Subgroups — C₃₁×#35100 #21491859

Order 7936.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2866	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2865	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2861	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2860	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2651	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2650	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2531	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2529	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2526	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2525	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2521	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2519	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2516	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2498	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2482	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2481	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2480	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2473	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2472	C₂	1	1	yes	maximal, characteristic
23	C₃₁×#2438	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#2411	C₂	1	1	yes	maximal, characteristic
25	C₃₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#2321	C₂	1	1	yes	maximal, characteristic
27	C₃₁×#2318	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#2312	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₃₁×#388	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#400	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#400	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#400	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#400	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#400	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#399	C₂²	1	1	yes	characteristic
53	C₃₁×#399	C₂²	1	1	yes	characteristic
54	C₃₁×#399	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#398	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#398	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#398	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#398	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#398	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#398	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#397	C₂²	1	1	yes	characteristic
62	C₃₁×#397	C₂²	1	1	yes	characteristic
63	C₃₁×#397	C₂²	1	1	yes	characteristic
64	C₃₁×#397	C₂²	1	1	yes	characteristic
65	C₃₁×#397	C₂²	1	1	yes	characteristic
66	C₃₁×#397	C₂²	1	1	yes	characteristic
67	C₃₁×#397	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#397	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#396	C₂²	1	1	yes	characteristic
70	C₃₁×#396	C₂²	1	1	yes	characteristic
71	C₃₁×#396	C₂²	1	1	yes	characteristic
72	C₃₁×#396	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#395	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#394	C₂²	1	1	yes	characteristic
75	C₃₁×#394	C₂²	1	1	yes	characteristic
76	C₃₁×#394	C₂²	1	1	yes	characteristic
77	C₃₁×#394	C₂²	1	1	yes	characteristic
78	C₃₁×#393	C₂²	1	1	yes	characteristic
79	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#390	C₂²	1	1	yes	characteristic
83	C₃₁×#390	C₂²	1	1	yes	characteristic
84	C₃₁×#390	C₂²	1	1	yes	characteristic
85	C₃₁×#390	C₂²	1	1	yes	characteristic
86	C₃₁×#390	C₂²	1	1	yes	characteristic
87	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#388	C₂²	1	1	yes	characteristic
92	C₃₁×#388	C₂²	1	1	yes	characteristic
93	C₃₁×#388	C₂²	1	1	yes	characteristic
94	C₃₁×#388	C₂²	1	1	yes	characteristic
95	C₃₁×#388	C₂²	1	1	yes	characteristic
96	C₃₁×#388	C₂²	1	1	yes	characteristic
97	C₃₁×#388	C₂²	1	1	yes	characteristic
98	C₃₁×#388	C₂²	1	1	yes	characteristic
99	C₃₁×#388	C₂²	1	1	yes	characteristic
100	C₃₁×#388	C₂²	1	1	yes	characteristic
101	C₃₁×#388	C₂²	1	1	yes	characteristic
102	C₃₁×#388	C₂²	1	1	yes	characteristic
103	C₃₁×#388	C₂²	1	1	yes	characteristic
104	C₃₁×#388	C₂²	1	1	yes	characteristic
105	C₃₁×#388	C₂²	1	1	yes	characteristic
106	C₃₁×#388	C₂²	1	1	yes	characteristic
107	C₃₁×#388	C₂²	1	1	yes	characteristic
108	C₃₁×#388	C₂²	1	1	yes	characteristic
109	C₃₁×#388	C₂²	1	1	yes	characteristic
110	C₃₁×#388	C₂²	1	1	yes	characteristic
111	C₃₁×#388	C₂²	1	1	yes	characteristic
112	C₃₁×#388	C₂²	1	1	yes	characteristic
113	C₃₁×#388	C₂²	1	1	yes	characteristic
114	C₃₁×#388	C₂²	1	1	yes	characteristic
115	C₃₁×#388	C₂²	1	1	yes	characteristic
116	C₃₁×#388	C₂²	1	1	yes	characteristic
117	C₃₁×#388	C₂²	1	1	yes	characteristic
118	C₃₁×#388	C₂²	1	1	yes	characteristic
119	C₃₁×#388	C₂²	1	1	yes	characteristic
120	C₃₁×#388	C₂²	1	1	yes	characteristic
121	C₃₁×#388	C₂²	1	1	yes	characteristic
122	C₃₁×#388	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#388	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#388	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#388	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#388	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#388	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#388	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
136	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
138	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
139	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
140	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
141	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
142	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
143	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
144	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
145	C₃₁×#386	C₂²	1	1	yes	characteristic
146	C₃₁×#386	C₂²	1	1	yes	characteristic
147	C₃₁×#386	C₂²	1	1	yes	characteristic
148	C₃₁×#386	C₂²	1	1	yes	characteristic
149	C₃₁×#386	C₂²	1	1	yes	characteristic
150	C₃₁×#386	C₂²	1	1	yes	characteristic
151	C₃₁×#385	C₂²	1	1	yes	characteristic
152	C₃₁×#385	C₂²	1	1	yes	characteristic
153	C₃₁×#385	C₂²	1	1	yes	characteristic
154	C₃₁×#385	C₂²	1	1	yes	characteristic
155	C₃₁×#385	C₂²	1	1	yes	characteristic
156	C₃₁×#385	C₂²	1	1	yes	characteristic
157	C₃₁×#383	C₂²	1	1	yes	characteristic, complemented
158	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
159	C₃₁×#381	C₂²	1	1	yes	characteristic
160	C₃₁×#381	C₂²	1	1	yes	characteristic, complemented
161	C₃₁×#380	C₂²	1	1	yes	characteristic
162	C₃₁×#380	C₂²	1	1	yes	characteristic
163	C₃₁×#380	C₂²	1	1	yes	characteristic
164	C₃₁×#380	C₂²	1	1	yes	characteristic, complemented
165	C₃₁×#379	C₂²	1	1	yes	characteristic
166	C₃₁×#379	C₂²	1	1	yes	characteristic
167	C₃₁×#379	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
169	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
170	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
171	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
172	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
173	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
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, complemented
180	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
181	C₃₁×#376	C₂²	1	1	yes	characteristic, complemented
182	C₃₁×#376	C₂²	1	1	yes	characteristic, complemented
183	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
184	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
185	C₄³×C₃₁	C₂²	1	1	yes	characteristic, complemented
186	C₄³×C₃₁	C₂²	1	1	yes	characteristic, complemented
187	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
189	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂²×D₄×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	C₃₁×#126	—	4	2	no	—
200	C₃₁×#126	—	4	2	no	—
201	C₃₁×#125	—	4	2	no	—
202	C₃₁×#124	—	4	2	no	—
203	C₃₁×#123	—	2	4	no	—
204	C₃₁×C₂²⋊Q₈	—	2	4	no	—
205	C₃₁×#120	—	2	4	no	—
206	C₄×D₄×C₃₁	—	2	4	no	—
207	C₃₁×#117	—	2	4	no	—
208	C₃₁×#117	—	2	4	no	—
209	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
210	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₁	—	2	4	no	—
243	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
245	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊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×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₃₁	—	2	4	no	—
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	C₂×C₄²×C₃₁	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	C₂⁴×C₃₁	—	2	2	no	—
358	C₂⁴×C₃₁	—	2	2	no	—
359	C₂⁴×C₃₁	—	2	2	no	—
360	C₂⁴×C₃₁	—	4	1	no	—
361	C₂⁴×C₃₁	—	4	1	no	—
362	C₂⁴×C₃₁	—	4	1	no	—
363	C₂⁴×C₃₁	—	4	1	no	—
364	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×Q₈×C₃₁	—	2	2	no	—
369	C₂×Q₈×C₃₁	—	4	1	no	—
370	C₂×Q₈×C₃₁	—	4	1	no	—
371	C₂×D₄×C₃₁	—	2	2	no	—
372	C₂×D₄×C₃₁	—	2	2	no	—
373	C₂×D₄×C₃₁	—	2	2	no	—
374	C₂×D₄×C₃₁	—	2	2	no	—
375	C₂×D₄×C₃₁	—	2	2	no	—
376	C₂×D₄×C₃₁	—	4	1	no	—
377	C₂×D₄×C₃₁	—	4	1	no	—
378	C₂×D₄×C₃₁	—	4	1	no	—
379	C₂×D₄×C₃₁	—	4	1	no	—
380	C₂²×C₄×C₃₁	—	2	2	no	—
381	C₂²×C₄×C₃₁	—	2	2	no	—
382	C₂²×C₄×C₃₁	—	2	2	no	—
383	C₂²×C₄×C₃₁	—	2	2	no	—
384	C₂²×C₄×C₃₁	—	2	2	no	—
385	C₂²×C₄×C₃₁	—	2	2	no	—
386	C₂²×C₄×C₃₁	—	2	2	no	—
387	C₂²×C₄×C₃₁	—	2	2	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	—	4	1	no	—
399	C₂²×C₄×C₃₁	#41	1	4	yes	—
400	C₂²×C₄×C₃₁	#41	1	4	yes	—
401	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₃₁	—	2	2	no	—
429	C₄⋊C₄×C₃₁	—	2	2	no	—
430	C₄⋊C₄×C₃₁	—	2	2	no	—
431	C₄⋊C₄×C₃₁	—	2	2	no	—
432	C₄⋊C₄×C₃₁	—	2	2	no	—
433	C₄⋊C₄×C₃₁	—	2	2	no	—
434	C₄⋊C₄×C₃₁	—	2	2	no	—
435	C₄⋊C₄×C₃₁	—	2	2	no	—
436	C₄⋊C₄×C₃₁	—	2	2	no	—
437	C₄⋊C₄×C₃₁	—	2	2	no	—
438	C₄⋊C₄×C₃₁	—	2	2	no	—
439	C₄⋊C₄×C₃₁	—	2	2	no	—
440	C₄⋊C₄×C₃₁	—	2	2	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	—	4	1	no	—
460	C₂²⋊C₄×C₃₁	—	2	2	no	—
461	C₂²⋊C₄×C₃₁	—	2	2	no	—
462	C₂²⋊C₄×C₃₁	—	2	2	no	—
463	C₂²⋊C₄×C₃₁	—	2	2	no	—
464	C₂²⋊C₄×C₃₁	—	2	2	no	—
465	C₂²⋊C₄×C₃₁	—	2	2	no	—
466	C₂²⋊C₄×C₃₁	—	2	2	no	—
467	C₂²⋊C₄×C₃₁	—	2	2	no	—
468	C₂²⋊C₄×C₃₁	—	2	2	no	—
469	C₂²⋊C₄×C₃₁	—	2	2	no	—
470	C₂²⋊C₄×C₃₁	—	2	2	no	—
471	C₂²⋊C₄×C₃₁	—	2	2	no	—
472	C₂²⋊C₄×C₃₁	—	2	2	no	—
473	C₂²⋊C₄×C₃₁	—	2	2	no	—
474	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	—	2	2	no	—
480	C₂²⋊C₄×C₃₁	—	2	2	no	—
481	C₂²⋊C₄×C₃₁	—	2	2	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	—	4	1	no	—
486	C₂²⋊C₄×C₃₁	—	4	1	no	—
487	C₂²⋊C₄×C₃₁	—	4	1	no	—
488	C₂²⋊C₄×C₃₁	—	4	1	no	—
489	C₂²⋊C₄×C₃₁	—	4	1	no	—
490	C₂²⋊C₄×C₃₁	—	4	1	no	—
491	C₂²⋊C₄×C₃₁	—	4	1	no	—
492	C₂²⋊C₄×C₃₁	—	4	1	no	—
493	C₂²⋊C₄×C₃₁	—	4	1	no	—
494	C₂²⋊C₄×C₃₁	—	4	1	no	—
495	C₂²⋊C₄×C₃₁	—	4	1	no	—
496	C₂²⋊C₄×C₃₁	—	4	1	no	—
497	C₂²⋊C₄×C₃₁	—	4	1	no	—
498	C₂²⋊C₄×C₃₁	—	4	1	no	—
499	C₂²⋊C₄×C₃₁	—	4	1	no	—
500	C₂²⋊C₄×C₃₁	—	4	1	no	—
501	C₂²⋊C₄×C₃₁	—	4	1	no	—
502	C₂²⋊C₄×C₃₁	—	4	1	no	—
503	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
504	C₄²×C₃₁	—	2	2	no	—
505	C₄²×C₃₁	—	2	2	no	—
506	C₄²×C₃₁	—	2	2	no	—
507	C₄²×C₃₁	—	2	2	no	—
508	C₄²×C₃₁	—	2	2	no	—
509	C₄²×C₃₁	—	2	2	no	—
510	C₄²×C₃₁	—	2	2	no	—
511	C₄²×C₃₁	—	2	2	no	—
512	C₄²×C₃₁	—	2	2	no	—
513	C₄²×C₃₁	—	2	2	no	—
514	C₄²×C₃₁	—	2	2	no	—
515	C₄²×C₃₁	—	4	1	no	—
516	C₄²×C₃₁	—	4	1	no	—
517	C₄²×C₃₁	—	4	1	no	—
518	C₄²×C₃₁	—	4	1	no	—
519	C₄²×C₃₁	—	4	1	no	—
520	C₄²×C₃₁	—	4	1	no	—
521	C₄²×C₃₁	—	4	1	no	—
522	C₄²×C₃₁	—	4	1	no	—
523	#35100	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	1	no	—
530	C₂³×C₃₁	—	2	1	no	—
531	C₂³×C₃₁	—	2	1	no	—
532	C₂³×C₃₁	—	2	1	no	—
533	C₂³×C₃₁	—	2	1	no	—
534	C₂³×C₃₁	—	2	1	no	—
535	C₂³×C₃₁	—	2	1	no	—
536	C₂³×C₃₁	—	2	1	no	—
537	C₂³×C₃₁	—	2	1	no	—
538	C₂³×C₃₁	—	2	1	no	—
539	C₂³×C₃₁	—	2	1	no	—
540	C₂³×C₃₁	—	2	1	no	—
541	C₂³×C₃₁	—	2	1	no	—
542	C₂³×C₃₁	—	2	1	no	—
543	C₂³×C₃₁	—	2	1	no	—
544	C₂³×C₃₁	—	2	1	no	—
545	C₂³×C₃₁	—	2	1	no	—
546	C₂³×C₃₁	—	2	1	no	—
547	C₂³×C₃₁	—	2	1	no	—
548	C₂³×C₃₁	—	2	1	no	—
549	C₂³×C₃₁	—	4	4	no	—
550	C₂³×C₃₁	—	4	4	no	—
551	C₂³×C₃₁	—	4	4	no	—
552	C₂³×C₃₁	—	8	2	no	—
553	C₂³×C₃₁	—	8	2	no	—
554	C₂³×C₃₁	—	8	2	no	—
555	C₂³×C₃₁	—	8	2	no	—
556	C₂³×C₃₁	C₂×#41	1	2	yes	—
557	C₂³×C₃₁	C₂×#41	1	2	yes	—
558	C₂³×C₃₁	C₂×#41	1	2	yes	—
559	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
560	Q₈×C₃₁	—	8	2	no	—
561	D₄×C₃₁	—	4	4	no	—
562	D₄×C₃₁	—	8	2	no	—
563	D₄×C₃₁	—	8	2	no	—
564	C₂×C₄×C₃₁	—	2	8	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	—	2	1	no	—
612	C₂×C₄×C₃₁	—	2	1	no	—
613	C₂×C₄×C₃₁	—	2	1	no	—
614	C₂×C₄×C₃₁	—	2	1	no	—
615	C₂×C₄×C₃₁	—	2	1	no	—
616	C₂×C₄×C₃₁	—	2	1	no	—
617	C₂×C₄×C₃₁	—	2	1	no	—
618	C₂×C₄×C₃₁	—	2	1	no	—
619	C₂×C₄×C₃₁	—	2	1	no	—
620	C₂×C₄×C₃₁	—	2	1	no	—
621	C₂×C₄×C₃₁	—	2	1	no	—
622	C₂×C₄×C₃₁	—	2	1	no	—
623	C₂×C₄×C₃₁	—	2	1	no	—
624	C₂×C₄×C₃₁	—	2	1	no	—
625	C₂×C₄×C₃₁	—	2	1	no	—
626	C₂×C₄×C₃₁	—	2	1	no	—
627	C₂×C₄×C₃₁	—	2	1	no	—
628	C₂×C₄×C₃₁	—	2	1	no	—
629	C₂×C₄×C₃₁	—	2	1	no	—
630	C₂×C₄×C₃₁	—	2	1	no	—
631	C₂×C₄×C₃₁	—	2	1	no	—
632	C₂×C₄×C₃₁	—	2	1	no	—
633	C₂×C₄×C₃₁	—	2	1	no	—
634	C₂×C₄×C₃₁	—	2	1	no	—
635	C₂×C₄×C₃₁	—	2	1	no	—
636	C₂×C₄×C₃₁	—	2	1	no	—
637	C₂×C₄×C₃₁	—	2	1	no	—
638	C₂×C₄×C₃₁	—	2	1	no	—
639	C₂×C₄×C₃₁	—	4	4	no	—
640	C₂×C₄×C₃₁	—	4	4	no	—
641	C₂×C₄×C₃₁	—	4	4	no	—
642	C₂×C₄×C₃₁	—	8	2	no	—
643	C₂×C₄×C₃₁	—	8	2	no	—
644	C₂×C₄×C₃₁	—	8	2	no	—
645	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
646	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
647	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
648	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
649	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
650	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
651	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
652	#2866	C₂×C₃₁	1	1	yes	characteristic, complemented
653	#2865	C₂×C₃₁	1	1	yes	characteristic, complemented
654	#2861	C₂×C₃₁	1	1	yes	characteristic, complemented
655	#2860	C₂×C₃₁	1	1	yes	characteristic, complemented
656	#2654	C₂×C₃₁	1	1	yes	characteristic, complemented
657	#2651	C₂×C₃₁	1	1	yes	characteristic, complemented
658	#2651	C₂×C₃₁	1	1	yes	characteristic, complemented
659	#2650	C₂×C₃₁	1	1	yes	characteristic, complemented
660	#2532	C₂×C₃₁	1	1	yes	characteristic, complemented
661	#2531	C₂×C₃₁	1	1	yes	characteristic, complemented
662	#2529	C₂×C₃₁	1	1	yes	characteristic, complemented
663	#2526	C₂×C₃₁	1	1	yes	characteristic, complemented
664	#2525	C₂×C₃₁	1	1	yes	characteristic, complemented
665	#2521	C₂×C₃₁	1	1	yes	characteristic, complemented
666	#2519	C₂×C₃₁	1	1	yes	characteristic, complemented
667	#2516	C₂×C₃₁	1	1	yes	characteristic, complemented
668	#2498	C₂×C₃₁	1	1	yes	characteristic, complemented
669	#2482	C₂×C₃₁	1	1	yes	characteristic, complemented
670	#2481	C₂×C₃₁	1	1	yes	characteristic, complemented
671	#2480	C₂×C₃₁	1	1	yes	characteristic, complemented
672	#2473	C₂×C₃₁	1	1	yes	characteristic, complemented
673	#2472	C₂×C₃₁	1	1	yes	characteristic
674	#2438	C₂×C₃₁	1	1	yes	characteristic, complemented
675	#2411	C₂×C₃₁	1	1	yes	characteristic
676	#2329	C₂×C₃₁	1	1	yes	characteristic, complemented
677	#2321	C₂×C₃₁	1	1	yes	characteristic
678	#2318	C₂×C₃₁	1	1	yes	characteristic, complemented
679	#2312	C₂×C₃₁	1	1	yes	characteristic, complemented
680	C₄×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
681	C₂×#388	C₂×C₃₁	1	1	yes	characteristic, complemented
682	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
683	C₂²×C₃₁	—	2	2	no	—
684	C₂²×C₃₁	—	2	2	no	—
685	C₂²×C₃₁	—	2	2	no	—
686	C₂²×C₃₁	—	2	2	no	—
687	C₂²×C₃₁	—	2	2	no	—
688	C₂²×C₃₁	—	2	2	no	—
689	C₂²×C₃₁	—	4	1	no	—
690	C₂²×C₃₁	—	4	1	no	—
691	C₂²×C₃₁	—	4	1	no	—
692	C₂²×C₃₁	—	4	1	no	—
693	C₂²×C₃₁	—	4	1	no	—
694	C₂²×C₃₁	—	4	1	no	—
695	C₂²×C₃₁	—	4	1	no	—
696	C₂²×C₃₁	—	4	1	no	—
697	C₂²×C₃₁	—	4	1	no	—
698	C₂²×C₃₁	—	4	1	no	—
699	C₂²×C₃₁	—	4	1	no	—
700	C₂²×C₃₁	—	4	1	no	—
701	C₂²×C₃₁	—	4	1	no	—
702	C₂²×C₃₁	—	4	1	no	—
703	C₂²×C₃₁	—	4	1	no	—
704	C₂²×C₃₁	—	4	1	no	—
705	C₂²×C₃₁	—	4	1	no	—
706	C₂²×C₃₁	—	4	1	no	—
707	C₂²×C₃₁	—	4	1	no	—
708	C₂²×C₃₁	—	4	1	no	—
709	C₂²×C₃₁	—	4	1	no	—
710	C₂²×C₃₁	—	8	8	no	—
711	C₂²×C₃₁	#529	1	4	yes	—
712	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
713	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
714	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
715	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
716	C₂²×C₃₁	#585	1	1	yes	characteristic
717	C₂²×C₃₁	#585	1	1	yes	characteristic
718	C₂²×C₃₁	#585	1	1	yes	characteristic
719	C₄×C₃₁	—	2	2	no	—
720	C₄×C₃₁	—	2	2	no	—
721	C₄×C₃₁	—	2	2	no	—
722	C₄×C₃₁	—	2	2	no	—
723	C₄×C₃₁	—	2	2	no	—
724	C₄×C₃₁	—	2	2	no	—
725	C₄×C₃₁	—	2	2	no	—
726	C₄×C₃₁	—	4	1	no	—
727	C₄×C₃₁	—	4	1	no	—
728	C₄×C₃₁	—	4	1	no	—
729	C₄×C₃₁	—	4	1	no	—
730	C₄×C₃₁	—	4	1	no	—
731	C₄×C₃₁	—	4	1	no	—
732	C₄×C₃₁	—	4	1	no	—
733	C₄×C₃₁	—	4	1	no	—
734	C₄×C₃₁	—	4	1	no	—
735	C₄×C₃₁	—	4	1	no	—
736	C₄×C₃₁	—	4	1	no	—
737	C₄×C₃₁	—	4	1	no	—
738	C₄×C₃₁	—	4	1	no	—
739	C₄×C₃₁	—	4	1	no	—
740	C₄×C₃₁	—	4	1	no	—
741	C₄×C₃₁	—	4	1	no	—
742	C₄×C₃₁	—	4	1	no	—
743	C₄×C₃₁	—	4	1	no	—
744	C₄×C₃₁	—	4	1	no	—
745	C₄×C₃₁	—	4	1	no	—
746	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
747	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic, complemented
748	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
749	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
750	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
751	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
752	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
753	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
754	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
755	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
756	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
757	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
758	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
759	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
760	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
761	#400	C₂²×C₃₁	1	1	yes	characteristic, complemented
762	#400	C₂²×C₃₁	1	1	yes	characteristic, complemented
763	#400	C₂²×C₃₁	1	1	yes	characteristic, complemented
764	#400	C₂²×C₃₁	1	1	yes	characteristic, complemented
765	#400	C₂²×C₃₁	1	1	yes	characteristic, complemented
766	#399	C₂²×C₃₁	1	1	yes	characteristic
767	#399	C₂²×C₃₁	1	1	yes	characteristic
768	#399	C₂²×C₃₁	1	1	yes	characteristic, complemented
769	#398	C₂²×C₃₁	1	1	yes	characteristic, complemented
770	#398	C₂²×C₃₁	1	1	yes	characteristic, complemented
771	#398	C₂²×C₃₁	1	1	yes	characteristic, complemented
772	#398	C₂²×C₃₁	1	1	yes	characteristic, complemented
773	#398	C₂²×C₃₁	1	1	yes	characteristic, complemented
774	#398	C₂²×C₃₁	1	1	yes	characteristic, complemented
775	#397	C₂²×C₃₁	1	1	yes	characteristic
776	#397	C₂²×C₃₁	1	1	yes	characteristic
777	#397	C₂²×C₃₁	1	1	yes	characteristic
778	#397	C₂²×C₃₁	1	1	yes	characteristic
779	#397	C₂²×C₃₁	1	1	yes	characteristic
780	#397	C₂²×C₃₁	1	1	yes	characteristic
781	#397	C₂²×C₃₁	1	1	yes	characteristic, complemented
782	#397	C₂²×C₃₁	1	1	yes	characteristic, complemented
783	#396	C₂²×C₃₁	1	1	yes	characteristic
784	#396	C₂²×C₃₁	1	1	yes	characteristic
785	#396	C₂²×C₃₁	1	1	yes	characteristic
786	#396	C₂²×C₃₁	1	1	yes	characteristic, complemented
787	#395	C₂²×C₃₁	1	1	yes	characteristic, complemented
788	#394	C₂²×C₃₁	1	1	yes	characteristic
789	#394	C₂²×C₃₁	1	1	yes	characteristic
790	#394	C₂²×C₃₁	1	1	yes	characteristic
791	#394	C₂²×C₃₁	1	1	yes	characteristic
792	#393	C₂²×C₃₁	1	1	yes	characteristic
793	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
794	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
795	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
796	#390	C₂²×C₃₁	1	1	yes	characteristic
797	#390	C₂²×C₃₁	1	1	yes	characteristic
798	#390	C₂²×C₃₁	1	1	yes	characteristic
799	#390	C₂²×C₃₁	1	1	yes	characteristic
800	#390	C₂²×C₃₁	1	1	yes	characteristic
801	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
802	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
803	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
804	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
805	#388	C₂²×C₃₁	1	1	yes	characteristic
806	#388	C₂²×C₃₁	1	1	yes	characteristic
807	#388	C₂²×C₃₁	1	1	yes	characteristic
808	#388	C₂²×C₃₁	1	1	yes	characteristic
809	#388	C₂²×C₃₁	1	1	yes	characteristic
810	#388	C₂²×C₃₁	1	1	yes	characteristic
811	#388	C₂²×C₃₁	1	1	yes	characteristic
812	#388	C₂²×C₃₁	1	1	yes	characteristic
813	#388	C₂²×C₃₁	1	1	yes	characteristic
814	#388	C₂²×C₃₁	1	1	yes	characteristic
815	#388	C₂²×C₃₁	1	1	yes	characteristic
816	#388	C₂²×C₃₁	1	1	yes	characteristic
817	#388	C₂²×C₃₁	1	1	yes	characteristic
818	#388	C₂²×C₃₁	1	1	yes	characteristic
819	#388	C₂²×C₃₁	1	1	yes	characteristic
820	#388	C₂²×C₃₁	1	1	yes	characteristic
821	#388	C₂²×C₃₁	1	1	yes	characteristic
822	#388	C₂²×C₃₁	1	1	yes	characteristic
823	#388	C₂²×C₃₁	1	1	yes	characteristic
824	#388	C₂²×C₃₁	1	1	yes	characteristic
825	#388	C₂²×C₃₁	1	1	yes	characteristic
826	#388	C₂²×C₃₁	1	1	yes	characteristic
827	#388	C₂²×C₃₁	1	1	yes	characteristic
828	#388	C₂²×C₃₁	1	1	yes	characteristic
829	#388	C₂²×C₃₁	1	1	yes	characteristic
830	#388	C₂²×C₃₁	1	1	yes	characteristic
831	#388	C₂²×C₃₁	1	1	yes	characteristic
832	#388	C₂²×C₃₁	1	1	yes	characteristic
833	#388	C₂²×C₃₁	1	1	yes	characteristic
834	#388	C₂²×C₃₁	1	1	yes	characteristic
835	#388	C₂²×C₃₁	1	1	yes	characteristic
836	#388	C₂²×C₃₁	1	1	yes	characteristic, complemented
837	#388	C₂²×C₃₁	1	1	yes	characteristic, complemented
838	#388	C₂²×C₃₁	1	1	yes	characteristic, complemented
839	#388	C₂²×C₃₁	1	1	yes	characteristic, complemented
840	#388	C₂²×C₃₁	1	1	yes	characteristic, complemented
841	#388	C₂²×C₃₁	1	1	yes	characteristic, complemented
842	#388	C₂²×C₃₁	1	1	yes	characteristic, complemented
843	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
844	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
845	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
846	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
847	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
848	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
849	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
850	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
851	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
852	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
853	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
854	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
855	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
856	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
857	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
858	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
859	#386	C₂²×C₃₁	1	1	yes	characteristic
860	#386	C₂²×C₃₁	1	1	yes	characteristic
861	#386	C₂²×C₃₁	1	1	yes	characteristic
862	#386	C₂²×C₃₁	1	1	yes	characteristic
863	#386	C₂²×C₃₁	1	1	yes	characteristic
864	#386	C₂²×C₃₁	1	1	yes	characteristic
865	#385	C₂²×C₃₁	1	1	yes	characteristic
866	#385	C₂²×C₃₁	1	1	yes	characteristic
867	#385	C₂²×C₃₁	1	1	yes	characteristic
868	#385	C₂²×C₃₁	1	1	yes	characteristic
869	#385	C₂²×C₃₁	1	1	yes	characteristic
870	#385	C₂²×C₃₁	1	1	yes	characteristic
871	#383	C₂²×C₃₁	1	1	yes	characteristic, complemented
872	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
873	#381	C₂²×C₃₁	1	1	yes	characteristic
874	#381	C₂²×C₃₁	1	1	yes	characteristic, complemented
875	#380	C₂²×C₃₁	1	1	yes	characteristic
876	#380	C₂²×C₃₁	1	1	yes	characteristic
877	#380	C₂²×C₃₁	1	1	yes	characteristic
878	#380	C₂²×C₃₁	1	1	yes	characteristic, complemented
879	#379	C₂²×C₃₁	1	1	yes	characteristic
880	#379	C₂²×C₃₁	1	1	yes	characteristic
881	#379	C₂²×C₃₁	1	1	yes	characteristic
882	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
883	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
884	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
885	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
886	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
887	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
888	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
889	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
890	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
891	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
892	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
893	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
894	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
895	#376	C₂²×C₃₁	1	1	yes	characteristic, complemented
896	#376	C₂²×C₃₁	1	1	yes	characteristic, complemented
897	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
898	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
899	C₄³	C₂²×C₃₁	1	1	yes	characteristic, complemented
900	C₄³	C₂²×C₃₁	1	1	yes	characteristic, complemented
901	C₂×C₃₁	—	2	4	no	—
902	C₂×C₃₁	—	8	1	no	—
903	C₂×C₃₁	—	8	1	no	—
904	C₂×C₃₁	—	8	1	no	—
905	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
906	C₂×C₃₁	#3455	1	1	yes	characteristic
907	C₂×C₃₁	#3460	1	1	yes	characteristic
908	C₂×C₃₁	#3491	1	1	yes	characteristic
909	C₂×C₃₁	#3494	1	1	yes	characteristic
910	C₂×C₃₁	#3514	1	1	yes	characteristic
911	C₂×C₃₁	#3521	1	1	yes	characteristic
912	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
913	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
914	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
915	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
916	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
917	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
918	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
919	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
920	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
921	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
922	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
923	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
924	#126	—	4	2	no	—
925	#126	—	4	2	no	—
926	#125	—	4	2	no	—
927	#124	—	4	2	no	—
928	#123	—	2	4	no	—
929	C₂²⋊Q₈	—	2	4	no	—
930	#120	—	2	4	no	—
931	C₄×D₄	—	2	4	no	—
932	#117	—	2	4	no	—
933	#117	—	2	4	no	—
934	C₂×C₄⋊C₄	—	4	2	no	—
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×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
967	C₂×C₂²⋊C₄	—	2	4	no	—
968	C₂×C₂²⋊C₄	—	2	4	no	—
969	C₂×C₂²⋊C₄	—	4	2	no	—
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×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
974	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
975	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
976	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
977	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
978	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
979	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
980	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
981	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
982	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
983	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
984	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
985	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
986	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
987	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
988	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
989	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
990	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
991	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
992	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
993	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
994	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
995	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
998	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1001	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1002	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1003	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1004	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1005	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1006	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1007	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1008	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1011	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1012	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1013	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1014	C₂×C₄²	—	2	4	no	—
1015	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1016	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1017	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1018	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1019	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1020	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1021	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1022	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1023	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1024	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1025	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1026	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1027	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1028	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1029	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1030	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1031	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1032	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1033	C₂×C₄²	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	#95	C₂³×C₃₁	1	1	yes	characteristic
1056	#95	C₂³×C₃₁	1	1	yes	characteristic
1057	#95	C₂³×C₃₁	1	1	yes	characteristic
1058	#95	C₂³×C₃₁	1	1	yes	characteristic
1059	#95	C₂³×C₃₁	1	1	yes	characteristic
1060	#95	C₂³×C₃₁	1	1	yes	characteristic
1061	#95	C₂³×C₃₁	1	1	yes	characteristic
1062	#95	C₂³×C₃₁	1	1	yes	characteristic
1063	#95	C₂³×C₃₁	1	1	yes	characteristic
1064	#95	C₂³×C₃₁	1	1	yes	characteristic
1065	#95	C₂³×C₃₁	1	1	yes	characteristic
1066	#95	C₂³×C₃₁	1	1	yes	characteristic
1067	#95	C₂³×C₃₁	1	1	yes	characteristic
1068	#95	C₂³×C₃₁	1	1	yes	characteristic
1069	#95	C₂³×C₃₁	1	1	yes	characteristic
1070	#95	C₂³×C₃₁	1	1	yes	characteristic
1071	#95	C₂³×C₃₁	1	1	yes	characteristic
1072	#95	C₂³×C₃₁	1	1	yes	characteristic
1073	#95	C₂³×C₃₁	1	1	yes	characteristic
1074	#95	C₂³×C₃₁	1	1	yes	characteristic
1075	#95	C₂³×C₃₁	1	1	yes	characteristic
1076	#95	C₂³×C₃₁	1	1	yes	characteristic
1077	#95	C₂³×C₃₁	1	1	yes	characteristic
1078	#95	C₂³×C₃₁	1	1	yes	characteristic
1079	#95	C₂³×C₃₁	1	1	yes	characteristic
1080	#95	C₂³×C₃₁	1	1	yes	characteristic
1081	#95	C₂³×C₃₁	1	1	yes	characteristic
1082	C₃₁	#35100	1	1	yes	characteristic, direct product factor, Sylow
1083	C₂⁴	—	2	2	no	—
1084	C₂⁴	—	2	2	no	—
1085	C₂⁴	—	2	2	no	—
1086	C₂⁴	—	4	1	no	—
1087	C₂⁴	—	4	1	no	—
1088	C₂⁴	—	4	1	no	—
1089	C₂⁴	—	4	1	no	—
1090	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1091	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1092	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1093	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1094	C₂×Q₈	—	2	2	no	—
1095	C₂×Q₈	—	4	1	no	—
1096	C₂×Q₈	—	4	1	no	—
1097	C₂×D₄	—	2	2	no	—
1098	C₂×D₄	—	2	2	no	—
1099	C₂×D₄	—	2	2	no	—
1100	C₂×D₄	—	2	2	no	—
1101	C₂×D₄	—	2	2	no	—
1102	C₂×D₄	—	4	1	no	—
1103	C₂×D₄	—	4	1	no	—
1104	C₂×D₄	—	4	1	no	—
1105	C₂×D₄	—	4	1	no	—
1106	C₂²×C₄	—	2	2	no	—
1107	C₂²×C₄	—	2	2	no	—
1108	C₂²×C₄	—	2	2	no	—
1109	C₂²×C₄	—	2	2	no	—
1110	C₂²×C₄	—	2	2	no	—
1111	C₂²×C₄	—	2	2	no	—
1112	C₂²×C₄	—	2	2	no	—
1113	C₂²×C₄	—	2	2	no	—
1114	C₂²×C₄	—	4	1	no	—
1115	C₂²×C₄	—	4	1	no	—
1116	C₂²×C₄	—	4	1	no	—
1117	C₂²×C₄	—	4	1	no	—
1118	C₂²×C₄	—	4	1	no	—
1119	C₂²×C₄	—	4	1	no	—
1120	C₂²×C₄	—	4	1	no	—
1121	C₂²×C₄	—	4	1	no	—
1122	C₂²×C₄	—	4	1	no	—
1123	C₂²×C₄	—	4	1	no	—
1124	C₂²×C₄	—	4	1	no	—
1125	C₂²×C₄	#41×C₃₁	1	4	yes	—
1126	C₂²×C₄	#41×C₃₁	1	4	yes	—
1127	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1128	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1129	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1130	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1131	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1132	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1133	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1134	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1135	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1136	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1137	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1138	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1139	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1140	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1141	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1142	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1143	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1144	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1145	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1146	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1147	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1148	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1149	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1150	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1151	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1152	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1153	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1154	C₄⋊C₄	—	2	2	no	—
1155	C₄⋊C₄	—	2	2	no	—
1156	C₄⋊C₄	—	2	2	no	—
1157	C₄⋊C₄	—	2	2	no	—
1158	C₄⋊C₄	—	2	2	no	—
1159	C₄⋊C₄	—	2	2	no	—
1160	C₄⋊C₄	—	2	2	no	—
1161	C₄⋊C₄	—	2	2	no	—
1162	C₄⋊C₄	—	2	2	no	—
1163	C₄⋊C₄	—	2	2	no	—
1164	C₄⋊C₄	—	2	2	no	—
1165	C₄⋊C₄	—	2	2	no	—
1166	C₄⋊C₄	—	2	2	no	—
1167	C₄⋊C₄	—	4	1	no	—
1168	C₄⋊C₄	—	4	1	no	—
1169	C₄⋊C₄	—	4	1	no	—
1170	C₄⋊C₄	—	4	1	no	—
1171	C₄⋊C₄	—	4	1	no	—
1172	C₄⋊C₄	—	4	1	no	—
1173	C₄⋊C₄	—	4	1	no	—
1174	C₄⋊C₄	—	4	1	no	—
1175	C₄⋊C₄	—	4	1	no	—
1176	C₄⋊C₄	—	4	1	no	—
1177	C₄⋊C₄	—	4	1	no	—
1178	C₄⋊C₄	—	4	1	no	—
1179	C₄⋊C₄	—	4	1	no	—
1180	C₄⋊C₄	—	4	1	no	—
1181	C₄⋊C₄	—	4	1	no	—
1182	C₄⋊C₄	—	4	1	no	—
1183	C₄⋊C₄	—	4	1	no	—
1184	C₄⋊C₄	—	4	1	no	—
1185	C₄⋊C₄	—	4	1	no	—
1186	C₂²⋊C₄	—	2	2	no	—
1187	C₂²⋊C₄	—	2	2	no	—
1188	C₂²⋊C₄	—	2	2	no	—
1189	C₂²⋊C₄	—	2	2	no	—
1190	C₂²⋊C₄	—	2	2	no	—
1191	C₂²⋊C₄	—	2	2	no	—
1192	C₂²⋊C₄	—	2	2	no	—
1193	C₂²⋊C₄	—	2	2	no	—
1194	C₂²⋊C₄	—	2	2	no	—
1195	C₂²⋊C₄	—	2	2	no	—
1196	C₂²⋊C₄	—	2	2	no	—
1197	C₂²⋊C₄	—	2	2	no	—
1198	C₂²⋊C₄	—	2	2	no	—
1199	C₂²⋊C₄	—	2	2	no	—
1200	C₂²⋊C₄	—	2	2	no	—
1201	C₂²⋊C₄	—	2	2	no	—
1202	C₂²⋊C₄	—	2	2	no	—
1203	C₂²⋊C₄	—	2	2	no	—
1204	C₂²⋊C₄	—	2	2	no	—
1205	C₂²⋊C₄	—	2	2	no	—
1206	C₂²⋊C₄	—	2	2	no	—
1207	C₂²⋊C₄	—	2	2	no	—
1208	C₂²⋊C₄	—	4	1	no	—
1209	C₂²⋊C₄	—	4	1	no	—
1210	C₂²⋊C₄	—	4	1	no	—
1211	C₂²⋊C₄	—	4	1	no	—
1212	C₂²⋊C₄	—	4	1	no	—
1213	C₂²⋊C₄	—	4	1	no	—
1214	C₂²⋊C₄	—	4	1	no	—
1215	C₂²⋊C₄	—	4	1	no	—
1216	C₂²⋊C₄	—	4	1	no	—
1217	C₂²⋊C₄	—	4	1	no	—
1218	C₂²⋊C₄	—	4	1	no	—
1219	C₂²⋊C₄	—	4	1	no	—
1220	C₂²⋊C₄	—	4	1	no	—
1221	C₂²⋊C₄	—	4	1	no	—
1222	C₂²⋊C₄	—	4	1	no	—
1223	C₂²⋊C₄	—	4	1	no	—
1224	C₂²⋊C₄	—	4	1	no	—
1225	C₂²⋊C₄	—	4	1	no	—
1226	C₂²⋊C₄	—	4	1	no	—
1227	C₂²⋊C₄	—	4	1	no	—
1228	C₂²⋊C₄	—	4	1	no	—
1229	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
1230	C₄²	—	2	2	no	—
1231	C₄²	—	2	2	no	—
1232	C₄²	—	2	2	no	—
1233	C₄²	—	2	2	no	—
1234	C₄²	—	2	2	no	—
1235	C₄²	—	2	2	no	—
1236	C₄²	—	2	2	no	—
1237	C₄²	—	2	2	no	—
1238	C₄²	—	2	2	no	—
1239	C₄²	—	2	2	no	—
1240	C₄²	—	2	2	no	—
1241	C₄²	—	4	1	no	—
1242	C₄²	—	4	1	no	—
1243	C₄²	—	4	1	no	—
1244	C₄²	—	4	1	no	—
1245	C₄²	—	4	1	no	—
1246	C₄²	—	4	1	no	—
1247	C₄²	—	4	1	no	—
1248	C₄²	—	4	1	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	2	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	2	1	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	1	no	—
1256	C₂³	—	2	1	no	—
1257	C₂³	—	2	1	no	—
1258	C₂³	—	2	1	no	—
1259	C₂³	—	2	1	no	—
1260	C₂³	—	2	1	no	—
1261	C₂³	—	2	1	no	—
1262	C₂³	—	2	1	no	—
1263	C₂³	—	2	1	no	—
1264	C₂³	—	2	1	no	—
1265	C₂³	—	2	1	no	—
1266	C₂³	—	2	1	no	—
1267	C₂³	—	2	1	no	—
1268	C₂³	—	2	1	no	—
1269	C₂³	—	2	1	no	—
1270	C₂³	—	2	1	no	—
1271	C₂³	—	2	1	no	—
1272	C₂³	—	2	1	no	—
1273	C₂³	—	2	1	no	—
1274	C₂³	—	4	4	no	—
1275	C₂³	—	4	4	no	—
1276	C₂³	—	4	4	no	—
1277	C₂³	—	8	2	no	—
1278	C₂³	—	8	2	no	—
1279	C₂³	—	8	2	no	—
1280	C₂³	—	8	2	no	—
1281	C₂³	C₂×#41×C₃₁	1	2	yes	—
1282	C₂³	C₂×#41×C₃₁	1	2	yes	—
1283	C₂³	C₂×#41×C₃₁	1	2	yes	—
1284	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1285	Q₈	—	8	2	no	—
1286	D₄	—	4	4	no	—
1287	D₄	—	8	2	no	—
1288	D₄	—	8	2	no	—
1289	C₂×C₄	—	2	8	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	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	4	4	no	—
1365	C₂×C₄	—	4	4	no	—
1366	C₂×C₄	—	4	4	no	—
1367	C₂×C₄	—	8	2	no	—
1368	C₂×C₄	—	8	2	no	—
1369	C₂×C₄	—	8	2	no	—
1370	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1371	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1372	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1373	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1374	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1375	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1376	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1377	C₂²	—	2	2	no	—
1378	C₂²	—	2	2	no	—
1379	C₂²	—	2	2	no	—
1380	C₂²	—	2	2	no	—
1381	C₂²	—	2	2	no	—
1382	C₂²	—	2	2	no	—
1383	C₂²	—	4	1	no	—
1384	C₂²	—	4	1	no	—
1385	C₂²	—	4	1	no	—
1386	C₂²	—	4	1	no	—
1387	C₂²	—	4	1	no	—
1388	C₂²	—	4	1	no	—
1389	C₂²	—	4	1	no	—
1390	C₂²	—	4	1	no	—
1391	C₂²	—	4	1	no	—
1392	C₂²	—	4	1	no	—
1393	C₂²	—	4	1	no	—
1394	C₂²	—	4	1	no	—
1395	C₂²	—	4	1	no	—
1396	C₂²	—	4	1	no	—
1397	C₂²	—	4	1	no	—
1398	C₂²	—	4	1	no	—
1399	C₂²	—	4	1	no	—
1400	C₂²	—	4	1	no	—
1401	C₂²	—	4	1	no	—
1402	C₂²	—	4	1	no	—
1403	C₂²	—	4	1	no	—
1404	C₂²	—	8	8	no	—
1405	C₂²	C₃₁×#529	1	4	yes	—
1406	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1407	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1408	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1409	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1410	C₂²	C₃₁×#585	1	1	yes	characteristic
1411	C₂²	C₃₁×#585	1	1	yes	characteristic
1412	C₂²	C₃₁×#585	1	1	yes	characteristic
1413	C₄	—	2	2	no	—
1414	C₄	—	2	2	no	—
1415	C₄	—	2	2	no	—
1416	C₄	—	2	2	no	—
1417	C₄	—	2	2	no	—
1418	C₄	—	2	2	no	—
1419	C₄	—	2	2	no	—
1420	C₄	—	4	1	no	—
1421	C₄	—	4	1	no	—
1422	C₄	—	4	1	no	—
1423	C₄	—	4	1	no	—
1424	C₄	—	4	1	no	—
1425	C₄	—	4	1	no	—
1426	C₄	—	4	1	no	—
1427	C₄	—	4	1	no	—
1428	C₄	—	4	1	no	—
1429	C₄	—	4	1	no	—
1430	C₄	—	4	1	no	—
1431	C₄	—	4	1	no	—
1432	C₄	—	4	1	no	—
1433	C₄	—	4	1	no	—
1434	C₄	—	4	1	no	—
1435	C₄	—	4	1	no	—
1436	C₄	—	4	1	no	—
1437	C₄	—	4	1	no	—
1438	C₄	—	4	1	no	—
1439	C₄	—	4	1	no	—
1440	C₂	—	2	4	no	—
1441	C₂	—	8	1	no	—
1442	C₂	—	8	1	no	—
1443	C₂	—	8	1	no	—
1444	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
1445	C₂	C₃₁×#3455	1	1	yes	characteristic
1446	C₂	C₃₁×#3460	1	1	yes	characteristic
1447	C₂	C₃₁×#3491	1	1	yes	characteristic
1448	C₂	C₃₁×#3494	1	1	yes	characteristic
1449	C₂	C₃₁×#3514	1	1	yes	characteristic
1450	C₂	C₃₁×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#120	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2866	C₂	semidirect
2. C₃₁×#2865	C₂	semidirect
3. C₃₁×#2861	C₂	semidirect
4. C₃₁×#2860	C₂	semidirect
5. C₃₁×#2654	C₂	semidirect
6. C₃₁×#2651	C₂	semidirect
7. C₃₁×#2651	C₂	semidirect
8. C₃₁×#2650	C₂	semidirect
9. C₃₁×#2532	C₂	semidirect
10. C₃₁×#2531	C₂	semidirect
11. C₃₁×#2529	C₂	semidirect
12. C₃₁×#2526	C₂	semidirect
13. C₃₁×#2525	C₂	semidirect
14. C₃₁×#2521	C₂	semidirect
15. C₃₁×#2519	C₂	semidirect
16. C₃₁×#2516	C₂	semidirect
17. C₃₁×#2498	C₂	semidirect
18. C₃₁×#2482	C₂	semidirect
19. C₃₁×#2481	C₂	semidirect
20. C₃₁×#2480	C₂	semidirect
21. C₃₁×#2473	C₂	semidirect
23. C₃₁×#2438	C₂	semidirect
25. C₃₁×#2329	C₂	semidirect
27. C₃₁×#2318	C₂	semidirect
28. C₃₁×#2312	C₂	semidirect
29. C₄×C₃₁×#123	C₂	semidirect
30. C₂×C₃₁×#388	C₂	semidirect
31. C₄×C₃₁×#117	C₂	semidirect
33. C₂×C₃₁×#126	C₂²	semidirect
34. C₂×C₃₁×#125	C₂²	semidirect
47. C₃₁×#400	C₂²	semidirect
48. C₃₁×#400	C₂²	semidirect
49. C₃₁×#400	C₂²	semidirect
50. C₃₁×#400	C₂²	semidirect
51. C₃₁×#400	C₂²	semidirect
54. C₃₁×#399	C₂²	semidirect
55. C₃₁×#398	C₂²	semidirect
56. C₃₁×#398	C₂²	semidirect
57. C₃₁×#398	C₂²	semidirect
58. C₃₁×#398	C₂²	semidirect
59. C₃₁×#398	C₂²	semidirect
60. C₃₁×#398	C₂²	semidirect
67. C₃₁×#397	C₂²	semidirect
68. C₃₁×#397	C₂²	semidirect
72. C₃₁×#396	C₂²	semidirect
73. C₃₁×#395	C₂²	semidirect
79. C₃₁×#391	C₂²	semidirect
80. C₃₁×#391	C₂²	semidirect
81. C₃₁×#391	C₂²	semidirect
87. C₃₁×#389	C₂²	semidirect
88. C₃₁×#389	C₂²	semidirect
89. C₃₁×#389	C₂²	semidirect
90. C₃₁×#389	C₂²	semidirect
122. C₃₁×#388	C₂²	semidirect
123. C₃₁×#388	C₂²	semidirect
124. C₃₁×#388	C₂²	semidirect
125. C₃₁×#388	C₂²	semidirect
126. C₃₁×#388	C₂²	semidirect
127. C₃₁×#388	C₂²	semidirect
128. C₃₁×#388	C₂²	semidirect
129. C₃₁×#387	C₂²	semidirect
130. C₃₁×#387	C₂²	semidirect
131. C₃₁×#387	C₂²	semidirect
132. C₃₁×#387	C₂²	semidirect
133. C₃₁×#387	C₂²	semidirect
134. C₃₁×#387	C₂²	semidirect
135. C₃₁×#387	C₂²	semidirect
136. C₃₁×#387	C₂²	semidirect
137. C₃₁×#387	C₂²	semidirect
138. C₃₁×#387	C₂²	semidirect
139. C₃₁×#387	C₂²	semidirect
140. C₃₁×#387	C₂²	semidirect
141. C₃₁×#387	C₂²	semidirect
142. C₃₁×#387	C₂²	semidirect
143. C₃₁×#387	C₂²	semidirect
144. C₃₁×#387	C₂²	semidirect
157. C₃₁×#383	C₂²	semidirect
158. C₃₁×#382	C₂²	semidirect
160. C₃₁×#381	C₂²	semidirect
164. C₃₁×#380	C₂²	semidirect
168. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
169. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
170. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
171. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
172. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
173. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
179. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
180. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
181. C₃₁×#376	C₂²	semidirect
182. C₃₁×#376	C₂²	semidirect
185. C₄³×C₃₁	C₂²	semidirect
186. C₄³×C₃₁	C₂²	semidirect
523. #35100	C₃₁	direct (N × H)
652. #2866	C₂×C₃₁	semidirect
653. #2865	C₂×C₃₁	semidirect
654. #2861	C₂×C₃₁	semidirect
655. #2860	C₂×C₃₁	semidirect
656. #2654	C₂×C₃₁	semidirect
657. #2651	C₂×C₃₁	semidirect
658. #2651	C₂×C₃₁	semidirect
659. #2650	C₂×C₃₁	semidirect
660. #2532	C₂×C₃₁	semidirect
661. #2531	C₂×C₃₁	semidirect
662. #2529	C₂×C₃₁	semidirect
663. #2526	C₂×C₃₁	semidirect
664. #2525	C₂×C₃₁	semidirect
665. #2521	C₂×C₃₁	semidirect
666. #2519	C₂×C₃₁	semidirect
667. #2516	C₂×C₃₁	semidirect
668. #2498	C₂×C₃₁	semidirect
669. #2482	C₂×C₃₁	semidirect
670. #2481	C₂×C₃₁	semidirect
671. #2480	C₂×C₃₁	semidirect
672. #2473	C₂×C₃₁	semidirect
674. #2438	C₂×C₃₁	semidirect
676. #2329	C₂×C₃₁	semidirect
678. #2318	C₂×C₃₁	semidirect
679. #2312	C₂×C₃₁	semidirect
680. C₄×#123	C₂×C₃₁	semidirect
681. C₂×#388	C₂×C₃₁	semidirect
682. C₄×#117	C₂×C₃₁	semidirect
747. C₂×#126	C₂²×C₃₁	semidirect
748. C₂×#125	C₂²×C₃₁	semidirect
761. #400	C₂²×C₃₁	semidirect
762. #400	C₂²×C₃₁	semidirect
763. #400	C₂²×C₃₁	semidirect
764. #400	C₂²×C₃₁	semidirect
765. #400	C₂²×C₃₁	semidirect
768. #399	C₂²×C₃₁	semidirect
769. #398	C₂²×C₃₁	semidirect
770. #398	C₂²×C₃₁	semidirect
771. #398	C₂²×C₃₁	semidirect
772. #398	C₂²×C₃₁	semidirect
773. #398	C₂²×C₃₁	semidirect
774. #398	C₂²×C₃₁	semidirect
781. #397	C₂²×C₃₁	semidirect
782. #397	C₂²×C₃₁	semidirect
786. #396	C₂²×C₃₁	semidirect
787. #395	C₂²×C₃₁	semidirect
793. #391	C₂²×C₃₁	semidirect
794. #391	C₂²×C₃₁	semidirect
795. #391	C₂²×C₃₁	semidirect
801. #389	C₂²×C₃₁	semidirect
802. #389	C₂²×C₃₁	semidirect
803. #389	C₂²×C₃₁	semidirect
804. #389	C₂²×C₃₁	semidirect
836. #388	C₂²×C₃₁	semidirect
837. #388	C₂²×C₃₁	semidirect
838. #388	C₂²×C₃₁	semidirect
839. #388	C₂²×C₃₁	semidirect
840. #388	C₂²×C₃₁	semidirect
841. #388	C₂²×C₃₁	semidirect
842. #388	C₂²×C₃₁	semidirect
843. #387	C₂²×C₃₁	semidirect
844. #387	C₂²×C₃₁	semidirect
845. #387	C₂²×C₃₁	semidirect
846. #387	C₂²×C₃₁	semidirect
847. #387	C₂²×C₃₁	semidirect
848. #387	C₂²×C₃₁	semidirect
849. #387	C₂²×C₃₁	semidirect
850. #387	C₂²×C₃₁	semidirect
851. #387	C₂²×C₃₁	semidirect
852. #387	C₂²×C₃₁	semidirect
853. #387	C₂²×C₃₁	semidirect
854. #387	C₂²×C₃₁	semidirect
855. #387	C₂²×C₃₁	semidirect
856. #387	C₂²×C₃₁	semidirect
857. #387	C₂²×C₃₁	semidirect
858. #387	C₂²×C₃₁	semidirect
871. #383	C₂²×C₃₁	semidirect
872. #382	C₂²×C₃₁	semidirect
874. #381	C₂²×C₃₁	semidirect
878. #380	C₂²×C₃₁	semidirect
882. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
883. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
884. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
885. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
886. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
887. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
893. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
894. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
895. #376	C₂²×C₃₁	semidirect
896. #376	C₂²×C₃₁	semidirect
899. C₄³	C₂²×C₃₁	semidirect
900. C₄³	C₂²×C₃₁	semidirect
1082. C₃₁	#35100	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2866	2
C₃₁×#2865	2
C₃₁×#2861	2
C₃₁×#2860	2
C₃₁×#2654	2
C₃₁×#2651	2
C₃₁×#2650	2
C₃₁×#2532	2
C₃₁×#2531	2
C₃₁×#2529	2
C₃₁×#2526	2
C₃₁×#2525	2
C₃₁×#2521	2
C₃₁×#2519	2
C₃₁×#2516	2
C₃₁×#2498	2
C₃₁×#2482	2
C₃₁×#2481	2
C₃₁×#2480	2
C₃₁×#2473	2
C₃₁×#2472	2
C₃₁×#2438	2
C₃₁×#2411	2
C₃₁×#2329	2
C₃₁×#2321	2
C₃₁×#2318	2
C₃₁×#2312	2
C₄×C₃₁×#123	2
C₂×C₃₁×#388	2
C₄×C₃₁×#117	2
#35100	31

Subgroups — C31×#35100 #21491859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35100 #21491859