Subgroups — C₁₃₁×#33753 #45719637

Order 33536.

642 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×#467×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#466×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2235×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2233×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2217×C₁₃₁	C₂	1	4	yes	maximal, complemented
6	#2187×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2185×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	C₂×C₂²⋊C₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
10	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Q₈×C₁₃₁	—	2	1	no	—
13	C₂×#121×C₁₃₁	—	2	1	no	—
14	C₂×SD₃₂×C₁₃₁	C₂²	1	4	yes	complemented
15	C₂²×C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
16	#467×C₁₃₁	—	2	1	no	—
17	#467×C₁₃₁	—	2	1	no	—
18	#467×C₁₃₁	C₂²	1	2	yes	—
19	#467×C₁₃₁	C₂²	1	2	yes	complemented
20	#466×C₁₃₁	—	2	1	no	—
21	#466×C₁₃₁	—	2	1	no	—
22	#466×C₁₃₁	C₂²	1	2	yes	—
23	#466×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×#103×C₁₃₁	—	2	1	no	—
27	C₂×#102×C₁₃₁	—	2	1	no	—
28	#367×C₁₃₁	C₂²	1	4	yes	complemented
29	#358×C₁₃₁	C₂²	1	4	yes	complemented
30	#357×C₁₃₁	C₂²	1	4	yes	complemented
31	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
32	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
33	C₂²×Q₈×C₁₃₁	—	2	1	no	—
34	C₂²×D₄×C₁₃₁	—	2	1	no	—
35	C₂²×D₄×C₁₃₁	—	4	1	no	—
36	C₂³×C₄×C₁₃₁	D₄	1	1	yes	characteristic
37	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
38	C₂×Q₁₆×C₁₃₁	—	4	2	no	—
39	C₂×Q₁₆×C₁₃₁	C₂³	1	2	yes	—
40	C₂×D₈×C₁₃₁	—	2	1	no	—
41	C₂×D₈×C₁₃₁	—	4	2	no	—
42	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₁	—	4	2	no	—
44	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
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⋊Q₈×C₁₃₁	—	2	2	no	—
51	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
52	C₂²⋊Q₈×C₁₃₁	—	4	1	no	—
53	C₂²⋊Q₈×C₁₃₁	—	4	1	no	—
54	#121×C₁₃₁	—	2	2	no	—
55	#121×C₁₃₁	—	2	2	no	—
56	#121×C₁₃₁	—	4	1	no	—
57	#121×C₁₃₁	—	4	1	no	—
58	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₁	—	4	1	no	—
61	C₂×C₂²⋊C₄×C₁₃₁	—	4	1	no	—
62	C₂×C₂²⋊C₄×C₁₃₁	—	4	1	no	—
63	SD₃₂×C₁₃₁	—	4	4	no	—
64	C₂×C₁₆×C₁₃₁	—	4	2	no	—
65	C₂×C₁₆×C₁₃₁	C₂³	1	4	yes	—
66	#107×C₁₃₁	—	2	1	no	—
67	#107×C₁₃₁	—	2	1	no	—
68	#107×C₁₃₁	C₂³	1	2	yes	—
69	#107×C₁₃₁	C₂³	1	2	yes	—
70	#103×C₁₃₁	—	2	2	no	—
71	#103×C₁₃₁	—	2	2	no	—
72	#102×C₁₃₁	—	2	2	no	—
73	#102×C₁₃₁	—	2	2	no	—
74	C₂⁴×C₁₃₁	—	4	1	no	—
75	C₂⁴×C₁₃₁	D₈	1	1	yes	characteristic
76	C₂×Q₈×C₁₃₁	—	2	2	no	—
77	C₂×Q₈×C₁₃₁	—	4	2	no	—
78	C₂×Q₈×C₁₃₁	—	4	2	no	—
79	C₂×Q₈×C₁₃₁	—	4	1	no	—
80	C₂×D₄×C₁₃₁	—	2	2	no	—
81	C₂×D₄×C₁₃₁	—	4	2	no	—
82	C₂×D₄×C₁₃₁	—	4	2	no	—
83	C₂×D₄×C₁₃₁	—	4	2	no	—
84	C₂×D₄×C₁₃₁	—	4	2	no	—
85	C₂×D₄×C₁₃₁	—	4	1	no	—
86	C₂×D₄×C₁₃₁	—	8	4	no	—
87	C₂²×C₄×C₁₃₁	—	4	1	no	—
88	C₂²×C₄×C₁₃₁	—	4	1	no	—
89	C₂²×C₄×C₁₃₁	—	4	1	no	—
90	C₂²×C₄×C₁₃₁	—	4	1	no	—
91	C₂²×C₄×C₁₃₁	—	4	1	no	—
92	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₁	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
98	Q₁₆×C₁₃₁	—	2	4	no	—
99	Q₁₆×C₁₃₁	—	4	2	no	—
100	D₈×C₁₃₁	—	2	4	no	—
101	D₈×C₁₃₁	—	4	2	no	—
102	C₂×C₈×C₁₃₁	—	2	2	no	—
103	C₂×C₈×C₁₃₁	—	2	2	no	—
104	C₂×C₈×C₁₃₁	—	2	2	no	—
105	C₂×C₈×C₁₃₁	—	4	1	no	—
106	C₂×C₈×C₁₃₁	—	4	1	no	—
107	C₂×C₈×C₁₃₁	—	4	1	no	—
108	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
112	C₄⋊C₄×C₁₃₁	—	2	2	no	—
113	C₄⋊C₄×C₁₃₁	—	2	2	no	—
114	C₄⋊C₄×C₁₃₁	—	4	1	no	—
115	C₄⋊C₄×C₁₃₁	—	4	1	no	—
116	C₄⋊C₄×C₁₃₁	—	4	2	no	—
117	C₄⋊C₄×C₁₃₁	—	4	2	no	—
118	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
119	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
121	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
122	C₁₆×C₁₃₁	—	2	4	no	—
123	C₂³×C₁₃₁	—	4	1	no	—
124	C₂³×C₁₃₁	—	4	1	no	—
125	C₂³×C₁₃₁	—	4	2	no	—
126	C₂³×C₁₃₁	—	8	2	no	—
127	C₂³×C₁₃₁	—	8	2	no	—
128	C₂³×C₁₃₁	—	8	2	no	—
129	C₂³×C₁₃₁	SD₃₂	1	4	yes	complemented
130	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
131	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
132	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
133	Q₈×C₁₃₁	—	4	2	no	—
134	Q₈×C₁₃₁	—	4	2	no	—
135	Q₈×C₁₃₁	—	8	2	no	—
136	D₄×C₁₃₁	—	4	2	no	—
137	D₄×C₁₃₁	—	4	2	no	—
138	D₄×C₁₃₁	—	8	2	no	—
139	D₄×C₁₃₁	—	8	4	no	—
140	D₄×C₁₃₁	—	8	4	no	—
141	C₂×C₄×C₁₃₁	—	2	1	no	—
142	C₂×C₄×C₁₃₁	—	2	1	no	—
143	C₂×C₄×C₁₃₁	—	2	1	no	—
144	C₂×C₄×C₁₃₁	—	2	1	no	—
145	C₂×C₄×C₁₃₁	—	2	1	no	—
146	C₂×C₄×C₁₃₁	—	2	1	no	—
147	C₂×C₄×C₁₃₁	—	4	1	no	—
148	C₂×C₄×C₁₃₁	—	4	1	no	—
149	C₂×C₄×C₁₃₁	—	4	1	no	—
150	C₂×C₄×C₁₃₁	—	4	2	no	—
151	C₂×C₄×C₁₃₁	—	4	2	no	—
152	C₂×C₄×C₁₃₁	—	4	2	no	—
153	C₂×C₄×C₁₃₁	—	8	2	no	—
154	C₂×C₄×C₁₃₁	—	8	2	no	—
155	C₂×C₄×C₁₃₁	—	8	2	no	—
156	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₁₃₁	—	2	1	no	—
161	C₈×C₁₃₁	—	2	1	no	—
162	C₈×C₁₃₁	—	2	1	no	—
163	C₈×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
164	C₂²×C₁₃₁	—	2	1	no	—
165	C₂²×C₁₃₁	—	2	1	no	—
166	C₂²×C₁₃₁	—	2	1	no	—
167	C₂²×C₁₃₁	—	2	1	no	—
168	C₂²×C₁₃₁	—	2	1	no	—
169	C₂²×C₁₃₁	—	2	1	no	—
170	C₂²×C₁₃₁	—	4	4	no	—
171	C₂²×C₁₃₁	—	8	2	no	—
172	C₂²×C₁₃₁	—	8	2	no	—
173	C₂²×C₁₃₁	—	8	2	no	—
174	C₂²×C₁₃₁	—	16	4	no	—
175	C₂²×C₁₃₁	C₂×SD₃₂	1	2	yes	—
176	C₂²×C₁₃₁	C₂×SD₃₂	1	2	yes	—
177	C₂²×C₁₃₁	C₂×SD₃₂	1	2	yes	—
178	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
179	C₄×C₁₃₁	—	2	1	no	—
180	C₄×C₁₃₁	—	2	1	no	—
181	C₄×C₁₃₁	—	2	1	no	—
182	C₄×C₁₃₁	—	8	2	no	—
183	C₄×C₁₃₁	—	8	2	no	—
184	C₄×C₁₃₁	—	8	2	no	—
185	C₄×C₁₃₁	#534	1	1	yes	characteristic
186	C₄×C₁₃₁	#575	1	1	yes	characteristic
187	C₂×C₁₃₁	—	2	2	no	—
188	C₂×C₁₃₁	—	2	2	no	—
189	C₂×C₁₃₁	—	2	2	no	—
190	C₂×C₁₃₁	—	16	2	no	—
191	C₂×C₁₃₁	#3186	1	1	yes	characteristic
192	C₂×C₁₃₁	C₂²×SD₃₂	1	1	yes	characteristic
193	C₂×C₁₃₁	#3414	1	1	yes	characteristic
194	#33753	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₁₃₁	#33753	1	1	yes	characteristic, direct product factor, Sylow
196	C₂×#467	C₂×C₁₃₁	1	1	yes	characteristic, complemented
197	C₂×#466	C₂×C₁₃₁	1	1	yes	characteristic
198	#2235	C₂×C₁₃₁	1	2	yes	complemented
199	#2233	C₂×C₁₃₁	1	2	yes	complemented
200	#2217	C₂×C₁₃₁	1	4	yes	complemented
201	#2187	C₂×C₁₃₁	1	2	yes	complemented
202	#2185	C₂×C₁₃₁	1	2	yes	complemented
203	C₂×C₂²⋊C₁₆	C₂×C₁₃₁	1	1	yes	characteristic, complemented
204	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
205	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
206	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
207	C₂×C₂²⋊Q₈	—	2	1	no	—
208	C₂×#121	—	2	1	no	—
209	C₂×SD₃₂	C₂²×C₁₃₁	1	4	yes	complemented
210	C₂²×C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
211	#467	—	2	1	no	—
212	#467	—	2	1	no	—
213	#467	C₂²×C₁₃₁	1	2	yes	—
214	#467	C₂²×C₁₃₁	1	2	yes	complemented
215	#466	—	2	1	no	—
216	#466	—	2	1	no	—
217	#466	C₂²×C₁₃₁	1	2	yes	—
218	#466	C₂²×C₁₃₁	1	2	yes	—
219	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
220	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
221	C₂×#103	—	2	1	no	—
222	C₂×#102	—	2	1	no	—
223	#367	C₂²×C₁₃₁	1	4	yes	complemented
224	#358	C₂²×C₁₃₁	1	4	yes	complemented
225	#357	C₂²×C₁₃₁	1	4	yes	complemented
226	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
227	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	—	4	1	no	—
231	C₂³×C₄	D₄×C₁₃₁	1	1	yes	characteristic
232	C₂×Q₁₆	—	2	1	no	—
233	C₂×Q₁₆	—	4	2	no	—
234	C₂×Q₁₆	C₂³×C₁₃₁	1	2	yes	—
235	C₂×D₈	—	2	1	no	—
236	C₂×D₈	—	4	2	no	—
237	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
238	C₂²×C₈	—	4	2	no	—
239	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
240	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
241	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
245	C₂²⋊Q₈	—	2	2	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	—	4	1	no	—
248	C₂²⋊Q₈	—	4	1	no	—
249	#121	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	—	4	1	no	—
252	#121	—	4	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	4	1	no	—
256	C₂×C₂²⋊C₄	—	4	1	no	—
257	C₂×C₂²⋊C₄	—	4	1	no	—
258	SD₃₂	—	4	4	no	—
259	C₂×C₁₆	—	4	2	no	—
260	C₂×C₁₆	C₂³×C₁₃₁	1	4	yes	—
261	#107	—	2	1	no	—
262	#107	—	2	1	no	—
263	#107	C₂³×C₁₃₁	1	2	yes	—
264	#107	C₂³×C₁₃₁	1	2	yes	—
265	#103	—	2	2	no	—
266	#103	—	2	2	no	—
267	#102	—	2	2	no	—
268	#102	—	2	2	no	—
269	C₂⁴	—	4	1	no	—
270	C₂⁴	D₈×C₁₃₁	1	1	yes	characteristic
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
288	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
289	C₂²×C₄	D₈×C₁₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
293	Q₁₆	—	2	4	no	—
294	Q₁₆	—	4	2	no	—
295	D₈	—	2	4	no	—
296	D₈	—	4	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
306	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₁₆	—	2	4	no	—
318	C₂³	—	4	1	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	—	8	2	no	—
323	C₂³	—	8	2	no	—
324	C₂³	SD₃₂×C₁₃₁	1	4	yes	complemented
325	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
326	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
327	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	8	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	4	no	—
335	D₄	—	8	4	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
352	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
353	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	16	4	no	—
370	C₂²	C₂×SD₃₂×C₁₃₁	1	2	yes	—
371	C₂²	C₂×SD₃₂×C₁₃₁	1	2	yes	—
372	C₂²	C₂×SD₃₂×C₁₃₁	1	2	yes	—
373	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	#534×C₁₃₁	1	1	yes	characteristic
381	C₄	#575×C₁₃₁	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	2	2	no	—
384	C₂	—	2	2	no	—
385	C₂	—	16	2	no	—
386	C₂	#3186×C₁₃₁	1	1	yes	characteristic
387	C₂	C₂²×SD₃₂×C₁₃₁	1	1	yes	characteristic
388	C₂	#3414×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
prime radical	C₂×#466×C₁₃₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂³×C₄×C₁₃₁ ◁ C₂³×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#467×C₁₃₁	C₂	semidirect
3. #2235×C₁₃₁	C₂	semidirect
4. #2233×C₁₃₁	C₂	semidirect
5. #2217×C₁₃₁	C₂	semidirect
6. #2187×C₁₃₁	C₂	semidirect
7. #2185×C₁₃₁	C₂	semidirect
8. C₂×C₂²⋊C₁₆×C₁₃₁	C₂	semidirect
9. C₂²×Q₁₆×C₁₃₁	C₂²	semidirect
14. C₂×SD₃₂×C₁₃₁	C₂²	semidirect
15. C₂²×C₁₆×C₁₃₁	C₂²	semidirect
19. #467×C₁₃₁	C₂²	semidirect
25. C₂×#107×C₁₃₁	C₂²	semidirect
28. #367×C₁₃₁	C₂²	semidirect
29. #358×C₁₃₁	C₂²	semidirect
30. #357×C₁₃₁	C₂²	semidirect
32. C₂²⋊C₁₆×C₁₃₁	C₂²	semidirect
129. C₂³×C₁₃₁	SD₃₂	semidirect
194. #33753	C₁₃₁	direct (N × H)
195. C₁₃₁	#33753	direct (N × H)
196. C₂×#467	C₂×C₁₃₁	semidirect
198. #2235	C₂×C₁₃₁	semidirect
199. #2233	C₂×C₁₃₁	semidirect
200. #2217	C₂×C₁₃₁	semidirect
201. #2187	C₂×C₁₃₁	semidirect
202. #2185	C₂×C₁₃₁	semidirect
203. C₂×C₂²⋊C₁₆	C₂×C₁₃₁	semidirect
204. C₂²×Q₁₆	C₂²×C₁₃₁	semidirect
209. C₂×SD₃₂	C₂²×C₁₃₁	semidirect
210. C₂²×C₁₆	C₂²×C₁₃₁	semidirect
214. #467	C₂²×C₁₃₁	semidirect
220. C₂×#107	C₂²×C₁₃₁	semidirect
223. #367	C₂²×C₁₃₁	semidirect
224. #358	C₂²×C₁₃₁	semidirect
225. #357	C₂²×C₁₃₁	semidirect
227. C₂²⋊C₁₆	C₂²×C₁₃₁	semidirect
324. C₂³	SD₃₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#467×C₁₃₁	2
C₂×#466×C₁₃₁	2
#2235×C₁₃₁	2
#2233×C₁₃₁	2
#2217×C₁₃₁	2
#2187×C₁₃₁	2
#2185×C₁₃₁	2
C₂×C₂²⋊C₁₆×C₁₃₁	2
#33753	131

Subgroups — C131×#33753 #45719637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33753 #45719637