Subgroups — C₁₃₁×#21596 #45707480

Order 33536.

894 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×M₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1984×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1939×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1917×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1851×C₁₃₁	C₂	1	2	yes	maximal
8	#1797×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#1771×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#1770×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1753×C₁₃₁	C₂	1	2	yes	maximal
12	C₂²×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₁₃₁	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₈×Q₈×C₁₃₁	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	2	yes	—
23	C₄×M₁₆×C₁₃₁	—	2	4	no	—
24	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
30	#391×C₁₃₁	C₄	1	1	yes	characteristic
31	#389×C₁₃₁	C₄	1	1	yes	characteristic
32	#387×C₁₃₁	C₄	1	2	yes	—
33	#385×C₁₃₁	C₄	1	2	yes	—
34	#380×C₁₃₁	C₄	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
38	#336×C₁₃₁	C₂²	1	2	yes	—
39	#336×C₁₃₁	C₂²	1	2	yes	—
40	#336×C₁₃₁	C₂²	1	2	yes	—
41	#336×C₁₃₁	C₂²	1	2	yes	—
42	#336×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₁₃₁	—	2	2	no	—
48	C₂×M₁₆×C₁₃₁	—	2	2	no	—
49	C₂×M₁₆×C₁₃₁	—	2	2	no	—
50	C₂×M₁₆×C₁₃₁	—	2	2	no	—
51	C₂×M₁₆×C₁₃₁	—	2	2	no	—
52	C₂×M₁₆×C₁₃₁	Q₈	1	4	yes	complemented
53	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
59	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
60	C₄×Q₈×C₁₃₁	—	2	2	no	—
61	C₄×Q₈×C₁₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₁₃₁	—	2	2	no	—
71	C₂×C₄²×C₁₃₁	—	2	2	no	—
72	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₁₃₁	—	2	4	no	—
79	C₄⋊C₈×C₁₃₁	—	2	4	no	—
80	C₄⋊C₈×C₁₃₁	—	2	2	no	—
81	C₄⋊C₈×C₁₃₁	—	2	2	no	—
82	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
83	#97×C₁₃₁	—	2	2	no	—
84	#97×C₁₃₁	—	2	2	no	—
85	#97×C₁₃₁	—	2	4	no	—
86	C₄×C₈×C₁₃₁	—	2	4	no	—
87	C₄×C₈×C₁₃₁	—	2	2	no	—
88	C₄×C₈×C₁₃₁	D₄	1	4	yes	—
89	#95×C₁₃₁	C₂×C₄	1	2	yes	—
90	#95×C₁₃₁	C₂×C₄	1	2	yes	—
91	#95×C₁₃₁	C₂×C₄	1	2	yes	—
92	#95×C₁₃₁	C₂×C₄	1	2	yes	—
93	#95×C₁₃₁	C₂×C₄	1	2	yes	—
94	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₃₁	—	2	2	no	—
96	C₂×Q₈×C₁₃₁	—	2	2	no	—
97	C₂×Q₈×C₁₃₁	M₁₆	1	4	yes	complemented
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	2	no	—
103	C₂²×C₄×C₁₃₁	—	2	2	no	—
104	C₂²×C₄×C₁₃₁	—	2	2	no	—
105	C₂²×C₄×C₁₃₁	—	2	2	no	—
106	C₂²×C₄×C₁₃₁	—	4	1	no	—
107	C₂²×C₄×C₁₃₁	—	4	1	no	—
108	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
119	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₁₃₁	—	2	8	no	—
121	M₁₆×C₁₃₁	—	2	8	no	—
122	C₂×C₈×C₁₃₁	—	2	1	no	—
123	C₂×C₈×C₁₃₁	—	2	1	no	—
124	C₂×C₈×C₁₃₁	—	2	1	no	—
125	C₂×C₈×C₁₃₁	—	2	1	no	—
126	C₂×C₈×C₁₃₁	—	2	1	no	—
127	C₂×C₈×C₁₃₁	—	2	1	no	—
128	C₂×C₈×C₁₃₁	—	2	2	no	—
129	C₂×C₈×C₁₃₁	—	2	2	no	—
130	C₂×C₈×C₁₃₁	—	2	2	no	—
131	C₂×C₈×C₁₃₁	—	2	2	no	—
132	C₂×C₈×C₁₃₁	—	2	2	no	—
133	C₂×C₈×C₁₃₁	—	2	2	no	—
134	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
137	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
138	C₂×C₈×C₁₃₁	#41	1	2	yes	—
139	C₂×C₈×C₁₃₁	#41	1	2	yes	—
140	C₄⋊C₄×C₁₃₁	—	2	4	no	—
141	C₄⋊C₄×C₁₃₁	—	2	2	no	—
142	C₄⋊C₄×C₁₃₁	—	2	2	no	—
143	C₄⋊C₄×C₁₃₁	—	2	4	no	—
144	C₄⋊C₄×C₁₃₁	—	2	2	no	—
145	C₄⋊C₄×C₁₃₁	—	4	2	no	—
146	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
147	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
148	C₄²×C₁₃₁	—	2	2	no	—
149	C₄²×C₁₃₁	—	2	2	no	—
150	C₄²×C₁₃₁	—	2	2	no	—
151	C₄²×C₁₃₁	—	2	1	no	—
152	C₄²×C₁₃₁	—	2	2	no	—
153	C₄²×C₁₃₁	—	2	2	no	—
154	C₄²×C₁₃₁	—	2	1	no	—
155	C₄²×C₁₃₁	—	2	2	no	—
156	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃₁	#41	1	2	yes	—
158	C₂³×C₁₃₁	—	2	1	no	—
159	C₂³×C₁₃₁	—	2	1	no	—
160	C₂³×C₁₃₁	—	2	1	no	—
161	C₂³×C₁₃₁	—	2	1	no	—
162	C₂³×C₁₃₁	—	2	1	no	—
163	C₂³×C₁₃₁	—	2	1	no	—
164	C₂³×C₁₃₁	C₄×Q₈	1	2	yes	—
165	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
166	Q₈×C₁₃₁	—	2	8	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	2	no	—
171	C₂×C₄×C₁₃₁	—	2	1	no	—
172	C₂×C₄×C₁₃₁	—	2	1	no	—
173	C₂×C₄×C₁₃₁	—	2	2	no	—
174	C₂×C₄×C₁₃₁	—	2	2	no	—
175	C₂×C₄×C₁₃₁	—	2	2	no	—
176	C₂×C₄×C₁₃₁	—	2	2	no	—
177	C₂×C₄×C₁₃₁	—	2	1	no	—
178	C₂×C₄×C₁₃₁	—	2	1	no	—
179	C₂×C₄×C₁₃₁	—	2	2	no	—
180	C₂×C₄×C₁₃₁	—	2	2	no	—
181	C₂×C₄×C₁₃₁	—	2	2	no	—
182	C₂×C₄×C₁₃₁	—	2	2	no	—
183	C₂×C₄×C₁₃₁	—	2	1	no	—
184	C₂×C₄×C₁₃₁	—	2	2	no	—
185	C₂×C₄×C₁₃₁	—	2	1	no	—
186	C₂×C₄×C₁₃₁	—	2	2	no	—
187	C₂×C₄×C₁₃₁	—	2	2	no	—
188	C₂×C₄×C₁₃₁	—	2	1	no	—
189	C₂×C₄×C₁₃₁	—	2	2	no	—
190	C₂×C₄×C₁₃₁	—	2	2	no	—
191	C₂×C₄×C₁₃₁	—	2	1	no	—
192	C₂×C₄×C₁₃₁	—	4	4	no	—
193	C₂×C₄×C₁₃₁	—	4	4	no	—
194	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₃₁	C₄×Q₈	1	2	yes	—
197	C₂×C₄×C₁₃₁	C₂×M₁₆	1	4	yes	—
198	C₂×C₄×C₁₃₁	C₂×M₁₆	1	2	yes	—
199	C₂×C₄×C₁₃₁	#131	1	2	yes	—
200	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
206	C₈×C₁₃₁	—	2	2	no	—
207	C₈×C₁₃₁	—	2	2	no	—
208	C₈×C₁₃₁	—	2	2	no	—
209	C₈×C₁₃₁	—	4	2	no	—
210	C₈×C₁₃₁	—	4	2	no	—
211	C₈×C₁₃₁	C₂²⋊Q₈	1	4	yes	complemented
212	C₂²×C₁₃₁	—	2	2	no	—
213	C₂²×C₁₃₁	—	2	2	no	—
214	C₂²×C₁₃₁	—	2	2	no	—
215	C₂²×C₁₃₁	—	4	1	no	—
216	C₂²×C₁₃₁	—	4	1	no	—
217	C₂²×C₁₃₁	—	4	1	no	—
218	C₂²×C₁₃₁	—	4	1	no	—
219	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₁₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
221	C₂²×C₁₃₁	C₄×#41	1	1	yes	characteristic
222	C₂²×C₁₃₁	C₂²×M₁₆	1	1	yes	characteristic
223	C₂²×C₁₃₁	C₂×#131	1	1	yes	characteristic
224	C₂²×C₁₃₁	#568	1	1	yes	characteristic
225	C₂²×C₁₃₁	#568	1	1	yes	characteristic
226	C₄×C₁₃₁	—	2	4	no	—
227	C₄×C₁₃₁	—	2	2	no	—
228	C₄×C₁₃₁	—	2	2	no	—
229	C₄×C₁₃₁	—	4	1	no	—
230	C₄×C₁₃₁	—	4	2	no	—
231	C₄×C₁₃₁	—	4	1	no	—
232	C₄×C₁₃₁	—	4	2	no	—
233	C₄×C₁₃₁	—	4	2	no	—
234	C₄×C₁₃₁	#435	1	4	yes	—
235	C₄×C₁₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
236	C₄×C₁₃₁	#525	1	1	yes	characteristic
237	C₄×C₁₃₁	#529	1	1	yes	characteristic
238	C₄×C₁₃₁	#533	1	1	yes	characteristic
239	C₂×C₁₃₁	—	4	2	no	—
240	C₂×C₁₃₁	C₄×C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₁₃₁	C₂×#435	1	1	yes	characteristic
242	C₂×C₁₃₁	#2930	1	1	yes	characteristic
243	C₂×C₁₃₁	#2962	1	1	yes	characteristic
244	C₂×C₁₃₁	Q₈×M₁₆	1	1	yes	characteristic
245	C₂×C₁₃₁	#2969	1	1	yes	characteristic
246	C₂×C₁₃₁	#2971	1	1	yes	characteristic
247	#21596	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₁₃₁	#21596	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×C₈×Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
250	C₂×C₄×M₁₆	C₂×C₁₃₁	1	1	yes	characteristic
251	C₄×C₂²⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic
252	#1984	C₂×C₁₃₁	1	1	yes	characteristic, complemented
253	#1939	C₂×C₁₃₁	1	1	yes	characteristic, complemented
254	#1917	C₂×C₁₃₁	1	2	yes	complemented
255	#1851	C₂×C₁₃₁	1	2	yes	—
256	#1797	C₂×C₁₃₁	1	1	yes	characteristic
257	#1771	C₂×C₁₃₁	1	2	yes	complemented
258	#1770	C₂×C₁₃₁	1	1	yes	characteristic, complemented
259	#1753	C₂×C₁₃₁	1	2	yes	—
260	C₂²×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
262	C₂×C₂²⋊Q₈	C₄×C₁₃₁	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
264	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
265	C₈×Q₈	—	2	4	no	—
266	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
269	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	2	yes	—
271	C₄×M₁₆	—	2	4	no	—
272	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
273	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
274	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
275	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
277	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
278	#391	C₄×C₁₃₁	1	1	yes	characteristic
279	#389	C₄×C₁₃₁	1	1	yes	characteristic
280	#387	C₄×C₁₃₁	1	2	yes	—
281	#385	C₄×C₁₃₁	1	2	yes	—
282	#380	C₄×C₁₃₁	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
284	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
285	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
286	#336	C₂²×C₁₃₁	1	2	yes	—
287	#336	C₂²×C₁₃₁	1	2	yes	—
288	#336	C₂²×C₁₃₁	1	2	yes	—
289	#336	C₂²×C₁₃₁	1	2	yes	—
290	#336	C₂²×C₁₃₁	1	2	yes	—
291	C₂²×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
292	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
293	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	Q₈×C₁₃₁	1	4	yes	complemented
301	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
302	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
307	C₂²⋊Q₈	—	2	4	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
312	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
313	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
321	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
323	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
324	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
326	C₄⋊C₈	—	2	4	no	—
327	C₄⋊C₈	—	2	4	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₂²⋊C₈	—	2	4	no	—
331	#97	—	2	2	no	—
332	#97	—	2	2	no	—
333	#97	—	2	4	no	—
334	C₄×C₈	—	2	4	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	D₄×C₁₃₁	1	4	yes	—
337	#95	C₂×C₄×C₁₃₁	1	2	yes	—
338	#95	C₂×C₄×C₁₃₁	1	2	yes	—
339	#95	C₂×C₄×C₁₃₁	1	2	yes	—
340	#95	C₂×C₄×C₁₃₁	1	2	yes	—
341	#95	C₂×C₄×C₁₃₁	1	2	yes	—
342	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	M₁₆×C₁₃₁	1	4	yes	complemented
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
360	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
361	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
366	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
368	M₁₆	—	2	8	no	—
369	M₁₆	—	2	8	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
384	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
385	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
386	C₂×C₈	#41×C₁₃₁	1	2	yes	—
387	C₂×C₈	#41×C₁₃₁	1	2	yes	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	2	no	—
404	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
405	C₄²	#41×C₁₃₁	1	2	yes	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	C₄×Q₈×C₁₃₁	1	2	yes	—
413	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
414	Q₈	—	2	8	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
443	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
444	C₂×C₄	C₄×Q₈×C₁₃₁	1	2	yes	—
445	C₂×C₄	C₂×M₁₆×C₁₃₁	1	4	yes	—
446	C₂×C₄	C₂×M₁₆×C₁₃₁	1	2	yes	—
447	C₂×C₄	#131×C₁₃₁	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
449	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₈	C₂²⋊Q₈×C₁₃₁	1	4	yes	complemented
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
468	C₂²	C₂×C₄×Q₈×C₁₃₁	1	1	yes	characteristic
469	C₂²	C₄×#41×C₁₃₁	1	1	yes	characteristic
470	C₂²	C₂²×M₁₆×C₁₃₁	1	1	yes	characteristic
471	C₂²	C₂×#131×C₁₃₁	1	1	yes	characteristic
472	C₂²	#568×C₁₃₁	1	1	yes	characteristic
473	C₂²	#568×C₁₃₁	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	4	no	—
476	C₄	—	2	2	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	#435×C₁₃₁	1	4	yes	—
483	C₄	C₂×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
484	C₄	#525×C₁₃₁	1	1	yes	characteristic
485	C₄	#529×C₁₃₁	1	1	yes	characteristic
486	C₄	#533×C₁₃₁	1	1	yes	characteristic
487	C₂	—	4	2	no	—
488	C₂	C₄×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
489	C₂	C₂×#435×C₁₃₁	1	1	yes	characteristic
490	C₂	#2930×C₁₃₁	1	1	yes	characteristic
491	C₂	#2962×C₁₃₁	1	1	yes	characteristic
492	C₂	Q₈×M₁₆×C₁₃₁	1	1	yes	characteristic
493	C₂	#2969×C₁₃₁	1	1	yes	characteristic
494	C₂	#2971×C₁₃₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Q₈×C₁₃₁	C₂	semidirect
4. #1984×C₁₃₁	C₂	semidirect
5. #1939×C₁₃₁	C₂	semidirect
6. #1917×C₁₃₁	C₂	semidirect
9. #1771×C₁₃₁	C₂	semidirect
10. #1770×C₁₃₁	C₂	semidirect
52. C₂×M₁₆×C₁₃₁	Q₈	semidirect
97. C₂×Q₈×C₁₃₁	M₁₆	semidirect
211. C₈×C₁₃₁	C₂²⋊Q₈	semidirect
247. #21596	C₁₃₁	direct (N × H)
248. C₁₃₁	#21596	direct (N × H)
249. C₂×C₈×Q₈	C₂×C₁₃₁	semidirect
252. #1984	C₂×C₁₃₁	semidirect
253. #1939	C₂×C₁₃₁	semidirect
254. #1917	C₂×C₁₃₁	semidirect
257. #1771	C₂×C₁₃₁	semidirect
258. #1770	C₂×C₁₃₁	semidirect
300. C₂×M₁₆	Q₈×C₁₃₁	semidirect
345. C₂×Q₈	M₁₆×C₁₃₁	semidirect
459. C₈	C₂²⋊Q₈×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Q₈×C₁₃₁	2
C₂×C₄×M₁₆×C₁₃₁	2
C₄×C₂²⋊Q₈×C₁₃₁	2
#1984×C₁₃₁	2
#1939×C₁₃₁	2
#1917×C₁₃₁	2
#1851×C₁₃₁	2
#1797×C₁₃₁	2
#1771×C₁₃₁	2
#1770×C₁₃₁	2
#1753×C₁₃₁	2
#21596	131

Subgroups — C131×#21596 #45707480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#21596 #45707480