Subgroups — C₁₃₁×#19468 #45705352

Order 33536.

672 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3208×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#3113×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#460×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2984×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1702×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1686×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1682×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1666×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1573×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1555×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	#1552×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₃₁	—	2	1	no	—
13	#533×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	#492×C₁₃₁	C₂²	1	2	yes	—
17	#486×C₁₃₁	C₂²	1	2	yes	—
18	#483×C₁₃₁	—	2	1	no	—
19	#475×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
20	#475×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
21	#462×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
22	#462×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
23	#460×C₁₃₁	—	2	1	no	—
24	#460×C₁₃₁	—	2	1	no	—
25	#460×C₁₃₁	—	2	2	no	—
26	#460×C₁₃₁	C₂²	1	2	yes	—
27	#460×C₁₃₁	C₂²	1	2	yes	—
28	#451×C₁₃₁	—	2	1	no	—
29	#450×C₁₃₁	—	2	1	no	—
30	#450×C₁₃₁	—	2	1	no	—
31	#446×C₁₃₁	—	2	2	no	—
32	#446×C₁₃₁	C₂²	1	2	yes	complemented
33	C₈×Q₈×C₁₃₁	C₂²	1	2	yes	complemented
34	#441×C₁₃₁	—	2	1	no	—
35	#441×C₁₃₁	—	2	1	no	—
36	#432×C₁₃₁	—	2	1	no	—
37	#432×C₁₃₁	C₂²	1	1	yes	characteristic
38	#432×C₁₃₁	C₂²	1	1	yes	characteristic
39	#431×C₁₃₁	—	2	1	no	—
40	#431×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
42	C₂×#102×C₁₃₁	—	2	1	no	—
43	#335×C₁₃₁	C₂²	1	2	yes	complemented
44	#334×C₁₃₁	C₂²	1	2	yes	complemented
45	#332×C₁₃₁	C₂²	1	2	yes	complemented
46	#332×C₁₃₁	C₂²	1	2	yes	complemented
47	#331×C₁₃₁	C₂²	1	2	yes	—
48	#331×C₁₃₁	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₃₁	—	2	1	no	—
51	C₂²×D₄×C₁₃₁	—	2	1	no	—
52	C₂²×D₄×C₁₃₁	—	2	1	no	—
53	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
54	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
55	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
56	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
57	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
58	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
59	C₂×SD₁₆×C₁₃₁	—	4	4	no	—
60	C₂²×C₈×C₁₃₁	—	2	1	no	—
61	C₄⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
63	#127×C₁₃₁	—	2	1	no	—
64	#127×C₁₃₁	—	2	1	no	—
65	#127×C₁₃₁	—	2	1	no	—
66	#127×C₁₃₁	C₂³	1	2	yes	—
67	#125×C₁₃₁	—	2	1	no	—
68	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
69	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
70	C₄×Q₈×C₁₃₁	—	2	1	no	—
71	C₄×Q₈×C₁₃₁	—	2	1	no	—
72	C₄×Q₈×C₁₃₁	—	2	1	no	—
73	C₄×Q₈×C₁₃₁	—	2	1	no	—
74	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
76	C₄×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₄×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
78	#117×C₁₃₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₃₁	—	2	1	no	—
82	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
83	#106×C₁₃₁	—	2	1	no	—
84	#106×C₁₃₁	—	2	1	no	—
85	C₄⋊C₈×C₁₃₁	—	2	2	no	—
86	C₄⋊C₈×C₁₃₁	—	2	2	no	—
87	C₄⋊C₈×C₁₃₁	—	2	1	no	—
88	C₄⋊C₈×C₁₃₁	D₄	1	2	yes	—
89	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
90	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
91	C₄⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
93	#103×C₁₃₁	—	2	1	no	—
94	#103×C₁₃₁	—	2	1	no	—
95	#103×C₁₃₁	—	2	1	no	—
96	#103×C₁₃₁	—	2	1	no	—
97	#102×C₁₃₁	—	2	2	no	—
98	#102×C₁₃₁	—	2	2	no	—
99	#102×C₁₃₁	—	2	2	no	—
100	#102×C₁₃₁	—	2	2	no	—
101	C₂²⋊C₈×C₁₃₁	—	2	1	no	—
102	C₂²⋊C₈×C₁₃₁	—	2	1	no	—
103	C₂²⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
104	C₂²⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
105	#97×C₁₃₁	—	2	2	no	—
106	#97×C₁₃₁	—	2	1	no	—
107	#97×C₁₃₁	—	2	1	no	—
108	C₄×C₈×C₁₃₁	—	2	2	no	—
109	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
110	C₂⁴×C₁₃₁	—	4	1	no	—
111	C₂×Q₈×C₁₃₁	—	2	1	no	—
112	C₂×Q₈×C₁₃₁	—	2	2	no	—
113	C₂×Q₈×C₁₃₁	—	2	1	no	—
114	C₂×Q₈×C₁₃₁	—	2	1	no	—
115	C₂×Q₈×C₁₃₁	—	4	1	no	—
116	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₁₃₁	—	2	2	no	—
119	C₂×D₄×C₁₃₁	—	2	2	no	—
120	C₂×D₄×C₁₃₁	—	2	2	no	—
121	C₂×D₄×C₁₃₁	—	4	2	no	—
122	C₂×D₄×C₁₃₁	—	4	2	no	—
123	C₂×D₄×C₁₃₁	—	4	1	no	—
124	C₂×D₄×C₁₃₁	—	4	1	no	—
125	C₂×D₄×C₁₃₁	—	4	1	no	—
126	C₂×D₄×C₁₃₁	—	8	2	no	—
127	C₂×D₄×C₁₃₁	—	8	2	no	—
128	C₂²×C₄×C₁₃₁	—	2	1	no	—
129	C₂²×C₄×C₁₃₁	—	2	1	no	—
130	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
133	Q₁₆×C₁₃₁	—	4	2	no	—
134	Q₁₆×C₁₃₁	—	4	2	no	—
135	SD₁₆×C₁₃₁	—	4	4	no	—
136	SD₁₆×C₁₃₁	—	4	4	no	—
137	SD₁₆×C₁₃₁	—	8	2	no	—
138	SD₁₆×C₁₃₁	—	8	2	no	—
139	C₂×C₈×C₁₃₁	—	2	2	no	—
140	C₂×C₈×C₁₃₁	—	2	1	no	—
141	C₂×C₈×C₁₃₁	—	2	1	no	—
142	C₂×C₈×C₁₃₁	—	2	2	no	—
143	C₂×C₈×C₁₃₁	—	4	2	no	—
144	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₁₃₁	—	2	1	no	—
147	C₄⋊C₄×C₁₃₁	—	2	1	no	—
148	C₄⋊C₄×C₁₃₁	—	2	1	no	—
149	C₄⋊C₄×C₁₃₁	—	2	1	no	—
150	C₄⋊C₄×C₁₃₁	—	2	1	no	—
151	C₄⋊C₄×C₁₃₁	—	2	1	no	—
152	C₄⋊C₄×C₁₃₁	—	2	1	no	—
153	C₄⋊C₄×C₁₃₁	—	2	1	no	—
154	C₄⋊C₄×C₁₃₁	—	2	1	no	—
155	C₄⋊C₄×C₁₃₁	—	4	1	no	—
156	C₄⋊C₄×C₁₃₁	—	4	1	no	—
157	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
158	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
159	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
160	C₄²×C₁₃₁	—	2	1	no	—
161	C₄²×C₁₃₁	—	2	1	no	—
162	C₄²×C₁₃₁	—	2	1	no	—
163	C₄²×C₁₃₁	—	2	1	no	—
164	C₄²×C₁₃₁	—	4	1	no	—
165	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₃₁	#41	1	1	yes	characteristic
168	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
169	C₂³×C₁₃₁	—	4	2	no	—
170	C₂³×C₁₃₁	—	8	2	no	—
171	C₂³×C₁₃₁	—	8	2	no	—
172	C₂³×C₁₃₁	—	8	2	no	—
173	C₂³×C₁₃₁	#121	1	1	yes	characteristic
174	Q₈×C₁₃₁	—	2	1	no	—
175	Q₈×C₁₃₁	—	2	1	no	—
176	Q₈×C₁₃₁	—	2	1	no	—
177	Q₈×C₁₃₁	—	4	2	no	—
178	Q₈×C₁₃₁	—	4	1	no	—
179	Q₈×C₁₃₁	—	4	1	no	—
180	Q₈×C₁₃₁	—	4	2	no	—
181	Q₈×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
182	D₄×C₁₃₁	—	4	2	no	—
183	D₄×C₁₃₁	—	4	2	no	—
184	D₄×C₁₃₁	—	4	2	no	—
185	D₄×C₁₃₁	—	4	2	no	—
186	D₄×C₁₃₁	—	8	2	no	—
187	D₄×C₁₃₁	—	8	2	no	—
188	D₄×C₁₃₁	—	8	2	no	—
189	D₄×C₁₃₁	—	8	2	no	—
190	C₂×C₄×C₁₃₁	—	2	1	no	—
191	C₂×C₄×C₁₃₁	—	2	2	no	—
192	C₂×C₄×C₁₃₁	—	2	1	no	—
193	C₂×C₄×C₁₃₁	—	2	1	no	—
194	C₂×C₄×C₁₃₁	—	2	2	no	—
195	C₂×C₄×C₁₃₁	—	2	1	no	—
196	C₂×C₄×C₁₃₁	—	2	1	no	—
197	C₂×C₄×C₁₃₁	—	2	1	no	—
198	C₂×C₄×C₁₃₁	—	4	2	no	—
199	C₂×C₄×C₁₃₁	—	4	2	no	—
200	C₂×C₄×C₁₃₁	—	4	1	no	—
201	C₂×C₄×C₁₃₁	—	4	1	no	—
202	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
205	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
208	C₈×C₁₃₁	—	2	2	no	—
209	C₈×C₁₃₁	—	2	2	no	—
210	C₈×C₁₃₁	—	4	2	no	—
211	C₈×C₁₃₁	—	4	1	no	—
212	C₈×C₁₃₁	—	4	1	no	—
213	C₈×C₁₃₁	—	4	2	no	—
214	C₂²×C₁₃₁	—	2	1	no	—
215	C₂²×C₁₃₁	—	2	1	no	—
216	C₂²×C₁₃₁	—	8	2	no	—
217	C₂²×C₁₃₁	—	8	2	no	—
218	C₂²×C₁₃₁	—	8	2	no	—
219	C₂²×C₁₃₁	—	16	4	no	—
220	C₂²×C₁₃₁	#471	1	2	yes	—
221	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
222	C₄×C₁₃₁	—	2	1	no	—
223	C₄×C₁₃₁	—	2	1	no	—
224	C₄×C₁₃₁	—	2	2	no	—
225	C₄×C₁₃₁	—	2	1	no	—
226	C₄×C₁₃₁	—	2	1	no	—
227	C₄×C₁₃₁	—	4	1	no	—
228	C₄×C₁₃₁	—	4	1	no	—
229	C₄×C₁₃₁	—	4	1	no	—
230	C₄×C₁₃₁	—	8	1	no	—
231	C₄×C₁₃₁	—	8	1	no	—
232	C₄×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₄×C₁₃₁	#575	1	1	yes	characteristic
234	C₄×C₁₃₁	#577	1	2	yes	—
235	C₂×C₁₃₁	—	2	2	no	—
236	C₂×C₁₃₁	—	16	2	no	—
237	C₂×C₁₃₁	#3043	1	1	yes	characteristic
238	C₂×C₁₃₁	#3055	1	1	yes	characteristic
239	C₂×C₁₃₁	C₂×#471	1	1	yes	characteristic
240	#19468	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₁₃₁	#19468	1	1	yes	characteristic, direct product factor, Sylow
242	#3208	C₂×C₁₃₁	1	1	yes	characteristic
243	#3113	C₂×C₁₃₁	1	1	yes	characteristic, complemented
244	C₂×#460	C₂×C₁₃₁	1	1	yes	characteristic
245	#2984	C₂×C₁₃₁	1	1	yes	characteristic, complemented
246	#1702	C₂×C₁₃₁	1	2	yes	complemented
247	#1686	C₂×C₁₃₁	1	2	yes	complemented
248	#1682	C₂×C₁₃₁	1	2	yes	complemented
249	#1666	C₂×C₁₃₁	1	2	yes	complemented
250	#1573	C₂×C₁₃₁	1	1	yes	characteristic, complemented
251	#1555	C₂×C₁₃₁	1	1	yes	characteristic
252	#1552	C₂×C₁₃₁	1	1	yes	characteristic, complemented
253	C₂²×SD₁₆	—	2	1	no	—
254	#533	C₂²×C₁₃₁	1	1	yes	characteristic
255	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
256	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
257	#492	C₂²×C₁₃₁	1	2	yes	—
258	#486	C₂²×C₁₃₁	1	2	yes	—
259	#483	—	2	1	no	—
260	#475	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
261	#475	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
262	#462	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
263	#462	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
264	#460	—	2	1	no	—
265	#460	—	2	1	no	—
266	#460	—	2	2	no	—
267	#460	C₂²×C₁₃₁	1	2	yes	—
268	#460	C₂²×C₁₃₁	1	2	yes	—
269	#451	—	2	1	no	—
270	#450	—	2	1	no	—
271	#450	—	2	1	no	—
272	#446	—	2	2	no	—
273	#446	C₂²×C₁₃₁	1	2	yes	complemented
274	C₈×Q₈	C₂²×C₁₃₁	1	2	yes	complemented
275	#441	—	2	1	no	—
276	#441	—	2	1	no	—
277	#432	—	2	1	no	—
278	#432	C₂²×C₁₃₁	1	1	yes	characteristic
279	#432	C₂²×C₁₃₁	1	1	yes	characteristic
280	#431	—	2	1	no	—
281	#431	C₂²×C₁₃₁	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
283	C₂×#102	—	2	1	no	—
284	#335	C₂²×C₁₃₁	1	2	yes	complemented
285	#334	C₂²×C₁₃₁	1	2	yes	complemented
286	#332	C₂²×C₁₃₁	1	2	yes	complemented
287	#332	C₂²×C₁₃₁	1	2	yes	complemented
288	#331	C₂²×C₁₃₁	1	2	yes	—
289	#331	C₂²×C₁₃₁	1	2	yes	—
290	C₂²×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂×Q₁₆	—	2	1	no	—
295	C₂×Q₁₆	—	2	1	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×SD₁₆	—	2	2	no	—
300	C₂×SD₁₆	—	4	4	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₄⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
303	C₄⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
304	#127	—	2	1	no	—
305	#127	—	2	1	no	—
306	#127	—	2	1	no	—
307	#127	C₂³×C₁₃₁	1	2	yes	—
308	#125	—	2	1	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	C₂²⋊Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×Q₈	—	2	1	no	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
316	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
317	C₄×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
318	C₄×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
319	#117	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
324	#106	—	2	1	no	—
325	#106	—	2	1	no	—
326	C₄⋊C₈	—	2	2	no	—
327	C₄⋊C₈	—	2	2	no	—
328	C₄⋊C₈	—	2	1	no	—
329	C₄⋊C₈	D₄×C₁₃₁	1	2	yes	—
330	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
331	C₄⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
332	C₄⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
333	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
334	#103	—	2	1	no	—
335	#103	—	2	1	no	—
336	#103	—	2	1	no	—
337	#103	—	2	1	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	#102	—	2	2	no	—
341	#102	—	2	2	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	1	no	—
344	C₂²⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
345	C₂²⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
346	#97	—	2	2	no	—
347	#97	—	2	1	no	—
348	#97	—	2	1	no	—
349	C₄×C₈	—	2	2	no	—
350	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
351	C₂⁴	—	4	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
358	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	8	2	no	—
368	C₂×D₄	—	8	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
373	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
374	Q₁₆	—	4	2	no	—
375	Q₁₆	—	4	2	no	—
376	SD₁₆	—	4	4	no	—
377	SD₁₆	—	4	4	no	—
378	SD₁₆	—	8	2	no	—
379	SD₁₆	—	8	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
386	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
400	C₂²⋊C₄	—	4	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	4	1	no	—
406	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
408	C₄²	#41×C₁₃₁	1	1	yes	characteristic
409	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
410	C₂³	—	4	2	no	—
411	C₂³	—	8	2	no	—
412	C₂³	—	8	2	no	—
413	C₂³	—	8	2	no	—
414	C₂³	#121×C₁₃₁	1	1	yes	characteristic
415	Q₈	—	2	1	no	—
416	Q₈	—	2	1	no	—
417	Q₈	—	2	1	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	2	no	—
422	Q₈	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	8	2	no	—
428	D₄	—	8	2	no	—
429	D₄	—	8	2	no	—
430	D₄	—	8	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
444	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
445	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
448	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	2	2	no	—
451	C₈	—	4	2	no	—
452	C₈	—	4	1	no	—
453	C₈	—	4	1	no	—
454	C₈	—	4	2	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	16	4	no	—
461	C₂²	#471×C₁₃₁	1	2	yes	—
462	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	1	no	—
473	C₄	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
474	C₄	#575×C₁₃₁	1	1	yes	characteristic
475	C₄	#577×C₁₃₁	1	2	yes	—
476	C₂	—	2	2	no	—
477	C₂	—	16	2	no	—
478	C₂	#3043×C₁₃₁	1	1	yes	characteristic
479	C₂	#3055×C₁₃₁	1	1	yes	characteristic
480	C₂	C₂×#471×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₁
prime radical	C₂×#127×C₁₃₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #3113×C₁₃₁	C₂	semidirect
4. #2984×C₁₃₁	C₂	semidirect
5. #1702×C₁₃₁	C₂	semidirect
6. #1686×C₁₃₁	C₂	semidirect
7. #1682×C₁₃₁	C₂	semidirect
8. #1666×C₁₃₁	C₂	semidirect
9. #1573×C₁₃₁	C₂	semidirect
11. #1552×C₁₃₁	C₂	semidirect
19. #475×C₁₃₁	C₂²	semidirect
20. #475×C₁₃₁	C₂²	semidirect
21. #462×C₁₃₁	C₂²	semidirect
22. #462×C₁₃₁	C₂²	semidirect
32. #446×C₁₃₁	C₂²	semidirect
33. C₈×Q₈×C₁₃₁	C₂²	semidirect
43. #335×C₁₃₁	C₂²	semidirect
44. #334×C₁₃₁	C₂²	semidirect
45. #332×C₁₃₁	C₂²	semidirect
46. #332×C₁₃₁	C₂²	semidirect
240. #19468	C₁₃₁	direct (N × H)
241. C₁₃₁	#19468	direct (N × H)
243. #3113	C₂×C₁₃₁	semidirect
245. #2984	C₂×C₁₃₁	semidirect
246. #1702	C₂×C₁₃₁	semidirect
247. #1686	C₂×C₁₃₁	semidirect
248. #1682	C₂×C₁₃₁	semidirect
249. #1666	C₂×C₁₃₁	semidirect
250. #1573	C₂×C₁₃₁	semidirect
252. #1552	C₂×C₁₃₁	semidirect
260. #475	C₂²×C₁₃₁	semidirect
261. #475	C₂²×C₁₃₁	semidirect
262. #462	C₂²×C₁₃₁	semidirect
263. #462	C₂²×C₁₃₁	semidirect
273. #446	C₂²×C₁₃₁	semidirect
274. C₈×Q₈	C₂²×C₁₃₁	semidirect
284. #335	C₂²×C₁₃₁	semidirect
285. #334	C₂²×C₁₃₁	semidirect
286. #332	C₂²×C₁₃₁	semidirect
287. #332	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3208×C₁₃₁	2
#3113×C₁₃₁	2
C₂×#460×C₁₃₁	2
#2984×C₁₃₁	2
#1702×C₁₃₁	2
#1686×C₁₃₁	2
#1682×C₁₃₁	2
#1666×C₁₃₁	2
#1573×C₁₃₁	2
#1555×C₁₃₁	2
#1552×C₁₃₁	2
#19468	131

Subgroups — C131×#19468 #45705352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#19468 #45705352