Subgroups — C₁₃₁×#34224 #45720108

Order 33536.

2330 conjugacy classes of subgroups.

The subgroup lattice has 686 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	#2373×C₁₃₁	C₂	1	4	yes	maximal, complemented
3	#2370×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2367×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2357×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2356×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2351×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2349×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2347×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2343×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2322×C₁₃₁	C₂	1	4	yes	maximal, complemented
12	#2318×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	C₄×C₂²⋊Q₈×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	C₄×#121×C₁₃₁	C₂	1	2	yes	maximal
15	#2283×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#2275×C₁₃₁	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	#529×C₁₃₁	C₄	1	16	yes	complemented
19	C₂×#126×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
35	#391×C₁₃₁	C₂²	1	2	yes	—
36	#390×C₁₃₁	C₂²	1	2	yes	—
37	#389×C₁₃₁	C₂²	1	2	yes	—
38	#389×C₁₃₁	C₂²	1	2	yes	—
39	#389×C₁₃₁	C₂²	1	4	yes	—
40	#389×C₁₃₁	C₂²	1	4	yes	—
41	#388×C₁₃₁	C₂²	1	4	yes	—
42	#388×C₁₃₁	C₂²	1	4	yes	—
43	#388×C₁₃₁	C₂²	1	4	yes	—
44	#388×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	#387×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	#383×C₁₃₁	C₂²	1	2	yes	—
54	#383×C₁₃₁	C₂²	1	2	yes	—
55	#382×C₁₃₁	C₂²	1	1	yes	characteristic
56	#382×C₁₃₁	C₂²	1	1	yes	characteristic
57	#382×C₁₃₁	C₂²	1	2	yes	—
58	#381×C₁₃₁	C₂²	1	2	yes	—
59	#381×C₁₃₁	C₂²	1	2	yes	—
60	#380×C₁₃₁	C₂²	1	2	yes	—
61	#380×C₁₃₁	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
63	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×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	4	yes	—
70	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	—
73	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
76	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
79	#376×C₁₃₁	C₂²	1	2	yes	—
80	#376×C₁₃₁	C₂²	1	2	yes	—
81	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
82	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
83	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
84	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃₁	C₂³	1	2	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	2	yes	—
90	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
94	#126×C₁₃₁	C₂×C₄	1	16	yes	complemented
95	#125×C₁₃₁	C₂×C₄	1	8	yes	complemented
96	#124×C₁₃₁	C₂×C₄	1	8	yes	complemented
97	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
98	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
99	#121×C₁₃₁	C₂×C₄	1	8	yes	—
100	C₄×Q₈×C₁₃₁	—	4	4	no	—
101	C₄×Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
102	C₄×D₄×C₁₃₁	—	2	16	no	—
103	C₄×D₄×C₁₃₁	—	4	4	no	—
104	C₄×D₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
105	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
106	#117×C₁₃₁	C₂×C₄	1	16	yes	complemented
107	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
108	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	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×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	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	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	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×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃₁	—	4	4	no	—
133	C₂×C₄²×C₁₃₁	C₂×C₄	1	8	yes	complemented
134	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
147	#95×C₁₃₁	C₂³	1	4	yes	—
148	#95×C₁₃₁	C₂³	1	2	yes	—
149	#95×C₁₃₁	C₂³	1	2	yes	—
150	#95×C₁₃₁	C₂³	1	4	yes	—
151	#95×C₁₃₁	C₂³	1	4	yes	—
152	#95×C₁₃₁	C₂³	1	4	yes	—
153	#95×C₁₃₁	C₂³	1	4	yes	—
154	#95×C₁₃₁	C₂³	1	2	yes	—
155	#95×C₁₃₁	C₂³	1	4	yes	—
156	#95×C₁₃₁	C₂³	1	4	yes	—
157	#95×C₁₃₁	C₂³	1	4	yes	—
158	#95×C₁₃₁	C₂³	1	1	yes	characteristic
159	#95×C₁₃₁	C₂³	1	1	yes	characteristic
160	#95×C₁₃₁	C₂³	1	2	yes	—
161	#95×C₁₃₁	C₂³	1	2	yes	—
162	#95×C₁₃₁	C₂³	1	1	yes	characteristic
163	#95×C₁₃₁	C₂³	1	1	yes	characteristic
164	#95×C₁₃₁	C₂³	1	2	yes	—
165	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
166	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
167	C₂×Q₈×C₁₃₁	—	2	2	no	—
168	C₂×Q₈×C₁₃₁	—	2	2	no	—
169	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₁₃₁	—	2	8	no	—
171	C₂×D₄×C₁₃₁	—	2	2	no	—
172	C₂×D₄×C₁₃₁	—	2	2	no	—
173	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
174	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₃₁	—	2	4	no	—
176	C₂²×C₄×C₁₃₁	—	2	2	no	—
177	C₂²×C₄×C₁₃₁	—	2	2	no	—
178	C₂²×C₄×C₁₃₁	—	2	4	no	—
179	C₂²×C₄×C₁₃₁	—	2	8	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	2	no	—
186	C₂²×C₄×C₁₃₁	—	4	4	no	—
187	C₂²×C₄×C₁₃₁	—	4	4	no	—
188	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
189	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
190	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
192	C₂²×C₄×C₁₃₁	#41	1	8	yes	—
193	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
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	1	yes	characteristic
208	C₄⋊C₄×C₁₃₁	—	2	4	no	—
209	C₄⋊C₄×C₁₃₁	—	2	4	no	—
210	C₄⋊C₄×C₁₃₁	—	2	4	no	—
211	C₄⋊C₄×C₁₃₁	—	2	4	no	—
212	C₄⋊C₄×C₁₃₁	—	2	8	no	—
213	C₄⋊C₄×C₁₃₁	—	2	4	no	—
214	C₄⋊C₄×C₁₃₁	—	2	4	no	—
215	C₄⋊C₄×C₁₃₁	—	4	4	no	—
216	C₄⋊C₄×C₁₃₁	—	4	4	no	—
217	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
218	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
219	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
221	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
222	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
223	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
224	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
225	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
226	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
227	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
229	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
230	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
231	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
232	C₄²×C₁₃₁	—	2	8	no	—
233	C₄²×C₁₃₁	—	2	4	no	—
234	C₄²×C₁₃₁	—	2	4	no	—
235	C₄²×C₁₃₁	—	4	2	no	—
236	C₄²×C₁₃₁	—	4	2	no	—
237	C₄²×C₁₃₁	—	4	4	no	—
238	C₄²×C₁₃₁	—	4	4	no	—
239	C₄²×C₁₃₁	—	4	4	no	—
240	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
241	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
242	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
243	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
244	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	—
245	C₂³×C₁₃₁	—	2	1	no	—
246	C₂³×C₁₃₁	—	2	1	no	—
247	C₂³×C₁₃₁	—	2	2	no	—
248	C₂³×C₁₃₁	—	2	4	no	—
249	C₂³×C₁₃₁	—	2	2	no	—
250	C₂³×C₁₃₁	—	2	2	no	—
251	C₂³×C₁₃₁	—	2	4	no	—
252	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
253	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
254	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
255	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
256	Q₈×C₁₃₁	—	2	8	no	—
257	D₄×C₁₃₁	—	2	16	no	—
258	D₄×C₁₃₁	—	2	8	no	—
259	C₂×C₄×C₁₃₁	—	2	8	no	—
260	C₂×C₄×C₁₃₁	—	2	4	no	—
261	C₂×C₄×C₁₃₁	—	2	2	no	—
262	C₂×C₄×C₁₃₁	—	2	2	no	—
263	C₂×C₄×C₁₃₁	—	2	2	no	—
264	C₂×C₄×C₁₃₁	—	2	2	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	2	no	—
269	C₂×C₄×C₁₃₁	—	2	2	no	—
270	C₂×C₄×C₁₃₁	—	2	2	no	—
271	C₂×C₄×C₁₃₁	—	2	4	no	—
272	C₂×C₄×C₁₃₁	—	2	2	no	—
273	C₂×C₄×C₁₃₁	—	2	2	no	—
274	C₂×C₄×C₁₃₁	—	2	8	no	—
275	C₂×C₄×C₁₃₁	—	2	4	no	—
276	C₂×C₄×C₁₃₁	—	2	4	no	—
277	C₂×C₄×C₁₃₁	—	2	2	no	—
278	C₂×C₄×C₁₃₁	—	2	2	no	—
279	C₂×C₄×C₁₃₁	—	2	2	no	—
280	C₂×C₄×C₁₃₁	—	2	2	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	—	2	4	no	—
285	C₂×C₄×C₁₃₁	—	2	2	no	—
286	C₂×C₄×C₁₃₁	—	2	2	no	—
287	C₂×C₄×C₁₃₁	—	4	4	no	—
288	C₂×C₄×C₁₃₁	—	4	8	no	—
289	C₂×C₄×C₁₃₁	—	4	8	no	—
290	C₂×C₄×C₁₃₁	—	4	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	2	yes	—
294	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	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	4	yes	—
299	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
300	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
302	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
303	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
304	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
305	C₂²×C₁₃₁	—	2	2	no	—
306	C₂²×C₁₃₁	—	2	2	no	—
307	C₂²×C₁₃₁	—	2	4	no	—
308	C₂²×C₁₃₁	—	2	4	no	—
309	C₂²×C₁₃₁	—	2	4	no	—
310	C₂²×C₁₃₁	—	2	4	no	—
311	C₂²×C₁₃₁	—	2	4	no	—
312	C₂²×C₁₃₁	—	4	4	no	—
313	C₂²×C₁₃₁	—	4	4	no	—
314	C₂²×C₁₃₁	C₄×#41	1	4	yes	—
315	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
316	C₂²×C₁₃₁	C₂²×#41	1	2	yes	—
317	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
319	C₂²×C₁₃₁	#585	1	2	yes	—
320	C₄×C₁₃₁	—	2	2	no	—
321	C₄×C₁₃₁	—	2	2	no	—
322	C₄×C₁₃₁	—	2	4	no	—
323	C₄×C₁₃₁	—	2	2	no	—
324	C₄×C₁₃₁	—	2	4	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	4	no	—
330	C₄×C₁₃₁	—	4	2	no	—
331	C₄×C₁₃₁	—	4	2	no	—
332	C₄×C₁₃₁	—	4	4	no	—
333	C₄×C₁₃₁	—	4	4	no	—
334	C₄×C₁₃₁	#520	1	4	yes	—
335	C₂×C₁₃₁	—	2	4	no	—
336	C₂×C₁₃₁	—	4	4	no	—
337	C₂×C₁₃₁	C₂×C₄×#41	1	1	yes	characteristic
338	C₂×C₁₃₁	C₂×#520	1	1	yes	characteristic
339	C₂×C₁₃₁	#3428	1	1	yes	characteristic
340	C₂×C₁₃₁	#3505	1	2	yes	—
341	C₂×C₁₃₁	#3507	1	2	yes	—
342	#34224	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₁₃₁	#34224	1	1	yes	characteristic, direct product factor, Sylow
344	C₂×#529	C₂×C₁₃₁	1	1	yes	characteristic
345	#2373	C₂×C₁₃₁	1	4	yes	complemented
346	#2370	C₂×C₁₃₁	1	2	yes	complemented
347	#2367	C₂×C₁₃₁	1	2	yes	complemented
348	#2357	C₂×C₁₃₁	1	1	yes	characteristic, complemented
349	#2356	C₂×C₁₃₁	1	1	yes	characteristic, complemented
350	#2351	C₂×C₁₃₁	1	1	yes	characteristic, complemented
351	#2349	C₂×C₁₃₁	1	1	yes	characteristic, complemented
352	#2347	C₂×C₁₃₁	1	2	yes	complemented
353	#2343	C₂×C₁₃₁	1	2	yes	complemented
354	#2322	C₂×C₁₃₁	1	4	yes	complemented
355	#2318	C₂×C₁₃₁	1	2	yes	complemented
356	C₄×C₂²⋊Q₈	C₂×C₁₃₁	1	2	yes	complemented
357	C₄×#121	C₂×C₁₃₁	1	2	yes	—
358	#2283	C₂×C₁₃₁	1	1	yes	characteristic, complemented
359	#2275	C₂×C₁₃₁	1	2	yes	complemented
360	C₂×C₄×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
361	#529	C₄×C₁₃₁	1	16	yes	complemented
362	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
363	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
364	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
365	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
366	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
367	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
368	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
369	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
370	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
371	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
372	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
374	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
375	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
376	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
377	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
378	#391	C₂²×C₁₃₁	1	2	yes	—
379	#390	C₂²×C₁₃₁	1	2	yes	—
380	#389	C₂²×C₁₃₁	1	4	yes	—
381	#389	C₂²×C₁₃₁	1	4	yes	—
382	#389	C₂²×C₁₃₁	1	2	yes	—
383	#389	C₂²×C₁₃₁	1	2	yes	—
384	#388	C₂²×C₁₃₁	1	4	yes	—
385	#388	C₂²×C₁₃₁	1	4	yes	—
386	#388	C₂²×C₁₃₁	1	4	yes	—
387	#388	C₂²×C₁₃₁	1	4	yes	—
388	#387	C₂²×C₁₃₁	1	4	yes	—
389	#387	C₂²×C₁₃₁	1	4	yes	—
390	#387	C₂²×C₁₃₁	1	4	yes	—
391	#387	C₂²×C₁₃₁	1	4	yes	—
392	#386	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	#383	C₂²×C₁₃₁	1	2	yes	—
397	#383	C₂²×C₁₃₁	1	2	yes	—
398	#382	C₂²×C₁₃₁	1	2	yes	—
399	#382	C₂²×C₁₃₁	1	1	yes	characteristic
400	#382	C₂²×C₁₃₁	1	1	yes	characteristic
401	#381	C₂²×C₁₃₁	1	2	yes	—
402	#381	C₂²×C₁₃₁	1	2	yes	—
403	#380	C₂²×C₁₃₁	1	2	yes	—
404	#380	C₂²×C₁₃₁	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
406	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
407	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	—
409	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
413	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
414	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
415	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	—
416	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
417	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
418	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
422	#376	C₂²×C₁₃₁	1	2	yes	—
423	#376	C₂²×C₁₃₁	1	2	yes	—
424	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
425	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
426	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
429	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
433	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
434	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
435	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
437	#126	C₂×C₄×C₁₃₁	1	16	yes	complemented
438	#125	C₂×C₄×C₁₃₁	1	8	yes	complemented
439	#124	C₂×C₄×C₁₃₁	1	8	yes	complemented
440	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
441	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
442	#121	C₂×C₄×C₁₃₁	1	8	yes	—
443	C₄×Q₈	—	4	4	no	—
444	C₄×Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
445	C₄×D₄	—	2	16	no	—
446	C₄×D₄	—	4	4	no	—
447	C₄×D₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
448	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
449	#117	C₂×C₄×C₁₃₁	1	16	yes	complemented
450	C₂×C₄⋊C₄	—	2	8	no	—
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	2	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	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
475	C₂×C₄²	—	4	4	no	—
476	C₂×C₄²	C₂×C₄×C₁₃₁	1	8	yes	complemented
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	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
481	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
482	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
483	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
484	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
485	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
487	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
490	#95	C₂³×C₁₃₁	1	1	yes	characteristic
491	#95	C₂³×C₁₃₁	1	1	yes	characteristic
492	#95	C₂³×C₁₃₁	1	2	yes	—
493	#95	C₂³×C₁₃₁	1	2	yes	—
494	#95	C₂³×C₁₃₁	1	4	yes	—
495	#95	C₂³×C₁₃₁	1	1	yes	characteristic
496	#95	C₂³×C₁₃₁	1	1	yes	characteristic
497	#95	C₂³×C₁₃₁	1	2	yes	—
498	#95	C₂³×C₁₃₁	1	2	yes	—
499	#95	C₂³×C₁₃₁	1	4	yes	—
500	#95	C₂³×C₁₃₁	1	4	yes	—
501	#95	C₂³×C₁₃₁	1	2	yes	—
502	#95	C₂³×C₁₃₁	1	2	yes	—
503	#95	C₂³×C₁₃₁	1	4	yes	—
504	#95	C₂³×C₁₃₁	1	4	yes	—
505	#95	C₂³×C₁₃₁	1	4	yes	—
506	#95	C₂³×C₁₃₁	1	4	yes	—
507	#95	C₂³×C₁₃₁	1	4	yes	—
508	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
509	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
517	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	8	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	4	no	—
530	C₂²×C₄	—	4	4	no	—
531	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
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	8	yes	—
535	C₂²×C₄	#41×C₁₃₁	1	8	yes	—
536	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
538	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	8	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	—	4	4	no	—
560	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
561	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
562	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
563	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
564	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
565	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
566	C₂²⋊C₄	—	2	8	no	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	4	4	no	—
569	C₂²⋊C₄	—	4	4	no	—
570	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
571	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
572	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
575	C₄²	—	2	8	no	—
576	C₄²	—	2	4	no	—
577	C₄²	—	2	4	no	—
578	C₄²	—	4	2	no	—
579	C₄²	—	4	2	no	—
580	C₄²	—	4	4	no	—
581	C₄²	—	4	4	no	—
582	C₄²	—	4	4	no	—
583	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
584	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
585	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
586	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
587	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	4	no	—
595	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
596	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
597	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
598	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
599	Q₈	—	2	8	no	—
600	D₄	—	2	16	no	—
601	D₄	—	2	8	no	—
602	C₂×C₄	—	2	8	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	4	8	no	—
632	C₂×C₄	—	4	8	no	—
633	C₂×C₄	—	4	8	no	—
634	C₂×C₄	—	8	8	no	—
635	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
636	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	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	2	yes	—
640	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
641	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
642	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
643	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
644	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
645	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
646	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
647	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
648	C₂²	—	2	4	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	4	no	—
654	C₂²	—	2	4	no	—
655	C₂²	—	4	4	no	—
656	C₂²	—	4	4	no	—
657	C₂²	C₄×#41×C₁₃₁	1	4	yes	—
658	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
659	C₂²	C₂²×#41×C₁₃₁	1	2	yes	—
660	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
661	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
662	C₂²	#585×C₁₃₁	1	2	yes	—
663	C₄	—	2	4	no	—
664	C₄	—	2	4	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	4	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	4	no	—
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	4	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	4	no	—
676	C₄	—	4	4	no	—
677	C₄	#520×C₁₃₁	1	4	yes	—
678	C₂	—	2	4	no	—
679	C₂	—	4	4	no	—
680	C₂	C₂×C₄×#41×C₁₃₁	1	1	yes	characteristic
681	C₂	C₂×#520×C₁₃₁	1	1	yes	characteristic
682	C₂	#3428×C₁₃₁	1	1	yes	characteristic
683	C₂	#3505×C₁₃₁	1	2	yes	—
684	C₂	#3507×C₁₃₁	1	2	yes	—

	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. #2373×C₁₃₁	C₂	semidirect
3. #2370×C₁₃₁	C₂	semidirect
4. #2367×C₁₃₁	C₂	semidirect
5. #2357×C₁₃₁	C₂	semidirect
6. #2356×C₁₃₁	C₂	semidirect
7. #2351×C₁₃₁	C₂	semidirect
8. #2349×C₁₃₁	C₂	semidirect
9. #2347×C₁₃₁	C₂	semidirect
10. #2343×C₁₃₁	C₂	semidirect
11. #2322×C₁₃₁	C₂	semidirect
12. #2318×C₁₃₁	C₂	semidirect
13. C₄×C₂²⋊Q₈×C₁₃₁	C₂	semidirect
15. #2283×C₁₃₁	C₂	semidirect
16. #2275×C₁₃₁	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₁₃₁	C₂	semidirect
18. #529×C₁₃₁	C₄	semidirect
94. #126×C₁₃₁	C₂×C₄	semidirect
95. #125×C₁₃₁	C₂×C₄	semidirect
96. #124×C₁₃₁	C₂×C₄	semidirect
97. #123×C₁₃₁	C₂×C₄	semidirect
98. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
101. C₄×Q₈×C₁₃₁	C₂×C₄	semidirect
104. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
105. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
106. #117×C₁₃₁	C₂×C₄	semidirect
133. C₂×C₄²×C₁₃₁	C₂×C₄	semidirect
342. #34224	C₁₃₁	direct (N × H)
343. C₁₃₁	#34224	direct (N × H)
345. #2373	C₂×C₁₃₁	semidirect
346. #2370	C₂×C₁₃₁	semidirect
347. #2367	C₂×C₁₃₁	semidirect
348. #2357	C₂×C₁₃₁	semidirect
349. #2356	C₂×C₁₃₁	semidirect
350. #2351	C₂×C₁₃₁	semidirect
351. #2349	C₂×C₁₃₁	semidirect
352. #2347	C₂×C₁₃₁	semidirect
353. #2343	C₂×C₁₃₁	semidirect
354. #2322	C₂×C₁₃₁	semidirect
355. #2318	C₂×C₁₃₁	semidirect
356. C₄×C₂²⋊Q₈	C₂×C₁₃₁	semidirect
358. #2283	C₂×C₁₃₁	semidirect
359. #2275	C₂×C₁₃₁	semidirect
360. C₂×C₄×C₄⋊C₄	C₂×C₁₃₁	semidirect
361. #529	C₄×C₁₃₁	semidirect
437. #126	C₂×C₄×C₁₃₁	semidirect
438. #125	C₂×C₄×C₁₃₁	semidirect
439. #124	C₂×C₄×C₁₃₁	semidirect
440. #123	C₂×C₄×C₁₃₁	semidirect
441. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
444. C₄×Q₈	C₂×C₄×C₁₃₁	semidirect
447. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
448. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
449. #117	C₂×C₄×C₁₃₁	semidirect
476. 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
#2373×C₁₃₁	2
#2370×C₁₃₁	2
#2367×C₁₃₁	2
#2357×C₁₃₁	2
#2356×C₁₃₁	2
#2351×C₁₃₁	2
#2349×C₁₃₁	2
#2347×C₁₃₁	2
#2343×C₁₃₁	2
#2322×C₁₃₁	2
#2318×C₁₃₁	2
C₄×C₂²⋊Q₈×C₁₃₁	2
C₄×#121×C₁₃₁	2
#2283×C₁₃₁	2
#2275×C₁₃₁	2
C₂×C₄×C₄⋊C₄×C₁₃₁	2
#34224	131

Subgroups — C131×#34224 #45720108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34224 #45720108