Subgroups — C₁₃₁×#26060 #45711944

Order 33536.

894 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#498×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#106×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2440×C₁₃₁	C₂	1	2	yes	maximal
4	#2084×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2058×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	#1853×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×C₄⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
15	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
16	#498×C₁₃₁	—	2	4	no	—
17	C₂×#106×C₁₃₁	—	2	4	no	—
18	C₂×#106×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	2	yes	—
22	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	#398×C₁₃₁	—	2	2	no	—
29	#395×C₁₃₁	—	2	2	no	—
30	#389×C₁₃₁	C₂²	1	2	yes	—
31	#389×C₁₃₁	C₂²	1	2	yes	—
32	#385×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	C₂²×Q₈×C₁₃₁	—	2	2	no	—
42	C₂³×C₄×C₁₃₁	—	2	2	no	—
43	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₁	—	2	2	no	—
45	C₂²×C₈×C₁₃₁	—	2	2	no	—
46	C₂²×C₈×C₁₃₁	Q₈	1	4	yes	complemented
47	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
52	C₄⋊Q₈×C₁₃₁	—	4	2	no	—
53	C₂²⋊Q₈×C₁₃₁	—	4	8	no	—
54	C₂×C₄⋊C₄×C₁₃₁	—	2	4	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	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
70	#106×C₁₃₁	—	2	2	no	—
71	#106×C₁₃₁	—	2	2	no	—
72	#106×C₁₃₁	—	2	2	no	—
73	#106×C₁₃₁	—	2	4	no	—
74	#106×C₁₃₁	—	2	4	no	—
75	#106×C₁₃₁	—	4	2	no	—
76	#106×C₁₃₁	D₄	1	4	yes	—
77	C₂²⋊C₈×C₁₃₁	Q₈	1	4	yes	complemented
78	C₄×C₈×C₁₃₁	—	2	2	no	—
79	C₄×C₈×C₁₃₁	—	2	2	no	—
80	#95×C₁₃₁	—	2	2	no	—
81	#95×C₁₃₁	—	2	2	no	—
82	#95×C₁₃₁	—	2	2	no	—
83	#95×C₁₃₁	D₄	1	2	yes	—
84	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₁₃₁	—	4	4	no	—
86	C₂×Q₈×C₁₃₁	—	4	4	no	—
87	C₂×Q₈×C₁₃₁	—	8	2	no	—
88	C₂²×C₄×C₁₃₁	—	2	1	no	—
89	C₂²×C₄×C₁₃₁	—	2	1	no	—
90	C₂²×C₄×C₁₃₁	—	2	1	no	—
91	C₂²×C₄×C₁₃₁	—	2	1	no	—
92	C₂²×C₄×C₁₃₁	—	2	2	no	—
93	C₂²×C₄×C₁₃₁	—	2	2	no	—
94	C₂²×C₄×C₁₃₁	—	2	2	no	—
95	C₂²×C₄×C₁₃₁	—	2	2	no	—
96	C₂²×C₄×C₁₃₁	—	4	4	no	—
97	C₂²×C₄×C₁₃₁	—	4	4	no	—
98	C₂²×C₄×C₁₃₁	—	8	2	no	—
99	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₁₃₁	—	2	1	no	—
106	C₂×C₈×C₁₃₁	—	2	1	no	—
107	C₂×C₈×C₁₃₁	—	2	1	no	—
108	C₂×C₈×C₁₃₁	—	2	1	no	—
109	C₂×C₈×C₁₃₁	—	2	1	no	—
110	C₂×C₈×C₁₃₁	—	2	1	no	—
111	C₂×C₈×C₁₃₁	—	2	8	no	—
112	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
114	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
116	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
117	C₂×C₈×C₁₃₁	#41	1	2	yes	—
118	C₄⋊C₄×C₁₃₁	—	2	2	no	—
119	C₄⋊C₄×C₁₃₁	—	2	2	no	—
120	C₄⋊C₄×C₁₃₁	—	2	2	no	—
121	C₄⋊C₄×C₁₃₁	—	2	2	no	—
122	C₄⋊C₄×C₁₃₁	—	2	2	no	—
123	C₄⋊C₄×C₁₃₁	—	2	2	no	—
124	C₄⋊C₄×C₁₃₁	—	2	2	no	—
125	C₄⋊C₄×C₁₃₁	—	4	4	no	—
126	C₄⋊C₄×C₁₃₁	—	4	4	no	—
127	C₄⋊C₄×C₁₃₁	—	4	4	no	—
128	C₄⋊C₄×C₁₃₁	—	4	4	no	—
129	C₄⋊C₄×C₁₃₁	—	4	4	no	—
130	C₄⋊C₄×C₁₃₁	—	8	2	no	—
131	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
132	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
133	C₂²⋊C₄×C₁₃₁	SD₁₆	1	8	yes	—
134	C₄²×C₁₃₁	—	2	1	no	—
135	C₄²×C₁₃₁	—	2	1	no	—
136	C₄²×C₁₃₁	—	2	1	no	—
137	C₄²×C₁₃₁	—	2	1	no	—
138	C₂³×C₁₃₁	—	2	1	no	—
139	C₂³×C₁₃₁	—	2	1	no	—
140	C₂³×C₁₃₁	—	2	2	no	—
141	C₂³×C₁₃₁	C₄⋊Q₈	1	2	yes	—
142	C₂³×C₁₃₁	C₂×SD₁₆	1	4	yes	—
143	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₁₃₁	—	8	8	no	—
145	C₂×C₄×C₁₃₁	—	2	2	no	—
146	C₂×C₄×C₁₃₁	—	2	1	no	—
147	C₂×C₄×C₁₃₁	—	2	2	no	—
148	C₂×C₄×C₁₃₁	—	2	1	no	—
149	C₂×C₄×C₁₃₁	—	2	2	no	—
150	C₂×C₄×C₁₃₁	—	2	2	no	—
151	C₂×C₄×C₁₃₁	—	2	2	no	—
152	C₂×C₄×C₁₃₁	—	2	2	no	—
153	C₂×C₄×C₁₃₁	—	2	2	no	—
154	C₂×C₄×C₁₃₁	—	2	2	no	—
155	C₂×C₄×C₁₃₁	—	2	4	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	—	4	2	no	—
163	C₂×C₄×C₁₃₁	—	4	2	no	—
164	C₂×C₄×C₁₃₁	—	4	2	no	—
165	C₂×C₄×C₁₃₁	—	4	2	no	—
166	C₂×C₄×C₁₃₁	—	4	2	no	—
167	C₂×C₄×C₁₃₁	—	8	8	no	—
168	C₂×C₄×C₁₃₁	C₄⋊Q₈	1	2	yes	—
169	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	4	yes	—
170	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	4	yes	—
171	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
177	C₈×C₁₃₁	—	2	2	no	—
178	C₈×C₁₃₁	—	2	2	no	—
179	C₈×C₁₃₁	—	2	2	no	—
180	C₈×C₁₃₁	C₂²⋊Q₈	1	4	yes	complemented
181	C₂²×C₁₃₁	—	2	4	no	—
182	C₂²×C₁₃₁	—	2	2	no	—
183	C₂²×C₁₃₁	—	2	2	no	—
184	C₂²×C₁₃₁	—	2	4	no	—
185	C₂²×C₁₃₁	#498	1	4	yes	complemented
186	C₂²×C₁₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
187	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
188	C₂²×C₁₃₁	#547	1	1	yes	characteristic
189	C₂²×C₁₃₁	C₂²×SD₁₆	1	2	yes	—
190	C₂²×C₁₃₁	#577	1	2	yes	—
191	C₄×C₁₃₁	—	2	4	no	—
192	C₄×C₁₃₁	—	2	2	no	—
193	C₄×C₁₃₁	—	2	4	no	—
194	C₄×C₁₃₁	—	4	4	no	—
195	C₄×C₁₃₁	—	8	2	no	—
196	C₄×C₁₃₁	—	8	2	no	—
197	C₄×C₁₃₁	—	8	2	no	—
198	C₄×C₁₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
199	C₄×C₁₃₁	#544	1	1	yes	characteristic
200	C₄×C₁₃₁	D₄×Q₈	1	1	yes	characteristic
201	C₄×C₁₃₁	#554	1	1	yes	characteristic
202	C₂×C₁₃₁	—	2	4	no	—
203	C₂×C₁₃₁	#2440	1	1	yes	characteristic
204	C₂×C₁₃₁	C₂×#498	1	1	yes	characteristic
205	C₂×C₁₃₁	#3163	1	1	yes	characteristic
206	C₂×C₁₃₁	D₄×SD₁₆	1	2	yes	—
207	C₂×C₁₃₁	#3335	1	2	yes	—
208	#26060	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₁₃₁	#26060	1	1	yes	characteristic, direct product factor, Sylow
210	C₂×#498	C₂×C₁₃₁	1	1	yes	characteristic, complemented
211	C₂²×#106	C₂×C₁₃₁	1	1	yes	characteristic
212	#2440	C₂×C₁₃₁	1	2	yes	—
213	#2084	C₂×C₁₃₁	1	2	yes	complemented
214	#2058	C₂×C₁₃₁	1	2	yes	complemented
215	#1941	C₂×C₁₃₁	1	1	yes	characteristic, complemented
216	#1941	C₂×C₁₃₁	1	1	yes	characteristic, complemented
217	#1853	C₂×C₁₃₁	1	2	yes	—
218	#1844	C₂×C₁₃₁	1	1	yes	characteristic, complemented
219	#1807	C₂×C₁₃₁	1	1	yes	characteristic
220	C₈×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic
221	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
222	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
223	C₂×C₂²⋊Q₈	—	2	2	no	—
224	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
225	#498	—	2	4	no	—
226	C₂×#106	—	2	4	no	—
227	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
228	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
229	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
230	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
231	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
232	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
233	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
234	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
237	#398	—	2	2	no	—
238	#395	—	2	2	no	—
239	#389	C₂²×C₁₃₁	1	2	yes	—
240	#389	C₂²×C₁₃₁	1	2	yes	—
241	#385	—	2	2	no	—
242	#384	C₂²×C₁₃₁	1	2	yes	—
243	#380	C₂²×C₁₃₁	1	2	yes	—
244	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
245	#340	C₂²×C₁₃₁	1	2	yes	—
246	#340	C₂²×C₁₃₁	1	2	yes	—
247	#340	C₂²×C₁₃₁	1	2	yes	—
248	#336	C₂²×C₁₃₁	1	1	yes	characteristic
249	#336	C₂²×C₁₃₁	1	1	yes	characteristic
250	C₂²×Q₈	—	2	2	no	—
251	C₂³×C₄	—	2	2	no	—
252	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	Q₈×C₁₃₁	1	4	yes	complemented
256	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
260	C₄⋊Q₈	—	2	4	no	—
261	C₄⋊Q₈	—	4	2	no	—
262	C₂²⋊Q₈	—	4	8	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	4	2	no	—
271	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
277	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
279	#106	—	2	2	no	—
280	#106	—	2	2	no	—
281	#106	—	2	2	no	—
282	#106	—	2	4	no	—
283	#106	—	2	4	no	—
284	#106	—	4	2	no	—
285	#106	D₄×C₁₃₁	1	4	yes	—
286	C₂²⋊C₈	Q₈×C₁₃₁	1	4	yes	complemented
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	D₄×C₁₃₁	1	2	yes	—
293	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
311	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
312	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	8	no	—
321	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
322	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
323	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
324	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
325	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
326	C₂×C₈	#41×C₁₃₁	1	2	yes	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	8	2	no	—
340	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	SD₁₆×C₁₃₁	1	8	yes	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	2	no	—
350	C₂³	C₄⋊Q₈×C₁₃₁	1	2	yes	—
351	C₂³	C₂×SD₁₆×C₁₃₁	1	4	yes	—
352	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
353	Q₈	—	8	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	8	8	no	—
377	C₂×C₄	C₄⋊Q₈×C₁₃₁	1	2	yes	—
378	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	4	yes	—
379	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	4	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
381	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
382	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
383	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
384	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
385	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
386	C₈	—	2	2	no	—
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	C₂²⋊Q₈×C₁₃₁	1	4	yes	complemented
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	#498×C₁₃₁	1	4	yes	complemented
395	C₂²	C₂×C₄⋊Q₈×C₁₃₁	1	1	yes	characteristic
396	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
397	C₂²	#547×C₁₃₁	1	1	yes	characteristic
398	C₂²	C₂²×SD₁₆×C₁₃₁	1	2	yes	—
399	C₂²	#577×C₁₃₁	1	2	yes	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	2	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₂×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
408	C₄	#544×C₁₃₁	1	1	yes	characteristic
409	C₄	D₄×Q₈×C₁₃₁	1	1	yes	characteristic
410	C₄	#554×C₁₃₁	1	1	yes	characteristic
411	C₂	—	2	4	no	—
412	C₂	#2440×C₁₃₁	1	1	yes	characteristic
413	C₂	C₂×#498×C₁₃₁	1	1	yes	characteristic
414	C₂	#3163×C₁₃₁	1	1	yes	characteristic
415	C₂	D₄×SD₁₆×C₁₃₁	1	2	yes	—
416	C₂	#3335×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×#498×C₁₃₁	C₂	semidirect
4. #2084×C₁₃₁	C₂	semidirect
5. #2058×C₁₃₁	C₂	semidirect
6. #1941×C₁₃₁	C₂	semidirect
7. #1941×C₁₃₁	C₂	semidirect
9. #1844×C₁₃₁	C₂	semidirect
46. C₂²×C₈×C₁₃₁	Q₈	semidirect
77. C₂²⋊C₈×C₁₃₁	Q₈	semidirect
180. C₈×C₁₃₁	C₂²⋊Q₈	semidirect
185. C₂²×C₁₃₁	#498	semidirect
208. #26060	C₁₃₁	direct (N × H)
209. C₁₃₁	#26060	direct (N × H)
210. C₂×#498	C₂×C₁₃₁	semidirect
213. #2084	C₂×C₁₃₁	semidirect
214. #2058	C₂×C₁₃₁	semidirect
215. #1941	C₂×C₁₃₁	semidirect
216. #1941	C₂×C₁₃₁	semidirect
218. #1844	C₂×C₁₃₁	semidirect
255. C₂²×C₈	Q₈×C₁₃₁	semidirect
286. C₂²⋊C₈	Q₈×C₁₃₁	semidirect
389. C₈	C₂²⋊Q₈×C₁₃₁	semidirect
394. C₂²	#498×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#498×C₁₃₁	2
C₂²×#106×C₁₃₁	2
#2440×C₁₃₁	2
#2084×C₁₃₁	2
#2058×C₁₃₁	2
#1941×C₁₃₁	2
#1853×C₁₃₁	2
#1844×C₁₃₁	2
#1807×C₁₃₁	2
C₈×C₂²⋊C₄×C₁₃₁	2
#26060	131

Subgroups — C131×#26060 #45711944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#26060 #45711944