Subgroups — C₃₁×#61256 #21518015

Order 7936.

1892 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3354	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3348	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3347	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3341	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3094	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3093	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2911	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
21	C₃₁×#555	—	2	1	no	—
22	C₃₁×#555	—	2	2	no	—
23	C₃₁×#555	—	2	1	no	—
24	C₃₁×#555	C₂²	1	2	yes	—
25	C₃₁×#555	C₂²	1	4	yes	—
26	C₃₁×#555	C₂²	1	2	yes	—
27	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#553	C₂²	1	2	yes	complemented
30	C₃₁×#552	—	2	1	no	—
31	C₃₁×#552	C₂²	1	2	yes	complemented
32	C₃₁×#551	—	2	2	no	—
33	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#546	—	2	1	no	—
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₃₁×#529	—	2	2	no	—
38	C₃₁×#529	—	2	1	no	—
39	C₂×C₃₁×#124	—	2	2	no	—
40	C₃₁×#525	C₂²	1	2	yes	—
41	C₂×C₃₁×#121	—	2	1	no	—
42	C₂×C₃₁×#121	C₂²	1	2	yes	—
43	C₄×#41×C₃₁	—	2	1	no	—
44	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#117	—	2	1	no	—
48	C₂×C₃₁×#117	C₂²	1	2	yes	—
49	C₂×C₃₁×#117	C₂²	1	2	yes	—
50	C₃₁×#501	C₂²	1	4	yes	complemented
51	C₃₁×#500	C₂²	1	2	yes	complemented
52	C₃₁×#498	C₂²	1	2	yes	complemented
53	C₃₁×#485	C₂²	1	4	yes	complemented
54	C₃₁×#485	C₂²	1	4	yes	complemented
55	C₃₁×#482	C₂²	1	4	yes	complemented
56	C₃₁×#482	C₂²	1	4	yes	complemented
57	C₃₁×#482	C₂²	1	4	yes	complemented
58	C₃₁×#482	C₂²	1	4	yes	complemented
59	C₃₁×#481	C₂²	1	4	yes	complemented
60	C₃₁×#480	C₂²	1	4	yes	complemented
61	C₃₁×#478	C₂²	1	4	yes	complemented
62	C₃₁×#477	C₂²	1	2	yes	complemented
63	C₃₁×#476	C₂²	1	2	yes	complemented
64	C₃₁×#476	C₂²	1	2	yes	complemented
65	C₃₁×#475	C₂²	1	2	yes	complemented
66	C₃₁×#474	C₂²	1	2	yes	complemented
67	C₃₁×#474	C₂²	1	2	yes	complemented
68	C₃₁×#469	C₂²	1	4	yes	complemented
69	C₃₁×#468	C₂²	1	4	yes	complemented
70	C₃₁×#466	C₂²	1	4	yes	complemented
71	C₃₁×#465	C₂²	1	4	yes	complemented
72	C₃₁×#442	C₂²	1	2	yes	complemented
73	C₃₁×#440	C₂²	1	2	yes	complemented
74	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
75	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
76	C₃₁×#436	C₂²	1	2	yes	complemented
77	C₃₁×#435	C₂²	1	4	yes	complemented
78	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
79	C₃₁×#428	C₂²	1	2	yes	—
80	C₃₁×#428	C₂²	1	2	yes	—
81	C₃₁×#428	C₂²	1	2	yes	—
82	C₃₁×#428	C₂²	1	2	yes	—
83	C₃₁×#428	C₂²	1	1	yes	characteristic
84	C₃₁×#428	C₂²	1	4	yes	complemented
85	C₃₁×#428	C₂²	1	4	yes	complemented
86	C₃₁×#427	C₂²	1	4	yes	complemented
87	C₃₁×#427	C₂²	1	4	yes	complemented
88	C₃₁×#423	C₂²	1	1	yes	characteristic
89	C₃₁×#418	C₂²	1	2	yes	—
90	C₃₁×#418	C₂²	1	1	yes	characteristic
91	C₃₁×#417	C₂²	1	2	yes	—
92	C₃₁×#417	C₂²	1	1	yes	characteristic
93	C₃₁×#407	C₂²	1	2	yes	—
94	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₃₁	—	2	1	no	—
98	C₂²×D₄×C₃₁	—	2	2	no	—
99	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
100	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₃₁	—	2	1	no	—
102	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
103	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
104	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×D₈×C₃₁	C₂³	1	2	yes	—
106	C₂×M₁₆×C₃₁	—	2	8	no	—
107	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
109	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
112	C₃₁×C₄⋊Q₈	—	2	1	no	—
113	C₃₁×C₄⋊Q₈	—	2	1	no	—
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#126	—	2	2	no	—
120	C₃₁×#126	—	2	2	no	—
121	C₃₁×#125	—	2	2	no	—
122	C₃₁×#125	—	2	1	no	—
123	C₃₁×#125	C₂³	1	2	yes	—
124	C₃₁×#124	—	2	1	no	—
125	C₃₁×#124	—	2	4	no	—
126	C₃₁×#124	—	2	4	no	—
127	C₃₁×#124	—	2	4	no	—
128	C₃₁×#124	—	2	4	no	—
129	C₃₁×#124	—	2	2	no	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×#123	—	2	2	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	1	no	—
136	C₃₁×C₂²⋊Q₈	—	2	1	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	4	no	—
143	C₃₁×#121	—	2	2	no	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	C₂³	1	4	yes	—
148	C₃₁×#121	C₂³	1	2	yes	—
149	C₃₁×#121	C₂³	1	4	yes	—
150	C₃₁×#121	C₂³	1	2	yes	—
151	C₃₁×#120	—	2	2	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
157	C₄×D₄×C₃₁	—	2	1	no	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	1	no	—
160	C₄×D₄×C₃₁	—	2	1	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
166	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
167	C₄×D₄×C₃₁	D₄	1	2	yes	—
168	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₃₁	C₂³	1	2	yes	—
170	C₄×D₄×C₃₁	C₂³	1	2	yes	—
171	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	C₂³	1	2	yes	—
174	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₃₁×#117	—	2	2	no	—
176	C₃₁×#117	—	2	2	no	—
177	C₃₁×#117	—	2	2	no	—
178	C₃₁×#117	—	2	2	no	—
179	C₃₁×#117	—	2	2	no	—
180	C₃₁×#117	—	2	2	no	—
181	C₃₁×#117	—	2	4	no	—
182	C₃₁×#117	—	2	1	no	—
183	C₃₁×#117	—	2	2	no	—
184	C₃₁×#117	—	2	1	no	—
185	C₃₁×#117	C₂³	1	1	yes	characteristic
186	C₃₁×#117	C₂³	1	2	yes	—
187	C₃₁×#117	C₂³	1	2	yes	—
188	C₃₁×#117	C₂³	1	2	yes	—
189	C₃₁×#117	C₂³	1	4	yes	—
190	C₃₁×#117	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
192	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
202	C₂×C₄²×C₃₁	—	2	2	no	—
203	C₂×C₄²×C₃₁	—	2	2	no	—
204	C₂×C₄²×C₃₁	—	2	1	no	—
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₃₁×#107	C₂³	1	2	yes	—
207	C₃₁×#107	C₂³	1	4	yes	—
208	C₃₁×#107	C₂³	1	4	yes	—
209	C₃₁×#107	C₂³	1	4	yes	—
210	C₃₁×#107	C₂³	1	4	yes	—
211	C₃₁×#106	C₂³	1	2	yes	—
212	C₃₁×#106	C₂³	1	4	yes	—
213	C₃₁×#106	C₂³	1	4	yes	—
214	C₃₁×#106	C₂³	1	4	yes	—
215	C₃₁×#106	C₂³	1	4	yes	—
216	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
217	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
218	C₃₁×#103	C₂³	1	2	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₃₁×#97	C₂³	1	2	yes	—
229	C₄×C₈×C₃₁	C₂³	1	2	yes	—
230	C₂⁴×C₃₁	—	2	1	no	—
231	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
232	#41×C₃₁	—	2	2	no	—
233	#41×C₃₁	—	2	2	no	—
234	#41×C₃₁	—	4	4	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	8	2	no	—
240	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₃₁	—	2	1	no	—
242	C₂×D₄×C₃₁	—	2	2	no	—
243	C₂×D₄×C₃₁	—	2	2	no	—
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	2	4	no	—
246	C₂×D₄×C₃₁	—	2	1	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	4	2	no	—
250	C₂×D₄×C₃₁	—	8	4	no	—
251	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₃₁	—	2	4	no	—
257	C₂²×C₄×C₃₁	—	2	4	no	—
258	C₂²×C₄×C₃₁	—	2	1	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	1	no	—
267	C₂²×C₄×C₃₁	—	4	4	no	—
268	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	SD₁₆×C₃₁	—	2	4	no	—
277	D₈×C₃₁	—	2	4	no	—
278	M₁₆×C₃₁	—	2	4	no	—
279	M₁₆×C₃₁	—	2	2	no	—
280	M₁₆×C₃₁	—	2	8	no	—
281	M₁₆×C₃₁	#41	1	4	yes	complemented
282	C₂×C₈×C₃₁	—	2	8	no	—
283	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
284	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
285	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
309	C₂²⋊C₄×C₃₁	—	2	1	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	4	no	—
312	C₂²⋊C₄×C₃₁	—	2	4	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	4	no	—
318	C₂²⋊C₄×C₃₁	—	2	4	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	1	no	—
323	C₂²⋊C₄×C₃₁	—	2	1	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	—	2	1	no	—
330	C₄²×C₃₁	—	2	4	no	—
331	C₄²×C₃₁	—	2	4	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	1	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	2	no	—
336	C₄²×C₃₁	—	2	1	no	—
337	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
341	#61256	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂³×C₃₁	—	2	4	no	—
343	C₂³×C₃₁	—	2	1	no	—
344	C₂³×C₃₁	—	2	2	no	—
345	C₂³×C₃₁	—	4	2	no	—
346	C₂³×C₃₁	—	4	2	no	—
347	C₂³×C₃₁	—	4	2	no	—
348	C₂³×C₃₁	—	4	2	no	—
349	C₂³×C₃₁	—	4	2	no	—
350	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
351	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
352	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	Q₈×C₃₁	—	2	1	no	—
354	Q₈×C₃₁	—	2	1	no	—
355	Q₈×C₃₁	—	4	2	no	—
356	Q₈×C₃₁	—	8	1	no	—
357	Q₈×C₃₁	—	8	2	no	—
358	Q₈×C₃₁	—	8	2	no	—
359	D₄×C₃₁	—	2	2	no	—
360	D₄×C₃₁	—	2	2	no	—
361	D₄×C₃₁	—	2	1	no	—
362	D₄×C₃₁	—	2	2	no	—
363	D₄×C₃₁	—	2	2	no	—
364	D₄×C₃₁	—	2	1	no	—
365	D₄×C₃₁	—	4	2	no	—
366	D₄×C₃₁	—	4	4	no	—
367	D₄×C₃₁	—	4	2	no	—
368	D₄×C₃₁	—	4	2	no	—
369	D₄×C₃₁	—	8	2	no	—
370	D₄×C₃₁	—	8	4	no	—
371	D₄×C₃₁	—	8	4	no	—
372	C₂×C₄×C₃₁	—	2	4	no	—
373	C₂×C₄×C₃₁	—	2	4	no	—
374	C₂×C₄×C₃₁	—	2	4	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	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	1	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	2	no	—
386	C₂×C₄×C₃₁	—	2	4	no	—
387	C₂×C₄×C₃₁	—	4	1	no	—
388	C₂×C₄×C₃₁	—	4	4	no	—
389	C₂×C₄×C₃₁	—	4	2	no	—
390	C₂×C₄×C₃₁	—	4	4	no	—
391	C₂×C₄×C₃₁	—	4	4	no	—
392	C₂×C₄×C₃₁	—	4	2	no	—
393	C₂×C₄×C₃₁	—	4	4	no	—
394	C₂×C₄×C₃₁	—	4	2	no	—
395	C₂×C₄×C₃₁	—	8	1	no	—
396	C₂×C₄×C₃₁	—	8	2	no	—
397	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
405	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
406	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
407	C₈×C₃₁	—	2	4	no	—
408	C₈×C₃₁	—	2	2	no	—
409	C₈×C₃₁	C₂×#41	1	4	yes	—
410	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
411	C₂×#555	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3357	C₂×C₃₁	1	2	yes	complemented
413	#3354	C₂×C₃₁	1	2	yes	complemented
414	#3348	C₂×C₃₁	1	4	yes	complemented
415	#3347	C₂×C₃₁	1	4	yes	complemented
416	#3341	C₂×C₃₁	1	2	yes	complemented
417	#3340	C₂×C₃₁	1	2	yes	complemented
418	#3165	C₂×C₃₁	1	1	yes	characteristic, complemented
419	#3094	C₂×C₃₁	1	2	yes	complemented
420	#3093	C₂×C₃₁	1	2	yes	complemented
421	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
423	#3055	C₂×C₃₁	1	2	yes	complemented
424	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
425	D₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
426	#2911	C₂×C₃₁	1	2	yes	complemented
427	C₂²×C₃₁	—	2	1	no	—
428	C₂²×C₃₁	—	2	1	no	—
429	C₂²×C₃₁	—	2	2	no	—
430	C₂²×C₃₁	—	2	2	no	—
431	C₂²×C₃₁	—	2	2	no	—
432	C₂²×C₃₁	—	2	2	no	—
433	C₂²×C₃₁	—	2	2	no	—
434	C₂²×C₃₁	—	2	2	no	—
435	C₂²×C₃₁	—	4	1	no	—
436	C₂²×C₃₁	—	4	2	no	—
437	C₂²×C₃₁	—	4	1	no	—
438	C₂²×C₃₁	—	4	2	no	—
439	C₂²×C₃₁	—	4	2	no	—
440	C₂²×C₃₁	—	4	1	no	—
441	C₂²×C₃₁	—	8	4	no	—
442	C₂²×C₃₁	—	8	4	no	—
443	C₂²×C₃₁	#547	1	2	yes	—
444	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₃₁	—	2	1	no	—
446	C₄×C₃₁	—	2	1	no	—
447	C₄×C₃₁	—	2	2	no	—
448	C₄×C₃₁	—	2	2	no	—
449	C₄×C₃₁	—	2	1	no	—
450	C₄×C₃₁	—	4	4	no	—
451	C₄×C₃₁	—	4	1	no	—
452	C₄×C₃₁	—	4	2	no	—
453	C₄×C₃₁	—	4	1	no	—
454	C₄×C₃₁	—	4	2	no	—
455	C₄×C₃₁	—	4	1	no	—
456	C₄×C₃₁	—	4	2	no	—
457	C₄×C₃₁	#547	1	2	yes	—
458	C₄×C₃₁	#575	1	2	yes	—
459	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
460	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
461	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
462	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
463	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
464	#555	—	2	1	no	—
465	#555	—	2	2	no	—
466	#555	—	2	1	no	—
467	#555	C₂²×C₃₁	1	2	yes	—
468	#555	C₂²×C₃₁	1	4	yes	—
469	#555	C₂²×C₃₁	1	2	yes	—
470	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
471	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
472	#553	C₂²×C₃₁	1	2	yes	complemented
473	#552	—	2	1	no	—
474	#552	C₂²×C₃₁	1	2	yes	complemented
475	#551	—	2	2	no	—
476	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	#546	—	2	1	no	—
478	#533	C₂²×C₃₁	1	1	yes	characteristic
479	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
480	#529	—	2	2	no	—
481	#529	—	2	1	no	—
482	C₂×#124	—	2	2	no	—
483	#525	C₂²×C₃₁	1	2	yes	—
484	C₂×#121	—	2	1	no	—
485	C₂×#121	C₂²×C₃₁	1	2	yes	—
486	C₄×#41	—	2	1	no	—
487	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
488	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
490	C₂×#117	—	2	1	no	—
491	C₂×#117	C₂²×C₃₁	1	2	yes	—
492	C₂×#117	C₂²×C₃₁	1	2	yes	—
493	#501	C₂²×C₃₁	1	4	yes	complemented
494	#500	C₂²×C₃₁	1	2	yes	complemented
495	#498	C₂²×C₃₁	1	2	yes	complemented
496	#485	C₂²×C₃₁	1	4	yes	complemented
497	#485	C₂²×C₃₁	1	4	yes	complemented
498	#482	C₂²×C₃₁	1	4	yes	complemented
499	#482	C₂²×C₃₁	1	4	yes	complemented
500	#482	C₂²×C₃₁	1	4	yes	complemented
501	#482	C₂²×C₃₁	1	4	yes	complemented
502	#481	C₂²×C₃₁	1	4	yes	complemented
503	#480	C₂²×C₃₁	1	4	yes	complemented
504	#478	C₂²×C₃₁	1	4	yes	complemented
505	#477	C₂²×C₃₁	1	2	yes	complemented
506	#476	C₂²×C₃₁	1	2	yes	complemented
507	#476	C₂²×C₃₁	1	2	yes	complemented
508	#475	C₂²×C₃₁	1	2	yes	complemented
509	#474	C₂²×C₃₁	1	2	yes	complemented
510	#474	C₂²×C₃₁	1	2	yes	complemented
511	#469	C₂²×C₃₁	1	4	yes	complemented
512	#468	C₂²×C₃₁	1	4	yes	complemented
513	#466	C₂²×C₃₁	1	4	yes	complemented
514	#465	C₂²×C₃₁	1	4	yes	complemented
515	#442	C₂²×C₃₁	1	2	yes	complemented
516	#440	C₂²×C₃₁	1	2	yes	complemented
517	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
518	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
519	#436	C₂²×C₃₁	1	2	yes	complemented
520	#435	C₂²×C₃₁	1	4	yes	complemented
521	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
522	#428	C₂²×C₃₁	1	2	yes	—
523	#428	C₂²×C₃₁	1	2	yes	—
524	#428	C₂²×C₃₁	1	2	yes	—
525	#428	C₂²×C₃₁	1	2	yes	—
526	#428	C₂²×C₃₁	1	1	yes	characteristic
527	#428	C₂²×C₃₁	1	4	yes	complemented
528	#428	C₂²×C₃₁	1	4	yes	complemented
529	#427	C₂²×C₃₁	1	4	yes	complemented
530	#427	C₂²×C₃₁	1	4	yes	complemented
531	#423	C₂²×C₃₁	1	1	yes	characteristic
532	#418	C₂²×C₃₁	1	2	yes	—
533	#418	C₂²×C₃₁	1	1	yes	characteristic
534	#417	C₂²×C₃₁	1	2	yes	—
535	#417	C₂²×C₃₁	1	1	yes	characteristic
536	#407	C₂²×C₃₁	1	2	yes	—
537	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
538	C₂×C₃₁	—	2	2	no	—
539	C₂×C₃₁	—	4	2	no	—
540	C₂×C₃₁	—	4	2	no	—
541	C₂×C₃₁	—	8	1	no	—
542	C₂×C₃₁	—	8	2	no	—
543	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
544	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
545	C₂×C₃₁	#3585	1	1	yes	characteristic
546	C₂×#41	—	2	1	no	—
547	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
548	C₂²×Q₈	—	2	1	no	—
549	C₂²×D₄	—	2	2	no	—
550	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
552	C₂³×C₄	—	2	1	no	—
553	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
554	AGL(1,ℤ/8)	—	2	4	no	—
555	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
556	C₂×D₈	C₂³×C₃₁	1	2	yes	—
557	C₂×M₁₆	—	2	8	no	—
558	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
559	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
560	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
561	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
562	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
569	#126	—	2	2	no	—
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#125	—	2	2	no	—
573	#125	—	2	1	no	—
574	#125	C₂³×C₃₁	1	2	yes	—
575	#124	—	2	1	no	—
576	#124	—	2	4	no	—
577	#124	—	2	4	no	—
578	#124	—	2	4	no	—
579	#124	—	2	4	no	—
580	#124	—	2	2	no	—
581	#123	—	2	2	no	—
582	#123	—	2	2	no	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
590	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	4	no	—
594	#121	—	2	2	no	—
595	#121	—	2	1	no	—
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	C₂³×C₃₁	1	4	yes	—
599	#121	C₂³×C₃₁	1	4	yes	—
600	#121	C₂³×C₃₁	1	2	yes	—
601	#121	C₂³×C₃₁	1	2	yes	—
602	#120	—	2	2	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
617	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
618	C₄×D₄	D₄×C₃₁	1	2	yes	—
619	C₄×D₄	C₂³×C₃₁	1	2	yes	—
620	C₄×D₄	C₂³×C₃₁	1	2	yes	—
621	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₃₁	1	2	yes	—
625	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
626	#117	—	2	2	no	—
627	#117	—	2	2	no	—
628	#117	—	2	2	no	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	—	2	2	no	—
632	#117	—	2	4	no	—
633	#117	—	2	1	no	—
634	#117	—	2	2	no	—
635	#117	—	2	1	no	—
636	#117	C₂³×C₃₁	1	1	yes	characteristic
637	#117	C₂³×C₃₁	1	2	yes	—
638	#117	C₂³×C₃₁	1	2	yes	—
639	#117	C₂³×C₃₁	1	2	yes	—
640	#117	C₂³×C₃₁	1	4	yes	—
641	#117	C₂³×C₃₁	1	4	yes	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
648	C₂×C₂²⋊C₄	—	2	2	no	—
649	C₂×C₂²⋊C₄	—	2	2	no	—
650	C₂×C₂²⋊C₄	—	2	2	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
653	C₂×C₄²	—	2	2	no	—
654	C₂×C₄²	—	2	2	no	—
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
657	#107	C₂³×C₃₁	1	2	yes	—
658	#107	C₂³×C₃₁	1	4	yes	—
659	#107	C₂³×C₃₁	1	4	yes	—
660	#107	C₂³×C₃₁	1	4	yes	—
661	#107	C₂³×C₃₁	1	4	yes	—
662	#106	C₂³×C₃₁	1	2	yes	—
663	#106	C₂³×C₃₁	1	4	yes	—
664	#106	C₂³×C₃₁	1	4	yes	—
665	#106	C₂³×C₃₁	1	4	yes	—
666	#106	C₂³×C₃₁	1	4	yes	—
667	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
668	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
669	#103	C₂³×C₃₁	1	2	yes	—
670	#103	C₂³×C₃₁	1	4	yes	—
671	#102	C₂³×C₃₁	1	2	yes	—
672	#102	C₂³×C₃₁	1	4	yes	—
673	#102	C₂³×C₃₁	1	2	yes	—
674	#102	C₂³×C₃₁	1	2	yes	—
675	#102	C₂³×C₃₁	1	4	yes	—
676	#102	C₂³×C₃₁	1	4	yes	—
677	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
678	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
679	#97	C₂³×C₃₁	1	2	yes	—
680	C₄×C₈	C₂³×C₃₁	1	2	yes	—
681	C₃₁	#61256	1	1	yes	characteristic, direct product factor, Sylow
682	C₂⁴	—	2	1	no	—
683	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
684	#41	—	2	2	no	—
685	#41	—	2	2	no	—
686	#41	—	4	4	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	8	2	no	—
692	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	8	4	no	—
703	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
704	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
705	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
706	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	4	4	no	—
720	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
724	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
728	SD₁₆	—	2	4	no	—
729	D₈	—	2	4	no	—
730	M₁₆	—	2	4	no	—
731	M₁₆	—	2	2	no	—
732	M₁₆	—	2	8	no	—
733	M₁₆	#41×C₃₁	1	4	yes	complemented
734	C₂×C₈	—	2	8	no	—
735	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
736	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
737	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
753	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
758	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
780	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
781	C₄²	—	2	1	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	1	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	1	no	—
789	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
790	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
791	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂³	—	2	4	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	2	no	—
800	C₂³	—	4	2	no	—
801	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
802	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
803	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
804	Q₈	—	2	1	no	—
805	Q₈	—	2	1	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	8	1	no	—
808	Q₈	—	8	2	no	—
809	Q₈	—	8	2	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	1	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	1	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	2	no	—
820	D₄	—	8	2	no	—
821	D₄	—	8	4	no	—
822	D₄	—	8	4	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	8	1	no	—
847	C₂×C₄	—	8	2	no	—
848	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
849	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
855	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
856	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
857	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
858	C₈	—	2	4	no	—
859	C₈	—	2	2	no	—
860	C₈	C₂×#41×C₃₁	1	4	yes	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	8	4	no	—
876	C₂²	—	8	4	no	—
877	C₂²	C₃₁×#547	1	2	yes	—
878	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	4	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	2	no	—
891	C₄	C₃₁×#547	1	2	yes	—
892	C₄	C₃₁×#575	1	2	yes	—
893	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
894	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
895	C₂	—	2	2	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	2	no	—
898	C₂	—	8	2	no	—
899	C₂	—	8	1	no	—
900	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
901	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
902	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 ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3475	C₂	semidirect
2. C₂×C₃₁×#555	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3354	C₂	semidirect
5. C₃₁×#3348	C₂	semidirect
6. C₃₁×#3347	C₂	semidirect
7. C₃₁×#3341	C₂	semidirect
8. C₃₁×#3340	C₂	semidirect
9. C₃₁×#3165	C₂	semidirect
10. C₃₁×#3094	C₂	semidirect
11. C₃₁×#3093	C₂	semidirect
12. C₃₁×#3079	C₂	semidirect
13. C₃₁×#3077	C₂	semidirect
14. C₃₁×#3055	C₂	semidirect
15. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
16. D₄×M₁₆×C₃₁	C₂	semidirect
17. C₃₁×#2911	C₂	semidirect
20. C₃₁×#556	C₂²	semidirect
27. C₃₁×#555	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
29. C₃₁×#553	C₂²	semidirect
31. C₃₁×#552	C₂²	semidirect
33. C₃₁×#547	C₂²	semidirect
50. C₃₁×#501	C₂²	semidirect
51. C₃₁×#500	C₂²	semidirect
52. C₃₁×#498	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
54. C₃₁×#485	C₂²	semidirect
55. C₃₁×#482	C₂²	semidirect
56. C₃₁×#482	C₂²	semidirect
57. C₃₁×#482	C₂²	semidirect
58. C₃₁×#482	C₂²	semidirect
59. C₃₁×#481	C₂²	semidirect
60. C₃₁×#480	C₂²	semidirect
61. C₃₁×#478	C₂²	semidirect
62. C₃₁×#477	C₂²	semidirect
63. C₃₁×#476	C₂²	semidirect
64. C₃₁×#476	C₂²	semidirect
65. C₃₁×#475	C₂²	semidirect
66. C₃₁×#474	C₂²	semidirect
67. C₃₁×#474	C₂²	semidirect
68. C₃₁×#469	C₂²	semidirect
69. C₃₁×#468	C₂²	semidirect
70. C₃₁×#466	C₂²	semidirect
71. C₃₁×#465	C₂²	semidirect
72. C₃₁×#442	C₂²	semidirect
73. C₃₁×#440	C₂²	semidirect
74. C₄×SD₁₆×C₃₁	C₂²	semidirect
75. C₄×D₈×C₃₁	C₂²	semidirect
76. C₃₁×#436	C₂²	semidirect
77. C₃₁×#435	C₂²	semidirect
78. C₈×D₄×C₃₁	C₂²	semidirect
84. C₃₁×#428	C₂²	semidirect
85. C₃₁×#428	C₂²	semidirect
86. C₃₁×#427	C₂²	semidirect
87. C₃₁×#427	C₂²	semidirect
281. M₁₆×C₃₁	#41	semidirect
341. #61256	C₃₁	direct (N × H)
410. #3475	C₂×C₃₁	semidirect
411. C₂×#555	C₂×C₃₁	semidirect
412. #3357	C₂×C₃₁	semidirect
413. #3354	C₂×C₃₁	semidirect
414. #3348	C₂×C₃₁	semidirect
415. #3347	C₂×C₃₁	semidirect
416. #3341	C₂×C₃₁	semidirect
417. #3340	C₂×C₃₁	semidirect
418. #3165	C₂×C₃₁	semidirect
419. #3094	C₂×C₃₁	semidirect
420. #3093	C₂×C₃₁	semidirect
421. #3079	C₂×C₃₁	semidirect
422. #3077	C₂×C₃₁	semidirect
423. #3055	C₂×C₃₁	semidirect
424. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
425. D₄×M₁₆	C₂×C₃₁	semidirect
426. #2911	C₂×C₃₁	semidirect
463. #556	C₂²×C₃₁	semidirect
470. #555	C₂²×C₃₁	semidirect
471. #554	C₂²×C₃₁	semidirect
472. #553	C₂²×C₃₁	semidirect
474. #552	C₂²×C₃₁	semidirect
476. #547	C₂²×C₃₁	semidirect
493. #501	C₂²×C₃₁	semidirect
494. #500	C₂²×C₃₁	semidirect
495. #498	C₂²×C₃₁	semidirect
496. #485	C₂²×C₃₁	semidirect
497. #485	C₂²×C₃₁	semidirect
498. #482	C₂²×C₃₁	semidirect
499. #482	C₂²×C₃₁	semidirect
500. #482	C₂²×C₃₁	semidirect
501. #482	C₂²×C₃₁	semidirect
502. #481	C₂²×C₃₁	semidirect
503. #480	C₂²×C₃₁	semidirect
504. #478	C₂²×C₃₁	semidirect
505. #477	C₂²×C₃₁	semidirect
506. #476	C₂²×C₃₁	semidirect
507. #476	C₂²×C₃₁	semidirect
508. #475	C₂²×C₃₁	semidirect
509. #474	C₂²×C₃₁	semidirect
510. #474	C₂²×C₃₁	semidirect
511. #469	C₂²×C₃₁	semidirect
512. #468	C₂²×C₃₁	semidirect
513. #466	C₂²×C₃₁	semidirect
514. #465	C₂²×C₃₁	semidirect
515. #442	C₂²×C₃₁	semidirect
516. #440	C₂²×C₃₁	semidirect
517. C₄×SD₁₆	C₂²×C₃₁	semidirect
518. C₄×D₈	C₂²×C₃₁	semidirect
519. #436	C₂²×C₃₁	semidirect
520. #435	C₂²×C₃₁	semidirect
521. C₈×D₄	C₂²×C₃₁	semidirect
527. #428	C₂²×C₃₁	semidirect
528. #428	C₂²×C₃₁	semidirect
529. #427	C₂²×C₃₁	semidirect
530. #427	C₂²×C₃₁	semidirect
681. C₃₁	#61256	direct (N × H)
733. M₁₆	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3475	2
C₂×C₃₁×#555	2
C₃₁×#3357	2
C₃₁×#3354	2
C₃₁×#3348	2
C₃₁×#3347	2
C₃₁×#3341	2
C₃₁×#3340	2
C₃₁×#3165	2
C₃₁×#3094	2
C₃₁×#3093	2
C₃₁×#3079	2
C₃₁×#3077	2
C₃₁×#3055	2
C₄×C₃₁×AGL(1,ℤ/8)	2
D₄×M₁₆×C₃₁	2
C₃₁×#2911	2
#61256	31

Subgroups — C31×#61256 #21518015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61256 #21518015