Subgroups — C₁₃₁×#34228 #45720112

Order 33536.

2726 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2368×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2364×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2358×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	#2357×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2353×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2343×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2339×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2333×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2332×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2318×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	C₄×#123×C₁₃₁	C₂	1	4	yes	maximal, complemented
13	C₂×#381×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#2275×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	#525×C₁₃₁	C₄	1	16	yes	complemented
19	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
33	#391×C₁₃₁	C₂²	1	4	yes	complemented
34	#390×C₁₃₁	C₂²	1	4	yes	—
35	#388×C₁₃₁	C₂²	1	4	yes	—
36	#388×C₁₃₁	C₂²	1	4	yes	—
37	#388×C₁₃₁	C₂²	1	4	yes	complemented
38	#388×C₁₃₁	C₂²	1	4	yes	complemented
39	#387×C₁₃₁	C₂²	1	4	yes	complemented
40	#387×C₁₃₁	C₂²	1	4	yes	complemented
41	#387×C₁₃₁	C₂²	1	4	yes	complemented
42	#387×C₁₃₁	C₂²	1	4	yes	complemented
43	#386×C₁₃₁	C₂²	1	4	yes	—
44	#386×C₁₃₁	C₂²	1	4	yes	—
45	#386×C₁₃₁	C₂²	1	4	yes	—
46	#386×C₁₃₁	C₂²	1	4	yes	complemented
47	#385×C₁₃₁	C₂²	1	4	yes	—
48	#385×C₁₃₁	C₂²	1	4	yes	—
49	#383×C₁₃₁	C₂²	1	2	yes	complemented
50	#382×C₁₃₁	C₂²	1	2	yes	complemented
51	#381×C₁₃₁	C₂²	1	2	yes	—
52	#381×C₁₃₁	C₂²	1	2	yes	—
53	#381×C₁₃₁	C₂²	1	2	yes	—
54	#381×C₁₃₁	C₂²	1	1	yes	characteristic
55	#381×C₁₃₁	C₂²	1	1	yes	characteristic
56	#381×C₁₃₁	C₂²	1	2	yes	complemented
57	#380×C₁₃₁	C₂²	1	2	yes	complemented
58	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
59	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
60	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
67	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
68	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
69	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
71	#376×C₁₃₁	C₂²	1	2	yes	complemented
72	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
73	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
74	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
75	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
76	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₂×#41×C₁₃₁	—	4	4	no	—
78	C₂×#41×C₁₃₁	C₂×C₄	1	8	yes	complemented
79	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃₁	—	4	4	no	—
85	C₂³×C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
86	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
87	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
96	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
97	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
98	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
99	#121×C₁₃₁	C₂×C₄	1	8	yes	complemented
100	#121×C₁₃₁	C₂×C₄	1	8	yes	complemented
101	#120×C₁₃₁	C₂×C₄	1	16	yes	complemented
102	C₄×D₄×C₁₃₁	—	2	16	no	—
103	C₄×D₄×C₁₃₁	—	4	8	no	—
104	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
105	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
106	#117×C₁₃₁	C₂×C₄	1	8	yes	complemented
107	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
115	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
116	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃₁	—	4	4	no	—
131	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
133	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
138	#95×C₁₃₁	C₂³	1	4	yes	—
139	#95×C₁₃₁	C₂³	1	4	yes	—
140	#95×C₁₃₁	C₂³	1	4	yes	—
141	#95×C₁₃₁	C₂³	1	4	yes	—
142	#95×C₁₃₁	C₂³	1	2	yes	—
143	#95×C₁₃₁	C₂³	1	4	yes	—
144	#95×C₁₃₁	C₂³	1	4	yes	—
145	#95×C₁₃₁	C₂³	1	4	yes	—
146	#95×C₁₃₁	C₂³	1	4	yes	—
147	#95×C₁₃₁	C₂³	1	2	yes	—
148	#95×C₁₃₁	C₂³	1	2	yes	—
149	#95×C₁₃₁	C₂³	1	2	yes	—
150	#95×C₁₃₁	C₂³	1	2	yes	—
151	#95×C₁₃₁	C₂³	1	2	yes	—
152	#95×C₁₃₁	C₂³	1	4	yes	—
153	C₂⁴×C₁₃₁	—	2	4	no	—
154	C₂⁴×C₁₃₁	—	2	4	no	—
155	C₂⁴×C₁₃₁	—	4	2	no	—
156	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
157	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
158	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
159	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
161	#41×C₁₃₁	—	4	16	no	—
162	C₂×Q₈×C₁₃₁	—	4	2	no	—
163	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
164	C₂×D₄×C₁₃₁	—	2	8	no	—
165	C₂×D₄×C₁₃₁	—	2	8	no	—
166	C₂×D₄×C₁₃₁	—	4	2	no	—
167	C₂×D₄×C₁₃₁	—	4	2	no	—
168	C₂×D₄×C₁₃₁	—	4	2	no	—
169	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₁₃₁	—	2	4	no	—
174	C₂²×C₄×C₁₃₁	—	2	4	no	—
175	C₂²×C₄×C₁₃₁	—	2	8	no	—
176	C₂²×C₄×C₁₃₁	—	2	8	no	—
177	C₂²×C₄×C₁₃₁	—	2	8	no	—
178	C₂²×C₄×C₁₃₁	—	2	8	no	—
179	C₂²×C₄×C₁₃₁	—	4	16	no	—
180	C₂²×C₄×C₁₃₁	—	4	2	no	—
181	C₂²×C₄×C₁₃₁	—	4	2	no	—
182	C₂²×C₄×C₁₃₁	—	4	2	no	—
183	C₂²×C₄×C₁₃₁	—	4	2	no	—
184	C₂²×C₄×C₁₃₁	—	4	4	no	—
185	C₂²×C₄×C₁₃₁	—	4	4	no	—
186	C₂²×C₄×C₁₃₁	—	4	4	no	—
187	C₂²×C₄×C₁₃₁	—	4	4	no	—
188	C₂²×C₄×C₁₃₁	—	4	4	no	—
189	C₂²×C₄×C₁₃₁	—	4	4	no	—
190	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
195	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
208	C₄⋊C₄×C₁₃₁	—	2	8	no	—
209	C₄⋊C₄×C₁₃₁	—	4	4	no	—
210	C₄⋊C₄×C₁₃₁	—	4	4	no	—
211	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
212	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
213	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
214	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
215	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
216	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
217	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
218	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
219	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
220	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
221	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
222	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
223	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
226	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₁₃₁	#41	1	8	yes	complemented
229	C₄²×C₁₃₁	—	2	8	no	—
230	C₄²×C₁₃₁	—	4	2	no	—
231	C₄²×C₁₃₁	—	4	4	no	—
232	C₄²×C₁₃₁	—	4	2	no	—
233	C₄²×C₁₃₁	—	4	4	no	—
234	C₄²×C₁₃₁	—	4	4	no	—
235	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	—
236	C₂³×C₁₃₁	—	2	2	no	—
237	C₂³×C₁₃₁	—	2	2	no	—
238	C₂³×C₁₃₁	—	2	2	no	—
239	C₂³×C₁₃₁	—	2	2	no	—
240	C₂³×C₁₃₁	—	2	8	no	—
241	C₂³×C₁₃₁	—	2	8	no	—
242	C₂³×C₁₃₁	—	2	2	no	—
243	C₂³×C₁₃₁	—	2	4	no	—
244	C₂³×C₁₃₁	—	2	2	no	—
245	C₂³×C₁₃₁	—	2	4	no	—
246	C₂³×C₁₃₁	—	2	2	no	—
247	C₂³×C₁₃₁	—	2	2	no	—
248	C₂³×C₁₃₁	—	2	2	no	—
249	C₂³×C₁₃₁	—	4	4	no	—
250	C₂³×C₁₃₁	—	4	16	no	—
251	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
252	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
253	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
254	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
255	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
256	C₂³×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
257	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
258	Q₈×C₁₃₁	—	4	4	no	—
259	D₄×C₁₃₁	—	2	16	no	—
260	D₄×C₁₃₁	—	2	16	no	—
261	D₄×C₁₃₁	—	4	8	no	—
262	D₄×C₁₃₁	—	4	4	no	—
263	C₂×C₄×C₁₃₁	—	2	8	no	—
264	C₂×C₄×C₁₃₁	—	2	8	no	—
265	C₂×C₄×C₁₃₁	—	2	4	no	—
266	C₂×C₄×C₁₃₁	—	2	4	no	—
267	C₂×C₄×C₁₃₁	—	2	2	no	—
268	C₂×C₄×C₁₃₁	—	2	2	no	—
269	C₂×C₄×C₁₃₁	—	2	4	no	—
270	C₂×C₄×C₁₃₁	—	2	2	no	—
271	C₂×C₄×C₁₃₁	—	2	2	no	—
272	C₂×C₄×C₁₃₁	—	2	2	no	—
273	C₂×C₄×C₁₃₁	—	2	4	no	—
274	C₂×C₄×C₁₃₁	—	2	2	no	—
275	C₂×C₄×C₁₃₁	—	2	4	no	—
276	C₂×C₄×C₁₃₁	—	2	4	no	—
277	C₂×C₄×C₁₃₁	—	2	4	no	—
278	C₂×C₄×C₁₃₁	—	2	4	no	—
279	C₂×C₄×C₁₃₁	—	2	4	no	—
280	C₂×C₄×C₁₃₁	—	2	4	no	—
281	C₂×C₄×C₁₃₁	—	2	4	no	—
282	C₂×C₄×C₁₃₁	—	2	4	no	—
283	C₂×C₄×C₁₃₁	—	2	4	no	—
284	C₂×C₄×C₁₃₁	—	4	4	no	—
285	C₂×C₄×C₁₃₁	—	4	4	no	—
286	C₂×C₄×C₁₃₁	—	4	4	no	—
287	C₂×C₄×C₁₃₁	—	4	4	no	—
288	C₂×C₄×C₁₃₁	—	4	8	no	—
289	C₂×C₄×C₁₃₁	—	4	16	no	—
290	C₂×C₄×C₁₃₁	—	8	8	no	—
291	C₂×C₄×C₁₃₁	—	8	8	no	—
292	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
298	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₁₃₁	C₂×#41	1	8	yes	—
300	C₂²×C₁₃₁	—	2	2	no	—
301	C₂²×C₁₃₁	—	2	2	no	—
302	C₂²×C₁₃₁	—	2	2	no	—
303	C₂²×C₁₃₁	—	2	2	no	—
304	C₂²×C₁₃₁	—	2	8	no	—
305	C₂²×C₁₃₁	—	2	8	no	—
306	C₂²×C₁₃₁	—	2	4	no	—
307	C₂²×C₁₃₁	—	2	2	no	—
308	C₂²×C₁₃₁	—	2	2	no	—
309	C₂²×C₁₃₁	—	2	4	no	—
310	C₂²×C₁₃₁	—	2	2	no	—
311	C₂²×C₁₃₁	—	2	4	no	—
312	C₂²×C₁₃₁	—	4	16	no	—
313	C₂²×C₁₃₁	—	4	4	no	—
314	C₂²×C₁₃₁	—	4	4	no	—
315	C₂²×C₁₃₁	—	4	4	no	—
316	C₂²×C₁₃₁	C₄×#41	1	4	yes	—
317	C₂²×C₁₃₁	#518	1	4	yes	—
318	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
319	C₂²×C₁₃₁	C₂²×#41	1	2	yes	—
320	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
321	C₂²×C₁₃₁	#585	1	2	yes	—
322	C₄×C₁₃₁	—	2	4	no	—
323	C₄×C₁₃₁	—	2	2	no	—
324	C₄×C₁₃₁	—	2	2	no	—
325	C₄×C₁₃₁	—	2	2	no	—
326	C₄×C₁₃₁	—	2	2	no	—
327	C₄×C₁₃₁	—	2	4	no	—
328	C₄×C₁₃₁	—	2	4	no	—
329	C₄×C₁₃₁	—	2	8	no	—
330	C₄×C₁₃₁	—	4	4	no	—
331	C₄×C₁₃₁	—	4	4	no	—
332	C₄×C₁₃₁	—	4	4	no	—
333	C₂×C₁₃₁	—	2	4	no	—
334	C₂×C₁₃₁	—	2	4	no	—
335	C₂×C₁₃₁	—	4	4	no	—
336	C₂×C₁₃₁	—	4	2	no	—
337	C₂×C₁₃₁	C₂×C₄×#41	1	1	yes	characteristic
338	C₂×C₁₃₁	C₂×#518	1	1	yes	characteristic
339	C₂×C₁₃₁	#3428	1	1	yes	characteristic
340	C₂×C₁₃₁	#3513	1	4	yes	—
341	#34228	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₁₃₁	#34228	1	1	yes	characteristic, direct product factor, Sylow
343	C₂×#525	C₂×C₁₃₁	1	1	yes	characteristic
344	#2368	C₂×C₁₃₁	1	2	yes	complemented
345	#2364	C₂×C₁₃₁	1	2	yes	complemented
346	#2358	C₂×C₁₃₁	1	4	yes	complemented
347	#2357	C₂×C₁₃₁	1	2	yes	complemented
348	#2353	C₂×C₁₃₁	1	2	yes	complemented
349	#2343	C₂×C₁₃₁	1	2	yes	complemented
350	#2339	C₂×C₁₃₁	1	2	yes	complemented
351	#2333	C₂×C₁₃₁	1	2	yes	complemented
352	#2332	C₂×C₁₃₁	1	2	yes	complemented
353	#2318	C₂×C₁₃₁	1	2	yes	complemented
354	C₄×#123	C₂×C₁₃₁	1	4	yes	complemented
355	C₂×#381	C₂×C₁₃₁	1	1	yes	characteristic, complemented
356	#2275	C₂×C₁₃₁	1	2	yes	complemented
357	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
358	C₂²×#41	C₂²×C₁₃₁	1	1	yes	characteristic
359	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
360	#525	C₄×C₁₃₁	1	16	yes	complemented
361	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
362	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
363	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
364	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
365	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
366	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
367	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
368	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
369	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
370	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
371	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
372	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
373	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
374	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
375	#391	C₂²×C₁₃₁	1	4	yes	complemented
376	#390	C₂²×C₁₃₁	1	4	yes	—
377	#388	C₂²×C₁₃₁	1	4	yes	—
378	#388	C₂²×C₁₃₁	1	4	yes	—
379	#388	C₂²×C₁₃₁	1	4	yes	complemented
380	#388	C₂²×C₁₃₁	1	4	yes	complemented
381	#387	C₂²×C₁₃₁	1	4	yes	complemented
382	#387	C₂²×C₁₃₁	1	4	yes	complemented
383	#387	C₂²×C₁₃₁	1	4	yes	complemented
384	#387	C₂²×C₁₃₁	1	4	yes	complemented
385	#386	C₂²×C₁₃₁	1	4	yes	—
386	#386	C₂²×C₁₃₁	1	4	yes	—
387	#386	C₂²×C₁₃₁	1	4	yes	—
388	#386	C₂²×C₁₃₁	1	4	yes	complemented
389	#385	C₂²×C₁₃₁	1	4	yes	—
390	#385	C₂²×C₁₃₁	1	4	yes	—
391	#383	C₂²×C₁₃₁	1	2	yes	complemented
392	#382	C₂²×C₁₃₁	1	2	yes	complemented
393	#381	C₂²×C₁₃₁	1	2	yes	—
394	#381	C₂²×C₁₃₁	1	2	yes	—
395	#381	C₂²×C₁₃₁	1	1	yes	characteristic
396	#381	C₂²×C₁₃₁	1	1	yes	characteristic
397	#381	C₂²×C₁₃₁	1	2	yes	—
398	#381	C₂²×C₁₃₁	1	2	yes	complemented
399	#380	C₂²×C₁₃₁	1	2	yes	complemented
400	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
401	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
402	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
403	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
404	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
405	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
406	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
407	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
408	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
411	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
412	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
413	#376	C₂²×C₁₃₁	1	2	yes	complemented
414	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
415	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
416	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
417	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
418	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
419	C₂×#41	—	4	4	no	—
420	C₂×#41	C₂×C₄×C₁₃₁	1	8	yes	complemented
421	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
422	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
423	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
424	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
425	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
426	C₂³×C₄	—	4	4	no	—
427	C₂³×C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
428	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
429	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
432	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
433	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
436	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
438	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
439	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
440	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
441	#121	C₂×C₄×C₁₃₁	1	8	yes	complemented
442	#121	C₂×C₄×C₁₃₁	1	8	yes	complemented
443	#120	C₂×C₄×C₁₃₁	1	16	yes	complemented
444	C₄×D₄	—	2	16	no	—
445	C₄×D₄	—	4	8	no	—
446	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
447	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
448	#117	C₂×C₄×C₁₃₁	1	8	yes	complemented
449	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
456	C₂×C₂²⋊C₄	—	2	8	no	—
457	C₂×C₂²⋊C₄	—	4	4	no	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
472	C₂×C₄²	—	4	4	no	—
473	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
474	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
475	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
476	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
477	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
478	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
479	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
480	#95	C₂³×C₁₃₁	1	2	yes	—
481	#95	C₂³×C₁₃₁	1	2	yes	—
482	#95	C₂³×C₁₃₁	1	2	yes	—
483	#95	C₂³×C₁₃₁	1	4	yes	—
484	#95	C₂³×C₁₃₁	1	2	yes	—
485	#95	C₂³×C₁₃₁	1	2	yes	—
486	#95	C₂³×C₁₃₁	1	4	yes	—
487	#95	C₂³×C₁₃₁	1	2	yes	—
488	#95	C₂³×C₁₃₁	1	4	yes	—
489	#95	C₂³×C₁₃₁	1	4	yes	—
490	#95	C₂³×C₁₃₁	1	4	yes	—
491	#95	C₂³×C₁₃₁	1	4	yes	—
492	#95	C₂³×C₁₃₁	1	4	yes	—
493	#95	C₂³×C₁₃₁	1	4	yes	—
494	#95	C₂³×C₁₃₁	1	4	yes	—
495	C₂⁴	—	2	4	no	—
496	C₂⁴	—	2	4	no	—
497	C₂⁴	—	4	2	no	—
498	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
499	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
500	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
501	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
502	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
503	#41	—	4	16	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
506	C₂×D₄	—	2	8	no	—
507	C₂×D₄	—	2	8	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
512	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
513	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
514	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	8	no	—
518	C₂²×C₄	—	2	8	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	4	16	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	4	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	—	4	4	no	—
529	C₂²×C₄	—	4	4	no	—
530	C₂²×C₄	—	4	4	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
533	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
534	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
535	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
536	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
537	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
538	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
540	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
550	C₄⋊C₄	—	2	8	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
555	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
556	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	8	no	—
560	C₂²⋊C₄	—	2	8	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	4	no	—
564	C₂²⋊C₄	—	4	4	no	—
565	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
569	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
570	C₂²⋊C₄	#41×C₁₃₁	1	8	yes	complemented
571	C₄²	—	2	8	no	—
572	C₄²	—	4	2	no	—
573	C₄²	—	4	4	no	—
574	C₄²	—	4	2	no	—
575	C₄²	—	4	4	no	—
576	C₄²	—	4	4	no	—
577	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	8	no	—
583	C₂³	—	2	8	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	4	4	no	—
592	C₂³	—	4	16	no	—
593	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
594	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
595	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
596	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
597	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
598	C₂³	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
599	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
600	Q₈	—	4	4	no	—
601	D₄	—	2	16	no	—
602	D₄	—	2	16	no	—
603	D₄	—	4	4	no	—
604	D₄	—	4	8	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	8	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	8	no	—
631	C₂×C₄	—	4	16	no	—
632	C₂×C₄	—	8	8	no	—
633	C₂×C₄	—	8	8	no	—
634	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
635	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
636	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
637	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
638	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
639	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
640	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
641	C₂×C₄	C₂×#41×C₁₃₁	1	8	yes	—
642	C₂²	—	2	8	no	—
643	C₂²	—	2	8	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	4	no	—
654	C₂²	—	4	16	no	—
655	C₂²	—	4	4	no	—
656	C₂²	—	4	4	no	—
657	C₂²	—	4	4	no	—
658	C₂²	C₄×#41×C₁₃₁	1	4	yes	—
659	C₂²	#518×C₁₃₁	1	4	yes	—
660	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
661	C₂²	C₂²×#41×C₁₃₁	1	2	yes	—
662	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
663	C₂²	#585×C₁₃₁	1	2	yes	—
664	C₄	—	2	8	no	—
665	C₄	—	2	4	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	4	no	—
671	C₄	—	2	4	no	—
672	C₄	—	4	4	no	—
673	C₄	—	4	4	no	—
674	C₄	—	4	4	no	—
675	C₂	—	2	4	no	—
676	C₂	—	2	4	no	—
677	C₂	—	4	2	no	—
678	C₂	—	4	4	no	—
679	C₂	C₂×C₄×#41×C₁₃₁	1	1	yes	characteristic
680	C₂	C₂×#518×C₁₃₁	1	1	yes	characteristic
681	C₂	#3428×C₁₃₁	1	1	yes	characteristic
682	C₂	#3513×C₁₃₁	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂×#525×C₁₃₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2368×C₁₃₁	C₂	semidirect
3. #2364×C₁₃₁	C₂	semidirect
4. #2358×C₁₃₁	C₂	semidirect
5. #2357×C₁₃₁	C₂	semidirect
6. #2353×C₁₃₁	C₂	semidirect
7. #2343×C₁₃₁	C₂	semidirect
8. #2339×C₁₃₁	C₂	semidirect
9. #2333×C₁₃₁	C₂	semidirect
10. #2332×C₁₃₁	C₂	semidirect
11. #2318×C₁₃₁	C₂	semidirect
12. C₄×#123×C₁₃₁	C₂	semidirect
13. C₂×#381×C₁₃₁	C₂	semidirect
14. #2275×C₁₃₁	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
18. #525×C₁₃₁	C₄	semidirect
33. #391×C₁₃₁	C₂²	semidirect
37. #388×C₁₃₁	C₂²	semidirect
38. #388×C₁₃₁	C₂²	semidirect
39. #387×C₁₃₁	C₂²	semidirect
40. #387×C₁₃₁	C₂²	semidirect
41. #387×C₁₃₁	C₂²	semidirect
42. #387×C₁₃₁	C₂²	semidirect
46. #386×C₁₃₁	C₂²	semidirect
49. #383×C₁₃₁	C₂²	semidirect
50. #382×C₁₃₁	C₂²	semidirect
56. #381×C₁₃₁	C₂²	semidirect
57. #380×C₁₃₁	C₂²	semidirect
58. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
59. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
60. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
68. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
69. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
71. #376×C₁₃₁	C₂²	semidirect
75. C₂×#95×C₁₃₁	C₂²	semidirect
78. C₂×#41×C₁₃₁	C₂×C₄	semidirect
85. C₂³×C₄×C₁₃₁	C₂×C₄	semidirect
96. #123×C₁₃₁	C₂×C₄	semidirect
97. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
98. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
99. #121×C₁₃₁	C₂×C₄	semidirect
100. #121×C₁₃₁	C₂×C₄	semidirect
101. #120×C₁₃₁	C₂×C₄	semidirect
104. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
105. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
106. #117×C₁₃₁	C₂×C₄	semidirect
228. C₂²⋊C₄×C₁₃₁	#41	semidirect
341. #34228	C₁₃₁	direct (N × H)
342. C₁₃₁	#34228	direct (N × H)
344. #2368	C₂×C₁₃₁	semidirect
345. #2364	C₂×C₁₃₁	semidirect
346. #2358	C₂×C₁₃₁	semidirect
347. #2357	C₂×C₁₃₁	semidirect
348. #2353	C₂×C₁₃₁	semidirect
349. #2343	C₂×C₁₃₁	semidirect
350. #2339	C₂×C₁₃₁	semidirect
351. #2333	C₂×C₁₃₁	semidirect
352. #2332	C₂×C₁₃₁	semidirect
353. #2318	C₂×C₁₃₁	semidirect
354. C₄×#123	C₂×C₁₃₁	semidirect
355. C₂×#381	C₂×C₁₃₁	semidirect
356. #2275	C₂×C₁₃₁	semidirect
357. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
360. #525	C₄×C₁₃₁	semidirect
375. #391	C₂²×C₁₃₁	semidirect
379. #388	C₂²×C₁₃₁	semidirect
380. #388	C₂²×C₁₃₁	semidirect
381. #387	C₂²×C₁₃₁	semidirect
382. #387	C₂²×C₁₃₁	semidirect
383. #387	C₂²×C₁₃₁	semidirect
384. #387	C₂²×C₁₃₁	semidirect
388. #386	C₂²×C₁₃₁	semidirect
391. #383	C₂²×C₁₃₁	semidirect
392. #382	C₂²×C₁₃₁	semidirect
398. #381	C₂²×C₁₃₁	semidirect
399. #380	C₂²×C₁₃₁	semidirect
400. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
401. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
402. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
410. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
411. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
412. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
413. #376	C₂²×C₁₃₁	semidirect
417. C₂×#95	C₂²×C₁₃₁	semidirect
420. C₂×#41	C₂×C₄×C₁₃₁	semidirect
427. C₂³×C₄	C₂×C₄×C₁₃₁	semidirect
438. #123	C₂×C₄×C₁₃₁	semidirect
439. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
440. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
441. #121	C₂×C₄×C₁₃₁	semidirect
442. #121	C₂×C₄×C₁₃₁	semidirect
443. #120	C₂×C₄×C₁₃₁	semidirect
446. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
447. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
448. #117	C₂×C₄×C₁₃₁	semidirect
570. C₂²⋊C₄	#41×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₃₁	2
#2368×C₁₃₁	2
#2364×C₁₃₁	2
#2358×C₁₃₁	2
#2357×C₁₃₁	2
#2353×C₁₃₁	2
#2343×C₁₃₁	2
#2339×C₁₃₁	2
#2333×C₁₃₁	2
#2332×C₁₃₁	2
#2318×C₁₃₁	2
C₄×#123×C₁₃₁	2
C₂×#381×C₁₃₁	2
#2275×C₁₃₁	2
C₂×C₄×C₂²⋊C₄×C₁₃₁	2
#34228	131

Subgroups — C131×#34228 #45720112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34228 #45720112