Subgroups — C₃₁×#35141 #21491900

Order 7936.

1528 conjugacy classes of subgroups.

The subgroup lattice has 1266 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
2	C₃₁×#2865	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2864	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2863	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2666	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2664	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2637	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#2634	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2585	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2585	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2573	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2556	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2525	C₂	1	1	yes	maximal, characteristic
14	C₃₁×#2525	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2524	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2524	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2520	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2520	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2519	C₂	1	1	yes	maximal, characteristic
20	C₃₁×#2515	C₂	1	1	yes	maximal, characteristic
21	C₃₁×#2469	C₂	1	1	yes	maximal, characteristic
22	C₃₁×#2465	C₂	1	1	yes	maximal, characteristic
23	C₃₁×#2462	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#2462	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#2336	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#2336	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#2334	C₂	1	1	yes	maximal, characteristic
28	C₃₁×#2332	C₂	1	1	yes	maximal, characteristic
29	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₃₁×#126	C₂	1	1	yes	maximal, characteristic
31	C₄²×Q₈×C₃₁	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
34	C₂×C₃₁×#125	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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#400	C₂²	1	1	yes	characteristic
42	C₃₁×#400	C₂²	1	1	yes	characteristic
43	C₃₁×#400	C₂²	1	1	yes	characteristic
44	C₃₁×#400	C₂²	1	1	yes	characteristic
45	C₃₁×#400	C₂²	1	1	yes	characteristic
46	C₃₁×#400	C₂²	1	1	yes	characteristic
47	C₃₁×#400	C₂²	1	1	yes	characteristic
48	C₃₁×#399	C₂²	1	1	yes	characteristic
49	C₃₁×#398	C₂²	1	1	yes	characteristic
50	C₃₁×#398	C₂²	1	1	yes	characteristic
51	C₃₁×#398	C₂²	1	1	yes	characteristic
52	C₃₁×#398	C₂²	1	1	yes	characteristic
53	C₃₁×#398	C₂²	1	1	yes	characteristic
54	C₃₁×#398	C₂²	1	1	yes	characteristic
55	C₃₁×#398	C₂²	1	1	yes	characteristic
56	C₃₁×#398	C₂²	1	1	yes	characteristic
57	C₃₁×#398	C₂²	1	1	yes	characteristic
58	C₃₁×#398	C₂²	1	1	yes	characteristic
59	C₃₁×#398	C₂²	1	1	yes	characteristic
60	C₃₁×#398	C₂²	1	1	yes	characteristic
61	C₃₁×#397	C₂²	1	1	yes	characteristic
62	C₃₁×#397	C₂²	1	1	yes	characteristic
63	C₃₁×#396	C₂²	1	1	yes	characteristic
64	C₃₁×#396	C₂²	1	1	yes	characteristic
65	C₃₁×#396	C₂²	1	1	yes	characteristic
66	C₃₁×#396	C₂²	1	1	yes	characteristic
67	C₃₁×#395	C₂²	1	1	yes	characteristic
68	C₃₁×#395	C₂²	1	1	yes	characteristic
69	C₃₁×#395	C₂²	1	1	yes	characteristic
70	C₃₁×#395	C₂²	1	1	yes	characteristic
71	C₃₁×#395	C₂²	1	1	yes	characteristic
72	C₃₁×#393	C₂²	1	1	yes	characteristic
73	C₃₁×#391	C₂²	1	1	yes	characteristic
74	C₃₁×#391	C₂²	1	1	yes	characteristic
75	C₃₁×#391	C₂²	1	1	yes	characteristic
76	C₃₁×#391	C₂²	1	1	yes	characteristic
77	C₃₁×#389	C₂²	1	1	yes	characteristic
78	C₃₁×#389	C₂²	1	1	yes	characteristic
79	C₃₁×#389	C₂²	1	1	yes	characteristic
80	C₃₁×#389	C₂²	1	1	yes	characteristic
81	C₃₁×#389	C₂²	1	1	yes	characteristic
82	C₃₁×#389	C₂²	1	1	yes	characteristic
83	C₃₁×#389	C₂²	1	1	yes	characteristic
84	C₃₁×#389	C₂²	1	1	yes	characteristic
85	C₃₁×#389	C₂²	1	1	yes	characteristic
86	C₃₁×#389	C₂²	1	1	yes	characteristic
87	C₃₁×#389	C₂²	1	1	yes	characteristic
88	C₃₁×#389	C₂²	1	1	yes	characteristic
89	C₃₁×#388	C₂²	1	1	yes	characteristic
90	C₃₁×#388	C₂²	1	1	yes	characteristic
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×#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×#387	C₂²	1	1	yes	characteristic
125	C₃₁×#387	C₂²	1	1	yes	characteristic
126	C₃₁×#387	C₂²	1	1	yes	characteristic
127	C₃₁×#387	C₂²	1	1	yes	characteristic
128	C₃₁×#387	C₂²	1	1	yes	characteristic
129	C₃₁×#387	C₂²	1	1	yes	characteristic
130	C₃₁×#387	C₂²	1	1	yes	characteristic
131	C₃₁×#387	C₂²	1	1	yes	characteristic
132	C₃₁×#387	C₂²	1	1	yes	characteristic
133	C₃₁×#387	C₂²	1	1	yes	characteristic
134	C₃₁×#387	C₂²	1	1	yes	characteristic
135	C₃₁×#387	C₂²	1	1	yes	characteristic
136	C₃₁×#387	C₂²	1	1	yes	characteristic
137	C₃₁×#387	C₂²	1	1	yes	characteristic
138	C₃₁×#387	C₂²	1	1	yes	characteristic
139	C₃₁×#387	C₂²	1	1	yes	characteristic
140	C₃₁×#387	C₂²	1	1	yes	characteristic
141	C₃₁×#387	C₂²	1	1	yes	characteristic
142	C₃₁×#387	C₂²	1	1	yes	characteristic
143	C₃₁×#387	C₂²	1	1	yes	characteristic
144	C₃₁×#387	C₂²	1	1	yes	characteristic
145	C₃₁×#387	C₂²	1	1	yes	characteristic
146	C₃₁×#387	C₂²	1	1	yes	characteristic
147	C₃₁×#387	C₂²	1	1	yes	characteristic
148	C₃₁×#387	C₂²	1	1	yes	characteristic
149	C₃₁×#387	C₂²	1	1	yes	characteristic
150	C₃₁×#387	C₂²	1	1	yes	characteristic
151	C₃₁×#385	C₂²	1	1	yes	characteristic
152	C₃₁×#385	C₂²	1	1	yes	characteristic
153	C₃₁×#383	C₂²	1	1	yes	characteristic
154	C₃₁×#383	C₂²	1	1	yes	characteristic
155	C₃₁×#383	C₂²	1	1	yes	characteristic
156	C₃₁×#383	C₂²	1	1	yes	characteristic
157	C₃₁×#383	C₂²	1	1	yes	characteristic
158	C₃₁×#382	C₂²	1	1	yes	characteristic
159	C₃₁×#382	C₂²	1	1	yes	characteristic
160	C₃₁×#382	C₂²	1	1	yes	characteristic
161	C₃₁×#382	C₂²	1	1	yes	characteristic
162	C₃₁×#381	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×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
173	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
174	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
175	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
176	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
179	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
180	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
184	C₄³×C₃₁	C₂²	1	1	yes	characteristic
185	C₄³×C₃₁	C₂²	1	1	yes	characteristic
186	C₄³×C₃₁	C₂²	1	1	yes	characteristic
187	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
189	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₃₁×#126	—	2	4	no	—
191	C₃₁×#126	—	2	4	no	—
192	C₃₁×#125	—	2	4	no	—
193	C₃₁×#125	—	2	4	no	—
194	C₃₁×#125	—	2	4	no	—
195	C₃₁×C₂²⋊Q₈	—	2	4	no	—
196	C₄×Q₈×C₃₁	—	2	4	no	—
197	C₄×Q₈×C₃₁	—	2	4	no	—
198	C₄×Q₈×C₃₁	—	2	4	no	—
199	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×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×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×C₄²×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
268	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
272	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
277	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
278	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
280	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
281	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
282	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#95	C₂³	1	1	yes	characteristic
288	C₃₁×#95	C₂³	1	1	yes	characteristic
289	C₃₁×#95	C₂³	1	1	yes	characteristic
290	C₃₁×#95	C₂³	1	1	yes	characteristic
291	C₃₁×#95	C₂³	1	1	yes	characteristic
292	C₃₁×#95	C₂³	1	1	yes	characteristic
293	C₃₁×#95	C₂³	1	1	yes	characteristic
294	C₃₁×#95	C₂³	1	1	yes	characteristic
295	C₃₁×#95	C₂³	1	1	yes	characteristic
296	C₃₁×#95	C₂³	1	1	yes	characteristic
297	C₃₁×#95	C₂³	1	1	yes	characteristic
298	C₃₁×#95	C₂³	1	1	yes	characteristic
299	C₃₁×#95	C₂³	1	1	yes	characteristic
300	C₃₁×#95	C₂³	1	1	yes	characteristic
301	C₃₁×#95	C₂³	1	1	yes	characteristic
302	C₃₁×#95	C₂³	1	1	yes	characteristic
303	C₃₁×#95	C₂³	1	1	yes	characteristic
304	C₃₁×#95	C₂³	1	1	yes	characteristic
305	C₃₁×#95	C₂³	1	1	yes	characteristic
306	C₃₁×#95	C₂³	1	1	yes	characteristic
307	C₃₁×#95	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	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×Q₈×C₃₁	—	2	2	no	—
353	C₂×Q₈×C₃₁	—	2	2	no	—
354	C₂×Q₈×C₃₁	—	2	2	no	—
355	C₂×Q₈×C₃₁	—	2	2	no	—
356	C₂×Q₈×C₃₁	—	4	1	no	—
357	C₂×Q₈×C₃₁	—	4	1	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	4	1	no	—
360	C₂²×C₄×C₃₁	—	4	1	no	—
361	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	2	no	—
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	2	no	—
415	C₄⋊C₄×C₃₁	—	2	2	no	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	—	2	2	no	—
420	C₄⋊C₄×C₃₁	—	2	2	no	—
421	C₄⋊C₄×C₃₁	—	2	2	no	—
422	C₄⋊C₄×C₃₁	—	2	2	no	—
423	C₄⋊C₄×C₃₁	—	2	2	no	—
424	C₄⋊C₄×C₃₁	—	2	2	no	—
425	C₄⋊C₄×C₃₁	—	4	1	no	—
426	C₄⋊C₄×C₃₁	—	4	1	no	—
427	C₄⋊C₄×C₃₁	—	4	1	no	—
428	C₄⋊C₄×C₃₁	—	4	1	no	—
429	C₄⋊C₄×C₃₁	—	4	1	no	—
430	C₄⋊C₄×C₃₁	—	4	1	no	—
431	C₄⋊C₄×C₃₁	—	4	1	no	—
432	C₄⋊C₄×C₃₁	—	4	1	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	#41	1	4	yes	—
438	C₄⋊C₄×C₃₁	#41	1	4	yes	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	—	2	2	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	2	no	—
445	C₂²⋊C₄×C₃₁	—	2	2	no	—
446	C₂²⋊C₄×C₃₁	—	2	2	no	—
447	C₂²⋊C₄×C₃₁	—	2	2	no	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	—	4	1	no	—
450	C₂²⋊C₄×C₃₁	—	4	1	no	—
451	C₂²⋊C₄×C₃₁	—	4	1	no	—
452	C₂²⋊C₄×C₃₁	—	4	1	no	—
453	C₄²×C₃₁	—	2	2	no	—
454	C₄²×C₃₁	—	2	2	no	—
455	C₄²×C₃₁	—	2	2	no	—
456	C₄²×C₃₁	—	2	2	no	—
457	C₄²×C₃₁	—	2	2	no	—
458	C₄²×C₃₁	—	2	2	no	—
459	C₄²×C₃₁	—	2	2	no	—
460	C₄²×C₃₁	—	2	2	no	—
461	C₄²×C₃₁	—	2	2	no	—
462	C₄²×C₃₁	—	2	2	no	—
463	C₄²×C₃₁	—	2	2	no	—
464	C₄²×C₃₁	—	2	2	no	—
465	C₄²×C₃₁	—	2	2	no	—
466	C₄²×C₃₁	—	2	2	no	—
467	C₄²×C₃₁	—	2	2	no	—
468	C₄²×C₃₁	—	4	1	no	—
469	C₄²×C₃₁	—	4	1	no	—
470	C₄²×C₃₁	—	4	1	no	—
471	C₄²×C₃₁	—	4	1	no	—
472	C₄²×C₃₁	—	4	1	no	—
473	C₄²×C₃₁	—	4	1	no	—
474	C₄²×C₃₁	—	4	1	no	—
475	C₄²×C₃₁	—	4	1	no	—
476	C₄²×C₃₁	—	4	1	no	—
477	C₄²×C₃₁	—	4	1	no	—
478	C₄²×C₃₁	#41	1	4	yes	—
479	#35141	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
480	C₂³×C₃₁	—	2	1	no	—
481	C₂³×C₃₁	—	2	1	no	—
482	C₂³×C₃₁	—	2	1	no	—
483	C₂³×C₃₁	—	2	1	no	—
484	C₂³×C₃₁	—	2	1	no	—
485	C₂³×C₃₁	—	2	1	no	—
486	C₂³×C₃₁	—	2	1	no	—
487	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
488	Q₈×C₃₁	—	2	8	no	—
489	Q₈×C₃₁	—	8	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	1	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	1	no	—
514	C₂×C₄×C₃₁	—	2	1	no	—
515	C₂×C₄×C₃₁	—	2	1	no	—
516	C₂×C₄×C₃₁	—	2	1	no	—
517	C₂×C₄×C₃₁	—	2	1	no	—
518	C₂×C₄×C₃₁	—	2	1	no	—
519	C₂×C₄×C₃₁	—	2	1	no	—
520	C₂×C₄×C₃₁	—	2	1	no	—
521	C₂×C₄×C₃₁	—	2	1	no	—
522	C₂×C₄×C₃₁	—	2	1	no	—
523	C₂×C₄×C₃₁	—	2	1	no	—
524	C₂×C₄×C₃₁	—	2	1	no	—
525	C₂×C₄×C₃₁	—	2	1	no	—
526	C₂×C₄×C₃₁	—	2	1	no	—
527	C₂×C₄×C₃₁	—	2	1	no	—
528	C₂×C₄×C₃₁	—	2	1	no	—
529	C₂×C₄×C₃₁	—	2	1	no	—
530	C₂×C₄×C₃₁	—	2	1	no	—
531	C₂×C₄×C₃₁	—	2	1	no	—
532	C₂×C₄×C₃₁	—	2	1	no	—
533	C₂×C₄×C₃₁	—	2	1	no	—
534	C₂×C₄×C₃₁	—	2	1	no	—
535	C₂×C₄×C₃₁	—	2	1	no	—
536	C₂×C₄×C₃₁	—	2	1	no	—
537	C₂×C₄×C₃₁	—	2	1	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	—	8	2	no	—
570	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
571	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
572	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
573	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
574	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
575	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
576	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
577	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
578	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
579	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
580	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
581	#2866	C₂×C₃₁	1	1	yes	characteristic
582	#2865	C₂×C₃₁	1	1	yes	characteristic
583	#2864	C₂×C₃₁	1	1	yes	characteristic, complemented
584	#2863	C₂×C₃₁	1	1	yes	characteristic, complemented
585	#2666	C₂×C₃₁	1	1	yes	characteristic, complemented
586	#2664	C₂×C₃₁	1	1	yes	characteristic
587	#2637	C₂×C₃₁	1	1	yes	characteristic
588	#2634	C₂×C₃₁	1	1	yes	characteristic, complemented
589	#2585	C₂×C₃₁	1	1	yes	characteristic, complemented
590	#2585	C₂×C₃₁	1	1	yes	characteristic, complemented
591	#2573	C₂×C₃₁	1	1	yes	characteristic
592	#2556	C₂×C₃₁	1	1	yes	characteristic
593	#2525	C₂×C₃₁	1	1	yes	characteristic
594	#2525	C₂×C₃₁	1	1	yes	characteristic
595	#2524	C₂×C₃₁	1	1	yes	characteristic, complemented
596	#2524	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#2520	C₂×C₃₁	1	1	yes	characteristic, complemented
598	#2520	C₂×C₃₁	1	1	yes	characteristic, complemented
599	#2519	C₂×C₃₁	1	1	yes	characteristic
600	#2515	C₂×C₃₁	1	1	yes	characteristic
601	#2469	C₂×C₃₁	1	1	yes	characteristic
602	#2465	C₂×C₃₁	1	1	yes	characteristic
603	#2462	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#2462	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#2336	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#2336	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#2334	C₂×C₃₁	1	1	yes	characteristic
608	#2332	C₂×C₃₁	1	1	yes	characteristic
609	C₄×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
610	C₄×#126	C₂×C₃₁	1	1	yes	characteristic
611	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
612	C₂²×C₃₁	—	4	1	no	—
613	C₂²×C₃₁	—	4	1	no	—
614	C₂²×C₃₁	—	4	1	no	—
615	C₂²×C₃₁	—	4	1	no	—
616	C₂²×C₃₁	—	4	1	no	—
617	C₂²×C₃₁	—	4	1	no	—
618	C₂²×C₃₁	—	4	1	no	—
619	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
620	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
621	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
622	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
623	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
624	C₂²×C₃₁	#585	1	1	yes	characteristic
625	C₂²×C₃₁	#585	1	1	yes	characteristic
626	C₄×C₃₁	—	2	2	no	—
627	C₄×C₃₁	—	2	2	no	—
628	C₄×C₃₁	—	2	2	no	—
629	C₄×C₃₁	—	2	2	no	—
630	C₄×C₃₁	—	2	2	no	—
631	C₄×C₃₁	—	2	2	no	—
632	C₄×C₃₁	—	2	2	no	—
633	C₄×C₃₁	—	2	2	no	—
634	C₄×C₃₁	—	2	2	no	—
635	C₄×C₃₁	—	2	2	no	—
636	C₄×C₃₁	—	2	2	no	—
637	C₄×C₃₁	—	4	1	no	—
638	C₄×C₃₁	—	4	1	no	—
639	C₄×C₃₁	—	4	1	no	—
640	C₄×C₃₁	—	4	1	no	—
641	C₄×C₃₁	—	4	1	no	—
642	C₄×C₃₁	—	4	1	no	—
643	C₄×C₃₁	—	4	1	no	—
644	C₄×C₃₁	—	4	1	no	—
645	C₄×C₃₁	—	4	1	no	—
646	C₄×C₃₁	—	4	1	no	—
647	C₄×C₃₁	—	4	1	no	—
648	C₄×C₃₁	—	4	1	no	—
649	C₄×C₃₁	—	4	1	no	—
650	C₄×C₃₁	—	4	1	no	—
651	C₄×C₃₁	—	4	1	no	—
652	C₄×C₃₁	—	4	1	no	—
653	C₄×C₃₁	—	4	1	no	—
654	C₄×C₃₁	—	4	1	no	—
655	C₄×C₃₁	—	4	1	no	—
656	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
657	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
658	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
659	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
660	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
661	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
662	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
663	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
664	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
665	#400	C₂²×C₃₁	1	1	yes	characteristic
666	#400	C₂²×C₃₁	1	1	yes	characteristic
667	#400	C₂²×C₃₁	1	1	yes	characteristic
668	#400	C₂²×C₃₁	1	1	yes	characteristic
669	#400	C₂²×C₃₁	1	1	yes	characteristic
670	#400	C₂²×C₃₁	1	1	yes	characteristic
671	#400	C₂²×C₃₁	1	1	yes	characteristic
672	#399	C₂²×C₃₁	1	1	yes	characteristic
673	#398	C₂²×C₃₁	1	1	yes	characteristic
674	#398	C₂²×C₃₁	1	1	yes	characteristic
675	#398	C₂²×C₃₁	1	1	yes	characteristic
676	#398	C₂²×C₃₁	1	1	yes	characteristic
677	#398	C₂²×C₃₁	1	1	yes	characteristic
678	#398	C₂²×C₃₁	1	1	yes	characteristic
679	#398	C₂²×C₃₁	1	1	yes	characteristic
680	#398	C₂²×C₃₁	1	1	yes	characteristic
681	#398	C₂²×C₃₁	1	1	yes	characteristic
682	#398	C₂²×C₃₁	1	1	yes	characteristic
683	#398	C₂²×C₃₁	1	1	yes	characteristic
684	#398	C₂²×C₃₁	1	1	yes	characteristic
685	#397	C₂²×C₃₁	1	1	yes	characteristic
686	#397	C₂²×C₃₁	1	1	yes	characteristic
687	#396	C₂²×C₃₁	1	1	yes	characteristic
688	#396	C₂²×C₃₁	1	1	yes	characteristic
689	#396	C₂²×C₃₁	1	1	yes	characteristic
690	#396	C₂²×C₃₁	1	1	yes	characteristic
691	#395	C₂²×C₃₁	1	1	yes	characteristic
692	#395	C₂²×C₃₁	1	1	yes	characteristic
693	#395	C₂²×C₃₁	1	1	yes	characteristic
694	#395	C₂²×C₃₁	1	1	yes	characteristic
695	#395	C₂²×C₃₁	1	1	yes	characteristic
696	#393	C₂²×C₃₁	1	1	yes	characteristic
697	#391	C₂²×C₃₁	1	1	yes	characteristic
698	#391	C₂²×C₃₁	1	1	yes	characteristic
699	#391	C₂²×C₃₁	1	1	yes	characteristic
700	#391	C₂²×C₃₁	1	1	yes	characteristic
701	#389	C₂²×C₃₁	1	1	yes	characteristic
702	#389	C₂²×C₃₁	1	1	yes	characteristic
703	#389	C₂²×C₃₁	1	1	yes	characteristic
704	#389	C₂²×C₃₁	1	1	yes	characteristic
705	#389	C₂²×C₃₁	1	1	yes	characteristic
706	#389	C₂²×C₃₁	1	1	yes	characteristic
707	#389	C₂²×C₃₁	1	1	yes	characteristic
708	#389	C₂²×C₃₁	1	1	yes	characteristic
709	#389	C₂²×C₃₁	1	1	yes	characteristic
710	#389	C₂²×C₃₁	1	1	yes	characteristic
711	#389	C₂²×C₃₁	1	1	yes	characteristic
712	#389	C₂²×C₃₁	1	1	yes	characteristic
713	#388	C₂²×C₃₁	1	1	yes	characteristic
714	#388	C₂²×C₃₁	1	1	yes	characteristic
715	#388	C₂²×C₃₁	1	1	yes	characteristic
716	#388	C₂²×C₃₁	1	1	yes	characteristic
717	#388	C₂²×C₃₁	1	1	yes	characteristic
718	#388	C₂²×C₃₁	1	1	yes	characteristic
719	#388	C₂²×C₃₁	1	1	yes	characteristic
720	#388	C₂²×C₃₁	1	1	yes	characteristic
721	#388	C₂²×C₃₁	1	1	yes	characteristic
722	#388	C₂²×C₃₁	1	1	yes	characteristic
723	#388	C₂²×C₃₁	1	1	yes	characteristic
724	#388	C₂²×C₃₁	1	1	yes	characteristic
725	#388	C₂²×C₃₁	1	1	yes	characteristic
726	#388	C₂²×C₃₁	1	1	yes	characteristic
727	#388	C₂²×C₃₁	1	1	yes	characteristic
728	#388	C₂²×C₃₁	1	1	yes	characteristic
729	#388	C₂²×C₃₁	1	1	yes	characteristic
730	#388	C₂²×C₃₁	1	1	yes	characteristic
731	#387	C₂²×C₃₁	1	1	yes	characteristic
732	#387	C₂²×C₃₁	1	1	yes	characteristic
733	#387	C₂²×C₃₁	1	1	yes	characteristic
734	#387	C₂²×C₃₁	1	1	yes	characteristic
735	#387	C₂²×C₃₁	1	1	yes	characteristic
736	#387	C₂²×C₃₁	1	1	yes	characteristic
737	#387	C₂²×C₃₁	1	1	yes	characteristic
738	#387	C₂²×C₃₁	1	1	yes	characteristic
739	#387	C₂²×C₃₁	1	1	yes	characteristic
740	#387	C₂²×C₃₁	1	1	yes	characteristic
741	#387	C₂²×C₃₁	1	1	yes	characteristic
742	#387	C₂²×C₃₁	1	1	yes	characteristic
743	#387	C₂²×C₃₁	1	1	yes	characteristic
744	#387	C₂²×C₃₁	1	1	yes	characteristic
745	#387	C₂²×C₃₁	1	1	yes	characteristic
746	#387	C₂²×C₃₁	1	1	yes	characteristic
747	#387	C₂²×C₃₁	1	1	yes	characteristic
748	#387	C₂²×C₃₁	1	1	yes	characteristic
749	#387	C₂²×C₃₁	1	1	yes	characteristic
750	#387	C₂²×C₃₁	1	1	yes	characteristic
751	#387	C₂²×C₃₁	1	1	yes	characteristic
752	#387	C₂²×C₃₁	1	1	yes	characteristic
753	#387	C₂²×C₃₁	1	1	yes	characteristic
754	#387	C₂²×C₃₁	1	1	yes	characteristic
755	#387	C₂²×C₃₁	1	1	yes	characteristic
756	#387	C₂²×C₃₁	1	1	yes	characteristic
757	#387	C₂²×C₃₁	1	1	yes	characteristic
758	#387	C₂²×C₃₁	1	1	yes	characteristic
759	#387	C₂²×C₃₁	1	1	yes	characteristic
760	#387	C₂²×C₃₁	1	1	yes	characteristic
761	#387	C₂²×C₃₁	1	1	yes	characteristic
762	#387	C₂²×C₃₁	1	1	yes	characteristic
763	#387	C₂²×C₃₁	1	1	yes	characteristic
764	#387	C₂²×C₃₁	1	1	yes	characteristic
765	#387	C₂²×C₃₁	1	1	yes	characteristic
766	#387	C₂²×C₃₁	1	1	yes	characteristic
767	#387	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	#385	C₂²×C₃₁	1	1	yes	characteristic
776	#385	C₂²×C₃₁	1	1	yes	characteristic
777	#383	C₂²×C₃₁	1	1	yes	characteristic
778	#383	C₂²×C₃₁	1	1	yes	characteristic
779	#383	C₂²×C₃₁	1	1	yes	characteristic
780	#383	C₂²×C₃₁	1	1	yes	characteristic
781	#383	C₂²×C₃₁	1	1	yes	characteristic
782	#382	C₂²×C₃₁	1	1	yes	characteristic
783	#382	C₂²×C₃₁	1	1	yes	characteristic
784	#382	C₂²×C₃₁	1	1	yes	characteristic
785	#382	C₂²×C₃₁	1	1	yes	characteristic
786	#381	C₂²×C₃₁	1	1	yes	characteristic
787	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
788	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
789	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
790	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
791	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
792	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
793	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
794	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
795	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
796	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
797	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
798	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
799	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
800	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
801	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
802	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
803	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
804	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
805	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
806	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
807	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
808	C₄³	C₂²×C₃₁	1	1	yes	characteristic
809	C₄³	C₂²×C₃₁	1	1	yes	characteristic
810	C₄³	C₂²×C₃₁	1	1	yes	characteristic
811	C₂×C₃₁	—	8	1	no	—
812	C₂×C₃₁	#3444	1	1	yes	characteristic
813	C₂×C₃₁	#3461	1	1	yes	characteristic
814	C₂×C₃₁	#3461	1	1	yes	characteristic
815	C₂×C₃₁	#3515	1	1	yes	characteristic
816	C₂×C₃₁	#3516	1	1	yes	characteristic
817	C₂×C₃₁	#3521	1	1	yes	characteristic
818	C₂×C₃₁	#3523	1	1	yes	characteristic
819	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
820	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
821	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
822	#126	—	2	4	no	—
823	#126	—	2	4	no	—
824	#125	—	2	4	no	—
825	#125	—	2	4	no	—
826	#125	—	2	4	no	—
827	C₂²⋊Q₈	—	2	4	no	—
828	C₄×Q₈	—	2	4	no	—
829	C₄×Q₈	—	2	4	no	—
830	C₄×Q₈	—	2	4	no	—
831	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
834	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
836	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
837	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
845	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
846	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
847	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
848	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
850	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
853	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
854	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
855	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
856	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
857	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
858	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
859	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
861	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
862	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
863	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
864	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
865	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
866	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
875	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
876	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
879	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
880	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
881	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
882	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
883	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
884	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
885	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
886	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
887	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
888	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
889	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
890	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
891	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
892	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
893	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
894	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
895	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
896	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
897	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
898	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
899	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
900	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
901	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
902	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
903	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
904	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
905	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
906	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
907	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
908	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
909	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
910	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
911	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
912	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
913	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
914	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
915	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
916	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
917	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
918	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
919	#95	C₂³×C₃₁	1	1	yes	characteristic
920	#95	C₂³×C₃₁	1	1	yes	characteristic
921	#95	C₂³×C₃₁	1	1	yes	characteristic
922	#95	C₂³×C₃₁	1	1	yes	characteristic
923	#95	C₂³×C₃₁	1	1	yes	characteristic
924	#95	C₂³×C₃₁	1	1	yes	characteristic
925	#95	C₂³×C₃₁	1	1	yes	characteristic
926	#95	C₂³×C₃₁	1	1	yes	characteristic
927	#95	C₂³×C₃₁	1	1	yes	characteristic
928	#95	C₂³×C₃₁	1	1	yes	characteristic
929	#95	C₂³×C₃₁	1	1	yes	characteristic
930	#95	C₂³×C₃₁	1	1	yes	characteristic
931	#95	C₂³×C₃₁	1	1	yes	characteristic
932	#95	C₂³×C₃₁	1	1	yes	characteristic
933	#95	C₂³×C₃₁	1	1	yes	characteristic
934	#95	C₂³×C₃₁	1	1	yes	characteristic
935	#95	C₂³×C₃₁	1	1	yes	characteristic
936	#95	C₂³×C₃₁	1	1	yes	characteristic
937	#95	C₂³×C₃₁	1	1	yes	characteristic
938	#95	C₂³×C₃₁	1	1	yes	characteristic
939	#95	C₂³×C₃₁	1	1	yes	characteristic
940	#95	C₂³×C₃₁	1	1	yes	characteristic
941	#95	C₂³×C₃₁	1	1	yes	characteristic
942	#95	C₂³×C₃₁	1	1	yes	characteristic
943	#95	C₂³×C₃₁	1	1	yes	characteristic
944	#95	C₂³×C₃₁	1	1	yes	characteristic
945	#95	C₂³×C₃₁	1	1	yes	characteristic
946	#95	C₂³×C₃₁	1	1	yes	characteristic
947	#95	C₂³×C₃₁	1	1	yes	characteristic
948	#95	C₂³×C₃₁	1	1	yes	characteristic
949	#95	C₂³×C₃₁	1	1	yes	characteristic
950	#95	C₂³×C₃₁	1	1	yes	characteristic
951	#95	C₂³×C₃₁	1	1	yes	characteristic
952	#95	C₂³×C₃₁	1	1	yes	characteristic
953	#95	C₂³×C₃₁	1	1	yes	characteristic
954	#95	C₂³×C₃₁	1	1	yes	characteristic
955	#95	C₂³×C₃₁	1	1	yes	characteristic
956	#95	C₂³×C₃₁	1	1	yes	characteristic
957	#95	C₂³×C₃₁	1	1	yes	characteristic
958	#95	C₂³×C₃₁	1	1	yes	characteristic
959	#95	C₂³×C₃₁	1	1	yes	characteristic
960	#95	C₂³×C₃₁	1	1	yes	characteristic
961	#95	C₂³×C₃₁	1	1	yes	characteristic
962	#95	C₂³×C₃₁	1	1	yes	characteristic
963	#95	C₂³×C₃₁	1	1	yes	characteristic
964	#95	C₂³×C₃₁	1	1	yes	characteristic
965	#95	C₂³×C₃₁	1	1	yes	characteristic
966	#95	C₂³×C₃₁	1	1	yes	characteristic
967	#95	C₂³×C₃₁	1	1	yes	characteristic
968	#95	C₂³×C₃₁	1	1	yes	characteristic
969	#95	C₂³×C₃₁	1	1	yes	characteristic
970	#95	C₂³×C₃₁	1	1	yes	characteristic
971	#95	C₂³×C₃₁	1	1	yes	characteristic
972	#95	C₂³×C₃₁	1	1	yes	characteristic
973	#95	C₂³×C₃₁	1	1	yes	characteristic
974	#95	C₂³×C₃₁	1	1	yes	characteristic
975	#95	C₂³×C₃₁	1	1	yes	characteristic
976	#95	C₂³×C₃₁	1	1	yes	characteristic
977	#95	C₂³×C₃₁	1	1	yes	characteristic
978	#95	C₂³×C₃₁	1	1	yes	characteristic
979	#95	C₂³×C₃₁	1	1	yes	characteristic
980	#95	C₂³×C₃₁	1	1	yes	characteristic
981	#95	C₂³×C₃₁	1	1	yes	characteristic
982	#95	C₂³×C₃₁	1	1	yes	characteristic
983	C₃₁	#35141	1	1	yes	characteristic, direct product factor, Sylow
984	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₂×Q₈	—	2	2	no	—
986	C₂×Q₈	—	2	2	no	—
987	C₂×Q₈	—	2	2	no	—
988	C₂×Q₈	—	2	2	no	—
989	C₂×Q₈	—	4	1	no	—
990	C₂×Q₈	—	4	1	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	4	1	no	—
993	C₂²×C₄	—	4	1	no	—
994	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
995	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1002	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1022	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1023	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	4	1	no	—
1059	C₄⋊C₄	—	4	1	no	—
1060	C₄⋊C₄	—	4	1	no	—
1061	C₄⋊C₄	—	4	1	no	—
1062	C₄⋊C₄	—	4	1	no	—
1063	C₄⋊C₄	—	4	1	no	—
1064	C₄⋊C₄	—	4	1	no	—
1065	C₄⋊C₄	—	4	1	no	—
1066	C₄⋊C₄	—	4	1	no	—
1067	C₄⋊C₄	—	4	1	no	—
1068	C₄⋊C₄	—	4	1	no	—
1069	C₄⋊C₄	—	4	1	no	—
1070	C₄⋊C₄	#41×C₃₁	1	4	yes	—
1071	C₄⋊C₄	#41×C₃₁	1	4	yes	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	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	C₄²	—	2	2	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	—	2	2	no	—
1091	C₄²	—	2	2	no	—
1092	C₄²	—	2	2	no	—
1093	C₄²	—	2	2	no	—
1094	C₄²	—	2	2	no	—
1095	C₄²	—	2	2	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	—	2	2	no	—
1101	C₄²	—	4	1	no	—
1102	C₄²	—	4	1	no	—
1103	C₄²	—	4	1	no	—
1104	C₄²	—	4	1	no	—
1105	C₄²	—	4	1	no	—
1106	C₄²	—	4	1	no	—
1107	C₄²	—	4	1	no	—
1108	C₄²	—	4	1	no	—
1109	C₄²	—	4	1	no	—
1110	C₄²	—	4	1	no	—
1111	C₄²	#41×C₃₁	1	4	yes	—
1112	C₂³	—	2	1	no	—
1113	C₂³	—	2	1	no	—
1114	C₂³	—	2	1	no	—
1115	C₂³	—	2	1	no	—
1116	C₂³	—	2	1	no	—
1117	C₂³	—	2	1	no	—
1118	C₂³	—	2	1	no	—
1119	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1120	Q₈	—	2	8	no	—
1121	Q₈	—	8	2	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	8	2	no	—
1202	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1203	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1204	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1205	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1206	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1207	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1208	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1209	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1210	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1211	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1212	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1221	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1222	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1223	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1224	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1225	C₂²	C₃₁×#585	1	1	yes	characteristic
1226	C₂²	C₃₁×#585	1	1	yes	characteristic
1227	C₄	—	2	2	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	2	2	no	—
1230	C₄	—	2	2	no	—
1231	C₄	—	2	2	no	—
1232	C₄	—	2	2	no	—
1233	C₄	—	2	2	no	—
1234	C₄	—	2	2	no	—
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	2	2	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₂	—	8	1	no	—
1258	C₂	C₃₁×#3444	1	1	yes	characteristic
1259	C₂	C₃₁×#3461	1	1	yes	characteristic
1260	C₂	C₃₁×#3461	1	1	yes	characteristic
1261	C₂	C₃₁×#3515	1	1	yes	characteristic
1262	C₂	C₃₁×#3516	1	1	yes	characteristic
1263	C₂	C₃₁×#3521	1	1	yes	characteristic
1264	C₂	C₃₁×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁴×C₃₁	C₂⁴
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
3. C₃₁×#2864	C₂	semidirect
4. C₃₁×#2863	C₂	semidirect
5. C₃₁×#2666	C₂	semidirect
8. C₃₁×#2634	C₂	semidirect
9. C₃₁×#2585	C₂	semidirect
10. C₃₁×#2585	C₂	semidirect
15. C₃₁×#2524	C₂	semidirect
16. C₃₁×#2524	C₂	semidirect
17. C₃₁×#2520	C₂	semidirect
18. C₃₁×#2520	C₂	semidirect
23. C₃₁×#2462	C₂	semidirect
24. C₃₁×#2462	C₂	semidirect
25. C₃₁×#2336	C₂	semidirect
26. C₃₁×#2336	C₂	semidirect
29. C₄×C₃₁×#125	C₂	semidirect
31. C₄²×Q₈×C₃₁	C₂	semidirect
479. #35141	C₃₁	direct (N × H)
583. #2864	C₂×C₃₁	semidirect
584. #2863	C₂×C₃₁	semidirect
585. #2666	C₂×C₃₁	semidirect
588. #2634	C₂×C₃₁	semidirect
589. #2585	C₂×C₃₁	semidirect
590. #2585	C₂×C₃₁	semidirect
595. #2524	C₂×C₃₁	semidirect
596. #2524	C₂×C₃₁	semidirect
597. #2520	C₂×C₃₁	semidirect
598. #2520	C₂×C₃₁	semidirect
603. #2462	C₂×C₃₁	semidirect
604. #2462	C₂×C₃₁	semidirect
605. #2336	C₂×C₃₁	semidirect
606. #2336	C₂×C₃₁	semidirect
609. C₄×#125	C₂×C₃₁	semidirect
611. C₄²×Q₈	C₂×C₃₁	semidirect
983. C₃₁	#35141	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×#2864	2
C₃₁×#2863	2
C₃₁×#2666	2
C₃₁×#2664	2
C₃₁×#2637	2
C₃₁×#2634	2
C₃₁×#2585	2
C₃₁×#2573	2
C₃₁×#2556	2
C₃₁×#2525	2
C₃₁×#2524	2
C₃₁×#2520	2
C₃₁×#2519	2
C₃₁×#2515	2
C₃₁×#2469	2
C₃₁×#2465	2
C₃₁×#2462	2
C₃₁×#2336	2
C₃₁×#2334	2
C₃₁×#2332	2
C₄×C₃₁×#125	2
C₄×C₃₁×#126	2
C₄²×Q₈×C₃₁	2
#35141	31

Subgroups — C31×#35141 #21491900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35141 #21491900