Subgroups — C₁₃₁×#25046 #45710930

Order 33536.

944 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#469×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#442×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2422×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2071×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2034×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1970×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1943×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1864×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1844×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1809×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1753×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#123×C₁₃₁	—	2	2	no	—
15	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
17	#469×C₁₃₁	—	2	4	no	—
18	#442×C₁₃₁	—	2	4	no	—
19	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
29	#397×C₁₃₁	—	2	2	no	—
30	#394×C₁₃₁	—	2	2	no	—
31	#390×C₁₃₁	C₂²	1	2	yes	—
32	#389×C₁₃₁	C₂²	1	2	yes	—
33	#385×C₁₃₁	—	2	2	no	—
34	#384×C₁₃₁	C₂²	1	2	yes	—
35	#380×C₁₃₁	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
37	#340×C₁₃₁	C₂²	1	2	yes	—
38	#340×C₁₃₁	C₂²	1	2	yes	—
39	#336×C₁₃₁	C₂²	1	1	yes	characteristic
40	#336×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃₁	—	2	2	no	—
42	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃₁	—	2	2	no	—
44	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₁₃₁	—	2	2	no	—
46	C₂×D₈×C₁₃₁	—	2	2	no	—
47	C₂×D₈×C₁₃₁	D₄	1	4	yes	—
48	C₂×M₁₆×C₁₃₁	—	2	2	no	—
49	C₂×M₁₆×C₁₃₁	—	2	2	no	—
50	C₂×M₁₆×C₁₃₁	—	2	2	no	—
51	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
55	#123×C₁₃₁	—	4	8	no	—
56	#121×C₁₃₁	—	2	4	no	—
57	#121×C₁₃₁	—	4	2	no	—
58	C₄×D₄×C₁₃₁	—	2	4	no	—
59	C₄×D₄×C₁₃₁	—	4	2	no	—
60	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	2	2	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	2	yes	—
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
72	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
74	#107×C₁₃₁	—	2	2	no	—
75	#106×C₁₃₁	—	2	2	no	—
76	#106×C₁₃₁	—	2	2	no	—
77	#106×C₁₃₁	—	4	2	no	—
78	#102×C₁₃₁	—	2	4	no	—
79	#102×C₁₃₁	—	2	4	no	—
80	#102×C₁₃₁	—	2	4	no	—
81	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
82	#97×C₁₃₁	—	2	2	no	—
83	C₄×C₈×C₁₃₁	—	2	2	no	—
84	#95×C₁₃₁	—	2	2	no	—
85	#95×C₁₃₁	—	2	2	no	—
86	#95×C₁₃₁	D₄	1	2	yes	—
87	C₂⁴×C₁₃₁	—	2	2	no	—
88	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₁₃₁	—	2	2	no	—
90	C₂×D₄×C₁₃₁	—	2	2	no	—
91	C₂×D₄×C₁₃₁	—	2	2	no	—
92	C₂×D₄×C₁₃₁	—	2	2	no	—
93	C₂×D₄×C₁₃₁	—	2	2	no	—
94	C₂×D₄×C₁₃₁	—	4	4	no	—
95	C₂×D₄×C₁₃₁	—	4	4	no	—
96	C₂×D₄×C₁₃₁	—	8	2	no	—
97	C₂×D₄×C₁₃₁	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₃₁	—	2	1	no	—
99	C₂²×C₄×C₁₃₁	—	2	1	no	—
100	C₂²×C₄×C₁₃₁	—	2	1	no	—
101	C₂²×C₄×C₁₃₁	—	2	1	no	—
102	C₂²×C₄×C₁₃₁	—	2	1	no	—
103	C₂²×C₄×C₁₃₁	—	2	1	no	—
104	C₂²×C₄×C₁₃₁	—	2	2	no	—
105	C₂²×C₄×C₁₃₁	—	2	2	no	—
106	C₂²×C₄×C₁₃₁	—	2	2	no	—
107	C₂²×C₄×C₁₃₁	—	4	4	no	—
108	C₂²×C₄×C₁₃₁	—	4	4	no	—
109	C₂²×C₄×C₁₃₁	—	8	2	no	—
110	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
114	D₈×C₁₃₁	—	2	8	no	—
115	M₁₆×C₁₃₁	—	4	4	no	—
116	C₂×C₈×C₁₃₁	—	2	1	no	—
117	C₂×C₈×C₁₃₁	—	2	1	no	—
118	C₂×C₈×C₁₃₁	—	2	1	no	—
119	C₂×C₈×C₁₃₁	—	2	1	no	—
120	C₂×C₈×C₁₃₁	—	2	1	no	—
121	C₂×C₈×C₁₃₁	—	2	1	no	—
122	C₂×C₈×C₁₃₁	—	2	1	no	—
123	C₂×C₈×C₁₃₁	—	2	1	no	—
124	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₃₁	#41	1	2	yes	—
126	C₂×C₈×C₁₃₁	#41	1	2	yes	—
127	C₂×C₈×C₁₃₁	#41	1	2	yes	—
128	C₄⋊C₄×C₁₃₁	—	2	2	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	—	2	2	no	—
134	C₄⋊C₄×C₁₃₁	—	4	4	no	—
135	C₄⋊C₄×C₁₃₁	—	4	4	no	—
136	C₄⋊C₄×C₁₃₁	—	8	2	no	—
137	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
138	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
139	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
140	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
141	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
142	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
143	C₄²×C₁₃₁	—	2	1	no	—
144	C₄²×C₁₃₁	—	2	1	no	—
145	C₄²×C₁₃₁	—	2	1	no	—
146	C₄²×C₁₃₁	—	2	1	no	—
147	C₂³×C₁₃₁	—	2	1	no	—
148	C₂³×C₁₃₁	—	2	4	no	—
149	C₂³×C₁₃₁	—	2	1	no	—
150	C₂³×C₁₃₁	—	2	1	no	—
151	C₂³×C₁₃₁	—	2	2	no	—
152	C₂³×C₁₃₁	—	2	2	no	—
153	C₂³×C₁₃₁	—	4	2	no	—
154	C₂³×C₁₃₁	—	4	2	no	—
155	C₂³×C₁₃₁	—	4	2	no	—
156	C₂³×C₁₃₁	—	4	2	no	—
157	C₂³×C₁₃₁	—	4	2	no	—
158	C₂³×C₁₃₁	—	4	2	no	—
159	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₁₃₁	—	2	4	no	—
161	D₄×C₁₃₁	—	2	4	no	—
162	D₄×C₁₃₁	—	4	2	no	—
163	D₄×C₁₃₁	—	4	2	no	—
164	D₄×C₁₃₁	—	8	8	no	—
165	C₂×C₄×C₁₃₁	—	2	2	no	—
166	C₂×C₄×C₁₃₁	—	2	2	no	—
167	C₂×C₄×C₁₃₁	—	2	1	no	—
168	C₂×C₄×C₁₃₁	—	2	2	no	—
169	C₂×C₄×C₁₃₁	—	2	1	no	—
170	C₂×C₄×C₁₃₁	—	2	1	no	—
171	C₂×C₄×C₁₃₁	—	2	2	no	—
172	C₂×C₄×C₁₃₁	—	2	2	no	—
173	C₂×C₄×C₁₃₁	—	4	1	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	—	4	2	no	—
185	C₂×C₄×C₁₃₁	—	4	2	no	—
186	C₂×C₄×C₁₃₁	—	8	8	no	—
187	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	4	yes	—
188	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
194	C₈×C₁₃₁	—	2	2	no	—
195	C₈×C₁₃₁	—	4	1	no	—
196	C₈×C₁₃₁	—	4	1	no	—
197	C₈×C₁₃₁	#123	1	4	yes	complemented
198	C₂²×C₁₃₁	—	4	2	no	—
199	C₂²×C₁₃₁	—	4	1	no	—
200	C₂²×C₁₃₁	—	4	1	no	—
201	C₂²×C₁₃₁	—	4	1	no	—
202	C₂²×C₁₃₁	—	4	4	no	—
203	C₂²×C₁₃₁	—	4	4	no	—
204	C₂²×C₁₃₁	—	4	2	no	—
205	C₂²×C₁₃₁	—	4	4	no	—
206	C₂²×C₁₃₁	—	8	2	no	—
207	C₂²×C₁₃₁	—	8	2	no	—
208	C₂²×C₁₃₁	—	8	2	no	—
209	C₂²×C₁₃₁	—	8	2	no	—
210	C₂²×C₁₃₁	#532	1	1	yes	characteristic
211	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
212	C₂²×C₁₃₁	#547	1	1	yes	characteristic
213	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
214	C₂²×C₁₃₁	#577	1	2	yes	—
215	C₄×C₁₃₁	—	2	4	no	—
216	C₄×C₁₃₁	—	4	1	no	—
217	C₄×C₁₃₁	—	4	2	no	—
218	C₄×C₁₃₁	—	8	2	no	—
219	C₄×C₁₃₁	—	8	2	no	—
220	C₄×C₁₃₁	—	8	2	no	—
221	C₄×C₁₃₁	C₂×#123	1	1	yes	characteristic
222	C₄×C₁₃₁	#542	1	1	yes	characteristic
223	C₄×C₁₃₁	#547	1	1	yes	characteristic
224	C₄×C₁₃₁	#553	1	1	yes	characteristic
225	C₂×C₁₃₁	—	8	1	no	—
226	C₂×C₁₃₁	—	8	4	no	—
227	C₂×C₁₃₁	#2422	1	1	yes	characteristic
228	C₂×C₁₃₁	#3173	1	1	yes	characteristic
229	C₂×C₁₃₁	#3184	1	1	yes	characteristic
230	C₂×C₁₃₁	#3272	1	2	yes	—
231	C₂×C₁₃₁	#3345	1	2	yes	—
232	#25046	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₁₃₁	#25046	1	1	yes	characteristic, direct product factor, Sylow
234	C₂×#469	C₂×C₁₃₁	1	1	yes	characteristic
235	C₂×#442	C₂×C₁₃₁	1	1	yes	characteristic, complemented
236	#2422	C₂×C₁₃₁	1	2	yes	complemented
237	#2071	C₂×C₁₃₁	1	2	yes	complemented
238	#2034	C₂×C₁₃₁	1	2	yes	complemented
239	#1970	C₂×C₁₃₁	1	1	yes	characteristic, complemented
240	#1943	C₂×C₁₃₁	1	1	yes	characteristic, complemented
241	#1864	C₂×C₁₃₁	1	2	yes	complemented
242	#1844	C₂×C₁₃₁	1	1	yes	characteristic, complemented
243	#1809	C₂×C₁₃₁	1	1	yes	characteristic, complemented
244	#1753	C₂×C₁₃₁	1	1	yes	characteristic, complemented
245	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
247	C₂×#123	—	2	2	no	—
248	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
250	#469	—	2	4	no	—
251	#442	—	2	4	no	—
252	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
253	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
254	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
255	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
256	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
257	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
258	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
260	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
262	#397	—	2	2	no	—
263	#394	—	2	2	no	—
264	#390	C₂²×C₁₃₁	1	2	yes	—
265	#389	C₂²×C₁₃₁	1	2	yes	—
266	#385	—	2	2	no	—
267	#384	C₂²×C₁₃₁	1	2	yes	—
268	#380	C₂²×C₁₃₁	1	2	yes	—
269	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
270	#340	C₂²×C₁₃₁	1	2	yes	—
271	#340	C₂²×C₁₃₁	1	2	yes	—
272	#336	C₂²×C₁₃₁	1	1	yes	characteristic
273	#336	C₂²×C₁₃₁	1	1	yes	characteristic
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
278	C₂×D₈	—	2	2	no	—
279	C₂×D₈	—	2	2	no	—
280	C₂×D₈	D₄×C₁₃₁	1	4	yes	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
288	#123	—	4	8	no	—
289	#121	—	2	4	no	—
290	#121	—	4	2	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	4	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
305	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
307	#107	—	2	2	no	—
308	#106	—	2	2	no	—
309	#106	—	2	2	no	—
310	#106	—	4	2	no	—
311	#102	—	2	4	no	—
312	#102	—	2	4	no	—
313	#102	—	2	4	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	#97	—	2	2	no	—
316	C₄×C₈	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	D₄×C₁₃₁	1	2	yes	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	8	2	no	—
330	C₂×D₄	C₂×D₄×C₁₃₁	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	8	2	no	—
343	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
347	D₈	—	2	8	no	—
348	M₁₆	—	4	4	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
358	C₂×C₈	#41×C₁₃₁	1	2	yes	—
359	C₂×C₈	#41×C₁₃₁	1	2	yes	—
360	C₂×C₈	#41×C₁₃₁	1	2	yes	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	8	8	no	—
420	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	4	yes	—
421	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
422	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
425	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
426	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
427	C₈	—	2	2	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	1	no	—
430	C₈	#123×C₁₃₁	1	4	yes	complemented
431	C₂²	—	4	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	#532×C₁₃₁	1	1	yes	characteristic
444	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
445	C₂²	#547×C₁₃₁	1	1	yes	characteristic
446	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
447	C₂²	#577×C₁₃₁	1	2	yes	—
448	C₄	—	2	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	2	no	—
454	C₄	C₂×#123×C₁₃₁	1	1	yes	characteristic
455	C₄	#542×C₁₃₁	1	1	yes	characteristic
456	C₄	#547×C₁₃₁	1	1	yes	characteristic
457	C₄	#553×C₁₃₁	1	1	yes	characteristic
458	C₂	—	8	1	no	—
459	C₂	—	8	4	no	—
460	C₂	#2422×C₁₃₁	1	1	yes	characteristic
461	C₂	#3173×C₁₃₁	1	1	yes	characteristic
462	C₂	#3184×C₁₃₁	1	1	yes	characteristic
463	C₂	#3272×C₁₃₁	1	2	yes	—
464	C₂	#3345×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#469×C₁₃₁	C₂
LCS	G ▷ C₂²×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. C₂×#442×C₁₃₁	C₂	semidirect
3. #2422×C₁₃₁	C₂	semidirect
4. #2071×C₁₃₁	C₂	semidirect
5. #2034×C₁₃₁	C₂	semidirect
6. #1970×C₁₃₁	C₂	semidirect
7. #1943×C₁₃₁	C₂	semidirect
8. #1864×C₁₃₁	C₂	semidirect
9. #1844×C₁₃₁	C₂	semidirect
10. #1809×C₁₃₁	C₂	semidirect
11. #1753×C₁₃₁	C₂	semidirect
197. C₈×C₁₃₁	#123	semidirect
232. #25046	C₁₃₁	direct (N × H)
233. C₁₃₁	#25046	direct (N × H)
235. C₂×#442	C₂×C₁₃₁	semidirect
236. #2422	C₂×C₁₃₁	semidirect
237. #2071	C₂×C₁₃₁	semidirect
238. #2034	C₂×C₁₃₁	semidirect
239. #1970	C₂×C₁₃₁	semidirect
240. #1943	C₂×C₁₃₁	semidirect
241. #1864	C₂×C₁₃₁	semidirect
242. #1844	C₂×C₁₃₁	semidirect
243. #1809	C₂×C₁₃₁	semidirect
244. #1753	C₂×C₁₃₁	semidirect
430. C₈	#123×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#469×C₁₃₁	2
C₂×#442×C₁₃₁	2
#2422×C₁₃₁	2
#2071×C₁₃₁	2
#2034×C₁₃₁	2
#1970×C₁₃₁	2
#1943×C₁₃₁	2
#1864×C₁₃₁	2
#1844×C₁₃₁	2
#1809×C₁₃₁	2
#1753×C₁₃₁	2
#25046	131

Subgroups — C131×#25046 #45710930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#25046 #45710930