Subgroups — C₃₁×#34472 #21491231

Order 7936.

2480 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#548	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2379	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2378	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2364	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2349	C₂	1	2	yes	maximal, complemented
10	D₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2337	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2329	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2325	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#548	C₄	1	16	yes	complemented
27	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#124	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₃₁×#121	C₂²	1	2	yes	—
32	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#391	C₂²	1	1	yes	characteristic
48	C₃₁×#391	C₂²	1	1	yes	characteristic
49	C₃₁×#391	C₂²	1	1	yes	characteristic
50	C₃₁×#391	C₂²	1	1	yes	characteristic
51	C₃₁×#391	C₂²	1	2	yes	—
52	C₃₁×#391	C₂²	1	2	yes	—
53	C₃₁×#391	C₂²	1	2	yes	—
54	C₃₁×#391	C₂²	1	1	yes	characteristic
55	C₃₁×#391	C₂²	1	1	yes	characteristic
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#390	C₂²	1	1	yes	characteristic
58	C₃₁×#390	C₂²	1	1	yes	characteristic
59	C₃₁×#389	C₂²	1	1	yes	characteristic
60	C₃₁×#389	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	2	yes	—
62	C₃₁×#389	C₂²	1	2	yes	—
63	C₃₁×#389	C₂²	1	2	yes	—
64	C₃₁×#388	C₂²	1	2	yes	—
65	C₃₁×#388	C₂²	1	2	yes	—
66	C₃₁×#388	C₂²	1	2	yes	—
67	C₃₁×#388	C₂²	1	2	yes	—
68	C₃₁×#388	C₂²	1	2	yes	—
69	C₃₁×#388	C₂²	1	2	yes	—
70	C₃₁×#388	C₂²	1	1	yes	characteristic
71	C₃₁×#388	C₂²	1	2	yes	—
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	1	yes	characteristic
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	1	yes	characteristic
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	1	yes	characteristic
82	C₃₁×#386	C₂²	1	2	yes	—
83	C₃₁×#386	C₂²	1	2	yes	—
84	C₃₁×#386	C₂²	1	2	yes	—
85	C₃₁×#386	C₂²	1	2	yes	—
86	C₃₁×#386	C₂²	1	1	yes	characteristic
87	C₃₁×#386	C₂²	1	2	yes	—
88	C₃₁×#386	C₂²	1	2	yes	—
89	C₃₁×#386	C₂²	1	1	yes	characteristic
90	C₃₁×#385	C₂²	1	1	yes	characteristic
91	C₃₁×#385	C₂²	1	2	yes	—
92	C₃₁×#385	C₂²	1	2	yes	—
93	C₃₁×#385	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×#385	C₂²	1	2	yes	—
98	C₃₁×#385	C₂²	1	1	yes	characteristic
99	C₃₁×#384	C₂²	1	1	yes	characteristic
100	C₃₁×#383	C₂²	1	2	yes	—
101	C₃₁×#382	C₂²	1	2	yes	—
102	C₃₁×#382	C₂²	1	2	yes	—
103	C₃₁×#381	C₂²	1	2	yes	—
104	C₃₁×#380	C₂²	1	2	yes	—
105	C₃₁×#380	C₂²	1	2	yes	—
106	C₃₁×#380	C₂²	1	1	yes	characteristic
107	C₃₁×#380	C₂²	1	2	yes	—
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	2	yes	—
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
120	C₃₁×#376	C₂²	1	1	yes	characteristic
121	C₂×C₃₁×#95	C₂²	1	2	yes	—
122	C₂×C₃₁×#95	C₂²	1	2	yes	—
123	C₂×C₃₁×#95	C₂²	1	2	yes	—
124	C₂×#41×C₃₁	—	4	2	no	—
125	C₂×#41×C₃₁	—	4	2	no	—
126	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
127	C₂²×Q₈×C₃₁	—	4	2	no	—
128	C₂²×Q₈×C₃₁	—	4	2	no	—
129	C₂²×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
135	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
137	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
142	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
146	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
147	C₃₁×#124	C₂×C₄	1	8	yes	complemented
148	C₃₁×#124	C₂×C₄	1	16	yes	complemented
149	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
150	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
151	C₃₁×#121	C₂×C₄	1	8	yes	complemented
152	C₃₁×#121	C₂×C₄	1	16	yes	complemented
153	C₄×Q₈×C₃₁	—	4	2	no	—
154	C₄×Q₈×C₃₁	—	4	2	no	—
155	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
156	C₄×D₄×C₃₁	—	4	2	no	—
157	C₄×D₄×C₃₁	—	4	2	no	—
158	C₄×D₄×C₃₁	—	4	4	no	—
159	C₄×D₄×C₃₁	—	4	4	no	—
160	C₄×D₄×C₃₁	—	4	4	no	—
161	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
162	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
163	C₃₁×#117	—	4	2	no	—
164	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
165	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
206	C₂×C₄²×C₃₁	—	4	2	no	—
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	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
214	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
215	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
216	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
218	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
232	C₃₁×#95	C₂³	1	1	yes	characteristic
233	C₃₁×#95	C₂³	1	1	yes	characteristic
234	C₃₁×#95	C₂³	1	1	yes	characteristic
235	C₃₁×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
240	C₃₁×#95	C₂³	1	2	yes	—
241	C₃₁×#95	C₂³	1	2	yes	—
242	C₃₁×#95	C₂³	1	1	yes	characteristic
243	C₃₁×#95	C₂³	1	1	yes	characteristic
244	C₃₁×#95	C₂³	1	2	yes	—
245	C₃₁×#95	C₂³	1	2	yes	—
246	C₃₁×#95	C₂³	1	2	yes	—
247	C₃₁×#95	C₂³	1	2	yes	—
248	C₃₁×#95	C₂³	1	1	yes	characteristic
249	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
251	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
252	#41×C₃₁	—	4	16	no	—
253	C₂×Q₈×C₃₁	—	2	2	no	—
254	C₂×Q₈×C₃₁	—	2	2	no	—
255	C₂×Q₈×C₃₁	—	2	2	no	—
256	C₂×Q₈×C₃₁	—	2	2	no	—
257	C₂×Q₈×C₃₁	—	4	2	no	—
258	C₂×Q₈×C₃₁	—	4	2	no	—
259	C₂×Q₈×C₃₁	—	4	16	no	—
260	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
261	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
262	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
263	C₂×D₄×C₃₁	—	2	4	no	—
264	C₂×D₄×C₃₁	—	2	2	no	—
265	C₂×D₄×C₃₁	—	2	2	no	—
266	C₂×D₄×C₃₁	—	2	4	no	—
267	C₂×D₄×C₃₁	—	2	2	no	—
268	C₂×D₄×C₃₁	—	2	2	no	—
269	C₂×D₄×C₃₁	—	4	2	no	—
270	C₂×D₄×C₃₁	—	4	2	no	—
271	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
272	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
273	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
274	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
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	2	no	—
279	C₂²×C₄×C₃₁	—	2	2	no	—
280	C₂²×C₄×C₃₁	—	2	2	no	—
281	C₂²×C₄×C₃₁	—	2	4	no	—
282	C₂²×C₄×C₃₁	—	2	2	no	—
283	C₂²×C₄×C₃₁	—	2	4	no	—
284	C₂²×C₄×C₃₁	—	4	1	no	—
285	C₂²×C₄×C₃₁	—	4	1	no	—
286	C₂²×C₄×C₃₁	—	4	1	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	—	4	2	no	—
292	C₂²×C₄×C₃₁	—	4	2	no	—
293	C₂²×C₄×C₃₁	—	4	2	no	—
294	C₂²×C₄×C₃₁	—	4	2	no	—
295	C₂²×C₄×C₃₁	—	4	2	no	—
296	C₂²×C₄×C₃₁	—	4	2	no	—
297	C₂²×C₄×C₃₁	—	4	2	no	—
298	C₂²×C₄×C₃₁	—	4	2	no	—
299	C₂²×C₄×C₃₁	—	4	2	no	—
300	C₂²×C₄×C₃₁	—	4	2	no	—
301	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
302	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
303	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
304	C₂²×C₄×C₃₁	C₂²×C₄	1	8	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	2	yes	—
311	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	4	2	no	—
331	C₄⋊C₄×C₃₁	—	4	2	no	—
332	C₄⋊C₄×C₃₁	—	4	1	no	—
333	C₄⋊C₄×C₃₁	—	4	2	no	—
334	C₄⋊C₄×C₃₁	—	4	1	no	—
335	C₄⋊C₄×C₃₁	—	4	1	no	—
336	C₄⋊C₄×C₃₁	—	4	2	no	—
337	C₄⋊C₄×C₃₁	—	4	2	no	—
338	C₄⋊C₄×C₃₁	—	4	2	no	—
339	C₄⋊C₄×C₃₁	—	4	2	no	—
340	C₄⋊C₄×C₃₁	—	4	2	no	—
341	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
342	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
343	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
344	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
345	C₂²⋊C₄×C₃₁	—	2	2	no	—
346	C₂²⋊C₄×C₃₁	—	2	4	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	4	2	no	—
350	C₂²⋊C₄×C₃₁	—	4	2	no	—
351	C₂²⋊C₄×C₃₁	—	4	1	no	—
352	C₂²⋊C₄×C₃₁	—	4	1	no	—
353	C₂²⋊C₄×C₃₁	—	4	1	no	—
354	C₂²⋊C₄×C₃₁	—	4	2	no	—
355	C₂²⋊C₄×C₃₁	—	4	2	no	—
356	C₂²⋊C₄×C₃₁	—	4	2	no	—
357	C₂²⋊C₄×C₃₁	—	4	2	no	—
358	C₂²⋊C₄×C₃₁	—	4	2	no	—
359	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
360	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
361	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
362	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
363	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
364	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
365	C₄²×C₃₁	—	2	2	no	—
366	C₄²×C₃₁	—	2	2	no	—
367	C₄²×C₃₁	—	2	2	no	—
368	C₄²×C₃₁	—	2	2	no	—
369	C₄²×C₃₁	—	4	1	no	—
370	C₄²×C₃₁	—	4	1	no	—
371	C₄²×C₃₁	—	4	2	no	—
372	C₄²×C₃₁	—	4	2	no	—
373	C₄²×C₃₁	—	4	2	no	—
374	C₄²×C₃₁	—	4	2	no	—
375	C₄²×C₃₁	—	4	2	no	—
376	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
377	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
378	#34472	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
379	C₂³×C₃₁	—	2	1	no	—
380	C₂³×C₃₁	—	2	1	no	—
381	C₂³×C₃₁	—	2	1	no	—
382	C₂³×C₃₁	—	2	1	no	—
383	C₂³×C₃₁	—	2	1	no	—
384	C₂³×C₃₁	—	2	2	no	—
385	C₂³×C₃₁	—	2	1	no	—
386	C₂³×C₃₁	—	2	2	no	—
387	C₂³×C₃₁	—	2	2	no	—
388	C₂³×C₃₁	—	2	1	no	—
389	C₂³×C₃₁	—	2	1	no	—
390	C₂³×C₃₁	—	2	2	no	—
391	C₂³×C₃₁	—	2	1	no	—
392	C₂³×C₃₁	—	2	2	no	—
393	C₂³×C₃₁	—	2	2	no	—
394	C₂³×C₃₁	—	2	1	no	—
395	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
396	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
397	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
398	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
399	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
400	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
401	Q₈×C₃₁	—	2	8	no	—
402	Q₈×C₃₁	—	2	8	no	—
403	Q₈×C₃₁	—	4	8	no	—
404	D₄×C₃₁	—	2	8	no	—
405	D₄×C₃₁	—	2	16	no	—
406	D₄×C₃₁	—	2	8	no	—
407	D₄×C₃₁	—	4	8	no	—
408	C₂×C₄×C₃₁	—	2	1	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	1	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	1	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	1	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	1	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	8	no	—
425	C₂×C₄×C₃₁	—	2	8	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	1	no	—
428	C₂×C₄×C₃₁	—	2	1	no	—
429	C₂×C₄×C₃₁	—	2	1	no	—
430	C₂×C₄×C₃₁	—	2	1	no	—
431	C₂×C₄×C₃₁	—	2	1	no	—
432	C₂×C₄×C₃₁	—	2	1	no	—
433	C₂×C₄×C₃₁	—	2	1	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	2	no	—
438	C₂×C₄×C₃₁	—	2	2	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	2	no	—
443	C₂×C₄×C₃₁	—	2	2	no	—
444	C₂×C₄×C₃₁	—	2	1	no	—
445	C₂×C₄×C₃₁	—	2	1	no	—
446	C₂×C₄×C₃₁	—	2	1	no	—
447	C₂×C₄×C₃₁	—	2	1	no	—
448	C₂×C₄×C₃₁	—	2	1	no	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	1	no	—
451	C₂×C₄×C₃₁	—	2	1	no	—
452	C₂×C₄×C₃₁	—	2	1	no	—
453	C₂×C₄×C₃₁	—	2	1	no	—
454	C₂×C₄×C₃₁	—	2	1	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	1	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	2	no	—
459	C₂×C₄×C₃₁	—	4	8	no	—
460	C₂×C₄×C₃₁	—	4	8	no	—
461	C₂×C₄×C₃₁	—	4	4	no	—
462	C₂×C₄×C₃₁	—	4	4	no	—
463	C₂×C₄×C₃₁	—	8	4	no	—
464	C₂×C₄×C₃₁	—	8	4	no	—
465	C₂×C₄×C₃₁	—	8	4	no	—
466	C₂×C₄×C₃₁	—	8	4	no	—
467	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
468	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
469	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
470	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
471	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
472	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
473	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
474	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
475	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
476	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
477	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
478	C₂×#548	C₂×C₃₁	1	1	yes	characteristic
479	#2379	C₂×C₃₁	1	2	yes	complemented
480	#2378	C₂×C₃₁	1	2	yes	complemented
481	#2367	C₂×C₃₁	1	1	yes	characteristic, complemented
482	#2364	C₂×C₃₁	1	2	yes	complemented
483	#2361	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#2360	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
486	#2349	C₂×C₃₁	1	2	yes	complemented
487	D₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
488	Q₈×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#2339	C₂×C₃₁	1	1	yes	characteristic, complemented
490	#2337	C₂×C₃₁	1	2	yes	complemented
491	#2329	C₂×C₃₁	1	2	yes	complemented
492	#2326	C₂×C₃₁	1	1	yes	characteristic, complemented
493	#2325	C₂×C₃₁	1	2	yes	complemented
494	#2323	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#2320	C₂×C₃₁	1	1	yes	characteristic, complemented
496	#2318	C₂×C₃₁	1	2	yes	complemented
497	#2311	C₂×C₃₁	1	1	yes	characteristic, complemented
498	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
499	C₂×#391	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#2290	C₂×C₃₁	1	1	yes	characteristic, complemented
501	C₂²×C₃₁	—	2	2	no	—
502	C₂²×C₃₁	—	2	2	no	—
503	C₂²×C₃₁	—	2	2	no	—
504	C₂²×C₃₁	—	2	2	no	—
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	2	2	no	—
507	C₂²×C₃₁	—	2	2	no	—
508	C₂²×C₃₁	—	2	4	no	—
509	C₂²×C₃₁	—	2	2	no	—
510	C₂²×C₃₁	—	2	4	no	—
511	C₂²×C₃₁	—	2	2	no	—
512	C₂²×C₃₁	—	2	4	no	—
513	C₂²×C₃₁	—	4	2	no	—
514	C₂²×C₃₁	—	4	1	no	—
515	C₂²×C₃₁	—	4	1	no	—
516	C₂²×C₃₁	—	4	2	no	—
517	C₂²×C₃₁	—	4	2	no	—
518	C₂²×C₃₁	—	4	1	no	—
519	C₂²×C₃₁	—	4	1	no	—
520	C₂²×C₃₁	—	4	2	no	—
521	C₂²×C₃₁	#520	1	4	yes	—
522	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
523	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
527	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
528	C₂²×C₃₁	#585	1	1	yes	characteristic
529	C₄×C₃₁	—	2	2	no	—
530	C₄×C₃₁	—	2	2	no	—
531	C₄×C₃₁	—	2	4	no	—
532	C₄×C₃₁	—	2	4	no	—
533	C₄×C₃₁	—	2	4	no	—
534	C₄×C₃₁	—	2	2	no	—
535	C₄×C₃₁	—	2	2	no	—
536	C₄×C₃₁	—	2	2	no	—
537	C₄×C₃₁	—	4	1	no	—
538	C₄×C₃₁	—	4	1	no	—
539	C₄×C₃₁	—	4	2	no	—
540	C₄×C₃₁	—	4	1	no	—
541	C₄×C₃₁	—	4	1	no	—
542	C₄×C₃₁	—	4	1	no	—
543	C₄×C₃₁	—	4	1	no	—
544	C₄×C₃₁	—	4	2	no	—
545	C₄×C₃₁	—	4	1	no	—
546	C₄×C₃₁	—	4	2	no	—
547	C₄×C₃₁	—	4	2	no	—
548	C₄×C₃₁	#518	1	4	yes	—
549	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
550	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
551	#548	C₄×C₃₁	1	16	yes	complemented
552	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
553	C₂×#124	C₂²×C₃₁	1	2	yes	—
554	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
555	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
556	C₂×#121	C₂²×C₃₁	1	2	yes	—
557	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
558	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
559	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
560	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
561	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
562	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
563	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
564	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
566	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
567	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
568	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
569	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
570	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
571	C₂²×C₄²	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	1	yes	characteristic
576	#391	C₂²×C₃₁	1	2	yes	—
577	#391	C₂²×C₃₁	1	2	yes	—
578	#391	C₂²×C₃₁	1	2	yes	—
579	#391	C₂²×C₃₁	1	1	yes	characteristic
580	#391	C₂²×C₃₁	1	1	yes	characteristic
581	#391	C₂²×C₃₁	1	2	yes	—
582	#390	C₂²×C₃₁	1	1	yes	characteristic
583	#390	C₂²×C₃₁	1	1	yes	characteristic
584	#389	C₂²×C₃₁	1	1	yes	characteristic
585	#389	C₂²×C₃₁	1	1	yes	characteristic
586	#389	C₂²×C₃₁	1	2	yes	—
587	#389	C₂²×C₃₁	1	2	yes	—
588	#389	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	#388	C₂²×C₃₁	1	2	yes	—
593	#388	C₂²×C₃₁	1	2	yes	—
594	#388	C₂²×C₃₁	1	2	yes	—
595	#388	C₂²×C₃₁	1	1	yes	characteristic
596	#388	C₂²×C₃₁	1	2	yes	—
597	#388	C₂²×C₃₁	1	2	yes	—
598	#388	C₂²×C₃₁	1	1	yes	characteristic
599	#387	C₂²×C₃₁	1	2	yes	—
600	#387	C₂²×C₃₁	1	2	yes	—
601	#387	C₂²×C₃₁	1	2	yes	—
602	#387	C₂²×C₃₁	1	2	yes	—
603	#387	C₂²×C₃₁	1	2	yes	—
604	#387	C₂²×C₃₁	1	1	yes	characteristic
605	#387	C₂²×C₃₁	1	2	yes	—
606	#387	C₂²×C₃₁	1	1	yes	characteristic
607	#386	C₂²×C₃₁	1	2	yes	—
608	#386	C₂²×C₃₁	1	2	yes	—
609	#386	C₂²×C₃₁	1	2	yes	—
610	#386	C₂²×C₃₁	1	2	yes	—
611	#386	C₂²×C₃₁	1	1	yes	characteristic
612	#386	C₂²×C₃₁	1	2	yes	—
613	#386	C₂²×C₃₁	1	2	yes	—
614	#386	C₂²×C₃₁	1	1	yes	characteristic
615	#385	C₂²×C₃₁	1	1	yes	characteristic
616	#385	C₂²×C₃₁	1	2	yes	—
617	#385	C₂²×C₃₁	1	2	yes	—
618	#385	C₂²×C₃₁	1	2	yes	—
619	#385	C₂²×C₃₁	1	2	yes	—
620	#385	C₂²×C₃₁	1	2	yes	—
621	#385	C₂²×C₃₁	1	2	yes	—
622	#385	C₂²×C₃₁	1	2	yes	—
623	#385	C₂²×C₃₁	1	1	yes	characteristic
624	#384	C₂²×C₃₁	1	1	yes	characteristic
625	#383	C₂²×C₃₁	1	2	yes	—
626	#382	C₂²×C₃₁	1	2	yes	—
627	#382	C₂²×C₃₁	1	2	yes	—
628	#381	C₂²×C₃₁	1	2	yes	—
629	#380	C₂²×C₃₁	1	2	yes	—
630	#380	C₂²×C₃₁	1	2	yes	—
631	#380	C₂²×C₃₁	1	1	yes	characteristic
632	#380	C₂²×C₃₁	1	2	yes	—
633	#380	C₂²×C₃₁	1	1	yes	characteristic
634	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
635	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
636	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
637	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
638	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
639	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
640	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
641	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
642	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
643	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
644	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
645	#376	C₂²×C₃₁	1	1	yes	characteristic
646	C₂×#95	C₂²×C₃₁	1	2	yes	—
647	C₂×#95	C₂²×C₃₁	1	2	yes	—
648	C₂×#95	C₂²×C₃₁	1	2	yes	—
649	C₂×C₃₁	—	2	4	no	—
650	C₂×C₃₁	—	4	2	no	—
651	C₂×C₃₁	—	4	4	no	—
652	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
653	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
654	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
655	C₂×C₃₁	#3536	1	1	yes	characteristic
656	C₂×C₃₁	#3541	1	1	yes	characteristic
657	C₂×C₃₁	#3552	1	1	yes	characteristic
658	C₂×C₃₁	#3558	1	1	yes	characteristic
659	C₂×#41	—	4	2	no	—
660	C₂×#41	—	4	2	no	—
661	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
662	C₂²×Q₈	—	4	2	no	—
663	C₂²×Q₈	—	4	2	no	—
664	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
665	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
666	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
667	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
668	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
669	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
670	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
671	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
672	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
673	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
674	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
675	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
676	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
677	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
678	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
679	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
680	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
681	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
682	#124	C₂×C₄×C₃₁	1	8	yes	complemented
683	#124	C₂×C₄×C₃₁	1	16	yes	complemented
684	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
685	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
686	#121	C₂×C₄×C₃₁	1	8	yes	complemented
687	#121	C₂×C₄×C₃₁	1	16	yes	complemented
688	C₄×Q₈	—	4	2	no	—
689	C₄×Q₈	—	4	2	no	—
690	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
691	C₄×D₄	—	4	2	no	—
692	C₄×D₄	—	4	2	no	—
693	C₄×D₄	—	4	4	no	—
694	C₄×D₄	—	4	4	no	—
695	C₄×D₄	—	4	4	no	—
696	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
697	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
698	#117	—	4	2	no	—
699	C₂×C₄⋊C₄	—	4	2	no	—
700	C₂×C₄⋊C₄	—	4	2	no	—
701	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
712	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
735	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
741	C₂×C₄²	—	4	2	no	—
742	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
747	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
748	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
749	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
750	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
751	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
755	#95	C₂³×C₃₁	1	1	yes	characteristic
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	#95	C₂³×C₃₁	1	2	yes	—
763	#95	C₂³×C₃₁	1	2	yes	—
764	#95	C₂³×C₃₁	1	2	yes	—
765	#95	C₂³×C₃₁	1	2	yes	—
766	#95	C₂³×C₃₁	1	1	yes	characteristic
767	#95	C₂³×C₃₁	1	1	yes	characteristic
768	#95	C₂³×C₃₁	1	1	yes	characteristic
769	#95	C₂³×C₃₁	1	1	yes	characteristic
770	#95	C₂³×C₃₁	1	1	yes	characteristic
771	#95	C₂³×C₃₁	1	2	yes	—
772	#95	C₂³×C₃₁	1	2	yes	—
773	#95	C₂³×C₃₁	1	1	yes	characteristic
774	#95	C₂³×C₃₁	1	2	yes	—
775	#95	C₂³×C₃₁	1	2	yes	—
776	#95	C₂³×C₃₁	1	2	yes	—
777	#95	C₂³×C₃₁	1	1	yes	characteristic
778	#95	C₂³×C₃₁	1	1	yes	characteristic
779	#95	C₂³×C₃₁	1	2	yes	—
780	#95	C₂³×C₃₁	1	2	yes	—
781	#95	C₂³×C₃₁	1	2	yes	—
782	#95	C₂³×C₃₁	1	2	yes	—
783	#95	C₂³×C₃₁	1	1	yes	characteristic
784	C₃₁	#34472	1	1	yes	characteristic, direct product factor, Sylow
785	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
787	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
788	#41	—	4	16	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	2	2	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	4	2	no	—
794	C₂×Q₈	—	4	2	no	—
795	C₂×Q₈	—	4	16	no	—
796	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
797	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
798	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
799	C₂×D₄	—	2	4	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	4	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
808	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
809	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
810	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	4	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	4	no	—
820	C₂²×C₄	—	4	1	no	—
821	C₂²×C₄	—	4	1	no	—
822	C₂²×C₄	—	4	1	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
838	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
839	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
840	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
841	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	4	2	no	—
867	C₄⋊C₄	—	4	2	no	—
868	C₄⋊C₄	—	4	1	no	—
869	C₄⋊C₄	—	4	2	no	—
870	C₄⋊C₄	—	4	1	no	—
871	C₄⋊C₄	—	4	1	no	—
872	C₄⋊C₄	—	4	2	no	—
873	C₄⋊C₄	—	4	2	no	—
874	C₄⋊C₄	—	4	2	no	—
875	C₄⋊C₄	—	4	2	no	—
876	C₄⋊C₄	—	4	2	no	—
877	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
878	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
879	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
880	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	4	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	4	2	no	—
887	C₂²⋊C₄	—	4	1	no	—
888	C₂²⋊C₄	—	4	1	no	—
889	C₂²⋊C₄	—	4	1	no	—
890	C₂²⋊C₄	—	4	2	no	—
891	C₂²⋊C₄	—	4	2	no	—
892	C₂²⋊C₄	—	4	2	no	—
893	C₂²⋊C₄	—	4	2	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
896	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
897	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
898	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	—	4	1	no	—
906	C₄²	—	4	1	no	—
907	C₄²	—	4	2	no	—
908	C₄²	—	4	2	no	—
909	C₄²	—	4	2	no	—
910	C₄²	—	4	2	no	—
911	C₄²	—	4	2	no	—
912	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
913	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	2	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	1	no	—
930	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
931	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
932	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
933	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
934	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
935	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
936	Q₈	—	2	8	no	—
937	Q₈	—	2	8	no	—
938	Q₈	—	4	8	no	—
939	D₄	—	2	8	no	—
940	D₄	—	2	16	no	—
941	D₄	—	2	8	no	—
942	D₄	—	4	8	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	8	no	—
960	C₂×C₄	—	2	8	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	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	4	8	no	—
995	C₂×C₄	—	4	8	no	—
996	C₂×C₄	—	4	4	no	—
997	C₂×C₄	—	4	4	no	—
998	C₂×C₄	—	8	4	no	—
999	C₂×C₄	—	8	4	no	—
1000	C₂×C₄	—	8	4	no	—
1001	C₂×C₄	—	8	4	no	—
1002	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1003	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1004	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1005	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1006	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1007	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1008	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1009	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1010	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1011	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1012	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	2	4	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	4	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	4	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	1	no	—
1031	C₂²	—	4	1	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	C₃₁×#520	1	4	yes	—
1034	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1035	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1036	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1037	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1038	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1039	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1040	C₂²	C₃₁×#585	1	1	yes	characteristic
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	4	no	—
1044	C₄	—	2	4	no	—
1045	C₄	—	2	4	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	C₃₁×#518	1	4	yes	—
1061	C₂	—	2	4	no	—
1062	C₂	—	4	2	no	—
1063	C₂	—	4	4	no	—
1064	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
1065	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
1066	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1067	C₂	C₃₁×#3536	1	1	yes	characteristic
1068	C₂	C₃₁×#3541	1	1	yes	characteristic
1069	C₂	C₃₁×#3552	1	1	yes	characteristic
1070	C₂	C₃₁×#3558	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#548	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×#2379	C₂	semidirect
3. C₃₁×#2378	C₂	semidirect
4. C₃₁×#2367	C₂	semidirect
5. C₃₁×#2364	C₂	semidirect
6. C₃₁×#2361	C₂	semidirect
7. C₃₁×#2360	C₂	semidirect
8. C₃₁×#2355	C₂	semidirect
9. C₃₁×#2349	C₂	semidirect
10. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
11. Q₈×C₂²⋊C₄×C₃₁	C₂	semidirect
12. C₃₁×#2339	C₂	semidirect
13. C₃₁×#2337	C₂	semidirect
14. C₃₁×#2329	C₂	semidirect
15. C₃₁×#2326	C₂	semidirect
16. C₃₁×#2325	C₂	semidirect
17. C₃₁×#2323	C₂	semidirect
18. C₃₁×#2320	C₂	semidirect
19. C₃₁×#2318	C₂	semidirect
20. C₃₁×#2311	C₂	semidirect
21. C₄×C₃₁×#121	C₂	semidirect
22. C₂×C₃₁×#391	C₂	semidirect
23. C₃₁×#2290	C₂	semidirect
26. C₃₁×#548	C₄	semidirect
126. C₂×#41×C₃₁	C₂×C₄	semidirect
129. C₂²×Q₈×C₃₁	C₂×C₄	semidirect
147. C₃₁×#124	C₂×C₄	semidirect
148. C₃₁×#124	C₂×C₄	semidirect
149. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
150. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
151. C₃₁×#121	C₂×C₄	semidirect
152. C₃₁×#121	C₂×C₄	semidirect
155. C₄×Q₈×C₃₁	C₂×C₄	semidirect
161. C₄×D₄×C₃₁	C₂×C₄	semidirect
162. C₄×D₄×C₃₁	C₂×C₄	semidirect
378. #34472	C₃₁	direct (N × H)
479. #2379	C₂×C₃₁	semidirect
480. #2378	C₂×C₃₁	semidirect
481. #2367	C₂×C₃₁	semidirect
482. #2364	C₂×C₃₁	semidirect
483. #2361	C₂×C₃₁	semidirect
484. #2360	C₂×C₃₁	semidirect
485. #2355	C₂×C₃₁	semidirect
486. #2349	C₂×C₃₁	semidirect
487. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
488. Q₈×C₂²⋊C₄	C₂×C₃₁	semidirect
489. #2339	C₂×C₃₁	semidirect
490. #2337	C₂×C₃₁	semidirect
491. #2329	C₂×C₃₁	semidirect
492. #2326	C₂×C₃₁	semidirect
493. #2325	C₂×C₃₁	semidirect
494. #2323	C₂×C₃₁	semidirect
495. #2320	C₂×C₃₁	semidirect
496. #2318	C₂×C₃₁	semidirect
497. #2311	C₂×C₃₁	semidirect
498. C₄×#121	C₂×C₃₁	semidirect
499. C₂×#391	C₂×C₃₁	semidirect
500. #2290	C₂×C₃₁	semidirect
551. #548	C₄×C₃₁	semidirect
661. C₂×#41	C₂×C₄×C₃₁	semidirect
664. C₂²×Q₈	C₂×C₄×C₃₁	semidirect
682. #124	C₂×C₄×C₃₁	semidirect
683. #124	C₂×C₄×C₃₁	semidirect
684. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
685. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
686. #121	C₂×C₄×C₃₁	semidirect
687. #121	C₂×C₄×C₃₁	semidirect
690. C₄×Q₈	C₂×C₄×C₃₁	semidirect
696. C₄×D₄	C₂×C₄×C₃₁	semidirect
697. C₄×D₄	C₂×C₄×C₃₁	semidirect
784. C₃₁	#34472	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×#548	2
C₃₁×#2379	2
C₃₁×#2378	2
C₃₁×#2367	2
C₃₁×#2364	2
C₃₁×#2361	2
C₃₁×#2360	2
C₃₁×#2355	2
C₃₁×#2349	2
D₄×C₄⋊C₄×C₃₁	2
Q₈×C₂²⋊C₄×C₃₁	2
C₃₁×#2339	2
C₃₁×#2337	2
C₃₁×#2329	2
C₃₁×#2326	2
C₃₁×#2325	2
C₃₁×#2323	2
C₃₁×#2320	2
C₃₁×#2318	2
C₃₁×#2311	2
C₄×C₃₁×#121	2
C₂×C₃₁×#391	2
C₃₁×#2290	2
#34472	31

Subgroups — C31×#34472 #21491231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34472 #21491231