Subgroups — C₁₃₁×#33594 #45719478

Order 33536.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3414×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	#3147×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#443×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2214×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2213×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2212×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	C₂×#364×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2148×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	C₂×#135×C₁₃₁	—	2	1	no	—
10	C₂×#135×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂×#135×C₁₃₁	C₂²	1	2	yes	—
12	C₂×#131×C₁₃₁	—	2	1	no	—
13	#532×C₁₃₁	—	2	1	no	—
14	#510×C₁₃₁	—	2	2	no	—
15	#510×C₁₃₁	C₂²	1	4	yes	—
16	#509×C₁₃₁	—	2	2	no	—
17	#509×C₁₃₁	C₂²	1	4	yes	—
18	#508×C₁₃₁	—	2	4	no	—
19	C₂×M₃₂×C₁₃₁	C₂²	1	2	yes	—
20	#495×C₁₃₁	—	2	1	no	—
21	#495×C₁₃₁	C₂²	1	2	yes	complemented
22	#494×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
23	#493×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
24	#492×C₁₃₁	—	2	1	no	—
25	#443×C₁₃₁	—	2	1	no	—
26	#443×C₁₃₁	—	2	1	no	—
27	#443×C₁₃₁	C₂²	1	2	yes	—
28	#443×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×#104×C₁₃₁	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
32	#364×C₁₃₁	C₂²	1	2	yes	complemented
33	#364×C₁₃₁	C₂²	1	2	yes	complemented
34	#362×C₁₃₁	C₂²	1	4	yes	complemented
35	#361×C₁₃₁	C₂²	1	4	yes	complemented
36	C₂×#41×C₁₃₁	—	2	1	no	—
37	C₂×#41×C₁₃₁	—	2	2	no	—
38	#135×C₁₃₁	—	2	1	no	—
39	#135×C₁₃₁	—	2	2	no	—
40	#135×C₁₃₁	—	2	2	no	—
41	#135×C₁₃₁	—	2	1	no	—
42	#135×C₁₃₁	—	2	2	no	—
43	#135×C₁₃₁	—	2	2	no	—
44	#135×C₁₃₁	—	4	1	no	—
45	#135×C₁₃₁	—	4	1	no	—
46	#135×C₁₃₁	—	4	1	no	—
47	#135×C₁₃₁	—	4	1	no	—
48	#135×C₁₃₁	D₄	1	2	yes	complemented
49	#135×C₁₃₁	C₂³	1	2	yes	—
50	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
51	C₂×Q₁₆×C₁₃₁	D₄	1	1	yes	characteristic, complemented
52	C₂×Q₁₆×C₁₃₁	C₂³	1	2	yes	—
53	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
54	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
55	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
56	C₂×D₈×C₁₃₁	—	2	1	no	—
57	C₂×D₈×C₁₃₁	D₄	1	1	yes	characteristic, complemented
58	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
59	#131×C₁₃₁	—	2	2	no	—
60	#131×C₁₃₁	—	2	2	no	—
61	#131×C₁₃₁	—	4	1	no	—
62	#131×C₁₃₁	—	4	1	no	—
63	C₂×M₁₆×C₁₃₁	—	2	1	no	—
64	C₂×M₁₆×C₁₃₁	—	4	1	no	—
65	C₂²×C₈×C₁₃₁	—	4	1	no	—
66	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
67	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
69	#127×C₁₃₁	—	2	1	no	—
70	#124×C₁₃₁	—	2	2	no	—
71	#121×C₁₃₁	—	4	2	no	—
72	C₄×D₄×C₁₃₁	—	4	2	no	—
73	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
74	Q₃₂×C₁₃₁	—	2	4	no	—
75	SD₃₂×C₁₃₁	—	2	4	no	—
76	SD₃₂×C₁₃₁	—	2	4	no	—
77	D₁₆×C₁₃₁	—	2	4	no	—
78	M₃₂×C₁₃₁	—	2	2	no	—
79	M₃₂×C₁₃₁	C₂³	1	4	yes	—
80	C₂×C₁₆×C₁₃₁	—	2	2	no	—
81	#108×C₁₃₁	—	2	1	no	—
82	#108×C₁₃₁	C₂³	1	2	yes	—
83	#104×C₁₃₁	—	2	2	no	—
84	#104×C₁₃₁	—	2	2	no	—
85	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
86	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
89	#41×C₁₃₁	—	2	2	no	—
90	#41×C₁₃₁	—	2	2	no	—
91	#41×C₁₃₁	—	4	1	no	—
92	#41×C₁₃₁	—	4	1	no	—
93	#41×C₁₃₁	—	4	2	no	—
94	#41×C₁₃₁	—	4	2	no	—
95	#41×C₁₃₁	—	4	2	no	—
96	#41×C₁₃₁	—	4	2	no	—
97	C₂×Q₈×C₁₃₁	—	2	1	no	—
98	C₂×Q₈×C₁₃₁	—	2	2	no	—
99	C₂×D₄×C₁₃₁	—	2	1	no	—
100	C₂×D₄×C₁₃₁	—	2	2	no	—
101	C₂×D₄×C₁₃₁	—	4	2	no	—
102	C₂×D₄×C₁₃₁	—	4	1	no	—
103	C₂×D₄×C₁₃₁	—	4	2	no	—
104	C₂²×C₄×C₁₃₁	—	2	1	no	—
105	C₂²×C₄×C₁₃₁	—	4	1	no	—
106	C₂²×C₄×C₁₃₁	—	4	2	no	—
107	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
108	Q₁₆×C₁₃₁	—	2	1	no	—
109	Q₁₆×C₁₃₁	—	2	2	no	—
110	Q₁₆×C₁₃₁	—	2	2	no	—
111	Q₁₆×C₁₃₁	—	4	1	no	—
112	Q₁₆×C₁₃₁	—	4	1	no	—
113	Q₁₆×C₁₃₁	C₂×D₄	1	2	yes	—
114	SD₁₆×C₁₃₁	—	2	2	no	—
115	SD₁₆×C₁₃₁	—	2	2	no	—
116	SD₁₆×C₁₃₁	—	4	2	no	—
117	SD₁₆×C₁₃₁	—	4	2	no	—
118	SD₁₆×C₁₃₁	—	4	2	no	—
119	SD₁₆×C₁₃₁	—	4	2	no	—
120	D₈×C₁₃₁	—	2	1	no	—
121	D₈×C₁₃₁	—	2	2	no	—
122	D₈×C₁₃₁	—	2	2	no	—
123	D₈×C₁₃₁	—	4	1	no	—
124	D₈×C₁₃₁	—	4	1	no	—
125	D₈×C₁₃₁	C₂×D₄	1	2	yes	—
126	M₁₆×C₁₃₁	—	2	2	no	—
127	M₁₆×C₁₃₁	—	4	1	no	—
128	M₁₆×C₁₃₁	—	4	2	no	—
129	M₁₆×C₁₃₁	—	4	2	no	—
130	C₂×C₈×C₁₃₁	—	4	1	no	—
131	C₂×C₈×C₁₃₁	—	4	2	no	—
132	C₂×C₈×C₁₃₁	—	4	2	no	—
133	C₂×C₈×C₁₃₁	D₈	1	1	yes	characteristic
134	C₂×C₈×C₁₃₁	D₈	1	1	yes	characteristic
135	C₂×C₈×C₁₃₁	D₈	1	1	yes	characteristic
136	C₂×C₈×C₁₃₁	D₈	1	1	yes	characteristic
137	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃₁	#41	1	1	yes	characteristic
143	C₂×C₈×C₁₃₁	#41	1	1	yes	characteristic
144	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
145	C₄⋊C₄×C₁₃₁	—	4	2	no	—
146	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
147	C₄²×C₁₃₁	—	2	1	no	—
148	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
150	C₁₆×C₁₃₁	—	2	4	no	—
151	C₂³×C₁₃₁	—	4	1	no	—
152	C₂³×C₁₃₁	—	4	2	no	—
153	C₂³×C₁₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
154	Q₈×C₁₃₁	—	2	2	no	—
155	Q₈×C₁₃₁	—	4	1	no	—
156	Q₈×C₁₃₁	—	4	2	no	—
157	Q₈×C₁₃₁	—	4	2	no	—
158	D₄×C₁₃₁	—	2	2	no	—
159	D₄×C₁₃₁	—	4	2	no	—
160	D₄×C₁₃₁	—	4	2	no	—
161	D₄×C₁₃₁	—	4	2	no	—
162	D₄×C₁₃₁	—	4	2	no	—
163	D₄×C₁₃₁	—	4	1	no	—
164	D₄×C₁₃₁	—	8	4	no	—
165	D₄×C₁₃₁	—	8	2	no	—
166	D₄×C₁₃₁	—	8	2	no	—
167	C₂×C₄×C₁₃₁	—	2	1	no	—
168	C₂×C₄×C₁₃₁	—	2	1	no	—
169	C₂×C₄×C₁₃₁	—	4	2	no	—
170	C₂×C₄×C₁₃₁	—	4	1	no	—
171	C₂×C₄×C₁₃₁	—	4	2	no	—
172	C₂×C₄×C₁₃₁	—	4	2	no	—
173	C₂×C₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	8	2	no	—
175	C₂×C₄×C₁₃₁	—	8	2	no	—
176	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₁₃₁	—	4	2	no	—
183	C₈×C₁₃₁	#121	1	1	yes	characteristic
184	C₈×C₁₃₁	#121	1	1	yes	characteristic
185	C₈×C₁₃₁	C₂×D₈	1	1	yes	characteristic
186	C₈×C₁₃₁	C₂×D₈	1	1	yes	characteristic
187	C₈×C₁₃₁	C₂×D₈	1	1	yes	characteristic
188	C₈×C₁₃₁	C₂×D₈	1	1	yes	characteristic
189	C₈×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₃₁	C₂×#41	1	1	yes	characteristic
191	C₂²×C₁₃₁	—	4	1	no	—
192	C₂²×C₁₃₁	—	4	2	no	—
193	C₂²×C₁₃₁	—	8	2	no	—
194	C₂²×C₁₃₁	—	8	4	no	—
195	C₂²×C₁₃₁	—	8	2	no	—
196	C₂²×C₁₃₁	#459	1	1	yes	characteristic
197	C₂²×C₁₃₁	#459	1	1	yes	characteristic
198	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₁₃₁	—	2	2	no	—
200	C₄×C₁₃₁	—	4	1	no	—
201	C₄×C₁₃₁	—	4	2	no	—
202	C₄×C₁₃₁	—	8	2	no	—
203	C₄×C₁₃₁	#459	1	1	yes	characteristic
204	C₄×C₁₃₁	#459	1	1	yes	characteristic
205	C₄×C₁₃₁	C₂×#121	1	1	yes	characteristic
206	C₄×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
207	C₂×C₁₃₁	—	2	1	no	—
208	C₂×C₁₃₁	—	2	1	no	—
209	C₂×C₁₃₁	—	2	1	no	—
210	C₂×C₁₃₁	—	8	2	no	—
211	C₂×C₁₃₁	—	16	2	no	—
212	C₂×C₁₃₁	C₂×#459	1	1	yes	characteristic
213	#33594	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₁₃₁	#33594	1	1	yes	characteristic, direct product factor, Sylow
215	#3414	C₂×C₁₃₁	1	2	yes	complemented
216	#3147	C₂×C₁₃₁	1	1	yes	characteristic, complemented
217	C₂×#443	C₂×C₁₃₁	1	1	yes	characteristic, complemented
218	#2214	C₂×C₁₃₁	1	2	yes	complemented
219	#2213	C₂×C₁₃₁	1	2	yes	complemented
220	#2212	C₂×C₁₃₁	1	4	yes	complemented
221	C₂×#364	C₂×C₁₃₁	1	1	yes	characteristic, complemented
222	#2148	C₂×C₁₃₁	1	2	yes	complemented
223	C₂×#135	—	2	1	no	—
224	C₂×#135	C₂²×C₁₃₁	1	1	yes	characteristic
225	C₂×#135	C₂²×C₁₃₁	1	2	yes	—
226	C₂×#131	—	2	1	no	—
227	#532	—	2	1	no	—
228	#510	—	2	2	no	—
229	#510	C₂²×C₁₃₁	1	4	yes	—
230	#509	—	2	2	no	—
231	#509	C₂²×C₁₃₁	1	4	yes	—
232	#508	—	2	4	no	—
233	C₂×M₃₂	C₂²×C₁₃₁	1	2	yes	—
234	#495	—	2	1	no	—
235	#495	C₂²×C₁₃₁	1	2	yes	complemented
236	#494	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
237	#493	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
238	#492	—	2	1	no	—
239	#443	—	2	1	no	—
240	#443	—	2	1	no	—
241	#443	C₂²×C₁₃₁	1	2	yes	—
242	#443	C₂²×C₁₃₁	1	2	yes	—
243	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
244	C₂×#104	—	2	1	no	—
245	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
246	#364	C₂²×C₁₃₁	1	2	yes	complemented
247	#364	C₂²×C₁₃₁	1	2	yes	complemented
248	#362	C₂²×C₁₃₁	1	4	yes	complemented
249	#361	C₂²×C₁₃₁	1	4	yes	complemented
250	C₂×#41	—	2	1	no	—
251	C₂×#41	—	2	2	no	—
252	#135	—	2	1	no	—
253	#135	—	2	2	no	—
254	#135	—	2	2	no	—
255	#135	—	2	1	no	—
256	#135	—	2	2	no	—
257	#135	—	2	2	no	—
258	#135	—	4	1	no	—
259	#135	—	4	1	no	—
260	#135	—	4	1	no	—
261	#135	—	4	1	no	—
262	#135	D₄×C₁₃₁	1	2	yes	complemented
263	#135	C₂³×C₁₃₁	1	2	yes	—
264	C₂×Q₁₆	—	2	1	no	—
265	C₂×Q₁₆	D₄×C₁₃₁	1	1	yes	characteristic, complemented
266	C₂×Q₁₆	C₂³×C₁₃₁	1	2	yes	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	C₂×SD₁₆	—	2	1	no	—
270	C₂×D₈	—	2	1	no	—
271	C₂×D₈	D₄×C₁₃₁	1	1	yes	characteristic, complemented
272	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
273	#131	—	2	2	no	—
274	#131	—	2	2	no	—
275	#131	—	4	1	no	—
276	#131	—	4	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	4	1	no	—
279	C₂²×C₈	—	4	1	no	—
280	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
282	C₄⋊Q₈	—	2	1	no	—
283	#127	—	2	1	no	—
284	#124	—	2	2	no	—
285	#121	—	4	2	no	—
286	C₄×D₄	—	4	2	no	—
287	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
288	Q₃₂	—	2	4	no	—
289	SD₃₂	—	2	4	no	—
290	SD₃₂	—	2	4	no	—
291	D₁₆	—	2	4	no	—
292	M₃₂	—	2	2	no	—
293	M₃₂	C₂³×C₁₃₁	1	4	yes	—
294	C₂×C₁₆	—	2	2	no	—
295	#108	—	2	1	no	—
296	#108	C₂³×C₁₃₁	1	2	yes	—
297	#104	—	2	2	no	—
298	#104	—	2	2	no	—
299	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
300	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
301	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
302	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	4	1	no	—
306	#41	—	4	1	no	—
307	#41	—	4	2	no	—
308	#41	—	4	2	no	—
309	#41	—	4	2	no	—
310	#41	—	4	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	2	2	no	—
324	Q₁₆	—	2	2	no	—
325	Q₁₆	—	4	1	no	—
326	Q₁₆	—	4	1	no	—
327	Q₁₆	C₂×D₄×C₁₃₁	1	2	yes	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	4	2	no	—
331	SD₁₆	—	4	2	no	—
332	SD₁₆	—	4	2	no	—
333	SD₁₆	—	4	2	no	—
334	D₈	—	2	1	no	—
335	D₈	—	2	2	no	—
336	D₈	—	2	2	no	—
337	D₈	—	4	1	no	—
338	D₈	—	4	1	no	—
339	D₈	C₂×D₄×C₁₃₁	1	2	yes	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	4	1	no	—
342	M₁₆	—	4	2	no	—
343	M₁₆	—	4	2	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	D₈×C₁₃₁	1	1	yes	characteristic
348	C₂×C₈	D₈×C₁₃₁	1	1	yes	characteristic
349	C₂×C₈	D₈×C₁₃₁	1	1	yes	characteristic
350	C₂×C₈	D₈×C₁₃₁	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
352	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
354	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
355	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
356	C₂×C₈	#41×C₁₃₁	1	1	yes	characteristic
357	C₂×C₈	#41×C₁₃₁	1	1	yes	characteristic
358	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
359	C₄⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
364	C₁₆	—	2	4	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	2	no	—
367	C₂³	AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	4	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
391	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
392	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
393	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
394	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
396	C₈	—	4	2	no	—
397	C₈	#121×C₁₃₁	1	1	yes	characteristic
398	C₈	#121×C₁₃₁	1	1	yes	characteristic
399	C₈	C₂×D₈×C₁₃₁	1	1	yes	characteristic
400	C₈	C₂×D₈×C₁₃₁	1	1	yes	characteristic
401	C₈	C₂×D₈×C₁₃₁	1	1	yes	characteristic
402	C₈	C₂×D₈×C₁₃₁	1	1	yes	characteristic
403	C₈	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
404	C₈	C₂×#41×C₁₃₁	1	1	yes	characteristic
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	#459×C₁₃₁	1	1	yes	characteristic
411	C₂²	#459×C₁₃₁	1	1	yes	characteristic
412	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	#459×C₁₃₁	1	1	yes	characteristic
418	C₄	#459×C₁₃₁	1	1	yes	characteristic
419	C₄	C₂×#121×C₁₃₁	1	1	yes	characteristic
420	C₄	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	8	2	no	—
425	C₂	—	16	2	no	—
426	C₂	C₂×#459×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃₁	#459
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
socle	C₂×C₁₃₁	C₂×#459
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₁ ◁ C₂²×C₄×C₁₃₁ ◁ C₂×C₄×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3414×C₁₃₁	C₂	semidirect
2. #3147×C₁₃₁	C₂	semidirect
3. C₂×#443×C₁₃₁	C₂	semidirect
4. #2214×C₁₃₁	C₂	semidirect
5. #2213×C₁₃₁	C₂	semidirect
6. #2212×C₁₃₁	C₂	semidirect
7. C₂×#364×C₁₃₁	C₂	semidirect
8. #2148×C₁₃₁	C₂	semidirect
21. #495×C₁₃₁	C₂²	semidirect
22. #494×C₁₃₁	C₂²	semidirect
23. #493×C₁₃₁	C₂²	semidirect
32. #364×C₁₃₁	C₂²	semidirect
33. #364×C₁₃₁	C₂²	semidirect
34. #362×C₁₃₁	C₂²	semidirect
35. #361×C₁₃₁	C₂²	semidirect
48. #135×C₁₃₁	D₄	semidirect
51. C₂×Q₁₆×C₁₃₁	D₄	semidirect
57. C₂×D₈×C₁₃₁	D₄	semidirect
213. #33594	C₁₃₁	direct (N × H)
214. C₁₃₁	#33594	direct (N × H)
215. #3414	C₂×C₁₃₁	semidirect
216. #3147	C₂×C₁₃₁	semidirect
217. C₂×#443	C₂×C₁₃₁	semidirect
218. #2214	C₂×C₁₃₁	semidirect
219. #2213	C₂×C₁₃₁	semidirect
220. #2212	C₂×C₁₃₁	semidirect
221. C₂×#364	C₂×C₁₃₁	semidirect
222. #2148	C₂×C₁₃₁	semidirect
235. #495	C₂²×C₁₃₁	semidirect
236. #494	C₂²×C₁₃₁	semidirect
237. #493	C₂²×C₁₃₁	semidirect
246. #364	C₂²×C₁₃₁	semidirect
247. #364	C₂²×C₁₃₁	semidirect
248. #362	C₂²×C₁₃₁	semidirect
249. #361	C₂²×C₁₃₁	semidirect
262. #135	D₄×C₁₃₁	semidirect
265. C₂×Q₁₆	D₄×C₁₃₁	semidirect
271. C₂×D₈	D₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3414×C₁₃₁	2
#3147×C₁₃₁	2
C₂×#443×C₁₃₁	2
#2214×C₁₃₁	2
#2213×C₁₃₁	2
#2212×C₁₃₁	2
C₂×#364×C₁₃₁	2
#2148×C₁₃₁	2
#33594	131

Subgroups — C131×#33594 #45719478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33594 #45719478