Subgroups — C₁₃₁×#33766 #45719650

Order 33536.

584 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3059×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3058×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2237×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2234×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2220×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2217×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2187×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2185×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2113×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
11	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×#131×C₁₃₁	C₂²	1	1	yes	characteristic
13	#536×C₁₃₁	—	2	1	no	—
14	#535×C₁₃₁	—	2	1	no	—
15	C₂×SD₃₂×C₁₃₁	C₂²	1	2	yes	—
16	C₂×SD₃₂×C₁₃₁	C₂²	1	2	yes	—
17	C₂×M₃₂×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
19	#470×C₁₃₁	—	2	1	no	—
20	#470×C₁₃₁	—	2	1	no	—
21	#469×C₁₃₁	—	2	1	no	—
22	#469×C₁₃₁	—	2	1	no	—
23	#467×C₁₃₁	C₂²	1	2	yes	—
24	#467×C₁₃₁	C₂²	1	2	yes	complemented
25	#466×C₁₃₁	C₂²	1	2	yes	—
26	#466×C₁₃₁	C₂²	1	2	yes	—
27	#427×C₁₃₁	C₂²	1	1	yes	characteristic
28	#427×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
29	#419×C₁₃₁	—	2	1	no	—
30	#418×C₁₃₁	—	2	1	no	—
31	#367×C₁₃₁	C₂²	1	2	yes	complemented
32	#366×C₁₃₁	C₂²	1	2	yes	complemented
33	#358×C₁₃₁	C₂²	1	2	yes	complemented
34	#358×C₁₃₁	C₂²	1	2	yes	complemented
35	#357×C₁₃₁	C₂²	1	2	yes	—
36	#357×C₁₃₁	C₂²	1	2	yes	—
37	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
38	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
39	C₂×#41×C₁₃₁	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃₁	—	2	1	no	—
41	C₂²×D₄×C₁₃₁	—	2	1	no	—
42	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
43	C₂×Q₁₆×C₁₃₁	—	4	1	no	—
44	C₂×Q₁₆×C₁₃₁	—	4	1	no	—
45	C₂×Q₁₆×C₁₃₁	C₂³	1	2	yes	—
46	C₂×D₈×C₁₃₁	—	2	1	no	—
47	C₂×D₈×C₁₃₁	—	4	1	no	—
48	C₂×D₈×C₁₃₁	—	4	1	no	—
49	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
50	#131×C₁₃₁	—	4	1	no	—
51	#131×C₁₃₁	—	4	1	no	—
52	C₂×M₁₆×C₁₃₁	D₄	1	1	yes	characteristic
53	C₂×M₁₆×C₁₃₁	D₄	1	1	yes	characteristic
54	C₂×M₁₆×C₁₃₁	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₁₃₁	—	4	1	no	—
59	#127×C₁₃₁	—	4	1	no	—
60	#124×C₁₃₁	—	4	1	no	—
61	#124×C₁₃₁	—	4	1	no	—
62	#123×C₁₃₁	—	4	1	no	—
63	#123×C₁₃₁	—	4	1	no	—
64	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
65	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
66	#121×C₁₃₁	—	2	2	no	—
67	#121×C₁₃₁	—	2	2	no	—
68	#120×C₁₃₁	—	4	1	no	—
69	#120×C₁₃₁	—	4	1	no	—
70	#117×C₁₃₁	—	2	1	no	—
71	#117×C₁₃₁	—	2	1	no	—
72	SD₃₂×C₁₃₁	—	4	2	no	—
73	SD₃₂×C₁₃₁	—	4	2	no	—
74	M₃₂×C₁₃₁	—	4	1	no	—
75	C₂×C₁₆×C₁₃₁	—	4	1	no	—
76	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
77	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
78	#107×C₁₃₁	C₂³	1	2	yes	—
79	#107×C₁₃₁	C₂³	1	2	yes	—
80	#106×C₁₃₁	—	2	1	no	—
81	#106×C₁₃₁	—	2	1	no	—
82	#103×C₁₃₁	—	2	2	no	—
83	#103×C₁₃₁	—	2	2	no	—
84	#102×C₁₃₁	—	2	2	no	—
85	#102×C₁₃₁	—	2	2	no	—
86	C₂⁴×C₁₃₁	—	4	1	no	—
87	#41×C₁₃₁	—	4	1	no	—
88	#41×C₁₃₁	—	4	1	no	—
89	C₂×Q₈×C₁₃₁	—	2	2	no	—
90	C₂×Q₈×C₁₃₁	—	4	2	no	—
91	C₂×Q₈×C₁₃₁	—	4	2	no	—
92	C₂×Q₈×C₁₃₁	—	4	1	no	—
93	C₂×Q₈×C₁₃₁	D₈	1	1	yes	characteristic
94	C₂×D₄×C₁₃₁	—	2	2	no	—
95	C₂×D₄×C₁₃₁	—	4	2	no	—
96	C₂×D₄×C₁₃₁	—	4	2	no	—
97	C₂×D₄×C₁₃₁	—	4	2	no	—
98	C₂×D₄×C₁₃₁	—	4	2	no	—
99	C₂×D₄×C₁₃₁	—	4	1	no	—
100	C₂×D₄×C₁₃₁	D₈	1	1	yes	characteristic
101	C₂×D₄×C₁₃₁	D₈	1	1	yes	characteristic
102	C₂×D₄×C₁₃₁	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₁	—	4	1	no	—
104	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	Q₁₆×C₁₃₁	—	2	2	no	—
108	Q₁₆×C₁₃₁	—	2	2	no	—
109	Q₁₆×C₁₃₁	—	4	2	no	—
110	D₈×C₁₃₁	—	2	2	no	—
111	D₈×C₁₃₁	—	2	2	no	—
112	D₈×C₁₃₁	—	4	2	no	—
113	M₁₆×C₁₃₁	—	4	1	no	—
114	M₁₆×C₁₃₁	—	4	1	no	—
115	M₁₆×C₁₃₁	—	4	1	no	—
116	C₂×C₈×C₁₃₁	—	2	1	no	—
117	C₂×C₈×C₁₃₁	—	2	1	no	—
118	C₂×C₈×C₁₃₁	—	2	1	no	—
119	C₂×C₈×C₁₃₁	—	2	1	no	—
120	C₂×C₈×C₁₃₁	—	2	1	no	—
121	C₂×C₈×C₁₃₁	—	2	1	no	—
122	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
126	C₄⋊C₄×C₁₃₁	—	2	2	no	—
127	C₄⋊C₄×C₁₃₁	—	2	2	no	—
128	C₄⋊C₄×C₁₃₁	—	4	2	no	—
129	C₄⋊C₄×C₁₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
131	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
132	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
134	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
135	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
136	C₄²×C₁₃₁	—	4	1	no	—
137	C₄²×C₁₃₁	—	4	1	no	—
138	C₁₆×C₁₃₁	—	2	2	no	—
139	C₁₆×C₁₃₁	—	2	2	no	—
140	C₂³×C₁₃₁	—	4	2	no	—
141	C₂³×C₁₃₁	—	8	2	no	—
142	C₂³×C₁₃₁	—	16	2	no	—
143	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
144	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
145	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₁₃₁	—	4	1	no	—
147	Q₈×C₁₃₁	—	4	2	no	—
148	Q₈×C₁₃₁	—	4	2	no	—
149	Q₈×C₁₃₁	—	8	2	no	—
150	D₄×C₁₃₁	—	4	1	no	—
151	D₄×C₁₃₁	—	4	1	no	—
152	D₄×C₁₃₁	—	4	1	no	—
153	D₄×C₁₃₁	—	4	2	no	—
154	D₄×C₁₃₁	—	4	2	no	—
155	D₄×C₁₃₁	—	8	2	no	—
156	D₄×C₁₃₁	—	16	2	no	—
157	D₄×C₁₃₁	—	16	2	no	—
158	C₂×C₄×C₁₃₁	—	2	1	no	—
159	C₂×C₄×C₁₃₁	—	2	1	no	—
160	C₂×C₄×C₁₃₁	—	2	1	no	—
161	C₂×C₄×C₁₃₁	—	2	1	no	—
162	C₂×C₄×C₁₃₁	—	2	1	no	—
163	C₂×C₄×C₁₃₁	—	2	1	no	—
164	C₂×C₄×C₁₃₁	—	4	2	no	—
165	C₂×C₄×C₁₃₁	—	4	2	no	—
166	C₂×C₄×C₁₃₁	—	4	2	no	—
167	C₂×C₄×C₁₃₁	—	8	2	no	—
168	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₁₃₁	—	2	1	no	—
173	C₈×C₁₃₁	—	2	1	no	—
174	C₈×C₁₃₁	—	2	1	no	—
175	C₈×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
176	C₈×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²×C₁₃₁	—	2	2	no	—
178	C₂²×C₁₃₁	—	2	2	no	—
179	C₂²×C₁₃₁	—	2	2	no	—
180	C₂²×C₁₃₁	—	2	1	no	—
181	C₂²×C₁₃₁	—	2	1	no	—
182	C₂²×C₁₃₁	—	2	1	no	—
183	C₂²×C₁₃₁	—	8	2	no	—
184	C₂²×C₁₃₁	—	8	2	no	—
185	C₂²×C₁₃₁	—	8	2	no	—
186	C₂²×C₁₃₁	—	16	4	no	—
187	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
188	C₄×C₁₃₁	—	2	1	no	—
189	C₄×C₁₃₁	—	2	1	no	—
190	C₄×C₁₃₁	—	2	1	no	—
191	C₄×C₁₃₁	—	8	2	no	—
192	C₄×C₁₃₁	—	8	2	no	—
193	C₄×C₁₃₁	—	8	2	no	—
194	C₄×C₁₃₁	#534	1	1	yes	characteristic
195	C₄×C₁₃₁	#575	1	1	yes	characteristic
196	C₂×C₁₃₁	—	4	1	no	—
197	C₂×C₁₃₁	—	4	1	no	—
198	C₂×C₁₃₁	—	4	1	no	—
199	C₂×C₁₃₁	—	16	2	no	—
200	C₂×C₁₃₁	#3186	1	1	yes	characteristic
201	C₂×C₁₃₁	#3416	1	2	yes	—
202	#33766	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₃₁	#33766	1	1	yes	characteristic, direct product factor, Sylow
204	#3059	C₂×C₁₃₁	1	1	yes	characteristic, complemented
205	#3058	C₂×C₁₃₁	1	1	yes	characteristic
206	#2237	C₂×C₁₃₁	1	2	yes	complemented
207	#2234	C₂×C₁₃₁	1	2	yes	complemented
208	#2220	C₂×C₁₃₁	1	2	yes	complemented
209	#2217	C₂×C₁₃₁	1	2	yes	complemented
210	#2187	C₂×C₁₃₁	1	2	yes	complemented
211	#2185	C₂×C₁₃₁	1	2	yes	complemented
212	#2113	C₂×C₁₃₁	1	1	yes	characteristic, complemented
213	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
214	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₂×#131	C₂²×C₁₃₁	1	1	yes	characteristic
216	#536	—	2	1	no	—
217	#535	—	2	1	no	—
218	C₂×SD₃₂	C₂²×C₁₃₁	1	2	yes	—
219	C₂×SD₃₂	C₂²×C₁₃₁	1	2	yes	—
220	C₂×M₃₂	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
221	C₂²×C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
222	#470	—	2	1	no	—
223	#470	—	2	1	no	—
224	#469	—	2	1	no	—
225	#469	—	2	1	no	—
226	#467	C₂²×C₁₃₁	1	2	yes	—
227	#467	C₂²×C₁₃₁	1	2	yes	complemented
228	#466	C₂²×C₁₃₁	1	2	yes	—
229	#466	C₂²×C₁₃₁	1	2	yes	—
230	#427	C₂²×C₁₃₁	1	1	yes	characteristic
231	#427	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
232	#419	—	2	1	no	—
233	#418	—	2	1	no	—
234	#367	C₂²×C₁₃₁	1	2	yes	complemented
235	#366	C₂²×C₁₃₁	1	2	yes	complemented
236	#358	C₂²×C₁₃₁	1	2	yes	complemented
237	#358	C₂²×C₁₃₁	1	2	yes	complemented
238	#357	C₂²×C₁₃₁	1	2	yes	—
239	#357	C₂²×C₁₃₁	1	2	yes	—
240	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
241	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
242	C₂×#41	D₄×C₁₃₁	1	1	yes	characteristic
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	—	4	1	no	—
247	C₂×Q₁₆	—	4	1	no	—
248	C₂×Q₁₆	C₂³×C₁₃₁	1	2	yes	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	4	1	no	—
251	C₂×D₈	—	4	1	no	—
252	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
253	#131	—	4	1	no	—
254	#131	—	4	1	no	—
255	C₂×M₁₆	D₄×C₁₃₁	1	1	yes	characteristic
256	C₂×M₁₆	D₄×C₁₃₁	1	1	yes	characteristic
257	C₂×M₁₆	D₄×C₁₃₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
261	C₄⋊Q₈	—	4	1	no	—
262	#127	—	4	1	no	—
263	#124	—	4	1	no	—
264	#124	—	4	1	no	—
265	#123	—	4	1	no	—
266	#123	—	4	1	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	#121	—	2	2	no	—
270	#121	—	2	2	no	—
271	#120	—	4	1	no	—
272	#120	—	4	1	no	—
273	#117	—	2	1	no	—
274	#117	—	2	1	no	—
275	SD₃₂	—	4	2	no	—
276	SD₃₂	—	4	2	no	—
277	M₃₂	—	4	1	no	—
278	C₂×C₁₆	—	4	1	no	—
279	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
280	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
281	#107	C₂³×C₁₃₁	1	2	yes	—
282	#107	C₂³×C₁₃₁	1	2	yes	—
283	#106	—	2	1	no	—
284	#106	—	2	1	no	—
285	#103	—	2	2	no	—
286	#103	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	C₂⁴	—	4	1	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	D₈×C₁₃₁	1	1	yes	characteristic
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	D₈×C₁₃₁	1	1	yes	characteristic
304	C₂×D₄	D₈×C₁₃₁	1	1	yes	characteristic
305	C₂×D₄	D₈×C₁₃₁	1	1	yes	characteristic
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	4	2	no	—
313	D₈	—	2	2	no	—
314	D₈	—	2	2	no	—
315	D₈	—	4	2	no	—
316	M₁₆	—	4	1	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
328	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₄²	—	4	1	no	—
340	C₄²	—	4	1	no	—
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	8	2	no	—
345	C₂³	—	16	2	no	—
346	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
347	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
348	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	8	2	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	16	2	no	—
360	D₄	—	16	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
373	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
379	C₈	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	#534×C₁₃₁	1	1	yes	characteristic
398	C₄	#575×C₁₃₁	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	4	1	no	—
402	C₂	—	16	2	no	—
403	C₂	#3186×C₁₃₁	1	1	yes	characteristic
404	C₂	#3416×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
prime radical	#3058×C₁₃₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×#41×C₁₃₁ ◁ C₂×#131×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3059×C₁₃₁	C₂	semidirect
3. #2237×C₁₃₁	C₂	semidirect
4. #2234×C₁₃₁	C₂	semidirect
5. #2220×C₁₃₁	C₂	semidirect
6. #2217×C₁₃₁	C₂	semidirect
7. #2187×C₁₃₁	C₂	semidirect
8. #2185×C₁₃₁	C₂	semidirect
9. #2113×C₁₃₁	C₂	semidirect
10. C₂²×Q₁₆×C₁₃₁	C₂²	semidirect
17. C₂×M₃₂×C₁₃₁	C₂²	semidirect
18. C₂²×C₁₆×C₁₃₁	C₂²	semidirect
24. #467×C₁₃₁	C₂²	semidirect
28. #427×C₁₃₁	C₂²	semidirect
31. #367×C₁₃₁	C₂²	semidirect
32. #366×C₁₃₁	C₂²	semidirect
33. #358×C₁₃₁	C₂²	semidirect
34. #358×C₁₃₁	C₂²	semidirect
38. C₂²⋊C₁₆×C₁₃₁	C₂²	semidirect
202. #33766	C₁₃₁	direct (N × H)
203. C₁₃₁	#33766	direct (N × H)
204. #3059	C₂×C₁₃₁	semidirect
206. #2237	C₂×C₁₃₁	semidirect
207. #2234	C₂×C₁₃₁	semidirect
208. #2220	C₂×C₁₃₁	semidirect
209. #2217	C₂×C₁₃₁	semidirect
210. #2187	C₂×C₁₃₁	semidirect
211. #2185	C₂×C₁₃₁	semidirect
212. #2113	C₂×C₁₃₁	semidirect
213. C₂²×Q₁₆	C₂²×C₁₃₁	semidirect
220. C₂×M₃₂	C₂²×C₁₃₁	semidirect
221. C₂²×C₁₆	C₂²×C₁₃₁	semidirect
227. #467	C₂²×C₁₃₁	semidirect
231. #427	C₂²×C₁₃₁	semidirect
234. #367	C₂²×C₁₃₁	semidirect
235. #366	C₂²×C₁₃₁	semidirect
236. #358	C₂²×C₁₃₁	semidirect
237. #358	C₂²×C₁₃₁	semidirect
241. C₂²⋊C₁₆	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3059×C₁₃₁	2
#3058×C₁₃₁	2
#2237×C₁₃₁	2
#2234×C₁₃₁	2
#2220×C₁₃₁	2
#2217×C₁₃₁	2
#2187×C₁₃₁	2
#2185×C₁₃₁	2
#2113×C₁₃₁	2
#33766	131

Subgroups — C131×#33766 #45719650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33766 #45719650