Subgroups — C₁₃₁×#29128 #45715012

Order 33536.

706 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2864×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#124×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2101×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2042×C₁₃₁	C₂	1	2	yes	maximal
5	#1936×C₁₃₁	C₂	1	2	yes	maximal
6	#1935×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1805×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1805×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1804×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	#1804×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	#1767×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
22	#391×C₁₃₁	C₂²	1	1	yes	characteristic
23	#390×C₁₃₁	C₂²	1	1	yes	characteristic
24	#389×C₁₃₁	C₂²	1	2	yes	—
25	#389×C₁₃₁	C₂²	1	2	yes	—
26	#388×C₁₃₁	—	2	2	no	—
27	#387×C₁₃₁	—	2	2	no	—
28	#387×C₁₃₁	—	2	2	no	—
29	#382×C₁₃₁	C₂²	1	1	yes	characteristic
30	#382×C₁₃₁	C₂²	1	1	yes	characteristic
31	#382×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
33	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
34	#340×C₁₃₁	C₂²	1	2	yes	—
35	#340×C₁₃₁	C₂²	1	2	yes	—
36	#340×C₁₃₁	C₂²	1	2	yes	—
37	#340×C₁₃₁	C₂²	1	2	yes	—
38	#336×C₁₃₁	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃₁	—	2	1	no	—
42	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
44	#124×C₁₃₁	—	2	2	no	—
45	#124×C₁₃₁	—	2	2	no	—
46	C₄×Q₈×C₁₃₁	—	2	2	no	—
47	C₄×Q₈×C₁₃₁	—	2	2	no	—
48	C₄×D₄×C₁₃₁	—	2	2	no	—
49	C₄×D₄×C₁₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
60	C₂×C₄²×C₁₃₁	—	2	1	no	—
61	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₁₃₁	—	2	2	no	—
67	C₄⋊C₈×C₁₃₁	—	2	2	no	—
68	#103×C₁₃₁	—	2	4	no	—
69	#103×C₁₃₁	—	4	2	no	—
70	#102×C₁₃₁	—	2	4	no	—
71	#102×C₁₃₁	—	4	2	no	—
72	#97×C₁₃₁	—	4	2	no	—
73	#95×C₁₃₁	—	2	2	no	—
74	#95×C₁₃₁	—	2	2	no	—
75	#95×C₁₃₁	—	2	2	no	—
76	#95×C₁₃₁	—	2	2	no	—
77	#95×C₁₃₁	—	2	1	no	—
78	#95×C₁₃₁	—	2	1	no	—
79	#95×C₁₃₁	—	2	1	no	—
80	#95×C₁₃₁	—	2	1	no	—
81	C₂⁴×C₁₃₁	—	2	1	no	—
82	C₂×Q₈×C₁₃₁	—	2	1	no	—
83	C₂×Q₈×C₁₃₁	—	2	1	no	—
84	C₂×Q₈×C₁₃₁	—	2	1	no	—
85	C₂×Q₈×C₁₃₁	—	2	1	no	—
86	C₂×Q₈×C₁₃₁	—	2	1	no	—
87	C₂×Q₈×C₁₃₁	#41	1	2	yes	—
88	C₂×D₄×C₁₃₁	—	2	1	no	—
89	C₂×D₄×C₁₃₁	—	2	1	no	—
90	C₂×D₄×C₁₃₁	—	2	1	no	—
91	C₂×D₄×C₁₃₁	—	2	1	no	—
92	C₂×D₄×C₁₃₁	—	2	1	no	—
93	C₂×D₄×C₁₃₁	#41	1	2	yes	—
94	C₂²×C₄×C₁₃₁	—	2	1	no	—
95	C₂²×C₄×C₁₃₁	—	2	1	no	—
96	C₂²×C₄×C₁₃₁	—	2	2	no	—
97	C₂²×C₄×C₁₃₁	—	2	2	no	—
98	C₂²×C₄×C₁₃₁	—	2	1	no	—
99	C₂²×C₄×C₁₃₁	—	4	4	no	—
100	C₂²×C₄×C₁₃₁	—	4	2	no	—
101	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₁₃₁	—	2	2	no	—
107	C₂×C₈×C₁₃₁	—	2	2	no	—
108	C₂×C₈×C₁₃₁	—	2	2	no	—
109	C₂×C₈×C₁₃₁	—	2	2	no	—
110	C₂×C₈×C₁₃₁	—	2	2	no	—
111	C₂×C₈×C₁₃₁	—	2	2	no	—
112	C₄⋊C₄×C₁₃₁	—	2	2	no	—
113	C₄⋊C₄×C₁₃₁	—	2	2	no	—
114	C₄⋊C₄×C₁₃₁	—	2	1	no	—
115	C₄⋊C₄×C₁₃₁	—	2	1	no	—
116	C₄⋊C₄×C₁₃₁	—	2	1	no	—
117	C₄⋊C₄×C₁₃₁	—	2	1	no	—
118	C₄⋊C₄×C₁₃₁	—	2	2	no	—
119	C₄⋊C₄×C₁₃₁	—	2	2	no	—
120	C₄⋊C₄×C₁₃₁	—	4	4	no	—
121	C₄⋊C₄×C₁₃₁	—	4	4	no	—
122	C₄⋊C₄×C₁₃₁	—	4	2	no	—
123	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
124	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
125	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
126	C₄²×C₁₃₁	—	2	1	no	—
127	C₄²×C₁₃₁	—	2	1	no	—
128	C₄²×C₁₃₁	—	2	1	no	—
129	C₄²×C₁₃₁	—	2	1	no	—
130	C₄²×C₁₃₁	—	4	2	no	—
131	C₄²×C₁₃₁	—	4	2	no	—
132	C₄²×C₁₃₁	—	4	2	no	—
133	C₄²×C₁₃₁	#41	1	2	yes	—
134	C₄²×C₁₃₁	#41	1	2	yes	—
135	C₂³×C₁₃₁	—	2	2	no	—
136	C₂³×C₁₃₁	—	4	1	no	—
137	C₂³×C₁₃₁	—	4	1	no	—
138	C₂³×C₁₃₁	—	4	2	no	—
139	C₂³×C₁₃₁	—	4	2	no	—
140	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₃₁	—	2	2	no	—
142	Q₈×C₁₃₁	—	2	2	no	—
143	Q₈×C₁₃₁	—	4	1	no	—
144	Q₈×C₁₃₁	—	4	1	no	—
145	D₄×C₁₃₁	—	2	2	no	—
146	D₄×C₁₃₁	—	2	2	no	—
147	D₄×C₁₃₁	—	4	1	no	—
148	D₄×C₁₃₁	—	4	1	no	—
149	C₂×C₄×C₁₃₁	—	2	2	no	—
150	C₂×C₄×C₁₃₁	—	2	2	no	—
151	C₂×C₄×C₁₃₁	—	2	2	no	—
152	C₂×C₄×C₁₃₁	—	2	2	no	—
153	C₂×C₄×C₁₃₁	—	2	2	no	—
154	C₂×C₄×C₁₃₁	—	2	2	no	—
155	C₂×C₄×C₁₃₁	—	2	2	no	—
156	C₂×C₄×C₁₃₁	—	2	2	no	—
157	C₂×C₄×C₁₃₁	—	2	2	no	—
158	C₂×C₄×C₁₃₁	—	4	1	no	—
159	C₂×C₄×C₁₃₁	—	4	1	no	—
160	C₂×C₄×C₁₃₁	—	4	2	no	—
161	C₂×C₄×C₁₃₁	—	4	1	no	—
162	C₂×C₄×C₁₃₁	—	4	1	no	—
163	C₂×C₄×C₁₃₁	—	4	2	no	—
164	C₂×C₄×C₁₃₁	—	4	2	no	—
165	C₂×C₄×C₁₃₁	—	4	2	no	—
166	C₂×C₄×C₁₃₁	—	4	2	no	—
167	C₂×C₄×C₁₃₁	—	4	2	no	—
168	C₂×C₄×C₁₃₁	—	4	2	no	—
169	C₂×C₄×C₁₃₁	—	4	2	no	—
170	C₂×C₄×C₁₃₁	—	8	4	no	—
171	C₂×C₄×C₁₃₁	#124	1	2	yes	—
172	C₂×C₄×C₁₃₁	#124	1	2	yes	—
173	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
179	C₈×C₁₃₁	—	4	2	no	—
180	C₈×C₁₃₁	—	4	2	no	—
181	C₂²×C₁₃₁	—	4	2	no	—
182	C₂²×C₁₃₁	—	4	4	no	—
183	C₂²×C₁₃₁	—	8	1	no	—
184	C₂²×C₁₃₁	—	8	1	no	—
185	C₂²×C₁₃₁	—	8	2	no	—
186	C₂²×C₁₃₁	#525	1	1	yes	characteristic
187	C₂²×C₁₃₁	C₂×#124	1	1	yes	characteristic
188	C₂²×C₁₃₁	#537	1	1	yes	characteristic
189	C₂²×C₁₃₁	#575	1	2	yes	—
190	C₂²×C₁₃₁	#575	1	2	yes	—
191	C₄×C₁₃₁	—	2	2	no	—
192	C₄×C₁₃₁	—	2	2	no	—
193	C₄×C₁₃₁	—	4	2	no	—
194	C₄×C₁₃₁	—	4	2	no	—
195	C₄×C₁₃₁	—	4	2	no	—
196	C₄×C₁₃₁	—	8	2	no	—
197	C₄×C₁₃₁	—	8	1	no	—
198	C₄×C₁₃₁	—	8	1	no	—
199	C₄×C₁₃₁	—	8	2	no	—
200	C₄×C₁₃₁	#552	1	1	yes	characteristic
201	C₄×C₁₃₁	#552	1	1	yes	characteristic
202	C₄×C₁₃₁	#553	1	1	yes	characteristic
203	C₄×C₁₃₁	#553	1	1	yes	characteristic
204	C₂×C₁₃₁	—	8	2	no	—
205	C₂×C₁₃₁	#2562	1	1	yes	characteristic
206	C₂×C₁₃₁	#3111	1	2	yes	—
207	C₂×C₁₃₁	#3135	1	1	yes	characteristic
208	C₂×C₁₃₁	#3140	1	1	yes	characteristic
209	C₂×C₁₃₁	#3256	1	2	yes	—
210	#29128	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₁₃₁	#29128	1	1	yes	characteristic, direct product factor, Sylow
212	#2864	C₂×C₁₃₁	1	1	yes	characteristic, complemented
213	C₄×#124	C₂×C₁₃₁	1	1	yes	characteristic
214	#2101	C₂×C₁₃₁	1	2	yes	complemented
215	#2042	C₂×C₁₃₁	1	2	yes	—
216	#1936	C₂×C₁₃₁	1	2	yes	—
217	#1935	C₂×C₁₃₁	1	2	yes	complemented
218	#1805	C₂×C₁₃₁	1	1	yes	characteristic, complemented
219	#1805	C₂×C₁₃₁	1	1	yes	characteristic, complemented
220	#1804	C₂×C₁₃₁	1	1	yes	characteristic
221	#1804	C₂×C₁₃₁	1	1	yes	characteristic
222	#1767	C₂×C₁₃₁	1	1	yes	characteristic, complemented
223	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
228	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
229	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
230	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
231	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
232	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
233	#391	C₂²×C₁₃₁	1	1	yes	characteristic
234	#390	C₂²×C₁₃₁	1	1	yes	characteristic
235	#389	C₂²×C₁₃₁	1	2	yes	—
236	#389	C₂²×C₁₃₁	1	2	yes	—
237	#388	—	2	2	no	—
238	#387	—	2	2	no	—
239	#387	—	2	2	no	—
240	#382	C₂²×C₁₃₁	1	1	yes	characteristic
241	#382	C₂²×C₁₃₁	1	1	yes	characteristic
242	#382	C₂²×C₁₃₁	1	1	yes	characteristic
243	C₄×C₂²⋊C₄	—	2	2	no	—
244	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
245	#340	C₂²×C₁₃₁	1	2	yes	—
246	#340	C₂²×C₁₃₁	1	2	yes	—
247	#340	C₂²×C₁₃₁	1	2	yes	—
248	#340	C₂²×C₁₃₁	1	2	yes	—
249	#336	C₂²×C₁₃₁	1	2	yes	—
250	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
251	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
254	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
255	#124	—	2	2	no	—
256	#124	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
273	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
274	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	#103	—	2	4	no	—
280	#103	—	4	2	no	—
281	#102	—	2	4	no	—
282	#102	—	4	2	no	—
283	#97	—	4	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	1	no	—
287	#95	—	2	1	no	—
288	#95	—	2	1	no	—
289	#95	—	2	1	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	C₂⁴	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	#41×C₁₃₁	1	2	yes	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	#41×C₁₃₁	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	4	2	no	—
342	C₄²	—	4	2	no	—
343	C₄²	—	4	2	no	—
344	C₄²	#41×C₁₃₁	1	2	yes	—
345	C₄²	#41×C₁₃₁	1	2	yes	—
346	C₂³	—	2	2	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	—	2	2	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	4	no	—
382	C₂×C₄	#124×C₁₃₁	1	2	yes	—
383	C₂×C₄	#124×C₁₃₁	1	2	yes	—
384	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
386	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
388	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
389	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	1	no	—
397	C₂²	#525×C₁₃₁	1	1	yes	characteristic
398	C₂²	C₂×#124×C₁₃₁	1	1	yes	characteristic
399	C₂²	#537×C₁₃₁	1	1	yes	characteristic
400	C₂²	#575×C₁₃₁	1	2	yes	—
401	C₂²	#575×C₁₃₁	1	2	yes	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	2	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	1	no	—
411	C₄	#552×C₁₃₁	1	1	yes	characteristic
412	C₄	#552×C₁₃₁	1	1	yes	characteristic
413	C₄	#553×C₁₃₁	1	1	yes	characteristic
414	C₄	#553×C₁₃₁	1	1	yes	characteristic
415	C₂	—	8	2	no	—
416	C₂	#2562×C₁₃₁	1	1	yes	characteristic
417	C₂	#3111×C₁₃₁	1	2	yes	—
418	C₂	#3135×C₁₃₁	1	1	yes	characteristic
419	C₂	#3140×C₁₃₁	1	1	yes	characteristic
420	C₂	#3256×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2864×C₁₃₁	C₂	semidirect
3. #2101×C₁₃₁	C₂	semidirect
6. #1935×C₁₃₁	C₂	semidirect
7. #1805×C₁₃₁	C₂	semidirect
8. #1805×C₁₃₁	C₂	semidirect
11. #1767×C₁₃₁	C₂	semidirect
210. #29128	C₁₃₁	direct (N × H)
211. C₁₃₁	#29128	direct (N × H)
212. #2864	C₂×C₁₃₁	semidirect
214. #2101	C₂×C₁₃₁	semidirect
217. #1935	C₂×C₁₃₁	semidirect
218. #1805	C₂×C₁₃₁	semidirect
219. #1805	C₂×C₁₃₁	semidirect
222. #1767	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2864×C₁₃₁	2
C₄×#124×C₁₃₁	2
#2101×C₁₃₁	2
#2042×C₁₃₁	2
#1936×C₁₃₁	2
#1935×C₁₃₁	2
#1805×C₁₃₁	2
#1804×C₁₃₁	2
#1767×C₁₃₁	2
#29128	131

Subgroups — C131×#29128 #45715012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29128 #45715012