Subgroups — C₃₁×#61349 #21518108

Order 7936.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3506	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×#3368	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2952	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#135	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×#555	—	2	1	no	—
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×#553	—	2	1	no	—
38	C₃₁×#553	—	2	1	no	—
39	C₃₁×#550	C₂²	1	2	yes	—
40	C₃₁×#547	—	2	1	no	—
41	C₃₁×#544	—	2	1	no	—
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#544	C₂²	1	1	yes	characteristic
44	C₃₁×#544	C₂²	1	1	yes	characteristic
45	C₃₁×#538	—	2	2	no	—
46	C₃₁×#535	C₂²	1	1	yes	characteristic
47	C₃₁×#535	C₂²	1	1	yes	characteristic
48	C₃₁×#533	—	2	1	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×#125	—	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×#491	C₂²	1	2	yes	complemented
61	C₃₁×#490	C₂²	1	2	yes	—
62	C₃₁×#490	C₂²	1	2	yes	—
63	C₃₁×#490	C₂²	1	2	yes	complemented
64	C₃₁×#489	C₂²	1	2	yes	—
65	C₃₁×#489	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	complemented
69	C₃₁×#488	C₂²	1	2	yes	complemented
70	C₃₁×#486	C₂²	1	2	yes	—
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×#478	C₂²	1	2	yes	—
75	C₃₁×#478	C₂²	1	2	yes	—
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	complemented
82	C₃₁×#475	C₂²	1	2	yes	complemented
83	C₃₁×#474	C₂²	1	2	yes	complemented
84	C₃₁×#464	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	2	yes	—
86	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	2	yes	—
90	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#460	C₂²	1	2	yes	—
95	C₃₁×#460	C₂²	1	2	yes	—
96	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#459	C₂²	1	2	yes	—
98	C₃₁×#459	C₂²	1	2	yes	—
99	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#446	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#446	C₂²	1	2	yes	complemented
103	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
104	C₃₁×#442	C₂²	1	2	yes	—
105	C₃₁×#442	C₂²	1	2	yes	complemented
106	C₃₁×#441	C₂²	1	2	yes	complemented
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₃₁×#440	C₂²	1	2	yes	complemented
110	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
114	C₄×D₈×C₃₁	C₂²	1	2	yes	—
115	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
116	C₃₁×#428	C₂²	1	1	yes	characteristic
117	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
119	C₃₁×#424	C₂²	1	1	yes	characteristic
120	C₃₁×#424	C₂²	1	1	yes	characteristic
121	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
122	C₃₁×#418	C₂²	1	1	yes	characteristic
123	C₃₁×#417	C₂²	1	1	yes	characteristic
124	C₃₁×#417	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic
126	C₃₁×#417	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×#405	C₂²	1	1	yes	characteristic
133	C₃₁×#405	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	C₃₁×#135	—	2	4	no	—
143	C₃₁×#135	—	2	4	no	—
144	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×D₈×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	—	2	2	no	—
159	C₃₁×C₄⋊Q₈	—	2	2	no	—
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	—	2	1	no	—
162	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×#127	C₂³	1	2	yes	—
168	C₃₁×#127	C₂³	1	2	yes	—
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#125	—	2	1	no	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	D₄	1	1	yes	characteristic
181	C₃₁×#125	D₄	1	1	yes	characteristic
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#125	C₂³	1	2	yes	—
184	C₃₁×#125	C₂³	1	2	yes	—
185	C₃₁×#125	C₂³	1	2	yes	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#124	C₂³	1	1	yes	characteristic
191	C₃₁×#124	C₂³	1	1	yes	characteristic
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	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	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	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	D₄	1	2	yes	—
206	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#120	—	2	2	no	—
217	C₃₁×#120	—	2	2	no	—
218	C₄×Q₈×C₃₁	—	2	2	no	—
219	C₄×Q₈×C₃₁	—	2	2	no	—
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	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	2	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	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	C₂³	1	1	yes	characteristic
255	C₃₁×#117	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	—	2	1	no	—
270	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#102	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	1	yes	characteristic
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	2	yes	—
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×#102	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₃₁	C₂³	1	2	yes	—
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	—	2	2	no	—
320	#41×C₃₁	—	2	2	no	—
321	#41×C₃₁	—	8	4	no	—
322	#41×C₃₁	#41	1	4	yes	complemented
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	1	yes	characteristic
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	1	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	2	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	—	8	2	no	—
361	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	Q₁₆×C₃₁	—	2	2	no	—
365	Q₁₆×C₃₁	—	2	2	no	—
366	SD₁₆×C₃₁	—	2	2	no	—
367	SD₁₆×C₃₁	—	2	2	no	—
368	SD₁₆×C₃₁	—	2	4	no	—
369	SD₁₆×C₃₁	—	2	2	no	—
370	SD₁₆×C₃₁	—	2	2	no	—
371	D₈×C₃₁	—	2	2	no	—
372	D₈×C₃₁	—	2	2	no	—
373	D₈×C₃₁	—	2	4	no	—
374	M₁₆×C₃₁	—	2	2	no	—
375	M₁₆×C₃₁	—	2	2	no	—
376	C₂×C₈×C₃₁	—	2	2	no	—
377	C₂×C₈×C₃₁	—	2	2	no	—
378	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
379	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	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	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	no	—
436	C₂²⋊C₄×C₃₁	—	2	1	no	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₄²×C₃₁	—	2	1	no	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	2	yes	—
450	C₄²×C₃₁	C₂⁴	1	2	yes	—
451	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
452	#61349	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	2	no	—
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	2	1	no	—
457	C₂³×C₃₁	—	4	2	no	—
458	C₂³×C₃₁	—	8	1	no	—
459	C₂³×C₃₁	—	8	1	no	—
460	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	2	1	no	—
463	Q₈×C₃₁	—	2	1	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	4	2	no	—
467	Q₈×C₃₁	—	4	2	no	—
468	Q₈×C₃₁	—	8	2	no	—
469	Q₈×C₃₁	—	8	2	no	—
470	Q₈×C₃₁	C₂×#41	1	2	yes	—
471	D₄×C₃₁	—	2	4	no	—
472	D₄×C₃₁	—	2	2	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	1	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	—	4	2	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	8	1	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	C₂×#41	1	2	yes	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	4	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	4	1	no	—
499	C₂×C₄×C₃₁	—	4	1	no	—
500	C₂×C₄×C₃₁	—	4	4	no	—
501	C₂×C₄×C₃₁	—	4	2	no	—
502	C₂×C₄×C₃₁	—	4	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	2	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	—	8	2	no	—
510	C₂×C₄×C₃₁	—	8	1	no	—
511	C₂×C₄×C₃₁	—	8	1	no	—
512	C₂×C₄×C₃₁	—	8	1	no	—
513	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
523	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
524	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
525	C₈×C₃₁	—	2	1	no	—
526	C₈×C₃₁	—	2	1	no	—
527	C₈×C₃₁	—	2	1	no	—
528	C₈×C₃₁	—	2	1	no	—
529	C₈×C₃₁	—	2	2	no	—
530	C₈×C₃₁	—	2	2	no	—
531	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3504	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3377	C₂×C₃₁	1	2	yes	complemented
534	#3376	C₂×C₃₁	1	2	yes	complemented
535	#3371	C₂×C₃₁	1	2	yes	complemented
536	#3370	C₂×C₃₁	1	2	yes	complemented
537	#3368	C₂×C₃₁	1	2	yes	complemented
538	#3366	C₂×C₃₁	1	2	yes	complemented
539	#3365	C₂×C₃₁	1	2	yes	complemented
540	#3361	C₂×C₃₁	1	2	yes	complemented
541	#3142	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
546	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3045	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3045	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#2962	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#2952	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
553	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
554	C₂²×C₃₁	—	2	1	no	—
555	C₂²×C₃₁	—	2	1	no	—
556	C₂²×C₃₁	—	2	2	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	2	no	—
562	C₂²×C₃₁	—	4	2	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	2	no	—
568	C₂²×C₃₁	—	8	4	no	—
569	C₂²×C₃₁	#548	1	2	yes	—
570	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
571	C₄×C₃₁	—	2	1	no	—
572	C₄×C₃₁	—	2	1	no	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	2	2	no	—
575	C₄×C₃₁	—	2	1	no	—
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	2	no	—
578	C₄×C₃₁	—	2	2	no	—
579	C₄×C₃₁	—	2	2	no	—
580	C₄×C₃₁	—	4	2	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	—	4	2	no	—
583	C₄×C₃₁	—	4	2	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	#548	1	2	yes	—
588	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
589	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
590	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
591	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
592	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
593	#559	C₂²×C₃₁	1	2	yes	—
594	#559	C₂²×C₃₁	1	2	yes	—
595	#557	C₂²×C₃₁	1	2	yes	complemented
596	#557	C₂²×C₃₁	1	2	yes	complemented
597	#556	C₂²×C₃₁	1	2	yes	—
598	#555	—	2	1	no	—
599	#554	—	2	2	no	—
600	#554	—	2	2	no	—
601	#554	C₂²×C₃₁	1	2	yes	complemented
602	#554	C₂²×C₃₁	1	2	yes	complemented
603	#553	—	2	1	no	—
604	#553	—	2	1	no	—
605	#550	C₂²×C₃₁	1	2	yes	—
606	#547	—	2	1	no	—
607	#544	—	2	1	no	—
608	#544	—	2	1	no	—
609	#544	C₂²×C₃₁	1	1	yes	characteristic
610	#544	C₂²×C₃₁	1	1	yes	characteristic
611	#538	—	2	2	no	—
612	#535	C₂²×C₃₁	1	1	yes	characteristic
613	#535	C₂²×C₃₁	1	1	yes	characteristic
614	#533	—	2	1	no	—
615	#533	C₂²×C₃₁	1	1	yes	characteristic
616	#532	C₂²×C₃₁	1	1	yes	characteristic
617	C₂×#125	—	2	1	no	—
618	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
619	#525	—	2	2	no	—
620	#520	C₂²×C₃₁	1	1	yes	characteristic
621	#520	C₂²×C₃₁	1	1	yes	characteristic
622	#520	C₂²×C₃₁	1	1	yes	characteristic
623	#520	C₂²×C₃₁	1	1	yes	characteristic
624	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
625	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
626	#491	C₂²×C₃₁	1	2	yes	complemented
627	#490	C₂²×C₃₁	1	2	yes	—
628	#490	C₂²×C₃₁	1	2	yes	—
629	#490	C₂²×C₃₁	1	2	yes	complemented
630	#489	C₂²×C₃₁	1	2	yes	—
631	#489	C₂²×C₃₁	1	2	yes	—
632	#488	C₂²×C₃₁	1	2	yes	—
633	#488	C₂²×C₃₁	1	2	yes	—
634	#488	C₂²×C₃₁	1	2	yes	complemented
635	#488	C₂²×C₃₁	1	2	yes	complemented
636	#486	C₂²×C₃₁	1	2	yes	—
637	#486	C₂²×C₃₁	1	2	yes	—
638	#479	C₂²×C₃₁	1	2	yes	complemented
639	#479	C₂²×C₃₁	1	2	yes	complemented
640	#478	C₂²×C₃₁	1	2	yes	—
641	#478	C₂²×C₃₁	1	2	yes	—
642	#478	C₂²×C₃₁	1	2	yes	—
643	#478	C₂²×C₃₁	1	2	yes	—
644	#478	C₂²×C₃₁	1	2	yes	complemented
645	#478	C₂²×C₃₁	1	2	yes	complemented
646	#477	C₂²×C₃₁	1	2	yes	complemented
647	#476	C₂²×C₃₁	1	2	yes	complemented
648	#475	C₂²×C₃₁	1	2	yes	complemented
649	#474	C₂²×C₃₁	1	2	yes	complemented
650	#464	C₂²×C₃₁	1	2	yes	—
651	#464	C₂²×C₃₁	1	2	yes	—
652	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#463	C₂²×C₃₁	1	2	yes	—
655	#463	C₂²×C₃₁	1	2	yes	—
656	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#460	C₂²×C₃₁	1	2	yes	—
661	#460	C₂²×C₃₁	1	2	yes	—
662	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#459	C₂²×C₃₁	1	2	yes	—
664	#459	C₂²×C₃₁	1	2	yes	—
665	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#446	C₂²×C₃₁	1	2	yes	complemented
667	#446	C₂²×C₃₁	1	2	yes	complemented
668	#446	C₂²×C₃₁	1	2	yes	complemented
669	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
670	#442	C₂²×C₃₁	1	2	yes	—
671	#442	C₂²×C₃₁	1	2	yes	complemented
672	#441	C₂²×C₃₁	1	2	yes	complemented
673	#440	C₂²×C₃₁	1	2	yes	—
674	#440	C₂²×C₃₁	1	2	yes	complemented
675	#440	C₂²×C₃₁	1	2	yes	complemented
676	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
677	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
678	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
679	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
680	C₄×D₈	C₂²×C₃₁	1	2	yes	—
681	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
682	#428	C₂²×C₃₁	1	1	yes	characteristic
683	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
684	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
685	#424	C₂²×C₃₁	1	1	yes	characteristic
686	#424	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
688	#418	C₂²×C₃₁	1	1	yes	characteristic
689	#417	C₂²×C₃₁	1	1	yes	characteristic
690	#417	C₂²×C₃₁	1	1	yes	characteristic
691	#417	C₂²×C₃₁	1	1	yes	characteristic
692	#417	C₂²×C₃₁	1	1	yes	characteristic
693	#417	C₂²×C₃₁	1	1	yes	characteristic
694	#416	C₂²×C₃₁	1	1	yes	characteristic
695	#416	C₂²×C₃₁	1	1	yes	characteristic
696	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
697	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
698	#405	C₂²×C₃₁	1	1	yes	characteristic
699	#405	C₂²×C₃₁	1	1	yes	characteristic
700	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
701	C₂×C₃₁	—	2	2	no	—
702	C₂×C₃₁	—	4	2	no	—
703	C₂×C₃₁	—	8	1	no	—
704	C₂×C₃₁	—	8	1	no	—
705	C₂×C₃₁	—	8	2	no	—
706	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
707	C₂×C₃₁	#3584	1	1	yes	characteristic
708	C₂×C₃₁	#3585	1	1	yes	characteristic
709	C₂×#41	—	2	2	no	—
710	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
712	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
713	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
714	C₂³×C₄	—	2	1	no	—
715	AGL(1,ℤ/8)	—	2	4	no	—
716	#135	—	2	4	no	—
717	#135	—	2	4	no	—
718	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
721	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
722	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
725	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×D₈	C₂³×C₃₁	1	2	yes	—
728	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
730	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
732	C₄⋊Q₈	—	2	2	no	—
733	C₄⋊Q₈	—	2	2	no	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
737	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
740	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
741	#127	C₂³×C₃₁	1	1	yes	characteristic
742	#127	C₂³×C₃₁	1	2	yes	—
743	#127	C₂³×C₃₁	1	2	yes	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	—	2	1	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	—	2	1	no	—
753	#125	—	2	1	no	—
754	#125	D₄×C₃₁	1	1	yes	characteristic
755	#125	D₄×C₃₁	1	1	yes	characteristic
756	#125	C₂³×C₃₁	1	2	yes	—
757	#125	C₂³×C₃₁	1	2	yes	—
758	#125	C₂³×C₃₁	1	2	yes	—
759	#125	C₂³×C₃₁	1	2	yes	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	C₂³×C₃₁	1	1	yes	characteristic
763	#124	C₂³×C₃₁	1	1	yes	characteristic
764	#124	C₂³×C₃₁	1	2	yes	—
765	#124	C₂³×C₃₁	1	2	yes	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
780	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	1	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#120	—	2	2	no	—
791	#120	—	2	2	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	2	no	—
794	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
797	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
798	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
799	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
800	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
801	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	C₂³×C₃₁	1	2	yes	—
815	C₄×D₄	C₂³×C₃₁	1	2	yes	—
816	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₃₁	1	2	yes	—
819	C₄×D₄	C₂³×C₃₁	1	2	yes	—
820	C₄×D₄	C₂³×C₃₁	1	2	yes	—
821	C₄×D₄	C₂³×C₃₁	1	2	yes	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	2	2	no	—
827	#117	—	2	1	no	—
828	#117	C₂³×C₃₁	1	1	yes	characteristic
829	#117	C₂³×C₃₁	1	1	yes	characteristic
830	#117	C₂³×C₃₁	1	1	yes	characteristic
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	—	2	2	no	—
839	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
842	C₂×C₂²⋊C₄	—	2	1	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
845	#107	C₂³×C₃₁	1	2	yes	—
846	#107	C₂³×C₃₁	1	2	yes	—
847	#107	C₂³×C₃₁	1	2	yes	—
848	#106	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	2	yes	—
850	#106	C₂³×C₃₁	1	2	yes	—
851	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
856	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
857	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
858	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	1	yes	characteristic
860	#103	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	2	yes	—
864	#103	C₂³×C₃₁	1	2	yes	—
865	#103	C₂³×C₃₁	1	2	yes	—
866	#103	C₂³×C₃₁	1	2	yes	—
867	#103	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	2	yes	—
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	1	yes	characteristic
874	#102	C₂³×C₃₁	1	1	yes	characteristic
875	#102	C₂³×C₃₁	1	1	yes	characteristic
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	2	yes	—
883	#97	C₂³×C₃₁	1	2	yes	—
884	#97	C₂³×C₃₁	1	2	yes	—
885	#97	C₂³×C₃₁	1	2	yes	—
886	C₄×C₈	C₂³×C₃₁	1	2	yes	—
887	C₄×C₈	C₂³×C₃₁	1	2	yes	—
888	C₄×C₈	C₂³×C₃₁	1	2	yes	—
889	C₃₁	#61349	1	1	yes	characteristic, direct product factor, Sylow
890	C₂⁴	—	2	1	no	—
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	8	4	no	—
897	#41	#41×C₃₁	1	4	yes	complemented
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
901	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
918	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	8	2	no	—
936	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
937	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
939	Q₁₆	—	2	2	no	—
940	Q₁₆	—	2	2	no	—
941	SD₁₆	—	2	2	no	—
942	SD₁₆	—	2	2	no	—
943	SD₁₆	—	2	4	no	—
944	SD₁₆	—	2	2	no	—
945	SD₁₆	—	2	2	no	—
946	D₈	—	2	2	no	—
947	D₈	—	2	2	no	—
948	D₈	—	2	4	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	2	2	no	—
951	C₂×C₈	—	2	2	no	—
952	C₂×C₈	—	2	2	no	—
953	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
954	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
957	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
985	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
995	C₂²⋊C₄	—	2	1	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	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1022	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₃₁	1	2	yes	—
1025	C₄²	C₂⁴×C₃₁	1	2	yes	—
1026	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	4	2	no	—
1032	C₂³	—	8	1	no	—
1033	C₂³	—	8	1	no	—
1034	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	4	2	no	—
1041	Q₈	—	4	2	no	—
1042	Q₈	—	8	2	no	—
1043	Q₈	—	8	2	no	—
1044	Q₈	C₂×#41×C₃₁	1	2	yes	—
1045	D₄	—	2	4	no	—
1046	D₄	—	2	2	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	8	1	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	C₂×#41×C₃₁	1	2	yes	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	4	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	4	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	8	1	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	1	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	1	no	—
1085	C₂×C₄	—	8	1	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1096	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1097	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1098	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1099	C₈	—	2	1	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₈	—	2	1	no	—
1103	C₈	—	2	2	no	—
1104	C₈	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	8	4	no	—
1120	C₂²	C₃₁×#548	1	2	yes	—
1121	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	C₃₁×#548	1	2	yes	—
1139	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1140	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1141	C₂	—	2	2	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	8	2	no	—
1144	C₂	—	8	1	no	—
1145	C₂	—	8	1	no	—
1146	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
1147	C₂	C₃₁×#3584	1	1	yes	characteristic
1148	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3506	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×#3368	C₂	semidirect
8. C₃₁×#3366	C₂	semidirect
9. C₃₁×#3365	C₂	semidirect
10. C₃₁×#3361	C₂	semidirect
11. C₃₁×#3142	C₂	semidirect
12. C₃₁×#3136	C₂	semidirect
13. C₃₁×#3136	C₂	semidirect
14. C₃₁×#3084	C₂	semidirect
15. C₃₁×#3083	C₂	semidirect
16. C₂×C₃₁×#478	C₂	semidirect
17. C₃₁×#3045	C₂	semidirect
18. C₃₁×#3045	C₂	semidirect
19. C₃₁×#3035	C₂	semidirect
20. C₃₁×#2962	C₂	semidirect
21. C₃₁×#2952	C₂	semidirect
22. C₃₁×#2951	C₂	semidirect
23. C₄×C₃₁×AGL(1,ℤ/8)	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×#490	C₂²	semidirect
68. C₃₁×#488	C₂²	semidirect
69. C₃₁×#488	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#477	C₂²	semidirect
81. C₃₁×#476	C₂²	semidirect
82. C₃₁×#475	C₂²	semidirect
83. C₃₁×#474	C₂²	semidirect
86. C₃₁×#464	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
90. C₃₁×#463	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#462	C₂²	semidirect
93. C₃₁×#461	C₂²	semidirect
96. C₃₁×#460	C₂²	semidirect
99. C₃₁×#459	C₂²	semidirect
100. C₃₁×#446	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
103. C₈×Q₈×C₃₁	C₂²	semidirect
105. C₃₁×#442	C₂²	semidirect
106. C₃₁×#441	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₃₁×#440	C₂²	semidirect
110. C₄×Q₁₆×C₃₁	C₂²	semidirect
112. C₄×SD₁₆×C₃₁	C₂²	semidirect
113. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₄×D₈×C₃₁	C₂²	semidirect
322. #41×C₃₁	#41	semidirect
452. #61349	C₃₁	direct (N × H)
531. #3506	C₂×C₃₁	semidirect
532. #3504	C₂×C₃₁	semidirect
533. #3377	C₂×C₃₁	semidirect
534. #3376	C₂×C₃₁	semidirect
535. #3371	C₂×C₃₁	semidirect
536. #3370	C₂×C₃₁	semidirect
537. #3368	C₂×C₃₁	semidirect
538. #3366	C₂×C₃₁	semidirect
539. #3365	C₂×C₃₁	semidirect
540. #3361	C₂×C₃₁	semidirect
541. #3142	C₂×C₃₁	semidirect
542. #3136	C₂×C₃₁	semidirect
543. #3136	C₂×C₃₁	semidirect
544. #3084	C₂×C₃₁	semidirect
545. #3083	C₂×C₃₁	semidirect
546. C₂×#478	C₂×C₃₁	semidirect
547. #3045	C₂×C₃₁	semidirect
548. #3045	C₂×C₃₁	semidirect
549. #3035	C₂×C₃₁	semidirect
550. #2962	C₂×C₃₁	semidirect
551. #2952	C₂×C₃₁	semidirect
552. #2951	C₂×C₃₁	semidirect
553. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
595. #557	C₂²×C₃₁	semidirect
596. #557	C₂²×C₃₁	semidirect
601. #554	C₂²×C₃₁	semidirect
602. #554	C₂²×C₃₁	semidirect
626. #491	C₂²×C₃₁	semidirect
629. #490	C₂²×C₃₁	semidirect
634. #488	C₂²×C₃₁	semidirect
635. #488	C₂²×C₃₁	semidirect
638. #479	C₂²×C₃₁	semidirect
639. #479	C₂²×C₃₁	semidirect
644. #478	C₂²×C₃₁	semidirect
645. #478	C₂²×C₃₁	semidirect
646. #477	C₂²×C₃₁	semidirect
647. #476	C₂²×C₃₁	semidirect
648. #475	C₂²×C₃₁	semidirect
649. #474	C₂²×C₃₁	semidirect
652. #464	C₂²×C₃₁	semidirect
653. #464	C₂²×C₃₁	semidirect
656. #463	C₂²×C₃₁	semidirect
657. #463	C₂²×C₃₁	semidirect
658. #462	C₂²×C₃₁	semidirect
659. #461	C₂²×C₃₁	semidirect
662. #460	C₂²×C₃₁	semidirect
665. #459	C₂²×C₃₁	semidirect
666. #446	C₂²×C₃₁	semidirect
667. #446	C₂²×C₃₁	semidirect
668. #446	C₂²×C₃₁	semidirect
669. C₈×Q₈	C₂²×C₃₁	semidirect
671. #442	C₂²×C₃₁	semidirect
672. #441	C₂²×C₃₁	semidirect
674. #440	C₂²×C₃₁	semidirect
675. #440	C₂²×C₃₁	semidirect
676. C₄×Q₁₆	C₂²×C₃₁	semidirect
678. C₄×SD₁₆	C₂²×C₃₁	semidirect
679. C₄×SD₁₆	C₂²×C₃₁	semidirect
681. C₄×D₈	C₂²×C₃₁	semidirect
889. C₃₁	#61349	direct (N × H)
897. #41	#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×#3506	2
C₃₁×#3504	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3365	2
C₃₁×#3361	2
C₃₁×#3142	2
C₃₁×#3136	2
C₃₁×#3084	2
C₃₁×#3083	2
C₂×C₃₁×#478	2
C₃₁×#3045	2
C₃₁×#3035	2
C₃₁×#2962	2
C₃₁×#2952	2
C₃₁×#2951	2
C₄×C₃₁×AGL(1,ℤ/8)	2
#61349	31

Subgroups — C31×#61349 #21518108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61349 #21518108