Subgroups — C₁₃₁×#34205 #45720089

Order 33536.

3642 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2364×C₁₃₁	C₂	1	4	yes	maximal, complemented
4	#2361×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	#2344×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2342×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	D₄×C₂²⋊C₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2325×C₁₃₁	C₂	1	4	yes	maximal, complemented
9	#2308×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	C₄×#121×C₁₃₁	C₂	1	4	yes	maximal, complemented
11	C₂×#380×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃₁	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×#121×C₁₃₁	C₄	1	16	yes	complemented
17	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
21	#518×C₁₃₁	—	2	16	no	—
22	C₂×C₄×D₄×C₁₃₁	C₂²	1	8	yes	complemented
23	C₂×C₄×D₄×C₁₃₁	C₂²	1	8	yes	complemented
24	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	complemented
25	C₂×#117×C₁₃₁	C₂²	1	4	yes	—
26	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
31	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	complemented
34	#390×C₁₃₁	C₂²	1	4	yes	complemented
35	#389×C₁₃₁	C₂²	1	4	yes	complemented
36	#388×C₁₃₁	C₂²	1	8	yes	complemented
37	#388×C₁₃₁	C₂²	1	8	yes	complemented
38	#387×C₁₃₁	C₂²	1	8	yes	complemented
39	#386×C₁₃₁	C₂²	1	8	yes	complemented
40	#386×C₁₃₁	C₂²	1	8	yes	complemented
41	#386×C₁₃₁	C₂²	1	8	yes	complemented
42	#385×C₁₃₁	C₂²	1	8	yes	complemented
43	#381×C₁₃₁	C₂²	1	4	yes	—
44	#380×C₁₃₁	C₂²	1	2	yes	—
45	#380×C₁₃₁	C₂²	1	2	yes	—
46	#380×C₁₃₁	C₂²	1	2	yes	complemented
47	#380×C₁₃₁	C₂²	1	2	yes	complemented
48	#379×C₁₃₁	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	8	yes	complemented
55	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
56	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
57	C₂⁵×C₁₃₁	C₂³	1	2	yes	—
58	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃₁	—	2	8	no	—
60	C₂²×D₄×C₁₃₁	—	2	8	no	—
61	C₂²×D₄×C₁₃₁	—	4	4	no	—
62	C₂²×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
63	C₂²×D₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
64	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
66	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃₁	—	4	4	no	—
69	C₂³×C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
70	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃₁	C₂³	1	8	yes	—
77	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
81	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
82	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
83	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
84	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
85	C₄×D₄×C₁₃₁	—	2	32	no	—
86	C₄×D₄×C₁₃₁	—	2	32	no	—
87	C₄×D₄×C₁₃₁	—	4	8	no	—
88	#117×C₁₃₁	—	2	16	no	—
89	C₂×C₄⋊C₄×C₁₃₁	—	4	4	no	—
90	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
91	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	8	yes	—
92	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
97	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₁₃₁	—	2	16	no	—
99	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
100	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	8	yes	complemented
101	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
108	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃₁	—	4	4	no	—
113	C₂×C₄²×C₁₃₁	C₂³	1	8	yes	—
114	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
116	#95×C₁₃₁	C₂³	1	4	yes	—
117	#95×C₁₃₁	C₂³	1	4	yes	—
118	#95×C₁₃₁	C₂³	1	8	yes	—
119	#95×C₁₃₁	C₂³	1	8	yes	—
120	#95×C₁₃₁	C₂³	1	4	yes	—
121	#95×C₁₃₁	C₂³	1	4	yes	—
122	C₂⁴×C₁₃₁	—	2	4	no	—
123	C₂⁴×C₁₃₁	—	2	4	no	—
124	C₂⁴×C₁₃₁	—	4	2	no	—
125	C₂⁴×C₁₃₁	—	4	2	no	—
126	C₂⁴×C₁₃₁	—	4	4	no	—
127	C₂⁴×C₁₃₁	—	4	4	no	—
128	C₂⁴×C₁₃₁	C₂²×C₄	1	8	yes	—
129	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
130	C₂⁴×C₁₃₁	C₂×D₄	1	4	yes	—
131	C₂⁴×C₁₃₁	#41	1	4	yes	—
132	C₂⁴×C₁₃₁	C₂⁴	1	4	yes	—
133	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
134	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
135	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
136	C₂×D₄×C₁₃₁	—	2	64	no	—
137	C₂×D₄×C₁₃₁	—	2	8	no	—
138	C₂×D₄×C₁₃₁	—	2	8	no	—
139	C₂×D₄×C₁₃₁	—	2	8	no	—
140	C₂×D₄×C₁₃₁	—	2	8	no	—
141	C₂×D₄×C₁₃₁	—	2	8	no	—
142	C₂×D₄×C₁₃₁	—	4	16	no	—
143	C₂×D₄×C₁₃₁	—	4	4	no	—
144	C₂×D₄×C₁₃₁	C₂²×C₄	1	16	yes	—
145	C₂×D₄×C₁₃₁	C₂²×C₄	1	16	yes	—
146	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
147	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
148	C₂²×C₄×C₁₃₁	—	2	4	no	—
149	C₂²×C₄×C₁₃₁	—	2	4	no	—
150	C₂²×C₄×C₁₃₁	—	2	4	no	—
151	C₂²×C₄×C₁₃₁	—	2	4	no	—
152	C₂²×C₄×C₁₃₁	—	2	4	no	—
153	C₂²×C₄×C₁₃₁	—	2	4	no	—
154	C₂²×C₄×C₁₃₁	—	2	8	no	—
155	C₂²×C₄×C₁₃₁	—	2	16	no	—
156	C₂²×C₄×C₁₃₁	—	4	16	no	—
157	C₂²×C₄×C₁₃₁	—	4	2	no	—
158	C₂²×C₄×C₁₃₁	—	4	2	no	—
159	C₂²×C₄×C₁₃₁	—	4	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	8	no	—
166	C₂²×C₄×C₁₃₁	—	4	8	no	—
167	C₂²×C₄×C₁₃₁	—	4	4	no	—
168	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	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	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₃₁	C₂×D₄	1	8	yes	complemented
176	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃₁	C₂⁴	1	8	yes	—
178	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
184	C₄⋊C₄×C₁₃₁	—	2	16	no	—
185	C₄⋊C₄×C₁₃₁	—	2	8	no	—
186	C₄⋊C₄×C₁₃₁	—	4	4	no	—
187	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
188	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
189	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
190	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
191	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
192	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
193	C₂²⋊C₄×C₁₃₁	—	2	16	no	—
194	C₂²⋊C₄×C₁₃₁	—	4	8	no	—
195	C₂²⋊C₄×C₁₃₁	—	4	8	no	—
196	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
197	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
198	C₂²⋊C₄×C₁₃₁	C₂×D₄	1	8	yes	—
199	C₂²⋊C₄×C₁₃₁	C₂×D₄	1	8	yes	complemented
200	C₄²×C₁₃₁	—	2	16	no	—
201	C₄²×C₁₃₁	—	2	8	no	—
202	C₄²×C₁₃₁	—	4	4	no	—
203	C₂³×C₁₃₁	—	2	2	no	—
204	C₂³×C₁₃₁	—	2	2	no	—
205	C₂³×C₁₃₁	—	2	2	no	—
206	C₂³×C₁₃₁	—	2	2	no	—
207	C₂³×C₁₃₁	—	2	2	no	—
208	C₂³×C₁₃₁	—	2	2	no	—
209	C₂³×C₁₃₁	—	2	4	no	—
210	C₂³×C₁₃₁	—	2	4	no	—
211	C₂³×C₁₃₁	—	2	8	no	—
212	C₂³×C₁₃₁	—	2	8	no	—
213	C₂³×C₁₃₁	—	2	16	no	—
214	C₂³×C₁₃₁	—	4	4	no	—
215	C₂³×C₁₃₁	—	4	4	no	—
216	C₂³×C₁₃₁	—	4	8	no	—
217	C₂³×C₁₃₁	—	4	8	no	—
218	C₂³×C₁₃₁	—	4	8	no	—
219	C₂³×C₁₃₁	—	4	8	no	—
220	C₂³×C₁₃₁	—	8	8	no	—
221	C₂³×C₁₃₁	—	8	8	no	—
222	C₂³×C₁₃₁	C₄×D₄	1	16	yes	complemented
223	C₂³×C₁₃₁	C₂³×C₄	1	8	yes	—
224	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
225	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
226	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
227	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
228	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
229	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
230	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
231	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
232	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
233	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
234	D₄×C₁₃₁	—	2	32	no	—
235	D₄×C₁₃₁	—	2	32	no	—
236	D₄×C₁₃₁	—	2	16	no	—
237	D₄×C₁₃₁	—	4	8	no	—
238	C₂×C₄×C₁₃₁	—	2	16	no	—
239	C₂×C₄×C₁₃₁	—	2	4	no	—
240	C₂×C₄×C₁₃₁	—	2	4	no	—
241	C₂×C₄×C₁₃₁	—	2	4	no	—
242	C₂×C₄×C₁₃₁	—	2	2	no	—
243	C₂×C₄×C₁₃₁	—	2	2	no	—
244	C₂×C₄×C₁₃₁	—	2	2	no	—
245	C₂×C₄×C₁₃₁	—	2	4	no	—
246	C₂×C₄×C₁₃₁	—	2	8	no	—
247	C₂×C₄×C₁₃₁	—	2	8	no	—
248	C₂×C₄×C₁₃₁	—	2	8	no	—
249	C₂×C₄×C₁₃₁	—	2	8	no	—
250	C₂×C₄×C₁₃₁	—	2	4	no	—
251	C₂×C₄×C₁₃₁	—	2	4	no	—
252	C₂×C₄×C₁₃₁	—	2	8	no	—
253	C₂×C₄×C₁₃₁	—	2	4	no	—
254	C₂×C₄×C₁₃₁	—	2	8	no	—
255	C₂×C₄×C₁₃₁	—	4	4	no	—
256	C₂×C₄×C₁₃₁	—	4	4	no	—
257	C₂×C₄×C₁₃₁	—	4	4	no	—
258	C₂×C₄×C₁₃₁	—	4	8	no	—
259	C₂×C₄×C₁₃₁	—	4	8	no	—
260	C₂×C₄×C₁₃₁	—	8	16	no	—
261	C₂×C₄×C₁₃₁	—	8	8	no	—
262	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
263	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
264	C₂×C₄×C₁₃₁	C₂³×C₄	1	8	yes	—
265	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
266	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
267	C₂×C₄×C₁₃₁	C₂²×D₄	1	8	yes	—
268	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
269	C₂²×C₁₃₁	—	2	2	no	—
270	C₂²×C₁₃₁	—	2	2	no	—
271	C₂²×C₁₃₁	—	2	2	no	—
272	C₂²×C₁₃₁	—	2	2	no	—
273	C₂²×C₁₃₁	—	2	2	no	—
274	C₂²×C₁₃₁	—	2	2	no	—
275	C₂²×C₁₃₁	—	2	4	no	—
276	C₂²×C₁₃₁	—	2	4	no	—
277	C₂²×C₁₃₁	—	2	4	no	—
278	C₂²×C₁₃₁	—	2	4	no	—
279	C₂²×C₁₃₁	—	2	4	no	—
280	C₂²×C₁₃₁	—	2	4	no	—
281	C₂²×C₁₃₁	—	2	8	no	—
282	C₂²×C₁₃₁	—	2	8	no	—
283	C₂²×C₁₃₁	—	2	8	no	—
284	C₂²×C₁₃₁	—	4	16	no	—
285	C₂²×C₁₃₁	—	4	8	no	—
286	C₂²×C₁₃₁	—	4	8	no	—
287	C₂²×C₁₃₁	—	8	16	no	—
288	C₂²×C₁₃₁	C₂×C₄×D₄	1	4	yes	—
289	C₂²×C₁₃₁	C₂×C₄×D₄	1	4	yes	—
290	C₂²×C₁₃₁	C₂×C₄×D₄	1	4	yes	—
291	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
292	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
293	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
294	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
295	C₂²×C₁₃₁	#585	1	2	yes	—
296	C₄×C₁₃₁	—	2	8	no	—
297	C₄×C₁₃₁	—	2	2	no	—
298	C₄×C₁₃₁	—	2	2	no	—
299	C₄×C₁₃₁	—	2	2	no	—
300	C₄×C₁₃₁	—	2	8	no	—
301	C₄×C₁₃₁	—	4	8	no	—
302	C₄×C₁₃₁	—	4	4	no	—
303	C₄×C₁₃₁	#518	1	4	yes	complemented
304	C₂×C₁₃₁	—	2	4	no	—
305	C₂×C₁₃₁	—	2	4	no	—
306	C₂×C₁₃₁	—	2	4	no	—
307	C₂×C₁₃₁	—	4	8	no	—
308	C₂×C₁₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
309	C₂×C₁₃₁	C₂×#518	1	1	yes	characteristic
310	C₂×C₁₃₁	#3428	1	1	yes	characteristic
311	C₂×C₁₃₁	#3496	1	2	yes	—
312	C₂×C₁₃₁	#3505	1	2	yes	—
313	#34205	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₁₃₁	#34205	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²×#121	C₂×C₁₃₁	1	1	yes	characteristic
316	C₂×#518	C₂×C₁₃₁	1	2	yes	complemented
317	#2364	C₂×C₁₃₁	1	4	yes	complemented
318	#2361	C₂×C₁₃₁	1	4	yes	complemented
319	#2344	C₂×C₁₃₁	1	2	yes	complemented
320	#2342	C₂×C₁₃₁	1	4	yes	complemented
321	D₄×C₂²⋊C₄	C₂×C₁₃₁	1	2	yes	complemented
322	#2325	C₂×C₁₃₁	1	4	yes	complemented
323	#2308	C₂×C₁₃₁	1	2	yes	complemented
324	C₄×#121	C₂×C₁₃₁	1	4	yes	complemented
325	C₂×#380	C₂×C₁₃₁	1	1	yes	characteristic, complemented
326	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
327	C₂³×D₄	C₂²×C₁₃₁	1	2	yes	—
328	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
329	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
330	C₂×#121	C₄×C₁₃₁	1	16	yes	complemented
331	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
332	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
333	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
334	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
335	#518	—	2	16	no	—
336	C₂×C₄×D₄	C₂²×C₁₃₁	1	8	yes	complemented
337	C₂×C₄×D₄	C₂²×C₁₃₁	1	8	yes	complemented
338	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	complemented
339	C₂×#117	C₂²×C₁₃₁	1	4	yes	—
340	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
341	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
342	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
343	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
344	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
345	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
346	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
347	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	complemented
348	#390	C₂²×C₁₃₁	1	4	yes	complemented
349	#389	C₂²×C₁₃₁	1	4	yes	complemented
350	#388	C₂²×C₁₃₁	1	8	yes	complemented
351	#388	C₂²×C₁₃₁	1	8	yes	complemented
352	#387	C₂²×C₁₃₁	1	8	yes	complemented
353	#386	C₂²×C₁₃₁	1	8	yes	complemented
354	#386	C₂²×C₁₃₁	1	8	yes	complemented
355	#386	C₂²×C₁₃₁	1	8	yes	complemented
356	#385	C₂²×C₁₃₁	1	8	yes	complemented
357	#381	C₂²×C₁₃₁	1	4	yes	—
358	#380	C₂²×C₁₃₁	1	2	yes	—
359	#380	C₂²×C₁₃₁	1	2	yes	—
360	#380	C₂²×C₁₃₁	1	2	yes	complemented
361	#380	C₂²×C₁₃₁	1	2	yes	complemented
362	#379	C₂²×C₁₃₁	1	4	yes	—
363	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
364	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
365	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
366	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	8	yes	complemented
367	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
368	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
369	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
370	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
371	C₂⁵	C₂³×C₁₃₁	1	2	yes	—
372	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
373	C₂²×D₄	—	2	8	no	—
374	C₂²×D₄	—	2	8	no	—
375	C₂²×D₄	—	4	4	no	—
376	C₂²×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
377	C₂²×D₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
378	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
379	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
380	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
381	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
382	C₂³×C₄	—	4	4	no	—
383	C₂³×C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
384	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
385	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
389	C₂³×C₄	C₂³×C₁₃₁	1	8	yes	—
390	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
391	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
395	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
396	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
397	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
398	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
399	C₄×D₄	—	2	32	no	—
400	C₄×D₄	—	2	32	no	—
401	C₄×D₄	—	4	8	no	—
402	#117	—	2	16	no	—
403	C₂×C₄⋊C₄	—	4	4	no	—
404	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
405	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	8	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
410	C₂×C₂²⋊C₄	—	2	8	no	—
411	C₂×C₂²⋊C₄	—	2	4	no	—
412	C₂×C₂²⋊C₄	—	2	16	no	—
413	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
414	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	8	yes	complemented
415	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
426	C₂×C₄²	—	4	4	no	—
427	C₂×C₄²	C₂³×C₁₃₁	1	8	yes	—
428	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
429	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
430	#95	C₂³×C₁₃₁	1	4	yes	—
431	#95	C₂³×C₁₃₁	1	4	yes	—
432	#95	C₂³×C₁₃₁	1	4	yes	—
433	#95	C₂³×C₁₃₁	1	4	yes	—
434	#95	C₂³×C₁₃₁	1	8	yes	—
435	#95	C₂³×C₁₃₁	1	8	yes	—
436	C₂⁴	—	2	4	no	—
437	C₂⁴	—	2	4	no	—
438	C₂⁴	—	4	2	no	—
439	C₂⁴	—	4	2	no	—
440	C₂⁴	—	4	4	no	—
441	C₂⁴	—	4	4	no	—
442	C₂⁴	C₂²×C₄×C₁₃₁	1	8	yes	—
443	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
444	C₂⁴	C₂×D₄×C₁₃₁	1	4	yes	—
445	C₂⁴	#41×C₁₃₁	1	4	yes	—
446	C₂⁴	C₂⁴×C₁₃₁	1	4	yes	—
447	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
448	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
449	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
450	C₂×D₄	—	2	64	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	4	16	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	C₂²×C₄×C₁₃₁	1	16	yes	—
459	C₂×D₄	C₂²×C₄×C₁₃₁	1	16	yes	—
460	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
461	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	2	16	no	—
470	C₂²×C₄	—	4	16	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	8	no	—
480	C₂²×C₄	—	4	8	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
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	C₂×D₄×C₁₃₁	1	8	yes	complemented
490	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₁₃₁	1	8	yes	—
492	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
498	C₄⋊C₄	—	2	16	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	4	4	no	—
501	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
502	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	2	8	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	16	no	—
508	C₂²⋊C₄	—	4	8	no	—
509	C₂²⋊C₄	—	4	8	no	—
510	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
511	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
512	C₂²⋊C₄	C₂×D₄×C₁₃₁	1	8	yes	—
513	C₂²⋊C₄	C₂×D₄×C₁₃₁	1	8	yes	complemented
514	C₄²	—	2	16	no	—
515	C₄²	—	2	8	no	—
516	C₄²	—	4	4	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	8	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	16	no	—
528	C₂³	—	4	4	no	—
529	C₂³	—	4	4	no	—
530	C₂³	—	4	8	no	—
531	C₂³	—	4	8	no	—
532	C₂³	—	4	8	no	—
533	C₂³	—	4	8	no	—
534	C₂³	—	8	8	no	—
535	C₂³	—	8	8	no	—
536	C₂³	C₄×D₄×C₁₃₁	1	16	yes	complemented
537	C₂³	C₂³×C₄×C₁₃₁	1	8	yes	—
538	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
539	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
540	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
541	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
542	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
543	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
544	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
545	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
546	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
547	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
548	D₄	—	2	32	no	—
549	D₄	—	2	32	no	—
550	D₄	—	2	16	no	—
551	D₄	—	4	8	no	—
552	C₂×C₄	—	2	16	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	8	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	—	8	16	no	—
575	C₂×C₄	—	8	8	no	—
576	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
577	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
578	C₂×C₄	C₂³×C₄×C₁₃₁	1	8	yes	—
579	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
580	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
581	C₂×C₄	C₂²×D₄×C₁₃₁	1	8	yes	—
582	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
583	C₂²	—	2	4	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	2	4	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	8	no	—
596	C₂²	—	2	8	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	4	16	no	—
599	C₂²	—	4	8	no	—
600	C₂²	—	4	8	no	—
601	C₂²	—	8	16	no	—
602	C₂²	C₂×C₄×D₄×C₁₃₁	1	4	yes	—
603	C₂²	C₂×C₄×D₄×C₁₃₁	1	4	yes	—
604	C₂²	C₂×C₄×D₄×C₁₃₁	1	4	yes	—
605	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
606	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
607	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
608	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
609	C₂²	#585×C₁₃₁	1	2	yes	—
610	C₄	—	2	8	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	8	no	—
615	C₄	—	4	4	no	—
616	C₄	—	4	8	no	—
617	C₄	#518×C₁₃₁	1	4	yes	complemented
618	C₂	—	2	4	no	—
619	C₂	—	2	4	no	—
620	C₂	—	2	4	no	—
621	C₂	—	4	8	no	—
622	C₂	C₂²×C₄×D₄×C₁₃₁	1	1	yes	characteristic
623	C₂	C₂×#518×C₁₃₁	1	1	yes	characteristic
624	C₂	#3428×C₁₃₁	1	1	yes	characteristic
625	C₂	#3496×C₁₃₁	1	2	yes	—
626	C₂	#3505×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂²×#121×C₁₃₁	C₂
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. C₂×#518×C₁₃₁	C₂	semidirect
3. #2364×C₁₃₁	C₂	semidirect
4. #2361×C₁₃₁	C₂	semidirect
5. #2344×C₁₃₁	C₂	semidirect
6. #2342×C₁₃₁	C₂	semidirect
7. D₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
8. #2325×C₁₃₁	C₂	semidirect
9. #2308×C₁₃₁	C₂	semidirect
10. C₄×#121×C₁₃₁	C₂	semidirect
11. C₂×#380×C₁₃₁	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
16. C₂×#121×C₁₃₁	C₄	semidirect
22. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
23. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
24. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
27. C₂²×C₄⋊C₄×C₁₃₁	C₂²	semidirect
33. C₂²×C₄²×C₁₃₁	C₂²	semidirect
34. #390×C₁₃₁	C₂²	semidirect
35. #389×C₁₃₁	C₂²	semidirect
36. #388×C₁₃₁	C₂²	semidirect
37. #388×C₁₃₁	C₂²	semidirect
38. #387×C₁₃₁	C₂²	semidirect
39. #386×C₁₃₁	C₂²	semidirect
40. #386×C₁₃₁	C₂²	semidirect
41. #386×C₁₃₁	C₂²	semidirect
42. #385×C₁₃₁	C₂²	semidirect
46. #380×C₁₃₁	C₂²	semidirect
47. #380×C₁₃₁	C₂²	semidirect
49. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
52. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
53. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
54. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
55. C₂×#95×C₁₃₁	C₂²	semidirect
56. C₂×#95×C₁₃₁	C₂²	semidirect
62. C₂²×D₄×C₁₃₁	C₂×C₄	semidirect
63. C₂²×D₄×C₁₃₁	C₂×C₄	semidirect
69. C₂³×C₄×C₁₃₁	C₂×C₄	semidirect
81. #121×C₁₃₁	C₂×C₄	semidirect
82. #121×C₁₃₁	C₂×C₄	semidirect
83. #121×C₁₃₁	C₂×C₄	semidirect
84. #121×C₁₃₁	C₂×C₄	semidirect
90. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
99. C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	semidirect
100. C₂×C₂²⋊C₄×C₁₃₁	D₄	semidirect
175. C₂²×C₄×C₁₃₁	C₂×D₄	semidirect
199. C₂²⋊C₄×C₁₃₁	C₂×D₄	semidirect
222. C₂³×C₁₃₁	C₄×D₄	semidirect
303. C₄×C₁₃₁	#518	semidirect
313. #34205	C₁₃₁	direct (N × H)
314. C₁₃₁	#34205	direct (N × H)
316. C₂×#518	C₂×C₁₃₁	semidirect
317. #2364	C₂×C₁₃₁	semidirect
318. #2361	C₂×C₁₃₁	semidirect
319. #2344	C₂×C₁₃₁	semidirect
320. #2342	C₂×C₁₃₁	semidirect
321. D₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
322. #2325	C₂×C₁₃₁	semidirect
323. #2308	C₂×C₁₃₁	semidirect
324. C₄×#121	C₂×C₁₃₁	semidirect
325. C₂×#380	C₂×C₁₃₁	semidirect
326. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
330. C₂×#121	C₄×C₁₃₁	semidirect
336. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
337. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
338. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
341. C₂²×C₄⋊C₄	C₂²×C₁₃₁	semidirect
347. C₂²×C₄²	C₂²×C₁₃₁	semidirect
348. #390	C₂²×C₁₃₁	semidirect
349. #389	C₂²×C₁₃₁	semidirect
350. #388	C₂²×C₁₃₁	semidirect
351. #388	C₂²×C₁₃₁	semidirect
352. #387	C₂²×C₁₃₁	semidirect
353. #386	C₂²×C₁₃₁	semidirect
354. #386	C₂²×C₁₃₁	semidirect
355. #386	C₂²×C₁₃₁	semidirect
356. #385	C₂²×C₁₃₁	semidirect
360. #380	C₂²×C₁₃₁	semidirect
361. #380	C₂²×C₁₃₁	semidirect
363. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
366. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
367. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
368. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
369. C₂×#95	C₂²×C₁₃₁	semidirect
370. C₂×#95	C₂²×C₁₃₁	semidirect
376. C₂²×D₄	C₂×C₄×C₁₃₁	semidirect
377. C₂²×D₄	C₂×C₄×C₁₃₁	semidirect
383. C₂³×C₄	C₂×C₄×C₁₃₁	semidirect
395. #121	C₂×C₄×C₁₃₁	semidirect
396. #121	C₂×C₄×C₁₃₁	semidirect
397. #121	C₂×C₄×C₁₃₁	semidirect
398. #121	C₂×C₄×C₁₃₁	semidirect
404. C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	semidirect
413. C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	semidirect
414. C₂×C₂²⋊C₄	D₄×C₁₃₁	semidirect
489. C₂²×C₄	C₂×D₄×C₁₃₁	semidirect
513. C₂²⋊C₄	C₂×D₄×C₁₃₁	semidirect
536. C₂³	C₄×D₄×C₁₃₁	semidirect
617. C₄	#518×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₁₃₁	2
C₂×#518×C₁₃₁	2
#2364×C₁₃₁	2
#2361×C₁₃₁	2
#2344×C₁₃₁	2
#2342×C₁₃₁	2
D₄×C₂²⋊C₄×C₁₃₁	2
#2325×C₁₃₁	2
#2308×C₁₃₁	2
C₄×#121×C₁₃₁	2
C₂×#380×C₁₃₁	2
C₂×C₄×C₂²⋊C₄×C₁₃₁	2
#34205	131

Subgroups — C131×#34205 #45720089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34205 #45720089