Subgroups — C₁₃₁×#29856 #45715740

Order 33536.

732 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#491×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#433×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2629×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2621×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2068×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2066×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2036×C₁₃₁	C₂	1	2	yes	maximal
8	#2035×C₁₃₁	C₂	1	2	yes	maximal
9	#1991×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1956×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1847×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
17	#491×C₁₃₁	—	2	4	no	—
18	#433×C₁₃₁	—	2	4	no	—
19	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
29	#398×C₁₃₁	—	2	2	no	—
30	#398×C₁₃₁	—	2	2	no	—
31	#397×C₁₃₁	—	2	2	no	—
32	#396×C₁₃₁	—	2	2	no	—
33	#391×C₁₃₁	C₂²	1	1	yes	characteristic
34	#391×C₁₃₁	C₂²	1	1	yes	characteristic
35	#389×C₁₃₁	C₂²	1	2	yes	—
36	#384×C₁₃₁	C₂²	1	1	yes	characteristic
37	#382×C₁₃₁	C₂²	1	1	yes	characteristic
38	#380×C₁₃₁	C₂²	1	2	yes	—
39	#340×C₁₃₁	C₂²	1	2	yes	—
40	#340×C₁₃₁	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
46	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
47	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
48	#125×C₁₃₁	—	2	2	no	—
49	#125×C₁₃₁	—	2	2	no	—
50	C₂²⋊Q₈×C₁₃₁	—	4	2	no	—
51	C₂²⋊Q₈×C₁₃₁	—	4	2	no	—
52	#117×C₁₃₁	—	2	2	no	—
53	#117×C₁₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₁	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
69	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
71	#107×C₁₃₁	—	4	2	no	—
72	#106×C₁₃₁	—	4	2	no	—
73	C₄⋊C₈×C₁₃₁	—	2	4	no	—
74	#103×C₁₃₁	—	2	4	no	—
75	#103×C₁₃₁	—	2	4	no	—
76	#103×C₁₃₁	—	4	2	no	—
77	#103×C₁₃₁	—	4	2	no	—
78	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
79	#97×C₁₃₁	D₄	1	4	yes	—
80	C₄×C₈×C₁₃₁	—	2	2	no	—
81	#95×C₁₃₁	—	2	2	no	—
82	#95×C₁₃₁	—	2	2	no	—
83	#95×C₁₃₁	—	2	2	no	—
84	#95×C₁₃₁	—	2	2	no	—
85	#95×C₁₃₁	—	2	2	no	—
86	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₁₃₁	—	2	1	no	—
88	C₂×Q₈×C₁₃₁	—	2	1	no	—
89	C₂×Q₈×C₁₃₁	—	2	1	no	—
90	C₂×Q₈×C₁₃₁	—	2	1	no	—
91	C₂×Q₈×C₁₃₁	—	2	2	no	—
92	C₂×Q₈×C₁₃₁	—	2	2	no	—
93	C₂×Q₈×C₁₃₁	—	2	2	no	—
94	C₂×Q₈×C₁₃₁	—	2	2	no	—
95	C₂²×C₄×C₁₃₁	—	2	1	no	—
96	C₂²×C₄×C₁₃₁	—	2	1	no	—
97	C₂²×C₄×C₁₃₁	—	2	2	no	—
98	C₂²×C₄×C₁₃₁	—	2	2	no	—
99	C₂²×C₄×C₁₃₁	—	2	1	no	—
100	C₂²×C₄×C₁₃₁	—	2	1	no	—
101	C₂²×C₄×C₁₃₁	—	2	2	no	—
102	C₂²×C₄×C₁₃₁	—	2	2	no	—
103	C₂²×C₄×C₁₃₁	—	2	1	no	—
104	C₂²×C₄×C₁₃₁	—	2	1	no	—
105	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₃₁	—	2	2	no	—
110	C₂×C₈×C₁₃₁	—	2	2	no	—
111	C₂×C₈×C₁₃₁	—	2	2	no	—
112	C₂×C₈×C₁₃₁	—	2	2	no	—
113	C₂×C₈×C₁₃₁	—	2	2	no	—
114	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
115	C₄⋊C₄×C₁₃₁	—	2	4	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	—	2	2	no	—
121	C₄⋊C₄×C₁₃₁	—	2	2	no	—
122	C₄⋊C₄×C₁₃₁	—	4	2	no	—
123	C₄⋊C₄×C₁₃₁	—	4	2	no	—
124	C₄⋊C₄×C₁₃₁	—	4	4	no	—
125	C₄⋊C₄×C₁₃₁	—	4	4	no	—
126	C₄⋊C₄×C₁₃₁	—	8	2	no	—
127	C₄⋊C₄×C₁₃₁	—	8	2	no	—
128	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
129	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
132	C₄²×C₁₃₁	—	2	1	no	—
133	C₄²×C₁₃₁	—	2	1	no	—
134	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
135	C₄²×C₁₃₁	#41	1	2	yes	—
136	C₂³×C₁₃₁	—	2	1	no	—
137	C₂³×C₁₃₁	—	2	1	no	—
138	C₂³×C₁₃₁	—	2	1	no	—
139	C₂³×C₁₃₁	—	2	2	no	—
140	C₂³×C₁₃₁	—	2	2	no	—
141	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₁₃₁	—	4	2	no	—
143	Q₈×C₁₃₁	—	4	2	no	—
144	Q₈×C₁₃₁	—	4	2	no	—
145	Q₈×C₁₃₁	—	4	2	no	—
146	C₂×C₄×C₁₃₁	—	2	2	no	—
147	C₂×C₄×C₁₃₁	—	2	2	no	—
148	C₂×C₄×C₁₃₁	—	2	2	no	—
149	C₂×C₄×C₁₃₁	—	2	1	no	—
150	C₂×C₄×C₁₃₁	—	2	1	no	—
151	C₂×C₄×C₁₃₁	—	2	1	no	—
152	C₂×C₄×C₁₃₁	—	2	2	no	—
153	C₂×C₄×C₁₃₁	—	2	2	no	—
154	C₂×C₄×C₁₃₁	—	4	2	no	—
155	C₂×C₄×C₁₃₁	—	4	2	no	—
156	C₂×C₄×C₁₃₁	—	4	2	no	—
157	C₂×C₄×C₁₃₁	—	4	1	no	—
158	C₂×C₄×C₁₃₁	—	4	1	no	—
159	C₂×C₄×C₁₃₁	—	4	1	no	—
160	C₂×C₄×C₁₃₁	—	4	1	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	1	no	—
165	C₂×C₄×C₁₃₁	—	4	1	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	—	4	2	no	—
171	C₂×C₄×C₁₃₁	—	4	2	no	—
172	C₂×C₄×C₁₃₁	#121	1	4	yes	—
173	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
176	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
177	C₈×C₁₃₁	—	2	4	no	—
178	C₈×C₁₃₁	—	4	2	no	—
179	C₂²×C₁₃₁	—	4	1	no	—
180	C₂²×C₁₃₁	—	4	1	no	—
181	C₂²×C₁₃₁	—	4	1	no	—
182	C₂²×C₁₃₁	—	4	2	no	—
183	C₂²×C₁₃₁	—	4	2	no	—
184	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
185	C₂²×C₁₃₁	#535	1	1	yes	characteristic
186	C₂²×C₁₃₁	#536	1	1	yes	characteristic
187	C₂²×C₁₃₁	#577	1	2	yes	—
188	C₂²×C₁₃₁	#578	1	2	yes	—
189	C₄×C₁₃₁	—	2	4	no	—
190	C₄×C₁₃₁	—	4	1	no	—
191	C₄×C₁₃₁	—	4	2	no	—
192	C₄×C₁₃₁	—	8	1	no	—
193	C₄×C₁₃₁	—	8	1	no	—
194	C₄×C₁₃₁	—	8	1	no	—
195	C₄×C₁₃₁	—	8	2	no	—
196	C₄×C₁₃₁	—	8	1	no	—
197	C₄×C₁₃₁	—	8	2	no	—
198	C₄×C₁₃₁	#537	1	2	yes	—
199	C₄×C₁₃₁	#542	1	2	yes	—
200	C₂×C₁₃₁	—	8	1	no	—
201	C₂×C₁₃₁	#2620	1	1	yes	characteristic
202	C₂×C₁₃₁	#3063	1	2	yes	—
203	C₂×C₁₃₁	#3221	1	1	yes	characteristic
204	C₂×C₁₃₁	#3223	1	1	yes	characteristic
205	C₂×C₁₃₁	#3242	1	2	yes	—
206	#29856	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₁₃₁	#29856	1	1	yes	characteristic, direct product factor, Sylow
208	C₂×#491	C₂×C₁₃₁	1	1	yes	characteristic, complemented
209	C₂×#433	C₂×C₁₃₁	1	1	yes	characteristic
210	#2629	C₂×C₁₃₁	1	1	yes	characteristic
211	#2621	C₂×C₁₃₁	1	1	yes	characteristic
212	#2068	C₂×C₁₃₁	1	2	yes	complemented
213	#2066	C₂×C₁₃₁	1	2	yes	complemented
214	#2036	C₂×C₁₃₁	1	2	yes	—
215	#2035	C₂×C₁₃₁	1	2	yes	—
216	#1991	C₂×C₁₃₁	1	1	yes	characteristic, complemented
217	#1956	C₂×C₁₃₁	1	1	yes	characteristic, complemented
218	#1847	C₂×C₁₃₁	1	1	yes	characteristic, complemented
219	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
220	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
221	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
223	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
224	#491	—	2	4	no	—
225	#433	—	2	4	no	—
226	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
227	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
228	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
229	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
230	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
231	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
232	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
233	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	2	yes	—
234	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
236	#398	—	2	2	no	—
237	#398	—	2	2	no	—
238	#397	—	2	2	no	—
239	#396	—	2	2	no	—
240	#391	C₂²×C₁₃₁	1	1	yes	characteristic
241	#391	C₂²×C₁₃₁	1	1	yes	characteristic
242	#389	C₂²×C₁₃₁	1	2	yes	—
243	#384	C₂²×C₁₃₁	1	1	yes	characteristic
244	#382	C₂²×C₁₃₁	1	1	yes	characteristic
245	#380	C₂²×C₁₃₁	1	2	yes	—
246	#340	C₂²×C₁₃₁	1	2	yes	—
247	#340	C₂²×C₁₃₁	1	2	yes	—
248	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
249	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	#125	—	2	2	no	—
256	#125	—	2	2	no	—
257	C₂²⋊Q₈	—	4	2	no	—
258	C₂²⋊Q₈	—	4	2	no	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	D₄×C₁₃₁	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
276	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
278	#107	—	4	2	no	—
279	#106	—	4	2	no	—
280	C₄⋊C₈	—	2	4	no	—
281	#103	—	2	4	no	—
282	#103	—	2	4	no	—
283	#103	—	4	2	no	—
284	#103	—	4	2	no	—
285	C₂²⋊C₈	—	2	4	no	—
286	#97	D₄×C₁₃₁	1	4	yes	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
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	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
316	C₂×C₈	—	2	2	no	—
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	C₂×D₄×C₁₃₁	1	4	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₄⋊C₄	—	8	2	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	8	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
342	C₄²	#41×C₁₃₁	1	2	yes	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	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	#121×C₁₃₁	1	4	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
382	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
383	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
384	C₈	—	2	4	no	—
385	C₈	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
392	C₂²	#535×C₁₃₁	1	1	yes	characteristic
393	C₂²	#536×C₁₃₁	1	1	yes	characteristic
394	C₂²	#577×C₁₃₁	1	2	yes	—
395	C₂²	#578×C₁₃₁	1	2	yes	—
396	C₄	—	2	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	1	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	1	no	—
405	C₄	#537×C₁₃₁	1	2	yes	—
406	C₄	#542×C₁₃₁	1	2	yes	—
407	C₂	—	8	1	no	—
408	C₂	#2620×C₁₃₁	1	1	yes	characteristic
409	C₂	#3063×C₁₃₁	1	2	yes	—
410	C₂	#3221×C₁₃₁	1	1	yes	characteristic
411	C₂	#3223×C₁₃₁	1	1	yes	characteristic
412	C₂	#3242×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂⁴×C₁₃₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₂×#117×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#491×C₁₃₁	C₂	semidirect
5. #2068×C₁₃₁	C₂	semidirect
6. #2066×C₁₃₁	C₂	semidirect
9. #1991×C₁₃₁	C₂	semidirect
10. #1956×C₁₃₁	C₂	semidirect
11. #1847×C₁₃₁	C₂	semidirect
206. #29856	C₁₃₁	direct (N × H)
207. C₁₃₁	#29856	direct (N × H)
208. C₂×#491	C₂×C₁₃₁	semidirect
212. #2068	C₂×C₁₃₁	semidirect
213. #2066	C₂×C₁₃₁	semidirect
216. #1991	C₂×C₁₃₁	semidirect
217. #1956	C₂×C₁₃₁	semidirect
218. #1847	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#491×C₁₃₁	2
C₂×#433×C₁₃₁	2
#2629×C₁₃₁	2
#2621×C₁₃₁	2
#2068×C₁₃₁	2
#2066×C₁₃₁	2
#2036×C₁₃₁	2
#2035×C₁₃₁	2
#1991×C₁₃₁	2
#1956×C₁₃₁	2
#1847×C₁₃₁	2
#29856	131

Subgroups — C131×#29856 #45715740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29856 #45715740