Subgroups — C₃₁×#61452 #21518211

Order 7936.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3265	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3180	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3112	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃₁×#440	C₂	1	2	yes	maximal, complemented
24	C₂²×#41×C₃₁	—	2	1	no	—
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#556	—	2	1	no	—
29	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#552	—	2	2	no	—
31	C₃₁×#552	C₂²	1	2	yes	complemented
32	C₃₁×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#548	—	2	1	no	—
36	C₃₁×#548	C₂²	1	2	yes	complemented
37	C₃₁×#547	—	2	1	no	—
38	C₃₁×#547	C₂²	1	1	yes	characteristic
39	C₃₁×#547	C₂²	1	2	yes	—
40	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#546	—	2	1	no	—
42	C₃₁×#546	—	2	2	no	—
43	D₄²×C₃₁	C₂²	1	2	yes	—
44	D₄²×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#533	—	2	1	no	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#532	C₂²	1	2	yes	—
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#529	—	2	2	no	—
50	C₃₁×#529	C₂²	1	2	yes	complemented
51	C₃₁×#525	—	2	2	no	—
52	C₃₁×#525	—	2	1	no	—
53	C₄×#41×C₃₁	—	2	1	no	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#496	C₂²	1	2	yes	complemented
62	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#490	C₂²	1	2	yes	complemented
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#484	C₂²	1	2	yes	complemented
68	C₃₁×#483	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	complemented
70	C₃₁×#480	C₂²	1	2	yes	complemented
71	C₃₁×#480	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#478	C₂²	1	2	yes	—
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#477	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#474	C₂²	1	1	yes	characteristic
79	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#474	C₂²	1	1	yes	characteristic, 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×#466	C₂²	1	2	yes	complemented
85	C₃₁×#465	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	complemented
87	C₃₁×#463	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#461	C₂²	1	1	yes	characteristic
90	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#460	C₂²	1	2	yes	complemented
92	C₃₁×#460	C₂²	1	2	yes	complemented
93	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#450	C₂²	1	2	yes	—
96	C₃₁×#450	C₂²	1	2	yes	—
97	C₃₁×#449	C₂²	1	2	yes	complemented
98	C₃₁×#448	C₂²	1	2	yes	complemented
99	C₃₁×#448	C₂²	1	2	yes	complemented
100	C₃₁×#447	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	1	yes	characteristic
104	C₃₁×#442	C₂²	1	2	yes	complemented
105	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	2	yes	—
109	C₃₁×#440	C₂²	1	1	yes	characteristic
110	C₃₁×#440	C₂²	1	2	yes	complemented
111	C₃₁×#440	C₂²	1	2	yes	complemented
112	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#440	C₂²	1	2	yes	complemented
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₃₁×#440	C₂²	1	2	yes	complemented
116	C₃₁×#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#435	C₂²	1	2	yes	complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#432	C₂²	1	2	yes	complemented
127	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
129	C₃₁×#418	C₂²	1	1	yes	characteristic
130	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	—
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	—	2	2	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	4	8	no	—
142	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₃₁	—	2	1	no	—
145	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₃₁	—	2	2	no	—
147	C₂²×D₄×C₃₁	—	2	1	no	—
148	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
149	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₃₁	—	2	2	no	—
151	C₂³×C₄×C₃₁	—	2	1	no	—
152	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
153	C₂×SD₁₆×C₃₁	—	2	8	no	—
154	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×D₈×C₃₁	C₂³	1	2	yes	—
164	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
167	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
168	C₃₁×C₄⋊Q₈	—	2	1	no	—
169	C₃₁×C₄⋊Q₈	—	2	1	no	—
170	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₃₁×#127	C₂³	1	1	yes	characteristic
175	C₃₁×#127	C₂³	1	2	yes	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#126	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	1	no	—
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	1	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#121	C₂³	1	2	yes	—
213	C₃₁×#121	C₂³	1	2	yes	—
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#120	—	2	2	no	—
216	C₃₁×#120	—	2	2	no	—
217	C₃₁×#120	—	2	2	no	—
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	2	no	—
220	C₄×Q₈×C₃₁	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
241	C₄×D₄×C₃₁	D₄	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	2	yes	—
250	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	D₄	1	2	yes	—
259	C₃₁×#117	D₄	1	1	yes	characteristic
260	C₃₁×#117	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
270	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#107	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	1	yes	characteristic
280	C₃₁×#106	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	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	1	yes	characteristic
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	1	yes	characteristic
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₃₁×#97	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
315	C₂⁴×C₃₁	—	2	1	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	8	no	—
321	#41×C₃₁	—	4	4	no	—
322	#41×C₃₁	—	4	8	no	—
323	#41×C₃₁	—	4	4	no	—
324	#41×C₃₁	—	4	4	no	—
325	#41×C₃₁	—	4	4	no	—
326	C₂×Q₈×C₃₁	—	2	2	no	—
327	C₂×Q₈×C₃₁	—	2	1	no	—
328	C₂×Q₈×C₃₁	—	2	2	no	—
329	C₂×Q₈×C₃₁	—	2	1	no	—
330	C₂×Q₈×C₃₁	—	2	4	no	—
331	C₂×Q₈×C₃₁	—	4	2	no	—
332	C₂×Q₈×C₃₁	—	4	4	no	—
333	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₃₁	—	2	4	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	2	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	1	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	1	no	—
347	C₂×D₄×C₃₁	—	2	2	no	—
348	C₂×D₄×C₃₁	—	2	1	no	—
349	C₂×D₄×C₃₁	—	4	2	no	—
350	C₂×D₄×C₃₁	—	4	1	no	—
351	C₂×D₄×C₃₁	—	4	8	no	—
352	C₂×D₄×C₃₁	—	4	4	no	—
353	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	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	1	no	—
366	C₂²×C₄×C₃₁	—	2	1	no	—
367	C₂²×C₄×C₃₁	—	2	1	no	—
368	C₂²×C₄×C₃₁	—	2	2	no	—
369	C₂²×C₄×C₃₁	—	2	2	no	—
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	2	1	no	—
373	C₂²×C₄×C₃₁	—	4	8	no	—
374	C₂²×C₄×C₃₁	—	4	4	no	—
375	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
380	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
381	SD₁₆×C₃₁	—	2	4	no	—
382	SD₁₆×C₃₁	—	2	2	no	—
383	SD₁₆×C₃₁	—	2	4	no	—
384	SD₁₆×C₃₁	—	2	4	no	—
385	SD₁₆×C₃₁	—	4	2	no	—
386	SD₁₆×C₃₁	—	4	2	no	—
387	SD₁₆×C₃₁	#41	1	4	yes	complemented
388	D₈×C₃₁	—	2	2	no	—
389	D₈×C₃₁	—	2	2	no	—
390	D₈×C₃₁	—	4	2	no	—
391	M₁₆×C₃₁	—	2	2	no	—
392	M₁₆×C₃₁	—	4	1	no	—
393	C₂×C₈×C₃₁	—	2	4	no	—
394	C₂×C₈×C₃₁	—	4	2	no	—
395	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
399	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
400	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	1	no	—
418	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	1	no	—
438	C₂²⋊C₄×C₃₁	—	2	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	1	no	—
440	C₂²⋊C₄×C₃₁	—	2	1	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
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	2	no	—
452	C₄²×C₃₁	—	2	2	no	—
453	C₄²×C₃₁	—	2	1	no	—
454	C₄²×C₃₁	—	2	2	no	—
455	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₃₁	C₂×D₄	1	2	yes	—
458	C₄²×C₃₁	C₂×D₄	1	2	yes	—
459	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
460	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
461	C₄²×C₃₁	C₂⁴	1	2	yes	—
462	#61452	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₂³×C₃₁	—	2	1	no	—
464	C₂³×C₃₁	—	2	1	no	—
465	C₂³×C₃₁	—	2	1	no	—
466	C₂³×C₃₁	—	2	2	no	—
467	C₂³×C₃₁	—	4	4	no	—
468	C₂³×C₃₁	—	4	2	no	—
469	C₂³×C₃₁	—	4	2	no	—
470	C₂³×C₃₁	—	4	4	no	—
471	C₂³×C₃₁	—	8	2	no	—
472	C₂³×C₃₁	—	8	1	no	—
473	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
474	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
475	Q₈×C₃₁	—	2	2	no	—
476	Q₈×C₃₁	—	2	1	no	—
477	Q₈×C₃₁	—	2	2	no	—
478	Q₈×C₃₁	—	2	2	no	—
479	Q₈×C₃₁	—	4	4	no	—
480	Q₈×C₃₁	—	4	4	no	—
481	Q₈×C₃₁	—	4	2	no	—
482	Q₈×C₃₁	—	4	2	no	—
483	Q₈×C₃₁	C₂×#41	1	2	yes	complemented
484	D₄×C₃₁	—	2	4	no	—
485	D₄×C₃₁	—	2	1	no	—
486	D₄×C₃₁	—	2	1	no	—
487	D₄×C₃₁	—	2	2	no	—
488	D₄×C₃₁	—	2	1	no	—
489	D₄×C₃₁	—	2	1	no	—
490	D₄×C₃₁	—	2	2	no	—
491	D₄×C₃₁	—	2	1	no	—
492	D₄×C₃₁	—	4	2	no	—
493	D₄×C₃₁	—	4	4	no	—
494	D₄×C₃₁	—	4	2	no	—
495	D₄×C₃₁	—	4	4	no	—
496	D₄×C₃₁	—	4	4	no	—
497	D₄×C₃₁	—	4	4	no	—
498	D₄×C₃₁	—	4	4	no	—
499	D₄×C₃₁	—	4	4	no	—
500	D₄×C₃₁	—	4	2	no	—
501	D₄×C₃₁	—	8	2	no	—
502	D₄×C₃₁	—	8	1	no	—
503	D₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
504	D₄×C₃₁	C₂×#41	1	2	yes	—
505	C₂×C₄×C₃₁	—	2	4	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
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	2	no	—
511	C₂×C₄×C₃₁	—	2	1	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	1	no	—
514	C₂×C₄×C₃₁	—	2	2	no	—
515	C₂×C₄×C₃₁	—	2	2	no	—
516	C₂×C₄×C₃₁	—	2	1	no	—
517	C₂×C₄×C₃₁	—	2	2	no	—
518	C₂×C₄×C₃₁	—	2	1	no	—
519	C₂×C₄×C₃₁	—	4	2	no	—
520	C₂×C₄×C₃₁	—	4	1	no	—
521	C₂×C₄×C₃₁	—	4	2	no	—
522	C₂×C₄×C₃₁	—	4	4	no	—
523	C₂×C₄×C₃₁	—	4	2	no	—
524	C₂×C₄×C₃₁	—	4	2	no	—
525	C₂×C₄×C₃₁	—	4	4	no	—
526	C₂×C₄×C₃₁	—	4	4	no	—
527	C₂×C₄×C₃₁	—	4	2	no	—
528	C₂×C₄×C₃₁	—	4	4	no	—
529	C₂×C₄×C₃₁	—	4	2	no	—
530	C₂×C₄×C₃₁	—	4	4	no	—
531	C₂×C₄×C₃₁	—	4	4	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	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
544	C₈×C₃₁	—	2	2	no	—
545	C₈×C₃₁	—	2	1	no	—
546	C₈×C₃₁	—	2	1	no	—
547	C₈×C₃₁	—	2	2	no	—
548	C₈×C₃₁	—	2	1	no	—
549	C₈×C₃₁	C₂×#41	1	2	yes	complemented
550	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
551	D₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3343	C₂×C₃₁	1	2	yes	complemented
557	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3310	C₂×C₃₁	1	2	yes	complemented
559	#3308	C₂×C₃₁	1	2	yes	complemented
560	#3298	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
562	D₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
563	#3265	C₂×C₃₁	1	2	yes	complemented
564	#3182	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#3180	C₂×C₃₁	1	2	yes	complemented
566	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
567	#3114	C₂×C₃₁	1	2	yes	complemented
568	#3112	C₂×C₃₁	1	2	yes	complemented
569	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
570	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
571	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
572	C₂×#440	C₂×C₃₁	1	2	yes	complemented
573	C₂²×C₃₁	—	2	2	no	—
574	C₂²×C₃₁	—	2	2	no	—
575	C₂²×C₃₁	—	2	1	no	—
576	C₂²×C₃₁	—	2	1	no	—
577	C₂²×C₃₁	—	2	2	no	—
578	C₂²×C₃₁	—	2	1	no	—
579	C₂²×C₃₁	—	4	1	no	—
580	C₂²×C₃₁	—	4	1	no	—
581	C₂²×C₃₁	—	4	1	no	—
582	C₂²×C₃₁	—	4	2	no	—
583	C₂²×C₃₁	—	4	1	no	—
584	C₂²×C₃₁	—	4	1	no	—
585	C₂²×C₃₁	—	4	1	no	—
586	C₂²×C₃₁	—	4	2	no	—
587	C₂²×C₃₁	—	4	2	no	—
588	C₂²×C₃₁	—	4	1	no	—
589	C₂²×C₃₁	—	4	1	no	—
590	C₂²×C₃₁	—	8	8	no	—
591	C₂²×C₃₁	—	8	4	no	—
592	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
593	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
594	C₄×C₃₁	—	2	1	no	—
595	C₄×C₃₁	—	2	2	no	—
596	C₄×C₃₁	—	2	1	no	—
597	C₄×C₃₁	—	2	1	no	—
598	C₄×C₃₁	—	2	2	no	—
599	C₄×C₃₁	—	2	2	no	—
600	C₄×C₃₁	—	2	1	no	—
601	C₄×C₃₁	—	2	2	no	—
602	C₄×C₃₁	—	4	1	no	—
603	C₄×C₃₁	—	4	2	no	—
604	C₄×C₃₁	—	4	1	no	—
605	C₄×C₃₁	—	4	1	no	—
606	C₄×C₃₁	—	4	2	no	—
607	C₄×C₃₁	—	4	1	no	—
608	C₄×C₃₁	—	4	2	no	—
609	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
610	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
611	C₄×C₃₁	#585	1	1	yes	characteristic
612	C₂²×#41	—	2	1	no	—
613	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
614	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
615	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#556	—	2	1	no	—
617	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#552	—	2	2	no	—
619	#552	C₂²×C₃₁	1	2	yes	complemented
620	#550	C₂²×C₃₁	1	1	yes	characteristic
621	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
622	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#548	—	2	1	no	—
624	#548	C₂²×C₃₁	1	2	yes	complemented
625	#547	—	2	1	no	—
626	#547	C₂²×C₃₁	1	1	yes	characteristic
627	#547	C₂²×C₃₁	1	2	yes	—
628	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#546	—	2	1	no	—
630	#546	—	2	2	no	—
631	D₄²	C₂²×C₃₁	1	2	yes	—
632	D₄²	C₂²×C₃₁	1	1	yes	characteristic
633	#533	—	2	1	no	—
634	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#532	C₂²×C₃₁	1	2	yes	—
636	#532	C₂²×C₃₁	1	1	yes	characteristic
637	#529	—	2	2	no	—
638	#529	C₂²×C₃₁	1	2	yes	complemented
639	#525	—	2	2	no	—
640	#525	—	2	1	no	—
641	C₄×#41	—	2	1	no	—
642	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
643	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
645	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
646	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
647	#501	C₂²×C₃₁	1	2	yes	complemented
648	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#496	C₂²×C₃₁	1	2	yes	complemented
650	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#490	C₂²×C₃₁	1	2	yes	complemented
652	#489	C₂²×C₃₁	1	2	yes	complemented
653	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#484	C₂²×C₃₁	1	2	yes	complemented
656	#483	C₂²×C₃₁	1	2	yes	complemented
657	#482	C₂²×C₃₁	1	2	yes	complemented
658	#480	C₂²×C₃₁	1	2	yes	complemented
659	#480	C₂²×C₃₁	1	2	yes	complemented
660	#480	C₂²×C₃₁	1	2	yes	complemented
661	#478	C₂²×C₃₁	1	2	yes	—
662	#478	C₂²×C₃₁	1	2	yes	complemented
663	#477	C₂²×C₃₁	1	2	yes	complemented
664	#477	C₂²×C₃₁	1	2	yes	complemented
665	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#474	C₂²×C₃₁	1	1	yes	characteristic
667	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#468	C₂²×C₃₁	1	2	yes	complemented
670	#468	C₂²×C₃₁	1	2	yes	complemented
671	#466	C₂²×C₃₁	1	2	yes	complemented
672	#466	C₂²×C₃₁	1	2	yes	complemented
673	#465	C₂²×C₃₁	1	2	yes	complemented
674	#465	C₂²×C₃₁	1	2	yes	complemented
675	#463	C₂²×C₃₁	1	2	yes	—
676	#463	C₂²×C₃₁	1	2	yes	complemented
677	#461	C₂²×C₃₁	1	1	yes	characteristic
678	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#460	C₂²×C₃₁	1	2	yes	complemented
680	#460	C₂²×C₃₁	1	2	yes	complemented
681	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#450	C₂²×C₃₁	1	2	yes	—
684	#450	C₂²×C₃₁	1	2	yes	—
685	#449	C₂²×C₃₁	1	2	yes	complemented
686	#448	C₂²×C₃₁	1	2	yes	complemented
687	#448	C₂²×C₃₁	1	2	yes	complemented
688	#447	C₂²×C₃₁	1	2	yes	—
689	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	#442	C₂²×C₃₁	1	1	yes	characteristic
692	#442	C₂²×C₃₁	1	2	yes	complemented
693	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#440	C₂²×C₃₁	1	2	yes	—
695	#440	C₂²×C₃₁	1	2	yes	—
696	#440	C₂²×C₃₁	1	2	yes	—
697	#440	C₂²×C₃₁	1	1	yes	characteristic
698	#440	C₂²×C₃₁	1	2	yes	complemented
699	#440	C₂²×C₃₁	1	2	yes	complemented
700	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#440	C₂²×C₃₁	1	2	yes	complemented
702	#440	C₂²×C₃₁	1	2	yes	complemented
703	#440	C₂²×C₃₁	1	2	yes	complemented
704	#440	C₂²×C₃₁	1	2	yes	complemented
705	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
706	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
708	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	#435	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	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	#432	C₂²×C₃₁	1	2	yes	complemented
715	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
717	#418	C₂²×C₃₁	1	1	yes	characteristic
718	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
720	C₂×#102	C₂²×C₃₁	1	2	yes	—
721	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
722	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
723	C₂×C₃₁	—	2	4	no	—
724	C₂×C₃₁	—	4	1	no	—
725	C₂×C₃₁	—	4	2	no	—
726	C₂×C₃₁	—	8	1	no	—
727	C₂×C₃₁	—	8	2	no	—
728	C₂×C₃₁	—	8	1	no	—
729	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
730	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
731	C₂×C₃₁	#3586	1	1	yes	characteristic
732	C₂×#41	—	2	1	no	—
733	C₂×#41	—	2	1	no	—
734	C₂×#41	—	2	2	no	—
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	2	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	4	8	no	—
739	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
740	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
741	C₂²×Q₈	—	2	1	no	—
742	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
743	C₂²×D₄	—	2	2	no	—
744	C₂²×D₄	—	2	1	no	—
745	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
746	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
747	C₂³×C₄	—	2	2	no	—
748	C₂³×C₄	—	2	1	no	—
749	AGL(1,ℤ/8)	—	2	4	no	—
750	C₂×SD₁₆	—	2	8	no	—
751	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
755	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
758	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
760	C₂×D₈	C₂³×C₃₁	1	2	yes	—
761	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
762	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
763	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
764	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
765	C₄⋊Q₈	—	2	1	no	—
766	C₄⋊Q₈	—	2	1	no	—
767	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
768	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
769	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
770	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
771	#127	C₂³×C₃₁	1	1	yes	characteristic
772	#127	C₂³×C₃₁	1	2	yes	—
773	#126	—	2	2	no	—
774	#126	—	2	2	no	—
775	#126	—	2	2	no	—
776	#125	—	2	2	no	—
777	#125	—	2	2	no	—
778	#125	—	2	1	no	—
779	#125	C₂³×C₃₁	1	2	yes	—
780	#124	—	2	2	no	—
781	#124	—	2	1	no	—
782	#124	—	2	2	no	—
783	#124	C₂³×C₃₁	1	2	yes	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	2	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	C₂³×C₃₁	1	2	yes	—
809	#121	C₂³×C₃₁	1	2	yes	—
810	#121	C₂³×C₃₁	1	2	yes	—
811	#121	C₂³×C₃₁	1	2	yes	—
812	#120	—	2	2	no	—
813	#120	—	2	2	no	—
814	#120	—	2	2	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	2	no	—
817	C₄×Q₈	—	2	2	no	—
818	C₄×Q₈	—	2	1	no	—
819	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
822	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
823	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
824	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
838	C₄×D₄	D₄×C₃₁	1	2	yes	—
839	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₃₁	1	2	yes	—
842	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₃₁	1	2	yes	—
844	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₃₁	1	2	yes	—
846	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
849	C₄×D₄	C₂³×C₃₁	1	2	yes	—
850	#117	—	2	1	no	—
851	#117	—	2	1	no	—
852	#117	—	2	2	no	—
853	#117	—	2	1	no	—
854	#117	—	2	2	no	—
855	#117	D₄×C₃₁	1	2	yes	—
856	#117	D₄×C₃₁	1	1	yes	characteristic
857	#117	C₂³×C₃₁	1	1	yes	characteristic
858	C₂×C₄⋊C₄	—	2	2	no	—
859	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
860	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
861	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
862	C₂×C₂²⋊C₄	—	2	2	no	—
863	C₂×C₂²⋊C₄	—	2	1	no	—
864	C₂×C₄²	—	2	2	no	—
865	C₂×C₄²	—	2	1	no	—
866	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
867	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
868	#107	C₂³×C₃₁	1	1	yes	characteristic
869	#107	C₂³×C₃₁	1	2	yes	—
870	#107	C₂³×C₃₁	1	2	yes	—
871	#107	C₂³×C₃₁	1	2	yes	—
872	#107	C₂³×C₃₁	1	1	yes	characteristic
873	#107	C₂³×C₃₁	1	2	yes	—
874	#107	C₂³×C₃₁	1	2	yes	—
875	#106	C₂³×C₃₁	1	1	yes	characteristic
876	#106	C₂³×C₃₁	1	1	yes	characteristic
877	#106	C₂³×C₃₁	1	2	yes	—
878	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
879	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
880	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
881	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
882	#103	C₂³×C₃₁	1	1	yes	characteristic
883	#103	C₂³×C₃₁	1	2	yes	—
884	#103	C₂³×C₃₁	1	2	yes	—
885	#103	C₂³×C₃₁	1	2	yes	—
886	#103	C₂³×C₃₁	1	1	yes	characteristic
887	#103	C₂³×C₃₁	1	2	yes	—
888	#103	C₂³×C₃₁	1	2	yes	—
889	#102	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
894	#102	C₂³×C₃₁	1	1	yes	characteristic
895	#102	C₂³×C₃₁	1	1	yes	characteristic
896	#102	C₂³×C₃₁	1	1	yes	characteristic
897	#102	C₂³×C₃₁	1	1	yes	characteristic
898	#102	C₂³×C₃₁	1	2	yes	—
899	#102	C₂³×C₃₁	1	2	yes	—
900	#102	C₂³×C₃₁	1	2	yes	—
901	#102	C₂³×C₃₁	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
905	#97	C₂³×C₃₁	1	1	yes	characteristic
906	#97	C₂³×C₃₁	1	2	yes	—
907	#97	C₂³×C₃₁	1	2	yes	—
908	#97	C₂³×C₃₁	1	2	yes	—
909	#97	C₂³×C₃₁	1	1	yes	characteristic
910	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
911	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
912	C₃₁	#61452	1	1	yes	characteristic, direct product factor, Sylow
913	C₂⁴	—	2	1	no	—
914	C₂⁴	—	2	2	no	—
915	#41	—	2	4	no	—
916	#41	—	2	2	no	—
917	#41	—	4	1	no	—
918	#41	—	4	8	no	—
919	#41	—	4	4	no	—
920	#41	—	4	8	no	—
921	#41	—	4	4	no	—
922	#41	—	4	4	no	—
923	#41	—	4	4	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	2	2	no	—
927	C₂×Q₈	—	2	1	no	—
928	C₂×Q₈	—	2	4	no	—
929	C₂×Q₈	—	4	2	no	—
930	C₂×Q₈	—	4	4	no	—
931	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
933	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×D₄	—	2	4	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	1	no	—
949	C₂×D₄	—	4	8	no	—
950	C₂×D₄	—	4	4	no	—
951	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
952	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
953	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
956	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	4	8	no	—
972	C₂²×C₄	—	4	4	no	—
973	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
974	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
975	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
976	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
978	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	SD₁₆	—	2	4	no	—
980	SD₁₆	—	2	2	no	—
981	SD₁₆	—	2	4	no	—
982	SD₁₆	—	2	4	no	—
983	SD₁₆	—	4	2	no	—
984	SD₁₆	—	4	2	no	—
985	SD₁₆	#41×C₃₁	1	4	yes	complemented
986	D₈	—	2	2	no	—
987	D₈	—	2	2	no	—
988	D₈	—	4	2	no	—
989	M₁₆	—	2	2	no	—
990	M₁₆	—	4	1	no	—
991	C₂×C₈	—	2	4	no	—
992	C₂×C₈	—	4	2	no	—
993	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
995	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
997	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
998	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1017	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1018	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1019	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1023	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1024	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	—	2	1	no	—
1052	C₄²	—	2	2	no	—
1053	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1054	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1055	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1056	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1057	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1058	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1059	C₄²	C₂⁴×C₃₁	1	2	yes	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	2	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	4	4	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	1	no	—
1070	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1072	Q₈	—	2	2	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	4	4	no	—
1077	Q₈	—	4	4	no	—
1078	Q₈	—	4	2	no	—
1079	Q₈	—	4	2	no	—
1080	Q₈	C₂×#41×C₃₁	1	2	yes	complemented
1081	D₄	—	2	4	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	4	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	4	no	—
1095	D₄	—	4	4	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	1	no	—
1100	D₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
1101	D₄	C₂×#41×C₃₁	1	2	yes	—
1102	C₂×C₄	—	2	4	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	4	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	4	no	—
1123	C₂×C₄	—	4	4	no	—
1124	C₂×C₄	—	4	2	no	—
1125	C₂×C₄	—	4	4	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	4	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1133	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1134	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1135	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1140	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1141	C₈	—	2	2	no	—
1142	C₈	—	2	1	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	2	2	no	—
1145	C₈	—	2	1	no	—
1146	C₈	C₂×#41×C₃₁	1	2	yes	complemented
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	2	no	—
1158	C₂²	—	4	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	8	8	no	—
1165	C₂²	—	8	4	no	—
1166	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
1167	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1168	C₄	—	2	1	no	—
1169	C₄	—	2	2	no	—
1170	C₄	—	2	2	no	—
1171	C₄	—	2	1	no	—
1172	C₄	—	2	2	no	—
1173	C₄	—	2	1	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	4	2	no	—
1177	C₄	—	4	1	no	—
1178	C₄	—	4	2	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	2	no	—
1182	C₄	—	4	1	no	—
1183	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
1184	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1185	C₄	C₃₁×#585	1	1	yes	characteristic
1186	C₂	—	2	4	no	—
1187	C₂	—	4	1	no	—
1188	C₂	—	4	2	no	—
1189	C₂	—	8	2	no	—
1190	C₂	—	8	1	no	—
1191	C₂	—	8	1	no	—
1192	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1193	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
1194	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×#3482	C₂	semidirect
2. D₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#3397	C₂	semidirect
4. C₃₁×#3386	C₂	semidirect
5. C₃₁×#3368	C₂	semidirect
6. C₃₁×#3367	C₂	semidirect
7. C₃₁×#3343	C₂	semidirect
8. C₃₁×#3334	C₂	semidirect
9. C₃₁×#3310	C₂	semidirect
10. C₃₁×#3308	C₂	semidirect
11. C₃₁×#3298	C₂	semidirect
12. C₃₁×#3294	C₂	semidirect
13. D₄×SD₁₆×C₃₁	C₂	semidirect
14. C₃₁×#3265	C₂	semidirect
15. C₃₁×#3182	C₂	semidirect
16. C₃₁×#3180	C₂	semidirect
17. C₃₁×#3115	C₂	semidirect
18. C₃₁×#3114	C₂	semidirect
19. C₃₁×#3112	C₂	semidirect
20. C₃₁×#3110	C₂	semidirect
21. C₃₁×#2970	C₂	semidirect
22. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
23. C₂×C₃₁×#440	C₂	semidirect
27. C₃₁×#557	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
31. C₃₁×#552	C₂²	semidirect
34. D₄×Q₈×C₃₁	C₂²	semidirect
36. C₃₁×#548	C₂²	semidirect
40. C₃₁×#547	C₂²	semidirect
46. C₃₁×#533	C₂²	semidirect
50. C₃₁×#529	C₂²	semidirect
55. C₄×#41×C₃₁	C₂²	semidirect
56. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#500	C₂²	semidirect
61. C₃₁×#496	C₂²	semidirect
62. C₃₁×#492	C₂²	semidirect
63. C₃₁×#490	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#484	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#480	C₂²	semidirect
71. C₃₁×#480	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#477	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
79. C₃₁×#474	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#468	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#466	C₂²	semidirect
84. C₃₁×#466	C₂²	semidirect
85. C₃₁×#465	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
91. C₃₁×#460	C₂²	semidirect
92. C₃₁×#460	C₂²	semidirect
93. C₃₁×#460	C₂²	semidirect
94. C₃₁×#459	C₂²	semidirect
97. C₃₁×#449	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
99. C₃₁×#448	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
104. C₃₁×#442	C₂²	semidirect
105. C₃₁×#442	C₂²	semidirect
110. C₃₁×#440	C₂²	semidirect
111. C₃₁×#440	C₂²	semidirect
112. C₃₁×#440	C₂²	semidirect
113. C₃₁×#440	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₃₁×#440	C₂²	semidirect
116. C₃₁×#440	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
121. C₃₁×#435	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#432	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₂×C₃₁×#107	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
131. C₂×C₃₁×#103	C₂²	semidirect
133. C₄×M₁₆×C₃₁	C₂²	semidirect
134. C₂×C₃₁×#97	C₂²	semidirect
387. SD₁₆×C₃₁	#41	semidirect
462. #61452	C₃₁	direct (N × H)
483. Q₈×C₃₁	C₂×#41	semidirect
503. D₄×C₃₁	AGL(1,ℤ/8)	semidirect
549. C₈×C₃₁	C₂×#41	semidirect
550. #3482	C₂×C₃₁	semidirect
551. D₄×#41	C₂×C₃₁	semidirect
552. #3397	C₂×C₃₁	semidirect
553. #3386	C₂×C₃₁	semidirect
554. #3368	C₂×C₃₁	semidirect
555. #3367	C₂×C₃₁	semidirect
556. #3343	C₂×C₃₁	semidirect
557. #3334	C₂×C₃₁	semidirect
558. #3310	C₂×C₃₁	semidirect
559. #3308	C₂×C₃₁	semidirect
560. #3298	C₂×C₃₁	semidirect
561. #3294	C₂×C₃₁	semidirect
562. D₄×SD₁₆	C₂×C₃₁	semidirect
563. #3265	C₂×C₃₁	semidirect
564. #3182	C₂×C₃₁	semidirect
565. #3180	C₂×C₃₁	semidirect
566. #3115	C₂×C₃₁	semidirect
567. #3114	C₂×C₃₁	semidirect
568. #3112	C₂×C₃₁	semidirect
569. #3110	C₂×C₃₁	semidirect
570. #2970	C₂×C₃₁	semidirect
571. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
572. C₂×#440	C₂×C₃₁	semidirect
615. #557	C₂²×C₃₁	semidirect
617. #556	C₂²×C₃₁	semidirect
619. #552	C₂²×C₃₁	semidirect
622. D₄×Q₈	C₂²×C₃₁	semidirect
624. #548	C₂²×C₃₁	semidirect
628. #547	C₂²×C₃₁	semidirect
634. #533	C₂²×C₃₁	semidirect
638. #529	C₂²×C₃₁	semidirect
643. C₄×#41	C₂²×C₃₁	semidirect
644. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
647. #501	C₂²×C₃₁	semidirect
648. #500	C₂²×C₃₁	semidirect
649. #496	C₂²×C₃₁	semidirect
650. #492	C₂²×C₃₁	semidirect
651. #490	C₂²×C₃₁	semidirect
652. #489	C₂²×C₃₁	semidirect
653. #487	C₂²×C₃₁	semidirect
654. #486	C₂²×C₃₁	semidirect
655. #484	C₂²×C₃₁	semidirect
656. #483	C₂²×C₃₁	semidirect
657. #482	C₂²×C₃₁	semidirect
658. #480	C₂²×C₃₁	semidirect
659. #480	C₂²×C₃₁	semidirect
660. #480	C₂²×C₃₁	semidirect
662. #478	C₂²×C₃₁	semidirect
663. #477	C₂²×C₃₁	semidirect
664. #477	C₂²×C₃₁	semidirect
665. #475	C₂²×C₃₁	semidirect
667. #474	C₂²×C₃₁	semidirect
668. #474	C₂²×C₃₁	semidirect
669. #468	C₂²×C₃₁	semidirect
670. #468	C₂²×C₃₁	semidirect
671. #466	C₂²×C₃₁	semidirect
672. #466	C₂²×C₃₁	semidirect
673. #465	C₂²×C₃₁	semidirect
674. #465	C₂²×C₃₁	semidirect
676. #463	C₂²×C₃₁	semidirect
678. #461	C₂²×C₃₁	semidirect
679. #460	C₂²×C₃₁	semidirect
680. #460	C₂²×C₃₁	semidirect
681. #460	C₂²×C₃₁	semidirect
682. #459	C₂²×C₃₁	semidirect
685. #449	C₂²×C₃₁	semidirect
686. #448	C₂²×C₃₁	semidirect
687. #448	C₂²×C₃₁	semidirect
689. #446	C₂²×C₃₁	semidirect
690. #446	C₂²×C₃₁	semidirect
692. #442	C₂²×C₃₁	semidirect
693. #442	C₂²×C₃₁	semidirect
698. #440	C₂²×C₃₁	semidirect
699. #440	C₂²×C₃₁	semidirect
700. #440	C₂²×C₃₁	semidirect
701. #440	C₂²×C₃₁	semidirect
702. #440	C₂²×C₃₁	semidirect
703. #440	C₂²×C₃₁	semidirect
704. #440	C₂²×C₃₁	semidirect
706. C₄×SD₁₆	C₂²×C₃₁	semidirect
708. C₄×D₈	C₂²×C₃₁	semidirect
709. #435	C₂²×C₃₁	semidirect
710. #435	C₂²×C₃₁	semidirect
711. C₈×D₄	C₂²×C₃₁	semidirect
712. C₈×D₄	C₂²×C₃₁	semidirect
713. #432	C₂²×C₃₁	semidirect
714. #432	C₂²×C₃₁	semidirect
715. #428	C₂²×C₃₁	semidirect
716. C₂×#107	C₂²×C₃₁	semidirect
718. #417	C₂²×C₃₁	semidirect
719. C₂×#103	C₂²×C₃₁	semidirect
721. C₄×M₁₆	C₂²×C₃₁	semidirect
722. C₂×#97	C₂²×C₃₁	semidirect
912. C₃₁	#61452	direct (N × H)
985. SD₁₆	#41×C₃₁	semidirect
1080. Q₈	C₂×#41×C₃₁	semidirect
1100. D₄	C₃₁×AGL(1,ℤ/8)	semidirect
1146. C₈	C₂×#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3482	2
D₄×#41×C₃₁	2
C₃₁×#3397	2
C₃₁×#3386	2
C₃₁×#3368	2
C₃₁×#3367	2
C₃₁×#3343	2
C₃₁×#3334	2
C₃₁×#3310	2
C₃₁×#3308	2
C₃₁×#3298	2
C₃₁×#3294	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3265	2
C₃₁×#3182	2
C₃₁×#3180	2
C₃₁×#3115	2
C₃₁×#3114	2
C₃₁×#3112	2
C₃₁×#3110	2
C₃₁×#2970	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₂×C₃₁×#440	2
#61452	31

Subgroups — C31×#61452 #21518211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61452 #21518211