Subgroups — C₁₃₁×#29828 #45715712

Order 33536.

842 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#476×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#461×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2862×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2293×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2066×C₁₃₁	C₂	1	4	yes	maximal, complemented
6	#2055×C₁₃₁	C₂	1	4	yes	maximal
7	#1987×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1981×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1842×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₁₃₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₃₁	—	2	1	no	—
15	#476×C₁₃₁	—	2	4	no	—
16	#461×C₁₃₁	—	2	4	no	—
17	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	4	yes	—
21	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#103×C₁₃₁	C₂²	1	4	yes	—
23	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
24	#391×C₁₃₁	—	2	2	no	—
25	#391×C₁₃₁	C₂²	1	4	yes	—
26	#390×C₁₃₁	C₂²	1	2	yes	—
27	#389×C₁₃₁	C₂²	1	2	yes	—
28	#388×C₁₃₁	—	2	2	no	—
29	#382×C₁₃₁	—	2	1	no	—
30	#382×C₁₃₁	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
33	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
34	#340×C₁₃₁	C₂²	1	4	yes	—
35	C₂²×Q₈×C₁₃₁	—	2	1	no	—
36	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₁	—	2	1	no	—
39	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
40	C₂×SD₁₆×C₁₃₁	—	4	4	no	—
41	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
43	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
44	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
45	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
46	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
47	C₄×D₄×C₁₃₁	—	2	2	no	—
48	C₄×D₄×C₁₃₁	D₄	1	4	yes	—
49	#117×C₁₃₁	—	4	4	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
60	C₂×C₄²×C₁₃₁	—	2	1	no	—
61	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
65	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
66	#106×C₁₃₁	—	2	4	no	—
67	C₄⋊C₈×C₁₃₁	—	2	2	no	—
68	C₄⋊C₈×C₁₃₁	—	2	2	no	—
69	C₄⋊C₈×C₁₃₁	—	4	4	no	—
70	#103×C₁₃₁	—	2	4	no	—
71	#103×C₁₃₁	—	4	4	no	—
72	#102×C₁₃₁	—	2	4	no	—
73	#95×C₁₃₁	—	2	1	no	—
74	#95×C₁₃₁	—	2	2	no	—
75	#95×C₁₃₁	—	2	4	no	—
76	#95×C₁₃₁	—	2	4	no	—
77	C₂⁴×C₁₃₁	—	2	1	no	—
78	C₂×Q₈×C₁₃₁	—	2	2	no	—
79	C₂×Q₈×C₁₃₁	—	2	2	no	—
80	C₂×Q₈×C₁₃₁	—	2	4	no	—
81	C₂×Q₈×C₁₃₁	—	2	4	no	—
82	C₂×Q₈×C₁₃₁	—	4	4	no	—
83	C₂×Q₈×C₁₃₁	—	4	2	no	—
84	C₂×D₄×C₁₃₁	—	2	1	no	—
85	C₂×D₄×C₁₃₁	—	2	2	no	—
86	C₂×D₄×C₁₃₁	—	2	2	no	—
87	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₃₁	—	2	1	no	—
89	C₂²×C₄×C₁₃₁	—	2	4	no	—
90	C₂²×C₄×C₁₃₁	—	2	2	no	—
91	C₂²×C₄×C₁₃₁	—	2	2	no	—
92	C₂²×C₄×C₁₃₁	—	2	2	no	—
93	C₂²×C₄×C₁₃₁	—	4	2	no	—
94	C₂²×C₄×C₁₃₁	—	4	2	no	—
95	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
100	SD₁₆×C₁₃₁	—	4	8	no	—
101	C₂×C₈×C₁₃₁	—	2	2	no	—
102	C₂×C₈×C₁₃₁	—	2	2	no	—
103	C₂×C₈×C₁₃₁	—	2	4	no	—
104	C₂×C₈×C₁₃₁	—	2	4	no	—
105	C₄⋊C₄×C₁₃₁	—	2	1	no	—
106	C₄⋊C₄×C₁₃₁	—	2	2	no	—
107	C₄⋊C₄×C₁₃₁	—	2	2	no	—
108	C₄⋊C₄×C₁₃₁	—	2	2	no	—
109	C₄⋊C₄×C₁₃₁	—	2	2	no	—
110	C₄⋊C₄×C₁₃₁	—	4	2	no	—
111	C₄⋊C₄×C₁₃₁	—	4	2	no	—
112	C₄⋊C₄×C₁₃₁	—	4	2	no	—
113	C₄⋊C₄×C₁₃₁	—	4	4	no	—
114	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
115	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
116	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
117	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
118	C₄²×C₁₃₁	—	2	2	no	—
119	C₄²×C₁₃₁	—	2	2	no	—
120	C₄²×C₁₃₁	—	2	2	no	—
121	C₄²×C₁₃₁	—	4	2	no	—
122	C₄²×C₁₃₁	—	4	2	no	—
123	C₄²×C₁₃₁	SD₁₆	1	4	yes	complemented
124	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
125	C₄²×C₁₃₁	#41	1	2	yes	—
126	C₂³×C₁₃₁	—	2	2	no	—
127	C₂³×C₁₃₁	—	4	2	no	—
128	C₂³×C₁₃₁	—	4	1	no	—
129	C₂³×C₁₃₁	—	4	1	no	—
130	C₂³×C₁₃₁	—	4	2	no	—
131	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₁₃₁	—	4	2	no	—
133	Q₈×C₁₃₁	—	4	2	no	—
134	Q₈×C₁₃₁	—	4	4	no	—
135	Q₈×C₁₃₁	—	8	4	no	—
136	D₄×C₁₃₁	—	2	2	no	—
137	D₄×C₁₃₁	—	2	2	no	—
138	D₄×C₁₃₁	—	4	2	no	—
139	C₂×C₄×C₁₃₁	—	2	2	no	—
140	C₂×C₄×C₁₃₁	—	2	2	no	—
141	C₂×C₄×C₁₃₁	—	2	2	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	—	4	1	no	—
147	C₂×C₄×C₁₃₁	—	4	1	no	—
148	C₂×C₄×C₁₃₁	—	4	8	no	—
149	C₂×C₄×C₁₃₁	—	4	2	no	—
150	C₂×C₄×C₁₃₁	—	4	2	no	—
151	C₂×C₄×C₁₃₁	—	4	2	no	—
152	C₂×C₄×C₁₃₁	—	4	4	no	—
153	C₂×C₄×C₁₃₁	—	4	2	no	—
154	C₂×C₄×C₁₃₁	—	4	2	no	—
155	C₂×C₄×C₁₃₁	—	4	4	no	—
156	C₂×C₄×C₁₃₁	#121	1	2	yes	—
157	C₂×C₄×C₁₃₁	#121	1	2	yes	—
158	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	4	yes	—
159	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₁₃₁	#137	1	2	yes	—
161	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
164	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
165	C₈×C₁₃₁	—	4	2	no	—
166	C₈×C₁₃₁	—	4	2	no	—
167	C₂²×C₁₃₁	—	4	2	no	—
168	C₂²×C₁₃₁	—	4	2	no	—
169	C₂²×C₁₃₁	—	4	2	no	—
170	C₂²×C₁₃₁	—	8	2	no	—
171	C₂²×C₁₃₁	—	8	2	no	—
172	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
173	C₂²×C₁₃₁	#537	1	2	yes	—
174	C₂²×C₁₃₁	C₂²×SD₁₆	1	1	yes	characteristic
175	C₂²×C₁₃₁	C₂×#137	1	1	yes	characteristic
176	C₂²×C₁₃₁	#575	1	2	yes	—
177	C₄×C₁₃₁	—	2	4	no	—
178	C₄×C₁₃₁	—	2	2	no	—
179	C₄×C₁₃₁	—	4	2	no	—
180	C₄×C₁₃₁	—	4	2	no	—
181	C₄×C₁₃₁	—	8	2	no	—
182	C₄×C₁₃₁	—	8	2	no	—
183	C₄×C₁₃₁	—	8	2	no	—
184	C₄×C₁₃₁	#461	1	4	yes	—
185	C₄×C₁₃₁	#535	1	1	yes	characteristic
186	C₄×C₁₃₁	#536	1	1	yes	characteristic
187	C₄×C₁₃₁	#542	1	2	yes	—
188	C₂×C₁₃₁	—	8	2	no	—
189	C₂×C₁₃₁	#2620	1	1	yes	characteristic
190	C₂×C₁₃₁	C₂×#461	1	1	yes	characteristic
191	C₂×C₁₃₁	#3040	1	1	yes	characteristic
192	C₂×C₁₃₁	#3246	1	2	yes	—
193	C₂×C₁₃₁	#3252	1	2	yes	—
194	#29828	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₁₃₁	#29828	1	1	yes	characteristic, direct product factor, Sylow
196	C₂×#476	C₂×C₁₃₁	1	1	yes	characteristic
197	C₂×#461	C₂×C₁₃₁	1	1	yes	characteristic
198	#2862	C₂×C₁₃₁	1	1	yes	characteristic, complemented
199	#2293	C₂×C₁₃₁	1	1	yes	characteristic
200	#2066	C₂×C₁₃₁	1	4	yes	complemented
201	#2055	C₂×C₁₃₁	1	4	yes	—
202	#1987	C₂×C₁₃₁	1	1	yes	characteristic, complemented
203	#1981	C₂×C₁₃₁	1	1	yes	characteristic, complemented
204	#1842	C₂×C₁₃₁	1	1	yes	characteristic, complemented
205	C₂²×SD₁₆	C₂²×C₁₃₁	1	2	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
209	C₂×#117	—	2	1	no	—
210	#476	—	2	4	no	—
211	#461	—	2	4	no	—
212	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	4	yes	—
216	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
217	C₂×#103	C₂²×C₁₃₁	1	4	yes	—
218	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
219	#391	—	2	2	no	—
220	#391	C₂²×C₁₃₁	1	4	yes	—
221	#390	C₂²×C₁₃₁	1	2	yes	—
222	#389	C₂²×C₁₃₁	1	2	yes	—
223	#388	—	2	2	no	—
224	#382	—	2	1	no	—
225	#382	—	2	1	no	—
226	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
227	C₄×C₂²⋊C₄	—	2	1	no	—
228	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
229	#340	C₂²×C₁₃₁	1	4	yes	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
232	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×SD₁₆	—	4	4	no	—
236	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
237	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	D₄×C₁₃₁	1	4	yes	—
244	#117	—	4	4	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
258	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
261	#106	—	2	4	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	4	4	no	—
265	#103	—	2	4	no	—
266	#103	—	4	4	no	—
267	#102	—	2	4	no	—
268	#95	—	2	2	no	—
269	#95	—	2	1	no	—
270	#95	—	2	4	no	—
271	#95	—	2	4	no	—
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
295	SD₁₆	—	4	8	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	4	no	—
309	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	4	2	no	—
317	C₄²	—	4	2	no	—
318	C₄²	SD₁₆×C₁₃₁	1	4	yes	complemented
319	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
320	C₄²	#41×C₁₃₁	1	2	yes	—
321	C₂³	—	2	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	2	no	—
326	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	4	4	no	—
330	Q₈	—	8	4	no	—
331	D₄	—	2	2	no	—
332	D₄	—	2	2	no	—
333	D₄	—	4	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	#121×C₁₃₁	1	2	yes	—
352	C₂×C₄	#121×C₁₃₁	1	2	yes	—
353	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	4	yes	—
354	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	2	yes	—
355	C₂×C₄	#137×C₁₃₁	1	2	yes	—
356	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
358	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
359	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
360	C₈	—	4	2	no	—
361	C₈	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
368	C₂²	#537×C₁₃₁	1	2	yes	—
369	C₂²	C₂²×SD₁₆×C₁₃₁	1	1	yes	characteristic
370	C₂²	C₂×#137×C₁₃₁	1	1	yes	characteristic
371	C₂²	#575×C₁₃₁	1	2	yes	—
372	C₄	—	2	4	no	—
373	C₄	—	2	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	2	no	—
376	C₄	—	8	2	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	2	no	—
379	C₄	#461×C₁₃₁	1	4	yes	—
380	C₄	#535×C₁₃₁	1	1	yes	characteristic
381	C₄	#536×C₁₃₁	1	1	yes	characteristic
382	C₄	#542×C₁₃₁	1	2	yes	—
383	C₂	—	8	2	no	—
384	C₂	#2620×C₁₃₁	1	1	yes	characteristic
385	C₂	C₂×#461×C₁₃₁	1	1	yes	characteristic
386	C₂	#3040×C₁₃₁	1	1	yes	characteristic
387	C₂	#3246×C₁₃₁	1	2	yes	—
388	C₂	#3252×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2862×C₁₃₁	C₂	semidirect
5. #2066×C₁₃₁	C₂	semidirect
7. #1987×C₁₃₁	C₂	semidirect
8. #1981×C₁₃₁	C₂	semidirect
9. #1842×C₁₃₁	C₂	semidirect
123. C₄²×C₁₃₁	SD₁₆	semidirect
194. #29828	C₁₃₁	direct (N × H)
195. C₁₃₁	#29828	direct (N × H)
198. #2862	C₂×C₁₃₁	semidirect
200. #2066	C₂×C₁₃₁	semidirect
202. #1987	C₂×C₁₃₁	semidirect
203. #1981	C₂×C₁₃₁	semidirect
204. #1842	C₂×C₁₃₁	semidirect
318. C₄²	SD₁₆×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#476×C₁₃₁	2
C₂×#461×C₁₃₁	2
#2862×C₁₃₁	2
#2293×C₁₃₁	2
#2066×C₁₃₁	2
#2055×C₁₃₁	2
#1987×C₁₃₁	2
#1981×C₁₃₁	2
#1842×C₁₃₁	2
#29828	131

Subgroups — C131×#29828 #45715712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29828 #45715712