Subgroups — C₃₁×#61283 #21518042

Order 7936.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3355	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3351	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2912	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
27	C₃₁×#559	—	2	1	no	—
28	C₃₁×#559	—	2	1	no	—
29	C₃₁×#556	—	2	1	no	—
30	C₃₁×#555	C₂²	1	2	yes	—
31	C₃₁×#553	—	2	2	no	—
32	C₃₁×#553	—	2	2	no	—
33	C₃₁×#553	C₂²	1	2	yes	—
34	C₃₁×#553	C₂²	1	2	yes	—
35	C₃₁×#553	C₂²	1	2	yes	complemented
36	C₃₁×#553	C₂²	1	2	yes	complemented
37	C₃₁×#552	C₂²	1	2	yes	complemented
38	C₃₁×#552	C₂²	1	2	yes	complemented
39	C₃₁×#550	—	2	1	no	—
40	C₃₁×#547	C₂²	1	2	yes	—
41	C₃₁×#541	—	2	1	no	—
42	C₃₁×#540	—	2	1	no	—
43	C₃₁×#538	—	2	2	no	—
44	C₃₁×#537	C₂²	1	1	yes	characteristic
45	C₃₁×#537	C₂²	1	1	yes	characteristic
46	C₃₁×#535	C₂²	1	1	yes	characteristic
47	C₃₁×#535	C₂²	1	1	yes	characteristic
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	—	2	1	no	—
52	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	2	no	—
54	C₃₁×#520	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	1	yes	characteristic
56	C₃₁×#520	C₂²	1	1	yes	characteristic
57	C₃₁×#520	C₂²	1	1	yes	characteristic
58	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
60	C₃₁×#501	C₂²	1	2	yes	complemented
61	C₃₁×#501	C₂²	1	2	yes	complemented
62	C₃₁×#499	C₂²	1	2	yes	complemented
63	C₃₁×#499	C₂²	1	2	yes	complemented
64	C₃₁×#485	C₂²	1	2	yes	complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#484	C₂²	1	2	yes	complemented
67	C₃₁×#483	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	—
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	2	yes	—
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#482	C₂²	1	2	yes	complemented
73	C₃₁×#482	C₂²	1	2	yes	complemented
74	C₃₁×#481	C₂²	1	2	yes	—
75	C₃₁×#481	C₂²	1	2	yes	—
76	C₃₁×#481	C₂²	1	2	yes	complemented
77	C₃₁×#480	C₂²	1	2	yes	—
78	C₃₁×#480	C₂²	1	2	yes	—
79	C₃₁×#480	C₂²	1	2	yes	complemented
80	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#478	C₂²	1	2	yes	—
83	C₃₁×#478	C₂²	1	2	yes	—
84	C₃₁×#478	C₂²	1	2	yes	—
85	C₃₁×#478	C₂²	1	2	yes	—
86	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#469	C₂²	1	2	yes	—
93	C₃₁×#469	C₂²	1	2	yes	—
94	C₃₁×#468	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#466	C₂²	1	2	yes	—
97	C₃₁×#466	C₂²	1	2	yes	—
98	C₃₁×#465	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#442	C₂²	1	2	yes	—
101	C₃₁×#440	C₂²	1	2	yes	—
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
103	C₄×D₈×C₃₁	C₂²	1	2	yes	—
104	C₃₁×#436	C₂²	1	2	yes	complemented
105	C₃₁×#435	C₂²	1	2	yes	complemented
106	C₃₁×#435	C₂²	1	2	yes	complemented
107	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
108	C₃₁×#428	C₂²	1	1	yes	characteristic
109	C₃₁×#428	C₂²	1	1	yes	characteristic
110	C₃₁×#428	C₂²	1	1	yes	characteristic
111	C₃₁×#428	C₂²	1	1	yes	characteristic
112	C₃₁×#428	C₂²	1	1	yes	characteristic
113	C₃₁×#428	C₂²	1	2	yes	complemented
114	C₃₁×#428	C₂²	1	2	yes	complemented
115	C₃₁×#428	C₂²	1	2	yes	complemented
116	C₃₁×#428	C₂²	1	2	yes	complemented
117	C₃₁×#427	C₂²	1	1	yes	characteristic
118	C₃₁×#427	C₂²	1	1	yes	characteristic
119	C₃₁×#427	C₂²	1	2	yes	complemented
120	C₃₁×#427	C₂²	1	2	yes	complemented
121	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
122	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
123	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
124	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
125	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₃₁×#418	C₂²	1	1	yes	characteristic
127	C₃₁×#417	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₃₁×#416	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
132	C₃₁×#408	C₂²	1	1	yes	characteristic
133	C₃₁×#408	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	2	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	—	2	1	no	—
141	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
142	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×D₈×C₃₁	C₂³	1	2	yes	—
144	C₃₁×#131	—	2	4	no	—
145	C₃₁×#131	—	2	4	no	—
146	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×#127	—	2	1	no	—
158	C₃₁×#127	—	2	1	no	—
159	C₃₁×#127	D₄	1	1	yes	characteristic
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	1	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	C₂³	1	2	yes	—
171	C₃₁×#125	C₂³	1	2	yes	—
172	C₃₁×#125	C₂³	1	1	yes	characteristic
173	C₃₁×#125	C₂³	1	1	yes	characteristic
174	C₃₁×#124	—	2	1	no	—
175	C₃₁×#124	—	2	1	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	D₄	1	1	yes	characteristic
179	C₃₁×#124	D₄	1	1	yes	characteristic
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×#123	—	2	2	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	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	—	2	1	no	—
197	C₃₁×#121	—	2	1	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	D₄	1	2	yes	—
205	C₃₁×#121	D₄	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#120	—	2	2	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	1	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	C₂³	1	1	yes	characteristic
249	C₃₁×#117	C₂³	1	1	yes	characteristic
250	C₃₁×#117	C₂³	1	1	yes	characteristic
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
265	C₂×C₄²×C₃₁	—	2	1	no	—
266	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	1	yes	characteristic
273	C₃₁×#107	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#107	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	1	yes	characteristic
281	C₃₁×#106	C₂³	1	2	yes	—
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×#106	C₂³	1	1	yes	characteristic
284	C₃₁×#106	C₂³	1	1	yes	characteristic
285	C₃₁×#106	C₂³	1	1	yes	characteristic
286	C₃₁×#106	C₂³	1	2	yes	—
287	C₃₁×#106	C₂³	1	2	yes	—
288	C₃₁×#106	C₂³	1	2	yes	—
289	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	2	yes	—
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₃₁×#97	C₂³	1	2	yes	—
314	C₄×C₈×C₃₁	C₂³	1	2	yes	—
315	C₂⁴×C₃₁	—	2	1	no	—
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	2	2	no	—
318	#41×C₃₁	—	2	2	no	—
319	#41×C₃₁	—	2	2	no	—
320	#41×C₃₁	—	2	2	no	—
321	#41×C₃₁	—	2	2	no	—
322	#41×C₃₁	—	8	4	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	2	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	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	2	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	—	8	2	no	—
359	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	SD₁₆×C₃₁	—	2	4	no	—
365	D₈×C₃₁	—	2	4	no	—
366	M₁₆×C₃₁	—	2	2	no	—
367	M₁₆×C₃₁	—	2	4	no	—
368	M₁₆×C₃₁	—	2	4	no	—
369	M₁₆×C₃₁	#41	1	4	yes	complemented
370	C₂×C₈×C₃₁	—	2	2	no	—
371	C₂×C₈×C₃₁	—	2	2	no	—
372	C₂×C₈×C₃₁	—	2	4	no	—
373	C₂×C₈×C₃₁	—	2	4	no	—
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
448	#61283	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	—	2	2	no	—
451	C₂³×C₃₁	—	4	2	no	—
452	C₂³×C₃₁	—	8	1	no	—
453	C₂³×C₃₁	—	8	1	no	—
454	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
455	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
456	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
457	Q₈×C₃₁	—	2	2	no	—
458	Q₈×C₃₁	—	2	2	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	4	2	no	—
462	Q₈×C₃₁	—	8	1	no	—
463	D₄×C₃₁	—	2	4	no	—
464	D₄×C₃₁	—	2	4	no	—
465	D₄×C₃₁	—	2	2	no	—
466	D₄×C₃₁	—	2	2	no	—
467	D₄×C₃₁	—	2	1	no	—
468	D₄×C₃₁	—	2	2	no	—
469	D₄×C₃₁	—	2	2	no	—
470	D₄×C₃₁	—	2	1	no	—
471	D₄×C₃₁	—	4	2	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	4	2	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	2	no	—
477	D₄×C₃₁	—	8	2	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	8	2	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	4	1	no	—
496	C₂×C₄×C₃₁	—	4	1	no	—
497	C₂×C₄×C₃₁	—	4	4	no	—
498	C₂×C₄×C₃₁	—	4	2	no	—
499	C₂×C₄×C₃₁	—	8	1	no	—
500	C₂×C₄×C₃₁	—	8	1	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	1	no	—
504	C₂×C₄×C₃₁	—	8	2	no	—
505	C₂×C₄×C₃₁	—	8	1	no	—
506	C₂×C₄×C₃₁	—	8	1	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
517	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
518	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	1	no	—
521	C₈×C₃₁	—	2	1	no	—
522	C₈×C₃₁	—	2	1	no	—
523	C₈×C₃₁	—	2	2	no	—
524	C₈×C₃₁	C₂×#41	1	4	yes	—
525	#3512	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3355	C₂×C₃₁	1	2	yes	complemented
528	#3351	C₂×C₃₁	1	2	yes	complemented
529	#3348	C₂×C₃₁	1	2	yes	complemented
530	#3347	C₂×C₃₁	1	2	yes	complemented
531	#3345	C₂×C₃₁	1	2	yes	complemented
532	#3343	C₂×C₃₁	1	2	yes	complemented
533	#3339	C₂×C₃₁	1	2	yes	complemented
534	#3337	C₂×C₃₁	1	2	yes	complemented
535	#3166	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3099	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
541	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3062	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3062	C₂×C₃₁	1	1	yes	characteristic, complemented
544	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#2935	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#2913	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#2912	C₂×C₃₁	1	1	yes	characteristic, complemented
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	1	no	—
550	C₂²×C₃₁	—	2	2	no	—
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	2	2	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	2	2	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	2	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	2	no	—
562	C₂²×C₃₁	—	8	4	no	—
563	C₂²×C₃₁	#547	1	2	yes	—
564	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
565	C₄×C₃₁	—	2	1	no	—
566	C₄×C₃₁	—	2	1	no	—
567	C₄×C₃₁	—	2	1	no	—
568	C₄×C₃₁	—	2	1	no	—
569	C₄×C₃₁	—	2	2	no	—
570	C₄×C₃₁	—	2	2	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	2	no	—
573	C₄×C₃₁	—	4	1	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	2	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	2	no	—
578	C₄×C₃₁	—	4	1	no	—
579	C₄×C₃₁	—	4	1	no	—
580	C₄×C₃₁	—	4	1	no	—
581	C₄×C₃₁	#547	1	2	yes	—
582	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
583	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
584	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
585	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
586	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
587	#559	—	2	1	no	—
588	#559	—	2	1	no	—
589	#556	—	2	1	no	—
590	#555	C₂²×C₃₁	1	2	yes	—
591	#553	—	2	2	no	—
592	#553	—	2	2	no	—
593	#553	C₂²×C₃₁	1	2	yes	—
594	#553	C₂²×C₃₁	1	2	yes	—
595	#553	C₂²×C₃₁	1	2	yes	complemented
596	#553	C₂²×C₃₁	1	2	yes	complemented
597	#552	C₂²×C₃₁	1	2	yes	complemented
598	#552	C₂²×C₃₁	1	2	yes	complemented
599	#550	—	2	1	no	—
600	#547	C₂²×C₃₁	1	2	yes	—
601	#541	—	2	1	no	—
602	#540	—	2	1	no	—
603	#538	—	2	2	no	—
604	#537	C₂²×C₃₁	1	1	yes	characteristic
605	#537	C₂²×C₃₁	1	1	yes	characteristic
606	#535	C₂²×C₃₁	1	1	yes	characteristic
607	#535	C₂²×C₃₁	1	1	yes	characteristic
608	#533	C₂²×C₃₁	1	1	yes	characteristic
609	#532	C₂²×C₃₁	1	1	yes	characteristic
610	#529	—	2	1	no	—
611	#529	—	2	1	no	—
612	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
613	#525	—	2	2	no	—
614	#520	C₂²×C₃₁	1	1	yes	characteristic
615	#520	C₂²×C₃₁	1	1	yes	characteristic
616	#520	C₂²×C₃₁	1	1	yes	characteristic
617	#520	C₂²×C₃₁	1	1	yes	characteristic
618	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
619	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
620	#501	C₂²×C₃₁	1	2	yes	complemented
621	#501	C₂²×C₃₁	1	2	yes	complemented
622	#499	C₂²×C₃₁	1	2	yes	complemented
623	#499	C₂²×C₃₁	1	2	yes	complemented
624	#485	C₂²×C₃₁	1	2	yes	complemented
625	#485	C₂²×C₃₁	1	2	yes	complemented
626	#484	C₂²×C₃₁	1	2	yes	complemented
627	#483	C₂²×C₃₁	1	2	yes	complemented
628	#482	C₂²×C₃₁	1	2	yes	—
629	#482	C₂²×C₃₁	1	2	yes	—
630	#482	C₂²×C₃₁	1	2	yes	—
631	#482	C₂²×C₃₁	1	2	yes	—
632	#482	C₂²×C₃₁	1	2	yes	complemented
633	#482	C₂²×C₃₁	1	2	yes	complemented
634	#481	C₂²×C₃₁	1	2	yes	—
635	#481	C₂²×C₃₁	1	2	yes	—
636	#481	C₂²×C₃₁	1	2	yes	complemented
637	#480	C₂²×C₃₁	1	2	yes	—
638	#480	C₂²×C₃₁	1	2	yes	—
639	#480	C₂²×C₃₁	1	2	yes	complemented
640	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#478	C₂²×C₃₁	1	2	yes	—
643	#478	C₂²×C₃₁	1	2	yes	—
644	#478	C₂²×C₃₁	1	2	yes	—
645	#478	C₂²×C₃₁	1	2	yes	—
646	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#469	C₂²×C₃₁	1	2	yes	—
653	#469	C₂²×C₃₁	1	2	yes	—
654	#468	C₂²×C₃₁	1	2	yes	—
655	#468	C₂²×C₃₁	1	2	yes	—
656	#466	C₂²×C₃₁	1	2	yes	—
657	#466	C₂²×C₃₁	1	2	yes	—
658	#465	C₂²×C₃₁	1	2	yes	—
659	#465	C₂²×C₃₁	1	2	yes	—
660	#442	C₂²×C₃₁	1	2	yes	—
661	#440	C₂²×C₃₁	1	2	yes	—
662	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
663	C₄×D₈	C₂²×C₃₁	1	2	yes	—
664	#436	C₂²×C₃₁	1	2	yes	complemented
665	#435	C₂²×C₃₁	1	2	yes	complemented
666	#435	C₂²×C₃₁	1	2	yes	complemented
667	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
668	#428	C₂²×C₃₁	1	1	yes	characteristic
669	#428	C₂²×C₃₁	1	1	yes	characteristic
670	#428	C₂²×C₃₁	1	1	yes	characteristic
671	#428	C₂²×C₃₁	1	1	yes	characteristic
672	#428	C₂²×C₃₁	1	1	yes	characteristic
673	#428	C₂²×C₃₁	1	2	yes	complemented
674	#428	C₂²×C₃₁	1	2	yes	complemented
675	#428	C₂²×C₃₁	1	2	yes	complemented
676	#428	C₂²×C₃₁	1	2	yes	complemented
677	#427	C₂²×C₃₁	1	1	yes	characteristic
678	#427	C₂²×C₃₁	1	1	yes	characteristic
679	#427	C₂²×C₃₁	1	2	yes	complemented
680	#427	C₂²×C₃₁	1	2	yes	complemented
681	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
682	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
683	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
684	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
685	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
686	#418	C₂²×C₃₁	1	1	yes	characteristic
687	#417	C₂²×C₃₁	1	1	yes	characteristic
688	#416	C₂²×C₃₁	1	1	yes	characteristic
689	#416	C₂²×C₃₁	1	1	yes	characteristic
690	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
691	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
692	#408	C₂²×C₃₁	1	1	yes	characteristic
693	#408	C₂²×C₃₁	1	1	yes	characteristic
694	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
695	C₂×C₃₁	—	2	2	no	—
696	C₂×C₃₁	—	4	2	no	—
697	C₂×C₃₁	—	4	2	no	—
698	C₂×C₃₁	—	8	1	no	—
699	C₂×C₃₁	—	8	2	no	—
700	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
701	C₂×C₃₁	#3584	1	1	yes	characteristic
702	C₂×C₃₁	#3585	1	1	yes	characteristic
703	C₂×#41	—	2	2	no	—
704	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
707	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
708	C₂³×C₄	—	2	1	no	—
709	AGL(1,ℤ/8)	—	2	4	no	—
710	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
711	C₂×D₈	C₂³×C₃₁	1	2	yes	—
712	#131	—	2	4	no	—
713	#131	—	2	4	no	—
714	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
716	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
718	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
721	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
722	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	#127	—	2	1	no	—
726	#127	—	2	1	no	—
727	#127	D₄×C₃₁	1	1	yes	characteristic
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	1	no	—
737	#125	—	2	1	no	—
738	#125	C₂³×C₃₁	1	2	yes	—
739	#125	C₂³×C₃₁	1	2	yes	—
740	#125	C₂³×C₃₁	1	1	yes	characteristic
741	#125	C₂³×C₃₁	1	1	yes	characteristic
742	#124	—	2	1	no	—
743	#124	—	2	1	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	D₄×C₃₁	1	1	yes	characteristic
747	#124	D₄×C₃₁	1	1	yes	characteristic
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	D₄×C₃₁	1	2	yes	—
773	#121	D₄×C₃₁	1	2	yes	—
774	#121	C₂³×C₃₁	1	2	yes	—
775	#121	C₂³×C₃₁	1	2	yes	—
776	#121	C₂³×C₃₁	1	2	yes	—
777	#121	C₂³×C₃₁	1	2	yes	—
778	#121	C₂³×C₃₁	1	2	yes	—
779	#121	C₂³×C₃₁	1	2	yes	—
780	#120	—	2	2	no	—
781	#120	—	2	2	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	C₂³×C₃₁	1	2	yes	—
807	C₄×D₄	C₂³×C₃₁	1	2	yes	—
808	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₃₁	1	2	yes	—
811	C₄×D₄	C₂³×C₃₁	1	2	yes	—
812	#117	—	2	2	no	—
813	#117	—	2	2	no	—
814	#117	—	2	2	no	—
815	#117	—	2	1	no	—
816	#117	C₂³×C₃₁	1	1	yes	characteristic
817	#117	C₂³×C₃₁	1	1	yes	characteristic
818	#117	C₂³×C₃₁	1	1	yes	characteristic
819	#117	C₂³×C₃₁	1	2	yes	—
820	#117	C₂³×C₃₁	1	2	yes	—
821	#117	C₂³×C₃₁	1	2	yes	—
822	#117	C₂³×C₃₁	1	2	yes	—
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	—	2	1	no	—
825	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
829	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
830	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
831	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
832	C₂×C₂²⋊C₄	—	2	1	no	—
833	C₂×C₄²	—	2	1	no	—
834	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
835	#107	C₂³×C₃₁	1	2	yes	—
836	#107	C₂³×C₃₁	1	2	yes	—
837	#107	C₂³×C₃₁	1	1	yes	characteristic
838	#107	C₂³×C₃₁	1	2	yes	—
839	#107	C₂³×C₃₁	1	2	yes	—
840	#107	C₂³×C₃₁	1	1	yes	characteristic
841	#107	C₂³×C₃₁	1	1	yes	characteristic
842	#107	C₂³×C₃₁	1	1	yes	characteristic
843	#107	C₂³×C₃₁	1	2	yes	—
844	#107	C₂³×C₃₁	1	2	yes	—
845	#107	C₂³×C₃₁	1	2	yes	—
846	#106	C₂³×C₃₁	1	2	yes	—
847	#106	C₂³×C₃₁	1	2	yes	—
848	#106	C₂³×C₃₁	1	1	yes	characteristic
849	#106	C₂³×C₃₁	1	2	yes	—
850	#106	C₂³×C₃₁	1	2	yes	—
851	#106	C₂³×C₃₁	1	1	yes	characteristic
852	#106	C₂³×C₃₁	1	1	yes	characteristic
853	#106	C₂³×C₃₁	1	1	yes	characteristic
854	#106	C₂³×C₃₁	1	2	yes	—
855	#106	C₂³×C₃₁	1	2	yes	—
856	#106	C₂³×C₃₁	1	2	yes	—
857	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	#103	C₂³×C₃₁	1	1	yes	characteristic
862	#103	C₂³×C₃₁	1	1	yes	characteristic
863	#103	C₂³×C₃₁	1	1	yes	characteristic
864	#103	C₂³×C₃₁	1	1	yes	characteristic
865	#103	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	#102	C₂³×C₃₁	1	1	yes	characteristic
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	1	yes	characteristic
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
881	#97	C₂³×C₃₁	1	2	yes	—
882	C₄×C₈	C₂³×C₃₁	1	2	yes	—
883	C₃₁	#61283	1	1	yes	characteristic, direct product factor, Sylow
884	C₂⁴	—	2	1	no	—
885	#41	—	2	2	no	—
886	#41	—	2	2	no	—
887	#41	—	2	2	no	—
888	#41	—	2	2	no	—
889	#41	—	2	2	no	—
890	#41	—	2	2	no	—
891	#41	—	8	4	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
895	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
908	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
909	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
910	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
911	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
912	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
913	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	8	2	no	—
928	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
929	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
930	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
931	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
932	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	SD₁₆	—	2	4	no	—
934	D₈	—	2	4	no	—
935	M₁₆	—	2	2	no	—
936	M₁₆	—	2	4	no	—
937	M₁₆	—	2	4	no	—
938	M₁₆	#41×C₃₁	1	4	yes	complemented
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	2	2	no	—
941	C₂×C₈	—	2	4	no	—
942	C₂×C₈	—	2	4	no	—
943	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
944	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1014	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	4	2	no	—
1020	C₂³	—	8	1	no	—
1021	C₂³	—	8	1	no	—
1022	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1023	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1024	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	8	1	no	—
1031	D₄	—	2	4	no	—
1032	D₄	—	2	4	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	1	no	—
1065	C₂×C₄	—	4	4	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	8	1	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	2	no	—
1071	C₂×C₄	—	8	1	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1084	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1085	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1086	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	C₂×#41×C₃₁	1	4	yes	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	8	4	no	—
1108	C₂²	C₃₁×#547	1	2	yes	—
1109	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1110	C₄	—	2	2	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	2	no	—
1126	C₄	C₃₁×#547	1	2	yes	—
1127	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1128	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1129	C₂	—	2	2	no	—
1130	C₂	—	4	2	no	—
1131	C₂	—	4	2	no	—
1132	C₂	—	8	2	no	—
1133	C₂	—	8	1	no	—
1134	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
1135	C₂	C₃₁×#3584	1	1	yes	characteristic
1136	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 ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3512	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3355	C₂	semidirect
4. C₃₁×#3351	C₂	semidirect
5. C₃₁×#3348	C₂	semidirect
6. C₃₁×#3347	C₂	semidirect
7. C₃₁×#3345	C₂	semidirect
8. C₃₁×#3343	C₂	semidirect
9. C₃₁×#3339	C₂	semidirect
10. C₃₁×#3337	C₂	semidirect
11. C₃₁×#3166	C₂	semidirect
12. C₃₁×#3099	C₂	semidirect
13. C₃₁×#3098	C₂	semidirect
14. C₃₁×#3096	C₂	semidirect
15. C₃₁×#3096	C₂	semidirect
16. C₃₁×#3076	C₂	semidirect
17. C₂×C₃₁×#478	C₂	semidirect
18. C₃₁×#3062	C₂	semidirect
19. C₃₁×#3062	C₂	semidirect
20. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
21. C₃₁×#2935	C₂	semidirect
22. C₃₁×#2913	C₂	semidirect
23. C₃₁×#2912	C₂	semidirect
35. C₃₁×#553	C₂²	semidirect
36. C₃₁×#553	C₂²	semidirect
37. C₃₁×#552	C₂²	semidirect
38. C₃₁×#552	C₂²	semidirect
60. C₃₁×#501	C₂²	semidirect
61. C₃₁×#501	C₂²	semidirect
62. C₃₁×#499	C₂²	semidirect
63. C₃₁×#499	C₂²	semidirect
64. C₃₁×#485	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#484	C₂²	semidirect
67. C₃₁×#483	C₂²	semidirect
72. C₃₁×#482	C₂²	semidirect
73. C₃₁×#482	C₂²	semidirect
76. C₃₁×#481	C₂²	semidirect
79. C₃₁×#480	C₂²	semidirect
80. C₃₁×#479	C₂²	semidirect
81. C₃₁×#479	C₂²	semidirect
86. C₃₁×#478	C₂²	semidirect
87. C₃₁×#478	C₂²	semidirect
88. C₃₁×#477	C₂²	semidirect
89. C₃₁×#476	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
104. C₃₁×#436	C₂²	semidirect
105. C₃₁×#435	C₂²	semidirect
106. C₃₁×#435	C₂²	semidirect
107. C₈×D₄×C₃₁	C₂²	semidirect
113. C₃₁×#428	C₂²	semidirect
114. C₃₁×#428	C₂²	semidirect
115. C₃₁×#428	C₂²	semidirect
116. C₃₁×#428	C₂²	semidirect
119. C₃₁×#427	C₂²	semidirect
120. C₃₁×#427	C₂²	semidirect
122. C₂×C₃₁×#107	C₂²	semidirect
124. C₂×C₃₁×#106	C₂²	semidirect
369. M₁₆×C₃₁	#41	semidirect
448. #61283	C₃₁	direct (N × H)
525. #3512	C₂×C₃₁	semidirect
526. #3506	C₂×C₃₁	semidirect
527. #3355	C₂×C₃₁	semidirect
528. #3351	C₂×C₃₁	semidirect
529. #3348	C₂×C₃₁	semidirect
530. #3347	C₂×C₃₁	semidirect
531. #3345	C₂×C₃₁	semidirect
532. #3343	C₂×C₃₁	semidirect
533. #3339	C₂×C₃₁	semidirect
534. #3337	C₂×C₃₁	semidirect
535. #3166	C₂×C₃₁	semidirect
536. #3099	C₂×C₃₁	semidirect
537. #3098	C₂×C₃₁	semidirect
538. #3096	C₂×C₃₁	semidirect
539. #3096	C₂×C₃₁	semidirect
540. #3076	C₂×C₃₁	semidirect
541. C₂×#478	C₂×C₃₁	semidirect
542. #3062	C₂×C₃₁	semidirect
543. #3062	C₂×C₃₁	semidirect
544. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
545. #2935	C₂×C₃₁	semidirect
546. #2913	C₂×C₃₁	semidirect
547. #2912	C₂×C₃₁	semidirect
595. #553	C₂²×C₃₁	semidirect
596. #553	C₂²×C₃₁	semidirect
597. #552	C₂²×C₃₁	semidirect
598. #552	C₂²×C₃₁	semidirect
620. #501	C₂²×C₃₁	semidirect
621. #501	C₂²×C₃₁	semidirect
622. #499	C₂²×C₃₁	semidirect
623. #499	C₂²×C₃₁	semidirect
624. #485	C₂²×C₃₁	semidirect
625. #485	C₂²×C₃₁	semidirect
626. #484	C₂²×C₃₁	semidirect
627. #483	C₂²×C₃₁	semidirect
632. #482	C₂²×C₃₁	semidirect
633. #482	C₂²×C₃₁	semidirect
636. #481	C₂²×C₃₁	semidirect
639. #480	C₂²×C₃₁	semidirect
640. #479	C₂²×C₃₁	semidirect
641. #479	C₂²×C₃₁	semidirect
646. #478	C₂²×C₃₁	semidirect
647. #478	C₂²×C₃₁	semidirect
648. #477	C₂²×C₃₁	semidirect
649. #476	C₂²×C₃₁	semidirect
650. #475	C₂²×C₃₁	semidirect
651. #474	C₂²×C₃₁	semidirect
664. #436	C₂²×C₃₁	semidirect
665. #435	C₂²×C₃₁	semidirect
666. #435	C₂²×C₃₁	semidirect
667. C₈×D₄	C₂²×C₃₁	semidirect
673. #428	C₂²×C₃₁	semidirect
674. #428	C₂²×C₃₁	semidirect
675. #428	C₂²×C₃₁	semidirect
676. #428	C₂²×C₃₁	semidirect
679. #427	C₂²×C₃₁	semidirect
680. #427	C₂²×C₃₁	semidirect
682. C₂×#107	C₂²×C₃₁	semidirect
684. C₂×#106	C₂²×C₃₁	semidirect
883. C₃₁	#61283	direct (N × H)
938. 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×#3512	2
C₃₁×#3506	2
C₃₁×#3355	2
C₃₁×#3351	2
C₃₁×#3348	2
C₃₁×#3347	2
C₃₁×#3345	2
C₃₁×#3343	2
C₃₁×#3339	2
C₃₁×#3337	2
C₃₁×#3166	2
C₃₁×#3099	2
C₃₁×#3098	2
C₃₁×#3096	2
C₃₁×#3076	2
C₂×C₃₁×#478	2
C₃₁×#3062	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₃₁×#2935	2
C₃₁×#2913	2
C₃₁×#2912	2
#61283	31

Subgroups — C31×#61283 #21518042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61283 #21518042