Subgroups — C₁₃₁×#17547 #45703431

Order 33536.

1166 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3519×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2974×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2275×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#1509×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1507×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1505×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1504×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1502×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1501×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#1500×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#327×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#555×C₁₃₁	C₄	1	1	yes	characteristic, complemented
13	#554×C₁₃₁	C₄	1	1	yes	characteristic, complemented
14	#553×C₁₃₁	—	2	1	no	—
15	#553×C₁₃₁	C₄	1	2	yes	complemented
16	#550×C₁₃₁	C₄	1	1	yes	characteristic, complemented
17	#546×C₁₃₁	—	2	2	no	—
18	#546×C₁₃₁	C₄	1	2	yes	complemented
19	D₄²×C₁₃₁	—	2	1	no	—
20	D₄²×C₁₃₁	C₄	1	1	yes	characteristic, complemented
21	#540×C₁₃₁	—	2	1	no	—
22	#538×C₁₃₁	—	2	2	no	—
23	#532×C₁₃₁	C₂²	1	1	yes	characteristic
24	#529×C₁₃₁	C₂²	1	1	yes	characteristic
25	#525×C₁₃₁	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
27	#518×C₁₃₁	—	2	1	no	—
28	C₂×C₄×D₄×C₁₃₁	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
30	#436×C₁₃₁	—	2	1	no	—
31	#435×C₁₃₁	—	2	2	no	—
32	C₈×D₄×C₁₃₁	—	2	1	no	—
33	#432×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
34	#431×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
35	#407×C₁₃₁	C₂²	1	2	yes	complemented
36	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	2	yes	complemented
37	C₄×C₄⋊C₄×C₁₃₁	—	2	1	no	—
38	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
40	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
41	#376×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
42	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
43	#328×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
44	#328×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
45	#328×C₁₃₁	C₂²	1	2	yes	complemented
46	#327×C₁₃₁	C₂²	1	1	yes	characteristic
47	#327×C₁₃₁	C₂²	1	2	yes	—
48	#327×C₁₃₁	C₂²	1	1	yes	characteristic
49	#327×C₁₃₁	C₂²	1	2	yes	complemented
50	#327×C₁₃₁	C₂²	1	2	yes	complemented
51	#327×C₁₃₁	C₂²	1	2	yes	complemented
52	#327×C₁₃₁	C₂²	1	2	yes	complemented
53	C₂×#41×C₁₃₁	—	2	1	no	—
54	C₂×#41×C₁₃₁	C₂×C₄	1	2	yes	complemented
55	C₂²×D₄×C₁₃₁	—	2	2	no	—
56	C₂²×D₄×C₁₃₁	—	2	1	no	—
57	C₂²×D₄×C₁₃₁	C₂×C₄	1	2	yes	complemented
58	C₂²×D₄×C₁₃₁	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₃₁	—	2	2	no	—
60	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₁₃₁	—	2	2	no	—
62	C₂²×C₈×C₁₃₁	—	2	2	no	—
63	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
64	#127×C₁₃₁	—	2	1	no	—
65	#127×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
66	#126×C₁₃₁	—	2	2	no	—
67	#126×C₁₃₁	—	2	1	no	—
68	#125×C₁₃₁	—	2	1	no	—
69	#125×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
70	#124×C₁₃₁	—	2	2	no	—
71	#124×C₁₃₁	—	2	1	no	—
72	#124×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
73	#123×C₁₃₁	—	2	2	no	—
74	#123×C₁₃₁	—	2	1	no	—
75	#123×C₁₃₁	—	2	2	no	—
76	#123×C₁₃₁	—	2	2	no	—
77	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
78	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	2	yes	complemented
79	C₂²⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
80	#121×C₁₃₁	—	2	2	no	—
81	#121×C₁₃₁	—	2	1	no	—
82	#121×C₁₃₁	—	2	2	no	—
83	#121×C₁₃₁	—	2	2	no	—
84	#121×C₁₃₁	—	2	1	no	—
85	#121×C₁₃₁	—	2	1	no	—
86	#121×C₁₃₁	—	2	2	no	—
87	#121×C₁₃₁	—	2	2	no	—
88	#121×C₁₃₁	C₂×C₄	1	2	yes	complemented
89	#121×C₁₃₁	C₂×C₄	1	2	yes	complemented
90	#121×C₁₃₁	C₂×C₄	1	2	yes	complemented
91	#121×C₁₃₁	C₂³	1	1	yes	characteristic
92	#121×C₁₃₁	C₂³	1	2	yes	—
93	#120×C₁₃₁	—	2	2	no	—
94	#120×C₁₃₁	—	2	2	no	—
95	#120×C₁₃₁	—	2	2	no	—
96	C₄×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
97	C₄×D₄×C₁₃₁	—	2	8	no	—
98	C₄×D₄×C₁₃₁	—	2	1	no	—
99	C₄×D₄×C₁₃₁	—	2	2	no	—
100	C₄×D₄×C₁₃₁	—	2	2	no	—
101	C₄×D₄×C₁₃₁	—	2	1	no	—
102	C₄×D₄×C₁₃₁	—	2	1	no	—
103	C₄×D₄×C₁₃₁	—	2	2	no	—
104	C₄×D₄×C₁₃₁	—	2	1	no	—
105	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
108	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
109	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	complemented
110	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
111	C₄×D₄×C₁₃₁	D₄	1	2	yes	—
112	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
113	#117×C₁₃₁	—	2	1	no	—
114	#117×C₁₃₁	—	2	1	no	—
115	#117×C₁₃₁	C₂×C₄	1	2	yes	complemented
116	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	complemented
118	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
120	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
121	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
122	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
123	C₂×C₄²×C₁₃₁	—	2	1	no	—
124	C₂×C₄²×C₁₃₁	—	2	1	no	—
125	C₂×C₄²×C₁₃₁	—	2	2	no	—
126	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
127	C₄⋊C₈×C₁₃₁	—	2	1	no	—
128	C₄⋊C₈×C₁₃₁	—	2	1	no	—
129	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
130	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
131	C₂²⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
132	C₂²⋊C₈×C₁₃₁	C₂³	1	2	yes	—
133	C₂²⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
134	#97×C₁₃₁	—	2	1	no	—
135	C₄×C₈×C₁₃₁	—	2	1	no	—
136	#95×C₁₃₁	—	2	2	no	—
137	#95×C₁₃₁	—	2	1	no	—
138	#95×C₁₃₁	C₂³	1	1	yes	characteristic
139	#95×C₁₃₁	C₂³	1	2	yes	—
140	#95×C₁₃₁	C₂³	1	1	yes	characteristic
141	C₂⁴×C₁₃₁	—	2	2	no	—
142	C₂⁴×C₁₃₁	C₂×D₄	1	2	yes	—
143	#41×C₁₃₁	—	8	1	no	—
144	#41×C₁₃₁	—	8	1	no	—
145	#41×C₁₃₁	—	8	2	no	—
146	C₂×Q₈×C₁₃₁	—	2	1	no	—
147	C₂×Q₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₁₃₁	—	2	4	no	—
149	C₂×D₄×C₁₃₁	—	2	2	no	—
150	C₂×D₄×C₁₃₁	—	2	2	no	—
151	C₂×D₄×C₁₃₁	—	2	1	no	—
152	C₂×D₄×C₁₃₁	—	2	2	no	—
153	C₂×D₄×C₁₃₁	—	2	2	no	—
154	C₂×D₄×C₁₃₁	—	2	2	no	—
155	C₂×D₄×C₁₃₁	—	2	1	no	—
156	C₂×D₄×C₁₃₁	—	2	1	no	—
157	C₂×D₄×C₁₃₁	—	2	2	no	—
158	C₂×D₄×C₁₃₁	—	4	4	no	—
159	C₂×D₄×C₁₃₁	—	8	2	no	—
160	C₂×D₄×C₁₃₁	—	8	2	no	—
161	C₂×D₄×C₁₃₁	—	8	2	no	—
162	C₂×D₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
163	C₂×D₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×D₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×D₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₁₃₁	—	2	1	no	—
168	C₂²×C₄×C₁₃₁	—	2	1	no	—
169	C₂²×C₄×C₁₃₁	—	2	2	no	—
170	C₂²×C₄×C₁₃₁	—	2	8	no	—
171	C₂²×C₄×C₁₃₁	—	2	2	no	—
172	C₂²×C₄×C₁₃₁	—	2	1	no	—
173	C₂²×C₄×C₁₃₁	—	2	2	no	—
174	C₂²×C₄×C₁₃₁	—	2	2	no	—
175	C₂²×C₄×C₁₃₁	—	8	2	no	—
176	C₂²×C₄×C₁₃₁	—	8	2	no	—
177	C₂²×C₄×C₁₃₁	—	8	2	no	—
178	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
179	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
180	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
186	M₁₆×C₁₃₁	—	8	2	no	—
187	C₂×C₈×C₁₃₁	—	2	1	no	—
188	C₂×C₈×C₁₃₁	—	2	1	no	—
189	C₂×C₈×C₁₃₁	—	2	2	no	—
190	C₂×C₈×C₁₃₁	—	8	2	no	—
191	C₄⋊C₄×C₁₃₁	—	2	4	no	—
192	C₄⋊C₄×C₁₃₁	—	2	2	no	—
193	C₄⋊C₄×C₁₃₁	—	2	1	no	—
194	C₄⋊C₄×C₁₃₁	—	2	1	no	—
195	C₄⋊C₄×C₁₃₁	—	2	1	no	—
196	C₄⋊C₄×C₁₃₁	—	2	2	no	—
197	C₄⋊C₄×C₁₃₁	—	2	1	no	—
198	C₄⋊C₄×C₁₃₁	—	2	1	no	—
199	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
202	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
204	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
206	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
207	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
208	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
209	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
210	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
211	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
212	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
213	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
214	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
215	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
216	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
217	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
218	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
219	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
220	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
221	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
222	C₄²×C₁₃₁	—	2	4	no	—
223	C₄²×C₁₃₁	—	2	2	no	—
224	C₄²×C₁₃₁	—	2	1	no	—
225	C₄²×C₁₃₁	—	8	1	no	—
226	C₄²×C₁₃₁	—	8	2	no	—
227	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
228	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
229	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
231	C₂³×C₁₃₁	—	2	2	no	—
232	C₂³×C₁₃₁	—	2	2	no	—
233	C₂³×C₁₃₁	—	2	4	no	—
234	C₂³×C₁₃₁	—	2	1	no	—
235	C₂³×C₁₃₁	—	2	2	no	—
236	C₂³×C₁₃₁	—	4	2	no	—
237	C₂³×C₁₃₁	—	4	4	no	—
238	C₂³×C₁₃₁	—	8	2	no	—
239	C₂³×C₁₃₁	—	8	2	no	—
240	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
241	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₁₃₁	—	4	1	no	—
244	Q₈×C₁₃₁	—	8	1	no	—
245	D₄×C₁₃₁	—	2	4	no	—
246	D₄×C₁₃₁	—	2	2	no	—
247	D₄×C₁₃₁	—	4	1	no	—
248	D₄×C₁₃₁	—	4	2	no	—
249	D₄×C₁₃₁	—	4	1	no	—
250	D₄×C₁₃₁	—	4	2	no	—
251	D₄×C₁₃₁	—	4	1	no	—
252	D₄×C₁₃₁	—	4	2	no	—
253	D₄×C₁₃₁	—	4	4	no	—
254	D₄×C₁₃₁	—	4	2	no	—
255	D₄×C₁₃₁	—	8	2	no	—
256	D₄×C₁₃₁	—	8	1	no	—
257	D₄×C₁₃₁	—	8	2	no	—
258	D₄×C₁₃₁	—	8	2	no	—
259	D₄×C₁₃₁	—	8	2	no	—
260	D₄×C₁₃₁	#104	1	4	yes	—
261	C₂×C₄×C₁₃₁	—	2	1	no	—
262	C₂×C₄×C₁₃₁	—	2	1	no	—
263	C₂×C₄×C₁₃₁	—	2	2	no	—
264	C₂×C₄×C₁₃₁	—	2	2	no	—
265	C₂×C₄×C₁₃₁	—	2	2	no	—
266	C₂×C₄×C₁₃₁	—	2	4	no	—
267	C₂×C₄×C₁₃₁	—	2	1	no	—
268	C₂×C₄×C₁₃₁	—	2	1	no	—
269	C₂×C₄×C₁₃₁	—	2	2	no	—
270	C₂×C₄×C₁₃₁	—	2	1	no	—
271	C₂×C₄×C₁₃₁	—	4	2	no	—
272	C₂×C₄×C₁₃₁	—	4	2	no	—
273	C₂×C₄×C₁₃₁	—	4	2	no	—
274	C₂×C₄×C₁₃₁	—	4	1	no	—
275	C₂×C₄×C₁₃₁	—	4	2	no	—
276	C₂×C₄×C₁₃₁	—	4	2	no	—
277	C₂×C₄×C₁₃₁	—	4	1	no	—
278	C₂×C₄×C₁₃₁	—	4	2	no	—
279	C₂×C₄×C₁₃₁	—	4	1	no	—
280	C₂×C₄×C₁₃₁	—	4	2	no	—
281	C₂×C₄×C₁₃₁	—	4	1	no	—
282	C₂×C₄×C₁₃₁	—	4	1	no	—
283	C₂×C₄×C₁₃₁	—	4	2	no	—
284	C₂×C₄×C₁₃₁	—	8	2	no	—
285	C₂×C₄×C₁₃₁	—	8	2	no	—
286	C₂×C₄×C₁₃₁	—	8	2	no	—
287	C₂×C₄×C₁₃₁	—	8	8	no	—
288	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
293	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
296	C₈×C₁₃₁	—	4	1	no	—
297	C₈×C₁₃₁	—	4	2	no	—
298	C₈×C₁₃₁	—	4	1	no	—
299	C₂²×C₁₃₁	—	2	1	no	—
300	C₂²×C₁₃₁	—	2	2	no	—
301	C₂²×C₁₃₁	—	2	2	no	—
302	C₂²×C₁₃₁	—	2	1	no	—
303	C₂²×C₁₃₁	—	2	2	no	—
304	C₂²×C₁₃₁	—	2	2	no	—
305	C₂²×C₁₃₁	—	2	2	no	—
306	C₂²×C₁₃₁	—	4	4	no	—
307	C₂²×C₁₃₁	—	4	4	no	—
308	C₂²×C₁₃₁	—	4	2	no	—
309	C₂²×C₁₃₁	—	4	1	no	—
310	C₂²×C₁₃₁	—	4	2	no	—
311	C₂²×C₁₃₁	—	4	1	no	—
312	C₂²×C₁₃₁	—	4	1	no	—
313	C₂²×C₁₃₁	—	4	2	no	—
314	C₂²×C₁₃₁	—	16	4	no	—
315	C₂²×C₁₃₁	C₂×#104	1	4	yes	—
316	C₂²×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₁₃₁	#576	1	1	yes	characteristic
318	C₂²×C₁₃₁	#577	1	1	yes	characteristic
319	C₄×C₁₃₁	—	2	1	no	—
320	C₄×C₁₃₁	—	2	1	no	—
321	C₄×C₁₃₁	—	2	2	no	—
322	C₄×C₁₃₁	—	2	2	no	—
323	C₄×C₁₃₁	—	2	1	no	—
324	C₄×C₁₃₁	—	2	1	no	—
325	C₄×C₁₃₁	—	2	1	no	—
326	C₄×C₁₃₁	—	4	2	no	—
327	C₄×C₁₃₁	—	4	4	no	—
328	C₄×C₁₃₁	—	4	2	no	—
329	C₄×C₁₃₁	—	4	1	no	—
330	C₄×C₁₃₁	—	4	1	no	—
331	C₄×C₁₃₁	—	4	2	no	—
332	C₄×C₁₃₁	—	4	1	no	—
333	C₄×C₁₃₁	C₂×#104	1	2	yes	—
334	C₂×C₁₃₁	—	2	1	no	—
335	C₂×C₁₃₁	—	2	1	no	—
336	C₂×C₁₃₁	—	2	4	no	—
337	C₂×C₁₃₁	—	4	2	no	—
338	C₂×C₁₃₁	—	8	2	no	—
339	C₂×C₁₃₁	—	8	1	no	—
340	C₂×C₁₃₁	#2883	1	1	yes	characteristic
341	C₂×C₁₃₁	#2897	1	1	yes	characteristic
342	C₂×C₁₃₁	C₂²×#104	1	1	yes	characteristic
343	#17547	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₁₃₁	#17547	1	1	yes	characteristic, direct product factor, Sylow
345	#3519	C₂×C₁₃₁	1	1	yes	characteristic
346	#2974	C₂×C₁₃₁	1	1	yes	characteristic, complemented
347	#2275	C₂×C₁₃₁	1	1	yes	characteristic, complemented
348	#1509	C₂×C₁₃₁	1	1	yes	characteristic, complemented
349	#1507	C₂×C₁₃₁	1	2	yes	complemented
350	#1505	C₂×C₁₃₁	1	1	yes	characteristic, complemented
351	#1504	C₂×C₁₃₁	1	2	yes	complemented
352	#1502	C₂×C₁₃₁	1	1	yes	characteristic, complemented
353	#1501	C₂×C₁₃₁	1	2	yes	complemented
354	#1500	C₂×C₁₃₁	1	1	yes	characteristic, complemented
355	C₂×#327	C₂×C₁₃₁	1	2	yes	complemented
356	#555	C₄×C₁₃₁	1	1	yes	characteristic, complemented
357	#554	C₄×C₁₃₁	1	1	yes	characteristic, complemented
358	#553	—	2	1	no	—
359	#553	C₄×C₁₃₁	1	2	yes	complemented
360	#550	C₄×C₁₃₁	1	1	yes	characteristic, complemented
361	#546	—	2	2	no	—
362	#546	C₄×C₁₃₁	1	2	yes	complemented
363	D₄²	—	2	1	no	—
364	D₄²	C₄×C₁₃₁	1	1	yes	characteristic, complemented
365	#540	—	2	1	no	—
366	#538	—	2	2	no	—
367	#532	C₂²×C₁₃₁	1	1	yes	characteristic
368	#529	C₂²×C₁₃₁	1	1	yes	characteristic
369	#525	C₂²×C₁₃₁	1	2	yes	—
370	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
371	#518	—	2	1	no	—
372	C₂×C₄×D₄	—	2	1	no	—
373	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
374	#436	—	2	1	no	—
375	#435	—	2	2	no	—
376	C₈×D₄	—	2	1	no	—
377	#432	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
378	#431	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
379	#407	C₂²×C₁₃₁	1	2	yes	complemented
380	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	2	yes	complemented
381	C₄×C₄⋊C₄	—	2	1	no	—
382	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
383	C₄×C₂²⋊C₄	—	2	2	no	—
384	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
385	#376	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
386	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
387	#328	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
388	#328	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
389	#328	C₂²×C₁₃₁	1	2	yes	complemented
390	#327	C₂²×C₁₃₁	1	1	yes	characteristic
391	#327	C₂²×C₁₃₁	1	2	yes	—
392	#327	C₂²×C₁₃₁	1	1	yes	characteristic
393	#327	C₂²×C₁₃₁	1	2	yes	complemented
394	#327	C₂²×C₁₃₁	1	2	yes	complemented
395	#327	C₂²×C₁₃₁	1	2	yes	complemented
396	#327	C₂²×C₁₃₁	1	2	yes	complemented
397	C₂×#41	—	2	1	no	—
398	C₂×#41	C₂×C₄×C₁₃₁	1	2	yes	complemented
399	C₂²×D₄	—	2	2	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	C₂×C₄×C₁₃₁	1	2	yes	complemented
402	C₂²×D₄	D₄×C₁₃₁	1	1	yes	characteristic
403	C₂³×C₄	—	2	2	no	—
404	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
405	C₂×M₁₆	—	2	2	no	—
406	C₂²×C₈	—	2	2	no	—
407	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
408	#127	—	2	1	no	—
409	#127	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
410	#126	—	2	2	no	—
411	#126	—	2	1	no	—
412	#125	—	2	1	no	—
413	#125	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
414	#124	—	2	2	no	—
415	#124	—	2	1	no	—
416	#124	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
417	#123	—	2	2	no	—
418	#123	—	2	1	no	—
419	#123	—	2	2	no	—
420	#123	—	2	2	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	2	yes	complemented
423	C₂²⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
424	#121	—	2	2	no	—
425	#121	—	2	1	no	—
426	#121	—	2	2	no	—
427	#121	—	2	2	no	—
428	#121	—	2	1	no	—
429	#121	—	2	1	no	—
430	#121	—	2	2	no	—
431	#121	—	2	2	no	—
432	#121	C₂×C₄×C₁₃₁	1	2	yes	complemented
433	#121	C₂×C₄×C₁₃₁	1	2	yes	complemented
434	#121	C₂×C₄×C₁₃₁	1	2	yes	complemented
435	#121	C₂³×C₁₃₁	1	1	yes	characteristic
436	#121	C₂³×C₁₃₁	1	2	yes	—
437	#120	—	2	2	no	—
438	#120	—	2	2	no	—
439	#120	—	2	2	no	—
440	C₄×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
441	C₄×D₄	—	2	8	no	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	—	2	1	no	—
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	—	2	1	no	—
449	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
450	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
451	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
452	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
453	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	complemented
454	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
455	C₄×D₄	D₄×C₁₃₁	1	2	yes	—
456	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
457	#117	—	2	1	no	—
458	#117	—	2	1	no	—
459	#117	C₂×C₄×C₁₃₁	1	2	yes	complemented
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	complemented
462	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	2	no	—
464	C₂×C₂²⋊C₄	—	2	2	no	—
465	C₂×C₂²⋊C₄	—	2	2	no	—
466	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	—	2	2	no	—
470	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
471	C₄⋊C₈	—	2	1	no	—
472	C₄⋊C₈	—	2	1	no	—
473	C₂²⋊C₈	—	2	2	no	—
474	C₂²⋊C₈	—	2	2	no	—
475	C₂²⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
476	C₂²⋊C₈	C₂³×C₁₃₁	1	2	yes	—
477	C₂²⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
478	#97	—	2	1	no	—
479	C₄×C₈	—	2	1	no	—
480	#95	—	2	2	no	—
481	#95	—	2	1	no	—
482	#95	C₂³×C₁₃₁	1	1	yes	characteristic
483	#95	C₂³×C₁₃₁	1	2	yes	—
484	#95	C₂³×C₁₃₁	1	1	yes	characteristic
485	C₂⁴	—	2	2	no	—
486	C₂⁴	C₂×D₄×C₁₃₁	1	2	yes	—
487	#41	—	8	1	no	—
488	#41	—	8	1	no	—
489	#41	—	8	2	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	8	2	no	—
504	C₂×D₄	—	8	2	no	—
505	C₂×D₄	—	8	2	no	—
506	C₂×D₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
507	C₂×D₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
508	C₂×D₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
509	C₂×D₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
510	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	8	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	8	2	no	—
520	C₂²×C₄	—	8	2	no	—
521	C₂²×C₄	—	8	2	no	—
522	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
523	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
524	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
527	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
528	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
530	M₁₆	—	8	2	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	2	no	—
534	C₂×C₈	—	8	2	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
544	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
545	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
546	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
548	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
563	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
564	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
565	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	8	1	no	—
570	C₄²	—	8	2	no	—
571	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
572	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
573	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
574	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	8	2	no	—
583	C₂³	—	8	2	no	—
584	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
585	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
586	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
587	Q₈	—	4	1	no	—
588	Q₈	—	8	1	no	—
589	D₄	—	2	4	no	—
590	D₄	—	2	2	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	4	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	2	no	—
599	D₄	—	8	2	no	—
600	D₄	—	8	1	no	—
601	D₄	—	8	2	no	—
602	D₄	—	8	2	no	—
603	D₄	—	8	2	no	—
604	D₄	#104×C₁₃₁	1	4	yes	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	8	2	no	—
629	C₂×C₄	—	8	2	no	—
630	C₂×C₄	—	8	2	no	—
631	C₂×C₄	—	8	8	no	—
632	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
633	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
634	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
635	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
636	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
637	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
638	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
640	C₈	—	4	1	no	—
641	C₈	—	4	2	no	—
642	C₈	—	4	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	4	4	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	16	4	no	—
659	C₂²	C₂×#104×C₁₃₁	1	4	yes	—
660	C₂²	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
661	C₂²	#576×C₁₃₁	1	1	yes	characteristic
662	C₂²	#577×C₁₃₁	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	1	no	—
677	C₄	C₂×#104×C₁₃₁	1	2	yes	—
678	C₂	—	2	1	no	—
679	C₂	—	2	1	no	—
680	C₂	—	2	4	no	—
681	C₂	—	4	2	no	—
682	C₂	—	8	1	no	—
683	C₂	—	8	2	no	—
684	C₂	#2883×C₁₃₁	1	1	yes	characteristic
685	C₂	#2897×C₁₃₁	1	1	yes	characteristic
686	C₂	C₂²×#104×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	#3519×C₁₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄×D₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2974×C₁₃₁	C₂	semidirect
3. #2275×C₁₃₁	C₂	semidirect
4. #1509×C₁₃₁	C₂	semidirect
5. #1507×C₁₃₁	C₂	semidirect
6. #1505×C₁₃₁	C₂	semidirect
7. #1504×C₁₃₁	C₂	semidirect
8. #1502×C₁₃₁	C₂	semidirect
9. #1501×C₁₃₁	C₂	semidirect
10. #1500×C₁₃₁	C₂	semidirect
11. C₂×#327×C₁₃₁	C₂	semidirect
12. #555×C₁₃₁	C₄	semidirect
13. #554×C₁₃₁	C₄	semidirect
15. #553×C₁₃₁	C₄	semidirect
16. #550×C₁₃₁	C₄	semidirect
18. #546×C₁₃₁	C₄	semidirect
20. D₄²×C₁₃₁	C₄	semidirect
33. #432×C₁₃₁	C₂²	semidirect
34. #431×C₁₃₁	C₂²	semidirect
35. #407×C₁₃₁	C₂²	semidirect
36. C₂×C₂²⋊C₈×C₁₃₁	C₂²	semidirect
38. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
40. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
41. #376×C₁₃₁	C₂²	semidirect
42. C₂×#95×C₁₃₁	C₂²	semidirect
43. #328×C₁₃₁	C₂²	semidirect
44. #328×C₁₃₁	C₂²	semidirect
45. #328×C₁₃₁	C₂²	semidirect
49. #327×C₁₃₁	C₂²	semidirect
50. #327×C₁₃₁	C₂²	semidirect
51. #327×C₁₃₁	C₂²	semidirect
52. #327×C₁₃₁	C₂²	semidirect
54. C₂×#41×C₁₃₁	C₂×C₄	semidirect
57. C₂²×D₄×C₁₃₁	C₂×C₄	semidirect
63. C₄⋊Q₈×C₁₃₁	C₂×C₄	semidirect
65. #127×C₁₃₁	C₂×C₄	semidirect
69. #125×C₁₃₁	C₂×C₄	semidirect
72. #124×C₁₃₁	C₂×C₄	semidirect
78. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
88. #121×C₁₃₁	C₂×C₄	semidirect
89. #121×C₁₃₁	C₂×C₄	semidirect
90. #121×C₁₃₁	C₂×C₄	semidirect
96. C₄×Q₈×C₁₃₁	C₂×C₄	semidirect
108. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
109. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
115. #117×C₁₃₁	C₂×C₄	semidirect
117. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
343. #17547	C₁₃₁	direct (N × H)
344. C₁₃₁	#17547	direct (N × H)
346. #2974	C₂×C₁₃₁	semidirect
347. #2275	C₂×C₁₃₁	semidirect
348. #1509	C₂×C₁₃₁	semidirect
349. #1507	C₂×C₁₃₁	semidirect
350. #1505	C₂×C₁₃₁	semidirect
351. #1504	C₂×C₁₃₁	semidirect
352. #1502	C₂×C₁₃₁	semidirect
353. #1501	C₂×C₁₃₁	semidirect
354. #1500	C₂×C₁₃₁	semidirect
355. C₂×#327	C₂×C₁₃₁	semidirect
356. #555	C₄×C₁₃₁	semidirect
357. #554	C₄×C₁₃₁	semidirect
359. #553	C₄×C₁₃₁	semidirect
360. #550	C₄×C₁₃₁	semidirect
362. #546	C₄×C₁₃₁	semidirect
364. D₄²	C₄×C₁₃₁	semidirect
377. #432	C₂²×C₁₃₁	semidirect
378. #431	C₂²×C₁₃₁	semidirect
379. #407	C₂²×C₁₃₁	semidirect
380. C₂×C₂²⋊C₈	C₂²×C₁₃₁	semidirect
382. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
384. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
385. #376	C₂²×C₁₃₁	semidirect
386. C₂×#95	C₂²×C₁₃₁	semidirect
387. #328	C₂²×C₁₃₁	semidirect
388. #328	C₂²×C₁₃₁	semidirect
389. #328	C₂²×C₁₃₁	semidirect
393. #327	C₂²×C₁₃₁	semidirect
394. #327	C₂²×C₁₃₁	semidirect
395. #327	C₂²×C₁₃₁	semidirect
396. #327	C₂²×C₁₃₁	semidirect
398. C₂×#41	C₂×C₄×C₁₃₁	semidirect
401. C₂²×D₄	C₂×C₄×C₁₃₁	semidirect
407. C₄⋊Q₈	C₂×C₄×C₁₃₁	semidirect
409. #127	C₂×C₄×C₁₃₁	semidirect
413. #125	C₂×C₄×C₁₃₁	semidirect
416. #124	C₂×C₄×C₁₃₁	semidirect
422. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
432. #121	C₂×C₄×C₁₃₁	semidirect
433. #121	C₂×C₄×C₁₃₁	semidirect
434. #121	C₂×C₄×C₁₃₁	semidirect
440. C₄×Q₈	C₂×C₄×C₁₃₁	semidirect
452. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
453. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
459. #117	C₂×C₄×C₁₃₁	semidirect
461. C₂×C₄⋊C₄	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
#3519×C₁₃₁	2
#2974×C₁₃₁	2
#2275×C₁₃₁	2
#1509×C₁₃₁	2
#1507×C₁₃₁	2
#1505×C₁₃₁	2
#1504×C₁₃₁	2
#1502×C₁₃₁	2
#1501×C₁₃₁	2
#1500×C₁₃₁	2
C₂×#327×C₁₃₁	2
#17547	131

Subgroups — C131×#17547 #45703431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#17547 #45703431