Subgroups — C₁₃₁×#17628 #45703512

Order 33536.

942 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3507×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2983×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2351×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#1518×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1517×C₁₃₁	C₂	1	1	yes	maximal, characteristic
6	#1512×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	#1509×C₁₃₁	C₂	1	4	yes	maximal, complemented
8	#1503×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1502×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	#559×C₁₃₁	C₄	1	2	yes	complemented
11	#557×C₁₃₁	C₄	1	2	yes	complemented
12	#556×C₁₃₁	—	2	2	no	—
13	#556×C₁₃₁	C₄	1	2	yes	complemented
14	#554×C₁₃₁	C₄	1	2	yes	complemented
15	#552×C₁₃₁	—	2	2	no	—
16	#539×C₁₃₁	—	2	2	no	—
17	#536×C₁₃₁	—	2	1	no	—
18	#533×C₁₃₁	C₂²	1	1	yes	characteristic
19	#532×C₁₃₁	C₂²	1	1	yes	characteristic
20	#529×C₁₃₁	C₂²	1	4	yes	—
21	#520×C₁₃₁	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₃₁	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
24	#446×C₁₃₁	—	2	2	no	—
25	#446×C₁₃₁	—	2	2	no	—
26	#432×C₁₃₁	C₂²	1	4	yes	—
27	#431×C₁₃₁	C₂²	1	1	yes	characteristic
28	#431×C₁₃₁	C₂²	1	1	yes	characteristic
29	#389×C₁₃₁	—	2	1	no	—
30	#389×C₁₃₁	—	2	2	no	—
31	#382×C₁₃₁	C₂²	1	2	yes	—
32	#382×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
35	#328×C₁₃₁	C₂²	1	2	yes	—
36	#328×C₁₃₁	C₂²	1	2	yes	—
37	#328×C₁₃₁	C₂²	1	4	yes	—
38	#327×C₁₃₁	C₂²	1	2	yes	—
39	#327×C₁₃₁	C₂²	1	2	yes	—
40	#327×C₁₃₁	C₂²	1	4	yes	—
41	C₂×#41×C₁₃₁	—	2	1	no	—
42	C₂²×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
43	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
44	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
45	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
46	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
47	#127×C₁₃₁	C₂×C₄	1	1	yes	characteristic
48	#126×C₁₃₁	—	2	4	no	—
49	#126×C₁₃₁	—	2	4	no	—
50	#125×C₁₃₁	—	2	4	no	—
51	#125×C₁₃₁	—	2	1	no	—
52	#125×C₁₃₁	C₂×C₄	1	4	yes	—
53	#124×C₁₃₁	—	2	2	no	—
54	#124×C₁₃₁	—	2	1	no	—
55	#124×C₁₃₁	C₂×C₄	1	4	yes	—
56	#123×C₁₃₁	—	2	4	no	—
57	#123×C₁₃₁	—	2	4	no	—
58	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
59	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
60	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
61	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
62	C₂²⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
63	#121×C₁₃₁	—	2	1	no	—
64	#121×C₁₃₁	C₂³	1	2	yes	—
65	C₄×Q₈×C₁₃₁	—	2	2	no	—
66	C₄×Q₈×C₁₃₁	—	2	1	no	—
67	C₄×Q₈×C₁₃₁	—	4	4	no	—
68	C₄×Q₈×C₁₃₁	C₂×C₄	1	4	yes	—
69	C₄×Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
70	C₄×Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
71	C₄×Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
72	C₄×Q₈×C₁₃₁	D₄	1	2	yes	—
73	C₄×Q₈×C₁₃₁	D₄	1	2	yes	—
74	C₄×D₄×C₁₃₁	—	2	4	no	—
75	C₄×D₄×C₁₃₁	—	2	2	no	—
76	C₄×D₄×C₁₃₁	—	2	1	no	—
77	C₄×D₄×C₁₃₁	C₂×C₄	1	4	yes	—
78	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
79	#117×C₁₃₁	—	2	1	no	—
80	#117×C₁₃₁	—	2	2	no	—
81	#117×C₁₃₁	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₃₁	D₄	1	2	yes	—
89	C₂×C₄²×C₁₃₁	—	2	2	no	—
90	C₂×C₄²×C₁₃₁	—	2	1	no	—
91	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
93	C₄⋊C₈×C₁₃₁	—	2	1	no	—
94	C₄⋊C₈×C₁₃₁	—	2	1	no	—
95	C₄⋊C₈×C₁₃₁	—	2	4	no	—
96	C₂²⋊C₈×C₁₃₁	C₂³	1	2	yes	—
97	C₂²⋊C₈×C₁₃₁	C₂³	1	2	yes	—
98	#97×C₁₃₁	—	2	4	no	—
99	C₄×C₈×C₁₃₁	—	2	1	no	—
100	C₄×C₈×C₁₃₁	—	2	1	no	—
101	#95×C₁₃₁	—	2	2	no	—
102	#95×C₁₃₁	—	2	1	no	—
103	#95×C₁₃₁	C₂³	1	1	yes	characteristic
104	#95×C₁₃₁	C₂³	1	1	yes	characteristic
105	#95×C₁₃₁	C₂³	1	2	yes	—
106	#41×C₁₃₁	—	4	2	no	—
107	#41×C₁₃₁	—	4	2	no	—
108	C₂×Q₈×C₁₃₁	—	2	1	no	—
109	C₂×Q₈×C₁₃₁	—	2	1	no	—
110	C₂×Q₈×C₁₃₁	—	2	2	no	—
111	C₂×Q₈×C₁₃₁	—	2	2	no	—
112	C₂×Q₈×C₁₃₁	C₂²⋊C₄	1	2	yes	—
113	C₂×Q₈×C₁₃₁	C₂²⋊C₄	1	2	yes	—
114	C₂×Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₁₃₁	—	2	2	no	—
116	C₂×D₄×C₁₃₁	—	2	1	no	—
117	C₂×D₄×C₁₃₁	—	2	1	no	—
118	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₃₁	—	2	1	no	—
120	C₂²×C₄×C₁₃₁	—	2	2	no	—
121	C₂²×C₄×C₁₃₁	—	2	4	no	—
122	C₂²×C₄×C₁₃₁	—	2	2	no	—
123	C₂²×C₄×C₁₃₁	—	2	1	no	—
124	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
129	C₂×C₈×C₁₃₁	—	2	2	no	—
130	C₂×C₈×C₁₃₁	—	2	2	no	—
131	C₄⋊C₄×C₁₃₁	—	2	1	no	—
132	C₄⋊C₄×C₁₃₁	—	2	4	no	—
133	C₄⋊C₄×C₁₃₁	—	2	1	no	—
134	C₄⋊C₄×C₁₃₁	—	2	4	no	—
135	C₄⋊C₄×C₁₃₁	—	2	1	no	—
136	C₄⋊C₄×C₁₃₁	—	2	1	no	—
137	C₄⋊C₄×C₁₃₁	—	2	2	no	—
138	C₄⋊C₄×C₁₃₁	—	2	4	no	—
139	C₄⋊C₄×C₁₃₁	—	2	2	no	—
140	C₄⋊C₄×C₁₃₁	—	4	4	no	—
141	C₄⋊C₄×C₁₃₁	—	4	2	no	—
142	C₄⋊C₄×C₁₃₁	—	4	4	no	—
143	C₄⋊C₄×C₁₃₁	—	4	2	no	—
144	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
145	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
146	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	4	yes	—
147	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	4	yes	—
148	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
149	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
150	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
151	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
152	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
153	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
154	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
155	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
156	C₄²×C₁₃₁	—	2	4	no	—
157	C₄²×C₁₃₁	—	2	2	no	—
158	C₄²×C₁₃₁	—	4	4	no	—
159	C₄²×C₁₃₁	—	4	2	no	—
160	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
162	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
166	C₂³×C₁₃₁	—	2	2	no	—
167	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₁₃₁	—	2	4	no	—
169	Q₈×C₁₃₁	—	2	4	no	—
170	Q₈×C₁₃₁	—	4	2	no	—
171	Q₈×C₁₃₁	—	4	2	no	—
172	Q₈×C₁₃₁	—	8	1	no	—
173	D₄×C₁₃₁	—	4	2	no	—
174	D₄×C₁₃₁	—	4	2	no	—
175	D₄×C₁₃₁	—	4	2	no	—
176	D₄×C₁₃₁	—	4	2	no	—
177	D₄×C₁₃₁	—	8	1	no	—
178	C₂×C₄×C₁₃₁	—	2	2	no	—
179	C₂×C₄×C₁₃₁	—	2	2	no	—
180	C₂×C₄×C₁₃₁	—	2	2	no	—
181	C₂×C₄×C₁₃₁	—	2	2	no	—
182	C₂×C₄×C₁₃₁	—	2	2	no	—
183	C₂×C₄×C₁₃₁	—	2	2	no	—
184	C₂×C₄×C₁₃₁	—	4	2	no	—
185	C₂×C₄×C₁₃₁	—	4	1	no	—
186	C₂×C₄×C₁₃₁	—	4	1	no	—
187	C₂×C₄×C₁₃₁	—	4	1	no	—
188	C₂×C₄×C₁₃₁	—	4	1	no	—
189	C₂×C₄×C₁₃₁	—	4	4	no	—
190	C₂×C₄×C₁₃₁	—	4	2	no	—
191	C₂×C₄×C₁₃₁	—	4	1	no	—
192	C₂×C₄×C₁₃₁	—	4	2	no	—
193	C₂×C₄×C₁₃₁	—	4	1	no	—
194	C₂×C₄×C₁₃₁	—	4	2	no	—
195	C₂×C₄×C₁₃₁	—	4	1	no	—
196	C₂×C₄×C₁₃₁	—	8	4	no	—
197	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
198	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
199	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₁₃₁	#137	1	2	yes	—
205	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
207	C₈×C₁₃₁	—	4	2	no	—
208	C₈×C₁₃₁	—	4	2	no	—
209	C₂²×C₁₃₁	—	2	1	no	—
210	C₂²×C₁₃₁	—	2	1	no	—
211	C₂²×C₁₃₁	—	4	2	no	—
212	C₂²×C₁₃₁	—	4	2	no	—
213	C₂²×C₁₃₁	—	4	2	no	—
214	C₂²×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₂²×C₁₃₁	C₂×#137	1	1	yes	characteristic
217	C₄×C₁₃₁	—	2	1	no	—
218	C₄×C₁₃₁	—	2	1	no	—
219	C₄×C₁₃₁	—	2	4	no	—
220	C₄×C₁₃₁	—	2	4	no	—
221	C₄×C₁₃₁	—	2	1	no	—
222	C₄×C₁₃₁	—	2	1	no	—
223	C₄×C₁₃₁	—	4	2	no	—
224	C₄×C₁₃₁	—	4	2	no	—
225	C₄×C₁₃₁	—	4	2	no	—
226	C₄×C₁₃₁	—	4	2	no	—
227	C₄×C₁₃₁	—	8	2	no	—
228	C₄×C₁₃₁	—	8	1	no	—
229	C₄×C₁₃₁	#417	1	2	yes	—
230	C₄×C₁₃₁	#417	1	2	yes	—
231	C₂×C₁₃₁	—	2	1	no	—
232	C₂×C₁₃₁	—	2	1	no	—
233	C₂×C₁₃₁	—	8	2	no	—
234	C₂×C₁₃₁	#2884	1	1	yes	characteristic
235	C₂×C₁₃₁	C₂×#417	1	1	yes	characteristic
236	C₂×C₁₃₁	#2901	1	1	yes	characteristic
237	#17628	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₁₃₁	#17628	1	1	yes	characteristic, direct product factor, Sylow
239	#3507	C₂×C₁₃₁	1	1	yes	characteristic
240	#2983	C₂×C₁₃₁	1	1	yes	characteristic, complemented
241	#2351	C₂×C₁₃₁	1	1	yes	characteristic, complemented
242	#1518	C₂×C₁₃₁	1	1	yes	characteristic, complemented
243	#1517	C₂×C₁₃₁	1	1	yes	characteristic
244	#1512	C₂×C₁₃₁	1	4	yes	complemented
245	#1509	C₂×C₁₃₁	1	4	yes	complemented
246	#1503	C₂×C₁₃₁	1	1	yes	characteristic, complemented
247	#1502	C₂×C₁₃₁	1	1	yes	characteristic
248	#559	C₄×C₁₃₁	1	2	yes	complemented
249	#557	C₄×C₁₃₁	1	2	yes	complemented
250	#556	—	2	2	no	—
251	#556	C₄×C₁₃₁	1	2	yes	complemented
252	#554	C₄×C₁₃₁	1	2	yes	complemented
253	#552	—	2	2	no	—
254	#539	—	2	2	no	—
255	#536	—	2	1	no	—
256	#533	C₂²×C₁₃₁	1	1	yes	characteristic
257	#532	C₂²×C₁₃₁	1	1	yes	characteristic
258	#529	C₂²×C₁₃₁	1	4	yes	—
259	#520	—	2	1	no	—
260	C₂×C₄×Q₈	—	2	1	no	—
261	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
262	#446	—	2	2	no	—
263	#446	—	2	2	no	—
264	#432	C₂²×C₁₃₁	1	4	yes	—
265	#431	C₂²×C₁₃₁	1	1	yes	characteristic
266	#431	C₂²×C₁₃₁	1	1	yes	characteristic
267	#389	—	2	1	no	—
268	#389	—	2	2	no	—
269	#382	C₂²×C₁₃₁	1	2	yes	—
270	#382	C₂²×C₁₃₁	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
273	#328	C₂²×C₁₃₁	1	2	yes	—
274	#328	C₂²×C₁₃₁	1	2	yes	—
275	#328	C₂²×C₁₃₁	1	4	yes	—
276	#327	C₂²×C₁₃₁	1	2	yes	—
277	#327	C₂²×C₁₃₁	1	2	yes	—
278	#327	C₂²×C₁₃₁	1	4	yes	—
279	C₂×#41	—	2	1	no	—
280	C₂²×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
283	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
284	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
285	#127	C₂×C₄×C₁₃₁	1	1	yes	characteristic
286	#126	—	2	4	no	—
287	#126	—	2	4	no	—
288	#125	—	2	4	no	—
289	#125	—	2	1	no	—
290	#125	C₂×C₄×C₁₃₁	1	4	yes	—
291	#124	—	2	2	no	—
292	#124	—	2	1	no	—
293	#124	C₂×C₄×C₁₃₁	1	4	yes	—
294	#123	—	2	4	no	—
295	#123	—	2	4	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
301	#121	—	2	1	no	—
302	#121	C₂³×C₁₃₁	1	2	yes	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	4	4	no	—
306	C₄×Q₈	C₂×C₄×C₁₃₁	1	4	yes	—
307	C₄×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
308	C₄×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
309	C₄×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
310	C₄×Q₈	D₄×C₁₃₁	1	2	yes	—
311	C₄×Q₈	D₄×C₁₃₁	1	2	yes	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	C₂×C₄×C₁₃₁	1	4	yes	—
316	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
317	#117	—	2	1	no	—
318	#117	—	2	2	no	—
319	#117	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₁₃₁	1	2	yes	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
330	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	—	2	4	no	—
334	C₂²⋊C₈	C₂³×C₁₃₁	1	2	yes	—
335	C₂²⋊C₈	C₂³×C₁₃₁	1	2	yes	—
336	#97	—	2	4	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	—	2	1	no	—
339	#95	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	C₂³×C₁₃₁	1	1	yes	characteristic
342	#95	C₂³×C₁₃₁	1	1	yes	characteristic
343	#95	C₂³×C₁₃₁	1	2	yes	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	C₂²⋊C₄×C₁₃₁	1	2	yes	—
351	C₂×Q₈	C₂²⋊C₄×C₁₃₁	1	2	yes	—
352	C₂×Q₈	C₂²×C₄×C₁₃₁	1	2	yes	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	4	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
383	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
384	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	4	yes	—
385	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	4	yes	—
386	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
387	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₄²	—	2	4	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	4	4	no	—
397	C₄²	—	4	2	no	—
398	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
399	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
400	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
401	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
402	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
403	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
404	C₂³	—	2	2	no	—
405	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	8	1	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	8	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	8	4	no	—
435	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
438	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
439	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
440	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
441	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
442	C₂×C₄	#137×C₁₃₁	1	2	yes	—
443	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
445	C₈	—	4	2	no	—
446	C₈	—	4	2	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
453	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
454	C₂²	C₂×#137×C₁₃₁	1	1	yes	characteristic
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	4	no	—
458	C₄	—	2	4	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	2	no	—
466	C₄	—	8	1	no	—
467	C₄	#417×C₁₃₁	1	2	yes	—
468	C₄	#417×C₁₃₁	1	2	yes	—
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	8	2	no	—
472	C₂	#2884×C₁₃₁	1	1	yes	characteristic
473	C₂	C₂×#417×C₁₃₁	1	1	yes	characteristic
474	C₂	#2901×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	#532×C₁₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄×Q₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2983×C₁₃₁	C₂	semidirect
3. #2351×C₁₃₁	C₂	semidirect
4. #1518×C₁₃₁	C₂	semidirect
6. #1512×C₁₃₁	C₂	semidirect
7. #1509×C₁₃₁	C₂	semidirect
8. #1503×C₁₃₁	C₂	semidirect
10. #559×C₁₃₁	C₄	semidirect
11. #557×C₁₃₁	C₄	semidirect
13. #556×C₁₃₁	C₄	semidirect
14. #554×C₁₃₁	C₄	semidirect
237. #17628	C₁₃₁	direct (N × H)
238. C₁₃₁	#17628	direct (N × H)
240. #2983	C₂×C₁₃₁	semidirect
241. #2351	C₂×C₁₃₁	semidirect
242. #1518	C₂×C₁₃₁	semidirect
244. #1512	C₂×C₁₃₁	semidirect
245. #1509	C₂×C₁₃₁	semidirect
246. #1503	C₂×C₁₃₁	semidirect
248. #559	C₄×C₁₃₁	semidirect
249. #557	C₄×C₁₃₁	semidirect
251. #556	C₄×C₁₃₁	semidirect
252. #554	C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3507×C₁₃₁	2
#2983×C₁₃₁	2
#2351×C₁₃₁	2
#1518×C₁₃₁	2
#1517×C₁₃₁	2
#1512×C₁₃₁	2
#1509×C₁₃₁	2
#1503×C₁₃₁	2
#1502×C₁₃₁	2
#17628	131

Subgroups — C131×#17628 #45703512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#17628 #45703512