Subgroups — C₃₁×#35030 #21491789

Order 7936.

1964 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2653	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2650	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2574	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2572	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2514	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2510	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2444	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2436	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2427	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2416	C₂	1	1	yes	maximal, characteristic
18	C₃₁×#2409	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2325	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
21	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#121	C₂²	1	2	yes	—
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#401	C₂²	1	2	yes	—
42	C₃₁×#400	C₂²	1	2	yes	—
43	C₃₁×#400	C₂²	1	2	yes	—
44	C₃₁×#400	C₂²	1	2	yes	—
45	C₃₁×#398	C₂²	1	2	yes	—
46	C₃₁×#397	C₂²	1	2	yes	—
47	C₃₁×#397	C₂²	1	2	yes	—
48	C₃₁×#397	C₂²	1	2	yes	—
49	C₃₁×#397	C₂²	1	2	yes	—
50	C₃₁×#396	C₂²	1	2	yes	—
51	C₃₁×#395	C₂²	1	2	yes	—
52	C₃₁×#394	C₂²	1	2	yes	—
53	C₃₁×#394	C₂²	1	2	yes	—
54	C₃₁×#393	C₂²	1	2	yes	—
55	C₃₁×#393	C₂²	1	2	yes	—
56	C₃₁×#393	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	2	yes	—
58	C₃₁×#391	C₂²	1	1	yes	characteristic
59	C₃₁×#391	C₂²	1	1	yes	characteristic
60	C₃₁×#391	C₂²	1	1	yes	characteristic
61	C₃₁×#391	C₂²	1	1	yes	characteristic
62	C₃₁×#391	C₂²	1	1	yes	characteristic
63	C₃₁×#391	C₂²	1	1	yes	characteristic
64	C₃₁×#391	C₂²	1	2	yes	—
65	C₃₁×#391	C₂²	1	1	yes	characteristic
66	C₃₁×#391	C₂²	1	1	yes	characteristic
67	C₃₁×#390	C₂²	1	1	yes	characteristic
68	C₃₁×#390	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	1	yes	characteristic
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#389	C₂²	1	1	yes	characteristic
73	C₃₁×#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×#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×#386	C₂²	1	2	yes	—
88	C₃₁×#386	C₂²	1	2	yes	—
89	C₃₁×#386	C₂²	1	2	yes	—
90	C₃₁×#386	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×#386	C₂²	1	2	yes	—
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	2	yes	—
97	C₃₁×#385	C₂²	1	2	yes	—
98	C₃₁×#385	C₂²	1	2	yes	—
99	C₃₁×#383	C₂²	1	2	yes	—
100	C₃₁×#383	C₂²	1	2	yes	—
101	C₃₁×#382	C₂²	1	2	yes	—
102	C₃₁×#382	C₂²	1	1	yes	characteristic
103	C₃₁×#381	C₂²	1	2	yes	—
104	C₃₁×#381	C₂²	1	2	yes	—
105	C₃₁×#380	C₂²	1	2	yes	—
106	C₃₁×#380	C₂²	1	2	yes	—
107	C₃₁×#380	C₂²	1	1	yes	characteristic
108	C₃₁×#380	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
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	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
120	C₂×C₃₁×#95	C₂²	1	2	yes	—
121	C₂×C₃₁×#95	C₂²	1	2	yes	—
122	C₄³×C₃₁	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	—	2	4	no	—
124	C₂²×Q₈×C₃₁	—	4	2	no	—
125	C₂²×Q₈×C₃₁	—	4	2	no	—
126	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
129	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
131	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
139	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
140	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₃₁×#125	—	4	2	no	—
143	C₃₁×#124	—	4	2	no	—
144	C₃₁×#124	—	4	2	no	—
145	C₃₁×C₂²⋊Q₈	—	4	2	no	—
146	C₃₁×C₂²⋊Q₈	—	4	2	no	—
147	C₃₁×#121	—	2	8	no	—
148	C₃₁×#121	—	2	4	no	—
149	C₃₁×#121	—	4	2	no	—
150	C₄×D₄×C₃₁	—	2	4	no	—
151	C₄×D₄×C₃₁	—	2	4	no	—
152	C₄×D₄×C₃₁	—	2	4	no	—
153	C₄×D₄×C₃₁	—	2	8	no	—
154	C₄×D₄×C₃₁	—	4	2	no	—
155	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊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	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×C₄²×C₃₁	—	4	2	no	—
195	C₂×C₄²×C₃₁	—	4	2	no	—
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₃₁	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	1	yes	characteristic
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	2	yes	—
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	1	yes	characteristic
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	1	yes	characteristic
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
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	C₃₁×#95	C₂³	1	2	yes	—
236	C₃₁×#95	C₂³	1	2	yes	—
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₃₁×#95	C₂³	1	1	yes	characteristic
239	C₃₁×#95	C₂³	1	1	yes	characteristic
240	C₃₁×#95	C₂³	1	2	yes	—
241	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
242	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×Q₈×C₃₁	—	2	4	no	—
245	C₂×Q₈×C₃₁	—	2	2	no	—
246	C₂×Q₈×C₃₁	—	2	2	no	—
247	C₂×Q₈×C₃₁	—	2	2	no	—
248	C₂×Q₈×C₃₁	—	2	2	no	—
249	C₂×Q₈×C₃₁	—	2	2	no	—
250	C₂×Q₈×C₃₁	—	2	2	no	—
251	C₂×Q₈×C₃₁	—	4	2	no	—
252	C₂×Q₈×C₃₁	—	4	2	no	—
253	C₂×Q₈×C₃₁	—	4	16	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	2	no	—
256	C₂×D₄×C₃₁	—	2	4	no	—
257	C₂×D₄×C₃₁	—	2	4	no	—
258	C₂×D₄×C₃₁	—	2	4	no	—
259	C₂×D₄×C₃₁	—	2	4	no	—
260	C₂×D₄×C₃₁	—	2	2	no	—
261	C₂×D₄×C₃₁	—	2	2	no	—
262	C₂×D₄×C₃₁	—	2	2	no	—
263	C₂×D₄×C₃₁	—	4	2	no	—
264	C₂×D₄×C₃₁	—	4	2	no	—
265	C₂×D₄×C₃₁	#41	1	4	yes	—
266	C₂²×C₄×C₃₁	—	2	2	no	—
267	C₂²×C₄×C₃₁	—	2	2	no	—
268	C₂²×C₄×C₃₁	—	2	2	no	—
269	C₂²×C₄×C₃₁	—	2	2	no	—
270	C₂²×C₄×C₃₁	—	2	4	no	—
271	C₂²×C₄×C₃₁	—	2	4	no	—
272	C₂²×C₄×C₃₁	—	2	2	no	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	2	2	no	—
275	C₂²×C₄×C₃₁	—	2	2	no	—
276	C₂²×C₄×C₃₁	—	2	2	no	—
277	C₂²×C₄×C₃₁	—	2	2	no	—
278	C₂²×C₄×C₃₁	—	2	4	no	—
279	C₂²×C₄×C₃₁	—	4	1	no	—
280	C₂²×C₄×C₃₁	—	4	1	no	—
281	C₂²×C₄×C₃₁	—	4	1	no	—
282	C₂²×C₄×C₃₁	—	4	1	no	—
283	C₂²×C₄×C₃₁	—	4	1	no	—
284	C₂²×C₄×C₃₁	—	4	1	no	—
285	C₂²×C₄×C₃₁	—	4	2	no	—
286	C₂²×C₄×C₃₁	—	4	2	no	—
287	C₂²×C₄×C₃₁	—	4	2	no	—
288	C₂²×C₄×C₃₁	—	4	2	no	—
289	C₂²×C₄×C₃₁	—	4	2	no	—
290	C₂²×C₄×C₃₁	—	4	2	no	—
291	C₂²×C₄×C₃₁	#41	1	4	yes	—
292	C₂²×C₄×C₃₁	#41	1	4	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₃₁	—	2	2	no	—
314	C₄⋊C₄×C₃₁	—	2	2	no	—
315	C₄⋊C₄×C₃₁	—	2	4	no	—
316	C₄⋊C₄×C₃₁	—	2	2	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	4	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	2	no	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	4	2	no	—
324	C₄⋊C₄×C₃₁	—	4	2	no	—
325	C₄⋊C₄×C₃₁	—	4	2	no	—
326	C₄⋊C₄×C₃₁	—	4	2	no	—
327	C₄⋊C₄×C₃₁	—	4	2	no	—
328	C₄⋊C₄×C₃₁	—	4	2	no	—
329	C₄⋊C₄×C₃₁	—	4	2	no	—
330	C₂²⋊C₄×C₃₁	—	2	2	no	—
331	C₂²⋊C₄×C₃₁	—	2	2	no	—
332	C₂²⋊C₄×C₃₁	—	2	4	no	—
333	C₂²⋊C₄×C₃₁	—	2	2	no	—
334	C₂²⋊C₄×C₃₁	—	2	2	no	—
335	C₂²⋊C₄×C₃₁	—	2	4	no	—
336	C₂²⋊C₄×C₃₁	—	2	2	no	—
337	C₂²⋊C₄×C₃₁	—	2	4	no	—
338	C₂²⋊C₄×C₃₁	—	2	2	no	—
339	C₂²⋊C₄×C₃₁	—	2	4	no	—
340	C₂²⋊C₄×C₃₁	—	2	4	no	—
341	C₂²⋊C₄×C₃₁	—	2	4	no	—
342	C₂²⋊C₄×C₃₁	—	4	2	no	—
343	C₂²⋊C₄×C₃₁	—	4	2	no	—
344	C₂²⋊C₄×C₃₁	—	4	2	no	—
345	C₂²⋊C₄×C₃₁	—	4	2	no	—
346	C₂²⋊C₄×C₃₁	—	4	2	no	—
347	C₂²⋊C₄×C₃₁	—	4	2	no	—
348	C₂²⋊C₄×C₃₁	—	4	2	no	—
349	C₂²⋊C₄×C₃₁	—	4	2	no	—
350	C₂²⋊C₄×C₃₁	—	4	2	no	—
351	C₄²×C₃₁	—	2	2	no	—
352	C₄²×C₃₁	—	2	2	no	—
353	C₄²×C₃₁	—	2	2	no	—
354	C₄²×C₃₁	—	2	4	no	—
355	C₄²×C₃₁	—	2	2	no	—
356	C₄²×C₃₁	—	2	2	no	—
357	C₄²×C₃₁	—	2	2	no	—
358	C₄²×C₃₁	—	2	2	no	—
359	C₄²×C₃₁	—	2	2	no	—
360	C₄²×C₃₁	—	4	1	no	—
361	C₄²×C₃₁	—	4	1	no	—
362	C₄²×C₃₁	—	4	1	no	—
363	C₄²×C₃₁	—	4	1	no	—
364	C₄²×C₃₁	—	4	1	no	—
365	#35030	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
366	C₂³×C₃₁	—	2	1	no	—
367	C₂³×C₃₁	—	2	1	no	—
368	C₂³×C₃₁	—	2	1	no	—
369	C₂³×C₃₁	—	2	1	no	—
370	C₂³×C₃₁	—	2	1	no	—
371	C₂³×C₃₁	—	2	1	no	—
372	C₂³×C₃₁	—	2	1	no	—
373	C₂³×C₃₁	—	2	1	no	—
374	C₂³×C₃₁	—	2	1	no	—
375	C₂³×C₃₁	—	2	1	no	—
376	C₂³×C₃₁	—	2	2	no	—
377	C₂³×C₃₁	—	2	2	no	—
378	C₂³×C₃₁	—	2	2	no	—
379	C₂³×C₃₁	—	2	2	no	—
380	C₂³×C₃₁	—	2	2	no	—
381	C₂³×C₃₁	—	2	2	no	—
382	C₂³×C₃₁	—	2	2	no	—
383	C₂³×C₃₁	C₂×#41	1	2	yes	—
384	C₂³×C₃₁	C₂×#41	1	2	yes	—
385	C₂³×C₃₁	C₂×#41	1	2	yes	—
386	C₂³×C₃₁	C₂×#41	1	2	yes	—
387	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
388	Q₈×C₃₁	—	4	8	no	—
389	Q₈×C₃₁	—	4	4	no	—
390	Q₈×C₃₁	—	4	4	no	—
391	D₄×C₃₁	—	2	8	no	—
392	D₄×C₃₁	—	4	8	no	—
393	D₄×C₃₁	—	4	4	no	—
394	D₄×C₃₁	—	8	4	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	1	no	—
398	C₂×C₄×C₃₁	—	2	1	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	1	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	8	no	—
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	1	no	—
413	C₂×C₄×C₃₁	—	2	1	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	1	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	1	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	1	no	—
425	C₂×C₄×C₃₁	—	2	1	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	1	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	1	no	—
430	C₂×C₄×C₃₁	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	1	no	—
438	C₂×C₄×C₃₁	—	2	1	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	1	no	—
441	C₂×C₄×C₃₁	—	2	1	no	—
442	C₂×C₄×C₃₁	—	2	1	no	—
443	C₂×C₄×C₃₁	—	2	1	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	2	1	no	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	4	4	no	—
449	C₂×C₄×C₃₁	—	4	4	no	—
450	C₂×C₄×C₃₁	—	4	4	no	—
451	C₂×C₄×C₃₁	—	4	4	no	—
452	C₂×C₄×C₃₁	—	4	8	no	—
453	C₂×C₄×C₃₁	—	4	4	no	—
454	C₂×C₄×C₃₁	—	8	4	no	—
455	C₂×C₄×C₃₁	—	8	4	no	—
456	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
457	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
458	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
459	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
460	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
461	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
462	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
463	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
464	#2863	C₂×C₃₁	1	1	yes	characteristic, complemented
465	#2861	C₂×C₃₁	1	1	yes	characteristic, complemented
466	#2855	C₂×C₃₁	1	1	yes	characteristic, complemented
467	#2850	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#2653	C₂×C₃₁	1	2	yes	complemented
469	#2650	C₂×C₃₁	1	2	yes	complemented
470	#2574	C₂×C₃₁	1	2	yes	complemented
471	#2572	C₂×C₃₁	1	2	yes	complemented
472	#2514	C₂×C₃₁	1	1	yes	characteristic, complemented
473	#2510	C₂×C₃₁	1	2	yes	complemented
474	#2489	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#2447	C₂×C₃₁	1	1	yes	characteristic, complemented
476	#2444	C₂×C₃₁	1	2	yes	complemented
477	#2442	C₂×C₃₁	1	1	yes	characteristic, complemented
478	#2436	C₂×C₃₁	1	1	yes	characteristic, complemented
479	#2427	C₂×C₃₁	1	1	yes	characteristic, complemented
480	#2416	C₂×C₃₁	1	1	yes	characteristic
481	#2409	C₂×C₃₁	1	1	yes	characteristic, complemented
482	#2325	C₂×C₃₁	1	2	yes	complemented
483	#2318	C₂×C₃₁	1	2	yes	complemented
484	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
485	C₂×#391	C₂×C₃₁	1	1	yes	characteristic, complemented
486	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
487	C₂²×C₃₁	—	2	2	no	—
488	C₂²×C₃₁	—	2	2	no	—
489	C₂²×C₃₁	—	2	2	no	—
490	C₂²×C₃₁	—	2	2	no	—
491	C₂²×C₃₁	—	2	2	no	—
492	C₂²×C₃₁	—	2	2	no	—
493	C₂²×C₃₁	—	2	2	no	—
494	C₂²×C₃₁	—	2	2	no	—
495	C₂²×C₃₁	—	2	2	no	—
496	C₂²×C₃₁	—	4	1	no	—
497	C₂²×C₃₁	—	4	1	no	—
498	C₂²×C₃₁	—	4	1	no	—
499	C₂²×C₃₁	—	4	1	no	—
500	C₂²×C₃₁	—	4	2	no	—
501	C₂²×C₃₁	—	4	2	no	—
502	C₂²×C₃₁	—	4	2	no	—
503	C₂²×C₃₁	—	4	2	no	—
504	C₂²×C₃₁	—	4	2	no	—
505	C₂²×C₃₁	—	4	2	no	—
506	C₂²×C₃₁	—	4	2	no	—
507	C₂²×C₃₁	#529	1	4	yes	—
508	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
509	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
510	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
511	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
512	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
514	C₂²×C₃₁	#585	1	1	yes	characteristic
515	C₄×C₃₁	—	2	2	no	—
516	C₄×C₃₁	—	2	2	no	—
517	C₄×C₃₁	—	2	2	no	—
518	C₄×C₃₁	—	2	2	no	—
519	C₄×C₃₁	—	2	2	no	—
520	C₄×C₃₁	—	4	2	no	—
521	C₄×C₃₁	—	4	1	no	—
522	C₄×C₃₁	—	4	2	no	—
523	C₄×C₃₁	—	4	2	no	—
524	C₄×C₃₁	—	4	1	no	—
525	C₄×C₃₁	—	4	1	no	—
526	C₄×C₃₁	—	4	2	no	—
527	C₄×C₃₁	—	4	1	no	—
528	C₄×C₃₁	—	4	2	no	—
529	C₄×C₃₁	—	4	1	no	—
530	C₄×C₃₁	—	4	2	no	—
531	C₄×C₃₁	—	4	2	no	—
532	C₄×C₃₁	—	4	1	no	—
533	C₄×C₃₁	—	4	1	no	—
534	C₄×C₃₁	#538	1	4	yes	—
535	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
536	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
537	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
538	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
539	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
540	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
541	C₂×#121	C₂²×C₃₁	1	2	yes	—
542	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
543	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
544	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
545	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
546	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
547	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
548	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
549	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
550	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
551	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
552	#401	C₂²×C₃₁	1	2	yes	—
553	#400	C₂²×C₃₁	1	2	yes	—
554	#400	C₂²×C₃₁	1	2	yes	—
555	#400	C₂²×C₃₁	1	2	yes	—
556	#398	C₂²×C₃₁	1	2	yes	—
557	#397	C₂²×C₃₁	1	2	yes	—
558	#397	C₂²×C₃₁	1	2	yes	—
559	#397	C₂²×C₃₁	1	2	yes	—
560	#397	C₂²×C₃₁	1	2	yes	—
561	#396	C₂²×C₃₁	1	2	yes	—
562	#395	C₂²×C₃₁	1	2	yes	—
563	#394	C₂²×C₃₁	1	2	yes	—
564	#394	C₂²×C₃₁	1	2	yes	—
565	#393	C₂²×C₃₁	1	2	yes	—
566	#393	C₂²×C₃₁	1	2	yes	—
567	#393	C₂²×C₃₁	1	2	yes	—
568	#391	C₂²×C₃₁	1	2	yes	—
569	#391	C₂²×C₃₁	1	1	yes	characteristic
570	#391	C₂²×C₃₁	1	1	yes	characteristic
571	#391	C₂²×C₃₁	1	1	yes	characteristic
572	#391	C₂²×C₃₁	1	1	yes	characteristic
573	#391	C₂²×C₃₁	1	1	yes	characteristic
574	#391	C₂²×C₃₁	1	1	yes	characteristic
575	#391	C₂²×C₃₁	1	2	yes	—
576	#391	C₂²×C₃₁	1	1	yes	characteristic
577	#391	C₂²×C₃₁	1	1	yes	characteristic
578	#390	C₂²×C₃₁	1	1	yes	characteristic
579	#390	C₂²×C₃₁	1	1	yes	characteristic
580	#389	C₂²×C₃₁	1	1	yes	characteristic
581	#389	C₂²×C₃₁	1	1	yes	characteristic
582	#389	C₂²×C₃₁	1	1	yes	characteristic
583	#389	C₂²×C₃₁	1	1	yes	characteristic
584	#388	C₂²×C₃₁	1	2	yes	—
585	#388	C₂²×C₃₁	1	2	yes	—
586	#388	C₂²×C₃₁	1	2	yes	—
587	#388	C₂²×C₃₁	1	2	yes	—
588	#388	C₂²×C₃₁	1	2	yes	—
589	#388	C₂²×C₃₁	1	2	yes	—
590	#388	C₂²×C₃₁	1	2	yes	—
591	#388	C₂²×C₃₁	1	2	yes	—
592	#387	C₂²×C₃₁	1	2	yes	—
593	#387	C₂²×C₃₁	1	2	yes	—
594	#387	C₂²×C₃₁	1	2	yes	—
595	#387	C₂²×C₃₁	1	2	yes	—
596	#387	C₂²×C₃₁	1	2	yes	—
597	#387	C₂²×C₃₁	1	2	yes	—
598	#386	C₂²×C₃₁	1	2	yes	—
599	#386	C₂²×C₃₁	1	2	yes	—
600	#386	C₂²×C₃₁	1	2	yes	—
601	#386	C₂²×C₃₁	1	2	yes	—
602	#386	C₂²×C₃₁	1	2	yes	—
603	#386	C₂²×C₃₁	1	2	yes	—
604	#386	C₂²×C₃₁	1	2	yes	—
605	#386	C₂²×C₃₁	1	2	yes	—
606	#385	C₂²×C₃₁	1	2	yes	—
607	#385	C₂²×C₃₁	1	2	yes	—
608	#385	C₂²×C₃₁	1	2	yes	—
609	#385	C₂²×C₃₁	1	2	yes	—
610	#383	C₂²×C₃₁	1	2	yes	—
611	#383	C₂²×C₃₁	1	2	yes	—
612	#382	C₂²×C₃₁	1	2	yes	—
613	#382	C₂²×C₃₁	1	1	yes	characteristic
614	#381	C₂²×C₃₁	1	2	yes	—
615	#381	C₂²×C₃₁	1	2	yes	—
616	#380	C₂²×C₃₁	1	2	yes	—
617	#380	C₂²×C₃₁	1	2	yes	—
618	#380	C₂²×C₃₁	1	1	yes	characteristic
619	#380	C₂²×C₃₁	1	1	yes	characteristic
620	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
621	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
622	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
623	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
624	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
625	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
626	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
627	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
628	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
629	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
630	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
631	C₂×#95	C₂²×C₃₁	1	2	yes	—
632	C₂×#95	C₂²×C₃₁	1	2	yes	—
633	C₄³	C₂²×C₃₁	1	1	yes	characteristic
634	C₂×C₃₁	—	2	4	no	—
635	C₂×C₃₁	—	4	2	no	—
636	C₂×C₃₁	—	8	2	no	—
637	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
638	C₂×C₃₁	C₂×#538	1	1	yes	characteristic
639	C₂×C₃₁	#3461	1	1	yes	characteristic
640	C₂×C₃₁	#3505	1	1	yes	characteristic
641	C₂×C₃₁	#3511	1	1	yes	characteristic
642	C₂×C₃₁	#3514	1	1	yes	characteristic
643	C₂×C₃₁	#3520	1	1	yes	characteristic
644	C₂²×Q₈	—	2	4	no	—
645	C₂²×Q₈	—	4	2	no	—
646	C₂²×Q₈	—	4	2	no	—
647	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
648	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
649	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
650	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
651	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
652	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
653	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
654	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
655	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
656	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
657	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
658	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
659	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
660	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
661	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
662	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
663	#125	—	4	2	no	—
664	#124	—	4	2	no	—
665	#124	—	4	2	no	—
666	C₂²⋊Q₈	—	4	2	no	—
667	C₂²⋊Q₈	—	4	2	no	—
668	#121	—	2	8	no	—
669	#121	—	2	4	no	—
670	#121	—	4	2	no	—
671	C₄×D₄	—	2	4	no	—
672	C₄×D₄	—	2	4	no	—
673	C₄×D₄	—	2	4	no	—
674	C₄×D₄	—	2	8	no	—
675	C₄×D₄	—	4	2	no	—
676	C₂×C₄⋊C₄	—	4	2	no	—
677	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
715	C₂×C₄²	—	4	2	no	—
716	C₂×C₄²	—	4	2	no	—
717	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
722	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
731	#95	C₂³×C₃₁	1	2	yes	—
732	#95	C₂³×C₃₁	1	2	yes	—
733	#95	C₂³×C₃₁	1	2	yes	—
734	#95	C₂³×C₃₁	1	2	yes	—
735	#95	C₂³×C₃₁	1	2	yes	—
736	#95	C₂³×C₃₁	1	2	yes	—
737	#95	C₂³×C₃₁	1	2	yes	—
738	#95	C₂³×C₃₁	1	2	yes	—
739	#95	C₂³×C₃₁	1	1	yes	characteristic
740	#95	C₂³×C₃₁	1	1	yes	characteristic
741	#95	C₂³×C₃₁	1	1	yes	characteristic
742	#95	C₂³×C₃₁	1	1	yes	characteristic
743	#95	C₂³×C₃₁	1	1	yes	characteristic
744	#95	C₂³×C₃₁	1	1	yes	characteristic
745	#95	C₂³×C₃₁	1	2	yes	—
746	#95	C₂³×C₃₁	1	2	yes	—
747	#95	C₂³×C₃₁	1	2	yes	—
748	#95	C₂³×C₃₁	1	2	yes	—
749	#95	C₂³×C₃₁	1	2	yes	—
750	#95	C₂³×C₃₁	1	2	yes	—
751	#95	C₂³×C₃₁	1	2	yes	—
752	#95	C₂³×C₃₁	1	2	yes	—
753	#95	C₂³×C₃₁	1	2	yes	—
754	#95	C₂³×C₃₁	1	2	yes	—
755	#95	C₂³×C₃₁	1	2	yes	—
756	#95	C₂³×C₃₁	1	2	yes	—
757	#95	C₂³×C₃₁	1	2	yes	—
758	#95	C₂³×C₃₁	1	2	yes	—
759	#95	C₂³×C₃₁	1	2	yes	—
760	#95	C₂³×C₃₁	1	2	yes	—
761	#95	C₂³×C₃₁	1	2	yes	—
762	C₃₁	#35030	1	1	yes	characteristic, direct product factor, Sylow
763	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
764	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
766	C₂×Q₈	—	2	4	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	—	2	2	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	4	2	no	—
774	C₂×Q₈	—	4	2	no	—
775	C₂×Q₈	—	4	16	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	4	2	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	#41×C₃₁	1	4	yes	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	4	1	no	—
802	C₂²×C₄	—	4	1	no	—
803	C₂²×C₄	—	4	1	no	—
804	C₂²×C₄	—	4	1	no	—
805	C₂²×C₄	—	4	1	no	—
806	C₂²×C₄	—	4	1	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	#41×C₃₁	1	4	yes	—
814	C₂²×C₄	#41×C₃₁	1	4	yes	—
815	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
819	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
820	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	4	2	no	—
846	C₄⋊C₄	—	4	2	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	4	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	4	1	no	—
883	C₄²	—	4	1	no	—
884	C₄²	—	4	1	no	—
885	C₄²	—	4	1	no	—
886	C₄²	—	4	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	C₂×#41×C₃₁	1	2	yes	—
905	C₂³	C₂×#41×C₃₁	1	2	yes	—
906	C₂³	C₂×#41×C₃₁	1	2	yes	—
907	C₂³	C₂×#41×C₃₁	1	2	yes	—
908	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
909	Q₈	—	4	8	no	—
910	Q₈	—	4	4	no	—
911	Q₈	—	4	4	no	—
912	D₄	—	2	8	no	—
913	D₄	—	4	8	no	—
914	D₄	—	4	4	no	—
915	D₄	—	8	4	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	8	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	4	4	no	—
970	C₂×C₄	—	4	4	no	—
971	C₂×C₄	—	4	4	no	—
972	C₂×C₄	—	4	4	no	—
973	C₂×C₄	—	4	8	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	8	4	no	—
976	C₂×C₄	—	8	4	no	—
977	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
978	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
979	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
980	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
981	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
982	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
983	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
984	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	C₃₁×#529	1	4	yes	—
1006	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1007	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1008	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1009	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1010	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1011	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1012	C₂²	C₃₁×#585	1	1	yes	characteristic
1013	C₄	—	2	2	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	2	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	1	no	—
1032	C₄	C₃₁×#538	1	4	yes	—
1033	C₂	—	2	4	no	—
1034	C₂	—	4	2	no	—
1035	C₂	—	8	2	no	—
1036	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
1037	C₂	C₂×C₃₁×#538	1	1	yes	characteristic
1038	C₂	C₃₁×#3461	1	1	yes	characteristic
1039	C₂	C₃₁×#3505	1	1	yes	characteristic
1040	C₂	C₃₁×#3511	1	1	yes	characteristic
1041	C₂	C₃₁×#3514	1	1	yes	characteristic
1042	C₂	C₃₁×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₃₁×#2416	C₂
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×#2863	C₂	semidirect
2. C₃₁×#2861	C₂	semidirect
3. C₃₁×#2855	C₂	semidirect
4. C₃₁×#2850	C₂	semidirect
5. C₃₁×#2653	C₂	semidirect
6. C₃₁×#2650	C₂	semidirect
7. C₃₁×#2574	C₂	semidirect
8. C₃₁×#2572	C₂	semidirect
9. C₃₁×#2514	C₂	semidirect
10. C₃₁×#2510	C₂	semidirect
11. C₃₁×#2489	C₂	semidirect
12. C₃₁×#2447	C₂	semidirect
13. C₃₁×#2444	C₂	semidirect
14. C₃₁×#2442	C₂	semidirect
15. C₃₁×#2436	C₂	semidirect
16. C₃₁×#2427	C₂	semidirect
18. C₃₁×#2409	C₂	semidirect
19. C₃₁×#2325	C₂	semidirect
20. C₃₁×#2318	C₂	semidirect
21. C₄×C₃₁×#121	C₂	semidirect
22. C₂×C₃₁×#391	C₂	semidirect
23. C₄²×D₄×C₃₁	C₂	semidirect
365. #35030	C₃₁	direct (N × H)
464. #2863	C₂×C₃₁	semidirect
465. #2861	C₂×C₃₁	semidirect
466. #2855	C₂×C₃₁	semidirect
467. #2850	C₂×C₃₁	semidirect
468. #2653	C₂×C₃₁	semidirect
469. #2650	C₂×C₃₁	semidirect
470. #2574	C₂×C₃₁	semidirect
471. #2572	C₂×C₃₁	semidirect
472. #2514	C₂×C₃₁	semidirect
473. #2510	C₂×C₃₁	semidirect
474. #2489	C₂×C₃₁	semidirect
475. #2447	C₂×C₃₁	semidirect
476. #2444	C₂×C₃₁	semidirect
477. #2442	C₂×C₃₁	semidirect
478. #2436	C₂×C₃₁	semidirect
479. #2427	C₂×C₃₁	semidirect
481. #2409	C₂×C₃₁	semidirect
482. #2325	C₂×C₃₁	semidirect
483. #2318	C₂×C₃₁	semidirect
484. C₄×#121	C₂×C₃₁	semidirect
485. C₂×#391	C₂×C₃₁	semidirect
486. C₄²×D₄	C₂×C₃₁	semidirect
762. C₃₁	#35030	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×#2863	2
C₃₁×#2861	2
C₃₁×#2855	2
C₃₁×#2850	2
C₃₁×#2653	2
C₃₁×#2650	2
C₃₁×#2574	2
C₃₁×#2572	2
C₃₁×#2514	2
C₃₁×#2510	2
C₃₁×#2489	2
C₃₁×#2447	2
C₃₁×#2444	2
C₃₁×#2442	2
C₃₁×#2436	2
C₃₁×#2427	2
C₃₁×#2416	2
C₃₁×#2409	2
C₃₁×#2325	2
C₃₁×#2318	2
C₄×C₃₁×#121	2
C₂×C₃₁×#391	2
C₄²×D₄×C₃₁	2
#35030	31

Subgroups — C31×#35030 #21491789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35030 #21491789