Subgroups — C₂×#1714×C₁₃₁ #45705489

Order 33536.

914 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#500×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#498×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#492×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#492×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#487×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#486×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1714×C₁₃₁	C₂	1	8	yes	maximal, direct product factor
8	C₂×#322×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₁₃₁	—	2	2	no	—
10	C₂²×SD₁₆×C₁₃₁	—	2	2	no	—
11	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
15	#500×C₁₃₁	—	2	2	no	—
16	#500×C₁₃₁	C₂²	1	4	yes	complemented
17	#498×C₁₃₁	—	2	2	no	—
18	#498×C₁₃₁	C₂²	1	4	yes	complemented
19	#492×C₁₃₁	—	2	2	no	—
20	#492×C₁₃₁	—	2	2	no	—
21	#492×C₁₃₁	C₂²	1	4	yes	—
22	#492×C₁₃₁	C₂²	1	4	yes	—
23	#487×C₁₃₁	—	2	2	no	—
24	#487×C₁₃₁	C₂²	1	4	yes	complemented
25	#486×C₁₃₁	—	2	2	no	—
26	#486×C₁₃₁	C₂²	1	4	yes	—
27	C₂×#107×C₁₃₁	—	2	2	no	—
28	C₂×#106×C₁₃₁	—	2	2	no	—
29	C₂×#103×C₁₃₁	—	2	2	no	—
30	C₂×#102×C₁₃₁	—	2	2	no	—
31	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
34	#322×C₁₃₁	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₁₃₁	—	2	1	no	—
36	C₂²×Q₈×C₁₃₁	—	2	1	no	—
37	C₂²×Q₈×C₁₃₁	—	2	1	no	—
38	C₂²×D₄×C₁₃₁	—	2	1	no	—
39	C₂²×D₄×C₁₃₁	—	2	1	no	—
40	C₂²×D₄×C₁₃₁	—	2	1	no	—
41	C₂×SD₁₆×C₁₃₁	—	2	8	no	—
42	C₂×SD₁₆×C₁₃₁	—	2	8	no	—
43	C₂×SD₁₆×C₁₃₁	—	4	8	no	—
44	C₂×SD₁₆×C₁₃₁	—	4	8	no	—
45	C₂²×C₈×C₁₃₁	D₄	1	2	yes	—
46	C₂²×C₈×C₁₃₁	D₄	1	2	yes	—
47	C₂²×C₈×C₁₃₁	D₄	1	2	yes	—
48	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
49	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
50	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
51	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
52	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
53	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
54	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
55	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
56	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
57	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
60	#127×C₁₃₁	—	2	1	no	—
61	#127×C₁₃₁	—	2	1	no	—
62	#127×C₁₃₁	—	2	1	no	—
63	#127×C₁₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
70	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
71	#107×C₁₃₁	—	2	8	no	—
72	#106×C₁₃₁	—	2	8	no	—
73	#103×C₁₃₁	—	2	8	no	—
74	#102×C₁₃₁	—	2	8	no	—
75	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
76	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
77	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
78	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
79	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
80	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
81	C₂⁴×C₁₃₁	—	4	1	no	—
82	C₂×Q₈×C₁₃₁	—	2	2	no	—
83	C₂×Q₈×C₁₃₁	—	2	2	no	—
84	C₂×Q₈×C₁₃₁	—	2	2	no	—
85	C₂×Q₈×C₁₃₁	—	4	1	no	—
86	C₂×Q₈×C₁₃₁	—	4	1	no	—
87	C₂×Q₈×C₁₃₁	—	4	1	no	—
88	C₂×Q₈×C₁₃₁	—	4	4	no	—
89	C₂×Q₈×C₁₃₁	—	4	4	no	—
90	C₂×Q₈×C₁₃₁	—	4	4	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	1	no	—
95	C₂×D₄×C₁₃₁	—	4	1	no	—
96	C₂×D₄×C₁₃₁	—	4	1	no	—
97	C₂×D₄×C₁₃₁	—	4	4	no	—
98	C₂×D₄×C₁₃₁	—	4	4	no	—
99	C₂×D₄×C₁₃₁	—	4	4	no	—
100	C₂²×C₄×C₁₃₁	—	4	1	no	—
101	C₂²×C₄×C₁₃₁	—	4	1	no	—
102	C₂²×C₄×C₁₃₁	—	4	1	no	—
103	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
106	SD₁₆×C₁₃₁	—	4	16	no	—
107	SD₁₆×C₁₃₁	—	4	16	no	—
108	C₂×C₈×C₁₃₁	—	2	4	no	—
109	C₂×C₈×C₁₃₁	—	2	4	no	—
110	C₂×C₈×C₁₃₁	SD₁₆	1	8	yes	complemented
111	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
112	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
113	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
114	C₄⋊C₄×C₁₃₁	—	2	2	no	—
115	C₄⋊C₄×C₁₃₁	—	2	2	no	—
116	C₄⋊C₄×C₁₃₁	—	2	2	no	—
117	C₄⋊C₄×C₁₃₁	—	2	2	no	—
118	C₄⋊C₄×C₁₃₁	—	2	2	no	—
119	C₄⋊C₄×C₁₃₁	—	2	2	no	—
120	C₄⋊C₄×C₁₃₁	—	4	1	no	—
121	C₄⋊C₄×C₁₃₁	—	4	1	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	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
130	C₂³×C₁₃₁	—	4	2	no	—
131	C₂³×C₁₃₁	—	8	2	no	—
132	C₂³×C₁₃₁	—	8	2	no	—
133	C₂³×C₁₃₁	—	8	2	no	—
134	C₂³×C₁₃₁	#127	1	1	yes	characteristic
135	Q₈×C₁₃₁	—	4	4	no	—
136	Q₈×C₁₃₁	—	4	4	no	—
137	Q₈×C₁₃₁	—	4	4	no	—
138	Q₈×C₁₃₁	—	8	2	no	—
139	Q₈×C₁₃₁	—	8	2	no	—
140	Q₈×C₁₃₁	—	8	2	no	—
141	D₄×C₁₃₁	—	4	4	no	—
142	D₄×C₁₃₁	—	4	4	no	—
143	D₄×C₁₃₁	—	4	4	no	—
144	D₄×C₁₃₁	—	8	2	no	—
145	D₄×C₁₃₁	—	8	2	no	—
146	D₄×C₁₃₁	—	8	2	no	—
147	C₂×C₄×C₁₃₁	—	4	2	no	—
148	C₂×C₄×C₁₃₁	—	4	2	no	—
149	C₂×C₄×C₁₃₁	—	4	2	no	—
150	C₂×C₄×C₁₃₁	—	8	2	no	—
151	C₂×C₄×C₁₃₁	—	8	2	no	—
152	C₂×C₄×C₁₃₁	—	8	2	no	—
153	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
154	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
155	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
156	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	4	yes	—
157	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	4	yes	—
158	C₂×C₄×C₁₃₁	#137	1	4	yes	—
159	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₈×C₁₃₁	—	2	4	no	—
163	C₈×C₁₃₁	—	2	4	no	—
164	C₈×C₁₃₁	C₂×SD₁₆	1	8	yes	complemented
165	C₂²×C₁₃₁	—	8	2	no	—
166	C₂²×C₁₃₁	—	8	2	no	—
167	C₂²×C₁₃₁	—	8	2	no	—
168	C₂²×C₁₃₁	—	16	4	no	—
169	C₂²×C₁₃₁	#492	1	2	yes	—
170	C₂²×C₁₃₁	#496	1	2	yes	—
171	C₂²×C₁₃₁	#497	1	2	yes	—
172	C₂²×C₁₃₁	C₂×#127	1	1	yes	characteristic
173	C₄×C₁₃₁	—	8	2	no	—
174	C₄×C₁₃₁	—	8	2	no	—
175	C₄×C₁₃₁	—	8	2	no	—
176	C₄×C₁₃₁	#492	1	2	yes	—
177	C₄×C₁₃₁	#496	1	2	yes	—
178	C₄×C₁₃₁	#497	1	2	yes	—
179	C₄×C₁₃₁	C₂²×SD₁₆	1	2	yes	—
180	C₄×C₁₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
181	C₄×C₁₃₁	C₂×#137	1	2	yes	—
182	C₂×C₁₃₁	—	16	2	no	—
183	C₂×C₁₃₁	#1714	1	4	yes	direct product factor
184	C₂×C₁₃₁	C₂×#492	1	1	yes	characteristic
185	C₂×C₁₃₁	C₂×#496	1	1	yes	characteristic
186	C₂×C₁₃₁	C₂×#497	1	1	yes	characteristic
187	C₂×#1714	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃₁	C₂×#1714	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#500	C₂×C₁₃₁	1	1	yes	characteristic, complemented
190	C₂×#498	C₂×C₁₃₁	1	1	yes	characteristic, complemented
191	C₂×#492	C₂×C₁₃₁	1	1	yes	characteristic
192	C₂×#492	C₂×C₁₃₁	1	1	yes	characteristic
193	C₂×#487	C₂×C₁₃₁	1	1	yes	characteristic, complemented
194	C₂×#486	C₂×C₁₃₁	1	1	yes	characteristic
195	#1714	C₂×C₁₃₁	1	8	yes	direct product factor
196	C₂×#322	C₂×C₁₃₁	1	1	yes	characteristic, complemented
197	C₂²×SD₁₆	—	2	2	no	—
198	C₂²×SD₁₆	—	2	2	no	—
199	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
201	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
202	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
203	#500	—	2	2	no	—
204	#500	C₂²×C₁₃₁	1	4	yes	complemented
205	#498	—	2	2	no	—
206	#498	C₂²×C₁₃₁	1	4	yes	complemented
207	#492	—	2	2	no	—
208	#492	—	2	2	no	—
209	#492	C₂²×C₁₃₁	1	4	yes	—
210	#492	C₂²×C₁₃₁	1	4	yes	—
211	#487	—	2	2	no	—
212	#487	C₂²×C₁₃₁	1	4	yes	complemented
213	#486	—	2	2	no	—
214	#486	C₂²×C₁₃₁	1	4	yes	—
215	C₂×#107	—	2	2	no	—
216	C₂×#106	—	2	2	no	—
217	C₂×#103	—	2	2	no	—
218	C₂×#102	—	2	2	no	—
219	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
222	#322	C₂²×C₁₃₁	1	4	yes	complemented
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	—	2	1	no	—
225	C₂²×Q₈	—	2	1	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂×SD₁₆	—	2	8	no	—
230	C₂×SD₁₆	—	2	8	no	—
231	C₂×SD₁₆	—	4	8	no	—
232	C₂×SD₁₆	—	4	8	no	—
233	C₂²×C₈	D₄×C₁₃₁	1	2	yes	—
234	C₂²×C₈	D₄×C₁₃₁	1	2	yes	—
235	C₂²×C₈	D₄×C₁₃₁	1	2	yes	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
246	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
247	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
248	#127	—	2	1	no	—
249	#127	—	2	1	no	—
250	#127	—	2	1	no	—
251	#127	C₂³×C₁₃₁	1	2	yes	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
259	#107	—	2	8	no	—
260	#106	—	2	8	no	—
261	#103	—	2	8	no	—
262	#102	—	2	8	no	—
263	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
264	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
265	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
266	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
267	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
268	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
269	C₂⁴	—	4	1	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	4	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	—	4	4	no	—
286	C₂×D₄	—	4	4	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
294	SD₁₆	—	4	16	no	—
295	SD₁₆	—	4	16	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	SD₁₆×C₁₃₁	1	8	yes	complemented
299	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
300	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
301	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
317	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
318	C₂³	—	4	2	no	—
319	C₂³	—	8	2	no	—
320	C₂³	—	8	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	#127×C₁₃₁	1	1	yes	characteristic
323	Q₈	—	4	4	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	4	4	no	—
326	Q₈	—	8	2	no	—
327	Q₈	—	8	2	no	—
328	Q₈	—	8	2	no	—
329	D₄	—	4	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	4	4	no	—
332	D₄	—	8	2	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
342	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
343	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	4	yes	—
345	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	4	yes	—
346	C₂×C₄	#137×C₁₃₁	1	4	yes	—
347	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
350	C₈	—	2	4	no	—
351	C₈	—	2	4	no	—
352	C₈	C₂×SD₁₆×C₁₃₁	1	8	yes	complemented
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	16	4	no	—
357	C₂²	#492×C₁₃₁	1	2	yes	—
358	C₂²	#496×C₁₃₁	1	2	yes	—
359	C₂²	#497×C₁₃₁	1	2	yes	—
360	C₂²	C₂×#127×C₁₃₁	1	1	yes	characteristic
361	C₄	—	8	2	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	2	no	—
364	C₄	#492×C₁₃₁	1	2	yes	—
365	C₄	#496×C₁₃₁	1	2	yes	—
366	C₄	#497×C₁₃₁	1	2	yes	—
367	C₄	C₂²×SD₁₆×C₁₃₁	1	2	yes	—
368	C₄	C₂×AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
369	C₄	C₂×#137×C₁₃₁	1	2	yes	—
370	C₂	—	16	2	no	—
371	C₂	#1714×C₁₃₁	1	4	yes	direct product factor
372	C₂	C₂×#492×C₁₃₁	1	1	yes	characteristic
373	C₂	C₂×#496×C₁₃₁	1	1	yes	characteristic
374	C₂	C₂×#497×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×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
1. C₂×#500×C₁₃₁	C₂	semidirect
2. C₂×#498×C₁₃₁	C₂	semidirect
5. C₂×#487×C₁₃₁	C₂	semidirect
7. #1714×C₁₃₁	C₂	direct (N × H)
8. C₂×#322×C₁₃₁	C₂	semidirect
16. #500×C₁₃₁	C₂²	semidirect
18. #498×C₁₃₁	C₂²	semidirect
24. #487×C₁₃₁	C₂²	semidirect
34. #322×C₁₃₁	C₂²	semidirect
110. C₂×C₈×C₁₃₁	SD₁₆	semidirect
164. C₈×C₁₃₁	C₂×SD₁₆	semidirect
183. C₂×C₁₃₁	#1714	direct (N × H)
187. C₂×#1714	C₁₃₁	direct (N × H)
188. C₁₃₁	C₂×#1714	direct (N × H)
189. C₂×#500	C₂×C₁₃₁	semidirect
190. C₂×#498	C₂×C₁₃₁	semidirect
193. C₂×#487	C₂×C₁₃₁	semidirect
195. #1714	C₂×C₁₃₁	direct (N × H)
196. C₂×#322	C₂×C₁₃₁	semidirect
204. #500	C₂²×C₁₃₁	semidirect
206. #498	C₂²×C₁₃₁	semidirect
212. #487	C₂²×C₁₃₁	semidirect
222. #322	C₂²×C₁₃₁	semidirect
298. C₂×C₈	SD₁₆×C₁₃₁	semidirect
352. C₈	C₂×SD₁₆×C₁₃₁	semidirect
371. C₂	#1714×C₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#500×C₁₃₁	2
C₂×#498×C₁₃₁	2
C₂×#492×C₁₃₁	2
C₂×#487×C₁₃₁	2
C₂×#486×C₁₃₁	2
#1714×C₁₃₁	2
C₂×#322×C₁₃₁	2
C₂×#1714	131

Subgroups — C2×#1714×C131 #45705489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1714×C₁₃₁ #45705489