Subgroups — C₁₃₁×#22607 #45708491

Order 33536.

692 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2924×C₁₃₁	C₂	1	2	yes	maximal
2	C₂×#427×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1946×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#1922×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	#1826×C₁₃₁	C₂	1	2	yes	maximal
6	#1810×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1773×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1752×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
11	#433×C₁₃₁	—	2	4	no	—
12	#432×C₁₃₁	—	2	2	no	—
13	#431×C₁₃₁	—	2	2	no	—
14	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
15	#427×C₁₃₁	C₄	1	1	yes	characteristic, complemented
16	#427×C₁₃₁	C₄	1	1	yes	characteristic, complemented
17	#427×C₁₃₁	C₄	1	2	yes	complemented
18	#427×C₁₃₁	C₂²	1	1	yes	characteristic
19	#427×C₁₃₁	C₂²	1	2	yes	—
20	#427×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#107×C₁₃₁	C₄	1	1	yes	characteristic, complemented
22	C₂×#107×C₁₃₁	C₄	1	1	yes	characteristic, complemented
23	C₂×#106×C₁₃₁	C₄	1	2	yes	complemented
24	#424×C₁₃₁	C₂²	1	4	yes	—
25	#407×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	#405×C₁₃₁	C₂²	1	4	yes	—
28	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
30	#341×C₁₃₁	C₂²	1	2	yes	—
31	#339×C₁₃₁	C₂²	1	4	yes	—
32	#339×C₁₃₁	C₂²	1	4	yes	—
33	#336×C₁₃₁	C₂²	1	2	yes	—
34	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₁₃₁	C₂³	1	4	yes	—
36	C₂²×C₈×C₁₃₁	—	2	4	no	—
37	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
44	#117×C₁₃₁	—	2	2	no	—
45	#117×C₁₃₁	—	2	2	no	—
46	#117×C₁₃₁	C₂×C₄	1	2	yes	—
47	#117×C₁₃₁	C₂×C₄	1	2	yes	—
48	#117×C₁₃₁	C₂³	1	2	yes	—
49	#117×C₁₃₁	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
54	C₂×C₄²×C₁₃₁	—	2	2	no	—
55	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
56	#108×C₁₃₁	—	2	4	no	—
57	#107×C₁₃₁	C₂×C₄	1	2	yes	—
58	#107×C₁₃₁	C₂×C₄	1	2	yes	—
59	#107×C₁₃₁	C₂×C₄	1	1	yes	characteristic
60	#107×C₁₃₁	C₂×C₄	1	1	yes	characteristic
61	#107×C₁₃₁	C₂×C₄	1	1	yes	characteristic
62	#107×C₁₃₁	C₂×C₄	1	1	yes	characteristic
63	#106×C₁₃₁	C₂×C₄	1	2	yes	—
64	#106×C₁₃₁	C₂×C₄	1	2	yes	—
65	#106×C₁₃₁	C₂×C₄	1	2	yes	—
66	#106×C₁₃₁	C₂×C₄	1	2	yes	—
67	C₄⋊C₈×C₁₃₁	—	2	4	no	—
68	C₄⋊C₈×C₁₃₁	—	2	4	no	—
69	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
70	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
71	C₂²⋊C₈×C₁₃₁	D₄	1	2	yes	—
72	C₂²⋊C₈×C₁₃₁	D₄	1	2	yes	—
73	#97×C₁₃₁	—	2	4	no	—
74	#97×C₁₃₁	—	2	4	no	—
75	C₄×C₈×C₁₃₁	—	2	4	no	—
76	#95×C₁₃₁	—	2	1	no	—
77	C₂⁴×C₁₃₁	#41	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₁	—	2	2	no	—
79	C₂²×C₄×C₁₃₁	—	2	2	no	—
80	C₂²×C₄×C₁₃₁	—	2	2	no	—
81	C₂²×C₄×C₁₃₁	—	2	2	no	—
82	C₂²×C₄×C₁₃₁	—	2	2	no	—
83	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
89	M₁₆×C₁₃₁	—	2	4	no	—
90	M₁₆×C₁₃₁	—	2	4	no	—
91	C₂×C₈×C₁₃₁	—	2	2	no	—
92	C₂×C₈×C₁₃₁	—	2	2	no	—
93	C₂×C₈×C₁₃₁	—	2	2	no	—
94	C₂×C₈×C₁₃₁	—	2	2	no	—
95	C₂×C₈×C₁₃₁	—	2	2	no	—
96	C₂×C₈×C₁₃₁	—	2	2	no	—
97	C₂×C₈×C₁₃₁	—	2	2	no	—
98	C₂×C₈×C₁₃₁	—	2	4	no	—
99	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
104	C₂×C₈×C₁₃₁	#41	1	4	yes	—
105	C₄⋊C₄×C₁₃₁	—	2	2	no	—
106	C₄⋊C₄×C₁₃₁	—	2	2	no	—
107	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
108	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
109	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
111	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
112	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
113	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
114	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
115	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
116	C₄²×C₁₃₁	—	2	2	no	—
117	C₄²×C₁₃₁	—	2	2	no	—
118	C₄²×C₁₃₁	—	2	2	no	—
119	C₄²×C₁₃₁	—	2	2	no	—
120	C₄²×C₁₃₁	—	2	2	no	—
121	C₄²×C₁₃₁	—	2	2	no	—
122	C₂³×C₁₃₁	—	2	2	no	—
123	C₂³×C₁₃₁	—	2	2	no	—
124	C₂³×C₁₃₁	—	4	1	no	—
125	C₂³×C₁₃₁	C₄×D₄	1	1	yes	characteristic
126	C₂³×C₁₃₁	C₄×D₄	1	1	yes	characteristic
127	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
128	C₂×C₄×C₁₃₁	—	2	2	no	—
129	C₂×C₄×C₁₃₁	—	2	1	no	—
130	C₂×C₄×C₁₃₁	—	2	1	no	—
131	C₂×C₄×C₁₃₁	—	2	1	no	—
132	C₂×C₄×C₁₃₁	—	2	1	no	—
133	C₂×C₄×C₁₃₁	—	2	2	no	—
134	C₂×C₄×C₁₃₁	—	2	2	no	—
135	C₂×C₄×C₁₃₁	—	2	2	no	—
136	C₂×C₄×C₁₃₁	—	2	2	no	—
137	C₂×C₄×C₁₃₁	—	2	2	no	—
138	C₂×C₄×C₁₃₁	—	2	2	no	—
139	C₂×C₄×C₁₃₁	—	4	4	no	—
140	C₂×C₄×C₁₃₁	—	4	2	no	—
141	C₂×C₄×C₁₃₁	—	4	2	no	—
142	C₂×C₄×C₁₃₁	—	4	2	no	—
143	C₂×C₄×C₁₃₁	—	8	2	no	—
144	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
149	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
150	C₈×C₁₃₁	—	2	1	no	—
151	C₈×C₁₃₁	—	2	1	no	—
152	C₈×C₁₃₁	—	2	4	no	—
153	C₈×C₁₃₁	—	4	4	no	—
154	C₈×C₁₃₁	#117	1	2	yes	—
155	C₈×C₁₃₁	#117	1	2	yes	—
156	C₂²×C₁₃₁	—	2	1	no	—
157	C₂²×C₁₃₁	—	2	1	no	—
158	C₂²×C₁₃₁	—	2	1	no	—
159	C₂²×C₁₃₁	—	2	1	no	—
160	C₂²×C₁₃₁	—	2	1	no	—
161	C₂²×C₁₃₁	—	2	1	no	—
162	C₂²×C₁₃₁	—	2	1	no	—
163	C₂²×C₁₃₁	—	4	4	no	—
164	C₂²×C₁₃₁	#444	1	2	yes	—
165	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₁₃₁	#552	1	2	yes	—
167	C₄×C₁₃₁	—	2	1	no	—
168	C₄×C₁₃₁	—	2	1	no	—
169	C₄×C₁₃₁	—	4	2	no	—
170	C₄×C₁₃₁	—	4	2	no	—
171	C₄×C₁₃₁	—	4	2	no	—
172	C₄×C₁₃₁	—	4	2	no	—
173	C₄×C₁₃₁	—	8	2	no	—
174	C₄×C₁₃₁	C₂×#117	1	1	yes	characteristic
175	C₄×C₁₃₁	#519	1	1	yes	characteristic
176	C₄×C₁₃₁	#547	1	2	yes	—
177	C₂×C₁₃₁	—	2	2	no	—
178	C₂×C₁₃₁	—	2	2	no	—
179	C₂×C₁₃₁	—	4	1	no	—
180	C₂×C₁₃₁	#2344	1	1	yes	characteristic
181	C₂×C₁₃₁	C₂×#444	1	1	yes	characteristic
182	C₂×C₁₃₁	#2957	1	1	yes	characteristic
183	#22607	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₁	#22607	1	1	yes	characteristic, direct product factor, Sylow
185	#2924	C₂×C₁₃₁	1	2	yes	—
186	C₂×#427	C₂×C₁₃₁	1	1	yes	characteristic
187	#1946	C₂×C₁₃₁	1	2	yes	complemented
188	#1922	C₂×C₁₃₁	1	4	yes	complemented
189	#1826	C₂×C₁₃₁	1	2	yes	—
190	#1810	C₂×C₁₃₁	1	1	yes	characteristic
191	#1773	C₂×C₁₃₁	1	2	yes	complemented
192	#1752	C₂×C₁₃₁	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
194	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
195	#433	—	2	4	no	—
196	#432	—	2	2	no	—
197	#431	—	2	2	no	—
198	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
199	#427	C₄×C₁₃₁	1	1	yes	characteristic, complemented
200	#427	C₄×C₁₃₁	1	1	yes	characteristic, complemented
201	#427	C₄×C₁₃₁	1	2	yes	complemented
202	#427	C₂²×C₁₃₁	1	2	yes	—
203	#427	C₂²×C₁₃₁	1	1	yes	characteristic
204	#427	C₂²×C₁₃₁	1	1	yes	characteristic
205	C₂×#107	C₄×C₁₃₁	1	1	yes	characteristic, complemented
206	C₂×#107	C₄×C₁₃₁	1	1	yes	characteristic, complemented
207	C₂×#106	C₄×C₁₃₁	1	2	yes	complemented
208	#424	C₂²×C₁₃₁	1	4	yes	—
209	#407	C₂²×C₁₃₁	1	2	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
211	#405	C₂²×C₁₃₁	1	4	yes	—
212	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
213	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
214	#341	C₂²×C₁₃₁	1	2	yes	—
215	#339	C₂²×C₁₃₁	1	4	yes	—
216	#339	C₂²×C₁₃₁	1	4	yes	—
217	#336	C₂²×C₁₃₁	1	2	yes	—
218	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
219	C₂×M₁₆	C₂³×C₁₃₁	1	4	yes	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
223	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
224	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
228	#117	—	2	2	no	—
229	#117	—	2	2	no	—
230	#117	C₂×C₄×C₁₃₁	1	2	yes	—
231	#117	C₂×C₄×C₁₃₁	1	2	yes	—
232	#117	C₂³×C₁₃₁	1	2	yes	—
233	#117	C₂³×C₁₃₁	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
240	#108	—	2	4	no	—
241	#107	C₂×C₄×C₁₃₁	1	2	yes	—
242	#107	C₂×C₄×C₁₃₁	1	2	yes	—
243	#107	C₂×C₄×C₁₃₁	1	1	yes	characteristic
244	#107	C₂×C₄×C₁₃₁	1	1	yes	characteristic
245	#107	C₂×C₄×C₁₃₁	1	1	yes	characteristic
246	#107	C₂×C₄×C₁₃₁	1	1	yes	characteristic
247	#106	C₂×C₄×C₁₃₁	1	2	yes	—
248	#106	C₂×C₄×C₁₃₁	1	2	yes	—
249	#106	C₂×C₄×C₁₃₁	1	2	yes	—
250	#106	C₂×C₄×C₁₃₁	1	2	yes	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	4	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₂²⋊C₈	D₄×C₁₃₁	1	2	yes	—
256	C₂²⋊C₈	D₄×C₁₃₁	1	2	yes	—
257	#97	—	2	4	no	—
258	#97	—	2	4	no	—
259	C₄×C₈	—	2	4	no	—
260	#95	—	2	1	no	—
261	C₂⁴	#41×C₁₃₁	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
271	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
272	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
273	M₁₆	—	2	4	no	—
274	M₁₆	—	2	4	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
284	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
285	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
286	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
287	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
288	C₂×C₈	#41×C₁₃₁	1	4	yes	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
292	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
293	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
294	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	4	1	no	—
309	C₂³	C₄×D₄×C₁₃₁	1	1	yes	characteristic
310	C₂³	C₄×D₄×C₁₃₁	1	1	yes	characteristic
311	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	8	2	no	—
328	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
329	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
330	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
333	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
334	C₈	—	2	1	no	—
335	C₈	—	2	1	no	—
336	C₈	—	2	4	no	—
337	C₈	—	4	4	no	—
338	C₈	#117×C₁₃₁	1	2	yes	—
339	C₈	#117×C₁₃₁	1	2	yes	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	4	4	no	—
348	C₂²	#444×C₁₃₁	1	2	yes	—
349	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
350	C₂²	#552×C₁₃₁	1	2	yes	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	—	8	2	no	—
358	C₄	C₂×#117×C₁₃₁	1	1	yes	characteristic
359	C₄	#519×C₁₃₁	1	1	yes	characteristic
360	C₄	#547×C₁₃₁	1	2	yes	—
361	C₂	—	2	2	no	—
362	C₂	—	2	2	no	—
363	C₂	—	4	1	no	—
364	C₂	#2344×C₁₃₁	1	1	yes	characteristic
365	C₂	C₂×#444×C₁₃₁	1	1	yes	characteristic
366	C₂	#2957×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂×C₄×D₄
prime radical	C₂⁴×C₁₃₁	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₂²⋊C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1946×C₁₃₁	C₂	semidirect
4. #1922×C₁₃₁	C₂	semidirect
7. #1773×C₁₃₁	C₂	semidirect
15. #427×C₁₃₁	C₄	semidirect
16. #427×C₁₃₁	C₄	semidirect
17. #427×C₁₃₁	C₄	semidirect
21. C₂×#107×C₁₃₁	C₄	semidirect
22. C₂×#107×C₁₃₁	C₄	semidirect
23. C₂×#106×C₁₃₁	C₄	semidirect
183. #22607	C₁₃₁	direct (N × H)
184. C₁₃₁	#22607	direct (N × H)
187. #1946	C₂×C₁₃₁	semidirect
188. #1922	C₂×C₁₃₁	semidirect
191. #1773	C₂×C₁₃₁	semidirect
199. #427	C₄×C₁₃₁	semidirect
200. #427	C₄×C₁₃₁	semidirect
201. #427	C₄×C₁₃₁	semidirect
205. C₂×#107	C₄×C₁₃₁	semidirect
206. C₂×#107	C₄×C₁₃₁	semidirect
207. C₂×#106	C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2924×C₁₃₁	2
C₂×#427×C₁₃₁	2
#1946×C₁₃₁	2
#1922×C₁₃₁	2
#1826×C₁₃₁	2
#1810×C₁₃₁	2
#1773×C₁₃₁	2
#1752×C₁₃₁	2
#22607	131

Subgroups — C131×#22607 #45708491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#22607 #45708491