Subgroups — C₁₃₁×#19232 #45705116

Order 33536.

652 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3246×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#3206×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#3165×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2935×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#1693×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1691×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1673×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1671×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1565×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1542×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#332×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₁₃₁	—	2	1	no	—
13	#533×C₁₃₁	C₂²	1	1	yes	characteristic
14	#532×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	#501×C₁₃₁	—	2	2	no	—
17	#500×C₁₃₁	C₂²	1	2	yes	—
18	#498×C₁₃₁	C₂²	1	2	yes	—
19	#492×C₁₃₁	—	2	1	no	—
20	#487×C₁₃₁	—	2	1	no	—
21	#476×C₁₃₁	C₂²	1	2	yes	—
22	#475×C₁₃₁	—	2	1	no	—
23	#465×C₁₃₁	—	2	2	no	—
24	#461×C₁₃₁	C₂²	1	2	yes	—
25	#461×C₁₃₁	C₂²	1	2	yes	—
26	#461×C₁₃₁	C₂²	1	2	yes	—
27	#460×C₁₃₁	—	2	1	no	—
28	#448×C₁₃₁	—	2	2	no	—
29	#436×C₁₃₁	C₂²	1	2	yes	—
30	#435×C₁₃₁	—	2	2	no	—
31	C₈×D₄×C₁₃₁	C₂²	1	2	yes	—
32	#431×C₁₃₁	C₂²	1	1	yes	characteristic
33	#428×C₁₃₁	—	2	1	no	—
34	#428×C₁₃₁	—	2	1	no	—
35	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
37	#408×C₁₃₁	—	2	1	no	—
38	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
39	#335×C₁₃₁	C₂²	1	2	yes	—
40	#334×C₁₃₁	C₂²	1	2	yes	—
41	#333×C₁₃₁	C₂²	1	1	yes	characteristic
42	#333×C₁₃₁	C₂²	1	1	yes	characteristic
43	#332×C₁₃₁	C₂²	1	2	yes	—
44	#332×C₁₃₁	C₂²	1	2	yes	—
45	#332×C₁₃₁	C₂²	1	1	yes	characteristic
46	#332×C₁₃₁	C₂²	1	1	yes	characteristic
47	C₂×#41×C₁₃₁	—	2	1	no	—
48	C₂²×Q₈×C₁₃₁	—	2	1	no	—
49	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
51	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
52	#131×C₁₃₁	—	4	4	no	—
53	C₂×M₁₆×C₁₃₁	—	2	2	no	—
54	C₂×M₁₆×C₁₃₁	D₄	1	1	yes	characteristic
55	C₂×M₁₆×C₁₃₁	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₁	—	2	1	no	—
57	C₂²×C₈×C₁₃₁	—	2	1	no	—
58	C₂²×C₈×C₁₃₁	—	2	2	no	—
59	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
60	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
61	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
62	C₄⋊Q₈×C₁₃₁	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
66	#127×C₁₃₁	D₄	1	1	yes	characteristic
67	#125×C₁₃₁	—	2	1	no	—
68	#124×C₁₃₁	—	2	1	no	—
69	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
70	C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
71	#121×C₁₃₁	—	2	1	no	—
72	#121×C₁₃₁	D₄	1	2	yes	—
73	C₄×Q₈×C₁₃₁	—	2	1	no	—
74	C₄×Q₈×C₁₃₁	—	2	1	no	—
75	C₄×D₄×C₁₃₁	—	2	1	no	—
76	C₄×D₄×C₁₃₁	C₂³	1	2	yes	—
77	#117×C₁₃₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
80	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
81	#107×C₁₃₁	—	2	2	no	—
82	#107×C₁₃₁	—	2	2	no	—
83	#106×C₁₃₁	—	2	2	no	—
84	#106×C₁₃₁	—	2	2	no	—
85	#106×C₁₃₁	—	2	2	no	—
86	C₄⋊C₈×C₁₃₁	—	2	1	no	—
87	C₄⋊C₈×C₁₃₁	—	2	1	no	—
88	C₄⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
91	C₄⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
93	#103×C₁₃₁	—	2	2	no	—
94	#103×C₁₃₁	—	2	2	no	—
95	#103×C₁₃₁	—	2	2	no	—
96	#102×C₁₃₁	—	2	2	no	—
97	C₂²⋊C₈×C₁₃₁	—	2	1	no	—
98	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
99	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
100	#97×C₁₃₁	D₄	1	2	yes	—
101	C₄×C₈×C₁₃₁	—	2	1	no	—
102	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
103	#41×C₁₃₁	—	4	2	no	—
104	#41×C₁₃₁	—	4	2	no	—
105	C₂×Q₈×C₁₃₁	—	2	1	no	—
106	C₂×Q₈×C₁₃₁	—	2	1	no	—
107	C₂×Q₈×C₁₃₁	—	2	2	no	—
108	C₂×Q₈×C₁₃₁	—	2	1	no	—
109	C₂×Q₈×C₁₃₁	—	4	1	no	—
110	C₂×Q₈×C₁₃₁	—	8	1	no	—
111	C₂×Q₈×C₁₃₁	—	8	1	no	—
112	C₂×D₄×C₁₃₁	—	2	2	no	—
113	C₂×D₄×C₁₃₁	—	2	1	no	—
114	C₂×D₄×C₁₃₁	—	2	1	no	—
115	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃₁	—	2	2	no	—
117	C₂²×C₄×C₁₃₁	—	4	1	no	—
118	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
121	SD₁₆×C₁₃₁	—	8	2	no	—
122	SD₁₆×C₁₃₁	—	8	2	no	—
123	SD₁₆×C₁₃₁	—	8	2	no	—
124	M₁₆×C₁₃₁	—	2	2	no	—
125	M₁₆×C₁₃₁	—	4	4	no	—
126	M₁₆×C₁₃₁	SD₁₆	1	4	yes	complemented
127	C₂×C₈×C₁₃₁	—	2	1	no	—
128	C₂×C₈×C₁₃₁	—	2	1	no	—
129	C₂×C₈×C₁₃₁	—	2	1	no	—
130	C₂×C₈×C₁₃₁	—	2	1	no	—
131	C₂×C₈×C₁₃₁	—	2	2	no	—
132	C₂×C₈×C₁₃₁	—	4	2	no	—
133	C₂×C₈×C₁₃₁	—	4	4	no	—
134	C₂×C₈×C₁₃₁	—	8	1	no	—
135	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₁₃₁	—	2	1	no	—
138	C₄⋊C₄×C₁₃₁	—	2	1	no	—
139	C₄⋊C₄×C₁₃₁	—	2	1	no	—
140	C₄⋊C₄×C₁₃₁	—	2	2	no	—
141	C₄⋊C₄×C₁₃₁	—	2	1	no	—
142	C₄⋊C₄×C₁₃₁	—	2	2	no	—
143	C₄⋊C₄×C₁₃₁	—	2	1	no	—
144	C₄⋊C₄×C₁₃₁	—	4	1	no	—
145	C₄⋊C₄×C₁₃₁	—	4	1	no	—
146	C₄⋊C₄×C₁₃₁	—	4	1	no	—
147	C₄⋊C₄×C₁₃₁	—	4	1	no	—
148	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
150	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
151	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
152	C₄²×C₁₃₁	—	4	1	no	—
153	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃₁	#41	1	1	yes	characteristic
156	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
157	C₂³×C₁₃₁	—	2	2	no	—
158	C₂³×C₁₃₁	#121	1	1	yes	characteristic
159	Q₈×C₁₃₁	—	4	2	no	—
160	Q₈×C₁₃₁	—	4	1	no	—
161	Q₈×C₁₃₁	—	4	2	no	—
162	Q₈×C₁₃₁	—	4	2	no	—
163	Q₈×C₁₃₁	—	4	1	no	—
164	Q₈×C₁₃₁	—	8	1	no	—
165	Q₈×C₁₃₁	—	8	2	no	—
166	D₄×C₁₃₁	—	2	2	no	—
167	D₄×C₁₃₁	—	2	2	no	—
168	D₄×C₁₃₁	—	4	4	no	—
169	D₄×C₁₃₁	—	4	2	no	—
170	D₄×C₁₃₁	—	8	1	no	—
171	C₂×C₄×C₁₃₁	—	2	1	no	—
172	C₂×C₄×C₁₃₁	—	2	1	no	—
173	C₂×C₄×C₁₃₁	—	2	2	no	—
174	C₂×C₄×C₁₃₁	—	4	1	no	—
175	C₂×C₄×C₁₃₁	—	4	2	no	—
176	C₂×C₄×C₁₃₁	—	4	2	no	—
177	C₂×C₄×C₁₃₁	—	4	1	no	—
178	C₂×C₄×C₁₃₁	—	4	1	no	—
179	C₂×C₄×C₁₃₁	—	4	2	no	—
180	C₂×C₄×C₁₃₁	—	8	2	no	—
181	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₁₃₁	#137	1	2	yes	—
186	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
189	C₈×C₁₃₁	—	2	2	no	—
190	C₈×C₁₃₁	—	4	1	no	—
191	C₈×C₁₃₁	—	4	1	no	—
192	C₈×C₁₃₁	—	4	2	no	—
193	C₈×C₁₃₁	—	4	1	no	—
194	C₈×C₁₃₁	—	4	1	no	—
195	C₈×C₁₃₁	C₂×SD₁₆	1	4	yes	—
196	C₂²×C₁₃₁	—	2	1	no	—
197	C₂²×C₁₃₁	—	2	1	no	—
198	C₂²×C₁₃₁	—	4	2	no	—
199	C₂²×C₁₃₁	—	4	2	no	—
200	C₂²×C₁₃₁	—	4	2	no	—
201	C₂²×C₁₃₁	#461	1	2	yes	—
202	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
203	C₄×C₁₃₁	—	2	1	no	—
204	C₄×C₁₃₁	—	2	1	no	—
205	C₄×C₁₃₁	—	2	1	no	—
206	C₄×C₁₃₁	—	4	2	no	—
207	C₄×C₁₃₁	—	8	2	no	—
208	C₄×C₁₃₁	—	8	1	no	—
209	C₄×C₁₃₁	—	8	1	no	—
210	C₄×C₁₃₁	#461	1	2	yes	—
211	C₄×C₁₃₁	C₂²×SD₁₆	1	1	yes	characteristic
212	C₄×C₁₃₁	C₂×#137	1	1	yes	characteristic
213	C₄×C₁₃₁	#576	1	1	yes	characteristic
214	C₄×C₁₃₁	#577	1	1	yes	characteristic
215	C₂×C₁₃₁	—	2	2	no	—
216	C₂×C₁₃₁	—	8	2	no	—
217	C₂×C₁₃₁	C₂×#461	1	1	yes	characteristic
218	C₂×C₁₃₁	#3062	1	1	yes	characteristic
219	C₂×C₁₃₁	#3069	1	1	yes	characteristic
220	#19232	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₁₃₁	#19232	1	1	yes	characteristic, direct product factor, Sylow
222	#3246	C₂×C₁₃₁	1	1	yes	characteristic
223	#3206	C₂×C₁₃₁	1	1	yes	characteristic
224	#3165	C₂×C₁₃₁	1	1	yes	characteristic, complemented
225	#2935	C₂×C₁₃₁	1	1	yes	characteristic
226	#1693	C₂×C₁₃₁	1	2	yes	complemented
227	#1691	C₂×C₁₃₁	1	2	yes	complemented
228	#1673	C₂×C₁₃₁	1	2	yes	complemented
229	#1671	C₂×C₁₃₁	1	2	yes	complemented
230	#1565	C₂×C₁₃₁	1	1	yes	characteristic, complemented
231	#1542	C₂×C₁₃₁	1	1	yes	characteristic, complemented
232	C₂×#332	C₂×C₁₃₁	1	1	yes	characteristic, complemented
233	C₂×#131	—	2	1	no	—
234	#533	C₂²×C₁₃₁	1	1	yes	characteristic
235	#532	C₂²×C₁₃₁	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
237	#501	—	2	2	no	—
238	#500	C₂²×C₁₃₁	1	2	yes	—
239	#498	C₂²×C₁₃₁	1	2	yes	—
240	#492	—	2	1	no	—
241	#487	—	2	1	no	—
242	#476	C₂²×C₁₃₁	1	2	yes	—
243	#475	—	2	1	no	—
244	#465	—	2	2	no	—
245	#461	C₂²×C₁₃₁	1	2	yes	—
246	#461	C₂²×C₁₃₁	1	2	yes	—
247	#461	C₂²×C₁₃₁	1	2	yes	—
248	#460	—	2	1	no	—
249	#448	—	2	2	no	—
250	#436	C₂²×C₁₃₁	1	2	yes	—
251	#435	—	2	2	no	—
252	C₈×D₄	C₂²×C₁₃₁	1	2	yes	—
253	#431	C₂²×C₁₃₁	1	1	yes	characteristic
254	#428	—	2	1	no	—
255	#428	—	2	1	no	—
256	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
258	#408	—	2	1	no	—
259	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
260	#335	C₂²×C₁₃₁	1	2	yes	—
261	#334	C₂²×C₁₃₁	1	2	yes	—
262	#333	C₂²×C₁₃₁	1	1	yes	characteristic
263	#333	C₂²×C₁₃₁	1	1	yes	characteristic
264	#332	C₂²×C₁₃₁	1	2	yes	—
265	#332	C₂²×C₁₃₁	1	2	yes	—
266	#332	C₂²×C₁₃₁	1	1	yes	characteristic
267	#332	C₂²×C₁₃₁	1	1	yes	characteristic
268	C₂×#41	—	2	1	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	2	2	no	—
273	#131	—	4	4	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	D₄×C₁₃₁	1	1	yes	characteristic
276	C₂×M₁₆	D₄×C₁₃₁	1	1	yes	characteristic
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	D₄×C₁₃₁	1	1	yes	characteristic
284	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
285	C₄⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
286	C₄⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
287	#127	D₄×C₁₃₁	1	1	yes	characteristic
288	#125	—	2	1	no	—
289	#124	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	#121	—	2	1	no	—
293	#121	D₄×C₁₃₁	1	2	yes	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	C₂³×C₁₃₁	1	2	yes	—
298	#117	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
302	#107	—	2	2	no	—
303	#107	—	2	2	no	—
304	#106	—	2	2	no	—
305	#106	—	2	2	no	—
306	#106	—	2	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	2	1	no	—
309	C₄⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
310	C₄⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
311	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
312	C₄⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
314	#103	—	2	2	no	—
315	#103	—	2	2	no	—
316	#103	—	2	2	no	—
317	#102	—	2	2	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	#97	D₄×C₁₃₁	1	2	yes	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	8	1	no	—
332	C₂×Q₈	—	8	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
341	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
342	SD₁₆	—	8	2	no	—
343	SD₁₆	—	8	2	no	—
344	SD₁₆	—	8	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	4	4	no	—
347	M₁₆	SD₁₆×C₁₃₁	1	4	yes	complemented
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	—	4	4	no	—
355	C₂×C₈	—	8	1	no	—
356	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
357	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₄²	—	4	1	no	—
374	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
375	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
376	C₄²	#41×C₁₃₁	1	1	yes	characteristic
377	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
378	C₂³	—	2	2	no	—
379	C₂³	#121×C₁₃₁	1	1	yes	characteristic
380	Q₈	—	4	2	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	1	no	—
385	Q₈	—	8	1	no	—
386	Q₈	—	8	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
403	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
404	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
405	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	2	yes	—
406	C₂×C₄	#137×C₁₃₁	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	C₂×SD₁₆×C₁₃₁	1	4	yes	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	#461×C₁₃₁	1	2	yes	—
423	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	#461×C₁₃₁	1	2	yes	—
432	C₄	C₂²×SD₁₆×C₁₃₁	1	1	yes	characteristic
433	C₄	C₂×#137×C₁₃₁	1	1	yes	characteristic
434	C₄	#576×C₁₃₁	1	1	yes	characteristic
435	C₄	#577×C₁₃₁	1	1	yes	characteristic
436	C₂	—	2	2	no	—
437	C₂	—	8	2	no	—
438	C₂	C₂×#461×C₁₃₁	1	1	yes	characteristic
439	C₂	#3062×C₁₃₁	1	1	yes	characteristic
440	C₂	#3069×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₁
prime radical	#532×C₁₃₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #3165×C₁₃₁	C₂	semidirect
5. #1693×C₁₃₁	C₂	semidirect
6. #1691×C₁₃₁	C₂	semidirect
7. #1673×C₁₃₁	C₂	semidirect
8. #1671×C₁₃₁	C₂	semidirect
9. #1565×C₁₃₁	C₂	semidirect
10. #1542×C₁₃₁	C₂	semidirect
11. C₂×#332×C₁₃₁	C₂	semidirect
126. M₁₆×C₁₃₁	SD₁₆	semidirect
220. #19232	C₁₃₁	direct (N × H)
221. C₁₃₁	#19232	direct (N × H)
224. #3165	C₂×C₁₃₁	semidirect
226. #1693	C₂×C₁₃₁	semidirect
227. #1691	C₂×C₁₃₁	semidirect
228. #1673	C₂×C₁₃₁	semidirect
229. #1671	C₂×C₁₃₁	semidirect
230. #1565	C₂×C₁₃₁	semidirect
231. #1542	C₂×C₁₃₁	semidirect
232. C₂×#332	C₂×C₁₃₁	semidirect
347. M₁₆	SD₁₆×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3246×C₁₃₁	2
#3206×C₁₃₁	2
#3165×C₁₃₁	2
#2935×C₁₃₁	2
#1693×C₁₃₁	2
#1691×C₁₃₁	2
#1673×C₁₃₁	2
#1671×C₁₃₁	2
#1565×C₁₃₁	2
#1542×C₁₃₁	2
C₂×#332×C₁₃₁	2
#19232	131

Subgroups — C131×#19232 #45705116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#19232 #45705116