Subgroups — C₁₃₁×#23189 #45709073

Order 33536.

1026 conjugacy classes of subgroups.

The subgroup lattice has 452 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×#442×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#441×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2367×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1983×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1972×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1971×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1880×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1877×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	C₄×#106×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1770×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₃₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
18	#495×C₁₃₁	C₄	1	8	yes	complemented
19	#442×C₁₃₁	—	2	4	no	—
20	#441×C₁₃₁	—	2	4	no	—
21	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
26	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
31	#391×C₁₃₁	C₂²	1	2	yes	—
32	#390×C₁₃₁	C₂²	1	2	yes	—
33	#388×C₁₃₁	—	2	2	no	—
34	#388×C₁₃₁	—	2	2	no	—
35	#385×C₁₃₁	—	2	2	no	—
36	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
39	#340×C₁₃₁	C₂²	1	2	yes	—
40	#336×C₁₃₁	C₂²	1	1	yes	characteristic
41	#336×C₁₃₁	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃₁	—	2	2	no	—
45	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	4	yes	complemented
48	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
49	C₂×SD₁₆×C₁₃₁	—	4	2	no	—
50	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	8	yes	complemented
51	C₂×D₈×C₁₃₁	—	2	2	no	—
52	C₂×D₈×C₁₃₁	—	2	2	no	—
53	C₂×D₈×C₁₃₁	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
58	#124×C₁₃₁	—	2	4	no	—
59	#124×C₁₃₁	C₂×C₄	1	8	yes	complemented
60	C₄×Q₈×C₁₃₁	—	2	4	no	—
61	C₄×Q₈×C₁₃₁	—	4	2	no	—
62	C₄×D₄×C₁₃₁	—	2	4	no	—
63	C₄×D₄×C₁₃₁	—	4	2	no	—
64	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₃₁	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
73	C₂×C₄²×C₁₃₁	—	2	2	no	—
74	C₂×C₄²×C₁₃₁	—	2	2	no	—
75	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
78	#106×C₁₃₁	—	2	2	no	—
79	#106×C₁₃₁	D₄	1	4	yes	—
80	C₄⋊C₈×C₁₃₁	—	2	2	no	—
81	#103×C₁₃₁	—	2	4	no	—
82	#103×C₁₃₁	—	4	2	no	—
83	#102×C₁₃₁	—	2	4	no	—
84	#102×C₁₃₁	—	4	2	no	—
85	#97×C₁₃₁	—	2	2	no	—
86	#97×C₁₃₁	—	2	2	no	—
87	C₄×C₈×C₁₃₁	C₂×C₄	1	4	yes	complemented
88	#95×C₁₃₁	—	2	2	no	—
89	#95×C₁₃₁	—	2	2	no	—
90	#95×C₁₃₁	—	2	2	no	—
91	#95×C₁₃₁	D₄	1	2	yes	—
92	C₂⁴×C₁₃₁	—	2	2	no	—
93	C₂×Q₈×C₁₃₁	—	2	2	no	—
94	C₂×Q₈×C₁₃₁	—	2	2	no	—
95	C₂×Q₈×C₁₃₁	—	2	2	no	—
96	C₂×Q₈×C₁₃₁	—	2	2	no	—
97	C₂×Q₈×C₁₃₁	—	2	2	no	—
98	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
99	C₂×D₄×C₁₃₁	—	2	2	no	—
100	C₂×D₄×C₁₃₁	—	2	2	no	—
101	C₂×D₄×C₁₃₁	—	2	2	no	—
102	C₂×D₄×C₁₃₁	—	2	2	no	—
103	C₂×D₄×C₁₃₁	—	2	2	no	—
104	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₃₁	—	2	2	no	—
106	C₂²×C₄×C₁₃₁	—	2	2	no	—
107	C₂²×C₄×C₁₃₁	—	2	2	no	—
108	C₂²×C₄×C₁₃₁	—	4	4	no	—
109	C₂²×C₄×C₁₃₁	—	4	4	no	—
110	C₂²×C₄×C₁₃₁	—	8	2	no	—
111	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
116	Q₁₆×C₁₃₁	—	2	8	no	—
117	SD₁₆×C₁₃₁	—	4	8	no	—
118	D₈×C₁₃₁	—	2	8	no	—
119	C₂×C₈×C₁₃₁	—	2	1	no	—
120	C₂×C₈×C₁₃₁	—	2	1	no	—
121	C₂×C₈×C₁₃₁	—	2	1	no	—
122	C₂×C₈×C₁₃₁	—	2	1	no	—
123	C₂×C₈×C₁₃₁	—	2	1	no	—
124	C₂×C₈×C₁₃₁	—	2	1	no	—
125	C₂×C₈×C₁₃₁	—	2	1	no	—
126	C₂×C₈×C₁₃₁	—	2	1	no	—
127	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃₁	#41	1	2	yes	—
131	C₄⋊C₄×C₁₃₁	—	2	2	no	—
132	C₄⋊C₄×C₁₃₁	—	2	2	no	—
133	C₄⋊C₄×C₁₃₁	—	2	2	no	—
134	C₄⋊C₄×C₁₃₁	—	4	2	no	—
135	C₄⋊C₄×C₁₃₁	—	4	4	no	—
136	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
137	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
138	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
139	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
140	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
141	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
142	C₄²×C₁₃₁	—	2	1	no	—
143	C₄²×C₁₃₁	—	2	1	no	—
144	C₄²×C₁₃₁	—	2	1	no	—
145	C₄²×C₁₃₁	—	2	1	no	—
146	C₄²×C₁₃₁	—	4	4	no	—
147	C₄²×C₁₃₁	—	8	2	no	—
148	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
149	C₄²×C₁₃₁	#41	1	2	yes	—
150	C₂³×C₁₃₁	—	2	4	no	—
151	C₂³×C₁₃₁	—	4	2	no	—
152	C₂³×C₁₃₁	—	4	2	no	—
153	C₂³×C₁₃₁	—	4	2	no	—
154	C₂³×C₁₃₁	—	4	2	no	—
155	C₂³×C₁₃₁	—	4	2	no	—
156	C₂³×C₁₃₁	—	4	2	no	—
157	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₃₁	—	2	4	no	—
159	Q₈×C₁₃₁	—	2	4	no	—
160	Q₈×C₁₃₁	—	4	2	no	—
161	Q₈×C₁₃₁	—	4	2	no	—
162	D₄×C₁₃₁	—	2	4	no	—
163	D₄×C₁₃₁	—	2	4	no	—
164	D₄×C₁₃₁	—	4	2	no	—
165	D₄×C₁₃₁	—	4	2	no	—
166	C₂×C₄×C₁₃₁	—	2	2	no	—
167	C₂×C₄×C₁₃₁	—	2	2	no	—
168	C₂×C₄×C₁₃₁	—	2	4	no	—
169	C₂×C₄×C₁₃₁	—	2	2	no	—
170	C₂×C₄×C₁₃₁	—	2	2	no	—
171	C₂×C₄×C₁₃₁	—	2	4	no	—
172	C₂×C₄×C₁₃₁	—	2	2	no	—
173	C₂×C₄×C₁₃₁	—	2	2	no	—
174	C₂×C₄×C₁₃₁	—	2	2	no	—
175	C₂×C₄×C₁₃₁	—	2	2	no	—
176	C₂×C₄×C₁₃₁	—	4	2	no	—
177	C₂×C₄×C₁₃₁	—	4	2	no	—
178	C₂×C₄×C₁₃₁	—	4	2	no	—
179	C₂×C₄×C₁₃₁	—	4	2	no	—
180	C₂×C₄×C₁₃₁	—	4	2	no	—
181	C₂×C₄×C₁₃₁	—	4	2	no	—
182	C₂×C₄×C₁₃₁	—	4	2	no	—
183	C₂×C₄×C₁₃₁	—	8	8	no	—
184	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
192	C₈×C₁₃₁	—	2	2	no	—
193	C₈×C₁₃₁	—	4	1	no	—
194	C₈×C₁₃₁	—	4	1	no	—
195	C₈×C₁₃₁	C₄×D₄	1	4	yes	—
196	C₂²×C₁₃₁	—	4	4	no	—
197	C₂²×C₁₃₁	—	4	4	no	—
198	C₂²×C₁₃₁	—	4	4	no	—
199	C₂²×C₁₃₁	—	8	2	no	—
200	C₂²×C₁₃₁	—	8	2	no	—
201	C₂²×C₁₃₁	—	8	2	no	—
202	C₂²×C₁₃₁	—	8	2	no	—
203	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
205	C₂²×C₁₃₁	#550	1	1	yes	characteristic
206	C₂²×C₁₃₁	#575	1	2	yes	—
207	C₂²×C₁₃₁	#577	1	2	yes	—
208	C₄×C₁₃₁	—	2	2	no	—
209	C₄×C₁₃₁	—	2	2	no	—
210	C₄×C₁₃₁	—	4	4	no	—
211	C₄×C₁₃₁	—	4	2	no	—
212	C₄×C₁₃₁	—	4	2	no	—
213	C₄×C₁₃₁	—	4	4	no	—
214	C₄×C₁₃₁	—	8	2	no	—
215	C₄×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₁₃₁	#518	1	1	yes	characteristic
217	C₄×C₁₃₁	#550	1	1	yes	characteristic
218	C₄×C₁₃₁	#559	1	1	yes	characteristic
219	C₂×C₁₃₁	—	8	4	no	—
220	C₂×C₁₃₁	#2366	1	1	yes	characteristic
221	C₂×C₁₃₁	#2943	1	1	yes	characteristic
222	C₂×C₁₃₁	#2952	1	1	yes	characteristic
223	C₂×C₁₃₁	#3275	1	2	yes	—
224	C₂×C₁₃₁	#3401	1	2	yes	—
225	#23189	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₁₃₁	#23189	1	1	yes	characteristic, direct product factor, Sylow
227	C₂×#495	C₂×C₁₃₁	1	1	yes	characteristic
228	C₂×#442	C₂×C₁₃₁	1	1	yes	characteristic
229	C₂×#441	C₂×C₁₃₁	1	1	yes	characteristic, complemented
230	#2367	C₂×C₁₃₁	1	2	yes	complemented
231	#1983	C₂×C₁₃₁	1	2	yes	complemented
232	#1972	C₂×C₁₃₁	1	1	yes	characteristic
233	#1971	C₂×C₁₃₁	1	1	yes	characteristic, complemented
234	#1880	C₂×C₁₃₁	1	2	yes	complemented
235	#1877	C₂×C₁₃₁	1	2	yes	complemented
236	C₄×#106	C₂×C₁₃₁	1	1	yes	characteristic, complemented
237	#1770	C₂×C₁₃₁	1	1	yes	characteristic, complemented
238	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
239	C₂²×SD₁₆	C₂²×C₁₃₁	1	2	yes	—
240	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
241	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
242	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
243	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
244	#495	C₄×C₁₃₁	1	8	yes	complemented
245	#442	—	2	4	no	—
246	#441	—	2	4	no	—
247	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
248	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
250	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
251	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
252	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
253	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
254	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
255	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
256	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
257	#391	C₂²×C₁₃₁	1	2	yes	—
258	#390	C₂²×C₁₃₁	1	2	yes	—
259	#388	—	2	2	no	—
260	#388	—	2	2	no	—
261	#385	—	2	2	no	—
262	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
263	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	—	2	2	no	—
265	#340	C₂²×C₁₃₁	1	2	yes	—
266	#336	C₂²×C₁₃₁	1	1	yes	characteristic
267	#336	C₂²×C₁₃₁	1	1	yes	characteristic
268	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
269	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
270	C₂³×C₄	—	2	2	no	—
271	C₂×Q₁₆	—	2	2	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	4	yes	complemented
274	C₂×SD₁₆	—	4	2	no	—
275	C₂×SD₁₆	—	4	2	no	—
276	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	8	yes	complemented
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	2	no	—
279	C₂×D₈	C₂×C₄×C₁₃₁	1	4	yes	—
280	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
284	#124	—	2	4	no	—
285	#124	C₂×C₄×C₁₃₁	1	8	yes	complemented
286	C₄×Q₈	—	2	4	no	—
287	C₄×Q₈	—	4	2	no	—
288	C₄×D₄	—	2	4	no	—
289	C₄×D₄	—	4	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	D₄×C₁₃₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
304	#106	—	2	2	no	—
305	#106	D₄×C₁₃₁	1	4	yes	—
306	C₄⋊C₈	—	2	2	no	—
307	#103	—	2	4	no	—
308	#103	—	4	2	no	—
309	#102	—	2	4	no	—
310	#102	—	4	2	no	—
311	#97	—	2	2	no	—
312	#97	—	2	2	no	—
313	C₄×C₈	C₂×C₄×C₁₃₁	1	4	yes	complemented
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	D₄×C₁₃₁	1	2	yes	—
318	C₂⁴	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	8	2	no	—
337	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
342	Q₁₆	—	2	8	no	—
343	SD₁₆	—	4	8	no	—
344	D₈	—	2	8	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
356	C₂×C₈	#41×C₁₃₁	1	2	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	4	4	no	—
373	C₄²	—	8	2	no	—
374	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
375	C₄²	#41×C₁₃₁	1	2	yes	—
376	C₂³	—	2	4	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	8	no	—
410	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
412	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
416	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
417	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	1	no	—
421	C₈	C₄×D₄×C₁₃₁	1	4	yes	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
430	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
431	C₂²	#550×C₁₃₁	1	1	yes	characteristic
432	C₂²	#575×C₁₃₁	1	2	yes	—
433	C₂²	#577×C₁₃₁	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	8	2	no	—
441	C₄	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
442	C₄	#518×C₁₃₁	1	1	yes	characteristic
443	C₄	#550×C₁₃₁	1	1	yes	characteristic
444	C₄	#559×C₁₃₁	1	1	yes	characteristic
445	C₂	—	8	4	no	—
446	C₂	#2366×C₁₃₁	1	1	yes	characteristic
447	C₂	#2943×C₁₃₁	1	1	yes	characteristic
448	C₂	#2952×C₁₃₁	1	1	yes	characteristic
449	C₂	#3275×C₁₃₁	1	2	yes	—
450	C₂	#3401×C₁₃₁	1	2	yes	—

	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
3. C₂×#441×C₁₃₁	C₂	semidirect
4. #2367×C₁₃₁	C₂	semidirect
5. #1983×C₁₃₁	C₂	semidirect
7. #1971×C₁₃₁	C₂	semidirect
8. #1880×C₁₃₁	C₂	semidirect
9. #1877×C₁₃₁	C₂	semidirect
10. C₄×#106×C₁₃₁	C₂	semidirect
11. #1770×C₁₃₁	C₂	semidirect
18. #495×C₁₃₁	C₄	semidirect
47. C₂×Q₁₆×C₁₃₁	C₂×C₄	semidirect
50. C₂×SD₁₆×C₁₃₁	C₂×C₄	semidirect
59. #124×C₁₃₁	C₂×C₄	semidirect
87. C₄×C₈×C₁₃₁	C₂×C₄	semidirect
225. #23189	C₁₃₁	direct (N × H)
226. C₁₃₁	#23189	direct (N × H)
229. C₂×#441	C₂×C₁₃₁	semidirect
230. #2367	C₂×C₁₃₁	semidirect
231. #1983	C₂×C₁₃₁	semidirect
233. #1971	C₂×C₁₃₁	semidirect
234. #1880	C₂×C₁₃₁	semidirect
235. #1877	C₂×C₁₃₁	semidirect
236. C₄×#106	C₂×C₁₃₁	semidirect
237. #1770	C₂×C₁₃₁	semidirect
244. #495	C₄×C₁₃₁	semidirect
273. C₂×Q₁₆	C₂×C₄×C₁₃₁	semidirect
276. C₂×SD₁₆	C₂×C₄×C₁₃₁	semidirect
285. #124	C₂×C₄×C₁₃₁	semidirect
313. 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×#442×C₁₃₁	2
C₂×#441×C₁₃₁	2
#2367×C₁₃₁	2
#1983×C₁₃₁	2
#1972×C₁₃₁	2
#1971×C₁₃₁	2
#1880×C₁₃₁	2
#1877×C₁₃₁	2
C₄×#106×C₁₃₁	2
#1770×C₁₃₁	2
#23189	131

Subgroups — C131×#23189 #45709073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#23189 #45709073