Subgroups — C₃₁×#35080 #21491839

Order 7936.

2154 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2847	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2653	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2649	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2510	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2495	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2494	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2472	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2450	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2427	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2426	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2423	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2422	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2418	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2337	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2335	C₂	1	2	yes	maximal, complemented
21	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃₁×#124	C₂²	1	2	yes	—
27	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×#123	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#120	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#401	C₂²	1	2	yes	complemented
45	C₃₁×#400	C₂²	1	2	yes	complemented
46	C₃₁×#400	C₂²	1	2	yes	complemented
47	C₃₁×#399	C₂²	1	2	yes	—
48	C₃₁×#398	C₂²	1	2	yes	complemented
49	C₃₁×#397	C₂²	1	2	yes	—
50	C₃₁×#397	C₂²	1	2	yes	—
51	C₃₁×#397	C₂²	1	2	yes	complemented
52	C₃₁×#397	C₂²	1	2	yes	complemented
53	C₃₁×#396	C₂²	1	2	yes	complemented
54	C₃₁×#394	C₂²	1	2	yes	—
55	C₃₁×#394	C₂²	1	2	yes	—
56	C₃₁×#394	C₂²	1	2	yes	—
57	C₃₁×#394	C₂²	1	2	yes	—
58	C₃₁×#393	C₂²	1	2	yes	—
59	C₃₁×#393	C₂²	1	2	yes	complemented
60	C₃₁×#391	C₂²	1	2	yes	complemented
61	C₃₁×#391	C₂²	1	2	yes	complemented
62	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#390	C₂²	1	2	yes	—
65	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#389	C₂²	1	2	yes	complemented
68	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	2	yes	—
75	C₃₁×#388	C₂²	1	2	yes	—
76	C₃₁×#388	C₂²	1	2	yes	complemented
77	C₃₁×#388	C₂²	1	2	yes	complemented
78	C₃₁×#388	C₂²	1	2	yes	complemented
79	C₃₁×#388	C₂²	1	2	yes	complemented
80	C₃₁×#388	C₂²	1	2	yes	complemented
81	C₃₁×#387	C₂²	1	2	yes	complemented
82	C₃₁×#387	C₂²	1	2	yes	complemented
83	C₃₁×#387	C₂²	1	2	yes	complemented
84	C₃₁×#386	C₂²	1	2	yes	—
85	C₃₁×#386	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×#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	complemented
96	C₃₁×#384	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#383	C₂²	1	2	yes	complemented
98	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#380	C₂²	1	1	yes	characteristic
100	C₃₁×#380	C₂²	1	1	yes	characteristic
101	C₃₁×#380	C₂²	1	1	yes	characteristic
102	C₃₁×#380	C₂²	1	1	yes	characteristic
103	C₃₁×#380	C₂²	1	1	yes	characteristic
104	C₃₁×#380	C₂²	1	1	yes	characteristic
105	C₃₁×#380	C₂²	1	2	yes	—
106	C₃₁×#380	C₂²	1	2	yes	complemented
107	C₃₁×#379	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
121	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
122	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
123	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
130	C₂³×C₄×C₃₁	—	2	4	no	—
131	C₂³×C₄×C₃₁	—	4	2	no	—
132	C₂³×C₄×C₃₁	—	4	2	no	—
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₃₁×C₄⋊Q₈	—	4	2	no	—
145	C₃₁×#124	—	2	8	no	—
146	C₃₁×#124	—	4	2	no	—
147	C₃₁×#123	—	2	8	no	—
148	C₃₁×C₂²⋊Q₈	—	2	4	no	—
149	C₃₁×C₂²⋊Q₈	—	4	4	no	—
150	C₃₁×C₂²⋊Q₈	—	4	2	no	—
151	C₃₁×C₂²⋊Q₈	—	4	2	no	—
152	C₃₁×#121	—	2	4	no	—
153	C₃₁×#121	—	4	2	no	—
154	C₃₁×#121	—	4	2	no	—
155	C₃₁×#120	—	4	4	no	—
156	C₄×Q₈×C₃₁	—	4	2	no	—
157	C₄×D₄×C₃₁	—	4	2	no	—
158	C₄×D₄×C₃₁	—	4	4	no	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
177	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×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	2	yes	—
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×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	—	4	2	no	—
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	2	yes	—
212	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	1	yes	characteristic
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	2	yes	—
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	1	yes	characteristic
226	C₃₁×#95	C₂³	1	1	yes	characteristic
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	1	yes	characteristic
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₃₁×#95	C₂³	1	2	yes	—
236	C₃₁×#95	C₂³	1	1	yes	characteristic
237	C₃₁×#95	C₂³	1	1	yes	characteristic
238	C₃₁×#95	C₂³	1	1	yes	characteristic
239	C₃₁×#95	C₂³	1	1	yes	characteristic
240	C₃₁×#95	C₂³	1	2	yes	—
241	C₃₁×#95	C₂³	1	2	yes	—
242	C₃₁×#95	C₂³	1	2	yes	—
243	C₃₁×#95	C₂³	1	2	yes	—
244	C₂⁴×C₃₁	—	2	2	no	—
245	C₂⁴×C₃₁	—	2	2	no	—
246	C₂⁴×C₃₁	—	2	2	no	—
247	C₂⁴×C₃₁	—	2	2	no	—
248	C₂⁴×C₃₁	—	2	2	no	—
249	C₂⁴×C₃₁	—	4	1	no	—
250	C₂⁴×C₃₁	—	4	1	no	—
251	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
252	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂×Q₈×C₃₁	—	2	2	no	—
256	C₂×Q₈×C₃₁	—	2	4	no	—
257	C₂×Q₈×C₃₁	—	2	2	no	—
258	C₂×Q₈×C₃₁	—	2	2	no	—
259	C₂×Q₈×C₃₁	—	4	2	no	—
260	C₂×Q₈×C₃₁	—	4	2	no	—
261	C₂×D₄×C₃₁	—	2	4	no	—
262	C₂×D₄×C₃₁	—	2	4	no	—
263	C₂×D₄×C₃₁	—	2	4	no	—
264	C₂×D₄×C₃₁	—	2	4	no	—
265	C₂×D₄×C₃₁	—	2	4	no	—
266	C₂×D₄×C₃₁	—	2	2	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	—	4	2	no	—
272	C₂×D₄×C₃₁	—	4	2	no	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	2	2	no	—
275	C₂²×C₄×C₃₁	—	2	2	no	—
276	C₂²×C₄×C₃₁	—	2	2	no	—
277	C₂²×C₄×C₃₁	—	2	2	no	—
278	C₂²×C₄×C₃₁	—	2	2	no	—
279	C₂²×C₄×C₃₁	—	2	2	no	—
280	C₂²×C₄×C₃₁	—	2	2	no	—
281	C₂²×C₄×C₃₁	—	2	2	no	—
282	C₂²×C₄×C₃₁	—	2	2	no	—
283	C₂²×C₄×C₃₁	—	2	2	no	—
284	C₂²×C₄×C₃₁	—	2	2	no	—
285	C₂²×C₄×C₃₁	—	2	2	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	—	2	2	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	2	4	no	—
293	C₂²×C₄×C₃₁	—	4	1	no	—
294	C₂²×C₄×C₃₁	—	4	1	no	—
295	C₂²×C₄×C₃₁	—	4	1	no	—
296	C₂²×C₄×C₃₁	—	4	1	no	—
297	C₂²×C₄×C₃₁	—	4	1	no	—
298	C₂²×C₄×C₃₁	—	4	1	no	—
299	C₂²×C₄×C₃₁	—	4	1	no	—
300	C₂²×C₄×C₃₁	—	4	1	no	—
301	C₂²×C₄×C₃₁	—	4	1	no	—
302	C₂²×C₄×C₃₁	—	4	1	no	—
303	C₂²×C₄×C₃₁	—	4	2	no	—
304	C₂²×C₄×C₃₁	—	4	2	no	—
305	C₂²×C₄×C₃₁	—	4	16	no	—
306	C₂²×C₄×C₃₁	#41	1	4	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	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	1	yes	characteristic
316	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	4	no	—
329	C₄⋊C₄×C₃₁	—	2	4	no	—
330	C₄⋊C₄×C₃₁	—	2	4	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	4	2	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	—	4	2	no	—
342	C₄⋊C₄×C₃₁	—	4	2	no	—
343	C₂²⋊C₄×C₃₁	—	2	2	no	—
344	C₂²⋊C₄×C₃₁	—	2	2	no	—
345	C₂²⋊C₄×C₃₁	—	2	4	no	—
346	C₂²⋊C₄×C₃₁	—	2	4	no	—
347	C₂²⋊C₄×C₃₁	—	2	4	no	—
348	C₂²⋊C₄×C₃₁	—	2	4	no	—
349	C₂²⋊C₄×C₃₁	—	2	4	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	4	no	—
355	C₂²⋊C₄×C₃₁	—	2	4	no	—
356	C₂²⋊C₄×C₃₁	—	2	4	no	—
357	C₂²⋊C₄×C₃₁	—	2	4	no	—
358	C₂²⋊C₄×C₃₁	—	4	2	no	—
359	C₂²⋊C₄×C₃₁	—	4	2	no	—
360	C₂²⋊C₄×C₃₁	—	4	2	no	—
361	C₂²⋊C₄×C₃₁	—	4	2	no	—
362	C₂²⋊C₄×C₃₁	—	4	2	no	—
363	C₂²⋊C₄×C₃₁	—	4	2	no	—
364	C₂²⋊C₄×C₃₁	—	4	2	no	—
365	C₂²⋊C₄×C₃₁	—	4	2	no	—
366	C₂²⋊C₄×C₃₁	—	4	2	no	—
367	C₂²⋊C₄×C₃₁	—	4	2	no	—
368	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
369	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
370	C₄²×C₃₁	—	2	4	no	—
371	C₄²×C₃₁	—	2	2	no	—
372	C₄²×C₃₁	—	2	2	no	—
373	C₄²×C₃₁	—	2	2	no	—
374	C₄²×C₃₁	—	2	2	no	—
375	C₄²×C₃₁	—	4	1	no	—
376	C₄²×C₃₁	—	4	1	no	—
377	C₄²×C₃₁	—	4	1	no	—
378	C₄²×C₃₁	—	4	1	no	—
379	C₄²×C₃₁	—	4	2	no	—
380	C₄²×C₃₁	—	4	2	no	—
381	#35080	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂³×C₃₁	—	2	1	no	—
383	C₂³×C₃₁	—	2	1	no	—
384	C₂³×C₃₁	—	2	1	no	—
385	C₂³×C₃₁	—	2	1	no	—
386	C₂³×C₃₁	—	2	8	no	—
387	C₂³×C₃₁	—	2	1	no	—
388	C₂³×C₃₁	—	2	1	no	—
389	C₂³×C₃₁	—	2	1	no	—
390	C₂³×C₃₁	—	2	1	no	—
391	C₂³×C₃₁	—	2	1	no	—
392	C₂³×C₃₁	—	2	1	no	—
393	C₂³×C₃₁	—	2	1	no	—
394	C₂³×C₃₁	—	2	1	no	—
395	C₂³×C₃₁	—	2	1	no	—
396	C₂³×C₃₁	—	2	1	no	—
397	C₂³×C₃₁	—	2	1	no	—
398	C₂³×C₃₁	—	2	1	no	—
399	C₂³×C₃₁	—	2	2	no	—
400	C₂³×C₃₁	—	2	2	no	—
401	C₂³×C₃₁	—	2	2	no	—
402	C₂³×C₃₁	—	2	2	no	—
403	C₂³×C₃₁	—	2	2	no	—
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	—	2	2	no	—
406	C₂³×C₃₁	—	4	4	no	—
407	C₂³×C₃₁	—	4	4	no	—
408	C₂³×C₃₁	—	4	4	no	—
409	C₂³×C₃₁	—	4	4	no	—
410	C₂³×C₃₁	—	4	4	no	—
411	C₂³×C₃₁	—	4	4	no	—
412	C₂³×C₃₁	C₂×#41	1	2	yes	—
413	C₂³×C₃₁	C₂×#41	1	2	yes	—
414	C₂³×C₃₁	C₂×#41	1	2	yes	—
415	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
416	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
417	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
418	Q₈×C₃₁	—	4	4	no	—
419	Q₈×C₃₁	—	8	4	no	—
420	D₄×C₃₁	—	4	8	no	—
421	D₄×C₃₁	—	4	4	no	—
422	D₄×C₃₁	—	8	4	no	—
423	D₄×C₃₁	—	8	4	no	—
424	C₂×C₄×C₃₁	—	2	1	no	—
425	C₂×C₄×C₃₁	—	2	1	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	1	no	—
428	C₂×C₄×C₃₁	—	2	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	8	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	1	no	—
439	C₂×C₄×C₃₁	—	2	1	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	2	no	—
445	C₂×C₄×C₃₁	—	2	2	no	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	1	no	—
449	C₂×C₄×C₃₁	—	2	1	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	2	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	2	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	2	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	1	no	—
465	C₂×C₄×C₃₁	—	2	1	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	2	1	no	—
471	C₂×C₄×C₃₁	—	2	1	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	4	4	no	—
475	C₂×C₄×C₃₁	—	4	4	no	—
476	C₂×C₄×C₃₁	—	4	4	no	—
477	C₂×C₄×C₃₁	—	4	4	no	—
478	C₂×C₄×C₃₁	—	4	4	no	—
479	C₂×C₄×C₃₁	—	4	4	no	—
480	C₂×C₄×C₃₁	—	4	4	no	—
481	C₂×C₄×C₃₁	—	4	4	no	—
482	C₂×C₄×C₃₁	—	4	4	no	—
483	C₂×C₄×C₃₁	—	8	4	no	—
484	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
485	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
486	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
487	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
488	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
489	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
490	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
491	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
492	#2857	C₂×C₃₁	1	1	yes	characteristic, complemented
493	#2850	C₂×C₃₁	1	1	yes	characteristic, complemented
494	#2848	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#2847	C₂×C₃₁	1	1	yes	characteristic
496	#2653	C₂×C₃₁	1	2	yes	complemented
497	#2649	C₂×C₃₁	1	2	yes	complemented
498	#2510	C₂×C₃₁	1	2	yes	complemented
499	#2495	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#2494	C₂×C₃₁	1	1	yes	characteristic, complemented
501	#2492	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#2491	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#2472	C₂×C₃₁	1	2	yes	complemented
504	#2450	C₂×C₃₁	1	2	yes	complemented
505	#2427	C₂×C₃₁	1	1	yes	characteristic, complemented
506	#2426	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#2423	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#2422	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#2418	C₂×C₃₁	1	2	yes	complemented
510	#2337	C₂×C₃₁	1	2	yes	complemented
511	#2335	C₂×C₃₁	1	2	yes	complemented
512	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
513	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
514	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
515	C₂²×C₃₁	—	2	2	no	—
516	C₂²×C₃₁	—	2	2	no	—
517	C₂²×C₃₁	—	2	2	no	—
518	C₂²×C₃₁	—	2	2	no	—
519	C₂²×C₃₁	—	2	2	no	—
520	C₂²×C₃₁	—	2	2	no	—
521	C₂²×C₃₁	—	2	2	no	—
522	C₂²×C₃₁	—	2	2	no	—
523	C₂²×C₃₁	—	2	2	no	—
524	C₂²×C₃₁	—	2	2	no	—
525	C₂²×C₃₁	—	2	2	no	—
526	C₂²×C₃₁	—	2	2	no	—
527	C₂²×C₃₁	—	4	16	no	—
528	C₂²×C₃₁	—	4	1	no	—
529	C₂²×C₃₁	—	4	1	no	—
530	C₂²×C₃₁	—	4	1	no	—
531	C₂²×C₃₁	—	4	1	no	—
532	C₂²×C₃₁	—	4	1	no	—
533	C₂²×C₃₁	—	4	1	no	—
534	C₂²×C₃₁	—	4	1	no	—
535	C₂²×C₃₁	—	4	1	no	—
536	C₂²×C₃₁	—	4	2	no	—
537	C₂²×C₃₁	—	4	2	no	—
538	C₂²×C₃₁	—	4	2	no	—
539	C₂²×C₃₁	—	4	2	no	—
540	C₂²×C₃₁	—	4	2	no	—
541	C₂²×C₃₁	—	4	2	no	—
542	C₂²×C₃₁	—	4	2	no	—
543	C₂²×C₃₁	#542	1	4	yes	—
544	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
545	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
546	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
547	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
551	C₄×C₃₁	—	2	2	no	—
552	C₄×C₃₁	—	2	2	no	—
553	C₄×C₃₁	—	2	2	no	—
554	C₄×C₃₁	—	2	2	no	—
555	C₄×C₃₁	—	2	2	no	—
556	C₄×C₃₁	—	4	2	no	—
557	C₄×C₃₁	—	4	1	no	—
558	C₄×C₃₁	—	4	1	no	—
559	C₄×C₃₁	—	4	2	no	—
560	C₄×C₃₁	—	4	2	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	—	4	2	no	—
564	C₄×C₃₁	—	4	2	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	2	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	#538	1	4	yes	—
570	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
571	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	C₂×#124	C₂²×C₃₁	1	2	yes	—
573	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	C₂×#123	C₂²×C₃₁	1	2	yes	—
575	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
576	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
577	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
578	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
579	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
580	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
581	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
582	C₂×#120	C₂²×C₃₁	1	2	yes	—
583	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
585	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
587	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
588	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
589	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
590	#401	C₂²×C₃₁	1	2	yes	complemented
591	#400	C₂²×C₃₁	1	2	yes	complemented
592	#400	C₂²×C₃₁	1	2	yes	complemented
593	#399	C₂²×C₃₁	1	2	yes	—
594	#398	C₂²×C₃₁	1	2	yes	complemented
595	#397	C₂²×C₃₁	1	2	yes	—
596	#397	C₂²×C₃₁	1	2	yes	—
597	#397	C₂²×C₃₁	1	2	yes	complemented
598	#397	C₂²×C₃₁	1	2	yes	complemented
599	#396	C₂²×C₃₁	1	2	yes	complemented
600	#394	C₂²×C₃₁	1	2	yes	—
601	#394	C₂²×C₃₁	1	2	yes	—
602	#394	C₂²×C₃₁	1	2	yes	—
603	#394	C₂²×C₃₁	1	2	yes	—
604	#393	C₂²×C₃₁	1	2	yes	—
605	#393	C₂²×C₃₁	1	2	yes	complemented
606	#391	C₂²×C₃₁	1	2	yes	complemented
607	#391	C₂²×C₃₁	1	2	yes	complemented
608	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	#390	C₂²×C₃₁	1	2	yes	—
611	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#389	C₂²×C₃₁	1	2	yes	complemented
614	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#388	C₂²×C₃₁	1	2	yes	—
619	#388	C₂²×C₃₁	1	2	yes	—
620	#388	C₂²×C₃₁	1	2	yes	—
621	#388	C₂²×C₃₁	1	2	yes	—
622	#388	C₂²×C₃₁	1	2	yes	complemented
623	#388	C₂²×C₃₁	1	2	yes	complemented
624	#388	C₂²×C₃₁	1	2	yes	complemented
625	#388	C₂²×C₃₁	1	2	yes	complemented
626	#388	C₂²×C₃₁	1	2	yes	complemented
627	#387	C₂²×C₃₁	1	2	yes	complemented
628	#387	C₂²×C₃₁	1	2	yes	complemented
629	#387	C₂²×C₃₁	1	2	yes	complemented
630	#386	C₂²×C₃₁	1	2	yes	—
631	#386	C₂²×C₃₁	1	2	yes	—
632	#386	C₂²×C₃₁	1	2	yes	—
633	#386	C₂²×C₃₁	1	2	yes	—
634	#386	C₂²×C₃₁	1	2	yes	—
635	#386	C₂²×C₃₁	1	2	yes	—
636	#386	C₂²×C₃₁	1	2	yes	—
637	#385	C₂²×C₃₁	1	2	yes	—
638	#385	C₂²×C₃₁	1	2	yes	—
639	#385	C₂²×C₃₁	1	2	yes	—
640	#385	C₂²×C₃₁	1	2	yes	—
641	#385	C₂²×C₃₁	1	2	yes	complemented
642	#384	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#383	C₂²×C₃₁	1	2	yes	complemented
644	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#380	C₂²×C₃₁	1	1	yes	characteristic
646	#380	C₂²×C₃₁	1	1	yes	characteristic
647	#380	C₂²×C₃₁	1	1	yes	characteristic
648	#380	C₂²×C₃₁	1	1	yes	characteristic
649	#380	C₂²×C₃₁	1	1	yes	characteristic
650	#380	C₂²×C₃₁	1	1	yes	characteristic
651	#380	C₂²×C₃₁	1	2	yes	—
652	#380	C₂²×C₃₁	1	2	yes	complemented
653	#379	C₂²×C₃₁	1	2	yes	—
654	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
655	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
658	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
659	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
660	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
661	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
662	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
663	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
664	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
665	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
666	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
667	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
668	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
669	C₂×C₃₁	—	2	4	no	—
670	C₂×C₃₁	—	4	2	no	—
671	C₂×C₃₁	—	4	2	no	—
672	C₂×C₃₁	—	8	2	no	—
673	C₂×C₃₁	#3444	1	1	yes	characteristic
674	C₂×C₃₁	C₂×#538	1	1	yes	characteristic
675	C₂×C₃₁	C₂×#542	1	1	yes	characteristic
676	C₂×C₃₁	#3519	1	1	yes	characteristic
677	C₂×C₃₁	#3519	1	1	yes	characteristic
678	C₂×C₃₁	#3520	1	1	yes	characteristic
679	C₂×C₃₁	#3520	1	1	yes	characteristic
680	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
681	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
682	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
683	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
684	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
685	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
686	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
687	C₂³×C₄	—	2	4	no	—
688	C₂³×C₄	—	4	2	no	—
689	C₂³×C₄	—	4	2	no	—
690	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
691	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
693	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
694	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
698	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
699	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
700	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
701	C₄⋊Q₈	—	4	2	no	—
702	#124	—	2	8	no	—
703	#124	—	4	2	no	—
704	#123	—	2	8	no	—
705	C₂²⋊Q₈	—	2	4	no	—
706	C₂²⋊Q₈	—	4	4	no	—
707	C₂²⋊Q₈	—	4	2	no	—
708	C₂²⋊Q₈	—	4	2	no	—
709	#121	—	2	4	no	—
710	#121	—	4	2	no	—
711	#121	—	4	2	no	—
712	#120	—	4	4	no	—
713	C₄×Q₈	—	4	2	no	—
714	C₄×D₄	—	4	2	no	—
715	C₄×D₄	—	4	4	no	—
716	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
733	C₂×C₂²⋊C₄	—	2	4	no	—
734	C₂×C₂²⋊C₄	—	2	4	no	—
735	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
762	C₂×C₄²	—	4	2	no	—
763	C₂×C₄²	—	4	2	no	—
764	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
765	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
767	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
770	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
771	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
775	#95	C₂³×C₃₁	1	1	yes	characteristic
776	#95	C₂³×C₃₁	1	1	yes	characteristic
777	#95	C₂³×C₃₁	1	1	yes	characteristic
778	#95	C₂³×C₃₁	1	1	yes	characteristic
779	#95	C₂³×C₃₁	1	1	yes	characteristic
780	#95	C₂³×C₃₁	1	1	yes	characteristic
781	#95	C₂³×C₃₁	1	1	yes	characteristic
782	#95	C₂³×C₃₁	1	1	yes	characteristic
783	#95	C₂³×C₃₁	1	2	yes	—
784	#95	C₂³×C₃₁	1	2	yes	—
785	#95	C₂³×C₃₁	1	2	yes	—
786	#95	C₂³×C₃₁	1	2	yes	—
787	#95	C₂³×C₃₁	1	2	yes	—
788	#95	C₂³×C₃₁	1	2	yes	—
789	#95	C₂³×C₃₁	1	2	yes	—
790	#95	C₂³×C₃₁	1	2	yes	—
791	#95	C₂³×C₃₁	1	2	yes	—
792	#95	C₂³×C₃₁	1	2	yes	—
793	#95	C₂³×C₃₁	1	2	yes	—
794	#95	C₂³×C₃₁	1	2	yes	—
795	#95	C₂³×C₃₁	1	2	yes	—
796	#95	C₂³×C₃₁	1	2	yes	—
797	#95	C₂³×C₃₁	1	2	yes	—
798	#95	C₂³×C₃₁	1	2	yes	—
799	#95	C₂³×C₃₁	1	2	yes	—
800	#95	C₂³×C₃₁	1	2	yes	—
801	C₃₁	#35080	1	1	yes	characteristic, direct product factor, Sylow
802	C₂⁴	—	2	2	no	—
803	C₂⁴	—	2	2	no	—
804	C₂⁴	—	2	2	no	—
805	C₂⁴	—	2	2	no	—
806	C₂⁴	—	2	2	no	—
807	C₂⁴	—	4	1	no	—
808	C₂⁴	—	4	1	no	—
809	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
810	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
811	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
812	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
813	C₂×Q₈	—	2	2	no	—
814	C₂×Q₈	—	2	4	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	4	2	no	—
818	C₂×Q₈	—	4	2	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	4	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	4	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	1	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	1	no	—
859	C₂²×C₄	—	4	1	no	—
860	C₂²×C₄	—	4	1	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	16	no	—
864	C₂²×C₄	#41×C₃₁	1	4	yes	—
865	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	4	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	4	2	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	2	no	—
896	C₄⋊C₄	—	4	2	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	—	4	2	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
927	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
928	C₄²	—	2	4	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	2	2	no	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	2	no	—
933	C₄²	—	4	1	no	—
934	C₄²	—	4	1	no	—
935	C₄²	—	4	1	no	—
936	C₄²	—	4	1	no	—
937	C₄²	—	4	2	no	—
938	C₄²	—	4	2	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	8	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	4	4	no	—
964	C₂³	—	4	4	no	—
965	C₂³	—	4	4	no	—
966	C₂³	—	4	4	no	—
967	C₂³	—	4	4	no	—
968	C₂³	—	4	4	no	—
969	C₂³	C₂×#41×C₃₁	1	2	yes	—
970	C₂³	C₂×#41×C₃₁	1	2	yes	—
971	C₂³	C₂×#41×C₃₁	1	2	yes	—
972	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
973	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
974	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
975	Q₈	—	4	4	no	—
976	Q₈	—	8	4	no	—
977	D₄	—	4	8	no	—
978	D₄	—	4	4	no	—
979	D₄	—	8	4	no	—
980	D₄	—	8	4	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	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	1	no	—
991	C₂×C₄	—	2	8	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	4	4	no	—
1037	C₂×C₄	—	4	4	no	—
1038	C₂×C₄	—	4	4	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	8	4	no	—
1041	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1042	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1043	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1044	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1045	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1046	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1047	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1048	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	4	16	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	C₃₁×#542	1	4	yes	—
1078	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1079	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1080	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1081	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1082	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1083	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1084	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	C₃₁×#538	1	4	yes	—
1104	C₂	—	2	4	no	—
1105	C₂	—	4	2	no	—
1106	C₂	—	4	2	no	—
1107	C₂	—	8	2	no	—
1108	C₂	C₃₁×#3444	1	1	yes	characteristic
1109	C₂	C₂×C₃₁×#538	1	1	yes	characteristic
1110	C₂	C₂×C₃₁×#542	1	1	yes	characteristic
1111	C₂	C₃₁×#3519	1	1	yes	characteristic
1112	C₂	C₃₁×#3519	1	1	yes	characteristic
1113	C₂	C₃₁×#3520	1	1	yes	characteristic
1114	C₂	C₃₁×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₃₁×#2847	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2857	C₂	semidirect
2. C₃₁×#2850	C₂	semidirect
3. C₃₁×#2848	C₂	semidirect
5. C₃₁×#2653	C₂	semidirect
6. C₃₁×#2649	C₂	semidirect
7. C₃₁×#2510	C₂	semidirect
8. C₃₁×#2495	C₂	semidirect
9. C₃₁×#2494	C₂	semidirect
10. C₃₁×#2492	C₂	semidirect
11. C₃₁×#2491	C₂	semidirect
12. C₃₁×#2472	C₂	semidirect
13. C₃₁×#2450	C₂	semidirect
14. C₃₁×#2427	C₂	semidirect
15. C₃₁×#2426	C₂	semidirect
16. C₃₁×#2423	C₂	semidirect
17. C₃₁×#2422	C₂	semidirect
18. C₃₁×#2418	C₂	semidirect
19. C₃₁×#2337	C₂	semidirect
20. C₃₁×#2335	C₂	semidirect
21. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
22. C₄×C₃₁×#121	C₂	semidirect
23. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
25. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₃₁×#124	C₂²	semidirect
37. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
39. C₂×C₄×D₄×C₃₁	C₂²	semidirect
44. C₃₁×#401	C₂²	semidirect
45. C₃₁×#400	C₂²	semidirect
46. C₃₁×#400	C₂²	semidirect
48. C₃₁×#398	C₂²	semidirect
51. C₃₁×#397	C₂²	semidirect
52. C₃₁×#397	C₂²	semidirect
53. C₃₁×#396	C₂²	semidirect
59. C₃₁×#393	C₂²	semidirect
60. C₃₁×#391	C₂²	semidirect
61. C₃₁×#391	C₂²	semidirect
62. C₃₁×#391	C₂²	semidirect
63. C₃₁×#391	C₂²	semidirect
65. C₃₁×#390	C₂²	semidirect
66. C₃₁×#390	C₂²	semidirect
67. C₃₁×#389	C₂²	semidirect
68. C₃₁×#389	C₂²	semidirect
69. C₃₁×#389	C₂²	semidirect
70. C₃₁×#389	C₂²	semidirect
71. C₃₁×#389	C₂²	semidirect
76. C₃₁×#388	C₂²	semidirect
77. C₃₁×#388	C₂²	semidirect
78. C₃₁×#388	C₂²	semidirect
79. C₃₁×#388	C₂²	semidirect
80. C₃₁×#388	C₂²	semidirect
81. C₃₁×#387	C₂²	semidirect
82. C₃₁×#387	C₂²	semidirect
83. C₃₁×#387	C₂²	semidirect
95. C₃₁×#385	C₂²	semidirect
96. C₃₁×#384	C₂²	semidirect
97. C₃₁×#383	C₂²	semidirect
98. C₃₁×#382	C₂²	semidirect
106. C₃₁×#380	C₂²	semidirect
108. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
109. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
110. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
381. #35080	C₃₁	direct (N × H)
492. #2857	C₂×C₃₁	semidirect
493. #2850	C₂×C₃₁	semidirect
494. #2848	C₂×C₃₁	semidirect
496. #2653	C₂×C₃₁	semidirect
497. #2649	C₂×C₃₁	semidirect
498. #2510	C₂×C₃₁	semidirect
499. #2495	C₂×C₃₁	semidirect
500. #2494	C₂×C₃₁	semidirect
501. #2492	C₂×C₃₁	semidirect
502. #2491	C₂×C₃₁	semidirect
503. #2472	C₂×C₃₁	semidirect
504. #2450	C₂×C₃₁	semidirect
505. #2427	C₂×C₃₁	semidirect
506. #2426	C₂×C₃₁	semidirect
507. #2423	C₂×C₃₁	semidirect
508. #2422	C₂×C₃₁	semidirect
509. #2418	C₂×C₃₁	semidirect
510. #2337	C₂×C₃₁	semidirect
511. #2335	C₂×C₃₁	semidirect
512. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
513. C₄×#121	C₂×C₃₁	semidirect
514. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
571. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
573. C₂×#124	C₂²×C₃₁	semidirect
583. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
585. C₂×C₄×D₄	C₂²×C₃₁	semidirect
590. #401	C₂²×C₃₁	semidirect
591. #400	C₂²×C₃₁	semidirect
592. #400	C₂²×C₃₁	semidirect
594. #398	C₂²×C₃₁	semidirect
597. #397	C₂²×C₃₁	semidirect
598. #397	C₂²×C₃₁	semidirect
599. #396	C₂²×C₃₁	semidirect
605. #393	C₂²×C₃₁	semidirect
606. #391	C₂²×C₃₁	semidirect
607. #391	C₂²×C₃₁	semidirect
608. #391	C₂²×C₃₁	semidirect
609. #391	C₂²×C₃₁	semidirect
611. #390	C₂²×C₃₁	semidirect
612. #390	C₂²×C₃₁	semidirect
613. #389	C₂²×C₃₁	semidirect
614. #389	C₂²×C₃₁	semidirect
615. #389	C₂²×C₃₁	semidirect
616. #389	C₂²×C₃₁	semidirect
617. #389	C₂²×C₃₁	semidirect
622. #388	C₂²×C₃₁	semidirect
623. #388	C₂²×C₃₁	semidirect
624. #388	C₂²×C₃₁	semidirect
625. #388	C₂²×C₃₁	semidirect
626. #388	C₂²×C₃₁	semidirect
627. #387	C₂²×C₃₁	semidirect
628. #387	C₂²×C₃₁	semidirect
629. #387	C₂²×C₃₁	semidirect
641. #385	C₂²×C₃₁	semidirect
642. #384	C₂²×C₃₁	semidirect
643. #383	C₂²×C₃₁	semidirect
644. #382	C₂²×C₃₁	semidirect
652. #380	C₂²×C₃₁	semidirect
654. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
655. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
656. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
666. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
801. C₃₁	#35080	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2857	2
C₃₁×#2850	2
C₃₁×#2848	2
C₃₁×#2847	2
C₃₁×#2653	2
C₃₁×#2649	2
C₃₁×#2510	2
C₃₁×#2495	2
C₃₁×#2494	2
C₃₁×#2492	2
C₃₁×#2491	2
C₃₁×#2472	2
C₃₁×#2450	2
C₃₁×#2427	2
C₃₁×#2426	2
C₃₁×#2423	2
C₃₁×#2422	2
C₃₁×#2418	2
C₃₁×#2337	2
C₃₁×#2335	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#121	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#35080	31

Subgroups — C31×#35080 #21491839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35080 #21491839