Subgroups — C₁₃₁×#17798 #45703682

Order 33536.

666 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2989×C₁₃₁	C₂	1	2	yes	maximal
2	C₄×#131×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1569×C₁₃₁	C₂	1	4	yes	maximal, complemented
4	#1568×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1566×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1565×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1564×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#334×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#131×C₁₃₁	C₄	1	1	yes	characteristic
10	C₂×#131×C₁₃₁	C₄	1	1	yes	characteristic
11	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
12	#446×C₁₃₁	—	2	2	no	—
13	#436×C₁₃₁	—	2	2	no	—
14	#435×C₁₃₁	—	2	4	no	—
15	#432×C₁₃₁	C₂²	1	4	yes	—
16	#431×C₁₃₁	C₂²	1	2	yes	—
17	#423×C₁₃₁	C₂²	1	4	yes	—
18	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
19	#405×C₁₃₁	C₄	1	1	yes	characteristic
20	#405×C₁₃₁	C₄	1	2	yes	—
21	#405×C₁₃₁	C₄	1	2	yes	—
22	#405×C₁₃₁	C₄	1	1	yes	characteristic
23	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₄×M₁₆×C₁₃₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
27	#335×C₁₃₁	C₂²	1	2	yes	—
28	#335×C₁₃₁	C₂²	1	4	yes	—
29	#334×C₁₃₁	C₂²	1	2	yes	—
30	#334×C₁₃₁	C₂²	1	2	yes	—
31	#334×C₁₃₁	C₂²	1	1	yes	characteristic
32	#334×C₁₃₁	C₂²	1	1	yes	characteristic
33	#334×C₁₃₁	C₂²	1	4	yes	—
34	C₂×#41×C₁₃₁	C₂×C₄	1	1	yes	characteristic
35	#131×C₁₃₁	—	2	4	no	—
36	#131×C₁₃₁	—	2	4	no	—
37	C₂×M₁₆×C₁₃₁	—	2	4	no	—
38	C₂×M₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₁	—	2	2	no	—
43	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
46	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
47	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
48	C₄×Q₈×C₁₃₁	Q₈	1	1	yes	characteristic
49	C₄×D₄×C₁₃₁	D₄	1	2	yes	—
50	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
51	C₄×D₄×C₁₃₁	Q₈	1	2	yes	—
52	C₄×D₄×C₁₃₁	Q₈	1	1	yes	characteristic
53	#117×C₁₃₁	C₂×C₄	1	2	yes	—
54	#117×C₁₃₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
57	C₄⋊C₈×C₁₃₁	—	2	2	no	—
58	C₄⋊C₈×C₁₃₁	—	2	4	no	—
59	C₄⋊C₈×C₁₃₁	C₂³	1	4	yes	—
60	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
61	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
62	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
63	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
64	#97×C₁₃₁	—	2	4	no	—
65	#97×C₁₃₁	C₂×C₄	1	2	yes	—
66	#97×C₁₃₁	C₂×C₄	1	2	yes	—
67	#97×C₁₃₁	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₃₁	—	2	2	no	—
69	C₄×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
70	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
76	#41×C₁₃₁	—	2	2	no	—
77	#41×C₁₃₁	—	2	2	no	—
78	C₂×Q₈×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂×D₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
80	C₂×D₄×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
87	M₁₆×C₁₃₁	—	2	2	no	—
88	M₁₆×C₁₃₁	—	2	4	no	—
89	M₁₆×C₁₃₁	—	2	4	no	—
90	M₁₆×C₁₃₁	—	8	4	no	—
91	M₁₆×C₁₃₁	M₁₆	1	4	yes	complemented
92	C₂×C₈×C₁₃₁	—	2	2	no	—
93	C₂×C₈×C₁₃₁	—	2	4	no	—
94	C₂×C₈×C₁₃₁	—	2	4	no	—
95	C₂×C₈×C₁₃₁	—	2	2	no	—
96	C₂×C₈×C₁₃₁	—	2	2	no	—
97	C₂×C₈×C₁₃₁	—	2	4	no	—
98	C₂×C₈×C₁₃₁	—	8	2	no	—
99	C₂×C₈×C₁₃₁	M₁₆	1	4	yes	complemented
100	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
106	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
107	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
109	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
110	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
111	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
112	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
113	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
115	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
117	C₄²×C₁₃₁	C₂×Q₈	1	2	yes	—
118	C₄²×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
120	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
121	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
122	Q₈×C₁₃₁	—	2	2	no	—
123	D₄×C₁₃₁	—	2	4	no	—
124	D₄×C₁₃₁	—	2	2	no	—
125	C₂×C₄×C₁₃₁	—	2	2	no	—
126	C₂×C₄×C₁₃₁	—	2	2	no	—
127	C₂×C₄×C₁₃₁	—	2	2	no	—
128	C₂×C₄×C₁₃₁	—	2	4	no	—
129	C₂×C₄×C₁₃₁	—	4	1	no	—
130	C₂×C₄×C₁₃₁	—	4	2	no	—
131	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
133	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃₁	C₂×M₁₆	1	2	yes	—
138	C₂×C₄×C₁₃₁	C₂×M₁₆	1	2	yes	—
139	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
142	C₈×C₁₃₁	—	2	1	no	—
143	C₈×C₁₃₁	—	2	1	no	—
144	C₈×C₁₃₁	—	2	2	no	—
145	C₈×C₁₃₁	—	4	2	no	—
146	C₈×C₁₃₁	—	4	4	no	—
147	C₈×C₁₃₁	—	4	2	no	—
148	C₈×C₁₃₁	C₂×M₁₆	1	2	yes	—
149	C₈×C₁₃₁	C₂×M₁₆	1	4	yes	—
150	C₈×C₁₃₁	C₂×M₁₆	1	2	yes	—
151	C₂²×C₁₃₁	—	2	1	no	—
152	C₂²×C₁₃₁	—	2	1	no	—
153	C₂²×C₁₃₁	—	2	2	no	—
154	C₂²×C₁₃₁	—	2	2	no	—
155	C₂²×C₁₃₁	—	2	2	no	—
156	C₂²×C₁₃₁	#423	1	2	yes	—
157	C₂²×C₁₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
158	C₄×C₁₃₁	—	2	2	no	—
159	C₄×C₁₃₁	—	2	1	no	—
160	C₄×C₁₃₁	—	2	2	no	—
161	C₄×C₁₃₁	—	2	1	no	—
162	C₄×C₁₃₁	—	2	1	no	—
163	C₄×C₁₃₁	—	2	2	no	—
164	C₄×C₁₃₁	#423	1	2	yes	—
165	C₄×C₁₃₁	C₂²×M₁₆	1	1	yes	characteristic
166	C₄×C₁₃₁	C₂²×M₁₆	1	1	yes	characteristic
167	C₄×C₁₃₁	#577	1	2	yes	—
168	C₂×C₁₃₁	—	2	2	no	—
169	C₂×C₁₃₁	—	4	2	no	—
170	C₂×C₁₃₁	C₂×#423	1	1	yes	characteristic
171	C₂×C₁₃₁	#2912	1	1	yes	characteristic
172	C₂×C₁₃₁	#2916	1	1	yes	characteristic
173	#17798	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₁₃₁	#17798	1	1	yes	characteristic, direct product factor, Sylow
175	#2989	C₂×C₁₃₁	1	2	yes	—
176	C₄×#131	C₂×C₁₃₁	1	1	yes	characteristic
177	#1569	C₂×C₁₃₁	1	4	yes	complemented
178	#1568	C₂×C₁₃₁	1	2	yes	complemented
179	#1566	C₂×C₁₃₁	1	2	yes	complemented
180	#1565	C₂×C₁₃₁	1	2	yes	complemented
181	#1564	C₂×C₁₃₁	1	1	yes	characteristic, complemented
182	C₂×#334	C₂×C₁₃₁	1	1	yes	characteristic, complemented
183	C₂×#131	C₄×C₁₃₁	1	1	yes	characteristic
184	C₂×#131	C₄×C₁₃₁	1	1	yes	characteristic
185	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
186	#446	—	2	2	no	—
187	#436	—	2	2	no	—
188	#435	—	2	4	no	—
189	#432	C₂²×C₁₃₁	1	4	yes	—
190	#431	C₂²×C₁₃₁	1	2	yes	—
191	#423	C₂²×C₁₃₁	1	4	yes	—
192	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
193	#405	C₄×C₁₃₁	1	1	yes	characteristic
194	#405	C₄×C₁₃₁	1	2	yes	—
195	#405	C₄×C₁₃₁	1	2	yes	—
196	#405	C₄×C₁₃₁	1	1	yes	characteristic
197	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
198	C₄×M₁₆	C₂²×C₁₃₁	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
201	#335	C₂²×C₁₃₁	1	2	yes	—
202	#335	C₂²×C₁₃₁	1	4	yes	—
203	#334	C₂²×C₁₃₁	1	2	yes	—
204	#334	C₂²×C₁₃₁	1	2	yes	—
205	#334	C₂²×C₁₃₁	1	1	yes	characteristic
206	#334	C₂²×C₁₃₁	1	1	yes	characteristic
207	#334	C₂²×C₁₃₁	1	4	yes	—
208	C₂×#41	C₂×C₄×C₁₃₁	1	1	yes	characteristic
209	#131	—	2	4	no	—
210	#131	—	2	4	no	—
211	C₂×M₁₆	—	2	4	no	—
212	C₂×M₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
213	C₂×M₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
214	C₂×M₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
215	C₂×M₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
218	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
219	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
220	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
221	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
222	C₄×Q₈	Q₈×C₁₃₁	1	1	yes	characteristic
223	C₄×D₄	D₄×C₁₃₁	1	2	yes	—
224	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
225	C₄×D₄	Q₈×C₁₃₁	1	2	yes	—
226	C₄×D₄	Q₈×C₁₃₁	1	1	yes	characteristic
227	#117	C₂×C₄×C₁₃₁	1	2	yes	—
228	#117	C₂×C₄×C₁₃₁	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
231	C₄⋊C₈	—	2	2	no	—
232	C₄⋊C₈	—	2	4	no	—
233	C₄⋊C₈	C₂³×C₁₃₁	1	4	yes	—
234	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
235	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
236	C₂²⋊C₈	—	2	2	no	—
237	C₂²⋊C₈	—	2	4	no	—
238	#97	—	2	4	no	—
239	#97	C₂×C₄×C₁₃₁	1	2	yes	—
240	#97	C₂×C₄×C₁₃₁	1	2	yes	—
241	#97	C₂×C₄×C₁₃₁	1	2	yes	—
242	C₄×C₈	—	2	2	no	—
243	C₄×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
244	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
245	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
246	C₄×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
247	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
248	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
249	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
250	#41	—	2	2	no	—
251	#41	—	2	2	no	—
252	C₂×Q₈	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
253	C₂×D₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
254	C₂×D₄	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
259	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
260	C₂²×C₄	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
261	M₁₆	—	2	2	no	—
262	M₁₆	—	2	4	no	—
263	M₁₆	—	2	4	no	—
264	M₁₆	—	8	4	no	—
265	M₁₆	M₁₆×C₁₃₁	1	4	yes	complemented
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	8	2	no	—
273	C₂×C₈	M₁₆×C₁₃₁	1	4	yes	complemented
274	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
275	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
276	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
277	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
278	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
279	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
280	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
281	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
282	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
283	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
284	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
285	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
286	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
287	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
288	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
289	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
290	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
291	C₄²	C₂×Q₈×C₁₃₁	1	2	yes	—
292	C₄²	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
293	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
294	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
295	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
296	Q₈	—	2	2	no	—
297	D₄	—	2	4	no	—
298	D₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
306	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
307	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
308	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
309	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
310	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
311	C₂×C₄	C₂×M₁₆×C₁₃₁	1	2	yes	—
312	C₂×C₄	C₂×M₁₆×C₁₃₁	1	2	yes	—
313	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
314	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
315	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
316	C₈	—	2	1	no	—
317	C₈	—	2	1	no	—
318	C₈	—	2	2	no	—
319	C₈	—	4	4	no	—
320	C₈	—	4	2	no	—
321	C₈	—	4	2	no	—
322	C₈	C₂×M₁₆×C₁₃₁	1	2	yes	—
323	C₈	C₂×M₁₆×C₁₃₁	1	4	yes	—
324	C₈	C₂×M₁₆×C₁₃₁	1	2	yes	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	#423×C₁₃₁	1	2	yes	—
331	C₂²	C₂²×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
332	C₄	—	2	2	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	2	no	—
338	C₄	#423×C₁₃₁	1	2	yes	—
339	C₄	C₂²×M₁₆×C₁₃₁	1	1	yes	characteristic
340	C₄	C₂²×M₁₆×C₁₃₁	1	1	yes	characteristic
341	C₄	#577×C₁₃₁	1	2	yes	—
342	C₂	—	2	2	no	—
343	C₂	—	4	2	no	—
344	C₂	C₂×#423×C₁₃₁	1	1	yes	characteristic
345	C₂	#2912×C₁₃₁	1	1	yes	characteristic
346	C₂	#2916×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₄²	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₁₃₁	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₄×#41×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1569×C₁₃₁	C₂	semidirect
4. #1568×C₁₃₁	C₂	semidirect
5. #1566×C₁₃₁	C₂	semidirect
6. #1565×C₁₃₁	C₂	semidirect
7. #1564×C₁₃₁	C₂	semidirect
8. C₂×#334×C₁₃₁	C₂	semidirect
91. M₁₆×C₁₃₁	M₁₆	semidirect
99. C₂×C₈×C₁₃₁	M₁₆	semidirect
173. #17798	C₁₃₁	direct (N × H)
174. C₁₃₁	#17798	direct (N × H)
177. #1569	C₂×C₁₃₁	semidirect
178. #1568	C₂×C₁₃₁	semidirect
179. #1566	C₂×C₁₃₁	semidirect
180. #1565	C₂×C₁₃₁	semidirect
181. #1564	C₂×C₁₃₁	semidirect
182. C₂×#334	C₂×C₁₃₁	semidirect
265. M₁₆	M₁₆×C₁₃₁	semidirect
273. C₂×C₈	M₁₆×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2989×C₁₃₁	2
C₄×#131×C₁₃₁	2
#1569×C₁₃₁	2
#1568×C₁₃₁	2
#1566×C₁₃₁	2
#1565×C₁₃₁	2
#1564×C₁₃₁	2
C₂×#334×C₁₃₁	2
#17798	131

Subgroups — C131×#17798 #45703682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#17798 #45703682