Subgroups — C₁₃₁×#26067 #45711951

Order 33536.

806 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#499×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#107×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2442×C₁₃₁	C₂	1	2	yes	maximal
4	#2085×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2059×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1942×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1942×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1853×C₁₃₁	C₂	1	2	yes	maximal
9	#1846×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1808×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	C₈×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₁	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
15	#499×C₁₃₁	—	2	4	no	—
16	C₂×#107×C₁₃₁	—	2	4	no	—
17	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	#400×C₁₃₁	—	2	2	no	—
28	#398×C₁₃₁	—	2	2	no	—
29	#389×C₁₃₁	C₂²	1	2	yes	—
30	#389×C₁₃₁	C₂²	1	2	yes	—
31	#385×C₁₃₁	—	2	2	no	—
32	#382×C₁₃₁	C₂²	1	2	yes	—
33	#380×C₁₃₁	—	2	2	no	—
34	#380×C₁₃₁	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
36	#340×C₁₃₁	C₂²	1	2	yes	—
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	C₂³×C₄×C₁₃₁	—	2	2	no	—
42	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃₁	—	2	2	no	—
44	C₂²×C₈×C₁₃₁	—	2	2	no	—
45	C₂²×C₈×C₁₃₁	Q₈	1	4	yes	—
46	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	#125×C₁₃₁	—	2	4	no	—
51	#125×C₁₃₁	—	4	2	no	—
52	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
68	#107×C₁₃₁	—	2	2	no	—
69	#107×C₁₃₁	—	2	2	no	—
70	#107×C₁₃₁	—	2	2	no	—
71	#107×C₁₃₁	—	2	4	no	—
72	#107×C₁₃₁	D₄	1	4	yes	—
73	#106×C₁₃₁	—	2	4	no	—
74	#106×C₁₃₁	—	4	2	no	—
75	C₂²⋊C₈×C₁₃₁	Q₈	1	4	yes	—
76	C₄×C₈×C₁₃₁	—	2	2	no	—
77	C₄×C₈×C₁₃₁	—	2	2	no	—
78	#95×C₁₃₁	—	2	2	no	—
79	#95×C₁₃₁	—	2	2	no	—
80	#95×C₁₃₁	—	2	2	no	—
81	#95×C₁₃₁	—	2	2	no	—
82	#95×C₁₃₁	—	2	2	no	—
83	#95×C₁₃₁	D₄	1	1	yes	characteristic
84	#95×C₁₃₁	D₄	1	1	yes	characteristic
85	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₁	—	2	1	no	—
87	C₂²×C₄×C₁₃₁	—	2	1	no	—
88	C₂²×C₄×C₁₃₁	—	2	1	no	—
89	C₂²×C₄×C₁₃₁	—	2	1	no	—
90	C₂²×C₄×C₁₃₁	—	2	2	no	—
91	C₂²×C₄×C₁₃₁	—	2	2	no	—
92	C₂²×C₄×C₁₃₁	—	2	2	no	—
93	C₂²×C₄×C₁₃₁	—	2	2	no	—
94	C₂²×C₄×C₁₃₁	—	4	4	no	—
95	C₂²×C₄×C₁₃₁	—	4	4	no	—
96	C₂²×C₄×C₁₃₁	—	8	2	no	—
97	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₁₃₁	—	2	1	no	—
106	C₂×C₈×C₁₃₁	—	2	1	no	—
107	C₂×C₈×C₁₃₁	—	2	1	no	—
108	C₂×C₈×C₁₃₁	—	2	1	no	—
109	C₂×C₈×C₁₃₁	—	2	1	no	—
110	C₂×C₈×C₁₃₁	—	2	1	no	—
111	C₂×C₈×C₁₃₁	—	2	8	no	—
112	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
114	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
116	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
117	C₂×C₈×C₁₃₁	#41	1	2	yes	—
118	C₄⋊C₄×C₁₃₁	—	2	2	no	—
119	C₄⋊C₄×C₁₃₁	—	2	2	no	—
120	C₄⋊C₄×C₁₃₁	—	2	2	no	—
121	C₄⋊C₄×C₁₃₁	—	2	2	no	—
122	C₄⋊C₄×C₁₃₁	—	2	2	no	—
123	C₄⋊C₄×C₁₃₁	—	2	2	no	—
124	C₄⋊C₄×C₁₃₁	—	2	2	no	—
125	C₄⋊C₄×C₁₃₁	—	4	4	no	—
126	C₄⋊C₄×C₁₃₁	—	4	4	no	—
127	C₄⋊C₄×C₁₃₁	—	4	4	no	—
128	C₄⋊C₄×C₁₃₁	—	8	2	no	—
129	C₄⋊C₄×C₁₃₁	—	8	2	no	—
130	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
131	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
132	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
133	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
134	C₄²×C₁₃₁	—	2	1	no	—
135	C₄²×C₁₃₁	—	2	1	no	—
136	C₄²×C₁₃₁	—	2	1	no	—
137	C₄²×C₁₃₁	—	2	1	no	—
138	C₂³×C₁₃₁	—	2	1	no	—
139	C₂³×C₁₃₁	—	2	1	no	—
140	C₂³×C₁₃₁	—	2	1	no	—
141	C₂³×C₁₃₁	—	2	1	no	—
142	C₂³×C₁₃₁	C₄⋊Q₈	1	2	yes	—
143	C₂³×C₁₃₁	#135	1	2	yes	—
144	C₂³×C₁₃₁	#135	1	2	yes	—
145	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₁	—	2	1	no	—
147	C₂×C₄×C₁₃₁	—	2	1	no	—
148	C₂×C₄×C₁₃₁	—	2	2	no	—
149	C₂×C₄×C₁₃₁	—	2	2	no	—
150	C₂×C₄×C₁₃₁	—	2	2	no	—
151	C₂×C₄×C₁₃₁	—	2	2	no	—
152	C₂×C₄×C₁₃₁	—	2	1	no	—
153	C₂×C₄×C₁₃₁	—	2	1	no	—
154	C₂×C₄×C₁₃₁	—	2	4	no	—
155	C₂×C₄×C₁₃₁	—	2	1	no	—
156	C₂×C₄×C₁₃₁	—	2	1	no	—
157	C₂×C₄×C₁₃₁	—	2	1	no	—
158	C₂×C₄×C₁₃₁	—	2	1	no	—
159	C₂×C₄×C₁₃₁	—	2	1	no	—
160	C₂×C₄×C₁₃₁	—	2	1	no	—
161	C₂×C₄×C₁₃₁	—	2	1	no	—
162	C₂×C₄×C₁₃₁	—	2	1	no	—
163	C₂×C₄×C₁₃₁	—	2	1	no	—
164	C₂×C₄×C₁₃₁	—	2	1	no	—
165	C₂×C₄×C₁₃₁	—	4	2	no	—
166	C₂×C₄×C₁₃₁	—	4	2	no	—
167	C₂×C₄×C₁₃₁	—	4	2	no	—
168	C₂×C₄×C₁₃₁	—	4	2	no	—
169	C₂×C₄×C₁₃₁	—	4	2	no	—
170	C₂×C₄×C₁₃₁	—	4	2	no	—
171	C₂×C₄×C₁₃₁	—	4	2	no	—
172	C₂×C₄×C₁₃₁	—	4	2	no	—
173	C₂×C₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	4	2	no	—
175	C₂×C₄×C₁₃₁	—	4	2	no	—
176	C₂×C₄×C₁₃₁	—	8	8	no	—
177	C₂×C₄×C₁₃₁	C₄⋊Q₈	1	2	yes	—
178	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
184	C₈×C₁₃₁	—	2	2	no	—
185	C₈×C₁₃₁	—	2	2	no	—
186	C₈×C₁₃₁	—	2	2	no	—
187	C₈×C₁₃₁	C₂²⋊Q₈	1	4	yes	—
188	C₂²×C₁₃₁	—	2	2	no	—
189	C₂²×C₁₃₁	—	2	2	no	—
190	C₂²×C₁₃₁	—	2	2	no	—
191	C₂²×C₁₃₁	—	2	2	no	—
192	C₂²×C₁₃₁	—	2	2	no	—
193	C₂²×C₁₃₁	—	2	2	no	—
194	C₂²×C₁₃₁	#499	1	4	yes	complemented
195	C₂²×C₁₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
196	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
197	C₂²×C₁₃₁	#547	1	1	yes	characteristic
198	C₂²×C₁₃₁	C₂×#135	1	1	yes	characteristic
199	C₂²×C₁₃₁	C₂×#135	1	1	yes	characteristic
200	C₂²×C₁₃₁	#576	1	1	yes	characteristic
201	C₂²×C₁₃₁	#578	1	1	yes	characteristic
202	C₄×C₁₃₁	—	2	2	no	—
203	C₄×C₁₃₁	—	4	1	no	—
204	C₄×C₁₃₁	—	4	1	no	—
205	C₄×C₁₃₁	—	4	1	no	—
206	C₄×C₁₃₁	—	4	4	no	—
207	C₄×C₁₃₁	—	4	1	no	—
208	C₄×C₁₃₁	—	8	2	no	—
209	C₄×C₁₃₁	—	8	2	no	—
210	C₄×C₁₃₁	—	8	2	no	—
211	C₄×C₁₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
212	C₄×C₁₃₁	#544	1	1	yes	characteristic
213	C₄×C₁₃₁	D₄×Q₈	1	1	yes	characteristic
214	C₄×C₁₃₁	#554	1	1	yes	characteristic
215	C₂×C₁₃₁	—	2	4	no	—
216	C₂×C₁₃₁	#2440	1	1	yes	characteristic
217	C₂×C₁₃₁	C₂×#499	1	1	yes	characteristic
218	C₂×C₁₃₁	#3164	1	1	yes	characteristic
219	C₂×C₁₃₁	#3280	1	1	yes	characteristic
220	C₂×C₁₃₁	#3285	1	1	yes	characteristic
221	C₂×C₁₃₁	#3336	1	1	yes	characteristic
222	C₂×C₁₃₁	#3339	1	1	yes	characteristic
223	#26067	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₁₃₁	#26067	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×#499	C₂×C₁₃₁	1	1	yes	characteristic, complemented
226	C₂²×#107	C₂×C₁₃₁	1	1	yes	characteristic
227	#2442	C₂×C₁₃₁	1	2	yes	—
228	#2085	C₂×C₁₃₁	1	2	yes	complemented
229	#2059	C₂×C₁₃₁	1	2	yes	complemented
230	#1942	C₂×C₁₃₁	1	1	yes	characteristic, complemented
231	#1942	C₂×C₁₃₁	1	1	yes	characteristic, complemented
232	#1853	C₂×C₁₃₁	1	2	yes	—
233	#1846	C₂×C₁₃₁	1	1	yes	characteristic, complemented
234	#1808	C₂×C₁₃₁	1	1	yes	characteristic
235	C₈×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic
236	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
237	C₂×#125	C₂²×C₁₃₁	1	2	yes	—
238	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
239	#499	—	2	4	no	—
240	C₂×#107	—	2	4	no	—
241	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
242	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
243	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
244	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
245	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
246	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
247	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
248	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
250	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
251	#400	—	2	2	no	—
252	#398	—	2	2	no	—
253	#389	C₂²×C₁₃₁	1	2	yes	—
254	#389	C₂²×C₁₃₁	1	2	yes	—
255	#385	—	2	2	no	—
256	#382	C₂²×C₁₃₁	1	2	yes	—
257	#380	—	2	2	no	—
258	#380	C₂²×C₁₃₁	1	2	yes	—
259	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
260	#340	C₂²×C₁₃₁	1	2	yes	—
261	#340	C₂²×C₁₃₁	1	2	yes	—
262	#340	C₂²×C₁₃₁	1	2	yes	—
263	#336	C₂²×C₁₃₁	1	1	yes	characteristic
264	#336	C₂²×C₁₃₁	1	1	yes	characteristic
265	C₂³×C₄	—	2	2	no	—
266	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	Q₈×C₁₃₁	1	4	yes	—
270	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
274	#125	—	2	4	no	—
275	#125	—	4	2	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	4	2	no	—
283	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#107	—	2	2	no	—
294	#107	—	2	2	no	—
295	#107	—	2	4	no	—
296	#107	D₄×C₁₃₁	1	4	yes	—
297	#106	—	2	4	no	—
298	#106	—	4	2	no	—
299	C₂²⋊C₈	Q₈×C₁₃₁	1	4	yes	—
300	C₄×C₈	—	2	2	no	—
301	C₄×C₈	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	D₄×C₁₃₁	1	1	yes	characteristic
308	#95	D₄×C₁₃₁	1	1	yes	characteristic
309	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	8	2	no	—
321	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
327	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
328	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
337	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
338	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
339	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
340	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
341	C₂×C₈	#41×C₁₃₁	1	2	yes	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄⋊C₄	—	8	2	no	—
353	C₄⋊C₄	—	8	2	no	—
354	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	C₄⋊Q₈×C₁₃₁	1	2	yes	—
367	C₂³	#135×C₁₃₁	1	2	yes	—
368	C₂³	#135×C₁₃₁	1	2	yes	—
369	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	8	no	—
401	C₂×C₄	C₄⋊Q₈×C₁₃₁	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
403	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
404	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
406	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
407	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	C₂²⋊Q₈×C₁₃₁	1	4	yes	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	#499×C₁₃₁	1	4	yes	complemented
419	C₂²	C₂×C₄⋊Q₈×C₁₃₁	1	1	yes	characteristic
420	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
421	C₂²	#547×C₁₃₁	1	1	yes	characteristic
422	C₂²	C₂×#135×C₁₃₁	1	1	yes	characteristic
423	C₂²	C₂×#135×C₁₃₁	1	1	yes	characteristic
424	C₂²	#576×C₁₃₁	1	1	yes	characteristic
425	C₂²	#578×C₁₃₁	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
436	C₄	#544×C₁₃₁	1	1	yes	characteristic
437	C₄	D₄×Q₈×C₁₃₁	1	1	yes	characteristic
438	C₄	#554×C₁₃₁	1	1	yes	characteristic
439	C₂	—	2	4	no	—
440	C₂	#2440×C₁₃₁	1	1	yes	characteristic
441	C₂	C₂×#499×C₁₃₁	1	1	yes	characteristic
442	C₂	#3164×C₁₃₁	1	1	yes	characteristic
443	C₂	#3280×C₁₃₁	1	1	yes	characteristic
444	C₂	#3285×C₁₃₁	1	1	yes	characteristic
445	C₂	#3336×C₁₃₁	1	1	yes	characteristic
446	C₂	#3339×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂⁴×C₁₃₁	C₂×D₄
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
1. C₂×#499×C₁₃₁	C₂	semidirect
4. #2085×C₁₃₁	C₂	semidirect
5. #2059×C₁₃₁	C₂	semidirect
6. #1942×C₁₃₁	C₂	semidirect
7. #1942×C₁₃₁	C₂	semidirect
9. #1846×C₁₃₁	C₂	semidirect
194. C₂²×C₁₃₁	#499	semidirect
223. #26067	C₁₃₁	direct (N × H)
224. C₁₃₁	#26067	direct (N × H)
225. C₂×#499	C₂×C₁₃₁	semidirect
228. #2085	C₂×C₁₃₁	semidirect
229. #2059	C₂×C₁₃₁	semidirect
230. #1942	C₂×C₁₃₁	semidirect
231. #1942	C₂×C₁₃₁	semidirect
233. #1846	C₂×C₁₃₁	semidirect
418. C₂²	#499×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#499×C₁₃₁	2
C₂²×#107×C₁₃₁	2
#2442×C₁₃₁	2
#2085×C₁₃₁	2
#2059×C₁₃₁	2
#1942×C₁₃₁	2
#1853×C₁₃₁	2
#1846×C₁₃₁	2
#1808×C₁₃₁	2
C₈×C₂²⋊C₄×C₁₃₁	2
#26067	131

Subgroups — C131×#26067 #45711951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#26067 #45711951