Subgroups — C₃₁×#35137 #21491896

Order 7936.

1722 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2850	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2653	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2650	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2532	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2527	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2514	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2513	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2492	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2491	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2477	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2474	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2452	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2451	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2421	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2420	C₂	1	1	yes	maximal, characteristic
19	C₃₁×#2337	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2332	C₂	1	2	yes	maximal, complemented
21	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#124	C₂²	1	2	yes	—
28	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#401	C₂²	1	2	yes	—
38	C₃₁×#400	C₂²	1	2	yes	—
39	C₃₁×#400	C₂²	1	2	yes	—
40	C₃₁×#400	C₂²	1	2	yes	—
41	C₃₁×#398	C₂²	1	2	yes	—
42	C₃₁×#397	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	2	yes	—
44	C₃₁×#397	C₂²	1	2	yes	—
45	C₃₁×#397	C₂²	1	2	yes	—
46	C₃₁×#396	C₂²	1	2	yes	—
47	C₃₁×#395	C₂²	1	2	yes	—
48	C₃₁×#394	C₂²	1	2	yes	—
49	C₃₁×#394	C₂²	1	2	yes	—
50	C₃₁×#393	C₂²	1	2	yes	—
51	C₃₁×#393	C₂²	1	2	yes	—
52	C₃₁×#393	C₂²	1	2	yes	—
53	C₃₁×#391	C₂²	1	2	yes	—
54	C₃₁×#391	C₂²	1	2	yes	—
55	C₃₁×#391	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	1	yes	characteristic
58	C₃₁×#391	C₂²	1	1	yes	characteristic
59	C₃₁×#391	C₂²	1	1	yes	characteristic
60	C₃₁×#391	C₂²	1	2	yes	—
61	C₃₁×#391	C₂²	1	2	yes	—
62	C₃₁×#391	C₂²	1	1	yes	characteristic
63	C₃₁×#390	C₂²	1	1	yes	characteristic
64	C₃₁×#390	C₂²	1	1	yes	characteristic
65	C₃₁×#390	C₂²	1	1	yes	characteristic
66	C₃₁×#390	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	1	yes	characteristic
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	1	yes	characteristic
71	C₃₁×#388	C₂²	1	2	yes	—
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	2	yes	—
75	C₃₁×#388	C₂²	1	2	yes	—
76	C₃₁×#388	C₂²	1	2	yes	—
77	C₃₁×#388	C₂²	1	2	yes	—
78	C₃₁×#388	C₂²	1	2	yes	—
79	C₃₁×#388	C₂²	1	2	yes	—
80	C₃₁×#388	C₂²	1	2	yes	—
81	C₃₁×#388	C₂²	1	2	yes	—
82	C₃₁×#388	C₂²	1	2	yes	—
83	C₃₁×#388	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×#386	C₂²	1	2	yes	—
92	C₃₁×#386	C₂²	1	2	yes	—
93	C₃₁×#386	C₂²	1	2	yes	—
94	C₃₁×#385	C₂²	1	2	yes	—
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	2	yes	—
97	C₃₁×#383	C₂²	1	2	yes	—
98	C₃₁×#382	C₂²	1	1	yes	characteristic
99	C₃₁×#382	C₂²	1	1	yes	characteristic
100	C₃₁×#382	C₂²	1	1	yes	characteristic
101	C₃₁×#382	C₂²	1	1	yes	characteristic
102	C₃₁×#381	C₂²	1	2	yes	—
103	C₃₁×#380	C₂²	1	1	yes	characteristic
104	C₃₁×#380	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₃₁×#376	C₂²	1	1	yes	characteristic
120	C₃₁×#376	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	2	yes	—
125	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
132	C₃₁×C₄⋊Q₈	—	4	2	no	—
133	C₃₁×C₄⋊Q₈	—	4	2	no	—
134	C₃₁×#125	—	2	4	no	—
135	C₃₁×#124	—	2	8	no	—
136	C₃₁×#124	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	8	no	—
138	C₃₁×C₂²⋊Q₈	—	4	2	no	—
139	C₃₁×#121	—	4	2	no	—
140	C₄×Q₈×C₃₁	—	4	2	no	—
141	C₄×D₄×C₃₁	—	4	2	no	—
142	C₃₁×#117	—	2	4	no	—
143	C₃₁×#117	—	2	4	no	—
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₃₁	—	2	4	no	—
184	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
193	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
208	C₃₁×#95	C₂³	1	2	yes	—
209	C₃₁×#95	C₂³	1	1	yes	characteristic
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	2	yes	—
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	1	yes	characteristic
226	C₃₁×#95	C₂³	1	1	yes	characteristic
227	C₃₁×#95	C₂³	1	1	yes	characteristic
228	C₃₁×#95	C₂³	1	1	yes	characteristic
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
236	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	4	no	—
239	C₂×Q₈×C₃₁	—	2	4	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	4	2	no	—
243	C₂×Q₈×C₃₁	—	4	2	no	—
244	C₂×Q₈×C₃₁	—	4	2	no	—
245	C₂×Q₈×C₃₁	—	4	2	no	—
246	C₂×D₄×C₃₁	—	2	4	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	4	2	no	—
251	C₂×D₄×C₃₁	—	4	2	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	4	no	—
260	C₂²×C₄×C₃₁	—	4	1	no	—
261	C₂²×C₄×C₃₁	—	4	1	no	—
262	C₂²×C₄×C₃₁	—	4	2	no	—
263	C₂²×C₄×C₃₁	—	4	2	no	—
264	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
289	C₄⋊C₄×C₃₁	—	2	4	no	—
290	C₄⋊C₄×C₃₁	—	2	4	no	—
291	C₄⋊C₄×C₃₁	—	2	4	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	4	2	no	—
299	C₄⋊C₄×C₃₁	—	4	2	no	—
300	C₄⋊C₄×C₃₁	—	4	2	no	—
301	C₄⋊C₄×C₃₁	—	4	2	no	—
302	C₄⋊C₄×C₃₁	—	4	2	no	—
303	C₄⋊C₄×C₃₁	—	4	2	no	—
304	C₄⋊C₄×C₃₁	#41	1	4	yes	—
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₃₁	—	2	4	no	—
312	C₂²⋊C₄×C₃₁	—	2	4	no	—
313	C₂²⋊C₄×C₃₁	—	2	4	no	—
314	C₂²⋊C₄×C₃₁	—	2	4	no	—
315	C₂²⋊C₄×C₃₁	—	4	2	no	—
316	C₂²⋊C₄×C₃₁	—	4	2	no	—
317	C₂²⋊C₄×C₃₁	—	4	2	no	—
318	C₂²⋊C₄×C₃₁	—	4	2	no	—
319	C₂²⋊C₄×C₃₁	—	4	2	no	—
320	C₂²⋊C₄×C₃₁	—	4	2	no	—
321	C₂²⋊C₄×C₃₁	—	4	2	no	—
322	C₂²⋊C₄×C₃₁	—	4	2	no	—
323	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
324	C₄²×C₃₁	—	2	2	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	2	2	no	—
327	C₄²×C₃₁	—	2	2	no	—
328	C₄²×C₃₁	—	2	2	no	—
329	C₄²×C₃₁	—	2	2	no	—
330	C₄²×C₃₁	—	2	2	no	—
331	C₄²×C₃₁	—	2	4	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	2	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	2	no	—
336	C₄²×C₃₁	—	4	1	no	—
337	C₄²×C₃₁	—	4	2	no	—
338	C₄²×C₃₁	—	4	1	no	—
339	C₄²×C₃₁	—	4	1	no	—
340	C₄²×C₃₁	—	4	1	no	—
341	C₄²×C₃₁	—	4	2	no	—
342	C₄²×C₃₁	#41	1	4	yes	—
343	#35137	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂³×C₃₁	—	2	1	no	—
345	C₂³×C₃₁	—	2	1	no	—
346	C₂³×C₃₁	—	2	1	no	—
347	C₂³×C₃₁	—	2	1	no	—
348	C₂³×C₃₁	—	2	1	no	—
349	C₂³×C₃₁	—	2	1	no	—
350	C₂³×C₃₁	—	2	2	no	—
351	C₂³×C₃₁	—	2	2	no	—
352	C₂³×C₃₁	—	2	2	no	—
353	C₂³×C₃₁	—	2	2	no	—
354	C₂³×C₃₁	—	2	2	no	—
355	C₂³×C₃₁	—	2	2	no	—
356	C₂³×C₃₁	—	2	2	no	—
357	C₂³×C₃₁	C₂×#41	1	2	yes	—
358	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
359	Q₈×C₃₁	—	4	4	no	—
360	Q₈×C₃₁	—	8	4	no	—
361	Q₈×C₃₁	—	8	4	no	—
362	D₄×C₃₁	—	4	4	no	—
363	D₄×C₃₁	—	8	4	no	—
364	C₂×C₄×C₃₁	—	2	8	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	1	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	1	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	1	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	1	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	2	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	1	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	1	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	1	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	1	no	—
412	C₂×C₄×C₃₁	—	2	1	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	4	4	no	—
419	C₂×C₄×C₃₁	—	4	4	no	—
420	C₂×C₄×C₃₁	—	8	4	no	—
421	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
422	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
423	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
424	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
425	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
426	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
427	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
428	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
429	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
430	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
431	#2862	C₂×C₃₁	1	1	yes	characteristic, complemented
432	#2861	C₂×C₃₁	1	1	yes	characteristic, complemented
433	#2851	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#2850	C₂×C₃₁	1	1	yes	characteristic
435	#2653	C₂×C₃₁	1	2	yes	complemented
436	#2650	C₂×C₃₁	1	2	yes	complemented
437	#2532	C₂×C₃₁	1	2	yes	complemented
438	#2527	C₂×C₃₁	1	2	yes	complemented
439	#2514	C₂×C₃₁	1	1	yes	characteristic, complemented
440	#2513	C₂×C₃₁	1	1	yes	characteristic, complemented
441	#2492	C₂×C₃₁	1	1	yes	characteristic, complemented
442	#2491	C₂×C₃₁	1	1	yes	characteristic
443	#2477	C₂×C₃₁	1	2	yes	complemented
444	#2474	C₂×C₃₁	1	2	yes	complemented
445	#2452	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#2451	C₂×C₃₁	1	1	yes	characteristic, complemented
447	#2421	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#2420	C₂×C₃₁	1	1	yes	characteristic
449	#2337	C₂×C₃₁	1	2	yes	complemented
450	#2332	C₂×C₃₁	1	2	yes	complemented
451	C₄×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
452	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
453	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
454	C₂²×C₃₁	—	2	2	no	—
455	C₂²×C₃₁	—	2	2	no	—
456	C₂²×C₃₁	—	2	2	no	—
457	C₂²×C₃₁	—	4	1	no	—
458	C₂²×C₃₁	—	4	1	no	—
459	C₂²×C₃₁	—	4	1	no	—
460	C₂²×C₃₁	—	4	1	no	—
461	C₂²×C₃₁	—	4	2	no	—
462	C₂²×C₃₁	—	4	2	no	—
463	C₂²×C₃₁	—	4	2	no	—
464	C₂²×C₃₁	—	4	2	no	—
465	C₂²×C₃₁	—	4	2	no	—
466	C₂²×C₃₁	—	4	2	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
469	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
470	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
473	C₂²×C₃₁	#585	1	1	yes	characteristic
474	C₂²×C₃₁	#585	1	1	yes	characteristic
475	C₄×C₃₁	—	2	2	no	—
476	C₄×C₃₁	—	2	2	no	—
477	C₄×C₃₁	—	2	2	no	—
478	C₄×C₃₁	—	2	2	no	—
479	C₄×C₃₁	—	2	2	no	—
480	C₄×C₃₁	—	2	2	no	—
481	C₄×C₃₁	—	2	2	no	—
482	C₄×C₃₁	—	4	2	no	—
483	C₄×C₃₁	—	4	1	no	—
484	C₄×C₃₁	—	4	2	no	—
485	C₄×C₃₁	—	4	2	no	—
486	C₄×C₃₁	—	4	1	no	—
487	C₄×C₃₁	—	4	1	no	—
488	C₄×C₃₁	—	4	2	no	—
489	C₄×C₃₁	—	4	2	no	—
490	C₄×C₃₁	—	4	2	no	—
491	C₄×C₃₁	—	4	2	no	—
492	C₄×C₃₁	—	4	1	no	—
493	C₄×C₃₁	—	4	1	no	—
494	C₄×C₃₁	—	4	1	no	—
495	C₄×C₃₁	#542	1	4	yes	—
496	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
497	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
498	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
499	C₂×#124	C₂²×C₃₁	1	2	yes	—
500	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
501	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
502	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
503	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
504	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
506	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
507	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
508	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
509	#401	C₂²×C₃₁	1	2	yes	—
510	#400	C₂²×C₃₁	1	2	yes	—
511	#400	C₂²×C₃₁	1	2	yes	—
512	#400	C₂²×C₃₁	1	2	yes	—
513	#398	C₂²×C₃₁	1	2	yes	—
514	#397	C₂²×C₃₁	1	2	yes	—
515	#397	C₂²×C₃₁	1	2	yes	—
516	#397	C₂²×C₃₁	1	2	yes	—
517	#397	C₂²×C₃₁	1	2	yes	—
518	#396	C₂²×C₃₁	1	2	yes	—
519	#395	C₂²×C₃₁	1	2	yes	—
520	#394	C₂²×C₃₁	1	2	yes	—
521	#394	C₂²×C₃₁	1	2	yes	—
522	#393	C₂²×C₃₁	1	2	yes	—
523	#393	C₂²×C₃₁	1	2	yes	—
524	#393	C₂²×C₃₁	1	2	yes	—
525	#391	C₂²×C₃₁	1	2	yes	—
526	#391	C₂²×C₃₁	1	2	yes	—
527	#391	C₂²×C₃₁	1	2	yes	—
528	#391	C₂²×C₃₁	1	2	yes	—
529	#391	C₂²×C₃₁	1	1	yes	characteristic
530	#391	C₂²×C₃₁	1	1	yes	characteristic
531	#391	C₂²×C₃₁	1	1	yes	characteristic
532	#391	C₂²×C₃₁	1	2	yes	—
533	#391	C₂²×C₃₁	1	2	yes	—
534	#391	C₂²×C₃₁	1	1	yes	characteristic
535	#390	C₂²×C₃₁	1	1	yes	characteristic
536	#390	C₂²×C₃₁	1	1	yes	characteristic
537	#390	C₂²×C₃₁	1	1	yes	characteristic
538	#390	C₂²×C₃₁	1	1	yes	characteristic
539	#389	C₂²×C₃₁	1	1	yes	characteristic
540	#389	C₂²×C₃₁	1	1	yes	characteristic
541	#389	C₂²×C₃₁	1	1	yes	characteristic
542	#389	C₂²×C₃₁	1	1	yes	characteristic
543	#388	C₂²×C₃₁	1	2	yes	—
544	#388	C₂²×C₃₁	1	2	yes	—
545	#388	C₂²×C₃₁	1	2	yes	—
546	#388	C₂²×C₃₁	1	2	yes	—
547	#388	C₂²×C₃₁	1	2	yes	—
548	#388	C₂²×C₃₁	1	2	yes	—
549	#388	C₂²×C₃₁	1	2	yes	—
550	#388	C₂²×C₃₁	1	2	yes	—
551	#388	C₂²×C₃₁	1	2	yes	—
552	#388	C₂²×C₃₁	1	2	yes	—
553	#388	C₂²×C₃₁	1	2	yes	—
554	#388	C₂²×C₃₁	1	2	yes	—
555	#388	C₂²×C₃₁	1	2	yes	—
556	#387	C₂²×C₃₁	1	2	yes	—
557	#387	C₂²×C₃₁	1	2	yes	—
558	#387	C₂²×C₃₁	1	2	yes	—
559	#387	C₂²×C₃₁	1	2	yes	—
560	#387	C₂²×C₃₁	1	2	yes	—
561	#387	C₂²×C₃₁	1	2	yes	—
562	#387	C₂²×C₃₁	1	2	yes	—
563	#386	C₂²×C₃₁	1	2	yes	—
564	#386	C₂²×C₃₁	1	2	yes	—
565	#386	C₂²×C₃₁	1	2	yes	—
566	#385	C₂²×C₃₁	1	2	yes	—
567	#385	C₂²×C₃₁	1	2	yes	—
568	#385	C₂²×C₃₁	1	2	yes	—
569	#383	C₂²×C₃₁	1	2	yes	—
570	#382	C₂²×C₃₁	1	1	yes	characteristic
571	#382	C₂²×C₃₁	1	1	yes	characteristic
572	#382	C₂²×C₃₁	1	1	yes	characteristic
573	#382	C₂²×C₃₁	1	1	yes	characteristic
574	#381	C₂²×C₃₁	1	2	yes	—
575	#380	C₂²×C₃₁	1	1	yes	characteristic
576	#380	C₂²×C₃₁	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
578	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
579	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
583	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
585	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
586	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
587	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
588	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
589	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
590	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
591	#376	C₂²×C₃₁	1	1	yes	characteristic
592	#376	C₂²×C₃₁	1	1	yes	characteristic
593	C₄³	C₂²×C₃₁	1	1	yes	characteristic
594	C₄³	C₂²×C₃₁	1	1	yes	characteristic
595	C₂×C₃₁	—	4	2	no	—
596	C₂×C₃₁	—	8	2	no	—
597	C₂×C₃₁	#3444	1	1	yes	characteristic
598	C₂×C₃₁	C₂×#542	1	1	yes	characteristic
599	C₂×C₃₁	#3455	1	1	yes	characteristic
600	C₂×C₃₁	#3514	1	1	yes	characteristic
601	C₂×C₃₁	#3514	1	1	yes	characteristic
602	C₂×C₃₁	#3515	1	1	yes	characteristic
603	C₂×C₃₁	#3518	1	1	yes	characteristic
604	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
605	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
606	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
607	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
608	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
609	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
612	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
613	C₄⋊Q₈	—	4	2	no	—
614	C₄⋊Q₈	—	4	2	no	—
615	#125	—	2	4	no	—
616	#124	—	2	8	no	—
617	#124	—	2	4	no	—
618	C₂²⋊Q₈	—	2	8	no	—
619	C₂²⋊Q₈	—	4	2	no	—
620	#121	—	4	2	no	—
621	C₄×Q₈	—	4	2	no	—
622	C₄×D₄	—	4	2	no	—
623	#117	—	2	4	no	—
624	#117	—	2	4	no	—
625	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₂×C₄²	—	2	4	no	—
665	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
671	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
678	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
683	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
684	#95	C₂³×C₃₁	1	1	yes	characteristic
685	#95	C₂³×C₃₁	1	1	yes	characteristic
686	#95	C₂³×C₃₁	1	1	yes	characteristic
687	#95	C₂³×C₃₁	1	1	yes	characteristic
688	#95	C₂³×C₃₁	1	1	yes	characteristic
689	#95	C₂³×C₃₁	1	1	yes	characteristic
690	#95	C₂³×C₃₁	1	1	yes	characteristic
691	#95	C₂³×C₃₁	1	1	yes	characteristic
692	#95	C₂³×C₃₁	1	2	yes	—
693	#95	C₂³×C₃₁	1	2	yes	—
694	#95	C₂³×C₃₁	1	2	yes	—
695	#95	C₂³×C₃₁	1	2	yes	—
696	#95	C₂³×C₃₁	1	2	yes	—
697	#95	C₂³×C₃₁	1	2	yes	—
698	#95	C₂³×C₃₁	1	2	yes	—
699	#95	C₂³×C₃₁	1	2	yes	—
700	#95	C₂³×C₃₁	1	2	yes	—
701	#95	C₂³×C₃₁	1	2	yes	—
702	#95	C₂³×C₃₁	1	2	yes	—
703	#95	C₂³×C₃₁	1	2	yes	—
704	#95	C₂³×C₃₁	1	2	yes	—
705	#95	C₂³×C₃₁	1	2	yes	—
706	#95	C₂³×C₃₁	1	2	yes	—
707	#95	C₂³×C₃₁	1	2	yes	—
708	#95	C₂³×C₃₁	1	2	yes	—
709	#95	C₂³×C₃₁	1	2	yes	—
710	#95	C₂³×C₃₁	1	2	yes	—
711	#95	C₂³×C₃₁	1	2	yes	—
712	#95	C₂³×C₃₁	1	2	yes	—
713	#95	C₂³×C₃₁	1	2	yes	—
714	#95	C₂³×C₃₁	1	2	yes	—
715	#95	C₂³×C₃₁	1	2	yes	—
716	C₃₁	#35137	1	1	yes	characteristic, direct product factor, Sylow
717	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
718	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	4	no	—
721	C₂×Q₈	—	2	4	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×Q₈	—	4	2	no	—
726	C₂×Q₈	—	4	2	no	—
727	C₂×Q₈	—	4	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	4	1	no	—
743	C₂²×C₄	—	4	1	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	#41×C₃₁	1	4	yes	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	4	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	4	1	no	—
819	C₄²	—	4	2	no	—
820	C₄²	—	4	1	no	—
821	C₄²	—	4	1	no	—
822	C₄²	—	4	1	no	—
823	C₄²	—	4	2	no	—
824	C₄²	#41×C₃₁	1	4	yes	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	C₂×#41×C₃₁	1	2	yes	—
839	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
840	Q₈	—	4	4	no	—
841	Q₈	—	8	4	no	—
842	Q₈	—	8	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	8	4	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	8	4	no	—
902	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
903	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
904	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
905	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
906	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
907	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
908	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
909	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
910	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
911	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
927	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
928	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
929	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
930	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
931	C₂²	C₃₁×#585	1	1	yes	characteristic
932	C₂²	C₃₁×#585	1	1	yes	characteristic
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	C₃₁×#542	1	4	yes	—
954	C₂	—	4	2	no	—
955	C₂	—	8	2	no	—
956	C₂	C₃₁×#3444	1	1	yes	characteristic
957	C₂	C₂×C₃₁×#542	1	1	yes	characteristic
958	C₂	C₃₁×#3455	1	1	yes	characteristic
959	C₂	C₃₁×#3514	1	1	yes	characteristic
960	C₂	C₃₁×#3514	1	1	yes	characteristic
961	C₂	C₃₁×#3515	1	1	yes	characteristic
962	C₂	C₃₁×#3518	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#121	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×#2862	C₂	semidirect
2. C₃₁×#2861	C₂	semidirect
3. C₃₁×#2851	C₂	semidirect
5. C₃₁×#2653	C₂	semidirect
6. C₃₁×#2650	C₂	semidirect
7. C₃₁×#2532	C₂	semidirect
8. C₃₁×#2527	C₂	semidirect
9. C₃₁×#2514	C₂	semidirect
10. C₃₁×#2513	C₂	semidirect
11. C₃₁×#2492	C₂	semidirect
13. C₃₁×#2477	C₂	semidirect
14. C₃₁×#2474	C₂	semidirect
15. C₃₁×#2452	C₂	semidirect
16. C₃₁×#2451	C₂	semidirect
17. C₃₁×#2421	C₂	semidirect
19. C₃₁×#2337	C₂	semidirect
20. C₃₁×#2332	C₂	semidirect
21. C₄×C₃₁×#125	C₂	semidirect
22. C₄×C₃₁×#124	C₂	semidirect
23. C₄×C₃₁×#117	C₂	semidirect
343. #35137	C₃₁	direct (N × H)
431. #2862	C₂×C₃₁	semidirect
432. #2861	C₂×C₃₁	semidirect
433. #2851	C₂×C₃₁	semidirect
435. #2653	C₂×C₃₁	semidirect
436. #2650	C₂×C₃₁	semidirect
437. #2532	C₂×C₃₁	semidirect
438. #2527	C₂×C₃₁	semidirect
439. #2514	C₂×C₃₁	semidirect
440. #2513	C₂×C₃₁	semidirect
441. #2492	C₂×C₃₁	semidirect
443. #2477	C₂×C₃₁	semidirect
444. #2474	C₂×C₃₁	semidirect
445. #2452	C₂×C₃₁	semidirect
446. #2451	C₂×C₃₁	semidirect
447. #2421	C₂×C₃₁	semidirect
449. #2337	C₂×C₃₁	semidirect
450. #2332	C₂×C₃₁	semidirect
451. C₄×#125	C₂×C₃₁	semidirect
452. C₄×#124	C₂×C₃₁	semidirect
453. C₄×#117	C₂×C₃₁	semidirect
716. C₃₁	#35137	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×#2862	2
C₃₁×#2861	2
C₃₁×#2851	2
C₃₁×#2850	2
C₃₁×#2653	2
C₃₁×#2650	2
C₃₁×#2532	2
C₃₁×#2527	2
C₃₁×#2514	2
C₃₁×#2513	2
C₃₁×#2492	2
C₃₁×#2491	2
C₃₁×#2477	2
C₃₁×#2474	2
C₃₁×#2452	2
C₃₁×#2451	2
C₃₁×#2421	2
C₃₁×#2420	2
C₃₁×#2337	2
C₃₁×#2332	2
C₄×C₃₁×#125	2
C₄×C₃₁×#124	2
C₄×C₃₁×#117	2
#35137	31

Subgroups — C31×#35137 #21491896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35137 #21491896