Subgroups — C₃₁×#62033 #21518792

Order 7936.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1188 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×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3272	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3260	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3045	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	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
27	C₃₁×#560	—	2	2	no	—
28	C₃₁×#559	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#552	—	2	2	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	C₂²	1	2	yes	complemented
36	C₃₁×#550	C₂²	1	1	yes	characteristic
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	C₃₁×#547	C₂²	1	2	yes	complemented
39	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	C₂²	1	2	yes	—
42	D₄²×C₃₁	—	2	1	no	—
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic
44	D₄²×C₃₁	C₂²	1	2	yes	—
45	C₃₁×#541	C₂²	1	2	yes	complemented
46	C₃₁×#540	—	2	1	no	—
47	C₃₁×#540	C₂²	1	2	yes	—
48	C₃₁×#539	—	2	2	no	—
49	C₃₁×#535	—	2	1	no	—
50	C₃₁×#535	C₂²	1	2	yes	—
51	C₃₁×#534	—	2	2	no	—
52	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
54	C₃₁×#529	—	2	1	no	—
55	C₃₁×#529	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic
57	C₂×C₃₁×#125	—	2	1	no	—
58	C₃₁×#520	C₂²	1	2	yes	complemented
59	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#497	C₂²	1	2	yes	complemented
61	C₃₁×#492	C₂²	1	1	yes	characteristic
62	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#492	C₂²	1	2	yes	complemented
64	C₃₁×#490	C₂²	1	2	yes	complemented
65	C₃₁×#488	C₂²	1	2	yes	complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic
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
70	C₃₁×#481	C₂²	1	2	yes	complemented
71	C₃₁×#480	C₂²	1	2	yes	complemented
72	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#470	C₂²	1	2	yes	complemented
80	C₃₁×#468	C₂²	1	2	yes	—
81	C₃₁×#468	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#465	C₂²	1	2	yes	complemented
84	C₃₁×#465	C₂²	1	2	yes	complemented
85	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#464	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#461	C₂²	1	2	yes	complemented
93	C₃₁×#461	C₂²	1	2	yes	complemented
94	C₃₁×#460	C₂²	1	1	yes	characteristic
95	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#460	C₂²	1	2	yes	complemented
97	C₃₁×#460	C₂²	1	2	yes	complemented
98	C₃₁×#460	C₂²	1	2	yes	complemented
99	C₃₁×#460	C₂²	1	2	yes	complemented
100	C₃₁×#459	C₂²	1	1	yes	characteristic
101	C₃₁×#459	C₂²	1	2	yes	complemented
102	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#459	C₂²	1	2	yes	complemented
104	C₃₁×#452	C₂²	1	2	yes	complemented
105	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	2	yes	complemented
108	C₃₁×#450	C₂²	1	2	yes	complemented
109	C₃₁×#450	C₂²	1	2	yes	complemented
110	C₃₁×#450	C₂²	1	2	yes	complemented
111	C₃₁×#449	C₂²	1	1	yes	characteristic
112	C₃₁×#449	C₂²	1	2	yes	complemented
113	C₃₁×#449	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×#440	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×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
122	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
124	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#436	C₂²	1	2	yes	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×#417	C₂²	1	2	yes	complemented
134	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₃₁	—	2	2	no	—
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
145	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
146	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
147	C₃₁×#135	—	4	4	no	—
148	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₃₁	C₂³	1	2	yes	—
161	C₂×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
163	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
164	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×#127	—	2	1	no	—
169	C₃₁×#127	—	2	1	no	—
170	C₃₁×#127	—	2	1	no	—
171	C₃₁×#127	C₂³	1	1	yes	characteristic
172	C₃₁×#127	C₂³	1	2	yes	—
173	C₃₁×#127	C₂³	1	1	yes	characteristic
174	C₃₁×#127	C₂³	1	2	yes	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#126	—	2	1	no	—
179	C₃₁×#126	D₄	1	2	yes	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	1	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	2	no	—
185	C₃₁×#125	—	2	2	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	D₄	1	1	yes	characteristic
188	C₃₁×#125	C₂³	1	2	yes	—
189	C₃₁×#125	C₂³	1	1	yes	characteristic
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×#123	—	2	2	no	—
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	1	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	1	no	—
219	C₃₁×#121	—	2	1	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	—	2	2	no	—
225	C₃₁×#121	D₄	1	1	yes	characteristic
226	C₃₁×#121	C₂³	1	1	yes	characteristic
227	C₃₁×#121	C₂³	1	2	yes	—
228	C₃₁×#121	C₂³	1	2	yes	—
229	C₃₁×#120	—	2	2	no	—
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	C₄×Q₈×C₃₁	—	2	1	no	—
236	C₄×Q₈×C₃₁	—	2	1	no	—
237	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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	1	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	—	2	2	no	—
250	C₄×D₄×C₃₁	—	2	2	no	—
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₃₁	C₂³	1	2	yes	—
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	2	no	—
261	C₃₁×#117	—	2	2	no	—
262	C₃₁×#117	—	2	1	no	—
263	C₃₁×#117	—	2	1	no	—
264	C₃₁×#117	C₂³	1	1	yes	characteristic
265	C₃₁×#117	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	1	yes	characteristic
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	2	yes	—
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	1	yes	characteristic
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	#41×C₃₁	—	2	4	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	—	4	2	no	—
323	#41×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	1	no	—
345	C₂×D₄×C₃₁	—	4	2	no	—
346	C₂×D₄×C₃₁	—	4	2	no	—
347	C₂×D₄×C₃₁	—	4	2	no	—
348	C₂×D₄×C₃₁	—	4	2	no	—
349	C₂×D₄×C₃₁	—	8	2	no	—
350	C₂×D₄×C₃₁	—	8	2	no	—
351	C₂×D₄×C₃₁	—	8	2	no	—
352	C₂×D₄×C₃₁	—	8	4	no	—
353	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
357	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
358	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	2	no	—
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	1	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	2	no	—
367	C₂²×C₄×C₃₁	—	2	2	no	—
368	C₂²×C₄×C₃₁	—	2	2	no	—
369	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
373	Q₁₆×C₃₁	—	4	1	no	—
374	Q₁₆×C₃₁	—	4	2	no	—
375	SD₁₆×C₃₁	—	2	2	no	—
376	SD₁₆×C₃₁	—	4	1	no	—
377	SD₁₆×C₃₁	—	4	2	no	—
378	SD₁₆×C₃₁	—	4	2	no	—
379	SD₁₆×C₃₁	—	4	2	no	—
380	SD₁₆×C₃₁	—	4	2	no	—
381	SD₁₆×C₃₁	—	4	2	no	—
382	SD₁₆×C₃₁	—	4	2	no	—
383	SD₁₆×C₃₁	—	4	2	no	—
384	D₈×C₃₁	—	2	4	no	—
385	D₈×C₃₁	—	2	2	no	—
386	D₈×C₃₁	—	2	4	no	—
387	M₁₆×C₃₁	—	4	2	no	—
388	M₁₆×C₃₁	—	4	2	no	—
389	C₂×C₈×C₃₁	—	4	2	no	—
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
395	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	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	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	1	no	—
437	C₂²⋊C₄×C₃₁	—	2	1	no	—
438	C₂²⋊C₄×C₃₁	—	2	1	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
449	C₄²×C₃₁	—	2	1	no	—
450	C₄²×C₃₁	—	2	1	no	—
451	C₄²×C₃₁	—	2	1	no	—
452	C₄²×C₃₁	—	2	2	no	—
453	C₄²×C₃₁	—	2	2	no	—
454	C₄²×C₃₁	—	2	1	no	—
455	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
458	C₄²×C₃₁	C₂⁴	1	2	yes	—
459	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
460	#62033	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂³×C₃₁	—	2	1	no	—
462	C₂³×C₃₁	—	2	2	no	—
463	C₂³×C₃₁	—	2	1	no	—
464	C₂³×C₃₁	—	2	2	no	—
465	C₂³×C₃₁	—	4	4	no	—
466	C₂³×C₃₁	—	8	2	no	—
467	C₂³×C₃₁	—	8	2	no	—
468	C₂³×C₃₁	—	8	2	no	—
469	C₂³×C₃₁	—	8	2	no	—
470	C₂³×C₃₁	—	8	2	no	—
471	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
472	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
473	Q₈×C₃₁	—	2	2	no	—
474	Q₈×C₃₁	—	2	1	no	—
475	Q₈×C₃₁	—	2	1	no	—
476	Q₈×C₃₁	—	2	2	no	—
477	Q₈×C₃₁	—	2	2	no	—
478	Q₈×C₃₁	—	2	1	no	—
479	Q₈×C₃₁	—	2	1	no	—
480	Q₈×C₃₁	—	8	1	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	1	no	—
483	D₄×C₃₁	—	2	2	no	—
484	D₄×C₃₁	—	2	2	no	—
485	D₄×C₃₁	—	2	1	no	—
486	D₄×C₃₁	—	2	1	no	—
487	D₄×C₃₁	—	2	2	no	—
488	D₄×C₃₁	—	2	2	no	—
489	D₄×C₃₁	—	4	2	no	—
490	D₄×C₃₁	—	4	4	no	—
491	D₄×C₃₁	—	4	2	no	—
492	D₄×C₃₁	—	4	2	no	—
493	D₄×C₃₁	—	4	2	no	—
494	D₄×C₃₁	—	4	2	no	—
495	D₄×C₃₁	—	8	2	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	—	8	2	no	—
498	D₄×C₃₁	—	8	1	no	—
499	D₄×C₃₁	—	8	1	no	—
500	D₄×C₃₁	—	8	2	no	—
501	D₄×C₃₁	—	8	2	no	—
502	D₄×C₃₁	—	8	2	no	—
503	D₄×C₃₁	—	8	2	no	—
504	D₄×C₃₁	—	8	2	no	—
505	D₄×C₃₁	—	8	2	no	—
506	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
507	C₂×C₄×C₃₁	—	2	2	no	—
508	C₂×C₄×C₃₁	—	2	2	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	2	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	1	no	—
514	C₂×C₄×C₃₁	—	2	1	no	—
515	C₂×C₄×C₃₁	—	2	2	no	—
516	C₂×C₄×C₃₁	—	2	1	no	—
517	C₂×C₄×C₃₁	—	2	1	no	—
518	C₂×C₄×C₃₁	—	2	2	no	—
519	C₂×C₄×C₃₁	—	2	1	no	—
520	C₂×C₄×C₃₁	—	4	1	no	—
521	C₂×C₄×C₃₁	—	4	4	no	—
522	C₂×C₄×C₃₁	—	4	2	no	—
523	C₂×C₄×C₃₁	—	4	2	no	—
524	C₂×C₄×C₃₁	—	4	2	no	—
525	C₂×C₄×C₃₁	—	8	1	no	—
526	C₂×C₄×C₃₁	—	8	2	no	—
527	C₂×C₄×C₃₁	—	8	2	no	—
528	C₂×C₄×C₃₁	—	8	2	no	—
529	C₂×C₄×C₃₁	—	8	2	no	—
530	C₂×C₄×C₃₁	—	8	2	no	—
531	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
540	C₈×C₃₁	—	2	1	no	—
541	C₈×C₃₁	—	2	2	no	—
542	C₈×C₃₁	—	2	1	no	—
543	C₈×C₃₁	—	2	2	no	—
544	C₈×C₃₁	—	2	1	no	—
545	C₈×C₃₁	—	2	1	no	—
546	#3543	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3392	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3323	C₂×C₃₁	1	2	yes	complemented
554	#3310	C₂×C₃₁	1	2	yes	complemented
555	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3284	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3272	C₂×C₃₁	1	2	yes	complemented
558	#3272	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3267	C₂×C₃₁	1	2	yes	complemented
560	#3260	C₂×C₃₁	1	2	yes	complemented
561	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3222	C₂×C₃₁	1	2	yes	complemented
563	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
564	#3119	C₂×C₃₁	1	2	yes	complemented
565	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
566	#3045	C₂×C₃₁	1	2	yes	complemented
567	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
569	C₂²×C₃₁	—	2	1	no	—
570	C₂²×C₃₁	—	2	2	no	—
571	C₂²×C₃₁	—	2	2	no	—
572	C₂²×C₃₁	—	2	1	no	—
573	C₂²×C₃₁	—	2	2	no	—
574	C₂²×C₃₁	—	2	1	no	—
575	C₂²×C₃₁	—	2	2	no	—
576	C₂²×C₃₁	—	4	1	no	—
577	C₂²×C₃₁	—	4	1	no	—
578	C₂²×C₃₁	—	4	2	no	—
579	C₂²×C₃₁	—	4	1	no	—
580	C₂²×C₃₁	—	4	2	no	—
581	C₂²×C₃₁	—	4	2	no	—
582	C₂²×C₃₁	—	4	2	no	—
583	C₂²×C₃₁	—	4	1	no	—
584	C₂²×C₃₁	—	4	1	no	—
585	C₂²×C₃₁	—	4	2	no	—
586	C₂²×C₃₁	—	4	2	no	—
587	C₂²×C₃₁	—	16	4	no	—
588	C₂²×C₃₁	—	16	4	no	—
589	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
590	C₄×C₃₁	—	2	1	no	—
591	C₄×C₃₁	—	2	1	no	—
592	C₄×C₃₁	—	2	2	no	—
593	C₄×C₃₁	—	2	2	no	—
594	C₄×C₃₁	—	2	1	no	—
595	C₄×C₃₁	—	2	1	no	—
596	C₄×C₃₁	—	2	2	no	—
597	C₄×C₃₁	—	4	1	no	—
598	C₄×C₃₁	—	4	1	no	—
599	C₄×C₃₁	—	4	2	no	—
600	C₄×C₃₁	—	4	1	no	—
601	C₄×C₃₁	—	4	2	no	—
602	C₄×C₃₁	—	4	1	no	—
603	C₄×C₃₁	—	4	1	no	—
604	C₄×C₃₁	—	4	1	no	—
605	C₄×C₃₁	#577	1	2	yes	—
606	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
607	C₄×C₃₁	#585	1	1	yes	characteristic
608	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
609	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
610	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
611	#560	—	2	2	no	—
612	#559	C₂²×C₃₁	1	1	yes	characteristic
613	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#553	—	2	1	no	—
617	#552	—	2	2	no	—
618	#552	—	2	1	no	—
619	#552	C₂²×C₃₁	1	2	yes	complemented
620	#550	C₂²×C₃₁	1	1	yes	characteristic
621	#550	C₂²×C₃₁	1	1	yes	characteristic
622	#547	C₂²×C₃₁	1	2	yes	complemented
623	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#546	—	2	1	no	—
625	#546	C₂²×C₃₁	1	2	yes	—
626	D₄²	—	2	1	no	—
627	D₄²	C₂²×C₃₁	1	1	yes	characteristic
628	D₄²	C₂²×C₃₁	1	2	yes	—
629	#541	C₂²×C₃₁	1	2	yes	complemented
630	#540	—	2	1	no	—
631	#540	C₂²×C₃₁	1	2	yes	—
632	#539	—	2	2	no	—
633	#535	—	2	1	no	—
634	#535	C₂²×C₃₁	1	2	yes	—
635	#534	—	2	2	no	—
636	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
638	#529	—	2	1	no	—
639	#529	C₂²×C₃₁	1	1	yes	characteristic
640	#529	C₂²×C₃₁	1	1	yes	characteristic
641	C₂×#125	—	2	1	no	—
642	#520	C₂²×C₃₁	1	2	yes	complemented
643	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#497	C₂²×C₃₁	1	2	yes	complemented
645	#492	C₂²×C₃₁	1	1	yes	characteristic
646	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#492	C₂²×C₃₁	1	2	yes	complemented
648	#490	C₂²×C₃₁	1	2	yes	complemented
649	#488	C₂²×C₃₁	1	2	yes	complemented
650	#486	C₂²×C₃₁	1	1	yes	characteristic
651	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#482	C₂²×C₃₁	1	1	yes	characteristic
654	#481	C₂²×C₃₁	1	2	yes	complemented
655	#480	C₂²×C₃₁	1	2	yes	complemented
656	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#479	C₂²×C₃₁	1	2	yes	complemented
658	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#478	C₂²×C₃₁	1	2	yes	complemented
660	#478	C₂²×C₃₁	1	2	yes	complemented
661	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#470	C₂²×C₃₁	1	2	yes	complemented
664	#468	C₂²×C₃₁	1	2	yes	—
665	#468	C₂²×C₃₁	1	2	yes	complemented
666	#468	C₂²×C₃₁	1	2	yes	complemented
667	#465	C₂²×C₃₁	1	2	yes	complemented
668	#465	C₂²×C₃₁	1	2	yes	complemented
669	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#464	C₂²×C₃₁	1	2	yes	complemented
671	#464	C₂²×C₃₁	1	2	yes	complemented
672	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#463	C₂²×C₃₁	1	2	yes	complemented
674	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#461	C₂²×C₃₁	1	2	yes	complemented
677	#461	C₂²×C₃₁	1	2	yes	complemented
678	#460	C₂²×C₃₁	1	1	yes	characteristic
679	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#460	C₂²×C₃₁	1	2	yes	complemented
681	#460	C₂²×C₃₁	1	2	yes	complemented
682	#460	C₂²×C₃₁	1	2	yes	complemented
683	#460	C₂²×C₃₁	1	2	yes	complemented
684	#459	C₂²×C₃₁	1	1	yes	characteristic
685	#459	C₂²×C₃₁	1	2	yes	complemented
686	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#459	C₂²×C₃₁	1	2	yes	complemented
688	#452	C₂²×C₃₁	1	2	yes	complemented
689	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	#452	C₂²×C₃₁	1	2	yes	complemented
691	#450	C₂²×C₃₁	1	2	yes	complemented
692	#450	C₂²×C₃₁	1	2	yes	complemented
693	#450	C₂²×C₃₁	1	2	yes	complemented
694	#450	C₂²×C₃₁	1	2	yes	complemented
695	#449	C₂²×C₃₁	1	1	yes	characteristic
696	#449	C₂²×C₃₁	1	2	yes	complemented
697	#449	C₂²×C₃₁	1	2	yes	complemented
698	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	#442	C₂²×C₃₁	1	2	yes	complemented
701	#440	C₂²×C₃₁	1	2	yes	complemented
702	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
706	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
708	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	#436	C₂²×C₃₁	1	2	yes	complemented
710	#435	C₂²×C₃₁	1	2	yes	complemented
711	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	#433	C₂²×C₃₁	1	2	yes	complemented
713	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	#424	C₂²×C₃₁	1	2	yes	complemented
715	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	#418	C₂²×C₃₁	1	2	yes	complemented
717	#417	C₂²×C₃₁	1	2	yes	complemented
718	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
719	C₂×C₃₁	—	4	2	no	—
720	C₂×C₃₁	—	4	1	no	—
721	C₂×C₃₁	—	4	2	no	—
722	C₂×C₃₁	—	8	2	no	—
723	C₂×C₃₁	—	8	2	no	—
724	C₂×C₃₁	—	8	1	no	—
725	C₂×C₃₁	#3488	1	1	yes	characteristic
726	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
727	C₂×C₃₁	#3585	1	1	yes	characteristic
728	C₂×#41	—	2	1	no	—
729	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×#41	C₂³×C₃₁	1	2	yes	—
731	C₂×#41	C₂³×C₃₁	1	2	yes	—
732	C₂²×D₄	—	2	2	no	—
733	C₂²×D₄	—	2	1	no	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
737	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
738	AGL(1,ℤ/8)	—	4	4	no	—
739	AGL(1,ℤ/8)	—	4	4	no	—
740	#135	—	4	4	no	—
741	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
742	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
752	C₂×D₈	C₂³×C₃₁	1	2	yes	—
753	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
754	C₂×D₈	C₂³×C₃₁	1	2	yes	—
755	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
756	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
757	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
758	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
760	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
761	#127	—	2	1	no	—
762	#127	—	2	1	no	—
763	#127	—	2	1	no	—
764	#127	C₂³×C₃₁	1	2	yes	—
765	#127	C₂³×C₃₁	1	1	yes	characteristic
766	#127	C₂³×C₃₁	1	1	yes	characteristic
767	#127	C₂³×C₃₁	1	2	yes	—
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	1	no	—
772	#126	D₄×C₃₁	1	2	yes	—
773	#125	—	2	2	no	—
774	#125	—	2	2	no	—
775	#125	—	2	1	no	—
776	#125	—	2	1	no	—
777	#125	—	2	2	no	—
778	#125	—	2	2	no	—
779	#125	—	2	1	no	—
780	#125	D₄×C₃₁	1	1	yes	characteristic
781	#125	C₂³×C₃₁	1	1	yes	characteristic
782	#125	C₂³×C₃₁	1	2	yes	—
783	#124	—	2	1	no	—
784	#124	D₄×C₃₁	1	1	yes	characteristic
785	#124	C₂³×C₃₁	1	1	yes	characteristic
786	#124	C₂³×C₃₁	1	2	yes	—
787	#123	—	2	2	no	—
788	#123	—	2	1	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	D₄×C₃₁	1	2	yes	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
802	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
803	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	D₄×C₃₁	1	1	yes	characteristic
819	#121	C₂³×C₃₁	1	1	yes	characteristic
820	#121	C₂³×C₃₁	1	2	yes	—
821	#121	C₂³×C₃₁	1	2	yes	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	C₄×Q₈	—	2	1	no	—
829	C₄×Q₈	—	2	1	no	—
830	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
833	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
834	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	2	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₃₁	1	2	yes	—
847	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₃₁	1	2	yes	—
849	C₄×D₄	C₂³×C₃₁	1	2	yes	—
850	C₄×D₄	C₂³×C₃₁	1	2	yes	—
851	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
852	#117	—	2	1	no	—
853	#117	—	2	2	no	—
854	#117	—	2	2	no	—
855	#117	—	2	1	no	—
856	#117	—	2	1	no	—
857	#117	C₂³×C₃₁	1	1	yes	characteristic
858	#117	C₂³×C₃₁	1	2	yes	—
859	C₂×C₄⋊C₄	—	2	2	no	—
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	—	2	2	no	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₄²	—	2	1	no	—
866	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
867	#107	C₂³×C₃₁	1	2	yes	—
868	#107	C₂³×C₃₁	1	1	yes	characteristic
869	#107	C₂³×C₃₁	1	1	yes	characteristic
870	#106	C₂³×C₃₁	1	1	yes	characteristic
871	#106	C₂³×C₃₁	1	1	yes	characteristic
872	#106	C₂³×C₃₁	1	2	yes	—
873	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
874	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
878	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
879	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
880	#103	C₂³×C₃₁	1	1	yes	characteristic
881	#103	C₂³×C₃₁	1	2	yes	—
882	#103	C₂³×C₃₁	1	2	yes	—
883	#103	C₂³×C₃₁	1	1	yes	characteristic
884	#103	C₂³×C₃₁	1	1	yes	characteristic
885	#103	C₂³×C₃₁	1	1	yes	characteristic
886	#103	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	1	yes	characteristic
888	#102	C₂³×C₃₁	1	2	yes	—
889	#102	C₂³×C₃₁	1	2	yes	—
890	#102	C₂³×C₃₁	1	2	yes	—
891	#102	C₂³×C₃₁	1	2	yes	—
892	#102	C₂³×C₃₁	1	2	yes	—
893	#102	C₂³×C₃₁	1	2	yes	—
894	#102	C₂³×C₃₁	1	2	yes	—
895	#102	C₂³×C₃₁	1	1	yes	characteristic
896	#102	C₂³×C₃₁	1	1	yes	characteristic
897	#102	C₂³×C₃₁	1	2	yes	—
898	#102	C₂³×C₃₁	1	1	yes	characteristic
899	#102	C₂³×C₃₁	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
902	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
904	#97	C₂³×C₃₁	1	2	yes	—
905	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
906	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₃₁	1	2	yes	—
908	C₃₁	#62033	1	1	yes	characteristic, direct product factor, Sylow
909	C₂⁴	—	2	2	no	—
910	C₂⁴	—	2	2	no	—
911	#41	—	2	4	no	—
912	#41	—	2	2	no	—
913	#41	—	4	1	no	—
914	#41	—	4	2	no	—
915	#41	—	4	2	no	—
916	#41	—	4	2	no	—
917	#41	—	8	2	no	—
918	C₂×Q₈	—	2	1	no	—
919	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
920	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	4	2	no	—
940	C₂×D₄	—	4	2	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	2	no	—
943	C₂×D₄	—	8	2	no	—
944	C₂×D₄	—	8	2	no	—
945	C₂×D₄	—	8	2	no	—
946	C₂×D₄	—	8	4	no	—
947	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
949	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
951	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
952	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
964	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
967	Q₁₆	—	4	1	no	—
968	Q₁₆	—	4	2	no	—
969	SD₁₆	—	2	2	no	—
970	SD₁₆	—	4	1	no	—
971	SD₁₆	—	4	2	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	SD₁₆	—	4	2	no	—
977	SD₁₆	—	4	2	no	—
978	D₈	—	2	4	no	—
979	D₈	—	2	2	no	—
980	D₈	—	2	4	no	—
981	M₁₆	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	C₂×C₈	—	4	2	no	—
984	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
989	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1010	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1011	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1012	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1014	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1015	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1039	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1041	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1042	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	2	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1052	C₄²	C₂⁴×C₃₁	1	2	yes	—
1053	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	—	8	2	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	—	8	2	no	—
1064	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1065	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	8	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	4	2	no	—
1083	D₄	—	4	4	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	1	no	—
1093	D₄	—	8	1	no	—
1094	D₄	—	8	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	4	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	—	8	2	no	—
1124	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1129	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1130	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1131	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1132	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1133	C₈	—	2	1	no	—
1134	C₈	—	2	2	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	2	no	—
1137	C₈	—	2	1	no	—
1138	C₈	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	1	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	16	4	no	—
1158	C₂²	—	16	4	no	—
1159	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	2	no	—
1175	C₄	C₃₁×#577	1	2	yes	—
1176	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1177	C₄	C₃₁×#585	1	1	yes	characteristic
1178	C₂	—	4	1	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	4	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	—	8	2	no	—
1183	C₂	—	8	2	no	—
1184	C₂	C₃₁×#3488	1	1	yes	characteristic
1185	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1186	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×#3515	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3392	C₂	semidirect
5. C₃₁×#3366	C₂	semidirect
6. C₃₁×#3361	C₂	semidirect
7. C₃₁×#3333	C₂	semidirect
8. C₃₁×#3323	C₂	semidirect
9. C₃₁×#3310	C₂	semidirect
10. C₃₁×#3295	C₂	semidirect
11. C₃₁×#3284	C₂	semidirect
12. C₃₁×#3272	C₂	semidirect
13. C₃₁×#3272	C₂	semidirect
14. C₃₁×#3267	C₂	semidirect
15. C₃₁×#3260	C₂	semidirect
16. C₃₁×#3252	C₂	semidirect
17. C₃₁×#3222	C₂	semidirect
18. C₃₁×#3208	C₂	semidirect
19. C₃₁×#3119	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3045	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. C₂×C₃₁×#135	C₂²	semidirect
29. C₃₁×#557	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
39. C₃₁×#547	C₂²	semidirect
45. C₃₁×#541	C₂²	semidirect
52. C₃₁×#533	C₂²	semidirect
58. C₃₁×#520	C₂²	semidirect
59. C₄×#41×C₃₁	C₂²	semidirect
60. C₃₁×#497	C₂²	semidirect
62. C₃₁×#492	C₂²	semidirect
63. C₃₁×#492	C₂²	semidirect
64. C₃₁×#490	C₂²	semidirect
65. C₃₁×#488	C₂²	semidirect
67. C₃₁×#486	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#480	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
79. C₃₁×#470	C₂²	semidirect
81. C₃₁×#468	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#465	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
85. C₃₁×#464	C₂²	semidirect
86. C₃₁×#464	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
91. C₃₁×#461	C₂²	semidirect
92. C₃₁×#461	C₂²	semidirect
93. C₃₁×#461	C₂²	semidirect
95. C₃₁×#460	C₂²	semidirect
96. C₃₁×#460	C₂²	semidirect
97. C₃₁×#460	C₂²	semidirect
98. C₃₁×#460	C₂²	semidirect
99. C₃₁×#460	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×#452	C₂²	semidirect
107. C₃₁×#450	C₂²	semidirect
108. C₃₁×#450	C₂²	semidirect
109. C₃₁×#450	C₂²	semidirect
110. C₃₁×#450	C₂²	semidirect
112. C₃₁×#449	C₂²	semidirect
113. C₃₁×#449	C₂²	semidirect
114. C₃₁×#446	C₂²	semidirect
115. C₈×Q₈×C₃₁	C₂²	semidirect
116. C₃₁×#442	C₂²	semidirect
117. C₃₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₃₁	C₂²	semidirect
119. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
121. C₄×SD₁₆×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×#417	C₂²	semidirect
134. C₂×C₃₁×#102	C₂²	semidirect
460. #62033	C₃₁	direct (N × H)
546. #3543	C₂×C₃₁	semidirect
547. #3515	C₂×C₃₁	semidirect
548. #3400	C₂×C₃₁	semidirect
549. #3392	C₂×C₃₁	semidirect
550. #3366	C₂×C₃₁	semidirect
551. #3361	C₂×C₃₁	semidirect
552. #3333	C₂×C₃₁	semidirect
553. #3323	C₂×C₃₁	semidirect
554. #3310	C₂×C₃₁	semidirect
555. #3295	C₂×C₃₁	semidirect
556. #3284	C₂×C₃₁	semidirect
557. #3272	C₂×C₃₁	semidirect
558. #3272	C₂×C₃₁	semidirect
559. #3267	C₂×C₃₁	semidirect
560. #3260	C₂×C₃₁	semidirect
561. #3252	C₂×C₃₁	semidirect
562. #3222	C₂×C₃₁	semidirect
563. #3208	C₂×C₃₁	semidirect
564. #3119	C₂×C₃₁	semidirect
565. #3102	C₂×C₃₁	semidirect
566. #3045	C₂×C₃₁	semidirect
567. #3038	C₂×C₃₁	semidirect
568. #2993	C₂×C₃₁	semidirect
608. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
609. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
610. C₂×#135	C₂²×C₃₁	semidirect
613. #557	C₂²×C₃₁	semidirect
614. #554	C₂²×C₃₁	semidirect
615. #554	C₂²×C₃₁	semidirect
619. #552	C₂²×C₃₁	semidirect
622. #547	C₂²×C₃₁	semidirect
623. #547	C₂²×C₃₁	semidirect
629. #541	C₂²×C₃₁	semidirect
636. #533	C₂²×C₃₁	semidirect
642. #520	C₂²×C₃₁	semidirect
643. C₄×#41	C₂²×C₃₁	semidirect
644. #497	C₂²×C₃₁	semidirect
646. #492	C₂²×C₃₁	semidirect
647. #492	C₂²×C₃₁	semidirect
648. #490	C₂²×C₃₁	semidirect
649. #488	C₂²×C₃₁	semidirect
651. #486	C₂²×C₃₁	semidirect
652. #485	C₂²×C₃₁	semidirect
654. #481	C₂²×C₃₁	semidirect
655. #480	C₂²×C₃₁	semidirect
656. #479	C₂²×C₃₁	semidirect
657. #479	C₂²×C₃₁	semidirect
658. #478	C₂²×C₃₁	semidirect
659. #478	C₂²×C₃₁	semidirect
660. #478	C₂²×C₃₁	semidirect
661. #477	C₂²×C₃₁	semidirect
662. #476	C₂²×C₃₁	semidirect
663. #470	C₂²×C₃₁	semidirect
665. #468	C₂²×C₃₁	semidirect
666. #468	C₂²×C₃₁	semidirect
667. #465	C₂²×C₃₁	semidirect
668. #465	C₂²×C₃₁	semidirect
669. #464	C₂²×C₃₁	semidirect
670. #464	C₂²×C₃₁	semidirect
671. #464	C₂²×C₃₁	semidirect
672. #463	C₂²×C₃₁	semidirect
673. #463	C₂²×C₃₁	semidirect
674. #462	C₂²×C₃₁	semidirect
675. #461	C₂²×C₃₁	semidirect
676. #461	C₂²×C₃₁	semidirect
677. #461	C₂²×C₃₁	semidirect
679. #460	C₂²×C₃₁	semidirect
680. #460	C₂²×C₃₁	semidirect
681. #460	C₂²×C₃₁	semidirect
682. #460	C₂²×C₃₁	semidirect
683. #460	C₂²×C₃₁	semidirect
685. #459	C₂²×C₃₁	semidirect
686. #459	C₂²×C₃₁	semidirect
687. #459	C₂²×C₃₁	semidirect
688. #452	C₂²×C₃₁	semidirect
689. #452	C₂²×C₃₁	semidirect
690. #452	C₂²×C₃₁	semidirect
691. #450	C₂²×C₃₁	semidirect
692. #450	C₂²×C₃₁	semidirect
693. #450	C₂²×C₃₁	semidirect
694. #450	C₂²×C₃₁	semidirect
696. #449	C₂²×C₃₁	semidirect
697. #449	C₂²×C₃₁	semidirect
698. #446	C₂²×C₃₁	semidirect
699. C₈×Q₈	C₂²×C₃₁	semidirect
700. #442	C₂²×C₃₁	semidirect
701. #440	C₂²×C₃₁	semidirect
702. C₄×Q₁₆	C₂²×C₃₁	semidirect
703. C₄×SD₁₆	C₂²×C₃₁	semidirect
704. C₄×SD₁₆	C₂²×C₃₁	semidirect
705. C₄×SD₁₆	C₂²×C₃₁	semidirect
706. C₄×D₈	C₂²×C₃₁	semidirect
707. C₄×D₈	C₂²×C₃₁	semidirect
708. #436	C₂²×C₃₁	semidirect
709. #436	C₂²×C₃₁	semidirect
710. #435	C₂²×C₃₁	semidirect
711. C₈×D₄	C₂²×C₃₁	semidirect
712. #433	C₂²×C₃₁	semidirect
713. #431	C₂²×C₃₁	semidirect
714. #424	C₂²×C₃₁	semidirect
715. #423	C₂²×C₃₁	semidirect
716. #418	C₂²×C₃₁	semidirect
717. #417	C₂²×C₃₁	semidirect
718. C₂×#102	C₂²×C₃₁	semidirect
908. C₃₁	#62033	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×#3515	2
C₃₁×#3400	2
C₃₁×#3392	2
C₃₁×#3366	2
C₃₁×#3361	2
C₃₁×#3333	2
C₃₁×#3323	2
C₃₁×#3310	2
C₃₁×#3295	2
C₃₁×#3284	2
C₃₁×#3272	2
C₃₁×#3267	2
C₃₁×#3260	2
C₃₁×#3252	2
C₃₁×#3222	2
C₃₁×#3208	2
C₃₁×#3119	2
C₃₁×#3102	2
C₃₁×#3045	2
C₃₁×#3038	2
C₃₁×#2993	2
#62033	31

Subgroups — C31×#62033 #21518792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62033 #21518792