Subgroups — C₃₁×#34459 #21491218

Order 7936.

2060 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#552	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2378	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2370	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2368	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2359	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#2359	C₂	1	1	yes	maximal, characteristic
11	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2349	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2344	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2343	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2343	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2343	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2336	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2334	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2334	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2330	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#2322	C₂	1	1	yes	maximal, characteristic
25	C₃₁×#2320	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#2318	C₂	1	1	yes	maximal, characteristic
27	C₃₁×#2317	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#2314	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₃₁×#123	C₂	1	1	yes	maximal, characteristic
30	C₃₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₃₁×#387	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#552	C₄	1	16	yes	complemented
33	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
49	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
54	C₃₁×#391	C₂²	1	1	yes	characteristic
55	C₃₁×#391	C₂²	1	1	yes	characteristic
56	C₃₁×#391	C₂²	1	1	yes	characteristic
57	C₃₁×#391	C₂²	1	1	yes	characteristic
58	C₃₁×#389	C₂²	1	1	yes	characteristic
59	C₃₁×#389	C₂²	1	1	yes	characteristic
60	C₃₁×#389	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	1	yes	characteristic
62	C₃₁×#389	C₂²	1	1	yes	characteristic
63	C₃₁×#389	C₂²	1	1	yes	characteristic
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	1	yes	characteristic
66	C₃₁×#389	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	1	yes	characteristic
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	1	yes	characteristic
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#389	C₂²	1	1	yes	characteristic
73	C₃₁×#389	C₂²	1	1	yes	characteristic
74	C₃₁×#389	C₂²	1	1	yes	characteristic
75	C₃₁×#389	C₂²	1	1	yes	characteristic
76	C₃₁×#388	C₂²	1	1	yes	characteristic
77	C₃₁×#388	C₂²	1	1	yes	characteristic
78	C₃₁×#388	C₂²	1	1	yes	characteristic
79	C₃₁×#388	C₂²	1	1	yes	characteristic
80	C₃₁×#388	C₂²	1	1	yes	characteristic
81	C₃₁×#388	C₂²	1	1	yes	characteristic
82	C₃₁×#388	C₂²	1	1	yes	characteristic
83	C₃₁×#388	C₂²	1	1	yes	characteristic
84	C₃₁×#388	C₂²	1	1	yes	characteristic
85	C₃₁×#388	C₂²	1	1	yes	characteristic
86	C₃₁×#387	C₂²	1	1	yes	characteristic
87	C₃₁×#387	C₂²	1	1	yes	characteristic
88	C₃₁×#387	C₂²	1	1	yes	characteristic
89	C₃₁×#387	C₂²	1	1	yes	characteristic
90	C₃₁×#387	C₂²	1	1	yes	characteristic
91	C₃₁×#387	C₂²	1	1	yes	characteristic
92	C₃₁×#387	C₂²	1	1	yes	characteristic
93	C₃₁×#387	C₂²	1	1	yes	characteristic
94	C₃₁×#387	C₂²	1	1	yes	characteristic
95	C₃₁×#387	C₂²	1	1	yes	characteristic
96	C₃₁×#387	C₂²	1	1	yes	characteristic
97	C₃₁×#387	C₂²	1	1	yes	characteristic
98	C₃₁×#387	C₂²	1	1	yes	characteristic
99	C₃₁×#387	C₂²	1	1	yes	characteristic
100	C₃₁×#387	C₂²	1	1	yes	characteristic
101	C₃₁×#387	C₂²	1	1	yes	characteristic
102	C₃₁×#387	C₂²	1	1	yes	characteristic
103	C₃₁×#387	C₂²	1	1	yes	characteristic
104	C₃₁×#387	C₂²	1	1	yes	characteristic
105	C₃₁×#387	C₂²	1	1	yes	characteristic
106	C₃₁×#387	C₂²	1	1	yes	characteristic
107	C₃₁×#387	C₂²	1	1	yes	characteristic
108	C₃₁×#387	C₂²	1	1	yes	characteristic
109	C₃₁×#387	C₂²	1	1	yes	characteristic
110	C₃₁×#387	C₂²	1	1	yes	characteristic
111	C₃₁×#387	C₂²	1	1	yes	characteristic
112	C₃₁×#387	C₂²	1	1	yes	characteristic
113	C₃₁×#387	C₂²	1	1	yes	characteristic
114	C₃₁×#387	C₂²	1	1	yes	characteristic
115	C₃₁×#387	C₂²	1	1	yes	characteristic
116	C₃₁×#387	C₂²	1	1	yes	characteristic
117	C₃₁×#387	C₂²	1	1	yes	characteristic
118	C₃₁×#387	C₂²	1	1	yes	characteristic
119	C₃₁×#387	C₂²	1	1	yes	characteristic
120	C₃₁×#387	C₂²	1	1	yes	characteristic
121	C₃₁×#387	C₂²	1	1	yes	characteristic
122	C₃₁×#387	C₂²	1	1	yes	characteristic
123	C₃₁×#387	C₂²	1	1	yes	characteristic
124	C₃₁×#386	C₂²	1	1	yes	characteristic
125	C₃₁×#386	C₂²	1	1	yes	characteristic
126	C₃₁×#385	C₂²	1	1	yes	characteristic
127	C₃₁×#385	C₂²	1	1	yes	characteristic
128	C₃₁×#385	C₂²	1	1	yes	characteristic
129	C₃₁×#385	C₂²	1	1	yes	characteristic
130	C₃₁×#385	C₂²	1	1	yes	characteristic
131	C₃₁×#385	C₂²	1	1	yes	characteristic
132	C₃₁×#385	C₂²	1	1	yes	characteristic
133	C₃₁×#385	C₂²	1	1	yes	characteristic
134	C₃₁×#385	C₂²	1	1	yes	characteristic
135	C₃₁×#385	C₂²	1	1	yes	characteristic
136	C₃₁×#385	C₂²	1	1	yes	characteristic
137	C₃₁×#385	C₂²	1	1	yes	characteristic
138	C₃₁×#385	C₂²	1	1	yes	characteristic
139	C₃₁×#385	C₂²	1	1	yes	characteristic
140	C₃₁×#384	C₂²	1	1	yes	characteristic
141	C₃₁×#384	C₂²	1	1	yes	characteristic
142	C₃₁×#383	C₂²	1	1	yes	characteristic
143	C₃₁×#383	C₂²	1	1	yes	characteristic
144	C₃₁×#383	C₂²	1	1	yes	characteristic
145	C₃₁×#382	C₂²	1	1	yes	characteristic
146	C₃₁×#382	C₂²	1	1	yes	characteristic
147	C₃₁×#382	C₂²	1	1	yes	characteristic
148	C₃₁×#382	C₂²	1	1	yes	characteristic
149	C₃₁×#382	C₂²	1	1	yes	characteristic
150	C₃₁×#382	C₂²	1	1	yes	characteristic
151	C₃₁×#381	C₂²	1	1	yes	characteristic
152	C₃₁×#381	C₂²	1	1	yes	characteristic
153	C₃₁×#381	C₂²	1	1	yes	characteristic
154	C₃₁×#380	C₂²	1	1	yes	characteristic
155	C₃₁×#380	C₂²	1	1	yes	characteristic
156	C₃₁×#380	C₂²	1	1	yes	characteristic
157	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
158	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
159	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
160	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
161	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
162	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
170	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
171	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
181	C₃₁×#376	C₂²	1	1	yes	characteristic
182	C₃₁×#376	C₂²	1	1	yes	characteristic
183	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
184	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
185	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
186	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
187	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
188	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
189	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
200	C₃₁×#126	C₂×C₄	1	8	yes	complemented
201	C₃₁×#126	C₂×C₄	1	8	yes	complemented
202	C₃₁×#125	C₂×C₄	1	8	yes	complemented
203	C₃₁×#125	C₂×C₄	1	8	yes	complemented
204	C₃₁×#125	C₂×C₄	1	8	yes	complemented
205	C₃₁×#123	C₂×C₄	1	8	yes	—
206	C₃₁×#123	C₂×C₄	1	8	yes	—
207	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
208	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
209	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
210	C₄×D₄×C₃₁	—	4	2	no	—
211	C₄×D₄×C₃₁	—	4	2	no	—
212	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
213	C₃₁×#117	—	4	2	no	—
214	C₃₁×#117	—	4	2	no	—
215	C₃₁×#117	C₂×C₄	1	8	yes	complemented
216	C₃₁×#117	C₂×C₄	1	8	yes	complemented
217	C₃₁×#117	C₂×C₄	1	8	yes	complemented
218	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
219	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
220	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
282	C₂×C₄²×C₃₁	—	4	2	no	—
283	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
285	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
287	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
288	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
308	C₃₁×#95	C₂³	1	1	yes	characteristic
309	C₃₁×#95	C₂³	1	1	yes	characteristic
310	C₃₁×#95	C₂³	1	1	yes	characteristic
311	C₃₁×#95	C₂³	1	1	yes	characteristic
312	C₃₁×#95	C₂³	1	1	yes	characteristic
313	C₃₁×#95	C₂³	1	1	yes	characteristic
314	C₃₁×#95	C₂³	1	1	yes	characteristic
315	C₃₁×#95	C₂³	1	1	yes	characteristic
316	C₃₁×#95	C₂³	1	1	yes	characteristic
317	C₃₁×#95	C₂³	1	1	yes	characteristic
318	C₃₁×#95	C₂³	1	1	yes	characteristic
319	C₃₁×#95	C₂³	1	1	yes	characteristic
320	C₃₁×#95	C₂³	1	1	yes	characteristic
321	C₃₁×#95	C₂³	1	1	yes	characteristic
322	C₃₁×#95	C₂³	1	1	yes	characteristic
323	C₃₁×#95	C₂³	1	1	yes	characteristic
324	C₃₁×#95	C₂³	1	1	yes	characteristic
325	C₃₁×#95	C₂³	1	1	yes	characteristic
326	C₃₁×#95	C₂³	1	1	yes	characteristic
327	C₃₁×#95	C₂³	1	1	yes	characteristic
328	C₃₁×#95	C₂³	1	1	yes	characteristic
329	C₃₁×#95	C₂³	1	1	yes	characteristic
330	C₃₁×#95	C₂³	1	1	yes	characteristic
331	C₃₁×#95	C₂³	1	1	yes	characteristic
332	C₃₁×#95	C₂³	1	1	yes	characteristic
333	C₃₁×#95	C₂³	1	1	yes	characteristic
334	C₃₁×#95	C₂³	1	1	yes	characteristic
335	C₃₁×#95	C₂³	1	1	yes	characteristic
336	C₃₁×#95	C₂³	1	1	yes	characteristic
337	C₃₁×#95	C₂³	1	1	yes	characteristic
338	C₃₁×#95	C₂³	1	1	yes	characteristic
339	C₃₁×#95	C₂³	1	1	yes	characteristic
340	C₃₁×#95	C₂³	1	1	yes	characteristic
341	C₃₁×#95	C₂³	1	1	yes	characteristic
342	C₃₁×#95	C₂³	1	1	yes	characteristic
343	C₃₁×#95	C₂³	1	1	yes	characteristic
344	C₃₁×#95	C₂³	1	1	yes	characteristic
345	C₃₁×#95	C₂³	1	1	yes	characteristic
346	C₃₁×#95	C₂³	1	1	yes	characteristic
347	C₃₁×#95	C₂³	1	1	yes	characteristic
348	C₃₁×#95	C₂³	1	1	yes	characteristic
349	C₃₁×#95	C₂³	1	1	yes	characteristic
350	C₃₁×#95	C₂³	1	1	yes	characteristic
351	C₃₁×#95	C₂³	1	1	yes	characteristic
352	C₃₁×#95	C₂³	1	1	yes	characteristic
353	C₃₁×#95	C₂³	1	1	yes	characteristic
354	C₃₁×#95	C₂³	1	1	yes	characteristic
355	C₃₁×#95	C₂³	1	1	yes	characteristic
356	C₃₁×#95	C₂³	1	1	yes	characteristic
357	C₃₁×#95	C₂³	1	1	yes	characteristic
358	C₃₁×#95	C₂³	1	1	yes	characteristic
359	C₃₁×#95	C₂³	1	1	yes	characteristic
360	C₃₁×#95	C₂³	1	1	yes	characteristic
361	C₃₁×#95	C₂³	1	1	yes	characteristic
362	C₃₁×#95	C₂³	1	1	yes	characteristic
363	C₃₁×#95	C₂³	1	1	yes	characteristic
364	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×Q₈×C₃₁	—	4	1	no	—
367	C₂×Q₈×C₃₁	—	4	1	no	—
368	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
369	C₂×D₄×C₃₁	—	2	2	no	—
370	C₂×D₄×C₃₁	—	2	2	no	—
371	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
372	C₂²×C₄×C₃₁	—	2	2	no	—
373	C₂²×C₄×C₃₁	—	2	2	no	—
374	C₂²×C₄×C₃₁	—	2	2	no	—
375	C₂²×C₄×C₃₁	—	2	2	no	—
376	C₂²×C₄×C₃₁	—	2	2	no	—
377	C₂²×C₄×C₃₁	—	2	2	no	—
378	C₂²×C₄×C₃₁	—	2	2	no	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	—	2	2	no	—
381	C₂²×C₄×C₃₁	—	2	2	no	—
382	C₂²×C₄×C₃₁	—	4	1	no	—
383	C₂²×C₄×C₃₁	—	4	1	no	—
384	C₂²×C₄×C₃₁	—	4	1	no	—
385	C₂²×C₄×C₃₁	—	4	1	no	—
386	C₂²×C₄×C₃₁	—	4	1	no	—
387	C₂²×C₄×C₃₁	—	4	1	no	—
388	C₂²×C₄×C₃₁	—	4	1	no	—
389	C₂²×C₄×C₃₁	—	4	1	no	—
390	C₂²×C₄×C₃₁	—	4	1	no	—
391	C₂²×C₄×C₃₁	—	4	1	no	—
392	C₂²×C₄×C₃₁	—	4	1	no	—
393	C₂²×C₄×C₃₁	—	4	1	no	—
394	C₂²×C₄×C₃₁	—	4	1	no	—
395	C₂²×C₄×C₃₁	—	4	1	no	—
396	C₂²×C₄×C₃₁	—	4	1	no	—
397	C₂²×C₄×C₃₁	—	4	1	no	—
398	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
399	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
400	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
401	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
402	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₃₁	—	2	2	no	—
432	C₄⋊C₄×C₃₁	—	2	2	no	—
433	C₄⋊C₄×C₃₁	—	4	1	no	—
434	C₄⋊C₄×C₃₁	—	4	1	no	—
435	C₄⋊C₄×C₃₁	—	4	1	no	—
436	C₄⋊C₄×C₃₁	—	4	1	no	—
437	C₄⋊C₄×C₃₁	—	4	1	no	—
438	C₄⋊C₄×C₃₁	—	4	1	no	—
439	C₄⋊C₄×C₃₁	—	4	1	no	—
440	C₄⋊C₄×C₃₁	—	4	1	no	—
441	C₄⋊C₄×C₃₁	—	4	1	no	—
442	C₄⋊C₄×C₃₁	—	4	1	no	—
443	C₄⋊C₄×C₃₁	—	4	1	no	—
444	C₄⋊C₄×C₃₁	—	4	1	no	—
445	C₄⋊C₄×C₃₁	—	4	1	no	—
446	C₄⋊C₄×C₃₁	—	4	1	no	—
447	C₄⋊C₄×C₃₁	—	4	1	no	—
448	C₄⋊C₄×C₃₁	—	4	1	no	—
449	C₄⋊C₄×C₃₁	—	4	1	no	—
450	C₄⋊C₄×C₃₁	—	4	1	no	—
451	C₄⋊C₄×C₃₁	—	4	1	no	—
452	C₄⋊C₄×C₃₁	—	4	1	no	—
453	C₄⋊C₄×C₃₁	—	4	1	no	—
454	C₄⋊C₄×C₃₁	—	4	1	no	—
455	C₄⋊C₄×C₃₁	—	4	1	no	—
456	C₄⋊C₄×C₃₁	—	4	1	no	—
457	C₄⋊C₄×C₃₁	—	4	1	no	—
458	C₄⋊C₄×C₃₁	—	4	1	no	—
459	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
460	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
461	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
462	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
463	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
464	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
465	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
466	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
467	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
468	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
469	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
470	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
471	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
472	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
473	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
474	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
475	C₂²⋊C₄×C₃₁	—	2	2	no	—
476	C₂²⋊C₄×C₃₁	—	2	2	no	—
477	C₂²⋊C₄×C₃₁	—	2	2	no	—
478	C₂²⋊C₄×C₃₁	—	2	2	no	—
479	C₂²⋊C₄×C₃₁	—	4	1	no	—
480	C₂²⋊C₄×C₃₁	—	4	1	no	—
481	C₂²⋊C₄×C₃₁	—	4	1	no	—
482	C₂²⋊C₄×C₃₁	—	4	1	no	—
483	C₂²⋊C₄×C₃₁	—	4	1	no	—
484	C₂²⋊C₄×C₃₁	—	4	1	no	—
485	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
486	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
487	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
488	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
489	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
490	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
491	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
492	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
493	C₄²×C₃₁	—	2	2	no	—
494	C₄²×C₃₁	—	4	1	no	—
495	C₄²×C₃₁	—	4	1	no	—
496	C₄²×C₃₁	—	4	1	no	—
497	C₄²×C₃₁	—	4	1	no	—
498	C₄²×C₃₁	—	4	1	no	—
499	C₄²×C₃₁	—	4	1	no	—
500	C₄²×C₃₁	—	4	1	no	—
501	C₄²×C₃₁	—	4	1	no	—
502	C₄²×C₃₁	—	4	1	no	—
503	C₄²×C₃₁	—	4	1	no	—
504	C₄²×C₃₁	—	4	1	no	—
505	C₄²×C₃₁	—	4	1	no	—
506	C₄²×C₃₁	—	4	1	no	—
507	C₄²×C₃₁	—	4	1	no	—
508	C₄²×C₃₁	—	4	1	no	—
509	C₄²×C₃₁	—	4	1	no	—
510	C₄²×C₃₁	—	4	1	no	—
511	C₄²×C₃₁	—	4	1	no	—
512	C₄²×C₃₁	—	4	1	no	—
513	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
514	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
515	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
516	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
517	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
518	#34459	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
519	C₂³×C₃₁	—	2	1	no	—
520	C₂³×C₃₁	—	2	1	no	—
521	C₂³×C₃₁	—	2	1	no	—
522	C₂³×C₃₁	—	2	1	no	—
523	C₂³×C₃₁	—	2	1	no	—
524	C₂³×C₃₁	—	2	1	no	—
525	C₂³×C₃₁	—	2	1	no	—
526	C₂³×C₃₁	—	2	1	no	—
527	C₂³×C₃₁	—	2	1	no	—
528	C₂³×C₃₁	—	2	1	no	—
529	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
530	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
531	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
532	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
533	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
534	Q₈×C₃₁	—	4	4	no	—
535	D₄×C₃₁	—	2	8	no	—
536	C₂×C₄×C₃₁	—	2	8	no	—
537	C₂×C₄×C₃₁	—	2	8	no	—
538	C₂×C₄×C₃₁	—	2	1	no	—
539	C₂×C₄×C₃₁	—	2	1	no	—
540	C₂×C₄×C₃₁	—	2	1	no	—
541	C₂×C₄×C₃₁	—	2	1	no	—
542	C₂×C₄×C₃₁	—	2	1	no	—
543	C₂×C₄×C₃₁	—	2	1	no	—
544	C₂×C₄×C₃₁	—	2	1	no	—
545	C₂×C₄×C₃₁	—	2	1	no	—
546	C₂×C₄×C₃₁	—	2	1	no	—
547	C₂×C₄×C₃₁	—	2	1	no	—
548	C₂×C₄×C₃₁	—	2	1	no	—
549	C₂×C₄×C₃₁	—	2	1	no	—
550	C₂×C₄×C₃₁	—	2	1	no	—
551	C₂×C₄×C₃₁	—	2	1	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	1	no	—
554	C₂×C₄×C₃₁	—	2	1	no	—
555	C₂×C₄×C₃₁	—	2	1	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	2	1	no	—
559	C₂×C₄×C₃₁	—	2	1	no	—
560	C₂×C₄×C₃₁	—	2	1	no	—
561	C₂×C₄×C₃₁	—	2	1	no	—
562	C₂×C₄×C₃₁	—	2	1	no	—
563	C₂×C₄×C₃₁	—	2	1	no	—
564	C₂×C₄×C₃₁	—	2	1	no	—
565	C₂×C₄×C₃₁	—	2	1	no	—
566	C₂×C₄×C₃₁	—	2	1	no	—
567	C₂×C₄×C₃₁	—	2	1	no	—
568	C₂×C₄×C₃₁	—	2	1	no	—
569	C₂×C₄×C₃₁	—	2	1	no	—
570	C₂×C₄×C₃₁	—	2	1	no	—
571	C₂×C₄×C₃₁	—	2	1	no	—
572	C₂×C₄×C₃₁	—	2	1	no	—
573	C₂×C₄×C₃₁	—	2	1	no	—
574	C₂×C₄×C₃₁	—	2	1	no	—
575	C₂×C₄×C₃₁	—	2	1	no	—
576	C₂×C₄×C₃₁	—	2	1	no	—
577	C₂×C₄×C₃₁	—	2	1	no	—
578	C₂×C₄×C₃₁	—	2	1	no	—
579	C₂×C₄×C₃₁	—	2	1	no	—
580	C₂×C₄×C₃₁	—	2	1	no	—
581	C₂×C₄×C₃₁	—	2	1	no	—
582	C₂×C₄×C₃₁	—	2	1	no	—
583	C₂×C₄×C₃₁	—	2	1	no	—
584	C₂×C₄×C₃₁	—	2	1	no	—
585	C₂×C₄×C₃₁	—	2	1	no	—
586	C₂×C₄×C₃₁	—	2	1	no	—
587	C₂×C₄×C₃₁	—	2	1	no	—
588	C₂×C₄×C₃₁	—	2	1	no	—
589	C₂×C₄×C₃₁	—	2	1	no	—
590	C₂×C₄×C₃₁	—	2	1	no	—
591	C₂×C₄×C₃₁	—	2	1	no	—
592	C₂×C₄×C₃₁	—	2	1	no	—
593	C₂×C₄×C₃₁	—	2	1	no	—
594	C₂×C₄×C₃₁	—	2	1	no	—
595	C₂×C₄×C₃₁	—	2	1	no	—
596	C₂×C₄×C₃₁	—	2	1	no	—
597	C₂×C₄×C₃₁	—	2	1	no	—
598	C₂×C₄×C₃₁	—	2	1	no	—
599	C₂×C₄×C₃₁	—	2	1	no	—
600	C₂×C₄×C₃₁	—	2	1	no	—
601	C₂×C₄×C₃₁	—	2	1	no	—
602	C₂×C₄×C₃₁	—	2	1	no	—
603	C₂×C₄×C₃₁	—	2	1	no	—
604	C₂×C₄×C₃₁	—	2	1	no	—
605	C₂×C₄×C₃₁	—	2	1	no	—
606	C₂×C₄×C₃₁	—	2	1	no	—
607	C₂×C₄×C₃₁	—	2	1	no	—
608	C₂×C₄×C₃₁	—	2	1	no	—
609	C₂×C₄×C₃₁	—	2	1	no	—
610	C₂×C₄×C₃₁	—	2	1	no	—
611	C₂×C₄×C₃₁	—	4	4	no	—
612	C₂×C₄×C₃₁	—	4	4	no	—
613	C₂×C₄×C₃₁	—	4	4	no	—
614	C₂×C₄×C₃₁	—	4	4	no	—
615	C₂×C₄×C₃₁	—	8	2	no	—
616	C₂×C₄×C₃₁	—	8	2	no	—
617	C₂×C₄×C₃₁	—	8	2	no	—
618	C₂×C₄×C₃₁	—	8	2	no	—
619	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
620	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
621	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
622	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
623	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
624	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
625	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
626	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
627	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
628	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
629	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
630	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
631	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
632	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
633	C₂×#552	C₂×C₃₁	1	1	yes	characteristic
634	#2383	C₂×C₃₁	1	1	yes	characteristic, complemented
635	#2382	C₂×C₃₁	1	1	yes	characteristic, complemented
636	#2382	C₂×C₃₁	1	1	yes	characteristic, complemented
637	#2378	C₂×C₃₁	1	1	yes	characteristic, complemented
638	#2373	C₂×C₃₁	1	1	yes	characteristic, complemented
639	#2370	C₂×C₃₁	1	1	yes	characteristic, complemented
640	#2368	C₂×C₃₁	1	1	yes	characteristic, complemented
641	#2359	C₂×C₃₁	1	1	yes	characteristic
642	#2359	C₂×C₃₁	1	1	yes	characteristic
643	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
644	#2349	C₂×C₃₁	1	1	yes	characteristic
645	#2344	C₂×C₃₁	1	1	yes	characteristic, complemented
646	#2343	C₂×C₃₁	1	1	yes	characteristic, complemented
647	#2343	C₂×C₃₁	1	1	yes	characteristic, complemented
648	#2343	C₂×C₃₁	1	1	yes	characteristic, complemented
649	#2336	C₂×C₃₁	1	1	yes	characteristic, complemented
650	#2336	C₂×C₃₁	1	1	yes	characteristic, complemented
651	#2334	C₂×C₃₁	1	1	yes	characteristic, complemented
652	#2334	C₂×C₃₁	1	1	yes	characteristic, complemented
653	#2330	C₂×C₃₁	1	1	yes	characteristic, complemented
654	#2329	C₂×C₃₁	1	1	yes	characteristic, complemented
655	#2329	C₂×C₃₁	1	1	yes	characteristic, complemented
656	#2322	C₂×C₃₁	1	1	yes	characteristic
657	#2320	C₂×C₃₁	1	1	yes	characteristic, complemented
658	#2318	C₂×C₃₁	1	1	yes	characteristic
659	#2317	C₂×C₃₁	1	1	yes	characteristic, complemented
660	#2314	C₂×C₃₁	1	1	yes	characteristic, complemented
661	C₄×#123	C₂×C₃₁	1	1	yes	characteristic
662	#2296	C₂×C₃₁	1	1	yes	characteristic, complemented
663	C₂×#387	C₂×C₃₁	1	1	yes	characteristic, complemented
664	C₂²×C₃₁	—	2	2	no	—
665	C₂²×C₃₁	—	2	2	no	—
666	C₂²×C₃₁	—	2	2	no	—
667	C₂²×C₃₁	—	2	2	no	—
668	C₂²×C₃₁	—	2	2	no	—
669	C₂²×C₃₁	—	2	2	no	—
670	C₂²×C₃₁	—	2	2	no	—
671	C₂²×C₃₁	—	2	2	no	—
672	C₂²×C₃₁	—	2	2	no	—
673	C₂²×C₃₁	—	4	1	no	—
674	C₂²×C₃₁	—	4	1	no	—
675	C₂²×C₃₁	—	4	1	no	—
676	C₂²×C₃₁	—	4	1	no	—
677	C₂²×C₃₁	#520	1	4	yes	—
678	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
679	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
681	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
682	C₂²×C₃₁	#585	1	1	yes	characteristic
683	C₂²×C₃₁	#585	1	1	yes	characteristic
684	C₂²×C₃₁	#585	1	1	yes	characteristic
685	C₄×C₃₁	—	2	2	no	—
686	C₄×C₃₁	—	2	2	no	—
687	C₄×C₃₁	—	2	2	no	—
688	C₄×C₃₁	—	2	2	no	—
689	C₄×C₃₁	—	2	2	no	—
690	C₄×C₃₁	—	2	2	no	—
691	C₄×C₃₁	—	2	2	no	—
692	C₄×C₃₁	—	2	2	no	—
693	C₄×C₃₁	—	2	2	no	—
694	C₄×C₃₁	—	2	2	no	—
695	C₄×C₃₁	—	2	2	no	—
696	C₄×C₃₁	—	2	2	no	—
697	C₄×C₃₁	—	2	2	no	—
698	C₄×C₃₁	—	2	2	no	—
699	C₄×C₃₁	—	4	1	no	—
700	C₄×C₃₁	—	4	1	no	—
701	C₄×C₃₁	—	4	1	no	—
702	C₄×C₃₁	—	4	1	no	—
703	C₄×C₃₁	—	4	1	no	—
704	C₄×C₃₁	—	4	1	no	—
705	C₄×C₃₁	—	4	1	no	—
706	C₄×C₃₁	—	4	1	no	—
707	C₄×C₃₁	—	4	1	no	—
708	C₄×C₃₁	—	4	1	no	—
709	C₄×C₃₁	—	4	1	no	—
710	C₄×C₃₁	—	4	1	no	—
711	C₄×C₃₁	—	4	1	no	—
712	C₄×C₃₁	—	4	1	no	—
713	C₄×C₃₁	—	4	1	no	—
714	#552	C₄×C₃₁	1	16	yes	complemented
715	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
716	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
717	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
718	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
719	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
720	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
721	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
722	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
723	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
724	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
725	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
726	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
727	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
728	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
729	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
730	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
731	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
732	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
733	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
734	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
735	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
736	#391	C₂²×C₃₁	1	1	yes	characteristic
737	#391	C₂²×C₃₁	1	1	yes	characteristic
738	#391	C₂²×C₃₁	1	1	yes	characteristic
739	#391	C₂²×C₃₁	1	1	yes	characteristic
740	#389	C₂²×C₃₁	1	1	yes	characteristic
741	#389	C₂²×C₃₁	1	1	yes	characteristic
742	#389	C₂²×C₃₁	1	1	yes	characteristic
743	#389	C₂²×C₃₁	1	1	yes	characteristic
744	#389	C₂²×C₃₁	1	1	yes	characteristic
745	#389	C₂²×C₃₁	1	1	yes	characteristic
746	#389	C₂²×C₃₁	1	1	yes	characteristic
747	#389	C₂²×C₃₁	1	1	yes	characteristic
748	#389	C₂²×C₃₁	1	1	yes	characteristic
749	#389	C₂²×C₃₁	1	1	yes	characteristic
750	#389	C₂²×C₃₁	1	1	yes	characteristic
751	#389	C₂²×C₃₁	1	1	yes	characteristic
752	#389	C₂²×C₃₁	1	1	yes	characteristic
753	#389	C₂²×C₃₁	1	1	yes	characteristic
754	#389	C₂²×C₃₁	1	1	yes	characteristic
755	#389	C₂²×C₃₁	1	1	yes	characteristic
756	#389	C₂²×C₃₁	1	1	yes	characteristic
757	#389	C₂²×C₃₁	1	1	yes	characteristic
758	#388	C₂²×C₃₁	1	1	yes	characteristic
759	#388	C₂²×C₃₁	1	1	yes	characteristic
760	#388	C₂²×C₃₁	1	1	yes	characteristic
761	#388	C₂²×C₃₁	1	1	yes	characteristic
762	#388	C₂²×C₃₁	1	1	yes	characteristic
763	#388	C₂²×C₃₁	1	1	yes	characteristic
764	#388	C₂²×C₃₁	1	1	yes	characteristic
765	#388	C₂²×C₃₁	1	1	yes	characteristic
766	#388	C₂²×C₃₁	1	1	yes	characteristic
767	#388	C₂²×C₃₁	1	1	yes	characteristic
768	#387	C₂²×C₃₁	1	1	yes	characteristic
769	#387	C₂²×C₃₁	1	1	yes	characteristic
770	#387	C₂²×C₃₁	1	1	yes	characteristic
771	#387	C₂²×C₃₁	1	1	yes	characteristic
772	#387	C₂²×C₃₁	1	1	yes	characteristic
773	#387	C₂²×C₃₁	1	1	yes	characteristic
774	#387	C₂²×C₃₁	1	1	yes	characteristic
775	#387	C₂²×C₃₁	1	1	yes	characteristic
776	#387	C₂²×C₃₁	1	1	yes	characteristic
777	#387	C₂²×C₃₁	1	1	yes	characteristic
778	#387	C₂²×C₃₁	1	1	yes	characteristic
779	#387	C₂²×C₃₁	1	1	yes	characteristic
780	#387	C₂²×C₃₁	1	1	yes	characteristic
781	#387	C₂²×C₃₁	1	1	yes	characteristic
782	#387	C₂²×C₃₁	1	1	yes	characteristic
783	#387	C₂²×C₃₁	1	1	yes	characteristic
784	#387	C₂²×C₃₁	1	1	yes	characteristic
785	#387	C₂²×C₃₁	1	1	yes	characteristic
786	#387	C₂²×C₃₁	1	1	yes	characteristic
787	#387	C₂²×C₃₁	1	1	yes	characteristic
788	#387	C₂²×C₃₁	1	1	yes	characteristic
789	#387	C₂²×C₃₁	1	1	yes	characteristic
790	#387	C₂²×C₃₁	1	1	yes	characteristic
791	#387	C₂²×C₃₁	1	1	yes	characteristic
792	#387	C₂²×C₃₁	1	1	yes	characteristic
793	#387	C₂²×C₃₁	1	1	yes	characteristic
794	#387	C₂²×C₃₁	1	1	yes	characteristic
795	#387	C₂²×C₃₁	1	1	yes	characteristic
796	#387	C₂²×C₃₁	1	1	yes	characteristic
797	#387	C₂²×C₃₁	1	1	yes	characteristic
798	#387	C₂²×C₃₁	1	1	yes	characteristic
799	#387	C₂²×C₃₁	1	1	yes	characteristic
800	#387	C₂²×C₃₁	1	1	yes	characteristic
801	#387	C₂²×C₃₁	1	1	yes	characteristic
802	#387	C₂²×C₃₁	1	1	yes	characteristic
803	#387	C₂²×C₃₁	1	1	yes	characteristic
804	#387	C₂²×C₃₁	1	1	yes	characteristic
805	#387	C₂²×C₃₁	1	1	yes	characteristic
806	#386	C₂²×C₃₁	1	1	yes	characteristic
807	#386	C₂²×C₃₁	1	1	yes	characteristic
808	#385	C₂²×C₃₁	1	1	yes	characteristic
809	#385	C₂²×C₃₁	1	1	yes	characteristic
810	#385	C₂²×C₃₁	1	1	yes	characteristic
811	#385	C₂²×C₃₁	1	1	yes	characteristic
812	#385	C₂²×C₃₁	1	1	yes	characteristic
813	#385	C₂²×C₃₁	1	1	yes	characteristic
814	#385	C₂²×C₃₁	1	1	yes	characteristic
815	#385	C₂²×C₃₁	1	1	yes	characteristic
816	#385	C₂²×C₃₁	1	1	yes	characteristic
817	#385	C₂²×C₃₁	1	1	yes	characteristic
818	#385	C₂²×C₃₁	1	1	yes	characteristic
819	#385	C₂²×C₃₁	1	1	yes	characteristic
820	#385	C₂²×C₃₁	1	1	yes	characteristic
821	#385	C₂²×C₃₁	1	1	yes	characteristic
822	#384	C₂²×C₃₁	1	1	yes	characteristic
823	#384	C₂²×C₃₁	1	1	yes	characteristic
824	#383	C₂²×C₃₁	1	1	yes	characteristic
825	#383	C₂²×C₃₁	1	1	yes	characteristic
826	#383	C₂²×C₃₁	1	1	yes	characteristic
827	#382	C₂²×C₃₁	1	1	yes	characteristic
828	#382	C₂²×C₃₁	1	1	yes	characteristic
829	#382	C₂²×C₃₁	1	1	yes	characteristic
830	#382	C₂²×C₃₁	1	1	yes	characteristic
831	#382	C₂²×C₃₁	1	1	yes	characteristic
832	#382	C₂²×C₃₁	1	1	yes	characteristic
833	#381	C₂²×C₃₁	1	1	yes	characteristic
834	#381	C₂²×C₃₁	1	1	yes	characteristic
835	#381	C₂²×C₃₁	1	1	yes	characteristic
836	#380	C₂²×C₃₁	1	1	yes	characteristic
837	#380	C₂²×C₃₁	1	1	yes	characteristic
838	#380	C₂²×C₃₁	1	1	yes	characteristic
839	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
840	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
841	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
842	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
843	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
844	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
845	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
846	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
847	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
848	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
849	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
850	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
851	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
852	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
853	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
854	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
855	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
856	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
857	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
858	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
859	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
860	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
861	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
862	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
863	#376	C₂²×C₃₁	1	1	yes	characteristic
864	#376	C₂²×C₃₁	1	1	yes	characteristic
865	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
866	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
867	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
868	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
869	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
870	C₂×C₃₁	—	2	4	no	—
871	C₂×C₃₁	—	4	2	no	—
872	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
873	C₂×C₃₁	#3428	1	1	yes	characteristic
874	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
875	C₂×C₃₁	#3533	1	1	yes	characteristic
876	C₂×C₃₁	#3535	1	1	yes	characteristic
877	C₂×C₃₁	#3563	1	1	yes	characteristic
878	C₂×C₃₁	#3564	1	1	yes	characteristic
879	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
880	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
881	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
882	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
883	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
884	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
885	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
886	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
887	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
888	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
889	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
890	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
891	#126	C₂×C₄×C₃₁	1	8	yes	complemented
892	#126	C₂×C₄×C₃₁	1	8	yes	complemented
893	#125	C₂×C₄×C₃₁	1	8	yes	complemented
894	#125	C₂×C₄×C₃₁	1	8	yes	complemented
895	#125	C₂×C₄×C₃₁	1	8	yes	complemented
896	#123	C₂×C₄×C₃₁	1	8	yes	—
897	#123	C₂×C₄×C₃₁	1	8	yes	—
898	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
899	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
900	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
901	C₄×D₄	—	4	2	no	—
902	C₄×D₄	—	4	2	no	—
903	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
904	#117	—	4	2	no	—
905	#117	—	4	2	no	—
906	#117	C₂×C₄×C₃₁	1	8	yes	complemented
907	#117	C₂×C₄×C₃₁	1	8	yes	complemented
908	#117	C₂×C₄×C₃₁	1	8	yes	complemented
909	C₂×C₄⋊C₄	—	4	2	no	—
910	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
911	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
912	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
913	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
914	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
921	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
924	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
925	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
926	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
927	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
928	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
929	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
930	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
934	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
935	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
936	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
937	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
938	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
953	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
954	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
955	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
956	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
957	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
958	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
959	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
960	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
961	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
962	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
963	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
964	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
966	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
967	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
968	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
970	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
971	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
972	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
973	C₂×C₄²	—	4	2	no	—
974	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
975	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
976	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
977	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
978	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
979	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
980	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
981	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
982	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
983	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
984	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
985	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
986	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
987	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
988	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
989	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
990	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
991	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
992	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
993	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
994	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
995	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
996	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
997	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
998	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
999	#95	C₂³×C₃₁	1	1	yes	characteristic
1000	#95	C₂³×C₃₁	1	1	yes	characteristic
1001	#95	C₂³×C₃₁	1	1	yes	characteristic
1002	#95	C₂³×C₃₁	1	1	yes	characteristic
1003	#95	C₂³×C₃₁	1	1	yes	characteristic
1004	#95	C₂³×C₃₁	1	1	yes	characteristic
1005	#95	C₂³×C₃₁	1	1	yes	characteristic
1006	#95	C₂³×C₃₁	1	1	yes	characteristic
1007	#95	C₂³×C₃₁	1	1	yes	characteristic
1008	#95	C₂³×C₃₁	1	1	yes	characteristic
1009	#95	C₂³×C₃₁	1	1	yes	characteristic
1010	#95	C₂³×C₃₁	1	1	yes	characteristic
1011	#95	C₂³×C₃₁	1	1	yes	characteristic
1012	#95	C₂³×C₃₁	1	1	yes	characteristic
1013	#95	C₂³×C₃₁	1	1	yes	characteristic
1014	#95	C₂³×C₃₁	1	1	yes	characteristic
1015	#95	C₂³×C₃₁	1	1	yes	characteristic
1016	#95	C₂³×C₃₁	1	1	yes	characteristic
1017	#95	C₂³×C₃₁	1	1	yes	characteristic
1018	#95	C₂³×C₃₁	1	1	yes	characteristic
1019	#95	C₂³×C₃₁	1	1	yes	characteristic
1020	#95	C₂³×C₃₁	1	1	yes	characteristic
1021	#95	C₂³×C₃₁	1	1	yes	characteristic
1022	#95	C₂³×C₃₁	1	1	yes	characteristic
1023	#95	C₂³×C₃₁	1	1	yes	characteristic
1024	#95	C₂³×C₃₁	1	1	yes	characteristic
1025	#95	C₂³×C₃₁	1	1	yes	characteristic
1026	#95	C₂³×C₃₁	1	1	yes	characteristic
1027	#95	C₂³×C₃₁	1	1	yes	characteristic
1028	#95	C₂³×C₃₁	1	1	yes	characteristic
1029	#95	C₂³×C₃₁	1	1	yes	characteristic
1030	#95	C₂³×C₃₁	1	1	yes	characteristic
1031	#95	C₂³×C₃₁	1	1	yes	characteristic
1032	#95	C₂³×C₃₁	1	1	yes	characteristic
1033	#95	C₂³×C₃₁	1	1	yes	characteristic
1034	#95	C₂³×C₃₁	1	1	yes	characteristic
1035	#95	C₂³×C₃₁	1	1	yes	characteristic
1036	#95	C₂³×C₃₁	1	1	yes	characteristic
1037	#95	C₂³×C₃₁	1	1	yes	characteristic
1038	#95	C₂³×C₃₁	1	1	yes	characteristic
1039	#95	C₂³×C₃₁	1	1	yes	characteristic
1040	#95	C₂³×C₃₁	1	1	yes	characteristic
1041	#95	C₂³×C₃₁	1	1	yes	characteristic
1042	#95	C₂³×C₃₁	1	1	yes	characteristic
1043	#95	C₂³×C₃₁	1	1	yes	characteristic
1044	#95	C₂³×C₃₁	1	1	yes	characteristic
1045	#95	C₂³×C₃₁	1	1	yes	characteristic
1046	#95	C₂³×C₃₁	1	1	yes	characteristic
1047	#95	C₂³×C₃₁	1	1	yes	characteristic
1048	#95	C₂³×C₃₁	1	1	yes	characteristic
1049	#95	C₂³×C₃₁	1	1	yes	characteristic
1050	#95	C₂³×C₃₁	1	1	yes	characteristic
1051	#95	C₂³×C₃₁	1	1	yes	characteristic
1052	#95	C₂³×C₃₁	1	1	yes	characteristic
1053	#95	C₂³×C₃₁	1	1	yes	characteristic
1054	#95	C₂³×C₃₁	1	1	yes	characteristic
1055	C₃₁	#34459	1	1	yes	characteristic, direct product factor, Sylow
1056	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1057	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1058	C₂×Q₈	—	4	1	no	—
1059	C₂×Q₈	—	4	1	no	—
1060	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
1061	C₂×D₄	—	2	2	no	—
1062	C₂×D₄	—	2	2	no	—
1063	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
1064	C₂²×C₄	—	2	2	no	—
1065	C₂²×C₄	—	2	2	no	—
1066	C₂²×C₄	—	2	2	no	—
1067	C₂²×C₄	—	2	2	no	—
1068	C₂²×C₄	—	2	2	no	—
1069	C₂²×C₄	—	2	2	no	—
1070	C₂²×C₄	—	2	2	no	—
1071	C₂²×C₄	—	2	2	no	—
1072	C₂²×C₄	—	2	2	no	—
1073	C₂²×C₄	—	2	2	no	—
1074	C₂²×C₄	—	4	1	no	—
1075	C₂²×C₄	—	4	1	no	—
1076	C₂²×C₄	—	4	1	no	—
1077	C₂²×C₄	—	4	1	no	—
1078	C₂²×C₄	—	4	1	no	—
1079	C₂²×C₄	—	4	1	no	—
1080	C₂²×C₄	—	4	1	no	—
1081	C₂²×C₄	—	4	1	no	—
1082	C₂²×C₄	—	4	1	no	—
1083	C₂²×C₄	—	4	1	no	—
1084	C₂²×C₄	—	4	1	no	—
1085	C₂²×C₄	—	4	1	no	—
1086	C₂²×C₄	—	4	1	no	—
1087	C₂²×C₄	—	4	1	no	—
1088	C₂²×C₄	—	4	1	no	—
1089	C₂²×C₄	—	4	1	no	—
1090	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
1091	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
1092	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
1093	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
1094	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1095	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1096	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1097	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1098	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1099	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1100	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1101	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1102	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1103	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1104	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1105	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1106	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1107	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1108	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1109	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1110	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1111	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1112	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1113	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1114	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1115	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1116	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1117	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1118	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1119	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1120	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1121	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1122	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1123	C₄⋊C₄	—	2	2	no	—
1124	C₄⋊C₄	—	2	2	no	—
1125	C₄⋊C₄	—	4	1	no	—
1126	C₄⋊C₄	—	4	1	no	—
1127	C₄⋊C₄	—	4	1	no	—
1128	C₄⋊C₄	—	4	1	no	—
1129	C₄⋊C₄	—	4	1	no	—
1130	C₄⋊C₄	—	4	1	no	—
1131	C₄⋊C₄	—	4	1	no	—
1132	C₄⋊C₄	—	4	1	no	—
1133	C₄⋊C₄	—	4	1	no	—
1134	C₄⋊C₄	—	4	1	no	—
1135	C₄⋊C₄	—	4	1	no	—
1136	C₄⋊C₄	—	4	1	no	—
1137	C₄⋊C₄	—	4	1	no	—
1138	C₄⋊C₄	—	4	1	no	—
1139	C₄⋊C₄	—	4	1	no	—
1140	C₄⋊C₄	—	4	1	no	—
1141	C₄⋊C₄	—	4	1	no	—
1142	C₄⋊C₄	—	4	1	no	—
1143	C₄⋊C₄	—	4	1	no	—
1144	C₄⋊C₄	—	4	1	no	—
1145	C₄⋊C₄	—	4	1	no	—
1146	C₄⋊C₄	—	4	1	no	—
1147	C₄⋊C₄	—	4	1	no	—
1148	C₄⋊C₄	—	4	1	no	—
1149	C₄⋊C₄	—	4	1	no	—
1150	C₄⋊C₄	—	4	1	no	—
1151	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1152	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1153	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1154	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1155	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1156	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1157	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1158	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1159	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1160	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1161	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1162	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1163	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1164	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1165	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1166	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1167	C₂²⋊C₄	—	2	2	no	—
1168	C₂²⋊C₄	—	2	2	no	—
1169	C₂²⋊C₄	—	2	2	no	—
1170	C₂²⋊C₄	—	2	2	no	—
1171	C₂²⋊C₄	—	4	1	no	—
1172	C₂²⋊C₄	—	4	1	no	—
1173	C₂²⋊C₄	—	4	1	no	—
1174	C₂²⋊C₄	—	4	1	no	—
1175	C₂²⋊C₄	—	4	1	no	—
1176	C₂²⋊C₄	—	4	1	no	—
1177	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1178	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1179	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1180	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1181	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1182	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1183	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1184	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1185	C₄²	—	2	2	no	—
1186	C₄²	—	4	1	no	—
1187	C₄²	—	4	1	no	—
1188	C₄²	—	4	1	no	—
1189	C₄²	—	4	1	no	—
1190	C₄²	—	4	1	no	—
1191	C₄²	—	4	1	no	—
1192	C₄²	—	4	1	no	—
1193	C₄²	—	4	1	no	—
1194	C₄²	—	4	1	no	—
1195	C₄²	—	4	1	no	—
1196	C₄²	—	4	1	no	—
1197	C₄²	—	4	1	no	—
1198	C₄²	—	4	1	no	—
1199	C₄²	—	4	1	no	—
1200	C₄²	—	4	1	no	—
1201	C₄²	—	4	1	no	—
1202	C₄²	—	4	1	no	—
1203	C₄²	—	4	1	no	—
1204	C₄²	—	4	1	no	—
1205	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
1206	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
1207	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
1208	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
1209	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
1210	C₂³	—	2	1	no	—
1211	C₂³	—	2	1	no	—
1212	C₂³	—	2	1	no	—
1213	C₂³	—	2	1	no	—
1214	C₂³	—	2	1	no	—
1215	C₂³	—	2	1	no	—
1216	C₂³	—	2	1	no	—
1217	C₂³	—	2	1	no	—
1218	C₂³	—	2	1	no	—
1219	C₂³	—	2	1	no	—
1220	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
1221	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
1222	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
1223	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
1224	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1225	Q₈	—	4	4	no	—
1226	D₄	—	2	8	no	—
1227	C₂×C₄	—	2	8	no	—
1228	C₂×C₄	—	2	8	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	2	1	no	—
1264	C₂×C₄	—	2	1	no	—
1265	C₂×C₄	—	2	1	no	—
1266	C₂×C₄	—	2	1	no	—
1267	C₂×C₄	—	2	1	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	2	1	no	—
1270	C₂×C₄	—	2	1	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	4	4	no	—
1303	C₂×C₄	—	4	4	no	—
1304	C₂×C₄	—	4	4	no	—
1305	C₂×C₄	—	4	4	no	—
1306	C₂×C₄	—	8	2	no	—
1307	C₂×C₄	—	8	2	no	—
1308	C₂×C₄	—	8	2	no	—
1309	C₂×C₄	—	8	2	no	—
1310	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1311	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1312	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1313	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1314	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1315	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1316	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1317	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1318	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1319	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1320	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1321	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1322	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1323	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1324	C₂²	—	2	2	no	—
1325	C₂²	—	2	2	no	—
1326	C₂²	—	2	2	no	—
1327	C₂²	—	2	2	no	—
1328	C₂²	—	2	2	no	—
1329	C₂²	—	2	2	no	—
1330	C₂²	—	2	2	no	—
1331	C₂²	—	2	2	no	—
1332	C₂²	—	2	2	no	—
1333	C₂²	—	4	1	no	—
1334	C₂²	—	4	1	no	—
1335	C₂²	—	4	1	no	—
1336	C₂²	—	4	1	no	—
1337	C₂²	C₃₁×#520	1	4	yes	—
1338	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1339	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1340	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1341	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1342	C₂²	C₃₁×#585	1	1	yes	characteristic
1343	C₂²	C₃₁×#585	1	1	yes	characteristic
1344	C₂²	C₃₁×#585	1	1	yes	characteristic
1345	C₄	—	2	2	no	—
1346	C₄	—	2	2	no	—
1347	C₄	—	2	2	no	—
1348	C₄	—	2	2	no	—
1349	C₄	—	2	2	no	—
1350	C₄	—	2	2	no	—
1351	C₄	—	2	2	no	—
1352	C₄	—	2	2	no	—
1353	C₄	—	2	2	no	—
1354	C₄	—	2	2	no	—
1355	C₄	—	2	2	no	—
1356	C₄	—	2	2	no	—
1357	C₄	—	2	2	no	—
1358	C₄	—	2	2	no	—
1359	C₄	—	4	1	no	—
1360	C₄	—	4	1	no	—
1361	C₄	—	4	1	no	—
1362	C₄	—	4	1	no	—
1363	C₄	—	4	1	no	—
1364	C₄	—	4	1	no	—
1365	C₄	—	4	1	no	—
1366	C₄	—	4	1	no	—
1367	C₄	—	4	1	no	—
1368	C₄	—	4	1	no	—
1369	C₄	—	4	1	no	—
1370	C₄	—	4	1	no	—
1371	C₄	—	4	1	no	—
1372	C₄	—	4	1	no	—
1373	C₄	—	4	1	no	—
1374	C₂	—	2	4	no	—
1375	C₂	—	4	2	no	—
1376	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
1377	C₂	C₃₁×#3428	1	1	yes	characteristic
1378	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1379	C₂	C₃₁×#3533	1	1	yes	characteristic
1380	C₂	C₃₁×#3535	1	1	yes	characteristic
1381	C₂	C₃₁×#3563	1	1	yes	characteristic
1382	C₂	C₃₁×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2383	C₂	semidirect
3. C₃₁×#2382	C₂	semidirect
4. C₃₁×#2382	C₂	semidirect
5. C₃₁×#2378	C₂	semidirect
6. C₃₁×#2373	C₂	semidirect
7. C₃₁×#2370	C₂	semidirect
8. C₃₁×#2368	C₂	semidirect
11. C₃₁×#2355	C₂	semidirect
13. C₃₁×#2344	C₂	semidirect
14. C₃₁×#2343	C₂	semidirect
15. C₃₁×#2343	C₂	semidirect
16. C₃₁×#2343	C₂	semidirect
17. C₃₁×#2336	C₂	semidirect
18. C₃₁×#2336	C₂	semidirect
19. C₃₁×#2334	C₂	semidirect
20. C₃₁×#2334	C₂	semidirect
21. C₃₁×#2330	C₂	semidirect
22. C₃₁×#2329	C₂	semidirect
23. C₃₁×#2329	C₂	semidirect
25. C₃₁×#2320	C₂	semidirect
27. C₃₁×#2317	C₂	semidirect
28. C₃₁×#2314	C₂	semidirect
30. C₃₁×#2296	C₂	semidirect
31. C₂×C₃₁×#387	C₂	semidirect
32. C₃₁×#552	C₄	semidirect
200. C₃₁×#126	C₂×C₄	semidirect
201. C₃₁×#126	C₂×C₄	semidirect
202. C₃₁×#125	C₂×C₄	semidirect
203. C₃₁×#125	C₂×C₄	semidirect
204. C₃₁×#125	C₂×C₄	semidirect
207. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
208. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
209. C₄×Q₈×C₃₁	C₂×C₄	semidirect
215. C₃₁×#117	C₂×C₄	semidirect
216. C₃₁×#117	C₂×C₄	semidirect
217. C₃₁×#117	C₂×C₄	semidirect
219. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
518. #34459	C₃₁	direct (N × H)
634. #2383	C₂×C₃₁	semidirect
635. #2382	C₂×C₃₁	semidirect
636. #2382	C₂×C₃₁	semidirect
637. #2378	C₂×C₃₁	semidirect
638. #2373	C₂×C₃₁	semidirect
639. #2370	C₂×C₃₁	semidirect
640. #2368	C₂×C₃₁	semidirect
643. #2355	C₂×C₃₁	semidirect
645. #2344	C₂×C₃₁	semidirect
646. #2343	C₂×C₃₁	semidirect
647. #2343	C₂×C₃₁	semidirect
648. #2343	C₂×C₃₁	semidirect
649. #2336	C₂×C₃₁	semidirect
650. #2336	C₂×C₃₁	semidirect
651. #2334	C₂×C₃₁	semidirect
652. #2334	C₂×C₃₁	semidirect
653. #2330	C₂×C₃₁	semidirect
654. #2329	C₂×C₃₁	semidirect
655. #2329	C₂×C₃₁	semidirect
657. #2320	C₂×C₃₁	semidirect
659. #2317	C₂×C₃₁	semidirect
660. #2314	C₂×C₃₁	semidirect
662. #2296	C₂×C₃₁	semidirect
663. C₂×#387	C₂×C₃₁	semidirect
714. #552	C₄×C₃₁	semidirect
891. #126	C₂×C₄×C₃₁	semidirect
892. #126	C₂×C₄×C₃₁	semidirect
893. #125	C₂×C₄×C₃₁	semidirect
894. #125	C₂×C₄×C₃₁	semidirect
895. #125	C₂×C₄×C₃₁	semidirect
898. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
899. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
900. C₄×Q₈	C₂×C₄×C₃₁	semidirect
906. #117	C₂×C₄×C₃₁	semidirect
907. #117	C₂×C₄×C₃₁	semidirect
908. #117	C₂×C₄×C₃₁	semidirect
910. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
1055. C₃₁	#34459	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#552	2
C₃₁×#2383	2
C₃₁×#2382	2
C₃₁×#2378	2
C₃₁×#2373	2
C₃₁×#2370	2
C₃₁×#2368	2
C₃₁×#2359	2
C₃₁×#2355	2
C₃₁×#2349	2
C₃₁×#2344	2
C₃₁×#2343	2
C₃₁×#2336	2
C₃₁×#2334	2
C₃₁×#2330	2
C₃₁×#2329	2
C₃₁×#2322	2
C₃₁×#2320	2
C₃₁×#2318	2
C₃₁×#2317	2
C₃₁×#2314	2
C₄×C₃₁×#123	2
C₃₁×#2296	2
C₂×C₃₁×#387	2
#34459	31

Subgroups — C31×#34459 #21491218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34459 #21491218