Subgroups — C₃₁×#62031 #21518790

Order 7936.

1960 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3273	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3041	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
27	C₃₁×#560	—	2	2	no	—
28	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#555	C₂²	1	2	yes	complemented
32	C₃₁×#551	—	2	2	no	—
33	C₃₁×#550	C₂²	1	1	yes	characteristic
34	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#546	—	2	1	no	—
38	C₃₁×#546	—	2	1	no	—
39	C₃₁×#546	C₂²	1	2	yes	complemented
40	C₃₁×#546	C₂²	1	2	yes	complemented
41	D₄²×C₃₁	—	2	1	no	—
42	D₄²×C₃₁	C₂²	1	1	yes	characteristic
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
44	D₄²×C₃₁	C₂²	1	2	yes	complemented
45	C₃₁×#542	C₂²	1	2	yes	complemented
46	C₃₁×#540	—	2	1	no	—
47	C₃₁×#540	C₂²	1	2	yes	complemented
48	C₃₁×#538	—	2	2	no	—
49	C₃₁×#535	—	2	1	no	—
50	C₃₁×#535	C₂²	1	2	yes	complemented
51	C₃₁×#534	—	2	2	no	—
52	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#529	—	2	1	no	—
55	C₃₁×#529	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃₁×#124	—	2	1	no	—
58	C₃₁×#518	C₂²	1	2	yes	complemented
59	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#496	C₂²	1	2	yes	complemented
61	C₃₁×#495	C₂²	1	2	yes	complemented
62	C₃₁×#493	C₂²	1	1	yes	characteristic
63	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	2	yes	complemented
67	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#476	C₂²	1	2	yes	complemented
76	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#474	C₂²	1	2	yes	complemented
79	C₃₁×#469	C₂²	1	2	yes	complemented
80	C₃₁×#469	C₂²	1	2	yes	complemented
81	C₃₁×#468	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	2	yes	complemented
84	C₃₁×#465	C₂²	1	2	yes	complemented
85	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#463	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#463	C₂²	1	2	yes	complemented
91	C₃₁×#463	C₂²	1	2	yes	complemented
92	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#460	C₂²	1	2	yes	complemented
96	C₃₁×#459	C₂²	1	1	yes	characteristic
97	C₃₁×#459	C₂²	1	2	yes	complemented
98	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#459	C₂²	1	2	yes	complemented
100	C₃₁×#459	C₂²	1	2	yes	complemented
101	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#459	C₂²	1	2	yes	complemented
103	C₃₁×#459	C₂²	1	2	yes	complemented
104	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#450	C₂²	1	2	yes	complemented
107	C₃₁×#449	C₂²	1	1	yes	characteristic
108	C₃₁×#449	C₂²	1	2	yes	complemented
109	C₃₁×#447	C₂²	1	2	yes	complemented
110	C₃₁×#447	C₂²	1	2	yes	complemented
111	C₃₁×#447	C₂²	1	2	yes	complemented
112	C₃₁×#447	C₂²	1	2	yes	complemented
113	C₃₁×#447	C₂²	1	2	yes	complemented
114	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#442	C₂²	1	2	yes	complemented
117	C₃₁×#442	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
123	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
124	C₃₁×#436	C₂²	1	2	yes	complemented
125	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#433	C₂²	1	2	yes	complemented
129	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#418	C₂²	1	2	yes	complemented
133	C₃₁×#418	C₂²	1	2	yes	complemented
134	C₃₁×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	—	2	2	no	—
142	C₂²×D₄×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	—	2	1	no	—
144	C₂²×D₄×C₃₁	—	2	1	no	—
145	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
147	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
148	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
149	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
150	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	—	4	4	no	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₃₁	C₂³	1	2	yes	—
160	C₂×D₈×C₃₁	C₂³	1	2	yes	—
161	C₂×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×D₈×C₃₁	C₂³	1	2	yes	—
163	C₂×D₈×C₃₁	C₂³	1	2	yes	—
164	C₂×D₈×C₃₁	C₂³	1	2	yes	—
165	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
166	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
167	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
168	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₃₁×#127	—	2	1	no	—
171	C₃₁×#127	—	2	1	no	—
172	C₃₁×#127	—	2	1	no	—
173	C₃₁×#127	C₂³	1	1	yes	characteristic
174	C₃₁×#127	C₂³	1	2	yes	—
175	C₃₁×#127	C₂³	1	2	yes	—
176	C₃₁×#127	C₂³	1	1	yes	characteristic
177	C₃₁×#127	C₂³	1	1	yes	characteristic
178	C₃₁×#126	—	2	2	no	—
179	C₃₁×#126	—	2	2	no	—
180	C₃₁×#126	—	2	1	no	—
181	C₃₁×#126	D₄	1	2	yes	—
182	C₃₁×#125	D₄	1	1	yes	characteristic
183	C₃₁×#125	C₂³	1	1	yes	characteristic
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	—	2	1	no	—
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	—	2	2	no	—
189	C₃₁×#124	—	2	2	no	—
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	D₄	1	1	yes	characteristic
192	C₃₁×#124	C₂³	1	1	yes	characteristic
193	C₃₁×#124	C₂³	1	2	yes	—
194	C₃₁×#124	C₂³	1	2	yes	—
195	C₃₁×#123	—	2	1	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	D₄	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	—	2	1	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	D₄	1	1	yes	characteristic
225	C₃₁×#121	C₂³	1	2	yes	—
226	C₃₁×#121	C₂³	1	2	yes	—
227	C₃₁×#121	C₂³	1	2	yes	—
228	C₃₁×#121	C₂³	1	2	yes	—
229	C₃₁×#121	C₂³	1	1	yes	characteristic
230	C₃₁×#120	—	2	2	no	—
231	C₃₁×#120	—	2	2	no	—
232	C₃₁×#120	—	2	2	no	—
233	C₃₁×#120	—	2	2	no	—
234	C₃₁×#120	—	2	2	no	—
235	C₃₁×#120	—	2	2	no	—
236	C₃₁×#120	—	2	2	no	—
237	C₃₁×#120	—	2	2	no	—
238	C₄×Q₈×C₃₁	—	2	1	no	—
239	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	2	no	—
247	C₄×D₄×C₃₁	—	2	2	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	—	2	1	no	—
250	C₄×D₄×C₃₁	—	2	1	no	—
251	C₄×D₄×C₃₁	—	2	1	no	—
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₄×D₄×C₃₁	C₂³	1	2	yes	—
257	C₄×D₄×C₃₁	C₂³	1	2	yes	—
258	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₃₁	C₂³	1	2	yes	—
260	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₃₁	C₂³	1	2	yes	—
262	C₃₁×#117	—	2	2	no	—
263	C₃₁×#117	—	2	1	no	—
264	C₃₁×#117	—	2	1	no	—
265	C₃₁×#117	C₂³	1	2	yes	—
266	C₃₁×#117	C₂³	1	1	yes	characteristic
267	C₃₁×#117	C₂³	1	2	yes	—
268	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂×C₄²×C₃₁	—	2	1	no	—
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	2	yes	—
315	C₂⁴×C₃₁	—	2	2	no	—
316	C₂⁴×C₃₁	—	2	2	no	—
317	C₂⁴×C₃₁	—	2	2	no	—
318	#41×C₃₁	—	2	2	no	—
319	#41×C₃₁	—	4	1	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	4	2	no	—
322	#41×C₃₁	—	8	2	no	—
323	#41×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	—	2	2	no	—
326	C₂×Q₈×C₃₁	—	8	2	no	—
327	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₃₁	—	2	4	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	1	no	—
346	C₂×D₄×C₃₁	—	2	2	no	—
347	C₂×D₄×C₃₁	—	2	2	no	—
348	C₂×D₄×C₃₁	—	2	2	no	—
349	C₂×D₄×C₃₁	—	2	2	no	—
350	C₂×D₄×C₃₁	—	2	1	no	—
351	C₂×D₄×C₃₁	—	4	2	no	—
352	C₂×D₄×C₃₁	—	4	2	no	—
353	C₂×D₄×C₃₁	—	4	2	no	—
354	C₂×D₄×C₃₁	—	4	2	no	—
355	C₂×D₄×C₃₁	—	4	2	no	—
356	C₂×D₄×C₃₁	—	8	2	no	—
357	C₂×D₄×C₃₁	—	8	2	no	—
358	C₂×D₄×C₃₁	—	8	2	no	—
359	C₂×D₄×C₃₁	—	8	2	no	—
360	C₂×D₄×C₃₁	—	8	4	no	—
361	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
365	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
366	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
367	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	—	2	1	no	—
369	C₂²×C₄×C₃₁	—	2	1	no	—
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	2	1	no	—
372	C₂²×C₄×C₃₁	—	2	2	no	—
373	C₂²×C₄×C₃₁	—	2	2	no	—
374	C₂²×C₄×C₃₁	—	2	2	no	—
375	C₂²×C₄×C₃₁	—	2	2	no	—
376	C₂²×C₄×C₃₁	—	2	2	no	—
377	C₂²×C₄×C₃₁	—	2	2	no	—
378	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
382	Q₁₆×C₃₁	—	4	1	no	—
383	SD₁₆×C₃₁	—	2	2	no	—
384	SD₁₆×C₃₁	—	4	1	no	—
385	SD₁₆×C₃₁	—	4	2	no	—
386	SD₁₆×C₃₁	—	4	2	no	—
387	SD₁₆×C₃₁	—	4	2	no	—
388	D₈×C₃₁	—	2	2	no	—
389	D₈×C₃₁	—	2	4	no	—
390	D₈×C₃₁	—	2	4	no	—
391	D₈×C₃₁	—	4	2	no	—
392	D₈×C₃₁	—	4	2	no	—
393	D₈×C₃₁	—	4	2	no	—
394	D₈×C₃₁	—	4	2	no	—
395	D₈×C₃₁	—	4	2	no	—
396	M₁₆×C₃₁	—	4	2	no	—
397	M₁₆×C₃₁	—	4	2	no	—
398	C₂×C₈×C₃₁	—	4	2	no	—
399	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
402	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	1	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	1	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	1	no	—
438	C₂²⋊C₄×C₃₁	—	2	1	no	—
439	C₂²⋊C₄×C₃₁	—	2	1	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	1	no	—
442	C₂²⋊C₄×C₃₁	—	2	2	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	2	no	—
445	C₂²⋊C₄×C₃₁	—	2	1	no	—
446	C₂²⋊C₄×C₃₁	—	2	2	no	—
447	C₂²⋊C₄×C₃₁	—	2	2	no	—
448	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
453	C₄²×C₃₁	—	2	1	no	—
454	C₄²×C₃₁	—	2	1	no	—
455	C₄²×C₃₁	—	2	1	no	—
456	C₄²×C₃₁	—	2	2	no	—
457	C₄²×C₃₁	—	2	1	no	—
458	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
461	C₄²×C₃₁	C₂⁴	1	2	yes	—
462	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
463	#62031	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
464	C₂³×C₃₁	—	2	1	no	—
465	C₂³×C₃₁	—	2	2	no	—
466	C₂³×C₃₁	—	2	2	no	—
467	C₂³×C₃₁	—	2	1	no	—
468	C₂³×C₃₁	—	2	2	no	—
469	C₂³×C₃₁	—	4	4	no	—
470	C₂³×C₃₁	—	4	4	no	—
471	C₂³×C₃₁	—	8	2	no	—
472	C₂³×C₃₁	—	8	2	no	—
473	C₂³×C₃₁	—	8	2	no	—
474	C₂³×C₃₁	—	8	2	no	—
475	C₂³×C₃₁	—	8	2	no	—
476	C₂³×C₃₁	—	8	2	no	—
477	C₂³×C₃₁	—	8	2	no	—
478	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
479	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
480	Q₈×C₃₁	—	2	2	no	—
481	Q₈×C₃₁	—	2	1	no	—
482	Q₈×C₃₁	—	2	1	no	—
483	Q₈×C₃₁	—	2	1	no	—
484	Q₈×C₃₁	—	2	1	no	—
485	Q₈×C₃₁	—	4	2	no	—
486	Q₈×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	2	2	no	—
488	D₄×C₃₁	—	2	1	no	—
489	D₄×C₃₁	—	2	2	no	—
490	D₄×C₃₁	—	2	2	no	—
491	D₄×C₃₁	—	2	2	no	—
492	D₄×C₃₁	—	2	1	no	—
493	D₄×C₃₁	—	2	2	no	—
494	D₄×C₃₁	—	2	2	no	—
495	D₄×C₃₁	—	2	2	no	—
496	D₄×C₃₁	—	2	1	no	—
497	D₄×C₃₁	—	4	2	no	—
498	D₄×C₃₁	—	4	4	no	—
499	D₄×C₃₁	—	4	2	no	—
500	D₄×C₃₁	—	4	2	no	—
501	D₄×C₃₁	—	4	2	no	—
502	D₄×C₃₁	—	4	2	no	—
503	D₄×C₃₁	—	4	2	no	—
504	D₄×C₃₁	—	8	1	no	—
505	D₄×C₃₁	—	8	2	no	—
506	D₄×C₃₁	—	8	2	no	—
507	D₄×C₃₁	—	8	2	no	—
508	D₄×C₃₁	—	8	1	no	—
509	D₄×C₃₁	—	8	1	no	—
510	D₄×C₃₁	—	8	2	no	—
511	D₄×C₃₁	—	8	2	no	—
512	D₄×C₃₁	—	8	2	no	—
513	D₄×C₃₁	—	8	2	no	—
514	D₄×C₃₁	—	8	2	no	—
515	D₄×C₃₁	—	8	2	no	—
516	D₄×C₃₁	—	8	2	no	—
517	D₄×C₃₁	—	8	2	no	—
518	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
519	C₂×C₄×C₃₁	—	2	2	no	—
520	C₂×C₄×C₃₁	—	2	2	no	—
521	C₂×C₄×C₃₁	—	2	1	no	—
522	C₂×C₄×C₃₁	—	2	1	no	—
523	C₂×C₄×C₃₁	—	2	2	no	—
524	C₂×C₄×C₃₁	—	2	1	no	—
525	C₂×C₄×C₃₁	—	2	1	no	—
526	C₂×C₄×C₃₁	—	2	1	no	—
527	C₂×C₄×C₃₁	—	2	1	no	—
528	C₂×C₄×C₃₁	—	2	1	no	—
529	C₂×C₄×C₃₁	—	2	2	no	—
530	C₂×C₄×C₃₁	—	2	1	no	—
531	C₂×C₄×C₃₁	—	4	1	no	—
532	C₂×C₄×C₃₁	—	4	2	no	—
533	C₂×C₄×C₃₁	—	4	2	no	—
534	C₂×C₄×C₃₁	—	4	2	no	—
535	C₂×C₄×C₃₁	—	8	1	no	—
536	C₂×C₄×C₃₁	—	8	2	no	—
537	C₂×C₄×C₃₁	—	8	2	no	—
538	C₂×C₄×C₃₁	—	8	2	no	—
539	C₂×C₄×C₃₁	—	8	2	no	—
540	C₂×C₄×C₃₁	—	8	2	no	—
541	C₂×C₄×C₃₁	—	8	2	no	—
542	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
551	C₈×C₃₁	—	2	1	no	—
552	C₈×C₃₁	—	2	2	no	—
553	C₈×C₃₁	—	2	2	no	—
554	C₈×C₃₁	—	2	1	no	—
555	C₈×C₃₁	—	2	1	no	—
556	C₈×C₃₁	—	2	1	no	—
557	#3543	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#3396	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
563	#3325	C₂×C₃₁	1	2	yes	complemented
564	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#3319	C₂×C₃₁	1	2	yes	complemented
566	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
567	D₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3274	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#3273	C₂×C₃₁	1	2	yes	complemented
570	#3264	C₂×C₃₁	1	2	yes	complemented
571	#3257	C₂×C₃₁	1	2	yes	complemented
572	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
573	#3224	C₂×C₃₁	1	2	yes	complemented
574	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
575	#3122	C₂×C₃₁	1	2	yes	complemented
576	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
577	#3041	C₂×C₃₁	1	2	yes	complemented
578	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
579	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
580	C₂²×C₃₁	—	2	1	no	—
581	C₂²×C₃₁	—	2	2	no	—
582	C₂²×C₃₁	—	2	1	no	—
583	C₂²×C₃₁	—	2	2	no	—
584	C₂²×C₃₁	—	2	2	no	—
585	C₂²×C₃₁	—	2	1	no	—
586	C₂²×C₃₁	—	2	2	no	—
587	C₂²×C₃₁	—	4	1	no	—
588	C₂²×C₃₁	—	4	1	no	—
589	C₂²×C₃₁	—	4	2	no	—
590	C₂²×C₃₁	—	4	2	no	—
591	C₂²×C₃₁	—	4	1	no	—
592	C₂²×C₃₁	—	4	2	no	—
593	C₂²×C₃₁	—	4	2	no	—
594	C₂²×C₃₁	—	4	2	no	—
595	C₂²×C₃₁	—	4	1	no	—
596	C₂²×C₃₁	—	4	2	no	—
597	C₂²×C₃₁	—	4	1	no	—
598	C₂²×C₃₁	—	4	2	no	—
599	C₂²×C₃₁	—	4	2	no	—
600	C₂²×C₃₁	—	4	2	no	—
601	C₂²×C₃₁	—	16	4	no	—
602	C₂²×C₃₁	—	16	4	no	—
603	C₂²×C₃₁	—	16	4	no	—
604	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
605	C₄×C₃₁	—	2	1	no	—
606	C₄×C₃₁	—	2	1	no	—
607	C₄×C₃₁	—	2	2	no	—
608	C₄×C₃₁	—	2	1	no	—
609	C₄×C₃₁	—	2	2	no	—
610	C₄×C₃₁	—	2	1	no	—
611	C₄×C₃₁	—	2	2	no	—
612	C₄×C₃₁	—	4	1	no	—
613	C₄×C₃₁	—	4	1	no	—
614	C₄×C₃₁	—	4	1	no	—
615	C₄×C₃₁	—	4	1	no	—
616	C₄×C₃₁	—	4	1	no	—
617	C₄×C₃₁	—	4	1	no	—
618	C₄×C₃₁	—	4	2	no	—
619	C₄×C₃₁	#576	1	2	yes	—
620	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
621	C₄×C₃₁	#585	1	1	yes	characteristic
622	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
623	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
624	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
625	#560	—	2	2	no	—
626	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#555	C₂²×C₃₁	1	2	yes	complemented
630	#551	—	2	2	no	—
631	#550	C₂²×C₃₁	1	1	yes	characteristic
632	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#548	—	2	1	no	—
635	#546	—	2	1	no	—
636	#546	—	2	1	no	—
637	#546	C₂²×C₃₁	1	2	yes	complemented
638	#546	C₂²×C₃₁	1	2	yes	complemented
639	D₄²	—	2	1	no	—
640	D₄²	C₂²×C₃₁	1	1	yes	characteristic
641	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	D₄²	C₂²×C₃₁	1	2	yes	complemented
643	#542	C₂²×C₃₁	1	2	yes	complemented
644	#540	—	2	1	no	—
645	#540	C₂²×C₃₁	1	2	yes	complemented
646	#538	—	2	2	no	—
647	#535	—	2	1	no	—
648	#535	C₂²×C₃₁	1	2	yes	complemented
649	#534	—	2	2	no	—
650	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#529	—	2	1	no	—
653	#529	C₂²×C₃₁	1	1	yes	characteristic
654	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	C₂×#124	—	2	1	no	—
656	#518	C₂²×C₃₁	1	2	yes	complemented
657	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#496	C₂²×C₃₁	1	2	yes	complemented
659	#495	C₂²×C₃₁	1	2	yes	complemented
660	#493	C₂²×C₃₁	1	1	yes	characteristic
661	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#489	C₂²×C₃₁	1	2	yes	complemented
663	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	#486	C₂²×C₃₁	1	2	yes	complemented
665	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#482	C₂²×C₃₁	1	2	yes	complemented
669	#482	C₂²×C₃₁	1	2	yes	complemented
670	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	#478	C₂²×C₃₁	1	2	yes	complemented
673	#476	C₂²×C₃₁	1	2	yes	complemented
674	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#474	C₂²×C₃₁	1	2	yes	complemented
677	#469	C₂²×C₃₁	1	2	yes	complemented
678	#469	C₂²×C₃₁	1	2	yes	complemented
679	#468	C₂²×C₃₁	1	2	yes	complemented
680	#468	C₂²×C₃₁	1	2	yes	complemented
681	#466	C₂²×C₃₁	1	2	yes	complemented
682	#465	C₂²×C₃₁	1	2	yes	complemented
683	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	#463	C₂²×C₃₁	1	2	yes	complemented
686	#463	C₂²×C₃₁	1	2	yes	complemented
687	#463	C₂²×C₃₁	1	2	yes	complemented
688	#463	C₂²×C₃₁	1	2	yes	complemented
689	#463	C₂²×C₃₁	1	2	yes	complemented
690	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#460	C₂²×C₃₁	1	2	yes	complemented
694	#459	C₂²×C₃₁	1	1	yes	characteristic
695	#459	C₂²×C₃₁	1	2	yes	complemented
696	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
697	#459	C₂²×C₃₁	1	2	yes	complemented
698	#459	C₂²×C₃₁	1	2	yes	complemented
699	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	#459	C₂²×C₃₁	1	2	yes	complemented
701	#459	C₂²×C₃₁	1	2	yes	complemented
702	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	#452	C₂²×C₃₁	1	2	yes	complemented
704	#450	C₂²×C₃₁	1	2	yes	complemented
705	#449	C₂²×C₃₁	1	1	yes	characteristic
706	#449	C₂²×C₃₁	1	2	yes	complemented
707	#447	C₂²×C₃₁	1	2	yes	complemented
708	#447	C₂²×C₃₁	1	2	yes	complemented
709	#447	C₂²×C₃₁	1	2	yes	complemented
710	#447	C₂²×C₃₁	1	2	yes	complemented
711	#447	C₂²×C₃₁	1	2	yes	complemented
712	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	#442	C₂²×C₃₁	1	2	yes	complemented
715	#442	C₂²×C₃₁	1	2	yes	complemented
716	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
721	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
722	#436	C₂²×C₃₁	1	2	yes	complemented
723	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
724	#435	C₂²×C₃₁	1	2	yes	complemented
725	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	#433	C₂²×C₃₁	1	2	yes	complemented
727	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	#424	C₂²×C₃₁	1	2	yes	complemented
729	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
730	#418	C₂²×C₃₁	1	2	yes	complemented
731	#418	C₂²×C₃₁	1	2	yes	complemented
732	#416	C₂²×C₃₁	1	2	yes	complemented
733	C₂×C₃₁	—	4	1	no	—
734	C₂×C₃₁	—	4	2	no	—
735	C₂×C₃₁	—	4	2	no	—
736	C₂×C₃₁	—	8	2	no	—
737	C₂×C₃₁	—	8	2	no	—
738	C₂×C₃₁	—	8	2	no	—
739	C₂×C₃₁	—	8	1	no	—
740	C₂×C₃₁	#3488	1	1	yes	characteristic
741	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
742	C₂×C₃₁	#3585	1	1	yes	characteristic
743	C₂×#41	—	2	1	no	—
744	C₂×#41	—	2	1	no	—
745	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
746	C₂×#41	C₂³×C₃₁	1	2	yes	—
747	C₂²×Q₈	—	2	1	no	—
748	C₂²×D₄	—	2	1	no	—
749	C₂²×D₄	—	2	2	no	—
750	C₂²×D₄	—	2	1	no	—
751	C₂²×D₄	—	2	1	no	—
752	C₂²×D₄	—	2	1	no	—
753	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
754	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
755	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
756	AGL(1,ℤ/8)	—	4	4	no	—
757	AGL(1,ℤ/8)	—	4	4	no	—
758	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
759	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
760	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
762	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
764	C₂×D₈	—	4	4	no	—
765	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
766	C₂×D₈	C₂³×C₃₁	1	2	yes	—
767	C₂×D₈	C₂³×C₃₁	1	2	yes	—
768	C₂×D₈	C₂³×C₃₁	1	2	yes	—
769	C₂×D₈	C₂³×C₃₁	1	2	yes	—
770	C₂×D₈	C₂³×C₃₁	1	2	yes	—
771	C₂×D₈	C₂³×C₃₁	1	2	yes	—
772	C₂×D₈	C₂³×C₃₁	1	2	yes	—
773	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
774	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
775	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
776	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
778	#127	—	2	1	no	—
779	#127	—	2	1	no	—
780	#127	—	2	1	no	—
781	#127	C₂³×C₃₁	1	2	yes	—
782	#127	C₂³×C₃₁	1	1	yes	characteristic
783	#127	C₂³×C₃₁	1	1	yes	characteristic
784	#127	C₂³×C₃₁	1	1	yes	characteristic
785	#127	C₂³×C₃₁	1	2	yes	—
786	#126	—	2	2	no	—
787	#126	—	2	2	no	—
788	#126	—	2	1	no	—
789	#126	D₄×C₃₁	1	2	yes	—
790	#125	D₄×C₃₁	1	1	yes	characteristic
791	#125	C₂³×C₃₁	1	1	yes	characteristic
792	#124	—	2	1	no	—
793	#124	—	2	1	no	—
794	#124	—	2	1	no	—
795	#124	—	2	2	no	—
796	#124	—	2	2	no	—
797	#124	—	2	2	no	—
798	#124	—	2	1	no	—
799	#124	D₄×C₃₁	1	1	yes	characteristic
800	#124	C₂³×C₃₁	1	1	yes	characteristic
801	#124	C₂³×C₃₁	1	2	yes	—
802	#124	C₂³×C₃₁	1	2	yes	—
803	#123	—	2	1	no	—
804	#123	—	2	2	no	—
805	#123	—	2	2	no	—
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	D₄×C₃₁	1	2	yes	—
812	C₂²⋊Q₈	—	2	1	no	—
813	C₂²⋊Q₈	—	2	2	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
816	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
817	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
818	#121	—	2	2	no	—
819	#121	—	2	1	no	—
820	#121	—	2	1	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	1	no	—
825	#121	—	2	1	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	—	2	2	no	—
832	#121	D₄×C₃₁	1	1	yes	characteristic
833	#121	C₂³×C₃₁	1	1	yes	characteristic
834	#121	C₂³×C₃₁	1	2	yes	—
835	#121	C₂³×C₃₁	1	2	yes	—
836	#121	C₂³×C₃₁	1	2	yes	—
837	#121	C₂³×C₃₁	1	2	yes	—
838	#120	—	2	2	no	—
839	#120	—	2	2	no	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	C₄×Q₈	—	2	1	no	—
847	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
848	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
849	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
850	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
861	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₃₁	1	2	yes	—
863	C₄×D₄	C₂³×C₃₁	1	2	yes	—
864	C₄×D₄	C₂³×C₃₁	1	2	yes	—
865	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
866	C₄×D₄	C₂³×C₃₁	1	2	yes	—
867	C₄×D₄	C₂³×C₃₁	1	2	yes	—
868	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₃₁	1	2	yes	—
870	#117	—	2	2	no	—
871	#117	—	2	1	no	—
872	#117	—	2	1	no	—
873	#117	C₂³×C₃₁	1	1	yes	characteristic
874	#117	C₂³×C₃₁	1	2	yes	—
875	#117	C₂³×C₃₁	1	2	yes	—
876	C₂×C₂²⋊C₄	—	2	2	no	—
877	C₂×C₂²⋊C₄	—	2	2	no	—
878	C₂×C₂²⋊C₄	—	2	2	no	—
879	C₂×C₂²⋊C₄	—	2	2	no	—
880	C₂×C₄²	—	2	1	no	—
881	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
882	#107	C₂³×C₃₁	1	1	yes	characteristic
883	#107	C₂³×C₃₁	1	1	yes	characteristic
884	#107	C₂³×C₃₁	1	2	yes	—
885	#106	C₂³×C₃₁	1	1	yes	characteristic
886	#106	C₂³×C₃₁	1	1	yes	characteristic
887	#106	C₂³×C₃₁	1	2	yes	—
888	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
889	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
892	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
893	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
894	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
895	#103	C₂³×C₃₁	1	1	yes	characteristic
896	#103	C₂³×C₃₁	1	2	yes	—
897	#103	C₂³×C₃₁	1	1	yes	characteristic
898	#103	C₂³×C₃₁	1	1	yes	characteristic
899	#103	C₂³×C₃₁	1	1	yes	characteristic
900	#102	C₂³×C₃₁	1	2	yes	—
901	#102	C₂³×C₃₁	1	2	yes	—
902	#102	C₂³×C₃₁	1	2	yes	—
903	#102	C₂³×C₃₁	1	1	yes	characteristic
904	#102	C₂³×C₃₁	1	2	yes	—
905	#102	C₂³×C₃₁	1	2	yes	—
906	#102	C₂³×C₃₁	1	2	yes	—
907	#102	C₂³×C₃₁	1	2	yes	—
908	#102	C₂³×C₃₁	1	1	yes	characteristic
909	#102	C₂³×C₃₁	1	1	yes	characteristic
910	#102	C₂³×C₃₁	1	2	yes	—
911	#102	C₂³×C₃₁	1	2	yes	—
912	#102	C₂³×C₃₁	1	1	yes	characteristic
913	#102	C₂³×C₃₁	1	2	yes	—
914	#102	C₂³×C₃₁	1	2	yes	—
915	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
916	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
917	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
919	#97	C₂³×C₃₁	1	2	yes	—
920	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
921	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
922	C₄×C₈	C₂³×C₃₁	1	2	yes	—
923	C₃₁	#62031	1	1	yes	characteristic, direct product factor, Sylow
924	C₂⁴	—	2	2	no	—
925	C₂⁴	—	2	2	no	—
926	C₂⁴	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	4	1	no	—
929	#41	—	4	2	no	—
930	#41	—	4	2	no	—
931	#41	—	8	2	no	—
932	#41	—	8	2	no	—
933	C₂×Q₈	—	2	1	no	—
934	C₂×Q₈	—	2	2	no	—
935	C₂×Q₈	—	8	2	no	—
936	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
937	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂×D₄	—	2	4	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	4	2	no	—
961	C₂×D₄	—	4	2	no	—
962	C₂×D₄	—	4	2	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	8	2	no	—
966	C₂×D₄	—	8	2	no	—
967	C₂×D₄	—	8	2	no	—
968	C₂×D₄	—	8	2	no	—
969	C₂×D₄	—	8	4	no	—
970	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
971	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
974	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
975	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
976	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
988	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
991	Q₁₆	—	4	1	no	—
992	SD₁₆	—	2	2	no	—
993	SD₁₆	—	4	1	no	—
994	SD₁₆	—	4	2	no	—
995	SD₁₆	—	4	2	no	—
996	SD₁₆	—	4	2	no	—
997	D₈	—	2	2	no	—
998	D₈	—	2	4	no	—
999	D₈	—	2	4	no	—
1000	D₈	—	4	2	no	—
1001	D₈	—	4	2	no	—
1002	D₈	—	4	2	no	—
1003	D₈	—	4	2	no	—
1004	D₈	—	4	2	no	—
1005	M₁₆	—	4	2	no	—
1006	M₁₆	—	4	2	no	—
1007	C₂×C₈	—	4	2	no	—
1008	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1010	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1011	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1012	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1013	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1024	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1025	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1026	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1027	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1028	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1029	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1030	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1031	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1033	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1059	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1060	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1061	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	1	no	—
1065	C₄²	—	2	2	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1068	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1069	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1070	C₄²	C₂⁴×C₃₁	1	2	yes	—
1071	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	4	4	no	—
1078	C₂³	—	4	4	no	—
1079	C₂³	—	8	2	no	—
1080	C₂³	—	8	2	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	—	8	2	no	—
1084	C₂³	—	8	2	no	—
1085	C₂³	—	8	2	no	—
1086	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1087	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	1	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	2	1	no	—
1093	Q₈	—	4	2	no	—
1094	Q₈	—	8	2	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	2	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	2	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	8	1	no	—
1113	D₄	—	8	2	no	—
1114	D₄	—	8	2	no	—
1115	D₄	—	8	2	no	—
1116	D₄	—	8	2	no	—
1117	D₄	—	8	1	no	—
1118	D₄	—	8	1	no	—
1119	D₄	—	8	2	no	—
1120	D₄	—	8	2	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	8	1	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	—	8	2	no	—
1146	C₂×C₄	—	8	2	no	—
1147	C₂×C₄	—	8	2	no	—
1148	C₂×C₄	—	8	2	no	—
1149	C₂×C₄	—	8	2	no	—
1150	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1151	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1152	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1153	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1154	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1155	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1156	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1157	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1158	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1159	C₈	—	2	1	no	—
1160	C₈	—	2	2	no	—
1161	C₈	—	2	2	no	—
1162	C₈	—	2	1	no	—
1163	C₈	—	2	1	no	—
1164	C₈	—	2	1	no	—
1165	C₂²	—	2	1	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	1	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	1	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	16	4	no	—
1187	C₂²	—	16	4	no	—
1188	C₂²	—	16	4	no	—
1189	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1190	C₄	—	2	1	no	—
1191	C₄	—	2	2	no	—
1192	C₄	—	2	1	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	1	no	—
1195	C₄	—	2	1	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	C₃₁×#576	1	2	yes	—
1205	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1206	C₄	C₃₁×#585	1	1	yes	characteristic
1207	C₂	—	4	1	no	—
1208	C₂	—	4	2	no	—
1209	C₂	—	4	2	no	—
1210	C₂	—	8	1	no	—
1211	C₂	—	8	2	no	—
1212	C₂	—	8	2	no	—
1213	C₂	—	8	2	no	—
1214	C₂	C₃₁×#3488	1	1	yes	characteristic
1215	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1216	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3543	C₂	semidirect
2. C₃₁×#3514	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3396	C₂	semidirect
5. C₃₁×#3373	C₂	semidirect
6. C₃₁×#3358	C₂	semidirect
7. C₃₁×#3325	C₂	semidirect
8. C₃₁×#3324	C₂	semidirect
9. C₃₁×#3319	C₂	semidirect
10. C₃₁×#3304	C₂	semidirect
11. D₄×D₈×C₃₁	C₂	semidirect
12. C₃₁×#3274	C₂	semidirect
13. C₃₁×#3273	C₂	semidirect
14. C₃₁×#3264	C₂	semidirect
15. C₃₁×#3257	C₂	semidirect
16. C₃₁×#3251	C₂	semidirect
17. C₃₁×#3224	C₂	semidirect
18. C₃₁×#3205	C₂	semidirect
19. C₃₁×#3122	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3041	C₂	semidirect
22. C₃₁×#3038	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
24. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂²×D₈×C₃₁	C₂²	semidirect
28. C₃₁×#559	C₂²	semidirect
29. C₃₁×#559	C₂²	semidirect
30. C₃₁×#556	C₂²	semidirect
31. C₃₁×#555	C₂²	semidirect
34. C₃₁×#550	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
39. C₃₁×#546	C₂²	semidirect
40. C₃₁×#546	C₂²	semidirect
43. D₄²×C₃₁	C₂²	semidirect
44. D₄²×C₃₁	C₂²	semidirect
45. C₃₁×#542	C₂²	semidirect
47. C₃₁×#540	C₂²	semidirect
50. C₃₁×#535	C₂²	semidirect
52. C₃₁×#532	C₂²	semidirect
53. C₂×C₃₁×#127	C₂²	semidirect
56. C₃₁×#529	C₂²	semidirect
58. C₃₁×#518	C₂²	semidirect
59. C₄×#41×C₃₁	C₂²	semidirect
60. C₃₁×#496	C₂²	semidirect
61. C₃₁×#495	C₂²	semidirect
63. C₃₁×#493	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#486	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#486	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#478	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#476	C₂²	semidirect
76. C₃₁×#475	C₂²	semidirect
77. C₃₁×#474	C₂²	semidirect
78. C₃₁×#474	C₂²	semidirect
79. C₃₁×#469	C₂²	semidirect
80. C₃₁×#469	C₂²	semidirect
81. C₃₁×#468	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#466	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
85. C₃₁×#464	C₂²	semidirect
86. C₃₁×#463	C₂²	semidirect
87. C₃₁×#463	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#463	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#460	C₂²	semidirect
93. C₃₁×#460	C₂²	semidirect
94. C₃₁×#460	C₂²	semidirect
95. C₃₁×#460	C₂²	semidirect
97. C₃₁×#459	C₂²	semidirect
98. C₃₁×#459	C₂²	semidirect
99. C₃₁×#459	C₂²	semidirect
100. C₃₁×#459	C₂²	semidirect
101. C₃₁×#459	C₂²	semidirect
102. C₃₁×#459	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
104. C₃₁×#452	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#450	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
109. C₃₁×#447	C₂²	semidirect
110. C₃₁×#447	C₂²	semidirect
111. C₃₁×#447	C₂²	semidirect
112. C₃₁×#447	C₂²	semidirect
113. C₃₁×#447	C₂²	semidirect
114. C₃₁×#446	C₂²	semidirect
115. C₈×Q₈×C₃₁	C₂²	semidirect
116. C₃₁×#442	C₂²	semidirect
117. C₃₁×#442	C₂²	semidirect
118. C₄×Q₁₆×C₃₁	C₂²	semidirect
119. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
121. C₄×D₈×C₃₁	C₂²	semidirect
122. C₄×D₈×C₃₁	C₂²	semidirect
123. C₄×D₈×C₃₁	C₂²	semidirect
124. C₃₁×#436	C₂²	semidirect
125. C₃₁×#436	C₂²	semidirect
126. C₃₁×#435	C₂²	semidirect
127. C₈×D₄×C₃₁	C₂²	semidirect
128. C₃₁×#433	C₂²	semidirect
129. C₃₁×#431	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
131. C₃₁×#423	C₂²	semidirect
132. C₃₁×#418	C₂²	semidirect
133. C₃₁×#418	C₂²	semidirect
134. C₃₁×#416	C₂²	semidirect
463. #62031	C₃₁	direct (N × H)
557. #3543	C₂×C₃₁	semidirect
558. #3514	C₂×C₃₁	semidirect
559. #3399	C₂×C₃₁	semidirect
560. #3396	C₂×C₃₁	semidirect
561. #3373	C₂×C₃₁	semidirect
562. #3358	C₂×C₃₁	semidirect
563. #3325	C₂×C₃₁	semidirect
564. #3324	C₂×C₃₁	semidirect
565. #3319	C₂×C₃₁	semidirect
566. #3304	C₂×C₃₁	semidirect
567. D₄×D₈	C₂×C₃₁	semidirect
568. #3274	C₂×C₃₁	semidirect
569. #3273	C₂×C₃₁	semidirect
570. #3264	C₂×C₃₁	semidirect
571. #3257	C₂×C₃₁	semidirect
572. #3251	C₂×C₃₁	semidirect
573. #3224	C₂×C₃₁	semidirect
574. #3205	C₂×C₃₁	semidirect
575. #3122	C₂×C₃₁	semidirect
576. #3102	C₂×C₃₁	semidirect
577. #3041	C₂×C₃₁	semidirect
578. #3038	C₂×C₃₁	semidirect
579. #2993	C₂×C₃₁	semidirect
622. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
623. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
624. C₂²×D₈	C₂²×C₃₁	semidirect
626. #559	C₂²×C₃₁	semidirect
627. #559	C₂²×C₃₁	semidirect
628. #556	C₂²×C₃₁	semidirect
629. #555	C₂²×C₃₁	semidirect
632. #550	C₂²×C₃₁	semidirect
633. D₄×Q₈	C₂²×C₃₁	semidirect
637. #546	C₂²×C₃₁	semidirect
638. #546	C₂²×C₃₁	semidirect
641. D₄²	C₂²×C₃₁	semidirect
642. D₄²	C₂²×C₃₁	semidirect
643. #542	C₂²×C₃₁	semidirect
645. #540	C₂²×C₃₁	semidirect
648. #535	C₂²×C₃₁	semidirect
650. #532	C₂²×C₃₁	semidirect
651. C₂×#127	C₂²×C₃₁	semidirect
654. #529	C₂²×C₃₁	semidirect
656. #518	C₂²×C₃₁	semidirect
657. C₄×#41	C₂²×C₃₁	semidirect
658. #496	C₂²×C₃₁	semidirect
659. #495	C₂²×C₃₁	semidirect
661. #493	C₂²×C₃₁	semidirect
662. #489	C₂²×C₃₁	semidirect
663. #486	C₂²×C₃₁	semidirect
664. #486	C₂²×C₃₁	semidirect
665. #486	C₂²×C₃₁	semidirect
666. #485	C₂²×C₃₁	semidirect
667. #482	C₂²×C₃₁	semidirect
668. #482	C₂²×C₃₁	semidirect
669. #482	C₂²×C₃₁	semidirect
670. #479	C₂²×C₃₁	semidirect
671. #478	C₂²×C₃₁	semidirect
672. #478	C₂²×C₃₁	semidirect
673. #476	C₂²×C₃₁	semidirect
674. #475	C₂²×C₃₁	semidirect
675. #474	C₂²×C₃₁	semidirect
676. #474	C₂²×C₃₁	semidirect
677. #469	C₂²×C₃₁	semidirect
678. #469	C₂²×C₃₁	semidirect
679. #468	C₂²×C₃₁	semidirect
680. #468	C₂²×C₃₁	semidirect
681. #466	C₂²×C₃₁	semidirect
682. #465	C₂²×C₃₁	semidirect
683. #464	C₂²×C₃₁	semidirect
684. #463	C₂²×C₃₁	semidirect
685. #463	C₂²×C₃₁	semidirect
686. #463	C₂²×C₃₁	semidirect
687. #463	C₂²×C₃₁	semidirect
688. #463	C₂²×C₃₁	semidirect
689. #463	C₂²×C₃₁	semidirect
690. #460	C₂²×C₃₁	semidirect
691. #460	C₂²×C₃₁	semidirect
692. #460	C₂²×C₃₁	semidirect
693. #460	C₂²×C₃₁	semidirect
695. #459	C₂²×C₃₁	semidirect
696. #459	C₂²×C₃₁	semidirect
697. #459	C₂²×C₃₁	semidirect
698. #459	C₂²×C₃₁	semidirect
699. #459	C₂²×C₃₁	semidirect
700. #459	C₂²×C₃₁	semidirect
701. #459	C₂²×C₃₁	semidirect
702. #452	C₂²×C₃₁	semidirect
703. #452	C₂²×C₃₁	semidirect
704. #450	C₂²×C₃₁	semidirect
706. #449	C₂²×C₃₁	semidirect
707. #447	C₂²×C₃₁	semidirect
708. #447	C₂²×C₃₁	semidirect
709. #447	C₂²×C₃₁	semidirect
710. #447	C₂²×C₃₁	semidirect
711. #447	C₂²×C₃₁	semidirect
712. #446	C₂²×C₃₁	semidirect
713. C₈×Q₈	C₂²×C₃₁	semidirect
714. #442	C₂²×C₃₁	semidirect
715. #442	C₂²×C₃₁	semidirect
716. C₄×Q₁₆	C₂²×C₃₁	semidirect
717. C₄×SD₁₆	C₂²×C₃₁	semidirect
718. C₄×SD₁₆	C₂²×C₃₁	semidirect
719. C₄×D₈	C₂²×C₃₁	semidirect
720. C₄×D₈	C₂²×C₃₁	semidirect
721. C₄×D₈	C₂²×C₃₁	semidirect
722. #436	C₂²×C₃₁	semidirect
723. #436	C₂²×C₃₁	semidirect
724. #435	C₂²×C₃₁	semidirect
725. C₈×D₄	C₂²×C₃₁	semidirect
726. #433	C₂²×C₃₁	semidirect
727. #431	C₂²×C₃₁	semidirect
728. #424	C₂²×C₃₁	semidirect
729. #423	C₂²×C₃₁	semidirect
730. #418	C₂²×C₃₁	semidirect
731. #418	C₂²×C₃₁	semidirect
732. #416	C₂²×C₃₁	semidirect
923. C₃₁	#62031	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×#3543	2
C₃₁×#3514	2
C₃₁×#3399	2
C₃₁×#3396	2
C₃₁×#3373	2
C₃₁×#3358	2
C₃₁×#3325	2
C₃₁×#3324	2
C₃₁×#3319	2
C₃₁×#3304	2
D₄×D₈×C₃₁	2
C₃₁×#3274	2
C₃₁×#3273	2
C₃₁×#3264	2
C₃₁×#3257	2
C₃₁×#3251	2
C₃₁×#3224	2
C₃₁×#3205	2
C₃₁×#3122	2
C₃₁×#3102	2
C₃₁×#3041	2
C₃₁×#3038	2
C₃₁×#2993	2
#62031	31

Subgroups — C31×#62031 #21518790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62031 #21518790