Subgroups — C₃₁×#36730 #21493489

Order 7936.

1950 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2848	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2847	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2746	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2745	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2738	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2737	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2701	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2700	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2687	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2686	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2639	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2510	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2472	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2450	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2418	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2325	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃₁×#381	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#124	C₂²	1	2	yes	—
22	C₂×C₃₁×#123	C₂²	1	2	yes	—
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#120	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#401	C₂²	1	2	yes	complemented
35	C₃₁×#400	C₂²	1	2	yes	complemented
36	C₃₁×#400	C₂²	1	2	yes	complemented
37	C₃₁×#400	C₂²	1	2	yes	complemented
38	C₃₁×#399	C₂²	1	2	yes	—
39	C₃₁×#398	C₂²	1	2	yes	complemented
40	C₃₁×#398	C₂²	1	2	yes	complemented
41	C₃₁×#398	C₂²	1	2	yes	complemented
42	C₃₁×#397	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	2	yes	—
44	C₃₁×#397	C₂²	1	2	yes	complemented
45	C₃₁×#397	C₂²	1	2	yes	complemented
46	C₃₁×#397	C₂²	1	2	yes	complemented
47	C₃₁×#396	C₂²	1	2	yes	complemented
48	C₃₁×#395	C₂²	1	2	yes	complemented
49	C₃₁×#395	C₂²	1	2	yes	complemented
50	C₃₁×#394	C₂²	1	2	yes	—
51	C₃₁×#394	C₂²	1	2	yes	—
52	C₃₁×#394	C₂²	1	2	yes	—
53	C₃₁×#394	C₂²	1	2	yes	—
54	C₃₁×#394	C₂²	1	2	yes	complemented
55	C₃₁×#393	C₂²	1	2	yes	—
56	C₃₁×#393	C₂²	1	2	yes	complemented
57	C₃₁×#393	C₂²	1	2	yes	complemented
58	C₃₁×#391	C₂²	1	2	yes	complemented
59	C₃₁×#391	C₂²	1	2	yes	complemented
60	C₃₁×#390	C₂²	1	2	yes	—
61	C₃₁×#389	C₂²	1	2	yes	complemented
62	C₃₁×#388	C₂²	1	2	yes	—
63	C₃₁×#388	C₂²	1	2	yes	—
64	C₃₁×#388	C₂²	1	2	yes	—
65	C₃₁×#388	C₂²	1	2	yes	—
66	C₃₁×#388	C₂²	1	2	yes	complemented
67	C₃₁×#388	C₂²	1	2	yes	complemented
68	C₃₁×#388	C₂²	1	2	yes	complemented
69	C₃₁×#387	C₂²	1	2	yes	complemented
70	C₃₁×#387	C₂²	1	2	yes	complemented
71	C₃₁×#387	C₂²	1	2	yes	complemented
72	C₃₁×#387	C₂²	1	2	yes	complemented
73	C₃₁×#387	C₂²	1	2	yes	complemented
74	C₃₁×#386	C₂²	1	2	yes	—
75	C₃₁×#386	C₂²	1	2	yes	—
76	C₃₁×#386	C₂²	1	2	yes	—
77	C₃₁×#386	C₂²	1	2	yes	—
78	C₃₁×#386	C₂²	1	2	yes	—
79	C₃₁×#386	C₂²	1	2	yes	—
80	C₃₁×#386	C₂²	1	2	yes	—
81	C₃₁×#386	C₂²	1	2	yes	complemented
82	C₃₁×#385	C₂²	1	2	yes	—
83	C₃₁×#385	C₂²	1	2	yes	—
84	C₃₁×#385	C₂²	1	2	yes	—
85	C₃₁×#385	C₂²	1	2	yes	—
86	C₃₁×#385	C₂²	1	2	yes	complemented
87	C₃₁×#385	C₂²	1	2	yes	complemented
88	C₃₁×#383	C₂²	1	2	yes	complemented
89	C₃₁×#381	C₂²	1	2	yes	—
90	C₃₁×#381	C₂²	1	2	yes	—
91	C₃₁×#381	C₂²	1	2	yes	—
92	C₃₁×#381	C₂²	1	2	yes	—
93	C₃₁×#380	C₂²	1	1	yes	characteristic
94	C₃₁×#380	C₂²	1	1	yes	characteristic
95	C₃₁×#380	C₂²	1	1	yes	characteristic
96	C₃₁×#380	C₂²	1	1	yes	characteristic
97	C₃₁×#380	C₂²	1	1	yes	characteristic
98	C₃₁×#380	C₂²	1	1	yes	characteristic
99	C₃₁×#380	C₂²	1	2	yes	—
100	C₃₁×#380	C₂²	1	2	yes	complemented
101	C₃₁×#379	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
103	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
104	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
105	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
106	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
107	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₃₁	—	2	4	no	—
115	C₂³×C₄×C₃₁	—	4	2	no	—
116	C₂³×C₄×C₃₁	—	4	2	no	—
117	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₃₁	C₂³	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	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₃₁×#124	—	4	4	no	—
129	C₃₁×#123	—	4	4	no	—
130	C₃₁×C₂²⋊Q₈	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	—	4	4	no	—
132	C₃₁×C₂²⋊Q₈	—	4	2	no	—
133	C₃₁×C₂²⋊Q₈	—	4	2	no	—
134	C₃₁×#121	—	2	4	no	—
135	C₃₁×#121	—	4	2	no	—
136	C₃₁×#121	—	4	2	no	—
137	C₃₁×#120	—	4	4	no	—
138	C₄×D₄×C₃₁	—	4	4	no	—
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	2	yes	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	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×C₂²⋊C₄×C₃₁	—	4	2	no	—
157	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
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	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×C₄²×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
183	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
184	C₃₁×#95	C₂³	1	2	yes	—
185	C₃₁×#95	C₂³	1	2	yes	—
186	C₃₁×#95	C₂³	1	2	yes	—
187	C₃₁×#95	C₂³	1	2	yes	—
188	C₃₁×#95	C₂³	1	2	yes	—
189	C₃₁×#95	C₂³	1	2	yes	—
190	C₃₁×#95	C₂³	1	2	yes	—
191	C₃₁×#95	C₂³	1	2	yes	—
192	C₃₁×#95	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
209	C₃₁×#95	C₂³	1	2	yes	—
210	C₂⁴×C₃₁	—	2	2	no	—
211	C₂⁴×C₃₁	—	2	2	no	—
212	C₂⁴×C₃₁	—	2	2	no	—
213	C₂⁴×C₃₁	—	2	2	no	—
214	C₂⁴×C₃₁	—	2	2	no	—
215	C₂⁴×C₃₁	—	4	1	no	—
216	C₂⁴×C₃₁	—	4	1	no	—
217	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
218	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂×Q₈×C₃₁	—	2	2	no	—
222	C₂×Q₈×C₃₁	—	4	1	no	—
223	C₂×Q₈×C₃₁	—	4	1	no	—
224	C₂×Q₈×C₃₁	—	4	2	no	—
225	C₂×Q₈×C₃₁	—	4	2	no	—
226	C₂×Q₈×C₃₁	—	4	2	no	—
227	C₂×D₄×C₃₁	—	2	4	no	—
228	C₂×D₄×C₃₁	—	2	4	no	—
229	C₂×D₄×C₃₁	—	2	4	no	—
230	C₂×D₄×C₃₁	—	2	4	no	—
231	C₂×D₄×C₃₁	—	2	4	no	—
232	C₂×D₄×C₃₁	—	2	2	no	—
233	C₂×D₄×C₃₁	—	4	2	no	—
234	C₂×D₄×C₃₁	—	4	2	no	—
235	C₂×D₄×C₃₁	—	4	1	no	—
236	C₂×D₄×C₃₁	—	4	1	no	—
237	C₂×D₄×C₃₁	—	4	2	no	—
238	C₂×D₄×C₃₁	—	4	2	no	—
239	C₂²×C₄×C₃₁	—	2	2	no	—
240	C₂²×C₄×C₃₁	—	2	2	no	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	2	2	no	—
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	—	2	2	no	—
245	C₂²×C₄×C₃₁	—	2	2	no	—
246	C₂²×C₄×C₃₁	—	2	2	no	—
247	C₂²×C₄×C₃₁	—	2	2	no	—
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	2	2	no	—
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	4	1	no	—
253	C₂²×C₄×C₃₁	—	4	1	no	—
254	C₂²×C₄×C₃₁	—	4	1	no	—
255	C₂²×C₄×C₃₁	—	4	1	no	—
256	C₂²×C₄×C₃₁	—	4	1	no	—
257	C₂²×C₄×C₃₁	—	4	1	no	—
258	C₂²×C₄×C₃₁	—	4	1	no	—
259	C₂²×C₄×C₃₁	—	4	1	no	—
260	C₂²×C₄×C₃₁	—	4	1	no	—
261	C₂²×C₄×C₃₁	—	4	1	no	—
262	C₂²×C₄×C₃₁	—	4	1	no	—
263	C₂²×C₄×C₃₁	—	4	1	no	—
264	C₂²×C₄×C₃₁	—	4	2	no	—
265	C₂²×C₄×C₃₁	—	4	2	no	—
266	C₂²×C₄×C₃₁	—	4	1	no	—
267	C₂²×C₄×C₃₁	—	4	2	no	—
268	C₂²×C₄×C₃₁	—	4	1	no	—
269	C₂²×C₄×C₃₁	—	4	1	no	—
270	C₂²×C₄×C₃₁	—	4	1	no	—
271	C₂²×C₄×C₃₁	—	4	16	no	—
272	C₂²×C₄×C₃₁	#41	1	4	yes	—
273	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	4	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	1	no	—
295	C₄⋊C₄×C₃₁	—	4	1	no	—
296	C₄⋊C₄×C₃₁	—	4	1	no	—
297	C₄⋊C₄×C₃₁	—	4	1	no	—
298	C₄⋊C₄×C₃₁	—	4	2	no	—
299	C₄⋊C₄×C₃₁	—	4	2	no	—
300	C₄⋊C₄×C₃₁	—	4	2	no	—
301	C₄⋊C₄×C₃₁	—	4	2	no	—
302	C₄⋊C₄×C₃₁	—	4	2	no	—
303	C₄⋊C₄×C₃₁	—	4	2	no	—
304	C₄⋊C₄×C₃₁	—	4	2	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	4	no	—
308	C₂²⋊C₄×C₃₁	—	2	4	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₃₁	—	2	4	no	—
312	C₂²⋊C₄×C₃₁	—	2	4	no	—
313	C₂²⋊C₄×C₃₁	—	4	2	no	—
314	C₂²⋊C₄×C₃₁	—	4	2	no	—
315	C₂²⋊C₄×C₃₁	—	4	2	no	—
316	C₂²⋊C₄×C₃₁	—	4	2	no	—
317	C₂²⋊C₄×C₃₁	—	4	2	no	—
318	C₂²⋊C₄×C₃₁	—	4	2	no	—
319	C₂²⋊C₄×C₃₁	—	4	2	no	—
320	C₂²⋊C₄×C₃₁	—	4	2	no	—
321	C₂²⋊C₄×C₃₁	—	4	2	no	—
322	C₂²⋊C₄×C₃₁	—	4	2	no	—
323	C₂²⋊C₄×C₃₁	—	4	2	no	—
324	C₂²⋊C₄×C₃₁	—	4	2	no	—
325	C₂²⋊C₄×C₃₁	—	4	2	no	—
326	C₂²⋊C₄×C₃₁	—	4	2	no	—
327	C₂²⋊C₄×C₃₁	—	4	2	no	—
328	C₄²×C₃₁	—	4	2	no	—
329	C₄²×C₃₁	—	4	2	no	—
330	C₄²×C₃₁	—	4	2	no	—
331	#36730	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂³×C₃₁	—	2	1	no	—
333	C₂³×C₃₁	—	2	1	no	—
334	C₂³×C₃₁	—	2	1	no	—
335	C₂³×C₃₁	—	2	1	no	—
336	C₂³×C₃₁	—	2	8	no	—
337	C₂³×C₃₁	—	2	1	no	—
338	C₂³×C₃₁	—	2	1	no	—
339	C₂³×C₃₁	—	2	1	no	—
340	C₂³×C₃₁	—	2	1	no	—
341	C₂³×C₃₁	—	2	1	no	—
342	C₂³×C₃₁	—	2	1	no	—
343	C₂³×C₃₁	—	2	1	no	—
344	C₂³×C₃₁	—	2	1	no	—
345	C₂³×C₃₁	—	2	1	no	—
346	C₂³×C₃₁	—	2	1	no	—
347	C₂³×C₃₁	—	2	1	no	—
348	C₂³×C₃₁	—	2	1	no	—
349	C₂³×C₃₁	—	2	2	no	—
350	C₂³×C₃₁	—	2	2	no	—
351	C₂³×C₃₁	—	2	2	no	—
352	C₂³×C₃₁	—	2	2	no	—
353	C₂³×C₃₁	—	2	2	no	—
354	C₂³×C₃₁	—	2	2	no	—
355	C₂³×C₃₁	—	2	2	no	—
356	C₂³×C₃₁	—	4	4	no	—
357	C₂³×C₃₁	—	4	4	no	—
358	C₂³×C₃₁	—	4	4	no	—
359	C₂³×C₃₁	—	4	4	no	—
360	C₂³×C₃₁	—	4	4	no	—
361	C₂³×C₃₁	—	4	4	no	—
362	C₂³×C₃₁	C₂×#41	1	2	yes	—
363	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
364	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
365	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
366	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
367	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
368	Q₈×C₃₁	—	8	2	no	—
369	Q₈×C₃₁	—	8	4	no	—
370	D₄×C₃₁	—	4	8	no	—
371	D₄×C₃₁	—	8	2	no	—
372	D₄×C₃₁	—	8	4	no	—
373	D₄×C₃₁	—	8	4	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	1	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	2	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	2	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	2	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	2	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	1	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	4	4	no	—
418	C₂×C₄×C₃₁	—	4	4	no	—
419	C₂×C₄×C₃₁	—	4	4	no	—
420	C₂×C₄×C₃₁	—	4	4	no	—
421	C₂×C₄×C₃₁	—	4	4	no	—
422	C₂×C₄×C₃₁	—	4	4	no	—
423	C₂×C₄×C₃₁	—	8	2	no	—
424	C₂×C₄×C₃₁	—	8	2	no	—
425	C₂×C₄×C₃₁	—	8	2	no	—
426	C₂×C₄×C₃₁	—	8	2	no	—
427	C₂×C₄×C₃₁	—	8	4	no	—
428	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
429	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
430	#2848	C₂×C₃₁	1	1	yes	characteristic, complemented
431	#2847	C₂×C₃₁	1	1	yes	characteristic
432	#2746	C₂×C₃₁	1	2	yes	complemented
433	#2745	C₂×C₃₁	1	2	yes	complemented
434	#2738	C₂×C₃₁	1	2	yes	complemented
435	#2737	C₂×C₃₁	1	2	yes	complemented
436	#2701	C₂×C₃₁	1	2	yes	complemented
437	#2700	C₂×C₃₁	1	2	yes	complemented
438	#2687	C₂×C₃₁	1	2	yes	complemented
439	#2686	C₂×C₃₁	1	2	yes	complemented
440	#2659	C₂×C₃₁	1	1	yes	characteristic, complemented
441	#2639	C₂×C₃₁	1	1	yes	characteristic, complemented
442	#2510	C₂×C₃₁	1	2	yes	complemented
443	#2472	C₂×C₃₁	1	2	yes	complemented
444	#2450	C₂×C₃₁	1	2	yes	complemented
445	#2418	C₂×C₃₁	1	2	yes	complemented
446	#2329	C₂×C₃₁	1	1	yes	characteristic, complemented
447	#2325	C₂×C₃₁	1	1	yes	characteristic, complemented
448	C₂×#381	C₂×C₃₁	1	1	yes	characteristic, complemented
449	C₂²×C₃₁	—	2	2	no	—
450	C₂²×C₃₁	—	2	2	no	—
451	C₂²×C₃₁	—	2	2	no	—
452	C₂²×C₃₁	—	2	2	no	—
453	C₂²×C₃₁	—	2	2	no	—
454	C₂²×C₃₁	—	2	2	no	—
455	C₂²×C₃₁	—	2	2	no	—
456	C₂²×C₃₁	—	2	2	no	—
457	C₂²×C₃₁	—	2	2	no	—
458	C₂²×C₃₁	—	2	2	no	—
459	C₂²×C₃₁	—	2	2	no	—
460	C₂²×C₃₁	—	2	2	no	—
461	C₂²×C₃₁	—	4	16	no	—
462	C₂²×C₃₁	—	4	1	no	—
463	C₂²×C₃₁	—	4	1	no	—
464	C₂²×C₃₁	—	4	1	no	—
465	C₂²×C₃₁	—	4	1	no	—
466	C₂²×C₃₁	—	4	1	no	—
467	C₂²×C₃₁	—	4	1	no	—
468	C₂²×C₃₁	—	4	1	no	—
469	C₂²×C₃₁	—	4	1	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	—	4	2	no	—
472	C₂²×C₃₁	—	4	2	no	—
473	C₂²×C₃₁	—	4	2	no	—
474	C₂²×C₃₁	—	4	2	no	—
475	C₂²×C₃₁	—	4	2	no	—
476	C₂²×C₃₁	—	4	2	no	—
477	C₂²×C₃₁	#542	1	4	yes	—
478	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
479	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂²×C₃₁	#585	1	1	yes	characteristic
484	C₂²×C₃₁	#585	1	1	yes	characteristic
485	C₄×C₃₁	—	2	2	no	—
486	C₄×C₃₁	—	2	2	no	—
487	C₄×C₃₁	—	4	2	no	—
488	C₄×C₃₁	—	4	1	no	—
489	C₄×C₃₁	—	4	1	no	—
490	C₄×C₃₁	—	4	2	no	—
491	C₄×C₃₁	—	4	2	no	—
492	C₄×C₃₁	—	4	2	no	—
493	C₄×C₃₁	—	4	2	no	—
494	C₄×C₃₁	—	4	2	no	—
495	C₄×C₃₁	—	4	2	no	—
496	C₄×C₃₁	—	4	2	no	—
497	C₄×C₃₁	—	4	2	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
501	C₂×#124	C₂²×C₃₁	1	2	yes	—
502	C₂×#123	C₂²×C₃₁	1	2	yes	—
503	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
504	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
505	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
506	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
507	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
508	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
509	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
510	C₂×#120	C₂²×C₃₁	1	2	yes	—
511	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
512	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
513	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
514	#401	C₂²×C₃₁	1	2	yes	complemented
515	#400	C₂²×C₃₁	1	2	yes	complemented
516	#400	C₂²×C₃₁	1	2	yes	complemented
517	#400	C₂²×C₃₁	1	2	yes	complemented
518	#399	C₂²×C₃₁	1	2	yes	—
519	#398	C₂²×C₃₁	1	2	yes	complemented
520	#398	C₂²×C₃₁	1	2	yes	complemented
521	#398	C₂²×C₃₁	1	2	yes	complemented
522	#397	C₂²×C₃₁	1	2	yes	—
523	#397	C₂²×C₃₁	1	2	yes	—
524	#397	C₂²×C₃₁	1	2	yes	complemented
525	#397	C₂²×C₃₁	1	2	yes	complemented
526	#397	C₂²×C₃₁	1	2	yes	complemented
527	#396	C₂²×C₃₁	1	2	yes	complemented
528	#395	C₂²×C₃₁	1	2	yes	complemented
529	#395	C₂²×C₃₁	1	2	yes	complemented
530	#394	C₂²×C₃₁	1	2	yes	—
531	#394	C₂²×C₃₁	1	2	yes	—
532	#394	C₂²×C₃₁	1	2	yes	—
533	#394	C₂²×C₃₁	1	2	yes	—
534	#394	C₂²×C₃₁	1	2	yes	complemented
535	#393	C₂²×C₃₁	1	2	yes	—
536	#393	C₂²×C₃₁	1	2	yes	complemented
537	#393	C₂²×C₃₁	1	2	yes	complemented
538	#391	C₂²×C₃₁	1	2	yes	complemented
539	#391	C₂²×C₃₁	1	2	yes	complemented
540	#390	C₂²×C₃₁	1	2	yes	—
541	#389	C₂²×C₃₁	1	2	yes	complemented
542	#388	C₂²×C₃₁	1	2	yes	—
543	#388	C₂²×C₃₁	1	2	yes	—
544	#388	C₂²×C₃₁	1	2	yes	—
545	#388	C₂²×C₃₁	1	2	yes	—
546	#388	C₂²×C₃₁	1	2	yes	complemented
547	#388	C₂²×C₃₁	1	2	yes	complemented
548	#388	C₂²×C₃₁	1	2	yes	complemented
549	#387	C₂²×C₃₁	1	2	yes	complemented
550	#387	C₂²×C₃₁	1	2	yes	complemented
551	#387	C₂²×C₃₁	1	2	yes	complemented
552	#387	C₂²×C₃₁	1	2	yes	complemented
553	#387	C₂²×C₃₁	1	2	yes	complemented
554	#386	C₂²×C₃₁	1	2	yes	—
555	#386	C₂²×C₃₁	1	2	yes	—
556	#386	C₂²×C₃₁	1	2	yes	—
557	#386	C₂²×C₃₁	1	2	yes	—
558	#386	C₂²×C₃₁	1	2	yes	—
559	#386	C₂²×C₃₁	1	2	yes	—
560	#386	C₂²×C₃₁	1	2	yes	—
561	#386	C₂²×C₃₁	1	2	yes	complemented
562	#385	C₂²×C₃₁	1	2	yes	—
563	#385	C₂²×C₃₁	1	2	yes	—
564	#385	C₂²×C₃₁	1	2	yes	—
565	#385	C₂²×C₃₁	1	2	yes	—
566	#385	C₂²×C₃₁	1	2	yes	complemented
567	#385	C₂²×C₃₁	1	2	yes	complemented
568	#383	C₂²×C₃₁	1	2	yes	complemented
569	#381	C₂²×C₃₁	1	2	yes	—
570	#381	C₂²×C₃₁	1	2	yes	—
571	#381	C₂²×C₃₁	1	2	yes	—
572	#381	C₂²×C₃₁	1	2	yes	—
573	#380	C₂²×C₃₁	1	1	yes	characteristic
574	#380	C₂²×C₃₁	1	1	yes	characteristic
575	#380	C₂²×C₃₁	1	1	yes	characteristic
576	#380	C₂²×C₃₁	1	1	yes	characteristic
577	#380	C₂²×C₃₁	1	1	yes	characteristic
578	#380	C₂²×C₃₁	1	1	yes	characteristic
579	#380	C₂²×C₃₁	1	2	yes	—
580	#380	C₂²×C₃₁	1	2	yes	complemented
581	#379	C₂²×C₃₁	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
583	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
584	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
585	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
586	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
587	C₂×C₃₁	—	2	4	no	—
588	C₂×C₃₁	—	4	2	no	—
589	C₂×C₃₁	—	4	2	no	—
590	C₂×C₃₁	—	8	2	no	—
591	C₂×C₃₁	C₂×#542	1	1	yes	characteristic
592	C₂×C₃₁	#3490	1	1	yes	characteristic
593	C₂×C₃₁	#3493	1	1	yes	characteristic
594	C₂×C₃₁	#3534	1	1	yes	characteristic
595	C₂×C₃₁	#3534	1	1	yes	characteristic
596	C₂×C₃₁	#3535	1	1	yes	characteristic
597	C₂×C₃₁	#3535	1	1	yes	characteristic
598	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
599	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
600	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
601	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
602	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
603	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
604	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
605	C₂³×C₄	—	2	4	no	—
606	C₂³×C₄	—	4	2	no	—
607	C₂³×C₄	—	4	2	no	—
608	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
618	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
619	#124	—	4	4	no	—
620	#123	—	4	4	no	—
621	C₂²⋊Q₈	—	2	4	no	—
622	C₂²⋊Q₈	—	4	4	no	—
623	C₂²⋊Q₈	—	4	2	no	—
624	C₂²⋊Q₈	—	4	2	no	—
625	#121	—	2	4	no	—
626	#121	—	4	2	no	—
627	#121	—	4	2	no	—
628	#120	—	4	4	no	—
629	C₄×D₄	—	4	4	no	—
630	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₂²⋊C₄	—	4	2	no	—
648	C₂×C₂²⋊C₄	—	4	2	no	—
649	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
673	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
674	C₂×C₄²	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	#95	C₂³×C₃₁	1	2	yes	—
687	#95	C₂³×C₃₁	1	2	yes	—
688	#95	C₂³×C₃₁	1	2	yes	—
689	#95	C₂³×C₃₁	1	2	yes	—
690	#95	C₂³×C₃₁	1	2	yes	—
691	#95	C₂³×C₃₁	1	2	yes	—
692	#95	C₂³×C₃₁	1	2	yes	—
693	#95	C₂³×C₃₁	1	2	yes	—
694	#95	C₂³×C₃₁	1	2	yes	—
695	#95	C₂³×C₃₁	1	2	yes	—
696	#95	C₂³×C₃₁	1	2	yes	—
697	#95	C₂³×C₃₁	1	2	yes	—
698	#95	C₂³×C₃₁	1	2	yes	—
699	#95	C₂³×C₃₁	1	2	yes	—
700	#95	C₂³×C₃₁	1	2	yes	—
701	C₃₁	#36730	1	1	yes	characteristic, direct product factor, Sylow
702	C₂⁴	—	2	2	no	—
703	C₂⁴	—	2	2	no	—
704	C₂⁴	—	2	2	no	—
705	C₂⁴	—	2	2	no	—
706	C₂⁴	—	2	2	no	—
707	C₂⁴	—	4	1	no	—
708	C₂⁴	—	4	1	no	—
709	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
710	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
711	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
712	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	4	1	no	—
715	C₂×Q₈	—	4	1	no	—
716	C₂×Q₈	—	4	2	no	—
717	C₂×Q₈	—	4	2	no	—
718	C₂×Q₈	—	4	2	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	1	no	—
728	C₂×D₄	—	4	1	no	—
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	4	1	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	—	4	1	no	—
748	C₂²×C₄	—	4	1	no	—
749	C₂²×C₄	—	4	1	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	1	no	—
752	C₂²×C₄	—	4	1	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	16	no	—
764	C₂²×C₄	#41×C₃₁	1	4	yes	—
765	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	1	no	—
787	C₄⋊C₄	—	4	1	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	—	4	1	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₄²	—	4	2	no	—
821	C₄²	—	4	2	no	—
822	C₄²	—	4	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	8	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	4	4	no	—
848	C₂³	—	4	4	no	—
849	C₂³	—	4	4	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	4	no	—
852	C₂³	—	4	4	no	—
853	C₂³	C₂×#41×C₃₁	1	2	yes	—
854	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
855	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
856	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
857	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
858	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
859	Q₈	—	8	2	no	—
860	Q₈	—	8	4	no	—
861	D₄	—	4	8	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	4	no	—
864	D₄	—	8	4	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	4	no	—
910	C₂×C₄	—	4	4	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	8	2	no	—
915	C₂×C₄	—	8	2	no	—
916	C₂×C₄	—	8	2	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	—	8	4	no	—
919	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
920	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	4	16	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	C₃₁×#542	1	4	yes	—
950	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
951	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
952	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
954	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
955	C₂²	C₃₁×#585	1	1	yes	characteristic
956	C₂²	C₃₁×#585	1	1	yes	characteristic
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₂	—	2	4	no	—
973	C₂	—	4	2	no	—
974	C₂	—	4	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₂×C₃₁×#542	1	1	yes	characteristic
977	C₂	C₃₁×#3490	1	1	yes	characteristic
978	C₂	C₃₁×#3493	1	1	yes	characteristic
979	C₂	C₃₁×#3534	1	1	yes	characteristic
980	C₂	C₃₁×#3534	1	1	yes	characteristic
981	C₂	C₃₁×#3535	1	1	yes	characteristic
982	C₂	C₃₁×#3535	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2848	C₂	semidirect
3. C₃₁×#2746	C₂	semidirect
4. C₃₁×#2745	C₂	semidirect
5. C₃₁×#2738	C₂	semidirect
6. C₃₁×#2737	C₂	semidirect
7. C₃₁×#2701	C₂	semidirect
8. C₃₁×#2700	C₂	semidirect
9. C₃₁×#2687	C₂	semidirect
10. C₃₁×#2686	C₂	semidirect
11. C₃₁×#2659	C₂	semidirect
12. C₃₁×#2639	C₂	semidirect
13. C₃₁×#2510	C₂	semidirect
14. C₃₁×#2472	C₂	semidirect
15. C₃₁×#2450	C₂	semidirect
16. C₃₁×#2418	C₂	semidirect
17. C₃₁×#2329	C₂	semidirect
18. C₃₁×#2325	C₂	semidirect
19. C₂×C₃₁×#381	C₂	semidirect
34. C₃₁×#401	C₂²	semidirect
35. C₃₁×#400	C₂²	semidirect
36. C₃₁×#400	C₂²	semidirect
37. C₃₁×#400	C₂²	semidirect
39. C₃₁×#398	C₂²	semidirect
40. C₃₁×#398	C₂²	semidirect
41. C₃₁×#398	C₂²	semidirect
44. C₃₁×#397	C₂²	semidirect
45. C₃₁×#397	C₂²	semidirect
46. C₃₁×#397	C₂²	semidirect
47. C₃₁×#396	C₂²	semidirect
48. C₃₁×#395	C₂²	semidirect
49. C₃₁×#395	C₂²	semidirect
54. C₃₁×#394	C₂²	semidirect
56. C₃₁×#393	C₂²	semidirect
57. C₃₁×#393	C₂²	semidirect
58. C₃₁×#391	C₂²	semidirect
59. C₃₁×#391	C₂²	semidirect
61. C₃₁×#389	C₂²	semidirect
66. C₃₁×#388	C₂²	semidirect
67. C₃₁×#388	C₂²	semidirect
68. C₃₁×#388	C₂²	semidirect
69. C₃₁×#387	C₂²	semidirect
70. C₃₁×#387	C₂²	semidirect
71. C₃₁×#387	C₂²	semidirect
72. C₃₁×#387	C₂²	semidirect
73. C₃₁×#387	C₂²	semidirect
81. C₃₁×#386	C₂²	semidirect
86. C₃₁×#385	C₂²	semidirect
87. C₃₁×#385	C₂²	semidirect
88. C₃₁×#383	C₂²	semidirect
100. C₃₁×#380	C₂²	semidirect
331. #36730	C₃₁	direct (N × H)
430. #2848	C₂×C₃₁	semidirect
432. #2746	C₂×C₃₁	semidirect
433. #2745	C₂×C₃₁	semidirect
434. #2738	C₂×C₃₁	semidirect
435. #2737	C₂×C₃₁	semidirect
436. #2701	C₂×C₃₁	semidirect
437. #2700	C₂×C₃₁	semidirect
438. #2687	C₂×C₃₁	semidirect
439. #2686	C₂×C₃₁	semidirect
440. #2659	C₂×C₃₁	semidirect
441. #2639	C₂×C₃₁	semidirect
442. #2510	C₂×C₃₁	semidirect
443. #2472	C₂×C₃₁	semidirect
444. #2450	C₂×C₃₁	semidirect
445. #2418	C₂×C₃₁	semidirect
446. #2329	C₂×C₃₁	semidirect
447. #2325	C₂×C₃₁	semidirect
448. C₂×#381	C₂×C₃₁	semidirect
514. #401	C₂²×C₃₁	semidirect
515. #400	C₂²×C₃₁	semidirect
516. #400	C₂²×C₃₁	semidirect
517. #400	C₂²×C₃₁	semidirect
519. #398	C₂²×C₃₁	semidirect
520. #398	C₂²×C₃₁	semidirect
521. #398	C₂²×C₃₁	semidirect
524. #397	C₂²×C₃₁	semidirect
525. #397	C₂²×C₃₁	semidirect
526. #397	C₂²×C₃₁	semidirect
527. #396	C₂²×C₃₁	semidirect
528. #395	C₂²×C₃₁	semidirect
529. #395	C₂²×C₃₁	semidirect
534. #394	C₂²×C₃₁	semidirect
536. #393	C₂²×C₃₁	semidirect
537. #393	C₂²×C₃₁	semidirect
538. #391	C₂²×C₃₁	semidirect
539. #391	C₂²×C₃₁	semidirect
541. #389	C₂²×C₃₁	semidirect
546. #388	C₂²×C₃₁	semidirect
547. #388	C₂²×C₃₁	semidirect
548. #388	C₂²×C₃₁	semidirect
549. #387	C₂²×C₃₁	semidirect
550. #387	C₂²×C₃₁	semidirect
551. #387	C₂²×C₃₁	semidirect
552. #387	C₂²×C₃₁	semidirect
553. #387	C₂²×C₃₁	semidirect
561. #386	C₂²×C₃₁	semidirect
566. #385	C₂²×C₃₁	semidirect
567. #385	C₂²×C₃₁	semidirect
568. #383	C₂²×C₃₁	semidirect
580. #380	C₂²×C₃₁	semidirect
701. C₃₁	#36730	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×#2848	2
C₃₁×#2847	2
C₃₁×#2746	2
C₃₁×#2745	2
C₃₁×#2738	2
C₃₁×#2737	2
C₃₁×#2701	2
C₃₁×#2700	2
C₃₁×#2687	2
C₃₁×#2686	2
C₃₁×#2659	2
C₃₁×#2639	2
C₃₁×#2510	2
C₃₁×#2472	2
C₃₁×#2450	2
C₃₁×#2418	2
C₃₁×#2329	2
C₃₁×#2325	2
C₂×C₃₁×#381	2
#36730	31

Subgroups — C31×#36730 #21493489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36730 #21493489