Subgroups — C₃₁×#61972 #21518731

Order 7936.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3401	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3371	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3327	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3323	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3312	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3310	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3308	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3306	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3277	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3275	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3270	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3270	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3266	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3265	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3256	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3250	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3219	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3211	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3117	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3111	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
36	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#559	C₂²	1	1	yes	characteristic
39	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#556	—	2	1	no	—
41	C₃₁×#556	C₂²	1	1	yes	characteristic
42	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#555	—	2	1	no	—
44	C₃₁×#552	—	2	1	no	—
45	C₃₁×#552	—	2	1	no	—
46	C₃₁×#552	C₂²	1	1	yes	characteristic
47	C₃₁×#552	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#551	—	2	1	no	—
49	C₃₁×#551	—	2	1	no	—
50	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
51	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#548	C₂²	1	1	yes	characteristic
53	C₃₁×#548	C₂²	1	1	yes	characteristic
54	C₃₁×#548	C₂²	1	1	yes	characteristic
55	C₃₁×#548	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#547	—	2	1	no	—
57	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#546	—	2	1	no	—
59	C₃₁×#546	C₂²	1	1	yes	characteristic
60	C₃₁×#546	C₂²	1	1	yes	characteristic
61	D₄²×C₃₁	C₂²	1	1	yes	characteristic
62	C₃₁×#542	—	2	1	no	—
63	C₃₁×#538	—	2	1	no	—
64	C₃₁×#538	—	2	1	no	—
65	C₃₁×#533	—	2	1	no	—
66	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#532	C₂²	1	1	yes	characteristic
68	C₃₁×#529	—	2	1	no	—
69	C₃₁×#529	—	2	1	no	—
70	C₃₁×#529	C₂²	1	1	yes	characteristic
71	C₃₁×#529	C₂²	1	1	yes	characteristic
72	C₃₁×#529	C₂²	1	1	yes	characteristic
73	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
77	C₃₁×#518	—	2	1	no	—
78	C₄×#41×C₃₁	—	2	1	no	—
79	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
80	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#497	C₂²	1	1	yes	characteristic
84	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#496	C₂²	1	1	yes	characteristic
87	C₃₁×#495	C₂²	1	1	yes	characteristic
88	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#490	C₂²	1	1	yes	characteristic
91	C₃₁×#489	C₂²	1	1	yes	characteristic
92	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#488	C₂²	1	1	yes	characteristic
94	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#482	C₂²	1	1	yes	characteristic
99	C₃₁×#481	C₂²	1	1	yes	characteristic
100	C₃₁×#480	C₂²	1	1	yes	characteristic
101	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#478	C₂²	1	1	yes	characteristic
107	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#469	C₂²	1	1	yes	characteristic
115	C₃₁×#468	C₂²	1	1	yes	characteristic
116	C₃₁×#468	C₂²	1	1	yes	characteristic
117	C₃₁×#468	C₂²	1	1	yes	characteristic
118	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#466	C₂²	1	1	yes	characteristic
121	C₃₁×#465	C₂²	1	1	yes	characteristic
122	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#464	C₂²	1	1	yes	characteristic
124	C₃₁×#464	C₂²	1	1	yes	characteristic
125	C₃₁×#464	C₂²	1	1	yes	characteristic
126	C₃₁×#464	C₂²	1	1	yes	characteristic
127	C₃₁×#464	C₂²	1	1	yes	characteristic
128	C₃₁×#464	C₂²	1	1	yes	characteristic
129	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
136	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
138	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
139	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
140	C₃₁×#463	C₂²	1	1	yes	characteristic
141	C₃₁×#463	C₂²	1	1	yes	characteristic
142	C₃₁×#463	C₂²	1	1	yes	characteristic
143	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
144	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
145	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
146	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
147	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
148	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
149	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
150	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
151	C₃₁×#460	C₂²	1	1	yes	characteristic
152	C₃₁×#460	C₂²	1	1	yes	characteristic
153	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
154	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
155	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
156	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
157	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
158	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
159	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
160	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
161	C₃₁×#450	C₂²	1	1	yes	characteristic
162	C₃₁×#450	C₂²	1	1	yes	characteristic
163	C₃₁×#450	C₂²	1	1	yes	characteristic
164	C₃₁×#449	C₂²	1	1	yes	characteristic
165	C₃₁×#449	C₂²	1	1	yes	characteristic, complemented
166	C₃₁×#449	C₂²	1	1	yes	characteristic, complemented
167	C₃₁×#448	C₂²	1	1	yes	characteristic
168	C₃₁×#448	C₂²	1	1	yes	characteristic
169	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
170	C₃₁×#447	C₂²	1	1	yes	characteristic
171	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
172	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
173	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
174	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
175	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
176	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
177	C₃₁×#440	C₂²	1	1	yes	characteristic
178	C₃₁×#440	C₂²	1	1	yes	characteristic
179	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
180	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
181	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
182	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
183	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
184	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
185	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
186	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
187	C₃₁×#435	C₂²	1	1	yes	characteristic
188	C₃₁×#435	C₂²	1	1	yes	characteristic
189	C₃₁×#435	C₂²	1	1	yes	characteristic, complemented
190	C₃₁×#435	C₂²	1	1	yes	characteristic, complemented
191	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
192	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
193	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
194	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
195	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
197	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
198	C₃₁×#418	C₂²	1	1	yes	characteristic
199	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
200	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
201	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
202	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	—	2	1	no	—
204	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
205	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
209	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
210	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₃₁	—	2	1	no	—
213	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
214	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
215	C₃₁×#137	—	4	2	no	—
216	C₃₁×#137	—	4	2	no	—
217	C₃₁×#137	—	4	2	no	—
218	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
219	C₂×Q₁₆×C₃₁	—	4	2	no	—
220	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆×C₃₁	—	4	2	no	—
230	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
239	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
240	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
241	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
242	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
243	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
244	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
245	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
246	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
248	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
249	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
250	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
251	C₃₁×C₄⋊Q₈	—	2	1	no	—
252	C₃₁×C₄⋊Q₈	—	2	1	no	—
253	C₃₁×C₄⋊Q₈	—	2	1	no	—
254	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
255	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
256	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
257	C₃₁×#127	C₂³	1	1	yes	characteristic
258	C₃₁×#126	—	2	1	no	—
259	C₃₁×#126	—	2	1	no	—
260	C₃₁×#126	—	2	1	no	—
261	C₃₁×#126	—	2	1	no	—
262	C₃₁×#126	—	2	1	no	—
263	C₃₁×#126	—	2	1	no	—
264	C₃₁×#126	—	2	1	no	—
265	C₃₁×#126	—	2	1	no	—
266	C₃₁×#126	—	2	1	no	—
267	C₃₁×#126	—	2	1	no	—
268	C₃₁×#126	—	2	1	no	—
269	C₃₁×#125	—	2	1	no	—
270	C₃₁×#125	—	2	1	no	—
271	C₃₁×#125	—	2	1	no	—
272	C₃₁×#125	—	2	1	no	—
273	C₃₁×#125	—	2	1	no	—
274	C₃₁×#125	C₂³	1	1	yes	characteristic
275	C₃₁×#125	C₂³	1	1	yes	characteristic
276	C₃₁×#125	C₂³	1	1	yes	characteristic
277	C₃₁×#124	—	2	1	no	—
278	C₃₁×#124	—	2	1	no	—
279	C₃₁×#124	—	2	1	no	—
280	C₃₁×#124	—	2	1	no	—
281	C₃₁×#124	—	2	1	no	—
282	C₃₁×#124	—	2	1	no	—
283	C₃₁×#124	—	2	1	no	—
284	C₃₁×#124	—	2	1	no	—
285	C₃₁×#124	—	2	1	no	—
286	C₃₁×#124	C₂³	1	1	yes	characteristic
287	C₃₁×#124	C₂³	1	1	yes	characteristic
288	C₃₁×#124	C₂³	1	1	yes	characteristic
289	C₃₁×#124	C₂³	1	1	yes	characteristic
290	C₃₁×#124	C₂³	1	1	yes	characteristic
291	C₃₁×#124	C₂³	1	1	yes	characteristic
292	C₃₁×#124	C₂³	1	1	yes	characteristic
293	C₃₁×#124	C₂³	1	1	yes	characteristic
294	C₃₁×#124	C₂³	1	1	yes	characteristic
295	C₃₁×#123	—	2	1	no	—
296	C₃₁×#123	—	2	1	no	—
297	C₃₁×#123	—	2	1	no	—
298	C₃₁×#123	—	2	1	no	—
299	C₃₁×#123	—	2	1	no	—
300	C₃₁×#123	—	2	1	no	—
301	C₃₁×#123	—	2	1	no	—
302	C₃₁×#123	—	2	1	no	—
303	C₃₁×#123	—	2	1	no	—
304	C₃₁×#123	—	2	1	no	—
305	C₃₁×#123	—	2	1	no	—
306	C₃₁×#123	—	2	1	no	—
307	C₃₁×#123	—	2	1	no	—
308	C₃₁×C₂²⋊Q₈	—	2	1	no	—
309	C₃₁×C₂²⋊Q₈	—	2	1	no	—
310	C₃₁×C₂²⋊Q₈	—	2	1	no	—
311	C₃₁×C₂²⋊Q₈	—	2	1	no	—
312	C₃₁×C₂²⋊Q₈	—	2	1	no	—
313	C₃₁×C₂²⋊Q₈	—	2	1	no	—
314	C₃₁×C₂²⋊Q₈	—	2	1	no	—
315	C₃₁×C₂²⋊Q₈	—	2	1	no	—
316	C₃₁×C₂²⋊Q₈	—	2	1	no	—
317	C₃₁×C₂²⋊Q₈	—	2	1	no	—
318	C₃₁×C₂²⋊Q₈	—	2	1	no	—
319	C₃₁×C₂²⋊Q₈	—	2	1	no	—
320	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
321	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
322	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
323	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
325	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
326	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
327	C₃₁×#121	—	2	1	no	—
328	C₃₁×#121	—	2	1	no	—
329	C₃₁×#121	—	2	1	no	—
330	C₃₁×#121	—	2	1	no	—
331	C₃₁×#121	—	2	1	no	—
332	C₃₁×#121	—	2	1	no	—
333	C₃₁×#121	—	2	1	no	—
334	C₃₁×#121	—	2	1	no	—
335	C₃₁×#121	—	2	1	no	—
336	C₃₁×#121	C₂³	1	1	yes	characteristic
337	C₃₁×#121	C₂³	1	1	yes	characteristic
338	C₃₁×#121	C₂³	1	1	yes	characteristic
339	C₃₁×#121	C₂³	1	1	yes	characteristic
340	C₃₁×#121	C₂³	1	1	yes	characteristic
341	C₃₁×#120	—	2	1	no	—
342	C₃₁×#120	—	2	1	no	—
343	C₃₁×#120	—	2	1	no	—
344	C₃₁×#120	—	2	1	no	—
345	C₄×Q₈×C₃₁	—	2	1	no	—
346	C₄×Q₈×C₃₁	—	2	1	no	—
347	C₄×Q₈×C₃₁	—	2	1	no	—
348	C₄×Q₈×C₃₁	—	2	1	no	—
349	C₄×Q₈×C₃₁	—	2	1	no	—
350	C₄×Q₈×C₃₁	—	2	1	no	—
351	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
352	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
354	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
355	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
356	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
357	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
358	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
359	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
360	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
361	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
362	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
363	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₃₁	—	2	1	no	—
365	C₄×D₄×C₃₁	—	2	1	no	—
366	C₄×D₄×C₃₁	—	2	1	no	—
367	C₄×D₄×C₃₁	—	2	1	no	—
368	C₄×D₄×C₃₁	—	2	1	no	—
369	C₄×D₄×C₃₁	—	2	1	no	—
370	C₄×D₄×C₃₁	—	2	1	no	—
371	C₄×D₄×C₃₁	—	2	1	no	—
372	C₄×D₄×C₃₁	—	2	1	no	—
373	C₄×D₄×C₃₁	—	2	1	no	—
374	C₄×D₄×C₃₁	—	2	1	no	—
375	C₄×D₄×C₃₁	—	2	1	no	—
376	C₄×D₄×C₃₁	—	2	1	no	—
377	C₄×D₄×C₃₁	—	2	1	no	—
378	C₄×D₄×C₃₁	—	2	1	no	—
379	C₄×D₄×C₃₁	—	2	1	no	—
380	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
381	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
382	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
383	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
384	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
385	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
386	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
387	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
388	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
389	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
390	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
391	C₃₁×#117	—	2	1	no	—
392	C₃₁×#117	—	2	1	no	—
393	C₃₁×#117	—	2	1	no	—
394	C₃₁×#117	—	2	1	no	—
395	C₃₁×#117	—	2	1	no	—
396	C₃₁×#117	—	2	1	no	—
397	C₃₁×#117	—	2	1	no	—
398	C₃₁×#117	—	2	1	no	—
399	C₃₁×#117	—	2	1	no	—
400	C₃₁×#117	—	2	1	no	—
401	C₃₁×#117	—	2	1	no	—
402	C₃₁×#117	D₄	1	1	yes	characteristic
403	C₃₁×#117	D₄	1	1	yes	characteristic
404	C₃₁×#117	D₄	1	1	yes	characteristic
405	C₃₁×#117	C₂³	1	1	yes	characteristic
406	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
408	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
409	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
410	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
411	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂×C₄²×C₃₁	—	2	1	no	—
417	C₂×C₄²×C₃₁	—	2	1	no	—
418	C₂×C₄²×C₃₁	—	2	1	no	—
419	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
420	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
421	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
422	C₃₁×#107	C₂³	1	1	yes	characteristic
423	C₃₁×#107	C₂³	1	1	yes	characteristic
424	C₃₁×#107	C₂³	1	1	yes	characteristic
425	C₃₁×#107	C₂³	1	1	yes	characteristic
426	C₃₁×#106	C₂³	1	1	yes	characteristic
427	C₃₁×#106	C₂³	1	1	yes	characteristic
428	C₃₁×#106	C₂³	1	1	yes	characteristic
429	C₃₁×#106	C₂³	1	1	yes	characteristic
430	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
434	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
435	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
436	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
437	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
438	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
439	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#103	C₂³	1	1	yes	characteristic
449	C₃₁×#103	C₂³	1	1	yes	characteristic
450	C₃₁×#103	C₂³	1	1	yes	characteristic
451	C₃₁×#103	C₂³	1	1	yes	characteristic
452	C₃₁×#103	C₂³	1	1	yes	characteristic
453	C₃₁×#103	C₂³	1	1	yes	characteristic
454	C₃₁×#103	C₂³	1	1	yes	characteristic
455	C₃₁×#103	C₂³	1	1	yes	characteristic
456	C₃₁×#103	C₂³	1	1	yes	characteristic
457	C₃₁×#103	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×#102	C₂³	1	1	yes	characteristic
463	C₃₁×#102	C₂³	1	1	yes	characteristic
464	C₃₁×#102	C₂³	1	1	yes	characteristic
465	C₃₁×#102	C₂³	1	1	yes	characteristic
466	C₃₁×#102	C₂³	1	1	yes	characteristic
467	C₃₁×#102	C₂³	1	1	yes	characteristic
468	C₃₁×#102	C₂³	1	1	yes	characteristic
469	C₃₁×#102	C₂³	1	1	yes	characteristic
470	C₃₁×#102	C₂³	1	1	yes	characteristic
471	C₃₁×#102	C₂³	1	1	yes	characteristic
472	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
474	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
475	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
476	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
477	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
478	C₃₁×#97	C₂³	1	1	yes	characteristic
479	C₃₁×#97	C₂³	1	1	yes	characteristic
480	C₃₁×#97	C₂³	1	1	yes	characteristic
481	C₃₁×#97	C₂³	1	1	yes	characteristic
482	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
483	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
484	C₂⁴×C₃₁	—	2	1	no	—
485	C₂⁴×C₃₁	—	2	1	no	—
486	#41×C₃₁	—	2	2	no	—
487	#41×C₃₁	—	4	2	no	—
488	#41×C₃₁	—	4	1	no	—
489	#41×C₃₁	—	4	1	no	—
490	#41×C₃₁	—	4	1	no	—
491	#41×C₃₁	—	4	1	no	—
492	#41×C₃₁	—	4	1	no	—
493	#41×C₃₁	—	4	4	no	—
494	C₂×Q₈×C₃₁	—	2	1	no	—
495	C₂×Q₈×C₃₁	—	2	1	no	—
496	C₂×Q₈×C₃₁	—	2	1	no	—
497	C₂×Q₈×C₃₁	—	2	1	no	—
498	C₂×Q₈×C₃₁	—	2	1	no	—
499	C₂×Q₈×C₃₁	—	2	2	no	—
500	C₂×Q₈×C₃₁	—	2	2	no	—
501	C₂×Q₈×C₃₁	—	4	1	no	—
502	C₂×Q₈×C₃₁	—	4	1	no	—
503	C₂×Q₈×C₃₁	—	4	1	no	—
504	C₂×Q₈×C₃₁	—	4	1	no	—
505	C₂×Q₈×C₃₁	—	4	1	no	—
506	C₂×Q₈×C₃₁	—	4	1	no	—
507	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
508	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
509	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
510	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
511	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
512	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
513	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
514	C₂×D₄×C₃₁	—	2	1	no	—
515	C₂×D₄×C₃₁	—	2	1	no	—
516	C₂×D₄×C₃₁	—	2	1	no	—
517	C₂×D₄×C₃₁	—	2	1	no	—
518	C₂×D₄×C₃₁	—	2	1	no	—
519	C₂×D₄×C₃₁	—	2	1	no	—
520	C₂×D₄×C₃₁	—	2	1	no	—
521	C₂×D₄×C₃₁	—	2	1	no	—
522	C₂×D₄×C₃₁	—	2	1	no	—
523	C₂×D₄×C₃₁	—	2	1	no	—
524	C₂×D₄×C₃₁	—	2	1	no	—
525	C₂×D₄×C₃₁	—	2	1	no	—
526	C₂×D₄×C₃₁	—	4	1	no	—
527	C₂×D₄×C₃₁	—	4	1	no	—
528	C₂×D₄×C₃₁	—	4	1	no	—
529	C₂×D₄×C₃₁	—	4	1	no	—
530	C₂×D₄×C₃₁	—	4	4	no	—
531	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
532	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
533	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
534	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
535	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
536	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
537	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
538	C₂²×C₄×C₃₁	—	2	1	no	—
539	C₂²×C₄×C₃₁	—	2	1	no	—
540	C₂²×C₄×C₃₁	—	2	1	no	—
541	C₂²×C₄×C₃₁	—	2	1	no	—
542	C₂²×C₄×C₃₁	—	2	1	no	—
543	C₂²×C₄×C₃₁	—	2	1	no	—
544	C₂²×C₄×C₃₁	—	2	1	no	—
545	C₂²×C₄×C₃₁	—	2	1	no	—
546	C₂²×C₄×C₃₁	—	2	1	no	—
547	C₂²×C₄×C₃₁	—	2	1	no	—
548	C₂²×C₄×C₃₁	—	2	1	no	—
549	C₂²×C₄×C₃₁	—	2	1	no	—
550	C₂²×C₄×C₃₁	—	2	1	no	—
551	C₂²×C₄×C₃₁	—	2	1	no	—
552	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
553	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
554	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
555	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
556	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
557	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
558	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
559	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
560	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
561	Q₁₆×C₃₁	—	2	2	no	—
562	Q₁₆×C₃₁	—	2	2	no	—
563	Q₁₆×C₃₁	—	2	2	no	—
564	Q₁₆×C₃₁	—	4	1	no	—
565	Q₁₆×C₃₁	—	4	1	no	—
566	Q₁₆×C₃₁	—	4	1	no	—
567	Q₁₆×C₃₁	—	4	1	no	—
568	Q₁₆×C₃₁	—	4	1	no	—
569	Q₁₆×C₃₁	—	4	1	no	—
570	SD₁₆×C₃₁	—	2	2	no	—
571	SD₁₆×C₃₁	—	2	2	no	—
572	SD₁₆×C₃₁	—	2	2	no	—
573	SD₁₆×C₃₁	—	4	1	no	—
574	SD₁₆×C₃₁	—	4	1	no	—
575	SD₁₆×C₃₁	—	4	1	no	—
576	SD₁₆×C₃₁	—	4	1	no	—
577	SD₁₆×C₃₁	—	4	1	no	—
578	SD₁₆×C₃₁	—	4	1	no	—
579	SD₁₆×C₃₁	—	4	1	no	—
580	SD₁₆×C₃₁	—	4	1	no	—
581	SD₁₆×C₃₁	—	4	1	no	—
582	D₈×C₃₁	—	4	1	no	—
583	D₈×C₃₁	—	4	1	no	—
584	D₈×C₃₁	—	4	1	no	—
585	M₁₆×C₃₁	—	4	1	no	—
586	M₁₆×C₃₁	—	4	1	no	—
587	M₁₆×C₃₁	—	4	1	no	—
588	M₁₆×C₃₁	—	4	1	no	—
589	C₂×C₈×C₃₁	—	4	1	no	—
590	C₂×C₈×C₃₁	—	4	1	no	—
591	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
592	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
593	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
594	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
595	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
596	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
597	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
598	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
599	C₄⋊C₄×C₃₁	—	2	1	no	—
600	C₄⋊C₄×C₃₁	—	2	1	no	—
601	C₄⋊C₄×C₃₁	—	2	1	no	—
602	C₄⋊C₄×C₃₁	—	2	1	no	—
603	C₄⋊C₄×C₃₁	—	2	1	no	—
604	C₄⋊C₄×C₃₁	—	2	1	no	—
605	C₄⋊C₄×C₃₁	—	2	1	no	—
606	C₄⋊C₄×C₃₁	—	2	1	no	—
607	C₄⋊C₄×C₃₁	—	2	1	no	—
608	C₄⋊C₄×C₃₁	—	2	1	no	—
609	C₄⋊C₄×C₃₁	—	2	1	no	—
610	C₄⋊C₄×C₃₁	—	2	1	no	—
611	C₄⋊C₄×C₃₁	—	2	1	no	—
612	C₄⋊C₄×C₃₁	—	2	1	no	—
613	C₄⋊C₄×C₃₁	—	2	1	no	—
614	C₄⋊C₄×C₃₁	—	2	1	no	—
615	C₄⋊C₄×C₃₁	—	2	1	no	—
616	C₄⋊C₄×C₃₁	—	2	1	no	—
617	C₄⋊C₄×C₃₁	—	2	1	no	—
618	C₄⋊C₄×C₃₁	—	2	1	no	—
619	C₄⋊C₄×C₃₁	—	2	1	no	—
620	C₄⋊C₄×C₃₁	—	2	1	no	—
621	C₄⋊C₄×C₃₁	—	2	1	no	—
622	C₄⋊C₄×C₃₁	—	2	1	no	—
623	C₄⋊C₄×C₃₁	—	2	1	no	—
624	C₄⋊C₄×C₃₁	—	2	1	no	—
625	C₄⋊C₄×C₃₁	—	2	1	no	—
626	C₄⋊C₄×C₃₁	—	2	1	no	—
627	C₄⋊C₄×C₃₁	—	2	1	no	—
628	C₄⋊C₄×C₃₁	—	2	1	no	—
629	C₄⋊C₄×C₃₁	—	2	1	no	—
630	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
631	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
632	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
634	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
635	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
636	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
637	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
639	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
640	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
642	C₂²⋊C₄×C₃₁	—	2	1	no	—
643	C₂²⋊C₄×C₃₁	—	2	1	no	—
644	C₂²⋊C₄×C₃₁	—	2	1	no	—
645	C₂²⋊C₄×C₃₁	—	2	1	no	—
646	C₂²⋊C₄×C₃₁	—	2	1	no	—
647	C₂²⋊C₄×C₃₁	—	2	1	no	—
648	C₂²⋊C₄×C₃₁	—	2	1	no	—
649	C₂²⋊C₄×C₃₁	—	2	1	no	—
650	C₂²⋊C₄×C₃₁	—	2	1	no	—
651	C₂²⋊C₄×C₃₁	—	2	1	no	—
652	C₂²⋊C₄×C₃₁	—	2	1	no	—
653	C₂²⋊C₄×C₃₁	—	2	1	no	—
654	C₂²⋊C₄×C₃₁	—	2	1	no	—
655	C₂²⋊C₄×C₃₁	—	2	1	no	—
656	C₂²⋊C₄×C₃₁	—	2	1	no	—
657	C₂²⋊C₄×C₃₁	—	2	1	no	—
658	C₂²⋊C₄×C₃₁	—	2	1	no	—
659	C₂²⋊C₄×C₃₁	—	2	1	no	—
660	C₂²⋊C₄×C₃₁	—	2	1	no	—
661	C₂²⋊C₄×C₃₁	—	2	1	no	—
662	C₂²⋊C₄×C₃₁	—	2	1	no	—
663	C₂²⋊C₄×C₃₁	—	2	1	no	—
664	C₂²⋊C₄×C₃₁	—	2	1	no	—
665	C₂²⋊C₄×C₃₁	—	2	1	no	—
666	C₂²⋊C₄×C₃₁	—	2	1	no	—
667	C₂²⋊C₄×C₃₁	—	2	1	no	—
668	C₂²⋊C₄×C₃₁	—	2	1	no	—
669	C₂²⋊C₄×C₃₁	—	2	1	no	—
670	C₂²⋊C₄×C₃₁	—	2	1	no	—
671	C₂²⋊C₄×C₃₁	—	2	1	no	—
672	C₂²⋊C₄×C₃₁	—	2	1	no	—
673	C₂²⋊C₄×C₃₁	—	2	1	no	—
674	C₂²⋊C₄×C₃₁	—	2	1	no	—
675	C₂²⋊C₄×C₃₁	—	2	1	no	—
676	C₂²⋊C₄×C₃₁	—	2	1	no	—
677	C₂²⋊C₄×C₃₁	—	2	1	no	—
678	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
679	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
680	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
681	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
682	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
683	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
684	C₄²×C₃₁	—	2	1	no	—
685	C₄²×C₃₁	—	2	1	no	—
686	C₄²×C₃₁	—	2	1	no	—
687	C₄²×C₃₁	—	2	1	no	—
688	C₄²×C₃₁	—	2	1	no	—
689	C₄²×C₃₁	—	2	1	no	—
690	C₄²×C₃₁	—	2	1	no	—
691	C₄²×C₃₁	—	2	1	no	—
692	C₄²×C₃₁	—	2	1	no	—
693	C₄²×C₃₁	—	2	1	no	—
694	C₄²×C₃₁	—	2	1	no	—
695	C₄²×C₃₁	—	2	1	no	—
696	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
697	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
698	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
699	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
700	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
701	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
702	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
703	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
704	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
705	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
706	#61972	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
707	C₂³×C₃₁	—	2	1	no	—
708	C₂³×C₃₁	—	2	1	no	—
709	C₂³×C₃₁	—	2	1	no	—
710	C₂³×C₃₁	—	2	1	no	—
711	C₂³×C₃₁	—	4	2	no	—
712	C₂³×C₃₁	—	4	2	no	—
713	C₂³×C₃₁	—	8	1	no	—
714	C₂³×C₃₁	—	8	1	no	—
715	C₂³×C₃₁	—	8	1	no	—
716	C₂³×C₃₁	—	8	1	no	—
717	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
718	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
719	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
720	Q₈×C₃₁	—	2	1	no	—
721	Q₈×C₃₁	—	2	1	no	—
722	Q₈×C₃₁	—	2	1	no	—
723	Q₈×C₃₁	—	2	1	no	—
724	Q₈×C₃₁	—	2	1	no	—
725	Q₈×C₃₁	—	2	1	no	—
726	Q₈×C₃₁	—	2	1	no	—
727	Q₈×C₃₁	—	2	1	no	—
728	Q₈×C₃₁	—	2	1	no	—
729	Q₈×C₃₁	—	2	1	no	—
730	Q₈×C₃₁	—	2	1	no	—
731	Q₈×C₃₁	—	4	1	no	—
732	Q₈×C₃₁	—	4	2	no	—
733	Q₈×C₃₁	—	4	2	no	—
734	Q₈×C₃₁	—	4	2	no	—
735	Q₈×C₃₁	—	8	1	no	—
736	Q₈×C₃₁	—	8	1	no	—
737	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
738	D₄×C₃₁	—	2	2	no	—
739	D₄×C₃₁	—	2	2	no	—
740	D₄×C₃₁	—	2	1	no	—
741	D₄×C₃₁	—	2	1	no	—
742	D₄×C₃₁	—	2	1	no	—
743	D₄×C₃₁	—	2	1	no	—
744	D₄×C₃₁	—	2	1	no	—
745	D₄×C₃₁	—	2	1	no	—
746	D₄×C₃₁	—	2	1	no	—
747	D₄×C₃₁	—	2	1	no	—
748	D₄×C₃₁	—	4	1	no	—
749	D₄×C₃₁	—	4	2	no	—
750	D₄×C₃₁	—	4	2	no	—
751	D₄×C₃₁	—	4	2	no	—
752	D₄×C₃₁	—	4	2	no	—
753	D₄×C₃₁	—	4	2	no	—
754	D₄×C₃₁	—	4	2	no	—
755	D₄×C₃₁	—	8	1	no	—
756	D₄×C₃₁	—	8	1	no	—
757	D₄×C₃₁	—	8	1	no	—
758	D₄×C₃₁	—	8	1	no	—
759	D₄×C₃₁	—	8	1	no	—
760	D₄×C₃₁	—	8	1	no	—
761	C₂×C₄×C₃₁	—	2	2	no	—
762	C₂×C₄×C₃₁	—	2	1	no	—
763	C₂×C₄×C₃₁	—	2	1	no	—
764	C₂×C₄×C₃₁	—	2	1	no	—
765	C₂×C₄×C₃₁	—	2	1	no	—
766	C₂×C₄×C₃₁	—	2	1	no	—
767	C₂×C₄×C₃₁	—	2	1	no	—
768	C₂×C₄×C₃₁	—	2	1	no	—
769	C₂×C₄×C₃₁	—	2	1	no	—
770	C₂×C₄×C₃₁	—	2	1	no	—
771	C₂×C₄×C₃₁	—	2	1	no	—
772	C₂×C₄×C₃₁	—	2	1	no	—
773	C₂×C₄×C₃₁	—	2	1	no	—
774	C₂×C₄×C₃₁	—	2	1	no	—
775	C₂×C₄×C₃₁	—	2	1	no	—
776	C₂×C₄×C₃₁	—	2	1	no	—
777	C₂×C₄×C₃₁	—	2	1	no	—
778	C₂×C₄×C₃₁	—	2	1	no	—
779	C₂×C₄×C₃₁	—	2	1	no	—
780	C₂×C₄×C₃₁	—	4	1	no	—
781	C₂×C₄×C₃₁	—	4	1	no	—
782	C₂×C₄×C₃₁	—	4	1	no	—
783	C₂×C₄×C₃₁	—	4	1	no	—
784	C₂×C₄×C₃₁	—	4	1	no	—
785	C₂×C₄×C₃₁	—	4	2	no	—
786	C₂×C₄×C₃₁	—	4	2	no	—
787	C₂×C₄×C₃₁	—	4	2	no	—
788	C₂×C₄×C₃₁	—	4	2	no	—
789	C₂×C₄×C₃₁	—	4	2	no	—
790	C₂×C₄×C₃₁	—	4	2	no	—
791	C₂×C₄×C₃₁	—	4	2	no	—
792	C₂×C₄×C₃₁	—	4	2	no	—
793	C₂×C₄×C₃₁	—	8	1	no	—
794	C₂×C₄×C₃₁	—	8	1	no	—
795	C₂×C₄×C₃₁	—	8	1	no	—
796	C₂×C₄×C₃₁	—	8	1	no	—
797	C₂×C₄×C₃₁	—	8	1	no	—
798	C₂×C₄×C₃₁	—	8	1	no	—
799	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
800	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
801	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
802	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
803	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
804	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
805	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
806	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
807	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
808	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
809	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
810	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
811	C₈×C₃₁	—	2	1	no	—
812	C₈×C₃₁	—	2	1	no	—
813	C₈×C₃₁	—	2	1	no	—
814	C₈×C₃₁	—	2	1	no	—
815	C₈×C₃₁	—	2	1	no	—
816	C₈×C₃₁	—	2	1	no	—
817	C₈×C₃₁	—	2	1	no	—
818	C₈×C₃₁	—	2	1	no	—
819	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
820	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
821	#3402	C₂×C₃₁	1	1	yes	characteristic, complemented
822	#3401	C₂×C₃₁	1	1	yes	characteristic, complemented
823	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
824	#3371	C₂×C₃₁	1	1	yes	characteristic, complemented
825	#3327	C₂×C₃₁	1	1	yes	characteristic, complemented
826	#3323	C₂×C₃₁	1	1	yes	characteristic, complemented
827	#3312	C₂×C₃₁	1	1	yes	characteristic, complemented
828	#3310	C₂×C₃₁	1	1	yes	characteristic, complemented
829	#3308	C₂×C₃₁	1	1	yes	characteristic, complemented
830	#3306	C₂×C₃₁	1	1	yes	characteristic, complemented
831	#3277	C₂×C₃₁	1	1	yes	characteristic, complemented
832	#3275	C₂×C₃₁	1	1	yes	characteristic, complemented
833	#3270	C₂×C₃₁	1	1	yes	characteristic, complemented
834	#3270	C₂×C₃₁	1	1	yes	characteristic, complemented
835	#3266	C₂×C₃₁	1	1	yes	characteristic, complemented
836	#3265	C₂×C₃₁	1	1	yes	characteristic, complemented
837	#3256	C₂×C₃₁	1	1	yes	characteristic, complemented
838	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
839	#3250	C₂×C₃₁	1	1	yes	characteristic, complemented
840	#3219	C₂×C₃₁	1	1	yes	characteristic, complemented
841	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
842	#3211	C₂×C₃₁	1	1	yes	characteristic, complemented
843	#3117	C₂×C₃₁	1	1	yes	characteristic, complemented
844	#3111	C₂×C₃₁	1	1	yes	characteristic, complemented
845	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
846	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
847	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
848	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
849	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
850	C₂²×C₃₁	—	2	1	no	—
851	C₂²×C₃₁	—	2	1	no	—
852	C₂²×C₃₁	—	2	1	no	—
853	C₂²×C₃₁	—	2	1	no	—
854	C₂²×C₃₁	—	2	1	no	—
855	C₂²×C₃₁	—	2	1	no	—
856	C₂²×C₃₁	—	2	1	no	—
857	C₂²×C₃₁	—	2	1	no	—
858	C₂²×C₃₁	—	4	1	no	—
859	C₂²×C₃₁	—	4	1	no	—
860	C₂²×C₃₁	—	4	1	no	—
861	C₂²×C₃₁	—	4	1	no	—
862	C₂²×C₃₁	—	4	1	no	—
863	C₂²×C₃₁	—	4	1	no	—
864	C₂²×C₃₁	—	4	1	no	—
865	C₂²×C₃₁	—	4	1	no	—
866	C₂²×C₃₁	—	4	1	no	—
867	C₂²×C₃₁	—	4	1	no	—
868	C₂²×C₃₁	—	4	1	no	—
869	C₂²×C₃₁	—	4	1	no	—
870	C₂²×C₃₁	—	16	2	no	—
871	C₂²×C₃₁	—	16	2	no	—
872	C₂²×C₃₁	#575	1	2	yes	—
873	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
874	C₄×C₃₁	—	2	1	no	—
875	C₄×C₃₁	—	2	1	no	—
876	C₄×C₃₁	—	2	1	no	—
877	C₄×C₃₁	—	2	1	no	—
878	C₄×C₃₁	—	2	1	no	—
879	C₄×C₃₁	—	2	1	no	—
880	C₄×C₃₁	—	2	1	no	—
881	C₄×C₃₁	—	2	2	no	—
882	C₄×C₃₁	—	2	1	no	—
883	C₄×C₃₁	—	2	1	no	—
884	C₄×C₃₁	—	2	1	no	—
885	C₄×C₃₁	—	2	1	no	—
886	C₄×C₃₁	—	4	1	no	—
887	C₄×C₃₁	—	4	1	no	—
888	C₄×C₃₁	—	4	1	no	—
889	C₄×C₃₁	—	4	1	no	—
890	C₄×C₃₁	—	4	1	no	—
891	C₄×C₃₁	—	4	1	no	—
892	C₄×C₃₁	—	4	1	no	—
893	C₄×C₃₁	—	4	1	no	—
894	C₄×C₃₁	—	4	1	no	—
895	C₄×C₃₁	—	4	1	no	—
896	C₄×C₃₁	—	4	1	no	—
897	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
898	C₄×C₃₁	#585	1	1	yes	characteristic
899	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
900	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
901	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
902	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
903	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
904	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
905	#559	C₂²×C₃₁	1	1	yes	characteristic
906	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
907	#556	—	2	1	no	—
908	#556	C₂²×C₃₁	1	1	yes	characteristic
909	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
910	#555	—	2	1	no	—
911	#552	—	2	1	no	—
912	#552	—	2	1	no	—
913	#552	C₂²×C₃₁	1	1	yes	characteristic
914	#552	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#551	—	2	1	no	—
916	#551	—	2	1	no	—
917	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
918	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
919	#548	C₂²×C₃₁	1	1	yes	characteristic
920	#548	C₂²×C₃₁	1	1	yes	characteristic
921	#548	C₂²×C₃₁	1	1	yes	characteristic
922	#548	C₂²×C₃₁	1	1	yes	characteristic, complemented
923	#547	—	2	1	no	—
924	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
925	#546	—	2	1	no	—
926	#546	C₂²×C₃₁	1	1	yes	characteristic
927	#546	C₂²×C₃₁	1	1	yes	characteristic
928	D₄²	C₂²×C₃₁	1	1	yes	characteristic
929	#542	—	2	1	no	—
930	#538	—	2	1	no	—
931	#538	—	2	1	no	—
932	#533	—	2	1	no	—
933	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
934	#532	C₂²×C₃₁	1	1	yes	characteristic
935	#529	—	2	1	no	—
936	#529	—	2	1	no	—
937	#529	C₂²×C₃₁	1	1	yes	characteristic
938	#529	C₂²×C₃₁	1	1	yes	characteristic
939	#529	C₂²×C₃₁	1	1	yes	characteristic
940	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
941	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
942	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
943	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
944	#518	—	2	1	no	—
945	C₄×#41	—	2	1	no	—
946	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
947	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
948	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
949	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
950	#497	C₂²×C₃₁	1	1	yes	characteristic
951	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
952	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
953	#496	C₂²×C₃₁	1	1	yes	characteristic
954	#495	C₂²×C₃₁	1	1	yes	characteristic
955	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
956	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
957	#490	C₂²×C₃₁	1	1	yes	characteristic
958	#489	C₂²×C₃₁	1	1	yes	characteristic
959	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
960	#488	C₂²×C₃₁	1	1	yes	characteristic
961	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
962	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
963	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
964	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
965	#482	C₂²×C₃₁	1	1	yes	characteristic
966	#481	C₂²×C₃₁	1	1	yes	characteristic
967	#480	C₂²×C₃₁	1	1	yes	characteristic
968	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
969	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
970	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
971	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
972	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
973	#478	C₂²×C₃₁	1	1	yes	characteristic
974	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
975	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
976	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
977	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
978	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
979	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
980	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
981	#469	C₂²×C₃₁	1	1	yes	characteristic
982	#468	C₂²×C₃₁	1	1	yes	characteristic
983	#468	C₂²×C₃₁	1	1	yes	characteristic
984	#468	C₂²×C₃₁	1	1	yes	characteristic
985	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
986	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
987	#466	C₂²×C₃₁	1	1	yes	characteristic
988	#465	C₂²×C₃₁	1	1	yes	characteristic
989	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
990	#464	C₂²×C₃₁	1	1	yes	characteristic
991	#464	C₂²×C₃₁	1	1	yes	characteristic
992	#464	C₂²×C₃₁	1	1	yes	characteristic
993	#464	C₂²×C₃₁	1	1	yes	characteristic
994	#464	C₂²×C₃₁	1	1	yes	characteristic
995	#464	C₂²×C₃₁	1	1	yes	characteristic
996	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
997	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
998	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
999	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
1000	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
1001	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
1002	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
1003	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
1004	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
1005	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
1006	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
1007	#463	C₂²×C₃₁	1	1	yes	characteristic
1008	#463	C₂²×C₃₁	1	1	yes	characteristic
1009	#463	C₂²×C₃₁	1	1	yes	characteristic
1010	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
1011	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
1012	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
1013	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
1014	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
1015	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
1016	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
1017	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
1018	#460	C₂²×C₃₁	1	1	yes	characteristic
1019	#460	C₂²×C₃₁	1	1	yes	characteristic
1020	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
1021	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
1022	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
1023	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
1024	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
1025	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
1026	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
1027	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
1028	#450	C₂²×C₃₁	1	1	yes	characteristic
1029	#450	C₂²×C₃₁	1	1	yes	characteristic
1030	#450	C₂²×C₃₁	1	1	yes	characteristic
1031	#449	C₂²×C₃₁	1	1	yes	characteristic
1032	#449	C₂²×C₃₁	1	1	yes	characteristic, complemented
1033	#449	C₂²×C₃₁	1	1	yes	characteristic, complemented
1034	#448	C₂²×C₃₁	1	1	yes	characteristic
1035	#448	C₂²×C₃₁	1	1	yes	characteristic
1036	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
1037	#447	C₂²×C₃₁	1	1	yes	characteristic
1038	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
1039	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
1040	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
1041	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
1042	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
1043	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
1044	#440	C₂²×C₃₁	1	1	yes	characteristic
1045	#440	C₂²×C₃₁	1	1	yes	characteristic
1046	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1047	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1048	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1049	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1050	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1051	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1052	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
1053	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
1054	#435	C₂²×C₃₁	1	1	yes	characteristic
1055	#435	C₂²×C₃₁	1	1	yes	characteristic
1056	#435	C₂²×C₃₁	1	1	yes	characteristic, complemented
1057	#435	C₂²×C₃₁	1	1	yes	characteristic, complemented
1058	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
1059	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
1060	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
1061	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
1062	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
1063	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
1064	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
1065	#418	C₂²×C₃₁	1	1	yes	characteristic
1066	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
1067	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
1068	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
1069	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
1070	C₂×C₃₁	—	2	2	no	—
1071	C₂×C₃₁	—	4	1	no	—
1072	C₂×C₃₁	—	4	1	no	—
1073	C₂×C₃₁	—	8	1	no	—
1074	C₂×C₃₁	—	8	1	no	—
1075	C₂×C₃₁	—	8	1	no	—
1076	C₂×C₃₁	—	8	1	no	—
1077	C₂×C₃₁	#3488	1	1	yes	characteristic
1078	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
1079	C₂×C₃₁	#3586	1	1	yes	characteristic
1080	C₂×#41	—	2	1	no	—
1081	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
1082	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1083	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1084	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1085	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1086	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1087	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1088	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1089	C₂²×D₄	—	2	1	no	—
1090	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
1091	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
1092	#137	—	4	2	no	—
1093	#137	—	4	2	no	—
1094	#137	—	4	2	no	—
1095	AGL(1,ℤ/8)	—	4	2	no	—
1096	C₂×Q₁₆	—	4	2	no	—
1097	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1098	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1099	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1100	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1101	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1102	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1103	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1104	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1105	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1106	C₂×SD₁₆	—	4	2	no	—
1107	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1108	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1109	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1110	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1111	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1112	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1113	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1114	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1115	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1116	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1117	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1118	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1119	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1120	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1121	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1122	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1123	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1124	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1125	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1126	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1127	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1128	C₄⋊Q₈	—	2	1	no	—
1129	C₄⋊Q₈	—	2	1	no	—
1130	C₄⋊Q₈	—	2	1	no	—
1131	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1132	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1133	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1134	#127	C₂³×C₃₁	1	1	yes	characteristic
1135	#126	—	2	1	no	—
1136	#126	—	2	1	no	—
1137	#126	—	2	1	no	—
1138	#126	—	2	1	no	—
1139	#126	—	2	1	no	—
1140	#126	—	2	1	no	—
1141	#126	—	2	1	no	—
1142	#126	—	2	1	no	—
1143	#126	—	2	1	no	—
1144	#126	—	2	1	no	—
1145	#126	—	2	1	no	—
1146	#125	—	2	1	no	—
1147	#125	—	2	1	no	—
1148	#125	—	2	1	no	—
1149	#125	—	2	1	no	—
1150	#125	—	2	1	no	—
1151	#125	C₂³×C₃₁	1	1	yes	characteristic
1152	#125	C₂³×C₃₁	1	1	yes	characteristic
1153	#125	C₂³×C₃₁	1	1	yes	characteristic
1154	#124	—	2	1	no	—
1155	#124	—	2	1	no	—
1156	#124	—	2	1	no	—
1157	#124	—	2	1	no	—
1158	#124	—	2	1	no	—
1159	#124	—	2	1	no	—
1160	#124	—	2	1	no	—
1161	#124	—	2	1	no	—
1162	#124	—	2	1	no	—
1163	#124	C₂³×C₃₁	1	1	yes	characteristic
1164	#124	C₂³×C₃₁	1	1	yes	characteristic
1165	#124	C₂³×C₃₁	1	1	yes	characteristic
1166	#124	C₂³×C₃₁	1	1	yes	characteristic
1167	#124	C₂³×C₃₁	1	1	yes	characteristic
1168	#124	C₂³×C₃₁	1	1	yes	characteristic
1169	#124	C₂³×C₃₁	1	1	yes	characteristic
1170	#124	C₂³×C₃₁	1	1	yes	characteristic
1171	#124	C₂³×C₃₁	1	1	yes	characteristic
1172	#123	—	2	1	no	—
1173	#123	—	2	1	no	—
1174	#123	—	2	1	no	—
1175	#123	—	2	1	no	—
1176	#123	—	2	1	no	—
1177	#123	—	2	1	no	—
1178	#123	—	2	1	no	—
1179	#123	—	2	1	no	—
1180	#123	—	2	1	no	—
1181	#123	—	2	1	no	—
1182	#123	—	2	1	no	—
1183	#123	—	2	1	no	—
1184	#123	—	2	1	no	—
1185	C₂²⋊Q₈	—	2	1	no	—
1186	C₂²⋊Q₈	—	2	1	no	—
1187	C₂²⋊Q₈	—	2	1	no	—
1188	C₂²⋊Q₈	—	2	1	no	—
1189	C₂²⋊Q₈	—	2	1	no	—
1190	C₂²⋊Q₈	—	2	1	no	—
1191	C₂²⋊Q₈	—	2	1	no	—
1192	C₂²⋊Q₈	—	2	1	no	—
1193	C₂²⋊Q₈	—	2	1	no	—
1194	C₂²⋊Q₈	—	2	1	no	—
1195	C₂²⋊Q₈	—	2	1	no	—
1196	C₂²⋊Q₈	—	2	1	no	—
1197	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1198	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1199	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1200	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1201	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1202	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1203	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1204	#121	—	2	1	no	—
1205	#121	—	2	1	no	—
1206	#121	—	2	1	no	—
1207	#121	—	2	1	no	—
1208	#121	—	2	1	no	—
1209	#121	—	2	1	no	—
1210	#121	—	2	1	no	—
1211	#121	—	2	1	no	—
1212	#121	—	2	1	no	—
1213	#121	C₂³×C₃₁	1	1	yes	characteristic
1214	#121	C₂³×C₃₁	1	1	yes	characteristic
1215	#121	C₂³×C₃₁	1	1	yes	characteristic
1216	#121	C₂³×C₃₁	1	1	yes	characteristic
1217	#121	C₂³×C₃₁	1	1	yes	characteristic
1218	#120	—	2	1	no	—
1219	#120	—	2	1	no	—
1220	#120	—	2	1	no	—
1221	#120	—	2	1	no	—
1222	C₄×Q₈	—	2	1	no	—
1223	C₄×Q₈	—	2	1	no	—
1224	C₄×Q₈	—	2	1	no	—
1225	C₄×Q₈	—	2	1	no	—
1226	C₄×Q₈	—	2	1	no	—
1227	C₄×Q₈	—	2	1	no	—
1228	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
1229	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1230	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1231	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1232	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1233	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1234	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1235	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1236	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1237	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1238	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1239	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1240	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1241	C₄×D₄	—	2	1	no	—
1242	C₄×D₄	—	2	1	no	—
1243	C₄×D₄	—	2	1	no	—
1244	C₄×D₄	—	2	1	no	—
1245	C₄×D₄	—	2	1	no	—
1246	C₄×D₄	—	2	1	no	—
1247	C₄×D₄	—	2	1	no	—
1248	C₄×D₄	—	2	1	no	—
1249	C₄×D₄	—	2	1	no	—
1250	C₄×D₄	—	2	1	no	—
1251	C₄×D₄	—	2	1	no	—
1252	C₄×D₄	—	2	1	no	—
1253	C₄×D₄	—	2	1	no	—
1254	C₄×D₄	—	2	1	no	—
1255	C₄×D₄	—	2	1	no	—
1256	C₄×D₄	—	2	1	no	—
1257	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
1258	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
1259	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
1260	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1261	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1262	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1263	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1264	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1265	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1266	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1267	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1268	#117	—	2	1	no	—
1269	#117	—	2	1	no	—
1270	#117	—	2	1	no	—
1271	#117	—	2	1	no	—
1272	#117	—	2	1	no	—
1273	#117	—	2	1	no	—
1274	#117	—	2	1	no	—
1275	#117	—	2	1	no	—
1276	#117	—	2	1	no	—
1277	#117	—	2	1	no	—
1278	#117	—	2	1	no	—
1279	#117	D₄×C₃₁	1	1	yes	characteristic
1280	#117	D₄×C₃₁	1	1	yes	characteristic
1281	#117	D₄×C₃₁	1	1	yes	characteristic
1282	#117	C₂³×C₃₁	1	1	yes	characteristic
1283	C₂×C₄⋊C₄	—	2	1	no	—
1284	C₂×C₄⋊C₄	—	2	1	no	—
1285	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1286	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1287	C₂×C₂²⋊C₄	—	2	1	no	—
1288	C₂×C₂²⋊C₄	—	2	1	no	—
1289	C₂×C₂²⋊C₄	—	2	1	no	—
1290	C₂×C₂²⋊C₄	—	2	1	no	—
1291	C₂×C₂²⋊C₄	—	2	1	no	—
1292	C₂×C₂²⋊C₄	—	2	1	no	—
1293	C₂×C₄²	—	2	1	no	—
1294	C₂×C₄²	—	2	1	no	—
1295	C₂×C₄²	—	2	1	no	—
1296	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1297	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1298	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1299	#107	C₂³×C₃₁	1	1	yes	characteristic
1300	#107	C₂³×C₃₁	1	1	yes	characteristic
1301	#107	C₂³×C₃₁	1	1	yes	characteristic
1302	#107	C₂³×C₃₁	1	1	yes	characteristic
1303	#106	C₂³×C₃₁	1	1	yes	characteristic
1304	#106	C₂³×C₃₁	1	1	yes	characteristic
1305	#106	C₂³×C₃₁	1	1	yes	characteristic
1306	#106	C₂³×C₃₁	1	1	yes	characteristic
1307	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1308	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1309	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1310	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1311	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1312	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1313	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1314	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1315	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1316	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1317	#103	C₂³×C₃₁	1	1	yes	characteristic
1318	#103	C₂³×C₃₁	1	1	yes	characteristic
1319	#103	C₂³×C₃₁	1	1	yes	characteristic
1320	#103	C₂³×C₃₁	1	1	yes	characteristic
1321	#103	C₂³×C₃₁	1	1	yes	characteristic
1322	#103	C₂³×C₃₁	1	1	yes	characteristic
1323	#103	C₂³×C₃₁	1	1	yes	characteristic
1324	#103	C₂³×C₃₁	1	1	yes	characteristic
1325	#103	C₂³×C₃₁	1	1	yes	characteristic
1326	#103	C₂³×C₃₁	1	1	yes	characteristic
1327	#103	C₂³×C₃₁	1	1	yes	characteristic
1328	#103	C₂³×C₃₁	1	1	yes	characteristic
1329	#103	C₂³×C₃₁	1	1	yes	characteristic
1330	#103	C₂³×C₃₁	1	1	yes	characteristic
1331	#103	C₂³×C₃₁	1	1	yes	characteristic
1332	#103	C₂³×C₃₁	1	1	yes	characteristic
1333	#103	C₂³×C₃₁	1	1	yes	characteristic
1334	#103	C₂³×C₃₁	1	1	yes	characteristic
1335	#102	C₂³×C₃₁	1	1	yes	characteristic
1336	#102	C₂³×C₃₁	1	1	yes	characteristic
1337	#102	C₂³×C₃₁	1	1	yes	characteristic
1338	#102	C₂³×C₃₁	1	1	yes	characteristic
1339	#102	C₂³×C₃₁	1	1	yes	characteristic
1340	#102	C₂³×C₃₁	1	1	yes	characteristic
1341	#102	C₂³×C₃₁	1	1	yes	characteristic
1342	#102	C₂³×C₃₁	1	1	yes	characteristic
1343	#102	C₂³×C₃₁	1	1	yes	characteristic
1344	#102	C₂³×C₃₁	1	1	yes	characteristic
1345	#102	C₂³×C₃₁	1	1	yes	characteristic
1346	#102	C₂³×C₃₁	1	1	yes	characteristic
1347	#102	C₂³×C₃₁	1	1	yes	characteristic
1348	#102	C₂³×C₃₁	1	1	yes	characteristic
1349	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1350	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1351	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1352	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1353	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1354	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1355	#97	C₂³×C₃₁	1	1	yes	characteristic
1356	#97	C₂³×C₃₁	1	1	yes	characteristic
1357	#97	C₂³×C₃₁	1	1	yes	characteristic
1358	#97	C₂³×C₃₁	1	1	yes	characteristic
1359	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1360	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1361	C₃₁	#61972	1	1	yes	characteristic, direct product factor, Sylow
1362	C₂⁴	—	2	1	no	—
1363	C₂⁴	—	2	1	no	—
1364	#41	—	2	2	no	—
1365	#41	—	4	2	no	—
1366	#41	—	4	1	no	—
1367	#41	—	4	1	no	—
1368	#41	—	4	1	no	—
1369	#41	—	4	1	no	—
1370	#41	—	4	1	no	—
1371	#41	—	4	4	no	—
1372	C₂×Q₈	—	2	1	no	—
1373	C₂×Q₈	—	2	1	no	—
1374	C₂×Q₈	—	2	1	no	—
1375	C₂×Q₈	—	2	1	no	—
1376	C₂×Q₈	—	2	1	no	—
1377	C₂×Q₈	—	2	2	no	—
1378	C₂×Q₈	—	2	2	no	—
1379	C₂×Q₈	—	4	1	no	—
1380	C₂×Q₈	—	4	1	no	—
1381	C₂×Q₈	—	4	1	no	—
1382	C₂×Q₈	—	4	1	no	—
1383	C₂×Q₈	—	4	1	no	—
1384	C₂×Q₈	—	4	1	no	—
1385	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1386	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1387	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1388	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1389	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1390	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1391	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1392	C₂×D₄	—	2	1	no	—
1393	C₂×D₄	—	2	1	no	—
1394	C₂×D₄	—	2	1	no	—
1395	C₂×D₄	—	2	1	no	—
1396	C₂×D₄	—	2	1	no	—
1397	C₂×D₄	—	2	1	no	—
1398	C₂×D₄	—	2	1	no	—
1399	C₂×D₄	—	2	1	no	—
1400	C₂×D₄	—	2	1	no	—
1401	C₂×D₄	—	2	1	no	—
1402	C₂×D₄	—	2	1	no	—
1403	C₂×D₄	—	2	1	no	—
1404	C₂×D₄	—	4	1	no	—
1405	C₂×D₄	—	4	1	no	—
1406	C₂×D₄	—	4	1	no	—
1407	C₂×D₄	—	4	1	no	—
1408	C₂×D₄	—	4	4	no	—
1409	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1410	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1411	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1412	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1413	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1414	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1415	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1416	C₂²×C₄	—	2	1	no	—
1417	C₂²×C₄	—	2	1	no	—
1418	C₂²×C₄	—	2	1	no	—
1419	C₂²×C₄	—	2	1	no	—
1420	C₂²×C₄	—	2	1	no	—
1421	C₂²×C₄	—	2	1	no	—
1422	C₂²×C₄	—	2	1	no	—
1423	C₂²×C₄	—	2	1	no	—
1424	C₂²×C₄	—	2	1	no	—
1425	C₂²×C₄	—	2	1	no	—
1426	C₂²×C₄	—	2	1	no	—
1427	C₂²×C₄	—	2	1	no	—
1428	C₂²×C₄	—	2	1	no	—
1429	C₂²×C₄	—	2	1	no	—
1430	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1431	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1432	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1433	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1434	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1435	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1436	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1437	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1438	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1439	Q₁₆	—	2	2	no	—
1440	Q₁₆	—	2	2	no	—
1441	Q₁₆	—	2	2	no	—
1442	Q₁₆	—	4	1	no	—
1443	Q₁₆	—	4	1	no	—
1444	Q₁₆	—	4	1	no	—
1445	Q₁₆	—	4	1	no	—
1446	Q₁₆	—	4	1	no	—
1447	Q₁₆	—	4	1	no	—
1448	SD₁₆	—	2	2	no	—
1449	SD₁₆	—	2	2	no	—
1450	SD₁₆	—	2	2	no	—
1451	SD₁₆	—	4	1	no	—
1452	SD₁₆	—	4	1	no	—
1453	SD₁₆	—	4	1	no	—
1454	SD₁₆	—	4	1	no	—
1455	SD₁₆	—	4	1	no	—
1456	SD₁₆	—	4	1	no	—
1457	SD₁₆	—	4	1	no	—
1458	SD₁₆	—	4	1	no	—
1459	SD₁₆	—	4	1	no	—
1460	D₈	—	4	1	no	—
1461	D₈	—	4	1	no	—
1462	D₈	—	4	1	no	—
1463	M₁₆	—	4	1	no	—
1464	M₁₆	—	4	1	no	—
1465	M₁₆	—	4	1	no	—
1466	M₁₆	—	4	1	no	—
1467	C₂×C₈	—	4	1	no	—
1468	C₂×C₈	—	4	1	no	—
1469	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1470	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1471	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1472	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1473	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1474	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1475	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1476	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1477	C₄⋊C₄	—	2	1	no	—
1478	C₄⋊C₄	—	2	1	no	—
1479	C₄⋊C₄	—	2	1	no	—
1480	C₄⋊C₄	—	2	1	no	—
1481	C₄⋊C₄	—	2	1	no	—
1482	C₄⋊C₄	—	2	1	no	—
1483	C₄⋊C₄	—	2	1	no	—
1484	C₄⋊C₄	—	2	1	no	—
1485	C₄⋊C₄	—	2	1	no	—
1486	C₄⋊C₄	—	2	1	no	—
1487	C₄⋊C₄	—	2	1	no	—
1488	C₄⋊C₄	—	2	1	no	—
1489	C₄⋊C₄	—	2	1	no	—
1490	C₄⋊C₄	—	2	1	no	—
1491	C₄⋊C₄	—	2	1	no	—
1492	C₄⋊C₄	—	2	1	no	—
1493	C₄⋊C₄	—	2	1	no	—
1494	C₄⋊C₄	—	2	1	no	—
1495	C₄⋊C₄	—	2	1	no	—
1496	C₄⋊C₄	—	2	1	no	—
1497	C₄⋊C₄	—	2	1	no	—
1498	C₄⋊C₄	—	2	1	no	—
1499	C₄⋊C₄	—	2	1	no	—
1500	C₄⋊C₄	—	2	1	no	—
1501	C₄⋊C₄	—	2	1	no	—
1502	C₄⋊C₄	—	2	1	no	—
1503	C₄⋊C₄	—	2	1	no	—
1504	C₄⋊C₄	—	2	1	no	—
1505	C₄⋊C₄	—	2	1	no	—
1506	C₄⋊C₄	—	2	1	no	—
1507	C₄⋊C₄	—	2	1	no	—
1508	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1509	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1510	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1511	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1512	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1513	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1514	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1515	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1516	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1517	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1518	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1519	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1520	C₂²⋊C₄	—	2	1	no	—
1521	C₂²⋊C₄	—	2	1	no	—
1522	C₂²⋊C₄	—	2	1	no	—
1523	C₂²⋊C₄	—	2	1	no	—
1524	C₂²⋊C₄	—	2	1	no	—
1525	C₂²⋊C₄	—	2	1	no	—
1526	C₂²⋊C₄	—	2	1	no	—
1527	C₂²⋊C₄	—	2	1	no	—
1528	C₂²⋊C₄	—	2	1	no	—
1529	C₂²⋊C₄	—	2	1	no	—
1530	C₂²⋊C₄	—	2	1	no	—
1531	C₂²⋊C₄	—	2	1	no	—
1532	C₂²⋊C₄	—	2	1	no	—
1533	C₂²⋊C₄	—	2	1	no	—
1534	C₂²⋊C₄	—	2	1	no	—
1535	C₂²⋊C₄	—	2	1	no	—
1536	C₂²⋊C₄	—	2	1	no	—
1537	C₂²⋊C₄	—	2	1	no	—
1538	C₂²⋊C₄	—	2	1	no	—
1539	C₂²⋊C₄	—	2	1	no	—
1540	C₂²⋊C₄	—	2	1	no	—
1541	C₂²⋊C₄	—	2	1	no	—
1542	C₂²⋊C₄	—	2	1	no	—
1543	C₂²⋊C₄	—	2	1	no	—
1544	C₂²⋊C₄	—	2	1	no	—
1545	C₂²⋊C₄	—	2	1	no	—
1546	C₂²⋊C₄	—	2	1	no	—
1547	C₂²⋊C₄	—	2	1	no	—
1548	C₂²⋊C₄	—	2	1	no	—
1549	C₂²⋊C₄	—	2	1	no	—
1550	C₂²⋊C₄	—	2	1	no	—
1551	C₂²⋊C₄	—	2	1	no	—
1552	C₂²⋊C₄	—	2	1	no	—
1553	C₂²⋊C₄	—	2	1	no	—
1554	C₂²⋊C₄	—	2	1	no	—
1555	C₂²⋊C₄	—	2	1	no	—
1556	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1557	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1558	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1559	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1560	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1561	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1562	C₄²	—	2	1	no	—
1563	C₄²	—	2	1	no	—
1564	C₄²	—	2	1	no	—
1565	C₄²	—	2	1	no	—
1566	C₄²	—	2	1	no	—
1567	C₄²	—	2	1	no	—
1568	C₄²	—	2	1	no	—
1569	C₄²	—	2	1	no	—
1570	C₄²	—	2	1	no	—
1571	C₄²	—	2	1	no	—
1572	C₄²	—	2	1	no	—
1573	C₄²	—	2	1	no	—
1574	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1575	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1576	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1577	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1578	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1579	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1580	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1581	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1582	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1583	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1584	C₂³	—	2	1	no	—
1585	C₂³	—	2	1	no	—
1586	C₂³	—	2	1	no	—
1587	C₂³	—	2	1	no	—
1588	C₂³	—	4	2	no	—
1589	C₂³	—	4	2	no	—
1590	C₂³	—	8	1	no	—
1591	C₂³	—	8	1	no	—
1592	C₂³	—	8	1	no	—
1593	C₂³	—	8	1	no	—
1594	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1595	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1596	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1597	Q₈	—	2	1	no	—
1598	Q₈	—	2	1	no	—
1599	Q₈	—	2	1	no	—
1600	Q₈	—	2	1	no	—
1601	Q₈	—	2	1	no	—
1602	Q₈	—	2	1	no	—
1603	Q₈	—	2	1	no	—
1604	Q₈	—	2	1	no	—
1605	Q₈	—	2	1	no	—
1606	Q₈	—	2	1	no	—
1607	Q₈	—	2	1	no	—
1608	Q₈	—	4	1	no	—
1609	Q₈	—	4	2	no	—
1610	Q₈	—	4	2	no	—
1611	Q₈	—	4	2	no	—
1612	Q₈	—	8	1	no	—
1613	Q₈	—	8	1	no	—
1614	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1615	D₄	—	2	2	no	—
1616	D₄	—	2	2	no	—
1617	D₄	—	2	1	no	—
1618	D₄	—	2	1	no	—
1619	D₄	—	2	1	no	—
1620	D₄	—	2	1	no	—
1621	D₄	—	2	1	no	—
1622	D₄	—	2	1	no	—
1623	D₄	—	2	1	no	—
1624	D₄	—	2	1	no	—
1625	D₄	—	4	1	no	—
1626	D₄	—	4	2	no	—
1627	D₄	—	4	2	no	—
1628	D₄	—	4	2	no	—
1629	D₄	—	4	2	no	—
1630	D₄	—	4	2	no	—
1631	D₄	—	4	2	no	—
1632	D₄	—	8	1	no	—
1633	D₄	—	8	1	no	—
1634	D₄	—	8	1	no	—
1635	D₄	—	8	1	no	—
1636	D₄	—	8	1	no	—
1637	D₄	—	8	1	no	—
1638	C₂×C₄	—	2	2	no	—
1639	C₂×C₄	—	2	1	no	—
1640	C₂×C₄	—	2	1	no	—
1641	C₂×C₄	—	2	1	no	—
1642	C₂×C₄	—	2	1	no	—
1643	C₂×C₄	—	2	1	no	—
1644	C₂×C₄	—	2	1	no	—
1645	C₂×C₄	—	2	1	no	—
1646	C₂×C₄	—	2	1	no	—
1647	C₂×C₄	—	2	1	no	—
1648	C₂×C₄	—	2	1	no	—
1649	C₂×C₄	—	2	1	no	—
1650	C₂×C₄	—	2	1	no	—
1651	C₂×C₄	—	2	1	no	—
1652	C₂×C₄	—	2	1	no	—
1653	C₂×C₄	—	2	1	no	—
1654	C₂×C₄	—	2	1	no	—
1655	C₂×C₄	—	2	1	no	—
1656	C₂×C₄	—	2	1	no	—
1657	C₂×C₄	—	4	1	no	—
1658	C₂×C₄	—	4	1	no	—
1659	C₂×C₄	—	4	1	no	—
1660	C₂×C₄	—	4	1	no	—
1661	C₂×C₄	—	4	1	no	—
1662	C₂×C₄	—	4	2	no	—
1663	C₂×C₄	—	4	2	no	—
1664	C₂×C₄	—	4	2	no	—
1665	C₂×C₄	—	4	2	no	—
1666	C₂×C₄	—	4	2	no	—
1667	C₂×C₄	—	4	2	no	—
1668	C₂×C₄	—	4	2	no	—
1669	C₂×C₄	—	4	2	no	—
1670	C₂×C₄	—	8	1	no	—
1671	C₂×C₄	—	8	1	no	—
1672	C₂×C₄	—	8	1	no	—
1673	C₂×C₄	—	8	1	no	—
1674	C₂×C₄	—	8	1	no	—
1675	C₂×C₄	—	8	1	no	—
1676	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1677	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1678	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1679	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1680	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1681	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1682	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1683	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1684	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1685	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1686	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1687	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1688	C₈	—	2	1	no	—
1689	C₈	—	2	1	no	—
1690	C₈	—	2	1	no	—
1691	C₈	—	2	1	no	—
1692	C₈	—	2	1	no	—
1693	C₈	—	2	1	no	—
1694	C₈	—	2	1	no	—
1695	C₈	—	2	1	no	—
1696	C₂²	—	2	1	no	—
1697	C₂²	—	2	1	no	—
1698	C₂²	—	2	1	no	—
1699	C₂²	—	2	1	no	—
1700	C₂²	—	2	1	no	—
1701	C₂²	—	2	1	no	—
1702	C₂²	—	2	1	no	—
1703	C₂²	—	2	1	no	—
1704	C₂²	—	4	1	no	—
1705	C₂²	—	4	1	no	—
1706	C₂²	—	4	1	no	—
1707	C₂²	—	4	1	no	—
1708	C₂²	—	4	1	no	—
1709	C₂²	—	4	1	no	—
1710	C₂²	—	4	1	no	—
1711	C₂²	—	4	1	no	—
1712	C₂²	—	4	1	no	—
1713	C₂²	—	4	1	no	—
1714	C₂²	—	4	1	no	—
1715	C₂²	—	4	1	no	—
1716	C₂²	—	16	2	no	—
1717	C₂²	—	16	2	no	—
1718	C₂²	C₃₁×#575	1	2	yes	—
1719	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1720	C₄	—	2	1	no	—
1721	C₄	—	2	1	no	—
1722	C₄	—	2	1	no	—
1723	C₄	—	2	2	no	—
1724	C₄	—	2	1	no	—
1725	C₄	—	2	1	no	—
1726	C₄	—	2	1	no	—
1727	C₄	—	2	1	no	—
1728	C₄	—	2	1	no	—
1729	C₄	—	2	1	no	—
1730	C₄	—	2	1	no	—
1731	C₄	—	2	1	no	—
1732	C₄	—	4	1	no	—
1733	C₄	—	4	1	no	—
1734	C₄	—	4	1	no	—
1735	C₄	—	4	1	no	—
1736	C₄	—	4	1	no	—
1737	C₄	—	4	1	no	—
1738	C₄	—	4	1	no	—
1739	C₄	—	4	1	no	—
1740	C₄	—	4	1	no	—
1741	C₄	—	4	1	no	—
1742	C₄	—	4	1	no	—
1743	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1744	C₄	C₃₁×#585	1	1	yes	characteristic
1745	C₂	—	2	2	no	—
1746	C₂	—	4	1	no	—
1747	C₂	—	4	1	no	—
1748	C₂	—	8	1	no	—
1749	C₂	—	8	1	no	—
1750	C₂	—	8	1	no	—
1751	C₂	—	8	1	no	—
1752	C₂	C₃₁×#3488	1	1	yes	characteristic
1753	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1754	C₂	C₃₁×#3586	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×#3514	C₂	semidirect
2. C₃₁×#3482	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3401	C₂	semidirect
5. C₃₁×#3377	C₂	semidirect
6. C₃₁×#3371	C₂	semidirect
7. C₃₁×#3327	C₂	semidirect
8. C₃₁×#3323	C₂	semidirect
9. C₃₁×#3312	C₂	semidirect
10. C₃₁×#3310	C₂	semidirect
11. C₃₁×#3308	C₂	semidirect
12. C₃₁×#3306	C₂	semidirect
13. C₃₁×#3277	C₂	semidirect
14. C₃₁×#3275	C₂	semidirect
15. C₃₁×#3270	C₂	semidirect
16. C₃₁×#3270	C₂	semidirect
17. C₃₁×#3266	C₂	semidirect
18. C₃₁×#3265	C₂	semidirect
19. C₃₁×#3256	C₂	semidirect
20. C₃₁×#3252	C₂	semidirect
21. C₃₁×#3250	C₂	semidirect
22. C₃₁×#3219	C₂	semidirect
23. C₃₁×#3215	C₂	semidirect
24. C₃₁×#3211	C₂	semidirect
25. C₃₁×#3117	C₂	semidirect
26. C₃₁×#3111	C₂	semidirect
27. C₃₁×#3108	C₂	semidirect
28. C₃₁×#3040	C₂	semidirect
29. C₃₁×#3037	C₂	semidirect
30. C₂×C₃₁×#464	C₂	semidirect
31. C₃₁×#2989	C₂	semidirect
32. C₂×C₃₁×#137	C₂²	semidirect
33. C₂×C₃₁×#137	C₂²	semidirect
34. C₂×C₃₁×#137	C₂²	semidirect
36. C₂²×Q₁₆×C₃₁	C₂²	semidirect
39. C₃₁×#557	C₂²	semidirect
42. C₃₁×#556	C₂²	semidirect
47. C₃₁×#552	C₂²	semidirect
51. D₄×Q₈×C₃₁	C₂²	semidirect
55. C₃₁×#548	C₂²	semidirect
57. C₃₁×#547	C₂²	semidirect
66. C₃₁×#533	C₂²	semidirect
73. C₃₁×#529	C₂²	semidirect
74. C₃₁×#529	C₂²	semidirect
80. C₄×#41×C₃₁	C₂²	semidirect
81. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
82. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
84. C₃₁×#497	C₂²	semidirect
85. C₃₁×#497	C₂²	semidirect
88. C₃₁×#495	C₂²	semidirect
89. C₃₁×#491	C₂²	semidirect
92. C₃₁×#489	C₂²	semidirect
94. C₃₁×#488	C₂²	semidirect
95. C₃₁×#485	C₂²	semidirect
96. C₃₁×#484	C₂²	semidirect
97. C₃₁×#483	C₂²	semidirect
101. C₃₁×#479	C₂²	semidirect
102. C₃₁×#479	C₂²	semidirect
103. C₃₁×#479	C₂²	semidirect
104. C₃₁×#479	C₂²	semidirect
105. C₃₁×#479	C₂²	semidirect
107. C₃₁×#478	C₂²	semidirect
108. C₃₁×#478	C₂²	semidirect
109. C₃₁×#477	C₂²	semidirect
110. C₃₁×#476	C₂²	semidirect
111. C₃₁×#470	C₂²	semidirect
112. C₃₁×#470	C₂²	semidirect
113. C₃₁×#470	C₂²	semidirect
118. C₃₁×#468	C₂²	semidirect
119. C₃₁×#467	C₂²	semidirect
122. C₃₁×#465	C₂²	semidirect
129. C₃₁×#464	C₂²	semidirect
130. C₃₁×#464	C₂²	semidirect
131. C₃₁×#464	C₂²	semidirect
132. C₃₁×#464	C₂²	semidirect
133. C₃₁×#464	C₂²	semidirect
134. C₃₁×#464	C₂²	semidirect
135. C₃₁×#464	C₂²	semidirect
136. C₃₁×#464	C₂²	semidirect
137. C₃₁×#464	C₂²	semidirect
138. C₃₁×#464	C₂²	semidirect
139. C₃₁×#464	C₂²	semidirect
143. C₃₁×#463	C₂²	semidirect
144. C₃₁×#463	C₂²	semidirect
145. C₃₁×#463	C₂²	semidirect
146. C₃₁×#463	C₂²	semidirect
147. C₃₁×#462	C₂²	semidirect
148. C₃₁×#462	C₂²	semidirect
149. C₃₁×#462	C₂²	semidirect
150. C₃₁×#461	C₂²	semidirect
153. C₃₁×#452	C₂²	semidirect
154. C₃₁×#452	C₂²	semidirect
155. C₃₁×#452	C₂²	semidirect
156. C₃₁×#451	C₂²	semidirect
157. C₃₁×#451	C₂²	semidirect
158. C₃₁×#451	C₂²	semidirect
159. C₃₁×#451	C₂²	semidirect
160. C₃₁×#451	C₂²	semidirect
165. C₃₁×#449	C₂²	semidirect
166. C₃₁×#449	C₂²	semidirect
169. C₃₁×#448	C₂²	semidirect
171. C₃₁×#446	C₂²	semidirect
172. C₃₁×#446	C₂²	semidirect
173. C₃₁×#442	C₂²	semidirect
174. C₃₁×#441	C₂²	semidirect
175. C₃₁×#441	C₂²	semidirect
176. C₃₁×#441	C₂²	semidirect
179. C₃₁×#440	C₂²	semidirect
180. C₃₁×#440	C₂²	semidirect
181. C₄×Q₁₆×C₃₁	C₂²	semidirect
182. C₄×Q₁₆×C₃₁	C₂²	semidirect
183. C₄×SD₁₆×C₃₁	C₂²	semidirect
184. C₄×SD₁₆×C₃₁	C₂²	semidirect
185. C₃₁×#436	C₂²	semidirect
186. C₃₁×#436	C₂²	semidirect
189. C₃₁×#435	C₂²	semidirect
190. C₃₁×#435	C₂²	semidirect
191. C₃₁×#432	C₂²	semidirect
192. C₃₁×#432	C₂²	semidirect
193. C₃₁×#431	C₂²	semidirect
194. C₃₁×#423	C₂²	semidirect
195. C₃₁×#423	C₂²	semidirect
196. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
197. C₃₁×#419	C₂²	semidirect
199. C₃₁×#417	C₂²	semidirect
200. C₃₁×#417	C₂²	semidirect
201. C₂×C₃₁×#103	C₂²	semidirect
706. #61972	C₃₁	direct (N × H)
819. #3514	C₂×C₃₁	semidirect
820. #3482	C₂×C₃₁	semidirect
821. #3402	C₂×C₃₁	semidirect
822. #3401	C₂×C₃₁	semidirect
823. #3377	C₂×C₃₁	semidirect
824. #3371	C₂×C₃₁	semidirect
825. #3327	C₂×C₃₁	semidirect
826. #3323	C₂×C₃₁	semidirect
827. #3312	C₂×C₃₁	semidirect
828. #3310	C₂×C₃₁	semidirect
829. #3308	C₂×C₃₁	semidirect
830. #3306	C₂×C₃₁	semidirect
831. #3277	C₂×C₃₁	semidirect
832. #3275	C₂×C₃₁	semidirect
833. #3270	C₂×C₃₁	semidirect
834. #3270	C₂×C₃₁	semidirect
835. #3266	C₂×C₃₁	semidirect
836. #3265	C₂×C₃₁	semidirect
837. #3256	C₂×C₃₁	semidirect
838. #3252	C₂×C₃₁	semidirect
839. #3250	C₂×C₃₁	semidirect
840. #3219	C₂×C₃₁	semidirect
841. #3215	C₂×C₃₁	semidirect
842. #3211	C₂×C₃₁	semidirect
843. #3117	C₂×C₃₁	semidirect
844. #3111	C₂×C₃₁	semidirect
845. #3108	C₂×C₃₁	semidirect
846. #3040	C₂×C₃₁	semidirect
847. #3037	C₂×C₃₁	semidirect
848. C₂×#464	C₂×C₃₁	semidirect
849. #2989	C₂×C₃₁	semidirect
899. C₂×#137	C₂²×C₃₁	semidirect
900. C₂×#137	C₂²×C₃₁	semidirect
901. C₂×#137	C₂²×C₃₁	semidirect
903. C₂²×Q₁₆	C₂²×C₃₁	semidirect
906. #557	C₂²×C₃₁	semidirect
909. #556	C₂²×C₃₁	semidirect
914. #552	C₂²×C₃₁	semidirect
918. D₄×Q₈	C₂²×C₃₁	semidirect
922. #548	C₂²×C₃₁	semidirect
924. #547	C₂²×C₃₁	semidirect
933. #533	C₂²×C₃₁	semidirect
940. #529	C₂²×C₃₁	semidirect
941. #529	C₂²×C₃₁	semidirect
947. C₄×#41	C₂²×C₃₁	semidirect
948. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
949. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
951. #497	C₂²×C₃₁	semidirect
952. #497	C₂²×C₃₁	semidirect
955. #495	C₂²×C₃₁	semidirect
956. #491	C₂²×C₃₁	semidirect
959. #489	C₂²×C₃₁	semidirect
961. #488	C₂²×C₃₁	semidirect
962. #485	C₂²×C₃₁	semidirect
963. #484	C₂²×C₃₁	semidirect
964. #483	C₂²×C₃₁	semidirect
968. #479	C₂²×C₃₁	semidirect
969. #479	C₂²×C₃₁	semidirect
970. #479	C₂²×C₃₁	semidirect
971. #479	C₂²×C₃₁	semidirect
972. #479	C₂²×C₃₁	semidirect
974. #478	C₂²×C₃₁	semidirect
975. #478	C₂²×C₃₁	semidirect
976. #477	C₂²×C₃₁	semidirect
977. #476	C₂²×C₃₁	semidirect
978. #470	C₂²×C₃₁	semidirect
979. #470	C₂²×C₃₁	semidirect
980. #470	C₂²×C₃₁	semidirect
985. #468	C₂²×C₃₁	semidirect
986. #467	C₂²×C₃₁	semidirect
989. #465	C₂²×C₃₁	semidirect
996. #464	C₂²×C₃₁	semidirect
997. #464	C₂²×C₃₁	semidirect
998. #464	C₂²×C₃₁	semidirect
999. #464	C₂²×C₃₁	semidirect
1000. #464	C₂²×C₃₁	semidirect
1001. #464	C₂²×C₃₁	semidirect
1002. #464	C₂²×C₃₁	semidirect
1003. #464	C₂²×C₃₁	semidirect
1004. #464	C₂²×C₃₁	semidirect
1005. #464	C₂²×C₃₁	semidirect
1006. #464	C₂²×C₃₁	semidirect
1010. #463	C₂²×C₃₁	semidirect
1011. #463	C₂²×C₃₁	semidirect
1012. #463	C₂²×C₃₁	semidirect
1013. #463	C₂²×C₃₁	semidirect
1014. #462	C₂²×C₃₁	semidirect
1015. #462	C₂²×C₃₁	semidirect
1016. #462	C₂²×C₃₁	semidirect
1017. #461	C₂²×C₃₁	semidirect
1020. #452	C₂²×C₃₁	semidirect
1021. #452	C₂²×C₃₁	semidirect
1022. #452	C₂²×C₃₁	semidirect
1023. #451	C₂²×C₃₁	semidirect
1024. #451	C₂²×C₃₁	semidirect
1025. #451	C₂²×C₃₁	semidirect
1026. #451	C₂²×C₃₁	semidirect
1027. #451	C₂²×C₃₁	semidirect
1032. #449	C₂²×C₃₁	semidirect
1033. #449	C₂²×C₃₁	semidirect
1036. #448	C₂²×C₃₁	semidirect
1038. #446	C₂²×C₃₁	semidirect
1039. #446	C₂²×C₃₁	semidirect
1040. #442	C₂²×C₃₁	semidirect
1041. #441	C₂²×C₃₁	semidirect
1042. #441	C₂²×C₃₁	semidirect
1043. #441	C₂²×C₃₁	semidirect
1046. #440	C₂²×C₃₁	semidirect
1047. #440	C₂²×C₃₁	semidirect
1048. C₄×Q₁₆	C₂²×C₃₁	semidirect
1049. C₄×Q₁₆	C₂²×C₃₁	semidirect
1050. C₄×SD₁₆	C₂²×C₃₁	semidirect
1051. C₄×SD₁₆	C₂²×C₃₁	semidirect
1052. #436	C₂²×C₃₁	semidirect
1053. #436	C₂²×C₃₁	semidirect
1056. #435	C₂²×C₃₁	semidirect
1057. #435	C₂²×C₃₁	semidirect
1058. #432	C₂²×C₃₁	semidirect
1059. #432	C₂²×C₃₁	semidirect
1060. #431	C₂²×C₃₁	semidirect
1061. #423	C₂²×C₃₁	semidirect
1062. #423	C₂²×C₃₁	semidirect
1063. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
1064. #419	C₂²×C₃₁	semidirect
1066. #417	C₂²×C₃₁	semidirect
1067. #417	C₂²×C₃₁	semidirect
1068. C₂×#103	C₂²×C₃₁	semidirect
1361. C₃₁	#61972	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3514	2
C₃₁×#3482	2
C₃₁×#3402	2
C₃₁×#3401	2
C₃₁×#3377	2
C₃₁×#3371	2
C₃₁×#3327	2
C₃₁×#3323	2
C₃₁×#3312	2
C₃₁×#3310	2
C₃₁×#3308	2
C₃₁×#3306	2
C₃₁×#3277	2
C₃₁×#3275	2
C₃₁×#3270	2
C₃₁×#3266	2
C₃₁×#3265	2
C₃₁×#3256	2
C₃₁×#3252	2
C₃₁×#3250	2
C₃₁×#3219	2
C₃₁×#3215	2
C₃₁×#3211	2
C₃₁×#3117	2
C₃₁×#3111	2
C₃₁×#3108	2
C₃₁×#3040	2
C₃₁×#3037	2
C₂×C₃₁×#464	2
C₃₁×#2989	2
#61972	31

Subgroups — C31×#61972 #21518731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61972 #21518731