Subgroups — C₃₁×#34478 #21491237

Order 7936.

2608 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#546	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×#2374	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×#2362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2342	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2335	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2324	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2312	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2309	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#546	C₄	1	16	yes	complemented
27	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#123	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#121	C₂²	1	2	yes	—
32	C₂×C₃₁×#120	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×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	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
40	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
45	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
46	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#390	C₂²	1	1	yes	characteristic
50	C₃₁×#390	C₂²	1	2	yes	—
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	2	yes	—
55	C₃₁×#390	C₂²	1	1	yes	characteristic
56	C₃₁×#390	C₂²	1	2	yes	—
57	C₃₁×#390	C₂²	1	1	yes	characteristic
58	C₃₁×#390	C₂²	1	2	yes	complemented
59	C₃₁×#390	C₂²	1	2	yes	complemented
60	C₃₁×#390	C₂²	1	2	yes	complemented
61	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#389	C₂²	1	2	yes	complemented
64	C₃₁×#388	C₂²	1	1	yes	characteristic
65	C₃₁×#388	C₂²	1	2	yes	—
66	C₃₁×#388	C₂²	1	2	yes	—
67	C₃₁×#388	C₂²	1	2	yes	—
68	C₃₁×#388	C₂²	1	2	yes	—
69	C₃₁×#388	C₂²	1	2	yes	—
70	C₃₁×#388	C₂²	1	1	yes	characteristic
71	C₃₁×#388	C₂²	1	2	yes	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	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×#388	C₂²	1	2	yes	complemented
82	C₃₁×#387	C₂²	1	2	yes	complemented
83	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#387	C₂²	1	2	yes	complemented
85	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#386	C₂²	1	1	yes	characteristic
87	C₃₁×#386	C₂²	1	2	yes	—
88	C₃₁×#386	C₂²	1	2	yes	—
89	C₃₁×#386	C₂²	1	1	yes	characteristic
90	C₃₁×#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×#385	C₂²	1	2	yes	complemented
95	C₃₁×#385	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#385	C₂²	1	2	yes	complemented
97	C₃₁×#385	C₂²	1	2	yes	complemented
98	C₃₁×#385	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#384	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#381	C₂²	1	2	yes	complemented
101	C₃₁×#380	C₂²	1	1	yes	characteristic
102	C₃₁×#380	C₂²	1	2	yes	complemented
103	C₃₁×#380	C₂²	1	2	yes	complemented
104	C₃₁×#380	C₂²	1	2	yes	complemented
105	C₃₁×#380	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#379	C₂²	1	2	yes	—
107	C₃₁×#379	C₂²	1	2	yes	—
108	C₃₁×#379	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
112	C₄×C₄⋊C₄×C₃₁	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×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	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	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
123	C₃₁×#376	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₃₁	C₂³	1	2	yes	—
125	C₂×#41×C₃₁	—	4	2	no	—
126	C₂×#41×C₃₁	—	4	2	no	—
127	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
128	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₃₁	—	4	2	no	—
130	C₂²×D₄×C₃₁	—	4	2	no	—
131	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
132	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
136	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
137	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
138	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
142	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
146	C₃₁×#124	C₂×C₄	1	8	yes	complemented
147	C₃₁×#123	C₂×C₄	1	16	yes	complemented
148	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
149	C₃₁×#121	C₂×C₄	1	8	yes	—
150	C₃₁×#121	C₂×C₄	1	16	yes	complemented
151	C₃₁×#120	C₂×C₄	1	16	yes	complemented
152	C₄×Q₈×C₃₁	—	4	2	no	—
153	C₄×Q₈×C₃₁	—	4	2	no	—
154	C₄×D₄×C₃₁	—	4	2	no	—
155	C₄×D₄×C₃₁	—	4	2	no	—
156	C₄×D₄×C₃₁	—	4	4	no	—
157	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
158	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
159	C₃₁×#117	—	4	2	no	—
160	C₃₁×#117	—	4	4	no	—
161	C₃₁×#117	—	4	2	no	—
162	C₃₁×#117	—	4	2	no	—
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	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	2	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	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	—	4	4	no	—
181	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
213	C₂×C₄²×C₃₁	—	4	2	no	—
214	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
218	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
222	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
223	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
224	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
225	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
226	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
227	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
228	C₃₁×#95	C₂³	1	1	yes	characteristic
229	C₃₁×#95	C₂³	1	1	yes	characteristic
230	C₃₁×#95	C₂³	1	1	yes	characteristic
231	C₃₁×#95	C₂³	1	1	yes	characteristic
232	C₃₁×#95	C₂³	1	1	yes	characteristic
233	C₃₁×#95	C₂³	1	1	yes	characteristic
234	C₃₁×#95	C₂³	1	1	yes	characteristic
235	C₃₁×#95	C₂³	1	1	yes	characteristic
236	C₃₁×#95	C₂³	1	2	yes	—
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₃₁×#95	C₂³	1	1	yes	characteristic
239	C₃₁×#95	C₂³	1	2	yes	—
240	C₃₁×#95	C₂³	1	2	yes	—
241	C₃₁×#95	C₂³	1	2	yes	—
242	C₃₁×#95	C₂³	1	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	C₂⁴×C₃₁	—	4	2	no	—
250	C₂⁴×C₃₁	—	4	2	no	—
251	C₂⁴×C₃₁	—	4	2	no	—
252	C₂⁴×C₃₁	—	4	2	no	—
253	C₂⁴×C₃₁	—	4	2	no	—
254	C₂⁴×C₃₁	—	4	2	no	—
255	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
256	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
258	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
259	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
260	#41×C₃₁	—	4	16	no	—
261	C₂×Q₈×C₃₁	—	2	2	no	—
262	C₂×Q₈×C₃₁	—	2	2	no	—
263	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
264	C₂×D₄×C₃₁	—	2	2	no	—
265	C₂×D₄×C₃₁	—	2	2	no	—
266	C₂×D₄×C₃₁	—	2	2	no	—
267	C₂×D₄×C₃₁	—	2	2	no	—
268	C₂×D₄×C₃₁	—	4	16	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	1	no	—
273	C₂×D₄×C₃₁	—	4	1	no	—
274	C₂×D₄×C₃₁	—	4	2	no	—
275	C₂×D₄×C₃₁	—	4	2	no	—
276	C₂×D₄×C₃₁	—	4	2	no	—
277	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
278	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
279	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
280	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
281	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
282	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
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	4	no	—
289	C₂²×C₄×C₃₁	—	4	1	no	—
290	C₂²×C₄×C₃₁	—	4	1	no	—
291	C₂²×C₄×C₃₁	—	4	2	no	—
292	C₂²×C₄×C₃₁	—	4	2	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	2	no	—
297	C₂²×C₄×C₃₁	—	4	2	no	—
298	C₂²×C₄×C₃₁	—	4	2	no	—
299	C₂²×C₄×C₃₁	—	4	2	no	—
300	C₂²×C₄×C₃₁	—	4	2	no	—
301	C₂²×C₄×C₃₁	—	4	2	no	—
302	C₂²×C₄×C₃₁	—	4	2	no	—
303	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
304	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
305	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
306	C₂²×C₄×C₃₁	C₂²×C₄	1	8	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	1	yes	characteristic
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	1	yes	characteristic
314	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
325	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	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	4	2	no	—
332	C₄⋊C₄×C₃₁	—	4	1	no	—
333	C₄⋊C₄×C₃₁	—	4	2	no	—
334	C₄⋊C₄×C₃₁	—	4	2	no	—
335	C₄⋊C₄×C₃₁	—	4	1	no	—
336	C₄⋊C₄×C₃₁	—	4	1	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	C₂²×C₄	1	4	yes	—
341	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
342	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
343	C₂²⋊C₄×C₃₁	—	2	2	no	—
344	C₂²⋊C₄×C₃₁	—	2	4	no	—
345	C₂²⋊C₄×C₃₁	—	4	2	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	—	4	2	no	—
350	C₂²⋊C₄×C₃₁	—	4	1	no	—
351	C₂²⋊C₄×C₃₁	—	4	2	no	—
352	C₂²⋊C₄×C₃₁	—	4	1	no	—
353	C₂²⋊C₄×C₃₁	—	4	2	no	—
354	C₂²⋊C₄×C₃₁	—	4	2	no	—
355	C₂²⋊C₄×C₃₁	—	4	2	no	—
356	C₂²⋊C₄×C₃₁	—	4	2	no	—
357	C₂²⋊C₄×C₃₁	—	4	1	no	—
358	C₂²⋊C₄×C₃₁	—	4	1	no	—
359	C₂²⋊C₄×C₃₁	—	4	1	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	C₂²×C₄	1	4	yes	—
368	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
369	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
370	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
371	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
372	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
373	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
374	C₄²×C₃₁	—	2	2	no	—
375	C₄²×C₃₁	—	2	2	no	—
376	C₄²×C₃₁	—	2	4	no	—
377	C₄²×C₃₁	—	2	2	no	—
378	C₄²×C₃₁	—	2	2	no	—
379	C₄²×C₃₁	—	4	1	no	—
380	C₄²×C₃₁	—	4	1	no	—
381	C₄²×C₃₁	—	4	2	no	—
382	C₄²×C₃₁	—	4	2	no	—
383	C₄²×C₃₁	—	4	2	no	—
384	C₄²×C₃₁	—	4	2	no	—
385	C₄²×C₃₁	—	4	2	no	—
386	C₄²×C₃₁	—	4	2	no	—
387	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
388	#34478	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂³×C₃₁	—	2	2	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	2	no	—
396	C₂³×C₃₁	—	2	2	no	—
397	C₂³×C₃₁	—	2	2	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	1	no	—
404	C₂³×C₃₁	—	2	1	no	—
405	C₂³×C₃₁	—	2	2	no	—
406	C₂³×C₃₁	—	2	2	no	—
407	C₂³×C₃₁	—	2	2	no	—
408	C₂³×C₃₁	—	2	2	no	—
409	C₂³×C₃₁	—	2	1	no	—
410	C₂³×C₃₁	—	2	1	no	—
411	C₂³×C₃₁	—	2	1	no	—
412	C₂³×C₃₁	—	2	1	no	—
413	C₂³×C₃₁	—	4	8	no	—
414	C₂³×C₃₁	—	4	8	no	—
415	C₂³×C₃₁	—	4	8	no	—
416	C₂³×C₃₁	—	8	4	no	—
417	C₂³×C₃₁	—	8	4	no	—
418	C₂³×C₃₁	—	8	4	no	—
419	C₂³×C₃₁	—	8	4	no	—
420	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
421	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
422	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
423	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
424	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
425	Q₈×C₃₁	—	2	8	no	—
426	D₄×C₃₁	—	2	8	no	—
427	D₄×C₃₁	—	2	8	no	—
428	D₄×C₃₁	—	4	8	no	—
429	D₄×C₃₁	—	4	4	no	—
430	D₄×C₃₁	—	4	8	no	—
431	D₄×C₃₁	—	4	8	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	1	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	2	no	—
438	C₂×C₄×C₃₁	—	2	2	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	1	no	—
443	C₂×C₄×C₃₁	—	2	1	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	2	1	no	—
446	C₂×C₄×C₃₁	—	2	8	no	—
447	C₂×C₄×C₃₁	—	2	8	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	2	no	—
454	C₂×C₄×C₃₁	—	2	1	no	—
455	C₂×C₄×C₃₁	—	2	1	no	—
456	C₂×C₄×C₃₁	—	2	1	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	2	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	2	no	—
464	C₂×C₄×C₃₁	—	2	1	no	—
465	C₂×C₄×C₃₁	—	2	2	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	1	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	2	no	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	1	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	1	no	—
481	C₂×C₄×C₃₁	—	4	8	no	—
482	C₂×C₄×C₃₁	—	4	8	no	—
483	C₂×C₄×C₃₁	—	4	4	no	—
484	C₂×C₄×C₃₁	—	4	4	no	—
485	C₂×C₄×C₃₁	—	8	4	no	—
486	C₂×C₄×C₃₁	—	8	4	no	—
487	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
488	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
489	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
490	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
491	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
492	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
493	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
494	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
495	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
496	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
497	C₂×#546	C₂×C₃₁	1	1	yes	characteristic
498	#2377	C₂×C₃₁	1	2	yes	complemented
499	#2375	C₂×C₃₁	1	2	yes	complemented
500	#2374	C₂×C₃₁	1	2	yes	complemented
501	#2367	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#2363	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#2362	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#2354	C₂×C₃₁	1	1	yes	characteristic, complemented
505	#2354	C₂×C₃₁	1	1	yes	characteristic, complemented
506	#2342	C₂×C₃₁	1	2	yes	complemented
507	#2341	C₂×C₃₁	1	1	yes	characteristic, complemented
508	D₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#2335	C₂×C₃₁	1	2	yes	complemented
510	#2326	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#2324	C₂×C₃₁	1	2	yes	complemented
512	#2323	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#2321	C₂×C₃₁	1	2	yes	complemented
514	#2319	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#2312	C₂×C₃₁	1	2	yes	complemented
516	#2309	C₂×C₃₁	1	1	yes	characteristic, complemented
517	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#2297	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#2290	C₂×C₃₁	1	1	yes	characteristic, complemented
520	C₂²×C₃₁	—	2	2	no	—
521	C₂²×C₃₁	—	2	2	no	—
522	C₂²×C₃₁	—	2	4	no	—
523	C₂²×C₃₁	—	2	4	no	—
524	C₂²×C₃₁	—	2	2	no	—
525	C₂²×C₃₁	—	2	2	no	—
526	C₂²×C₃₁	—	2	4	no	—
527	C₂²×C₃₁	—	2	4	no	—
528	C₂²×C₃₁	—	2	4	no	—
529	C₂²×C₃₁	—	2	2	no	—
530	C₂²×C₃₁	—	2	4	no	—
531	C₂²×C₃₁	—	2	2	no	—
532	C₂²×C₃₁	—	4	1	no	—
533	C₂²×C₃₁	—	4	2	no	—
534	C₂²×C₃₁	—	4	2	no	—
535	C₂²×C₃₁	—	4	1	no	—
536	C₂²×C₃₁	—	4	1	no	—
537	C₂²×C₃₁	—	4	2	no	—
538	C₂²×C₃₁	—	4	2	no	—
539	C₂²×C₃₁	—	4	1	no	—
540	C₂²×C₃₁	—	4	2	no	—
541	C₂²×C₃₁	—	4	1	no	—
542	C₂²×C₃₁	—	4	2	no	—
543	C₂²×C₃₁	—	4	1	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	2	no	—
546	C₂²×C₃₁	—	4	2	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	8	16	no	—
549	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
550	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
552	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂²×C₃₁	#585	1	1	yes	characteristic
554	C₂²×C₃₁	#585	1	1	yes	characteristic
555	C₂²×C₃₁	#585	1	1	yes	characteristic
556	C₄×C₃₁	—	2	2	no	—
557	C₄×C₃₁	—	2	2	no	—
558	C₄×C₃₁	—	2	4	no	—
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	2	2	no	—
561	C₄×C₃₁	—	2	4	no	—
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	4	1	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	1	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	2	no	—
569	C₄×C₃₁	—	4	2	no	—
570	C₄×C₃₁	—	4	2	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	#518	1	4	yes	—
575	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
576	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
577	#546	C₄×C₃₁	1	16	yes	complemented
578	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
579	C₂×#123	C₂²×C₃₁	1	2	yes	—
580	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
581	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
582	C₂×#121	C₂²×C₃₁	1	2	yes	—
583	C₂×#120	C₂²×C₃₁	1	2	yes	—
584	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
585	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
587	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
588	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
589	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
590	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
591	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
592	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
593	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
594	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
595	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
596	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
597	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#390	C₂²×C₃₁	1	1	yes	characteristic
601	#390	C₂²×C₃₁	1	2	yes	—
602	#390	C₂²×C₃₁	1	1	yes	characteristic
603	#390	C₂²×C₃₁	1	1	yes	characteristic
604	#390	C₂²×C₃₁	1	1	yes	characteristic
605	#390	C₂²×C₃₁	1	2	yes	—
606	#390	C₂²×C₃₁	1	1	yes	characteristic
607	#390	C₂²×C₃₁	1	2	yes	—
608	#390	C₂²×C₃₁	1	1	yes	characteristic
609	#390	C₂²×C₃₁	1	2	yes	complemented
610	#390	C₂²×C₃₁	1	2	yes	complemented
611	#390	C₂²×C₃₁	1	2	yes	complemented
612	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	#389	C₂²×C₃₁	1	2	yes	complemented
615	#388	C₂²×C₃₁	1	1	yes	characteristic
616	#388	C₂²×C₃₁	1	2	yes	—
617	#388	C₂²×C₃₁	1	2	yes	—
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	1	yes	characteristic
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	#388	C₂²×C₃₁	1	2	yes	complemented
628	#388	C₂²×C₃₁	1	2	yes	complemented
629	#388	C₂²×C₃₁	1	2	yes	complemented
630	#388	C₂²×C₃₁	1	2	yes	complemented
631	#388	C₂²×C₃₁	1	2	yes	complemented
632	#388	C₂²×C₃₁	1	2	yes	complemented
633	#387	C₂²×C₃₁	1	2	yes	complemented
634	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#387	C₂²×C₃₁	1	2	yes	complemented
636	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#386	C₂²×C₃₁	1	1	yes	characteristic
638	#386	C₂²×C₃₁	1	2	yes	—
639	#386	C₂²×C₃₁	1	2	yes	—
640	#386	C₂²×C₃₁	1	1	yes	characteristic
641	#386	C₂²×C₃₁	1	2	yes	complemented
642	#386	C₂²×C₃₁	1	2	yes	complemented
643	#386	C₂²×C₃₁	1	2	yes	complemented
644	#386	C₂²×C₃₁	1	2	yes	complemented
645	#385	C₂²×C₃₁	1	2	yes	complemented
646	#385	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#385	C₂²×C₃₁	1	2	yes	complemented
648	#385	C₂²×C₃₁	1	2	yes	complemented
649	#385	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#384	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#381	C₂²×C₃₁	1	2	yes	complemented
652	#380	C₂²×C₃₁	1	1	yes	characteristic
653	#380	C₂²×C₃₁	1	2	yes	complemented
654	#380	C₂²×C₃₁	1	2	yes	complemented
655	#380	C₂²×C₃₁	1	2	yes	complemented
656	#380	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#379	C₂²×C₃₁	1	2	yes	—
658	#379	C₂²×C₃₁	1	2	yes	—
659	#379	C₂²×C₃₁	1	2	yes	—
660	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
663	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
664	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
667	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
668	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
669	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
670	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
671	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
673	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
674	#376	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	C₂×C₃₁	—	4	2	no	—
676	C₂×C₃₁	—	4	4	no	—
677	C₂×C₃₁	—	4	4	no	—
678	C₂×C₃₁	—	4	2	no	—
679	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
680	C₂×C₃₁	#3428	1	1	yes	characteristic
681	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂×C₃₁	#3540	1	1	yes	characteristic
683	C₂×C₃₁	#3542	1	1	yes	characteristic
684	C₂×C₃₁	#3546	1	1	yes	characteristic
685	C₂×C₃₁	#3562	1	1	yes	characteristic
686	C₂⁵	C₂³×C₃₁	1	2	yes	—
687	C₂×#41	—	4	2	no	—
688	C₂×#41	—	4	2	no	—
689	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
690	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₂²×D₄	—	4	2	no	—
692	C₂²×D₄	—	4	2	no	—
693	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
694	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
695	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
696	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
697	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
698	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
699	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
700	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
702	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
703	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
704	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
705	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
706	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
707	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
708	#124	C₂×C₄×C₃₁	1	8	yes	complemented
709	#123	C₂×C₄×C₃₁	1	16	yes	complemented
710	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
711	#121	C₂×C₄×C₃₁	1	8	yes	—
712	#121	C₂×C₄×C₃₁	1	16	yes	complemented
713	#120	C₂×C₄×C₃₁	1	16	yes	complemented
714	C₄×Q₈	—	4	2	no	—
715	C₄×Q₈	—	4	2	no	—
716	C₄×D₄	—	4	2	no	—
717	C₄×D₄	—	4	2	no	—
718	C₄×D₄	—	4	4	no	—
719	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
720	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
721	#117	—	4	2	no	—
722	#117	—	4	4	no	—
723	#117	—	4	2	no	—
724	#117	—	4	2	no	—
725	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
742	C₂×C₂²⋊C₄	—	4	4	no	—
743	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
744	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
749	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
768	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
769	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
775	C₂×C₄²	—	4	2	no	—
776	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
777	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
779	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
780	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
781	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
782	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
783	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
784	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
785	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
786	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
787	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
788	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
789	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
790	#95	C₂³×C₃₁	1	1	yes	characteristic
791	#95	C₂³×C₃₁	1	1	yes	characteristic
792	#95	C₂³×C₃₁	1	1	yes	characteristic
793	#95	C₂³×C₃₁	1	1	yes	characteristic
794	#95	C₂³×C₃₁	1	1	yes	characteristic
795	#95	C₂³×C₃₁	1	1	yes	characteristic
796	#95	C₂³×C₃₁	1	1	yes	characteristic
797	#95	C₂³×C₃₁	1	1	yes	characteristic
798	#95	C₂³×C₃₁	1	2	yes	—
799	#95	C₂³×C₃₁	1	2	yes	—
800	#95	C₂³×C₃₁	1	1	yes	characteristic
801	#95	C₂³×C₃₁	1	2	yes	—
802	#95	C₂³×C₃₁	1	2	yes	—
803	#95	C₂³×C₃₁	1	2	yes	—
804	#95	C₂³×C₃₁	1	2	yes	—
805	#95	C₂³×C₃₁	1	2	yes	—
806	#95	C₂³×C₃₁	1	2	yes	—
807	#95	C₂³×C₃₁	1	2	yes	—
808	#95	C₂³×C₃₁	1	2	yes	—
809	#95	C₂³×C₃₁	1	2	yes	—
810	#95	C₂³×C₃₁	1	1	yes	characteristic
811	C₃₁	#34478	1	1	yes	characteristic, direct product factor, Sylow
812	C₂⁴	—	4	2	no	—
813	C₂⁴	—	4	2	no	—
814	C₂⁴	—	4	2	no	—
815	C₂⁴	—	4	2	no	—
816	C₂⁴	—	4	2	no	—
817	C₂⁴	—	4	2	no	—
818	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
819	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
820	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
821	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
822	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
823	#41	—	4	16	no	—
824	C₂×Q₈	—	2	2	no	—
825	C₂×Q₈	—	2	2	no	—
826	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	4	16	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	1	no	—
836	C₂×D₄	—	4	1	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
841	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
842	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
843	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
844	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
845	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
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	2	no	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	1	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
867	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
868	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
869	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
870	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
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	2	yes	—
884	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	2	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	1	no	—
896	C₄⋊C₄	—	4	2	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	—	4	1	no	—
899	C₄⋊C₄	—	4	1	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₄⋊C₄	—	4	2	no	—
902	C₄⋊C₄	—	4	2	no	—
903	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
904	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
905	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	1	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	1	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	1	no	—
921	C₂²⋊C₄	—	4	1	no	—
922	C₂²⋊C₄	—	4	1	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	—	4	2	no	—
929	C₂²⋊C₄	—	4	2	no	—
930	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
931	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
932	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
933	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
934	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
935	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
936	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	2	no	—
939	C₄²	—	2	4	no	—
940	C₄²	—	2	2	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	4	1	no	—
943	C₄²	—	4	1	no	—
944	C₄²	—	4	2	no	—
945	C₄²	—	4	2	no	—
946	C₄²	—	4	2	no	—
947	C₄²	—	4	2	no	—
948	C₄²	—	4	2	no	—
949	C₄²	—	4	2	no	—
950	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	4	8	no	—
976	C₂³	—	4	8	no	—
977	C₂³	—	4	8	no	—
978	C₂³	—	8	4	no	—
979	C₂³	—	8	4	no	—
980	C₂³	—	8	4	no	—
981	C₂³	—	8	4	no	—
982	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
983	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
984	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
985	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
986	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
987	Q₈	—	2	8	no	—
988	D₄	—	2	8	no	—
989	D₄	—	2	8	no	—
990	D₄	—	4	8	no	—
991	D₄	—	4	4	no	—
992	D₄	—	4	8	no	—
993	D₄	—	4	8	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	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	8	no	—
1009	C₂×C₄	—	2	8	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	4	8	no	—
1044	C₂×C₄	—	4	8	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	8	4	no	—
1048	C₂×C₄	—	8	4	no	—
1049	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1050	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1051	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1052	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1053	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1054	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1055	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1056	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1057	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1058	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	4	no	—
1062	C₂²	—	2	4	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	4	no	—
1066	C₂²	—	2	4	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	8	16	no	—
1088	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1089	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1090	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1091	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1092	C₂²	C₃₁×#585	1	1	yes	characteristic
1093	C₂²	C₃₁×#585	1	1	yes	characteristic
1094	C₂²	C₃₁×#585	1	1	yes	characteristic
1095	C₄	—	2	2	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	4	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	4	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	C₃₁×#518	1	4	yes	—
1114	C₂	—	4	2	no	—
1115	C₂	—	4	4	no	—
1116	C₂	—	4	4	no	—
1117	C₂	—	4	2	no	—
1118	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
1119	C₂	C₃₁×#3428	1	1	yes	characteristic
1120	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1121	C₂	C₃₁×#3540	1	1	yes	characteristic
1122	C₂	C₃₁×#3542	1	1	yes	characteristic
1123	C₂	C₃₁×#3546	1	1	yes	characteristic
1124	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×#546	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×#2374	C₂	semidirect
5. C₃₁×#2367	C₂	semidirect
6. C₃₁×#2363	C₂	semidirect
7. C₃₁×#2362	C₂	semidirect
8. C₃₁×#2354	C₂	semidirect
9. C₃₁×#2354	C₂	semidirect
10. C₃₁×#2342	C₂	semidirect
11. C₃₁×#2341	C₂	semidirect
12. D₄×C₂²⋊C₄×C₃₁	C₂	semidirect
13. C₃₁×#2335	C₂	semidirect
14. C₃₁×#2326	C₂	semidirect
15. C₃₁×#2324	C₂	semidirect
16. C₃₁×#2323	C₂	semidirect
17. C₃₁×#2321	C₂	semidirect
18. C₃₁×#2319	C₂	semidirect
19. C₃₁×#2312	C₂	semidirect
20. C₃₁×#2309	C₂	semidirect
21. C₄×C₃₁×#121	C₂	semidirect
22. C₃₁×#2297	C₂	semidirect
23. C₃₁×#2290	C₂	semidirect
26. C₃₁×#546	C₄	semidirect
33. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
34. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
39. C₂×C₄×D₄×C₃₁	C₂²	semidirect
42. C₂×C₃₁×#117	C₂²	semidirect
43. C₂×C₃₁×#117	C₂²	semidirect
46. C₂²×C₄²×C₃₁	C₂²	semidirect
47. C₃₁×#391	C₂²	semidirect
48. C₃₁×#391	C₂²	semidirect
58. C₃₁×#390	C₂²	semidirect
59. C₃₁×#390	C₂²	semidirect
60. C₃₁×#390	C₂²	semidirect
61. C₃₁×#389	C₂²	semidirect
62. C₃₁×#389	C₂²	semidirect
63. C₃₁×#389	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×#388	C₂²	semidirect
80. C₃₁×#388	C₂²	semidirect
81. C₃₁×#388	C₂²	semidirect
82. C₃₁×#387	C₂²	semidirect
83. C₃₁×#387	C₂²	semidirect
84. C₃₁×#387	C₂²	semidirect
85. C₃₁×#387	C₂²	semidirect
90. C₃₁×#386	C₂²	semidirect
91. C₃₁×#386	C₂²	semidirect
92. C₃₁×#386	C₂²	semidirect
93. C₃₁×#386	C₂²	semidirect
94. C₃₁×#385	C₂²	semidirect
95. C₃₁×#385	C₂²	semidirect
96. C₃₁×#385	C₂²	semidirect
97. C₃₁×#385	C₂²	semidirect
98. C₃₁×#385	C₂²	semidirect
99. C₃₁×#384	C₂²	semidirect
100. C₃₁×#381	C₂²	semidirect
102. C₃₁×#380	C₂²	semidirect
103. C₃₁×#380	C₂²	semidirect
104. C₃₁×#380	C₂²	semidirect
105. C₃₁×#380	C₂²	semidirect
109. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
110. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
111. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
112. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
113. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
114. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
116. C₄×C₂²⋊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
127. C₂×#41×C₃₁	C₂×C₄	semidirect
131. C₂²×D₄×C₃₁	C₂×C₄	semidirect
146. C₃₁×#124	C₂×C₄	semidirect
147. C₃₁×#123	C₂×C₄	semidirect
148. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
150. C₃₁×#121	C₂×C₄	semidirect
151. C₃₁×#120	C₂×C₄	semidirect
157. C₄×D₄×C₃₁	C₂×C₄	semidirect
158. C₄×D₄×C₃₁	C₂×C₄	semidirect
181. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
388. #34478	C₃₁	direct (N × H)
498. #2377	C₂×C₃₁	semidirect
499. #2375	C₂×C₃₁	semidirect
500. #2374	C₂×C₃₁	semidirect
501. #2367	C₂×C₃₁	semidirect
502. #2363	C₂×C₃₁	semidirect
503. #2362	C₂×C₃₁	semidirect
504. #2354	C₂×C₃₁	semidirect
505. #2354	C₂×C₃₁	semidirect
506. #2342	C₂×C₃₁	semidirect
507. #2341	C₂×C₃₁	semidirect
508. D₄×C₂²⋊C₄	C₂×C₃₁	semidirect
509. #2335	C₂×C₃₁	semidirect
510. #2326	C₂×C₃₁	semidirect
511. #2324	C₂×C₃₁	semidirect
512. #2323	C₂×C₃₁	semidirect
513. #2321	C₂×C₃₁	semidirect
514. #2319	C₂×C₃₁	semidirect
515. #2312	C₂×C₃₁	semidirect
516. #2309	C₂×C₃₁	semidirect
517. C₄×#121	C₂×C₃₁	semidirect
518. #2297	C₂×C₃₁	semidirect
519. #2290	C₂×C₃₁	semidirect
577. #546	C₄×C₃₁	semidirect
584. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
585. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
590. C₂×C₄×D₄	C₂²×C₃₁	semidirect
593. C₂×#117	C₂²×C₃₁	semidirect
594. C₂×#117	C₂²×C₃₁	semidirect
597. C₂²×C₄²	C₂²×C₃₁	semidirect
598. #391	C₂²×C₃₁	semidirect
599. #391	C₂²×C₃₁	semidirect
609. #390	C₂²×C₃₁	semidirect
610. #390	C₂²×C₃₁	semidirect
611. #390	C₂²×C₃₁	semidirect
612. #389	C₂²×C₃₁	semidirect
613. #389	C₂²×C₃₁	semidirect
614. #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. #388	C₂²×C₃₁	semidirect
628. #388	C₂²×C₃₁	semidirect
629. #388	C₂²×C₃₁	semidirect
630. #388	C₂²×C₃₁	semidirect
631. #388	C₂²×C₃₁	semidirect
632. #388	C₂²×C₃₁	semidirect
633. #387	C₂²×C₃₁	semidirect
634. #387	C₂²×C₃₁	semidirect
635. #387	C₂²×C₃₁	semidirect
636. #387	C₂²×C₃₁	semidirect
641. #386	C₂²×C₃₁	semidirect
642. #386	C₂²×C₃₁	semidirect
643. #386	C₂²×C₃₁	semidirect
644. #386	C₂²×C₃₁	semidirect
645. #385	C₂²×C₃₁	semidirect
646. #385	C₂²×C₃₁	semidirect
647. #385	C₂²×C₃₁	semidirect
648. #385	C₂²×C₃₁	semidirect
649. #385	C₂²×C₃₁	semidirect
650. #384	C₂²×C₃₁	semidirect
651. #381	C₂²×C₃₁	semidirect
653. #380	C₂²×C₃₁	semidirect
654. #380	C₂²×C₃₁	semidirect
655. #380	C₂²×C₃₁	semidirect
656. #380	C₂²×C₃₁	semidirect
660. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
661. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
662. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
663. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
664. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
665. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
667. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
668. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
669. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
670. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
671. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
672. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
673. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
674. #376	C₂²×C₃₁	semidirect
689. C₂×#41	C₂×C₄×C₃₁	semidirect
693. C₂²×D₄	C₂×C₄×C₃₁	semidirect
708. #124	C₂×C₄×C₃₁	semidirect
709. #123	C₂×C₄×C₃₁	semidirect
710. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
712. #121	C₂×C₄×C₃₁	semidirect
713. #120	C₂×C₄×C₃₁	semidirect
719. C₄×D₄	C₂×C₄×C₃₁	semidirect
720. C₄×D₄	C₂×C₄×C₃₁	semidirect
743. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
811. C₃₁	#34478	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×#546	2
C₃₁×#2377	2
C₃₁×#2375	2
C₃₁×#2374	2
C₃₁×#2367	2
C₃₁×#2363	2
C₃₁×#2362	2
C₃₁×#2354	2
C₃₁×#2342	2
C₃₁×#2341	2
D₄×C₂²⋊C₄×C₃₁	2
C₃₁×#2335	2
C₃₁×#2326	2
C₃₁×#2324	2
C₃₁×#2323	2
C₃₁×#2321	2
C₃₁×#2319	2
C₃₁×#2312	2
C₃₁×#2309	2
C₄×C₃₁×#121	2
C₃₁×#2297	2
C₃₁×#2290	2
#34478	31

Subgroups — C31×#34478 #21491237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34478 #21491237