Subgroups — C₁₃₁×#17386 #45703270

Order 33536.

1080 conjugacy classes of subgroups.

The subgroup lattice has 592 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	#2973×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2972×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#1473×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1471×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1469×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1468×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1459×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	C₂×#323×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#538×C₁₃₁	—	2	4	no	—
11	#538×C₁₃₁	—	2	4	no	—
12	C₂×#126×C₁₃₁	C₄	1	1	yes	characteristic
13	C₂×#126×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₁₃₁	C₄	1	1	yes	characteristic
15	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×#123×C₁₃₁	C₄	1	1	yes	characteristic
17	C₂×#123×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₁₃₁	C₄	1	1	yes	characteristic
19	C₂×#121×C₁₃₁	C₄	1	1	yes	characteristic
20	C₂×#121×C₁₃₁	C₄	1	1	yes	characteristic
21	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#120×C₁₃₁	C₄	1	1	yes	characteristic
23	C₂×#120×C₁₃₁	C₄	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
27	#435×C₁₃₁	—	2	4	no	—
28	C₈×D₄×C₁₃₁	—	2	4	no	—
29	#432×C₁₃₁	C₂²	1	2	yes	complemented
30	#431×C₁₃₁	C₂²	1	2	yes	complemented
31	#407×C₁₃₁	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	2	yes	complemented
35	#324×C₁₃₁	C₂²	1	4	yes	complemented
36	#323×C₁₃₁	C₂²	1	4	yes	—
37	#323×C₁₃₁	C₂²	1	4	yes	—
38	#323×C₁₃₁	C₂²	1	4	yes	complemented
39	C₂⁵×C₁₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₁₃₁	—	2	2	no	—
53	C₂²×C₈×C₁₃₁	—	2	2	no	—
54	C₂²×C₈×C₁₃₁	—	2	2	no	—
55	C₂²×C₈×C₁₃₁	—	2	2	no	—
56	#126×C₁₃₁	—	2	4	no	—
57	#126×C₁₃₁	—	2	2	no	—
58	#126×C₁₃₁	—	2	2	no	—
59	#124×C₁₃₁	—	2	4	no	—
60	#124×C₁₃₁	—	2	2	no	—
61	#124×C₁₃₁	—	2	2	no	—
62	#123×C₁₃₁	—	2	2	no	—
63	#123×C₁₃₁	—	2	2	no	—
64	#123×C₁₃₁	—	2	4	no	—
65	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
66	#121×C₁₃₁	—	2	4	no	—
67	#121×C₁₃₁	—	2	2	no	—
68	#121×C₁₃₁	—	2	2	no	—
69	#121×C₁₃₁	—	2	4	no	—
70	#120×C₁₃₁	—	2	4	no	—
71	#120×C₁₃₁	—	2	4	no	—
72	C₄×D₄×C₁₃₁	—	2	2	no	—
73	C₄×D₄×C₁₃₁	—	2	2	no	—
74	C₄×D₄×C₁₃₁	D₄	1	4	yes	—
75	C₄×D₄×C₁₃₁	D₄	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₁₃₁	—	2	2	no	—
101	C₄⋊C₈×C₁₃₁	—	2	2	no	—
102	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
103	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
104	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
105	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
106	C₂²⋊C₈×C₁₃₁	C₂³	1	4	yes	—
107	C₂²⋊C₈×C₁₃₁	C₂³	1	4	yes	—
108	#97×C₁₃₁	—	2	2	no	—
109	C₄×C₈×C₁₃₁	—	2	2	no	—
110	C₂⁴×C₁₃₁	—	2	2	no	—
111	C₂⁴×C₁₃₁	—	2	4	no	—
112	C₂⁴×C₁₃₁	—	8	1	no	—
113	C₂⁴×C₁₃₁	—	8	1	no	—
114	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
115	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
116	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
117	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
118	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×Q₈×C₁₃₁	—	2	2	no	—
120	C₂×Q₈×C₁₃₁	—	8	1	no	—
121	C₂×D₄×C₁₃₁	—	2	4	no	—
122	C₂×D₄×C₁₃₁	—	2	2	no	—
123	C₂×D₄×C₁₃₁	—	2	4	no	—
124	C₂×D₄×C₁₃₁	—	2	2	no	—
125	C₂×D₄×C₁₃₁	—	2	2	no	—
126	C₂×D₄×C₁₃₁	—	2	2	no	—
127	C₂×D₄×C₁₃₁	—	2	2	no	—
128	C₂×D₄×C₁₃₁	—	2	2	no	—
129	C₂×D₄×C₁₃₁	—	8	1	no	—
130	C₂×D₄×C₁₃₁	—	8	1	no	—
131	C₂×D₄×C₁₃₁	—	8	1	no	—
132	C₂×D₄×C₁₃₁	—	8	1	no	—
133	C₂×D₄×C₁₃₁	—	8	1	no	—
134	C₂×D₄×C₁₃₁	C₂²⋊C₄	1	4	yes	—
135	C₂²×C₄×C₁₃₁	—	2	2	no	—
136	C₂²×C₄×C₁₃₁	—	2	2	no	—
137	C₂²×C₄×C₁₃₁	—	8	1	no	—
138	C₂²×C₄×C₁₃₁	—	8	1	no	—
139	C₂²×C₄×C₁₃₁	—	8	1	no	—
140	C₂²×C₄×C₁₃₁	—	8	1	no	—
141	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
155	M₁₆×C₁₃₁	—	8	2	no	—
156	C₂×C₈×C₁₃₁	—	2	4	no	—
157	C₂×C₈×C₁₃₁	—	2	4	no	—
158	C₂×C₈×C₁₃₁	—	8	2	no	—
159	C₂×C₈×C₁₃₁	—	8	2	no	—
160	C₂×C₈×C₁₃₁	—	8	2	no	—
161	C₄⋊C₄×C₁₃₁	—	2	2	no	—
162	C₄⋊C₄×C₁₃₁	—	2	2	no	—
163	C₄⋊C₄×C₁₃₁	—	2	2	no	—
164	C₄⋊C₄×C₁₃₁	—	2	2	no	—
165	C₄⋊C₄×C₁₃₁	—	2	1	no	—
166	C₄⋊C₄×C₁₃₁	—	2	1	no	—
167	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	4	yes	—
168	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
169	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
170	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
171	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
172	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
173	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
174	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
175	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
176	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
177	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
178	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
179	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
180	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
181	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
182	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
183	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	4	yes	—
184	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	4	yes	—
185	C₄²×C₁₃₁	—	2	2	no	—
186	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
187	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
188	C₂³×C₁₃₁	—	2	2	no	—
189	C₂³×C₁₃₁	—	2	1	no	—
190	C₂³×C₁₃₁	—	2	1	no	—
191	C₂³×C₁₃₁	—	2	1	no	—
192	C₂³×C₁₃₁	—	2	2	no	—
193	C₂³×C₁₃₁	—	2	2	no	—
194	C₂³×C₁₃₁	—	2	2	no	—
195	C₂³×C₁₃₁	—	4	1	no	—
196	C₂³×C₁₃₁	—	4	1	no	—
197	C₂³×C₁₃₁	—	4	1	no	—
198	C₂³×C₁₃₁	—	4	1	no	—
199	C₂³×C₁₃₁	—	4	1	no	—
200	C₂³×C₁₃₁	—	4	1	no	—
201	C₂³×C₁₃₁	—	4	1	no	—
202	C₂³×C₁₃₁	—	4	1	no	—
203	C₂³×C₁₃₁	—	4	1	no	—
204	C₂³×C₁₃₁	—	4	1	no	—
205	C₂³×C₁₃₁	—	4	4	no	—
206	C₂³×C₁₃₁	—	8	2	no	—
207	C₂³×C₁₃₁	—	8	2	no	—
208	C₂³×C₁₃₁	—	8	8	no	—
209	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂³×C₁₃₁	#131	1	4	yes	—
212	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
213	Q₈×C₁₃₁	—	8	2	no	—
214	D₄×C₁₃₁	—	2	8	no	—
215	D₄×C₁₃₁	—	4	4	no	—
216	D₄×C₁₃₁	—	8	2	no	—
217	D₄×C₁₃₁	—	8	2	no	—
218	D₄×C₁₃₁	—	8	2	no	—
219	D₄×C₁₃₁	—	8	2	no	—
220	D₄×C₁₃₁	—	8	2	no	—
221	C₂×C₄×C₁₃₁	—	2	2	no	—
222	C₂×C₄×C₁₃₁	—	2	1	no	—
223	C₂×C₄×C₁₃₁	—	2	1	no	—
224	C₂×C₄×C₁₃₁	—	2	1	no	—
225	C₂×C₄×C₁₃₁	—	2	1	no	—
226	C₂×C₄×C₁₃₁	—	2	1	no	—
227	C₂×C₄×C₁₃₁	—	2	2	no	—
228	C₂×C₄×C₁₃₁	—	4	2	no	—
229	C₂×C₄×C₁₃₁	—	4	2	no	—
230	C₂×C₄×C₁₃₁	—	4	2	no	—
231	C₂×C₄×C₁₃₁	—	4	2	no	—
232	C₂×C₄×C₁₃₁	—	4	1	no	—
233	C₂×C₄×C₁₃₁	—	4	1	no	—
234	C₂×C₄×C₁₃₁	—	4	1	no	—
235	C₂×C₄×C₁₃₁	—	4	1	no	—
236	C₂×C₄×C₁₃₁	—	4	1	no	—
237	C₂×C₄×C₁₃₁	—	4	1	no	—
238	C₂×C₄×C₁₃₁	—	4	1	no	—
239	C₂×C₄×C₁₃₁	—	4	1	no	—
240	C₂×C₄×C₁₃₁	—	8	2	no	—
241	C₂×C₄×C₁₃₁	—	8	2	no	—
242	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
243	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
244	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
248	C₈×C₁₃₁	—	4	4	no	—
249	C₈×C₁₃₁	—	4	4	no	—
250	C₂²×C₁₃₁	—	2	1	no	—
251	C₂²×C₁₃₁	—	2	2	no	—
252	C₂²×C₁₃₁	—	2	1	no	—
253	C₂²×C₁₃₁	—	2	2	no	—
254	C₂²×C₁₃₁	—	2	2	no	—
255	C₂²×C₁₃₁	—	2	2	no	—
256	C₂²×C₁₃₁	—	2	2	no	—
257	C₂²×C₁₃₁	—	4	4	no	—
258	C₂²×C₁₃₁	—	4	1	no	—
259	C₂²×C₁₃₁	—	4	1	no	—
260	C₂²×C₁₃₁	—	4	1	no	—
261	C₂²×C₁₃₁	—	4	1	no	—
262	C₂²×C₁₃₁	—	4	1	no	—
263	C₂²×C₁₃₁	—	4	1	no	—
264	C₂²×C₁₃₁	—	4	1	no	—
265	C₂²×C₁₃₁	—	4	1	no	—
266	C₂²×C₁₃₁	—	4	1	no	—
267	C₂²×C₁₃₁	—	8	2	no	—
268	C₂²×C₁₃₁	—	8	2	no	—
269	C₂²×C₁₃₁	—	8	2	no	—
270	C₂²×C₁₃₁	—	8	2	no	—
271	C₂²×C₁₃₁	—	8	8	no	—
272	C₂²×C₁₃₁	#408	1	4	yes	—
273	C₂²×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×C₁₃₁	C₂×#131	1	2	yes	—
275	C₄×C₁₃₁	—	2	2	no	—
276	C₄×C₁₃₁	—	2	1	no	—
277	C₄×C₁₃₁	—	2	1	no	—
278	C₄×C₁₃₁	—	2	2	no	—
279	C₄×C₁₃₁	—	2	2	no	—
280	C₄×C₁₃₁	—	2	2	no	—
281	C₄×C₁₃₁	—	4	1	no	—
282	C₄×C₁₃₁	—	4	1	no	—
283	C₄×C₁₃₁	—	4	1	no	—
284	C₄×C₁₃₁	—	4	1	no	—
285	C₄×C₁₃₁	—	4	1	no	—
286	C₂×C₁₃₁	—	2	2	no	—
287	C₂×C₁₃₁	—	2	4	no	—
288	C₂×C₁₃₁	—	4	2	no	—
289	C₂×C₁₃₁	—	8	1	no	—
290	C₂×C₁₃₁	—	8	1	no	—
291	C₂×C₁₃₁	—	8	1	no	—
292	C₂×C₁₃₁	C₂×#408	1	1	yes	characteristic
293	C₂×C₁₃₁	#2883	1	1	yes	characteristic
294	C₂×C₁₃₁	#2888	1	1	yes	characteristic
295	#17386	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₁₃₁	#17386	1	1	yes	characteristic, direct product factor, Sylow
297	C₂×#538	C₂×C₁₃₁	1	1	yes	characteristic
298	#2973	C₂×C₁₃₁	1	1	yes	characteristic, complemented
299	#2972	C₂×C₁₃₁	1	1	yes	characteristic, complemented
300	#1473	C₂×C₁₃₁	1	2	yes	complemented
301	#1471	C₂×C₁₃₁	1	2	yes	complemented
302	#1469	C₂×C₁₃₁	1	2	yes	complemented
303	#1468	C₂×C₁₃₁	1	2	yes	complemented
304	#1459	C₂×C₁₃₁	1	2	yes	complemented
305	C₂×#323	C₂×C₁₃₁	1	2	yes	complemented
306	#538	—	2	4	no	—
307	#538	—	2	4	no	—
308	C₂×#126	C₄×C₁₃₁	1	1	yes	characteristic
309	C₂×#126	C₂²×C₁₃₁	1	1	yes	characteristic
310	C₂×#124	C₄×C₁₃₁	1	1	yes	characteristic
311	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
312	C₂×#123	C₄×C₁₃₁	1	1	yes	characteristic
313	C₂×#123	C₂²×C₁₃₁	1	1	yes	characteristic
314	C₂×C₂²⋊Q₈	C₄×C₁₃₁	1	1	yes	characteristic
315	C₂×#121	C₄×C₁₃₁	1	1	yes	characteristic
316	C₂×#121	C₄×C₁₃₁	1	1	yes	characteristic
317	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
318	C₂×#120	C₄×C₁₃₁	1	1	yes	characteristic
319	C₂×#120	C₄×C₁₃₁	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
321	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
322	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
323	#435	—	2	4	no	—
324	C₈×D₄	—	2	4	no	—
325	#432	C₂²×C₁₃₁	1	2	yes	complemented
326	#431	C₂²×C₁₃₁	1	2	yes	complemented
327	#407	C₂²×C₁₃₁	1	2	yes	complemented
328	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	2	yes	—
329	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	2	yes	—
330	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	2	yes	complemented
331	#324	C₂²×C₁₃₁	1	4	yes	complemented
332	#323	C₂²×C₁₃₁	1	4	yes	—
333	#323	C₂²×C₁₃₁	1	4	yes	—
334	#323	C₂²×C₁₃₁	1	4	yes	complemented
335	C₂⁵	C₂×C₄×C₁₃₁	1	1	yes	characteristic
336	C₂²×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
337	C₂²×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
338	C₂²×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
339	C₂²×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
340	C₂²×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
341	C₂²×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
342	C₂²×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
343	C₂²×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
344	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
345	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
348	C₂×M₁₆	—	2	2	no	—
349	C₂²×C₈	—	2	2	no	—
350	C₂²×C₈	—	2	2	no	—
351	C₂²×C₈	—	2	2	no	—
352	#126	—	2	4	no	—
353	#126	—	2	2	no	—
354	#126	—	2	2	no	—
355	#124	—	2	4	no	—
356	#124	—	2	2	no	—
357	#124	—	2	2	no	—
358	#123	—	2	2	no	—
359	#123	—	2	2	no	—
360	#123	—	2	4	no	—
361	C₂²⋊Q₈	—	2	4	no	—
362	#121	—	2	4	no	—
363	#121	—	2	2	no	—
364	#121	—	2	2	no	—
365	#121	—	2	4	no	—
366	#120	—	2	4	no	—
367	#120	—	2	4	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	D₄×C₁₃₁	1	4	yes	—
371	C₄×D₄	D₄×C₁₃₁	1	4	yes	—
372	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
394	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
396	C₄⋊C₈	—	2	2	no	—
397	C₄⋊C₈	—	2	2	no	—
398	C₂²⋊C₈	—	2	2	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	C₂²⋊C₈	—	2	2	no	—
401	C₂²⋊C₈	—	2	2	no	—
402	C₂²⋊C₈	C₂³×C₁₃₁	1	4	yes	—
403	C₂²⋊C₈	C₂³×C₁₃₁	1	4	yes	—
404	#97	—	2	2	no	—
405	C₄×C₈	—	2	2	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	8	1	no	—
409	C₂⁴	—	8	1	no	—
410	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
411	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
412	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
413	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
414	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	8	1	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	8	1	no	—
426	C₂×D₄	—	8	1	no	—
427	C₂×D₄	—	8	1	no	—
428	C₂×D₄	—	8	1	no	—
429	C₂×D₄	—	8	1	no	—
430	C₂×D₄	C₂²⋊C₄×C₁₃₁	1	4	yes	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	8	1	no	—
434	C₂²×C₄	—	8	1	no	—
435	C₂²×C₄	—	8	1	no	—
436	C₂²×C₄	—	8	1	no	—
437	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
442	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
443	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
451	M₁₆	—	8	2	no	—
452	C₂×C₈	—	2	4	no	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	—	8	2	no	—
455	C₂×C₈	—	8	2	no	—
456	C₂×C₈	—	8	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	4	yes	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	4	yes	—
480	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	4	yes	—
481	C₄²	—	2	2	no	—
482	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
483	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	4	no	—
502	C₂³	—	8	2	no	—
503	C₂³	—	8	2	no	—
504	C₂³	—	8	8	no	—
505	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
506	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
507	C₂³	#131×C₁₃₁	1	4	yes	—
508	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
509	Q₈	—	8	2	no	—
510	D₄	—	2	8	no	—
511	D₄	—	4	4	no	—
512	D₄	—	8	2	no	—
513	D₄	—	8	2	no	—
514	D₄	—	8	2	no	—
515	D₄	—	8	2	no	—
516	D₄	—	8	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	8	2	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
539	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
540	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
541	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
544	C₈	—	4	4	no	—
545	C₈	—	4	4	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	2	no	—
567	C₂²	—	8	8	no	—
568	C₂²	#408×C₁₃₁	1	4	yes	—
569	C₂²	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
570	C₂²	C₂×#131×C₁₃₁	1	2	yes	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₂	—	2	2	no	—
583	C₂	—	2	4	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	1	no	—
586	C₂	—	8	1	no	—
587	C₂	—	8	1	no	—
588	C₂	C₂×#408×C₁₃₁	1	1	yes	characteristic
589	C₂	#2883×C₁₃₁	1	1	yes	characteristic
590	C₂	#2888×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#538×C₁₃₁	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ 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. #2973×C₁₃₁	C₂	semidirect
3. #2972×C₁₃₁	C₂	semidirect
4. #1473×C₁₃₁	C₂	semidirect
5. #1471×C₁₃₁	C₂	semidirect
6. #1469×C₁₃₁	C₂	semidirect
7. #1468×C₁₃₁	C₂	semidirect
8. #1459×C₁₃₁	C₂	semidirect
9. C₂×#323×C₁₃₁	C₂	semidirect
29. #432×C₁₃₁	C₂²	semidirect
30. #431×C₁₃₁	C₂²	semidirect
31. #407×C₁₃₁	C₂²	semidirect
34. C₂×C₂²⋊C₈×C₁₃₁	C₂²	semidirect
35. #324×C₁₃₁	C₂²	semidirect
38. #323×C₁₃₁	C₂²	semidirect
295. #17386	C₁₃₁	direct (N × H)
296. C₁₃₁	#17386	direct (N × H)
298. #2973	C₂×C₁₃₁	semidirect
299. #2972	C₂×C₁₃₁	semidirect
300. #1473	C₂×C₁₃₁	semidirect
301. #1471	C₂×C₁₃₁	semidirect
302. #1469	C₂×C₁₃₁	semidirect
303. #1468	C₂×C₁₃₁	semidirect
304. #1459	C₂×C₁₃₁	semidirect
305. C₂×#323	C₂×C₁₃₁	semidirect
325. #432	C₂²×C₁₃₁	semidirect
326. #431	C₂²×C₁₃₁	semidirect
327. #407	C₂²×C₁₃₁	semidirect
330. C₂×C₂²⋊C₈	C₂²×C₁₃₁	semidirect
331. #324	C₂²×C₁₃₁	semidirect
334. #323	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
#2973×C₁₃₁	2
#2972×C₁₃₁	2
#1473×C₁₃₁	2
#1471×C₁₃₁	2
#1469×C₁₃₁	2
#1468×C₁₃₁	2
#1459×C₁₃₁	2
C₂×#323×C₁₃₁	2
#17386	131

Subgroups — C131×#17386 #45703270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#17386 #45703270