Subgroups — C₃₁×#61493 #21518252

Order 7936.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3303	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
23	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
26	C₃₁×#559	C₂²	1	1	yes	characteristic
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#556	C₂²	1	1	yes	characteristic
29	C₃₁×#555	C₂²	1	2	yes	—
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#552	—	2	2	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	C₂²	1	2	yes	complemented
36	C₃₁×#551	—	2	2	no	—
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#548	—	2	1	no	—
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#547	C₂²	1	2	yes	complemented
41	C₃₁×#546	—	2	1	no	—
42	C₃₁×#546	C₂²	1	2	yes	—
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#541	C₂²	1	2	yes	complemented
46	C₃₁×#539	—	2	2	no	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×#125	—	2	1	no	—
54	C₂×C₃₁×#124	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	complemented
56	C₃₁×#518	C₂²	1	2	yes	—
57	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
58	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#497	C₂²	1	2	yes	complemented
62	C₃₁×#492	C₂²	1	1	yes	characteristic
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#487	C₂²	1	2	yes	complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#485	C₂²	1	2	yes	complemented
70	C₃₁×#483	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#478	C₂²	1	2	yes	—
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	2	yes	complemented
78	C₃₁×#475	C₂²	1	2	yes	complemented
79	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#470	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	—
83	C₃₁×#467	C₂²	1	2	yes	complemented
84	C₃₁×#465	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	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#461	C₂²	1	1	yes	characteristic
91	C₃₁×#461	C₂²	1	2	yes	—
92	C₃₁×#461	C₂²	1	2	yes	complemented
93	C₃₁×#460	C₂²	1	1	yes	characteristic
94	C₃₁×#459	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#452	C₂²	1	2	yes	complemented
97	C₃₁×#450	C₂²	1	2	yes	—
98	C₃₁×#450	C₂²	1	2	yes	—
99	C₃₁×#449	C₂²	1	2	yes	—
100	C₃₁×#449	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	complemented
105	C₃₁×#441	C₂²	1	2	yes	complemented
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	complemented
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
110	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#416	C₂²	1	1	yes	characteristic
130	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#416	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	—
133	C₃₁×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
142	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
143	C₃₁×#135	—	2	4	no	—
144	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	C₂³	1	2	yes	—
153	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#127	C₂³	1	1	yes	characteristic
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	D₄	1	2	yes	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	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	1	no	—
177	C₃₁×#125	D₄	1	1	yes	characteristic
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	D₄	1	1	yes	characteristic
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
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	D₄	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	D₄	1	1	yes	characteristic
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#120	—	2	2	no	—
217	C₃₁×#120	—	2	2	no	—
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
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	1	yes	characteristic
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	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	1	no	—
255	C₃₁×#117	C₂³	1	1	yes	characteristic
256	C₃₁×#117	C₂³	1	1	yes	characteristic
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	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	1	yes	characteristic
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	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	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	C₂⁴×C₃₁	—	2	2	no	—
315	#41×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	2	4	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	1	no	—
320	#41×C₃₁	—	4	1	no	—
321	#41×C₃₁	—	8	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	8	2	no	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₃₁	—	2	4	no	—
331	C₂×D₄×C₃₁	—	2	1	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	1	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	4	2	no	—
340	C₂×D₄×C₃₁	—	8	2	no	—
341	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
344	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₃₁	—	2	2	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	2	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
362	Q₁₆×C₃₁	—	2	2	no	—
363	Q₁₆×C₃₁	—	4	2	no	—
364	SD₁₆×C₃₁	—	2	2	no	—
365	SD₁₆×C₃₁	—	2	2	no	—
366	SD₁₆×C₃₁	—	2	4	no	—
367	SD₁₆×C₃₁	—	2	4	no	—
368	SD₁₆×C₃₁	—	4	2	no	—
369	SD₁₆×C₃₁	—	4	2	no	—
370	D₈×C₃₁	—	2	4	no	—
371	D₈×C₃₁	#41	1	4	yes	complemented
372	M₁₆×C₃₁	—	2	4	no	—
373	C₂×C₈×C₃₁	—	2	2	no	—
374	C₂×C₈×C₃₁	—	4	1	no	—
375	C₂×C₈×C₃₁	—	4	2	no	—
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
381	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
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	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	1	no	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
451	C₄²×C₃₁	C₂⁴	1	2	yes	—
452	#61493	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	1	no	—
455	C₂³×C₃₁	—	2	2	no	—
456	C₂³×C₃₁	—	4	4	no	—
457	C₂³×C₃₁	—	8	2	no	—
458	C₂³×C₃₁	—	8	2	no	—
459	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
460	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	2	1	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	2	no	—
467	Q₈×C₃₁	—	2	1	no	—
468	Q₈×C₃₁	—	4	2	no	—
469	Q₈×C₃₁	—	8	1	no	—
470	Q₈×C₃₁	—	8	2	no	—
471	D₄×C₃₁	—	2	2	no	—
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	—	4	2	no	—
477	D₄×C₃₁	—	4	4	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	4	4	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	8	1	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	C₂×#41	1	2	yes	—
486	D₄×C₃₁	C₂×#41	1	2	yes	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	4	1	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	4	4	no	—
505	C₂×C₄×C₃₁	—	4	2	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	8	1	no	—
508	C₂×C₄×C₃₁	—	8	1	no	—
509	C₂×C₄×C₃₁	—	8	2	no	—
510	C₂×C₄×C₃₁	—	8	2	no	—
511	C₂×C₄×C₃₁	—	8	2	no	—
512	C₂×C₄×C₃₁	—	8	2	no	—
513	C₂×C₄×C₃₁	—	8	2	no	—
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	1	yes	characteristic
517	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
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	C₂⁵	1	1	yes	characteristic
523	C₈×C₃₁	—	2	1	no	—
524	C₈×C₃₁	—	2	2	no	—
525	C₈×C₃₁	—	2	1	no	—
526	C₈×C₃₁	—	2	1	no	—
527	C₈×C₃₁	—	2	2	no	—
528	C₈×C₃₁	C₂×#41	1	2	yes	—
529	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3359	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3348	C₂×C₃₁	1	2	yes	complemented
537	#3303	C₂×C₃₁	1	2	yes	complemented
538	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3296	C₂×C₃₁	1	2	yes	complemented
540	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3272	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3267	C₂×C₃₁	1	2	yes	complemented
543	#3178	C₂×C₃₁	1	2	yes	complemented
544	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3125	C₂×C₃₁	1	2	yes	complemented
546	#3123	C₂×C₃₁	1	2	yes	complemented
547	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#2946	C₂×C₃₁	1	2	yes	complemented
551	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
552	C₂²×C₃₁	—	2	1	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	2	1	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	2	2	no	—
557	C₂²×C₃₁	—	2	2	no	—
558	C₂²×C₃₁	—	2	1	no	—
559	C₂²×C₃₁	—	2	2	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	2	no	—
565	C₂²×C₃₁	—	4	2	no	—
566	C₂²×C₃₁	—	4	2	no	—
567	C₂²×C₃₁	—	16	4	no	—
568	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
569	C₄×C₃₁	—	2	1	no	—
570	C₄×C₃₁	—	2	1	no	—
571	C₄×C₃₁	—	2	2	no	—
572	C₄×C₃₁	—	2	1	no	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	2	1	no	—
575	C₄×C₃₁	—	2	2	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	1	no	—
578	C₄×C₃₁	—	4	2	no	—
579	C₄×C₃₁	—	4	1	no	—
580	C₄×C₃₁	—	4	2	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	—	4	1	no	—
583	C₄×C₃₁	—	4	1	no	—
584	C₄×C₃₁	—	4	2	no	—
585	C₄×C₃₁	#577	1	2	yes	—
586	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
587	C₄×C₃₁	#585	1	1	yes	characteristic
588	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
589	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
590	#559	C₂²×C₃₁	1	1	yes	characteristic
591	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
592	#556	C₂²×C₃₁	1	1	yes	characteristic
593	#555	C₂²×C₃₁	1	2	yes	—
594	#554	C₂²×C₃₁	1	1	yes	characteristic
595	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
596	#553	—	2	1	no	—
597	#552	—	2	2	no	—
598	#552	—	2	1	no	—
599	#552	C₂²×C₃₁	1	2	yes	complemented
600	#551	—	2	2	no	—
601	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
602	#548	—	2	1	no	—
603	#547	C₂²×C₃₁	1	1	yes	characteristic
604	#547	C₂²×C₃₁	1	2	yes	complemented
605	#546	—	2	1	no	—
606	#546	C₂²×C₃₁	1	2	yes	—
607	D₄²	C₂²×C₃₁	1	1	yes	characteristic
608	#542	C₂²×C₃₁	1	2	yes	—
609	#541	C₂²×C₃₁	1	2	yes	complemented
610	#539	—	2	2	no	—
611	#538	—	2	2	no	—
612	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#532	C₂²×C₃₁	1	1	yes	characteristic
614	#529	—	2	1	no	—
615	#529	—	2	1	no	—
616	#529	C₂²×C₃₁	1	1	yes	characteristic
617	C₂×#125	—	2	1	no	—
618	C₂×#124	—	2	1	no	—
619	#520	C₂²×C₃₁	1	2	yes	complemented
620	#518	C₂²×C₃₁	1	2	yes	—
621	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
622	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#501	C₂²×C₃₁	1	2	yes	complemented
624	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#497	C₂²×C₃₁	1	2	yes	complemented
626	#492	C₂²×C₃₁	1	1	yes	characteristic
627	#488	C₂²×C₃₁	1	2	yes	complemented
628	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#487	C₂²×C₃₁	1	2	yes	complemented
630	#486	C₂²×C₃₁	1	1	yes	characteristic
631	#485	C₂²×C₃₁	1	2	yes	complemented
632	#485	C₂²×C₃₁	1	2	yes	complemented
633	#485	C₂²×C₃₁	1	2	yes	complemented
634	#483	C₂²×C₃₁	1	2	yes	complemented
635	#482	C₂²×C₃₁	1	2	yes	complemented
636	#481	C₂²×C₃₁	1	2	yes	—
637	#478	C₂²×C₃₁	1	2	yes	—
638	#478	C₂²×C₃₁	1	2	yes	complemented
639	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#476	C₂²×C₃₁	1	1	yes	characteristic
641	#476	C₂²×C₃₁	1	2	yes	complemented
642	#475	C₂²×C₃₁	1	2	yes	complemented
643	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#470	C₂²×C₃₁	1	2	yes	complemented
646	#468	C₂²×C₃₁	1	2	yes	—
647	#467	C₂²×C₃₁	1	2	yes	complemented
648	#465	C₂²×C₃₁	1	2	yes	—
649	#465	C₂²×C₃₁	1	2	yes	complemented
650	#465	C₂²×C₃₁	1	2	yes	complemented
651	#464	C₂²×C₃₁	1	2	yes	complemented
652	#463	C₂²×C₃₁	1	2	yes	complemented
653	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#461	C₂²×C₃₁	1	1	yes	characteristic
655	#461	C₂²×C₃₁	1	2	yes	—
656	#461	C₂²×C₃₁	1	2	yes	complemented
657	#460	C₂²×C₃₁	1	1	yes	characteristic
658	#459	C₂²×C₃₁	1	1	yes	characteristic
659	#452	C₂²×C₃₁	1	2	yes	—
660	#452	C₂²×C₃₁	1	2	yes	complemented
661	#450	C₂²×C₃₁	1	2	yes	—
662	#450	C₂²×C₃₁	1	2	yes	—
663	#449	C₂²×C₃₁	1	2	yes	—
664	#449	C₂²×C₃₁	1	2	yes	complemented
665	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#442	C₂²×C₃₁	1	2	yes	—
668	#442	C₂²×C₃₁	1	2	yes	complemented
669	#441	C₂²×C₃₁	1	2	yes	complemented
670	#440	C₂²×C₃₁	1	2	yes	—
671	#440	C₂²×C₃₁	1	2	yes	complemented
672	#440	C₂²×C₃₁	1	2	yes	complemented
673	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
676	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
677	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
680	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
682	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
683	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
684	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
685	#436	C₂²×C₃₁	1	1	yes	characteristic
686	#435	C₂²×C₃₁	1	2	yes	complemented
687	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
688	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
689	#433	C₂²×C₃₁	1	2	yes	complemented
690	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	#428	C₂²×C₃₁	1	2	yes	complemented
692	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#416	C₂²×C₃₁	1	1	yes	characteristic
694	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#416	C₂²×C₃₁	1	2	yes	complemented
696	C₂×#102	C₂²×C₃₁	1	2	yes	—
697	#405	C₂²×C₃₁	1	2	yes	complemented
698	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₂×C₃₁	—	4	1	no	—
700	C₂×C₃₁	—	4	2	no	—
701	C₂×C₃₁	—	4	2	no	—
702	C₂×C₃₁	—	4	2	no	—
703	C₂×C₃₁	—	8	2	no	—
704	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
705	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
706	C₂×C₃₁	#3584	1	1	yes	characteristic
707	C₂×#41	—	2	1	no	—
708	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
710	C₂×#41	C₂³×C₃₁	1	2	yes	—
711	C₂²×Q₈	—	2	1	no	—
712	C₂²×D₄	—	2	1	no	—
713	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
714	AGL(1,ℤ/8)	—	2	8	no	—
715	#135	—	2	4	no	—
716	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
724	C₂×D₈	C₂³×C₃₁	1	2	yes	—
725	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
727	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
730	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
732	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
735	#127	C₂³×C₃₁	1	1	yes	characteristic
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	D₄×C₃₁	1	2	yes	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	1	no	—
745	#125	—	2	1	no	—
746	#125	—	2	2	no	—
747	#125	—	2	2	no	—
748	#125	—	2	1	no	—
749	#125	D₄×C₃₁	1	1	yes	characteristic
750	#125	C₂³×C₃₁	1	2	yes	—
751	#124	—	2	1	no	—
752	#124	—	2	1	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	1	no	—
757	#124	D₄×C₃₁	1	1	yes	characteristic
758	#124	C₂³×C₃₁	1	2	yes	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	D₄×C₃₁	1	2	yes	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	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	D₄×C₃₁	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	D₄×C₃₁	1	1	yes	characteristic
786	#121	C₂³×C₃₁	1	2	yes	—
787	#121	C₂³×C₃₁	1	2	yes	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
798	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
799	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₃₁	1	2	yes	—
816	C₄×D₄	C₂³×C₃₁	1	2	yes	—
817	C₄×D₄	C₂³×C₃₁	1	2	yes	—
818	C₄×D₄	C₂³×C₃₁	1	2	yes	—
819	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₃₁	1	2	yes	—
821	#117	—	2	1	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	C₂³×C₃₁	1	1	yes	characteristic
828	#117	C₂³×C₃₁	1	1	yes	characteristic
829	#117	C₂³×C₃₁	1	2	yes	—
830	#117	C₂³×C₃₁	1	2	yes	—
831	C₂×C₄⋊C₄	—	2	2	no	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	—	2	2	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₂²⋊C₄	—	2	2	no	—
838	C₂×C₂²⋊C₄	—	2	2	no	—
839	C₂×C₄²	—	2	1	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
842	#107	C₂³×C₃₁	1	1	yes	characteristic
843	#107	C₂³×C₃₁	1	1	yes	characteristic
844	#107	C₂³×C₃₁	1	2	yes	—
845	#107	C₂³×C₃₁	1	2	yes	—
846	#106	C₂³×C₃₁	1	1	yes	characteristic
847	#106	C₂³×C₃₁	1	1	yes	characteristic
848	#106	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	2	yes	—
850	#106	C₂³×C₃₁	1	2	yes	—
851	#106	C₂³×C₃₁	1	2	yes	—
852	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
855	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	1	yes	characteristic
857	#103	C₂³×C₃₁	1	1	yes	characteristic
858	#103	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	2	yes	—
862	#103	C₂³×C₃₁	1	2	yes	—
863	#103	C₂³×C₃₁	1	2	yes	—
864	#103	C₂³×C₃₁	1	2	yes	—
865	#103	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	1	yes	characteristic
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	#102	C₂³×C₃₁	1	1	yes	characteristic
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
879	#97	C₂³×C₃₁	1	2	yes	—
880	#97	C₂³×C₃₁	1	2	yes	—
881	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₃₁	1	2	yes	—
886	C₃₁	#61493	1	1	yes	characteristic, direct product factor, Sylow
887	C₂⁴	—	2	2	no	—
888	#41	—	2	2	no	—
889	#41	—	2	2	no	—
890	#41	—	2	4	no	—
891	#41	—	4	2	no	—
892	#41	—	4	1	no	—
893	#41	—	4	1	no	—
894	#41	—	8	2	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	8	2	no	—
899	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
900	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂×D₄	—	2	4	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	8	2	no	—
914	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
915	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
916	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
917	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
935	Q₁₆	—	2	2	no	—
936	Q₁₆	—	4	2	no	—
937	SD₁₆	—	2	2	no	—
938	SD₁₆	—	2	2	no	—
939	SD₁₆	—	2	4	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	4	2	no	—
942	SD₁₆	—	4	2	no	—
943	D₈	—	2	4	no	—
944	D₈	#41×C₃₁	1	4	yes	complemented
945	M₁₆	—	2	4	no	—
946	C₂×C₈	—	2	2	no	—
947	C₂×C₈	—	4	1	no	—
948	C₂×C₈	—	4	2	no	—
949	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
953	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
954	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
977	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₃₁	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1021	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₃₁	1	2	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	4	4	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	—	8	2	no	—
1031	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1032	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	4	2	no	—
1041	Q₈	—	8	1	no	—
1042	Q₈	—	8	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	4	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	1	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	C₂×#41×C₃₁	1	2	yes	—
1058	D₄	C₂×#41×C₃₁	1	2	yes	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	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	—	2	2	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	4	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	8	1	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1093	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1094	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	C₂×#41×C₃₁	1	2	yes	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	1	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	16	4	no	—
1117	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	C₃₁×#577	1	2	yes	—
1135	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1136	C₄	C₃₁×#585	1	1	yes	characteristic
1137	C₂	—	4	2	no	—
1138	C₂	—	4	1	no	—
1139	C₂	—	4	2	no	—
1140	C₂	—	4	2	no	—
1141	C₂	—	8	2	no	—
1142	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1143	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1144	C₂	C₃₁×#3584	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3515	C₂	semidirect
2. C₃₁×#3514	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. C₃₁×#3361	C₂	semidirect
6. C₃₁×#3359	C₂	semidirect
7. C₃₁×#3356	C₂	semidirect
8. C₃₁×#3348	C₂	semidirect
9. C₃₁×#3303	C₂	semidirect
10. C₃₁×#3302	C₂	semidirect
11. C₃₁×#3296	C₂	semidirect
12. C₃₁×#3295	C₂	semidirect
13. C₃₁×#3272	C₂	semidirect
14. C₃₁×#3267	C₂	semidirect
15. C₃₁×#3178	C₂	semidirect
16. C₃₁×#3167	C₂	semidirect
17. C₃₁×#3125	C₂	semidirect
18. C₃₁×#3123	C₂	semidirect
19. C₃₁×#3116	C₂	semidirect
20. C₃₁×#3115	C₂	semidirect
21. C₃₁×#2966	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₄×C₃₁×#135	C₂	semidirect
27. C₃₁×#557	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
40. C₃₁×#547	C₂²	semidirect
45. C₃₁×#541	C₂²	semidirect
48. C₃₁×#533	C₂²	semidirect
55. C₃₁×#520	C₂²	semidirect
58. C₄×#41×C₃₁	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#497	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#485	C₂²	semidirect
70. C₃₁×#483	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
77. C₃₁×#476	C₂²	semidirect
78. C₃₁×#475	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
83. C₃₁×#467	C₂²	semidirect
85. C₃₁×#465	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
92. C₃₁×#461	C₂²	semidirect
96. C₃₁×#452	C₂²	semidirect
100. C₃₁×#449	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
104. C₃₁×#442	C₂²	semidirect
105. C₃₁×#441	C₂²	semidirect
107. C₃₁×#440	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₄×Q₁₆×C₃₁	C₂²	semidirect
110. C₄×Q₁₆×C₃₁	C₂²	semidirect
114. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₃₁×#427	C₂²	semidirect
130. C₃₁×#416	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
371. D₈×C₃₁	#41	semidirect
452. #61493	C₃₁	direct (N × H)
529. #3515	C₂×C₃₁	semidirect
530. #3514	C₂×C₃₁	semidirect
531. #3400	C₂×C₃₁	semidirect
532. #3384	C₂×C₃₁	semidirect
533. #3361	C₂×C₃₁	semidirect
534. #3359	C₂×C₃₁	semidirect
535. #3356	C₂×C₃₁	semidirect
536. #3348	C₂×C₃₁	semidirect
537. #3303	C₂×C₃₁	semidirect
538. #3302	C₂×C₃₁	semidirect
539. #3296	C₂×C₃₁	semidirect
540. #3295	C₂×C₃₁	semidirect
541. #3272	C₂×C₃₁	semidirect
542. #3267	C₂×C₃₁	semidirect
543. #3178	C₂×C₃₁	semidirect
544. #3167	C₂×C₃₁	semidirect
545. #3125	C₂×C₃₁	semidirect
546. #3123	C₂×C₃₁	semidirect
547. #3116	C₂×C₃₁	semidirect
548. #3115	C₂×C₃₁	semidirect
549. #2966	C₂×C₃₁	semidirect
550. #2946	C₂×C₃₁	semidirect
551. C₄×#135	C₂×C₃₁	semidirect
591. #557	C₂²×C₃₁	semidirect
595. #554	C₂²×C₃₁	semidirect
599. #552	C₂²×C₃₁	semidirect
604. #547	C₂²×C₃₁	semidirect
609. #541	C₂²×C₃₁	semidirect
612. #533	C₂²×C₃₁	semidirect
619. #520	C₂²×C₃₁	semidirect
622. C₄×#41	C₂²×C₃₁	semidirect
623. #501	C₂²×C₃₁	semidirect
624. #498	C₂²×C₃₁	semidirect
625. #497	C₂²×C₃₁	semidirect
627. #488	C₂²×C₃₁	semidirect
628. #487	C₂²×C₃₁	semidirect
629. #487	C₂²×C₃₁	semidirect
631. #485	C₂²×C₃₁	semidirect
632. #485	C₂²×C₃₁	semidirect
633. #485	C₂²×C₃₁	semidirect
634. #483	C₂²×C₃₁	semidirect
635. #482	C₂²×C₃₁	semidirect
638. #478	C₂²×C₃₁	semidirect
639. #477	C₂²×C₃₁	semidirect
641. #476	C₂²×C₃₁	semidirect
642. #475	C₂²×C₃₁	semidirect
643. #475	C₂²×C₃₁	semidirect
644. #474	C₂²×C₃₁	semidirect
645. #470	C₂²×C₃₁	semidirect
647. #467	C₂²×C₃₁	semidirect
649. #465	C₂²×C₃₁	semidirect
650. #465	C₂²×C₃₁	semidirect
651. #464	C₂²×C₃₁	semidirect
652. #463	C₂²×C₃₁	semidirect
653. #462	C₂²×C₃₁	semidirect
656. #461	C₂²×C₃₁	semidirect
660. #452	C₂²×C₃₁	semidirect
664. #449	C₂²×C₃₁	semidirect
665. #446	C₂²×C₃₁	semidirect
666. C₈×Q₈	C₂²×C₃₁	semidirect
668. #442	C₂²×C₃₁	semidirect
669. #441	C₂²×C₃₁	semidirect
671. #440	C₂²×C₃₁	semidirect
672. #440	C₂²×C₃₁	semidirect
673. C₄×Q₁₆	C₂²×C₃₁	semidirect
674. C₄×Q₁₆	C₂²×C₃₁	semidirect
678. C₄×SD₁₆	C₂²×C₃₁	semidirect
679. C₄×SD₁₆	C₂²×C₃₁	semidirect
680. C₄×SD₁₆	C₂²×C₃₁	semidirect
681. C₄×SD₁₆	C₂²×C₃₁	semidirect
684. C₄×D₈	C₂²×C₃₁	semidirect
686. #435	C₂²×C₃₁	semidirect
688. C₈×D₄	C₂²×C₃₁	semidirect
689. #433	C₂²×C₃₁	semidirect
690. #432	C₂²×C₃₁	semidirect
691. #428	C₂²×C₃₁	semidirect
692. #427	C₂²×C₃₁	semidirect
694. #416	C₂²×C₃₁	semidirect
695. #416	C₂²×C₃₁	semidirect
697. #405	C₂²×C₃₁	semidirect
698. C₂×C₄×C₈	C₂²×C₃₁	semidirect
886. C₃₁	#61493	direct (N × H)
944. D₈	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3515	2
C₃₁×#3514	2
C₃₁×#3400	2
C₃₁×#3384	2
C₃₁×#3361	2
C₃₁×#3359	2
C₃₁×#3356	2
C₃₁×#3348	2
C₃₁×#3303	2
C₃₁×#3302	2
C₃₁×#3296	2
C₃₁×#3295	2
C₃₁×#3272	2
C₃₁×#3267	2
C₃₁×#3178	2
C₃₁×#3167	2
C₃₁×#3125	2
C₃₁×#3123	2
C₃₁×#3116	2
C₃₁×#3115	2
C₃₁×#2966	2
C₃₁×#2946	2
C₄×C₃₁×#135	2
#61493	31

Subgroups — C31×#61493 #21518252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61493 #21518252