Subgroups — C₃₁×#35142 #21491901

Order 7936.

1542 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2851	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2851	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2655	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2652	C₂	1	2	yes	maximal
7	C₃₁×#2533	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2528	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2509	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2508	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2507	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2506	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2497	C₂	1	1	yes	maximal, characteristic
14	C₃₁×#2496	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2495	C₂	1	1	yes	maximal, characteristic
16	C₃₁×#2494	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#2478	C₂	1	2	yes	maximal
18	C₃₁×#2475	C₂	1	2	yes	maximal
19	C₃₁×#2336	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2334	C₂	1	2	yes	maximal
21	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
24	C₂×C₃₁×#126	C₂²	1	2	yes	—
25	C₂×C₃₁×#125	C₂²	1	2	yes	—
26	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#401	C₂²	1	2	yes	—
32	C₃₁×#400	C₂²	1	2	yes	—
33	C₃₁×#400	C₂²	1	2	yes	—
34	C₃₁×#400	C₂²	1	2	yes	—
35	C₃₁×#400	C₂²	1	2	yes	—
36	C₃₁×#400	C₂²	1	2	yes	—
37	C₃₁×#400	C₂²	1	2	yes	—
38	C₃₁×#400	C₂²	1	2	yes	—
39	C₃₁×#398	C₂²	1	2	yes	—
40	C₃₁×#398	C₂²	1	2	yes	—
41	C₃₁×#398	C₂²	1	2	yes	—
42	C₃₁×#398	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	2	yes	—
44	C₃₁×#397	C₂²	1	2	yes	—
45	C₃₁×#397	C₂²	1	2	yes	—
46	C₃₁×#396	C₂²	1	2	yes	—
47	C₃₁×#389	C₂²	1	2	yes	—
48	C₃₁×#389	C₂²	1	2	yes	—
49	C₃₁×#389	C₂²	1	2	yes	—
50	C₃₁×#389	C₂²	1	2	yes	—
51	C₃₁×#389	C₂²	1	1	yes	characteristic
52	C₃₁×#389	C₂²	1	1	yes	characteristic
53	C₃₁×#389	C₂²	1	1	yes	characteristic
54	C₃₁×#389	C₂²	1	1	yes	characteristic
55	C₃₁×#389	C₂²	1	2	yes	—
56	C₃₁×#389	C₂²	1	2	yes	—
57	C₃₁×#389	C₂²	1	1	yes	characteristic
58	C₃₁×#389	C₂²	1	1	yes	characteristic
59	C₃₁×#389	C₂²	1	1	yes	characteristic
60	C₃₁×#389	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	1	yes	characteristic
62	C₃₁×#389	C₂²	1	1	yes	characteristic
63	C₃₁×#389	C₂²	1	1	yes	characteristic
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#388	C₂²	1	2	yes	—
66	C₃₁×#388	C₂²	1	2	yes	—
67	C₃₁×#388	C₂²	1	2	yes	—
68	C₃₁×#387	C₂²	1	2	yes	—
69	C₃₁×#387	C₂²	1	2	yes	—
70	C₃₁×#387	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	2	yes	—
82	C₃₁×#387	C₂²	1	2	yes	—
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#387	C₂²	1	2	yes	—
87	C₃₁×#385	C₂²	1	2	yes	—
88	C₃₁×#385	C₂²	1	2	yes	—
89	C₃₁×#385	C₂²	1	2	yes	—
90	C₃₁×#385	C₂²	1	2	yes	—
91	C₃₁×#384	C₂²	1	1	yes	characteristic
92	C₃₁×#384	C₂²	1	1	yes	characteristic
93	C₃₁×#383	C₂²	1	2	yes	—
94	C₃₁×#382	C₂²	1	2	yes	—
95	C₃₁×#382	C₂²	1	1	yes	characteristic
96	C₃₁×#382	C₂²	1	1	yes	characteristic
97	C₃₁×#382	C₂²	1	1	yes	characteristic
98	C₃₁×#382	C₂²	1	1	yes	characteristic
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	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊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	C₃₁×#376	C₂²	1	1	yes	characteristic
120	C₃₁×#376	C₂²	1	1	yes	characteristic
121	C₄³×C₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₃₁	C₂²	1	1	yes	characteristic
123	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₃₁×#126	—	2	8	no	—
127	C₃₁×#125	—	2	8	no	—
128	C₃₁×#125	—	2	4	no	—
129	C₃₁×#125	—	2	4	no	—
130	C₃₁×#117	—	2	4	no	—
131	C₃₁×#117	—	2	4	no	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₃₁	—	2	4	no	—
173	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
191	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
192	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
193	C₃₁×#95	C₂³	1	2	yes	—
194	C₃₁×#95	C₂³	1	2	yes	—
195	C₃₁×#95	C₂³	1	2	yes	—
196	C₃₁×#95	C₂³	1	2	yes	—
197	C₃₁×#95	C₂³	1	2	yes	—
198	C₃₁×#95	C₂³	1	2	yes	—
199	C₃₁×#95	C₂³	1	2	yes	—
200	C₃₁×#95	C₂³	1	2	yes	—
201	C₃₁×#95	C₂³	1	2	yes	—
202	C₃₁×#95	C₂³	1	2	yes	—
203	C₃₁×#95	C₂³	1	1	yes	characteristic
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₃₁×#95	C₂³	1	2	yes	—
206	C₃₁×#95	C₂³	1	2	yes	—
207	C₃₁×#95	C₂³	1	2	yes	—
208	C₃₁×#95	C₂³	1	1	yes	characteristic
209	C₃₁×#95	C₂³	1	1	yes	characteristic
210	C₃₁×#95	C₂³	1	1	yes	characteristic
211	C₃₁×#95	C₂³	1	2	yes	—
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₃₁×#95	C₂³	1	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	2	yes	—
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	1	yes	characteristic
220	C₃₁×#95	C₂³	1	1	yes	characteristic
221	C₃₁×#95	C₂³	1	1	yes	characteristic
222	C₃₁×#95	C₂³	1	1	yes	characteristic
223	C₃₁×#95	C₂³	1	2	yes	—
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	2	yes	—
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₃₁	—	2	2	no	—
231	C₂²×C₄×C₃₁	—	2	2	no	—
232	C₂²×C₄×C₃₁	—	2	2	no	—
233	C₂²×C₄×C₃₁	—	2	2	no	—
234	C₂²×C₄×C₃₁	—	2	2	no	—
235	C₂²×C₄×C₃₁	—	2	2	no	—
236	C₂²×C₄×C₃₁	—	2	2	no	—
237	C₂²×C₄×C₃₁	—	4	1	no	—
238	C₂²×C₄×C₃₁	—	4	1	no	—
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
261	C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	2	4	no	—
266	C₄⋊C₄×C₃₁	—	2	4	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	4	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	4	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	4	no	—
278	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	2	4	no	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	4	2	no	—
285	C₄⋊C₄×C₃₁	—	4	2	no	—
286	C₄⋊C₄×C₃₁	—	4	2	no	—
287	C₄⋊C₄×C₃₁	—	4	2	no	—
288	C₄⋊C₄×C₃₁	—	4	2	no	—
289	C₄⋊C₄×C₃₁	—	4	2	no	—
290	C₄⋊C₄×C₃₁	—	4	2	no	—
291	C₄⋊C₄×C₃₁	—	4	2	no	—
292	C₄⋊C₄×C₃₁	#41	1	4	yes	—
293	C₂²⋊C₄×C₃₁	—	2	2	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	2	no	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	—	4	2	no	—
299	C₂²⋊C₄×C₃₁	—	4	2	no	—
300	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
301	C₄²×C₃₁	—	2	2	no	—
302	C₄²×C₃₁	—	2	2	no	—
303	C₄²×C₃₁	—	2	2	no	—
304	C₄²×C₃₁	—	2	2	no	—
305	C₄²×C₃₁	—	2	2	no	—
306	C₄²×C₃₁	—	2	2	no	—
307	C₄²×C₃₁	—	2	2	no	—
308	C₄²×C₃₁	—	2	4	no	—
309	C₄²×C₃₁	—	2	4	no	—
310	C₄²×C₃₁	—	2	2	no	—
311	C₄²×C₃₁	—	2	2	no	—
312	C₄²×C₃₁	—	2	2	no	—
313	C₄²×C₃₁	—	2	2	no	—
314	C₄²×C₃₁	—	4	1	no	—
315	C₄²×C₃₁	—	4	2	no	—
316	C₄²×C₃₁	—	4	2	no	—
317	C₄²×C₃₁	—	4	1	no	—
318	C₄²×C₃₁	—	4	1	no	—
319	C₄²×C₃₁	—	4	1	no	—
320	C₄²×C₃₁	#41	1	4	yes	—
321	#35142	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₃₁	—	2	1	no	—
323	C₂³×C₃₁	—	2	1	no	—
324	C₂³×C₃₁	—	2	1	no	—
325	C₂³×C₃₁	—	2	1	no	—
326	C₂³×C₃₁	—	2	1	no	—
327	C₂³×C₃₁	—	2	1	no	—
328	C₂³×C₃₁	C₂×#41	1	2	yes	—
329	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
330	C₂×C₄×C₃₁	—	2	8	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	1	no	—
333	C₂×C₄×C₃₁	—	2	1	no	—
334	C₂×C₄×C₃₁	—	2	1	no	—
335	C₂×C₄×C₃₁	—	2	1	no	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	1	no	—
338	C₂×C₄×C₃₁	—	2	1	no	—
339	C₂×C₄×C₃₁	—	2	1	no	—
340	C₂×C₄×C₃₁	—	2	1	no	—
341	C₂×C₄×C₃₁	—	2	1	no	—
342	C₂×C₄×C₃₁	—	2	1	no	—
343	C₂×C₄×C₃₁	—	2	1	no	—
344	C₂×C₄×C₃₁	—	2	1	no	—
345	C₂×C₄×C₃₁	—	2	1	no	—
346	C₂×C₄×C₃₁	—	2	1	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	1	no	—
349	C₂×C₄×C₃₁	—	2	1	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	1	no	—
352	C₂×C₄×C₃₁	—	2	1	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	1	no	—
364	C₂×C₄×C₃₁	—	2	1	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	1	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	4	4	no	—
388	C₂×C₄×C₃₁	—	4	4	no	—
389	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
390	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
391	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
392	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
393	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
394	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
395	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
396	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
397	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
398	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
399	#2864	C₂×C₃₁	1	1	yes	characteristic, complemented
400	#2859	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#2851	C₂×C₃₁	1	1	yes	characteristic
402	#2851	C₂×C₃₁	1	1	yes	characteristic
403	#2655	C₂×C₃₁	1	2	yes	complemented
404	#2652	C₂×C₃₁	1	2	yes	—
405	#2533	C₂×C₃₁	1	2	yes	complemented
406	#2528	C₂×C₃₁	1	2	yes	complemented
407	#2509	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#2508	C₂×C₃₁	1	1	yes	characteristic, complemented
409	#2507	C₂×C₃₁	1	1	yes	characteristic, complemented
410	#2506	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#2497	C₂×C₃₁	1	1	yes	characteristic
412	#2496	C₂×C₃₁	1	1	yes	characteristic
413	#2495	C₂×C₃₁	1	1	yes	characteristic
414	#2494	C₂×C₃₁	1	1	yes	characteristic
415	#2478	C₂×C₃₁	1	2	yes	—
416	#2475	C₂×C₃₁	1	2	yes	—
417	#2336	C₂×C₃₁	1	2	yes	complemented
418	#2334	C₂×C₃₁	1	2	yes	—
419	C₄×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
420	C₄×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
421	C₄×#117	C₂×C₃₁	1	1	yes	characteristic
422	C₂²×C₃₁	—	2	2	no	—
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	2	2	no	—
425	C₂²×C₃₁	—	4	1	no	—
426	C₂²×C₃₁	—	4	1	no	—
427	C₂²×C₃₁	—	4	1	no	—
428	C₂²×C₃₁	—	4	1	no	—
429	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
431	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
432	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
434	C₂²×C₃₁	#585	1	1	yes	characteristic
435	C₂²×C₃₁	#585	1	1	yes	characteristic
436	C₄×C₃₁	—	2	2	no	—
437	C₄×C₃₁	—	2	2	no	—
438	C₄×C₃₁	—	2	2	no	—
439	C₄×C₃₁	—	2	2	no	—
440	C₄×C₃₁	—	2	2	no	—
441	C₄×C₃₁	—	2	2	no	—
442	C₄×C₃₁	—	2	2	no	—
443	C₄×C₃₁	—	4	2	no	—
444	C₄×C₃₁	—	4	2	no	—
445	C₄×C₃₁	—	4	1	no	—
446	C₄×C₃₁	—	4	2	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	—	4	2	no	—
450	C₄×C₃₁	—	4	1	no	—
451	C₄×C₃₁	—	4	1	no	—
452	C₄×C₃₁	—	4	2	no	—
453	C₄×C₃₁	—	4	2	no	—
454	C₄×C₃₁	—	4	1	no	—
455	C₄×C₃₁	—	4	1	no	—
456	C₄×C₃₁	—	4	2	no	—
457	C₄×C₃₁	#541	1	4	yes	—
458	C₂×#126	C₂²×C₃₁	1	2	yes	—
459	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
460	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
461	C₂×#125	C₂²×C₃₁	1	2	yes	—
462	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
463	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
464	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
465	#401	C₂²×C₃₁	1	2	yes	—
466	#400	C₂²×C₃₁	1	2	yes	—
467	#400	C₂²×C₃₁	1	2	yes	—
468	#400	C₂²×C₃₁	1	2	yes	—
469	#400	C₂²×C₃₁	1	2	yes	—
470	#400	C₂²×C₃₁	1	2	yes	—
471	#400	C₂²×C₃₁	1	2	yes	—
472	#400	C₂²×C₃₁	1	2	yes	—
473	#398	C₂²×C₃₁	1	2	yes	—
474	#398	C₂²×C₃₁	1	2	yes	—
475	#398	C₂²×C₃₁	1	2	yes	—
476	#398	C₂²×C₃₁	1	2	yes	—
477	#397	C₂²×C₃₁	1	2	yes	—
478	#397	C₂²×C₃₁	1	2	yes	—
479	#397	C₂²×C₃₁	1	2	yes	—
480	#396	C₂²×C₃₁	1	2	yes	—
481	#389	C₂²×C₃₁	1	1	yes	characteristic
482	#389	C₂²×C₃₁	1	1	yes	characteristic
483	#389	C₂²×C₃₁	1	1	yes	characteristic
484	#389	C₂²×C₃₁	1	1	yes	characteristic
485	#389	C₂²×C₃₁	1	2	yes	—
486	#389	C₂²×C₃₁	1	2	yes	—
487	#389	C₂²×C₃₁	1	2	yes	—
488	#389	C₂²×C₃₁	1	2	yes	—
489	#389	C₂²×C₃₁	1	1	yes	characteristic
490	#389	C₂²×C₃₁	1	1	yes	characteristic
491	#389	C₂²×C₃₁	1	1	yes	characteristic
492	#389	C₂²×C₃₁	1	1	yes	characteristic
493	#389	C₂²×C₃₁	1	2	yes	—
494	#389	C₂²×C₃₁	1	2	yes	—
495	#389	C₂²×C₃₁	1	1	yes	characteristic
496	#389	C₂²×C₃₁	1	1	yes	characteristic
497	#389	C₂²×C₃₁	1	1	yes	characteristic
498	#389	C₂²×C₃₁	1	1	yes	characteristic
499	#388	C₂²×C₃₁	1	2	yes	—
500	#388	C₂²×C₃₁	1	2	yes	—
501	#388	C₂²×C₃₁	1	2	yes	—
502	#387	C₂²×C₃₁	1	2	yes	—
503	#387	C₂²×C₃₁	1	2	yes	—
504	#387	C₂²×C₃₁	1	2	yes	—
505	#387	C₂²×C₃₁	1	2	yes	—
506	#387	C₂²×C₃₁	1	2	yes	—
507	#387	C₂²×C₃₁	1	2	yes	—
508	#387	C₂²×C₃₁	1	2	yes	—
509	#387	C₂²×C₃₁	1	2	yes	—
510	#387	C₂²×C₃₁	1	2	yes	—
511	#387	C₂²×C₃₁	1	2	yes	—
512	#387	C₂²×C₃₁	1	2	yes	—
513	#387	C₂²×C₃₁	1	2	yes	—
514	#387	C₂²×C₃₁	1	2	yes	—
515	#387	C₂²×C₃₁	1	2	yes	—
516	#387	C₂²×C₃₁	1	2	yes	—
517	#387	C₂²×C₃₁	1	2	yes	—
518	#387	C₂²×C₃₁	1	2	yes	—
519	#387	C₂²×C₃₁	1	2	yes	—
520	#387	C₂²×C₃₁	1	2	yes	—
521	#385	C₂²×C₃₁	1	2	yes	—
522	#385	C₂²×C₃₁	1	2	yes	—
523	#385	C₂²×C₃₁	1	2	yes	—
524	#385	C₂²×C₃₁	1	2	yes	—
525	#384	C₂²×C₃₁	1	1	yes	characteristic
526	#384	C₂²×C₃₁	1	1	yes	characteristic
527	#383	C₂²×C₃₁	1	2	yes	—
528	#382	C₂²×C₃₁	1	1	yes	characteristic
529	#382	C₂²×C₃₁	1	1	yes	characteristic
530	#382	C₂²×C₃₁	1	2	yes	—
531	#382	C₂²×C₃₁	1	1	yes	characteristic
532	#382	C₂²×C₃₁	1	1	yes	characteristic
533	#380	C₂²×C₃₁	1	1	yes	characteristic
534	#380	C₂²×C₃₁	1	1	yes	characteristic
535	#380	C₂²×C₃₁	1	1	yes	characteristic
536	#380	C₂²×C₃₁	1	1	yes	characteristic
537	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
538	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
539	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
540	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
541	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
542	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
543	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
545	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
546	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
547	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
548	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
549	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
550	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
551	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
552	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
553	#376	C₂²×C₃₁	1	1	yes	characteristic
554	#376	C₂²×C₃₁	1	1	yes	characteristic
555	C₄³	C₂²×C₃₁	1	1	yes	characteristic
556	C₄³	C₂²×C₃₁	1	1	yes	characteristic
557	C₂×C₃₁	—	4	2	no	—
558	C₂×C₃₁	#3444	1	1	yes	characteristic
559	C₂×C₃₁	C₂×#541	1	1	yes	characteristic
560	C₂×C₃₁	#3455	1	1	yes	characteristic
561	C₂×C₃₁	#3515	1	1	yes	characteristic
562	C₂×C₃₁	#3515	1	1	yes	characteristic
563	C₂×C₃₁	#3515	1	1	yes	characteristic
564	C₂×C₃₁	#3518	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
568	#126	—	2	8	no	—
569	#125	—	2	8	no	—
570	#125	—	2	4	no	—
571	#125	—	2	4	no	—
572	#117	—	2	4	no	—
573	#117	—	2	4	no	—
574	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
614	C₂×C₄²	—	2	4	no	—
615	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
620	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
621	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
633	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
634	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
635	#95	C₂³×C₃₁	1	1	yes	characteristic
636	#95	C₂³×C₃₁	1	1	yes	characteristic
637	#95	C₂³×C₃₁	1	1	yes	characteristic
638	#95	C₂³×C₃₁	1	1	yes	characteristic
639	#95	C₂³×C₃₁	1	1	yes	characteristic
640	#95	C₂³×C₃₁	1	1	yes	characteristic
641	#95	C₂³×C₃₁	1	1	yes	characteristic
642	#95	C₂³×C₃₁	1	1	yes	characteristic
643	#95	C₂³×C₃₁	1	2	yes	—
644	#95	C₂³×C₃₁	1	2	yes	—
645	#95	C₂³×C₃₁	1	2	yes	—
646	#95	C₂³×C₃₁	1	2	yes	—
647	#95	C₂³×C₃₁	1	2	yes	—
648	#95	C₂³×C₃₁	1	2	yes	—
649	#95	C₂³×C₃₁	1	2	yes	—
650	#95	C₂³×C₃₁	1	2	yes	—
651	#95	C₂³×C₃₁	1	2	yes	—
652	#95	C₂³×C₃₁	1	2	yes	—
653	#95	C₂³×C₃₁	1	2	yes	—
654	#95	C₂³×C₃₁	1	2	yes	—
655	#95	C₂³×C₃₁	1	2	yes	—
656	#95	C₂³×C₃₁	1	2	yes	—
657	#95	C₂³×C₃₁	1	2	yes	—
658	#95	C₂³×C₃₁	1	2	yes	—
659	#95	C₂³×C₃₁	1	2	yes	—
660	#95	C₂³×C₃₁	1	2	yes	—
661	#95	C₂³×C₃₁	1	2	yes	—
662	#95	C₂³×C₃₁	1	2	yes	—
663	#95	C₂³×C₃₁	1	2	yes	—
664	#95	C₂³×C₃₁	1	2	yes	—
665	#95	C₂³×C₃₁	1	2	yes	—
666	#95	C₂³×C₃₁	1	2	yes	—
667	#95	C₂³×C₃₁	1	2	yes	—
668	#95	C₂³×C₃₁	1	2	yes	—
669	#95	C₂³×C₃₁	1	2	yes	—
670	#95	C₂³×C₃₁	1	2	yes	—
671	C₃₁	#35142	1	1	yes	characteristic, direct product factor, Sylow
672	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	#41×C₃₁	1	4	yes	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	4	1	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	1	no	—
761	C₄²	—	4	1	no	—
762	C₄²	—	4	1	no	—
763	C₄²	#41×C₃₁	1	4	yes	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	C₂×#41×C₃₁	1	2	yes	—
771	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
772	C₂×C₄	—	2	8	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
832	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
833	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
834	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
835	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
836	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
837	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
838	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
839	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
840	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
849	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
850	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
851	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
852	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
853	C₂²	C₃₁×#585	1	1	yes	characteristic
854	C₂²	C₃₁×#585	1	1	yes	characteristic
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	C₃₁×#541	1	4	yes	—
877	C₂	—	4	2	no	—
878	C₂	C₃₁×#3444	1	1	yes	characteristic
879	C₂	C₂×C₃₁×#541	1	1	yes	characteristic
880	C₂	C₃₁×#3455	1	1	yes	characteristic
881	C₂	C₃₁×#3515	1	1	yes	characteristic
882	C₂	C₃₁×#3515	1	1	yes	characteristic
883	C₂	C₃₁×#3515	1	1	yes	characteristic
884	C₂	C₃₁×#3518	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁴×C₃₁	C₂⁴
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×#2864	C₂	semidirect
2. C₃₁×#2859	C₂	semidirect
5. C₃₁×#2655	C₂	semidirect
7. C₃₁×#2533	C₂	semidirect
8. C₃₁×#2528	C₂	semidirect
9. C₃₁×#2509	C₂	semidirect
10. C₃₁×#2508	C₂	semidirect
11. C₃₁×#2507	C₂	semidirect
12. C₃₁×#2506	C₂	semidirect
19. C₃₁×#2336	C₂	semidirect
21. C₄×C₃₁×#125	C₂	semidirect
22. C₄×C₃₁×#125	C₂	semidirect
321. #35142	C₃₁	direct (N × H)
399. #2864	C₂×C₃₁	semidirect
400. #2859	C₂×C₃₁	semidirect
403. #2655	C₂×C₃₁	semidirect
405. #2533	C₂×C₃₁	semidirect
406. #2528	C₂×C₃₁	semidirect
407. #2509	C₂×C₃₁	semidirect
408. #2508	C₂×C₃₁	semidirect
409. #2507	C₂×C₃₁	semidirect
410. #2506	C₂×C₃₁	semidirect
417. #2336	C₂×C₃₁	semidirect
419. C₄×#125	C₂×C₃₁	semidirect
420. C₄×#125	C₂×C₃₁	semidirect
671. C₃₁	#35142	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×#2864	2
C₃₁×#2859	2
C₃₁×#2851	2
C₃₁×#2655	2
C₃₁×#2652	2
C₃₁×#2533	2
C₃₁×#2528	2
C₃₁×#2509	2
C₃₁×#2508	2
C₃₁×#2507	2
C₃₁×#2506	2
C₃₁×#2497	2
C₃₁×#2496	2
C₃₁×#2495	2
C₃₁×#2494	2
C₃₁×#2478	2
C₃₁×#2475	2
C₃₁×#2336	2
C₃₁×#2334	2
C₄×C₃₁×#125	2
C₄×C₃₁×#117	2
#35142	31

Subgroups — C31×#35142 #21491901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35142 #21491901