Subgroups — C₁₃₁×#35093 #45720977

Order 33536.

2434 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2854×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2849×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2627×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2622×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2618×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2478×C₁₃₁	C₂	1	4	yes	maximal, complemented
10	#2476×C₁₃₁	C₂	1	4	yes	maximal, complemented
11	#2474×C₁₃₁	C₂	1	4	yes	maximal, complemented
12	#2470×C₁₃₁	C₂	1	4	yes	maximal, complemented
13	#2322×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	#2312×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#123×C₁₃₁	C₂	1	2	yes	maximal, complemented
16	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
17	#538×C₁₃₁	—	2	8	no	—
18	C₂×#126×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#117×C₁₃₁	—	2	8	no	—
29	C₂×#117×C₁₃₁	C₂²	1	4	yes	—
30	C₂×#117×C₁₃₁	C₂²	1	4	yes	—
31	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
37	#400×C₁₃₁	C₂²	1	2	yes	complemented
38	#398×C₁₃₁	C₂²	1	4	yes	complemented
39	#398×C₁₃₁	C₂²	1	2	yes	complemented
40	#397×C₁₃₁	C₂²	1	4	yes	—
41	#397×C₁₃₁	C₂²	1	4	yes	—
42	#396×C₁₃₁	C₂²	1	4	yes	complemented
43	#395×C₁₃₁	C₂²	1	2	yes	complemented
44	#394×C₁₃₁	C₂²	1	4	yes	—
45	#394×C₁₃₁	C₂²	1	4	yes	—
46	#394×C₁₃₁	C₂²	1	2	yes	complemented
47	#391×C₁₃₁	C₂²	1	2	yes	complemented
48	#390×C₁₃₁	C₂²	1	2	yes	complemented
49	#389×C₁₃₁	C₂²	1	2	yes	complemented
50	#389×C₁₃₁	C₂²	1	4	yes	complemented
51	#389×C₁₃₁	C₂²	1	2	yes	complemented
52	#388×C₁₃₁	C₂²	1	4	yes	—
53	#388×C₁₃₁	C₂²	1	4	yes	—
54	#388×C₁₃₁	C₂²	1	4	yes	complemented
55	#388×C₁₃₁	C₂²	1	4	yes	complemented
56	#388×C₁₃₁	C₂²	1	4	yes	complemented
57	#387×C₁₃₁	C₂²	1	4	yes	complemented
58	#387×C₁₃₁	C₂²	1	4	yes	complemented
59	#387×C₁₃₁	C₂²	1	4	yes	complemented
60	#386×C₁₃₁	C₂²	1	4	yes	—
61	#386×C₁₃₁	C₂²	1	4	yes	—
62	#386×C₁₃₁	C₂²	1	2	yes	—
63	#386×C₁₃₁	C₂²	1	2	yes	—
64	#385×C₁₃₁	C₂²	1	4	yes	—
65	#385×C₁₃₁	C₂²	1	4	yes	—
66	#385×C₁₃₁	C₂²	1	2	yes	—
67	#385×C₁₃₁	C₂²	1	2	yes	—
68	#385×C₁₃₁	C₂²	1	4	yes	complemented
69	#381×C₁₃₁	C₂²	1	2	yes	—
70	#381×C₁₃₁	C₂²	1	2	yes	—
71	#380×C₁₃₁	C₂²	1	1	yes	characteristic
72	#380×C₁₃₁	C₂²	1	1	yes	characteristic
73	#379×C₁₃₁	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
77	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃₁	—	2	4	no	—
84	C₂³×C₄×C₁₃₁	—	2	4	no	—
85	C₂³×C₄×C₁₃₁	—	2	4	no	—
86	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
87	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
94	#126×C₁₃₁	—	2	8	no	—
95	#124×C₁₃₁	—	2	8	no	—
96	#123×C₁₃₁	—	2	8	no	—
97	#123×C₁₃₁	—	2	8	no	—
98	#123×C₁₃₁	—	2	8	no	—
99	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
100	#121×C₁₃₁	—	2	4	no	—
101	#121×C₁₃₁	—	2	8	no	—
102	#120×C₁₃₁	—	2	8	no	—
103	C₄×D₄×C₁₃₁	—	2	8	no	—
104	#117×C₁₃₁	—	2	16	no	—
105	#117×C₁₃₁	—	2	16	no	—
106	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
107	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
108	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	8	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃₁	—	2	4	no	—
140	C₂×C₄²×C₁₃₁	—	2	4	no	—
141	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
146	#95×C₁₃₁	C₂³	1	2	yes	—
147	#95×C₁₃₁	C₂³	1	4	yes	—
148	#95×C₁₃₁	C₂³	1	2	yes	—
149	#95×C₁₃₁	C₂³	1	4	yes	—
150	#95×C₁₃₁	C₂³	1	4	yes	—
151	#95×C₁₃₁	C₂³	1	4	yes	—
152	#95×C₁₃₁	C₂³	1	4	yes	—
153	#95×C₁₃₁	C₂³	1	4	yes	—
154	#95×C₁₃₁	C₂³	1	4	yes	—
155	#95×C₁₃₁	C₂³	1	4	yes	—
156	#95×C₁₃₁	C₂³	1	4	yes	—
157	C₂⁴×C₁₃₁	—	2	2	no	—
158	C₂⁴×C₁₃₁	—	2	2	no	—
159	C₂⁴×C₁₃₁	—	4	2	no	—
160	C₂⁴×C₁₃₁	—	4	2	no	—
161	C₂⁴×C₁₃₁	C₂×D₄	1	4	yes	—
162	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
163	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
164	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
165	C₂×Q₈×C₁₃₁	—	2	2	no	—
166	C₂×Q₈×C₁₃₁	—	4	2	no	—
167	C₂×D₄×C₁₃₁	—	2	4	no	—
168	C₂×D₄×C₁₃₁	—	2	4	no	—
169	C₂×D₄×C₁₃₁	—	2	4	no	—
170	C₂×D₄×C₁₃₁	—	2	4	no	—
171	C₂×D₄×C₁₃₁	—	2	4	no	—
172	C₂×D₄×C₁₃₁	—	2	2	no	—
173	C₂×D₄×C₁₃₁	—	4	2	no	—
174	C₂×D₄×C₁₃₁	—	4	4	no	—
175	C₂×D₄×C₁₃₁	—	4	4	no	—
176	C₂²×C₄×C₁₃₁	—	2	32	no	—
177	C₂²×C₄×C₁₃₁	—	2	2	no	—
178	C₂²×C₄×C₁₃₁	—	2	2	no	—
179	C₂²×C₄×C₁₃₁	—	2	8	no	—
180	C₂²×C₄×C₁₃₁	—	2	2	no	—
181	C₂²×C₄×C₁₃₁	—	2	2	no	—
182	C₂²×C₄×C₁₃₁	—	2	8	no	—
183	C₂²×C₄×C₁₃₁	—	2	8	no	—
184	C₂²×C₄×C₁₃₁	—	2	2	no	—
185	C₂²×C₄×C₁₃₁	—	2	2	no	—
186	C₂²×C₄×C₁₃₁	—	2	4	no	—
187	C₂²×C₄×C₁₃₁	—	4	2	no	—
188	C₂²×C₄×C₁₃₁	—	4	2	no	—
189	C₂²×C₄×C₁₃₁	—	4	2	no	—
190	C₂²×C₄×C₁₃₁	—	4	2	no	—
191	C₂²×C₄×C₁₃₁	—	4	4	no	—
192	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
193	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
195	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
196	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
208	C₄⋊C₄×C₁₃₁	—	2	8	no	—
209	C₄⋊C₄×C₁₃₁	—	2	4	no	—
210	C₄⋊C₄×C₁₃₁	—	2	4	no	—
211	C₄⋊C₄×C₁₃₁	—	2	4	no	—
212	C₄⋊C₄×C₁₃₁	—	2	4	no	—
213	C₄⋊C₄×C₁₃₁	—	2	2	no	—
214	C₄⋊C₄×C₁₃₁	—	2	2	no	—
215	C₄⋊C₄×C₁₃₁	—	2	8	no	—
216	C₄⋊C₄×C₁₃₁	—	2	8	no	—
217	C₄⋊C₄×C₁₃₁	—	4	2	no	—
218	C₄⋊C₄×C₁₃₁	—	4	2	no	—
219	C₄⋊C₄×C₁₃₁	—	4	4	no	—
220	C₄⋊C₄×C₁₃₁	—	4	4	no	—
221	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
222	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
223	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
224	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
225	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
226	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
227	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
228	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
229	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
230	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
231	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
232	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
233	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
234	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
235	C₂²⋊C₄×C₁₃₁	C₂×D₄	1	8	yes	—
236	C₂²⋊C₄×C₁₃₁	C₂×D₄	1	8	yes	—
237	C₄²×C₁₃₁	—	2	8	no	—
238	C₄²×C₁₃₁	—	2	4	no	—
239	C₄²×C₁₃₁	—	2	4	no	—
240	C₄²×C₁₃₁	—	2	4	no	—
241	C₄²×C₁₃₁	—	4	4	no	—
242	C₂³×C₁₃₁	—	2	2	no	—
243	C₂³×C₁₃₁	—	2	2	no	—
244	C₂³×C₁₃₁	—	2	8	no	—
245	C₂³×C₁₃₁	—	2	2	no	—
246	C₂³×C₁₃₁	—	2	2	no	—
247	C₂³×C₁₃₁	—	2	4	no	—
248	C₂³×C₁₃₁	—	2	4	no	—
249	C₂³×C₁₃₁	—	2	2	no	—
250	C₂³×C₁₃₁	—	2	2	no	—
251	C₂³×C₁₃₁	—	2	2	no	—
252	C₂³×C₁₃₁	—	2	4	no	—
253	C₂³×C₁₃₁	—	2	4	no	—
254	C₂³×C₁₃₁	—	4	4	no	—
255	C₂³×C₁₃₁	—	4	4	no	—
256	C₂³×C₁₃₁	—	4	8	no	—
257	C₂³×C₁₃₁	—	4	8	no	—
258	C₂³×C₁₃₁	C₂²×D₄	1	4	yes	—
259	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
260	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
261	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
262	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
263	Q₈×C₁₃₁	—	8	2	no	—
264	D₄×C₁₃₁	—	4	8	no	—
265	D₄×C₁₃₁	—	8	2	no	—
266	D₄×C₁₃₁	—	8	4	no	—
267	D₄×C₁₃₁	—	8	4	no	—
268	C₂×C₄×C₁₃₁	—	2	32	no	—
269	C₂×C₄×C₁₃₁	—	2	8	no	—
270	C₂×C₄×C₁₃₁	—	2	8	no	—
271	C₂×C₄×C₁₃₁	—	2	2	no	—
272	C₂×C₄×C₁₃₁	—	2	2	no	—
273	C₂×C₄×C₁₃₁	—	2	2	no	—
274	C₂×C₄×C₁₃₁	—	2	2	no	—
275	C₂×C₄×C₁₃₁	—	2	4	no	—
276	C₂×C₄×C₁₃₁	—	2	2	no	—
277	C₂×C₄×C₁₃₁	—	2	2	no	—
278	C₂×C₄×C₁₃₁	—	2	2	no	—
279	C₂×C₄×C₁₃₁	—	2	2	no	—
280	C₂×C₄×C₁₃₁	—	2	2	no	—
281	C₂×C₄×C₁₃₁	—	2	2	no	—
282	C₂×C₄×C₁₃₁	—	2	2	no	—
283	C₂×C₄×C₁₃₁	—	2	4	no	—
284	C₂×C₄×C₁₃₁	—	2	4	no	—
285	C₂×C₄×C₁₃₁	—	2	2	no	—
286	C₂×C₄×C₁₃₁	—	2	2	no	—
287	C₂×C₄×C₁₃₁	—	2	4	no	—
288	C₂×C₄×C₁₃₁	—	2	4	no	—
289	C₂×C₄×C₁₃₁	—	2	4	no	—
290	C₂×C₄×C₁₃₁	—	2	2	no	—
291	C₂×C₄×C₁₃₁	—	2	4	no	—
292	C₂×C₄×C₁₃₁	—	2	4	no	—
293	C₂×C₄×C₁₃₁	—	2	2	no	—
294	C₂×C₄×C₁₃₁	—	2	4	no	—
295	C₂×C₄×C₁₃₁	—	2	4	no	—
296	C₂×C₄×C₁₃₁	—	4	4	no	—
297	C₂×C₄×C₁₃₁	—	4	4	no	—
298	C₂×C₄×C₁₃₁	—	4	4	no	—
299	C₂×C₄×C₁₃₁	—	4	4	no	—
300	C₂×C₄×C₁₃₁	—	8	4	no	—
301	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
305	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
306	C₂²×C₁₃₁	—	2	4	no	—
307	C₂²×C₁₃₁	—	2	2	no	—
308	C₂²×C₁₃₁	—	2	2	no	—
309	C₂²×C₁₃₁	—	2	4	no	—
310	C₂²×C₁₃₁	—	2	4	no	—
311	C₂²×C₁₃₁	—	2	4	no	—
312	C₂²×C₁₃₁	—	2	4	no	—
313	C₂²×C₁₃₁	—	4	16	no	—
314	C₂²×C₁₃₁	—	4	4	no	—
315	C₂²×C₁₃₁	—	4	4	no	—
316	C₂²×C₁₃₁	—	4	2	no	—
317	C₂²×C₁₃₁	—	4	4	no	—
318	C₂²×C₁₃₁	—	4	2	no	—
319	C₂²×C₁₃₁	—	4	2	no	—
320	C₂²×C₁₃₁	—	4	4	no	—
321	C₂²×C₁₃₁	#525	1	4	yes	—
322	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
323	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
324	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
325	C₂²×C₁₃₁	#585	1	2	yes	—
326	C₂²×C₁₃₁	#585	1	2	yes	—
327	C₄×C₁₃₁	—	2	4	no	—
328	C₄×C₁₃₁	—	2	4	no	—
329	C₄×C₁₃₁	—	2	4	no	—
330	C₄×C₁₃₁	—	2	2	no	—
331	C₄×C₁₃₁	—	2	2	no	—
332	C₄×C₁₃₁	—	4	2	no	—
333	C₄×C₁₃₁	—	4	4	no	—
334	C₄×C₁₃₁	—	4	2	no	—
335	C₄×C₁₃₁	—	4	2	no	—
336	C₄×C₁₃₁	—	4	2	no	—
337	C₄×C₁₃₁	—	4	2	no	—
338	C₄×C₁₃₁	—	4	4	no	—
339	C₂×C₁₃₁	—	2	4	no	—
340	C₂×C₁₃₁	—	4	4	no	—
341	C₂×C₁₃₁	—	8	2	no	—
342	C₂×C₁₃₁	C₂×#525	1	1	yes	characteristic
343	C₂×C₁₃₁	#3455	1	2	yes	—
344	C₂×C₁₃₁	#3485	1	1	yes	characteristic
345	C₂×C₁₃₁	#3485	1	1	yes	characteristic
346	C₂×C₁₃₁	#3493	1	2	yes	—
347	#35093	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₁₃₁	#35093	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×#538	C₂×C₁₃₁	1	1	yes	characteristic
350	C₂²×#117	C₂×C₁₃₁	1	1	yes	characteristic, complemented
351	#2855	C₂×C₁₃₁	1	1	yes	characteristic, complemented
352	#2854	C₂×C₁₃₁	1	1	yes	characteristic, complemented
353	#2849	C₂×C₁₃₁	1	2	yes	complemented
354	#2627	C₂×C₁₃₁	1	1	yes	characteristic, complemented
355	#2622	C₂×C₁₃₁	1	2	yes	complemented
356	#2618	C₂×C₁₃₁	1	1	yes	characteristic, complemented
357	#2478	C₂×C₁₃₁	1	4	yes	complemented
358	#2476	C₂×C₁₃₁	1	4	yes	complemented
359	#2474	C₂×C₁₃₁	1	4	yes	complemented
360	#2470	C₂×C₁₃₁	1	4	yes	complemented
361	#2322	C₂×C₁₃₁	1	2	yes	complemented
362	#2312	C₂×C₁₃₁	1	1	yes	characteristic, complemented
363	C₄×#123	C₂×C₁₃₁	1	2	yes	complemented
364	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
365	#538	—	2	8	no	—
366	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
367	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
368	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
369	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
370	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
371	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
372	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
373	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
374	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
376	C₂×#117	—	2	8	no	—
377	C₂×#117	C₂²×C₁₃₁	1	4	yes	—
378	C₂×#117	C₂²×C₁₃₁	1	4	yes	—
379	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
380	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
381	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
382	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
383	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
384	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
385	#400	C₂²×C₁₃₁	1	2	yes	complemented
386	#398	C₂²×C₁₃₁	1	2	yes	complemented
387	#398	C₂²×C₁₃₁	1	4	yes	complemented
388	#397	C₂²×C₁₃₁	1	4	yes	—
389	#397	C₂²×C₁₃₁	1	4	yes	—
390	#396	C₂²×C₁₃₁	1	4	yes	complemented
391	#395	C₂²×C₁₃₁	1	2	yes	complemented
392	#394	C₂²×C₁₃₁	1	4	yes	—
393	#394	C₂²×C₁₃₁	1	4	yes	—
394	#394	C₂²×C₁₃₁	1	2	yes	complemented
395	#391	C₂²×C₁₃₁	1	2	yes	complemented
396	#390	C₂²×C₁₃₁	1	2	yes	complemented
397	#389	C₂²×C₁₃₁	1	4	yes	complemented
398	#389	C₂²×C₁₃₁	1	2	yes	complemented
399	#389	C₂²×C₁₃₁	1	2	yes	complemented
400	#388	C₂²×C₁₃₁	1	4	yes	—
401	#388	C₂²×C₁₃₁	1	4	yes	—
402	#388	C₂²×C₁₃₁	1	4	yes	complemented
403	#388	C₂²×C₁₃₁	1	4	yes	complemented
404	#388	C₂²×C₁₃₁	1	4	yes	complemented
405	#387	C₂²×C₁₃₁	1	4	yes	complemented
406	#387	C₂²×C₁₃₁	1	4	yes	complemented
407	#387	C₂²×C₁₃₁	1	4	yes	complemented
408	#386	C₂²×C₁₃₁	1	2	yes	—
409	#386	C₂²×C₁₃₁	1	4	yes	—
410	#386	C₂²×C₁₃₁	1	4	yes	—
411	#386	C₂²×C₁₃₁	1	2	yes	—
412	#385	C₂²×C₁₃₁	1	2	yes	—
413	#385	C₂²×C₁₃₁	1	4	yes	—
414	#385	C₂²×C₁₃₁	1	4	yes	—
415	#385	C₂²×C₁₃₁	1	2	yes	—
416	#385	C₂²×C₁₃₁	1	4	yes	complemented
417	#381	C₂²×C₁₃₁	1	2	yes	—
418	#381	C₂²×C₁₃₁	1	2	yes	—
419	#380	C₂²×C₁₃₁	1	1	yes	characteristic
420	#380	C₂²×C₁₃₁	1	1	yes	characteristic
421	#379	C₂²×C₁₃₁	1	2	yes	—
422	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
423	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
425	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
426	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
428	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
429	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
430	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
431	C₂³×C₄	—	2	4	no	—
432	C₂³×C₄	—	2	4	no	—
433	C₂³×C₄	—	2	4	no	—
434	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
435	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
440	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
442	#126	—	2	8	no	—
443	#124	—	2	8	no	—
444	#123	—	2	8	no	—
445	#123	—	2	8	no	—
446	#123	—	2	8	no	—
447	C₂²⋊Q₈	—	2	4	no	—
448	#121	—	2	4	no	—
449	#121	—	2	8	no	—
450	#120	—	2	8	no	—
451	C₄×D₄	—	2	8	no	—
452	#117	—	2	16	no	—
453	#117	—	2	16	no	—
454	C₂×C₄⋊C₄	—	2	4	no	—
455	C₂×C₄⋊C₄	—	2	4	no	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
469	C₂×C₂²⋊C₄	—	2	4	no	—
470	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	8	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
487	C₂×C₄²	—	2	4	no	—
488	C₂×C₄²	—	2	4	no	—
489	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
490	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
491	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
492	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
493	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
494	#95	C₂³×C₁₃₁	1	4	yes	—
495	#95	C₂³×C₁₃₁	1	4	yes	—
496	#95	C₂³×C₁₃₁	1	4	yes	—
497	#95	C₂³×C₁₃₁	1	4	yes	—
498	#95	C₂³×C₁₃₁	1	4	yes	—
499	#95	C₂³×C₁₃₁	1	2	yes	—
500	#95	C₂³×C₁₃₁	1	2	yes	—
501	#95	C₂³×C₁₃₁	1	4	yes	—
502	#95	C₂³×C₁₃₁	1	4	yes	—
503	#95	C₂³×C₁₃₁	1	4	yes	—
504	#95	C₂³×C₁₃₁	1	4	yes	—
505	C₂⁴	—	2	2	no	—
506	C₂⁴	—	2	2	no	—
507	C₂⁴	—	4	2	no	—
508	C₂⁴	—	4	2	no	—
509	C₂⁴	C₂×D₄×C₁₃₁	1	4	yes	—
510	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
511	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
512	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
513	C₂×Q₈	—	2	2	no	—
514	C₂×Q₈	—	4	2	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	4	4	no	—
523	C₂×D₄	—	4	4	no	—
524	C₂²×C₄	—	2	32	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	8	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	8	no	—
531	C₂²×C₄	—	2	8	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
541	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
542	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
543	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
546	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
556	C₄⋊C₄	—	2	8	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	8	no	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	—	4	2	no	—
567	C₄⋊C₄	—	4	4	no	—
568	C₄⋊C₄	—	4	4	no	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	—	4	4	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	—	4	4	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	C₂×D₄×C₁₃₁	1	8	yes	—
584	C₂²⋊C₄	C₂×D₄×C₁₃₁	1	8	yes	—
585	C₄²	—	2	8	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	4	4	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	8	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	4	no	—
596	C₂³	—	2	4	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	4	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	4	4	no	—
603	C₂³	—	4	4	no	—
604	C₂³	—	4	8	no	—
605	C₂³	—	4	8	no	—
606	C₂³	C₂²×D₄×C₁₃₁	1	4	yes	—
607	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
608	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
609	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
610	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
611	Q₈	—	8	2	no	—
612	D₄	—	4	8	no	—
613	D₄	—	8	2	no	—
614	D₄	—	8	4	no	—
615	D₄	—	8	4	no	—
616	C₂×C₄	—	2	32	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	8	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	4	4	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	8	4	no	—
649	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
650	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
652	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
653	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
654	C₂²	—	2	4	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	4	no	—
661	C₂²	—	4	16	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	4	no	—
669	C₂²	#525×C₁₃₁	1	4	yes	—
670	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
671	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
672	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
673	C₂²	#585×C₁₃₁	1	2	yes	—
674	C₂²	#585×C₁₃₁	1	2	yes	—
675	C₄	—	2	4	no	—
676	C₄	—	2	4	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	4	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	4	no	—
687	C₂	—	2	4	no	—
688	C₂	—	4	4	no	—
689	C₂	—	8	2	no	—
690	C₂	C₂×#525×C₁₃₁	1	1	yes	characteristic
691	C₂	#3455×C₁₃₁	1	2	yes	—
692	C₂	#3485×C₁₃₁	1	1	yes	characteristic
693	C₂	#3485×C₁₃₁	1	1	yes	characteristic
694	C₂	#3493×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂×#538×C₁₃₁	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₁₃₁	C₂	semidirect
3. #2855×C₁₃₁	C₂	semidirect
4. #2854×C₁₃₁	C₂	semidirect
5. #2849×C₁₃₁	C₂	semidirect
6. #2627×C₁₃₁	C₂	semidirect
7. #2622×C₁₃₁	C₂	semidirect
8. #2618×C₁₃₁	C₂	semidirect
9. #2478×C₁₃₁	C₂	semidirect
10. #2476×C₁₃₁	C₂	semidirect
11. #2474×C₁₃₁	C₂	semidirect
12. #2470×C₁₃₁	C₂	semidirect
13. #2322×C₁₃₁	C₂	semidirect
14. #2312×C₁₃₁	C₂	semidirect
15. C₄×#123×C₁₃₁	C₂	semidirect
37. #400×C₁₃₁	C₂²	semidirect
38. #398×C₁₃₁	C₂²	semidirect
39. #398×C₁₃₁	C₂²	semidirect
42. #396×C₁₃₁	C₂²	semidirect
43. #395×C₁₃₁	C₂²	semidirect
46. #394×C₁₃₁	C₂²	semidirect
47. #391×C₁₃₁	C₂²	semidirect
48. #390×C₁₃₁	C₂²	semidirect
49. #389×C₁₃₁	C₂²	semidirect
50. #389×C₁₃₁	C₂²	semidirect
51. #389×C₁₃₁	C₂²	semidirect
54. #388×C₁₃₁	C₂²	semidirect
55. #388×C₁₃₁	C₂²	semidirect
56. #388×C₁₃₁	C₂²	semidirect
57. #387×C₁₃₁	C₂²	semidirect
58. #387×C₁₃₁	C₂²	semidirect
59. #387×C₁₃₁	C₂²	semidirect
68. #385×C₁₃₁	C₂²	semidirect
74. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
347. #35093	C₁₃₁	direct (N × H)
348. C₁₃₁	#35093	direct (N × H)
350. C₂²×#117	C₂×C₁₃₁	semidirect
351. #2855	C₂×C₁₃₁	semidirect
352. #2854	C₂×C₁₃₁	semidirect
353. #2849	C₂×C₁₃₁	semidirect
354. #2627	C₂×C₁₃₁	semidirect
355. #2622	C₂×C₁₃₁	semidirect
356. #2618	C₂×C₁₃₁	semidirect
357. #2478	C₂×C₁₃₁	semidirect
358. #2476	C₂×C₁₃₁	semidirect
359. #2474	C₂×C₁₃₁	semidirect
360. #2470	C₂×C₁₃₁	semidirect
361. #2322	C₂×C₁₃₁	semidirect
362. #2312	C₂×C₁₃₁	semidirect
363. C₄×#123	C₂×C₁₃₁	semidirect
385. #400	C₂²×C₁₃₁	semidirect
386. #398	C₂²×C₁₃₁	semidirect
387. #398	C₂²×C₁₃₁	semidirect
390. #396	C₂²×C₁₃₁	semidirect
391. #395	C₂²×C₁₃₁	semidirect
394. #394	C₂²×C₁₃₁	semidirect
395. #391	C₂²×C₁₃₁	semidirect
396. #390	C₂²×C₁₃₁	semidirect
397. #389	C₂²×C₁₃₁	semidirect
398. #389	C₂²×C₁₃₁	semidirect
399. #389	C₂²×C₁₃₁	semidirect
402. #388	C₂²×C₁₃₁	semidirect
403. #388	C₂²×C₁₃₁	semidirect
404. #388	C₂²×C₁₃₁	semidirect
405. #387	C₂²×C₁₃₁	semidirect
406. #387	C₂²×C₁₃₁	semidirect
407. #387	C₂²×C₁₃₁	semidirect
416. #385	C₂²×C₁₃₁	semidirect
422. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
424. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#538×C₁₃₁	2
C₂²×#117×C₁₃₁	2
#2855×C₁₃₁	2
#2854×C₁₃₁	2
#2849×C₁₃₁	2
#2627×C₁₃₁	2
#2622×C₁₃₁	2
#2618×C₁₃₁	2
#2478×C₁₃₁	2
#2476×C₁₃₁	2
#2474×C₁₃₁	2
#2470×C₁₃₁	2
#2322×C₁₃₁	2
#2312×C₁₃₁	2
C₄×#123×C₁₃₁	2
#35093	131

Subgroups — C131×#35093 #45720977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#35093 #45720977