Subgroups — C₃₁×#34503 #21491262

Order 7936.

2140 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#555	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2381	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2377	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2367	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2364	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2353	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2343	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2343	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2337	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2333	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2327	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2325	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2314	C₂	1	2	yes	maximal, complemented
18	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2298	C₂	1	2	yes	maximal, complemented
20	C₃₁×#555	C₄	1	16	yes	complemented
21	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#124	C₂²	1	2	yes	—
24	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#121	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	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×D₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₃₁×#117	C₂²	1	2	yes	—
34	C₂×C₃₁×#117	C₂²	1	2	yes	—
35	C₃₁×#391	C₂²	1	1	yes	characteristic
36	C₃₁×#391	C₂²	1	1	yes	characteristic
37	C₃₁×#391	C₂²	1	1	yes	characteristic
38	C₃₁×#391	C₂²	1	2	yes	—
39	C₃₁×#391	C₂²	1	1	yes	characteristic
40	C₃₁×#390	C₂²	1	1	yes	characteristic
41	C₃₁×#390	C₂²	1	2	yes	—
42	C₃₁×#390	C₂²	1	1	yes	characteristic
43	C₃₁×#388	C₂²	1	2	yes	—
44	C₃₁×#388	C₂²	1	2	yes	—
45	C₃₁×#388	C₂²	1	2	yes	—
46	C₃₁×#388	C₂²	1	2	yes	—
47	C₃₁×#388	C₂²	1	2	yes	—
48	C₃₁×#388	C₂²	1	2	yes	—
49	C₃₁×#388	C₂²	1	2	yes	—
50	C₃₁×#388	C₂²	1	2	yes	—
51	C₃₁×#388	C₂²	1	2	yes	—
52	C₃₁×#388	C₂²	1	2	yes	—
53	C₃₁×#388	C₂²	1	2	yes	—
54	C₃₁×#388	C₂²	1	2	yes	—
55	C₃₁×#387	C₂²	1	2	yes	—
56	C₃₁×#387	C₂²	1	2	yes	—
57	C₃₁×#387	C₂²	1	2	yes	—
58	C₃₁×#387	C₂²	1	2	yes	—
59	C₃₁×#387	C₂²	1	2	yes	—
60	C₃₁×#387	C₂²	1	2	yes	—
61	C₃₁×#387	C₂²	1	2	yes	—
62	C₃₁×#387	C₂²	1	2	yes	—
63	C₃₁×#387	C₂²	1	2	yes	—
64	C₃₁×#387	C₂²	1	2	yes	—
65	C₃₁×#387	C₂²	1	2	yes	—
66	C₃₁×#387	C₂²	1	2	yes	—
67	C₃₁×#386	C₂²	1	2	yes	—
68	C₃₁×#386	C₂²	1	2	yes	—
69	C₃₁×#386	C₂²	1	2	yes	—
70	C₃₁×#386	C₂²	1	2	yes	—
71	C₃₁×#386	C₂²	1	2	yes	—
72	C₃₁×#386	C₂²	1	2	yes	—
73	C₃₁×#386	C₂²	1	2	yes	—
74	C₃₁×#386	C₂²	1	2	yes	—
75	C₃₁×#385	C₂²	1	2	yes	—
76	C₃₁×#385	C₂²	1	2	yes	—
77	C₃₁×#385	C₂²	1	2	yes	—
78	C₃₁×#385	C₂²	1	2	yes	—
79	C₃₁×#385	C₂²	1	2	yes	—
80	C₃₁×#385	C₂²	1	2	yes	—
81	C₃₁×#384	C₂²	1	1	yes	characteristic
82	C₃₁×#383	C₂²	1	2	yes	—
83	C₃₁×#383	C₂²	1	2	yes	—
84	C₃₁×#382	C₂²	1	2	yes	—
85	C₃₁×#382	C₂²	1	1	yes	characteristic
86	C₃₁×#382	C₂²	1	1	yes	characteristic
87	C₃₁×#381	C₂²	1	2	yes	—
88	C₃₁×#381	C₂²	1	2	yes	—
89	C₃₁×#380	C₂²	1	2	yes	—
90	C₃₁×#380	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₃₁×#376	C₂²	1	1	yes	characteristic
103	C₃₁×#376	C₂²	1	1	yes	characteristic
104	C₃₁×#376	C₂²	1	2	yes	—
105	C₂×C₃₁×#95	C₂²	1	2	yes	—
106	C₂×C₃₁×#95	C₂²	1	2	yes	—
107	C₄³×C₃₁	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
114	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
115	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
116	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
119	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
120	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
121	C₃₁×#124	C₂×C₄	1	8	yes	complemented
122	C₃₁×#124	C₂×C₄	1	16	yes	complemented
123	C₃₁×#124	C₂×C₄	1	8	yes	complemented
124	C₃₁×#121	C₂×C₄	1	16	yes	complemented
125	C₃₁×#121	C₂×C₄	1	16	yes	complemented
126	C₄×Q₈×C₃₁	—	4	2	no	—
127	C₄×Q₈×C₃₁	—	4	2	no	—
128	C₄×D₄×C₃₁	—	4	2	no	—
129	C₄×D₄×C₃₁	—	4	2	no	—
130	C₄×D₄×C₃₁	—	4	4	no	—
131	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
132	C₃₁×#117	C₂×C₄	1	16	yes	complemented
133	C₃₁×#117	C₂×C₄	1	16	yes	complemented
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
171	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₃₁×#95	C₂³	1	2	yes	—
184	C₃₁×#95	C₂³	1	2	yes	—
185	C₃₁×#95	C₂³	1	2	yes	—
186	C₃₁×#95	C₂³	1	2	yes	—
187	C₃₁×#95	C₂³	1	2	yes	—
188	C₃₁×#95	C₂³	1	2	yes	—
189	C₃₁×#95	C₂³	1	2	yes	—
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	2	yes	—
209	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
210	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
211	C₂×Q₈×C₃₁	—	4	1	no	—
212	C₂×Q₈×C₃₁	—	4	1	no	—
213	C₂×Q₈×C₃₁	—	4	1	no	—
214	C₂×Q₈×C₃₁	—	4	1	no	—
215	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
216	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
217	C₂×D₄×C₃₁	—	4	1	no	—
218	C₂×D₄×C₃₁	—	4	1	no	—
219	C₂×D₄×C₃₁	—	4	2	no	—
220	C₂×D₄×C₃₁	—	4	1	no	—
221	C₂×D₄×C₃₁	—	4	1	no	—
222	C₂×D₄×C₃₁	—	4	2	no	—
223	C₂×D₄×C₃₁	—	4	2	no	—
224	C₂×D₄×C₃₁	—	4	2	no	—
225	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
226	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
228	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
229	C₂²×C₄×C₃₁	—	2	4	no	—
230	C₂²×C₄×C₃₁	—	4	2	no	—
231	C₂²×C₄×C₃₁	—	4	2	no	—
232	C₂²×C₄×C₃₁	—	4	2	no	—
233	C₂²×C₄×C₃₁	—	4	2	no	—
234	C₂²×C₄×C₃₁	—	4	2	no	—
235	C₂²×C₄×C₃₁	—	4	2	no	—
236	C₂²×C₄×C₃₁	—	4	2	no	—
237	C₂²×C₄×C₃₁	—	4	2	no	—
238	C₂²×C₄×C₃₁	—	4	2	no	—
239	C₂²×C₄×C₃₁	—	4	2	no	—
240	C₂²×C₄×C₃₁	—	4	2	no	—
241	C₂²×C₄×C₃₁	—	4	2	no	—
242	C₂²×C₄×C₃₁	—	4	2	no	—
243	C₂²×C₄×C₃₁	—	4	2	no	—
244	C₂²×C₄×C₃₁	—	4	2	no	—
245	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
246	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	4	2	no	—
266	C₄⋊C₄×C₃₁	—	4	2	no	—
267	C₄⋊C₄×C₃₁	—	4	2	no	—
268	C₄⋊C₄×C₃₁	—	4	2	no	—
269	C₄⋊C₄×C₃₁	—	4	2	no	—
270	C₄⋊C₄×C₃₁	—	4	1	no	—
271	C₄⋊C₄×C₃₁	—	4	1	no	—
272	C₄⋊C₄×C₃₁	—	4	1	no	—
273	C₄⋊C₄×C₃₁	—	4	1	no	—
274	C₄⋊C₄×C₃₁	—	4	1	no	—
275	C₄⋊C₄×C₃₁	—	4	1	no	—
276	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
277	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
278	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	4	2	no	—
281	C₂²⋊C₄×C₃₁	—	4	2	no	—
282	C₂²⋊C₄×C₃₁	—	4	2	no	—
283	C₂²⋊C₄×C₃₁	—	4	2	no	—
284	C₂²⋊C₄×C₃₁	—	4	2	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	C₂²×C₄	1	8	yes	—
292	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
293	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
294	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
295	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
296	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
297	C₄²×C₃₁	—	2	2	no	—
298	C₄²×C₃₁	—	2	2	no	—
299	C₄²×C₃₁	—	2	2	no	—
300	C₄²×C₃₁	—	4	2	no	—
301	C₄²×C₃₁	—	4	2	no	—
302	C₄²×C₃₁	—	4	2	no	—
303	C₄²×C₃₁	—	4	2	no	—
304	C₄²×C₃₁	—	4	1	no	—
305	C₄²×C₃₁	—	4	1	no	—
306	C₄²×C₃₁	—	4	1	no	—
307	C₄²×C₃₁	—	4	2	no	—
308	C₄²×C₃₁	—	4	2	no	—
309	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
310	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
311	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
312	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
313	#34503	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₂³×C₃₁	—	2	2	no	—
315	C₂³×C₃₁	—	2	2	no	—
316	C₂³×C₃₁	—	2	2	no	—
317	C₂³×C₃₁	—	2	2	no	—
318	C₂³×C₃₁	—	2	2	no	—
319	C₂³×C₃₁	—	2	2	no	—
320	C₂³×C₃₁	—	2	2	no	—
321	C₂³×C₃₁	—	2	2	no	—
322	C₂³×C₃₁	—	2	2	no	—
323	C₂³×C₃₁	—	2	2	no	—
324	C₂³×C₃₁	—	2	2	no	—
325	C₂³×C₃₁	—	2	2	no	—
326	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
327	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
328	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
329	Q₈×C₃₁	—	4	4	no	—
330	Q₈×C₃₁	—	4	4	no	—
331	D₄×C₃₁	—	4	8	no	—
332	D₄×C₃₁	—	4	4	no	—
333	D₄×C₃₁	—	4	4	no	—
334	D₄×C₃₁	—	4	8	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	2	no	—
341	C₂×C₄×C₃₁	—	2	2	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	1	no	—
351	C₂×C₄×C₃₁	—	2	1	no	—
352	C₂×C₄×C₃₁	—	2	1	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	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	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	4	8	no	—
375	C₂×C₄×C₃₁	—	4	8	no	—
376	C₂×C₄×C₃₁	—	8	4	no	—
377	C₂×C₄×C₃₁	—	8	4	no	—
378	C₂×C₄×C₃₁	—	8	4	no	—
379	C₂×C₄×C₃₁	—	8	4	no	—
380	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
381	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
382	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
383	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
384	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
385	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
386	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
387	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
388	C₂×#555	C₂×C₃₁	1	1	yes	characteristic
389	#2381	C₂×C₃₁	1	1	yes	characteristic, complemented
390	#2379	C₂×C₃₁	1	1	yes	characteristic, complemented
391	#2377	C₂×C₃₁	1	2	yes	complemented
392	#2372	C₂×C₃₁	1	1	yes	characteristic, complemented
393	#2367	C₂×C₃₁	1	2	yes	complemented
394	#2364	C₂×C₃₁	1	2	yes	complemented
395	#2353	C₂×C₃₁	1	2	yes	complemented
396	#2343	C₂×C₃₁	1	2	yes	complemented
397	#2343	C₂×C₃₁	1	2	yes	complemented
398	#2337	C₂×C₃₁	1	2	yes	complemented
399	#2333	C₂×C₃₁	1	2	yes	complemented
400	#2327	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#2326	C₂×C₃₁	1	1	yes	characteristic, complemented
402	#2325	C₂×C₃₁	1	2	yes	complemented
403	#2318	C₂×C₃₁	1	2	yes	complemented
404	#2314	C₂×C₃₁	1	2	yes	complemented
405	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#2298	C₂×C₃₁	1	2	yes	complemented
407	C₂²×C₃₁	—	2	4	no	—
408	C₂²×C₃₁	—	2	4	no	—
409	C₂²×C₃₁	—	2	4	no	—
410	C₂²×C₃₁	—	2	4	no	—
411	C₂²×C₃₁	—	2	4	no	—
412	C₂²×C₃₁	—	2	4	no	—
413	C₂²×C₃₁	—	4	2	no	—
414	C₂²×C₃₁	—	4	2	no	—
415	C₂²×C₃₁	—	4	2	no	—
416	C₂²×C₃₁	—	4	2	no	—
417	C₂²×C₃₁	—	4	2	no	—
418	C₂²×C₃₁	—	4	2	no	—
419	C₂²×C₃₁	—	4	2	no	—
420	C₂²×C₃₁	—	4	2	no	—
421	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
422	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
423	C₂²×C₃₁	#585	1	2	yes	—
424	C₂²×C₃₁	#585	1	2	yes	—
425	C₂²×C₃₁	#585	1	1	yes	characteristic
426	C₄×C₃₁	—	2	4	no	—
427	C₄×C₃₁	—	2	4	no	—
428	C₄×C₃₁	—	2	4	no	—
429	C₄×C₃₁	—	2	2	no	—
430	C₄×C₃₁	—	2	2	no	—
431	C₄×C₃₁	—	2	4	no	—
432	C₄×C₃₁	—	2	2	no	—
433	C₄×C₃₁	—	2	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	2	no	—
439	C₄×C₃₁	—	4	1	no	—
440	C₄×C₃₁	—	4	2	no	—
441	C₄×C₃₁	—	4	2	no	—
442	C₄×C₃₁	—	4	2	no	—
443	#555	C₄×C₃₁	1	16	yes	complemented
444	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
445	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
446	C₂×#124	C₂²×C₃₁	1	2	yes	—
447	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×#121	C₂²×C₃₁	1	2	yes	—
449	C₂×#121	C₂²×C₃₁	1	2	yes	—
450	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
451	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
454	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
456	C₂×#117	C₂²×C₃₁	1	2	yes	—
457	C₂×#117	C₂²×C₃₁	1	2	yes	—
458	#391	C₂²×C₃₁	1	1	yes	characteristic
459	#391	C₂²×C₃₁	1	1	yes	characteristic
460	#391	C₂²×C₃₁	1	1	yes	characteristic
461	#391	C₂²×C₃₁	1	2	yes	—
462	#391	C₂²×C₃₁	1	1	yes	characteristic
463	#390	C₂²×C₃₁	1	1	yes	characteristic
464	#390	C₂²×C₃₁	1	2	yes	—
465	#390	C₂²×C₃₁	1	1	yes	characteristic
466	#388	C₂²×C₃₁	1	2	yes	—
467	#388	C₂²×C₃₁	1	2	yes	—
468	#388	C₂²×C₃₁	1	2	yes	—
469	#388	C₂²×C₃₁	1	2	yes	—
470	#388	C₂²×C₃₁	1	2	yes	—
471	#388	C₂²×C₃₁	1	2	yes	—
472	#388	C₂²×C₃₁	1	2	yes	—
473	#388	C₂²×C₃₁	1	2	yes	—
474	#388	C₂²×C₃₁	1	2	yes	—
475	#388	C₂²×C₃₁	1	2	yes	—
476	#388	C₂²×C₃₁	1	2	yes	—
477	#388	C₂²×C₃₁	1	2	yes	—
478	#387	C₂²×C₃₁	1	2	yes	—
479	#387	C₂²×C₃₁	1	2	yes	—
480	#387	C₂²×C₃₁	1	2	yes	—
481	#387	C₂²×C₃₁	1	2	yes	—
482	#387	C₂²×C₃₁	1	2	yes	—
483	#387	C₂²×C₃₁	1	2	yes	—
484	#387	C₂²×C₃₁	1	2	yes	—
485	#387	C₂²×C₃₁	1	2	yes	—
486	#387	C₂²×C₃₁	1	2	yes	—
487	#387	C₂²×C₃₁	1	2	yes	—
488	#387	C₂²×C₃₁	1	2	yes	—
489	#387	C₂²×C₃₁	1	2	yes	—
490	#386	C₂²×C₃₁	1	2	yes	—
491	#386	C₂²×C₃₁	1	2	yes	—
492	#386	C₂²×C₃₁	1	2	yes	—
493	#386	C₂²×C₃₁	1	2	yes	—
494	#386	C₂²×C₃₁	1	2	yes	—
495	#386	C₂²×C₃₁	1	2	yes	—
496	#386	C₂²×C₃₁	1	2	yes	—
497	#386	C₂²×C₃₁	1	2	yes	—
498	#385	C₂²×C₃₁	1	2	yes	—
499	#385	C₂²×C₃₁	1	2	yes	—
500	#385	C₂²×C₃₁	1	2	yes	—
501	#385	C₂²×C₃₁	1	2	yes	—
502	#385	C₂²×C₃₁	1	2	yes	—
503	#385	C₂²×C₃₁	1	2	yes	—
504	#384	C₂²×C₃₁	1	1	yes	characteristic
505	#383	C₂²×C₃₁	1	2	yes	—
506	#383	C₂²×C₃₁	1	2	yes	—
507	#382	C₂²×C₃₁	1	2	yes	—
508	#382	C₂²×C₃₁	1	1	yes	characteristic
509	#382	C₂²×C₃₁	1	1	yes	characteristic
510	#381	C₂²×C₃₁	1	2	yes	—
511	#381	C₂²×C₃₁	1	2	yes	—
512	#380	C₂²×C₃₁	1	2	yes	—
513	#380	C₂²×C₃₁	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
515	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
516	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
517	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
525	#376	C₂²×C₃₁	1	1	yes	characteristic
526	#376	C₂²×C₃₁	1	1	yes	characteristic
527	#376	C₂²×C₃₁	1	2	yes	—
528	C₂×#95	C₂²×C₃₁	1	2	yes	—
529	C₂×#95	C₂²×C₃₁	1	2	yes	—
530	C₄³	C₂²×C₃₁	1	1	yes	characteristic
531	C₂×C₃₁	—	4	4	no	—
532	C₂×C₃₁	—	4	4	no	—
533	C₂×C₃₁	#3428	1	2	yes	—
534	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
535	C₂×C₃₁	#3545	1	1	yes	characteristic
536	C₂×C₃₁	#3551	1	1	yes	characteristic
537	C₂×C₃₁	#3566	1	2	yes	—
538	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
539	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
542	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
544	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
545	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
546	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
547	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
548	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
549	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
550	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
551	#124	C₂×C₄×C₃₁	1	8	yes	complemented
552	#124	C₂×C₄×C₃₁	1	16	yes	complemented
553	#124	C₂×C₄×C₃₁	1	8	yes	complemented
554	#121	C₂×C₄×C₃₁	1	16	yes	complemented
555	#121	C₂×C₄×C₃₁	1	16	yes	complemented
556	C₄×Q₈	—	4	2	no	—
557	C₄×Q₈	—	4	2	no	—
558	C₄×D₄	—	4	2	no	—
559	C₄×D₄	—	4	2	no	—
560	C₄×D₄	—	4	4	no	—
561	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
562	#117	C₂×C₄×C₃₁	1	16	yes	complemented
563	#117	C₂×C₄×C₃₁	1	16	yes	complemented
564	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
597	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
601	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
602	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
603	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
604	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
606	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
613	#95	C₂³×C₃₁	1	2	yes	—
614	#95	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
620	#95	C₂³×C₃₁	1	2	yes	—
621	#95	C₂³×C₃₁	1	2	yes	—
622	#95	C₂³×C₃₁	1	2	yes	—
623	#95	C₂³×C₃₁	1	2	yes	—
624	#95	C₂³×C₃₁	1	2	yes	—
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	C₃₁	#34503	1	1	yes	characteristic, direct product factor, Sylow
640	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
641	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
642	C₂×Q₈	—	4	1	no	—
643	C₂×Q₈	—	4	1	no	—
644	C₂×Q₈	—	4	1	no	—
645	C₂×Q₈	—	4	1	no	—
646	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
647	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
648	C₂×D₄	—	4	1	no	—
649	C₂×D₄	—	4	1	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	1	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
657	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
658	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
659	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
677	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
678	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	1	no	—
702	C₄⋊C₄	—	4	1	no	—
703	C₄⋊C₄	—	4	1	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	1	no	—
707	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
708	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
709	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
723	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
724	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
725	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
726	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
727	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	4	2	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₄²	—	4	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	C₂²×C₄×C₃₁	1	4	yes	—
741	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
742	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
743	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
757	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
758	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
759	Q₈	—	4	4	no	—
760	Q₈	—	4	4	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	4	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	8	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	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	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	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	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	8	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	—	8	4	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	—	8	4	no	—
810	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
811	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
812	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
813	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
814	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
815	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
816	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
817	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
833	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
834	C₂²	C₃₁×#585	1	2	yes	—
835	C₂²	C₃₁×#585	1	2	yes	—
836	C₂²	C₃₁×#585	1	1	yes	characteristic
837	C₄	—	2	4	no	—
838	C₄	—	2	4	no	—
839	C₄	—	2	4	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	4	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₂	—	4	4	no	—
855	C₂	—	4	4	no	—
856	C₂	C₃₁×#3428	1	2	yes	—
857	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
858	C₂	C₃₁×#3545	1	1	yes	characteristic
859	C₂	C₃₁×#3551	1	1	yes	characteristic
860	C₂	C₃₁×#3566	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#555	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2381	C₂	semidirect
3. C₃₁×#2379	C₂	semidirect
4. C₃₁×#2377	C₂	semidirect
5. C₃₁×#2372	C₂	semidirect
6. C₃₁×#2367	C₂	semidirect
7. C₃₁×#2364	C₂	semidirect
8. C₃₁×#2353	C₂	semidirect
9. C₃₁×#2343	C₂	semidirect
10. C₃₁×#2343	C₂	semidirect
11. C₃₁×#2337	C₂	semidirect
12. C₃₁×#2333	C₂	semidirect
13. C₃₁×#2327	C₂	semidirect
14. C₃₁×#2326	C₂	semidirect
15. C₃₁×#2325	C₂	semidirect
16. C₃₁×#2318	C₂	semidirect
17. C₃₁×#2314	C₂	semidirect
18. C₄×C₃₁×#124	C₂	semidirect
19. C₃₁×#2298	C₂	semidirect
20. C₃₁×#555	C₄	semidirect
120. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
121. C₃₁×#124	C₂×C₄	semidirect
122. C₃₁×#124	C₂×C₄	semidirect
123. C₃₁×#124	C₂×C₄	semidirect
124. C₃₁×#121	C₂×C₄	semidirect
125. C₃₁×#121	C₂×C₄	semidirect
131. C₄×D₄×C₃₁	C₂×C₄	semidirect
132. C₃₁×#117	C₂×C₄	semidirect
133. C₃₁×#117	C₂×C₄	semidirect
313. #34503	C₃₁	direct (N × H)
389. #2381	C₂×C₃₁	semidirect
390. #2379	C₂×C₃₁	semidirect
391. #2377	C₂×C₃₁	semidirect
392. #2372	C₂×C₃₁	semidirect
393. #2367	C₂×C₃₁	semidirect
394. #2364	C₂×C₃₁	semidirect
395. #2353	C₂×C₃₁	semidirect
396. #2343	C₂×C₃₁	semidirect
397. #2343	C₂×C₃₁	semidirect
398. #2337	C₂×C₃₁	semidirect
399. #2333	C₂×C₃₁	semidirect
400. #2327	C₂×C₃₁	semidirect
401. #2326	C₂×C₃₁	semidirect
402. #2325	C₂×C₃₁	semidirect
403. #2318	C₂×C₃₁	semidirect
404. #2314	C₂×C₃₁	semidirect
405. C₄×#124	C₂×C₃₁	semidirect
406. #2298	C₂×C₃₁	semidirect
443. #555	C₄×C₃₁	semidirect
550. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
551. #124	C₂×C₄×C₃₁	semidirect
552. #124	C₂×C₄×C₃₁	semidirect
553. #124	C₂×C₄×C₃₁	semidirect
554. #121	C₂×C₄×C₃₁	semidirect
555. #121	C₂×C₄×C₃₁	semidirect
561. C₄×D₄	C₂×C₄×C₃₁	semidirect
562. #117	C₂×C₄×C₃₁	semidirect
563. #117	C₂×C₄×C₃₁	semidirect
639. C₃₁	#34503	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#555	2
C₃₁×#2381	2
C₃₁×#2379	2
C₃₁×#2377	2
C₃₁×#2372	2
C₃₁×#2367	2
C₃₁×#2364	2
C₃₁×#2353	2
C₃₁×#2343	2
C₃₁×#2337	2
C₃₁×#2333	2
C₃₁×#2327	2
C₃₁×#2326	2
C₃₁×#2325	2
C₃₁×#2318	2
C₃₁×#2314	2
C₄×C₃₁×#124	2
C₃₁×#2298	2
#34503	31

Subgroups — C31×#34503 #21491262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34503 #21491262