Subgroups — C₃₁×#61961 #21518720

Order 7936.

2178 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3332	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3306	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3274	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3264	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3253	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3214	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3109	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3036	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	—	2	1	no	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
21	C₃₁×#559	—	2	1	no	—
22	C₃₁×#559	C₂²	1	2	yes	complemented
23	C₃₁×#550	—	2	1	no	—
24	C₃₁×#550	C₂²	1	2	yes	complemented
25	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
26	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#548	—	2	1	no	—
28	C₃₁×#547	C₂²	1	2	yes	—
29	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#546	—	2	2	no	—
31	C₃₁×#546	—	2	1	no	—
32	C₃₁×#546	—	2	2	no	—
33	C₃₁×#546	C₂²	1	4	yes	complemented
34	D₄²×C₃₁	C₂²	1	2	yes	—
35	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#540	—	2	2	no	—
37	C₃₁×#535	—	2	1	no	—
38	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₃₁×#532	C₂²	1	2	yes	complemented
41	C₃₁×#532	C₂²	1	2	yes	complemented
42	C₃₁×#532	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#525	—	2	1	no	—
45	C₃₁×#525	—	2	2	no	—
46	C₃₁×#518	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
50	C₃₁×#496	C₂²	1	4	yes	complemented
51	C₃₁×#493	C₂²	1	2	yes	complemented
52	C₃₁×#489	C₂²	1	4	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	complemented
54	C₃₁×#483	C₂²	1	2	yes	complemented
55	C₃₁×#481	C₂²	1	4	yes	complemented
56	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#476	C₂²	1	2	yes	complemented
59	C₃₁×#476	C₂²	1	4	yes	complemented
60	C₃₁×#475	C₂²	1	2	yes	complemented
61	C₃₁×#469	C₂²	1	4	yes	complemented
62	C₃₁×#469	C₂²	1	4	yes	complemented
63	C₃₁×#465	C₂²	1	4	yes	complemented
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#463	C₂²	1	4	yes	complemented
66	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#461	C₂²	1	2	yes	complemented
69	C₃₁×#460	C₂²	1	2	yes	complemented
70	C₃₁×#459	C₂²	1	2	yes	—
71	C₃₁×#459	C₂²	1	2	yes	—
72	C₃₁×#459	C₂²	1	2	yes	complemented
73	C₃₁×#459	C₂²	1	2	yes	complemented
74	C₃₁×#459	C₂²	1	4	yes	complemented
75	C₃₁×#459	C₂²	1	2	yes	complemented
76	C₃₁×#459	C₂²	1	2	yes	complemented
77	C₃₁×#450	C₂²	1	2	yes	—
78	C₃₁×#449	C₂²	1	4	yes	complemented
79	C₃₁×#449	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	4	yes	complemented
81	C₃₁×#447	C₂²	1	4	yes	complemented
82	C₃₁×#446	C₂²	1	2	yes	complemented
83	C₃₁×#442	C₂²	1	4	yes	complemented
84	C₃₁×#442	C₂²	1	4	yes	complemented
85	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
87	C₃₁×#436	C₂²	1	2	yes	complemented
88	C₃₁×#435	C₂²	1	4	yes	complemented
89	C₃₁×#432	C₂²	1	2	yes	complemented
90	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#423	C₂²	1	2	yes	complemented
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#417	C₂²	1	4	yes	complemented
94	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	1	no	—
98	C₂×#41×C₃₁	—	2	1	no	—
99	C₂×#41×C₃₁	—	2	2	no	—
100	C₂×#41×C₃₁	—	2	2	no	—
101	C₂×#41×C₃₁	—	4	8	no	—
102	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
103	C₂×#41×C₃₁	C₂³	1	4	yes	—
104	C₂²×Q₈×C₃₁	—	2	1	no	—
105	C₂²×D₄×C₃₁	—	2	2	no	—
106	C₂²×D₄×C₃₁	—	2	1	no	—
107	C₂²×D₄×C₃₁	—	2	1	no	—
108	C₂²×D₄×C₃₁	—	2	1	no	—
109	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂³×C₄×C₃₁	—	2	1	no	—
113	C₂³×C₄×C₃₁	—	2	2	no	—
114	C₃₁×AGL(1,ℤ/8)	—	4	8	no	—
115	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
118	C₂×D₈×C₃₁	—	4	4	no	—
119	C₂×D₈×C₃₁	C₂³	1	4	yes	—
120	C₂×D₈×C₃₁	C₂³	1	4	yes	—
121	C₂×D₈×C₃₁	C₂³	1	4	yes	—
122	C₂×D₈×C₃₁	C₂³	1	4	yes	—
123	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
124	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
125	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₃₁×#127	—	2	2	no	—
130	C₃₁×#127	—	2	1	no	—
131	C₃₁×#127	—	2	1	no	—
132	C₃₁×#127	C₂³	1	2	yes	—
133	C₃₁×#127	C₂³	1	2	yes	—
134	C₃₁×#127	C₂³	1	2	yes	—
135	C₃₁×#127	C₂³	1	1	yes	characteristic
136	C₃₁×#125	—	2	1	no	—
137	C₃₁×#124	—	2	2	no	—
138	C₃₁×#124	—	2	1	no	—
139	C₃₁×#124	—	2	2	no	—
140	C₃₁×#124	—	2	2	no	—
141	C₃₁×#124	C₂³	1	4	yes	—
142	C₃₁×#123	—	2	4	no	—
143	C₃₁×#123	—	2	4	no	—
144	C₃₁×#123	—	2	2	no	—
145	C₃₁×#123	—	2	2	no	—
146	C₃₁×#123	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	1	no	—
148	C₃₁×C₂²⋊Q₈	—	2	1	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	—	2	2	no	—
151	C₃₁×C₂²⋊Q₈	—	2	1	no	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×#121	—	2	1	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	2	no	—
158	C₃₁×#121	—	2	2	no	—
159	C₃₁×#121	—	2	1	no	—
160	C₃₁×#121	—	2	1	no	—
161	C₃₁×#121	—	2	2	no	—
162	C₃₁×#121	—	2	4	no	—
163	C₃₁×#121	—	2	4	no	—
164	C₃₁×#121	C₂³	1	2	yes	—
165	C₃₁×#121	C₂³	1	4	yes	—
166	C₃₁×#121	C₂³	1	2	yes	—
167	C₃₁×#121	C₂³	1	2	yes	—
168	C₃₁×#120	—	2	4	no	—
169	C₃₁×#120	—	2	2	no	—
170	C₃₁×#120	—	2	2	no	—
171	C₃₁×#120	—	2	2	no	—
172	C₄×Q₈×C₃₁	—	2	1	no	—
173	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
175	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	1	no	—
185	C₄×D₄×C₃₁	—	2	2	no	—
186	C₄×D₄×C₃₁	—	2	2	no	—
187	C₄×D₄×C₃₁	D₄	1	2	yes	—
188	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
189	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₃₁	C₂³	1	4	yes	—
192	C₄×D₄×C₃₁	C₂³	1	2	yes	—
193	C₄×D₄×C₃₁	C₂³	1	2	yes	—
194	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₃₁	C₂³	1	2	yes	—
197	C₄×D₄×C₃₁	C₂³	1	2	yes	—
198	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
199	C₃₁×#117	—	2	1	no	—
200	C₃₁×#117	D₄	1	1	yes	characteristic
201	C₃₁×#117	D₄	1	2	yes	—
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
209	C₃₁×#106	C₂³	1	2	yes	—
210	C₃₁×#106	C₂³	1	2	yes	—
211	C₃₁×#106	C₂³	1	4	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
216	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₃₁×#103	C₂³	1	2	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	2	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×#102	C₂³	1	2	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×#102	C₂³	1	4	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₃₁×#97	C₂³	1	4	yes	—
230	C₄×C₈×C₃₁	C₂³	1	2	yes	—
231	C₂⁴×C₃₁	—	2	2	no	—
232	C₂⁴×C₃₁	—	2	1	no	—
233	C₂⁴×C₃₁	—	2	2	no	—
234	#41×C₃₁	—	2	4	no	—
235	#41×C₃₁	—	4	8	no	—
236	#41×C₃₁	—	4	4	no	—
237	#41×C₃₁	—	4	4	no	—
238	#41×C₃₁	—	4	8	no	—
239	#41×C₃₁	—	4	4	no	—
240	#41×C₃₁	—	4	4	no	—
241	#41×C₃₁	—	4	4	no	—
242	#41×C₃₁	—	8	4	no	—
243	C₂×Q₈×C₃₁	—	2	1	no	—
244	C₂×Q₈×C₃₁	—	2	2	no	—
245	C₂×Q₈×C₃₁	—	2	1	no	—
246	C₂×Q₈×C₃₁	—	4	4	no	—
247	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
248	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	4	no	—
255	C₂×D₄×C₃₁	—	2	4	no	—
256	C₂×D₄×C₃₁	—	2	2	no	—
257	C₂×D₄×C₃₁	—	2	1	no	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	2	2	no	—
261	C₂×D₄×C₃₁	—	2	2	no	—
262	C₂×D₄×C₃₁	—	2	1	no	—
263	C₂×D₄×C₃₁	—	2	2	no	—
264	C₂×D₄×C₃₁	—	2	1	no	—
265	C₂×D₄×C₃₁	—	2	2	no	—
266	C₂×D₄×C₃₁	—	2	2	no	—
267	C₂×D₄×C₃₁	—	4	1	no	—
268	C₂×D₄×C₃₁	—	4	2	no	—
269	C₂×D₄×C₃₁	—	4	2	no	—
270	C₂×D₄×C₃₁	—	4	2	no	—
271	C₂×D₄×C₃₁	—	4	8	no	—
272	C₂×D₄×C₃₁	—	4	4	no	—
273	C₂×D₄×C₃₁	—	4	4	no	—
274	C₂×D₄×C₃₁	—	8	2	no	—
275	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
277	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
278	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₃₁	—	2	2	no	—
282	C₂²×C₄×C₃₁	—	2	1	no	—
283	C₂²×C₄×C₃₁	—	2	1	no	—
284	C₂²×C₄×C₃₁	—	2	1	no	—
285	C₂²×C₄×C₃₁	—	2	2	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	1	no	—
288	C₂²×C₄×C₃₁	—	2	2	no	—
289	C₂²×C₄×C₃₁	—	2	1	no	—
290	C₂²×C₄×C₃₁	—	2	4	no	—
291	C₂²×C₄×C₃₁	—	2	4	no	—
292	C₂²×C₄×C₃₁	—	4	8	no	—
293	C₂²×C₄×C₃₁	—	4	4	no	—
294	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	SD₁₆×C₃₁	—	2	4	no	—
301	SD₁₆×C₃₁	—	4	2	no	—
302	SD₁₆×C₃₁	—	4	4	no	—
303	D₈×C₃₁	—	2	8	no	—
304	D₈×C₃₁	—	4	4	no	—
305	D₈×C₃₁	—	4	4	no	—
306	D₈×C₃₁	—	4	4	no	—
307	M₁₆×C₃₁	—	4	4	no	—
308	C₂×C₈×C₃₁	—	4	2	no	—
309	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
310	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
311	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
312	C₄⋊C₄×C₃₁	—	2	2	no	—
313	C₄⋊C₄×C₃₁	—	2	1	no	—
314	C₄⋊C₄×C₃₁	—	2	1	no	—
315	C₄⋊C₄×C₃₁	—	2	1	no	—
316	C₄⋊C₄×C₃₁	—	2	1	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	1	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	2	no	—
321	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
324	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
325	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
328	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
329	C₂²⋊C₄×C₃₁	—	2	2	no	—
330	C₂²⋊C₄×C₃₁	—	2	1	no	—
331	C₂²⋊C₄×C₃₁	—	2	4	no	—
332	C₂²⋊C₄×C₃₁	—	2	4	no	—
333	C₂²⋊C₄×C₃₁	—	2	2	no	—
334	C₂²⋊C₄×C₃₁	—	2	1	no	—
335	C₂²⋊C₄×C₃₁	—	2	2	no	—
336	C₂²⋊C₄×C₃₁	—	2	1	no	—
337	C₂²⋊C₄×C₃₁	—	2	1	no	—
338	C₂²⋊C₄×C₃₁	—	2	2	no	—
339	C₂²⋊C₄×C₃₁	—	2	2	no	—
340	C₂²⋊C₄×C₃₁	—	2	2	no	—
341	C₂²⋊C₄×C₃₁	—	2	2	no	—
342	C₂²⋊C₄×C₃₁	—	2	4	no	—
343	C₂²⋊C₄×C₃₁	—	2	4	no	—
344	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
345	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
346	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
347	C₄²×C₃₁	—	2	2	no	—
348	C₄²×C₃₁	C₂×D₄	1	2	yes	—
349	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₃₁	C₂×D₄	1	2	yes	—
351	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₄²×C₃₁	C₂⁴	1	2	yes	—
354	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
355	#61961	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
356	C₂³×C₃₁	—	2	1	no	—
357	C₂³×C₃₁	—	2	4	no	—
358	C₂³×C₃₁	—	2	1	no	—
359	C₂³×C₃₁	—	2	2	no	—
360	C₂³×C₃₁	—	4	2	no	—
361	C₂³×C₃₁	—	4	4	no	—
362	C₂³×C₃₁	—	4	4	no	—
363	C₂³×C₃₁	—	4	2	no	—
364	C₂³×C₃₁	—	4	4	no	—
365	C₂³×C₃₁	—	8	1	no	—
366	C₂³×C₃₁	—	8	2	no	—
367	C₂³×C₃₁	—	8	2	no	—
368	C₂³×C₃₁	—	8	2	no	—
369	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
370	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
371	Q₈×C₃₁	—	2	2	no	—
372	Q₈×C₃₁	—	2	2	no	—
373	Q₈×C₃₁	—	2	2	no	—
374	Q₈×C₃₁	—	4	4	no	—
375	Q₈×C₃₁	—	4	2	no	—
376	Q₈×C₃₁	—	4	2	no	—
377	D₄×C₃₁	—	2	4	no	—
378	D₄×C₃₁	—	2	2	no	—
379	D₄×C₃₁	—	2	4	no	—
380	D₄×C₃₁	—	2	1	no	—
381	D₄×C₃₁	—	2	2	no	—
382	D₄×C₃₁	—	2	1	no	—
383	D₄×C₃₁	—	2	2	no	—
384	D₄×C₃₁	—	2	4	no	—
385	D₄×C₃₁	—	2	1	no	—
386	D₄×C₃₁	—	4	4	no	—
387	D₄×C₃₁	—	4	2	no	—
388	D₄×C₃₁	—	4	4	no	—
389	D₄×C₃₁	—	4	4	no	—
390	D₄×C₃₁	—	4	4	no	—
391	D₄×C₃₁	—	4	4	no	—
392	D₄×C₃₁	—	4	4	no	—
393	D₄×C₃₁	—	4	4	no	—
394	D₄×C₃₁	—	4	4	no	—
395	D₄×C₃₁	—	4	2	no	—
396	D₄×C₃₁	—	8	2	no	—
397	D₄×C₃₁	—	8	1	no	—
398	D₄×C₃₁	—	8	2	no	—
399	D₄×C₃₁	—	8	2	no	—
400	D₄×C₃₁	—	8	4	no	—
401	D₄×C₃₁	—	8	4	no	—
402	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
403	C₂×C₄×C₃₁	—	2	4	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	1	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	1	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	1	no	—
413	C₂×C₄×C₃₁	—	4	1	no	—
414	C₂×C₄×C₃₁	—	4	2	no	—
415	C₂×C₄×C₃₁	—	4	4	no	—
416	C₂×C₄×C₃₁	—	4	4	no	—
417	C₂×C₄×C₃₁	—	4	4	no	—
418	C₂×C₄×C₃₁	—	4	2	no	—
419	C₂×C₄×C₃₁	—	4	2	no	—
420	C₂×C₄×C₃₁	—	4	2	no	—
421	C₂×C₄×C₃₁	—	4	2	no	—
422	C₂×C₄×C₃₁	—	4	4	no	—
423	C₂×C₄×C₃₁	—	4	2	no	—
424	C₂×C₄×C₃₁	—	8	4	no	—
425	C₂×C₄×C₃₁	—	8	4	no	—
426	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
427	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
436	C₈×C₃₁	—	2	4	no	—
437	C₈×C₃₁	—	2	2	no	—
438	C₈×C₃₁	—	2	2	no	—
439	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
440	D₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
441	#3399	C₂×C₃₁	1	2	yes	complemented
442	#3373	C₂×C₃₁	1	2	yes	complemented
443	#3332	C₂×C₃₁	1	2	yes	complemented
444	#3306	C₂×C₃₁	1	4	yes	complemented
445	#3274	C₂×C₃₁	1	2	yes	complemented
446	#3264	C₂×C₃₁	1	4	yes	complemented
447	#3253	C₂×C₃₁	1	2	yes	complemented
448	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#3214	C₂×C₃₁	1	2	yes	complemented
450	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
451	#3109	C₂×C₃₁	1	2	yes	complemented
452	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#3036	C₂×C₃₁	1	2	yes	complemented
454	C₂×#459	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
456	C₂²×C₃₁	—	2	1	no	—
457	C₂²×C₃₁	—	2	1	no	—
458	C₂²×C₃₁	—	2	2	no	—
459	C₂²×C₃₁	—	2	2	no	—
460	C₂²×C₃₁	—	2	2	no	—
461	C₂²×C₃₁	—	2	2	no	—
462	C₂²×C₃₁	—	4	1	no	—
463	C₂²×C₃₁	—	4	1	no	—
464	C₂²×C₃₁	—	4	4	no	—
465	C₂²×C₃₁	—	4	1	no	—
466	C₂²×C₃₁	—	4	2	no	—
467	C₂²×C₃₁	—	4	4	no	—
468	C₂²×C₃₁	—	4	1	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	—	4	1	no	—
472	C₂²×C₃₁	—	4	4	no	—
473	C₂²×C₃₁	—	8	4	no	—
474	C₂²×C₃₁	—	8	8	no	—
475	C₂²×C₃₁	—	16	4	no	—
476	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
477	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
478	C₄×C₃₁	—	2	1	no	—
479	C₄×C₃₁	—	2	2	no	—
480	C₄×C₃₁	—	2	1	no	—
481	C₄×C₃₁	—	2	2	no	—
482	C₄×C₃₁	—	2	1	no	—
483	C₄×C₃₁	—	2	2	no	—
484	C₄×C₃₁	—	4	2	no	—
485	C₄×C₃₁	—	4	2	no	—
486	C₄×C₃₁	—	4	1	no	—
487	C₄×C₃₁	—	4	2	no	—
488	C₄×C₃₁	—	4	1	no	—
489	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
490	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
491	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₄×C₃₁	#585	1	1	yes	characteristic
493	C₂²×#41	—	2	1	no	—
494	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
495	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
496	#559	—	2	1	no	—
497	#559	C₂²×C₃₁	1	2	yes	complemented
498	#550	—	2	1	no	—
499	#550	C₂²×C₃₁	1	2	yes	complemented
500	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
501	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
502	#548	—	2	1	no	—
503	#547	C₂²×C₃₁	1	2	yes	—
504	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
505	#546	—	2	2	no	—
506	#546	—	2	1	no	—
507	#546	—	2	2	no	—
508	#546	C₂²×C₃₁	1	4	yes	complemented
509	D₄²	C₂²×C₃₁	1	2	yes	—
510	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
511	#540	—	2	2	no	—
512	#535	—	2	1	no	—
513	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	#532	C₂²×C₃₁	1	1	yes	characteristic
515	#532	C₂²×C₃₁	1	2	yes	complemented
516	#532	C₂²×C₃₁	1	2	yes	complemented
517	#532	C₂²×C₃₁	1	2	yes	complemented
518	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
519	#525	—	2	1	no	—
520	#525	—	2	2	no	—
521	#518	—	2	1	no	—
522	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
525	#496	C₂²×C₃₁	1	4	yes	complemented
526	#493	C₂²×C₃₁	1	2	yes	complemented
527	#489	C₂²×C₃₁	1	4	yes	complemented
528	#486	C₂²×C₃₁	1	2	yes	complemented
529	#483	C₂²×C₃₁	1	2	yes	complemented
530	#481	C₂²×C₃₁	1	4	yes	complemented
531	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
533	#476	C₂²×C₃₁	1	2	yes	complemented
534	#476	C₂²×C₃₁	1	4	yes	complemented
535	#475	C₂²×C₃₁	1	2	yes	complemented
536	#469	C₂²×C₃₁	1	4	yes	complemented
537	#469	C₂²×C₃₁	1	4	yes	complemented
538	#465	C₂²×C₃₁	1	4	yes	complemented
539	#463	C₂²×C₃₁	1	4	yes	complemented
540	#463	C₂²×C₃₁	1	4	yes	complemented
541	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
542	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
543	#461	C₂²×C₃₁	1	2	yes	complemented
544	#460	C₂²×C₃₁	1	2	yes	complemented
545	#459	C₂²×C₃₁	1	2	yes	—
546	#459	C₂²×C₃₁	1	2	yes	—
547	#459	C₂²×C₃₁	1	2	yes	complemented
548	#459	C₂²×C₃₁	1	2	yes	complemented
549	#459	C₂²×C₃₁	1	4	yes	complemented
550	#459	C₂²×C₃₁	1	2	yes	complemented
551	#459	C₂²×C₃₁	1	2	yes	complemented
552	#450	C₂²×C₃₁	1	2	yes	—
553	#449	C₂²×C₃₁	1	4	yes	complemented
554	#449	C₂²×C₃₁	1	4	yes	complemented
555	#447	C₂²×C₃₁	1	4	yes	complemented
556	#447	C₂²×C₃₁	1	4	yes	complemented
557	#446	C₂²×C₃₁	1	2	yes	complemented
558	#442	C₂²×C₃₁	1	4	yes	complemented
559	#442	C₂²×C₃₁	1	4	yes	complemented
560	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
561	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
562	#436	C₂²×C₃₁	1	2	yes	complemented
563	#435	C₂²×C₃₁	1	4	yes	complemented
564	#432	C₂²×C₃₁	1	2	yes	complemented
565	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
566	#423	C₂²×C₃₁	1	2	yes	complemented
567	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	#417	C₂²×C₃₁	1	4	yes	complemented
569	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
570	C₂×C₃₁	—	2	2	no	—
571	C₂×C₃₁	—	4	2	no	—
572	C₂×C₃₁	—	4	2	no	—
573	C₂×C₃₁	—	8	1	no	—
574	C₂×C₃₁	—	8	2	no	—
575	C₂×C₃₁	—	8	4	no	—
576	C₂×C₃₁	#3488	1	1	yes	characteristic
577	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
578	C₂×C₃₁	#3585	1	1	yes	characteristic
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	2	no	—
581	C₂×#41	—	2	1	no	—
582	C₂×#41	—	2	1	no	—
583	C₂×#41	—	2	2	no	—
584	C₂×#41	—	2	2	no	—
585	C₂×#41	—	4	8	no	—
586	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
587	C₂×#41	C₂³×C₃₁	1	4	yes	—
588	C₂²×Q₈	—	2	1	no	—
589	C₂²×D₄	—	2	2	no	—
590	C₂²×D₄	—	2	1	no	—
591	C₂²×D₄	—	2	1	no	—
592	C₂²×D₄	—	2	1	no	—
593	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
594	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
595	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
596	C₂³×C₄	—	2	1	no	—
597	C₂³×C₄	—	2	2	no	—
598	AGL(1,ℤ/8)	—	4	8	no	—
599	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
601	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
602	C₂×D₈	—	4	4	no	—
603	C₂×D₈	C₂³×C₃₁	1	4	yes	—
604	C₂×D₈	C₂³×C₃₁	1	4	yes	—
605	C₂×D₈	C₂³×C₃₁	1	4	yes	—
606	C₂×D₈	C₂³×C₃₁	1	4	yes	—
607	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
608	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
609	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
610	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
611	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
612	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
613	#127	—	2	2	no	—
614	#127	—	2	1	no	—
615	#127	—	2	1	no	—
616	#127	C₂³×C₃₁	1	2	yes	—
617	#127	C₂³×C₃₁	1	2	yes	—
618	#127	C₂³×C₃₁	1	1	yes	characteristic
619	#127	C₂³×C₃₁	1	2	yes	—
620	#125	—	2	1	no	—
621	#124	—	2	2	no	—
622	#124	—	2	1	no	—
623	#124	—	2	2	no	—
624	#124	—	2	2	no	—
625	#124	C₂³×C₃₁	1	4	yes	—
626	#123	—	2	4	no	—
627	#123	—	2	4	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	C₂²⋊Q₈	—	2	1	no	—
632	C₂²⋊Q₈	—	2	1	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	1	no	—
636	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
637	#121	—	2	1	no	—
638	#121	—	2	2	no	—
639	#121	—	2	2	no	—
640	#121	—	2	2	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	1	no	—
644	#121	—	2	1	no	—
645	#121	—	2	2	no	—
646	#121	—	2	4	no	—
647	#121	—	2	4	no	—
648	#121	C₂³×C₃₁	1	2	yes	—
649	#121	C₂³×C₃₁	1	2	yes	—
650	#121	C₂³×C₃₁	1	2	yes	—
651	#121	C₂³×C₃₁	1	4	yes	—
652	#120	—	2	4	no	—
653	#120	—	2	2	no	—
654	#120	—	2	2	no	—
655	#120	—	2	2	no	—
656	C₄×Q₈	—	2	1	no	—
657	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
658	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
659	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	1	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	D₄×C₃₁	1	2	yes	—
672	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
673	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
674	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
675	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
676	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
677	C₄×D₄	C₂³×C₃₁	1	2	yes	—
678	C₄×D₄	C₂³×C₃₁	1	2	yes	—
679	C₄×D₄	C₂³×C₃₁	1	2	yes	—
680	C₄×D₄	C₂³×C₃₁	1	4	yes	—
681	C₄×D₄	C₂³×C₃₁	1	2	yes	—
682	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
683	#117	—	2	1	no	—
684	#117	D₄×C₃₁	1	1	yes	characteristic
685	#117	D₄×C₃₁	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
688	C₂×C₂²⋊C₄	—	2	1	no	—
689	C₂×C₂²⋊C₄	—	2	2	no	—
690	C₂×C₂²⋊C₄	—	2	4	no	—
691	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
693	#106	C₂³×C₃₁	1	2	yes	—
694	#106	C₂³×C₃₁	1	2	yes	—
695	#106	C₂³×C₃₁	1	4	yes	—
696	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
697	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
698	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
699	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
700	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
701	#103	C₂³×C₃₁	1	2	yes	—
702	#103	C₂³×C₃₁	1	4	yes	—
703	#103	C₂³×C₃₁	1	2	yes	—
704	#102	C₂³×C₃₁	1	4	yes	—
705	#102	C₂³×C₃₁	1	4	yes	—
706	#102	C₂³×C₃₁	1	4	yes	—
707	#102	C₂³×C₃₁	1	2	yes	—
708	#102	C₂³×C₃₁	1	2	yes	—
709	#102	C₂³×C₃₁	1	4	yes	—
710	#102	C₂³×C₃₁	1	4	yes	—
711	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
713	#97	C₂³×C₃₁	1	4	yes	—
714	C₄×C₈	C₂³×C₃₁	1	2	yes	—
715	C₃₁	#61961	1	1	yes	characteristic, direct product factor, Sylow
716	C₂⁴	—	2	2	no	—
717	C₂⁴	—	2	1	no	—
718	C₂⁴	—	2	2	no	—
719	#41	—	2	4	no	—
720	#41	—	4	8	no	—
721	#41	—	4	4	no	—
722	#41	—	4	4	no	—
723	#41	—	4	8	no	—
724	#41	—	4	4	no	—
725	#41	—	4	4	no	—
726	#41	—	4	4	no	—
727	#41	—	8	4	no	—
728	C₂×Q₈	—	2	1	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	1	no	—
731	C₂×Q₈	—	4	4	no	—
732	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
733	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	4	1	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	8	no	—
757	C₂×D₄	—	4	4	no	—
758	C₂×D₄	—	4	4	no	—
759	C₂×D₄	—	8	2	no	—
760	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
761	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
763	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
764	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
765	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	4	8	no	—
778	C₂²×C₄	—	4	4	no	—
779	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
781	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
782	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
785	SD₁₆	—	2	4	no	—
786	SD₁₆	—	4	2	no	—
787	SD₁₆	—	4	4	no	—
788	D₈	—	2	8	no	—
789	D₈	—	4	4	no	—
790	D₈	—	4	4	no	—
791	D₈	—	4	4	no	—
792	M₁₆	—	4	4	no	—
793	C₂×C₈	—	4	2	no	—
794	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
795	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
796	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
807	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
808	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
809	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
811	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
812	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
813	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	1	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	1	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	1	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
830	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
831	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
832	C₄²	—	2	2	no	—
833	C₄²	C₂×D₄×C₃₁	1	2	yes	—
834	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
835	C₄²	C₂×D₄×C₃₁	1	2	yes	—
836	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
837	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
838	C₄²	C₂⁴×C₃₁	1	2	yes	—
839	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
840	C₂³	—	2	1	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	4	2	no	—
845	C₂³	—	4	4	no	—
846	C₂³	—	4	4	no	—
847	C₂³	—	4	2	no	—
848	C₂³	—	4	4	no	—
849	C₂³	—	8	1	no	—
850	C₂³	—	8	2	no	—
851	C₂³	—	8	2	no	—
852	C₂³	—	8	2	no	—
853	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
854	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	4	no	—
859	Q₈	—	4	2	no	—
860	Q₈	—	4	2	no	—
861	D₄	—	2	4	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	4	no	—
864	D₄	—	2	1	no	—
865	D₄	—	2	2	no	—
866	D₄	—	2	1	no	—
867	D₄	—	2	2	no	—
868	D₄	—	2	4	no	—
869	D₄	—	2	1	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	2	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	4	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	2	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	1	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	4	no	—
885	D₄	—	8	4	no	—
886	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	2	no	—
903	C₂×C₄	—	4	2	no	—
904	C₂×C₄	—	4	2	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	2	no	—
908	C₂×C₄	—	8	4	no	—
909	C₂×C₄	—	8	4	no	—
910	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
911	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
916	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
917	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
918	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
919	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
920	C₈	—	2	4	no	—
921	C₈	—	2	2	no	—
922	C₈	—	2	2	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	4	no	—
932	C₂²	—	4	1	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	4	no	—
937	C₂²	—	4	4	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	8	4	no	—
941	C₂²	—	8	8	no	—
942	C₂²	—	16	4	no	—
943	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
944	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
945	C₄	—	2	2	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	1	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	1	no	—
955	C₄	—	4	2	no	—
956	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
957	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
958	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
959	C₄	C₃₁×#585	1	1	yes	characteristic
960	C₂	—	2	2	no	—
961	C₂	—	4	2	no	—
962	C₂	—	4	2	no	—
963	C₂	—	8	1	no	—
964	C₂	—	8	2	no	—
965	C₂	—	8	4	no	—
966	C₂	C₃₁×#3488	1	1	yes	characteristic
967	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
968	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. D₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3373	C₂	semidirect
5. C₃₁×#3332	C₂	semidirect
6. C₃₁×#3306	C₂	semidirect
7. C₃₁×#3274	C₂	semidirect
8. C₃₁×#3264	C₂	semidirect
9. C₃₁×#3253	C₂	semidirect
10. C₃₁×#3246	C₂	semidirect
11. C₃₁×#3214	C₂	semidirect
12. C₃₁×#3205	C₂	semidirect
13. C₃₁×#3109	C₂	semidirect
14. C₃₁×#3101	C₂	semidirect
15. C₃₁×#3036	C₂	semidirect
16. C₂×C₃₁×#459	C₂	semidirect
17. C₃₁×#2989	C₂	semidirect
19. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
22. C₃₁×#559	C₂²	semidirect
24. C₃₁×#550	C₂²	semidirect
25. C₃₁×#550	C₂²	semidirect
26. D₄×Q₈×C₃₁	C₂²	semidirect
29. C₃₁×#547	C₂²	semidirect
33. C₃₁×#546	C₂²	semidirect
35. D₄²×C₃₁	C₂²	semidirect
38. C₃₁×#533	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
41. C₃₁×#532	C₂²	semidirect
42. C₃₁×#532	C₂²	semidirect
43. C₂×C₃₁×#127	C₂²	semidirect
49. C₂×C₄×D₄×C₃₁	C₂²	semidirect
50. C₃₁×#496	C₂²	semidirect
51. C₃₁×#493	C₂²	semidirect
52. C₃₁×#489	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
54. C₃₁×#483	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
56. C₃₁×#476	C₂²	semidirect
57. C₃₁×#476	C₂²	semidirect
58. C₃₁×#476	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#469	C₂²	semidirect
62. C₃₁×#469	C₂²	semidirect
63. C₃₁×#465	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
65. C₃₁×#463	C₂²	semidirect
66. C₃₁×#461	C₂²	semidirect
67. C₃₁×#461	C₂²	semidirect
68. C₃₁×#461	C₂²	semidirect
69. C₃₁×#460	C₂²	semidirect
72. C₃₁×#459	C₂²	semidirect
73. C₃₁×#459	C₂²	semidirect
74. C₃₁×#459	C₂²	semidirect
75. C₃₁×#459	C₂²	semidirect
76. C₃₁×#459	C₂²	semidirect
78. C₃₁×#449	C₂²	semidirect
79. C₃₁×#449	C₂²	semidirect
80. C₃₁×#447	C₂²	semidirect
81. C₃₁×#447	C₂²	semidirect
82. C₃₁×#446	C₂²	semidirect
83. C₃₁×#442	C₂²	semidirect
84. C₃₁×#442	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₄×SD₁₆×C₃₁	C₂²	semidirect
87. C₃₁×#436	C₂²	semidirect
88. C₃₁×#435	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
90. C₃₁×#431	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
93. C₃₁×#417	C₂²	semidirect
94. C₂×C₃₁×#102	C₂²	semidirect
355. #61961	C₃₁	direct (N × H)
426. C₂×C₄×C₃₁	AGL(1,ℤ/8)	semidirect
439. #3508	C₂×C₃₁	semidirect
440. D₄×#41	C₂×C₃₁	semidirect
441. #3399	C₂×C₃₁	semidirect
442. #3373	C₂×C₃₁	semidirect
443. #3332	C₂×C₃₁	semidirect
444. #3306	C₂×C₃₁	semidirect
445. #3274	C₂×C₃₁	semidirect
446. #3264	C₂×C₃₁	semidirect
447. #3253	C₂×C₃₁	semidirect
448. #3246	C₂×C₃₁	semidirect
449. #3214	C₂×C₃₁	semidirect
450. #3205	C₂×C₃₁	semidirect
451. #3109	C₂×C₃₁	semidirect
452. #3101	C₂×C₃₁	semidirect
453. #3036	C₂×C₃₁	semidirect
454. C₂×#459	C₂×C₃₁	semidirect
455. #2989	C₂×C₃₁	semidirect
494. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
497. #559	C₂²×C₃₁	semidirect
499. #550	C₂²×C₃₁	semidirect
500. #550	C₂²×C₃₁	semidirect
501. D₄×Q₈	C₂²×C₃₁	semidirect
504. #547	C₂²×C₃₁	semidirect
508. #546	C₂²×C₃₁	semidirect
510. D₄²	C₂²×C₃₁	semidirect
513. #533	C₂²×C₃₁	semidirect
515. #532	C₂²×C₃₁	semidirect
516. #532	C₂²×C₃₁	semidirect
517. #532	C₂²×C₃₁	semidirect
518. C₂×#127	C₂²×C₃₁	semidirect
524. C₂×C₄×D₄	C₂²×C₃₁	semidirect
525. #496	C₂²×C₃₁	semidirect
526. #493	C₂²×C₃₁	semidirect
527. #489	C₂²×C₃₁	semidirect
528. #486	C₂²×C₃₁	semidirect
529. #483	C₂²×C₃₁	semidirect
530. #481	C₂²×C₃₁	semidirect
531. #476	C₂²×C₃₁	semidirect
532. #476	C₂²×C₃₁	semidirect
533. #476	C₂²×C₃₁	semidirect
534. #476	C₂²×C₃₁	semidirect
535. #475	C₂²×C₃₁	semidirect
536. #469	C₂²×C₃₁	semidirect
537. #469	C₂²×C₃₁	semidirect
538. #465	C₂²×C₃₁	semidirect
539. #463	C₂²×C₃₁	semidirect
540. #463	C₂²×C₃₁	semidirect
541. #461	C₂²×C₃₁	semidirect
542. #461	C₂²×C₃₁	semidirect
543. #461	C₂²×C₃₁	semidirect
544. #460	C₂²×C₃₁	semidirect
547. #459	C₂²×C₃₁	semidirect
548. #459	C₂²×C₃₁	semidirect
549. #459	C₂²×C₃₁	semidirect
550. #459	C₂²×C₃₁	semidirect
551. #459	C₂²×C₃₁	semidirect
553. #449	C₂²×C₃₁	semidirect
554. #449	C₂²×C₃₁	semidirect
555. #447	C₂²×C₃₁	semidirect
556. #447	C₂²×C₃₁	semidirect
557. #446	C₂²×C₃₁	semidirect
558. #442	C₂²×C₃₁	semidirect
559. #442	C₂²×C₃₁	semidirect
560. C₄×SD₁₆	C₂²×C₃₁	semidirect
561. C₄×SD₁₆	C₂²×C₃₁	semidirect
562. #436	C₂²×C₃₁	semidirect
563. #435	C₂²×C₃₁	semidirect
564. #432	C₂²×C₃₁	semidirect
565. #431	C₂²×C₃₁	semidirect
566. #423	C₂²×C₃₁	semidirect
567. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
568. #417	C₂²×C₃₁	semidirect
569. C₂×#102	C₂²×C₃₁	semidirect
715. C₃₁	#61961	direct (N × H)
910. C₂×C₄	C₃₁×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3508	2
D₄×#41×C₃₁	2
C₃₁×#3399	2
C₃₁×#3373	2
C₃₁×#3332	2
C₃₁×#3306	2
C₃₁×#3274	2
C₃₁×#3264	2
C₃₁×#3253	2
C₃₁×#3246	2
C₃₁×#3214	2
C₃₁×#3205	2
C₃₁×#3109	2
C₃₁×#3101	2
C₃₁×#3036	2
C₂×C₃₁×#459	2
C₃₁×#2989	2
#61961	31

Subgroups — C31×#61961 #21518720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61961 #21518720