Subgroups — C₁₃₁×#34381 #45720265

Order 33536.

2134 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#126×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2383×C₁₃₁	C₂	1	4	yes	maximal, complemented
3	#2373×C₁₃₁	C₂	1	4	yes	maximal, complemented
4	#2345×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2344×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2342×C₁₃₁	C₂	1	2	yes	maximal
7	#2342×C₁₃₁	C₂	1	2	yes	maximal
8	#2334×C₁₃₁	C₂	1	4	yes	maximal, complemented
9	#2334×C₁₃₁	C₂	1	4	yes	maximal, complemented
10	#2316×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#2315×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	#2313×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#2312×C₁₃₁	C₂	1	1	yes	maximal, characteristic
14	#2285×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#2283×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#126×C₁₃₁	C₄	1	16	yes	complemented
17	C₂×#126×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#126×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#126×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#126×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
31	#389×C₁₃₁	C₂²	1	4	yes	complemented
32	#389×C₁₃₁	C₂²	1	4	yes	complemented
33	#389×C₁₃₁	C₂²	1	4	yes	complemented
34	#389×C₁₃₁	C₂²	1	4	yes	complemented
35	#388×C₁₃₁	C₂²	1	4	yes	—
36	#388×C₁₃₁	C₂²	1	4	yes	—
37	#388×C₁₃₁	C₂²	1	4	yes	—
38	#388×C₁₃₁	C₂²	1	4	yes	—
39	#388×C₁₃₁	C₂²	1	4	yes	—
40	#388×C₁₃₁	C₂²	1	4	yes	—
41	#387×C₁₃₁	C₂²	1	4	yes	complemented
42	#387×C₁₃₁	C₂²	1	4	yes	complemented
43	#387×C₁₃₁	C₂²	1	4	yes	complemented
44	#387×C₁₃₁	C₂²	1	4	yes	complemented
45	#387×C₁₃₁	C₂²	1	4	yes	complemented
46	#387×C₁₃₁	C₂²	1	4	yes	complemented
47	#385×C₁₃₁	C₂²	1	4	yes	—
48	#385×C₁₃₁	C₂²	1	4	yes	—
49	#385×C₁₃₁	C₂²	1	4	yes	—
50	#385×C₁₃₁	C₂²	1	4	yes	—
51	#384×C₁₃₁	C₂²	1	2	yes	complemented
52	#383×C₁₃₁	C₂²	1	2	yes	complemented
53	#382×C₁₃₁	C₂²	1	2	yes	complemented
54	#382×C₁₃₁	C₂²	1	2	yes	complemented
55	#381×C₁₃₁	C₂²	1	2	yes	—
56	#381×C₁₃₁	C₂²	1	2	yes	—
57	#380×C₁₃₁	C₂²	1	1	yes	characteristic
58	#380×C₁₃₁	C₂²	1	1	yes	characteristic
59	#380×C₁₃₁	C₂²	1	1	yes	characteristic
60	#380×C₁₃₁	C₂²	1	1	yes	characteristic
61	#380×C₁₃₁	C₂²	1	2	yes	—
62	#380×C₁₃₁	C₂²	1	2	yes	—
63	#380×C₁₃₁	C₂²	1	2	yes	—
64	#379×C₁₃₁	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
66	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
67	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
68	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
69	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
70	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
75	#376×C₁₃₁	C₂²	1	2	yes	complemented
76	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
84	#126×C₁₃₁	C₂×C₄	1	16	yes	complemented
85	#126×C₁₃₁	C₂×C₄	1	16	yes	complemented
86	#126×C₁₃₁	C₂×C₄	1	16	yes	complemented
87	#126×C₁₃₁	C₂×C₄	1	16	yes	complemented
88	#117×C₁₃₁	—	4	4	no	—
89	#117×C₁₃₁	—	4	4	no	—
90	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
91	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
92	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
93	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
109	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	—
110	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	—
111	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	—
112	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃₁	C₂×C₄	1	8	yes	complemented
126	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
127	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
128	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
135	#95×C₁₃₁	C₂³	1	2	yes	—
136	#95×C₁₃₁	C₂³	1	4	yes	—
137	#95×C₁₃₁	C₂³	1	2	yes	—
138	#95×C₁₃₁	C₂³	1	4	yes	—
139	#95×C₁₃₁	C₂³	1	4	yes	—
140	#95×C₁₃₁	C₂³	1	4	yes	—
141	#95×C₁₃₁	C₂³	1	4	yes	—
142	#95×C₁₃₁	C₂³	1	4	yes	—
143	#95×C₁₃₁	C₂³	1	4	yes	—
144	#95×C₁₃₁	C₂³	1	4	yes	—
145	#95×C₁₃₁	C₂³	1	4	yes	—
146	#95×C₁₃₁	C₂³	1	2	yes	—
147	#95×C₁₃₁	C₂³	1	2	yes	—
148	#95×C₁₃₁	C₂³	1	4	yes	—
149	C₂⁴×C₁₃₁	—	2	2	no	—
150	C₂⁴×C₁₃₁	—	2	2	no	—
151	C₂⁴×C₁₃₁	—	4	2	no	—
152	C₂⁴×C₁₃₁	—	4	2	no	—
153	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
154	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
155	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃₁	—	2	2	no	—
157	C₂²×C₄×C₁₃₁	—	2	2	no	—
158	C₂²×C₄×C₁₃₁	—	2	2	no	—
159	C₂²×C₄×C₁₃₁	—	2	2	no	—
160	C₂²×C₄×C₁₃₁	—	4	2	no	—
161	C₂²×C₄×C₁₃₁	—	4	2	no	—
162	C₂²×C₄×C₁₃₁	—	4	2	no	—
163	C₂²×C₄×C₁₃₁	—	4	2	no	—
164	C₂²×C₄×C₁₃₁	—	4	4	no	—
165	C₂²×C₄×C₁₃₁	—	4	4	no	—
166	C₂²×C₄×C₁₃₁	—	4	4	no	—
167	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
172	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
186	C₄⋊C₄×C₁₃₁	—	4	4	no	—
187	C₄⋊C₄×C₁₃₁	—	4	4	no	—
188	C₄⋊C₄×C₁₃₁	—	4	2	no	—
189	C₄⋊C₄×C₁₃₁	—	4	4	no	—
190	C₄⋊C₄×C₁₃₁	—	4	2	no	—
191	C₄⋊C₄×C₁₃₁	—	4	2	no	—
192	C₄⋊C₄×C₁₃₁	—	4	2	no	—
193	C₄⋊C₄×C₁₃₁	—	4	4	no	—
194	C₄⋊C₄×C₁₃₁	—	4	4	no	—
195	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
196	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
197	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
198	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
199	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
200	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
201	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
202	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
203	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
204	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
205	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
206	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
207	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
208	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
209	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
210	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
211	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
212	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
213	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
214	C₄²×C₁₃₁	—	4	4	no	—
215	C₄²×C₁₃₁	—	4	4	no	—
216	C₄²×C₁₃₁	—	4	4	no	—
217	C₄²×C₁₃₁	—	4	4	no	—
218	C₄²×C₁₃₁	—	4	4	no	—
219	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
220	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
221	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
222	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
223	C₂³×C₁₃₁	—	2	2	no	—
224	C₂³×C₁₃₁	—	2	2	no	—
225	C₂³×C₁₃₁	—	2	2	no	—
226	C₂³×C₁₃₁	—	2	2	no	—
227	C₂³×C₁₃₁	—	2	4	no	—
228	C₂³×C₁₃₁	—	2	4	no	—
229	C₂³×C₁₃₁	—	2	8	no	—
230	C₂³×C₁₃₁	—	4	4	no	—
231	C₂³×C₁₃₁	—	4	4	no	—
232	C₂³×C₁₃₁	—	8	4	no	—
233	C₂³×C₁₃₁	—	8	4	no	—
234	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
235	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
236	C₂³×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
237	C₂³×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
238	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
239	C₂×C₄×C₁₃₁	—	2	8	no	—
240	C₂×C₄×C₁₃₁	—	2	8	no	—
241	C₂×C₄×C₁₃₁	—	2	1	no	—
242	C₂×C₄×C₁₃₁	—	2	2	no	—
243	C₂×C₄×C₁₃₁	—	2	1	no	—
244	C₂×C₄×C₁₃₁	—	2	1	no	—
245	C₂×C₄×C₁₃₁	—	2	2	no	—
246	C₂×C₄×C₁₃₁	—	2	1	no	—
247	C₂×C₄×C₁₃₁	—	2	2	no	—
248	C₂×C₄×C₁₃₁	—	2	4	no	—
249	C₂×C₄×C₁₃₁	—	2	4	no	—
250	C₂×C₄×C₁₃₁	—	2	2	no	—
251	C₂×C₄×C₁₃₁	—	2	2	no	—
252	C₂×C₄×C₁₃₁	—	2	2	no	—
253	C₂×C₄×C₁₃₁	—	2	4	no	—
254	C₂×C₄×C₁₃₁	—	2	4	no	—
255	C₂×C₄×C₁₃₁	—	2	4	no	—
256	C₂×C₄×C₁₃₁	—	2	4	no	—
257	C₂×C₄×C₁₃₁	—	2	4	no	—
258	C₂×C₄×C₁₃₁	—	2	4	no	—
259	C₂×C₄×C₁₃₁	—	2	4	no	—
260	C₂×C₄×C₁₃₁	—	2	4	no	—
261	C₂×C₄×C₁₃₁	—	2	4	no	—
262	C₂×C₄×C₁₃₁	—	2	4	no	—
263	C₂×C₄×C₁₃₁	—	2	4	no	—
264	C₂×C₄×C₁₃₁	—	2	4	no	—
265	C₂×C₄×C₁₃₁	—	4	4	no	—
266	C₂×C₄×C₁₃₁	—	4	4	no	—
267	C₂×C₄×C₁₃₁	—	4	4	no	—
268	C₂×C₄×C₁₃₁	—	4	4	no	—
269	C₂×C₄×C₁₃₁	—	8	8	no	—
270	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
271	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
272	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
273	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
274	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
275	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
276	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
277	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
278	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
279	C₂²×C₁₃₁	—	2	2	no	—
280	C₂²×C₁₃₁	—	2	2	no	—
281	C₂²×C₁₃₁	—	2	4	no	—
282	C₂²×C₁₃₁	—	2	4	no	—
283	C₂²×C₁₃₁	—	2	4	no	—
284	C₂²×C₁₃₁	—	2	4	no	—
285	C₂²×C₁₃₁	—	2	4	no	—
286	C₂²×C₁₃₁	—	4	4	no	—
287	C₂²×C₁₃₁	—	4	4	no	—
288	C₂²×C₁₃₁	—	8	8	no	—
289	C₂²×C₁₃₁	#520	1	4	yes	—
290	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
291	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
292	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
293	C₂²×C₁₃₁	#585	1	2	yes	—
294	C₂²×C₁₃₁	#585	1	2	yes	—
295	C₄×C₁₃₁	—	2	2	no	—
296	C₄×C₁₃₁	—	2	4	no	—
297	C₄×C₁₃₁	—	2	2	no	—
298	C₄×C₁₃₁	—	2	2	no	—
299	C₄×C₁₃₁	—	2	4	no	—
300	C₄×C₁₃₁	—	2	4	no	—
301	C₄×C₁₃₁	—	2	2	no	—
302	C₄×C₁₃₁	—	2	2	no	—
303	C₄×C₁₃₁	—	2	2	no	—
304	C₄×C₁₃₁	—	4	4	no	—
305	C₄×C₁₃₁	—	4	4	no	—
306	C₄×C₁₃₁	—	4	4	no	—
307	C₄×C₁₃₁	—	4	4	no	—
308	C₂×C₁₃₁	—	2	4	no	—
309	C₂×C₁₃₁	—	4	4	no	—
310	C₂×C₁₃₁	C₂×#520	1	1	yes	characteristic
311	C₂×C₁₃₁	#3428	1	1	yes	characteristic
312	C₂×C₁₃₁	#3428	1	1	yes	characteristic
313	C₂×C₁₃₁	#3560	1	2	yes	—
314	C₂×C₁₃₁	#3564	1	2	yes	—
315	#34381	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₁₃₁	#34381	1	1	yes	characteristic, direct product factor, Sylow
317	C₂²×#126	C₂×C₁₃₁	1	1	yes	characteristic
318	#2383	C₂×C₁₃₁	1	4	yes	complemented
319	#2373	C₂×C₁₃₁	1	4	yes	complemented
320	#2345	C₂×C₁₃₁	1	2	yes	complemented
321	#2344	C₂×C₁₃₁	1	2	yes	complemented
322	#2342	C₂×C₁₃₁	1	2	yes	—
323	#2342	C₂×C₁₃₁	1	2	yes	—
324	#2334	C₂×C₁₃₁	1	4	yes	complemented
325	#2334	C₂×C₁₃₁	1	4	yes	complemented
326	#2316	C₂×C₁₃₁	1	1	yes	characteristic, complemented
327	#2315	C₂×C₁₃₁	1	1	yes	characteristic
328	#2313	C₂×C₁₃₁	1	1	yes	characteristic, complemented
329	#2312	C₂×C₁₃₁	1	1	yes	characteristic
330	#2285	C₂×C₁₃₁	1	1	yes	characteristic, complemented
331	#2283	C₂×C₁₃₁	1	1	yes	characteristic, complemented
332	C₂×#126	C₄×C₁₃₁	1	16	yes	complemented
333	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
334	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
335	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
336	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
337	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
338	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
339	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
340	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
341	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
342	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
343	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
346	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
347	#389	C₂²×C₁₃₁	1	4	yes	complemented
348	#389	C₂²×C₁₃₁	1	4	yes	complemented
349	#389	C₂²×C₁₃₁	1	4	yes	complemented
350	#389	C₂²×C₁₃₁	1	4	yes	complemented
351	#388	C₂²×C₁₃₁	1	4	yes	—
352	#388	C₂²×C₁₃₁	1	4	yes	—
353	#388	C₂²×C₁₃₁	1	4	yes	—
354	#388	C₂²×C₁₃₁	1	4	yes	—
355	#388	C₂²×C₁₃₁	1	4	yes	—
356	#388	C₂²×C₁₃₁	1	4	yes	—
357	#387	C₂²×C₁₃₁	1	4	yes	complemented
358	#387	C₂²×C₁₃₁	1	4	yes	complemented
359	#387	C₂²×C₁₃₁	1	4	yes	complemented
360	#387	C₂²×C₁₃₁	1	4	yes	complemented
361	#387	C₂²×C₁₃₁	1	4	yes	complemented
362	#387	C₂²×C₁₃₁	1	4	yes	complemented
363	#385	C₂²×C₁₃₁	1	4	yes	—
364	#385	C₂²×C₁₃₁	1	4	yes	—
365	#385	C₂²×C₁₃₁	1	4	yes	—
366	#385	C₂²×C₁₃₁	1	4	yes	—
367	#384	C₂²×C₁₃₁	1	2	yes	complemented
368	#383	C₂²×C₁₃₁	1	2	yes	complemented
369	#382	C₂²×C₁₃₁	1	2	yes	complemented
370	#382	C₂²×C₁₃₁	1	2	yes	complemented
371	#381	C₂²×C₁₃₁	1	2	yes	—
372	#381	C₂²×C₁₃₁	1	2	yes	—
373	#380	C₂²×C₁₃₁	1	1	yes	characteristic
374	#380	C₂²×C₁₃₁	1	1	yes	characteristic
375	#380	C₂²×C₁₃₁	1	1	yes	characteristic
376	#380	C₂²×C₁₃₁	1	1	yes	characteristic
377	#380	C₂²×C₁₃₁	1	2	yes	—
378	#380	C₂²×C₁₃₁	1	2	yes	—
379	#380	C₂²×C₁₃₁	1	2	yes	—
380	#379	C₂²×C₁₃₁	1	2	yes	—
381	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
382	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
383	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
384	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
385	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
386	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
387	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
388	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
389	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
390	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
391	#376	C₂²×C₁₃₁	1	2	yes	complemented
392	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
396	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
400	#126	C₂×C₄×C₁₃₁	1	16	yes	complemented
401	#126	C₂×C₄×C₁₃₁	1	16	yes	complemented
402	#126	C₂×C₄×C₁₃₁	1	16	yes	complemented
403	#126	C₂×C₄×C₁₃₁	1	16	yes	complemented
404	#117	—	4	4	no	—
405	#117	—	4	4	no	—
406	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
407	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
408	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
409	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
424	C₂×C₂²⋊C₄	—	4	4	no	—
425	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	—
426	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	—
427	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
441	C₂×C₄²	C₂×C₄×C₁₃₁	1	8	yes	complemented
442	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
443	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
444	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
445	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
446	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
447	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
451	#95	C₂³×C₁₃₁	1	4	yes	—
452	#95	C₂³×C₁₃₁	1	2	yes	—
453	#95	C₂³×C₁₃₁	1	2	yes	—
454	#95	C₂³×C₁₃₁	1	4	yes	—
455	#95	C₂³×C₁₃₁	1	4	yes	—
456	#95	C₂³×C₁₃₁	1	4	yes	—
457	#95	C₂³×C₁₃₁	1	4	yes	—
458	#95	C₂³×C₁₃₁	1	4	yes	—
459	#95	C₂³×C₁₃₁	1	4	yes	—
460	#95	C₂³×C₁₃₁	1	2	yes	—
461	#95	C₂³×C₁₃₁	1	2	yes	—
462	#95	C₂³×C₁₃₁	1	4	yes	—
463	#95	C₂³×C₁₃₁	1	4	yes	—
464	#95	C₂³×C₁₃₁	1	4	yes	—
465	C₂⁴	—	2	2	no	—
466	C₂⁴	—	2	2	no	—
467	C₂⁴	—	4	2	no	—
468	C₂⁴	—	4	2	no	—
469	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
470	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
471	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	—	4	4	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	—	4	4	no	—
483	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
484	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
485	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
486	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
487	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
488	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
490	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
502	C₄⋊C₄	—	4	4	no	—
503	C₄⋊C₄	—	4	4	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	4	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	4	no	—
510	C₄⋊C₄	—	4	4	no	—
511	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
512	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
513	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
514	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
515	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
516	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	4	4	no	—
522	C₂²⋊C₄	—	4	4	no	—
523	C₂²⋊C₄	—	4	4	no	—
524	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
525	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
526	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
527	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
528	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
529	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
530	C₄²	—	4	4	no	—
531	C₄²	—	4	4	no	—
532	C₄²	—	4	4	no	—
533	C₄²	—	4	4	no	—
534	C₄²	—	4	4	no	—
535	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
536	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
537	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
538	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	4	4	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	8	4	no	—
549	C₂³	—	8	4	no	—
550	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
551	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
552	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
553	C₂³	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
554	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	8	8	no	—
586	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
587	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
588	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
589	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
590	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
591	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
592	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
593	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
594	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	8	8	no	—
605	C₂²	#520×C₁₃₁	1	4	yes	—
606	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
607	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
608	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
609	C₂²	#585×C₁₃₁	1	2	yes	—
610	C₂²	#585×C₁₃₁	1	2	yes	—
611	C₄	—	2	2	no	—
612	C₄	—	2	4	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	4	no	—
616	C₄	—	2	4	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	4	4	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	4	no	—
623	C₄	—	4	4	no	—
624	C₂	—	2	4	no	—
625	C₂	—	4	4	no	—
626	C₂	C₂×#520×C₁₃₁	1	1	yes	characteristic
627	C₂	#3428×C₁₃₁	1	1	yes	characteristic
628	C₂	#3428×C₁₃₁	1	1	yes	characteristic
629	C₂	#3560×C₁₃₁	1	2	yes	—
630	C₂	#3564×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂⁵×C₁₃₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2383×C₁₃₁	C₂	semidirect
3. #2373×C₁₃₁	C₂	semidirect
4. #2345×C₁₃₁	C₂	semidirect
5. #2344×C₁₃₁	C₂	semidirect
8. #2334×C₁₃₁	C₂	semidirect
9. #2334×C₁₃₁	C₂	semidirect
10. #2316×C₁₃₁	C₂	semidirect
12. #2313×C₁₃₁	C₂	semidirect
14. #2285×C₁₃₁	C₂	semidirect
15. #2283×C₁₃₁	C₂	semidirect
16. C₂×#126×C₁₃₁	C₄	semidirect
31. #389×C₁₃₁	C₂²	semidirect
32. #389×C₁₃₁	C₂²	semidirect
33. #389×C₁₃₁	C₂²	semidirect
34. #389×C₁₃₁	C₂²	semidirect
41. #387×C₁₃₁	C₂²	semidirect
42. #387×C₁₃₁	C₂²	semidirect
43. #387×C₁₃₁	C₂²	semidirect
44. #387×C₁₃₁	C₂²	semidirect
45. #387×C₁₃₁	C₂²	semidirect
46. #387×C₁₃₁	C₂²	semidirect
51. #384×C₁₃₁	C₂²	semidirect
52. #383×C₁₃₁	C₂²	semidirect
53. #382×C₁₃₁	C₂²	semidirect
54. #382×C₁₃₁	C₂²	semidirect
65. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
66. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
67. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
68. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
69. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
75. #376×C₁₃₁	C₂²	semidirect
84. #126×C₁₃₁	C₂×C₄	semidirect
85. #126×C₁₃₁	C₂×C₄	semidirect
86. #126×C₁₃₁	C₂×C₄	semidirect
87. #126×C₁₃₁	C₂×C₄	semidirect
90. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
91. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
92. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
125. C₂×C₄²×C₁₃₁	C₂×C₄	semidirect
315. #34381	C₁₃₁	direct (N × H)
316. C₁₃₁	#34381	direct (N × H)
318. #2383	C₂×C₁₃₁	semidirect
319. #2373	C₂×C₁₃₁	semidirect
320. #2345	C₂×C₁₃₁	semidirect
321. #2344	C₂×C₁₃₁	semidirect
324. #2334	C₂×C₁₃₁	semidirect
325. #2334	C₂×C₁₃₁	semidirect
326. #2316	C₂×C₁₃₁	semidirect
328. #2313	C₂×C₁₃₁	semidirect
330. #2285	C₂×C₁₃₁	semidirect
331. #2283	C₂×C₁₃₁	semidirect
332. C₂×#126	C₄×C₁₃₁	semidirect
347. #389	C₂²×C₁₃₁	semidirect
348. #389	C₂²×C₁₃₁	semidirect
349. #389	C₂²×C₁₃₁	semidirect
350. #389	C₂²×C₁₃₁	semidirect
357. #387	C₂²×C₁₃₁	semidirect
358. #387	C₂²×C₁₃₁	semidirect
359. #387	C₂²×C₁₃₁	semidirect
360. #387	C₂²×C₁₃₁	semidirect
361. #387	C₂²×C₁₃₁	semidirect
362. #387	C₂²×C₁₃₁	semidirect
367. #384	C₂²×C₁₃₁	semidirect
368. #383	C₂²×C₁₃₁	semidirect
369. #382	C₂²×C₁₃₁	semidirect
370. #382	C₂²×C₁₃₁	semidirect
381. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
382. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
383. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
384. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
385. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
391. #376	C₂²×C₁₃₁	semidirect
400. #126	C₂×C₄×C₁₃₁	semidirect
401. #126	C₂×C₄×C₁₃₁	semidirect
402. #126	C₂×C₄×C₁₃₁	semidirect
403. #126	C₂×C₄×C₁₃₁	semidirect
406. C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	semidirect
407. C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	semidirect
408. C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	semidirect
441. C₂×C₄²	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
C₂²×#126×C₁₃₁	2
#2383×C₁₃₁	2
#2373×C₁₃₁	2
#2345×C₁₃₁	2
#2344×C₁₃₁	2
#2342×C₁₃₁	2
#2334×C₁₃₁	2
#2316×C₁₃₁	2
#2315×C₁₃₁	2
#2313×C₁₃₁	2
#2312×C₁₃₁	2
#2285×C₁₃₁	2
#2283×C₁₃₁	2
#34381	131

Subgroups — C131×#34381 #45720265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34381 #45720265