Subgroups — C₁₃₁×#34382 #45720266

Order 33536.

2218 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×#529×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2382×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2379×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2359×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	#2355×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2352×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2352×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	D₄×C₄⋊C₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2334×C₁₃₁	C₂	1	4	yes	maximal, complemented
10	#2329×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2325×C₁₃₁	C₂	1	2	yes	maximal
12	#2317×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2314×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	#2285×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#382×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#529×C₁₃₁	C₄	1	16	yes	complemented
17	C₂×#126×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
34	#391×C₁₃₁	C₂²	1	4	yes	—
35	#389×C₁₃₁	C₂²	1	4	yes	—
36	#389×C₁₃₁	C₂²	1	4	yes	—
37	#389×C₁₃₁	C₂²	1	4	yes	—
38	#388×C₁₃₁	C₂²	1	4	yes	—
39	#388×C₁₃₁	C₂²	1	4	yes	—
40	#388×C₁₃₁	C₂²	1	4	yes	—
41	#388×C₁₃₁	C₂²	1	4	yes	—
42	#387×C₁₃₁	C₂²	1	4	yes	—
43	#387×C₁₃₁	C₂²	1	4	yes	—
44	#387×C₁₃₁	C₂²	1	4	yes	—
45	#387×C₁₃₁	C₂²	1	4	yes	—
46	#387×C₁₃₁	C₂²	1	4	yes	—
47	#387×C₁₃₁	C₂²	1	4	yes	—
48	#386×C₁₃₁	C₂²	1	4	yes	—
49	#386×C₁₃₁	C₂²	1	4	yes	—
50	#385×C₁₃₁	C₂²	1	4	yes	—
51	#385×C₁₃₁	C₂²	1	4	yes	—
52	#385×C₁₃₁	C₂²	1	4	yes	—
53	#385×C₁₃₁	C₂²	1	4	yes	—
54	#384×C₁₃₁	C₂²	1	1	yes	characteristic
55	#384×C₁₃₁	C₂²	1	1	yes	characteristic
56	#384×C₁₃₁	C₂²	1	2	yes	—
57	#382×C₁₃₁	C₂²	1	2	yes	—
58	#382×C₁₃₁	C₂²	1	2	yes	—
59	#382×C₁₃₁	C₂²	1	2	yes	—
60	#382×C₁₃₁	C₂²	1	2	yes	—
61	#382×C₁₃₁	C₂²	1	2	yes	—
62	#382×C₁₃₁	C₂²	1	2	yes	—
63	#380×C₁₃₁	C₂²	1	2	yes	—
64	#380×C₁₃₁	C₂²	1	2	yes	—
65	#380×C₁₃₁	C₂²	1	2	yes	—
66	#380×C₁₃₁	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	—
72	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
73	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
74	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
75	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
76	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
86	#126×C₁₃₁	C₂×C₄	1	16	yes	complemented
87	#125×C₁₃₁	C₂×C₄	1	8	yes	complemented
88	#124×C₁₃₁	C₂×C₄	1	8	yes	complemented
89	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
90	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
91	#121×C₁₃₁	C₂×C₄	1	8	yes	—
92	C₄×Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
93	C₄×D₄×C₁₃₁	—	4	8	no	—
94	C₄×D₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
95	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
96	#117×C₁₃₁	—	4	4	no	—
97	#117×C₁₃₁	—	4	4	no	—
98	#117×C₁₃₁	C₂×C₄	1	16	yes	complemented
99	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
100	C₂×C₄⋊C₄×C₁₃₁	—	4	4	no	—
101	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
102	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	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	4	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	C₂×C₄	1	8	yes	complemented
131	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
133	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
134	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
140	#95×C₁₃₁	C₂³	1	4	yes	—
141	#95×C₁₃₁	C₂³	1	4	yes	—
142	#95×C₁₃₁	C₂³	1	4	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	4	yes	—
148	#95×C₁₃₁	C₂³	1	4	yes	—
149	#95×C₁₃₁	C₂³	1	4	yes	—
150	#95×C₁₃₁	C₂³	1	4	yes	—
151	#95×C₁₃₁	C₂³	1	4	yes	—
152	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
153	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
154	C₂×Q₈×C₁₃₁	—	4	1	no	—
155	C₂×Q₈×C₁₃₁	—	4	1	no	—
156	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
157	C₂×D₄×C₁₃₁	—	2	4	no	—
158	C₂×D₄×C₁₃₁	—	2	4	no	—
159	C₂×D₄×C₁₃₁	—	4	1	no	—
160	C₂×D₄×C₁₃₁	—	4	1	no	—
161	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
162	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
163	C₂²×C₄×C₁₃₁	—	2	2	no	—
164	C₂²×C₄×C₁₃₁	—	2	2	no	—
165	C₂²×C₄×C₁₃₁	—	2	2	no	—
166	C₂²×C₄×C₁₃₁	—	2	4	no	—
167	C₂²×C₄×C₁₃₁	—	2	2	no	—
168	C₂²×C₄×C₁₃₁	—	2	4	no	—
169	C₂²×C₄×C₁₃₁	—	2	4	no	—
170	C₂²×C₄×C₁₃₁	—	2	4	no	—
171	C₂²×C₄×C₁₃₁	—	4	1	no	—
172	C₂²×C₄×C₁₃₁	—	4	1	no	—
173	C₂²×C₄×C₁₃₁	—	4	2	no	—
174	C₂²×C₄×C₁₃₁	—	4	4	no	—
175	C₂²×C₄×C₁₃₁	—	4	2	no	—
176	C₂²×C₄×C₁₃₁	—	4	4	no	—
177	C₂²×C₄×C₁₃₁	—	4	2	no	—
178	C₂²×C₄×C₁₃₁	—	4	4	no	—
179	C₂²×C₄×C₁₃₁	—	4	2	no	—
180	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
183	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
197	C₄⋊C₄×C₁₃₁	—	2	4	no	—
198	C₄⋊C₄×C₁₃₁	—	2	4	no	—
199	C₄⋊C₄×C₁₃₁	—	2	4	no	—
200	C₄⋊C₄×C₁₃₁	—	2	4	no	—
201	C₄⋊C₄×C₁₃₁	—	4	4	no	—
202	C₄⋊C₄×C₁₃₁	—	4	2	no	—
203	C₄⋊C₄×C₁₃₁	—	4	2	no	—
204	C₄⋊C₄×C₁₃₁	—	4	2	no	—
205	C₄⋊C₄×C₁₃₁	—	4	2	no	—
206	C₄⋊C₄×C₁₃₁	—	4	4	no	—
207	C₄⋊C₄×C₁₃₁	—	4	2	no	—
208	C₄⋊C₄×C₁₃₁	—	4	2	no	—
209	C₄⋊C₄×C₁₃₁	—	4	4	no	—
210	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
211	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	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	4	yes	—
215	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
216	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
217	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
218	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
219	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
220	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
221	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
223	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
225	C₄²×C₁₃₁	—	4	4	no	—
226	C₄²×C₁₃₁	—	4	4	no	—
227	C₄²×C₁₃₁	—	4	4	no	—
228	C₄²×C₁₃₁	—	4	4	no	—
229	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
230	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
231	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
232	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
233	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	—
234	C₂³×C₁₃₁	—	2	1	no	—
235	C₂³×C₁₃₁	—	2	1	no	—
236	C₂³×C₁₃₁	—	2	1	no	—
237	C₂³×C₁₃₁	—	2	1	no	—
238	C₂³×C₁₃₁	—	2	2	no	—
239	C₂³×C₁₃₁	—	2	2	no	—
240	C₂³×C₁₃₁	—	2	2	no	—
241	C₂³×C₁₃₁	—	2	2	no	—
242	C₂³×C₁₃₁	—	2	2	no	—
243	C₂³×C₁₃₁	—	2	2	no	—
244	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
245	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
246	C₂³×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
247	C₂³×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
248	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
249	Q₈×C₁₃₁	—	4	4	no	—
250	D₄×C₁₃₁	—	2	16	no	—
251	D₄×C₁₃₁	—	4	4	no	—
252	C₂×C₄×C₁₃₁	—	2	8	no	—
253	C₂×C₄×C₁₃₁	—	2	1	no	—
254	C₂×C₄×C₁₃₁	—	2	2	no	—
255	C₂×C₄×C₁₃₁	—	2	2	no	—
256	C₂×C₄×C₁₃₁	—	2	1	no	—
257	C₂×C₄×C₁₃₁	—	2	1	no	—
258	C₂×C₄×C₁₃₁	—	2	2	no	—
259	C₂×C₄×C₁₃₁	—	2	1	no	—
260	C₂×C₄×C₁₃₁	—	2	1	no	—
261	C₂×C₄×C₁₃₁	—	2	1	no	—
262	C₂×C₄×C₁₃₁	—	2	2	no	—
263	C₂×C₄×C₁₃₁	—	2	2	no	—
264	C₂×C₄×C₁₃₁	—	2	1	no	—
265	C₂×C₄×C₁₃₁	—	2	1	no	—
266	C₂×C₄×C₁₃₁	—	2	2	no	—
267	C₂×C₄×C₁₃₁	—	2	1	no	—
268	C₂×C₄×C₁₃₁	—	2	1	no	—
269	C₂×C₄×C₁₃₁	—	2	8	no	—
270	C₂×C₄×C₁₃₁	—	2	16	no	—
271	C₂×C₄×C₁₃₁	—	2	4	no	—
272	C₂×C₄×C₁₃₁	—	2	4	no	—
273	C₂×C₄×C₁₃₁	—	2	4	no	—
274	C₂×C₄×C₁₃₁	—	2	4	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	—	4	4	no	—
284	C₂×C₄×C₁₃₁	—	8	4	no	—
285	C₂×C₄×C₁₃₁	—	8	4	no	—
286	C₂×C₄×C₁₃₁	—	8	8	no	—
287	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	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	H(5,𝔽₂)	1	2	yes	—
297	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
298	C₂²×C₁₃₁	—	2	2	no	—
299	C₂²×C₁₃₁	—	2	2	no	—
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	4	no	—
305	C₂²×C₁₃₁	—	2	4	no	—
306	C₂²×C₁₃₁	—	2	4	no	—
307	C₂²×C₁₃₁	—	4	2	no	—
308	C₂²×C₁₃₁	—	4	2	no	—
309	C₂²×C₁₃₁	—	4	2	no	—
310	C₂²×C₁₃₁	—	4	2	no	—
311	C₂²×C₁₃₁	#520	1	4	yes	—
312	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
313	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂²×C₁₃₁	#585	1	1	yes	characteristic
318	C₂²×C₁₃₁	#585	1	1	yes	characteristic
319	C₄×C₁₃₁	—	2	2	no	—
320	C₄×C₁₃₁	—	2	2	no	—
321	C₄×C₁₃₁	—	2	4	no	—
322	C₄×C₁₃₁	—	2	2	no	—
323	C₄×C₁₃₁	—	2	4	no	—
324	C₄×C₁₃₁	—	2	2	no	—
325	C₄×C₁₃₁	—	2	2	no	—
326	C₄×C₁₃₁	—	2	4	no	—
327	C₄×C₁₃₁	—	4	4	no	—
328	C₄×C₁₃₁	—	4	4	no	—
329	C₄×C₁₃₁	—	4	4	no	—
330	C₄×C₁₃₁	—	4	4	no	—
331	C₄×C₁₃₁	#520	1	4	yes	—
332	C₂×C₁₃₁	—	2	4	no	—
333	C₂×C₁₃₁	—	4	4	no	—
334	C₂×C₁₃₁	C₂×#520	1	1	yes	characteristic
335	C₂×C₁₃₁	C₂×#520	1	1	yes	characteristic
336	C₂×C₁₃₁	#3428	1	1	yes	characteristic
337	C₂×C₁₃₁	#3558	1	1	yes	characteristic
338	C₂×C₁₃₁	#3559	1	1	yes	characteristic
339	C₂×C₁₃₁	#3561	1	1	yes	characteristic
340	C₂×C₁₃₁	#3563	1	1	yes	characteristic
341	#34382	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₁₃₁	#34382	1	1	yes	characteristic, direct product factor, Sylow
343	C₂×#529	C₂×C₁₃₁	1	1	yes	characteristic
344	#2382	C₂×C₁₃₁	1	2	yes	complemented
345	#2379	C₂×C₁₃₁	1	2	yes	complemented
346	#2359	C₂×C₁₃₁	1	4	yes	complemented
347	#2355	C₂×C₁₃₁	1	2	yes	complemented
348	#2352	C₂×C₁₃₁	1	2	yes	complemented
349	#2352	C₂×C₁₃₁	1	2	yes	complemented
350	D₄×C₄⋊C₄	C₂×C₁₃₁	1	2	yes	complemented
351	#2334	C₂×C₁₃₁	1	4	yes	complemented
352	#2329	C₂×C₁₃₁	1	2	yes	complemented
353	#2325	C₂×C₁₃₁	1	2	yes	—
354	#2317	C₂×C₁₃₁	1	2	yes	complemented
355	#2314	C₂×C₁₃₁	1	2	yes	complemented
356	#2285	C₂×C₁₃₁	1	1	yes	characteristic, complemented
357	C₂×#382	C₂×C₁₃₁	1	1	yes	characteristic, complemented
358	#529	C₄×C₁₃₁	1	16	yes	complemented
359	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
360	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
361	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
362	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
364	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
365	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
366	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
367	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
368	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
369	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
370	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
371	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
372	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
373	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
374	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
375	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
376	#391	C₂²×C₁₃₁	1	4	yes	—
377	#389	C₂²×C₁₃₁	1	4	yes	—
378	#389	C₂²×C₁₃₁	1	4	yes	—
379	#389	C₂²×C₁₃₁	1	4	yes	—
380	#388	C₂²×C₁₃₁	1	4	yes	—
381	#388	C₂²×C₁₃₁	1	4	yes	—
382	#388	C₂²×C₁₃₁	1	4	yes	—
383	#388	C₂²×C₁₃₁	1	4	yes	—
384	#387	C₂²×C₁₃₁	1	4	yes	—
385	#387	C₂²×C₁₃₁	1	4	yes	—
386	#387	C₂²×C₁₃₁	1	4	yes	—
387	#387	C₂²×C₁₃₁	1	4	yes	—
388	#387	C₂²×C₁₃₁	1	4	yes	—
389	#387	C₂²×C₁₃₁	1	4	yes	—
390	#386	C₂²×C₁₃₁	1	4	yes	—
391	#386	C₂²×C₁₃₁	1	4	yes	—
392	#385	C₂²×C₁₃₁	1	4	yes	—
393	#385	C₂²×C₁₃₁	1	4	yes	—
394	#385	C₂²×C₁₃₁	1	4	yes	—
395	#385	C₂²×C₁₃₁	1	4	yes	—
396	#384	C₂²×C₁₃₁	1	1	yes	characteristic
397	#384	C₂²×C₁₃₁	1	1	yes	characteristic
398	#384	C₂²×C₁₃₁	1	2	yes	—
399	#382	C₂²×C₁₃₁	1	2	yes	—
400	#382	C₂²×C₁₃₁	1	2	yes	—
401	#382	C₂²×C₁₃₁	1	2	yes	—
402	#382	C₂²×C₁₃₁	1	2	yes	—
403	#382	C₂²×C₁₃₁	1	2	yes	—
404	#382	C₂²×C₁₃₁	1	2	yes	—
405	#380	C₂²×C₁₃₁	1	2	yes	—
406	#380	C₂²×C₁₃₁	1	2	yes	—
407	#380	C₂²×C₁₃₁	1	2	yes	—
408	#380	C₂²×C₁₃₁	1	2	yes	—
409	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
411	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	—
413	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
415	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
416	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
417	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
418	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
419	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
420	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
423	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
425	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
426	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
427	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
428	#126	C₂×C₄×C₁₃₁	1	16	yes	complemented
429	#125	C₂×C₄×C₁₃₁	1	8	yes	complemented
430	#124	C₂×C₄×C₁₃₁	1	8	yes	complemented
431	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
432	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
433	#121	C₂×C₄×C₁₃₁	1	8	yes	—
434	C₄×Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
435	C₄×D₄	—	4	8	no	—
436	C₄×D₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
437	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
438	#117	—	4	4	no	—
439	#117	—	4	4	no	—
440	#117	C₂×C₄×C₁₃₁	1	16	yes	complemented
441	C₂×C₄⋊C₄	—	4	2	no	—
442	C₂×C₄⋊C₄	—	4	4	no	—
443	C₂×C₄⋊C₄	—	4	2	no	—
444	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	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	4	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	C₂×C₄×C₁₃₁	1	8	yes	complemented
473	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
474	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
475	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
476	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
477	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
479	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
482	#95	C₂³×C₁₃₁	1	4	yes	—
483	#95	C₂³×C₁₃₁	1	4	yes	—
484	#95	C₂³×C₁₃₁	1	4	yes	—
485	#95	C₂³×C₁₃₁	1	4	yes	—
486	#95	C₂³×C₁₃₁	1	4	yes	—
487	#95	C₂³×C₁₃₁	1	4	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	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
495	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
496	C₂×Q₈	—	4	1	no	—
497	C₂×Q₈	—	4	1	no	—
498	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	4	1	no	—
502	C₂×D₄	—	4	1	no	—
503	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
504	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	4	1	no	—
514	C₂²×C₄	—	4	1	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
524	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
525	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	4	4	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	4	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
553	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	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	4	yes	—
557	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
567	C₄²	—	4	4	no	—
568	C₄²	—	4	4	no	—
569	C₄²	—	4	4	no	—
570	C₄²	—	4	4	no	—
571	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
572	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
573	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
574	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
575	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
587	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
588	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
589	C₂³	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
590	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
591	Q₈	—	4	4	no	—
592	D₄	—	2	16	no	—
593	D₄	—	4	4	no	—
594	C₂×C₄	—	2	8	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	8	no	—
612	C₂×C₄	—	2	16	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	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	—	4	4	no	—
626	C₂×C₄	—	8	4	no	—
627	C₂×C₄	—	8	4	no	—
628	C₂×C₄	—	8	8	no	—
629	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
631	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
632	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
634	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	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	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
639	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	#520×C₁₃₁	1	4	yes	—
654	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
655	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
656	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
657	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
658	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
659	C₂²	#585×C₁₃₁	1	1	yes	characteristic
660	C₂²	#585×C₁₃₁	1	1	yes	characteristic
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	4	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	4	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	4	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	4	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	4	no	—
673	C₄	#520×C₁₃₁	1	4	yes	—
674	C₂	—	2	4	no	—
675	C₂	—	4	4	no	—
676	C₂	C₂×#520×C₁₃₁	1	1	yes	characteristic
677	C₂	C₂×#520×C₁₃₁	1	1	yes	characteristic
678	C₂	#3428×C₁₃₁	1	1	yes	characteristic
679	C₂	#3558×C₁₃₁	1	1	yes	characteristic
680	C₂	#3559×C₁₃₁	1	1	yes	characteristic
681	C₂	#3561×C₁₃₁	1	1	yes	characteristic
682	C₂	#3563×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂×#121×C₁₃₁	C₂²
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. #2382×C₁₃₁	C₂	semidirect
3. #2379×C₁₃₁	C₂	semidirect
4. #2359×C₁₃₁	C₂	semidirect
5. #2355×C₁₃₁	C₂	semidirect
6. #2352×C₁₃₁	C₂	semidirect
7. #2352×C₁₃₁	C₂	semidirect
8. D₄×C₄⋊C₄×C₁₃₁	C₂	semidirect
9. #2334×C₁₃₁	C₂	semidirect
10. #2329×C₁₃₁	C₂	semidirect
12. #2317×C₁₃₁	C₂	semidirect
13. #2314×C₁₃₁	C₂	semidirect
14. #2285×C₁₃₁	C₂	semidirect
15. C₂×#382×C₁₃₁	C₂	semidirect
16. #529×C₁₃₁	C₄	semidirect
86. #126×C₁₃₁	C₂×C₄	semidirect
87. #125×C₁₃₁	C₂×C₄	semidirect
88. #124×C₁₃₁	C₂×C₄	semidirect
89. #123×C₁₃₁	C₂×C₄	semidirect
90. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
92. C₄×Q₈×C₁₃₁	C₂×C₄	semidirect
94. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
95. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
98. #117×C₁₃₁	C₂×C₄	semidirect
130. C₂×C₄²×C₁₃₁	C₂×C₄	semidirect
341. #34382	C₁₃₁	direct (N × H)
342. C₁₃₁	#34382	direct (N × H)
344. #2382	C₂×C₁₃₁	semidirect
345. #2379	C₂×C₁₃₁	semidirect
346. #2359	C₂×C₁₃₁	semidirect
347. #2355	C₂×C₁₃₁	semidirect
348. #2352	C₂×C₁₃₁	semidirect
349. #2352	C₂×C₁₃₁	semidirect
350. D₄×C₄⋊C₄	C₂×C₁₃₁	semidirect
351. #2334	C₂×C₁₃₁	semidirect
352. #2329	C₂×C₁₃₁	semidirect
354. #2317	C₂×C₁₃₁	semidirect
355. #2314	C₂×C₁₃₁	semidirect
356. #2285	C₂×C₁₃₁	semidirect
357. C₂×#382	C₂×C₁₃₁	semidirect
358. #529	C₄×C₁₃₁	semidirect
428. #126	C₂×C₄×C₁₃₁	semidirect
429. #125	C₂×C₄×C₁₃₁	semidirect
430. #124	C₂×C₄×C₁₃₁	semidirect
431. #123	C₂×C₄×C₁₃₁	semidirect
432. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
434. C₄×Q₈	C₂×C₄×C₁₃₁	semidirect
436. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
437. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
440. #117	C₂×C₄×C₁₃₁	semidirect
472. C₂×C₄²	C₂×C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₁₃₁	2
#2382×C₁₃₁	2
#2379×C₁₃₁	2
#2359×C₁₃₁	2
#2355×C₁₃₁	2
#2352×C₁₃₁	2
D₄×C₄⋊C₄×C₁₃₁	2
#2334×C₁₃₁	2
#2329×C₁₃₁	2
#2325×C₁₃₁	2
#2317×C₁₃₁	2
#2314×C₁₃₁	2
#2285×C₁₃₁	2
C₂×#382×C₁₃₁	2
#34382	131

Subgroups — C131×#34382 #45720266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34382 #45720266