Subgroups — C₁₃₁×#11388 #45697272

Order 33536.

878 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#1742×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1740×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1736×C₁₃₁	C₂	1	2	yes	maximal
5	#1733×C₁₃₁	C₂	1	2	yes	maximal
6	C₂²×M₁₆×C₁₃₁	C₂²	1	2	yes	—
7	#544×C₁₃₁	—	2	4	no	—
8	#544×C₁₃₁	—	2	4	no	—
9	C₂×C₄⋊Q₈×C₁₃₁	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₁₃₁	C₄	1	2	yes	complemented
11	C₂×#125×C₁₃₁	—	2	1	no	—
12	C₂×#125×C₁₃₁	C₄	1	2	yes	complemented
13	C₂×C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
14	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
15	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	#343×C₁₃₁	—	2	1	no	—
19	#343×C₁₃₁	—	2	1	no	—
20	#342×C₁₃₁	—	2	2	no	—
21	#340×C₁₃₁	—	2	4	no	—
22	#339×C₁₃₁	—	2	4	no	—
23	C₂²×Q₈×C₁₃₁	—	2	2	no	—
24	C₂³×C₄×C₁₃₁	—	2	1	no	—
25	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
26	C₂×M₁₆×C₁₃₁	—	2	2	no	—
27	C₂×M₁₆×C₁₃₁	—	2	2	no	—
28	C₂×M₁₆×C₁₃₁	—	2	2	no	—
29	C₂×M₁₆×C₁₃₁	—	2	2	no	—
30	C₂×M₁₆×C₁₃₁	—	2	2	no	—
31	C₂×M₁₆×C₁₃₁	Q₈	1	4	yes	complemented
32	C₂²×C₈×C₁₃₁	—	2	2	no	—
33	C₄⋊Q₈×C₁₃₁	—	2	8	no	—
34	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
35	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
36	#125×C₁₃₁	—	2	8	no	—
37	#125×C₁₃₁	—	2	4	no	—
38	#125×C₁₃₁	—	2	4	no	—
39	C₂²⋊Q₈×C₁₃₁	—	2	16	no	—
40	#117×C₁₃₁	—	2	2	no	—
41	#117×C₁₃₁	—	2	2	no	—
42	#117×C₁₃₁	—	2	2	no	—
43	#117×C₁₃₁	—	2	2	no	—
44	#117×C₁₃₁	—	2	2	no	—
45	#117×C₁₃₁	—	2	2	no	—
46	#117×C₁₃₁	D₄	1	4	yes	—
47	#117×C₁₃₁	Q₈	1	4	yes	complemented
48	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₃₁	D₄	1	4	yes	—
60	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃₁	—	2	1	no	—
64	C₂×C₄²×C₁₃₁	—	2	2	no	—
65	C₂×C₄²×C₁₃₁	C₂×C₄	1	2	yes	—
66	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
67	C₂×Q₈×C₁₃₁	—	2	8	no	—
68	C₂×Q₈×C₁₃₁	—	8	4	no	—
69	C₂²×C₄×C₁₃₁	—	2	1	no	—
70	C₂²×C₄×C₁₃₁	—	2	1	no	—
71	C₂²×C₄×C₁₃₁	—	2	2	no	—
72	C₂²×C₄×C₁₃₁	—	2	4	no	—
73	C₂²×C₄×C₁₃₁	—	4	2	no	—
74	C₂²×C₄×C₁₃₁	—	8	2	no	—
75	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
77	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
84	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
85	M₁₆×C₁₃₁	—	2	4	no	—
86	M₁₆×C₁₃₁	—	2	4	no	—
87	M₁₆×C₁₃₁	—	4	2	no	—
88	M₁₆×C₁₃₁	—	4	2	no	—
89	C₂×C₈×C₁₃₁	—	2	4	no	—
90	C₂×C₈×C₁₃₁	—	4	2	no	—
91	C₂×C₈×C₁₃₁	—	4	2	no	—
92	C₄⋊C₄×C₁₃₁	—	2	8	no	—
93	C₄⋊C₄×C₁₃₁	—	2	8	no	—
94	C₄⋊C₄×C₁₃₁	—	2	8	no	—
95	C₄⋊C₄×C₁₃₁	—	2	2	no	—
96	C₄⋊C₄×C₁₃₁	—	2	1	no	—
97	C₄⋊C₄×C₁₃₁	—	2	1	no	—
98	C₄⋊C₄×C₁₃₁	—	2	4	no	—
99	C₄⋊C₄×C₁₃₁	—	2	2	no	—
100	C₄⋊C₄×C₁₃₁	—	2	2	no	—
101	C₄⋊C₄×C₁₃₁	—	2	4	no	—
102	C₄⋊C₄×C₁₃₁	—	4	2	no	—
103	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	4	yes	—
104	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
105	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
106	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
107	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
108	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
109	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
110	C₄²×C₁₃₁	—	2	2	no	—
111	C₄²×C₁₃₁	—	2	2	no	—
112	C₄²×C₁₃₁	—	2	4	no	—
113	C₄²×C₁₃₁	—	2	4	no	—
114	C₄²×C₁₃₁	—	4	2	no	—
115	C₂³×C₁₃₁	—	4	1	no	—
116	C₂³×C₁₃₁	—	4	1	no	—
117	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂³×C₁₃₁	#120	1	2	yes	—
119	C₂³×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
120	C₂³×C₁₃₁	#124	1	1	yes	characteristic
121	C₂³×C₁₃₁	C₄⋊Q₈	1	1	yes	characteristic
122	Q₈×C₁₃₁	—	8	8	no	—
123	C₂×C₄×C₁₃₁	—	2	2	no	—
124	C₂×C₄×C₁₃₁	—	2	2	no	—
125	C₂×C₄×C₁₃₁	—	2	2	no	—
126	C₂×C₄×C₁₃₁	—	2	2	no	—
127	C₂×C₄×C₁₃₁	—	2	4	no	—
128	C₂×C₄×C₁₃₁	—	4	2	no	—
129	C₂×C₄×C₁₃₁	—	4	4	no	—
130	C₂×C₄×C₁₃₁	—	4	2	no	—
131	C₂×C₄×C₁₃₁	—	4	2	no	—
132	C₂×C₄×C₁₃₁	—	4	2	no	—
133	C₂×C₄×C₁₃₁	—	4	4	no	—
134	C₂×C₄×C₁₃₁	—	8	4	no	—
135	C₂×C₄×C₁₃₁	—	8	2	no	—
136	C₂×C₄×C₁₃₁	—	8	2	no	—
137	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃₁	C₄×Q₈	1	2	yes	—
140	C₂×C₄×C₁₃₁	C₄×Q₈	1	2	yes	—
141	C₂×C₄×C₁₃₁	#120	1	2	yes	—
142	C₂×C₄×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
144	C₂×C₄×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
145	C₂×C₄×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₁₃₁	#124	1	2	yes	—
148	C₂×C₄×C₁₃₁	#124	1	2	yes	—
149	C₂×C₄×C₁₃₁	#124	1	1	yes	characteristic
150	C₂×C₄×C₁₃₁	C₄⋊Q₈	1	2	yes	—
151	C₂×C₄×C₁₃₁	C₄⋊Q₈	1	2	yes	—
152	C₂×C₄×C₁₃₁	C₄⋊Q₈	1	1	yes	characteristic
153	C₈×C₁₃₁	—	4	4	no	—
154	C₂²×C₁₃₁	—	2	1	no	—
155	C₂²×C₁₃₁	—	2	2	no	—
156	C₂²×C₁₃₁	—	2	1	no	—
157	C₂²×C₁₃₁	—	2	2	no	—
158	C₂²×C₁₃₁	—	4	2	no	—
159	C₂²×C₁₃₁	—	4	1	no	—
160	C₂²×C₁₃₁	—	4	1	no	—
161	C₂²×C₁₃₁	#379	1	1	yes	characteristic
162	C₂²×C₁₃₁	#391	1	1	yes	characteristic
163	C₂²×C₁₃₁	#391	1	1	yes	characteristic
164	C₂²×C₁₃₁	#393	1	2	yes	—
165	C₂²×C₁₃₁	#395	1	2	yes	—
166	C₄×C₁₃₁	—	4	4	no	—
167	C₄×C₁₃₁	—	4	2	no	—
168	C₄×C₁₃₁	—	4	2	no	—
169	C₄×C₁₃₁	—	4	2	no	—
170	C₄×C₁₃₁	—	4	2	no	—
171	C₄×C₁₃₁	—	8	4	no	—
172	C₄×C₁₃₁	#391	1	2	yes	—
173	C₄×C₁₃₁	#391	1	2	yes	—
174	C₄×C₁₃₁	#393	1	2	yes	—
175	C₄×C₁₃₁	#395	1	2	yes	—
176	C₂×C₁₃₁	—	2	2	no	—
177	C₂×C₁₃₁	—	2	1	no	—
178	C₂×C₁₃₁	—	2	1	no	—
179	C₂×C₁₃₁	—	2	2	no	—
180	C₂×C₁₃₁	#1446	1	1	yes	characteristic
181	C₂×C₁₃₁	#1795	1	1	yes	characteristic
182	C₂×C₁₃₁	#1796	1	1	yes	characteristic
183	#11388	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₁	#11388	1	1	yes	characteristic, direct product factor, Sylow
185	C₂×#544	C₂×C₁₃₁	1	1	yes	characteristic
186	#1742	C₂×C₁₃₁	1	1	yes	characteristic
187	#1740	C₂×C₁₃₁	1	1	yes	characteristic
188	#1736	C₂×C₁₃₁	1	2	yes	—
189	#1733	C₂×C₁₃₁	1	2	yes	—
190	C₂²×M₁₆	C₂²×C₁₃₁	1	2	yes	—
191	#544	—	2	4	no	—
192	#544	—	2	4	no	—
193	C₂×C₄⋊Q₈	—	2	1	no	—
194	C₂×C₄⋊Q₈	C₄×C₁₃₁	1	2	yes	complemented
195	C₂×#125	—	2	1	no	—
196	C₂×#125	C₄×C₁₃₁	1	2	yes	complemented
197	C₂×C₂²⋊Q₈	—	2	2	no	—
198	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
199	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
200	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
201	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
202	#343	—	2	1	no	—
203	#343	—	2	1	no	—
204	#342	—	2	2	no	—
205	#340	—	2	4	no	—
206	#339	—	2	4	no	—
207	C₂²×Q₈	—	2	2	no	—
208	C₂³×C₄	—	2	1	no	—
209	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	—	2	2	no	—
212	C₂×M₁₆	—	2	2	no	—
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	Q₈×C₁₃₁	1	4	yes	complemented
216	C₂²×C₈	—	2	2	no	—
217	C₄⋊Q₈	—	2	8	no	—
218	C₄⋊Q₈	—	2	4	no	—
219	C₄⋊Q₈	—	2	4	no	—
220	#125	—	2	8	no	—
221	#125	—	2	4	no	—
222	#125	—	2	4	no	—
223	C₂²⋊Q₈	—	2	16	no	—
224	#117	—	2	2	no	—
225	#117	—	2	2	no	—
226	#117	—	2	2	no	—
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	—	2	2	no	—
230	#117	D₄×C₁₃₁	1	4	yes	—
231	#117	Q₈×C₁₃₁	1	4	yes	complemented
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
242	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
243	C₂×C₄⋊C₄	D₄×C₁₃₁	1	4	yes	—
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	C₂×C₄×C₁₃₁	1	2	yes	—
250	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
251	C₂×Q₈	—	2	8	no	—
252	C₂×Q₈	—	8	4	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	8	2	no	—
259	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
260	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
266	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
267	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
268	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
269	M₁₆	—	2	4	no	—
270	M₁₆	—	2	4	no	—
271	M₁₆	—	4	2	no	—
272	M₁₆	—	4	2	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	4	2	no	—
275	C₂×C₈	—	4	2	no	—
276	C₄⋊C₄	—	2	8	no	—
277	C₄⋊C₄	—	2	8	no	—
278	C₄⋊C₄	—	2	8	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	4	2	no	—
287	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	4	yes	—
288	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
289	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
290	C₂²⋊C₄	—	2	4	no	—
291	C₂²⋊C₄	—	2	4	no	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	4	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	4	2	no	—
299	C₂³	—	4	1	no	—
300	C₂³	—	4	1	no	—
301	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
302	C₂³	#120×C₁₃₁	1	2	yes	—
303	C₂³	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
304	C₂³	#124×C₁₃₁	1	1	yes	characteristic
305	C₂³	C₄⋊Q₈×C₁₃₁	1	1	yes	characteristic
306	Q₈	—	8	8	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	8	4	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	—	8	2	no	—
321	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
322	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
323	C₂×C₄	C₄×Q₈×C₁₃₁	1	2	yes	—
324	C₂×C₄	C₄×Q₈×C₁₃₁	1	2	yes	—
325	C₂×C₄	#120×C₁₃₁	1	2	yes	—
326	C₂×C₄	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
327	C₂×C₄	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
328	C₂×C₄	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
329	C₂×C₄	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
330	C₂×C₄	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
331	C₂×C₄	#124×C₁₃₁	1	2	yes	—
332	C₂×C₄	#124×C₁₃₁	1	2	yes	—
333	C₂×C₄	#124×C₁₃₁	1	1	yes	characteristic
334	C₂×C₄	C₄⋊Q₈×C₁₃₁	1	2	yes	—
335	C₂×C₄	C₄⋊Q₈×C₁₃₁	1	2	yes	—
336	C₂×C₄	C₄⋊Q₈×C₁₃₁	1	1	yes	characteristic
337	C₈	—	4	4	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	#379×C₁₃₁	1	1	yes	characteristic
346	C₂²	#391×C₁₃₁	1	1	yes	characteristic
347	C₂²	#391×C₁₃₁	1	1	yes	characteristic
348	C₂²	#393×C₁₃₁	1	2	yes	—
349	C₂²	#395×C₁₃₁	1	2	yes	—
350	C₄	—	4	4	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	8	4	no	—
356	C₄	#391×C₁₃₁	1	2	yes	—
357	C₄	#391×C₁₃₁	1	2	yes	—
358	C₄	#393×C₁₃₁	1	2	yes	—
359	C₄	#395×C₁₃₁	1	2	yes	—
360	C₂	—	2	2	no	—
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	2	2	no	—
364	C₂	#1446×C₁₃₁	1	1	yes	characteristic
365	C₂	#1795×C₁₃₁	1	1	yes	characteristic
366	C₂	#1796×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₁
prime radical	C₂⁴×C₁₃₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂³×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₂×C₄⋊Q₈×C₁₃₁	C₄	semidirect
12. C₂×#125×C₁₃₁	C₄	semidirect
31. C₂×M₁₆×C₁₃₁	Q₈	semidirect
47. #117×C₁₃₁	Q₈	semidirect
183. #11388	C₁₃₁	direct (N × H)
184. C₁₃₁	#11388	direct (N × H)
194. C₂×C₄⋊Q₈	C₄×C₁₃₁	semidirect
196. C₂×#125	C₄×C₁₃₁	semidirect
215. C₂×M₁₆	Q₈×C₁₃₁	semidirect
231. #117	Q₈×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#544×C₁₃₁	2
#1742×C₁₃₁	2
#1740×C₁₃₁	2
#1736×C₁₃₁	2
#1733×C₁₃₁	2
#11388	131

Subgroups — C131×#11388 #45697272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#11388 #45697272