Subgroups — C₁₃₁×#33423 #45719307

Order 33536.

590 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#131×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2164×C₁₃₁	C₂	1	4	yes	maximal, complemented
3	#2163×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2162×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2150×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄⋊C₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2113×C₁₃₁	C₂	1	2	yes	maximal
8	#2108×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	C₂×#131×C₁₃₁	C₄	1	1	yes	characteristic
10	C₂×#131×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₄×#41×C₁₃₁	C₄	1	1	yes	characteristic
12	C₂×M₃₂×C₁₃₁	C₂²	1	2	yes	—
13	C₂²×C₁₆×C₁₃₁	C₂²	1	2	yes	—
14	#405×C₁₃₁	C₄	1	1	yes	characteristic
15	#405×C₁₃₁	C₄	1	2	yes	—
16	#405×C₁₃₁	C₂²	1	1	yes	characteristic
17	#405×C₁₃₁	C₂²	1	2	yes	—
18	C₄×M₁₆×C₁₃₁	C₄	1	2	yes	—
19	C₄×M₁₆×C₁₃₁	C₄	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
22	C₄⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₄⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
25	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
26	C₄⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
27	C₂²⋊C₁₆×C₁₃₁	C₂²	1	4	yes	—
28	C₂²⋊C₁₆×C₁₃₁	C₂²	1	4	yes	—
29	#346×C₁₃₁	C₂²	1	4	yes	—
30	C₄×C₁₆×C₁₃₁	C₂²	1	4	yes	—
31	C₂×#41×C₁₃₁	C₂×C₄	1	1	yes	characteristic
32	#131×C₁₃₁	—	2	4	no	—
33	#131×C₁₃₁	—	2	2	no	—
34	#131×C₁₃₁	—	2	2	no	—
35	C₂×M₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
36	C₂×M₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
37	C₂×M₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
43	C₄×Q₈×C₁₃₁	C₈	1	1	yes	characteristic
44	C₄×Q₈×C₁₃₁	C₈	1	1	yes	characteristic
45	C₄×D₄×C₁₃₁	C₈	1	2	yes	—
46	C₄×D₄×C₁₃₁	C₈	1	1	yes	characteristic
47	C₄×D₄×C₁₃₁	C₈	1	2	yes	—
48	C₄×D₄×C₁₃₁	C₈	1	1	yes	characteristic
49	#117×C₁₃₁	C₂×C₄	1	2	yes	—
50	#117×C₁₃₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
53	M₃₂×C₁₃₁	—	2	4	no	—
54	C₂×C₁₆×C₁₃₁	—	2	4	no	—
55	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
56	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
57	C₂×C₁₆×C₁₃₁	C₂³	1	4	yes	—
58	#97×C₁₃₁	C₂×C₄	1	2	yes	—
59	#97×C₁₃₁	C₂×C₄	1	2	yes	—
60	#97×C₁₃₁	C₂×C₄	1	2	yes	—
61	C₄×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
62	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
63	C₄×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
64	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
65	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
66	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
67	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
68	#41×C₁₃₁	—	2	2	no	—
69	#41×C₁₃₁	—	2	2	no	—
70	C₂×Q₈×C₁₃₁	C₂×C₈	1	1	yes	characteristic
71	C₂×D₄×C₁₃₁	C₂×C₈	1	2	yes	—
72	C₂×D₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₁	C₂×C₈	1	2	yes	—
74	C₂²×C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₁	C₂×C₈	1	2	yes	—
76	C₂²×C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
79	M₁₆×C₁₃₁	—	2	2	no	—
80	M₁₆×C₁₃₁	—	2	4	no	—
81	M₁₆×C₁₃₁	—	2	4	no	—
82	M₁₆×C₁₃₁	M₁₆	1	4	yes	—
83	C₂×C₈×C₁₃₁	—	2	2	no	—
84	C₂×C₈×C₁₃₁	—	2	4	no	—
85	C₂×C₈×C₁₃₁	—	2	2	no	—
86	C₂×C₈×C₁₃₁	—	2	2	no	—
87	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
92	C₂×C₈×C₁₃₁	#41	1	2	yes	—
93	C₂×C₈×C₁₃₁	#41	1	2	yes	—
94	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
95	C₄⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
96	C₄⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
97	C₄⋊C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
98	C₄⋊C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
99	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
100	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
101	C₂²⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
102	C₄²×C₁₃₁	C₂×C₈	1	2	yes	—
103	C₄²×C₁₃₁	C₂×C₈	1	1	yes	characteristic
104	C₄²×C₁₃₁	C₂×C₈	1	2	yes	—
105	C₄²×C₁₃₁	C₂×C₈	1	1	yes	characteristic
106	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
108	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
109	C₁₆×C₁₃₁	—	2	2	no	—
110	C₁₆×C₁₃₁	—	2	2	no	—
111	C₁₆×C₁₃₁	—	2	4	no	—
112	C₂³×C₁₃₁	C₂²×C₈	1	2	yes	—
113	C₂³×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
114	Q₈×C₁₃₁	—	2	2	no	—
115	D₄×C₁₃₁	—	2	4	no	—
116	D₄×C₁₃₁	—	2	2	no	—
117	C₂×C₄×C₁₃₁	—	2	2	no	—
118	C₂×C₄×C₁₃₁	—	2	2	no	—
119	C₂×C₄×C₁₃₁	—	2	2	no	—
120	C₂×C₄×C₁₃₁	—	2	4	no	—
121	C₂×C₄×C₁₃₁	—	4	1	no	—
122	C₂×C₄×C₁₃₁	—	4	2	no	—
123	C₂×C₄×C₁₃₁	#117	1	2	yes	—
124	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
125	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
126	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
127	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
128	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
129	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
130	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
131	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
132	C₂×C₄×C₁₃₁	C₂×M₁₆	1	2	yes	—
133	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
134	C₈×C₁₃₁	—	2	2	no	—
135	C₈×C₁₃₁	—	2	1	no	—
136	C₈×C₁₃₁	—	2	1	no	—
137	C₈×C₁₃₁	#117	1	2	yes	—
138	C₈×C₁₃₁	C₂×M₁₆	1	4	yes	—
139	C₈×C₁₃₁	C₂×#41	1	1	yes	characteristic
140	C₈×C₁₃₁	C₂×#41	1	1	yes	characteristic
141	C₂²×C₁₃₁	—	2	1	no	—
142	C₂²×C₁₃₁	—	2	1	no	—
143	C₂²×C₁₃₁	—	2	2	no	—
144	C₂²×C₁₃₁	—	2	2	no	—
145	C₂²×C₁₃₁	—	2	2	no	—
146	C₂²×C₁₃₁	#431	1	2	yes	—
147	C₂²×C₁₃₁	C₂³×C₈	1	1	yes	characteristic
148	C₄×C₁₃₁	—	2	1	no	—
149	C₄×C₁₃₁	—	2	2	no	—
150	C₄×C₁₃₁	—	2	1	no	—
151	C₄×C₁₃₁	—	2	1	no	—
152	C₄×C₁₃₁	—	2	2	no	—
153	C₄×C₁₃₁	—	2	2	no	—
154	C₄×C₁₃₁	#431	1	2	yes	—
155	C₄×C₁₃₁	#504	1	2	yes	—
156	C₄×C₁₃₁	C₂×#117	1	1	yes	characteristic
157	C₄×C₁₃₁	C₂²×M₁₆	1	1	yes	characteristic
158	C₂×C₁₃₁	—	2	2	no	—
159	C₂×C₁₃₁	—	4	2	no	—
160	C₂×C₁₃₁	C₂×#431	1	1	yes	characteristic
161	C₂×C₁₃₁	C₂×#504	1	1	yes	characteristic
162	C₂×C₁₃₁	#3407	1	1	yes	characteristic
163	#33423	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₁₃₁	#33423	1	1	yes	characteristic, direct product factor, Sylow
165	C₄×#131	C₂×C₁₃₁	1	1	yes	characteristic
166	#2164	C₂×C₁₃₁	1	4	yes	complemented
167	#2163	C₂×C₁₃₁	1	2	yes	complemented
168	#2162	C₂×C₁₃₁	1	2	yes	complemented
169	#2150	C₂×C₁₃₁	1	1	yes	characteristic, complemented
170	C₂×C₄⋊C₁₆	C₂×C₁₃₁	1	1	yes	characteristic, complemented
171	#2113	C₂×C₁₃₁	1	2	yes	—
172	#2108	C₂×C₁₃₁	1	2	yes	complemented
173	C₂×#131	C₄×C₁₃₁	1	1	yes	characteristic
174	C₂×#131	C₂²×C₁₃₁	1	1	yes	characteristic
175	C₄×#41	C₄×C₁₃₁	1	1	yes	characteristic
176	C₂×M₃₂	C₂²×C₁₃₁	1	2	yes	—
177	C₂²×C₁₆	C₂²×C₁₃₁	1	2	yes	—
178	#405	C₄×C₁₃₁	1	1	yes	characteristic
179	#405	C₄×C₁₃₁	1	2	yes	—
180	#405	C₂²×C₁₃₁	1	1	yes	characteristic
181	#405	C₂²×C₁₃₁	1	2	yes	—
182	C₄×M₁₆	C₄×C₁₃₁	1	2	yes	—
183	C₄×M₁₆	C₄×C₁₃₁	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
186	C₄⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
187	C₄⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
188	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
189	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
190	C₄⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
191	C₂²⋊C₁₆	C₂²×C₁₃₁	1	4	yes	—
192	C₂²⋊C₁₆	C₂²×C₁₃₁	1	4	yes	—
193	#346	C₂²×C₁₃₁	1	4	yes	—
194	C₄×C₁₆	C₂²×C₁₃₁	1	4	yes	—
195	C₂×#41	C₂×C₄×C₁₃₁	1	1	yes	characteristic
196	#131	—	2	4	no	—
197	#131	—	2	2	no	—
198	#131	—	2	2	no	—
199	C₂×M₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
200	C₂×M₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
201	C₂×M₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
202	C₂×M₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
203	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
204	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
205	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
206	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
207	C₄×Q₈	C₈×C₁₃₁	1	1	yes	characteristic
208	C₄×Q₈	C₈×C₁₃₁	1	1	yes	characteristic
209	C₄×D₄	C₈×C₁₃₁	1	2	yes	—
210	C₄×D₄	C₈×C₁₃₁	1	1	yes	characteristic
211	C₄×D₄	C₈×C₁₃₁	1	2	yes	—
212	C₄×D₄	C₈×C₁₃₁	1	1	yes	characteristic
213	#117	C₂×C₄×C₁₃₁	1	2	yes	—
214	#117	C₂×C₄×C₁₃₁	1	1	yes	characteristic
215	C₂×C₄²	C₂×C₄×C₁₃₁	1	2	yes	—
216	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
217	M₃₂	—	2	4	no	—
218	C₂×C₁₆	—	2	4	no	—
219	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
220	C₂×C₁₆	C₂³×C₁₃₁	1	4	yes	—
221	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
222	#97	C₂×C₄×C₁₃₁	1	2	yes	—
223	#97	C₂×C₄×C₁₃₁	1	2	yes	—
224	#97	C₂×C₄×C₁₃₁	1	2	yes	—
225	C₄×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
226	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
227	C₄×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
228	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
229	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
230	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
231	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
232	#41	—	2	2	no	—
233	#41	—	2	2	no	—
234	C₂×Q₈	C₂×C₈×C₁₃₁	1	1	yes	characteristic
235	C₂×D₄	C₂×C₈×C₁₃₁	1	2	yes	—
236	C₂×D₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
237	C₂²×C₄	C₂×C₈×C₁₃₁	1	2	yes	—
238	C₂²×C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
239	C₂²×C₄	C₂×C₈×C₁₃₁	1	2	yes	—
240	C₂²×C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
243	M₁₆	—	2	2	no	—
244	M₁₆	—	2	4	no	—
245	M₁₆	—	2	4	no	—
246	M₁₆	M₁₆×C₁₃₁	1	4	yes	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
252	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
253	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
254	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
255	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
256	C₂×C₈	#41×C₁₃₁	1	2	yes	—
257	C₂×C₈	#41×C₁₃₁	1	2	yes	—
258	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
259	C₄⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
260	C₄⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
261	C₄⋊C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
262	C₄⋊C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
263	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
264	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
265	C₂²⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
266	C₄²	C₂×C₈×C₁₃₁	1	2	yes	—
267	C₄²	C₂×C₈×C₁₃₁	1	1	yes	characteristic
268	C₄²	C₂×C₈×C₁₃₁	1	2	yes	—
269	C₄²	C₂×C₈×C₁₃₁	1	1	yes	characteristic
270	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
271	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
272	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
273	C₁₆	—	2	2	no	—
274	C₁₆	—	2	2	no	—
275	C₁₆	—	2	4	no	—
276	C₂³	C₂²×C₈×C₁₃₁	1	2	yes	—
277	C₂³	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
278	Q₈	—	2	2	no	—
279	D₄	—	2	4	no	—
280	D₄	—	2	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	#117×C₁₃₁	1	2	yes	—
288	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
289	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
290	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
291	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
292	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
293	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
294	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
295	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
296	C₂×C₄	C₂×M₁₆×C₁₃₁	1	2	yes	—
297	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
298	C₈	—	2	2	no	—
299	C₈	—	2	1	no	—
300	C₈	—	2	1	no	—
301	C₈	#117×C₁₃₁	1	2	yes	—
302	C₈	C₂×M₁₆×C₁₃₁	1	4	yes	—
303	C₈	C₂×#41×C₁₃₁	1	1	yes	characteristic
304	C₈	C₂×#41×C₁₃₁	1	1	yes	characteristic
305	C₂²	—	2	1	no	—
306	C₂²	—	2	1	no	—
307	C₂²	—	2	2	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	2	2	no	—
310	C₂²	#431×C₁₃₁	1	2	yes	—
311	C₂²	C₂³×C₈×C₁₃₁	1	1	yes	characteristic
312	C₄	—	2	1	no	—
313	C₄	—	2	2	no	—
314	C₄	—	2	1	no	—
315	C₄	—	2	1	no	—
316	C₄	—	2	2	no	—
317	C₄	—	2	2	no	—
318	C₄	#431×C₁₃₁	1	2	yes	—
319	C₄	#504×C₁₃₁	1	2	yes	—
320	C₄	C₂×#117×C₁₃₁	1	1	yes	characteristic
321	C₄	C₂²×M₁₆×C₁₃₁	1	1	yes	characteristic
322	C₂	—	2	2	no	—
323	C₂	—	4	2	no	—
324	C₂	C₂×#431×C₁₃₁	1	1	yes	characteristic
325	C₂	C₂×#504×C₁₃₁	1	1	yes	characteristic
326	C₂	#3407×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂³×C₈
prime radical	C₂×#41×C₁₃₁	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2164×C₁₃₁	C₂	semidirect
3. #2163×C₁₃₁	C₂	semidirect
4. #2162×C₁₃₁	C₂	semidirect
5. #2150×C₁₃₁	C₂	semidirect
6. C₂×C₄⋊C₁₆×C₁₃₁	C₂	semidirect
8. #2108×C₁₃₁	C₂	semidirect
163. #33423	C₁₃₁	direct (N × H)
164. C₁₃₁	#33423	direct (N × H)
166. #2164	C₂×C₁₃₁	semidirect
167. #2163	C₂×C₁₃₁	semidirect
168. #2162	C₂×C₁₃₁	semidirect
169. #2150	C₂×C₁₃₁	semidirect
170. C₂×C₄⋊C₁₆	C₂×C₁₃₁	semidirect
172. #2108	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×#131×C₁₃₁	2
#2164×C₁₃₁	2
#2163×C₁₃₁	2
#2162×C₁₃₁	2
#2150×C₁₃₁	2
C₂×C₄⋊C₁₆×C₁₃₁	2
#2113×C₁₃₁	2
#2108×C₁₃₁	2
#33423	131

Subgroups — C131×#33423 #45719307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33423 #45719307