Subgroups — C₁₃₁×#19682 #45705566

Order 33536.

754 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3209×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3208×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#3170×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#3165×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#3138×C₁₃₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#486×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1722×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1720×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1720×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#1719×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1451×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₁₃₁	C₂²	1	1	yes	characteristic
13	#533×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
16	#501×C₁₃₁	—	2	2	no	—
17	#500×C₁₃₁	C₂²	1	2	yes	complemented
18	#500×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
19	#498×C₁₃₁	C₂²	1	2	yes	complemented
20	#494×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
21	#494×C₁₃₁	C₂²	1	2	yes	complemented
22	#492×C₁₃₁	C₂²	1	2	yes	—
23	#490×C₁₃₁	—	2	2	no	—
24	#487×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
25	#487×C₁₃₁	C₂²	1	2	yes	complemented
26	#487×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
27	#486×C₁₃₁	—	2	2	no	—
28	#486×C₁₃₁	C₂²	1	2	yes	—
29	#486×C₁₃₁	C₂²	1	2	yes	—
30	#486×C₁₃₁	C₂²	1	2	yes	—
31	#486×C₁₃₁	C₂²	1	2	yes	—
32	#486×C₁₃₁	C₂²	1	2	yes	—
33	#467×C₁₃₁	—	2	2	no	—
34	#462×C₁₃₁	—	2	2	no	—
35	#460×C₁₃₁	—	2	2	no	—
36	#451×C₁₃₁	—	2	2	no	—
37	#450×C₁₃₁	—	2	2	no	—
38	C₄×Q₁₆×C₁₃₁	—	2	2	no	—
39	#431×C₁₃₁	C₂²	1	1	yes	characteristic
40	#428×C₁₃₁	—	2	2	no	—
41	#418×C₁₃₁	—	2	2	no	—
42	C₂×#102×C₁₃₁	—	2	2	no	—
43	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
45	#322×C₁₃₁	C₂²	1	2	yes	complemented
46	#322×C₁₃₁	C₂²	1	2	yes	complemented
47	C₂²×Q₈×C₁₃₁	—	2	1	no	—
48	C₂²×D₄×C₁₃₁	—	2	1	no	—
49	C₂²×D₄×C₁₃₁	—	2	1	no	—
50	C₂²×D₄×C₁₃₁	—	2	1	no	—
51	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
52	C₂×Q₁₆×C₁₃₁	—	2	4	no	—
53	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
54	C₂×M₁₆×C₁₃₁	D₄	1	2	yes	—
55	C₂²×C₈×C₁₃₁	D₄	1	2	yes	—
56	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
57	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
58	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
59	C₄⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₄⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
63	C₄⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
64	#127×C₁₃₁	—	2	1	no	—
65	#127×C₁₃₁	—	2	1	no	—
66	#127×C₁₃₁	—	2	1	no	—
67	#127×C₁₃₁	C₂³	1	2	yes	—
68	#125×C₁₃₁	—	2	1	no	—
69	#125×C₁₃₁	—	2	1	no	—
70	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
71	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
72	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
73	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
74	C₄×Q₈×C₁₃₁	—	2	1	no	—
75	C₄×Q₈×C₁₃₁	—	2	1	no	—
76	C₄×Q₈×C₁₃₁	—	2	1	no	—
77	C₄×Q₈×C₁₃₁	—	2	1	no	—
78	#117×C₁₃₁	—	2	1	no	—
79	#117×C₁₃₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
82	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
83	#107×C₁₃₁	—	2	4	no	—
84	#107×C₁₃₁	—	2	2	no	—
85	#106×C₁₃₁	—	2	4	no	—
86	C₄⋊C₈×C₁₃₁	D₄	1	2	yes	—
87	#103×C₁₃₁	—	2	2	no	—
88	#103×C₁₃₁	—	2	2	no	—
89	#103×C₁₃₁	—	2	4	no	—
90	#102×C₁₃₁	—	2	4	no	—
91	#102×C₁₃₁	—	2	4	no	—
92	#102×C₁₃₁	—	2	4	no	—
93	#102×C₁₃₁	—	2	4	no	—
94	#102×C₁₃₁	—	2	4	no	—
95	C₂²⋊C₈×C₁₃₁	D₄	1	2	yes	—
96	#97×C₁₃₁	D₄	1	2	yes	—
97	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
98	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
101	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
102	C₂⁴×C₁₃₁	—	4	1	no	—
103	C₂×Q₈×C₁₃₁	—	2	1	no	—
104	C₂×Q₈×C₁₃₁	—	2	1	no	—
105	C₂×Q₈×C₁₃₁	—	2	2	no	—
106	C₂×Q₈×C₁₃₁	—	2	1	no	—
107	C₂×Q₈×C₁₃₁	—	2	1	no	—
108	C₂×Q₈×C₁₃₁	—	4	1	no	—
109	C₂×Q₈×C₁₃₁	—	8	2	no	—
110	C₂×D₄×C₁₃₁	—	2	2	no	—
111	C₂×D₄×C₁₃₁	—	2	2	no	—
112	C₂×D₄×C₁₃₁	—	2	2	no	—
113	C₂×D₄×C₁₃₁	—	4	4	no	—
114	C₂×D₄×C₁₃₁	—	4	1	no	—
115	C₂×D₄×C₁₃₁	—	4	1	no	—
116	C₂×D₄×C₁₃₁	—	4	1	no	—
117	C₂×D₄×C₁₃₁	—	4	4	no	—
118	C₂×D₄×C₁₃₁	—	8	2	no	—
119	C₂²×C₄×C₁₃₁	—	4	1	no	—
120	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
123	Q₁₆×C₁₃₁	—	4	4	no	—
124	Q₁₆×C₁₃₁	—	8	4	no	—
125	SD₁₆×C₁₃₁	—	8	4	no	—
126	M₁₆×C₁₃₁	—	2	4	no	—
127	C₂×C₈×C₁₃₁	—	4	2	no	—
128	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₁₃₁	—	2	2	no	—
133	C₄⋊C₄×C₁₃₁	—	2	1	no	—
134	C₄⋊C₄×C₁₃₁	—	2	1	no	—
135	C₄⋊C₄×C₁₃₁	—	2	1	no	—
136	C₄⋊C₄×C₁₃₁	—	2	1	no	—
137	C₄⋊C₄×C₁₃₁	—	2	1	no	—
138	C₄⋊C₄×C₁₃₁	—	2	1	no	—
139	C₄⋊C₄×C₁₃₁	—	2	1	no	—
140	C₄⋊C₄×C₁₃₁	—	2	2	no	—
141	C₄⋊C₄×C₁₃₁	—	2	1	no	—
142	C₄⋊C₄×C₁₃₁	—	4	1	no	—
143	C₄⋊C₄×C₁₃₁	—	4	1	no	—
144	C₄⋊C₄×C₁₃₁	—	4	1	no	—
145	C₄⋊C₄×C₁₃₁	—	4	1	no	—
146	C₄⋊C₄×C₁₃₁	—	4	1	no	—
147	C₄⋊C₄×C₁₃₁	—	4	1	no	—
148	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
149	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
150	C₄²×C₁₃₁	—	4	1	no	—
151	C₄²×C₁₃₁	—	4	1	no	—
152	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
156	C₂³×C₁₃₁	—	4	2	no	—
157	C₂³×C₁₃₁	—	8	2	no	—
158	C₂³×C₁₃₁	—	8	2	no	—
159	C₂³×C₁₃₁	—	8	2	no	—
160	C₂³×C₁₃₁	#127	1	1	yes	characteristic
161	Q₈×C₁₃₁	—	4	2	no	—
162	Q₈×C₁₃₁	—	4	2	no	—
163	Q₈×C₁₃₁	—	4	2	no	—
164	Q₈×C₁₃₁	—	4	2	no	—
165	Q₈×C₁₃₁	—	4	4	no	—
166	Q₈×C₁₃₁	—	8	2	no	—
167	D₄×C₁₃₁	—	4	4	no	—
168	D₄×C₁₃₁	—	4	4	no	—
169	D₄×C₁₃₁	—	4	4	no	—
170	D₄×C₁₃₁	—	8	2	no	—
171	D₄×C₁₃₁	—	8	2	no	—
172	D₄×C₁₃₁	—	8	2	no	—
173	C₂×C₄×C₁₃₁	—	2	2	no	—
174	C₂×C₄×C₁₃₁	—	2	2	no	—
175	C₂×C₄×C₁₃₁	—	4	1	no	—
176	C₂×C₄×C₁₃₁	—	4	1	no	—
177	C₂×C₄×C₁₃₁	—	4	1	no	—
178	C₂×C₄×C₁₃₁	—	4	1	no	—
179	C₂×C₄×C₁₃₁	—	4	2	no	—
180	C₂×C₄×C₁₃₁	—	8	2	no	—
181	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
182	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
183	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
184	C₂×C₄×C₁₃₁	#137	1	4	yes	—
185	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₁₃₁	—	2	4	no	—
189	C₈×C₁₃₁	—	2	2	no	—
190	C₈×C₁₃₁	—	2	2	no	—
191	C₈×C₁₃₁	—	2	4	no	—
192	C₂²×C₁₃₁	—	2	1	no	—
193	C₂²×C₁₃₁	—	2	1	no	—
194	C₂²×C₁₃₁	—	8	2	no	—
195	C₂²×C₁₃₁	—	8	2	no	—
196	C₂²×C₁₃₁	—	8	2	no	—
197	C₂²×C₁₃₁	—	16	4	no	—
198	C₂²×C₁₃₁	#497	1	2	yes	—
199	C₂²×C₁₃₁	C₂×#127	1	1	yes	characteristic
200	C₄×C₁₃₁	—	2	1	no	—
201	C₄×C₁₃₁	—	2	1	no	—
202	C₄×C₁₃₁	—	8	1	no	—
203	C₄×C₁₃₁	—	8	1	no	—
204	C₄×C₁₃₁	—	8	2	no	—
205	C₄×C₁₃₁	—	8	1	no	—
206	C₄×C₁₃₁	—	8	1	no	—
207	C₄×C₁₃₁	#497	1	2	yes	—
208	C₄×C₁₃₁	C₂×#137	1	2	yes	—
209	C₄×C₁₃₁	#575	1	2	yes	—
210	C₄×C₁₃₁	#576	1	2	yes	—
211	C₂×C₁₃₁	—	2	2	no	—
212	C₂×C₁₃₁	—	16	2	no	—
213	C₂×C₁₃₁	C₂×#497	1	1	yes	characteristic
214	C₂×C₁₃₁	#3153	1	1	yes	characteristic
215	C₂×C₁₃₁	#3155	1	1	yes	characteristic
216	#19682	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₁₃₁	#19682	1	1	yes	characteristic, direct product factor, Sylow
218	#3209	C₂×C₁₃₁	1	1	yes	characteristic, complemented
219	#3208	C₂×C₁₃₁	1	1	yes	characteristic
220	#3170	C₂×C₁₃₁	1	1	yes	characteristic, complemented
221	#3165	C₂×C₁₃₁	1	1	yes	characteristic, complemented
222	#3138	C₂×C₁₃₁	1	1	yes	characteristic
223	C₂×#486	C₂×C₁₃₁	1	1	yes	characteristic
224	#1722	C₂×C₁₃₁	1	2	yes	complemented
225	#1720	C₂×C₁₃₁	1	2	yes	complemented
226	#1720	C₂×C₁₃₁	1	2	yes	complemented
227	#1719	C₂×C₁₃₁	1	2	yes	complemented
228	#1451	C₂×C₁₃₁	1	1	yes	characteristic, complemented
229	#533	C₂²×C₁₃₁	1	1	yes	characteristic
230	#533	C₂²×C₁₃₁	1	1	yes	characteristic
231	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
232	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
233	#501	—	2	2	no	—
234	#500	C₂²×C₁₃₁	1	2	yes	complemented
235	#500	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
236	#498	C₂²×C₁₃₁	1	2	yes	complemented
237	#494	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
238	#494	C₂²×C₁₃₁	1	2	yes	complemented
239	#492	C₂²×C₁₃₁	1	2	yes	—
240	#490	—	2	2	no	—
241	#487	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
242	#487	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
243	#487	C₂²×C₁₃₁	1	2	yes	complemented
244	#486	—	2	2	no	—
245	#486	C₂²×C₁₃₁	1	2	yes	—
246	#486	C₂²×C₁₃₁	1	2	yes	—
247	#486	C₂²×C₁₃₁	1	2	yes	—
248	#486	C₂²×C₁₃₁	1	2	yes	—
249	#486	C₂²×C₁₃₁	1	2	yes	—
250	#467	—	2	2	no	—
251	#462	—	2	2	no	—
252	#460	—	2	2	no	—
253	#451	—	2	2	no	—
254	#450	—	2	2	no	—
255	C₄×Q₁₆	—	2	2	no	—
256	#431	C₂²×C₁₃₁	1	1	yes	characteristic
257	#428	—	2	2	no	—
258	#418	—	2	2	no	—
259	C₂×#102	—	2	2	no	—
260	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
262	#322	C₂²×C₁₃₁	1	2	yes	complemented
263	#322	C₂²×C₁₃₁	1	2	yes	complemented
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	2	4	no	—
270	C₂×SD₁₆	—	2	4	no	—
271	C₂×M₁₆	D₄×C₁₃₁	1	2	yes	—
272	C₂²×C₈	D₄×C₁₃₁	1	2	yes	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
277	C₄⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
278	C₄⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
279	C₄⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
281	#127	—	2	1	no	—
282	#127	—	2	1	no	—
283	#127	—	2	1	no	—
284	#127	C₂³×C₁₃₁	1	2	yes	—
285	#125	—	2	1	no	—
286	#125	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	#117	—	2	1	no	—
296	#117	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
300	#107	—	2	4	no	—
301	#107	—	2	2	no	—
302	#106	—	2	4	no	—
303	C₄⋊C₈	D₄×C₁₃₁	1	2	yes	—
304	#103	—	2	2	no	—
305	#103	—	2	2	no	—
306	#103	—	2	4	no	—
307	#102	—	2	4	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	#102	—	2	4	no	—
311	#102	—	2	4	no	—
312	C₂²⋊C₈	D₄×C₁₃₁	1	2	yes	—
313	#97	D₄×C₁₃₁	1	2	yes	—
314	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
315	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
316	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
317	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
318	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
319	C₂⁴	—	4	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	8	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	—	8	2	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
340	Q₁₆	—	4	4	no	—
341	Q₁₆	—	8	4	no	—
342	SD₁₆	—	8	4	no	—
343	M₁₆	—	2	4	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
346	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
347	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
348	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₄²	—	4	1	no	—
368	C₄²	—	4	1	no	—
369	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
370	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
371	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
372	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
373	C₂³	—	4	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	—	8	2	no	—
376	C₂³	—	8	2	no	—
377	C₂³	#127×C₁₃₁	1	1	yes	characteristic
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	4	no	—
383	Q₈	—	8	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	4	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
399	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
400	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
401	C₂×C₄	#137×C₁₃₁	1	4	yes	—
402	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
405	C₈	—	2	4	no	—
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	2	4	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	16	4	no	—
415	C₂²	#497×C₁₃₁	1	2	yes	—
416	C₂²	C₂×#127×C₁₃₁	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	#497×C₁₃₁	1	2	yes	—
425	C₄	C₂×#137×C₁₃₁	1	2	yes	—
426	C₄	#575×C₁₃₁	1	2	yes	—
427	C₄	#576×C₁₃₁	1	2	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	16	2	no	—
430	C₂	C₂×#497×C₁₃₁	1	1	yes	characteristic
431	C₂	#3153×C₁₃₁	1	1	yes	characteristic
432	C₂	#3155×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#127
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
1. #3209×C₁₃₁	C₂	semidirect
3. #3170×C₁₃₁	C₂	semidirect
4. #3165×C₁₃₁	C₂	semidirect
7. #1722×C₁₃₁	C₂	semidirect
8. #1720×C₁₃₁	C₂	semidirect
9. #1720×C₁₃₁	C₂	semidirect
10. #1719×C₁₃₁	C₂	semidirect
11. #1451×C₁₃₁	C₂	semidirect
17. #500×C₁₃₁	C₂²	semidirect
18. #500×C₁₃₁	C₂²	semidirect
19. #498×C₁₃₁	C₂²	semidirect
20. #494×C₁₃₁	C₂²	semidirect
21. #494×C₁₃₁	C₂²	semidirect
24. #487×C₁₃₁	C₂²	semidirect
25. #487×C₁₃₁	C₂²	semidirect
26. #487×C₁₃₁	C₂²	semidirect
45. #322×C₁₃₁	C₂²	semidirect
46. #322×C₁₃₁	C₂²	semidirect
216. #19682	C₁₃₁	direct (N × H)
217. C₁₃₁	#19682	direct (N × H)
218. #3209	C₂×C₁₃₁	semidirect
220. #3170	C₂×C₁₃₁	semidirect
221. #3165	C₂×C₁₃₁	semidirect
224. #1722	C₂×C₁₃₁	semidirect
225. #1720	C₂×C₁₃₁	semidirect
226. #1720	C₂×C₁₃₁	semidirect
227. #1719	C₂×C₁₃₁	semidirect
228. #1451	C₂×C₁₃₁	semidirect
234. #500	C₂²×C₁₃₁	semidirect
235. #500	C₂²×C₁₃₁	semidirect
236. #498	C₂²×C₁₃₁	semidirect
237. #494	C₂²×C₁₃₁	semidirect
238. #494	C₂²×C₁₃₁	semidirect
241. #487	C₂²×C₁₃₁	semidirect
242. #487	C₂²×C₁₃₁	semidirect
243. #487	C₂²×C₁₃₁	semidirect
262. #322	C₂²×C₁₃₁	semidirect
263. #322	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3209×C₁₃₁	2
#3208×C₁₃₁	2
#3170×C₁₃₁	2
#3165×C₁₃₁	2
#3138×C₁₃₁	2
C₂×#486×C₁₃₁	2
#1722×C₁₃₁	2
#1720×C₁₃₁	2
#1719×C₁₃₁	2
#1451×C₁₃₁	2
#19682	131

Subgroups — C131×#19682 #45705566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#19682 #45705566