Subgroups — C₁₃₁×#23191 #45709075

Order 33536.

1026 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#495×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#440×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2367×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#1983×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1973×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1879×C₁₃₁	C₂	1	2	yes	maximal
7	#1878×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	C₄×#107×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1770×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₁₃₁	C₂²	1	2	yes	—
12	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
16	#495×C₁₃₁	C₄	1	8	yes	complemented
17	#440×C₁₃₁	—	2	8	no	—
18	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	#391×C₁₃₁	C₂²	1	2	yes	—
28	#390×C₁₃₁	C₂²	1	2	yes	—
29	#388×C₁₃₁	—	2	2	no	—
30	#388×C₁₃₁	—	2	2	no	—
31	#385×C₁₃₁	—	2	2	no	—
32	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
35	#340×C₁₃₁	C₂²	1	2	yes	—
36	#336×C₁₃₁	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
38	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃₁	—	2	2	no	—
40	C₂×Q₁₆×C₁₃₁	—	4	1	no	—
41	C₂×Q₁₆×C₁₃₁	—	4	1	no	—
42	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	4	yes	complemented
43	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
44	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
45	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	8	yes	complemented
46	C₂×D₈×C₁₃₁	—	4	1	no	—
47	C₂×D₈×C₁₃₁	—	4	1	no	—
48	C₂×D₈×C₁₃₁	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	#124×C₁₃₁	—	2	4	no	—
53	#124×C₁₃₁	C₂×C₄	1	8	yes	complemented
54	C₄×Q₈×C₁₃₁	—	2	4	no	—
55	C₄×Q₈×C₁₃₁	—	4	2	no	—
56	C₄×D₄×C₁₃₁	—	2	4	no	—
57	C₄×D₄×C₁₃₁	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
68	C₂×C₄²×C₁₃₁	—	2	2	no	—
69	C₂×C₄²×C₁₃₁	—	2	2	no	—
70	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
72	#107×C₁₃₁	—	2	2	no	—
73	#107×C₁₃₁	D₄	1	4	yes	—
74	C₄⋊C₈×C₁₃₁	—	2	2	no	—
75	#103×C₁₃₁	—	2	4	no	—
76	#103×C₁₃₁	—	4	2	no	—
77	#102×C₁₃₁	—	2	4	no	—
78	#102×C₁₃₁	—	4	2	no	—
79	#97×C₁₃₁	—	2	4	no	—
80	C₄×C₈×C₁₃₁	C₂×C₄	1	4	yes	complemented
81	#95×C₁₃₁	—	2	2	no	—
82	#95×C₁₃₁	—	2	2	no	—
83	#95×C₁₃₁	—	2	2	no	—
84	#95×C₁₃₁	D₄	1	2	yes	—
85	C₂⁴×C₁₃₁	—	2	2	no	—
86	C₂×Q₈×C₁₃₁	—	2	2	no	—
87	C₂×Q₈×C₁₃₁	—	2	2	no	—
88	C₂×Q₈×C₁₃₁	—	2	2	no	—
89	C₂×Q₈×C₁₃₁	—	2	2	no	—
90	C₂×Q₈×C₁₃₁	—	2	2	no	—
91	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
92	C₂×D₄×C₁₃₁	—	2	2	no	—
93	C₂×D₄×C₁₃₁	—	2	2	no	—
94	C₂×D₄×C₁₃₁	—	2	2	no	—
95	C₂×D₄×C₁₃₁	—	2	2	no	—
96	C₂×D₄×C₁₃₁	—	2	2	no	—
97	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₃₁	—	2	2	no	—
99	C₂²×C₄×C₁₃₁	—	2	2	no	—
100	C₂²×C₄×C₁₃₁	—	2	2	no	—
101	C₂²×C₄×C₁₃₁	—	4	4	no	—
102	C₂²×C₄×C₁₃₁	—	4	4	no	—
103	C₂²×C₄×C₁₃₁	—	8	2	no	—
104	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
108	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
109	Q₁₆×C₁₃₁	—	4	4	no	—
110	SD₁₆×C₁₃₁	—	2	16	no	—
111	D₈×C₁₃₁	—	4	4	no	—
112	C₂×C₈×C₁₃₁	—	2	1	no	—
113	C₂×C₈×C₁₃₁	—	2	1	no	—
114	C₂×C₈×C₁₃₁	—	2	2	no	—
115	C₂×C₈×C₁₃₁	—	2	2	no	—
116	C₂×C₈×C₁₃₁	—	2	2	no	—
117	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₃₁	#41	1	2	yes	—
121	C₄⋊C₄×C₁₃₁	—	2	2	no	—
122	C₄⋊C₄×C₁₃₁	—	2	2	no	—
123	C₄⋊C₄×C₁₃₁	—	2	2	no	—
124	C₄⋊C₄×C₁₃₁	—	4	1	no	—
125	C₄⋊C₄×C₁₃₁	—	4	1	no	—
126	C₄⋊C₄×C₁₃₁	—	4	4	no	—
127	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
128	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
129	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
130	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
131	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
132	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
133	C₄²×C₁₃₁	—	2	2	no	—
134	C₄²×C₁₃₁	—	2	2	no	—
135	C₄²×C₁₃₁	—	4	4	no	—
136	C₄²×C₁₃₁	—	8	2	no	—
137	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
138	C₄²×C₁₃₁	#41	1	2	yes	—
139	C₂³×C₁₃₁	—	2	4	no	—
140	C₂³×C₁₃₁	—	4	2	no	—
141	C₂³×C₁₃₁	—	4	2	no	—
142	C₂³×C₁₃₁	—	4	2	no	—
143	C₂³×C₁₃₁	—	4	2	no	—
144	C₂³×C₁₃₁	—	4	2	no	—
145	C₂³×C₁₃₁	—	4	2	no	—
146	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₃₁	—	2	4	no	—
148	Q₈×C₁₃₁	—	2	4	no	—
149	Q₈×C₁₃₁	—	4	2	no	—
150	Q₈×C₁₃₁	—	4	2	no	—
151	D₄×C₁₃₁	—	2	4	no	—
152	D₄×C₁₃₁	—	2	4	no	—
153	D₄×C₁₃₁	—	4	2	no	—
154	D₄×C₁₃₁	—	4	2	no	—
155	C₂×C₄×C₁₃₁	—	2	1	no	—
156	C₂×C₄×C₁₃₁	—	2	1	no	—
157	C₂×C₄×C₁₃₁	—	2	1	no	—
158	C₂×C₄×C₁₃₁	—	2	1	no	—
159	C₂×C₄×C₁₃₁	—	2	4	no	—
160	C₂×C₄×C₁₃₁	—	2	2	no	—
161	C₂×C₄×C₁₃₁	—	2	2	no	—
162	C₂×C₄×C₁₃₁	—	2	4	no	—
163	C₂×C₄×C₁₃₁	—	2	2	no	—
164	C₂×C₄×C₁₃₁	—	2	2	no	—
165	C₂×C₄×C₁₃₁	—	2	2	no	—
166	C₂×C₄×C₁₃₁	—	2	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	—	4	2	no	—
173	C₂×C₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	8	8	no	—
175	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
183	C₈×C₁₃₁	—	2	2	no	—
184	C₈×C₁₃₁	—	4	2	no	—
185	C₈×C₁₃₁	C₄×D₄	1	4	yes	—
186	C₂²×C₁₃₁	—	4	4	no	—
187	C₂²×C₁₃₁	—	4	4	no	—
188	C₂²×C₁₃₁	—	4	4	no	—
189	C₂²×C₁₃₁	—	8	2	no	—
190	C₂²×C₁₃₁	—	8	2	no	—
191	C₂²×C₁₃₁	—	8	2	no	—
192	C₂²×C₁₃₁	—	8	2	no	—
193	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
195	C₂²×C₁₃₁	#550	1	1	yes	characteristic
196	C₂²×C₁₃₁	#575	1	1	yes	characteristic
197	C₂²×C₁₃₁	#575	1	1	yes	characteristic
198	C₂²×C₁₃₁	#576	1	1	yes	characteristic
199	C₂²×C₁₃₁	#578	1	1	yes	characteristic
200	C₄×C₁₃₁	—	2	2	no	—
201	C₄×C₁₃₁	—	2	2	no	—
202	C₄×C₁₃₁	—	4	4	no	—
203	C₄×C₁₃₁	—	4	2	no	—
204	C₄×C₁₃₁	—	4	4	no	—
205	C₄×C₁₃₁	—	4	2	no	—
206	C₄×C₁₃₁	—	8	2	no	—
207	C₄×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
208	C₄×C₁₃₁	#518	1	1	yes	characteristic
209	C₄×C₁₃₁	#550	1	1	yes	characteristic
210	C₄×C₁₃₁	#559	1	1	yes	characteristic
211	C₂×C₁₃₁	—	8	4	no	—
212	C₂×C₁₃₁	#2366	1	1	yes	characteristic
213	C₂×C₁₃₁	#2943	1	1	yes	characteristic
214	C₂×C₁₃₁	#2951	1	1	yes	characteristic
215	C₂×C₁₃₁	#3273	1	1	yes	characteristic
216	C₂×C₁₃₁	#3277	1	1	yes	characteristic
217	C₂×C₁₃₁	#3402	1	1	yes	characteristic
218	C₂×C₁₃₁	#3403	1	1	yes	characteristic
219	#23191	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₁₃₁	#23191	1	1	yes	characteristic, direct product factor, Sylow
221	C₂×#495	C₂×C₁₃₁	1	1	yes	characteristic
222	C₂×#440	C₂×C₁₃₁	1	2	yes	complemented
223	#2367	C₂×C₁₃₁	1	2	yes	complemented
224	#1983	C₂×C₁₃₁	1	2	yes	complemented
225	#1973	C₂×C₁₃₁	1	2	yes	complemented
226	#1879	C₂×C₁₃₁	1	2	yes	—
227	#1878	C₂×C₁₃₁	1	2	yes	complemented
228	C₄×#107	C₂×C₁₃₁	1	1	yes	characteristic, complemented
229	#1770	C₂×C₁₃₁	1	1	yes	characteristic, complemented
230	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
231	C₂²×SD₁₆	C₂²×C₁₃₁	1	2	yes	—
232	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
233	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
234	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
235	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
236	#495	C₄×C₁₃₁	1	8	yes	complemented
237	#440	—	2	8	no	—
238	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
239	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
241	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
242	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
243	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
244	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
245	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
246	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
247	#391	C₂²×C₁₃₁	1	2	yes	—
248	#390	C₂²×C₁₃₁	1	2	yes	—
249	#388	—	2	2	no	—
250	#388	—	2	2	no	—
251	#385	—	2	2	no	—
252	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
253	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
254	C₄×C₂²⋊C₄	—	2	2	no	—
255	#340	C₂²×C₁₃₁	1	2	yes	—
256	#336	C₂²×C₁₃₁	1	2	yes	—
257	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
258	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
259	C₂³×C₄	—	2	2	no	—
260	C₂×Q₁₆	—	4	1	no	—
261	C₂×Q₁₆	—	4	1	no	—
262	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	4	yes	complemented
263	C₂×SD₁₆	—	2	4	no	—
264	C₂×SD₁₆	—	2	4	no	—
265	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	8	yes	complemented
266	C₂×D₈	—	4	1	no	—
267	C₂×D₈	—	4	1	no	—
268	C₂×D₈	C₂×C₄×C₁₃₁	1	4	yes	—
269	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
272	#124	—	2	4	no	—
273	#124	C₂×C₄×C₁₃₁	1	8	yes	complemented
274	C₄×Q₈	—	2	4	no	—
275	C₄×Q₈	—	4	2	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	—	4	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
280	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#107	D₄×C₁₃₁	1	4	yes	—
294	C₄⋊C₈	—	2	2	no	—
295	#103	—	2	4	no	—
296	#103	—	4	2	no	—
297	#102	—	2	4	no	—
298	#102	—	4	2	no	—
299	#97	—	2	4	no	—
300	C₄×C₈	C₂×C₄×C₁₃₁	1	4	yes	complemented
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	D₄×C₁₃₁	1	2	yes	—
305	C₂⁴	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	8	2	no	—
324	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
329	Q₁₆	—	4	4	no	—
330	SD₁₆	—	2	16	no	—
331	D₈	—	4	4	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
338	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
340	C₂×C₈	#41×C₁₃₁	1	2	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	4	4	no	—
352	C₂²⋊C₄	—	8	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	4	4	no	—
356	C₄²	—	8	2	no	—
357	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
358	C₄²	#41×C₁₃₁	1	2	yes	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
367	Q₈	—	2	4	no	—
368	Q₈	—	2	4	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	8	no	—
395	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
396	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
397	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
400	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
401	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
402	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	4	2	no	—
405	C₈	C₄×D₄×C₁₃₁	1	4	yes	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
414	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
415	C₂²	#550×C₁₃₁	1	1	yes	characteristic
416	C₂²	#575×C₁₃₁	1	1	yes	characteristic
417	C₂²	#575×C₁₃₁	1	1	yes	characteristic
418	C₂²	#576×C₁₃₁	1	1	yes	characteristic
419	C₂²	#578×C₁₃₁	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	8	2	no	—
427	C₄	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
428	C₄	#518×C₁₃₁	1	1	yes	characteristic
429	C₄	#550×C₁₃₁	1	1	yes	characteristic
430	C₄	#559×C₁₃₁	1	1	yes	characteristic
431	C₂	—	8	4	no	—
432	C₂	#2366×C₁₃₁	1	1	yes	characteristic
433	C₂	#2943×C₁₃₁	1	1	yes	characteristic
434	C₂	#2951×C₁₃₁	1	1	yes	characteristic
435	C₂	#3273×C₁₃₁	1	1	yes	characteristic
436	C₂	#3277×C₁₃₁	1	1	yes	characteristic
437	C₂	#3402×C₁₃₁	1	1	yes	characteristic
438	C₂	#3403×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₈×C₁₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄×C₄⋊C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#440×C₁₃₁	C₂	semidirect
3. #2367×C₁₃₁	C₂	semidirect
4. #1983×C₁₃₁	C₂	semidirect
5. #1973×C₁₃₁	C₂	semidirect
7. #1878×C₁₃₁	C₂	semidirect
8. C₄×#107×C₁₃₁	C₂	semidirect
9. #1770×C₁₃₁	C₂	semidirect
16. #495×C₁₃₁	C₄	semidirect
42. C₂×Q₁₆×C₁₃₁	C₂×C₄	semidirect
45. C₂×SD₁₆×C₁₃₁	C₂×C₄	semidirect
53. #124×C₁₃₁	C₂×C₄	semidirect
80. C₄×C₈×C₁₃₁	C₂×C₄	semidirect
219. #23191	C₁₃₁	direct (N × H)
220. C₁₃₁	#23191	direct (N × H)
222. C₂×#440	C₂×C₁₃₁	semidirect
223. #2367	C₂×C₁₃₁	semidirect
224. #1983	C₂×C₁₃₁	semidirect
225. #1973	C₂×C₁₃₁	semidirect
227. #1878	C₂×C₁₃₁	semidirect
228. C₄×#107	C₂×C₁₃₁	semidirect
229. #1770	C₂×C₁₃₁	semidirect
236. #495	C₄×C₁₃₁	semidirect
262. C₂×Q₁₆	C₂×C₄×C₁₃₁	semidirect
265. C₂×SD₁₆	C₂×C₄×C₁₃₁	semidirect
273. #124	C₂×C₄×C₁₃₁	semidirect
300. C₄×C₈	C₂×C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#495×C₁₃₁	2
C₂×#440×C₁₃₁	2
#2367×C₁₃₁	2
#1983×C₁₃₁	2
#1973×C₁₃₁	2
#1879×C₁₃₁	2
#1878×C₁₃₁	2
C₄×#107×C₁₃₁	2
#1770×C₁₃₁	2
#23191	131

Subgroups — C131×#23191 #45709075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#23191 #45709075