Subgroups — C₃₁×#34471 #21491230

Order 7936.

3112 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2377	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2375	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2358	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2333	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2328	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2309	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2308	C₂	1	2	yes	maximal, complemented
21	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
25	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
26	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
27	D₄²×C₃₁	C₄	1	16	yes	complemented
28	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#121	C₂²	1	2	yes	—
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#120	C₂²	1	2	yes	—
33	C₂×C₃₁×#120	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
37	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
47	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
48	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
50	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#390	C₂²	1	1	yes	characteristic
52	C₃₁×#390	C₂²	1	1	yes	characteristic
53	C₃₁×#390	C₂²	1	1	yes	characteristic
54	C₃₁×#390	C₂²	1	1	yes	characteristic
55	C₃₁×#390	C₂²	1	2	yes	complemented
56	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#390	C₂²	1	2	yes	complemented
58	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#390	C₂²	1	2	yes	complemented
60	C₃₁×#390	C₂²	1	2	yes	complemented
61	C₃₁×#390	C₂²	1	2	yes	complemented
62	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#390	C₂²	1	2	yes	complemented
64	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#390	C₂²	1	2	yes	complemented
66	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#388	C₂²	1	2	yes	complemented
69	C₃₁×#388	C₂²	1	2	yes	complemented
70	C₃₁×#388	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#388	C₂²	1	2	yes	complemented
72	C₃₁×#388	C₂²	1	2	yes	complemented
73	C₃₁×#388	C₂²	1	2	yes	complemented
74	C₃₁×#388	C₂²	1	2	yes	complemented
75	C₃₁×#388	C₂²	1	2	yes	complemented
76	C₃₁×#388	C₂²	1	2	yes	complemented
77	C₃₁×#388	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#388	C₂²	1	2	yes	complemented
79	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#387	C₂²	1	2	yes	complemented
81	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#386	C₂²	1	1	yes	characteristic
83	C₃₁×#386	C₂²	1	2	yes	—
84	C₃₁×#386	C₂²	1	1	yes	characteristic
85	C₃₁×#386	C₂²	1	2	yes	complemented
86	C₃₁×#386	C₂²	1	2	yes	complemented
87	C₃₁×#386	C₂²	1	2	yes	complemented
88	C₃₁×#386	C₂²	1	2	yes	complemented
89	C₃₁×#386	C₂²	1	2	yes	complemented
90	C₃₁×#386	C₂²	1	2	yes	complemented
91	C₃₁×#386	C₂²	1	2	yes	complemented
92	C₃₁×#386	C₂²	1	2	yes	complemented
93	C₃₁×#386	C₂²	1	2	yes	complemented
94	C₃₁×#386	C₂²	1	2	yes	complemented
95	C₃₁×#386	C₂²	1	2	yes	complemented
96	C₃₁×#386	C₂²	1	2	yes	complemented
97	C₃₁×#386	C₂²	1	2	yes	complemented
98	C₃₁×#386	C₂²	1	2	yes	complemented
99	C₃₁×#385	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#385	C₂²	1	2	yes	complemented
101	C₃₁×#385	C₂²	1	2	yes	complemented
102	C₃₁×#385	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#381	C₂²	1	2	yes	complemented
105	C₃₁×#381	C₂²	1	2	yes	complemented
106	C₃₁×#380	C₂²	1	2	yes	complemented
107	C₃₁×#380	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#380	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#379	C₂²	1	2	yes	complemented
110	C₃₁×#379	C₂²	1	2	yes	complemented
111	C₃₁×#379	C₂²	1	2	yes	complemented
112	C₃₁×#379	C₂²	1	2	yes	complemented
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#376	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₃₁	C₂³	1	2	yes	—
125	C₂⁵×C₃₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₃₁	—	4	2	no	—
127	C₂²×D₄×C₃₁	—	4	2	no	—
128	C₂²×D₄×C₃₁	—	4	2	no	—
129	C₂²×D₄×C₃₁	—	4	2	no	—
130	C₂²×D₄×C₃₁	—	4	4	no	—
131	C₂²×D₄×C₃₁	—	4	4	no	—
132	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
133	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
134	C₂²×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
135	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
138	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
150	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
151	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
152	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
153	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
154	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
155	C₃₁×#127	C₂×C₄	1	8	yes	complemented
156	C₃₁×#121	C₂×C₄	1	8	yes	complemented
157	C₃₁×#121	C₂×C₄	1	8	yes	complemented
158	C₃₁×#121	C₂×C₄	1	16	yes	complemented
159	C₃₁×#120	C₂×C₄	1	16	yes	complemented
160	C₃₁×#120	C₂×C₄	1	16	yes	complemented
161	C₄×D₄×C₃₁	—	4	2	no	—
162	C₄×D₄×C₃₁	—	4	2	no	—
163	C₄×D₄×C₃₁	—	4	2	no	—
164	C₄×D₄×C₃₁	—	4	2	no	—
165	C₄×D₄×C₃₁	—	4	4	no	—
166	C₄×D₄×C₃₁	—	4	4	no	—
167	C₄×D₄×C₃₁	—	4	4	no	—
168	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
169	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
170	C₃₁×#117	—	4	2	no	—
171	C₃₁×#117	—	4	2	no	—
172	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
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	1	yes	characteristic
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
187	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
188	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
189	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
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	1	yes	characteristic
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	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
224	C₂×C₄²×C₃₁	—	4	2	no	—
225	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
232	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
233	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
234	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
235	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
241	C₃₁×#95	C₂³	1	1	yes	characteristic
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	C₃₁×#95	C₂³	1	2	yes	—
247	C₃₁×#95	C₂³	1	2	yes	—
248	C₃₁×#95	C₂³	1	1	yes	characteristic
249	C₃₁×#95	C₂³	1	1	yes	characteristic
250	C₃₁×#95	C₂³	1	1	yes	characteristic
251	C₃₁×#95	C₂³	1	2	yes	—
252	C₃₁×#95	C₂³	1	1	yes	characteristic
253	C₃₁×#95	C₂³	1	2	yes	—
254	C₃₁×#95	C₂³	1	2	yes	—
255	C₂⁴×C₃₁	—	2	4	no	—
256	C₂⁴×C₃₁	—	2	4	no	—
257	C₂⁴×C₃₁	—	4	2	no	—
258	C₂⁴×C₃₁	—	4	2	no	—
259	C₂⁴×C₃₁	—	4	2	no	—
260	C₂⁴×C₃₁	—	4	2	no	—
261	C₂⁴×C₃₁	—	4	2	no	—
262	C₂⁴×C₃₁	—	4	2	no	—
263	C₂⁴×C₃₁	—	4	2	no	—
264	C₂⁴×C₃₁	—	4	2	no	—
265	C₂⁴×C₃₁	—	4	2	no	—
266	C₂⁴×C₃₁	—	4	2	no	—
267	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
268	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
269	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
270	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
271	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
272	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
273	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂×D₄×C₃₁	—	2	4	no	—
275	C₂×D₄×C₃₁	—	2	4	no	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	2	2	no	—
279	C₂×D₄×C₃₁	—	2	2	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	2	2	no	—
282	C₂×D₄×C₃₁	—	2	2	no	—
283	C₂×D₄×C₃₁	—	2	2	no	—
284	C₂×D₄×C₃₁	—	4	16	no	—
285	C₂×D₄×C₃₁	—	4	16	no	—
286	C₂×D₄×C₃₁	—	4	2	no	—
287	C₂×D₄×C₃₁	—	4	2	no	—
288	C₂×D₄×C₃₁	—	4	2	no	—
289	C₂×D₄×C₃₁	—	4	2	no	—
290	C₂×D₄×C₃₁	—	4	2	no	—
291	C₂×D₄×C₃₁	—	4	2	no	—
292	C₂×D₄×C₃₁	—	4	2	no	—
293	C₂×D₄×C₃₁	—	4	2	no	—
294	C₂×D₄×C₃₁	—	4	2	no	—
295	C₂×D₄×C₃₁	—	4	2	no	—
296	C₂×D₄×C₃₁	—	4	32	no	—
297	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
298	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
299	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
300	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
301	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
302	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
303	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
304	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
305	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
306	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
307	C₂²×C₄×C₃₁	—	2	2	no	—
308	C₂²×C₄×C₃₁	—	2	2	no	—
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	—	2	2	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	—	2	2	no	—
313	C₂²×C₄×C₃₁	—	2	4	no	—
314	C₂²×C₄×C₃₁	—	2	2	no	—
315	C₂²×C₄×C₃₁	—	2	4	no	—
316	C₂²×C₄×C₃₁	—	4	1	no	—
317	C₂²×C₄×C₃₁	—	4	1	no	—
318	C₂²×C₄×C₃₁	—	4	1	no	—
319	C₂²×C₄×C₃₁	—	4	2	no	—
320	C₂²×C₄×C₃₁	—	4	2	no	—
321	C₂²×C₄×C₃₁	—	4	2	no	—
322	C₂²×C₄×C₃₁	—	4	2	no	—
323	C₂²×C₄×C₃₁	—	4	2	no	—
324	C₂²×C₄×C₃₁	—	4	2	no	—
325	C₂²×C₄×C₃₁	—	4	2	no	—
326	C₂²×C₄×C₃₁	—	4	2	no	—
327	C₂²×C₄×C₃₁	—	4	2	no	—
328	C₂²×C₄×C₃₁	—	4	2	no	—
329	C₂²×C₄×C₃₁	—	4	2	no	—
330	C₂²×C₄×C₃₁	—	4	2	no	—
331	C₂²×C₄×C₃₁	—	4	2	no	—
332	C₂²×C₄×C₃₁	—	4	2	no	—
333	C₂²×C₄×C₃₁	—	4	2	no	—
334	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
335	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
336	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
337	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	4	2	no	—
361	C₄⋊C₄×C₃₁	—	4	1	no	—
362	C₄⋊C₄×C₃₁	—	4	1	no	—
363	C₄⋊C₄×C₃₁	—	4	1	no	—
364	C₄⋊C₄×C₃₁	—	4	2	no	—
365	C₄⋊C₄×C₃₁	—	4	2	no	—
366	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
367	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	4	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	4	no	—
373	C₂²⋊C₄×C₃₁	—	2	4	no	—
374	C₂²⋊C₄×C₃₁	—	4	2	no	—
375	C₂²⋊C₄×C₃₁	—	4	2	no	—
376	C₂²⋊C₄×C₃₁	—	4	2	no	—
377	C₂²⋊C₄×C₃₁	—	4	2	no	—
378	C₂²⋊C₄×C₃₁	—	4	2	no	—
379	C₂²⋊C₄×C₃₁	—	4	2	no	—
380	C₂²⋊C₄×C₃₁	—	4	2	no	—
381	C₂²⋊C₄×C₃₁	—	4	2	no	—
382	C₂²⋊C₄×C₃₁	—	4	2	no	—
383	C₂²⋊C₄×C₃₁	—	4	2	no	—
384	C₂²⋊C₄×C₃₁	—	4	2	no	—
385	C₂²⋊C₄×C₃₁	—	4	2	no	—
386	C₂²⋊C₄×C₃₁	—	4	1	no	—
387	C₂²⋊C₄×C₃₁	—	4	1	no	—
388	C₂²⋊C₄×C₃₁	—	4	1	no	—
389	C₂²⋊C₄×C₃₁	—	4	2	no	—
390	C₂²⋊C₄×C₃₁	—	4	2	no	—
391	C₂²⋊C₄×C₃₁	—	4	2	no	—
392	C₂²⋊C₄×C₃₁	—	4	2	no	—
393	C₂²⋊C₄×C₃₁	—	4	2	no	—
394	C₂²⋊C₄×C₃₁	—	4	2	no	—
395	C₂²⋊C₄×C₃₁	—	4	2	no	—
396	C₂²⋊C₄×C₃₁	—	4	2	no	—
397	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
398	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
399	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
400	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
401	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
402	C₄²×C₃₁	—	2	2	no	—
403	C₄²×C₃₁	—	2	2	no	—
404	C₄²×C₃₁	—	2	2	no	—
405	C₄²×C₃₁	—	2	2	no	—
406	C₄²×C₃₁	—	4	1	no	—
407	C₄²×C₃₁	—	4	1	no	—
408	C₄²×C₃₁	—	4	2	no	—
409	C₄²×C₃₁	—	4	2	no	—
410	C₄²×C₃₁	—	4	2	no	—
411	C₄²×C₃₁	—	4	2	no	—
412	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
413	#34471	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₂³×C₃₁	—	2	1	no	—
415	C₂³×C₃₁	—	2	1	no	—
416	C₂³×C₃₁	—	2	1	no	—
417	C₂³×C₃₁	—	2	1	no	—
418	C₂³×C₃₁	—	2	1	no	—
419	C₂³×C₃₁	—	2	2	no	—
420	C₂³×C₃₁	—	2	2	no	—
421	C₂³×C₃₁	—	2	1	no	—
422	C₂³×C₃₁	—	2	1	no	—
423	C₂³×C₃₁	—	2	2	no	—
424	C₂³×C₃₁	—	2	2	no	—
425	C₂³×C₃₁	—	2	2	no	—
426	C₂³×C₃₁	—	2	2	no	—
427	C₂³×C₃₁	—	2	2	no	—
428	C₂³×C₃₁	—	2	2	no	—
429	C₂³×C₃₁	—	2	2	no	—
430	C₂³×C₃₁	—	2	2	no	—
431	C₂³×C₃₁	—	2	2	no	—
432	C₂³×C₃₁	—	2	2	no	—
433	C₂³×C₃₁	—	2	2	no	—
434	C₂³×C₃₁	—	2	2	no	—
435	C₂³×C₃₁	—	2	1	no	—
436	C₂³×C₃₁	—	2	1	no	—
437	C₂³×C₃₁	—	2	2	no	—
438	C₂³×C₃₁	—	2	2	no	—
439	C₂³×C₃₁	—	2	1	no	—
440	C₂³×C₃₁	—	2	2	no	—
441	C₂³×C₃₁	—	2	2	no	—
442	C₂³×C₃₁	—	2	16	no	—
443	C₂³×C₃₁	—	4	8	no	—
444	C₂³×C₃₁	—	4	8	no	—
445	C₂³×C₃₁	—	4	8	no	—
446	C₂³×C₃₁	—	4	8	no	—
447	C₂³×C₃₁	—	4	8	no	—
448	C₂³×C₃₁	—	8	4	no	—
449	C₂³×C₃₁	—	8	4	no	—
450	C₂³×C₃₁	—	8	4	no	—
451	C₂³×C₃₁	—	8	4	no	—
452	C₂³×C₃₁	—	8	4	no	—
453	C₂³×C₃₁	—	8	4	no	—
454	C₂³×C₃₁	—	8	4	no	—
455	C₂³×C₃₁	—	8	4	no	—
456	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
457	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
458	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
459	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
460	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
461	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
462	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
463	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
464	D₄×C₃₁	—	2	8	no	—
465	D₄×C₃₁	—	2	16	no	—
466	D₄×C₃₁	—	2	8	no	—
467	D₄×C₃₁	—	2	8	no	—
468	D₄×C₃₁	—	2	8	no	—
469	D₄×C₃₁	—	4	8	no	—
470	D₄×C₃₁	—	4	8	no	—
471	D₄×C₃₁	—	4	8	no	—
472	D₄×C₃₁	—	4	8	no	—
473	D₄×C₃₁	—	4	8	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	1	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	8	no	—
487	C₂×C₄×C₃₁	—	2	8	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	2	2	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	2	no	—
512	C₂×C₄×C₃₁	—	2	2	no	—
513	C₂×C₄×C₃₁	—	2	1	no	—
514	C₂×C₄×C₃₁	—	2	1	no	—
515	C₂×C₄×C₃₁	—	2	2	no	—
516	C₂×C₄×C₃₁	—	2	1	no	—
517	C₂×C₄×C₃₁	—	2	1	no	—
518	C₂×C₄×C₃₁	—	2	2	no	—
519	C₂×C₄×C₃₁	—	2	1	no	—
520	C₂×C₄×C₃₁	—	2	1	no	—
521	C₂×C₄×C₃₁	—	4	8	no	—
522	C₂×C₄×C₃₁	—	4	4	no	—
523	C₂×C₄×C₃₁	—	4	4	no	—
524	C₂×C₄×C₃₁	—	8	4	no	—
525	C₂×C₄×C₃₁	—	8	4	no	—
526	C₂×C₄×C₃₁	—	8	4	no	—
527	C₂×C₄×C₃₁	—	8	4	no	—
528	C₂×C₄×C₃₁	—	8	4	no	—
529	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
530	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
531	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
532	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
533	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
534	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
535	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
536	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
537	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
538	C₂×D₄²	C₂×C₃₁	1	1	yes	characteristic
539	#2377	C₂×C₃₁	1	2	yes	complemented
540	#2375	C₂×C₃₁	1	2	yes	complemented
541	#2366	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#2363	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#2361	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#2358	C₂×C₃₁	1	2	yes	complemented
545	#2357	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#2352	C₂×C₃₁	1	1	yes	characteristic, complemented
547	D₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
548	D₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
549	D₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#2333	C₂×C₃₁	1	2	yes	complemented
551	#2328	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#2324	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#2321	C₂×C₃₁	1	2	yes	complemented
554	#2321	C₂×C₃₁	1	2	yes	complemented
555	#2319	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#2309	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#2308	C₂×C₃₁	1	2	yes	complemented
558	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
559	C₂×#390	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#2290	C₂×C₃₁	1	1	yes	characteristic, complemented
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	2	2	no	—
565	C₂²×C₃₁	—	2	2	no	—
566	C₂²×C₃₁	—	2	2	no	—
567	C₂²×C₃₁	—	2	2	no	—
568	C₂²×C₃₁	—	2	4	no	—
569	C₂²×C₃₁	—	2	2	no	—
570	C₂²×C₃₁	—	2	4	no	—
571	C₂²×C₃₁	—	2	4	no	—
572	C₂²×C₃₁	—	2	4	no	—
573	C₂²×C₃₁	—	2	4	no	—
574	C₂²×C₃₁	—	2	4	no	—
575	C₂²×C₃₁	—	2	4	no	—
576	C₂²×C₃₁	—	2	4	no	—
577	C₂²×C₃₁	—	2	2	no	—
578	C₂²×C₃₁	—	2	4	no	—
579	C₂²×C₃₁	—	4	2	no	—
580	C₂²×C₃₁	—	4	2	no	—
581	C₂²×C₃₁	—	4	1	no	—
582	C₂²×C₃₁	—	4	2	no	—
583	C₂²×C₃₁	—	4	2	no	—
584	C₂²×C₃₁	—	4	2	no	—
585	C₂²×C₃₁	—	4	1	no	—
586	C₂²×C₃₁	—	4	2	no	—
587	C₂²×C₃₁	—	4	2	no	—
588	C₂²×C₃₁	—	4	2	no	—
589	C₂²×C₃₁	—	4	1	no	—
590	C₂²×C₃₁	—	4	2	no	—
591	C₂²×C₃₁	—	4	2	no	—
592	C₂²×C₃₁	—	4	2	no	—
593	C₂²×C₃₁	—	4	1	no	—
594	C₂²×C₃₁	—	4	2	no	—
595	C₂²×C₃₁	—	8	16	no	—
596	C₂²×C₃₁	—	8	16	no	—
597	C₂²×C₃₁	#518	1	4	yes	—
598	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
599	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
600	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
603	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	C₂²×C₃₁	#585	1	1	yes	characteristic
605	C₄×C₃₁	—	2	2	no	—
606	C₄×C₃₁	—	2	2	no	—
607	C₄×C₃₁	—	2	2	no	—
608	C₄×C₃₁	—	2	4	no	—
609	C₄×C₃₁	—	2	2	no	—
610	C₄×C₃₁	—	2	2	no	—
611	C₄×C₃₁	—	4	1	no	—
612	C₄×C₃₁	—	4	1	no	—
613	C₄×C₃₁	—	4	2	no	—
614	C₄×C₃₁	—	4	1	no	—
615	C₄×C₃₁	—	4	1	no	—
616	C₄×C₃₁	—	4	1	no	—
617	C₄×C₃₁	—	4	2	no	—
618	C₄×C₃₁	—	4	1	no	—
619	C₄×C₃₁	—	4	2	no	—
620	C₄×C₃₁	—	4	2	no	—
621	C₄×C₃₁	—	4	1	no	—
622	C₄×C₃₁	#518	1	4	yes	—
623	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
624	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
625	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
626	D₄²	C₄×C₃₁	1	16	yes	complemented
627	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
628	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
629	C₂×#121	C₂²×C₃₁	1	2	yes	—
630	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
631	C₂×#120	C₂²×C₃₁	1	2	yes	—
632	C₂×#120	C₂²×C₃₁	1	2	yes	—
633	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
634	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
635	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
636	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
637	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
641	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
646	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
647	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
648	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
649	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#390	C₂²×C₃₁	1	1	yes	characteristic
651	#390	C₂²×C₃₁	1	1	yes	characteristic
652	#390	C₂²×C₃₁	1	1	yes	characteristic
653	#390	C₂²×C₃₁	1	1	yes	characteristic
654	#390	C₂²×C₃₁	1	2	yes	complemented
655	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#390	C₂²×C₃₁	1	2	yes	complemented
657	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#390	C₂²×C₃₁	1	2	yes	complemented
659	#390	C₂²×C₃₁	1	2	yes	complemented
660	#390	C₂²×C₃₁	1	2	yes	complemented
661	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#390	C₂²×C₃₁	1	2	yes	complemented
663	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	#390	C₂²×C₃₁	1	2	yes	complemented
665	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#388	C₂²×C₃₁	1	2	yes	complemented
668	#388	C₂²×C₃₁	1	2	yes	complemented
669	#388	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#388	C₂²×C₃₁	1	2	yes	complemented
671	#388	C₂²×C₃₁	1	2	yes	complemented
672	#388	C₂²×C₃₁	1	2	yes	complemented
673	#388	C₂²×C₃₁	1	2	yes	complemented
674	#388	C₂²×C₃₁	1	2	yes	complemented
675	#388	C₂²×C₃₁	1	2	yes	complemented
676	#388	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#388	C₂²×C₃₁	1	2	yes	complemented
678	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#387	C₂²×C₃₁	1	2	yes	complemented
680	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#386	C₂²×C₃₁	1	1	yes	characteristic
682	#386	C₂²×C₃₁	1	2	yes	—
683	#386	C₂²×C₃₁	1	1	yes	characteristic
684	#386	C₂²×C₃₁	1	2	yes	complemented
685	#386	C₂²×C₃₁	1	2	yes	complemented
686	#386	C₂²×C₃₁	1	2	yes	complemented
687	#386	C₂²×C₃₁	1	2	yes	complemented
688	#386	C₂²×C₃₁	1	2	yes	complemented
689	#386	C₂²×C₃₁	1	2	yes	complemented
690	#386	C₂²×C₃₁	1	2	yes	complemented
691	#386	C₂²×C₃₁	1	2	yes	complemented
692	#386	C₂²×C₃₁	1	2	yes	complemented
693	#386	C₂²×C₃₁	1	2	yes	complemented
694	#386	C₂²×C₃₁	1	2	yes	complemented
695	#386	C₂²×C₃₁	1	2	yes	complemented
696	#386	C₂²×C₃₁	1	2	yes	complemented
697	#386	C₂²×C₃₁	1	2	yes	complemented
698	#385	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#385	C₂²×C₃₁	1	2	yes	complemented
700	#385	C₂²×C₃₁	1	2	yes	complemented
701	#385	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	#381	C₂²×C₃₁	1	2	yes	complemented
704	#381	C₂²×C₃₁	1	2	yes	complemented
705	#380	C₂²×C₃₁	1	2	yes	complemented
706	#380	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	#380	C₂²×C₃₁	1	1	yes	characteristic, complemented
708	#379	C₂²×C₃₁	1	2	yes	complemented
709	#379	C₂²×C₃₁	1	2	yes	complemented
710	#379	C₂²×C₃₁	1	2	yes	complemented
711	#379	C₂²×C₃₁	1	2	yes	complemented
712	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
717	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
718	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
719	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
720	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
722	#376	C₂²×C₃₁	1	1	yes	characteristic, complemented
723	C₂×C₃₁	—	2	4	no	—
724	C₂×C₃₁	—	4	4	no	—
725	C₂×C₃₁	—	4	4	no	—
726	C₂×C₃₁	—	4	2	no	—
727	C₂×C₃₁	—	4	4	no	—
728	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
729	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
730	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
731	C₂×C₃₁	#3537	1	1	yes	characteristic
732	C₂×C₃₁	#3542	1	1	yes	characteristic
733	C₂×C₃₁	#3543	1	1	yes	characteristic
734	C₂×C₃₁	#3558	1	1	yes	characteristic
735	C₂⁵	C₂³×C₃₁	1	2	yes	—
736	C₂⁵	C₂³×C₃₁	1	2	yes	—
737	C₂²×D₄	—	4	2	no	—
738	C₂²×D₄	—	4	2	no	—
739	C₂²×D₄	—	4	2	no	—
740	C₂²×D₄	—	4	2	no	—
741	C₂²×D₄	—	4	4	no	—
742	C₂²×D₄	—	4	4	no	—
743	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
744	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
745	C₂²×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
746	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
747	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
748	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
749	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
750	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
751	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
752	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
753	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
754	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
755	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
756	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
757	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
758	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
759	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
760	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
761	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
762	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
763	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
764	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
765	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
766	#127	C₂×C₄×C₃₁	1	8	yes	complemented
767	#121	C₂×C₄×C₃₁	1	8	yes	complemented
768	#121	C₂×C₄×C₃₁	1	8	yes	complemented
769	#121	C₂×C₄×C₃₁	1	16	yes	complemented
770	#120	C₂×C₄×C₃₁	1	16	yes	complemented
771	#120	C₂×C₄×C₃₁	1	16	yes	complemented
772	C₄×D₄	—	4	2	no	—
773	C₄×D₄	—	4	2	no	—
774	C₄×D₄	—	4	2	no	—
775	C₄×D₄	—	4	2	no	—
776	C₄×D₄	—	4	4	no	—
777	C₄×D₄	—	4	4	no	—
778	C₄×D₄	—	4	4	no	—
779	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
780	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
781	#117	—	4	2	no	—
782	#117	—	4	2	no	—
783	C₂×C₄⋊C₄	—	4	2	no	—
784	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
790	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
793	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
794	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
797	C₂×C₂²⋊C₄	—	4	4	no	—
798	C₂×C₂²⋊C₄	—	4	4	no	—
799	C₂×C₂²⋊C₄	—	4	4	no	—
800	C₂×C₂²⋊C₄	—	4	4	no	—
801	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
803	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
828	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
830	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
831	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
832	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
833	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
834	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
835	C₂×C₄²	—	4	2	no	—
836	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
837	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
838	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
839	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
841	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
842	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
843	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
844	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
845	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
846	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
847	#95	C₂³×C₃₁	1	1	yes	characteristic
848	#95	C₂³×C₃₁	1	1	yes	characteristic
849	#95	C₂³×C₃₁	1	1	yes	characteristic
850	#95	C₂³×C₃₁	1	1	yes	characteristic
851	#95	C₂³×C₃₁	1	1	yes	characteristic
852	#95	C₂³×C₃₁	1	1	yes	characteristic
853	#95	C₂³×C₃₁	1	2	yes	—
854	#95	C₂³×C₃₁	1	2	yes	—
855	#95	C₂³×C₃₁	1	2	yes	—
856	#95	C₂³×C₃₁	1	2	yes	—
857	#95	C₂³×C₃₁	1	2	yes	—
858	#95	C₂³×C₃₁	1	2	yes	—
859	#95	C₂³×C₃₁	1	1	yes	characteristic
860	#95	C₂³×C₃₁	1	1	yes	characteristic
861	#95	C₂³×C₃₁	1	1	yes	characteristic
862	#95	C₂³×C₃₁	1	2	yes	—
863	#95	C₂³×C₃₁	1	1	yes	characteristic
864	#95	C₂³×C₃₁	1	2	yes	—
865	#95	C₂³×C₃₁	1	2	yes	—
866	C₃₁	#34471	1	1	yes	characteristic, direct product factor, Sylow
867	C₂⁴	—	2	4	no	—
868	C₂⁴	—	2	4	no	—
869	C₂⁴	—	4	2	no	—
870	C₂⁴	—	4	2	no	—
871	C₂⁴	—	4	2	no	—
872	C₂⁴	—	4	2	no	—
873	C₂⁴	—	4	2	no	—
874	C₂⁴	—	4	2	no	—
875	C₂⁴	—	4	2	no	—
876	C₂⁴	—	4	2	no	—
877	C₂⁴	—	4	2	no	—
878	C₂⁴	—	4	2	no	—
879	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
880	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
881	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
883	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
884	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
885	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
886	C₂×D₄	—	2	4	no	—
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	4	16	no	—
897	C₂×D₄	—	4	16	no	—
898	C₂×D₄	—	4	2	no	—
899	C₂×D₄	—	4	2	no	—
900	C₂×D₄	—	4	2	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	2	no	—
904	C₂×D₄	—	4	2	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	32	no	—
909	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
910	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
911	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
912	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
913	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
914	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
915	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
916	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
917	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
918	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	4	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	4	no	—
928	C₂²×C₄	—	4	1	no	—
929	C₂²×C₄	—	4	1	no	—
930	C₂²×C₄	—	4	1	no	—
931	C₂²×C₄	—	4	2	no	—
932	C₂²×C₄	—	4	2	no	—
933	C₂²×C₄	—	4	2	no	—
934	C₂²×C₄	—	4	2	no	—
935	C₂²×C₄	—	4	2	no	—
936	C₂²×C₄	—	4	2	no	—
937	C₂²×C₄	—	4	2	no	—
938	C₂²×C₄	—	4	2	no	—
939	C₂²×C₄	—	4	2	no	—
940	C₂²×C₄	—	4	2	no	—
941	C₂²×C₄	—	4	2	no	—
942	C₂²×C₄	—	4	2	no	—
943	C₂²×C₄	—	4	2	no	—
944	C₂²×C₄	—	4	2	no	—
945	C₂²×C₄	—	4	2	no	—
946	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
947	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
948	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
949	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
957	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
960	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	4	2	no	—
973	C₄⋊C₄	—	4	1	no	—
974	C₄⋊C₄	—	4	1	no	—
975	C₄⋊C₄	—	4	1	no	—
976	C₄⋊C₄	—	4	2	no	—
977	C₄⋊C₄	—	4	2	no	—
978	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
979	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	2	4	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	4	2	no	—
997	C₂²⋊C₄	—	4	2	no	—
998	C₂²⋊C₄	—	4	1	no	—
999	C₂²⋊C₄	—	4	1	no	—
1000	C₂²⋊C₄	—	4	1	no	—
1001	C₂²⋊C₄	—	4	2	no	—
1002	C₂²⋊C₄	—	4	2	no	—
1003	C₂²⋊C₄	—	4	2	no	—
1004	C₂²⋊C₄	—	4	2	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1010	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
1011	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1012	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
1013	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	4	1	no	—
1019	C₄²	—	4	1	no	—
1020	C₄²	—	4	2	no	—
1021	C₄²	—	4	2	no	—
1022	C₄²	—	4	2	no	—
1023	C₄²	—	4	2	no	—
1024	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	2	no	—
1053	C₂³	—	2	16	no	—
1054	C₂³	—	4	8	no	—
1055	C₂³	—	4	8	no	—
1056	C₂³	—	4	8	no	—
1057	C₂³	—	4	8	no	—
1058	C₂³	—	4	8	no	—
1059	C₂³	—	8	4	no	—
1060	C₂³	—	8	4	no	—
1061	C₂³	—	8	4	no	—
1062	C₂³	—	8	4	no	—
1063	C₂³	—	8	4	no	—
1064	C₂³	—	8	4	no	—
1065	C₂³	—	8	4	no	—
1066	C₂³	—	8	4	no	—
1067	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
1068	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
1069	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
1070	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
1071	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
1072	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
1073	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
1074	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1075	D₄	—	2	8	no	—
1076	D₄	—	2	16	no	—
1077	D₄	—	2	8	no	—
1078	D₄	—	2	8	no	—
1079	D₄	—	2	8	no	—
1080	D₄	—	4	8	no	—
1081	D₄	—	4	8	no	—
1082	D₄	—	4	8	no	—
1083	D₄	—	4	8	no	—
1084	D₄	—	4	8	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	8	no	—
1098	C₂×C₄	—	2	8	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	4	8	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	8	4	no	—
1136	C₂×C₄	—	8	4	no	—
1137	C₂×C₄	—	8	4	no	—
1138	C₂×C₄	—	8	4	no	—
1139	C₂×C₄	—	8	4	no	—
1140	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1141	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1142	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1143	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1144	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1145	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1146	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1147	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1148	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	4	no	—
1160	C₂²	—	2	4	no	—
1161	C₂²	—	2	4	no	—
1162	C₂²	—	2	4	no	—
1163	C₂²	—	2	4	no	—
1164	C₂²	—	2	4	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	4	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	8	16	no	—
1184	C₂²	—	8	16	no	—
1185	C₂²	C₃₁×#518	1	4	yes	—
1186	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1187	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1188	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1189	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1191	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1192	C₂²	C₃₁×#585	1	1	yes	characteristic
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	4	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	C₃₁×#518	1	4	yes	—
1211	C₂	—	2	4	no	—
1212	C₂	—	4	2	no	—
1213	C₂	—	4	4	no	—
1214	C₂	—	4	4	no	—
1215	C₂	—	4	4	no	—
1216	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
1217	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
1218	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1219	C₂	C₃₁×#3537	1	1	yes	characteristic
1220	C₂	C₃₁×#3542	1	1	yes	characteristic
1221	C₂	C₃₁×#3543	1	1	yes	characteristic
1222	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×D₄²×C₃₁	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×#2377	C₂	semidirect
3. C₃₁×#2375	C₂	semidirect
4. C₃₁×#2366	C₂	semidirect
5. C₃₁×#2363	C₂	semidirect
6. C₃₁×#2361	C₂	semidirect
7. C₃₁×#2358	C₂	semidirect
8. C₃₁×#2357	C₂	semidirect
9. C₃₁×#2352	C₂	semidirect
10. D₄×C₂²⋊C₄×C₃₁	C₂	semidirect
11. D₄×C₂²⋊C₄×C₃₁	C₂	semidirect
12. D₄×C₂²⋊C₄×C₃₁	C₂	semidirect
13. C₃₁×#2333	C₂	semidirect
14. C₃₁×#2328	C₂	semidirect
15. C₃₁×#2324	C₂	semidirect
16. C₃₁×#2321	C₂	semidirect
17. C₃₁×#2321	C₂	semidirect
18. C₃₁×#2319	C₂	semidirect
19. C₃₁×#2309	C₂	semidirect
20. C₃₁×#2308	C₂	semidirect
21. C₄×C₃₁×#121	C₂	semidirect
22. C₂×C₃₁×#390	C₂	semidirect
23. C₃₁×#2290	C₂	semidirect
27. D₄²×C₃₁	C₄	semidirect
36. C₂×C₄×D₄×C₃₁	C₂²	semidirect
37. C₂×C₄×D₄×C₃₁	C₂²	semidirect
38. C₂×C₄×D₄×C₃₁	C₂²	semidirect
39. C₂×C₄×D₄×C₃₁	C₂²	semidirect
40. C₂×C₄×D₄×C₃₁	C₂²	semidirect
41. C₂×C₄×D₄×C₃₁	C₂²	semidirect
42. C₂×C₄×D₄×C₃₁	C₂²	semidirect
43. C₂×C₃₁×#117	C₂²	semidirect
44. C₂×C₃₁×#117	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
46. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
47. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
50. C₂²×C₄²×C₃₁	C₂²	semidirect
55. C₃₁×#390	C₂²	semidirect
56. C₃₁×#390	C₂²	semidirect
57. C₃₁×#390	C₂²	semidirect
58. C₃₁×#390	C₂²	semidirect
59. C₃₁×#390	C₂²	semidirect
60. C₃₁×#390	C₂²	semidirect
61. C₃₁×#390	C₂²	semidirect
62. C₃₁×#390	C₂²	semidirect
63. C₃₁×#390	C₂²	semidirect
64. C₃₁×#390	C₂²	semidirect
65. C₃₁×#390	C₂²	semidirect
66. C₃₁×#389	C₂²	semidirect
67. C₃₁×#389	C₂²	semidirect
68. C₃₁×#388	C₂²	semidirect
69. C₃₁×#388	C₂²	semidirect
70. C₃₁×#388	C₂²	semidirect
71. C₃₁×#388	C₂²	semidirect
72. C₃₁×#388	C₂²	semidirect
73. C₃₁×#388	C₂²	semidirect
74. C₃₁×#388	C₂²	semidirect
75. C₃₁×#388	C₂²	semidirect
76. C₃₁×#388	C₂²	semidirect
77. C₃₁×#388	C₂²	semidirect
78. C₃₁×#388	C₂²	semidirect
79. C₃₁×#387	C₂²	semidirect
80. C₃₁×#387	C₂²	semidirect
81. C₃₁×#387	C₂²	semidirect
85. C₃₁×#386	C₂²	semidirect
86. C₃₁×#386	C₂²	semidirect
87. C₃₁×#386	C₂²	semidirect
88. C₃₁×#386	C₂²	semidirect
89. C₃₁×#386	C₂²	semidirect
90. C₃₁×#386	C₂²	semidirect
91. C₃₁×#386	C₂²	semidirect
92. C₃₁×#386	C₂²	semidirect
93. C₃₁×#386	C₂²	semidirect
94. C₃₁×#386	C₂²	semidirect
95. C₃₁×#386	C₂²	semidirect
96. C₃₁×#386	C₂²	semidirect
97. C₃₁×#386	C₂²	semidirect
98. C₃₁×#386	C₂²	semidirect
99. C₃₁×#385	C₂²	semidirect
100. C₃₁×#385	C₂²	semidirect
101. C₃₁×#385	C₂²	semidirect
102. C₃₁×#385	C₂²	semidirect
103. C₃₁×#382	C₂²	semidirect
104. C₃₁×#381	C₂²	semidirect
105. C₃₁×#381	C₂²	semidirect
106. C₃₁×#380	C₂²	semidirect
107. C₃₁×#380	C₂²	semidirect
108. C₃₁×#380	C₂²	semidirect
109. C₃₁×#379	C₂²	semidirect
110. C₃₁×#379	C₂²	semidirect
111. C₃₁×#379	C₂²	semidirect
112. C₃₁×#379	C₂²	semidirect
113. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
114. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
115. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
116. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
117. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
123. C₃₁×#376	C₂²	semidirect
132. C₂²×D₄×C₃₁	C₂×C₄	semidirect
133. C₂²×D₄×C₃₁	C₂×C₄	semidirect
134. C₂²×D₄×C₃₁	C₂×C₄	semidirect
155. C₃₁×#127	C₂×C₄	semidirect
156. C₃₁×#121	C₂×C₄	semidirect
157. C₃₁×#121	C₂×C₄	semidirect
158. C₃₁×#121	C₂×C₄	semidirect
159. C₃₁×#120	C₂×C₄	semidirect
160. C₃₁×#120	C₂×C₄	semidirect
168. C₄×D₄×C₃₁	C₂×C₄	semidirect
169. C₄×D₄×C₃₁	C₂×C₄	semidirect
413. #34471	C₃₁	direct (N × H)
539. #2377	C₂×C₃₁	semidirect
540. #2375	C₂×C₃₁	semidirect
541. #2366	C₂×C₃₁	semidirect
542. #2363	C₂×C₃₁	semidirect
543. #2361	C₂×C₃₁	semidirect
544. #2358	C₂×C₃₁	semidirect
545. #2357	C₂×C₃₁	semidirect
546. #2352	C₂×C₃₁	semidirect
547. D₄×C₂²⋊C₄	C₂×C₃₁	semidirect
548. D₄×C₂²⋊C₄	C₂×C₃₁	semidirect
549. D₄×C₂²⋊C₄	C₂×C₃₁	semidirect
550. #2333	C₂×C₃₁	semidirect
551. #2328	C₂×C₃₁	semidirect
552. #2324	C₂×C₃₁	semidirect
553. #2321	C₂×C₃₁	semidirect
554. #2321	C₂×C₃₁	semidirect
555. #2319	C₂×C₃₁	semidirect
556. #2309	C₂×C₃₁	semidirect
557. #2308	C₂×C₃₁	semidirect
558. C₄×#121	C₂×C₃₁	semidirect
559. C₂×#390	C₂×C₃₁	semidirect
560. #2290	C₂×C₃₁	semidirect
626. D₄²	C₄×C₃₁	semidirect
635. C₂×C₄×D₄	C₂²×C₃₁	semidirect
636. C₂×C₄×D₄	C₂²×C₃₁	semidirect
637. C₂×C₄×D₄	C₂²×C₃₁	semidirect
638. C₂×C₄×D₄	C₂²×C₃₁	semidirect
639. C₂×C₄×D₄	C₂²×C₃₁	semidirect
640. C₂×C₄×D₄	C₂²×C₃₁	semidirect
641. C₂×C₄×D₄	C₂²×C₃₁	semidirect
642. C₂×#117	C₂²×C₃₁	semidirect
643. C₂×#117	C₂²×C₃₁	semidirect
644. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
645. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
646. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
647. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
648. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
649. C₂²×C₄²	C₂²×C₃₁	semidirect
654. #390	C₂²×C₃₁	semidirect
655. #390	C₂²×C₃₁	semidirect
656. #390	C₂²×C₃₁	semidirect
657. #390	C₂²×C₃₁	semidirect
658. #390	C₂²×C₃₁	semidirect
659. #390	C₂²×C₃₁	semidirect
660. #390	C₂²×C₃₁	semidirect
661. #390	C₂²×C₃₁	semidirect
662. #390	C₂²×C₃₁	semidirect
663. #390	C₂²×C₃₁	semidirect
664. #390	C₂²×C₃₁	semidirect
665. #389	C₂²×C₃₁	semidirect
666. #389	C₂²×C₃₁	semidirect
667. #388	C₂²×C₃₁	semidirect
668. #388	C₂²×C₃₁	semidirect
669. #388	C₂²×C₃₁	semidirect
670. #388	C₂²×C₃₁	semidirect
671. #388	C₂²×C₃₁	semidirect
672. #388	C₂²×C₃₁	semidirect
673. #388	C₂²×C₃₁	semidirect
674. #388	C₂²×C₃₁	semidirect
675. #388	C₂²×C₃₁	semidirect
676. #388	C₂²×C₃₁	semidirect
677. #388	C₂²×C₃₁	semidirect
678. #387	C₂²×C₃₁	semidirect
679. #387	C₂²×C₃₁	semidirect
680. #387	C₂²×C₃₁	semidirect
684. #386	C₂²×C₃₁	semidirect
685. #386	C₂²×C₃₁	semidirect
686. #386	C₂²×C₃₁	semidirect
687. #386	C₂²×C₃₁	semidirect
688. #386	C₂²×C₃₁	semidirect
689. #386	C₂²×C₃₁	semidirect
690. #386	C₂²×C₃₁	semidirect
691. #386	C₂²×C₃₁	semidirect
692. #386	C₂²×C₃₁	semidirect
693. #386	C₂²×C₃₁	semidirect
694. #386	C₂²×C₃₁	semidirect
695. #386	C₂²×C₃₁	semidirect
696. #386	C₂²×C₃₁	semidirect
697. #386	C₂²×C₃₁	semidirect
698. #385	C₂²×C₃₁	semidirect
699. #385	C₂²×C₃₁	semidirect
700. #385	C₂²×C₃₁	semidirect
701. #385	C₂²×C₃₁	semidirect
702. #382	C₂²×C₃₁	semidirect
703. #381	C₂²×C₃₁	semidirect
704. #381	C₂²×C₃₁	semidirect
705. #380	C₂²×C₃₁	semidirect
706. #380	C₂²×C₃₁	semidirect
707. #380	C₂²×C₃₁	semidirect
708. #379	C₂²×C₃₁	semidirect
709. #379	C₂²×C₃₁	semidirect
710. #379	C₂²×C₃₁	semidirect
711. #379	C₂²×C₃₁	semidirect
712. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
713. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
714. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
715. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
716. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
717. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
718. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
719. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
720. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
721. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
722. #376	C₂²×C₃₁	semidirect
743. C₂²×D₄	C₂×C₄×C₃₁	semidirect
744. C₂²×D₄	C₂×C₄×C₃₁	semidirect
745. C₂²×D₄	C₂×C₄×C₃₁	semidirect
766. #127	C₂×C₄×C₃₁	semidirect
767. #121	C₂×C₄×C₃₁	semidirect
768. #121	C₂×C₄×C₃₁	semidirect
769. #121	C₂×C₄×C₃₁	semidirect
770. #120	C₂×C₄×C₃₁	semidirect
771. #120	C₂×C₄×C₃₁	semidirect
779. C₄×D₄	C₂×C₄×C₃₁	semidirect
780. C₄×D₄	C₂×C₄×C₃₁	semidirect
866. C₃₁	#34471	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×D₄²×C₃₁	2
C₃₁×#2377	2
C₃₁×#2375	2
C₃₁×#2366	2
C₃₁×#2363	2
C₃₁×#2361	2
C₃₁×#2358	2
C₃₁×#2357	2
C₃₁×#2352	2
D₄×C₂²⋊C₄×C₃₁	2
C₃₁×#2333	2
C₃₁×#2328	2
C₃₁×#2324	2
C₃₁×#2321	2
C₃₁×#2319	2
C₃₁×#2309	2
C₃₁×#2308	2
C₄×C₃₁×#121	2
C₂×C₃₁×#390	2
C₃₁×#2290	2
#34471	31

Subgroups — C31×#34471 #21491230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34471 #21491230