Subgroups — C₃₁×#61331 #21518090

Order 7936.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#488	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic
19	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
27	C₃₁×#559	C₂²	1	2	yes	—
28	C₃₁×#559	C₂²	1	2	yes	—
29	C₃₁×#557	C₂²	1	2	yes	complemented
30	C₃₁×#557	C₂²	1	2	yes	complemented
31	C₃₁×#556	C₂²	1	2	yes	—
32	C₃₁×#556	C₂²	1	2	yes	—
33	C₃₁×#554	—	2	2	no	—
34	C₃₁×#554	—	2	2	no	—
35	C₃₁×#554	C₂²	1	2	yes	complemented
36	C₃₁×#554	C₂²	1	2	yes	complemented
37	C₃₁×#551	—	2	2	no	—
38	C₃₁×#551	—	2	2	no	—
39	C₃₁×#544	—	2	1	no	—
40	C₃₁×#544	—	2	1	no	—
41	C₃₁×#544	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	1	yes	characteristic
43	C₃₁×#542	—	2	1	no	—
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#536	C₂²	1	1	yes	characteristic
46	C₃₁×#535	C₂²	1	1	yes	characteristic
47	C₃₁×#533	—	2	1	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#529	—	2	1	no	—
50	C₃₁×#529	—	2	1	no	—
51	C₂×C₃₁×#125	—	2	1	no	—
52	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
54	C₃₁×#520	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	1	yes	characteristic
56	C₃₁×#519	C₂²	1	1	yes	characteristic
57	C₃₁×#518	C₂²	1	1	yes	characteristic
58	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
59	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
60	C₃₁×#491	C₂²	1	2	yes	complemented
61	C₃₁×#490	C₂²	1	2	yes	—
62	C₃₁×#489	C₂²	1	2	yes	—
63	C₃₁×#489	C₂²	1	2	yes	complemented
64	C₃₁×#488	C₂²	1	2	yes	—
65	C₃₁×#488	C₂²	1	2	yes	—
66	C₃₁×#488	C₂²	1	2	yes	—
67	C₃₁×#488	C₂²	1	2	yes	—
68	C₃₁×#488	C₂²	1	2	yes	—
69	C₃₁×#488	C₂²	1	2	yes	complemented
70	C₃₁×#487	C₂²	1	2	yes	complemented
71	C₃₁×#486	C₂²	1	2	yes	—
72	C₃₁×#479	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#477	C₂²	1	2	yes	complemented
81	C₃₁×#476	C₂²	1	2	yes	—
82	C₃₁×#475	C₂²	1	2	yes	complemented
83	C₃₁×#474	C₂²	1	2	yes	—
84	C₃₁×#464	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	2	yes	—
86	C₃₁×#464	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	2	yes	—
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	2	yes	complemented
92	C₃₁×#462	C₂²	1	2	yes	complemented
93	C₃₁×#461	C₂²	1	2	yes	complemented
94	C₃₁×#460	C₂²	1	2	yes	—
95	C₃₁×#459	C₂²	1	2	yes	—
96	C₃₁×#446	C₂²	1	2	yes	complemented
97	C₃₁×#446	C₂²	1	2	yes	complemented
98	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
99	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
100	C₃₁×#442	C₂²	1	2	yes	—
101	C₃₁×#441	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	—
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
109	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₈×C₃₁	C₂²	1	2	yes	—
114	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#428	C₂²	1	1	yes	characteristic
117	C₃₁×#428	C₂²	1	1	yes	characteristic
118	C₃₁×#427	C₂²	1	1	yes	characteristic
119	C₃₁×#424	C₂²	1	1	yes	characteristic
120	C₃₁×#424	C₂²	1	1	yes	characteristic
121	C₃₁×#423	C₂²	1	1	yes	characteristic
122	C₃₁×#419	C₂²	1	1	yes	characteristic
123	C₃₁×#418	C₂²	1	1	yes	characteristic
124	C₃₁×#417	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic
126	C₃₁×#416	C₂²	1	1	yes	characteristic
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
129	C₂×C₃₁×#103	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×#405	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₃₁×#137	—	2	4	no	—
140	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
141	C₃₁×#135	—	2	4	no	—
142	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	—	2	2	no	—
155	C₃₁×C₄⋊Q₈	—	2	2	no	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×#127	C₂³	1	2	yes	—
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×#125	—	2	1	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	—	2	1	no	—
176	C₃₁×#125	D₄	1	1	yes	characteristic
177	C₃₁×#125	D₄	1	1	yes	characteristic
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#125	C₂³	1	2	yes	—
180	C₃₁×#125	C₂³	1	2	yes	—
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#124	C₂³	1	2	yes	—
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
208	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
209	C₃₁×#121	—	2	1	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#120	—	2	2	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	2	no	—
215	C₄×Q₈×C₃₁	—	2	2	no	—
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	1	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	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	no	—
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	—	2	2	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	C₂³	1	1	yes	characteristic
252	C₃₁×#117	C₂³	1	1	yes	characteristic
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	1	yes	characteristic
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	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	#41	1	4	yes	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
338	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	Q₁₆×C₃₁	—	2	2	no	—
357	Q₁₆×C₃₁	—	2	4	no	—
358	SD₁₆×C₃₁	—	2	2	no	—
359	SD₁₆×C₃₁	—	2	4	no	—
360	SD₁₆×C₃₁	—	2	2	no	—
361	SD₁₆×C₃₁	—	2	4	no	—
362	D₈×C₃₁	—	2	2	no	—
363	D₈×C₃₁	—	2	4	no	—
364	M₁₆×C₃₁	—	2	2	no	—
365	M₁₆×C₃₁	—	2	2	no	—
366	C₂×C₈×C₃₁	—	2	2	no	—
367	C₂×C₈×C₃₁	—	2	2	no	—
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
373	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
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	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
446	C₄²×C₃₁	C₂⁴	1	2	yes	—
447	C₄²×C₃₁	C₂⁴	1	2	yes	—
448	#61331	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	—	2	1	no	—
452	C₂³×C₃₁	—	4	2	no	—
453	C₂³×C₃₁	—	8	1	no	—
454	C₂³×C₃₁	—	8	1	no	—
455	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	2	no	—
458	Q₈×C₃₁	—	2	1	no	—
459	Q₈×C₃₁	—	2	2	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	4	2	no	—
462	Q₈×C₃₁	—	4	2	no	—
463	Q₈×C₃₁	—	4	2	no	—
464	Q₈×C₃₁	—	8	2	no	—
465	Q₈×C₃₁	—	8	2	no	—
466	Q₈×C₃₁	C₂×#41	1	2	yes	—
467	D₄×C₃₁	—	2	4	no	—
468	D₄×C₃₁	—	2	2	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	1	no	—
471	D₄×C₃₁	—	2	2	no	—
472	D₄×C₃₁	—	2	1	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	C₂×#41	1	2	yes	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	4	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	4	1	no	—
489	C₂×C₄×C₃₁	—	4	1	no	—
490	C₂×C₄×C₃₁	—	4	2	no	—
491	C₂×C₄×C₃₁	—	4	2	no	—
492	C₂×C₄×C₃₁	—	8	1	no	—
493	C₂×C₄×C₃₁	—	8	1	no	—
494	C₂×C₄×C₃₁	—	8	1	no	—
495	C₂×C₄×C₃₁	—	8	1	no	—
496	C₂×C₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	—	8	1	no	—
501	C₂×C₄×C₃₁	—	8	1	no	—
502	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
512	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
513	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
514	C₈×C₃₁	—	2	1	no	—
515	C₈×C₃₁	—	2	1	no	—
516	C₈×C₃₁	—	2	2	no	—
517	C₈×C₃₁	—	2	2	no	—
518	C₈×C₃₁	—	2	1	no	—
519	C₈×C₃₁	—	2	1	no	—
520	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3504	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3377	C₂×C₃₁	1	2	yes	complemented
523	#3376	C₂×C₃₁	1	2	yes	complemented
524	#3371	C₂×C₃₁	1	2	yes	complemented
525	#3370	C₂×C₃₁	1	2	yes	complemented
526	#3365	C₂×C₃₁	1	2	yes	complemented
527	#3364	C₂×C₃₁	1	2	yes	complemented
528	#3361	C₂×C₃₁	1	2	yes	complemented
529	#3360	C₂×C₃₁	1	2	yes	complemented
530	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
532	C₂×#488	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3080	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3045	C₂×C₃₁	1	1	yes	characteristic
538	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#2960	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#2947	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#2946	C₂×C₃₁	1	1	yes	characteristic, complemented
542	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
543	C₂²×C₃₁	—	2	1	no	—
544	C₂²×C₃₁	—	2	1	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	1	no	—
550	C₂²×C₃₁	—	4	2	no	—
551	C₂²×C₃₁	—	4	2	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	2	no	—
554	C₂²×C₃₁	—	16	2	no	—
555	C₂²×C₃₁	#548	1	2	yes	—
556	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
557	C₄×C₃₁	—	2	1	no	—
558	C₄×C₃₁	—	2	1	no	—
559	C₄×C₃₁	—	2	1	no	—
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	2	no	—
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	2	no	—
565	C₄×C₃₁	—	2	2	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	2	no	—
569	C₄×C₃₁	—	4	2	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	#548	1	2	yes	—
575	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
576	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
577	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
578	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
579	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
580	#559	C₂²×C₃₁	1	2	yes	—
581	#559	C₂²×C₃₁	1	2	yes	—
582	#557	C₂²×C₃₁	1	2	yes	complemented
583	#557	C₂²×C₃₁	1	2	yes	complemented
584	#556	C₂²×C₃₁	1	2	yes	—
585	#556	C₂²×C₃₁	1	2	yes	—
586	#554	—	2	2	no	—
587	#554	—	2	2	no	—
588	#554	C₂²×C₃₁	1	2	yes	complemented
589	#554	C₂²×C₃₁	1	2	yes	complemented
590	#551	—	2	2	no	—
591	#551	—	2	2	no	—
592	#544	—	2	1	no	—
593	#544	—	2	1	no	—
594	#544	C₂²×C₃₁	1	1	yes	characteristic
595	#544	C₂²×C₃₁	1	1	yes	characteristic
596	#542	—	2	1	no	—
597	#542	—	2	1	no	—
598	#536	C₂²×C₃₁	1	1	yes	characteristic
599	#535	C₂²×C₃₁	1	1	yes	characteristic
600	#533	—	2	1	no	—
601	#533	C₂²×C₃₁	1	1	yes	characteristic
602	#529	—	2	1	no	—
603	#529	—	2	1	no	—
604	C₂×#125	—	2	1	no	—
605	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
606	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
607	#520	C₂²×C₃₁	1	1	yes	characteristic
608	#520	C₂²×C₃₁	1	1	yes	characteristic
609	#519	C₂²×C₃₁	1	1	yes	characteristic
610	#518	C₂²×C₃₁	1	1	yes	characteristic
611	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
612	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
613	#491	C₂²×C₃₁	1	2	yes	complemented
614	#490	C₂²×C₃₁	1	2	yes	—
615	#489	C₂²×C₃₁	1	2	yes	—
616	#489	C₂²×C₃₁	1	2	yes	complemented
617	#488	C₂²×C₃₁	1	2	yes	—
618	#488	C₂²×C₃₁	1	2	yes	—
619	#488	C₂²×C₃₁	1	2	yes	—
620	#488	C₂²×C₃₁	1	2	yes	—
621	#488	C₂²×C₃₁	1	2	yes	—
622	#488	C₂²×C₃₁	1	2	yes	complemented
623	#487	C₂²×C₃₁	1	2	yes	complemented
624	#486	C₂²×C₃₁	1	2	yes	—
625	#479	C₂²×C₃₁	1	2	yes	complemented
626	#479	C₂²×C₃₁	1	2	yes	complemented
627	#479	C₂²×C₃₁	1	2	yes	complemented
628	#479	C₂²×C₃₁	1	2	yes	complemented
629	#478	C₂²×C₃₁	1	2	yes	—
630	#478	C₂²×C₃₁	1	2	yes	—
631	#478	C₂²×C₃₁	1	2	yes	complemented
632	#478	C₂²×C₃₁	1	2	yes	complemented
633	#477	C₂²×C₃₁	1	2	yes	complemented
634	#476	C₂²×C₃₁	1	2	yes	—
635	#475	C₂²×C₃₁	1	2	yes	complemented
636	#474	C₂²×C₃₁	1	2	yes	—
637	#464	C₂²×C₃₁	1	2	yes	—
638	#464	C₂²×C₃₁	1	2	yes	—
639	#464	C₂²×C₃₁	1	2	yes	—
640	#464	C₂²×C₃₁	1	2	yes	complemented
641	#463	C₂²×C₃₁	1	2	yes	—
642	#463	C₂²×C₃₁	1	2	yes	—
643	#463	C₂²×C₃₁	1	2	yes	—
644	#463	C₂²×C₃₁	1	2	yes	complemented
645	#462	C₂²×C₃₁	1	2	yes	complemented
646	#461	C₂²×C₃₁	1	2	yes	complemented
647	#460	C₂²×C₃₁	1	2	yes	—
648	#459	C₂²×C₃₁	1	2	yes	—
649	#446	C₂²×C₃₁	1	2	yes	complemented
650	#446	C₂²×C₃₁	1	2	yes	complemented
651	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
652	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
653	#442	C₂²×C₃₁	1	2	yes	—
654	#441	C₂²×C₃₁	1	2	yes	complemented
655	#440	C₂²×C₃₁	1	2	yes	—
656	#440	C₂²×C₃₁	1	2	yes	complemented
657	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
659	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
661	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
663	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	C₄×D₈	C₂²×C₃₁	1	2	yes	—
667	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#428	C₂²×C₃₁	1	1	yes	characteristic
670	#428	C₂²×C₃₁	1	1	yes	characteristic
671	#427	C₂²×C₃₁	1	1	yes	characteristic
672	#424	C₂²×C₃₁	1	1	yes	characteristic
673	#424	C₂²×C₃₁	1	1	yes	characteristic
674	#423	C₂²×C₃₁	1	1	yes	characteristic
675	#419	C₂²×C₃₁	1	1	yes	characteristic
676	#418	C₂²×C₃₁	1	1	yes	characteristic
677	#417	C₂²×C₃₁	1	1	yes	characteristic
678	#417	C₂²×C₃₁	1	1	yes	characteristic
679	#416	C₂²×C₃₁	1	1	yes	characteristic
680	#416	C₂²×C₃₁	1	1	yes	characteristic
681	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
682	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
683	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
684	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
685	#405	C₂²×C₃₁	1	1	yes	characteristic
686	#405	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
688	C₂×C₃₁	—	2	2	no	—
689	C₂×C₃₁	—	4	2	no	—
690	C₂×C₃₁	—	8	1	no	—
691	C₂×C₃₁	—	8	2	no	—
692	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
693	C₂×C₃₁	#3584	1	1	yes	characteristic
694	C₂×C₃₁	#3584	1	1	yes	characteristic
695	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
697	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
698	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
699	#137	—	2	4	no	—
700	AGL(1,ℤ/8)	—	2	4	no	—
701	#135	—	2	4	no	—
702	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
708	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₃₁	1	2	yes	—
710	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
712	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
719	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
722	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
723	#127	C₂³×C₃₁	1	2	yes	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	—	2	1	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	1	no	—
735	#125	—	2	1	no	—
736	#125	D₄×C₃₁	1	1	yes	characteristic
737	#125	D₄×C₃₁	1	1	yes	characteristic
738	#125	C₂³×C₃₁	1	2	yes	—
739	#125	C₂³×C₃₁	1	2	yes	—
740	#125	C₂³×C₃₁	1	2	yes	—
741	#125	C₂³×C₃₁	1	2	yes	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	1	no	—
745	#124	—	2	1	no	—
746	#124	C₂³×C₃₁	1	2	yes	—
747	#124	C₂³×C₃₁	1	2	yes	—
748	#124	C₂³×C₃₁	1	2	yes	—
749	#124	C₂³×C₃₁	1	2	yes	—
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	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
768	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
769	#121	—	2	1	no	—
770	#121	—	2	1	no	—
771	#120	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	2	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
781	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
782	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
783	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
784	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	2	yes	—
802	C₄×D₄	C₂³×C₃₁	1	2	yes	—
803	C₄×D₄	C₂³×C₃₁	1	2	yes	—
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	—	2	2	no	—
807	#117	—	2	2	no	—
808	#117	—	2	2	no	—
809	#117	—	2	1	no	—
810	#117	—	2	1	no	—
811	#117	C₂³×C₃₁	1	1	yes	characteristic
812	#117	C₂³×C₃₁	1	1	yes	characteristic
813	#117	C₂³×C₃₁	1	1	yes	characteristic
814	#117	C₂³×C₃₁	1	1	yes	characteristic
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	—	2	2	no	—
820	C₂×C₄⋊C₄	—	2	2	no	—
821	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
822	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₂×C₂²⋊C₄	—	2	1	no	—
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	C₂×C₄²	—	2	1	no	—
827	C₂×C₄²	—	2	1	no	—
828	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
829	#107	C₂³×C₃₁	1	1	yes	characteristic
830	#107	C₂³×C₃₁	1	1	yes	characteristic
831	#107	C₂³×C₃₁	1	2	yes	—
832	#107	C₂³×C₃₁	1	2	yes	—
833	#106	C₂³×C₃₁	1	1	yes	characteristic
834	#106	C₂³×C₃₁	1	1	yes	characteristic
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	2	yes	—
837	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
840	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
841	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
842	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	2	yes	—
846	#103	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	1	yes	characteristic
848	#103	C₂³×C₃₁	1	1	yes	characteristic
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	2	yes	—
852	#103	C₂³×C₃₁	1	2	yes	—
853	#103	C₂³×C₃₁	1	2	yes	—
854	#103	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	2	yes	—
857	#102	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	2	yes	—
859	#102	C₂³×C₃₁	1	1	yes	characteristic
860	#102	C₂³×C₃₁	1	1	yes	characteristic
861	#102	C₂³×C₃₁	1	1	yes	characteristic
862	#102	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	2	yes	—
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	2	yes	—
867	#97	C₂³×C₃₁	1	2	yes	—
868	#97	C₂³×C₃₁	1	2	yes	—
869	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₃₁	1	2	yes	—
874	C₄×C₈	C₂³×C₃₁	1	2	yes	—
875	C₃₁	#61331	1	1	yes	characteristic, direct product factor, Sylow
876	C₂⁴	—	2	1	no	—
877	#41	—	2	2	no	—
878	#41	—	2	2	no	—
879	#41	—	2	2	no	—
880	#41	#41×C₃₁	1	4	yes	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
887	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
899	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
915	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
917	Q₁₆	—	2	2	no	—
918	Q₁₆	—	2	4	no	—
919	SD₁₆	—	2	2	no	—
920	SD₁₆	—	2	4	no	—
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	2	4	no	—
923	D₈	—	2	2	no	—
924	D₈	—	2	4	no	—
925	M₁₆	—	2	2	no	—
926	M₁₆	—	2	2	no	—
927	C₂×C₈	—	2	2	no	—
928	C₂×C₈	—	2	2	no	—
929	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
934	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
964	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₃₁	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1004	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₃₁	1	2	yes	—
1008	C₄²	C₂⁴×C₃₁	1	2	yes	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	8	1	no	—
1014	C₂³	—	8	1	no	—
1015	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	2	no	—
1026	Q₈	C₂×#41×C₃₁	1	2	yes	—
1027	D₄	—	2	4	no	—
1028	D₄	—	2	2	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	C₂×#41×C₃₁	1	2	yes	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	4	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	—	4	1	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	8	1	no	—
1053	C₂×C₄	—	8	1	no	—
1054	C₂×C₄	—	8	1	no	—
1055	C₂×C₄	—	8	1	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	2	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1064	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1072	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1073	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	16	2	no	—
1092	C₂²	C₃₁×#548	1	2	yes	—
1093	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1094	C₄	—	2	2	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	C₃₁×#548	1	2	yes	—
1112	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1113	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1114	C₂	—	2	2	no	—
1115	C₂	—	4	2	no	—
1116	C₂	—	8	2	no	—
1117	C₂	—	8	1	no	—
1118	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
1119	C₂	C₃₁×#3584	1	1	yes	characteristic
1120	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3045	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3510	C₂	semidirect
2. C₃₁×#3504	C₂	semidirect
3. C₃₁×#3377	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3371	C₂	semidirect
6. C₃₁×#3370	C₂	semidirect
7. C₃₁×#3365	C₂	semidirect
8. C₃₁×#3364	C₂	semidirect
9. C₃₁×#3361	C₂	semidirect
10. C₃₁×#3360	C₂	semidirect
11. C₃₁×#3137	C₂	semidirect
12. C₃₁×#3136	C₂	semidirect
13. C₂×C₃₁×#488	C₂	semidirect
14. C₃₁×#3082	C₂	semidirect
15. C₃₁×#3081	C₂	semidirect
16. C₃₁×#3080	C₂	semidirect
17. C₃₁×#3046	C₂	semidirect
19. C₃₁×#3040	C₂	semidirect
20. C₃₁×#2960	C₂	semidirect
21. C₃₁×#2947	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₄×C₃₁×#135	C₂	semidirect
29. C₃₁×#557	C₂²	semidirect
30. C₃₁×#557	C₂²	semidirect
35. C₃₁×#554	C₂²	semidirect
36. C₃₁×#554	C₂²	semidirect
60. C₃₁×#491	C₂²	semidirect
63. C₃₁×#489	C₂²	semidirect
69. C₃₁×#488	C₂²	semidirect
70. C₃₁×#487	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#477	C₂²	semidirect
82. C₃₁×#475	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#462	C₂²	semidirect
93. C₃₁×#461	C₂²	semidirect
96. C₃₁×#446	C₂²	semidirect
97. C₃₁×#446	C₂²	semidirect
98. C₈×Q₈×C₃₁	C₂²	semidirect
99. C₈×Q₈×C₃₁	C₂²	semidirect
101. C₃₁×#441	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₄×Q₁₆×C₃₁	C₂²	semidirect
105. C₄×Q₁₆×C₃₁	C₂²	semidirect
106. C₄×Q₁₆×C₃₁	C₂²	semidirect
108. C₄×SD₁₆×C₃₁	C₂²	semidirect
109. C₄×SD₁₆×C₃₁	C₂²	semidirect
110. C₄×SD₁₆×C₃₁	C₂²	semidirect
111. C₄×SD₁₆×C₃₁	C₂²	semidirect
112. C₄×SD₁₆×C₃₁	C₂²	semidirect
114. C₄×D₈×C₃₁	C₂²	semidirect
115. C₄×D₈×C₃₁	C₂²	semidirect
448. #61331	C₃₁	direct (N × H)
520. #3510	C₂×C₃₁	semidirect
521. #3504	C₂×C₃₁	semidirect
522. #3377	C₂×C₃₁	semidirect
523. #3376	C₂×C₃₁	semidirect
524. #3371	C₂×C₃₁	semidirect
525. #3370	C₂×C₃₁	semidirect
526. #3365	C₂×C₃₁	semidirect
527. #3364	C₂×C₃₁	semidirect
528. #3361	C₂×C₃₁	semidirect
529. #3360	C₂×C₃₁	semidirect
530. #3137	C₂×C₃₁	semidirect
531. #3136	C₂×C₃₁	semidirect
532. C₂×#488	C₂×C₃₁	semidirect
533. #3082	C₂×C₃₁	semidirect
534. #3081	C₂×C₃₁	semidirect
535. #3080	C₂×C₃₁	semidirect
536. #3046	C₂×C₃₁	semidirect
538. #3040	C₂×C₃₁	semidirect
539. #2960	C₂×C₃₁	semidirect
540. #2947	C₂×C₃₁	semidirect
541. #2946	C₂×C₃₁	semidirect
542. C₄×#135	C₂×C₃₁	semidirect
582. #557	C₂²×C₃₁	semidirect
583. #557	C₂²×C₃₁	semidirect
588. #554	C₂²×C₃₁	semidirect
589. #554	C₂²×C₃₁	semidirect
613. #491	C₂²×C₃₁	semidirect
616. #489	C₂²×C₃₁	semidirect
622. #488	C₂²×C₃₁	semidirect
623. #487	C₂²×C₃₁	semidirect
625. #479	C₂²×C₃₁	semidirect
626. #479	C₂²×C₃₁	semidirect
627. #479	C₂²×C₃₁	semidirect
628. #479	C₂²×C₃₁	semidirect
631. #478	C₂²×C₃₁	semidirect
632. #478	C₂²×C₃₁	semidirect
633. #477	C₂²×C₃₁	semidirect
635. #475	C₂²×C₃₁	semidirect
640. #464	C₂²×C₃₁	semidirect
644. #463	C₂²×C₃₁	semidirect
645. #462	C₂²×C₃₁	semidirect
646. #461	C₂²×C₃₁	semidirect
649. #446	C₂²×C₃₁	semidirect
650. #446	C₂²×C₃₁	semidirect
651. C₈×Q₈	C₂²×C₃₁	semidirect
652. C₈×Q₈	C₂²×C₃₁	semidirect
654. #441	C₂²×C₃₁	semidirect
656. #440	C₂²×C₃₁	semidirect
657. C₄×Q₁₆	C₂²×C₃₁	semidirect
658. C₄×Q₁₆	C₂²×C₃₁	semidirect
659. C₄×Q₁₆	C₂²×C₃₁	semidirect
661. C₄×SD₁₆	C₂²×C₃₁	semidirect
662. C₄×SD₁₆	C₂²×C₃₁	semidirect
663. C₄×SD₁₆	C₂²×C₃₁	semidirect
664. C₄×SD₁₆	C₂²×C₃₁	semidirect
665. C₄×SD₁₆	C₂²×C₃₁	semidirect
667. C₄×D₈	C₂²×C₃₁	semidirect
668. C₄×D₈	C₂²×C₃₁	semidirect
875. C₃₁	#61331	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3510	2
C₃₁×#3504	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3365	2
C₃₁×#3364	2
C₃₁×#3361	2
C₃₁×#3360	2
C₃₁×#3137	2
C₃₁×#3136	2
C₂×C₃₁×#488	2
C₃₁×#3082	2
C₃₁×#3081	2
C₃₁×#3080	2
C₃₁×#3046	2
C₃₁×#3045	2
C₃₁×#3040	2
C₃₁×#2960	2
C₃₁×#2947	2
C₃₁×#2946	2
C₄×C₃₁×#135	2
#61331	31

Subgroups — C31×#61331 #21518090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61331 #21518090