Subgroups — C₃₁×#34496 #21491255

Order 7936.

2344 conjugacy classes of subgroups.

The subgroup lattice has 1052 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×#2378	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2372	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2353	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2352	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×#2333	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2329	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2319	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2310	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2293	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	2	yes	—
28	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
32	C₂×C₃₁×#121	C₂²	1	2	yes	—
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	1	yes	characteristic
37	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#391	C₂²	1	1	yes	characteristic
45	C₃₁×#391	C₂²	1	1	yes	characteristic
46	C₃₁×#391	C₂²	1	2	yes	—
47	C₃₁×#391	C₂²	1	1	yes	characteristic
48	C₃₁×#391	C₂²	1	1	yes	characteristic
49	C₃₁×#391	C₂²	1	2	yes	—
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	1	yes	characteristic
54	C₃₁×#390	C₂²	1	1	yes	characteristic
55	C₃₁×#390	C₂²	1	1	yes	characteristic
56	C₃₁×#390	C₂²	1	2	yes	—
57	C₃₁×#390	C₂²	1	2	yes	—
58	C₃₁×#390	C₂²	1	1	yes	characteristic
59	C₃₁×#390	C₂²	1	1	yes	characteristic
60	C₃₁×#389	C₂²	1	2	yes	—
61	C₃₁×#389	C₂²	1	2	yes	—
62	C₃₁×#389	C₂²	1	1	yes	characteristic
63	C₃₁×#389	C₂²	1	1	yes	characteristic
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	1	yes	characteristic
66	C₃₁×#388	C₂²	1	1	yes	characteristic
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	2	yes	—
71	C₃₁×#388	C₂²	1	2	yes	—
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	1	yes	characteristic
75	C₃₁×#388	C₂²	1	2	yes	—
76	C₃₁×#388	C₂²	1	1	yes	characteristic
77	C₃₁×#388	C₂²	1	1	yes	characteristic
78	C₃₁×#388	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	2	yes	—
82	C₃₁×#387	C₂²	1	2	yes	—
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#386	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×#385	C₂²	1	2	yes	—
94	C₃₁×#385	C₂²	1	2	yes	—
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#383	C₂²	1	2	yes	—
97	C₃₁×#382	C₂²	1	1	yes	characteristic
98	C₃₁×#381	C₂²	1	2	yes	—
99	C₃₁×#381	C₂²	1	2	yes	—
100	C₃₁×#381	C₂²	1	2	yes	—
101	C₃₁×#380	C₂²	1	2	yes	—
102	C₃₁×#380	C₂²	1	2	yes	—
103	C₃₁×#380	C₂²	1	2	yes	—
104	C₃₁×#380	C₂²	1	1	yes	characteristic
105	C₃₁×#380	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
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	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
120	C₃₁×#376	C₂²	1	2	yes	—
121	C₃₁×#376	C₂²	1	2	yes	—
122	C₂×C₃₁×#95	C₂²	1	2	yes	—
123	C₄³×C₃₁	C₂²	1	1	yes	characteristic
124	C₂×#41×C₃₁	—	4	2	no	—
125	C₂×#41×C₃₁	—	4	2	no	—
126	C₂×#41×C₃₁	C₂×C₄	1	8	yes	—
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	2	yes	—
140	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
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	C₃₁×#124	C₂×C₄	1	8	yes	complemented
145	C₃₁×#124	C₂×C₄	1	16	yes	complemented
146	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
147	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
148	C₃₁×#121	C₂×C₄	1	8	yes	complemented
149	C₃₁×#121	C₂×C₄	1	16	yes	complemented
150	C₄×Q₈×C₃₁	—	4	2	no	—
151	C₄×Q₈×C₃₁	—	4	2	no	—
152	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
153	C₄×D₄×C₃₁	—	4	2	no	—
154	C₄×D₄×C₃₁	—	4	2	no	—
155	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
156	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
157	C₃₁×#117	—	4	2	no	—
158	C₃₁×#117	—	4	2	no	—
159	C₃₁×#117	—	4	2	no	—
160	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
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	1	yes	characteristic
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×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	2	yes	—
209	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
210	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
211	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
218	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	1	yes	characteristic
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	1	yes	characteristic
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	2	yes	—
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	1	yes	characteristic
231	C₃₁×#95	C₂³	1	1	yes	characteristic
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
239	C₃₁×#95	C₂³	1	2	yes	—
240	C₃₁×#95	C₂³	1	1	yes	characteristic
241	C₃₁×#95	C₂³	1	2	yes	—
242	C₃₁×#95	C₂³	1	2	yes	—
243	C₃₁×#95	C₂³	1	2	yes	—
244	C₃₁×#95	C₂³	1	2	yes	—
245	C₃₁×#95	C₂³	1	2	yes	—
246	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
249	#41×C₃₁	—	4	16	no	—
250	C₂×Q₈×C₃₁	—	2	2	no	—
251	C₂×Q₈×C₃₁	—	2	2	no	—
252	C₂×Q₈×C₃₁	—	2	2	no	—
253	C₂×Q₈×C₃₁	—	2	2	no	—
254	C₂×Q₈×C₃₁	—	4	2	no	—
255	C₂×Q₈×C₃₁	—	4	2	no	—
256	C₂×Q₈×C₃₁	—	4	16	no	—
257	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
258	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
259	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
260	C₂×D₄×C₃₁	—	2	2	no	—
261	C₂×D₄×C₃₁	—	2	2	no	—
262	C₂×D₄×C₃₁	—	4	2	no	—
263	C₂×D₄×C₃₁	—	4	1	no	—
264	C₂×D₄×C₃₁	—	4	1	no	—
265	C₂×D₄×C₃₁	—	4	2	no	—
266	C₂×D₄×C₃₁	—	4	2	no	—
267	C₂×D₄×C₃₁	—	4	2	no	—
268	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
269	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
270	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
271	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
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	4	no	—
277	C₂²×C₄×C₃₁	—	4	2	no	—
278	C₂²×C₄×C₃₁	—	4	2	no	—
279	C₂²×C₄×C₃₁	—	4	2	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	C₂²×C₄	1	4	yes	—
290	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
291	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
292	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
316	C₄⋊C₄×C₃₁	—	2	2	no	—
317	C₄⋊C₄×C₃₁	—	4	2	no	—
318	C₄⋊C₄×C₃₁	—	4	1	no	—
319	C₄⋊C₄×C₃₁	—	4	1	no	—
320	C₄⋊C₄×C₃₁	—	4	2	no	—
321	C₄⋊C₄×C₃₁	—	4	2	no	—
322	C₄⋊C₄×C₃₁	—	4	1	no	—
323	C₄⋊C₄×C₃₁	—	4	1	no	—
324	C₄⋊C₄×C₃₁	—	4	1	no	—
325	C₄⋊C₄×C₃₁	—	4	1	no	—
326	C₄⋊C₄×C₃₁	—	4	2	no	—
327	C₄⋊C₄×C₃₁	—	4	2	no	—
328	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
329	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
330	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
331	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
332	C₂²⋊C₄×C₃₁	—	2	2	no	—
333	C₂²⋊C₄×C₃₁	—	2	2	no	—
334	C₂²⋊C₄×C₃₁	—	4	2	no	—
335	C₂²⋊C₄×C₃₁	—	4	1	no	—
336	C₂²⋊C₄×C₃₁	—	4	2	no	—
337	C₂²⋊C₄×C₃₁	—	4	1	no	—
338	C₂²⋊C₄×C₃₁	—	4	2	no	—
339	C₂²⋊C₄×C₃₁	—	4	2	no	—
340	C₂²⋊C₄×C₃₁	—	4	2	no	—
341	C₂²⋊C₄×C₃₁	—	4	2	no	—
342	C₂²⋊C₄×C₃₁	—	4	1	no	—
343	C₂²⋊C₄×C₃₁	—	4	1	no	—
344	C₂²⋊C₄×C₃₁	—	4	1	no	—
345	C₂²⋊C₄×C₃₁	—	4	1	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	C₂²×C₄	1	4	yes	—
350	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
351	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
352	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
354	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
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	2	no	—
362	C₄²×C₃₁	—	4	1	no	—
363	C₄²×C₃₁	—	4	2	no	—
364	C₄²×C₃₁	—	4	2	no	—
365	C₄²×C₃₁	—	4	1	no	—
366	C₄²×C₃₁	—	4	2	no	—
367	C₄²×C₃₁	—	4	2	no	—
368	C₄²×C₃₁	—	4	2	no	—
369	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
370	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
371	#34496	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
372	C₂³×C₃₁	—	2	1	no	—
373	C₂³×C₃₁	—	2	1	no	—
374	C₂³×C₃₁	—	2	1	no	—
375	C₂³×C₃₁	—	2	2	no	—
376	C₂³×C₃₁	—	2	2	no	—
377	C₂³×C₃₁	—	2	1	no	—
378	C₂³×C₃₁	—	2	1	no	—
379	C₂³×C₃₁	—	2	1	no	—
380	C₂³×C₃₁	—	2	2	no	—
381	C₂³×C₃₁	—	2	1	no	—
382	C₂³×C₃₁	—	2	2	no	—
383	C₂³×C₃₁	—	2	2	no	—
384	C₂³×C₃₁	—	2	1	no	—
385	C₂³×C₃₁	—	2	1	no	—
386	C₂³×C₃₁	—	2	1	no	—
387	C₂³×C₃₁	—	2	2	no	—
388	C₂³×C₃₁	—	2	1	no	—
389	C₂³×C₃₁	—	2	1	no	—
390	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
391	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
392	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
393	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
394	Q₈×C₃₁	—	2	8	no	—
395	Q₈×C₃₁	—	2	8	no	—
396	Q₈×C₃₁	—	4	8	no	—
397	D₄×C₃₁	—	2	8	no	—
398	D₄×C₃₁	—	4	4	no	—
399	D₄×C₃₁	—	4	8	no	—
400	D₄×C₃₁	—	4	8	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	1	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	2	no	—
410	C₂×C₄×C₃₁	—	2	1	no	—
411	C₂×C₄×C₃₁	—	2	1	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	1	no	—
414	C₂×C₄×C₃₁	—	2	1	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	8	no	—
418	C₂×C₄×C₃₁	—	2	8	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	1	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	2	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	2	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	2	no	—
434	C₂×C₄×C₃₁	—	2	1	no	—
435	C₂×C₄×C₃₁	—	2	1	no	—
436	C₂×C₄×C₃₁	—	2	1	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	2	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	2	no	—
443	C₂×C₄×C₃₁	—	2	1	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	2	no	—
448	C₂×C₄×C₃₁	—	2	2	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	—	4	8	no	—
453	C₂×C₄×C₃₁	—	4	8	no	—
454	C₂×C₄×C₃₁	—	8	4	no	—
455	C₂×C₄×C₃₁	—	8	4	no	—
456	C₂×C₄×C₃₁	—	8	4	no	—
457	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
459	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
460	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
461	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
463	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
466	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
467	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
468	C₂×#548	C₂×C₃₁	1	1	yes	characteristic
469	#2378	C₂×C₃₁	1	2	yes	complemented
470	#2377	C₂×C₃₁	1	2	yes	complemented
471	#2372	C₂×C₃₁	1	2	yes	complemented
472	#2367	C₂×C₃₁	1	1	yes	characteristic, complemented
473	#2363	C₂×C₃₁	1	1	yes	characteristic, complemented
474	#2360	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#2356	C₂×C₃₁	1	1	yes	characteristic, complemented
476	#2353	C₂×C₃₁	1	2	yes	complemented
477	#2352	C₂×C₃₁	1	1	yes	characteristic, complemented
478	Q₈×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
479	#2339	C₂×C₃₁	1	1	yes	characteristic, complemented
480	#2337	C₂×C₃₁	1	2	yes	complemented
481	#2333	C₂×C₃₁	1	2	yes	complemented
482	#2329	C₂×C₃₁	1	2	yes	complemented
483	#2324	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#2323	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#2319	C₂×C₃₁	1	2	yes	complemented
486	#2311	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#2310	C₂×C₃₁	1	1	yes	characteristic, complemented
488	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
490	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
491	C₂²×C₃₁	—	2	2	no	—
492	C₂²×C₃₁	—	2	2	no	—
493	C₂²×C₃₁	—	2	4	no	—
494	C₂²×C₃₁	—	2	2	no	—
495	C₂²×C₃₁	—	2	2	no	—
496	C₂²×C₃₁	—	2	4	no	—
497	C₂²×C₃₁	—	2	2	no	—
498	C₂²×C₃₁	—	2	2	no	—
499	C₂²×C₃₁	—	2	4	no	—
500	C₂²×C₃₁	—	4	1	no	—
501	C₂²×C₃₁	—	4	1	no	—
502	C₂²×C₃₁	—	4	2	no	—
503	C₂²×C₃₁	—	4	2	no	—
504	C₂²×C₃₁	—	4	1	no	—
505	C₂²×C₃₁	—	4	1	no	—
506	C₂²×C₃₁	—	4	2	no	—
507	C₂²×C₃₁	—	4	1	no	—
508	C₂²×C₃₁	—	4	1	no	—
509	C₂²×C₃₁	—	4	1	no	—
510	C₂²×C₃₁	—	4	1	no	—
511	C₂²×C₃₁	—	4	2	no	—
512	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
513	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
516	C₂²×C₃₁	#585	1	1	yes	characteristic
517	C₂²×C₃₁	#585	1	1	yes	characteristic
518	C₂²×C₃₁	#585	1	1	yes	characteristic
519	C₄×C₃₁	—	2	2	no	—
520	C₄×C₃₁	—	2	2	no	—
521	C₄×C₃₁	—	2	4	no	—
522	C₄×C₃₁	—	2	4	no	—
523	C₄×C₃₁	—	2	4	no	—
524	C₄×C₃₁	—	2	2	no	—
525	C₄×C₃₁	—	2	2	no	—
526	C₄×C₃₁	—	2	2	no	—
527	C₄×C₃₁	—	4	1	no	—
528	C₄×C₃₁	—	4	1	no	—
529	C₄×C₃₁	—	4	1	no	—
530	C₄×C₃₁	—	4	1	no	—
531	C₄×C₃₁	—	4	1	no	—
532	C₄×C₃₁	—	4	2	no	—
533	C₄×C₃₁	—	4	1	no	—
534	C₄×C₃₁	—	4	2	no	—
535	C₄×C₃₁	—	4	1	no	—
536	C₄×C₃₁	—	4	2	no	—
537	C₄×C₃₁	—	4	2	no	—
538	C₄×C₃₁	#518	1	4	yes	—
539	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
540	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
541	#548	C₄×C₃₁	1	16	yes	complemented
542	C₂×#124	C₂²×C₃₁	1	2	yes	—
543	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
544	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
545	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
546	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
547	C₂×#121	C₂²×C₃₁	1	2	yes	—
548	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
549	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
550	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
552	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
553	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
554	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
555	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
556	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
557	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
558	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
559	#391	C₂²×C₃₁	1	1	yes	characteristic
560	#391	C₂²×C₃₁	1	1	yes	characteristic
561	#391	C₂²×C₃₁	1	2	yes	—
562	#391	C₂²×C₃₁	1	1	yes	characteristic
563	#391	C₂²×C₃₁	1	1	yes	characteristic
564	#391	C₂²×C₃₁	1	2	yes	—
565	#391	C₂²×C₃₁	1	1	yes	characteristic
566	#391	C₂²×C₃₁	1	2	yes	—
567	#391	C₂²×C₃₁	1	2	yes	—
568	#391	C₂²×C₃₁	1	1	yes	characteristic
569	#390	C₂²×C₃₁	1	1	yes	characteristic
570	#390	C₂²×C₃₁	1	1	yes	characteristic
571	#390	C₂²×C₃₁	1	2	yes	—
572	#390	C₂²×C₃₁	1	2	yes	—
573	#390	C₂²×C₃₁	1	1	yes	characteristic
574	#390	C₂²×C₃₁	1	1	yes	characteristic
575	#389	C₂²×C₃₁	1	2	yes	—
576	#389	C₂²×C₃₁	1	2	yes	—
577	#389	C₂²×C₃₁	1	1	yes	characteristic
578	#389	C₂²×C₃₁	1	1	yes	characteristic
579	#389	C₂²×C₃₁	1	1	yes	characteristic
580	#389	C₂²×C₃₁	1	1	yes	characteristic
581	#388	C₂²×C₃₁	1	1	yes	characteristic
582	#388	C₂²×C₃₁	1	2	yes	—
583	#388	C₂²×C₃₁	1	2	yes	—
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	1	yes	characteristic
590	#388	C₂²×C₃₁	1	2	yes	—
591	#388	C₂²×C₃₁	1	1	yes	characteristic
592	#388	C₂²×C₃₁	1	1	yes	characteristic
593	#388	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	#387	C₂²×C₃₁	1	2	yes	—
599	#387	C₂²×C₃₁	1	2	yes	—
600	#387	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	#386	C₂²×C₃₁	1	2	yes	—
607	#386	C₂²×C₃₁	1	2	yes	—
608	#385	C₂²×C₃₁	1	2	yes	—
609	#385	C₂²×C₃₁	1	2	yes	—
610	#385	C₂²×C₃₁	1	2	yes	—
611	#383	C₂²×C₃₁	1	2	yes	—
612	#382	C₂²×C₃₁	1	1	yes	characteristic
613	#381	C₂²×C₃₁	1	2	yes	—
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	2	yes	—
619	#380	C₂²×C₃₁	1	1	yes	characteristic
620	#380	C₂²×C₃₁	1	1	yes	characteristic
621	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
622	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
623	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
624	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
625	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
626	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
627	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
628	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
629	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
630	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
631	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
632	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
633	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
634	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
635	#376	C₂²×C₃₁	1	2	yes	—
636	#376	C₂²×C₃₁	1	2	yes	—
637	C₂×#95	C₂²×C₃₁	1	2	yes	—
638	C₄³	C₂²×C₃₁	1	1	yes	characteristic
639	C₂×C₃₁	—	4	2	no	—
640	C₂×C₃₁	—	4	2	no	—
641	C₂×C₃₁	—	4	4	no	—
642	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
643	C₂×C₃₁	#3428	1	1	yes	characteristic
644	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
645	C₂×C₃₁	#3547	1	1	yes	characteristic
646	C₂×C₃₁	#3551	1	1	yes	characteristic
647	C₂×C₃₁	#3561	1	1	yes	characteristic
648	C₂×C₃₁	#3562	1	1	yes	characteristic
649	C₂×#41	—	4	2	no	—
650	C₂×#41	—	4	2	no	—
651	C₂×#41	C₂×C₄×C₃₁	1	8	yes	—
652	C₂²×Q₈	—	4	2	no	—
653	C₂²×Q₈	—	4	2	no	—
654	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
655	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
656	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
657	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
658	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
659	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
660	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
661	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
662	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
663	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
665	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
666	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
667	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
668	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
669	#124	C₂×C₄×C₃₁	1	8	yes	complemented
670	#124	C₂×C₄×C₃₁	1	16	yes	complemented
671	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
672	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
673	#121	C₂×C₄×C₃₁	1	8	yes	complemented
674	#121	C₂×C₄×C₃₁	1	16	yes	complemented
675	C₄×Q₈	—	4	2	no	—
676	C₄×Q₈	—	4	2	no	—
677	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
678	C₄×D₄	—	4	2	no	—
679	C₄×D₄	—	4	2	no	—
680	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
681	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
682	#117	—	4	2	no	—
683	#117	—	4	2	no	—
684	#117	—	4	2	no	—
685	C₂×C₄⋊C₄	—	4	2	no	—
686	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
734	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
735	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
736	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
740	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
741	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
742	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
756	#95	C₂³×C₃₁	1	1	yes	characteristic
757	#95	C₂³×C₃₁	1	2	yes	—
758	#95	C₂³×C₃₁	1	2	yes	—
759	#95	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
766	#95	C₂³×C₃₁	1	2	yes	—
767	#95	C₂³×C₃₁	1	2	yes	—
768	#95	C₂³×C₃₁	1	2	yes	—
769	#95	C₂³×C₃₁	1	2	yes	—
770	#95	C₂³×C₃₁	1	2	yes	—
771	C₃₁	#34496	1	1	yes	characteristic, direct product factor, Sylow
772	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
774	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
775	#41	—	4	16	no	—
776	C₂×Q₈	—	2	2	no	—
777	C₂×Q₈	—	2	2	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	4	2	no	—
781	C₂×Q₈	—	4	2	no	—
782	C₂×Q₈	—	4	16	no	—
783	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
784	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
785	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	1	no	—
790	C₂×D₄	—	4	1	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
795	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
796	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
797	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	2	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	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
816	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
817	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
818	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
819	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
820	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	2	yes	—
831	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	4	2	no	—
844	C₄⋊C₄	—	4	1	no	—
845	C₄⋊C₄	—	4	1	no	—
846	C₄⋊C₄	—	4	2	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	1	no	—
849	C₄⋊C₄	—	4	1	no	—
850	C₄⋊C₄	—	4	1	no	—
851	C₄⋊C₄	—	4	1	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
855	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
856	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
857	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	1	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	1	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	1	no	—
869	C₂²⋊C₄	—	4	1	no	—
870	C₂²⋊C₄	—	4	1	no	—
871	C₂²⋊C₄	—	4	1	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
876	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
877	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	4	1	no	—
887	C₄²	—	4	2	no	—
888	C₄²	—	4	1	no	—
889	C₄²	—	4	2	no	—
890	C₄²	—	4	2	no	—
891	C₄²	—	4	1	no	—
892	C₄²	—	4	2	no	—
893	C₄²	—	4	2	no	—
894	C₄²	—	4	2	no	—
895	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
896	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	1	no	—
915	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
916	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
917	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
918	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
919	Q₈	—	2	8	no	—
920	Q₈	—	2	8	no	—
921	Q₈	—	4	8	no	—
922	D₄	—	2	8	no	—
923	D₄	—	4	4	no	—
924	D₄	—	4	8	no	—
925	D₄	—	4	8	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	8	no	—
943	C₂×C₄	—	2	8	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	1	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	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	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	—	4	8	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	8	4	no	—
980	C₂×C₄	—	8	4	no	—
981	C₂×C₄	—	8	4	no	—
982	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
984	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
985	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
986	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
987	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
988	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
989	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
990	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
991	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
992	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	4	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	4	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1015	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1016	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1017	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1018	C₂²	C₃₁×#585	1	1	yes	characteristic
1019	C₂²	C₃₁×#585	1	1	yes	characteristic
1020	C₂²	C₃₁×#585	1	1	yes	characteristic
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	4	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	4	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	2	2	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	1	no	—
1040	C₄	C₃₁×#518	1	4	yes	—
1041	C₂	—	4	2	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	4	4	no	—
1044	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
1045	C₂	C₃₁×#3428	1	1	yes	characteristic
1046	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1047	C₂	C₃₁×#3547	1	1	yes	characteristic
1048	C₂	C₃₁×#3551	1	1	yes	characteristic
1049	C₂	C₃₁×#3561	1	1	yes	characteristic
1050	C₂	C₃₁×#3562	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×#2378	C₂	semidirect
3. C₃₁×#2377	C₂	semidirect
4. C₃₁×#2372	C₂	semidirect
5. C₃₁×#2367	C₂	semidirect
6. C₃₁×#2363	C₂	semidirect
7. C₃₁×#2360	C₂	semidirect
8. C₃₁×#2356	C₂	semidirect
9. C₃₁×#2353	C₂	semidirect
10. C₃₁×#2352	C₂	semidirect
11. Q₈×C₂²⋊C₄×C₃₁	C₂	semidirect
12. C₃₁×#2339	C₂	semidirect
13. C₃₁×#2337	C₂	semidirect
14. C₃₁×#2333	C₂	semidirect
15. C₃₁×#2329	C₂	semidirect
16. C₃₁×#2324	C₂	semidirect
17. C₃₁×#2323	C₂	semidirect
18. C₃₁×#2319	C₂	semidirect
19. C₃₁×#2311	C₂	semidirect
20. C₃₁×#2310	C₂	semidirect
21. C₄×C₃₁×#124	C₂	semidirect
22. C₃₁×#2295	C₂	semidirect
23. C₃₁×#2293	C₂	semidirect
26. C₃₁×#548	C₄	semidirect
129. C₂²×Q₈×C₃₁	C₂×C₄	semidirect
144. C₃₁×#124	C₂×C₄	semidirect
145. C₃₁×#124	C₂×C₄	semidirect
146. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
147. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
148. C₃₁×#121	C₂×C₄	semidirect
149. C₃₁×#121	C₂×C₄	semidirect
152. C₄×Q₈×C₃₁	C₂×C₄	semidirect
155. C₄×D₄×C₃₁	C₂×C₄	semidirect
156. C₄×D₄×C₃₁	C₂×C₄	semidirect
371. #34496	C₃₁	direct (N × H)
469. #2378	C₂×C₃₁	semidirect
470. #2377	C₂×C₃₁	semidirect
471. #2372	C₂×C₃₁	semidirect
472. #2367	C₂×C₃₁	semidirect
473. #2363	C₂×C₃₁	semidirect
474. #2360	C₂×C₃₁	semidirect
475. #2356	C₂×C₃₁	semidirect
476. #2353	C₂×C₃₁	semidirect
477. #2352	C₂×C₃₁	semidirect
478. Q₈×C₂²⋊C₄	C₂×C₃₁	semidirect
479. #2339	C₂×C₃₁	semidirect
480. #2337	C₂×C₃₁	semidirect
481. #2333	C₂×C₃₁	semidirect
482. #2329	C₂×C₃₁	semidirect
483. #2324	C₂×C₃₁	semidirect
484. #2323	C₂×C₃₁	semidirect
485. #2319	C₂×C₃₁	semidirect
486. #2311	C₂×C₃₁	semidirect
487. #2310	C₂×C₃₁	semidirect
488. C₄×#124	C₂×C₃₁	semidirect
489. #2295	C₂×C₃₁	semidirect
490. #2293	C₂×C₃₁	semidirect
541. #548	C₄×C₃₁	semidirect
654. C₂²×Q₈	C₂×C₄×C₃₁	semidirect
669. #124	C₂×C₄×C₃₁	semidirect
670. #124	C₂×C₄×C₃₁	semidirect
671. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
672. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
673. #121	C₂×C₄×C₃₁	semidirect
674. #121	C₂×C₄×C₃₁	semidirect
677. C₄×Q₈	C₂×C₄×C₃₁	semidirect
680. C₄×D₄	C₂×C₄×C₃₁	semidirect
681. C₄×D₄	C₂×C₄×C₃₁	semidirect
771. C₃₁	#34496	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×#2378	2
C₃₁×#2377	2
C₃₁×#2372	2
C₃₁×#2367	2
C₃₁×#2363	2
C₃₁×#2360	2
C₃₁×#2356	2
C₃₁×#2353	2
C₃₁×#2352	2
Q₈×C₂²⋊C₄×C₃₁	2
C₃₁×#2339	2
C₃₁×#2337	2
C₃₁×#2333	2
C₃₁×#2329	2
C₃₁×#2324	2
C₃₁×#2323	2
C₃₁×#2319	2
C₃₁×#2311	2
C₃₁×#2310	2
C₄×C₃₁×#124	2
C₃₁×#2295	2
C₃₁×#2293	2
#34496	31

Subgroups — C31×#34496 #21491255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34496 #21491255