Subgroups — C₃₁×#35116 #21491875

Order 7936.

1648 conjugacy classes of subgroups.

The subgroup lattice has 910 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×#2860	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2860	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2654	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2637	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2584	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2580	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2566	C₂	1	1	yes	maximal, characteristic
11	C₃₁×#2519	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2513	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2512	C₂	1	1	yes	maximal, characteristic
14	C₃₁×#2508	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2507	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2478	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2475	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2469	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
21	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic
23	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#126	C₂²	1	2	yes	—
25	C₂×C₃₁×#126	C₂²	1	2	yes	—
26	C₂×C₃₁×#126	C₂²	1	2	yes	—
27	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#125	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#117	C₂²	1	2	yes	—
34	C₃₁×#400	C₂²	1	2	yes	—
35	C₃₁×#400	C₂²	1	2	yes	—
36	C₃₁×#399	C₂²	1	2	yes	—
37	C₃₁×#398	C₂²	1	2	yes	—
38	C₃₁×#398	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×#397	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	2	yes	—
44	C₃₁×#397	C₂²	1	2	yes	—
45	C₃₁×#396	C₂²	1	2	yes	—
46	C₃₁×#396	C₂²	1	2	yes	—
47	C₃₁×#396	C₂²	1	2	yes	—
48	C₃₁×#395	C₂²	1	2	yes	—
49	C₃₁×#393	C₂²	1	2	yes	—
50	C₃₁×#390	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
56	C₃₁×#389	C₂²	1	1	yes	characteristic
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	2	yes	—
61	C₃₁×#389	C₂²	1	2	yes	—
62	C₃₁×#389	C₂²	1	1	yes	characteristic
63	C₃₁×#389	C₂²	1	1	yes	characteristic
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	1	yes	characteristic
66	C₃₁×#389	C₂²	1	2	yes	—
67	C₃₁×#389	C₂²	1	2	yes	—
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	2	yes	—
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#389	C₂²	1	1	yes	characteristic
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	2	yes	—
75	C₃₁×#388	C₂²	1	2	yes	—
76	C₃₁×#388	C₂²	1	2	yes	—
77	C₃₁×#388	C₂²	1	2	yes	—
78	C₃₁×#388	C₂²	1	2	yes	—
79	C₃₁×#388	C₂²	1	2	yes	—
80	C₃₁×#388	C₂²	1	2	yes	—
81	C₃₁×#388	C₂²	1	2	yes	—
82	C₃₁×#388	C₂²	1	2	yes	—
83	C₃₁×#388	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×#387	C₂²	1	2	yes	—
88	C₃₁×#387	C₂²	1	2	yes	—
89	C₃₁×#387	C₂²	1	2	yes	—
90	C₃₁×#387	C₂²	1	2	yes	—
91	C₃₁×#387	C₂²	1	2	yes	—
92	C₃₁×#387	C₂²	1	2	yes	—
93	C₃₁×#387	C₂²	1	2	yes	—
94	C₃₁×#385	C₂²	1	2	yes	—
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	2	yes	—
97	C₃₁×#385	C₂²	1	2	yes	—
98	C₃₁×#384	C₂²	1	1	yes	characteristic
99	C₃₁×#384	C₂²	1	1	yes	characteristic
100	C₃₁×#382	C₂²	1	1	yes	characteristic
101	C₃₁×#382	C₂²	1	1	yes	characteristic
102	C₃₁×#382	C₂²	1	1	yes	characteristic
103	C₃₁×#382	C₂²	1	2	yes	—
104	C₃₁×#382	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	1	yes	characteristic
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
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×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
120	C₄³×C₃₁	C₂²	1	1	yes	characteristic
121	C₄³×C₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₃₁	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
126	C₃₁×#126	—	2	8	no	—
127	C₃₁×#126	—	2	8	no	—
128	C₃₁×#126	—	4	4	no	—
129	C₃₁×#125	—	2	4	no	—
130	C₃₁×#125	—	4	4	no	—
131	C₄×Q₈×C₃₁	—	2	4	no	—
132	C₄×Q₈×C₃₁	—	2	4	no	—
133	C₄×Q₈×C₃₁	—	2	4	no	—
134	C₄×D₄×C₃₁	—	2	4	no	—
135	C₃₁×#117	—	4	4	no	—
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	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×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	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
209	C₃₁×#95	C₂³	1	2	yes	—
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	1	yes	characteristic
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₃₁×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	2	yes	—
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	1	yes	characteristic
226	C₃₁×#95	C₂³	1	1	yes	characteristic
227	C₃₁×#95	C₂³	1	1	yes	characteristic
228	C₃₁×#95	C₂³	1	1	yes	characteristic
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×D₄×C₃₁	—	2	2	no	—
237	C₂×D₄×C₃₁	—	2	2	no	—
238	C₂×D₄×C₃₁	—	2	2	no	—
239	C₂²×C₄×C₃₁	—	2	4	no	—
240	C₂²×C₄×C₃₁	—	4	2	no	—
241	C₂²×C₄×C₃₁	—	4	2	no	—
242	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₃₁	—	2	2	no	—
265	C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	2	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	4	no	—
274	C₄⋊C₄×C₃₁	—	2	4	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	4	no	—
281	C₄⋊C₄×C₃₁	—	2	4	no	—
282	C₄⋊C₄×C₃₁	—	2	4	no	—
283	C₄⋊C₄×C₃₁	—	2	4	no	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	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	—	4	2	no	—
293	C₄⋊C₄×C₃₁	—	4	2	no	—
294	C₄⋊C₄×C₃₁	—	4	2	no	—
295	C₄⋊C₄×C₃₁	—	4	2	no	—
296	C₄⋊C₄×C₃₁	—	4	2	no	—
297	C₄⋊C₄×C₃₁	#41	1	4	yes	—
298	C₂²⋊C₄×C₃₁	—	2	4	no	—
299	C₂²⋊C₄×C₃₁	—	2	4	no	—
300	C₂²⋊C₄×C₃₁	—	2	4	no	—
301	C₂²⋊C₄×C₃₁	—	2	4	no	—
302	C₂²⋊C₄×C₃₁	—	2	4	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	4	2	no	—
307	C₂²⋊C₄×C₃₁	—	4	2	no	—
308	C₂²⋊C₄×C₃₁	—	4	2	no	—
309	C₂²⋊C₄×C₃₁	—	4	2	no	—
310	C₂²⋊C₄×C₃₁	—	4	2	no	—
311	C₄²×C₃₁	—	2	2	no	—
312	C₄²×C₃₁	—	2	2	no	—
313	C₄²×C₃₁	—	2	2	no	—
314	C₄²×C₃₁	—	2	2	no	—
315	C₄²×C₃₁	—	2	2	no	—
316	C₄²×C₃₁	—	2	2	no	—
317	C₄²×C₃₁	—	2	2	no	—
318	C₄²×C₃₁	—	2	4	no	—
319	C₄²×C₃₁	—	2	2	no	—
320	C₄²×C₃₁	—	2	2	no	—
321	C₄²×C₃₁	—	2	2	no	—
322	C₄²×C₃₁	—	2	2	no	—
323	C₄²×C₃₁	—	2	2	no	—
324	C₄²×C₃₁	—	2	2	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	4	1	no	—
327	C₄²×C₃₁	—	4	1	no	—
328	C₄²×C₃₁	—	4	1	no	—
329	C₄²×C₃₁	—	4	2	no	—
330	C₄²×C₃₁	—	4	2	no	—
331	C₄²×C₃₁	#41	1	4	yes	—
332	C₄²×C₃₁	#41	1	4	yes	—
333	#35116	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₃₁	—	2	2	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	2	2	no	—
337	C₂³×C₃₁	—	2	2	no	—
338	C₂³×C₃₁	—	2	2	no	—
339	C₂³×C₃₁	—	2	2	no	—
340	C₂³×C₃₁	—	2	2	no	—
341	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
342	Q₈×C₃₁	—	2	8	no	—
343	D₄×C₃₁	—	4	4	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	1	no	—
348	C₂×C₄×C₃₁	—	2	1	no	—
349	C₂×C₄×C₃₁	—	2	1	no	—
350	C₂×C₄×C₃₁	—	2	1	no	—
351	C₂×C₄×C₃₁	—	2	1	no	—
352	C₂×C₄×C₃₁	—	2	1	no	—
353	C₂×C₄×C₃₁	—	2	1	no	—
354	C₂×C₄×C₃₁	—	2	1	no	—
355	C₂×C₄×C₃₁	—	2	1	no	—
356	C₂×C₄×C₃₁	—	2	1	no	—
357	C₂×C₄×C₃₁	—	2	1	no	—
358	C₂×C₄×C₃₁	—	2	1	no	—
359	C₂×C₄×C₃₁	—	2	1	no	—
360	C₂×C₄×C₃₁	—	2	1	no	—
361	C₂×C₄×C₃₁	—	2	1	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	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	1	no	—
368	C₂×C₄×C₃₁	—	2	1	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	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	1	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	2	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	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	2	no	—
392	C₂×C₄×C₃₁	—	2	1	no	—
393	C₂×C₄×C₃₁	—	2	1	no	—
394	C₂×C₄×C₃₁	—	2	2	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	4	8	no	—
399	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
400	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
401	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
402	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
403	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
404	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
405	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
406	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
407	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
408	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
409	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
410	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
411	#2864	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#2860	C₂×C₃₁	1	1	yes	characteristic
413	#2860	C₂×C₃₁	1	1	yes	characteristic
414	#2859	C₂×C₃₁	1	1	yes	characteristic, complemented
415	#2654	C₂×C₃₁	1	2	yes	complemented
416	#2637	C₂×C₃₁	1	2	yes	complemented
417	#2584	C₂×C₃₁	1	1	yes	characteristic, complemented
418	#2580	C₂×C₃₁	1	1	yes	characteristic
419	#2570	C₂×C₃₁	1	1	yes	characteristic, complemented
420	#2566	C₂×C₃₁	1	1	yes	characteristic
421	#2519	C₂×C₃₁	1	2	yes	complemented
422	#2513	C₂×C₃₁	1	1	yes	characteristic
423	#2512	C₂×C₃₁	1	1	yes	characteristic
424	#2508	C₂×C₃₁	1	1	yes	characteristic, complemented
425	#2507	C₂×C₃₁	1	1	yes	characteristic, complemented
426	#2478	C₂×C₃₁	1	2	yes	complemented
427	#2475	C₂×C₃₁	1	2	yes	complemented
428	#2469	C₂×C₃₁	1	2	yes	complemented
429	#2334	C₂×C₃₁	1	2	yes	complemented
430	#2334	C₂×C₃₁	1	2	yes	complemented
431	C₄×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
432	#2293	C₂×C₃₁	1	1	yes	characteristic
433	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
434	C₂²×C₃₁	—	4	2	no	—
435	C₂²×C₃₁	—	4	2	no	—
436	C₂²×C₃₁	—	4	2	no	—
437	C₂²×C₃₁	—	4	2	no	—
438	C₂²×C₃₁	—	4	2	no	—
439	C₂²×C₃₁	—	4	2	no	—
440	C₂²×C₃₁	—	4	2	no	—
441	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
442	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
443	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
444	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
447	C₂²×C₃₁	#585	1	1	yes	characteristic
448	C₄×C₃₁	—	2	2	no	—
449	C₄×C₃₁	—	2	2	no	—
450	C₄×C₃₁	—	2	2	no	—
451	C₄×C₃₁	—	2	2	no	—
452	C₄×C₃₁	—	2	2	no	—
453	C₄×C₃₁	—	2	2	no	—
454	C₄×C₃₁	—	2	2	no	—
455	C₄×C₃₁	—	2	2	no	—
456	C₄×C₃₁	—	2	2	no	—
457	C₄×C₃₁	—	4	2	no	—
458	C₄×C₃₁	—	4	1	no	—
459	C₄×C₃₁	—	4	1	no	—
460	C₄×C₃₁	—	4	2	no	—
461	C₄×C₃₁	—	4	2	no	—
462	C₄×C₃₁	—	4	2	no	—
463	C₄×C₃₁	—	4	1	no	—
464	C₄×C₃₁	—	4	1	no	—
465	C₄×C₃₁	—	4	2	no	—
466	C₄×C₃₁	—	4	1	no	—
467	C₄×C₃₁	—	4	2	no	—
468	C₄×C₃₁	—	4	2	no	—
469	C₄×C₃₁	#541	1	4	yes	—
470	C₂×#126	C₂²×C₃₁	1	2	yes	—
471	C₂×#126	C₂²×C₃₁	1	2	yes	—
472	C₂×#126	C₂²×C₃₁	1	2	yes	—
473	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
474	C₂×#125	C₂²×C₃₁	1	2	yes	—
475	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
476	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
477	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
478	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
479	C₂×#117	C₂²×C₃₁	1	2	yes	—
480	#400	C₂²×C₃₁	1	2	yes	—
481	#400	C₂²×C₃₁	1	2	yes	—
482	#399	C₂²×C₃₁	1	2	yes	—
483	#398	C₂²×C₃₁	1	2	yes	—
484	#398	C₂²×C₃₁	1	2	yes	—
485	#398	C₂²×C₃₁	1	2	yes	—
486	#398	C₂²×C₃₁	1	2	yes	—
487	#398	C₂²×C₃₁	1	2	yes	—
488	#397	C₂²×C₃₁	1	2	yes	—
489	#397	C₂²×C₃₁	1	2	yes	—
490	#397	C₂²×C₃₁	1	2	yes	—
491	#396	C₂²×C₃₁	1	2	yes	—
492	#396	C₂²×C₃₁	1	2	yes	—
493	#396	C₂²×C₃₁	1	2	yes	—
494	#395	C₂²×C₃₁	1	2	yes	—
495	#393	C₂²×C₃₁	1	2	yes	—
496	#390	C₂²×C₃₁	1	1	yes	characteristic
497	#390	C₂²×C₃₁	1	1	yes	characteristic
498	#390	C₂²×C₃₁	1	1	yes	characteristic
499	#390	C₂²×C₃₁	1	1	yes	characteristic
500	#390	C₂²×C₃₁	1	1	yes	characteristic
501	#390	C₂²×C₃₁	1	1	yes	characteristic
502	#389	C₂²×C₃₁	1	1	yes	characteristic
503	#389	C₂²×C₃₁	1	1	yes	characteristic
504	#389	C₂²×C₃₁	1	1	yes	characteristic
505	#389	C₂²×C₃₁	1	1	yes	characteristic
506	#389	C₂²×C₃₁	1	1	yes	characteristic
507	#389	C₂²×C₃₁	1	1	yes	characteristic
508	#389	C₂²×C₃₁	1	2	yes	—
509	#389	C₂²×C₃₁	1	2	yes	—
510	#389	C₂²×C₃₁	1	1	yes	characteristic
511	#389	C₂²×C₃₁	1	1	yes	characteristic
512	#389	C₂²×C₃₁	1	1	yes	characteristic
513	#389	C₂²×C₃₁	1	1	yes	characteristic
514	#389	C₂²×C₃₁	1	2	yes	—
515	#389	C₂²×C₃₁	1	2	yes	—
516	#389	C₂²×C₃₁	1	1	yes	characteristic
517	#389	C₂²×C₃₁	1	2	yes	—
518	#389	C₂²×C₃₁	1	1	yes	characteristic
519	#388	C₂²×C₃₁	1	2	yes	—
520	#388	C₂²×C₃₁	1	2	yes	—
521	#388	C₂²×C₃₁	1	2	yes	—
522	#388	C₂²×C₃₁	1	2	yes	—
523	#388	C₂²×C₃₁	1	2	yes	—
524	#388	C₂²×C₃₁	1	2	yes	—
525	#388	C₂²×C₃₁	1	2	yes	—
526	#388	C₂²×C₃₁	1	2	yes	—
527	#388	C₂²×C₃₁	1	2	yes	—
528	#388	C₂²×C₃₁	1	2	yes	—
529	#388	C₂²×C₃₁	1	2	yes	—
530	#387	C₂²×C₃₁	1	2	yes	—
531	#387	C₂²×C₃₁	1	2	yes	—
532	#387	C₂²×C₃₁	1	2	yes	—
533	#387	C₂²×C₃₁	1	2	yes	—
534	#387	C₂²×C₃₁	1	2	yes	—
535	#387	C₂²×C₃₁	1	2	yes	—
536	#387	C₂²×C₃₁	1	2	yes	—
537	#387	C₂²×C₃₁	1	2	yes	—
538	#387	C₂²×C₃₁	1	2	yes	—
539	#387	C₂²×C₃₁	1	2	yes	—
540	#385	C₂²×C₃₁	1	2	yes	—
541	#385	C₂²×C₃₁	1	2	yes	—
542	#385	C₂²×C₃₁	1	2	yes	—
543	#385	C₂²×C₃₁	1	2	yes	—
544	#384	C₂²×C₃₁	1	1	yes	characteristic
545	#384	C₂²×C₃₁	1	1	yes	characteristic
546	#382	C₂²×C₃₁	1	1	yes	characteristic
547	#382	C₂²×C₃₁	1	1	yes	characteristic
548	#382	C₂²×C₃₁	1	1	yes	characteristic
549	#382	C₂²×C₃₁	1	2	yes	—
550	#382	C₂²×C₃₁	1	2	yes	—
551	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
552	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
560	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
563	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
565	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
566	C₄³	C₂²×C₃₁	1	1	yes	characteristic
567	C₄³	C₂²×C₃₁	1	1	yes	characteristic
568	C₄³	C₂²×C₃₁	1	1	yes	characteristic
569	C₂×C₃₁	—	8	2	no	—
570	C₂×C₃₁	#3444	1	1	yes	characteristic
571	C₂×C₃₁	C₂×#541	1	1	yes	characteristic
572	C₂×C₃₁	#3460	1	1	yes	characteristic
573	C₂×C₃₁	#3507	1	1	yes	characteristic
574	C₂×C₃₁	#3511	1	1	yes	characteristic
575	C₂×C₃₁	#3515	1	1	yes	characteristic
576	C₂×C₃₁	#3522	1	1	yes	characteristic
577	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
580	#126	—	2	8	no	—
581	#126	—	2	8	no	—
582	#126	—	4	4	no	—
583	#125	—	2	4	no	—
584	#125	—	4	4	no	—
585	C₄×Q₈	—	2	4	no	—
586	C₄×Q₈	—	2	4	no	—
587	C₄×Q₈	—	2	4	no	—
588	C₄×D₄	—	2	4	no	—
589	#117	—	4	4	no	—
590	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
637	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
648	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
657	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
659	#95	C₂³×C₃₁	1	2	yes	—
660	#95	C₂³×C₃₁	1	2	yes	—
661	#95	C₂³×C₃₁	1	1	yes	characteristic
662	#95	C₂³×C₃₁	1	1	yes	characteristic
663	#95	C₂³×C₃₁	1	1	yes	characteristic
664	#95	C₂³×C₃₁	1	1	yes	characteristic
665	#95	C₂³×C₃₁	1	1	yes	characteristic
666	#95	C₂³×C₃₁	1	1	yes	characteristic
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	#95	C₂³×C₃₁	1	2	yes	—
672	#95	C₂³×C₃₁	1	2	yes	—
673	#95	C₂³×C₃₁	1	2	yes	—
674	#95	C₂³×C₃₁	1	2	yes	—
675	#95	C₂³×C₃₁	1	2	yes	—
676	#95	C₂³×C₃₁	1	2	yes	—
677	#95	C₂³×C₃₁	1	2	yes	—
678	#95	C₂³×C₃₁	1	2	yes	—
679	#95	C₂³×C₃₁	1	2	yes	—
680	#95	C₂³×C₃₁	1	2	yes	—
681	#95	C₂³×C₃₁	1	2	yes	—
682	#95	C₂³×C₃₁	1	2	yes	—
683	#95	C₂³×C₃₁	1	2	yes	—
684	#95	C₂³×C₃₁	1	2	yes	—
685	#95	C₂³×C₃₁	1	2	yes	—
686	C₃₁	#35116	1	1	yes	characteristic, direct product factor, Sylow
687	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	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	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	#41×C₃₁	1	4	yes	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	4	1	no	—
782	C₄²	—	4	1	no	—
783	C₄²	—	4	1	no	—
784	C₄²	—	4	2	no	—
785	C₄²	—	4	2	no	—
786	C₄²	#41×C₃₁	1	4	yes	—
787	C₄²	#41×C₃₁	1	4	yes	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
796	Q₈	—	2	8	no	—
797	D₄	—	4	4	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	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	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	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	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
854	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
855	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
856	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
857	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
858	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
859	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
860	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
861	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
862	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
863	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
864	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
873	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
874	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
875	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
876	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
877	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
878	C₂²	C₃₁×#585	1	1	yes	characteristic
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	C₃₁×#541	1	4	yes	—
901	C₂	—	8	2	no	—
902	C₂	C₃₁×#3444	1	1	yes	characteristic
903	C₂	C₂×C₃₁×#541	1	1	yes	characteristic
904	C₂	C₃₁×#3460	1	1	yes	characteristic
905	C₂	C₃₁×#3507	1	1	yes	characteristic
906	C₂	C₃₁×#3511	1	1	yes	characteristic
907	C₂	C₃₁×#3515	1	1	yes	characteristic
908	C₂	C₃₁×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
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
4. C₃₁×#2859	C₂	semidirect
5. C₃₁×#2654	C₂	semidirect
6. C₃₁×#2637	C₂	semidirect
7. C₃₁×#2584	C₂	semidirect
9. C₃₁×#2570	C₂	semidirect
11. C₃₁×#2519	C₂	semidirect
14. C₃₁×#2508	C₂	semidirect
15. C₃₁×#2507	C₂	semidirect
16. C₃₁×#2478	C₂	semidirect
17. C₃₁×#2475	C₂	semidirect
18. C₃₁×#2469	C₂	semidirect
19. C₃₁×#2334	C₂	semidirect
20. C₃₁×#2334	C₂	semidirect
21. C₄×C₃₁×#125	C₂	semidirect
23. C₄²×Q₈×C₃₁	C₂	semidirect
333. #35116	C₃₁	direct (N × H)
411. #2864	C₂×C₃₁	semidirect
414. #2859	C₂×C₃₁	semidirect
415. #2654	C₂×C₃₁	semidirect
416. #2637	C₂×C₃₁	semidirect
417. #2584	C₂×C₃₁	semidirect
419. #2570	C₂×C₃₁	semidirect
421. #2519	C₂×C₃₁	semidirect
424. #2508	C₂×C₃₁	semidirect
425. #2507	C₂×C₃₁	semidirect
426. #2478	C₂×C₃₁	semidirect
427. #2475	C₂×C₃₁	semidirect
428. #2469	C₂×C₃₁	semidirect
429. #2334	C₂×C₃₁	semidirect
430. #2334	C₂×C₃₁	semidirect
431. C₄×#125	C₂×C₃₁	semidirect
433. C₄²×Q₈	C₂×C₃₁	semidirect
686. C₃₁	#35116	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×#2860	2
C₃₁×#2859	2
C₃₁×#2654	2
C₃₁×#2637	2
C₃₁×#2584	2
C₃₁×#2580	2
C₃₁×#2570	2
C₃₁×#2566	2
C₃₁×#2519	2
C₃₁×#2513	2
C₃₁×#2512	2
C₃₁×#2508	2
C₃₁×#2507	2
C₃₁×#2478	2
C₃₁×#2475	2
C₃₁×#2469	2
C₃₁×#2334	2
C₄×C₃₁×#125	2
C₃₁×#2293	2
C₄²×Q₈×C₃₁	2
#35116	31

Subgroups — C31×#35116 #21491875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35116 #21491875