Subgroups — C₁₃₁×#33269 #45719153

Order 33536.

762 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2860×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	#1972×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1972×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1970×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#1944×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1943×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1941×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1936×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1936×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#1934×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	C₄×#97×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#126×C₁₃₁	—	2	2	no	—
14	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	#390×C₁₃₁	C₂²	1	2	yes	—
27	#390×C₁₃₁	C₂²	1	2	yes	—
28	#390×C₁₃₁	C₂²	1	2	yes	—
29	#389×C₁₃₁	C₂²	1	2	yes	—
30	#389×C₁₃₁	C₂²	1	2	yes	—
31	#389×C₁₃₁	C₂²	1	2	yes	—
32	#388×C₁₃₁	—	2	2	no	—
33	#388×C₁₃₁	—	2	2	no	—
34	#388×C₁₃₁	—	2	2	no	—
35	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
36	#340×C₁₃₁	C₂²	1	2	yes	—
37	#340×C₁₃₁	C₂²	1	2	yes	—
38	#340×C₁₃₁	C₂²	1	2	yes	—
39	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
40	C₂×D₈×C₁₃₁	—	2	2	no	—
41	C₂×D₈×C₁₃₁	—	2	2	no	—
42	C₂×D₈×C₁₃₁	—	2	2	no	—
43	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
47	#126×C₁₃₁	—	4	8	no	—
48	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
60	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
61	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
65	#107×C₁₃₁	—	2	2	no	—
66	#106×C₁₃₁	—	2	2	no	—
67	#106×C₁₃₁	—	2	2	no	—
68	#102×C₁₃₁	—	2	4	no	—
69	#102×C₁₃₁	—	2	4	no	—
70	#102×C₁₃₁	—	2	4	no	—
71	#97×C₁₃₁	—	2	2	no	—
72	#97×C₁₃₁	—	2	2	no	—
73	#97×C₁₃₁	—	2	2	no	—
74	#97×C₁₃₁	—	2	2	no	—
75	C₄×C₈×C₁₃₁	—	2	2	no	—
76	C₄×C₈×C₁₃₁	—	2	2	no	—
77	#95×C₁₃₁	—	2	2	no	—
78	#95×C₁₃₁	—	2	2	no	—
79	#95×C₁₃₁	—	2	2	no	—
80	C₂⁴×C₁₃₁	—	2	2	no	—
81	C₂×D₄×C₁₃₁	—	2	2	no	—
82	C₂×D₄×C₁₃₁	—	2	2	no	—
83	C₂×D₄×C₁₃₁	—	2	2	no	—
84	C₂×D₄×C₁₃₁	—	2	2	no	—
85	C₂×D₄×C₁₃₁	—	2	2	no	—
86	C₂×D₄×C₁₃₁	—	2	2	no	—
87	C₂²×C₄×C₁₃₁	—	2	2	no	—
88	C₂²×C₄×C₁₃₁	—	2	2	no	—
89	C₂²×C₄×C₁₃₁	—	2	2	no	—
90	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
95	D₈×C₁₃₁	—	4	4	no	—
96	C₂×C₈×C₁₃₁	—	2	1	no	—
97	C₂×C₈×C₁₃₁	—	2	1	no	—
98	C₂×C₈×C₁₃₁	—	2	1	no	—
99	C₂×C₈×C₁₃₁	—	2	1	no	—
100	C₂×C₈×C₁₃₁	—	2	1	no	—
101	C₂×C₈×C₁₃₁	—	2	1	no	—
102	C₂×C₈×C₁₃₁	#41	1	2	yes	—
103	C₂×C₈×C₁₃₁	#41	1	2	yes	—
104	C₂×C₈×C₁₃₁	#41	1	2	yes	—
105	C₂×C₈×C₁₃₁	#41	1	2	yes	—
106	C₂×C₈×C₁₃₁	#41	1	2	yes	—
107	C₂×C₈×C₁₃₁	#41	1	2	yes	—
108	C₄⋊C₄×C₁₃₁	—	2	2	no	—
109	C₄⋊C₄×C₁₃₁	—	2	2	no	—
110	C₄⋊C₄×C₁₃₁	—	2	2	no	—
111	C₄⋊C₄×C₁₃₁	—	2	2	no	—
112	C₄⋊C₄×C₁₃₁	—	2	2	no	—
113	C₄⋊C₄×C₁₃₁	—	2	2	no	—
114	C₄⋊C₄×C₁₃₁	—	4	4	no	—
115	C₄⋊C₄×C₁₃₁	—	4	4	no	—
116	C₄⋊C₄×C₁₃₁	—	4	4	no	—
117	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
118	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
119	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
120	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
121	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
122	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
123	C₄²×C₁₃₁	—	2	4	no	—
124	C₄²×C₁₃₁	—	2	1	no	—
125	C₄²×C₁₃₁	—	2	1	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	C₂³×C₁₃₁	—	4	2	no	—
132	C₂³×C₁₃₁	—	4	2	no	—
133	C₂³×C₁₃₁	—	4	2	no	—
134	C₂³×C₁₃₁	—	4	2	no	—
135	C₂³×C₁₃₁	—	4	2	no	—
136	C₂³×C₁₃₁	—	4	2	no	—
137	C₂³×C₁₃₁	—	4	2	no	—
138	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
139	D₄×C₁₃₁	—	4	2	no	—
140	D₄×C₁₃₁	—	4	2	no	—
141	D₄×C₁₃₁	—	4	2	no	—
142	D₄×C₁₃₁	—	4	2	no	—
143	C₂×C₄×C₁₃₁	—	2	2	no	—
144	C₂×C₄×C₁₃₁	—	2	2	no	—
145	C₂×C₄×C₁₃₁	—	2	2	no	—
146	C₂×C₄×C₁₃₁	—	2	1	no	—
147	C₂×C₄×C₁₃₁	—	2	1	no	—
148	C₂×C₄×C₁₃₁	—	2	2	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	—	4	2	no	—
153	C₂×C₄×C₁₃₁	—	4	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	2	no	—
158	C₂×C₄×C₁₃₁	—	4	2	no	—
159	C₂×C₄×C₁₃₁	—	4	2	no	—
160	C₂×C₄×C₁₃₁	—	4	2	no	—
161	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	4	yes	—
162	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
168	C₈×C₁₃₁	—	2	2	no	—
169	C₈×C₁₃₁	—	2	2	no	—
170	C₈×C₁₃₁	—	2	2	no	—
171	C₈×C₁₃₁	#126	1	4	yes	complemented
172	C₂²×C₁₃₁	—	8	2	no	—
173	C₂²×C₁₃₁	—	8	2	no	—
174	C₂²×C₁₃₁	—	8	2	no	—
175	C₂²×C₁₃₁	—	8	2	no	—
176	C₂²×C₁₃₁	—	8	2	no	—
177	C₂²×C₁₃₁	—	8	2	no	—
178	C₂²×C₁₃₁	—	8	2	no	—
179	C₂²×C₁₃₁	#532	1	1	yes	characteristic
180	C₂²×C₁₃₁	#532	1	1	yes	characteristic
181	C₂²×C₁₃₁	#532	1	1	yes	characteristic
182	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
183	C₂²×C₁₃₁	#575	1	2	yes	—
184	C₄×C₁₃₁	—	2	4	no	—
185	C₄×C₁₃₁	—	4	2	no	—
186	C₄×C₁₃₁	—	4	1	no	—
187	C₄×C₁₃₁	—	4	1	no	—
188	C₄×C₁₃₁	—	8	2	no	—
189	C₄×C₁₃₁	—	8	2	no	—
190	C₄×C₁₃₁	—	8	2	no	—
191	C₄×C₁₃₁	C₂×#126	1	1	yes	characteristic
192	C₄×C₁₃₁	#529	1	1	yes	characteristic
193	C₄×C₁₃₁	#529	1	1	yes	characteristic
194	C₄×C₁₃₁	#529	1	1	yes	characteristic
195	C₂×C₁₃₁	—	16	2	no	—
196	C₂×C₁₃₁	#2860	1	1	yes	characteristic
197	C₂×C₁₃₁	#3171	1	2	yes	—
198	C₂×C₁₃₁	#3180	1	2	yes	—
199	C₂×C₁₃₁	#3183	1	1	yes	characteristic
200	C₂×C₁₃₁	#3184	1	1	yes	characteristic
201	#33269	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₁₃₁	#33269	1	1	yes	characteristic, direct product factor, Sylow
203	#2860	C₂×C₁₃₁	1	2	yes	complemented
204	#1972	C₂×C₁₃₁	1	1	yes	characteristic
205	#1972	C₂×C₁₃₁	1	1	yes	characteristic
206	#1970	C₂×C₁₃₁	1	1	yes	characteristic
207	#1944	C₂×C₁₃₁	1	1	yes	characteristic, complemented
208	#1943	C₂×C₁₃₁	1	1	yes	characteristic, complemented
209	#1941	C₂×C₁₃₁	1	1	yes	characteristic, complemented
210	#1936	C₂×C₁₃₁	1	2	yes	complemented
211	#1936	C₂×C₁₃₁	1	2	yes	complemented
212	#1934	C₂×C₁₃₁	1	2	yes	complemented
213	C₄×#97	C₂×C₁₃₁	1	1	yes	characteristic, complemented
214	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₂×#126	—	2	2	no	—
216	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
217	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
218	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
219	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
220	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
221	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
222	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
223	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
224	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
225	C₂×#97	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	#390	C₂²×C₁₃₁	1	2	yes	—
229	#390	C₂²×C₁₃₁	1	2	yes	—
230	#390	C₂²×C₁₃₁	1	2	yes	—
231	#389	C₂²×C₁₃₁	1	2	yes	—
232	#389	C₂²×C₁₃₁	1	2	yes	—
233	#389	C₂²×C₁₃₁	1	2	yes	—
234	#388	—	2	2	no	—
235	#388	—	2	2	no	—
236	#388	—	2	2	no	—
237	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
238	#340	C₂²×C₁₃₁	1	2	yes	—
239	#340	C₂²×C₁₃₁	1	2	yes	—
240	#340	C₂²×C₁₃₁	1	2	yes	—
241	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
242	C₂×D₈	—	2	2	no	—
243	C₂×D₈	—	2	2	no	—
244	C₂×D₈	—	2	2	no	—
245	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
249	#126	—	4	8	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
263	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
264	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
267	#107	—	2	2	no	—
268	#106	—	2	2	no	—
269	#106	—	2	2	no	—
270	#102	—	2	4	no	—
271	#102	—	2	4	no	—
272	#102	—	2	4	no	—
273	#97	—	2	2	no	—
274	#97	—	2	2	no	—
275	#97	—	2	2	no	—
276	#97	—	2	2	no	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	C₂⁴	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
297	D₈	—	4	4	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	#41×C₁₃₁	1	2	yes	—
305	C₂×C₈	#41×C₁₃₁	1	2	yes	—
306	C₂×C₈	#41×C₁₃₁	1	2	yes	—
307	C₂×C₈	#41×C₁₃₁	1	2	yes	—
308	C₂×C₈	#41×C₁₃₁	1	2	yes	—
309	C₂×C₈	#41×C₁₃₁	1	2	yes	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₂²⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	4	yes	—
364	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
366	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
369	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	2	no	—
372	C₈	—	2	2	no	—
373	C₈	#126×C₁₃₁	1	4	yes	complemented
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	#532×C₁₃₁	1	1	yes	characteristic
382	C₂²	#532×C₁₃₁	1	1	yes	characteristic
383	C₂²	#532×C₁₃₁	1	1	yes	characteristic
384	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
385	C₂²	#575×C₁₃₁	1	2	yes	—
386	C₄	—	2	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	2	no	—
393	C₄	C₂×#126×C₁₃₁	1	1	yes	characteristic
394	C₄	#529×C₁₃₁	1	1	yes	characteristic
395	C₄	#529×C₁₃₁	1	1	yes	characteristic
396	C₄	#529×C₁₃₁	1	1	yes	characteristic
397	C₂	—	16	2	no	—
398	C₂	#2860×C₁₃₁	1	1	yes	characteristic
399	C₂	#3171×C₁₃₁	1	2	yes	—
400	C₂	#3180×C₁₃₁	1	2	yes	—
401	C₂	#3183×C₁₃₁	1	1	yes	characteristic
402	C₂	#3184×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₈×C₁₃₁	C₂²
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. #2860×C₁₃₁	C₂	semidirect
5. #1944×C₁₃₁	C₂	semidirect
6. #1943×C₁₃₁	C₂	semidirect
7. #1941×C₁₃₁	C₂	semidirect
8. #1936×C₁₃₁	C₂	semidirect
9. #1936×C₁₃₁	C₂	semidirect
10. #1934×C₁₃₁	C₂	semidirect
11. C₄×#97×C₁₃₁	C₂	semidirect
171. C₈×C₁₃₁	#126	semidirect
201. #33269	C₁₃₁	direct (N × H)
202. C₁₃₁	#33269	direct (N × H)
203. #2860	C₂×C₁₃₁	semidirect
207. #1944	C₂×C₁₃₁	semidirect
208. #1943	C₂×C₁₃₁	semidirect
209. #1941	C₂×C₁₃₁	semidirect
210. #1936	C₂×C₁₃₁	semidirect
211. #1936	C₂×C₁₃₁	semidirect
212. #1934	C₂×C₁₃₁	semidirect
213. C₄×#97	C₂×C₁₃₁	semidirect
373. C₈	#126×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2860×C₁₃₁	2
#1972×C₁₃₁	2
#1970×C₁₃₁	2
#1944×C₁₃₁	2
#1943×C₁₃₁	2
#1941×C₁₃₁	2
#1936×C₁₃₁	2
#1934×C₁₃₁	2
C₄×#97×C₁₃₁	2
#33269	131

Subgroups — C131×#33269 #45719153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33269 #45719153