Subgroups — C₁₃₁×#32823 #45718707

Order 33536.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2864×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#2858×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2092×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2073×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2067×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2065×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2058×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2057×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2041×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	#2041×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	#1831×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₁₃₁	—	2	1	no	—
15	C₂×#124×C₁₃₁	—	2	1	no	—
16	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
17	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
23	#390×C₁₃₁	—	2	1	no	—
24	#390×C₁₃₁	—	2	1	no	—
25	#390×C₁₃₁	C₂²	1	2	yes	—
26	#390×C₁₃₁	C₂²	1	2	yes	—
27	#389×C₁₃₁	C₂²	1	1	yes	characteristic
28	#389×C₁₃₁	C₂²	1	1	yes	characteristic
29	#389×C₁₃₁	C₂²	1	1	yes	characteristic
30	#389×C₁₃₁	C₂²	1	1	yes	characteristic
31	#387×C₁₃₁	—	2	1	no	—
32	#387×C₁₃₁	—	2	1	no	—
33	#387×C₁₃₁	—	2	1	no	—
34	#387×C₁₃₁	—	2	1	no	—
35	#382×C₁₃₁	C₂²	1	1	yes	characteristic
36	#382×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
38	#340×C₁₃₁	C₂²	1	2	yes	—
39	#340×C₁₃₁	C₂²	1	2	yes	—
40	#336×C₁₃₁	C₂²	1	1	yes	characteristic
41	#336×C₁₃₁	C₂²	1	1	yes	characteristic
42	#336×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₁	—	2	1	no	—
44	C₂²×D₄×C₁₃₁	—	2	1	no	—
45	C₂²×D₄×C₁₃₁	—	2	1	no	—
46	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₁₃₁	—	4	2	no	—
50	#127×C₁₃₁	—	4	2	no	—
51	#124×C₁₃₁	—	4	4	no	—
52	#124×C₁₃₁	—	4	4	no	—
53	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
67	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
74	#107×C₁₃₁	—	4	2	no	—
75	#106×C₁₃₁	—	4	2	no	—
76	C₄⋊C₈×C₁₃₁	—	4	2	no	—
77	#102×C₁₃₁	—	4	2	no	—
78	#102×C₁₃₁	—	4	2	no	—
79	#102×C₁₃₁	—	4	2	no	—
80	#102×C₁₃₁	—	4	2	no	—
81	#95×C₁₃₁	—	2	1	no	—
82	#95×C₁₃₁	—	2	1	no	—
83	#95×C₁₃₁	—	2	1	no	—
84	#95×C₁₃₁	—	2	1	no	—
85	#95×C₁₃₁	—	2	1	no	—
86	#95×C₁₃₁	—	2	1	no	—
87	#95×C₁₃₁	—	2	1	no	—
88	#95×C₁₃₁	—	2	1	no	—
89	C₂⁴×C₁₃₁	—	2	2	no	—
90	C₂×Q₈×C₁₃₁	—	4	2	no	—
91	C₂×Q₈×C₁₃₁	—	4	2	no	—
92	C₂×Q₈×C₁₃₁	—	4	2	no	—
93	C₂×D₄×C₁₃₁	—	2	2	no	—
94	C₂×D₄×C₁₃₁	—	2	2	no	—
95	C₂×D₄×C₁₃₁	—	2	2	no	—
96	C₂×D₄×C₁₃₁	—	2	2	no	—
97	C₂×D₄×C₁₃₁	—	2	2	no	—
98	C₂×D₄×C₁₃₁	—	2	2	no	—
99	C₂×D₄×C₁₃₁	—	4	2	no	—
100	C₂×D₄×C₁₃₁	—	4	2	no	—
101	C₂×D₄×C₁₃₁	—	4	2	no	—
102	C₂×D₄×C₁₃₁	—	4	2	no	—
103	C₂×D₄×C₁₃₁	—	4	2	no	—
104	C₂×D₄×C₁₃₁	—	4	2	no	—
105	C₂²×C₄×C₁₃₁	—	2	1	no	—
106	C₂²×C₄×C₁₃₁	—	2	1	no	—
107	C₂²×C₄×C₁₃₁	—	2	1	no	—
108	C₂²×C₄×C₁₃₁	—	2	1	no	—
109	C₂²×C₄×C₁₃₁	—	2	2	no	—
110	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₁₃₁	—	2	2	no	—
118	C₂×C₈×C₁₃₁	—	2	2	no	—
119	C₂×C₈×C₁₃₁	—	2	2	no	—
120	C₂×C₈×C₁₃₁	—	2	2	no	—
121	C₂×C₈×C₁₃₁	—	2	2	no	—
122	C₂×C₈×C₁₃₁	—	2	2	no	—
123	C₄⋊C₄×C₁₃₁	—	2	1	no	—
124	C₄⋊C₄×C₁₃₁	—	2	1	no	—
125	C₄⋊C₄×C₁₃₁	—	2	2	no	—
126	C₄⋊C₄×C₁₃₁	—	2	2	no	—
127	C₄⋊C₄×C₁₃₁	—	2	2	no	—
128	C₄⋊C₄×C₁₃₁	—	2	2	no	—
129	C₄⋊C₄×C₁₃₁	—	2	1	no	—
130	C₄⋊C₄×C₁₃₁	—	2	1	no	—
131	C₄⋊C₄×C₁₃₁	—	4	2	no	—
132	C₄⋊C₄×C₁₃₁	—	4	2	no	—
133	C₄⋊C₄×C₁₃₁	—	4	2	no	—
134	C₄⋊C₄×C₁₃₁	—	4	2	no	—
135	C₄⋊C₄×C₁₃₁	—	4	2	no	—
136	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
137	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
138	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
139	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
140	C₄²×C₁₃₁	—	2	2	no	—
141	C₄²×C₁₃₁	—	2	2	no	—
142	C₄²×C₁₃₁	—	2	2	no	—
143	C₄²×C₁₃₁	—	2	1	no	—
144	C₄²×C₁₃₁	—	2	2	no	—
145	C₄²×C₁₃₁	—	2	1	no	—
146	C₄²×C₁₃₁	—	2	2	no	—
147	C₄²×C₁₃₁	—	4	1	no	—
148	C₂³×C₁₃₁	—	4	2	no	—
149	C₂³×C₁₃₁	—	4	2	no	—
150	C₂³×C₁₃₁	—	4	2	no	—
151	C₂³×C₁₃₁	—	4	2	no	—
152	C₂³×C₁₃₁	—	4	2	no	—
153	C₂³×C₁₃₁	—	4	2	no	—
154	C₂³×C₁₃₁	—	4	2	no	—
155	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₃₁	—	8	4	no	—
157	D₄×C₁₃₁	—	4	2	no	—
158	D₄×C₁₃₁	—	4	2	no	—
159	D₄×C₁₃₁	—	4	2	no	—
160	D₄×C₁₃₁	—	4	2	no	—
161	D₄×C₁₃₁	—	8	4	no	—
162	D₄×C₁₃₁	—	8	4	no	—
163	C₂×C₄×C₁₃₁	—	2	1	no	—
164	C₂×C₄×C₁₃₁	—	2	1	no	—
165	C₂×C₄×C₁₃₁	—	2	1	no	—
166	C₂×C₄×C₁₃₁	—	2	1	no	—
167	C₂×C₄×C₁₃₁	—	2	1	no	—
168	C₂×C₄×C₁₃₁	—	2	1	no	—
169	C₂×C₄×C₁₃₁	—	2	1	no	—
170	C₂×C₄×C₁₃₁	—	2	1	no	—
171	C₂×C₄×C₁₃₁	—	2	1	no	—
172	C₂×C₄×C₁₃₁	—	2	1	no	—
173	C₂×C₄×C₁₃₁	—	2	1	no	—
174	C₂×C₄×C₁₃₁	—	2	1	no	—
175	C₂×C₄×C₁₃₁	—	2	1	no	—
176	C₂×C₄×C₁₃₁	—	2	1	no	—
177	C₂×C₄×C₁₃₁	—	2	1	no	—
178	C₂×C₄×C₁₃₁	—	4	2	no	—
179	C₂×C₄×C₁₃₁	—	4	1	no	—
180	C₂×C₄×C₁₃₁	—	4	1	no	—
181	C₂×C₄×C₁₃₁	—	4	1	no	—
182	C₂×C₄×C₁₃₁	—	4	1	no	—
183	C₂×C₄×C₁₃₁	—	4	1	no	—
184	C₂×C₄×C₁₃₁	—	4	1	no	—
185	C₂×C₄×C₁₃₁	—	4	2	no	—
186	C₂×C₄×C₁₃₁	—	4	2	no	—
187	C₂×C₄×C₁₃₁	—	4	1	no	—
188	C₂×C₄×C₁₃₁	—	4	1	no	—
189	C₂×C₄×C₁₃₁	—	4	1	no	—
190	C₂×C₄×C₁₃₁	—	4	1	no	—
191	C₂×C₄×C₁₃₁	—	4	1	no	—
192	C₂×C₄×C₁₃₁	—	4	1	no	—
193	C₂×C₄×C₁₃₁	#135	1	2	yes	—
194	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
195	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
198	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
199	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₁₃₁	—	4	2	no	—
201	C₈×C₁₃₁	—	4	2	no	—
202	C₂²×C₁₃₁	—	8	2	no	—
203	C₂²×C₁₃₁	—	8	2	no	—
204	C₂²×C₁₃₁	—	8	2	no	—
205	C₂²×C₁₃₁	—	8	2	no	—
206	C₂²×C₁₃₁	—	8	2	no	—
207	C₂²×C₁₃₁	—	8	2	no	—
208	C₂²×C₁₃₁	—	8	2	no	—
209	C₂²×C₁₃₁	#535	1	1	yes	characteristic
210	C₂²×C₁₃₁	#536	1	1	yes	characteristic
211	C₂²×C₁₃₁	#537	1	1	yes	characteristic
212	C₂²×C₁₃₁	C₂×#135	1	1	yes	characteristic
213	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂²×C₁₃₁	#575	1	1	yes	characteristic
216	C₄×C₁₃₁	—	2	2	no	—
217	C₄×C₁₃₁	—	2	2	no	—
218	C₄×C₁₃₁	—	2	2	no	—
219	C₄×C₁₃₁	—	4	1	no	—
220	C₄×C₁₃₁	—	4	1	no	—
221	C₄×C₁₃₁	—	4	1	no	—
222	C₄×C₁₃₁	—	8	1	no	—
223	C₄×C₁₃₁	—	8	1	no	—
224	C₄×C₁₃₁	—	8	2	no	—
225	C₄×C₁₃₁	—	8	1	no	—
226	C₄×C₁₃₁	—	8	1	no	—
227	C₄×C₁₃₁	#562	1	2	yes	—
228	C₄×C₁₃₁	#563	1	2	yes	—
229	C₂×C₁₃₁	—	16	2	no	—
230	C₂×C₁₃₁	#2820	1	1	yes	characteristic
231	C₂×C₁₃₁	#3211	1	1	yes	characteristic
232	C₂×C₁₃₁	#3217	1	1	yes	characteristic
233	C₂×C₁₃₁	#3228	1	1	yes	characteristic
234	C₂×C₁₃₁	#3235	1	1	yes	characteristic
235	C₂×C₁₃₁	#3247	1	1	yes	characteristic
236	C₂×C₁₃₁	#3251	1	1	yes	characteristic
237	#32823	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₁₃₁	#32823	1	1	yes	characteristic, direct product factor, Sylow
239	#2864	C₂×C₁₃₁	1	1	yes	characteristic, complemented
240	#2858	C₂×C₁₃₁	1	1	yes	characteristic
241	#2092	C₂×C₁₃₁	1	2	yes	complemented
242	#2073	C₂×C₁₃₁	1	2	yes	complemented
243	#2067	C₂×C₁₃₁	1	2	yes	complemented
244	#2065	C₂×C₁₃₁	1	2	yes	complemented
245	#2058	C₂×C₁₃₁	1	1	yes	characteristic, complemented
246	#2057	C₂×C₁₃₁	1	1	yes	characteristic, complemented
247	#2041	C₂×C₁₃₁	1	1	yes	characteristic
248	#2041	C₂×C₁₃₁	1	1	yes	characteristic
249	#1831	C₂×C₁₃₁	1	1	yes	characteristic, complemented
250	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
251	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
252	C₂×#124	—	2	1	no	—
253	C₂×#124	—	2	1	no	—
254	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
255	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
256	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
257	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
258	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
259	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
260	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
261	#390	—	2	1	no	—
262	#390	—	2	1	no	—
263	#390	C₂²×C₁₃₁	1	2	yes	—
264	#390	C₂²×C₁₃₁	1	2	yes	—
265	#389	C₂²×C₁₃₁	1	1	yes	characteristic
266	#389	C₂²×C₁₃₁	1	1	yes	characteristic
267	#389	C₂²×C₁₃₁	1	1	yes	characteristic
268	#389	C₂²×C₁₃₁	1	1	yes	characteristic
269	#387	—	2	1	no	—
270	#387	—	2	1	no	—
271	#387	—	2	1	no	—
272	#387	—	2	1	no	—
273	#382	C₂²×C₁₃₁	1	1	yes	characteristic
274	#382	C₂²×C₁₃₁	1	1	yes	characteristic
275	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
276	#340	C₂²×C₁₃₁	1	2	yes	—
277	#340	C₂²×C₁₃₁	1	2	yes	—
278	#336	C₂²×C₁₃₁	1	1	yes	characteristic
279	#336	C₂²×C₁₃₁	1	1	yes	characteristic
280	#336	C₂²×C₁₃₁	1	2	yes	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
286	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
287	C₄⋊Q₈	—	4	2	no	—
288	#127	—	4	2	no	—
289	#124	—	4	4	no	—
290	#124	—	4	4	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
306	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
307	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
312	#107	—	4	2	no	—
313	#106	—	4	2	no	—
314	C₄⋊C₈	—	4	2	no	—
315	#102	—	4	2	no	—
316	#102	—	4	2	no	—
317	#102	—	4	2	no	—
318	#102	—	4	2	no	—
319	#95	—	2	1	no	—
320	#95	—	2	1	no	—
321	#95	—	2	1	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	1	no	—
326	#95	—	2	1	no	—
327	C₂⁴	—	2	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	1	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
394	Q₈	—	8	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	8	4	no	—
400	D₄	—	8	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	#135×C₁₃₁	1	2	yes	—
432	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
433	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
434	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
435	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
436	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
437	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
438	C₈	—	4	2	no	—
439	C₈	—	4	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	#535×C₁₃₁	1	1	yes	characteristic
448	C₂²	#536×C₁₃₁	1	1	yes	characteristic
449	C₂²	#537×C₁₃₁	1	1	yes	characteristic
450	C₂²	C₂×#135×C₁₃₁	1	1	yes	characteristic
451	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
452	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
453	C₂²	#575×C₁₃₁	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	1	no	—
463	C₄	—	8	2	no	—
464	C₄	—	8	1	no	—
465	C₄	#562×C₁₃₁	1	2	yes	—
466	C₄	#563×C₁₃₁	1	2	yes	—
467	C₂	—	16	2	no	—
468	C₂	#2820×C₁₃₁	1	1	yes	characteristic
469	C₂	#3211×C₁₃₁	1	1	yes	characteristic
470	C₂	#3217×C₁₃₁	1	1	yes	characteristic
471	C₂	#3228×C₁₃₁	1	1	yes	characteristic
472	C₂	#3235×C₁₃₁	1	1	yes	characteristic
473	C₂	#3247×C₁₃₁	1	1	yes	characteristic
474	C₂	#3251×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#127×C₁₃₁	C₂²
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
1. #2864×C₁₃₁	C₂	semidirect
3. #2092×C₁₃₁	C₂	semidirect
4. #2073×C₁₃₁	C₂	semidirect
5. #2067×C₁₃₁	C₂	semidirect
6. #2065×C₁₃₁	C₂	semidirect
7. #2058×C₁₃₁	C₂	semidirect
8. #2057×C₁₃₁	C₂	semidirect
11. #1831×C₁₃₁	C₂	semidirect
237. #32823	C₁₃₁	direct (N × H)
238. C₁₃₁	#32823	direct (N × H)
239. #2864	C₂×C₁₃₁	semidirect
241. #2092	C₂×C₁₃₁	semidirect
242. #2073	C₂×C₁₃₁	semidirect
243. #2067	C₂×C₁₃₁	semidirect
244. #2065	C₂×C₁₃₁	semidirect
245. #2058	C₂×C₁₃₁	semidirect
246. #2057	C₂×C₁₃₁	semidirect
249. #1831	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2864×C₁₃₁	2
#2858×C₁₃₁	2
#2092×C₁₃₁	2
#2073×C₁₃₁	2
#2067×C₁₃₁	2
#2065×C₁₃₁	2
#2058×C₁₃₁	2
#2057×C₁₃₁	2
#2041×C₁₃₁	2
#1831×C₁₃₁	2
#32823	131

Subgroups — C131×#32823 #45718707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#32823 #45718707