#22562	131

Subgroups — C131×#22562 #45708446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#22562 #45708446