Subgroups — C₁₃₁×#35117 #45721001

Order 33536.

1664 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2863×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#2862×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2861×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2860×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2650×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2637×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2592×C₁₃₁	C₂	1	1	yes	maximal, characteristic
8	#2581×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2550×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#2545×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	#2532×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#2529×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2515×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	#2465×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	#2453×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#2452×C₁₃₁	C₂	1	1	yes	maximal, characteristic
17	#2447×C₁₃₁	C₂	1	1	yes	maximal, characteristic
18	#2446×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
19	#2334×C₁₃₁	C₂	1	2	yes	maximal, complemented
20	#2332×C₁₃₁	C₂	1	2	yes	maximal, complemented
21	C₄×#124×C₁₃₁	C₂	1	1	yes	maximal, characteristic
22	#2295×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×#126×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
37	#400×C₁₃₁	C₂²	1	2	yes	—
38	#400×C₁₃₁	C₂²	1	2	yes	—
39	#400×C₁₃₁	C₂²	1	2	yes	—
40	#398×C₁₃₁	C₂²	1	2	yes	—
41	#398×C₁₃₁	C₂²	1	2	yes	—
42	#398×C₁₃₁	C₂²	1	2	yes	—
43	#397×C₁₃₁	C₂²	1	2	yes	—
44	#397×C₁₃₁	C₂²	1	2	yes	—
45	#397×C₁₃₁	C₂²	1	2	yes	—
46	#396×C₁₃₁	C₂²	1	2	yes	—
47	#396×C₁₃₁	C₂²	1	2	yes	—
48	#396×C₁₃₁	C₂²	1	2	yes	—
49	#395×C₁₃₁	C₂²	1	2	yes	—
50	#395×C₁₃₁	C₂²	1	2	yes	—
51	#393×C₁₃₁	C₂²	1	2	yes	—
52	#393×C₁₃₁	C₂²	1	2	yes	—
53	#391×C₁₃₁	C₂²	1	2	yes	—
54	#391×C₁₃₁	C₂²	1	2	yes	—
55	#391×C₁₃₁	C₂²	1	1	yes	characteristic
56	#391×C₁₃₁	C₂²	1	1	yes	characteristic
57	#391×C₁₃₁	C₂²	1	1	yes	characteristic
58	#391×C₁₃₁	C₂²	1	1	yes	characteristic
59	#391×C₁₃₁	C₂²	1	1	yes	characteristic
60	#391×C₁₃₁	C₂²	1	1	yes	characteristic
61	#391×C₁₃₁	C₂²	1	2	yes	—
62	#391×C₁₃₁	C₂²	1	1	yes	characteristic
63	#391×C₁₃₁	C₂²	1	1	yes	characteristic
64	#390×C₁₃₁	C₂²	1	1	yes	characteristic
65	#390×C₁₃₁	C₂²	1	1	yes	characteristic
66	#390×C₁₃₁	C₂²	1	1	yes	characteristic
67	#390×C₁₃₁	C₂²	1	1	yes	characteristic
68	#389×C₁₃₁	C₂²	1	2	yes	—
69	#389×C₁₃₁	C₂²	1	1	yes	characteristic
70	#389×C₁₃₁	C₂²	1	1	yes	characteristic
71	#389×C₁₃₁	C₂²	1	1	yes	characteristic
72	#389×C₁₃₁	C₂²	1	1	yes	characteristic
73	#389×C₁₃₁	C₂²	1	1	yes	characteristic
74	#389×C₁₃₁	C₂²	1	1	yes	characteristic
75	#389×C₁₃₁	C₂²	1	2	yes	—
76	#388×C₁₃₁	C₂²	1	2	yes	—
77	#388×C₁₃₁	C₂²	1	2	yes	—
78	#388×C₁₃₁	C₂²	1	2	yes	—
79	#388×C₁₃₁	C₂²	1	2	yes	—
80	#388×C₁₃₁	C₂²	1	2	yes	—
81	#388×C₁₃₁	C₂²	1	2	yes	—
82	#388×C₁₃₁	C₂²	1	2	yes	—
83	#388×C₁₃₁	C₂²	1	2	yes	—
84	#388×C₁₃₁	C₂²	1	2	yes	—
85	#388×C₁₃₁	C₂²	1	2	yes	—
86	#388×C₁₃₁	C₂²	1	2	yes	—
87	#388×C₁₃₁	C₂²	1	2	yes	—
88	#388×C₁₃₁	C₂²	1	2	yes	—
89	#387×C₁₃₁	C₂²	1	2	yes	—
90	#387×C₁₃₁	C₂²	1	2	yes	—
91	#387×C₁₃₁	C₂²	1	2	yes	—
92	#387×C₁₃₁	C₂²	1	2	yes	—
93	#387×C₁₃₁	C₂²	1	2	yes	—
94	#387×C₁₃₁	C₂²	1	2	yes	—
95	#387×C₁₃₁	C₂²	1	2	yes	—
96	#387×C₁₃₁	C₂²	1	2	yes	—
97	#387×C₁₃₁	C₂²	1	2	yes	—
98	#387×C₁₃₁	C₂²	1	2	yes	—
99	#385×C₁₃₁	C₂²	1	2	yes	—
100	#385×C₁₃₁	C₂²	1	2	yes	—
101	#383×C₁₃₁	C₂²	1	2	yes	—
102	#382×C₁₃₁	C₂²	1	2	yes	—
103	#382×C₁₃₁	C₂²	1	1	yes	characteristic
104	#382×C₁₃₁	C₂²	1	2	yes	—
105	#381×C₁₃₁	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
119	#376×C₁₃₁	C₂²	1	2	yes	—
120	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
121	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₁₃₁	—	4	2	no	—
130	C₄⋊Q₈×C₁₃₁	—	4	2	no	—
131	#126×C₁₃₁	—	2	8	no	—
132	#125×C₁₃₁	—	4	2	no	—
133	#124×C₁₃₁	—	2	4	no	—
134	#124×C₁₃₁	—	4	2	no	—
135	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
136	C₄×Q₈×C₁₃₁	—	2	4	no	—
137	C₄×Q₈×C₁₃₁	—	2	4	no	—
138	C₄×Q₈×C₁₃₁	—	2	4	no	—
139	C₄×Q₈×C₁₃₁	—	2	4	no	—
140	C₄×Q₈×C₁₃₁	—	4	2	no	—
141	C₄×D₄×C₁₃₁	—	4	2	no	—
142	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
204	#95×C₁₃₁	C₂³	1	1	yes	characteristic
205	#95×C₁₃₁	C₂³	1	2	yes	—
206	#95×C₁₃₁	C₂³	1	2	yes	—
207	#95×C₁₃₁	C₂³	1	2	yes	—
208	#95×C₁₃₁	C₂³	1	2	yes	—
209	#95×C₁₃₁	C₂³	1	1	yes	characteristic
210	#95×C₁₃₁	C₂³	1	2	yes	—
211	#95×C₁₃₁	C₂³	1	2	yes	—
212	#95×C₁₃₁	C₂³	1	2	yes	—
213	#95×C₁₃₁	C₂³	1	2	yes	—
214	#95×C₁₃₁	C₂³	1	2	yes	—
215	#95×C₁₃₁	C₂³	1	2	yes	—
216	#95×C₁₃₁	C₂³	1	2	yes	—
217	#95×C₁₃₁	C₂³	1	2	yes	—
218	#95×C₁₃₁	C₂³	1	2	yes	—
219	#95×C₁₃₁	C₂³	1	2	yes	—
220	#95×C₁₃₁	C₂³	1	2	yes	—
221	#95×C₁₃₁	C₂³	1	2	yes	—
222	#95×C₁₃₁	C₂³	1	2	yes	—
223	#95×C₁₃₁	C₂³	1	2	yes	—
224	#95×C₁₃₁	C₂³	1	2	yes	—
225	#95×C₁₃₁	C₂³	1	2	yes	—
226	#95×C₁₃₁	C₂³	1	2	yes	—
227	#95×C₁₃₁	C₂³	1	2	yes	—
228	#95×C₁₃₁	C₂³	1	2	yes	—
229	#95×C₁₃₁	C₂³	1	2	yes	—
230	#95×C₁₃₁	C₂³	1	1	yes	characteristic
231	#95×C₁₃₁	C₂³	1	2	yes	—
232	#95×C₁₃₁	C₂³	1	1	yes	characteristic
233	#95×C₁₃₁	C₂³	1	1	yes	characteristic
234	#95×C₁₃₁	C₂³	1	1	yes	characteristic
235	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₁₃₁	—	2	2	no	—
237	C₂×Q₈×C₁₃₁	—	2	2	no	—
238	C₂×Q₈×C₁₃₁	—	2	2	no	—
239	C₂×Q₈×C₁₃₁	—	2	2	no	—
240	C₂×Q₈×C₁₃₁	—	2	2	no	—
241	C₂×Q₈×C₁₃₁	—	2	4	no	—
242	C₂×Q₈×C₁₃₁	—	2	2	no	—
243	C₂×Q₈×C₁₃₁	—	2	2	no	—
244	C₂×Q₈×C₁₃₁	—	2	2	no	—
245	C₂×Q₈×C₁₃₁	—	2	2	no	—
246	C₂×Q₈×C₁₃₁	—	4	2	no	—
247	C₂×Q₈×C₁₃₁	—	4	2	no	—
248	C₂×D₄×C₁₃₁	—	2	2	no	—
249	C₂×D₄×C₁₃₁	—	2	2	no	—
250	C₂×D₄×C₁₃₁	—	2	2	no	—
251	C₂²×C₄×C₁₃₁	—	2	4	no	—
252	C₂²×C₄×C₁₃₁	—	4	2	no	—
253	C₂²×C₄×C₁₃₁	—	4	2	no	—
254	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₁₃₁	—	2	2	no	—
277	C₄⋊C₄×C₁₃₁	—	2	2	no	—
278	C₄⋊C₄×C₁₃₁	—	2	2	no	—
279	C₄⋊C₄×C₁₃₁	—	2	2	no	—
280	C₄⋊C₄×C₁₃₁	—	2	2	no	—
281	C₄⋊C₄×C₁₃₁	—	2	2	no	—
282	C₄⋊C₄×C₁₃₁	—	2	2	no	—
283	C₄⋊C₄×C₁₃₁	—	2	2	no	—
284	C₄⋊C₄×C₁₃₁	—	2	2	no	—
285	C₄⋊C₄×C₁₃₁	—	2	4	no	—
286	C₄⋊C₄×C₁₃₁	—	2	4	no	—
287	C₄⋊C₄×C₁₃₁	—	2	4	no	—
288	C₄⋊C₄×C₁₃₁	—	2	4	no	—
289	C₄⋊C₄×C₁₃₁	—	2	4	no	—
290	C₄⋊C₄×C₁₃₁	—	2	4	no	—
291	C₄⋊C₄×C₁₃₁	—	2	2	no	—
292	C₄⋊C₄×C₁₃₁	—	2	2	no	—
293	C₄⋊C₄×C₁₃₁	—	2	2	no	—
294	C₄⋊C₄×C₁₃₁	—	2	2	no	—
295	C₄⋊C₄×C₁₃₁	—	4	2	no	—
296	C₄⋊C₄×C₁₃₁	—	4	2	no	—
297	C₄⋊C₄×C₁₃₁	—	4	2	no	—
298	C₄⋊C₄×C₁₃₁	—	4	2	no	—
299	C₄⋊C₄×C₁₃₁	—	4	2	no	—
300	C₄⋊C₄×C₁₃₁	—	4	2	no	—
301	C₄⋊C₄×C₁₃₁	—	4	2	no	—
302	C₄⋊C₄×C₁₃₁	#41	1	4	yes	—
303	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
308	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
309	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
312	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
313	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
314	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
315	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
316	C₄²×C₁₃₁	—	2	2	no	—
317	C₄²×C₁₃₁	—	2	2	no	—
318	C₄²×C₁₃₁	—	2	2	no	—
319	C₄²×C₁₃₁	—	2	2	no	—
320	C₄²×C₁₃₁	—	2	2	no	—
321	C₄²×C₁₃₁	—	2	2	no	—
322	C₄²×C₁₃₁	—	2	2	no	—
323	C₄²×C₁₃₁	—	2	4	no	—
324	C₄²×C₁₃₁	—	2	2	no	—
325	C₄²×C₁₃₁	—	2	2	no	—
326	C₄²×C₁₃₁	—	2	2	no	—
327	C₄²×C₁₃₁	—	2	2	no	—
328	C₄²×C₁₃₁	—	2	2	no	—
329	C₄²×C₁₃₁	—	2	2	no	—
330	C₄²×C₁₃₁	—	2	2	no	—
331	C₄²×C₁₃₁	—	4	1	no	—
332	C₄²×C₁₃₁	—	4	1	no	—
333	C₄²×C₁₃₁	—	4	1	no	—
334	C₄²×C₁₃₁	—	4	2	no	—
335	C₄²×C₁₃₁	—	4	2	no	—
336	C₄²×C₁₃₁	#41	1	4	yes	—
337	C₄²×C₁₃₁	#41	1	4	yes	—
338	C₂³×C₁₃₁	—	2	2	no	—
339	C₂³×C₁₃₁	—	2	2	no	—
340	C₂³×C₁₃₁	—	2	2	no	—
341	C₂³×C₁₃₁	—	2	2	no	—
342	C₂³×C₁₃₁	—	2	2	no	—
343	C₂³×C₁₃₁	—	2	2	no	—
344	C₂³×C₁₃₁	—	2	2	no	—
345	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
346	Q₈×C₁₃₁	—	2	8	no	—
347	Q₈×C₁₃₁	—	4	4	no	—
348	Q₈×C₁₃₁	—	4	4	no	—
349	Q₈×C₁₃₁	—	8	4	no	—
350	D₄×C₁₃₁	—	4	4	no	—
351	C₂×C₄×C₁₃₁	—	2	1	no	—
352	C₂×C₄×C₁₃₁	—	2	1	no	—
353	C₂×C₄×C₁₃₁	—	2	1	no	—
354	C₂×C₄×C₁₃₁	—	2	1	no	—
355	C₂×C₄×C₁₃₁	—	2	1	no	—
356	C₂×C₄×C₁₃₁	—	2	1	no	—
357	C₂×C₄×C₁₃₁	—	2	1	no	—
358	C₂×C₄×C₁₃₁	—	2	1	no	—
359	C₂×C₄×C₁₃₁	—	2	1	no	—
360	C₂×C₄×C₁₃₁	—	2	1	no	—
361	C₂×C₄×C₁₃₁	—	2	1	no	—
362	C₂×C₄×C₁₃₁	—	2	1	no	—
363	C₂×C₄×C₁₃₁	—	2	1	no	—
364	C₂×C₄×C₁₃₁	—	2	1	no	—
365	C₂×C₄×C₁₃₁	—	2	1	no	—
366	C₂×C₄×C₁₃₁	—	2	1	no	—
367	C₂×C₄×C₁₃₁	—	2	1	no	—
368	C₂×C₄×C₁₃₁	—	2	1	no	—
369	C₂×C₄×C₁₃₁	—	2	2	no	—
370	C₂×C₄×C₁₃₁	—	2	1	no	—
371	C₂×C₄×C₁₃₁	—	2	1	no	—
372	C₂×C₄×C₁₃₁	—	2	1	no	—
373	C₂×C₄×C₁₃₁	—	2	1	no	—
374	C₂×C₄×C₁₃₁	—	2	1	no	—
375	C₂×C₄×C₁₃₁	—	2	2	no	—
376	C₂×C₄×C₁₃₁	—	2	2	no	—
377	C₂×C₄×C₁₃₁	—	2	2	no	—
378	C₂×C₄×C₁₃₁	—	2	2	no	—
379	C₂×C₄×C₁₃₁	—	2	2	no	—
380	C₂×C₄×C₁₃₁	—	2	2	no	—
381	C₂×C₄×C₁₃₁	—	2	2	no	—
382	C₂×C₄×C₁₃₁	—	2	2	no	—
383	C₂×C₄×C₁₃₁	—	2	1	no	—
384	C₂×C₄×C₁₃₁	—	2	1	no	—
385	C₂×C₄×C₁₃₁	—	2	1	no	—
386	C₂×C₄×C₁₃₁	—	2	2	no	—
387	C₂×C₄×C₁₃₁	—	2	2	no	—
388	C₂×C₄×C₁₃₁	—	2	2	no	—
389	C₂×C₄×C₁₃₁	—	2	2	no	—
390	C₂×C₄×C₁₃₁	—	2	2	no	—
391	C₂×C₄×C₁₃₁	—	2	1	no	—
392	C₂×C₄×C₁₃₁	—	2	1	no	—
393	C₂×C₄×C₁₃₁	—	2	1	no	—
394	C₂×C₄×C₁₃₁	—	2	1	no	—
395	C₂×C₄×C₁₃₁	—	2	2	no	—
396	C₂×C₄×C₁₃₁	—	2	2	no	—
397	C₂×C₄×C₁₃₁	—	2	2	no	—
398	C₂×C₄×C₁₃₁	—	2	2	no	—
399	C₂×C₄×C₁₃₁	—	2	1	no	—
400	C₂×C₄×C₁₃₁	—	2	1	no	—
401	C₂×C₄×C₁₃₁	—	2	2	no	—
402	C₂×C₄×C₁₃₁	—	2	2	no	—
403	C₂×C₄×C₁₃₁	—	2	1	no	—
404	C₂×C₄×C₁₃₁	—	2	2	no	—
405	C₂×C₄×C₁₃₁	—	8	4	no	—
406	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
407	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
408	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
409	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
410	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
411	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
412	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
413	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
414	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
415	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
416	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
417	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
418	C₂²×C₁₃₁	—	4	2	no	—
419	C₂²×C₁₃₁	—	4	2	no	—
420	C₂²×C₁₃₁	—	4	2	no	—
421	C₂²×C₁₃₁	—	4	2	no	—
422	C₂²×C₁₃₁	—	4	2	no	—
423	C₂²×C₁₃₁	—	4	2	no	—
424	C₂²×C₁₃₁	—	4	2	no	—
425	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
427	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
428	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
430	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
431	C₂²×C₁₃₁	#585	1	1	yes	characteristic
432	C₄×C₁₃₁	—	2	2	no	—
433	C₄×C₁₃₁	—	2	2	no	—
434	C₄×C₁₃₁	—	2	2	no	—
435	C₄×C₁₃₁	—	2	2	no	—
436	C₄×C₁₃₁	—	2	2	no	—
437	C₄×C₁₃₁	—	2	2	no	—
438	C₄×C₁₃₁	—	2	2	no	—
439	C₄×C₁₃₁	—	2	2	no	—
440	C₄×C₁₃₁	—	2	2	no	—
441	C₄×C₁₃₁	—	4	2	no	—
442	C₄×C₁₃₁	—	4	2	no	—
443	C₄×C₁₃₁	—	4	2	no	—
444	C₄×C₁₃₁	—	4	1	no	—
445	C₄×C₁₃₁	—	4	1	no	—
446	C₄×C₁₃₁	—	4	2	no	—
447	C₄×C₁₃₁	—	4	1	no	—
448	C₄×C₁₃₁	—	4	1	no	—
449	C₄×C₁₃₁	—	4	2	no	—
450	C₄×C₁₃₁	—	4	1	no	—
451	C₄×C₁₃₁	—	4	2	no	—
452	C₄×C₁₃₁	—	4	2	no	—
453	C₄×C₁₃₁	#542	1	4	yes	—
454	C₂×C₁₃₁	—	8	2	no	—
455	C₂×C₁₃₁	#3444	1	1	yes	characteristic
456	C₂×C₁₃₁	C₂×#542	1	1	yes	characteristic
457	C₂×C₁₃₁	#3461	1	1	yes	characteristic
458	C₂×C₁₃₁	#3507	1	1	yes	characteristic
459	C₂×C₁₃₁	#3511	1	1	yes	characteristic
460	C₂×C₁₃₁	#3514	1	1	yes	characteristic
461	C₂×C₁₃₁	#3523	1	1	yes	characteristic
462	#35117	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₁₃₁	#35117	1	1	yes	characteristic, direct product factor, Sylow
464	#2863	C₂×C₁₃₁	1	1	yes	characteristic, complemented
465	#2862	C₂×C₁₃₁	1	1	yes	characteristic, complemented
466	#2861	C₂×C₁₃₁	1	1	yes	characteristic
467	#2860	C₂×C₁₃₁	1	1	yes	characteristic
468	#2650	C₂×C₁₃₁	1	2	yes	complemented
469	#2637	C₂×C₁₃₁	1	2	yes	complemented
470	#2592	C₂×C₁₃₁	1	1	yes	characteristic
471	#2581	C₂×C₁₃₁	1	1	yes	characteristic, complemented
472	#2550	C₂×C₁₃₁	1	1	yes	characteristic, complemented
473	#2545	C₂×C₁₃₁	1	1	yes	characteristic
474	#2532	C₂×C₁₃₁	1	2	yes	complemented
475	#2529	C₂×C₁₃₁	1	2	yes	complemented
476	#2515	C₂×C₁₃₁	1	2	yes	complemented
477	#2465	C₂×C₁₃₁	1	2	yes	complemented
478	#2453	C₂×C₁₃₁	1	1	yes	characteristic, complemented
479	#2452	C₂×C₁₃₁	1	1	yes	characteristic
480	#2447	C₂×C₁₃₁	1	1	yes	characteristic
481	#2446	C₂×C₁₃₁	1	1	yes	characteristic, complemented
482	#2334	C₂×C₁₃₁	1	2	yes	complemented
483	#2332	C₂×C₁₃₁	1	2	yes	complemented
484	C₄×#124	C₂×C₁₃₁	1	1	yes	characteristic
485	#2295	C₂×C₁₃₁	1	1	yes	characteristic, complemented
486	C₄²×Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
487	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
488	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
489	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
490	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
491	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
492	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
493	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
494	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
495	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
496	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
497	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
498	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
500	#400	C₂²×C₁₃₁	1	2	yes	—
501	#400	C₂²×C₁₃₁	1	2	yes	—
502	#400	C₂²×C₁₃₁	1	2	yes	—
503	#398	C₂²×C₁₃₁	1	2	yes	—
504	#398	C₂²×C₁₃₁	1	2	yes	—
505	#398	C₂²×C₁₃₁	1	2	yes	—
506	#397	C₂²×C₁₃₁	1	2	yes	—
507	#397	C₂²×C₁₃₁	1	2	yes	—
508	#397	C₂²×C₁₃₁	1	2	yes	—
509	#396	C₂²×C₁₃₁	1	2	yes	—
510	#396	C₂²×C₁₃₁	1	2	yes	—
511	#396	C₂²×C₁₃₁	1	2	yes	—
512	#395	C₂²×C₁₃₁	1	2	yes	—
513	#395	C₂²×C₁₃₁	1	2	yes	—
514	#393	C₂²×C₁₃₁	1	2	yes	—
515	#393	C₂²×C₁₃₁	1	2	yes	—
516	#391	C₂²×C₁₃₁	1	1	yes	characteristic
517	#391	C₂²×C₁₃₁	1	1	yes	characteristic
518	#391	C₂²×C₁₃₁	1	2	yes	—
519	#391	C₂²×C₁₃₁	1	2	yes	—
520	#391	C₂²×C₁₃₁	1	1	yes	characteristic
521	#391	C₂²×C₁₃₁	1	1	yes	characteristic
522	#391	C₂²×C₁₃₁	1	1	yes	characteristic
523	#391	C₂²×C₁₃₁	1	1	yes	characteristic
524	#391	C₂²×C₁₃₁	1	2	yes	—
525	#391	C₂²×C₁₃₁	1	1	yes	characteristic
526	#391	C₂²×C₁₃₁	1	1	yes	characteristic
527	#390	C₂²×C₁₃₁	1	1	yes	characteristic
528	#390	C₂²×C₁₃₁	1	1	yes	characteristic
529	#390	C₂²×C₁₃₁	1	1	yes	characteristic
530	#390	C₂²×C₁₃₁	1	1	yes	characteristic
531	#389	C₂²×C₁₃₁	1	1	yes	characteristic
532	#389	C₂²×C₁₃₁	1	1	yes	characteristic
533	#389	C₂²×C₁₃₁	1	2	yes	—
534	#389	C₂²×C₁₃₁	1	2	yes	—
535	#389	C₂²×C₁₃₁	1	1	yes	characteristic
536	#389	C₂²×C₁₃₁	1	1	yes	characteristic
537	#389	C₂²×C₁₃₁	1	1	yes	characteristic
538	#389	C₂²×C₁₃₁	1	1	yes	characteristic
539	#388	C₂²×C₁₃₁	1	2	yes	—
540	#388	C₂²×C₁₃₁	1	2	yes	—
541	#388	C₂²×C₁₃₁	1	2	yes	—
542	#388	C₂²×C₁₃₁	1	2	yes	—
543	#388	C₂²×C₁₃₁	1	2	yes	—
544	#388	C₂²×C₁₃₁	1	2	yes	—
545	#388	C₂²×C₁₃₁	1	2	yes	—
546	#388	C₂²×C₁₃₁	1	2	yes	—
547	#388	C₂²×C₁₃₁	1	2	yes	—
548	#388	C₂²×C₁₃₁	1	2	yes	—
549	#388	C₂²×C₁₃₁	1	2	yes	—
550	#388	C₂²×C₁₃₁	1	2	yes	—
551	#388	C₂²×C₁₃₁	1	2	yes	—
552	#387	C₂²×C₁₃₁	1	2	yes	—
553	#387	C₂²×C₁₃₁	1	2	yes	—
554	#387	C₂²×C₁₃₁	1	2	yes	—
555	#387	C₂²×C₁₃₁	1	2	yes	—
556	#387	C₂²×C₁₃₁	1	2	yes	—
557	#387	C₂²×C₁₃₁	1	2	yes	—
558	#387	C₂²×C₁₃₁	1	2	yes	—
559	#387	C₂²×C₁₃₁	1	2	yes	—
560	#387	C₂²×C₁₃₁	1	2	yes	—
561	#387	C₂²×C₁₃₁	1	2	yes	—
562	#385	C₂²×C₁₃₁	1	2	yes	—
563	#385	C₂²×C₁₃₁	1	2	yes	—
564	#383	C₂²×C₁₃₁	1	2	yes	—
565	#382	C₂²×C₁₃₁	1	1	yes	characteristic
566	#382	C₂²×C₁₃₁	1	2	yes	—
567	#382	C₂²×C₁₃₁	1	2	yes	—
568	#381	C₂²×C₁₃₁	1	2	yes	—
569	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
571	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
572	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
580	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
582	#376	C₂²×C₁₃₁	1	2	yes	—
583	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
584	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
585	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
586	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
587	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
588	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
589	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
590	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
591	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
592	C₄⋊Q₈	—	4	2	no	—
593	C₄⋊Q₈	—	4	2	no	—
594	#126	—	2	8	no	—
595	#125	—	4	2	no	—
596	#124	—	2	4	no	—
597	#124	—	4	2	no	—
598	C₂²⋊Q₈	—	2	8	no	—
599	C₄×Q₈	—	2	4	no	—
600	C₄×Q₈	—	2	4	no	—
601	C₄×Q₈	—	2	4	no	—
602	C₄×Q₈	—	2	4	no	—
603	C₄×Q₈	—	4	2	no	—
604	C₄×D₄	—	4	2	no	—
605	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
654	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
661	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
665	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
667	#95	C₂³×C₁₃₁	1	2	yes	—
668	#95	C₂³×C₁₃₁	1	2	yes	—
669	#95	C₂³×C₁₃₁	1	2	yes	—
670	#95	C₂³×C₁₃₁	1	2	yes	—
671	#95	C₂³×C₁₃₁	1	2	yes	—
672	#95	C₂³×C₁₃₁	1	2	yes	—
673	#95	C₂³×C₁₃₁	1	2	yes	—
674	#95	C₂³×C₁₃₁	1	2	yes	—
675	#95	C₂³×C₁₃₁	1	1	yes	characteristic
676	#95	C₂³×C₁₃₁	1	1	yes	characteristic
677	#95	C₂³×C₁₃₁	1	1	yes	characteristic
678	#95	C₂³×C₁₃₁	1	1	yes	characteristic
679	#95	C₂³×C₁₃₁	1	1	yes	characteristic
680	#95	C₂³×C₁₃₁	1	1	yes	characteristic
681	#95	C₂³×C₁₃₁	1	2	yes	—
682	#95	C₂³×C₁₃₁	1	2	yes	—
683	#95	C₂³×C₁₃₁	1	2	yes	—
684	#95	C₂³×C₁₃₁	1	2	yes	—
685	#95	C₂³×C₁₃₁	1	2	yes	—
686	#95	C₂³×C₁₃₁	1	2	yes	—
687	#95	C₂³×C₁₃₁	1	2	yes	—
688	#95	C₂³×C₁₃₁	1	2	yes	—
689	#95	C₂³×C₁₃₁	1	2	yes	—
690	#95	C₂³×C₁₃₁	1	2	yes	—
691	#95	C₂³×C₁₃₁	1	2	yes	—
692	#95	C₂³×C₁₃₁	1	2	yes	—
693	#95	C₂³×C₁₃₁	1	2	yes	—
694	#95	C₂³×C₁₃₁	1	2	yes	—
695	#95	C₂³×C₁₃₁	1	2	yes	—
696	#95	C₂³×C₁₃₁	1	2	yes	—
697	#95	C₂³×C₁₃₁	1	2	yes	—
698	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	4	2	no	—
710	C₂×Q₈	—	4	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	#41×C₁₃₁	1	4	yes	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	4	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	4	1	no	—
795	C₄²	—	4	1	no	—
796	C₄²	—	4	1	no	—
797	C₄²	—	4	2	no	—
798	C₄²	—	4	2	no	—
799	C₄²	#41×C₁₃₁	1	4	yes	—
800	C₄²	#41×C₁₃₁	1	4	yes	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
809	Q₈	—	2	8	no	—
810	Q₈	—	4	4	no	—
811	Q₈	—	4	4	no	—
812	Q₈	—	8	4	no	—
813	D₄	—	4	4	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	8	4	no	—
869	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
870	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
871	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
872	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
873	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
874	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
875	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
876	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
877	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
878	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
879	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
880	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
889	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
890	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
891	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
892	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
893	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
894	C₂²	#585×C₁₃₁	1	1	yes	characteristic
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	1	no	—
916	C₄	#542×C₁₃₁	1	4	yes	—
917	C₂	—	8	2	no	—
918	C₂	#3444×C₁₃₁	1	1	yes	characteristic
919	C₂	C₂×#542×C₁₃₁	1	1	yes	characteristic
920	C₂	#3461×C₁₃₁	1	1	yes	characteristic
921	C₂	#3507×C₁₃₁	1	1	yes	characteristic
922	C₂	#3511×C₁₃₁	1	1	yes	characteristic
923	C₂	#3514×C₁₃₁	1	1	yes	characteristic
924	C₂	#3523×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2863×C₁₃₁	C₂	semidirect
2. #2862×C₁₃₁	C₂	semidirect
5. #2650×C₁₃₁	C₂	semidirect
6. #2637×C₁₃₁	C₂	semidirect
8. #2581×C₁₃₁	C₂	semidirect
9. #2550×C₁₃₁	C₂	semidirect
11. #2532×C₁₃₁	C₂	semidirect
12. #2529×C₁₃₁	C₂	semidirect
13. #2515×C₁₃₁	C₂	semidirect
14. #2465×C₁₃₁	C₂	semidirect
15. #2453×C₁₃₁	C₂	semidirect
18. #2446×C₁₃₁	C₂	semidirect
19. #2334×C₁₃₁	C₂	semidirect
20. #2332×C₁₃₁	C₂	semidirect
22. #2295×C₁₃₁	C₂	semidirect
23. C₄²×Q₈×C₁₃₁	C₂	semidirect
462. #35117	C₁₃₁	direct (N × H)
463. C₁₃₁	#35117	direct (N × H)
464. #2863	C₂×C₁₃₁	semidirect
465. #2862	C₂×C₁₃₁	semidirect
468. #2650	C₂×C₁₃₁	semidirect
469. #2637	C₂×C₁₃₁	semidirect
471. #2581	C₂×C₁₃₁	semidirect
472. #2550	C₂×C₁₃₁	semidirect
474. #2532	C₂×C₁₃₁	semidirect
475. #2529	C₂×C₁₃₁	semidirect
476. #2515	C₂×C₁₃₁	semidirect
477. #2465	C₂×C₁₃₁	semidirect
478. #2453	C₂×C₁₃₁	semidirect
481. #2446	C₂×C₁₃₁	semidirect
482. #2334	C₂×C₁₃₁	semidirect
483. #2332	C₂×C₁₃₁	semidirect
485. #2295	C₂×C₁₃₁	semidirect
486. C₄²×Q₈	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2863×C₁₃₁	2
#2862×C₁₃₁	2
#2861×C₁₃₁	2
#2860×C₁₃₁	2
#2650×C₁₃₁	2
#2637×C₁₃₁	2
#2592×C₁₃₁	2
#2581×C₁₃₁	2
#2550×C₁₃₁	2
#2545×C₁₃₁	2
#2532×C₁₃₁	2
#2529×C₁₃₁	2
#2515×C₁₃₁	2
#2465×C₁₃₁	2
#2453×C₁₃₁	2
#2452×C₁₃₁	2
#2447×C₁₃₁	2
#2446×C₁₃₁	2
#2334×C₁₃₁	2
#2332×C₁₃₁	2
C₄×#124×C₁₃₁	2
#2295×C₁₃₁	2
C₄²×Q₈×C₁₃₁	2
#35117	131

Subgroups — C131×#35117 #45721001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#35117 #45721001