Subgroups — C₁₃₁×#21455 #45707339

Order 33536.

1436 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#451×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#441×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	C₄×C₂²⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#1878×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1872×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1865×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1853×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#1787×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	#1763×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1749×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₃₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃₁	—	2	8	no	—
16	C₂×C₄×Q₈×C₁₃₁	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₃₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₃₁	—	2	1	no	—
22	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃₁	—	2	1	no	—
24	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
25	#451×C₁₃₁	C₄	1	8	yes	complemented
26	#441×C₁₃₁	—	2	8	no	—
27	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
31	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
35	#391×C₁₃₁	C₂²	1	1	yes	characteristic
36	#389×C₁₃₁	C₂²	1	1	yes	characteristic
37	#387×C₁₃₁	—	2	1	no	—
38	#385×C₁₃₁	—	2	1	no	—
39	#380×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₁₃₁	—	2	1	no	—
41	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
43	#340×C₁₃₁	C₂²	1	2	yes	—
44	#340×C₁₃₁	C₂²	1	2	yes	—
45	#336×C₁₃₁	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₃₁	—	2	4	no	—
47	C₂²×Q₈×C₁₃₁	—	2	4	no	—
48	C₂²×Q₈×C₁₃₁	—	2	1	no	—
49	C₂²×Q₈×C₁₃₁	—	2	2	no	—
50	C₂²×Q₈×C₁₃₁	C₂×C₄	1	4	yes	—
51	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃₁	—	2	1	no	—
54	C₂³×C₄×C₁₃₁	—	2	1	no	—
55	C₂³×C₄×C₁₃₁	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃₁	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
58	C₂×Q₁₆×C₁₃₁	—	2	4	no	—
59	C₂×Q₁₆×C₁₃₁	—	2	4	no	—
60	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	8	yes	complemented
61	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
63	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
64	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	4	yes	—
65	C₄×Q₈×C₁₃₁	—	2	8	no	—
66	C₄×Q₈×C₁₃₁	—	2	8	no	—
67	C₄×Q₈×C₁₃₁	—	2	4	no	—
68	C₄×Q₈×C₁₃₁	—	2	4	no	—
69	C₄×Q₈×C₁₃₁	—	2	4	no	—
70	C₄×Q₈×C₁₃₁	—	2	4	no	—
71	C₄×Q₈×C₁₃₁	D₄	1	8	yes	—
72	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
73	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
78	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
86	C₂×C₄²×C₁₃₁	—	2	8	no	—
87	C₂×C₄²×C₁₃₁	—	2	2	no	—
88	C₂×C₄²×C₁₃₁	—	2	2	no	—
89	C₂×C₄²×C₁₃₁	—	2	4	no	—
90	C₂×C₄²×C₁₃₁	—	2	1	no	—
91	C₂×C₄²×C₁₃₁	—	2	1	no	—
92	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
96	#106×C₁₃₁	—	2	4	no	—
97	#103×C₁₃₁	—	2	4	no	—
98	#103×C₁₃₁	—	2	4	no	—
99	#103×C₁₃₁	—	2	4	no	—
100	#103×C₁₃₁	C₂×C₄	1	8	yes	complemented
101	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
102	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	4	yes	—
103	#97×C₁₃₁	—	2	4	no	—
104	#95×C₁₃₁	—	2	1	no	—
105	#95×C₁₃₁	—	2	1	no	—
106	#95×C₁₃₁	—	2	1	no	—
107	#95×C₁₃₁	—	2	1	no	—
108	#95×C₁₃₁	—	2	1	no	—
109	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₃₁	—	2	4	no	—
111	C₂×Q₈×C₁₃₁	—	2	16	no	—
112	C₂×Q₈×C₁₃₁	—	2	4	no	—
113	C₂×Q₈×C₁₃₁	—	2	16	no	—
114	C₂×Q₈×C₁₃₁	—	2	4	no	—
115	C₂×Q₈×C₁₃₁	—	2	2	no	—
116	C₂×Q₈×C₁₃₁	—	2	2	no	—
117	C₂×Q₈×C₁₃₁	—	2	2	no	—
118	C₂×Q₈×C₁₃₁	—	2	1	no	—
119	C₂×Q₈×C₁₃₁	—	2	2	no	—
120	C₂×Q₈×C₁₃₁	—	2	2	no	—
121	C₂×Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
122	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
123	C₂×Q₈×C₁₃₁	C₂×D₄	1	4	yes	—
124	C₂×Q₈×C₁₃₁	#41	1	4	yes	—
125	C₂²×C₄×C₁₃₁	—	2	4	no	—
126	C₂²×C₄×C₁₃₁	—	2	4	no	—
127	C₂²×C₄×C₁₃₁	—	2	4	no	—
128	C₂²×C₄×C₁₃₁	—	2	2	no	—
129	C₂²×C₄×C₁₃₁	—	2	2	no	—
130	C₂²×C₄×C₁₃₁	—	2	2	no	—
131	C₂²×C₄×C₁₃₁	—	2	2	no	—
132	C₂²×C₄×C₁₃₁	—	2	2	no	—
133	C₂²×C₄×C₁₃₁	—	2	2	no	—
134	C₂²×C₄×C₁₃₁	—	2	4	no	—
135	C₂²×C₄×C₁₃₁	—	2	2	no	—
136	C₂²×C₄×C₁₃₁	—	2	1	no	—
137	C₂²×C₄×C₁₃₁	—	2	1	no	—
138	C₂²×C₄×C₁₃₁	—	2	2	no	—
139	C₂²×C₄×C₁₃₁	—	2	2	no	—
140	C₂²×C₄×C₁₃₁	—	2	1	no	—
141	C₂²×C₄×C₁₃₁	—	2	1	no	—
142	C₂²×C₄×C₁₃₁	—	4	1	no	—
143	C₂²×C₄×C₁₃₁	—	4	2	no	—
144	C₂²×C₄×C₁₃₁	—	4	2	no	—
145	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
152	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
153	Q₁₆×C₁₃₁	—	2	16	no	—
154	C₂×C₈×C₁₃₁	—	2	2	no	—
155	C₂×C₈×C₁₃₁	—	2	2	no	—
156	C₂×C₈×C₁₃₁	—	2	2	no	—
157	C₂×C₈×C₁₃₁	—	2	2	no	—
158	C₂×C₈×C₁₃₁	—	2	2	no	—
159	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
160	C₄⋊C₄×C₁₃₁	—	2	8	no	—
161	C₄⋊C₄×C₁₃₁	—	2	4	no	—
162	C₄⋊C₄×C₁₃₁	—	2	4	no	—
163	C₄⋊C₄×C₁₃₁	—	2	8	no	—
164	C₄⋊C₄×C₁₃₁	—	2	2	no	—
165	C₄⋊C₄×C₁₃₁	—	2	1	no	—
166	C₄⋊C₄×C₁₃₁	—	2	2	no	—
167	C₄⋊C₄×C₁₃₁	—	2	2	no	—
168	C₄⋊C₄×C₁₃₁	—	4	2	no	—
169	C₄⋊C₄×C₁₃₁	—	4	2	no	—
170	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
171	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
172	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
173	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
174	C₄²×C₁₃₁	—	2	8	no	—
175	C₄²×C₁₃₁	—	2	8	no	—
176	C₄²×C₁₃₁	—	2	2	no	—
177	C₄²×C₁₃₁	—	2	2	no	—
178	C₄²×C₁₃₁	—	2	2	no	—
179	C₄²×C₁₃₁	—	4	2	no	—
180	C₄²×C₁₃₁	—	4	2	no	—
181	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
182	C₂³×C₁₃₁	—	2	1	no	—
183	C₂³×C₁₃₁	—	2	1	no	—
184	C₂³×C₁₃₁	—	2	1	no	—
185	C₂³×C₁₃₁	—	2	1	no	—
186	C₂³×C₁₃₁	C₄×D₄	1	2	yes	—
187	C₂³×C₁₃₁	#137	1	2	yes	—
188	C₂³×C₁₃₁	#137	1	2	yes	—
189	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₃₁	—	2	16	no	—
191	Q₈×C₁₃₁	—	2	4	no	—
192	Q₈×C₁₃₁	—	2	4	no	—
193	Q₈×C₁₃₁	—	2	4	no	—
194	Q₈×C₁₃₁	—	2	4	no	—
195	Q₈×C₁₃₁	—	4	2	no	—
196	Q₈×C₁₃₁	C₄×D₄	1	8	yes	—
197	C₂×C₄×C₁₃₁	—	2	8	no	—
198	C₂×C₄×C₁₃₁	—	2	16	no	—
199	C₂×C₄×C₁₃₁	—	2	4	no	—
200	C₂×C₄×C₁₃₁	—	2	1	no	—
201	C₂×C₄×C₁₃₁	—	2	4	no	—
202	C₂×C₄×C₁₃₁	—	2	1	no	—
203	C₂×C₄×C₁₃₁	—	2	4	no	—
204	C₂×C₄×C₁₃₁	—	2	1	no	—
205	C₂×C₄×C₁₃₁	—	2	1	no	—
206	C₂×C₄×C₁₃₁	—	2	1	no	—
207	C₂×C₄×C₁₃₁	—	2	1	no	—
208	C₂×C₄×C₁₃₁	—	2	1	no	—
209	C₂×C₄×C₁₃₁	—	2	1	no	—
210	C₂×C₄×C₁₃₁	—	2	4	no	—
211	C₂×C₄×C₁₃₁	—	2	4	no	—
212	C₂×C₄×C₁₃₁	—	2	2	no	—
213	C₂×C₄×C₁₃₁	—	2	2	no	—
214	C₂×C₄×C₁₃₁	—	2	1	no	—
215	C₂×C₄×C₁₃₁	—	2	4	no	—
216	C₂×C₄×C₁₃₁	—	2	1	no	—
217	C₂×C₄×C₁₃₁	—	2	1	no	—
218	C₂×C₄×C₁₃₁	—	4	4	no	—
219	C₂×C₄×C₁₃₁	—	4	8	no	—
220	C₂×C₄×C₁₃₁	—	4	1	no	—
221	C₂×C₄×C₁₃₁	—	4	1	no	—
222	C₂×C₄×C₁₃₁	—	4	1	no	—
223	C₂×C₄×C₁₃₁	—	4	2	no	—
224	C₂×C₄×C₁₃₁	—	4	1	no	—
225	C₂×C₄×C₁₃₁	—	4	2	no	—
226	C₂×C₄×C₁₃₁	—	4	1	no	—
227	C₂×C₄×C₁₃₁	—	4	1	no	—
228	C₂×C₄×C₁₃₁	—	4	1	no	—
229	C₂×C₄×C₁₃₁	—	4	1	no	—
230	C₂×C₄×C₁₃₁	—	4	1	no	—
231	C₂×C₄×C₁₃₁	—	4	1	no	—
232	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
233	C₂×C₄×C₁₃₁	#120	1	2	yes	—
234	C₂×C₄×C₁₃₁	#120	1	2	yes	—
235	C₂×C₄×C₁₃₁	#137	1	2	yes	—
236	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
239	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
240	C₈×C₁₃₁	—	2	4	no	—
241	C₈×C₁₃₁	—	4	2	no	—
242	C₂²×C₁₃₁	—	2	2	no	—
243	C₂²×C₁₃₁	—	2	2	no	—
244	C₂²×C₁₃₁	—	2	2	no	—
245	C₂²×C₁₃₁	—	2	2	no	—
246	C₂²×C₁₃₁	—	2	2	no	—
247	C₂²×C₁₃₁	—	2	2	no	—
248	C₂²×C₁₃₁	#441	1	4	yes	complemented
249	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂²×C₁₃₁	C₂×#120	1	1	yes	characteristic
251	C₂²×C₁₃₁	#525	1	1	yes	characteristic
252	C₂²×C₁₃₁	C₂×#137	1	1	yes	characteristic
253	C₂²×C₁₃₁	C₂×#137	1	1	yes	characteristic
254	C₂²×C₁₃₁	C₂×#137	1	1	yes	characteristic
255	C₂²×C₁₃₁	#575	1	1	yes	characteristic
256	C₄×C₁₃₁	—	2	2	no	—
257	C₄×C₁₃₁	—	2	2	no	—
258	C₄×C₁₃₁	—	2	2	no	—
259	C₄×C₁₃₁	—	2	8	no	—
260	C₄×C₁₃₁	—	2	2	no	—
261	C₄×C₁₃₁	—	4	2	no	—
262	C₄×C₁₃₁	—	4	1	no	—
263	C₄×C₁₃₁	—	4	4	no	—
264	C₄×C₁₃₁	—	4	2	no	—
265	C₄×C₁₃₁	—	8	1	no	—
266	C₄×C₁₃₁	—	8	1	no	—
267	C₄×C₁₃₁	C₂×C₄×D₄	1	2	yes	—
268	C₄×C₁₃₁	#525	1	2	yes	—
269	C₂×C₁₃₁	—	2	4	no	—
270	C₂×C₁₃₁	C₄×#120	1	1	yes	characteristic
271	C₂×C₁₃₁	C₂×#441	1	1	yes	characteristic
272	C₂×C₁₃₁	C₄×#137	1	1	yes	characteristic
273	C₂×C₁₃₁	#3004	1	1	yes	characteristic
274	C₂×C₁₃₁	#3007	1	1	yes	characteristic
275	C₂×C₁₃₁	#3113	1	1	yes	characteristic
276	C₂×C₁₃₁	#3117	1	1	yes	characteristic
277	#21455	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₁₃₁	#21455	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²×C₄×Q₈	C₂×C₁₃₁	1	1	yes	characteristic
280	C₂×#451	C₂×C₁₃₁	1	1	yes	characteristic
281	C₂×#441	C₂×C₁₃₁	1	2	yes	complemented
282	C₄×C₂²⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic
283	#1878	C₂×C₁₃₁	1	2	yes	complemented
284	#1872	C₂×C₁₃₁	1	1	yes	characteristic
285	#1865	C₂×C₁₃₁	1	2	yes	complemented
286	#1853	C₂×C₁₃₁	1	1	yes	characteristic
287	#1787	C₂×C₁₃₁	1	1	yes	characteristic
288	#1763	C₂×C₁₃₁	1	2	yes	complemented
289	#1749	C₂×C₁₃₁	1	1	yes	characteristic
290	C₂³×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
291	C₂²×Q₁₆	C₂²×C₁₃₁	1	2	yes	—
292	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
293	C₂×C₄×Q₈	—	2	8	no	—
294	C₂×C₄×Q₈	—	2	1	no	—
295	C₂×C₄×Q₈	—	2	1	no	—
296	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
297	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
299	C₂²×C₄⋊C₄	—	2	1	no	—
300	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
301	C₂²×C₄²	—	2	1	no	—
302	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
303	#451	C₄×C₁₃₁	1	8	yes	complemented
304	#441	—	2	8	no	—
305	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
306	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
307	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
308	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
309	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
312	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
313	#391	C₂²×C₁₃₁	1	1	yes	characteristic
314	#389	C₂²×C₁₃₁	1	1	yes	characteristic
315	#387	—	2	1	no	—
316	#385	—	2	1	no	—
317	#380	C₂²×C₁₃₁	1	1	yes	characteristic
318	C₄×C₄⋊C₄	—	2	1	no	—
319	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
320	C₄×C₂²⋊C₄	—	2	1	no	—
321	#340	C₂²×C₁₃₁	1	2	yes	—
322	#340	C₂²×C₁₃₁	1	2	yes	—
323	#336	C₂²×C₁₃₁	1	2	yes	—
324	C₂²×Q₈	—	2	4	no	—
325	C₂²×Q₈	—	2	4	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	—	2	2	no	—
328	C₂²×Q₈	C₂×C₄×C₁₃₁	1	4	yes	—
329	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
330	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	D₄×C₁₃₁	1	1	yes	characteristic
334	C₂³×C₄	D₄×C₁₃₁	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
336	C₂×Q₁₆	—	2	4	no	—
337	C₂×Q₁₆	—	2	4	no	—
338	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	8	yes	complemented
339	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
340	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	4	yes	—
343	C₄×Q₈	—	2	8	no	—
344	C₄×Q₈	—	2	8	no	—
345	C₄×Q₈	—	2	4	no	—
346	C₄×Q₈	—	2	4	no	—
347	C₄×Q₈	—	2	4	no	—
348	C₄×Q₈	—	2	4	no	—
349	C₄×Q₈	D₄×C₁₃₁	1	8	yes	—
350	C₂×C₄⋊C₄	—	2	8	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	8	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	4	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
371	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
374	#106	—	2	4	no	—
375	#103	—	2	4	no	—
376	#103	—	2	4	no	—
377	#103	—	2	4	no	—
378	#103	C₂×C₄×C₁₃₁	1	8	yes	complemented
379	C₂²⋊C₈	—	2	2	no	—
380	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	4	yes	—
381	#97	—	2	4	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	16	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	16	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	C₂²×C₄×C₁₃₁	1	2	yes	—
400	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
401	C₂×Q₈	C₂×D₄×C₁₃₁	1	4	yes	—
402	C₂×Q₈	#41×C₁₃₁	1	4	yes	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	4	1	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
429	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
431	Q₁₆	—	2	16	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
449	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	4	2	no	—
452	C₄²	—	2	8	no	—
453	C₄²	—	2	8	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	4	2	no	—
458	C₄²	—	4	2	no	—
459	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	C₄×D₄×C₁₃₁	1	2	yes	—
465	C₂³	#137×C₁₃₁	1	2	yes	—
466	C₂³	#137×C₁₃₁	1	2	yes	—
467	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
468	Q₈	—	2	16	no	—
469	Q₈	—	2	4	no	—
470	Q₈	—	2	4	no	—
471	Q₈	—	2	4	no	—
472	Q₈	—	2	4	no	—
473	Q₈	—	4	2	no	—
474	Q₈	C₄×D₄×C₁₃₁	1	8	yes	—
475	C₂×C₄	—	2	16	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
511	C₂×C₄	#120×C₁₃₁	1	2	yes	—
512	C₂×C₄	#120×C₁₃₁	1	2	yes	—
513	C₂×C₄	#137×C₁₃₁	1	2	yes	—
514	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
516	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
517	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
518	C₈	—	2	4	no	—
519	C₈	—	4	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	#441×C₁₃₁	1	4	yes	complemented
527	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
528	C₂²	C₂×#120×C₁₃₁	1	1	yes	characteristic
529	C₂²	#525×C₁₃₁	1	1	yes	characteristic
530	C₂²	C₂×#137×C₁₃₁	1	1	yes	characteristic
531	C₂²	C₂×#137×C₁₃₁	1	1	yes	characteristic
532	C₂²	C₂×#137×C₁₃₁	1	1	yes	characteristic
533	C₂²	#575×C₁₃₁	1	1	yes	characteristic
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	8	no	—
538	C₄	—	2	2	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	4	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	1	no	—
545	C₄	C₂×C₄×D₄×C₁₃₁	1	2	yes	—
546	C₄	#525×C₁₃₁	1	2	yes	—
547	C₂	—	2	4	no	—
548	C₂	C₄×#120×C₁₃₁	1	1	yes	characteristic
549	C₂	C₂×#441×C₁₃₁	1	1	yes	characteristic
550	C₂	C₄×#137×C₁₃₁	1	1	yes	characteristic
551	C₂	#3004×C₁₃₁	1	1	yes	characteristic
552	C₂	#3007×C₁₃₁	1	1	yes	characteristic
553	C₂	#3113×C₁₃₁	1	1	yes	characteristic
554	C₂	#3117×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂⁴×C₁₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₂²×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#441×C₁₃₁	C₂	semidirect
5. #1878×C₁₃₁	C₂	semidirect
7. #1865×C₁₃₁	C₂	semidirect
10. #1763×C₁₃₁	C₂	semidirect
25. #451×C₁₃₁	C₄	semidirect
60. C₂×Q₁₆×C₁₃₁	C₂×C₄	semidirect
100. #103×C₁₃₁	C₂×C₄	semidirect
248. C₂²×C₁₃₁	#441	semidirect
277. #21455	C₁₃₁	direct (N × H)
278. C₁₃₁	#21455	direct (N × H)
281. C₂×#441	C₂×C₁₃₁	semidirect
283. #1878	C₂×C₁₃₁	semidirect
285. #1865	C₂×C₁₃₁	semidirect
288. #1763	C₂×C₁₃₁	semidirect
303. #451	C₄×C₁₃₁	semidirect
338. C₂×Q₁₆	C₂×C₄×C₁₃₁	semidirect
378. #103	C₂×C₄×C₁₃₁	semidirect
526. C₂²	#441×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₃₁	2
C₂×#451×C₁₃₁	2
C₂×#441×C₁₃₁	2
C₄×C₂²⋊Q₈×C₁₃₁	2
#1878×C₁₃₁	2
#1872×C₁₃₁	2
#1865×C₁₃₁	2
#1853×C₁₃₁	2
#1787×C₁₃₁	2
#1763×C₁₃₁	2
#1749×C₁₃₁	2
#21455	131

Subgroups — C131×#21455 #45707339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#21455 #45707339