Subgroups — C₃₁×#36581 #21493340

Order 7936.

2988 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2847	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2591	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2579	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2487	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2481	C₂	1	4	yes	maximal, complemented
10	C₃₁×#2443	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2442	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2416	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2361	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2352	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2345	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×#120	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#120	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#553	—	2	8	no	—
21	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
22	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
24	C₂×C₃₁×#121	C₂²	1	2	yes	—
25	C₂×C₃₁×#121	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#121	C₂²	1	4	yes	—
28	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃₁×#120	C₂²	1	2	yes	—
30	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄⋊C₄×C₃₁	—	2	8	no	—
38	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
42	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#400	C₂²	1	4	yes	complemented
45	C₃₁×#400	C₂²	1	2	yes	complemented
46	C₃₁×#399	C₂²	1	2	yes	complemented
47	C₃₁×#398	C₂²	1	4	yes	complemented
48	C₃₁×#397	C₂²	1	4	yes	complemented
49	C₃₁×#396	C₂²	1	4	yes	complemented
50	C₃₁×#394	C₂²	1	4	yes	complemented
51	C₃₁×#390	C₂²	1	2	yes	complemented
52	C₃₁×#389	C₂²	1	2	yes	complemented
53	C₃₁×#389	C₂²	1	2	yes	complemented
54	C₃₁×#388	C₂²	1	4	yes	complemented
55	C₃₁×#388	C₂²	1	4	yes	complemented
56	C₃₁×#387	C₂²	1	4	yes	complemented
57	C₃₁×#387	C₂²	1	4	yes	complemented
58	C₃₁×#386	C₂²	1	2	yes	—
59	C₃₁×#386	C₂²	1	2	yes	—
60	C₃₁×#386	C₂²	1	2	yes	—
61	C₃₁×#386	C₂²	1	4	yes	—
62	C₃₁×#386	C₂²	1	4	yes	—
63	C₃₁×#386	C₂²	1	4	yes	—
64	C₃₁×#386	C₂²	1	1	yes	characteristic
65	C₃₁×#386	C₂²	1	2	yes	—
66	C₃₁×#386	C₂²	1	4	yes	—
67	C₃₁×#386	C₂²	1	2	yes	—
68	C₃₁×#385	C₂²	1	1	yes	characteristic
69	C₃₁×#385	C₂²	1	2	yes	—
70	C₃₁×#385	C₂²	1	4	yes	—
71	C₃₁×#385	C₂²	1	2	yes	—
72	C₃₁×#385	C₂²	1	4	yes	complemented
73	C₃₁×#382	C₂²	1	2	yes	complemented
74	C₃₁×#380	C₂²	1	2	yes	—
75	C₃₁×#380	C₂²	1	1	yes	characteristic
76	C₃₁×#380	C₂²	1	2	yes	—
77	C₃₁×#380	C₂²	1	4	yes	—
78	C₃₁×#380	C₂²	1	2	yes	complemented
79	C₃₁×#379	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
85	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
87	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₃₁	—	2	4	no	—
93	C₂³×C₄×C₃₁	—	2	8	no	—
94	C₂³×C₄×C₃₁	—	2	8	no	—
95	C₂³×C₄×C₃₁	—	4	8	no	—
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
98	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
103	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
104	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
105	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
106	C₃₁×#126	—	2	8	no	—
107	C₃₁×#125	—	2	4	no	—
108	C₃₁×#123	—	2	8	no	—
109	C₃₁×#121	—	2	8	no	—
110	C₃₁×#121	—	2	4	no	—
111	C₃₁×#121	—	2	8	no	—
112	C₃₁×#121	—	2	4	no	—
113	C₃₁×#121	—	4	8	no	—
114	C₃₁×#120	—	2	8	no	—
115	C₃₁×#120	—	2	4	no	—
116	C₄×D₄×C₃₁	—	2	8	no	—
117	C₄×D₄×C₃₁	—	2	4	no	—
118	C₄×D₄×C₃₁	—	2	8	no	—
119	C₄×D₄×C₃₁	—	2	4	no	—
120	C₄×D₄×C₃₁	—	4	8	no	—
121	C₃₁×#117	—	2	4	no	—
122	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
123	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
124	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
125	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
126	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
127	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	complemented
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	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	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
161	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
165	C₃₁×#95	C₂³	1	4	yes	—
166	C₃₁×#95	C₂³	1	2	yes	—
167	C₃₁×#95	C₂³	1	4	yes	—
168	C₃₁×#95	C₂³	1	4	yes	—
169	C₃₁×#95	C₂³	1	2	yes	—
170	C₃₁×#95	C₂³	1	4	yes	—
171	C₃₁×#95	C₂³	1	2	yes	—
172	C₃₁×#95	C₂³	1	2	yes	—
173	C₃₁×#95	C₂³	1	4	yes	—
174	C₃₁×#95	C₂³	1	4	yes	—
175	C₃₁×#95	C₂³	1	4	yes	—
176	C₂⁴×C₃₁	—	2	2	no	—
177	C₂⁴×C₃₁	—	2	4	no	—
178	C₂⁴×C₃₁	—	2	4	no	—
179	C₂⁴×C₃₁	—	2	2	no	—
180	C₂⁴×C₃₁	#41	1	4	yes	—
181	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
183	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
184	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
185	C₂×D₄×C₃₁	—	2	4	no	—
186	C₂×D₄×C₃₁	—	2	2	no	—
187	C₂×D₄×C₃₁	—	2	4	no	—
188	C₂×D₄×C₃₁	—	2	4	no	—
189	C₂×D₄×C₃₁	—	2	2	no	—
190	C₂×D₄×C₃₁	—	2	4	no	—
191	C₂×D₄×C₃₁	—	2	8	no	—
192	C₂×D₄×C₃₁	—	2	8	no	—
193	C₂×D₄×C₃₁	—	2	8	no	—
194	C₂×D₄×C₃₁	—	2	4	no	—
195	C₂×D₄×C₃₁	—	2	4	no	—
196	C₂×D₄×C₃₁	—	2	2	no	—
197	C₂×D₄×C₃₁	—	2	2	no	—
198	C₂×D₄×C₃₁	—	2	4	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	4	4	no	—
201	C₂²×C₄×C₃₁	—	2	32	no	—
202	C₂²×C₄×C₃₁	—	2	2	no	—
203	C₂²×C₄×C₃₁	—	2	4	no	—
204	C₂²×C₄×C₃₁	—	2	4	no	—
205	C₂²×C₄×C₃₁	—	2	4	no	—
206	C₂²×C₄×C₃₁	—	2	4	no	—
207	C₂²×C₄×C₃₁	—	2	4	no	—
208	C₂²×C₄×C₃₁	—	2	4	no	—
209	C₂²×C₄×C₃₁	—	2	4	no	—
210	C₂²×C₄×C₃₁	—	2	4	no	—
211	C₂²×C₄×C₃₁	—	2	8	no	—
212	C₂²×C₄×C₃₁	—	2	8	no	—
213	C₂²×C₄×C₃₁	—	2	8	no	—
214	C₂²×C₄×C₃₁	—	2	8	no	—
215	C₂²×C₄×C₃₁	—	2	2	no	—
216	C₂²×C₄×C₃₁	—	2	4	no	—
217	C₂²×C₄×C₃₁	—	2	4	no	—
218	C₂²×C₄×C₃₁	—	4	4	no	—
219	C₂²×C₄×C₃₁	—	4	4	no	—
220	C₂²×C₄×C₃₁	—	4	4	no	—
221	C₂²×C₄×C₃₁	—	4	4	no	—
222	C₂²×C₄×C₃₁	—	4	4	no	—
223	C₂²×C₄×C₃₁	—	4	32	no	—
224	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
225	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
226	C₂²×C₄×C₃₁	#41	1	8	yes	—
227	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₄⋊C₄×C₃₁	—	2	8	no	—
241	C₄⋊C₄×C₃₁	—	2	8	no	—
242	C₄⋊C₄×C₃₁	—	2	4	no	—
243	C₄⋊C₄×C₃₁	—	2	4	no	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	—	2	4	no	—
246	C₄⋊C₄×C₃₁	—	2	2	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	4	4	no	—
251	C₄⋊C₄×C₃₁	—	4	4	no	—
252	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
253	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
254	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
255	C₂²⋊C₄×C₃₁	—	2	2	no	—
256	C₂²⋊C₄×C₃₁	—	2	4	no	—
257	C₂²⋊C₄×C₃₁	—	2	4	no	—
258	C₂²⋊C₄×C₃₁	—	2	2	no	—
259	C₂²⋊C₄×C₃₁	—	2	8	no	—
260	C₂²⋊C₄×C₃₁	—	2	4	no	—
261	C₂²⋊C₄×C₃₁	—	2	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	8	no	—
270	C₂²⋊C₄×C₃₁	—	4	4	no	—
271	C₂²⋊C₄×C₃₁	—	4	4	no	—
272	C₂²⋊C₄×C₃₁	—	4	4	no	—
273	C₄²×C₃₁	—	2	4	no	—
274	C₄²×C₃₁	—	2	2	no	—
275	C₄²×C₃₁	—	2	4	no	—
276	C₄²×C₃₁	—	4	4	no	—
277	#36581	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₃₁	—	2	8	no	—
279	C₂³×C₃₁	—	2	8	no	—
280	C₂³×C₃₁	—	2	16	no	—
281	C₂³×C₃₁	—	2	8	no	—
282	C₂³×C₃₁	—	2	16	no	—
283	C₂³×C₃₁	—	2	2	no	—
284	C₂³×C₃₁	—	2	2	no	—
285	C₂³×C₃₁	—	2	2	no	—
286	C₂³×C₃₁	—	2	2	no	—
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	1	no	—
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	2	4	no	—
293	C₂³×C₃₁	—	2	1	no	—
294	C₂³×C₃₁	—	2	2	no	—
295	C₂³×C₃₁	—	2	4	no	—
296	C₂³×C₃₁	—	2	2	no	—
297	C₂³×C₃₁	—	2	1	no	—
298	C₂³×C₃₁	—	2	2	no	—
299	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
300	C₂³×C₃₁	C₂×#41	1	2	yes	—
301	C₂³×C₃₁	C₂×#41	1	4	yes	—
302	C₂³×C₃₁	C₂×#41	1	4	yes	—
303	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
304	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
305	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
306	D₄×C₃₁	—	4	8	no	—
307	D₄×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	4	8	no	—
309	D₄×C₃₁	—	4	16	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	8	4	no	—
312	C₂×C₄×C₃₁	—	2	16	no	—
313	C₂×C₄×C₃₁	—	2	8	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	2	4	no	—
319	C₂×C₄×C₃₁	—	2	8	no	—
320	C₂×C₄×C₃₁	—	2	16	no	—
321	C₂×C₄×C₃₁	—	2	1	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	1	no	—
324	C₂×C₄×C₃₁	—	2	1	no	—
325	C₂×C₄×C₃₁	—	2	4	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	1	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	4	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	4	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	4	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	4	no	—
339	C₂×C₄×C₃₁	—	2	4	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	1	no	—
343	C₂×C₄×C₃₁	—	4	8	no	—
344	C₂×C₄×C₃₁	—	4	16	no	—
345	C₂×C₄×C₃₁	—	4	16	no	—
346	C₂×C₄×C₃₁	—	4	8	no	—
347	C₂×C₄×C₃₁	—	4	4	no	—
348	C₂×C₄×C₃₁	—	8	4	no	—
349	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
352	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
354	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
355	C₂×#553	C₂×C₃₁	1	1	yes	characteristic, complemented
356	C₂³×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#2847	C₂×C₃₁	1	2	yes	complemented
358	#2847	C₂×C₃₁	1	1	yes	characteristic, complemented
359	#2591	C₂×C₃₁	1	2	yes	complemented
360	#2579	C₂×C₃₁	1	2	yes	complemented
361	#2504	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#2487	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#2481	C₂×C₃₁	1	4	yes	complemented
364	#2443	C₂×C₃₁	1	4	yes	complemented
365	#2442	C₂×C₃₁	1	2	yes	complemented
366	#2416	C₂×C₃₁	1	2	yes	complemented
367	#2361	C₂×C₃₁	1	2	yes	complemented
368	#2352	C₂×C₃₁	1	2	yes	complemented
369	#2345	C₂×C₃₁	1	1	yes	characteristic, complemented
370	C₄×#120	C₂×C₃₁	1	2	yes	complemented
371	C₄×#120	C₂×C₃₁	1	1	yes	characteristic, complemented
372	C₂²×C₃₁	—	2	32	no	—
373	C₂²×C₃₁	—	2	2	no	—
374	C₂²×C₃₁	—	2	4	no	—
375	C₂²×C₃₁	—	2	4	no	—
376	C₂²×C₃₁	—	2	4	no	—
377	C₂²×C₃₁	—	2	4	no	—
378	C₂²×C₃₁	—	2	2	no	—
379	C₂²×C₃₁	—	2	4	no	—
380	C₂²×C₃₁	—	2	4	no	—
381	C₂²×C₃₁	—	2	4	no	—
382	C₂²×C₃₁	—	2	4	no	—
383	C₂²×C₃₁	—	4	1	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	—	4	1	no	—
386	C₂²×C₃₁	—	4	2	no	—
387	C₂²×C₃₁	—	4	2	no	—
388	C₂²×C₃₁	—	4	4	no	—
389	C₂²×C₃₁	—	4	2	no	—
390	C₂²×C₃₁	—	4	1	no	—
391	C₂²×C₃₁	—	4	2	no	—
392	C₂²×C₃₁	—	4	4	no	—
393	C₂²×C₃₁	#548	1	4	yes	—
394	C₂²×C₃₁	#553	1	8	yes	complemented
395	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
396	C₂²×C₃₁	C₂²×#41	1	2	yes	—
397	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
398	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
399	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
400	C₄×C₃₁	—	2	2	no	—
401	C₄×C₃₁	—	2	4	no	—
402	C₄×C₃₁	—	2	4	no	—
403	C₄×C₃₁	—	2	4	no	—
404	C₄×C₃₁	—	4	1	no	—
405	C₄×C₃₁	—	4	2	no	—
406	C₄×C₃₁	—	4	1	no	—
407	C₄×C₃₁	—	4	2	no	—
408	C₄×C₃₁	—	4	4	no	—
409	C₄×C₃₁	—	4	4	no	—
410	C₄×C₃₁	—	4	1	no	—
411	C₄×C₃₁	—	4	2	no	—
412	C₄×C₃₁	#525	1	4	yes	—
413	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
414	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
415	#553	—	2	8	no	—
416	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
417	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
418	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
419	C₂×#121	C₂²×C₃₁	1	2	yes	—
420	C₂×#121	C₂²×C₃₁	1	2	yes	—
421	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
422	C₂×#121	C₂²×C₃₁	1	4	yes	—
423	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	C₂×#120	C₂²×C₃₁	1	2	yes	—
425	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
427	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
430	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
431	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
432	C₂²×C₄⋊C₄	—	2	8	no	—
433	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
434	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
435	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
436	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
437	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
439	#400	C₂²×C₃₁	1	4	yes	complemented
440	#400	C₂²×C₃₁	1	2	yes	complemented
441	#399	C₂²×C₃₁	1	2	yes	complemented
442	#398	C₂²×C₃₁	1	4	yes	complemented
443	#397	C₂²×C₃₁	1	4	yes	complemented
444	#396	C₂²×C₃₁	1	4	yes	complemented
445	#394	C₂²×C₃₁	1	4	yes	complemented
446	#390	C₂²×C₃₁	1	2	yes	complemented
447	#389	C₂²×C₃₁	1	2	yes	complemented
448	#389	C₂²×C₃₁	1	2	yes	complemented
449	#388	C₂²×C₃₁	1	4	yes	complemented
450	#388	C₂²×C₃₁	1	4	yes	complemented
451	#387	C₂²×C₃₁	1	4	yes	complemented
452	#387	C₂²×C₃₁	1	4	yes	complemented
453	#386	C₂²×C₃₁	1	2	yes	—
454	#386	C₂²×C₃₁	1	2	yes	—
455	#386	C₂²×C₃₁	1	1	yes	characteristic
456	#386	C₂²×C₃₁	1	2	yes	—
457	#386	C₂²×C₃₁	1	2	yes	—
458	#386	C₂²×C₃₁	1	4	yes	—
459	#386	C₂²×C₃₁	1	4	yes	—
460	#386	C₂²×C₃₁	1	4	yes	—
461	#386	C₂²×C₃₁	1	4	yes	—
462	#386	C₂²×C₃₁	1	2	yes	—
463	#385	C₂²×C₃₁	1	1	yes	characteristic
464	#385	C₂²×C₃₁	1	2	yes	—
465	#385	C₂²×C₃₁	1	4	yes	—
466	#385	C₂²×C₃₁	1	2	yes	—
467	#385	C₂²×C₃₁	1	4	yes	complemented
468	#382	C₂²×C₃₁	1	2	yes	complemented
469	#380	C₂²×C₃₁	1	2	yes	—
470	#380	C₂²×C₃₁	1	1	yes	characteristic
471	#380	C₂²×C₃₁	1	2	yes	—
472	#380	C₂²×C₃₁	1	4	yes	—
473	#380	C₂²×C₃₁	1	2	yes	complemented
474	#379	C₂²×C₃₁	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
476	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
477	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
478	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
479	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
480	C₂×C₃₁	—	2	4	no	—
481	C₂×C₃₁	—	2	8	no	—
482	C₂×C₃₁	—	8	1	no	—
483	C₂×C₃₁	—	8	2	no	—
484	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
485	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
486	C₂×C₃₁	C₂×#553	1	2	yes	—
487	C₂×C₃₁	#3484	1	1	yes	characteristic
488	C₂×C₃₁	#3492	1	2	yes	—
489	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
491	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
493	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
494	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
495	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
496	C₂³×C₄	—	2	4	no	—
497	C₂³×C₄	—	2	8	no	—
498	C₂³×C₄	—	2	8	no	—
499	C₂³×C₄	—	4	8	no	—
500	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
502	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
504	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
505	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
507	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
508	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
509	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
510	#126	—	2	8	no	—
511	#125	—	2	4	no	—
512	#123	—	2	8	no	—
513	#121	—	2	8	no	—
514	#121	—	2	4	no	—
515	#121	—	2	8	no	—
516	#121	—	2	4	no	—
517	#121	—	4	8	no	—
518	#120	—	2	8	no	—
519	#120	—	2	4	no	—
520	C₄×D₄	—	2	8	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	8	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	4	8	no	—
525	#117	—	2	4	no	—
526	C₂×C₄⋊C₄	—	2	8	no	—
527	C₂×C₄⋊C₄	—	2	4	no	—
528	C₂×C₄⋊C₄	—	2	8	no	—
529	C₂×C₄⋊C₄	—	2	8	no	—
530	C₂×C₄⋊C₄	—	2	16	no	—
531	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	complemented
532	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
543	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
565	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
566	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
568	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
569	#95	C₂³×C₃₁	1	4	yes	—
570	#95	C₂³×C₃₁	1	4	yes	—
571	#95	C₂³×C₃₁	1	2	yes	—
572	#95	C₂³×C₃₁	1	2	yes	—
573	#95	C₂³×C₃₁	1	4	yes	—
574	#95	C₂³×C₃₁	1	2	yes	—
575	#95	C₂³×C₃₁	1	4	yes	—
576	#95	C₂³×C₃₁	1	4	yes	—
577	#95	C₂³×C₃₁	1	2	yes	—
578	#95	C₂³×C₃₁	1	4	yes	—
579	#95	C₂³×C₃₁	1	4	yes	—
580	C₃₁	#36581	1	1	yes	characteristic, direct product factor, Sylow
581	C₂⁴	—	2	2	no	—
582	C₂⁴	—	2	4	no	—
583	C₂⁴	—	2	4	no	—
584	C₂⁴	—	2	2	no	—
585	C₂⁴	#41×C₃₁	1	4	yes	—
586	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
587	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
588	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
589	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	8	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂²×C₄	—	2	32	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	8	no	—
617	C₂²×C₄	—	2	8	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	2	8	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	32	no	—
629	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
630	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
631	C₂²×C₄	#41×C₃₁	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
639	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
645	C₄⋊C₄	—	2	8	no	—
646	C₄⋊C₄	—	2	8	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	4	4	no	—
656	C₄⋊C₄	—	4	4	no	—
657	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
658	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
659	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	8	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	8	no	—
675	C₂²⋊C₄	—	4	4	no	—
676	C₂²⋊C₄	—	4	4	no	—
677	C₂²⋊C₄	—	4	4	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	4	4	no	—
682	C₂³	—	2	8	no	—
683	C₂³	—	2	8	no	—
684	C₂³	—	2	16	no	—
685	C₂³	—	2	8	no	—
686	C₂³	—	2	16	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	4	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	2	no	—
703	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
704	C₂³	C₂×#41×C₃₁	1	2	yes	—
705	C₂³	C₂×#41×C₃₁	1	4	yes	—
706	C₂³	C₂×#41×C₃₁	1	4	yes	—
707	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
708	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
709	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
710	D₄	—	4	8	no	—
711	D₄	—	4	4	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	16	no	—
714	D₄	—	4	4	no	—
715	D₄	—	8	4	no	—
716	C₂×C₄	—	2	16	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	8	no	—
724	C₂×C₄	—	2	16	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	4	8	no	—
748	C₂×C₄	—	4	16	no	—
749	C₂×C₄	—	4	16	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	8	4	no	—
753	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
755	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
756	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
757	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
758	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
759	C₂²	—	2	32	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	4	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	4	no	—
780	C₂²	C₃₁×#548	1	4	yes	—
781	C₂²	C₃₁×#553	1	8	yes	complemented
782	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
783	C₂²	C₂²×#41×C₃₁	1	2	yes	—
784	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
785	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
786	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
787	C₄	—	2	2	no	—
788	C₄	—	2	4	no	—
789	C₄	—	2	4	no	—
790	C₄	—	2	4	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	4	no	—
796	C₄	—	4	4	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	2	no	—
799	C₄	C₃₁×#525	1	4	yes	—
800	C₂	—	2	4	no	—
801	C₂	—	2	8	no	—
802	C₂	—	8	1	no	—
803	C₂	—	8	2	no	—
804	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
805	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
806	C₂	C₂×C₃₁×#553	1	2	yes	—
807	C₂	C₃₁×#3484	1	1	yes	characteristic
808	C₂	C₃₁×#3492	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
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. C₂×C₃₁×#553	C₂	semidirect
2. C₂³×C₄⋊C₄×C₃₁	C₂	semidirect
3. C₃₁×#2847	C₂	semidirect
4. C₃₁×#2847	C₂	semidirect
5. C₃₁×#2591	C₂	semidirect
6. C₃₁×#2579	C₂	semidirect
7. C₃₁×#2504	C₂	semidirect
8. C₃₁×#2487	C₂	semidirect
9. C₃₁×#2481	C₂	semidirect
10. C₃₁×#2443	C₂	semidirect
11. C₃₁×#2442	C₂	semidirect
12. C₃₁×#2416	C₂	semidirect
13. C₃₁×#2361	C₂	semidirect
14. C₃₁×#2352	C₂	semidirect
15. C₃₁×#2345	C₂	semidirect
16. C₄×C₃₁×#120	C₂	semidirect
17. C₄×C₃₁×#120	C₂	semidirect
21. C₂×C₃₁×#126	C₂²	semidirect
22. C₂×C₃₁×#125	C₂²	semidirect
23. C₂×C₃₁×#123	C₂²	semidirect
28. C₂×C₃₁×#121	C₂²	semidirect
35. C₂×C₄×D₄×C₃₁	C₂²	semidirect
36. C₂×C₃₁×#117	C₂²	semidirect
44. C₃₁×#400	C₂²	semidirect
45. C₃₁×#400	C₂²	semidirect
46. C₃₁×#399	C₂²	semidirect
47. C₃₁×#398	C₂²	semidirect
48. C₃₁×#397	C₂²	semidirect
49. C₃₁×#396	C₂²	semidirect
50. C₃₁×#394	C₂²	semidirect
51. C₃₁×#390	C₂²	semidirect
52. C₃₁×#389	C₂²	semidirect
53. C₃₁×#389	C₂²	semidirect
54. C₃₁×#388	C₂²	semidirect
55. C₃₁×#388	C₂²	semidirect
56. C₃₁×#387	C₂²	semidirect
57. C₃₁×#387	C₂²	semidirect
72. C₃₁×#385	C₂²	semidirect
73. C₃₁×#382	C₂²	semidirect
78. C₃₁×#380	C₂²	semidirect
80. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
127. C₂×C₄⋊C₄×C₃₁	D₄	semidirect
277. #36581	C₃₁	direct (N × H)
355. C₂×#553	C₂×C₃₁	semidirect
356. C₂³×C₄⋊C₄	C₂×C₃₁	semidirect
357. #2847	C₂×C₃₁	semidirect
358. #2847	C₂×C₃₁	semidirect
359. #2591	C₂×C₃₁	semidirect
360. #2579	C₂×C₃₁	semidirect
361. #2504	C₂×C₃₁	semidirect
362. #2487	C₂×C₃₁	semidirect
363. #2481	C₂×C₃₁	semidirect
364. #2443	C₂×C₃₁	semidirect
365. #2442	C₂×C₃₁	semidirect
366. #2416	C₂×C₃₁	semidirect
367. #2361	C₂×C₃₁	semidirect
368. #2352	C₂×C₃₁	semidirect
369. #2345	C₂×C₃₁	semidirect
370. C₄×#120	C₂×C₃₁	semidirect
371. C₄×#120	C₂×C₃₁	semidirect
394. C₂²×C₃₁	#553	semidirect
416. C₂×#126	C₂²×C₃₁	semidirect
417. C₂×#125	C₂²×C₃₁	semidirect
418. C₂×#123	C₂²×C₃₁	semidirect
423. C₂×#121	C₂²×C₃₁	semidirect
430. C₂×C₄×D₄	C₂²×C₃₁	semidirect
431. C₂×#117	C₂²×C₃₁	semidirect
439. #400	C₂²×C₃₁	semidirect
440. #400	C₂²×C₃₁	semidirect
441. #399	C₂²×C₃₁	semidirect
442. #398	C₂²×C₃₁	semidirect
443. #397	C₂²×C₃₁	semidirect
444. #396	C₂²×C₃₁	semidirect
445. #394	C₂²×C₃₁	semidirect
446. #390	C₂²×C₃₁	semidirect
447. #389	C₂²×C₃₁	semidirect
448. #389	C₂²×C₃₁	semidirect
449. #388	C₂²×C₃₁	semidirect
450. #388	C₂²×C₃₁	semidirect
451. #387	C₂²×C₃₁	semidirect
452. #387	C₂²×C₃₁	semidirect
467. #385	C₂²×C₃₁	semidirect
468. #382	C₂²×C₃₁	semidirect
473. #380	C₂²×C₃₁	semidirect
475. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
531. C₂×C₄⋊C₄	D₄×C₃₁	semidirect
580. C₃₁	#36581	direct (N × H)
781. C₂²	C₃₁×#553	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#553	2
C₂³×C₄⋊C₄×C₃₁	2
C₃₁×#2847	2
C₃₁×#2591	2
C₃₁×#2579	2
C₃₁×#2504	2
C₃₁×#2487	2
C₃₁×#2481	2
C₃₁×#2443	2
C₃₁×#2442	2
C₃₁×#2416	2
C₃₁×#2361	2
C₃₁×#2352	2
C₃₁×#2345	2
C₄×C₃₁×#120	2
#36581	31

Subgroups — C31×#36581 #21493340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36581 #21493340