Subgroups — C₁₃₁×#8979 #45694863

Order 33536.

660 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#460×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#1982×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1957×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈⋊C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1296×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1279×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₁₃₁	—	2	1	no	—
9	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃₁	—	2	1	no	—
11	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	#460×C₁₃₁	—	2	2	no	—
13	#460×C₁₃₁	C₄	1	4	yes	complemented
14	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×#102×C₁₃₁	—	2	1	no	—
17	C₂×#102×C₁₃₁	—	2	1	no	—
18	C₂×#102×C₁₃₁	—	2	1	no	—
19	C₂×#102×C₁₃₁	—	2	2	no	—
20	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	#389×C₁₃₁	—	2	1	no	—
22	#389×C₁₃₁	—	2	2	no	—
23	#384×C₁₃₁	—	2	1	no	—
24	#384×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₃₁	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
27	Q₈⋊C₈×C₁₃₁	—	2	2	no	—
28	C₂²×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₃₁	—	2	1	no	—
30	C₂²×D₄×C₁₃₁	—	2	1	no	—
31	C₂²×D₄×C₁₃₁	—	2	1	no	—
32	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
33	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
34	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
35	C₂²×C₈×C₁₃₁	—	2	1	no	—
36	C₂²×C₈×C₁₃₁	—	2	1	no	—
37	C₂²×C₈×C₁₃₁	—	2	1	no	—
38	#127×C₁₃₁	—	2	1	no	—
39	#127×C₁₃₁	—	2	1	no	—
40	#127×C₁₃₁	—	2	1	no	—
41	#127×C₁₃₁	C₂×C₄	1	2	yes	—
42	C₄×Q₈×C₁₃₁	—	2	1	no	—
43	C₄×Q₈×C₁₃₁	—	2	1	no	—
44	C₄×Q₈×C₁₃₁	—	4	2	no	—
45	C₄×Q₈×C₁₃₁	—	4	2	no	—
46	C₄×Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
47	C₄×Q₈×C₁₃₁	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₁	D₄	1	2	yes	—
57	C₂×C₄²×C₁₃₁	—	2	1	no	—
58	C₂×C₄²×C₁₃₁	—	2	2	no	—
59	C₂×C₄²×C₁₃₁	—	2	1	no	—
60	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₁₃₁	—	2	1	no	—
62	C₄⋊C₈×C₁₃₁	—	2	1	no	—
63	C₄⋊C₈×C₁₃₁	—	2	1	no	—
64	C₄⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
65	#102×C₁₃₁	—	2	4	no	—
66	#102×C₁₃₁	—	4	2	no	—
67	#102×C₁₃₁	—	4	4	no	—
68	#102×C₁₃₁	—	4	2	no	—
69	C₄×C₈×C₁₃₁	—	2	1	no	—
70	C₄×C₈×C₁₃₁	—	2	1	no	—
71	#95×C₁₃₁	—	2	2	no	—
72	#95×C₁₃₁	—	2	1	no	—
73	C₂⁴×C₁₃₁	—	4	1	no	—
74	C₂×Q₈×C₁₃₁	—	2	1	no	—
75	C₂×Q₈×C₁₃₁	—	2	1	no	—
76	C₂×Q₈×C₁₃₁	—	2	1	no	—
77	C₂×Q₈×C₁₃₁	C₂²⋊C₄	1	2	yes	—
78	C₂×Q₈×C₁₃₁	D₈	1	2	yes	—
79	C₂×Q₈×C₁₃₁	SD₁₆	1	2	yes	—
80	C₂×D₄×C₁₃₁	—	2	2	no	—
81	C₂×D₄×C₁₃₁	—	2	2	no	—
82	C₂×D₄×C₁₃₁	—	2	2	no	—
83	C₂×D₄×C₁₃₁	—	4	2	no	—
84	C₂×D₄×C₁₃₁	—	4	2	no	—
85	C₂×D₄×C₁₃₁	—	4	1	no	—
86	C₂×D₄×C₁₃₁	—	4	1	no	—
87	C₂×D₄×C₁₃₁	—	4	1	no	—
88	C₂×D₄×C₁₃₁	—	4	1	no	—
89	C₂×D₄×C₁₃₁	—	4	1	no	—
90	C₂×D₄×C₁₃₁	—	4	1	no	—
91	C₂×D₄×C₁₃₁	—	4	1	no	—
92	C₂×D₄×C₁₃₁	—	4	1	no	—
93	C₂×D₄×C₁₃₁	—	4	1	no	—
94	C₂×D₄×C₁₃₁	—	4	1	no	—
95	C₂×D₄×C₁₃₁	—	4	1	no	—
96	C₂²×C₄×C₁₃₁	—	2	1	no	—
97	C₂²×C₄×C₁₃₁	—	2	1	no	—
98	C₂²×C₄×C₁₃₁	—	2	1	no	—
99	C₂²×C₄×C₁₃₁	—	2	1	no	—
100	C₂²×C₄×C₁₃₁	—	2	2	no	—
101	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
104	SD₁₆×C₁₃₁	—	4	8	no	—
105	C₂×C₈×C₁₃₁	—	2	2	no	—
106	C₂×C₈×C₁₃₁	—	2	2	no	—
107	C₂×C₈×C₁₃₁	—	4	1	no	—
108	C₂×C₈×C₁₃₁	—	4	1	no	—
109	C₂×C₈×C₁₃₁	—	4	1	no	—
110	C₂×C₈×C₁₃₁	—	4	1	no	—
111	C₂×C₈×C₁₃₁	—	4	1	no	—
112	C₂×C₈×C₁₃₁	—	4	1	no	—
113	C₂×C₈×C₁₃₁	—	4	1	no	—
114	C₄⋊C₄×C₁₃₁	—	2	2	no	—
115	C₄⋊C₄×C₁₃₁	—	2	2	no	—
116	C₄⋊C₄×C₁₃₁	—	2	1	no	—
117	C₄⋊C₄×C₁₃₁	—	2	1	no	—
118	C₄⋊C₄×C₁₃₁	—	2	1	no	—
119	C₄⋊C₄×C₁₃₁	—	2	1	no	—
120	C₄⋊C₄×C₁₃₁	—	4	2	no	—
121	C₄⋊C₄×C₁₃₁	—	4	4	no	—
122	C₄⋊C₄×C₁₃₁	—	4	1	no	—
123	C₄⋊C₄×C₁₃₁	—	4	1	no	—
124	C₄⋊C₄×C₁₃₁	—	4	1	no	—
125	C₄⋊C₄×C₁₃₁	—	4	1	no	—
126	C₄⋊C₄×C₁₃₁	—	8	2	no	—
127	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
128	C₄⋊C₄×C₁₃₁	SD₁₆	1	2	yes	complemented
129	C₄²×C₁₃₁	—	2	2	no	—
130	C₄²×C₁₃₁	—	2	2	no	—
131	C₄²×C₁₃₁	—	4	4	no	—
132	C₄²×C₁₃₁	—	4	1	no	—
133	C₄²×C₁₃₁	—	4	1	no	—
134	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃₁	#41	1	1	yes	characteristic
137	C₄²×C₁₃₁	#41	1	1	yes	characteristic
138	C₂³×C₁₃₁	—	4	2	no	—
139	C₂³×C₁₃₁	—	8	1	no	—
140	C₂³×C₁₃₁	—	8	1	no	—
141	C₂³×C₁₃₁	—	8	1	no	—
142	C₂³×C₁₃₁	—	8	1	no	—
143	C₂³×C₁₃₁	—	8	1	no	—
144	C₂³×C₁₃₁	—	8	1	no	—
145	C₂³×C₁₃₁	#120	1	1	yes	characteristic
146	Q₈×C₁₃₁	—	2	2	no	—
147	Q₈×C₁₃₁	—	2	2	no	—
148	Q₈×C₁₃₁	—	2	2	no	—
149	Q₈×C₁₃₁	#102	1	4	yes	complemented
150	D₄×C₁₃₁	—	4	4	no	—
151	D₄×C₁₃₁	—	4	2	no	—
152	D₄×C₁₃₁	—	4	2	no	—
153	D₄×C₁₃₁	—	4	2	no	—
154	D₄×C₁₃₁	—	4	2	no	—
155	D₄×C₁₃₁	—	8	2	no	—
156	D₄×C₁₃₁	—	8	1	no	—
157	D₄×C₁₃₁	—	8	1	no	—
158	D₄×C₁₃₁	—	8	1	no	—
159	D₄×C₁₃₁	—	8	1	no	—
160	C₂×C₄×C₁₃₁	—	2	2	no	—
161	C₂×C₄×C₁₃₁	—	2	2	no	—
162	C₂×C₄×C₁₃₁	—	2	2	no	—
163	C₂×C₄×C₁₃₁	—	2	1	no	—
164	C₂×C₄×C₁₃₁	—	2	1	no	—
165	C₂×C₄×C₁₃₁	—	2	2	no	—
166	C₂×C₄×C₁₃₁	—	2	2	no	—
167	C₂×C₄×C₁₃₁	—	4	1	no	—
168	C₂×C₄×C₁₃₁	—	4	1	no	—
169	C₂×C₄×C₁₃₁	—	4	1	no	—
170	C₂×C₄×C₁₃₁	—	4	1	no	—
171	C₂×C₄×C₁₃₁	—	4	2	no	—
172	C₂×C₄×C₁₃₁	—	4	1	no	—
173	C₂×C₄×C₁₃₁	—	4	1	no	—
174	C₂×C₄×C₁₃₁	—	4	2	no	—
175	C₂×C₄×C₁₃₁	—	4	2	no	—
176	C₂×C₄×C₁₃₁	—	4	1	no	—
177	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₃₁	#123	1	1	yes	characteristic
183	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	1	yes	characteristic
185	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	1	yes	characteristic
186	C₂×C₄×C₁₃₁	#135	1	1	yes	characteristic
187	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₄×C₁₃₁	#137	1	1	yes	characteristic
190	C₂×C₄×C₁₃₁	#137	1	1	yes	characteristic
191	C₈×C₁₃₁	—	4	2	no	—
192	C₈×C₁₃₁	—	4	2	no	—
193	C₈×C₁₃₁	—	8	1	no	—
194	C₂²×C₁₃₁	—	8	2	no	—
195	C₂²×C₁₃₁	—	8	2	no	—
196	C₂²×C₁₃₁	—	8	2	no	—
197	C₂²×C₁₃₁	—	16	1	no	—
198	C₂²×C₁₃₁	—	16	1	no	—
199	C₂²×C₁₃₁	—	16	1	no	—
200	C₂²×C₁₃₁	—	16	1	no	—
201	C₂²×C₁₃₁	#386	1	1	yes	characteristic
202	C₂²×C₁₃₁	#447	1	1	yes	characteristic
203	C₂²×C₁₃₁	#448	1	1	yes	characteristic
204	C₂²×C₁₃₁	#448	1	1	yes	characteristic
205	C₂²×C₁₃₁	#449	1	1	yes	characteristic
206	C₂²×C₁₃₁	#453	1	1	yes	characteristic
207	C₂²×C₁₃₁	#454	1	1	yes	characteristic
208	C₄×C₁₃₁	—	2	4	no	—
209	C₄×C₁₃₁	—	2	1	no	—
210	C₄×C₁₃₁	—	2	1	no	—
211	C₄×C₁₃₁	—	4	2	no	—
212	C₄×C₁₃₁	—	4	2	no	—
213	C₄×C₁₃₁	—	8	1	no	—
214	C₄×C₁₃₁	—	8	2	no	—
215	C₄×C₁₃₁	C₂×#102	1	1	yes	characteristic
216	C₄×C₁₃₁	#417	1	1	yes	characteristic
217	C₄×C₁₃₁	C₄×SD₁₆	1	1	yes	characteristic
218	C₄×C₁₃₁	#440	1	1	yes	characteristic
219	C₄×C₁₃₁	#460	1	1	yes	characteristic
220	C₄×C₁₃₁	#464	1	1	yes	characteristic
221	C₄×C₁₃₁	#480	1	1	yes	characteristic
222	C₄×C₁₃₁	#481	1	1	yes	characteristic
223	C₂×C₁₃₁	—	16	2	no	—
224	C₂×C₁₃₁	#1621	1	1	yes	characteristic
225	C₂×C₁₃₁	#1623	1	1	yes	characteristic
226	C₂×C₁₃₁	#1626	1	1	yes	characteristic
227	C₂×C₁₃₁	#1627	1	1	yes	characteristic
228	C₂×C₁₃₁	#1874	1	1	yes	characteristic
229	C₂×C₁₃₁	#1880	1	1	yes	characteristic
230	C₂×C₁₃₁	#1883	1	1	yes	characteristic
231	#8979	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₁₃₁	#8979	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×#460	C₂×C₁₃₁	1	1	yes	characteristic
234	Q₈×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
235	#1982	C₂×C₁₃₁	1	1	yes	characteristic
236	#1957	C₂×C₁₃₁	1	1	yes	characteristic
237	C₂×Q₈⋊C₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
238	#1296	C₂×C₁₃₁	1	1	yes	characteristic, complemented
239	#1279	C₂×C₁₃₁	1	1	yes	characteristic, complemented
240	C₂²×SD₁₆	—	2	1	no	—
241	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
242	C₂×C₄×Q₈	—	2	1	no	—
243	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
244	#460	—	2	2	no	—
245	#460	C₄×C₁₃₁	1	4	yes	complemented
246	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
248	C₂×#102	—	2	1	no	—
249	C₂×#102	—	2	2	no	—
250	C₂×#102	—	2	1	no	—
251	C₂×#102	—	2	1	no	—
252	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
253	#389	—	2	1	no	—
254	#389	—	2	2	no	—
255	#384	—	2	1	no	—
256	#384	C₂²×C₁₃₁	1	1	yes	characteristic
257	C₄×C₄⋊C₄	—	2	1	no	—
258	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
259	Q₈⋊C₈	—	2	2	no	—
260	C₂²×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂×SD₁₆	—	2	4	no	—
265	C₂×SD₁₆	—	4	2	no	—
266	C₂×SD₁₆	—	4	2	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	C₂×C₄×C₁₃₁	1	2	yes	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	—	4	2	no	—
277	C₄×Q₈	—	4	2	no	—
278	C₄×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
279	C₄×Q₈	D₄×C₁₃₁	1	2	yes	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
286	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
287	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
288	C₂×C₄⋊C₄	D₄×C₁₃₁	1	2	yes	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
297	#102	—	2	4	no	—
298	#102	—	4	2	no	—
299	#102	—	4	4	no	—
300	#102	—	4	2	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	2	1	no	—
303	#95	—	2	2	no	—
304	#95	—	2	1	no	—
305	C₂⁴	—	4	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	C₂²⋊C₄×C₁₃₁	1	2	yes	—
310	C₂×Q₈	D₈×C₁₃₁	1	2	yes	—
311	C₂×Q₈	SD₁₆×C₁₃₁	1	2	yes	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
336	SD₁₆	—	4	8	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	8	2	no	—
359	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
360	C₄⋊C₄	SD₁₆×C₁₃₁	1	2	yes	complemented
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
367	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
368	C₄²	#41×C₁₃₁	1	1	yes	characteristic
369	C₄²	#41×C₁₃₁	1	1	yes	characteristic
370	C₂³	—	4	2	no	—
371	C₂³	—	8	1	no	—
372	C₂³	—	8	1	no	—
373	C₂³	—	8	1	no	—
374	C₂³	—	8	1	no	—
375	C₂³	—	8	1	no	—
376	C₂³	—	8	1	no	—
377	C₂³	#120×C₁₃₁	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	#102×C₁₃₁	1	4	yes	complemented
382	D₄	—	4	4	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	1	no	—
389	D₄	—	8	1	no	—
390	D₄	—	8	1	no	—
391	D₄	—	8	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
410	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
411	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
412	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
413	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
414	C₂×C₄	#123×C₁₃₁	1	1	yes	characteristic
415	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
416	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	1	yes	characteristic
417	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	1	yes	characteristic
418	C₂×C₄	#135×C₁₃₁	1	1	yes	characteristic
419	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
420	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
421	C₂×C₄	#137×C₁₃₁	1	1	yes	characteristic
422	C₂×C₄	#137×C₁₃₁	1	1	yes	characteristic
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	8	1	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	16	1	no	—
430	C₂²	—	16	1	no	—
431	C₂²	—	16	1	no	—
432	C₂²	—	16	1	no	—
433	C₂²	#386×C₁₃₁	1	1	yes	characteristic
434	C₂²	#447×C₁₃₁	1	1	yes	characteristic
435	C₂²	#448×C₁₃₁	1	1	yes	characteristic
436	C₂²	#448×C₁₃₁	1	1	yes	characteristic
437	C₂²	#449×C₁₃₁	1	1	yes	characteristic
438	C₂²	#453×C₁₃₁	1	1	yes	characteristic
439	C₂²	#454×C₁₃₁	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	2	no	—
447	C₄	C₂×#102×C₁₃₁	1	1	yes	characteristic
448	C₄	#417×C₁₃₁	1	1	yes	characteristic
449	C₄	C₄×SD₁₆×C₁₃₁	1	1	yes	characteristic
450	C₄	#440×C₁₃₁	1	1	yes	characteristic
451	C₄	#460×C₁₃₁	1	1	yes	characteristic
452	C₄	#464×C₁₃₁	1	1	yes	characteristic
453	C₄	#480×C₁₃₁	1	1	yes	characteristic
454	C₄	#481×C₁₃₁	1	1	yes	characteristic
455	C₂	—	16	2	no	—
456	C₂	#1621×C₁₃₁	1	1	yes	characteristic
457	C₂	#1623×C₁₃₁	1	1	yes	characteristic
458	C₂	#1626×C₁₃₁	1	1	yes	characteristic
459	C₂	#1627×C₁₃₁	1	1	yes	characteristic
460	C₂	#1874×C₁₃₁	1	1	yes	characteristic
461	C₂	#1880×C₁₃₁	1	1	yes	characteristic
462	C₂	#1883×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	#120
commutator	C₄²	C₂²×C₄×C₁₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₁
prime radical	C₂×#127×C₁₃₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₄⋊C₄×C₁₃₁	C₂	semidirect
5. C₂×Q₈⋊C₈×C₁₃₁	C₂	semidirect
6. #1296×C₁₃₁	C₂	semidirect
7. #1279×C₁₃₁	C₂	semidirect
13. #460×C₁₃₁	C₄	semidirect
128. C₄⋊C₄×C₁₃₁	SD₁₆	semidirect
149. Q₈×C₁₃₁	#102	semidirect
231. #8979	C₁₃₁	direct (N × H)
232. C₁₃₁	#8979	direct (N × H)
234. Q₈×C₄⋊C₄	C₂×C₁₃₁	semidirect
237. C₂×Q₈⋊C₈	C₂×C₁₃₁	semidirect
238. #1296	C₂×C₁₃₁	semidirect
239. #1279	C₂×C₁₃₁	semidirect
245. #460	C₄×C₁₃₁	semidirect
360. C₄⋊C₄	SD₁₆×C₁₃₁	semidirect
381. Q₈	#102×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#460×C₁₃₁	2
Q₈×C₄⋊C₄×C₁₃₁	2
#1982×C₁₃₁	2
#1957×C₁₃₁	2
C₂×Q₈⋊C₈×C₁₃₁	2
#1296×C₁₃₁	2
#1279×C₁₃₁	2
#8979	131

Subgroups — C131×#8979 #45694863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#8979 #45694863