Subgroups — C₁₃₁×#26063 #45711947

Order 33536.

778 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#499×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#427×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2441×C₁₃₁	C₂	1	2	yes	maximal
4	#2083×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2059×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1941×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1941×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1854×C₁₃₁	C₂	1	2	yes	maximal
9	#1844×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1807×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	C₈×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₁	C₂²	1	2	yes	—
14	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
15	#499×C₁₃₁	—	2	4	no	—
16	#427×C₁₃₁	—	2	4	no	—
17	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	#399×C₁₃₁	—	2	2	no	—
28	#396×C₁₃₁	—	2	2	no	—
29	#389×C₁₃₁	—	2	2	no	—
30	#389×C₁₃₁	C₂²	1	2	yes	—
31	#389×C₁₃₁	C₂²	1	2	yes	—
32	#387×C₁₃₁	—	2	2	no	—
33	#384×C₁₃₁	C₂²	1	2	yes	—
34	#380×C₁₃₁	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
36	#340×C₁₃₁	C₂²	1	2	yes	—
37	#340×C₁₃₁	C₂²	1	2	yes	—
38	#340×C₁₃₁	C₂²	1	2	yes	—
39	#336×C₁₃₁	C₂²	1	1	yes	characteristic
40	#336×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₁	—	2	2	no	—
43	C₂²×C₈×C₁₃₁	—	2	2	no	—
44	C₂²×C₈×C₁₃₁	Q₈	1	4	yes	—
45	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	#125×C₁₃₁	—	2	4	no	—
50	#125×C₁₃₁	—	4	2	no	—
51	#117×C₁₃₁	—	2	4	no	—
52	#117×C₁₃₁	—	4	2	no	—
53	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
66	C₂×C₄²×C₁₃₁	—	2	2	no	—
67	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
69	#107×C₁₃₁	—	2	4	no	—
70	#107×C₁₃₁	—	2	4	no	—
71	#106×C₁₃₁	—	2	2	no	—
72	#106×C₁₃₁	—	2	2	no	—
73	#106×C₁₃₁	—	2	2	no	—
74	#106×C₁₃₁	—	4	2	no	—
75	#106×C₁₃₁	D₄	1	4	yes	—
76	C₂²⋊C₈×C₁₃₁	Q₈	1	4	yes	—
77	C₄×C₈×C₁₃₁	—	2	2	no	—
78	C₄×C₈×C₁₃₁	—	2	2	no	—
79	#95×C₁₃₁	—	2	2	no	—
80	#95×C₁₃₁	—	2	2	no	—
81	#95×C₁₃₁	—	2	2	no	—
82	#95×C₁₃₁	D₄	1	2	yes	—
83	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₁	—	2	1	no	—
85	C₂²×C₄×C₁₃₁	—	2	1	no	—
86	C₂²×C₄×C₁₃₁	—	2	1	no	—
87	C₂²×C₄×C₁₃₁	—	2	1	no	—
88	C₂²×C₄×C₁₃₁	—	2	2	no	—
89	C₂²×C₄×C₁₃₁	—	2	2	no	—
90	C₂²×C₄×C₁₃₁	—	2	2	no	—
91	C₂²×C₄×C₁₃₁	—	2	2	no	—
92	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₁₃₁	—	2	1	no	—
99	C₂×C₈×C₁₃₁	—	2	1	no	—
100	C₂×C₈×C₁₃₁	—	2	1	no	—
101	C₂×C₈×C₁₃₁	—	2	1	no	—
102	C₂×C₈×C₁₃₁	—	2	1	no	—
103	C₂×C₈×C₁₃₁	—	2	1	no	—
104	C₂×C₈×C₁₃₁	—	2	8	no	—
105	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
107	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
108	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
109	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
110	C₂×C₈×C₁₃₁	#41	1	2	yes	—
111	C₄⋊C₄×C₁₃₁	—	2	2	no	—
112	C₄⋊C₄×C₁₃₁	—	2	2	no	—
113	C₄⋊C₄×C₁₃₁	—	2	2	no	—
114	C₄⋊C₄×C₁₃₁	—	2	2	no	—
115	C₄⋊C₄×C₁₃₁	—	2	2	no	—
116	C₄⋊C₄×C₁₃₁	—	2	2	no	—
117	C₄⋊C₄×C₁₃₁	—	2	2	no	—
118	C₄⋊C₄×C₁₃₁	—	4	4	no	—
119	C₄⋊C₄×C₁₃₁	—	4	4	no	—
120	C₄⋊C₄×C₁₃₁	—	4	4	no	—
121	C₄⋊C₄×C₁₃₁	—	4	4	no	—
122	C₄⋊C₄×C₁₃₁	—	8	2	no	—
123	C₄⋊C₄×C₁₃₁	—	8	2	no	—
124	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
125	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
126	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
127	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
128	C₄²×C₁₃₁	—	2	1	no	—
129	C₄²×C₁₃₁	—	2	1	no	—
130	C₄²×C₁₃₁	—	2	1	no	—
131	C₄²×C₁₃₁	—	2	1	no	—
132	C₄²×C₁₃₁	—	4	4	no	—
133	C₂³×C₁₃₁	—	2	1	no	—
134	C₂³×C₁₃₁	—	2	1	no	—
135	C₂³×C₁₃₁	—	2	2	no	—
136	C₂³×C₁₃₁	—	2	2	no	—
137	C₂³×C₁₃₁	C₄⋊Q₈	1	2	yes	—
138	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃₁	—	2	1	no	—
140	C₂×C₄×C₁₃₁	—	2	2	no	—
141	C₂×C₄×C₁₃₁	—	2	1	no	—
142	C₂×C₄×C₁₃₁	—	2	2	no	—
143	C₂×C₄×C₁₃₁	—	2	2	no	—
144	C₂×C₄×C₁₃₁	—	2	2	no	—
145	C₂×C₄×C₁₃₁	—	2	2	no	—
146	C₂×C₄×C₁₃₁	—	2	2	no	—
147	C₂×C₄×C₁₃₁	—	2	2	no	—
148	C₂×C₄×C₁₃₁	—	2	4	no	—
149	C₂×C₄×C₁₃₁	—	2	2	no	—
150	C₂×C₄×C₁₃₁	—	2	2	no	—
151	C₂×C₄×C₁₃₁	—	4	2	no	—
152	C₂×C₄×C₁₃₁	—	4	2	no	—
153	C₂×C₄×C₁₃₁	—	4	2	no	—
154	C₂×C₄×C₁₃₁	—	4	2	no	—
155	C₂×C₄×C₁₃₁	—	4	2	no	—
156	C₂×C₄×C₁₃₁	—	4	2	no	—
157	C₂×C₄×C₁₃₁	—	4	2	no	—
158	C₂×C₄×C₁₃₁	—	4	2	no	—
159	C₂×C₄×C₁₃₁	—	4	2	no	—
160	C₂×C₄×C₁₃₁	—	4	2	no	—
161	C₂×C₄×C₁₃₁	—	4	2	no	—
162	C₂×C₄×C₁₃₁	C₄⋊Q₈	1	2	yes	—
163	C₂×C₄×C₁₃₁	#135	1	4	yes	—
164	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
170	C₈×C₁₃₁	—	2	2	no	—
171	C₈×C₁₃₁	—	2	2	no	—
172	C₈×C₁₃₁	—	2	2	no	—
173	C₈×C₁₃₁	C₂²⋊Q₈	1	4	yes	—
174	C₂²×C₁₃₁	—	2	2	no	—
175	C₂²×C₁₃₁	—	2	2	no	—
176	C₂²×C₁₃₁	—	2	2	no	—
177	C₂²×C₁₃₁	—	4	2	no	—
178	C₂²×C₁₃₁	—	4	2	no	—
179	C₂²×C₁₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
180	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
181	C₂²×C₁₃₁	#547	1	1	yes	characteristic
182	C₂²×C₁₃₁	C₂×#135	1	2	yes	—
183	C₂²×C₁₃₁	#577	1	2	yes	—
184	C₄×C₁₃₁	—	2	4	no	—
185	C₄×C₁₃₁	—	2	2	no	—
186	C₄×C₁₃₁	—	4	2	no	—
187	C₄×C₁₃₁	—	4	4	no	—
188	C₄×C₁₃₁	—	8	2	no	—
189	C₄×C₁₃₁	—	8	2	no	—
190	C₄×C₁₃₁	—	8	2	no	—
191	C₄×C₁₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
192	C₄×C₁₃₁	#544	1	1	yes	characteristic
193	C₄×C₁₃₁	D₄×Q₈	1	1	yes	characteristic
194	C₄×C₁₃₁	#554	1	1	yes	characteristic
195	C₂×C₁₃₁	—	4	2	no	—
196	C₂×C₁₃₁	#2440	1	1	yes	characteristic
197	C₂×C₁₃₁	#3160	1	1	yes	characteristic
198	C₂×C₁₃₁	#3163	1	1	yes	characteristic
199	C₂×C₁₃₁	#3284	1	2	yes	—
200	C₂×C₁₃₁	#3337	1	2	yes	—
201	#26063	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₁₃₁	#26063	1	1	yes	characteristic, direct product factor, Sylow
203	C₂×#499	C₂×C₁₃₁	1	1	yes	characteristic, complemented
204	C₂×#427	C₂×C₁₃₁	1	1	yes	characteristic
205	#2441	C₂×C₁₃₁	1	2	yes	—
206	#2083	C₂×C₁₃₁	1	2	yes	complemented
207	#2059	C₂×C₁₃₁	1	2	yes	complemented
208	#1941	C₂×C₁₃₁	1	1	yes	characteristic, complemented
209	#1941	C₂×C₁₃₁	1	1	yes	characteristic, complemented
210	#1854	C₂×C₁₃₁	1	2	yes	—
211	#1844	C₂×C₁₃₁	1	1	yes	characteristic, complemented
212	#1807	C₂×C₁₃₁	1	1	yes	characteristic
213	C₈×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic
214	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₂×#125	C₂²×C₁₃₁	1	2	yes	—
216	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
217	#499	—	2	4	no	—
218	#427	—	2	4	no	—
219	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
220	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
221	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
222	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
223	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
224	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
225	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
229	#399	—	2	2	no	—
230	#396	—	2	2	no	—
231	#389	—	2	2	no	—
232	#389	C₂²×C₁₃₁	1	2	yes	—
233	#389	C₂²×C₁₃₁	1	2	yes	—
234	#387	—	2	2	no	—
235	#384	C₂²×C₁₃₁	1	2	yes	—
236	#380	C₂²×C₁₃₁	1	2	yes	—
237	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
238	#340	C₂²×C₁₃₁	1	2	yes	—
239	#340	C₂²×C₁₃₁	1	2	yes	—
240	#340	C₂²×C₁₃₁	1	2	yes	—
241	#336	C₂²×C₁₃₁	1	1	yes	characteristic
242	#336	C₂²×C₁₃₁	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	Q₈×C₁₃₁	1	4	yes	—
247	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
251	#125	—	2	4	no	—
252	#125	—	4	2	no	—
253	#117	—	2	4	no	—
254	#117	—	4	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
271	#107	—	2	4	no	—
272	#107	—	2	4	no	—
273	#106	—	2	2	no	—
274	#106	—	2	2	no	—
275	#106	—	2	2	no	—
276	#106	—	4	2	no	—
277	#106	D₄×C₁₃₁	1	4	yes	—
278	C₂²⋊C₈	Q₈×C₁₃₁	1	4	yes	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	D₄×C₁₃₁	1	2	yes	—
285	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
297	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
298	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
299	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	8	no	—
307	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
308	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
309	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
310	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
311	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
312	C₂×C₈	#41×C₁₃₁	1	2	yes	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₄⋊C₄	—	4	4	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₄⋊C₄	—	8	2	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	8	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	4	4	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	C₄⋊Q₈×C₁₃₁	1	2	yes	—
340	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	C₄⋊Q₈×C₁₃₁	1	2	yes	—
365	C₂×C₄	#135×C₁₃₁	1	4	yes	—
366	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
367	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
368	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
369	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
370	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
371	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
372	C₈	—	2	2	no	—
373	C₈	—	2	2	no	—
374	C₈	—	2	2	no	—
375	C₈	C₂²⋊Q₈×C₁₃₁	1	4	yes	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	C₂×C₄⋊Q₈×C₁₃₁	1	1	yes	characteristic
382	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
383	C₂²	#547×C₁₃₁	1	1	yes	characteristic
384	C₂²	C₂×#135×C₁₃₁	1	2	yes	—
385	C₂²	#577×C₁₃₁	1	2	yes	—
386	C₄	—	2	4	no	—
387	C₄	—	2	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	2	no	—
393	C₄	C₂×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
394	C₄	#544×C₁₃₁	1	1	yes	characteristic
395	C₄	D₄×Q₈×C₁₃₁	1	1	yes	characteristic
396	C₄	#554×C₁₃₁	1	1	yes	characteristic
397	C₂	—	4	2	no	—
398	C₂	#2440×C₁₃₁	1	1	yes	characteristic
399	C₂	#3160×C₁₃₁	1	1	yes	characteristic
400	C₂	#3163×C₁₃₁	1	1	yes	characteristic
401	C₂	#3284×C₁₃₁	1	2	yes	—
402	C₂	#3337×C₁₃₁	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×#499×C₁₃₁	C₂	semidirect
4. #2083×C₁₃₁	C₂	semidirect
5. #2059×C₁₃₁	C₂	semidirect
6. #1941×C₁₃₁	C₂	semidirect
7. #1941×C₁₃₁	C₂	semidirect
9. #1844×C₁₃₁	C₂	semidirect
201. #26063	C₁₃₁	direct (N × H)
202. C₁₃₁	#26063	direct (N × H)
203. C₂×#499	C₂×C₁₃₁	semidirect
206. #2083	C₂×C₁₃₁	semidirect
207. #2059	C₂×C₁₃₁	semidirect
208. #1941	C₂×C₁₃₁	semidirect
209. #1941	C₂×C₁₃₁	semidirect
211. #1844	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#499×C₁₃₁	2
C₂×#427×C₁₃₁	2
#2441×C₁₃₁	2
#2083×C₁₃₁	2
#2059×C₁₃₁	2
#1941×C₁₃₁	2
#1854×C₁₃₁	2
#1844×C₁₃₁	2
#1807×C₁₃₁	2
C₈×C₂²⋊C₄×C₁₃₁	2
#26063	131

Subgroups — C131×#26063 #45711947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#26063 #45711947