Subgroups — C₁₃₁×#25034 #45710918

Order 33536.

962 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#466×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2422×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2071×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2033×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1970×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1942×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1862×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1845×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1808×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#123×C₁₃₁	—	2	2	no	—
15	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
17	#466×C₁₃₁	—	2	4	no	—
18	C₄×D₈×C₁₃₁	—	2	4	no	—
19	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
29	#397×C₁₃₁	—	2	2	no	—
30	#394×C₁₃₁	—	2	2	no	—
31	#390×C₁₃₁	C₂²	1	2	yes	—
32	#389×C₁₃₁	C₂²	1	2	yes	—
33	#385×C₁₃₁	—	2	2	no	—
34	#384×C₁₃₁	C₂²	1	2	yes	—
35	#380×C₁₃₁	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
37	#340×C₁₃₁	C₂²	1	2	yes	—
38	#340×C₁₃₁	C₂²	1	2	yes	—
39	#336×C₁₃₁	C₂²	1	1	yes	characteristic
40	#336×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃₁	—	2	2	no	—
42	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃₁	—	2	2	no	—
44	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₁₃₁	—	2	2	no	—
46	C₂×D₈×C₁₃₁	—	2	2	no	—
47	C₂×D₈×C₁₃₁	D₄	1	4	yes	—
48	C₂²×C₈×C₁₃₁	—	2	2	no	—
49	C₂²×C₈×C₁₃₁	—	2	2	no	—
50	C₂²×C₈×C₁₃₁	—	2	2	no	—
51	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
55	#123×C₁₃₁	—	4	8	no	—
56	#121×C₁₃₁	—	2	4	no	—
57	#121×C₁₃₁	—	4	2	no	—
58	C₄×D₄×C₁₃₁	—	2	4	no	—
59	C₄×D₄×C₁₃₁	—	4	2	no	—
60	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
75	#107×C₁₃₁	—	2	2	no	—
76	#107×C₁₃₁	—	2	2	no	—
77	#107×C₁₃₁	—	2	2	no	—
78	#107×C₁₃₁	—	4	2	no	—
79	#102×C₁₃₁	—	2	4	no	—
80	#102×C₁₃₁	—	2	4	no	—
81	#102×C₁₃₁	—	2	4	no	—
82	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
83	C₄×C₈×C₁₃₁	—	2	2	no	—
84	C₄×C₈×C₁₃₁	—	2	2	no	—
85	#95×C₁₃₁	—	2	2	no	—
86	#95×C₁₃₁	—	2	2	no	—
87	#95×C₁₃₁	D₄	1	1	yes	characteristic
88	#95×C₁₃₁	D₄	1	1	yes	characteristic
89	C₂⁴×C₁₃₁	—	2	2	no	—
90	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂×D₄×C₁₃₁	—	2	2	no	—
92	C₂×D₄×C₁₃₁	—	2	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	—	4	4	no	—
97	C₂×D₄×C₁₃₁	—	4	4	no	—
98	C₂×D₄×C₁₃₁	—	8	2	no	—
99	C₂×D₄×C₁₃₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₁₃₁	—	2	1	no	—
101	C₂²×C₄×C₁₃₁	—	2	1	no	—
102	C₂²×C₄×C₁₃₁	—	2	1	no	—
103	C₂²×C₄×C₁₃₁	—	2	1	no	—
104	C₂²×C₄×C₁₃₁	—	2	1	no	—
105	C₂²×C₄×C₁₃₁	—	2	1	no	—
106	C₂²×C₄×C₁₃₁	—	2	2	no	—
107	C₂²×C₄×C₁₃₁	—	2	2	no	—
108	C₂²×C₄×C₁₃₁	—	2	2	no	—
109	C₂²×C₄×C₁₃₁	—	4	4	no	—
110	C₂²×C₄×C₁₃₁	—	4	4	no	—
111	C₂²×C₄×C₁₃₁	—	8	2	no	—
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	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
118	D₈×C₁₃₁	—	2	8	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	—	2	1	no	—
123	C₂×C₈×C₁₃₁	—	2	1	no	—
124	C₂×C₈×C₁₃₁	—	2	1	no	—
125	C₂×C₈×C₁₃₁	—	2	1	no	—
126	C₂×C₈×C₁₃₁	—	2	1	no	—
127	C₂×C₈×C₁₃₁	—	4	4	no	—
128	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃₁	#41	1	2	yes	—
130	C₂×C₈×C₁₃₁	#41	1	2	yes	—
131	C₂×C₈×C₁₃₁	#41	1	2	yes	—
132	C₄⋊C₄×C₁₃₁	—	2	2	no	—
133	C₄⋊C₄×C₁₃₁	—	2	2	no	—
134	C₄⋊C₄×C₁₃₁	—	2	2	no	—
135	C₄⋊C₄×C₁₃₁	—	2	2	no	—
136	C₄⋊C₄×C₁₃₁	—	2	2	no	—
137	C₄⋊C₄×C₁₃₁	—	2	2	no	—
138	C₄⋊C₄×C₁₃₁	—	4	4	no	—
139	C₄⋊C₄×C₁₃₁	—	4	4	no	—
140	C₄⋊C₄×C₁₃₁	—	8	2	no	—
141	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
142	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
143	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
144	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
145	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
146	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
147	C₂²⋊C₄×C₁₃₁	D₈	1	4	yes	complemented
148	C₄²×C₁₃₁	—	2	1	no	—
149	C₄²×C₁₃₁	—	2	1	no	—
150	C₄²×C₁₃₁	—	2	1	no	—
151	C₄²×C₁₃₁	—	2	1	no	—
152	C₂³×C₁₃₁	—	2	1	no	—
153	C₂³×C₁₃₁	—	2	1	no	—
154	C₂³×C₁₃₁	—	2	1	no	—
155	C₂³×C₁₃₁	—	2	1	no	—
156	C₂³×C₁₃₁	—	2	1	no	—
157	C₂³×C₁₃₁	—	2	1	no	—
158	C₂³×C₁₃₁	—	2	4	no	—
159	C₂³×C₁₃₁	—	4	2	no	—
160	C₂³×C₁₃₁	—	4	2	no	—
161	C₂³×C₁₃₁	—	4	2	no	—
162	C₂³×C₁₃₁	—	4	2	no	—
163	C₂³×C₁₃₁	—	4	2	no	—
164	C₂³×C₁₃₁	—	4	2	no	—
165	C₂³×C₁₃₁	C₂×D₈	1	2	yes	—
166	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
167	D₄×C₁₃₁	—	2	4	no	—
168	D₄×C₁₃₁	—	2	4	no	—
169	D₄×C₁₃₁	—	4	2	no	—
170	D₄×C₁₃₁	—	4	2	no	—
171	D₄×C₁₃₁	—	8	8	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	—	2	1	no	—
179	C₂×C₄×C₁₃₁	—	2	1	no	—
180	C₂×C₄×C₁₃₁	—	2	1	no	—
181	C₂×C₄×C₁₃₁	—	2	1	no	—
182	C₂×C₄×C₁₃₁	—	2	1	no	—
183	C₂×C₄×C₁₃₁	—	2	1	no	—
184	C₂×C₄×C₁₃₁	—	4	1	no	—
185	C₂×C₄×C₁₃₁	—	4	1	no	—
186	C₂×C₄×C₁₃₁	—	4	1	no	—
187	C₂×C₄×C₁₃₁	—	4	1	no	—
188	C₂×C₄×C₁₃₁	—	4	2	no	—
189	C₂×C₄×C₁₃₁	—	4	2	no	—
190	C₂×C₄×C₁₃₁	—	4	2	no	—
191	C₂×C₄×C₁₃₁	—	4	2	no	—
192	C₂×C₄×C₁₃₁	—	4	2	no	—
193	C₂×C₄×C₁₃₁	—	4	2	no	—
194	C₂×C₄×C₁₃₁	—	4	2	no	—
195	C₂×C₄×C₁₃₁	—	4	2	no	—
196	C₂×C₄×C₁₃₁	—	4	2	no	—
197	C₂×C₄×C₁₃₁	—	8	8	no	—
198	C₂×C₄×C₁₃₁	C₂×D₈	1	2	yes	—
199	C₂×C₄×C₁₃₁	C₂×D₈	1	2	yes	—
200	C₂×C₄×C₁₃₁	#135	1	2	yes	—
201	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
207	C₈×C₁₃₁	—	2	2	no	—
208	C₈×C₁₃₁	—	4	1	no	—
209	C₈×C₁₃₁	—	4	1	no	—
210	C₈×C₁₃₁	#123	1	4	yes	complemented
211	C₂²×C₁₃₁	—	2	2	no	—
212	C₂²×C₁₃₁	—	2	2	no	—
213	C₂²×C₁₃₁	—	2	2	no	—
214	C₂²×C₁₃₁	—	4	1	no	—
215	C₂²×C₁₃₁	—	4	1	no	—
216	C₂²×C₁₃₁	—	4	1	no	—
217	C₂²×C₁₃₁	—	4	1	no	—
218	C₂²×C₁₃₁	—	4	4	no	—
219	C₂²×C₁₃₁	—	4	4	no	—
220	C₂²×C₁₃₁	—	4	4	no	—
221	C₂²×C₁₃₁	—	8	2	no	—
222	C₂²×C₁₃₁	—	8	2	no	—
223	C₂²×C₁₃₁	—	8	2	no	—
224	C₂²×C₁₃₁	—	8	2	no	—
225	C₂²×C₁₃₁	#532	1	1	yes	characteristic
226	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
227	C₂²×C₁₃₁	#547	1	1	yes	characteristic
228	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
229	C₂²×C₁₃₁	C₂×#135	1	1	yes	characteristic
230	C₂²×C₁₃₁	#576	1	1	yes	characteristic
231	C₂²×C₁₃₁	#578	1	1	yes	characteristic
232	C₄×C₁₃₁	—	2	2	no	—
233	C₄×C₁₃₁	—	2	2	no	—
234	C₄×C₁₃₁	—	2	2	no	—
235	C₄×C₁₃₁	—	4	1	no	—
236	C₄×C₁₃₁	—	4	1	no	—
237	C₄×C₁₃₁	—	8	2	no	—
238	C₄×C₁₃₁	—	8	2	no	—
239	C₄×C₁₃₁	—	8	2	no	—
240	C₄×C₁₃₁	C₂×#123	1	1	yes	characteristic
241	C₄×C₁₃₁	#542	1	1	yes	characteristic
242	C₄×C₁₃₁	#547	1	1	yes	characteristic
243	C₄×C₁₃₁	#553	1	1	yes	characteristic
244	C₂×C₁₃₁	—	4	2	no	—
245	C₂×C₁₃₁	—	8	4	no	—
246	C₂×C₁₃₁	#2422	1	1	yes	characteristic
247	C₂×C₁₃₁	#3169	1	1	yes	characteristic
248	C₂×C₁₃₁	#3175	1	1	yes	characteristic
249	C₂×C₁₃₁	D₄×D₈	1	1	yes	characteristic
250	C₂×C₁₃₁	#3283	1	1	yes	characteristic
251	C₂×C₁₃₁	#3334	1	1	yes	characteristic
252	C₂×C₁₃₁	#3339	1	1	yes	characteristic
253	#25034	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₁₃₁	#25034	1	1	yes	characteristic, direct product factor, Sylow
255	C₂×#466	C₂×C₁₃₁	1	1	yes	characteristic
256	C₂×C₄×D₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
257	#2422	C₂×C₁₃₁	1	2	yes	complemented
258	#2071	C₂×C₁₃₁	1	2	yes	complemented
259	#2033	C₂×C₁₃₁	1	2	yes	complemented
260	#1970	C₂×C₁₃₁	1	1	yes	characteristic, complemented
261	#1942	C₂×C₁₃₁	1	1	yes	characteristic, complemented
262	#1862	C₂×C₁₃₁	1	2	yes	complemented
263	#1845	C₂×C₁₃₁	1	1	yes	characteristic, complemented
264	#1808	C₂×C₁₃₁	1	1	yes	characteristic, complemented
265	C₈×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
266	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
267	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
268	C₂×#123	—	2	2	no	—
269	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
270	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
271	#466	—	2	4	no	—
272	C₄×D₈	—	2	4	no	—
273	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
274	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
275	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
276	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
277	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
278	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
279	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
280	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
283	#397	—	2	2	no	—
284	#394	—	2	2	no	—
285	#390	C₂²×C₁₃₁	1	2	yes	—
286	#389	C₂²×C₁₃₁	1	2	yes	—
287	#385	—	2	2	no	—
288	#384	C₂²×C₁₃₁	1	2	yes	—
289	#380	C₂²×C₁₃₁	1	2	yes	—
290	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
291	#340	C₂²×C₁₃₁	1	2	yes	—
292	#340	C₂²×C₁₃₁	1	2	yes	—
293	#336	C₂²×C₁₃₁	1	1	yes	characteristic
294	#336	C₂²×C₁₃₁	1	1	yes	characteristic
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
299	C₂×D₈	—	2	2	no	—
300	C₂×D₈	—	2	2	no	—
301	C₂×D₈	D₄×C₁₃₁	1	4	yes	—
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
309	#123	—	4	8	no	—
310	#121	—	2	4	no	—
311	#121	—	4	2	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	4	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
329	#107	—	2	2	no	—
330	#107	—	2	2	no	—
331	#107	—	2	2	no	—
332	#107	—	4	2	no	—
333	#102	—	2	4	no	—
334	#102	—	2	4	no	—
335	#102	—	2	4	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₄×C₈	—	2	2	no	—
338	C₄×C₈	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	#95	D₄×C₁₃₁	1	1	yes	characteristic
342	#95	D₄×C₁₃₁	1	1	yes	characteristic
343	C₂⁴	—	2	2	no	—
344	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	8	2	no	—
353	C₂×D₄	C₂×D₄×C₁₃₁	1	4	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	8	2	no	—
366	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
372	D₈	—	2	8	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	4	4	no	—
382	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
383	C₂×C₈	#41×C₁₃₁	1	2	yes	—
384	C₂×C₈	#41×C₁₃₁	1	2	yes	—
385	C₂×C₈	#41×C₁₃₁	1	2	yes	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	4	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	8	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	D₈×C₁₃₁	1	4	yes	complemented
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	C₂×D₈×C₁₃₁	1	2	yes	—
420	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
421	D₄	—	2	4	no	—
422	D₄	—	2	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	8	8	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	8	no	—
452	C₂×C₄	C₂×D₈×C₁₃₁	1	2	yes	—
453	C₂×C₄	C₂×D₈×C₁₃₁	1	2	yes	—
454	C₂×C₄	#135×C₁₃₁	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
457	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
459	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
460	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	4	1	no	—
463	C₈	—	4	1	no	—
464	C₈	#123×C₁₃₁	1	4	yes	complemented
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	#532×C₁₃₁	1	1	yes	characteristic
480	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
481	C₂²	#547×C₁₃₁	1	1	yes	characteristic
482	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
483	C₂²	C₂×#135×C₁₃₁	1	1	yes	characteristic
484	C₂²	#576×C₁₃₁	1	1	yes	characteristic
485	C₂²	#578×C₁₃₁	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	8	2	no	—
492	C₄	—	8	2	no	—
493	C₄	—	8	2	no	—
494	C₄	C₂×#123×C₁₃₁	1	1	yes	characteristic
495	C₄	#542×C₁₃₁	1	1	yes	characteristic
496	C₄	#547×C₁₃₁	1	1	yes	characteristic
497	C₄	#553×C₁₃₁	1	1	yes	characteristic
498	C₂	—	4	2	no	—
499	C₂	—	8	4	no	—
500	C₂	#2422×C₁₃₁	1	1	yes	characteristic
501	C₂	#3169×C₁₃₁	1	1	yes	characteristic
502	C₂	#3175×C₁₃₁	1	1	yes	characteristic
503	C₂	D₄×D₈×C₁₃₁	1	1	yes	characteristic
504	C₂	#3283×C₁₃₁	1	1	yes	characteristic
505	C₂	#3334×C₁₃₁	1	1	yes	characteristic
506	C₂	#3339×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#466×C₁₃₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄×C₂²⋊C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₁₃₁	C₂	semidirect
3. #2422×C₁₃₁	C₂	semidirect
4. #2071×C₁₃₁	C₂	semidirect
5. #2033×C₁₃₁	C₂	semidirect
6. #1970×C₁₃₁	C₂	semidirect
7. #1942×C₁₃₁	C₂	semidirect
8. #1862×C₁₃₁	C₂	semidirect
9. #1845×C₁₃₁	C₂	semidirect
10. #1808×C₁₃₁	C₂	semidirect
11. C₈×C₂²⋊C₄×C₁₃₁	C₂	semidirect
147. C₂²⋊C₄×C₁₃₁	D₈	semidirect
210. C₈×C₁₃₁	#123	semidirect
253. #25034	C₁₃₁	direct (N × H)
254. C₁₃₁	#25034	direct (N × H)
256. C₂×C₄×D₈	C₂×C₁₃₁	semidirect
257. #2422	C₂×C₁₃₁	semidirect
258. #2071	C₂×C₁₃₁	semidirect
259. #2033	C₂×C₁₃₁	semidirect
260. #1970	C₂×C₁₃₁	semidirect
261. #1942	C₂×C₁₃₁	semidirect
262. #1862	C₂×C₁₃₁	semidirect
263. #1845	C₂×C₁₃₁	semidirect
264. #1808	C₂×C₁₃₁	semidirect
265. C₈×C₂²⋊C₄	C₂×C₁₃₁	semidirect
401. C₂²⋊C₄	D₈×C₁₃₁	semidirect
464. C₈	#123×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#466×C₁₃₁	2
C₂×C₄×D₈×C₁₃₁	2
#2422×C₁₃₁	2
#2071×C₁₃₁	2
#2033×C₁₃₁	2
#1970×C₁₃₁	2
#1942×C₁₃₁	2
#1862×C₁₃₁	2
#1845×C₁₃₁	2
#1808×C₁₃₁	2
C₈×C₂²⋊C₄×C₁₃₁	2
#25034	131

Subgroups — C131×#25034 #45710918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#25034 #45710918