Subgroups — C₃₁×#61459 #21518218

Order 7936.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3180	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3115	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2943	C₂	1	2	yes	maximal, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#135	C₂²	1	2	yes	—
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#555	—	2	2	no	—
29	C₃₁×#555	—	2	1	no	—
30	C₃₁×#555	C₂²	1	1	yes	characteristic
31	C₃₁×#555	C₂²	1	2	yes	—
32	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#554	C₂²	1	1	yes	characteristic
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#552	—	2	1	no	—
36	C₃₁×#552	C₂²	1	2	yes	—
37	C₃₁×#551	—	2	2	no	—
38	C₃₁×#550	—	2	1	no	—
39	C₃₁×#550	C₂²	1	2	yes	—
40	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#547	C₂²	1	1	yes	characteristic
43	C₃₁×#546	C₂²	1	2	yes	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#532	—	2	1	no	—
46	C₃₁×#532	—	2	2	no	—
47	C₃₁×#532	C₂²	1	1	yes	characteristic
48	C₃₁×#532	C₂²	1	2	yes	complemented
49	C₃₁×#529	—	2	2	no	—
50	C₃₁×#529	C₂²	1	2	yes	—
51	C₃₁×#525	—	2	1	no	—
52	C₄×#41×C₃₁	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	2	yes	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
56	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₃₁×#117	—	2	1	no	—
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#496	C₂²	1	2	yes	—
62	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#490	C₂²	1	2	yes	complemented
64	C₃₁×#489	C₂²	1	2	yes	—
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#476	C₂²	1	1	yes	characteristic
77	C₃₁×#476	C₂²	1	1	yes	characteristic
78	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#475	C₂²	1	2	yes	complemented
80	C₃₁×#474	C₂²	1	2	yes	—
81	C₃₁×#468	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	—
83	C₃₁×#466	C₂²	1	2	yes	—
84	C₃₁×#466	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#460	C₂²	1	2	yes	complemented
92	C₃₁×#459	C₂²	1	1	yes	characteristic
93	C₃₁×#459	C₂²	1	1	yes	characteristic
94	C₃₁×#459	C₂²	1	2	yes	—
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#452	C₂²	1	2	yes	complemented
97	C₃₁×#449	C₂²	1	2	yes	—
98	C₃₁×#449	C₂²	1	2	yes	—
99	C₃₁×#449	C₂²	1	2	yes	—
100	C₃₁×#447	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	—
105	C₃₁×#442	C₂²	1	2	yes	—
106	C₃₁×#442	C₂²	1	1	yes	characteristic
107	C₃₁×#442	C₂²	1	1	yes	characteristic
108	C₃₁×#441	C₂²	1	2	yes	complemented
109	C₃₁×#441	C₂²	1	2	yes	complemented
110	C₃₁×#440	C₂²	1	1	yes	characteristic
111	C₃₁×#440	C₂²	1	2	yes	—
112	C₃₁×#440	C₂²	1	1	yes	characteristic
113	C₃₁×#440	C₂²	1	2	yes	complemented
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₃₁×#440	C₂²	1	2	yes	complemented
116	C₃₁×#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#435	C₂²	1	2	yes	—
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#432	C₂²	1	1	yes	characteristic
126	C₃₁×#432	C₂²	1	2	yes	complemented
127	C₃₁×#428	C₂²	1	1	yes	characteristic
128	C₃₁×#427	C₂²	1	2	yes	complemented
129	C₃₁×#418	C₂²	1	1	yes	characteristic
130	C₃₁×#417	C₂²	1	1	yes	characteristic
131	C₃₁×#416	C₂²	1	2	yes	—
132	C₃₁×#416	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₃₁	—	2	1	no	—
144	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
145	C₃₁×#135	—	2	8	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	—	2	2	no	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×#127	—	2	2	no	—
167	C₃₁×#127	—	2	1	no	—
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#127	C₂³	1	2	yes	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	C₂³	1	2	yes	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×#121	—	2	1	no	—
194	C₃₁×#121	—	2	1	no	—
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	1	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	—	2	2	no	—
205	C₃₁×#121	C₂³	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×#120	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
213	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	1	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	2	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	2	no	—
232	C₄×D₄×C₃₁	D₄	1	2	yes	—
233	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	2	no	—
255	C₃₁×#117	D₄	1	1	yes	characteristic
256	C₃₁×#117	D₄	1	2	yes	—
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₃₁×#117	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
269	C₂×C₄²×C₃₁	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	1	yes	characteristic
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	1	yes	characteristic
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	1	yes	characteristic
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₂⁴×C₃₁	—	2	1	no	—
315	#41×C₃₁	—	2	4	no	—
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	2	4	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	2	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	4	1	no	—
322	#41×C₃₁	—	4	4	no	—
323	#41×C₃₁	—	8	2	no	—
324	#41×C₃₁	—	8	4	no	—
325	C₂×Q₈×C₃₁	—	2	1	no	—
326	C₂×Q₈×C₃₁	—	2	2	no	—
327	C₂×Q₈×C₃₁	—	2	1	no	—
328	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	1	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	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	1	no	—
344	C₂×D₄×C₃₁	—	4	1	no	—
345	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
350	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	2	no	—
364	C₂²×C₄×C₃₁	—	4	4	no	—
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
369	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
371	Q₁₆×C₃₁	—	2	4	no	—
372	SD₁₆×C₃₁	—	2	2	no	—
373	SD₁₆×C₃₁	—	2	4	no	—
374	SD₁₆×C₃₁	—	4	2	no	—
375	SD₁₆×C₃₁	—	4	2	no	—
376	SD₁₆×C₃₁	#41	1	4	yes	complemented
377	D₈×C₃₁	—	2	4	no	—
378	D₈×C₃₁	—	2	2	no	—
379	D₈×C₃₁	—	2	2	no	—
380	D₈×C₃₁	—	4	2	no	—
381	M₁₆×C₃₁	—	2	2	no	—
382	M₁₆×C₃₁	—	4	1	no	—
383	C₂×C₈×C₃₁	—	2	4	no	—
384	C₂×C₈×C₃₁	—	4	2	no	—
385	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	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	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	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	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	2	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	—	2	1	no	—
447	C₄²×C₃₁	C₂×D₄	1	2	yes	—
448	C₄²×C₃₁	C₂×D₄	1	2	yes	—
449	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₃₁	C₂⁴	1	2	yes	—
454	#61459	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	2	1	no	—
457	C₂³×C₃₁	—	2	1	no	—
458	C₂³×C₃₁	—	2	2	no	—
459	C₂³×C₃₁	—	4	2	no	—
460	C₂³×C₃₁	—	4	2	no	—
461	C₂³×C₃₁	—	8	1	no	—
462	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
463	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
464	Q₈×C₃₁	—	2	2	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	2	no	—
467	Q₈×C₃₁	—	2	2	no	—
468	Q₈×C₃₁	—	8	1	no	—
469	Q₈×C₃₁	—	8	2	no	—
470	Q₈×C₃₁	—	8	1	no	—
471	Q₈×C₃₁	C₂×#41	1	2	yes	—
472	D₄×C₃₁	—	2	2	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	2	1	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	4	4	no	—
483	D₄×C₃₁	—	4	2	no	—
484	D₄×C₃₁	—	4	4	no	—
485	D₄×C₃₁	—	4	4	no	—
486	D₄×C₃₁	—	4	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	1	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	2	no	—
491	D₄×C₃₁	—	8	2	no	—
492	D₄×C₃₁	—	8	2	no	—
493	D₄×C₃₁	C₂×#41	1	2	yes	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	2	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	4	2	no	—
509	C₂×C₄×C₃₁	—	4	1	no	—
510	C₂×C₄×C₃₁	—	4	4	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	4	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	4	4	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	4	4	no	—
518	C₂×C₄×C₃₁	—	4	2	no	—
519	C₂×C₄×C₃₁	—	4	2	no	—
520	C₂×C₄×C₃₁	—	4	2	no	—
521	C₂×C₄×C₃₁	—	4	2	no	—
522	C₂×C₄×C₃₁	—	8	2	no	—
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
532	C₈×C₃₁	—	2	2	no	—
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	1	no	—
535	C₈×C₃₁	—	2	2	no	—
536	C₈×C₃₁	—	2	1	no	—
537	C₈×C₃₁	C₂×#41	1	2	yes	—
538	#3483	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3348	C₂×C₃₁	1	2	yes	complemented
545	#3341	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3319	C₂×C₃₁	1	2	yes	complemented
547	#3317	C₂×C₃₁	1	2	yes	complemented
548	#3305	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3284	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3268	C₂×C₃₁	1	2	yes	complemented
552	#3182	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3180	C₂×C₃₁	1	2	yes	complemented
554	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3115	C₂×C₃₁	1	2	yes	complemented
556	#3111	C₂×C₃₁	1	2	yes	complemented
557	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
559	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#2943	C₂×C₃₁	1	2	yes	complemented
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	2	1	no	—
565	C₂²×C₃₁	—	2	2	no	—
566	C₂²×C₃₁	—	2	1	no	—
567	C₂²×C₃₁	—	2	2	no	—
568	C₂²×C₃₁	—	4	1	no	—
569	C₂²×C₃₁	—	4	1	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	1	no	—
574	C₂²×C₃₁	—	4	2	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	4	1	no	—
577	C₂²×C₃₁	—	4	2	no	—
578	C₂²×C₃₁	—	4	1	no	—
579	C₂²×C₃₁	—	8	4	no	—
580	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
581	C₄×C₃₁	—	2	1	no	—
582	C₄×C₃₁	—	2	2	no	—
583	C₄×C₃₁	—	2	1	no	—
584	C₄×C₃₁	—	2	2	no	—
585	C₄×C₃₁	—	2	1	no	—
586	C₄×C₃₁	—	2	2	no	—
587	C₄×C₃₁	—	2	1	no	—
588	C₄×C₃₁	—	2	2	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	2	no	—
591	C₄×C₃₁	—	4	2	no	—
592	C₄×C₃₁	—	4	2	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	1	no	—
595	C₄×C₃₁	—	4	1	no	—
596	C₄×C₃₁	#575	1	2	yes	—
597	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
598	C₄×C₃₁	#585	1	1	yes	characteristic
599	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
600	C₂×#135	C₂²×C₃₁	1	2	yes	—
601	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#556	C₂²×C₃₁	1	1	yes	characteristic
603	#555	—	2	2	no	—
604	#555	—	2	1	no	—
605	#555	C₂²×C₃₁	1	1	yes	characteristic
606	#555	C₂²×C₃₁	1	2	yes	—
607	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	#554	C₂²×C₃₁	1	1	yes	characteristic
609	#553	—	2	1	no	—
610	#552	—	2	1	no	—
611	#552	C₂²×C₃₁	1	2	yes	—
612	#551	—	2	2	no	—
613	#550	—	2	1	no	—
614	#550	C₂²×C₃₁	1	2	yes	—
615	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#547	C₂²×C₃₁	1	1	yes	characteristic
618	#546	C₂²×C₃₁	1	2	yes	—
619	#533	C₂²×C₃₁	1	1	yes	characteristic
620	#532	—	2	1	no	—
621	#532	—	2	2	no	—
622	#532	C₂²×C₃₁	1	1	yes	characteristic
623	#532	C₂²×C₃₁	1	2	yes	complemented
624	#529	—	2	2	no	—
625	#529	C₂²×C₃₁	1	2	yes	—
626	#525	—	2	1	no	—
627	C₄×#41	—	2	1	no	—
628	C₄×#41	C₂²×C₃₁	1	2	yes	—
629	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
630	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
631	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
632	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
633	C₂×#117	—	2	1	no	—
634	#501	C₂²×C₃₁	1	2	yes	complemented
635	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#496	C₂²×C₃₁	1	2	yes	—
637	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#490	C₂²×C₃₁	1	2	yes	complemented
639	#489	C₂²×C₃₁	1	2	yes	—
640	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#485	C₂²×C₃₁	1	2	yes	—
643	#485	C₂²×C₃₁	1	2	yes	complemented
644	#482	C₂²×C₃₁	1	2	yes	—
645	#482	C₂²×C₃₁	1	2	yes	complemented
646	#482	C₂²×C₃₁	1	2	yes	complemented
647	#481	C₂²×C₃₁	1	2	yes	—
648	#479	C₂²×C₃₁	1	2	yes	complemented
649	#478	C₂²×C₃₁	1	2	yes	complemented
650	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#476	C₂²×C₃₁	1	1	yes	characteristic
652	#476	C₂²×C₃₁	1	1	yes	characteristic
653	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#475	C₂²×C₃₁	1	2	yes	complemented
655	#474	C₂²×C₃₁	1	2	yes	—
656	#468	C₂²×C₃₁	1	2	yes	—
657	#468	C₂²×C₃₁	1	2	yes	—
658	#466	C₂²×C₃₁	1	2	yes	—
659	#466	C₂²×C₃₁	1	2	yes	—
660	#465	C₂²×C₃₁	1	2	yes	complemented
661	#465	C₂²×C₃₁	1	2	yes	complemented
662	#464	C₂²×C₃₁	1	2	yes	—
663	#463	C₂²×C₃₁	1	2	yes	—
664	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#460	C₂²×C₃₁	1	2	yes	complemented
667	#459	C₂²×C₃₁	1	1	yes	characteristic
668	#459	C₂²×C₃₁	1	1	yes	characteristic
669	#459	C₂²×C₃₁	1	2	yes	—
670	#452	C₂²×C₃₁	1	2	yes	—
671	#452	C₂²×C₃₁	1	2	yes	complemented
672	#449	C₂²×C₃₁	1	2	yes	—
673	#449	C₂²×C₃₁	1	2	yes	—
674	#449	C₂²×C₃₁	1	2	yes	—
675	#447	C₂²×C₃₁	1	2	yes	—
676	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#442	C₂²×C₃₁	1	2	yes	—
679	#442	C₂²×C₃₁	1	2	yes	—
680	#442	C₂²×C₃₁	1	2	yes	—
681	#442	C₂²×C₃₁	1	1	yes	characteristic
682	#442	C₂²×C₃₁	1	1	yes	characteristic
683	#441	C₂²×C₃₁	1	2	yes	complemented
684	#441	C₂²×C₃₁	1	2	yes	complemented
685	#440	C₂²×C₃₁	1	1	yes	characteristic
686	#440	C₂²×C₃₁	1	2	yes	—
687	#440	C₂²×C₃₁	1	1	yes	characteristic
688	#440	C₂²×C₃₁	1	2	yes	complemented
689	#440	C₂²×C₃₁	1	2	yes	complemented
690	#440	C₂²×C₃₁	1	2	yes	complemented
691	#440	C₂²×C₃₁	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
693	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
694	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
695	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
696	#435	C₂²×C₃₁	1	2	yes	—
697	#435	C₂²×C₃₁	1	2	yes	—
698	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	#432	C₂²×C₃₁	1	1	yes	characteristic
701	#432	C₂²×C₃₁	1	2	yes	complemented
702	#428	C₂²×C₃₁	1	1	yes	characteristic
703	#427	C₂²×C₃₁	1	2	yes	complemented
704	#418	C₂²×C₃₁	1	1	yes	characteristic
705	#417	C₂²×C₃₁	1	1	yes	characteristic
706	#416	C₂²×C₃₁	1	2	yes	—
707	#416	C₂²×C₃₁	1	2	yes	complemented
708	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
709	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
710	C₂×C₃₁	—	4	2	no	—
711	C₂×C₃₁	—	4	1	no	—
712	C₂×C₃₁	—	4	2	no	—
713	C₂×C₃₁	—	8	1	no	—
714	C₂×C₃₁	—	8	2	no	—
715	C₂×C₃₁	—	8	1	no	—
716	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
717	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
718	C₂×C₃₁	#3585	1	1	yes	characteristic
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	2	no	—
722	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
723	C₂×#41	C₂³×C₃₁	1	2	yes	—
724	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×#41	C₂³×C₃₁	1	2	yes	—
726	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
727	C₂³×C₄	—	2	1	no	—
728	AGL(1,ℤ/8)	—	2	4	no	—
729	#135	—	2	8	no	—
730	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
736	C₂×D₈	C₂³×C₃₁	1	2	yes	—
737	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₃₁	1	2	yes	—
740	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
742	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
743	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	2	2	no	—
746	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
749	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
750	#127	—	2	2	no	—
751	#127	—	2	1	no	—
752	#127	C₂³×C₃₁	1	1	yes	characteristic
753	#127	C₂³×C₃₁	1	2	yes	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	1	no	—
759	#125	C₂³×C₃₁	1	2	yes	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	1	no	—
765	#124	—	2	2	no	—
766	#124	C₂³×C₃₁	1	2	yes	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
777	#121	—	2	1	no	—
778	#121	—	2	1	no	—
779	#121	—	2	2	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	C₂³×C₃₁	1	2	yes	—
790	#121	C₂³×C₃₁	1	2	yes	—
791	#121	C₂³×C₃₁	1	2	yes	—
792	#121	C₂³×C₃₁	1	2	yes	—
793	#120	—	2	2	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
799	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
801	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
802	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	D₄×C₃₁	1	2	yes	—
817	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₃₁	1	2	yes	—
824	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₃₁	1	2	yes	—
826	C₄×D₄	C₂³×C₃₁	1	2	yes	—
827	C₄×D₄	C₂³×C₃₁	1	2	yes	—
828	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	—	2	2	no	—
833	#117	—	2	1	no	—
834	#117	—	2	2	no	—
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	D₄×C₃₁	1	1	yes	characteristic
840	#117	D₄×C₃₁	1	2	yes	—
841	#117	C₂³×C₃₁	1	2	yes	—
842	#117	C₂³×C₃₁	1	1	yes	characteristic
843	#117	C₂³×C₃₁	1	2	yes	—
844	C₂×C₄⋊C₄	—	2	1	no	—
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	—	2	1	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₄²	—	2	2	no	—
850	C₂×C₄²	—	2	1	no	—
851	C₂×C₄²	—	2	2	no	—
852	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
853	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
854	#107	C₂³×C₃₁	1	1	yes	characteristic
855	#107	C₂³×C₃₁	1	2	yes	—
856	#107	C₂³×C₃₁	1	1	yes	characteristic
857	#107	C₂³×C₃₁	1	2	yes	—
858	#107	C₂³×C₃₁	1	2	yes	—
859	#106	C₂³×C₃₁	1	2	yes	—
860	#106	C₂³×C₃₁	1	2	yes	—
861	#106	C₂³×C₃₁	1	1	yes	characteristic
862	#106	C₂³×C₃₁	1	1	yes	characteristic
863	#106	C₂³×C₃₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
867	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
868	#103	C₂³×C₃₁	1	2	yes	—
869	#103	C₂³×C₃₁	1	2	yes	—
870	#103	C₂³×C₃₁	1	1	yes	characteristic
871	#103	C₂³×C₃₁	1	2	yes	—
872	#103	C₂³×C₃₁	1	1	yes	characteristic
873	#103	C₂³×C₃₁	1	2	yes	—
874	#103	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
880	#102	C₂³×C₃₁	1	1	yes	characteristic
881	#102	C₂³×C₃₁	1	1	yes	characteristic
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	1	yes	characteristic
884	#102	C₂³×C₃₁	1	2	yes	—
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
891	#97	C₂³×C₃₁	1	1	yes	characteristic
892	#97	C₂³×C₃₁	1	2	yes	—
893	#97	C₂³×C₃₁	1	2	yes	—
894	#97	C₂³×C₃₁	1	2	yes	—
895	#97	C₂³×C₃₁	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
898	C₃₁	#61459	1	1	yes	characteristic, direct product factor, Sylow
899	C₂⁴	—	2	1	no	—
900	#41	—	2	4	no	—
901	#41	—	2	2	no	—
902	#41	—	2	4	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	1	no	—
907	#41	—	4	4	no	—
908	#41	—	8	2	no	—
909	#41	—	8	4	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	4	1	no	—
930	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
931	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
932	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	4	4	no	—
950	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
951	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
953	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
954	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
956	Q₁₆	—	2	4	no	—
957	SD₁₆	—	2	2	no	—
958	SD₁₆	—	2	4	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	#41×C₃₁	1	4	yes	complemented
962	D₈	—	2	4	no	—
963	D₈	—	2	2	no	—
964	D₈	—	2	2	no	—
965	D₈	—	4	2	no	—
966	M₁₆	—	2	2	no	—
967	M₁₆	—	4	1	no	—
968	C₂×C₈	—	2	4	no	—
969	C₂×C₈	—	4	2	no	—
970	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
974	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
975	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	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	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1033	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1034	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₃₁	1	2	yes	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	4	2	no	—
1044	C₂³	—	4	2	no	—
1045	C₂³	—	8	1	no	—
1046	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1047	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	8	1	no	—
1053	Q₈	—	8	2	no	—
1054	Q₈	—	8	1	no	—
1055	Q₈	C₂×#41×C₃₁	1	2	yes	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	4	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	1	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	C₂×#41×C₃₁	1	2	yes	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	4	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	4	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1115	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1116	C₈	—	2	2	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₈	—	2	1	no	—
1121	C₈	C₂×#41×C₃₁	1	2	yes	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	8	4	no	—
1141	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	2	no	—
1145	C₄	—	2	1	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	2	no	—
1157	C₄	C₃₁×#575	1	2	yes	—
1158	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1159	C₄	C₃₁×#585	1	1	yes	characteristic
1160	C₂	—	4	1	no	—
1161	C₂	—	4	2	no	—
1162	C₂	—	4	2	no	—
1163	C₂	—	8	1	no	—
1164	C₂	—	8	1	no	—
1165	C₂	—	8	2	no	—
1166	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1167	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1168	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3483	C₂	semidirect
2. C₃₁×#3475	C₂	semidirect
3. C₃₁×#3397	C₂	semidirect
4. C₃₁×#3385	C₂	semidirect
5. C₃₁×#3369	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3348	C₂	semidirect
8. C₃₁×#3341	C₂	semidirect
9. C₃₁×#3319	C₂	semidirect
10. C₃₁×#3317	C₂	semidirect
11. C₃₁×#3305	C₂	semidirect
12. C₃₁×#3303	C₂	semidirect
13. C₃₁×#3284	C₂	semidirect
14. C₃₁×#3268	C₂	semidirect
15. C₃₁×#3182	C₂	semidirect
16. C₃₁×#3180	C₂	semidirect
17. C₃₁×#3116	C₂	semidirect
18. C₃₁×#3115	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#3109	C₂	semidirect
21. C₃₁×#2970	C₂	semidirect
22. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
23. C₃₁×#2943	C₂	semidirect
26. Q₈²×C₃₁	C₂²	semidirect
32. C₃₁×#555	C₂²	semidirect
40. C₃₁×#550	C₂²	semidirect
41. C₃₁×#550	C₂²	semidirect
48. C₃₁×#532	C₂²	semidirect
56. C₄×#41×C₃₁	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#500	C₂²	semidirect
62. C₃₁×#492	C₂²	semidirect
63. C₃₁×#490	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
85. C₃₁×#465	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
91. C₃₁×#460	C₂²	semidirect
96. C₃₁×#452	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
108. C₃₁×#441	C₂²	semidirect
109. C₃₁×#441	C₂²	semidirect
113. C₃₁×#440	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₃₁×#440	C₂²	semidirect
116. C₃₁×#440	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
128. C₃₁×#427	C₂²	semidirect
132. C₃₁×#416	C₂²	semidirect
134. C₂×C₃₁×#97	C₂²	semidirect
376. SD₁₆×C₃₁	#41	semidirect
454. #61459	C₃₁	direct (N × H)
538. #3483	C₂×C₃₁	semidirect
539. #3475	C₂×C₃₁	semidirect
540. #3397	C₂×C₃₁	semidirect
541. #3385	C₂×C₃₁	semidirect
542. #3369	C₂×C₃₁	semidirect
543. #3366	C₂×C₃₁	semidirect
544. #3348	C₂×C₃₁	semidirect
545. #3341	C₂×C₃₁	semidirect
546. #3319	C₂×C₃₁	semidirect
547. #3317	C₂×C₃₁	semidirect
548. #3305	C₂×C₃₁	semidirect
549. #3303	C₂×C₃₁	semidirect
550. #3284	C₂×C₃₁	semidirect
551. #3268	C₂×C₃₁	semidirect
552. #3182	C₂×C₃₁	semidirect
553. #3180	C₂×C₃₁	semidirect
554. #3116	C₂×C₃₁	semidirect
555. #3115	C₂×C₃₁	semidirect
556. #3111	C₂×C₃₁	semidirect
557. #3109	C₂×C₃₁	semidirect
558. #2970	C₂×C₃₁	semidirect
559. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
560. #2943	C₂×C₃₁	semidirect
601. Q₈²	C₂²×C₃₁	semidirect
607. #555	C₂²×C₃₁	semidirect
615. #550	C₂²×C₃₁	semidirect
616. #550	C₂²×C₃₁	semidirect
623. #532	C₂²×C₃₁	semidirect
631. C₄×#41	C₂²×C₃₁	semidirect
634. #501	C₂²×C₃₁	semidirect
635. #500	C₂²×C₃₁	semidirect
637. #492	C₂²×C₃₁	semidirect
638. #490	C₂²×C₃₁	semidirect
640. #487	C₂²×C₃₁	semidirect
641. #486	C₂²×C₃₁	semidirect
643. #485	C₂²×C₃₁	semidirect
645. #482	C₂²×C₃₁	semidirect
646. #482	C₂²×C₃₁	semidirect
648. #479	C₂²×C₃₁	semidirect
649. #478	C₂²×C₃₁	semidirect
650. #477	C₂²×C₃₁	semidirect
653. #476	C₂²×C₃₁	semidirect
654. #475	C₂²×C₃₁	semidirect
660. #465	C₂²×C₃₁	semidirect
661. #465	C₂²×C₃₁	semidirect
664. #462	C₂²×C₃₁	semidirect
665. #461	C₂²×C₃₁	semidirect
666. #460	C₂²×C₃₁	semidirect
671. #452	C₂²×C₃₁	semidirect
676. #446	C₂²×C₃₁	semidirect
677. #446	C₂²×C₃₁	semidirect
683. #441	C₂²×C₃₁	semidirect
684. #441	C₂²×C₃₁	semidirect
688. #440	C₂²×C₃₁	semidirect
689. #440	C₂²×C₃₁	semidirect
690. #440	C₂²×C₃₁	semidirect
691. #440	C₂²×C₃₁	semidirect
698. C₈×D₄	C₂²×C₃₁	semidirect
699. C₈×D₄	C₂²×C₃₁	semidirect
701. #432	C₂²×C₃₁	semidirect
703. #427	C₂²×C₃₁	semidirect
707. #416	C₂²×C₃₁	semidirect
709. C₂×#97	C₂²×C₃₁	semidirect
898. C₃₁	#61459	direct (N × H)
961. SD₁₆	#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×#3483	2
C₃₁×#3475	2
C₃₁×#3397	2
C₃₁×#3385	2
C₃₁×#3369	2
C₃₁×#3366	2
C₃₁×#3348	2
C₃₁×#3341	2
C₃₁×#3319	2
C₃₁×#3317	2
C₃₁×#3305	2
C₃₁×#3303	2
C₃₁×#3284	2
C₃₁×#3268	2
C₃₁×#3182	2
C₃₁×#3180	2
C₃₁×#3116	2
C₃₁×#3115	2
C₃₁×#3111	2
C₃₁×#3109	2
C₃₁×#2970	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₃₁×#2943	2
#61459	31

Subgroups — C31×#61459 #21518218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61459 #21518218