Subgroups — C₁₃₁×#19273 #45705157

Order 33536.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3160×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3116×C₁₃₁	C₂	1	2	yes	maximal
3	C₈×#41×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1676×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1675×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1674×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1673×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1672×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1671×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#1568×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1554×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#533×C₁₃₁	C₂²	1	2	yes	—
13	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
14	#500×C₁₃₁	C₂²	1	1	yes	characteristic
15	#500×C₁₃₁	C₂²	1	1	yes	characteristic
16	#499×C₁₃₁	—	2	1	no	—
17	#499×C₁₃₁	—	2	1	no	—
18	#498×C₁₃₁	C₂²	1	2	yes	—
19	#485×C₁₃₁	—	2	2	no	—
20	#477×C₁₃₁	C₂²	1	2	yes	—
21	#476×C₁₃₁	C₂²	1	2	yes	—
22	#462×C₁₃₁	C₂²	1	2	yes	—
23	#461×C₁₃₁	C₂²	1	2	yes	—
24	#452×C₁₃₁	—	2	2	no	—
25	C₈×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₈×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	#441×C₁₃₁	—	2	2	no	—
28	#440×C₁₃₁	—	2	2	no	—
29	C₈×D₄×C₁₃₁	—	2	1	no	—
30	C₈×D₄×C₁₃₁	—	2	1	no	—
31	C₈×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₈×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
33	#432×C₁₃₁	C₂²	1	2	yes	—
34	#431×C₁₃₁	—	2	1	no	—
35	#431×C₁₃₁	C₂²	1	1	yes	characteristic
36	#427×C₁₃₁	—	2	1	no	—
37	#427×C₁₃₁	—	2	1	no	—
38	C₂×C₄×C₈×C₁₃₁	—	2	1	no	—
39	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
40	#335×C₁₃₁	C₂²	1	1	yes	characteristic
41	#335×C₁₃₁	C₂²	1	1	yes	characteristic
42	#334×C₁₃₁	C₂²	1	2	yes	—
43	#333×C₁₃₁	C₂²	1	2	yes	—
44	#333×C₁₃₁	C₂²	1	2	yes	—
45	#332×C₁₃₁	C₂²	1	2	yes	—
46	#332×C₁₃₁	C₂²	1	2	yes	—
47	C₂×#41×C₁₃₁	D₄	1	1	yes	characteristic
48	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
49	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
50	C₂²×C₈×C₁₃₁	—	2	1	no	—
51	C₂²×C₈×C₁₃₁	—	2	1	no	—
52	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
56	#125×C₁₃₁	—	2	2	no	—
57	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
58	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
59	C₄×Q₈×C₁₃₁	—	2	2	no	—
60	C₄×Q₈×C₁₃₁	—	2	2	no	—
61	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
62	C₄×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₃₁	—	2	1	no	—
64	C₄×D₄×C₁₃₁	—	2	1	no	—
65	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
66	C₄×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
67	#117×C₁₃₁	—	2	1	no	—
68	#117×C₁₃₁	—	2	2	no	—
69	#117×C₁₃₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₁	—	2	1	no	—
71	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
72	#107×C₁₃₁	—	2	1	no	—
73	#107×C₁₃₁	—	2	1	no	—
74	#107×C₁₃₁	—	2	1	no	—
75	#107×C₁₃₁	—	2	1	no	—
76	#107×C₁₃₁	—	2	2	no	—
77	#106×C₁₃₁	—	2	2	no	—
78	#106×C₁₃₁	—	2	2	no	—
79	#106×C₁₃₁	—	2	2	no	—
80	C₄⋊C₈×C₁₃₁	—	2	1	no	—
81	C₄⋊C₈×C₁₃₁	—	2	1	no	—
82	C₄⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₁₃₁	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
85	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
86	#103×C₁₃₁	—	2	2	no	—
87	#103×C₁₃₁	—	2	2	no	—
88	#103×C₁₃₁	—	2	2	no	—
89	#102×C₁₃₁	—	2	2	no	—
90	C₂²⋊C₈×C₁₃₁	—	2	1	no	—
91	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
92	C₂²⋊C₈×C₁₃₁	—	2	1	no	—
93	C₂²⋊C₈×C₁₃₁	—	2	1	no	—
94	#97×C₁₃₁	—	2	2	no	—
95	C₄×C₈×C₁₃₁	—	2	1	no	—
96	C₄×C₈×C₁₃₁	—	2	1	no	—
97	C₄×C₈×C₁₃₁	—	2	1	no	—
98	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
99	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
100	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
102	#41×C₁₃₁	—	2	2	no	—
103	#41×C₁₃₁	—	2	2	no	—
104	C₂×Q₈×C₁₃₁	—	2	2	no	—
105	C₂×Q₈×C₁₃₁	—	2	2	no	—
106	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₁₃₁	—	2	1	no	—
108	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₁	—	2	1	no	—
110	C₂²×C₄×C₁₃₁	—	2	1	no	—
111	C₂²×C₄×C₁₃₁	—	2	1	no	—
112	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
115	Q₁₆×C₁₃₁	—	4	4	no	—
116	SD₁₆×C₁₃₁	—	4	4	no	—
117	C₂×C₈×C₁₃₁	—	2	2	no	—
118	C₂×C₈×C₁₃₁	—	2	2	no	—
119	C₂×C₈×C₁₃₁	—	2	1	no	—
120	C₂×C₈×C₁₃₁	—	2	1	no	—
121	C₂×C₈×C₁₃₁	—	2	2	no	—
122	C₂×C₈×C₁₃₁	—	2	2	no	—
123	C₂×C₈×C₁₃₁	—	4	2	no	—
124	C₂×C₈×C₁₃₁	—	4	2	no	—
125	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₁₃₁	—	2	1	no	—
130	C₄⋊C₄×C₁₃₁	—	2	1	no	—
131	C₄⋊C₄×C₁₃₁	—	2	2	no	—
132	C₄⋊C₄×C₁₃₁	—	2	2	no	—
133	C₄⋊C₄×C₁₃₁	—	2	2	no	—
134	C₄⋊C₄×C₁₃₁	—	2	2	no	—
135	C₄⋊C₄×C₁₃₁	—	4	2	no	—
136	C₄⋊C₄×C₁₃₁	—	4	2	no	—
137	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
138	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
140	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
141	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
142	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
143	C₄²×C₁₃₁	—	2	1	no	—
144	C₄²×C₁₃₁	—	2	1	no	—
145	C₄²×C₁₃₁	—	2	1	no	—
146	C₄²×C₁₃₁	—	4	2	no	—
147	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₃₁	#41	1	1	yes	characteristic
150	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
151	C₂³×C₁₃₁	—	2	1	no	—
152	C₂³×C₁₃₁	#121	1	1	yes	characteristic
153	Q₈×C₁₃₁	—	2	1	no	—
154	Q₈×C₁₃₁	—	4	2	no	—
155	Q₈×C₁₃₁	—	4	2	no	—
156	Q₈×C₁₃₁	—	8	2	no	—
157	Q₈×C₁₃₁	#135	1	2	yes	—
158	D₄×C₁₃₁	—	2	4	no	—
159	D₄×C₁₃₁	—	2	1	no	—
160	D₄×C₁₃₁	#135	1	2	yes	—
161	C₂×C₄×C₁₃₁	—	2	4	no	—
162	C₂×C₄×C₁₃₁	—	2	1	no	—
163	C₂×C₄×C₁₃₁	—	2	1	no	—
164	C₂×C₄×C₁₃₁	—	2	1	no	—
165	C₂×C₄×C₁₃₁	—	2	1	no	—
166	C₂×C₄×C₁₃₁	—	2	1	no	—
167	C₂×C₄×C₁₃₁	—	2	1	no	—
168	C₂×C₄×C₁₃₁	—	2	1	no	—
169	C₂×C₄×C₁₃₁	—	4	1	no	—
170	C₂×C₄×C₁₃₁	—	4	2	no	—
171	C₂×C₄×C₁₃₁	—	4	1	no	—
172	C₂×C₄×C₁₃₁	—	4	1	no	—
173	C₂×C₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	4	2	no	—
175	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
181	C₈×C₁₃₁	—	2	1	no	—
182	C₈×C₁₃₁	—	2	1	no	—
183	C₈×C₁₃₁	—	4	2	no	—
184	C₈×C₁₃₁	—	4	2	no	—
185	C₈×C₁₃₁	—	4	1	no	—
186	C₈×C₁₃₁	—	4	1	no	—
187	C₈×C₁₃₁	#137	1	2	yes	—
188	C₈×C₁₃₁	#137	1	2	yes	—
189	C₂²×C₁₃₁	—	2	1	no	—
190	C₂²×C₁₃₁	—	2	1	no	—
191	C₂²×C₁₃₁	—	2	2	no	—
192	C₂²×C₁₃₁	—	2	1	no	—
193	C₂²×C₁₃₁	—	4	1	no	—
194	C₂²×C₁₃₁	—	4	1	no	—
195	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
196	C₄×C₁₃₁	—	2	1	no	—
197	C₄×C₁₃₁	—	2	1	no	—
198	C₄×C₁₃₁	—	2	2	no	—
199	C₄×C₁₃₁	—	2	1	no	—
200	C₄×C₁₃₁	—	2	1	no	—
201	C₄×C₁₃₁	—	4	1	no	—
202	C₄×C₁₃₁	—	4	1	no	—
203	C₄×C₁₃₁	—	8	2	no	—
204	C₄×C₁₃₁	—	8	2	no	—
205	C₄×C₁₃₁	C₂×#135	1	1	yes	characteristic
206	C₄×C₁₃₁	C₂×#135	1	1	yes	characteristic
207	C₄×C₁₃₁	C₂×#137	1	1	yes	characteristic
208	C₄×C₁₃₁	C₂×#137	1	1	yes	characteristic
209	C₂×C₁₃₁	—	4	1	no	—
210	C₂×C₁₃₁	—	4	2	no	—
211	C₂×C₁₃₁	#3039	1	1	yes	characteristic
212	C₂×C₁₃₁	#3050	1	1	yes	characteristic
213	C₂×C₁₃₁	#3067	1	1	yes	characteristic
214	#19273	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₁₃₁	#19273	1	1	yes	characteristic, direct product factor, Sylow
216	#3160	C₂×C₁₃₁	1	1	yes	characteristic, complemented
217	#3116	C₂×C₁₃₁	1	2	yes	—
218	C₈×#41	C₂×C₁₃₁	1	1	yes	characteristic
219	#1676	C₂×C₁₃₁	1	1	yes	characteristic, complemented
220	#1675	C₂×C₁₃₁	1	1	yes	characteristic, complemented
221	#1674	C₂×C₁₃₁	1	1	yes	characteristic, complemented
222	#1673	C₂×C₁₃₁	1	1	yes	characteristic, complemented
223	#1672	C₂×C₁₃₁	1	2	yes	complemented
224	#1671	C₂×C₁₃₁	1	2	yes	complemented
225	#1568	C₂×C₁₃₁	1	1	yes	characteristic, complemented
226	#1554	C₂×C₁₃₁	1	2	yes	complemented
227	#533	C₂²×C₁₃₁	1	2	yes	—
228	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
229	#500	C₂²×C₁₃₁	1	1	yes	characteristic
230	#500	C₂²×C₁₃₁	1	1	yes	characteristic
231	#499	—	2	1	no	—
232	#499	—	2	1	no	—
233	#498	C₂²×C₁₃₁	1	2	yes	—
234	#485	—	2	2	no	—
235	#477	C₂²×C₁₃₁	1	2	yes	—
236	#476	C₂²×C₁₃₁	1	2	yes	—
237	#462	C₂²×C₁₃₁	1	2	yes	—
238	#461	C₂²×C₁₃₁	1	2	yes	—
239	#452	—	2	2	no	—
240	C₈×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
241	C₈×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
242	#441	—	2	2	no	—
243	#440	—	2	2	no	—
244	C₈×D₄	—	2	1	no	—
245	C₈×D₄	—	2	1	no	—
246	C₈×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
247	C₈×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
248	#432	C₂²×C₁₃₁	1	2	yes	—
249	#431	—	2	1	no	—
250	#431	C₂²×C₁₃₁	1	1	yes	characteristic
251	#427	—	2	1	no	—
252	#427	—	2	1	no	—
253	C₂×C₄×C₈	—	2	1	no	—
254	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
255	#335	C₂²×C₁₃₁	1	1	yes	characteristic
256	#335	C₂²×C₁₃₁	1	1	yes	characteristic
257	#334	C₂²×C₁₃₁	1	2	yes	—
258	#333	C₂²×C₁₃₁	1	2	yes	—
259	#333	C₂²×C₁₃₁	1	2	yes	—
260	#332	C₂²×C₁₃₁	1	2	yes	—
261	#332	C₂²×C₁₃₁	1	2	yes	—
262	C₂×#41	D₄×C₁₃₁	1	1	yes	characteristic
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
268	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
269	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
270	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
271	#125	—	2	2	no	—
272	C₂²⋊Q₈	—	2	2	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
277	C₄×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
281	C₄×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	—	2	2	no	—
284	#117	D₄×C₁₃₁	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#107	—	2	2	no	—
292	#106	—	2	2	no	—
293	#106	—	2	2	no	—
294	#106	—	2	2	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
298	C₄⋊C₈	C₂³×C₁₃₁	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
300	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
301	#103	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#102	—	2	2	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	#97	—	2	2	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
314	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
315	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
316	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
329	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
330	Q₁₆	—	4	4	no	—
331	SD₁₆	—	4	4	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
341	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
342	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
343	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
353	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	4	2	no	—
362	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
364	C₄²	#41×C₁₃₁	1	1	yes	characteristic
365	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
366	C₂³	—	2	1	no	—
367	C₂³	#121×C₁₃₁	1	1	yes	characteristic
368	Q₈	—	2	1	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	2	no	—
372	Q₈	#135×C₁₃₁	1	2	yes	—
373	D₄	—	2	4	no	—
374	D₄	—	2	1	no	—
375	D₄	#135×C₁₃₁	1	2	yes	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
391	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
392	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
395	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	2	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	1	no	—
401	C₈	—	4	1	no	—
402	C₈	#137×C₁₃₁	1	2	yes	—
403	C₈	#137×C₁₃₁	1	2	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	2	no	—
420	C₄	C₂×#135×C₁₃₁	1	1	yes	characteristic
421	C₄	C₂×#135×C₁₃₁	1	1	yes	characteristic
422	C₄	C₂×#137×C₁₃₁	1	1	yes	characteristic
423	C₄	C₂×#137×C₁₃₁	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#3039×C₁₃₁	1	1	yes	characteristic
427	C₂	#3050×C₁₃₁	1	1	yes	characteristic
428	C₂	#3067×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₁
prime radical	C₂×#41×C₁₃₁	D₄
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
1. #3160×C₁₃₁	C₂	semidirect
4. #1676×C₁₃₁	C₂	semidirect
5. #1675×C₁₃₁	C₂	semidirect
6. #1674×C₁₃₁	C₂	semidirect
7. #1673×C₁₃₁	C₂	semidirect
8. #1672×C₁₃₁	C₂	semidirect
9. #1671×C₁₃₁	C₂	semidirect
10. #1568×C₁₃₁	C₂	semidirect
11. #1554×C₁₃₁	C₂	semidirect
214. #19273	C₁₃₁	direct (N × H)
215. C₁₃₁	#19273	direct (N × H)
216. #3160	C₂×C₁₃₁	semidirect
219. #1676	C₂×C₁₃₁	semidirect
220. #1675	C₂×C₁₃₁	semidirect
221. #1674	C₂×C₁₃₁	semidirect
222. #1673	C₂×C₁₃₁	semidirect
223. #1672	C₂×C₁₃₁	semidirect
224. #1671	C₂×C₁₃₁	semidirect
225. #1568	C₂×C₁₃₁	semidirect
226. #1554	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3160×C₁₃₁	2
#3116×C₁₃₁	2
C₈×#41×C₁₃₁	2
#1676×C₁₃₁	2
#1675×C₁₃₁	2
#1674×C₁₃₁	2
#1673×C₁₃₁	2
#1672×C₁₃₁	2
#1671×C₁₃₁	2
#1568×C₁₃₁	2
#1554×C₁₃₁	2
#19273	131

Subgroups — C131×#19273 #45705157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#19273 #45705157