Subgroups — C₃₁×#35115 #21491874

Order 7936.

1500 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2864	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2863	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2863	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2859	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2655	C₂	1	2	yes	maximal
6	C₃₁×#2634	C₂	1	2	yes	maximal
7	C₃₁×#2584	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#2581	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2570	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#2565	C₂	1	1	yes	maximal, characteristic
11	C₃₁×#2533	C₂	1	2	yes	maximal
12	C₃₁×#2528	C₂	1	2	yes	maximal
13	C₃₁×#2524	C₂	1	2	yes	maximal
14	C₃₁×#2514	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2511	C₂	1	1	yes	maximal, characteristic
16	C₃₁×#2509	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#2506	C₂	1	1	yes	maximal, characteristic
18	C₃₁×#2462	C₂	1	2	yes	maximal
19	C₃₁×#2336	C₂	1	2	yes	maximal
20	C₃₁×#2336	C₂	1	2	yes	maximal
21	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic
22	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic
23	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
24	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#125	C₂²	1	2	yes	—
26	C₂×C₃₁×#125	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#401	C₂²	1	2	yes	—
32	C₃₁×#400	C₂²	1	2	yes	—
33	C₃₁×#400	C₂²	1	2	yes	—
34	C₃₁×#400	C₂²	1	2	yes	—
35	C₃₁×#400	C₂²	1	2	yes	—
36	C₃₁×#400	C₂²	1	2	yes	—
37	C₃₁×#400	C₂²	1	2	yes	—
38	C₃₁×#400	C₂²	1	2	yes	—
39	C₃₁×#400	C₂²	1	2	yes	—
40	C₃₁×#398	C₂²	1	2	yes	—
41	C₃₁×#398	C₂²	1	2	yes	—
42	C₃₁×#398	C₂²	1	2	yes	—
43	C₃₁×#398	C₂²	1	2	yes	—
44	C₃₁×#398	C₂²	1	2	yes	—
45	C₃₁×#395	C₂²	1	2	yes	—
46	C₃₁×#395	C₂²	1	2	yes	—
47	C₃₁×#391	C₂²	1	1	yes	characteristic
48	C₃₁×#391	C₂²	1	1	yes	characteristic
49	C₃₁×#391	C₂²	1	1	yes	characteristic
50	C₃₁×#391	C₂²	1	1	yes	characteristic
51	C₃₁×#391	C₂²	1	1	yes	characteristic
52	C₃₁×#391	C₂²	1	1	yes	characteristic
53	C₃₁×#389	C₂²	1	1	yes	characteristic
54	C₃₁×#389	C₂²	1	1	yes	characteristic
55	C₃₁×#389	C₂²	1	1	yes	characteristic
56	C₃₁×#389	C₂²	1	1	yes	characteristic
57	C₃₁×#389	C₂²	1	2	yes	—
58	C₃₁×#389	C₂²	1	2	yes	—
59	C₃₁×#389	C₂²	1	1	yes	characteristic
60	C₃₁×#389	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	1	yes	characteristic
62	C₃₁×#389	C₂²	1	1	yes	characteristic
63	C₃₁×#389	C₂²	1	2	yes	—
64	C₃₁×#389	C₂²	1	2	yes	—
65	C₃₁×#389	C₂²	1	1	yes	characteristic
66	C₃₁×#389	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	2	yes	—
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#387	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	2	yes	—
82	C₃₁×#387	C₂²	1	2	yes	—
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#387	C₂²	1	2	yes	—
87	C₃₁×#387	C₂²	1	2	yes	—
88	C₃₁×#387	C₂²	1	2	yes	—
89	C₃₁×#387	C₂²	1	2	yes	—
90	C₃₁×#387	C₂²	1	2	yes	—
91	C₃₁×#387	C₂²	1	2	yes	—
92	C₃₁×#387	C₂²	1	2	yes	—
93	C₃₁×#387	C₂²	1	2	yes	—
94	C₃₁×#387	C₂²	1	2	yes	—
95	C₃₁×#384	C₂²	1	1	yes	characteristic
96	C₃₁×#384	C₂²	1	1	yes	characteristic
97	C₃₁×#383	C₂²	1	2	yes	—
98	C₃₁×#383	C₂²	1	2	yes	—
99	C₃₁×#383	C₂²	1	2	yes	—
100	C₃₁×#382	C₂²	1	1	yes	characteristic
101	C₃₁×#382	C₂²	1	1	yes	characteristic
102	C₃₁×#382	C₂²	1	1	yes	characteristic
103	C₃₁×#382	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₃₁×#376	C₂²	1	2	yes	—
120	C₄³×C₃₁	C₂²	1	1	yes	characteristic
121	C₄³×C₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₃₁	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₃₁×#125	—	2	8	no	—
126	C₃₁×#125	—	2	4	no	—
127	C₃₁×#125	—	2	8	no	—
128	C₄×Q₈×C₃₁	—	2	4	no	—
129	C₄×Q₈×C₃₁	—	2	4	no	—
130	C₄×Q₈×C₃₁	—	2	4	no	—
131	C₄×Q₈×C₃₁	—	2	4	no	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
188	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₃₁×#95	C₂³	1	2	yes	—
191	C₃₁×#95	C₂³	1	2	yes	—
192	C₃₁×#95	C₂³	1	2	yes	—
193	C₃₁×#95	C₂³	1	2	yes	—
194	C₃₁×#95	C₂³	1	2	yes	—
195	C₃₁×#95	C₂³	1	2	yes	—
196	C₃₁×#95	C₂³	1	2	yes	—
197	C₃₁×#95	C₂³	1	2	yes	—
198	C₃₁×#95	C₂³	1	2	yes	—
199	C₃₁×#95	C₂³	1	2	yes	—
200	C₃₁×#95	C₂³	1	2	yes	—
201	C₃₁×#95	C₂³	1	2	yes	—
202	C₃₁×#95	C₂³	1	2	yes	—
203	C₃₁×#95	C₂³	1	2	yes	—
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₃₁×#95	C₂³	1	2	yes	—
206	C₃₁×#95	C₂³	1	2	yes	—
207	C₃₁×#95	C₂³	1	2	yes	—
208	C₃₁×#95	C₂³	1	1	yes	characteristic
209	C₃₁×#95	C₂³	1	2	yes	—
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	1	yes	characteristic
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₃₁×#95	C₂³	1	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	2	yes	—
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	1	yes	characteristic
221	C₃₁×#95	C₂³	1	1	yes	characteristic
222	C₃₁×#95	C₂³	1	1	yes	characteristic
223	C₃₁×#95	C₂³	1	1	yes	characteristic
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	2	yes	—
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₂×Q₈×C₃₁	—	2	2	no	—
230	C₂×Q₈×C₃₁	—	2	2	no	—
231	C₂×Q₈×C₃₁	—	2	2	no	—
232	C₂×Q₈×C₃₁	—	2	2	no	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₄⋊C₄×C₃₁	—	2	2	no	—
265	C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	4	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	4	no	—
273	C₄⋊C₄×C₃₁	—	2	4	no	—
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	—	2	4	no	—
276	C₄⋊C₄×C₃₁	—	2	4	no	—
277	C₄⋊C₄×C₃₁	—	2	4	no	—
278	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	2	4	no	—
280	C₄⋊C₄×C₃₁	—	2	4	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	4	no	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	4	2	no	—
289	C₄⋊C₄×C₃₁	—	4	2	no	—
290	C₄⋊C₄×C₃₁	—	4	2	no	—
291	C₄⋊C₄×C₃₁	—	4	2	no	—
292	C₄⋊C₄×C₃₁	#41	1	4	yes	—
293	C₄²×C₃₁	—	2	2	no	—
294	C₄²×C₃₁	—	2	2	no	—
295	C₄²×C₃₁	—	2	2	no	—
296	C₄²×C₃₁	—	2	2	no	—
297	C₄²×C₃₁	—	2	2	no	—
298	C₄²×C₃₁	—	2	2	no	—
299	C₄²×C₃₁	—	2	2	no	—
300	C₄²×C₃₁	—	2	4	no	—
301	C₄²×C₃₁	—	2	4	no	—
302	C₄²×C₃₁	—	2	2	no	—
303	C₄²×C₃₁	—	2	2	no	—
304	C₄²×C₃₁	—	2	2	no	—
305	C₄²×C₃₁	—	2	2	no	—
306	C₄²×C₃₁	—	2	2	no	—
307	C₄²×C₃₁	—	2	2	no	—
308	C₄²×C₃₁	—	2	2	no	—
309	C₄²×C₃₁	—	4	1	no	—
310	C₄²×C₃₁	—	4	1	no	—
311	C₄²×C₃₁	—	4	1	no	—
312	C₄²×C₃₁	—	4	2	no	—
313	C₄²×C₃₁	—	4	2	no	—
314	C₄²×C₃₁	#41	1	4	yes	—
315	C₄²×C₃₁	#41	1	4	yes	—
316	#35115	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
318	Q₈×C₃₁	—	2	8	no	—
319	Q₈×C₃₁	—	4	4	no	—
320	C₂×C₄×C₃₁	—	2	1	no	—
321	C₂×C₄×C₃₁	—	2	1	no	—
322	C₂×C₄×C₃₁	—	2	1	no	—
323	C₂×C₄×C₃₁	—	2	1	no	—
324	C₂×C₄×C₃₁	—	2	1	no	—
325	C₂×C₄×C₃₁	—	2	1	no	—
326	C₂×C₄×C₃₁	—	2	1	no	—
327	C₂×C₄×C₃₁	—	2	1	no	—
328	C₂×C₄×C₃₁	—	2	1	no	—
329	C₂×C₄×C₃₁	—	2	1	no	—
330	C₂×C₄×C₃₁	—	2	1	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	1	no	—
333	C₂×C₄×C₃₁	—	2	1	no	—
334	C₂×C₄×C₃₁	—	2	1	no	—
335	C₂×C₄×C₃₁	—	2	1	no	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	1	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	1	no	—
341	C₂×C₄×C₃₁	—	2	1	no	—
342	C₂×C₄×C₃₁	—	2	1	no	—
343	C₂×C₄×C₃₁	—	2	1	no	—
344	C₂×C₄×C₃₁	—	2	1	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	2	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	2	1	no	—
356	C₂×C₄×C₃₁	—	2	1	no	—
357	C₂×C₄×C₃₁	—	2	1	no	—
358	C₂×C₄×C₃₁	—	2	1	no	—
359	C₂×C₄×C₃₁	—	2	1	no	—
360	C₂×C₄×C₃₁	—	2	1	no	—
361	C₂×C₄×C₃₁	—	2	1	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	1	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
378	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
379	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
380	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
381	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
382	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
383	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
384	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
385	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
386	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
387	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
388	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
389	#2864	C₂×C₃₁	1	1	yes	characteristic
390	#2863	C₂×C₃₁	1	1	yes	characteristic
391	#2863	C₂×C₃₁	1	1	yes	characteristic
392	#2859	C₂×C₃₁	1	1	yes	characteristic
393	#2655	C₂×C₃₁	1	2	yes	—
394	#2634	C₂×C₃₁	1	2	yes	—
395	#2584	C₂×C₃₁	1	1	yes	characteristic
396	#2581	C₂×C₃₁	1	1	yes	characteristic
397	#2570	C₂×C₃₁	1	1	yes	characteristic
398	#2565	C₂×C₃₁	1	1	yes	characteristic
399	#2533	C₂×C₃₁	1	2	yes	—
400	#2528	C₂×C₃₁	1	2	yes	—
401	#2524	C₂×C₃₁	1	2	yes	—
402	#2514	C₂×C₃₁	1	1	yes	characteristic
403	#2511	C₂×C₃₁	1	1	yes	characteristic
404	#2509	C₂×C₃₁	1	1	yes	characteristic
405	#2506	C₂×C₃₁	1	1	yes	characteristic
406	#2462	C₂×C₃₁	1	2	yes	—
407	#2336	C₂×C₃₁	1	2	yes	—
408	#2336	C₂×C₃₁	1	2	yes	—
409	C₄×#125	C₂×C₃₁	1	1	yes	characteristic
410	#2295	C₂×C₃₁	1	1	yes	characteristic
411	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic
412	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
414	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
415	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
417	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
418	C₂²×C₃₁	#585	1	1	yes	characteristic
419	C₄×C₃₁	—	2	2	no	—
420	C₄×C₃₁	—	2	2	no	—
421	C₄×C₃₁	—	2	2	no	—
422	C₄×C₃₁	—	2	2	no	—
423	C₄×C₃₁	—	2	2	no	—
424	C₄×C₃₁	—	2	2	no	—
425	C₄×C₃₁	—	2	2	no	—
426	C₄×C₃₁	—	2	2	no	—
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	4	2	no	—
429	C₄×C₃₁	—	4	2	no	—
430	C₄×C₃₁	—	4	2	no	—
431	C₄×C₃₁	—	4	1	no	—
432	C₄×C₃₁	—	4	1	no	—
433	C₄×C₃₁	—	4	2	no	—
434	C₄×C₃₁	—	4	2	no	—
435	C₄×C₃₁	—	4	2	no	—
436	C₄×C₃₁	—	4	1	no	—
437	C₄×C₃₁	—	4	1	no	—
438	C₄×C₃₁	—	4	1	no	—
439	C₄×C₃₁	—	4	2	no	—
440	C₄×C₃₁	—	4	2	no	—
441	C₄×C₃₁	#541	1	4	yes	—
442	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×#125	C₂²×C₃₁	1	2	yes	—
444	C₂×#125	C₂²×C₃₁	1	2	yes	—
445	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
447	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
449	#401	C₂²×C₃₁	1	2	yes	—
450	#400	C₂²×C₃₁	1	2	yes	—
451	#400	C₂²×C₃₁	1	2	yes	—
452	#400	C₂²×C₃₁	1	2	yes	—
453	#400	C₂²×C₃₁	1	2	yes	—
454	#400	C₂²×C₃₁	1	2	yes	—
455	#400	C₂²×C₃₁	1	2	yes	—
456	#400	C₂²×C₃₁	1	2	yes	—
457	#400	C₂²×C₃₁	1	2	yes	—
458	#398	C₂²×C₃₁	1	2	yes	—
459	#398	C₂²×C₃₁	1	2	yes	—
460	#398	C₂²×C₃₁	1	2	yes	—
461	#398	C₂²×C₃₁	1	2	yes	—
462	#398	C₂²×C₃₁	1	2	yes	—
463	#395	C₂²×C₃₁	1	2	yes	—
464	#395	C₂²×C₃₁	1	2	yes	—
465	#391	C₂²×C₃₁	1	1	yes	characteristic
466	#391	C₂²×C₃₁	1	1	yes	characteristic
467	#391	C₂²×C₃₁	1	1	yes	characteristic
468	#391	C₂²×C₃₁	1	1	yes	characteristic
469	#391	C₂²×C₃₁	1	1	yes	characteristic
470	#391	C₂²×C₃₁	1	1	yes	characteristic
471	#389	C₂²×C₃₁	1	1	yes	characteristic
472	#389	C₂²×C₃₁	1	1	yes	characteristic
473	#389	C₂²×C₃₁	1	1	yes	characteristic
474	#389	C₂²×C₃₁	1	1	yes	characteristic
475	#389	C₂²×C₃₁	1	1	yes	characteristic
476	#389	C₂²×C₃₁	1	1	yes	characteristic
477	#389	C₂²×C₃₁	1	2	yes	—
478	#389	C₂²×C₃₁	1	2	yes	—
479	#389	C₂²×C₃₁	1	1	yes	characteristic
480	#389	C₂²×C₃₁	1	1	yes	characteristic
481	#389	C₂²×C₃₁	1	1	yes	characteristic
482	#389	C₂²×C₃₁	1	1	yes	characteristic
483	#389	C₂²×C₃₁	1	2	yes	—
484	#389	C₂²×C₃₁	1	2	yes	—
485	#389	C₂²×C₃₁	1	1	yes	characteristic
486	#389	C₂²×C₃₁	1	2	yes	—
487	#389	C₂²×C₃₁	1	1	yes	characteristic
488	#387	C₂²×C₃₁	1	2	yes	—
489	#387	C₂²×C₃₁	1	2	yes	—
490	#387	C₂²×C₃₁	1	2	yes	—
491	#387	C₂²×C₃₁	1	2	yes	—
492	#387	C₂²×C₃₁	1	2	yes	—
493	#387	C₂²×C₃₁	1	2	yes	—
494	#387	C₂²×C₃₁	1	2	yes	—
495	#387	C₂²×C₃₁	1	2	yes	—
496	#387	C₂²×C₃₁	1	2	yes	—
497	#387	C₂²×C₃₁	1	2	yes	—
498	#387	C₂²×C₃₁	1	2	yes	—
499	#387	C₂²×C₃₁	1	2	yes	—
500	#387	C₂²×C₃₁	1	2	yes	—
501	#387	C₂²×C₃₁	1	2	yes	—
502	#387	C₂²×C₃₁	1	2	yes	—
503	#387	C₂²×C₃₁	1	2	yes	—
504	#387	C₂²×C₃₁	1	2	yes	—
505	#387	C₂²×C₃₁	1	2	yes	—
506	#387	C₂²×C₃₁	1	2	yes	—
507	#387	C₂²×C₃₁	1	2	yes	—
508	#387	C₂²×C₃₁	1	2	yes	—
509	#387	C₂²×C₃₁	1	2	yes	—
510	#387	C₂²×C₃₁	1	2	yes	—
511	#387	C₂²×C₃₁	1	2	yes	—
512	#387	C₂²×C₃₁	1	2	yes	—
513	#384	C₂²×C₃₁	1	1	yes	characteristic
514	#384	C₂²×C₃₁	1	1	yes	characteristic
515	#383	C₂²×C₃₁	1	2	yes	—
516	#383	C₂²×C₃₁	1	2	yes	—
517	#383	C₂²×C₃₁	1	2	yes	—
518	#382	C₂²×C₃₁	1	1	yes	characteristic
519	#382	C₂²×C₃₁	1	1	yes	characteristic
520	#382	C₂²×C₃₁	1	1	yes	characteristic
521	#382	C₂²×C₃₁	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
523	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
524	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
525	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
526	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
527	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
528	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
529	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
530	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
531	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
532	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
533	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
535	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
536	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
537	#376	C₂²×C₃₁	1	2	yes	—
538	C₄³	C₂²×C₃₁	1	1	yes	characteristic
539	C₄³	C₂²×C₃₁	1	1	yes	characteristic
540	C₄³	C₂²×C₃₁	1	1	yes	characteristic
541	C₂×C₃₁	#3444	1	1	yes	characteristic
542	C₂×C₃₁	C₂×#541	1	1	yes	characteristic
543	C₂×C₃₁	#3461	1	1	yes	characteristic
544	C₂×C₃₁	#3507	1	1	yes	characteristic
545	C₂×C₃₁	#3509	1	1	yes	characteristic
546	C₂×C₃₁	#3515	1	1	yes	characteristic
547	C₂×C₃₁	#3523	1	1	yes	characteristic
548	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
550	#125	—	2	8	no	—
551	#125	—	2	4	no	—
552	#125	—	2	8	no	—
553	C₄×Q₈	—	2	4	no	—
554	C₄×Q₈	—	2	4	no	—
555	C₄×Q₈	—	2	4	no	—
556	C₄×Q₈	—	2	4	no	—
557	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
600	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
601	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
612	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
613	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
615	#95	C₂³×C₃₁	1	2	yes	—
616	#95	C₂³×C₃₁	1	2	yes	—
617	#95	C₂³×C₃₁	1	2	yes	—
618	#95	C₂³×C₃₁	1	2	yes	—
619	#95	C₂³×C₃₁	1	1	yes	characteristic
620	#95	C₂³×C₃₁	1	1	yes	characteristic
621	#95	C₂³×C₃₁	1	1	yes	characteristic
622	#95	C₂³×C₃₁	1	1	yes	characteristic
623	#95	C₂³×C₃₁	1	1	yes	characteristic
624	#95	C₂³×C₃₁	1	1	yes	characteristic
625	#95	C₂³×C₃₁	1	2	yes	—
626	#95	C₂³×C₃₁	1	2	yes	—
627	#95	C₂³×C₃₁	1	2	yes	—
628	#95	C₂³×C₃₁	1	2	yes	—
629	#95	C₂³×C₃₁	1	2	yes	—
630	#95	C₂³×C₃₁	1	2	yes	—
631	#95	C₂³×C₃₁	1	2	yes	—
632	#95	C₂³×C₃₁	1	2	yes	—
633	#95	C₂³×C₃₁	1	2	yes	—
634	#95	C₂³×C₃₁	1	2	yes	—
635	#95	C₂³×C₃₁	1	2	yes	—
636	#95	C₂³×C₃₁	1	2	yes	—
637	#95	C₂³×C₃₁	1	2	yes	—
638	#95	C₂³×C₃₁	1	2	yes	—
639	#95	C₂³×C₃₁	1	2	yes	—
640	#95	C₂³×C₃₁	1	2	yes	—
641	#95	C₂³×C₃₁	1	2	yes	—
642	#95	C₂³×C₃₁	1	2	yes	—
643	#95	C₂³×C₃₁	1	2	yes	—
644	#95	C₂³×C₃₁	1	2	yes	—
645	#95	C₂³×C₃₁	1	2	yes	—
646	#95	C₂³×C₃₁	1	2	yes	—
647	#95	C₂³×C₃₁	1	2	yes	—
648	#95	C₂³×C₃₁	1	2	yes	—
649	#95	C₂³×C₃₁	1	2	yes	—
650	#95	C₂³×C₃₁	1	2	yes	—
651	#95	C₂³×C₃₁	1	2	yes	—
652	#95	C₂³×C₃₁	1	2	yes	—
653	#95	C₂³×C₃₁	1	2	yes	—
654	C₃₁	#35115	1	1	yes	characteristic, direct product factor, Sylow
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	#41×C₃₁	1	4	yes	—
719	C₄²	—	2	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	4	1	no	—
736	C₄²	—	4	1	no	—
737	C₄²	—	4	1	no	—
738	C₄²	—	4	2	no	—
739	C₄²	—	4	2	no	—
740	C₄²	#41×C₃₁	1	4	yes	—
741	C₄²	#41×C₃₁	1	4	yes	—
742	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
743	Q₈	—	2	8	no	—
744	Q₈	—	4	4	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
803	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
804	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
805	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
806	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
807	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
808	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
809	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
810	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
811	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
812	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
813	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
814	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
815	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
816	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
817	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
818	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
819	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
820	C₂²	C₃₁×#585	1	1	yes	characteristic
821	C₄	—	2	2	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	2	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	C₃₁×#541	1	4	yes	—
844	C₂	C₃₁×#3444	1	1	yes	characteristic
845	C₂	C₂×C₃₁×#541	1	1	yes	characteristic
846	C₂	C₃₁×#3461	1	1	yes	characteristic
847	C₂	C₃₁×#3507	1	1	yes	characteristic
848	C₂	C₃₁×#3509	1	1	yes	characteristic
849	C₂	C₃₁×#3515	1	1	yes	characteristic
850	C₂	C₃₁×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
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
316. #35115	C₃₁	direct (N × H)
654. C₃₁	#35115	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×#2864	2
C₃₁×#2863	2
C₃₁×#2859	2
C₃₁×#2655	2
C₃₁×#2634	2
C₃₁×#2584	2
C₃₁×#2581	2
C₃₁×#2570	2
C₃₁×#2565	2
C₃₁×#2533	2
C₃₁×#2528	2
C₃₁×#2524	2
C₃₁×#2514	2
C₃₁×#2511	2
C₃₁×#2509	2
C₃₁×#2506	2
C₃₁×#2462	2
C₃₁×#2336	2
C₄×C₃₁×#125	2
C₃₁×#2295	2
C₄²×Q₈×C₃₁	2
#35115	31

Subgroups — C31×#35115 #21491874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35115 #21491874