Subgroups — C₃₁×#36706 #21493465

Order 7936.

3038 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2691	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2676	C₂	1	4	yes	maximal, complemented
7	C₃₁×#2675	C₂	1	4	yes	maximal, complemented
8	C₃₁×#2671	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2626	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2617	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2579	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2410	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2410	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2408	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2315	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#538	—	2	8	no	—
21	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
22	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₃₁×#121	—	2	8	no	—
27	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#121	C₂²	1	4	yes	—
29	C₂×C₃₁×#121	C₂²	1	4	yes	—
30	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
31	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
32	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
33	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
34	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
35	C₂×C₃₁×#120	C₂²	1	2	yes	—
36	C₂×C₃₁×#120	C₂²	1	2	yes	—
37	C₂×C₃₁×#120	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₃₁×#399	C₂²	1	2	yes	complemented
44	C₃₁×#398	C₂²	1	4	yes	complemented
45	C₃₁×#397	C₂²	1	2	yes	complemented
46	C₃₁×#396	C₂²	1	4	yes	complemented
47	C₃₁×#396	C₂²	1	4	yes	complemented
48	C₃₁×#394	C₂²	1	4	yes	complemented
49	C₃₁×#394	C₂²	1	4	yes	complemented
50	C₃₁×#394	C₂²	1	4	yes	complemented
51	C₃₁×#394	C₂²	1	4	yes	complemented
52	C₃₁×#393	C₂²	1	2	yes	complemented
53	C₃₁×#392	C₂²	1	2	yes	complemented
54	C₃₁×#392	C₂²	1	4	yes	complemented
55	C₃₁×#392	C₂²	1	4	yes	complemented
56	C₃₁×#392	C₂²	1	4	yes	complemented
57	C₃₁×#390	C₂²	1	4	yes	complemented
58	C₃₁×#387	C₂²	1	4	yes	complemented
59	C₃₁×#386	C₂²	1	2	yes	—
60	C₃₁×#386	C₂²	1	2	yes	—
61	C₃₁×#386	C₂²	1	4	yes	complemented
62	C₃₁×#386	C₂²	1	4	yes	complemented
63	C₃₁×#386	C₂²	1	4	yes	complemented
64	C₃₁×#385	C₂²	1	2	yes	—
65	C₃₁×#385	C₂²	1	2	yes	—
66	C₃₁×#385	C₂²	1	4	yes	complemented
67	C₃₁×#385	C₂²	1	4	yes	complemented
68	C₃₁×#385	C₂²	1	4	yes	complemented
69	C₃₁×#385	C₂²	1	4	yes	complemented
70	C₃₁×#380	C₂²	1	2	yes	—
71	C₃₁×#380	C₂²	1	1	yes	characteristic
72	C₃₁×#380	C₂²	1	1	yes	characteristic
73	C₃₁×#380	C₂²	1	2	yes	complemented
74	C₃₁×#380	C₂²	1	2	yes	complemented
75	C₃₁×#379	C₂²	1	2	yes	—
76	C₃₁×#379	C₂²	1	2	yes	—
77	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
78	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
79	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₃₁	—	2	4	no	—
82	C₂²×D₄×C₃₁	—	2	4	no	—
83	C₂²×D₄×C₃₁	—	2	4	no	—
84	C₂²×D₄×C₃₁	—	4	4	no	—
85	C₂²×D₄×C₃₁	—	4	4	no	—
86	C₂²×D₄×C₃₁	—	4	4	no	—
87	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
88	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
89	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
94	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
96	C₂³×C₄×C₃₁	—	2	4	no	—
97	C₂³×C₄×C₃₁	—	4	4	no	—
98	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
103	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
104	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
106	C₃₁×#126	—	2	8	no	—
107	C₃₁×#124	—	2	8	no	—
108	C₃₁×#123	—	2	8	no	—
109	C₃₁×C₂²⋊Q₈	—	2	4	no	—
110	C₃₁×C₂²⋊Q₈	—	4	4	no	—
111	C₃₁×#121	—	2	4	no	—
112	C₃₁×#121	—	2	16	no	—
113	C₃₁×#121	—	2	16	no	—
114	C₃₁×#121	—	2	8	no	—
115	C₃₁×#121	—	4	4	no	—
116	C₃₁×#121	—	4	8	no	—
117	C₃₁×#121	—	4	8	no	—
118	C₃₁×#121	—	4	8	no	—
119	C₃₁×#120	—	2	8	no	—
120	C₃₁×#120	—	4	4	no	—
121	C₃₁×#120	—	4	4	no	—
122	C₄×D₄×C₃₁	—	2	8	no	—
123	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
136	C₂×C₂²⋊C₄×C₃₁	D₄	1	8	yes	complemented
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
158	C₃₁×#95	C₂³	1	4	yes	—
159	C₃₁×#95	C₂³	1	4	yes	—
160	C₃₁×#95	C₂³	1	2	yes	—
161	C₃₁×#95	C₂³	1	4	yes	—
162	C₃₁×#95	C₂³	1	4	yes	—
163	C₃₁×#95	C₂³	1	2	yes	—
164	C₃₁×#95	C₂³	1	4	yes	—
165	C₂⁴×C₃₁	—	2	2	no	—
166	C₂⁴×C₃₁	—	2	4	no	—
167	C₂⁴×C₃₁	—	2	2	no	—
168	C₂⁴×C₃₁	—	2	2	no	—
169	C₂⁴×C₃₁	—	2	2	no	—
170	C₂⁴×C₃₁	—	2	2	no	—
171	C₂⁴×C₃₁	—	2	2	no	—
172	C₂⁴×C₃₁	—	2	2	no	—
173	C₂⁴×C₃₁	—	2	2	no	—
174	C₂⁴×C₃₁	—	4	2	no	—
175	C₂⁴×C₃₁	—	4	2	no	—
176	C₂⁴×C₃₁	—	4	2	no	—
177	C₂⁴×C₃₁	—	4	2	no	—
178	C₂⁴×C₃₁	—	4	2	no	—
179	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
180	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
181	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
182	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
183	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
184	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
185	C₂×Q₈×C₃₁	—	2	2	no	—
186	C₂×Q₈×C₃₁	—	4	2	no	—
187	C₂×D₄×C₃₁	—	2	4	no	—
188	C₂×D₄×C₃₁	—	2	8	no	—
189	C₂×D₄×C₃₁	—	2	8	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	4	no	—
194	C₂×D₄×C₃₁	—	2	4	no	—
195	C₂×D₄×C₃₁	—	2	4	no	—
196	C₂×D₄×C₃₁	—	2	8	no	—
197	C₂×D₄×C₃₁	—	2	8	no	—
198	C₂×D₄×C₃₁	—	2	2	no	—
199	C₂×D₄×C₃₁	—	2	8	no	—
200	C₂×D₄×C₃₁	—	4	4	no	—
201	C₂×D₄×C₃₁	—	4	4	no	—
202	C₂×D₄×C₃₁	—	4	4	no	—
203	C₂×D₄×C₃₁	—	4	16	no	—
204	C₂×D₄×C₃₁	—	4	4	no	—
205	C₂×D₄×C₃₁	—	4	4	no	—
206	C₂×D₄×C₃₁	—	4	2	no	—
207	C₂×D₄×C₃₁	—	4	4	no	—
208	C₂×D₄×C₃₁	—	4	4	no	—
209	C₂×D₄×C₃₁	—	4	4	no	—
210	C₂×D₄×C₃₁	—	4	4	no	—
211	C₂×D₄×C₃₁	—	4	4	no	—
212	C₂×D₄×C₃₁	—	4	16	no	—
213	C₂×D₄×C₃₁	—	4	16	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	4	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	4	no	—
218	C₂²×C₄×C₃₁	—	2	4	no	—
219	C₂²×C₄×C₃₁	—	2	4	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	4	2	no	—
223	C₂²×C₄×C₃₁	—	4	2	no	—
224	C₂²×C₄×C₃₁	—	4	2	no	—
225	C₂²×C₄×C₃₁	—	4	2	no	—
226	C₂²×C₄×C₃₁	—	4	2	no	—
227	C₂²×C₄×C₃₁	—	4	4	no	—
228	C₂²×C₄×C₃₁	—	4	4	no	—
229	C₂²×C₄×C₃₁	—	4	4	no	—
230	C₂²×C₄×C₃₁	—	4	4	no	—
231	C₂²×C₄×C₃₁	—	4	16	no	—
232	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
244	C₄⋊C₄×C₃₁	—	2	8	no	—
245	C₄⋊C₄×C₃₁	—	2	4	no	—
246	C₄⋊C₄×C₃₁	—	2	4	no	—
247	C₄⋊C₄×C₃₁	—	2	2	no	—
248	C₄⋊C₄×C₃₁	—	2	2	no	—
249	C₄⋊C₄×C₃₁	—	2	8	no	—
250	C₄⋊C₄×C₃₁	—	4	2	no	—
251	C₄⋊C₄×C₃₁	—	4	4	no	—
252	C₄⋊C₄×C₃₁	—	4	4	no	—
253	C₄⋊C₄×C₃₁	—	4	2	no	—
254	C₂²⋊C₄×C₃₁	—	2	4	no	—
255	C₂²⋊C₄×C₃₁	—	2	4	no	—
256	C₂²⋊C₄×C₃₁	—	2	4	no	—
257	C₂²⋊C₄×C₃₁	—	2	4	no	—
258	C₂²⋊C₄×C₃₁	—	2	4	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	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	8	no	—
265	C₂²⋊C₄×C₃₁	—	4	4	no	—
266	C₂²⋊C₄×C₃₁	—	4	4	no	—
267	C₂²⋊C₄×C₃₁	—	4	4	no	—
268	C₂²⋊C₄×C₃₁	—	4	4	no	—
269	C₂²⋊C₄×C₃₁	—	4	4	no	—
270	C₂²⋊C₄×C₃₁	—	4	4	no	—
271	C₂²⋊C₄×C₃₁	—	4	4	no	—
272	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
273	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
274	C₄²×C₃₁	—	2	4	no	—
275	#36706	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₃₁	—	2	2	no	—
277	C₂³×C₃₁	—	2	2	no	—
278	C₂³×C₃₁	—	2	8	no	—
279	C₂³×C₃₁	—	2	2	no	—
280	C₂³×C₃₁	—	2	2	no	—
281	C₂³×C₃₁	—	2	2	no	—
282	C₂³×C₃₁	—	2	2	no	—
283	C₂³×C₃₁	—	2	2	no	—
284	C₂³×C₃₁	—	2	4	no	—
285	C₂³×C₃₁	—	2	4	no	—
286	C₂³×C₃₁	—	2	2	no	—
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	8	no	—
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	2	4	no	—
293	C₂³×C₃₁	—	2	2	no	—
294	C₂³×C₃₁	—	2	4	no	—
295	C₂³×C₃₁	—	2	4	no	—
296	C₂³×C₃₁	—	2	4	no	—
297	C₂³×C₃₁	—	2	2	no	—
298	C₂³×C₃₁	—	2	2	no	—
299	C₂³×C₃₁	—	2	2	no	—
300	C₂³×C₃₁	—	4	4	no	—
301	C₂³×C₃₁	—	4	4	no	—
302	C₂³×C₃₁	—	4	8	no	—
303	C₂³×C₃₁	—	4	8	no	—
304	C₂³×C₃₁	—	4	4	no	—
305	C₂³×C₃₁	—	4	4	no	—
306	C₂³×C₃₁	—	4	4	no	—
307	C₂³×C₃₁	—	4	4	no	—
308	C₂³×C₃₁	—	4	4	no	—
309	C₂³×C₃₁	—	8	4	no	—
310	C₂³×C₃₁	—	8	4	no	—
311	C₂³×C₃₁	—	8	4	no	—
312	C₂³×C₃₁	—	8	4	no	—
313	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
314	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
315	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
316	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
317	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
318	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
319	Q₈×C₃₁	—	8	2	no	—
320	D₄×C₃₁	—	4	16	no	—
321	D₄×C₃₁	—	4	16	no	—
322	D₄×C₃₁	—	4	16	no	—
323	D₄×C₃₁	—	4	8	no	—
324	D₄×C₃₁	—	8	2	no	—
325	D₄×C₃₁	—	8	4	no	—
326	D₄×C₃₁	—	8	4	no	—
327	D₄×C₃₁	—	8	8	no	—
328	D₄×C₃₁	—	8	8	no	—
329	C₂×C₄×C₃₁	—	2	8	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	2	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	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	4	no	—
340	C₂×C₄×C₃₁	—	2	4	no	—
341	C₂×C₄×C₃₁	—	2	4	no	—
342	C₂×C₄×C₃₁	—	2	4	no	—
343	C₂×C₄×C₃₁	—	2	4	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	4	no	—
346	C₂×C₄×C₃₁	—	2	4	no	—
347	C₂×C₄×C₃₁	—	2	4	no	—
348	C₂×C₄×C₃₁	—	2	4	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	4	4	no	—
351	C₂×C₄×C₃₁	—	4	4	no	—
352	C₂×C₄×C₃₁	—	4	8	no	—
353	C₂×C₄×C₃₁	—	4	8	no	—
354	C₂×C₄×C₃₁	—	4	4	no	—
355	C₂×C₄×C₃₁	—	8	4	no	—
356	C₂×C₄×C₃₁	—	8	8	no	—
357	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
358	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
361	C₂×#538	C₂×C₃₁	1	1	yes	characteristic, complemented
362	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#2848	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#2847	C₂×C₃₁	1	1	yes	characteristic, complemented
365	#2691	C₂×C₃₁	1	4	yes	complemented
366	#2676	C₂×C₃₁	1	4	yes	complemented
367	#2675	C₂×C₃₁	1	4	yes	complemented
368	#2671	C₂×C₃₁	1	4	yes	complemented
369	#2626	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#2617	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#2579	C₂×C₃₁	1	2	yes	complemented
372	#2410	C₂×C₃₁	1	2	yes	complemented
373	#2410	C₂×C₃₁	1	2	yes	complemented
374	#2408	C₂×C₃₁	1	2	yes	complemented
375	#2315	C₂×C₃₁	1	1	yes	characteristic, complemented
376	C₂²×C₃₁	—	2	2	no	—
377	C₂²×C₃₁	—	2	2	no	—
378	C₂²×C₃₁	—	2	4	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	—	2	4	no	—
384	C₂²×C₃₁	—	2	4	no	—
385	C₂²×C₃₁	—	2	4	no	—
386	C₂²×C₃₁	—	4	16	no	—
387	C₂²×C₃₁	—	4	2	no	—
388	C₂²×C₃₁	—	4	2	no	—
389	C₂²×C₃₁	—	4	2	no	—
390	C₂²×C₃₁	—	4	4	no	—
391	C₂²×C₃₁	—	4	4	no	—
392	C₂²×C₃₁	—	4	2	no	—
393	C₂²×C₃₁	—	4	2	no	—
394	C₂²×C₃₁	—	4	2	no	—
395	C₂²×C₃₁	—	4	2	no	—
396	C₂²×C₃₁	—	4	2	no	—
397	C₂²×C₃₁	—	4	2	no	—
398	C₂²×C₃₁	—	4	2	no	—
399	C₂²×C₃₁	—	4	4	no	—
400	C₂²×C₃₁	—	4	4	no	—
401	C₂²×C₃₁	—	4	4	no	—
402	C₂²×C₃₁	—	4	4	no	—
403	C₂²×C₃₁	—	8	8	no	—
404	C₂²×C₃₁	—	8	8	no	—
405	C₂²×C₃₁	#537	1	4	yes	—
406	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
407	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
409	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
410	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
411	C₄×C₃₁	—	2	4	no	—
412	C₄×C₃₁	—	2	2	no	—
413	C₄×C₃₁	—	2	2	no	—
414	C₄×C₃₁	—	2	4	no	—
415	C₄×C₃₁	—	4	2	no	—
416	C₄×C₃₁	—	4	2	no	—
417	C₄×C₃₁	—	4	2	no	—
418	C₄×C₃₁	—	4	2	no	—
419	C₄×C₃₁	—	4	4	no	—
420	C₄×C₃₁	—	4	4	no	—
421	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
422	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
423	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
424	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
425	#538	—	2	8	no	—
426	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
427	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
428	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
429	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
431	C₂×#121	—	2	8	no	—
432	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
433	C₂×#121	C₂²×C₃₁	1	4	yes	—
434	C₂×#121	C₂²×C₃₁	1	4	yes	—
435	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
436	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
437	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
438	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
439	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
440	C₂×#120	C₂²×C₃₁	1	2	yes	—
441	C₂×#120	C₂²×C₃₁	1	2	yes	—
442	C₂×#120	C₂²×C₃₁	1	2	yes	—
443	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
444	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
445	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
446	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
447	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
448	#399	C₂²×C₃₁	1	2	yes	complemented
449	#398	C₂²×C₃₁	1	4	yes	complemented
450	#397	C₂²×C₃₁	1	2	yes	complemented
451	#396	C₂²×C₃₁	1	4	yes	complemented
452	#396	C₂²×C₃₁	1	4	yes	complemented
453	#394	C₂²×C₃₁	1	4	yes	complemented
454	#394	C₂²×C₃₁	1	4	yes	complemented
455	#394	C₂²×C₃₁	1	4	yes	complemented
456	#394	C₂²×C₃₁	1	4	yes	complemented
457	#393	C₂²×C₃₁	1	2	yes	complemented
458	#392	C₂²×C₃₁	1	2	yes	complemented
459	#392	C₂²×C₃₁	1	4	yes	complemented
460	#392	C₂²×C₃₁	1	4	yes	complemented
461	#392	C₂²×C₃₁	1	4	yes	complemented
462	#390	C₂²×C₃₁	1	4	yes	complemented
463	#387	C₂²×C₃₁	1	4	yes	complemented
464	#386	C₂²×C₃₁	1	2	yes	—
465	#386	C₂²×C₃₁	1	2	yes	—
466	#386	C₂²×C₃₁	1	4	yes	complemented
467	#386	C₂²×C₃₁	1	4	yes	complemented
468	#386	C₂²×C₃₁	1	4	yes	complemented
469	#385	C₂²×C₃₁	1	2	yes	—
470	#385	C₂²×C₃₁	1	2	yes	—
471	#385	C₂²×C₃₁	1	4	yes	complemented
472	#385	C₂²×C₃₁	1	4	yes	complemented
473	#385	C₂²×C₃₁	1	4	yes	complemented
474	#385	C₂²×C₃₁	1	4	yes	complemented
475	#380	C₂²×C₃₁	1	2	yes	—
476	#380	C₂²×C₃₁	1	1	yes	characteristic
477	#380	C₂²×C₃₁	1	1	yes	characteristic
478	#380	C₂²×C₃₁	1	2	yes	complemented
479	#380	C₂²×C₃₁	1	2	yes	complemented
480	#379	C₂²×C₃₁	1	2	yes	—
481	#379	C₂²×C₃₁	1	2	yes	—
482	C₂×C₃₁	—	2	4	no	—
483	C₂×C₃₁	—	4	4	no	—
484	C₂×C₃₁	—	4	4	no	—
485	C₂×C₃₁	—	8	2	no	—
486	C₂×C₃₁	—	8	2	no	—
487	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
488	C₂×C₃₁	#3484	1	1	yes	characteristic
489	C₂×C₃₁	#3484	1	1	yes	characteristic
490	C₂×C₃₁	#3536	1	2	yes	—
491	C₂×C₃₁	#3537	1	2	yes	—
492	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
493	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
494	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
496	C₂²×D₄	—	2	4	no	—
497	C₂²×D₄	—	2	4	no	—
498	C₂²×D₄	—	2	4	no	—
499	C₂²×D₄	—	4	4	no	—
500	C₂²×D₄	—	4	4	no	—
501	C₂²×D₄	—	4	4	no	—
502	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
503	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
504	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
505	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
506	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
507	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
508	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
509	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
511	C₂³×C₄	—	2	4	no	—
512	C₂³×C₄	—	4	4	no	—
513	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
515	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
516	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
518	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
519	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
521	#126	—	2	8	no	—
522	#124	—	2	8	no	—
523	#123	—	2	8	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	4	4	no	—
526	#121	—	2	4	no	—
527	#121	—	2	16	no	—
528	#121	—	2	16	no	—
529	#121	—	2	8	no	—
530	#121	—	4	4	no	—
531	#121	—	4	8	no	—
532	#121	—	4	8	no	—
533	#121	—	4	8	no	—
534	#120	—	2	8	no	—
535	#120	—	4	4	no	—
536	#120	—	4	4	no	—
537	C₄×D₄	—	2	8	no	—
538	C₂×C₄⋊C₄	—	2	4	no	—
539	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	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	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂×C₂²⋊C₄	—	2	4	no	—
550	C₂×C₂²⋊C₄	—	4	4	no	—
551	C₂×C₂²⋊C₄	D₄×C₃₁	1	8	yes	complemented
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	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	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	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
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×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
572	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
573	#95	C₂³×C₃₁	1	2	yes	—
574	#95	C₂³×C₃₁	1	4	yes	—
575	#95	C₂³×C₃₁	1	2	yes	—
576	#95	C₂³×C₃₁	1	4	yes	—
577	#95	C₂³×C₃₁	1	4	yes	—
578	#95	C₂³×C₃₁	1	4	yes	—
579	#95	C₂³×C₃₁	1	4	yes	—
580	C₃₁	#36706	1	1	yes	characteristic, direct product factor, Sylow
581	C₂⁴	—	2	2	no	—
582	C₂⁴	—	2	4	no	—
583	C₂⁴	—	2	2	no	—
584	C₂⁴	—	2	2	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	4	2	no	—
591	C₂⁴	—	4	2	no	—
592	C₂⁴	—	4	2	no	—
593	C₂⁴	—	4	2	no	—
594	C₂⁴	—	4	2	no	—
595	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
596	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
597	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
598	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
599	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
600	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	4	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	8	no	—
605	C₂×D₄	—	2	8	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	8	no	—
608	C₂×D₄	—	2	8	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	8	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	8	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	4	16	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	—	4	4	no	—
622	C₂×D₄	—	4	2	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	16	no	—
629	C₂×D₄	—	4	16	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	—	4	16	no	—
648	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
649	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
650	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
652	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
653	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
660	C₄⋊C₄	—	2	8	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	8	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₄⋊C₄	—	4	4	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	8	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	8	no	—
681	C₂²⋊C₄	—	4	4	no	—
682	C₂²⋊C₄	—	4	4	no	—
683	C₂²⋊C₄	—	4	4	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	4	4	no	—
688	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
689	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
690	C₄²	—	2	4	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	8	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	4	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	8	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	4	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	4	8	no	—
718	C₂³	—	4	8	no	—
719	C₂³	—	4	4	no	—
720	C₂³	—	4	4	no	—
721	C₂³	—	4	4	no	—
722	C₂³	—	4	4	no	—
723	C₂³	—	4	4	no	—
724	C₂³	—	8	4	no	—
725	C₂³	—	8	4	no	—
726	C₂³	—	8	4	no	—
727	C₂³	—	8	4	no	—
728	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
729	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
730	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
731	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
732	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
733	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
734	Q₈	—	8	2	no	—
735	D₄	—	4	16	no	—
736	D₄	—	4	16	no	—
737	D₄	—	4	16	no	—
738	D₄	—	4	8	no	—
739	D₄	—	8	2	no	—
740	D₄	—	8	4	no	—
741	D₄	—	8	4	no	—
742	D₄	—	8	8	no	—
743	D₄	—	8	8	no	—
744	C₂×C₄	—	2	8	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	8	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	8	4	no	—
771	C₂×C₄	—	8	8	no	—
772	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
773	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
774	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
775	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	4	no	—
782	C₂²	—	2	4	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	4	16	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	4	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	4	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	8	8	no	—
804	C₂²	—	8	8	no	—
805	C₂²	C₃₁×#537	1	4	yes	—
806	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
807	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
808	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
809	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
810	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
811	C₄	—	2	4	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	4	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	4	no	—
820	C₄	—	4	4	no	—
821	C₂	—	2	4	no	—
822	C₂	—	4	4	no	—
823	C₂	—	4	4	no	—
824	C₂	—	8	2	no	—
825	C₂	—	8	2	no	—
826	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
827	C₂	C₃₁×#3484	1	1	yes	characteristic
828	C₂	C₃₁×#3484	1	1	yes	characteristic
829	C₂	C₃₁×#3536	1	2	yes	—
830	C₂	C₃₁×#3537	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×#538	C₂	semidirect
2. C₂²×C₃₁×#121	C₂	semidirect
3. C₃₁×#2848	C₂	semidirect
4. C₃₁×#2847	C₂	semidirect
5. C₃₁×#2691	C₂	semidirect
6. C₃₁×#2676	C₂	semidirect
7. C₃₁×#2675	C₂	semidirect
8. C₃₁×#2671	C₂	semidirect
9. C₃₁×#2626	C₂	semidirect
10. C₃₁×#2617	C₂	semidirect
11. C₃₁×#2579	C₂	semidirect
12. C₃₁×#2410	C₂	semidirect
13. C₃₁×#2410	C₂	semidirect
14. C₃₁×#2408	C₂	semidirect
15. C₃₁×#2315	C₂	semidirect
21. C₂×C₃₁×#126	C₂²	semidirect
22. C₂×C₃₁×#124	C₂²	semidirect
23. C₂×C₃₁×#123	C₂²	semidirect
25. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₃₁×#121	C₂²	semidirect
31. C₂×C₃₁×#121	C₂²	semidirect
32. C₂×C₃₁×#121	C₂²	semidirect
33. C₂×C₃₁×#121	C₂²	semidirect
34. C₂×C₃₁×#121	C₂²	semidirect
43. C₃₁×#399	C₂²	semidirect
44. C₃₁×#398	C₂²	semidirect
45. C₃₁×#397	C₂²	semidirect
46. C₃₁×#396	C₂²	semidirect
47. C₃₁×#396	C₂²	semidirect
48. C₃₁×#394	C₂²	semidirect
49. C₃₁×#394	C₂²	semidirect
50. C₃₁×#394	C₂²	semidirect
51. C₃₁×#394	C₂²	semidirect
52. C₃₁×#393	C₂²	semidirect
53. C₃₁×#392	C₂²	semidirect
54. C₃₁×#392	C₂²	semidirect
55. C₃₁×#392	C₂²	semidirect
56. C₃₁×#392	C₂²	semidirect
57. C₃₁×#390	C₂²	semidirect
58. C₃₁×#387	C₂²	semidirect
61. C₃₁×#386	C₂²	semidirect
62. C₃₁×#386	C₂²	semidirect
63. C₃₁×#386	C₂²	semidirect
66. C₃₁×#385	C₂²	semidirect
67. C₃₁×#385	C₂²	semidirect
68. C₃₁×#385	C₂²	semidirect
69. C₃₁×#385	C₂²	semidirect
73. C₃₁×#380	C₂²	semidirect
74. C₃₁×#380	C₂²	semidirect
136. C₂×C₂²⋊C₄×C₃₁	D₄	semidirect
275. #36706	C₃₁	direct (N × H)
361. C₂×#538	C₂×C₃₁	semidirect
362. C₂²×#121	C₂×C₃₁	semidirect
363. #2848	C₂×C₃₁	semidirect
364. #2847	C₂×C₃₁	semidirect
365. #2691	C₂×C₃₁	semidirect
366. #2676	C₂×C₃₁	semidirect
367. #2675	C₂×C₃₁	semidirect
368. #2671	C₂×C₃₁	semidirect
369. #2626	C₂×C₃₁	semidirect
370. #2617	C₂×C₃₁	semidirect
371. #2579	C₂×C₃₁	semidirect
372. #2410	C₂×C₃₁	semidirect
373. #2410	C₂×C₃₁	semidirect
374. #2408	C₂×C₃₁	semidirect
375. #2315	C₂×C₃₁	semidirect
426. C₂×#126	C₂²×C₃₁	semidirect
427. C₂×#124	C₂²×C₃₁	semidirect
428. C₂×#123	C₂²×C₃₁	semidirect
430. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
435. C₂×#121	C₂²×C₃₁	semidirect
436. C₂×#121	C₂²×C₃₁	semidirect
437. C₂×#121	C₂²×C₃₁	semidirect
438. C₂×#121	C₂²×C₃₁	semidirect
439. C₂×#121	C₂²×C₃₁	semidirect
448. #399	C₂²×C₃₁	semidirect
449. #398	C₂²×C₃₁	semidirect
450. #397	C₂²×C₃₁	semidirect
451. #396	C₂²×C₃₁	semidirect
452. #396	C₂²×C₃₁	semidirect
453. #394	C₂²×C₃₁	semidirect
454. #394	C₂²×C₃₁	semidirect
455. #394	C₂²×C₃₁	semidirect
456. #394	C₂²×C₃₁	semidirect
457. #393	C₂²×C₃₁	semidirect
458. #392	C₂²×C₃₁	semidirect
459. #392	C₂²×C₃₁	semidirect
460. #392	C₂²×C₃₁	semidirect
461. #392	C₂²×C₃₁	semidirect
462. #390	C₂²×C₃₁	semidirect
463. #387	C₂²×C₃₁	semidirect
466. #386	C₂²×C₃₁	semidirect
467. #386	C₂²×C₃₁	semidirect
468. #386	C₂²×C₃₁	semidirect
471. #385	C₂²×C₃₁	semidirect
472. #385	C₂²×C₃₁	semidirect
473. #385	C₂²×C₃₁	semidirect
474. #385	C₂²×C₃₁	semidirect
478. #380	C₂²×C₃₁	semidirect
479. #380	C₂²×C₃₁	semidirect
551. C₂×C₂²⋊C₄	D₄×C₃₁	semidirect
580. C₃₁	#36706	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#538	2
C₂²×C₃₁×#121	2
C₃₁×#2848	2
C₃₁×#2847	2
C₃₁×#2691	2
C₃₁×#2676	2
C₃₁×#2675	2
C₃₁×#2671	2
C₃₁×#2626	2
C₃₁×#2617	2
C₃₁×#2579	2
C₃₁×#2410	2
C₃₁×#2408	2
C₃₁×#2315	2
#36706	31

Subgroups — C31×#36706 #21493465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36706 #21493465