Subgroups — C₁₃₁×#35038 #45720922

Order 33536.

2100 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2861×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#2860×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2856×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2855×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2648×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2635×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2595×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2559×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2511×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#2490×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#2467×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#2456×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2445×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#2441×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#2431×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#2427×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#2414×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	#2407×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
19	#2335×C₁₃₁	C₂	1	2	yes	maximal, complemented
20	#2333×C₁₃₁	C₂	1	2	yes	maximal, complemented
21	C₄×#121×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
22	#2297×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×#127×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×#123×C₁₃₁	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
33	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
35	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
41	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
44	#400×C₁₃₁	C₂²	1	2	yes	—
45	#400×C₁₃₁	C₂²	1	2	yes	—
46	#399×C₁₃₁	C₂²	1	2	yes	—
47	#397×C₁₃₁	C₂²	1	2	yes	—
48	#397×C₁₃₁	C₂²	1	2	yes	—
49	#396×C₁₃₁	C₂²	1	2	yes	—
50	#394×C₁₃₁	C₂²	1	2	yes	—
51	#394×C₁₃₁	C₂²	1	2	yes	—
52	#394×C₁₃₁	C₂²	1	2	yes	—
53	#394×C₁₃₁	C₂²	1	2	yes	—
54	#394×C₁₃₁	C₂²	1	2	yes	—
55	#394×C₁₃₁	C₂²	1	2	yes	—
56	#392×C₁₃₁	C₂²	1	2	yes	—
57	#392×C₁₃₁	C₂²	1	2	yes	—
58	#392×C₁₃₁	C₂²	1	2	yes	—
59	#392×C₁₃₁	C₂²	1	2	yes	—
60	#391×C₁₃₁	C₂²	1	1	yes	characteristic
61	#391×C₁₃₁	C₂²	1	1	yes	characteristic
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	2	yes	—
66	#390×C₁₃₁	C₂²	1	1	yes	characteristic
67	#390×C₁₃₁	C₂²	1	1	yes	characteristic
68	#390×C₁₃₁	C₂²	1	1	yes	characteristic
69	#390×C₁₃₁	C₂²	1	2	yes	—
70	#390×C₁₃₁	C₂²	1	2	yes	—
71	#390×C₁₃₁	C₂²	1	2	yes	—
72	#390×C₁₃₁	C₂²	1	1	yes	characteristic
73	#390×C₁₃₁	C₂²	1	1	yes	characteristic
74	#389×C₁₃₁	C₂²	1	1	yes	characteristic
75	#389×C₁₃₁	C₂²	1	1	yes	characteristic
76	#389×C₁₃₁	C₂²	1	2	yes	—
77	#389×C₁₃₁	C₂²	1	1	yes	characteristic
78	#389×C₁₃₁	C₂²	1	1	yes	characteristic
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	#386×C₁₃₁	C₂²	1	2	yes	—
95	#386×C₁₃₁	C₂²	1	2	yes	—
96	#386×C₁₃₁	C₂²	1	2	yes	—
97	#386×C₁₃₁	C₂²	1	2	yes	—
98	#386×C₁₃₁	C₂²	1	2	yes	—
99	#386×C₁₃₁	C₂²	1	2	yes	—
100	#386×C₁₃₁	C₂²	1	2	yes	—
101	#386×C₁₃₁	C₂²	1	2	yes	—
102	#385×C₁₃₁	C₂²	1	2	yes	—
103	#385×C₁₃₁	C₂²	1	2	yes	—
104	#384×C₁₃₁	C₂²	1	1	yes	characteristic
105	#381×C₁₃₁	C₂²	1	2	yes	—
106	#380×C₁₃₁	C₂²	1	1	yes	characteristic
107	#380×C₁₃₁	C₂²	1	1	yes	characteristic
108	#380×C₁₃₁	C₂²	1	2	yes	—
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×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
122	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
123	C₂×#41×C₁₃₁	—	2	4	no	—
124	C₂×#41×C₁₃₁	—	4	2	no	—
125	C₂×#41×C₁₃₁	—	4	2	no	—
126	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
132	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
134	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
135	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
144	#127×C₁₃₁	—	4	2	no	—
145	#126×C₁₃₁	—	4	4	no	—
146	#125×C₁₃₁	—	4	2	no	—
147	#124×C₁₃₁	—	4	2	no	—
148	#123×C₁₃₁	—	2	8	no	—
149	C₂²⋊Q₈×C₁₃₁	—	4	2	no	—
150	#121×C₁₃₁	—	2	4	no	—
151	#121×C₁₃₁	—	2	8	no	—
152	#121×C₁₃₁	—	4	4	no	—
153	#121×C₁₃₁	—	4	2	no	—
154	#121×C₁₃₁	—	4	2	no	—
155	C₄×D₄×C₁₃₁	—	2	4	no	—
156	C₄×D₄×C₁₃₁	—	2	4	no	—
157	C₄×D₄×C₁₃₁	—	2	4	no	—
158	C₄×D₄×C₁₃₁	—	4	2	no	—
159	C₄×D₄×C₁₃₁	—	4	4	no	—
160	#117×C₁₃₁	—	4	2	no	—
161	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
206	C₂×C₄²×C₁₃₁	—	4	2	no	—
207	C₂×C₄²×C₁₃₁	—	4	2	no	—
208	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
219	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
220	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
231	#95×C₁₃₁	C₂³	1	1	yes	characteristic
232	#95×C₁₃₁	C₂³	1	2	yes	—
233	#95×C₁₃₁	C₂³	1	2	yes	—
234	#95×C₁₃₁	C₂³	1	1	yes	characteristic
235	#95×C₁₃₁	C₂³	1	2	yes	—
236	#95×C₁₃₁	C₂³	1	2	yes	—
237	#95×C₁₃₁	C₂³	1	2	yes	—
238	#95×C₁₃₁	C₂³	1	2	yes	—
239	#95×C₁₃₁	C₂³	1	2	yes	—
240	#95×C₁₃₁	C₂³	1	1	yes	characteristic
241	#95×C₁₃₁	C₂³	1	1	yes	characteristic
242	#95×C₁₃₁	C₂³	1	1	yes	characteristic
243	#95×C₁₃₁	C₂³	1	1	yes	characteristic
244	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
245	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
246	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
248	#41×C₁₃₁	—	4	16	no	—
249	C₂×Q₈×C₁₃₁	—	2	2	no	—
250	C₂×Q₈×C₁₃₁	—	2	2	no	—
251	C₂×Q₈×C₁₃₁	—	2	2	no	—
252	C₂×D₄×C₁₃₁	—	2	2	no	—
253	C₂×D₄×C₁₃₁	—	2	2	no	—
254	C₂×D₄×C₁₃₁	—	2	4	no	—
255	C₂×D₄×C₁₃₁	—	2	4	no	—
256	C₂×D₄×C₁₃₁	—	2	4	no	—
257	C₂×D₄×C₁₃₁	—	2	4	no	—
258	C₂×D₄×C₁₃₁	—	2	2	no	—
259	C₂×D₄×C₁₃₁	—	2	2	no	—
260	C₂×D₄×C₁₃₁	—	2	2	no	—
261	C₂×D₄×C₁₃₁	—	2	4	no	—
262	C₂×D₄×C₁₃₁	—	2	4	no	—
263	C₂×D₄×C₁₃₁	—	2	2	no	—
264	C₂×D₄×C₁₃₁	—	2	2	no	—
265	C₂×D₄×C₁₃₁	—	2	2	no	—
266	C₂×D₄×C₁₃₁	—	2	2	no	—
267	C₂×D₄×C₁₃₁	—	4	2	no	—
268	C₂×D₄×C₁₃₁	—	4	2	no	—
269	C₂×D₄×C₁₃₁	—	4	2	no	—
270	C₂×D₄×C₁₃₁	—	4	2	no	—
271	C₂×D₄×C₁₃₁	—	4	2	no	—
272	C₂×D₄×C₁₃₁	—	4	2	no	—
273	C₂×D₄×C₁₃₁	—	4	2	no	—
274	C₂×D₄×C₁₃₁	—	4	2	no	—
275	C₂×D₄×C₁₃₁	—	4	2	no	—
276	C₂×D₄×C₁₃₁	—	4	2	no	—
277	C₂×D₄×C₁₃₁	—	4	2	no	—
278	C₂×D₄×C₁₃₁	—	4	2	no	—
279	C₂²×C₄×C₁₃₁	—	2	2	no	—
280	C₂²×C₄×C₁₃₁	—	2	2	no	—
281	C₂²×C₄×C₁₃₁	—	2	2	no	—
282	C₂²×C₄×C₁₃₁	—	2	2	no	—
283	C₂²×C₄×C₁₃₁	—	2	2	no	—
284	C₂²×C₄×C₁₃₁	—	2	2	no	—
285	C₂²×C₄×C₁₃₁	—	2	4	no	—
286	C₂²×C₄×C₁₃₁	—	2	2	no	—
287	C₂²×C₄×C₁₃₁	—	2	2	no	—
288	C₂²×C₄×C₁₃₁	—	2	2	no	—
289	C₂²×C₄×C₁₃₁	—	2	2	no	—
290	C₂²×C₄×C₁₃₁	—	2	4	no	—
291	C₂²×C₄×C₁₃₁	—	4	1	no	—
292	C₂²×C₄×C₁₃₁	—	4	1	no	—
293	C₂²×C₄×C₁₃₁	—	4	1	no	—
294	C₂²×C₄×C₁₃₁	—	4	1	no	—
295	C₂²×C₄×C₁₃₁	—	4	1	no	—
296	C₂²×C₄×C₁₃₁	—	4	1	no	—
297	C₂²×C₄×C₁₃₁	—	4	2	no	—
298	C₂²×C₄×C₁₃₁	—	4	2	no	—
299	C₂²×C₄×C₁₃₁	—	4	2	no	—
300	C₂²×C₄×C₁₃₁	—	4	2	no	—
301	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
302	C₂²×C₄×C₁₃₁	#41	1	4	yes	complemented
303	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₁₃₁	—	2	2	no	—
323	C₄⋊C₄×C₁₃₁	—	2	2	no	—
324	C₄⋊C₄×C₁₃₁	—	2	4	no	—
325	C₄⋊C₄×C₁₃₁	—	2	2	no	—
326	C₄⋊C₄×C₁₃₁	—	2	4	no	—
327	C₄⋊C₄×C₁₃₁	—	2	2	no	—
328	C₄⋊C₄×C₁₃₁	—	2	2	no	—
329	C₄⋊C₄×C₁₃₁	—	2	2	no	—
330	C₄⋊C₄×C₁₃₁	—	2	4	no	—
331	C₄⋊C₄×C₁₃₁	—	2	2	no	—
332	C₄⋊C₄×C₁₃₁	—	4	2	no	—
333	C₄⋊C₄×C₁₃₁	—	4	2	no	—
334	C₄⋊C₄×C₁₃₁	—	4	2	no	—
335	C₄⋊C₄×C₁₃₁	—	4	2	no	—
336	C₄⋊C₄×C₁₃₁	—	4	2	no	—
337	C₄⋊C₄×C₁₃₁	—	4	2	no	—
338	C₄⋊C₄×C₁₃₁	#41	1	4	yes	complemented
339	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
340	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
341	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
342	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
343	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
344	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
345	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
346	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
347	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
348	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
349	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
350	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
351	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
352	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
353	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
354	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
355	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
356	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
357	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
358	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
359	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
360	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
361	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
362	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
363	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
364	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
365	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
366	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
367	C₄²×C₁₃₁	—	2	2	no	—
368	C₄²×C₁₃₁	—	2	2	no	—
369	C₄²×C₁₃₁	—	2	2	no	—
370	C₄²×C₁₃₁	—	2	2	no	—
371	C₄²×C₁₃₁	—	2	2	no	—
372	C₄²×C₁₃₁	—	2	2	no	—
373	C₄²×C₁₃₁	—	2	2	no	—
374	C₄²×C₁₃₁	—	2	2	no	—
375	C₄²×C₁₃₁	—	4	1	no	—
376	C₄²×C₁₃₁	—	4	1	no	—
377	C₄²×C₁₃₁	—	4	1	no	—
378	C₄²×C₁₃₁	—	4	1	no	—
379	C₄²×C₁₃₁	—	4	1	no	—
380	C₄²×C₁₃₁	—	4	2	no	—
381	C₄²×C₁₃₁	—	4	2	no	—
382	C₂³×C₁₃₁	—	2	1	no	—
383	C₂³×C₁₃₁	—	2	1	no	—
384	C₂³×C₁₃₁	—	2	1	no	—
385	C₂³×C₁₃₁	—	2	1	no	—
386	C₂³×C₁₃₁	—	2	1	no	—
387	C₂³×C₁₃₁	—	2	1	no	—
388	C₂³×C₁₃₁	—	2	1	no	—
389	C₂³×C₁₃₁	—	2	1	no	—
390	C₂³×C₁₃₁	—	2	1	no	—
391	C₂³×C₁₃₁	—	2	1	no	—
392	C₂³×C₁₃₁	—	2	1	no	—
393	C₂³×C₁₃₁	—	2	1	no	—
394	C₂³×C₁₃₁	—	2	2	no	—
395	C₂³×C₁₃₁	—	2	2	no	—
396	C₂³×C₁₃₁	—	2	2	no	—
397	C₂³×C₁₃₁	—	2	2	no	—
398	C₂³×C₁₃₁	—	2	2	no	—
399	C₂³×C₁₃₁	—	2	2	no	—
400	C₂³×C₁₃₁	—	2	2	no	—
401	C₂³×C₁₃₁	—	2	2	no	—
402	C₂³×C₁₃₁	—	2	2	no	—
403	C₂³×C₁₃₁	—	2	2	no	—
404	C₂³×C₁₃₁	—	2	2	no	—
405	C₂³×C₁₃₁	—	2	2	no	—
406	C₂³×C₁₃₁	—	2	2	no	—
407	C₂³×C₁₃₁	—	2	2	no	—
408	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
409	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
410	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
411	Q₈×C₁₃₁	—	4	4	no	—
412	D₄×C₁₃₁	—	2	8	no	—
413	D₄×C₁₃₁	—	4	8	no	—
414	D₄×C₁₃₁	—	4	8	no	—
415	D₄×C₁₃₁	—	4	4	no	—
416	D₄×C₁₃₁	—	4	4	no	—
417	D₄×C₁₃₁	—	8	4	no	—
418	D₄×C₁₃₁	—	8	4	no	—
419	D₄×C₁₃₁	—	8	4	no	—
420	D₄×C₁₃₁	—	8	4	no	—
421	C₂×C₄×C₁₃₁	—	2	1	no	—
422	C₂×C₄×C₁₃₁	—	2	1	no	—
423	C₂×C₄×C₁₃₁	—	2	1	no	—
424	C₂×C₄×C₁₃₁	—	2	1	no	—
425	C₂×C₄×C₁₃₁	—	2	1	no	—
426	C₂×C₄×C₁₃₁	—	2	1	no	—
427	C₂×C₄×C₁₃₁	—	2	1	no	—
428	C₂×C₄×C₁₃₁	—	2	1	no	—
429	C₂×C₄×C₁₃₁	—	2	1	no	—
430	C₂×C₄×C₁₃₁	—	2	1	no	—
431	C₂×C₄×C₁₃₁	—	2	1	no	—
432	C₂×C₄×C₁₃₁	—	2	1	no	—
433	C₂×C₄×C₁₃₁	—	2	1	no	—
434	C₂×C₄×C₁₃₁	—	2	1	no	—
435	C₂×C₄×C₁₃₁	—	2	8	no	—
436	C₂×C₄×C₁₃₁	—	2	1	no	—
437	C₂×C₄×C₁₃₁	—	2	1	no	—
438	C₂×C₄×C₁₃₁	—	2	1	no	—
439	C₂×C₄×C₁₃₁	—	2	2	no	—
440	C₂×C₄×C₁₃₁	—	2	1	no	—
441	C₂×C₄×C₁₃₁	—	2	1	no	—
442	C₂×C₄×C₁₃₁	—	2	2	no	—
443	C₂×C₄×C₁₃₁	—	2	2	no	—
444	C₂×C₄×C₁₃₁	—	2	2	no	—
445	C₂×C₄×C₁₃₁	—	2	2	no	—
446	C₂×C₄×C₁₃₁	—	2	2	no	—
447	C₂×C₄×C₁₃₁	—	2	1	no	—
448	C₂×C₄×C₁₃₁	—	2	1	no	—
449	C₂×C₄×C₁₃₁	—	2	1	no	—
450	C₂×C₄×C₁₃₁	—	2	1	no	—
451	C₂×C₄×C₁₃₁	—	2	1	no	—
452	C₂×C₄×C₁₃₁	—	2	1	no	—
453	C₂×C₄×C₁₃₁	—	2	2	no	—
454	C₂×C₄×C₁₃₁	—	2	2	no	—
455	C₂×C₄×C₁₃₁	—	2	2	no	—
456	C₂×C₄×C₁₃₁	—	2	2	no	—
457	C₂×C₄×C₁₃₁	—	2	2	no	—
458	C₂×C₄×C₁₃₁	—	2	1	no	—
459	C₂×C₄×C₁₃₁	—	2	2	no	—
460	C₂×C₄×C₁₃₁	—	2	2	no	—
461	C₂×C₄×C₁₃₁	—	2	2	no	—
462	C₂×C₄×C₁₃₁	—	2	2	no	—
463	C₂×C₄×C₁₃₁	—	2	2	no	—
464	C₂×C₄×C₁₃₁	—	2	1	no	—
465	C₂×C₄×C₁₃₁	—	2	1	no	—
466	C₂×C₄×C₁₃₁	—	2	2	no	—
467	C₂×C₄×C₁₃₁	—	2	1	no	—
468	C₂×C₄×C₁₃₁	—	2	2	no	—
469	C₂×C₄×C₁₃₁	—	4	4	no	—
470	C₂×C₄×C₁₃₁	—	4	4	no	—
471	C₂×C₄×C₁₃₁	—	4	4	no	—
472	C₂×C₄×C₁₃₁	—	4	4	no	—
473	C₂×C₄×C₁₃₁	—	4	8	no	—
474	C₂×C₄×C₁₃₁	—	4	4	no	—
475	C₂×C₄×C₁₃₁	—	8	4	no	—
476	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
477	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
478	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
479	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
480	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
481	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
482	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
483	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
484	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
485	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
486	C₂²×C₁₃₁	—	2	2	no	—
487	C₂²×C₁₃₁	—	2	2	no	—
488	C₂²×C₁₃₁	—	2	2	no	—
489	C₂²×C₁₃₁	—	2	2	no	—
490	C₂²×C₁₃₁	—	2	2	no	—
491	C₂²×C₁₃₁	—	2	2	no	—
492	C₂²×C₁₃₁	—	4	1	no	—
493	C₂²×C₁₃₁	—	4	1	no	—
494	C₂²×C₁₃₁	—	4	1	no	—
495	C₂²×C₁₃₁	—	4	1	no	—
496	C₂²×C₁₃₁	—	4	1	no	—
497	C₂²×C₁₃₁	—	4	1	no	—
498	C₂²×C₁₃₁	—	4	1	no	—
499	C₂²×C₁₃₁	—	4	1	no	—
500	C₂²×C₁₃₁	—	4	2	no	—
501	C₂²×C₁₃₁	—	4	2	no	—
502	C₂²×C₁₃₁	—	4	2	no	—
503	C₂²×C₁₃₁	—	4	2	no	—
504	C₂²×C₁₃₁	—	4	2	no	—
505	C₂²×C₁₃₁	—	4	2	no	—
506	C₂²×C₁₃₁	—	4	2	no	—
507	C₂²×C₁₃₁	—	4	2	no	—
508	C₂²×C₁₃₁	—	4	2	no	—
509	C₂²×C₁₃₁	—	4	2	no	—
510	C₂²×C₁₃₁	—	4	2	no	—
511	C₂²×C₁₃₁	—	4	2	no	—
512	C₂²×C₁₃₁	—	4	2	no	—
513	C₂²×C₁₃₁	—	4	2	no	—
514	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
515	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
516	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
517	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
520	C₂²×C₁₃₁	#585	1	1	yes	characteristic
521	C₄×C₁₃₁	—	2	2	no	—
522	C₄×C₁₃₁	—	2	2	no	—
523	C₄×C₁₃₁	—	2	2	no	—
524	C₄×C₁₃₁	—	2	2	no	—
525	C₄×C₁₃₁	—	2	2	no	—
526	C₄×C₁₃₁	—	2	2	no	—
527	C₄×C₁₃₁	—	2	2	no	—
528	C₄×C₁₃₁	—	4	1	no	—
529	C₄×C₁₃₁	—	4	2	no	—
530	C₄×C₁₃₁	—	4	1	no	—
531	C₄×C₁₃₁	—	4	2	no	—
532	C₄×C₁₃₁	—	4	1	no	—
533	C₄×C₁₃₁	—	4	1	no	—
534	C₄×C₁₃₁	—	4	2	no	—
535	C₄×C₁₃₁	—	4	2	no	—
536	C₄×C₁₃₁	—	4	1	no	—
537	C₄×C₁₃₁	—	4	2	no	—
538	C₄×C₁₃₁	—	4	2	no	—
539	C₄×C₁₃₁	#538	1	4	yes	—
540	C₂×C₁₃₁	—	4	2	no	—
541	C₂×C₁₃₁	—	4	2	no	—
542	C₂×C₁₃₁	—	8	2	no	—
543	C₂×C₁₃₁	—	8	2	no	—
544	C₂×C₁₃₁	#3444	1	1	yes	characteristic
545	C₂×C₁₃₁	C₂×#538	1	1	yes	characteristic
546	C₂×C₁₃₁	#3460	1	1	yes	characteristic
547	C₂×C₁₃₁	#3505	1	1	yes	characteristic
548	C₂×C₁₃₁	#3508	1	1	yes	characteristic
549	C₂×C₁₃₁	#3517	1	1	yes	characteristic
550	C₂×C₁₃₁	#3519	1	1	yes	characteristic
551	#35038	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
552	C₁₃₁	#35038	1	1	yes	characteristic, direct product factor, Sylow
553	#2861	C₂×C₁₃₁	1	1	yes	characteristic, complemented
554	#2860	C₂×C₁₃₁	1	1	yes	characteristic, complemented
555	#2856	C₂×C₁₃₁	1	1	yes	characteristic, complemented
556	#2855	C₂×C₁₃₁	1	1	yes	characteristic, complemented
557	#2648	C₂×C₁₃₁	1	2	yes	complemented
558	#2635	C₂×C₁₃₁	1	2	yes	complemented
559	#2595	C₂×C₁₃₁	1	2	yes	complemented
560	#2559	C₂×C₁₃₁	1	2	yes	complemented
561	#2511	C₂×C₁₃₁	1	1	yes	characteristic, complemented
562	#2490	C₂×C₁₃₁	1	1	yes	characteristic, complemented
563	#2467	C₂×C₁₃₁	1	2	yes	complemented
564	#2456	C₂×C₁₃₁	1	2	yes	complemented
565	#2445	C₂×C₁₃₁	1	1	yes	characteristic, complemented
566	#2441	C₂×C₁₃₁	1	1	yes	characteristic, complemented
567	#2431	C₂×C₁₃₁	1	1	yes	characteristic, complemented
568	#2427	C₂×C₁₃₁	1	1	yes	characteristic, complemented
569	#2414	C₂×C₁₃₁	1	1	yes	characteristic, complemented
570	#2407	C₂×C₁₃₁	1	1	yes	characteristic, complemented
571	#2335	C₂×C₁₃₁	1	2	yes	complemented
572	#2333	C₂×C₁₃₁	1	2	yes	complemented
573	C₄×#121	C₂×C₁₃₁	1	1	yes	characteristic, complemented
574	#2297	C₂×C₁₃₁	1	1	yes	characteristic, complemented
575	C₄²×D₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
576	C₂²×#41	C₂²×C₁₃₁	1	1	yes	characteristic
577	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
578	C₂×#126	C₂²×C₁₃₁	1	2	yes	—
579	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
580	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
581	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
582	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
583	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
584	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
585	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
586	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
587	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
588	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
589	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
590	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
591	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
592	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
593	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
594	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
595	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
596	#400	C₂²×C₁₃₁	1	2	yes	—
597	#400	C₂²×C₁₃₁	1	2	yes	—
598	#399	C₂²×C₁₃₁	1	2	yes	—
599	#397	C₂²×C₁₃₁	1	2	yes	—
600	#397	C₂²×C₁₃₁	1	2	yes	—
601	#396	C₂²×C₁₃₁	1	2	yes	—
602	#394	C₂²×C₁₃₁	1	2	yes	—
603	#394	C₂²×C₁₃₁	1	2	yes	—
604	#394	C₂²×C₁₃₁	1	2	yes	—
605	#394	C₂²×C₁₃₁	1	2	yes	—
606	#394	C₂²×C₁₃₁	1	2	yes	—
607	#394	C₂²×C₁₃₁	1	2	yes	—
608	#392	C₂²×C₁₃₁	1	2	yes	—
609	#392	C₂²×C₁₃₁	1	2	yes	—
610	#392	C₂²×C₁₃₁	1	2	yes	—
611	#392	C₂²×C₁₃₁	1	2	yes	—
612	#391	C₂²×C₁₃₁	1	1	yes	characteristic
613	#391	C₂²×C₁₃₁	1	1	yes	characteristic
614	#391	C₂²×C₁₃₁	1	1	yes	characteristic
615	#391	C₂²×C₁₃₁	1	1	yes	characteristic
616	#390	C₂²×C₁₃₁	1	2	yes	—
617	#390	C₂²×C₁₃₁	1	2	yes	—
618	#390	C₂²×C₁₃₁	1	2	yes	—
619	#390	C₂²×C₁₃₁	1	2	yes	—
620	#390	C₂²×C₁₃₁	1	1	yes	characteristic
621	#390	C₂²×C₁₃₁	1	1	yes	characteristic
622	#390	C₂²×C₁₃₁	1	1	yes	characteristic
623	#390	C₂²×C₁₃₁	1	1	yes	characteristic
624	#390	C₂²×C₁₃₁	1	1	yes	characteristic
625	#390	C₂²×C₁₃₁	1	1	yes	characteristic
626	#389	C₂²×C₁₃₁	1	2	yes	—
627	#389	C₂²×C₁₃₁	1	1	yes	characteristic
628	#389	C₂²×C₁₃₁	1	1	yes	characteristic
629	#389	C₂²×C₁₃₁	1	1	yes	characteristic
630	#389	C₂²×C₁₃₁	1	1	yes	characteristic
631	#388	C₂²×C₁₃₁	1	2	yes	—
632	#388	C₂²×C₁₃₁	1	2	yes	—
633	#388	C₂²×C₁₃₁	1	2	yes	—
634	#388	C₂²×C₁₃₁	1	2	yes	—
635	#388	C₂²×C₁₃₁	1	2	yes	—
636	#388	C₂²×C₁₃₁	1	2	yes	—
637	#388	C₂²×C₁₃₁	1	2	yes	—
638	#388	C₂²×C₁₃₁	1	2	yes	—
639	#388	C₂²×C₁₃₁	1	2	yes	—
640	#388	C₂²×C₁₃₁	1	2	yes	—
641	#387	C₂²×C₁₃₁	1	2	yes	—
642	#387	C₂²×C₁₃₁	1	2	yes	—
643	#387	C₂²×C₁₃₁	1	2	yes	—
644	#387	C₂²×C₁₃₁	1	2	yes	—
645	#387	C₂²×C₁₃₁	1	2	yes	—
646	#386	C₂²×C₁₃₁	1	2	yes	—
647	#386	C₂²×C₁₃₁	1	2	yes	—
648	#386	C₂²×C₁₃₁	1	2	yes	—
649	#386	C₂²×C₁₃₁	1	2	yes	—
650	#386	C₂²×C₁₃₁	1	2	yes	—
651	#386	C₂²×C₁₃₁	1	2	yes	—
652	#386	C₂²×C₁₃₁	1	2	yes	—
653	#386	C₂²×C₁₃₁	1	2	yes	—
654	#385	C₂²×C₁₃₁	1	2	yes	—
655	#385	C₂²×C₁₃₁	1	2	yes	—
656	#384	C₂²×C₁₃₁	1	1	yes	characteristic
657	#381	C₂²×C₁₃₁	1	2	yes	—
658	#380	C₂²×C₁₃₁	1	2	yes	—
659	#380	C₂²×C₁₃₁	1	1	yes	characteristic
660	#380	C₂²×C₁₃₁	1	1	yes	characteristic
661	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
662	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
663	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
664	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
665	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
666	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
667	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
668	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
669	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
670	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
671	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
672	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
673	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
674	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
675	C₂×#41	—	2	4	no	—
676	C₂×#41	—	4	2	no	—
677	C₂×#41	—	4	2	no	—
678	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
679	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
680	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
681	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
682	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
683	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
684	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
685	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
686	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
687	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
688	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
689	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
690	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
691	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
693	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
694	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
695	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
696	#127	—	4	2	no	—
697	#126	—	4	4	no	—
698	#125	—	4	2	no	—
699	#124	—	4	2	no	—
700	#123	—	2	8	no	—
701	C₂²⋊Q₈	—	4	2	no	—
702	#121	—	2	4	no	—
703	#121	—	2	8	no	—
704	#121	—	4	4	no	—
705	#121	—	4	2	no	—
706	#121	—	4	2	no	—
707	C₄×D₄	—	2	4	no	—
708	C₄×D₄	—	2	4	no	—
709	C₄×D₄	—	2	4	no	—
710	C₄×D₄	—	4	2	no	—
711	C₄×D₄	—	4	4	no	—
712	#117	—	4	2	no	—
713	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
733	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
734	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
735	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
758	C₂×C₄²	—	4	2	no	—
759	C₂×C₄²	—	4	2	no	—
760	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
765	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
769	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
770	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
775	#95	C₂³×C₁₃₁	1	1	yes	characteristic
776	#95	C₂³×C₁₃₁	1	1	yes	characteristic
777	#95	C₂³×C₁₃₁	1	1	yes	characteristic
778	#95	C₂³×C₁₃₁	1	1	yes	characteristic
779	#95	C₂³×C₁₃₁	1	1	yes	characteristic
780	#95	C₂³×C₁₃₁	1	1	yes	characteristic
781	#95	C₂³×C₁₃₁	1	2	yes	—
782	#95	C₂³×C₁₃₁	1	2	yes	—
783	#95	C₂³×C₁₃₁	1	2	yes	—
784	#95	C₂³×C₁₃₁	1	2	yes	—
785	#95	C₂³×C₁₃₁	1	2	yes	—
786	#95	C₂³×C₁₃₁	1	2	yes	—
787	#95	C₂³×C₁₃₁	1	2	yes	—
788	#95	C₂³×C₁₃₁	1	2	yes	—
789	#95	C₂³×C₁₃₁	1	2	yes	—
790	#95	C₂³×C₁₃₁	1	2	yes	—
791	#95	C₂³×C₁₃₁	1	2	yes	—
792	#95	C₂³×C₁₃₁	1	2	yes	—
793	#95	C₂³×C₁₃₁	1	2	yes	—
794	#95	C₂³×C₁₃₁	1	2	yes	—
795	#95	C₂³×C₁₃₁	1	2	yes	—
796	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
797	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
798	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
799	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
800	#41	—	4	16	no	—
801	C₂×Q₈	—	2	2	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	4	no	—
843	C₂²×C₄	—	4	1	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	1	no	—
846	C₂²×C₄	—	4	1	no	—
847	C₂²×C₄	—	4	1	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
854	C₂²×C₄	#41×C₁₃₁	1	4	yes	complemented
855	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
863	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	4	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	4	2	no	—
885	C₄⋊C₄	—	4	2	no	—
886	C₄⋊C₄	—	4	2	no	—
887	C₄⋊C₄	—	4	2	no	—
888	C₄⋊C₄	—	4	2	no	—
889	C₄⋊C₄	—	4	2	no	—
890	C₄⋊C₄	#41×C₁₃₁	1	4	yes	complemented
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	2	no	—
921	C₄²	—	2	2	no	—
922	C₄²	—	2	2	no	—
923	C₄²	—	2	2	no	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	4	1	no	—
928	C₄²	—	4	1	no	—
929	C₄²	—	4	1	no	—
930	C₄²	—	4	1	no	—
931	C₄²	—	4	1	no	—
932	C₄²	—	4	2	no	—
933	C₄²	—	4	2	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
961	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
962	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
963	Q₈	—	4	4	no	—
964	D₄	—	2	8	no	—
965	D₄	—	4	8	no	—
966	D₄	—	4	8	no	—
967	D₄	—	4	4	no	—
968	D₄	—	4	4	no	—
969	D₄	—	8	4	no	—
970	D₄	—	8	4	no	—
971	D₄	—	8	4	no	—
972	D₄	—	8	4	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	8	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	4	4	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	—	4	8	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	—	8	4	no	—
1028	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1029	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1030	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1031	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1032	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1033	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1034	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1035	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
1036	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
1037	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
1067	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
1068	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
1069	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
1070	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
1071	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
1072	C₂²	#585×C₁₃₁	1	1	yes	characteristic
1073	C₄	—	2	2	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	#538×C₁₃₁	1	4	yes	—
1092	C₂	—	4	2	no	—
1093	C₂	—	4	2	no	—
1094	C₂	—	8	2	no	—
1095	C₂	—	8	2	no	—
1096	C₂	#3444×C₁₃₁	1	1	yes	characteristic
1097	C₂	C₂×#538×C₁₃₁	1	1	yes	characteristic
1098	C₂	#3460×C₁₃₁	1	1	yes	characteristic
1099	C₂	#3505×C₁₃₁	1	1	yes	characteristic
1100	C₂	#3508×C₁₃₁	1	1	yes	characteristic
1101	C₂	#3517×C₁₃₁	1	1	yes	characteristic
1102	C₂	#3519×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
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. #2861×C₁₃₁	C₂	semidirect
2. #2860×C₁₃₁	C₂	semidirect
3. #2856×C₁₃₁	C₂	semidirect
4. #2855×C₁₃₁	C₂	semidirect
5. #2648×C₁₃₁	C₂	semidirect
6. #2635×C₁₃₁	C₂	semidirect
7. #2595×C₁₃₁	C₂	semidirect
8. #2559×C₁₃₁	C₂	semidirect
9. #2511×C₁₃₁	C₂	semidirect
10. #2490×C₁₃₁	C₂	semidirect
11. #2467×C₁₃₁	C₂	semidirect
12. #2456×C₁₃₁	C₂	semidirect
13. #2445×C₁₃₁	C₂	semidirect
14. #2441×C₁₃₁	C₂	semidirect
15. #2431×C₁₃₁	C₂	semidirect
16. #2427×C₁₃₁	C₂	semidirect
17. #2414×C₁₃₁	C₂	semidirect
18. #2407×C₁₃₁	C₂	semidirect
19. #2335×C₁₃₁	C₂	semidirect
20. #2333×C₁₃₁	C₂	semidirect
21. C₄×#121×C₁₃₁	C₂	semidirect
22. #2297×C₁₃₁	C₂	semidirect
23. C₄²×D₄×C₁₃₁	C₂	semidirect
302. C₂²×C₄×C₁₃₁	#41	semidirect
338. C₄⋊C₄×C₁₃₁	#41	semidirect
551. #35038	C₁₃₁	direct (N × H)
552. C₁₃₁	#35038	direct (N × H)
553. #2861	C₂×C₁₃₁	semidirect
554. #2860	C₂×C₁₃₁	semidirect
555. #2856	C₂×C₁₃₁	semidirect
556. #2855	C₂×C₁₃₁	semidirect
557. #2648	C₂×C₁₃₁	semidirect
558. #2635	C₂×C₁₃₁	semidirect
559. #2595	C₂×C₁₃₁	semidirect
560. #2559	C₂×C₁₃₁	semidirect
561. #2511	C₂×C₁₃₁	semidirect
562. #2490	C₂×C₁₃₁	semidirect
563. #2467	C₂×C₁₃₁	semidirect
564. #2456	C₂×C₁₃₁	semidirect
565. #2445	C₂×C₁₃₁	semidirect
566. #2441	C₂×C₁₃₁	semidirect
567. #2431	C₂×C₁₃₁	semidirect
568. #2427	C₂×C₁₃₁	semidirect
569. #2414	C₂×C₁₃₁	semidirect
570. #2407	C₂×C₁₃₁	semidirect
571. #2335	C₂×C₁₃₁	semidirect
572. #2333	C₂×C₁₃₁	semidirect
573. C₄×#121	C₂×C₁₃₁	semidirect
574. #2297	C₂×C₁₃₁	semidirect
575. C₄²×D₄	C₂×C₁₃₁	semidirect
854. C₂²×C₄	#41×C₁₃₁	semidirect
890. C₄⋊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
#2861×C₁₃₁	2
#2860×C₁₃₁	2
#2856×C₁₃₁	2
#2855×C₁₃₁	2
#2648×C₁₃₁	2
#2635×C₁₃₁	2
#2595×C₁₃₁	2
#2559×C₁₃₁	2
#2511×C₁₃₁	2
#2490×C₁₃₁	2
#2467×C₁₃₁	2
#2456×C₁₃₁	2
#2445×C₁₃₁	2
#2441×C₁₃₁	2
#2431×C₁₃₁	2
#2427×C₁₃₁	2
#2414×C₁₃₁	2
#2407×C₁₃₁	2
#2335×C₁₃₁	2
#2333×C₁₃₁	2
C₄×#121×C₁₃₁	2
#2297×C₁₃₁	2
C₄²×D₄×C₁₃₁	2
#35038	131

Subgroups — C131×#35038 #45720922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#35038 #45720922