Subgroups — C₃₁×#61464 #21518223

Order 7936.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3351	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3273	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3183	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2971	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#555	C₂²	1	1	yes	characteristic
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#553	C₂²	1	2	yes	—
35	C₃₁×#552	—	2	1	no	—
36	C₃₁×#552	C₂²	1	2	yes	complemented
37	C₃₁×#551	—	2	2	no	—
38	C₃₁×#551	—	2	2	no	—
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	C₂²	1	2	yes	—
42	C₃₁×#546	C₂²	1	2	yes	complemented
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#532	C₂²	1	1	yes	characteristic
46	C₃₁×#529	—	2	1	no	—
47	C₃₁×#529	—	2	2	no	—
48	C₃₁×#529	C₂²	1	2	yes	complemented
49	C₃₁×#529	C₂²	1	2	yes	complemented
50	C₃₁×#525	—	2	1	no	—
51	C₃₁×#525	—	2	2	no	—
52	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
53	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
55	C₂×C₄×D₄×C₃₁	—	2	1	no	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
58	C₂×C₃₁×#117	—	2	1	no	—
59	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#499	C₂²	1	2	yes	complemented
61	C₃₁×#495	C₂²	1	2	yes	complemented
62	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#488	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#483	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#470	C₂²	1	2	yes	complemented
82	C₃₁×#469	C₂²	1	2	yes	—
83	C₃₁×#468	C₂²	1	2	yes	complemented
84	C₃₁×#468	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	complemented
86	C₃₁×#468	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#463	C₂²	1	2	yes	complemented
91	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#459	C₂²	1	1	yes	characteristic
94	C₃₁×#459	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#452	C₂²	1	2	yes	complemented
97	C₃₁×#450	C₂²	1	2	yes	complemented
98	C₃₁×#449	C₂²	1	2	yes	—
99	C₃₁×#447	C₂²	1	2	yes	—
100	C₃₁×#447	C₂²	1	2	yes	complemented
101	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	1	yes	characteristic
104	C₃₁×#442	C₂²	1	1	yes	characteristic
105	C₃₁×#442	C₂²	1	2	yes	complemented
106	C₃₁×#442	C₂²	1	2	yes	complemented
107	C₃₁×#441	C₂²	1	2	yes	complemented
108	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#440	C₂²	1	2	yes	complemented
110	C₃₁×#440	C₂²	1	2	yes	complemented
111	C₃₁×#440	C₂²	1	2	yes	complemented
112	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
117	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	2	yes	—
120	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#436	C₂²	1	2	yes	complemented
123	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#436	C₂²	1	2	yes	complemented
125	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#432	C₂²	1	2	yes	complemented
127	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#428	C₂²	1	2	yes	complemented
129	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#418	C₂²	1	2	yes	complemented
131	C₃₁×#417	C₂²	1	1	yes	characteristic
132	C₃₁×#417	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
134	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	—	2	1	no	—
143	C₂³×C₄×C₃₁	—	2	2	no	—
144	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
145	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#127	C₂³	1	1	yes	characteristic
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	—	2	1	no	—
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#125	C₂³	1	2	yes	—
174	C₃₁×#124	—	2	1	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	C₂³	1	2	yes	—
178	C₃₁×#124	C₂³	1	2	yes	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	1	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#120	—	2	2	no	—
208	C₃₁×#120	—	2	2	no	—
209	C₃₁×#120	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
212	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	1	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
232	C₄×D₄×C₃₁	D₄	1	2	yes	—
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	2	yes	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	D₄	1	1	yes	characteristic
254	C₃₁×#117	D₄	1	2	yes	—
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₃₁×#117	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
262	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	2	no	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	1	yes	characteristic
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	1	yes	characteristic
292	C₃₁×#102	C₂³	1	1	yes	characteristic
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	1	yes	characteristic
308	C₃₁×#97	C₂³	1	1	yes	characteristic
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	2	yes	—
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₂⁴×C₃₁	—	2	1	no	—
315	C₂⁴×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	4	no	—
317	#41×C₃₁	—	2	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	1	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	8	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	4	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	4	2	no	—
339	C₂×D₄×C₃₁	—	4	1	no	—
340	C₂×D₄×C₃₁	—	4	4	no	—
341	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
345	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	4	4	no	—
362	C₂²×C₄×C₃₁	—	8	4	no	—
363	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	Q₁₆×C₃₁	—	4	2	no	—
370	SD₁₆×C₃₁	—	2	2	no	—
371	SD₁₆×C₃₁	—	2	4	no	—
372	SD₁₆×C₃₁	—	2	4	no	—
373	SD₁₆×C₃₁	—	2	2	no	—
374	SD₁₆×C₃₁	—	4	2	no	—
375	D₈×C₃₁	—	2	4	no	—
376	D₈×C₃₁	—	2	2	no	—
377	D₈×C₃₁	—	4	2	no	—
378	D₈×C₃₁	#41	1	4	yes	complemented
379	M₁₆×C₃₁	—	2	2	no	—
380	M₁₆×C₃₁	—	2	4	no	—
381	M₁₆×C₃₁	—	4	2	no	—
382	M₁₆×C₃₁	—	4	1	no	—
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
385	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
388	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	—	2	1	no	—
447	C₄²×C₃₁	C₂×D₄	1	2	yes	—
448	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₃₁	C₂×D₄	1	2	yes	—
450	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₃₁	C₂⁴	1	2	yes	—
452	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
454	#61464	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	2	1	no	—
457	C₂³×C₃₁	—	2	1	no	—
458	C₂³×C₃₁	—	2	2	no	—
459	C₂³×C₃₁	—	4	2	no	—
460	C₂³×C₃₁	—	4	4	no	—
461	C₂³×C₃₁	—	4	2	no	—
462	C₂³×C₃₁	—	4	4	no	—
463	C₂³×C₃₁	—	8	2	no	—
464	C₂³×C₃₁	—	8	1	no	—
465	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
466	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₃₁	—	2	2	no	—
468	Q₈×C₃₁	—	2	1	no	—
469	Q₈×C₃₁	—	2	2	no	—
470	Q₈×C₃₁	—	2	2	no	—
471	Q₈×C₃₁	—	2	1	no	—
472	Q₈×C₃₁	—	8	1	no	—
473	Q₈×C₃₁	—	8	1	no	—
474	D₄×C₃₁	—	2	2	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	2	2	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	2	1	no	—
479	D₄×C₃₁	—	2	1	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	4	4	no	—
484	D₄×C₃₁	—	4	4	no	—
485	D₄×C₃₁	—	4	2	no	—
486	D₄×C₃₁	—	4	4	no	—
487	D₄×C₃₁	—	4	2	no	—
488	D₄×C₃₁	—	8	1	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	2	no	—
491	D₄×C₃₁	C₂×#41	1	2	yes	—
492	D₄×C₃₁	C₂×#41	1	2	yes	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	2	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	4	1	no	—
509	C₂×C₄×C₃₁	—	4	4	no	—
510	C₂×C₄×C₃₁	—	4	2	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	4	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	4	2	no	—
518	C₂×C₄×C₃₁	—	4	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	—	8	2	no	—
522	C₂×C₄×C₃₁	—	8	2	no	—
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	2	no	—
534	C₈×C₃₁	—	2	1	no	—
535	C₈×C₃₁	—	2	2	no	—
536	C₈×C₃₁	—	2	1	no	—
537	C₈×C₃₁	C₂×#41	1	2	yes	—
538	#3481	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3394	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3351	C₂×C₃₁	1	2	yes	complemented
546	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3323	C₂×C₃₁	1	2	yes	complemented
549	#3322	C₂×C₃₁	1	2	yes	complemented
550	#3273	C₂×C₃₁	1	2	yes	complemented
551	#3272	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3183	C₂×C₃₁	1	2	yes	complemented
553	#3182	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3114	C₂×C₃₁	1	2	yes	complemented
556	#3111	C₂×C₃₁	1	2	yes	complemented
557	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#2971	C₂×C₃₁	1	1	yes	characteristic, complemented
559	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
560	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	2	yes	complemented
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	2	1	no	—
565	C₂²×C₃₁	—	2	2	no	—
566	C₂²×C₃₁	—	2	2	no	—
567	C₂²×C₃₁	—	2	1	no	—
568	C₂²×C₃₁	—	2	2	no	—
569	C₂²×C₃₁	—	4	1	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	4	1	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	4	2	no	—
577	C₂²×C₃₁	—	4	1	no	—
578	C₂²×C₃₁	—	4	2	no	—
579	C₂²×C₃₁	—	8	4	no	—
580	C₂²×C₃₁	—	8	8	no	—
581	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
582	C₄×C₃₁	—	2	1	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	2	1	no	—
585	C₄×C₃₁	—	2	2	no	—
586	C₄×C₃₁	—	2	1	no	—
587	C₄×C₃₁	—	2	1	no	—
588	C₄×C₃₁	—	2	2	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	2	no	—
591	C₄×C₃₁	—	4	2	no	—
592	C₄×C₃₁	—	4	1	no	—
593	C₄×C₃₁	—	4	2	no	—
594	C₄×C₃₁	—	4	1	no	—
595	C₄×C₃₁	—	4	1	no	—
596	C₄×C₃₁	—	4	1	no	—
597	C₄×C₃₁	#575	1	2	yes	—
598	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
599	C₄×C₃₁	#585	1	1	yes	characteristic
600	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
601	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
602	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	#555	C₂²×C₃₁	1	1	yes	characteristic
605	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
607	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	#553	—	2	1	no	—
609	#553	—	2	1	no	—
610	#553	C₂²×C₃₁	1	2	yes	—
611	#552	—	2	1	no	—
612	#552	C₂²×C₃₁	1	2	yes	complemented
613	#551	—	2	2	no	—
614	#551	—	2	2	no	—
615	#547	C₂²×C₃₁	1	1	yes	characteristic
616	#546	—	2	1	no	—
617	#546	C₂²×C₃₁	1	2	yes	—
618	#546	C₂²×C₃₁	1	2	yes	complemented
619	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#532	C₂²×C₃₁	1	1	yes	characteristic
622	#529	—	2	1	no	—
623	#529	—	2	2	no	—
624	#529	C₂²×C₃₁	1	2	yes	complemented
625	#529	C₂²×C₃₁	1	2	yes	complemented
626	#525	—	2	1	no	—
627	#525	—	2	2	no	—
628	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
629	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
630	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
631	C₂×C₄×D₄	—	2	1	no	—
632	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
634	C₂×#117	—	2	1	no	—
635	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#499	C₂²×C₃₁	1	2	yes	complemented
637	#495	C₂²×C₃₁	1	2	yes	complemented
638	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#488	C₂²×C₃₁	1	2	yes	complemented
640	#488	C₂²×C₃₁	1	2	yes	complemented
641	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#485	C₂²×C₃₁	1	2	yes	complemented
644	#485	C₂²×C₃₁	1	2	yes	complemented
645	#483	C₂²×C₃₁	1	2	yes	complemented
646	#482	C₂²×C₃₁	1	2	yes	complemented
647	#481	C₂²×C₃₁	1	2	yes	complemented
648	#480	C₂²×C₃₁	1	2	yes	complemented
649	#479	C₂²×C₃₁	1	2	yes	complemented
650	#478	C₂²×C₃₁	1	2	yes	complemented
651	#478	C₂²×C₃₁	1	2	yes	complemented
652	#478	C₂²×C₃₁	1	2	yes	complemented
653	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#470	C₂²×C₃₁	1	2	yes	complemented
658	#469	C₂²×C₃₁	1	2	yes	—
659	#468	C₂²×C₃₁	1	2	yes	complemented
660	#468	C₂²×C₃₁	1	2	yes	complemented
661	#468	C₂²×C₃₁	1	2	yes	complemented
662	#468	C₂²×C₃₁	1	2	yes	complemented
663	#464	C₂²×C₃₁	1	2	yes	complemented
664	#463	C₂²×C₃₁	1	2	yes	—
665	#463	C₂²×C₃₁	1	2	yes	complemented
666	#463	C₂²×C₃₁	1	2	yes	complemented
667	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#459	C₂²×C₃₁	1	1	yes	characteristic
670	#459	C₂²×C₃₁	1	1	yes	characteristic
671	#452	C₂²×C₃₁	1	2	yes	—
672	#452	C₂²×C₃₁	1	2	yes	complemented
673	#450	C₂²×C₃₁	1	2	yes	complemented
674	#449	C₂²×C₃₁	1	2	yes	—
675	#447	C₂²×C₃₁	1	2	yes	—
676	#447	C₂²×C₃₁	1	2	yes	complemented
677	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#442	C₂²×C₃₁	1	1	yes	characteristic
680	#442	C₂²×C₃₁	1	1	yes	characteristic
681	#442	C₂²×C₃₁	1	2	yes	complemented
682	#442	C₂²×C₃₁	1	2	yes	complemented
683	#441	C₂²×C₃₁	1	2	yes	complemented
684	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	#440	C₂²×C₃₁	1	2	yes	complemented
686	#440	C₂²×C₃₁	1	2	yes	complemented
687	#440	C₂²×C₃₁	1	2	yes	complemented
688	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
693	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
694	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
695	C₄×D₈	C₂²×C₃₁	1	2	yes	—
696	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
697	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#436	C₂²×C₃₁	1	2	yes	complemented
699	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	#436	C₂²×C₃₁	1	2	yes	complemented
701	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#432	C₂²×C₃₁	1	2	yes	complemented
703	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	#428	C₂²×C₃₁	1	2	yes	complemented
705	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#418	C₂²×C₃₁	1	2	yes	complemented
707	#417	C₂²×C₃₁	1	1	yes	characteristic
708	#417	C₂²×C₃₁	1	2	yes	complemented
709	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
710	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
711	C₂×C₃₁	—	4	2	no	—
712	C₂×C₃₁	—	4	1	no	—
713	C₂×C₃₁	—	4	2	no	—
714	C₂×C₃₁	—	4	2	no	—
715	C₂×C₃₁	—	8	2	no	—
716	C₂×C₃₁	—	8	1	no	—
717	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
718	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
719	C₂×C₃₁	#3585	1	1	yes	characteristic
720	C₂×#41	—	2	1	no	—
721	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
722	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×#41	C₂³×C₃₁	1	2	yes	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
726	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
727	C₂³×C₄	—	2	1	no	—
728	C₂³×C₄	—	2	2	no	—
729	AGL(1,ℤ/8)	—	2	8	no	—
730	AGL(1,ℤ/8)	—	2	4	no	—
731	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
736	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
737	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₃₁	1	2	yes	—
739	C₂×D₈	C₂³×C₃₁	1	2	yes	—
740	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
742	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
745	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
748	#127	C₂³×C₃₁	1	1	yes	characteristic
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#125	—	2	2	no	—
755	#125	—	2	1	no	—
756	#125	—	2	1	no	—
757	#125	C₂³×C₃₁	1	2	yes	—
758	#125	C₂³×C₃₁	1	2	yes	—
759	#124	—	2	1	no	—
760	#124	—	2	2	no	—
761	#124	—	2	1	no	—
762	#124	C₂³×C₃₁	1	2	yes	—
763	#124	C₂³×C₃₁	1	2	yes	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	C₂³×C₃₁	1	2	yes	—
790	#121	C₂³×C₃₁	1	2	yes	—
791	#121	C₂³×C₃₁	1	2	yes	—
792	#120	—	2	2	no	—
793	#120	—	2	2	no	—
794	#120	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
800	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
801	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
817	C₄×D₄	D₄×C₃₁	1	2	yes	—
818	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₃₁	1	2	yes	—
822	C₄×D₄	C₂³×C₃₁	1	2	yes	—
823	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₃₁	1	2	yes	—
825	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₃₁	1	2	yes	—
828	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₃₁	1	2	yes	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	—	2	2	no	—
834	#117	—	2	2	no	—
835	#117	—	2	1	no	—
836	#117	—	2	2	no	—
837	#117	—	2	2	no	—
838	#117	D₄×C₃₁	1	1	yes	characteristic
839	#117	D₄×C₃₁	1	2	yes	—
840	#117	C₂³×C₃₁	1	1	yes	characteristic
841	#117	C₂³×C₃₁	1	2	yes	—
842	C₂×C₄⋊C₄	—	2	1	no	—
843	C₂×C₄⋊C₄	—	2	1	no	—
844	C₂×C₄⋊C₄	—	2	1	no	—
845	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
846	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₂²⋊C₄	—	2	1	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₄²	—	2	2	no	—
852	C₂×C₄²	—	2	1	no	—
853	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
854	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
855	#107	C₂³×C₃₁	1	1	yes	characteristic
856	#107	C₂³×C₃₁	1	2	yes	—
857	#107	C₂³×C₃₁	1	1	yes	characteristic
858	#107	C₂³×C₃₁	1	2	yes	—
859	#107	C₂³×C₃₁	1	2	yes	—
860	#106	C₂³×C₃₁	1	1	yes	characteristic
861	#106	C₂³×C₃₁	1	1	yes	characteristic
862	#106	C₂³×C₃₁	1	2	yes	—
863	#106	C₂³×C₃₁	1	2	yes	—
864	#106	C₂³×C₃₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
869	#103	C₂³×C₃₁	1	1	yes	characteristic
870	#103	C₂³×C₃₁	1	1	yes	characteristic
871	#103	C₂³×C₃₁	1	2	yes	—
872	#103	C₂³×C₃₁	1	2	yes	—
873	#103	C₂³×C₃₁	1	2	yes	—
874	#103	C₂³×C₃₁	1	2	yes	—
875	#103	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	1	yes	characteristic
877	#102	C₂³×C₃₁	1	1	yes	characteristic
878	#102	C₂³×C₃₁	1	1	yes	characteristic
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	1	yes	characteristic
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	2	yes	—
884	#102	C₂³×C₃₁	1	1	yes	characteristic
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	2	yes	—
888	#102	C₂³×C₃₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
892	#97	C₂³×C₃₁	1	1	yes	characteristic
893	#97	C₂³×C₃₁	1	1	yes	characteristic
894	#97	C₂³×C₃₁	1	2	yes	—
895	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₃₁	1	2	yes	—
898	C₄×C₈	C₂³×C₃₁	1	2	yes	—
899	C₃₁	#61464	1	1	yes	characteristic, direct product factor, Sylow
900	C₂⁴	—	2	1	no	—
901	C₂⁴	—	2	2	no	—
902	#41	—	2	4	no	—
903	#41	—	2	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	1	no	—
906	#41	—	4	2	no	—
907	#41	—	8	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	4	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	4	2	no	—
925	C₂×D₄	—	4	1	no	—
926	C₂×D₄	—	4	4	no	—
927	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
928	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
931	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
932	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	4	4	no	—
948	C₂²×C₄	—	8	4	no	—
949	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
950	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
951	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
954	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	Q₁₆	—	4	2	no	—
956	SD₁₆	—	2	2	no	—
957	SD₁₆	—	2	4	no	—
958	SD₁₆	—	2	4	no	—
959	SD₁₆	—	2	2	no	—
960	SD₁₆	—	4	2	no	—
961	D₈	—	2	4	no	—
962	D₈	—	2	2	no	—
963	D₈	—	4	2	no	—
964	D₈	#41×C₃₁	1	4	yes	complemented
965	M₁₆	—	2	4	no	—
966	M₁₆	—	2	2	no	—
967	M₁₆	—	4	2	no	—
968	M₁₆	—	4	1	no	—
969	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
971	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
974	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1034	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1036	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₃₁	1	2	yes	—
1038	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	2	no	—
1045	C₂³	—	4	4	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	4	4	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	—	8	1	no	—
1050	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1051	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	8	1	no	—
1058	Q₈	—	8	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	4	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	C₂×#41×C₃₁	1	2	yes	—
1077	D₄	C₂×#41×C₃₁	1	2	yes	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1116	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1117	C₈	—	2	1	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	1	no	—
1122	C₈	C₂×#41×C₃₁	1	2	yes	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	8	8	no	—
1142	C₂²	—	8	4	no	—
1143	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1144	C₄	—	2	2	no	—
1145	C₄	—	2	1	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	2	no	—
1159	C₄	C₃₁×#575	1	2	yes	—
1160	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1161	C₄	C₃₁×#585	1	1	yes	characteristic
1162	C₂	—	4	1	no	—
1163	C₂	—	4	2	no	—
1164	C₂	—	4	2	no	—
1165	C₂	—	4	2	no	—
1166	C₂	—	8	1	no	—
1167	C₂	—	8	2	no	—
1168	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1169	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1170	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×#3481	C₂	semidirect
2. C₃₁×#3475	C₂	semidirect
3. C₃₁×#3394	C₂	semidirect
4. C₃₁×#3380	C₂	semidirect
5. C₃₁×#3361	C₂	semidirect
6. C₃₁×#3360	C₂	semidirect
7. C₃₁×#3357	C₂	semidirect
8. C₃₁×#3351	C₂	semidirect
9. C₃₁×#3331	C₂	semidirect
10. C₃₁×#3325	C₂	semidirect
11. C₃₁×#3323	C₂	semidirect
12. C₃₁×#3322	C₂	semidirect
13. C₃₁×#3273	C₂	semidirect
14. C₃₁×#3272	C₂	semidirect
15. C₃₁×#3183	C₂	semidirect
16. C₃₁×#3182	C₂	semidirect
17. C₃₁×#3116	C₂	semidirect
18. C₃₁×#3114	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#3109	C₂	semidirect
21. C₃₁×#2971	C₂	semidirect
22. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
23. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
26. C₃₁×#559	C₂²	semidirect
27. C₃₁×#556	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
36. C₃₁×#552	C₂²	semidirect
42. C₃₁×#546	C₂²	semidirect
43. D₄²×C₃₁	C₂²	semidirect
44. C₃₁×#533	C₂²	semidirect
48. C₃₁×#529	C₂²	semidirect
49. C₃₁×#529	C₂²	semidirect
54. C₄×#41×C₃₁	C₂²	semidirect
56. C₂×C₄×D₄×C₃₁	C₂²	semidirect
57. C₂×C₄×D₄×C₃₁	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
60. C₃₁×#499	C₂²	semidirect
61. C₃₁×#495	C₂²	semidirect
62. C₃₁×#492	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#488	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
79. C₃₁×#476	C₂²	semidirect
80. C₃₁×#476	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
83. C₃₁×#468	C₂²	semidirect
84. C₃₁×#468	C₂²	semidirect
85. C₃₁×#468	C₂²	semidirect
86. C₃₁×#468	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#463	C₂²	semidirect
91. C₃₁×#462	C₂²	semidirect
92. C₃₁×#461	C₂²	semidirect
96. C₃₁×#452	C₂²	semidirect
97. C₃₁×#450	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₈×Q₈×C₃₁	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
105. C₃₁×#442	C₂²	semidirect
106. C₃₁×#442	C₂²	semidirect
107. C₃₁×#441	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₃₁×#440	C₂²	semidirect
110. C₃₁×#440	C₂²	semidirect
111. C₃₁×#440	C₂²	semidirect
112. C₃₁×#440	C₂²	semidirect
113. C₄×SD₁₆×C₃₁	C₂²	semidirect
114. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
123. C₃₁×#436	C₂²	semidirect
124. C₃₁×#436	C₂²	semidirect
125. C₃₁×#432	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₃₁×#428	C₂²	semidirect
129. C₃₁×#418	C₂²	semidirect
130. C₃₁×#418	C₂²	semidirect
132. C₃₁×#417	C₂²	semidirect
133. C₄×M₁₆×C₃₁	C₂²	semidirect
134. C₄×M₁₆×C₃₁	C₂²	semidirect
378. D₈×C₃₁	#41	semidirect
454. #61464	C₃₁	direct (N × H)
538. #3481	C₂×C₃₁	semidirect
539. #3475	C₂×C₃₁	semidirect
540. #3394	C₂×C₃₁	semidirect
541. #3380	C₂×C₃₁	semidirect
542. #3361	C₂×C₃₁	semidirect
543. #3360	C₂×C₃₁	semidirect
544. #3357	C₂×C₃₁	semidirect
545. #3351	C₂×C₃₁	semidirect
546. #3331	C₂×C₃₁	semidirect
547. #3325	C₂×C₃₁	semidirect
548. #3323	C₂×C₃₁	semidirect
549. #3322	C₂×C₃₁	semidirect
550. #3273	C₂×C₃₁	semidirect
551. #3272	C₂×C₃₁	semidirect
552. #3183	C₂×C₃₁	semidirect
553. #3182	C₂×C₃₁	semidirect
554. #3116	C₂×C₃₁	semidirect
555. #3114	C₂×C₃₁	semidirect
556. #3111	C₂×C₃₁	semidirect
557. #3109	C₂×C₃₁	semidirect
558. #2971	C₂×C₃₁	semidirect
559. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
560. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
602. #559	C₂²×C₃₁	semidirect
603. #556	C₂²×C₃₁	semidirect
605. #554	C₂²×C₃₁	semidirect
606. #554	C₂²×C₃₁	semidirect
607. #554	C₂²×C₃₁	semidirect
612. #552	C₂²×C₃₁	semidirect
618. #546	C₂²×C₃₁	semidirect
619. D₄²	C₂²×C₃₁	semidirect
620. #533	C₂²×C₃₁	semidirect
624. #529	C₂²×C₃₁	semidirect
625. #529	C₂²×C₃₁	semidirect
630. C₄×#41	C₂²×C₃₁	semidirect
632. C₂×C₄×D₄	C₂²×C₃₁	semidirect
633. C₂×C₄×D₄	C₂²×C₃₁	semidirect
635. #500	C₂²×C₃₁	semidirect
636. #499	C₂²×C₃₁	semidirect
637. #495	C₂²×C₃₁	semidirect
638. #492	C₂²×C₃₁	semidirect
639. #488	C₂²×C₃₁	semidirect
640. #488	C₂²×C₃₁	semidirect
641. #487	C₂²×C₃₁	semidirect
642. #486	C₂²×C₃₁	semidirect
643. #485	C₂²×C₃₁	semidirect
644. #485	C₂²×C₃₁	semidirect
645. #483	C₂²×C₃₁	semidirect
646. #482	C₂²×C₃₁	semidirect
647. #481	C₂²×C₃₁	semidirect
648. #480	C₂²×C₃₁	semidirect
649. #479	C₂²×C₃₁	semidirect
650. #478	C₂²×C₃₁	semidirect
651. #478	C₂²×C₃₁	semidirect
652. #478	C₂²×C₃₁	semidirect
653. #477	C₂²×C₃₁	semidirect
654. #476	C₂²×C₃₁	semidirect
655. #476	C₂²×C₃₁	semidirect
656. #476	C₂²×C₃₁	semidirect
657. #470	C₂²×C₃₁	semidirect
659. #468	C₂²×C₃₁	semidirect
660. #468	C₂²×C₃₁	semidirect
661. #468	C₂²×C₃₁	semidirect
662. #468	C₂²×C₃₁	semidirect
663. #464	C₂²×C₃₁	semidirect
665. #463	C₂²×C₃₁	semidirect
666. #463	C₂²×C₃₁	semidirect
667. #462	C₂²×C₃₁	semidirect
668. #461	C₂²×C₃₁	semidirect
672. #452	C₂²×C₃₁	semidirect
673. #450	C₂²×C₃₁	semidirect
676. #447	C₂²×C₃₁	semidirect
677. C₈×Q₈	C₂²×C₃₁	semidirect
678. C₈×Q₈	C₂²×C₃₁	semidirect
681. #442	C₂²×C₃₁	semidirect
682. #442	C₂²×C₃₁	semidirect
683. #441	C₂²×C₃₁	semidirect
684. #440	C₂²×C₃₁	semidirect
685. #440	C₂²×C₃₁	semidirect
686. #440	C₂²×C₃₁	semidirect
687. #440	C₂²×C₃₁	semidirect
688. #440	C₂²×C₃₁	semidirect
689. C₄×SD₁₆	C₂²×C₃₁	semidirect
690. C₄×SD₁₆	C₂²×C₃₁	semidirect
691. C₄×SD₁₆	C₂²×C₃₁	semidirect
692. C₄×SD₁₆	C₂²×C₃₁	semidirect
696. C₄×D₈	C₂²×C₃₁	semidirect
697. #436	C₂²×C₃₁	semidirect
698. #436	C₂²×C₃₁	semidirect
699. #436	C₂²×C₃₁	semidirect
700. #436	C₂²×C₃₁	semidirect
701. #432	C₂²×C₃₁	semidirect
702. #432	C₂²×C₃₁	semidirect
703. #428	C₂²×C₃₁	semidirect
704. #428	C₂²×C₃₁	semidirect
705. #418	C₂²×C₃₁	semidirect
706. #418	C₂²×C₃₁	semidirect
708. #417	C₂²×C₃₁	semidirect
709. C₄×M₁₆	C₂²×C₃₁	semidirect
710. C₄×M₁₆	C₂²×C₃₁	semidirect
899. C₃₁	#61464	direct (N × H)
964. D₈	#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×#3481	2
C₃₁×#3475	2
C₃₁×#3394	2
C₃₁×#3380	2
C₃₁×#3361	2
C₃₁×#3360	2
C₃₁×#3357	2
C₃₁×#3351	2
C₃₁×#3331	2
C₃₁×#3325	2
C₃₁×#3323	2
C₃₁×#3322	2
C₃₁×#3273	2
C₃₁×#3272	2
C₃₁×#3183	2
C₃₁×#3182	2
C₃₁×#3116	2
C₃₁×#3114	2
C₃₁×#3111	2
C₃₁×#3109	2
C₃₁×#2971	2
C₄×C₃₁×AGL(1,ℤ/8)	2
#61464	31

Subgroups — C31×#61464 #21518223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61464 #21518223