Subgroups — C₁₃₁×#29905 #45715789

Order 33536.

730 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	#3011×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2889×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2082×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2080×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2049×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2047×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1915×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1909×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1868×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1858×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1796×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂×2₋¹⁺⁴×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#137×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
15	#568×C₁₃₁	C₂²	1	1	yes	characteristic
16	#568×C₁₃₁	C₂²	1	1	yes	characteristic
17	#536×C₁₃₁	C₂²	1	1	yes	characteristic
18	#452×C₁₃₁	—	2	2	no	—
19	#451×C₁₃₁	—	2	2	no	—
20	#430×C₁₃₁	C₂²	1	2	yes	—
21	#424×C₁₃₁	C₂²	1	2	yes	—
22	#421×C₁₃₁	C₂²	1	2	yes	—
23	#419×C₁₃₁	C₂²	1	1	yes	characteristic
24	#419×C₁₃₁	C₂²	1	2	yes	—
25	#419×C₁₃₁	C₂²	1	2	yes	—
26	#416×C₁₃₁	C₂²	1	1	yes	characteristic
27	#413×C₁₃₁	—	2	2	no	—
28	#413×C₁₃₁	C₂²	1	2	yes	—
29	#413×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×#101×C₁₃₁	—	2	2	no	—
31	C₂×#101×C₁₃₁	C₂²	1	2	yes	—
32	C₂×#101×C₁₃₁	C₂²	1	2	yes	—
33	#410×C₁₃₁	C₂²	1	1	yes	characteristic
34	#408×C₁₃₁	C₂²	1	1	yes	characteristic
35	#344×C₁₃₁	C₂²	1	2	yes	—
36	#344×C₁₃₁	C₂²	1	2	yes	—
37	#341×C₁₃₁	C₂²	1	2	yes	—
38	H(3,ℤ/4)×C₁₃₁	C₂²	1	2	yes	—
39	2₋¹⁺⁴×C₁₃₁	—	4	2	no	—
40	2₋¹⁺⁴×C₁₃₁	—	4	2	no	—
41	C₂×#41×C₁₃₁	—	2	1	no	—
42	C₂×#41×C₁₃₁	—	2	2	no	—
43	C₂×#41×C₁₃₁	D₄	1	2	yes	—
44	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃₁	—	2	1	no	—
47	C₂²×Q₈×C₁₃₁	D₄	1	2	yes	—
48	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	#137×C₁₃₁	—	4	2	no	—
51	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
52	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
53	C₂×Q₁₆×C₁₃₁	—	4	2	no	—
54	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
55	#131×C₁₃₁	—	4	2	no	—
56	#131×C₁₃₁	—	4	2	no	—
57	C₂×M₁₆×C₁₃₁	—	2	2	no	—
58	C₂×M₁₆×C₁₃₁	—	2	2	no	—
59	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
62	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
65	#124×C₁₃₁	—	2	1	no	—
66	#123×C₁₃₁	—	2	2	no	—
67	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
68	#117×C₁₃₁	C₂³	1	2	yes	—
69	#117×C₁₃₁	C₂³	1	1	yes	characteristic
70	#108×C₁₃₁	—	4	2	no	—
71	C₄⋊C₈×C₁₃₁	—	4	2	no	—
72	#104×C₁₃₁	—	4	2	no	—
73	#103×C₁₃₁	—	2	1	no	—
74	#103×C₁₃₁	—	2	2	no	—
75	#103×C₁₃₁	—	4	2	no	—
76	#103×C₁₃₁	—	4	2	no	—
77	#102×C₁₃₁	—	2	1	no	—
78	#101×C₁₃₁	—	2	2	no	—
79	#101×C₁₃₁	—	2	4	no	—
80	#101×C₁₃₁	—	2	1	no	—
81	#101×C₁₃₁	—	4	2	no	—
82	#100×C₁₃₁	—	2	2	no	—
83	#100×C₁₃₁	—	2	1	no	—
84	#99×C₁₃₁	—	2	2	no	—
85	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
86	#41×C₁₃₁	—	2	2	no	—
87	#41×C₁₃₁	—	2	2	no	—
88	#41×C₁₃₁	—	2	2	no	—
89	#41×C₁₃₁	—	2	2	no	—
90	#41×C₁₃₁	—	4	2	no	—
91	#41×C₁₃₁	—	4	2	no	—
92	#41×C₁₃₁	—	4	8	no	—
93	#41×C₁₃₁	—	4	4	no	—
94	C₂×Q₈×C₁₃₁	—	2	2	no	—
95	C₂×Q₈×C₁₃₁	—	2	1	no	—
96	C₂×Q₈×C₁₃₁	—	2	1	no	—
97	C₂×Q₈×C₁₃₁	—	2	1	no	—
98	C₂×Q₈×C₁₃₁	—	2	2	no	—
99	C₂×Q₈×C₁₃₁	—	2	2	no	—
100	C₂×Q₈×C₁₃₁	—	2	2	no	—
101	C₂×Q₈×C₁₃₁	—	2	2	no	—
102	C₂×Q₈×C₁₃₁	—	4	2	no	—
103	C₂×Q₈×C₁₃₁	—	4	2	no	—
104	C₂×Q₈×C₁₃₁	—	4	4	no	—
105	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₃₁	C₂×D₄	1	2	yes	—
107	C₂×Q₈×C₁₃₁	#41	1	1	yes	characteristic
108	C₂×D₄×C₁₃₁	—	2	2	no	—
109	C₂×D₄×C₁₃₁	—	2	1	no	—
110	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×D₄×C₁₃₁	#41	1	2	yes	—
112	C₂×D₄×C₁₃₁	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₁	—	2	2	no	—
114	C₂²×C₄×C₁₃₁	—	2	1	no	—
115	C₂²×C₄×C₁₃₁	—	2	2	no	—
116	C₂²×C₄×C₁₃₁	—	2	1	no	—
117	C₂²×C₄×C₁₃₁	—	2	1	no	—
118	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
120	Q₁₆×C₁₃₁	—	4	4	no	—
121	Q₁₆×C₁₃₁	—	4	2	no	—
122	SD₁₆×C₁₃₁	—	4	2	no	—
123	M₁₆×C₁₃₁	—	2	2	no	—
124	M₁₆×C₁₃₁	—	2	2	no	—
125	M₁₆×C₁₃₁	—	2	2	no	—
126	M₁₆×C₁₃₁	—	2	2	no	—
127	M₁₆×C₁₃₁	—	2	2	no	—
128	M₁₆×C₁₃₁	—	2	2	no	—
129	M₁₆×C₁₃₁	—	2	2	no	—
130	M₁₆×C₁₃₁	—	4	2	no	—
131	M₁₆×C₁₃₁	—	4	2	no	—
132	C₂×C₈×C₁₃₁	—	2	1	no	—
133	C₂×C₈×C₁₃₁	—	2	1	no	—
134	C₂×C₈×C₁₃₁	—	2	2	no	—
135	C₂×C₈×C₁₃₁	—	2	2	no	—
136	C₂×C₈×C₁₃₁	—	2	2	no	—
137	C₂×C₈×C₁₃₁	—	2	2	no	—
138	C₂×C₈×C₁₃₁	—	4	2	no	—
139	C₂×C₈×C₁₃₁	—	4	2	no	—
140	C₄⋊C₄×C₁₃₁	—	2	1	no	—
141	C₄⋊C₄×C₁₃₁	—	2	2	no	—
142	C₄⋊C₄×C₁₃₁	—	4	2	no	—
143	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
144	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
145	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
146	C₄²×C₁₃₁	—	2	1	no	—
147	C₄²×C₁₃₁	—	2	2	no	—
148	C₂³×C₁₃₁	—	2	1	no	—
149	C₂³×C₁₃₁	#123	1	2	yes	—
150	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
151	Q₈×C₁₃₁	—	2	2	no	—
152	Q₈×C₁₃₁	—	2	2	no	—
153	Q₈×C₁₃₁	—	2	1	no	—
154	Q₈×C₁₃₁	—	2	2	no	—
155	Q₈×C₁₃₁	—	2	1	no	—
156	Q₈×C₁₃₁	—	4	4	no	—
157	Q₈×C₁₃₁	—	4	2	no	—
158	Q₈×C₁₃₁	—	4	1	no	—
159	Q₈×C₁₃₁	—	4	1	no	—
160	Q₈×C₁₃₁	—	4	2	no	—
161	D₄×C₁₃₁	—	2	4	no	—
162	D₄×C₁₃₁	—	2	1	no	—
163	D₄×C₁₃₁	—	2	1	no	—
164	D₄×C₁₃₁	—	2	2	no	—
165	D₄×C₁₃₁	—	4	4	no	—
166	D₄×C₁₃₁	—	4	2	no	—
167	C₂×C₄×C₁₃₁	—	2	2	no	—
168	C₂×C₄×C₁₃₁	—	2	2	no	—
169	C₂×C₄×C₁₃₁	—	2	1	no	—
170	C₂×C₄×C₁₃₁	—	2	2	no	—
171	C₂×C₄×C₁₃₁	—	4	4	no	—
172	C₂×C₄×C₁₃₁	—	4	4	no	—
173	C₂×C₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	4	2	no	—
175	C₂×C₄×C₁₃₁	—	4	1	no	—
176	C₂×C₄×C₁₃₁	—	4	1	no	—
177	C₂×C₄×C₁₃₁	—	4	2	no	—
178	C₂×C₄×C₁₃₁	—	4	2	no	—
179	C₂×C₄×C₁₃₁	#123	1	2	yes	—
180	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
184	C₈×C₁₃₁	—	4	1	no	—
185	C₈×C₁₃₁	—	4	2	no	—
186	C₈×C₁₃₁	—	4	2	no	—
187	C₈×C₁₃₁	—	4	1	no	—
188	C₈×C₁₃₁	—	4	2	no	—
189	C₂²×C₁₃₁	—	2	2	no	—
190	C₂²×C₁₃₁	—	4	1	no	—
191	C₂²×C₁₃₁	—	4	2	no	—
192	C₂²×C₁₃₁	—	4	1	no	—
193	C₂²×C₁₃₁	—	8	1	no	—
194	C₂²×C₁₃₁	C₂×#123	1	1	yes	characteristic
195	C₂²×C₁₃₁	#538	1	2	yes	—
196	C₄×C₁₃₁	—	2	2	no	—
197	C₄×C₁₃₁	—	4	2	no	—
198	C₄×C₁₃₁	—	4	1	no	—
199	C₄×C₁₃₁	—	8	1	no	—
200	C₄×C₁₃₁	—	8	2	no	—
201	C₄×C₁₃₁	—	8	1	no	—
202	C₄×C₁₃₁	#534	1	1	yes	characteristic
203	C₄×C₁₃₁	#534	1	1	yes	characteristic
204	C₄×C₁₃₁	#538	1	2	yes	—
205	C₂×C₁₃₁	—	2	1	no	—
206	C₂×C₁₃₁	—	2	2	no	—
207	C₂×C₁₃₁	—	4	2	no	—
208	C₂×C₁₃₁	—	8	1	no	—
209	C₂×C₁₃₁	#2622	1	1	yes	characteristic
210	#29905	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₁₃₁	#29905	1	1	yes	characteristic, direct product factor, Sylow
212	#3011	C₂×C₁₃₁	1	1	yes	characteristic
213	#2889	C₂×C₁₃₁	1	1	yes	characteristic
214	#2082	C₂×C₁₃₁	1	2	yes	complemented
215	#2080	C₂×C₁₃₁	1	2	yes	complemented
216	#2049	C₂×C₁₃₁	1	2	yes	complemented
217	#2047	C₂×C₁₃₁	1	2	yes	complemented
218	#1915	C₂×C₁₃₁	1	1	yes	characteristic, complemented
219	#1909	C₂×C₁₃₁	1	1	yes	characteristic, complemented
220	#1868	C₂×C₁₃₁	1	1	yes	characteristic, complemented
221	#1858	C₂×C₁₃₁	1	1	yes	characteristic, complemented
222	#1796	C₂×C₁₃₁	1	1	yes	characteristic
223	C₂×2₋¹⁺⁴	C₂²×C₁₃₁	1	1	yes	characteristic
224	C₂×#137	C₂²×C₁₃₁	1	1	yes	characteristic
225	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
226	#568	C₂²×C₁₃₁	1	1	yes	characteristic
227	#568	C₂²×C₁₃₁	1	1	yes	characteristic
228	#536	C₂²×C₁₃₁	1	1	yes	characteristic
229	#452	—	2	2	no	—
230	#451	—	2	2	no	—
231	#430	C₂²×C₁₃₁	1	2	yes	—
232	#424	C₂²×C₁₃₁	1	2	yes	—
233	#421	C₂²×C₁₃₁	1	2	yes	—
234	#419	C₂²×C₁₃₁	1	1	yes	characteristic
235	#419	C₂²×C₁₃₁	1	2	yes	—
236	#419	C₂²×C₁₃₁	1	2	yes	—
237	#416	C₂²×C₁₃₁	1	1	yes	characteristic
238	#413	—	2	2	no	—
239	#413	C₂²×C₁₃₁	1	2	yes	—
240	#413	C₂²×C₁₃₁	1	1	yes	characteristic
241	C₂×#101	—	2	2	no	—
242	C₂×#101	C₂²×C₁₃₁	1	2	yes	—
243	C₂×#101	C₂²×C₁₃₁	1	2	yes	—
244	#410	C₂²×C₁₃₁	1	1	yes	characteristic
245	#408	C₂²×C₁₃₁	1	1	yes	characteristic
246	#344	C₂²×C₁₃₁	1	2	yes	—
247	#344	C₂²×C₁₃₁	1	2	yes	—
248	#341	C₂²×C₁₃₁	1	2	yes	—
249	H(3,ℤ/4)	C₂²×C₁₃₁	1	2	yes	—
250	2₋¹⁺⁴	—	4	2	no	—
251	2₋¹⁺⁴	—	4	2	no	—
252	C₂×#41	—	2	1	no	—
253	C₂×#41	—	2	2	no	—
254	C₂×#41	D₄×C₁₃₁	1	2	yes	—
255	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
256	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	D₄×C₁₃₁	1	2	yes	—
259	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
260	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
261	#137	—	4	2	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	—	2	1	no	—
264	C₂×Q₁₆	—	4	2	no	—
265	C₂×SD₁₆	—	2	1	no	—
266	#131	—	4	2	no	—
267	#131	—	4	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
271	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
272	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
273	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
274	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	1	no	—
276	#124	—	2	1	no	—
277	#123	—	2	2	no	—
278	C₂²⋊Q₈	—	2	2	no	—
279	#117	C₂³×C₁₃₁	1	1	yes	characteristic
280	#117	C₂³×C₁₃₁	1	2	yes	—
281	#108	—	4	2	no	—
282	C₄⋊C₈	—	4	2	no	—
283	#104	—	4	2	no	—
284	#103	—	2	1	no	—
285	#103	—	2	2	no	—
286	#103	—	4	2	no	—
287	#103	—	4	2	no	—
288	#102	—	2	1	no	—
289	#101	—	2	2	no	—
290	#101	—	2	4	no	—
291	#101	—	2	1	no	—
292	#101	—	4	2	no	—
293	#100	—	2	2	no	—
294	#100	—	2	1	no	—
295	#99	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	—	4	2	no	—
302	#41	—	4	2	no	—
303	#41	—	4	8	no	—
304	#41	—	4	4	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	4	no	—
316	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
317	C₂×Q₈	C₂×D₄×C₁₃₁	1	2	yes	—
318	C₂×Q₈	#41×C₁₃₁	1	1	yes	characteristic
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
322	C₂×D₄	#41×C₁₃₁	1	2	yes	—
323	C₂×D₄	#41×C₁₃₁	1	1	yes	characteristic
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
331	Q₁₆	—	4	4	no	—
332	Q₁₆	—	4	2	no	—
333	SD₁₆	—	4	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	4	2	no	—
342	M₁₆	—	4	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	4	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	2	no	—
359	C₂³	—	2	1	no	—
360	C₂³	#123×C₁₃₁	1	2	yes	—
361	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	2	1	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	4	4	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	2	2	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	#123×C₁₃₁	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
393	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
394	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
395	C₈	—	4	1	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₂×#123×C₁₃₁	1	1	yes	characteristic
406	C₂²	#538×C₁₃₁	1	2	yes	—
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	1	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	1	no	—
413	C₄	#534×C₁₃₁	1	1	yes	characteristic
414	C₄	#534×C₁₃₁	1	1	yes	characteristic
415	C₄	#538×C₁₃₁	1	2	yes	—
416	C₂	—	2	1	no	—
417	C₂	—	2	2	no	—
418	C₂	—	4	2	no	—
419	C₂	—	8	1	no	—
420	C₂	#2622×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₁	#2622
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×2₋¹⁺⁴×C₁₃₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2082×C₁₃₁	C₂	semidirect
4. #2080×C₁₃₁	C₂	semidirect
5. #2049×C₁₃₁	C₂	semidirect
6. #2047×C₁₃₁	C₂	semidirect
7. #1915×C₁₃₁	C₂	semidirect
8. #1909×C₁₃₁	C₂	semidirect
9. #1868×C₁₃₁	C₂	semidirect
10. #1858×C₁₃₁	C₂	semidirect
210. #29905	C₁₃₁	direct (N × H)
211. C₁₃₁	#29905	direct (N × H)
214. #2082	C₂×C₁₃₁	semidirect
215. #2080	C₂×C₁₃₁	semidirect
216. #2049	C₂×C₁₃₁	semidirect
217. #2047	C₂×C₁₃₁	semidirect
218. #1915	C₂×C₁₃₁	semidirect
219. #1909	C₂×C₁₃₁	semidirect
220. #1868	C₂×C₁₃₁	semidirect
221. #1858	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3011×C₁₃₁	2
#2889×C₁₃₁	2
#2082×C₁₃₁	2
#2080×C₁₃₁	2
#2049×C₁₃₁	2
#2047×C₁₃₁	2
#1915×C₁₃₁	2
#1909×C₁₃₁	2
#1868×C₁₃₁	2
#1858×C₁₃₁	2
#1796×C₁₃₁	2
#29905	131

Subgroups — C131×#29905 #45715789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29905 #45715789