Subgroups — C₃₁×#62132 #21518891

Order 7936.

1944 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3386	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3343	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3334	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3308	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3238	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3112	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#477	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×2₋¹⁺⁴	—	2	1	no	—
19	C₃₁×#557	C₂²	1	1	yes	characteristic
20	C₃₁×#556	—	2	1	no	—
21	C₃₁×#556	C₂²	1	1	yes	characteristic
22	C₃₁×#552	—	2	2	no	—
23	C₃₁×#552	C₂²	1	2	yes	—
24	D₄×Q₈×C₃₁	—	2	1	no	—
25	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
26	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#548	C₂²	1	2	yes	—
28	C₃₁×#547	—	2	1	no	—
29	C₃₁×#547	—	2	1	no	—
30	C₃₁×#547	—	2	2	no	—
31	C₃₁×#547	C₂²	1	1	yes	characteristic
32	C₃₁×#547	C₂²	1	2	yes	—
33	C₃₁×#547	C₂²	1	4	yes	—
34	C₃₁×#536	—	2	2	no	—
35	C₃₁×#536	—	2	1	no	—
36	C₃₁×#533	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	2	yes	—
40	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
42	C₃₁×#529	—	2	2	no	—
43	C₃₁×#529	C₂²	1	2	yes	—
44	C₄×#41×C₃₁	—	2	1	no	—
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
48	C₃₁×#501	C₂²	1	4	yes	—
49	C₃₁×#500	C₂²	1	2	yes	—
50	C₃₁×#489	C₂²	1	4	yes	—
51	C₃₁×#487	C₂²	1	2	yes	—
52	C₃₁×#484	C₂²	1	4	yes	—
53	C₃₁×#483	C₂²	1	4	yes	—
54	C₃₁×#482	C₂²	1	2	yes	—
55	C₃₁×#480	C₂²	1	4	yes	—
56	C₃₁×#480	C₂²	1	4	yes	—
57	C₃₁×#478	C₂²	1	4	yes	—
58	C₃₁×#477	C₂²	1	2	yes	—
59	C₃₁×#477	C₂²	1	4	yes	—
60	C₃₁×#477	C₂²	1	1	yes	characteristic
61	C₃₁×#477	C₂²	1	2	yes	—
62	C₃₁×#477	C₂²	1	4	yes	—
63	C₃₁×#477	C₂²	1	2	yes	—
64	C₃₁×#477	C₂²	1	2	yes	—
65	C₃₁×#476	C₂²	1	2	yes	—
66	C₃₁×#476	C₂²	1	1	yes	characteristic
67	C₃₁×#475	C₂²	1	2	yes	—
68	C₃₁×#474	C₂²	1	2	yes	—
69	C₃₁×#474	C₂²	1	2	yes	—
70	C₃₁×#468	C₂²	1	4	yes	—
71	C₃₁×#466	C₂²	1	4	yes	—
72	C₃₁×#465	C₂²	1	4	yes	—
73	C₃₁×#463	C₂²	1	4	yes	—
74	C₃₁×#461	C₂²	1	2	yes	—
75	C₃₁×#460	C₂²	1	1	yes	characteristic
76	C₃₁×#460	C₂²	1	2	yes	—
77	C₃₁×#459	C₂²	1	1	yes	characteristic
78	C₃₁×#449	C₂²	1	2	yes	—
79	C₃₁×#448	C₂²	1	4	yes	—
80	C₃₁×#446	C₂²	1	2	yes	—
81	C₃₁×#440	C₂²	1	4	yes	—
82	C₃₁×#440	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
84	C₄×D₈×C₃₁	C₂²	1	2	yes	—
85	C₃₁×#435	C₂²	1	4	yes	—
86	C₈×D₄×C₃₁	C₂²	1	2	yes	—
87	C₃₁×#432	C₂²	1	2	yes	—
88	C₃₁×#431	C₂²	1	1	yes	characteristic
89	C₃₁×#428	C₂²	1	2	yes	—
90	C₂×C₃₁×#107	C₂²	1	4	yes	—
91	C₃₁×#423	C₂²	1	1	yes	characteristic
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
93	C₃₁×#417	C₂²	1	2	yes	—
94	C₂×C₃₁×#103	C₂²	1	4	yes	—
95	C₃₁×2₋¹⁺⁴	—	4	8	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	—	2	4	no	—
98	C₂×#41×C₃₁	—	2	2	no	—
99	C₂×#41×C₃₁	—	2	2	no	—
100	C₂×#41×C₃₁	—	2	1	no	—
101	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
102	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₃₁	—	2	2	no	—
104	C₂²×Q₈×C₃₁	—	2	2	no	—
105	C₂²×Q₈×C₃₁	—	2	1	no	—
106	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×D₈×C₃₁	C₂³	1	2	yes	—
110	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
111	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
112	C₃₁×C₄⋊Q₈	—	2	1	no	—
113	C₃₁×C₄⋊Q₈	—	2	1	no	—
114	C₃₁×C₄⋊Q₈	—	2	1	no	—
115	C₃₁×C₄⋊Q₈	—	2	2	no	—
116	C₃₁×C₄⋊Q₈	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	—	2	2	no	—
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
124	C₃₁×#127	C₂³	1	1	yes	characteristic
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#125	—	2	2	no	—
129	C₃₁×#125	—	2	2	no	—
130	C₃₁×#125	—	2	1	no	—
131	C₃₁×#125	C₂³	1	2	yes	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#124	—	2	1	no	—
134	C₃₁×#124	—	2	2	no	—
135	C₃₁×#124	C₂³	1	2	yes	—
136	C₃₁×#123	—	2	2	no	—
137	C₃₁×#123	—	2	2	no	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	2	4	no	—
140	C₃₁×#123	—	2	4	no	—
141	C₃₁×#123	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	1	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	4	no	—
148	C₃₁×C₂²⋊Q₈	—	2	4	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	—	2	2	no	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	1	no	—
156	C₃₁×#121	C₂³	1	4	yes	—
157	C₃₁×#121	C₂³	1	2	yes	—
158	C₃₁×#121	C₂³	1	2	yes	—
159	C₄×Q₈×C₃₁	—	2	1	no	—
160	C₄×Q₈×C₃₁	—	2	2	no	—
161	C₄×Q₈×C₃₁	—	2	2	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
178	C₄×D₄×C₃₁	D₄	1	2	yes	—
179	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₃₁	C₂³	1	2	yes	—
181	C₄×D₄×C₃₁	C₂³	1	4	yes	—
182	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₃₁×#117	—	2	1	no	—
186	C₃₁×#117	—	2	1	no	—
187	C₃₁×#117	—	2	2	no	—
188	C₃₁×#117	—	2	1	no	—
189	C₃₁×#117	—	2	2	no	—
190	C₃₁×#117	D₄	1	2	yes	—
191	C₃₁×#117	D₄	1	1	yes	characteristic
192	C₃₁×#117	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
194	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
195	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	—	2	2	no	—
200	C₂×C₄²×C₃₁	—	2	1	no	—
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₃₁×#107	C₂³	1	2	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#107	C₂³	1	4	yes	—
206	C₃₁×#107	C₂³	1	4	yes	—
207	C₃₁×#107	C₂³	1	4	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×#106	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₃₁×#103	C₂³	1	2	yes	—
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₃₁×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₃₁	C₂³	1	2	yes	—
229	#41×C₃₁	—	2	4	no	—
230	#41×C₃₁	—	2	2	no	—
231	#41×C₃₁	—	4	1	no	—
232	#41×C₃₁	—	4	8	no	—
233	#41×C₃₁	—	4	4	no	—
234	#41×C₃₁	—	4	16	no	—
235	#41×C₃₁	—	4	4	no	—
236	#41×C₃₁	—	4	8	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	1	no	—
239	C₂×Q₈×C₃₁	—	2	4	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	1	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	—	2	4	no	—
244	C₂×Q₈×C₃₁	—	4	2	no	—
245	C₂×Q₈×C₃₁	—	4	8	no	—
246	C₂×Q₈×C₃₁	—	4	4	no	—
247	C₂×Q₈×C₃₁	—	4	8	no	—
248	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
249	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
250	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	4	no	—
255	C₂×D₄×C₃₁	—	2	1	no	—
256	C₂×D₄×C₃₁	—	2	1	no	—
257	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	2	4	no	—
265	C₂²×C₄×C₃₁	—	2	1	no	—
266	C₂²×C₄×C₃₁	—	2	1	no	—
267	C₂²×C₄×C₃₁	—	2	1	no	—
268	C₂²×C₄×C₃₁	—	2	4	no	—
269	C₂²×C₄×C₃₁	—	2	2	no	—
270	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	SD₁₆×C₃₁	—	2	4	no	—
277	SD₁₆×C₃₁	—	4	4	no	—
278	D₈×C₃₁	—	4	2	no	—
279	M₁₆×C₃₁	—	4	2	no	—
280	C₂×C₈×C₃₁	—	4	4	no	—
281	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
282	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
283	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	4	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	4	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	1	no	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	1	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	1	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
327	C₄²×C₃₁	—	2	1	no	—
328	C₄²×C₃₁	—	2	1	no	—
329	C₄²×C₃₁	—	2	2	no	—
330	C₄²×C₃₁	—	2	2	no	—
331	C₄²×C₃₁	—	2	1	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₃₁	C₂×D₄	1	2	yes	—
336	C₄²×C₃₁	C₂×D₄	1	2	yes	—
337	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₄²×C₃₁	C₂⁴	1	2	yes	—
339	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
340	#62132	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂³×C₃₁	—	2	1	no	—
342	C₂³×C₃₁	—	2	2	no	—
343	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
345	Q₈×C₃₁	—	2	2	no	—
346	Q₈×C₃₁	—	2	1	no	—
347	Q₈×C₃₁	—	2	2	no	—
348	Q₈×C₃₁	—	2	2	no	—
349	Q₈×C₃₁	—	4	4	no	—
350	Q₈×C₃₁	—	4	4	no	—
351	Q₈×C₃₁	—	4	2	no	—
352	Q₈×C₃₁	—	4	8	no	—
353	Q₈×C₃₁	—	4	4	no	—
354	Q₈×C₃₁	—	4	2	no	—
355	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	complemented
356	D₄×C₃₁	—	2	4	no	—
357	D₄×C₃₁	—	2	2	no	—
358	D₄×C₃₁	—	2	1	no	—
359	D₄×C₃₁	—	2	1	no	—
360	D₄×C₃₁	—	2	2	no	—
361	D₄×C₃₁	—	4	2	no	—
362	D₄×C₃₁	—	4	2	no	—
363	D₄×C₃₁	—	4	4	no	—
364	D₄×C₃₁	—	4	4	no	—
365	D₄×C₃₁	—	4	8	no	—
366	D₄×C₃₁	—	4	2	no	—
367	D₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
368	C₂×C₄×C₃₁	—	2	4	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	4	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	4	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	4	2	no	—
384	C₂×C₄×C₃₁	—	4	4	no	—
385	C₂×C₄×C₃₁	—	4	8	no	—
386	C₂×C₄×C₃₁	—	4	4	no	—
387	C₂×C₄×C₃₁	—	4	8	no	—
388	C₂×C₄×C₃₁	—	4	4	no	—
389	C₂×C₄×C₃₁	—	4	4	no	—
390	C₂×C₄×C₃₁	—	4	2	no	—
391	C₂×C₄×C₃₁	—	4	2	no	—
392	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
401	C₈×C₃₁	—	2	2	no	—
402	C₈×C₃₁	—	2	2	no	—
403	C₈×C₃₁	—	2	4	no	—
404	#3499	C₂×C₃₁	1	1	yes	characteristic, complemented
405	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#3386	C₂×C₃₁	1	2	yes	complemented
407	#3367	C₂×C₃₁	1	2	yes	complemented
408	#3343	C₂×C₃₁	1	4	yes	complemented
409	#3334	C₂×C₃₁	1	2	yes	complemented
410	#3308	C₂×C₃₁	1	4	yes	complemented
411	#3298	C₂×C₃₁	1	2	yes	complemented
412	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
413	#3247	C₂×C₃₁	1	2	yes	complemented
414	#3238	C₂×C₃₁	1	2	yes	complemented
415	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#3112	C₂×C₃₁	1	2	yes	complemented
417	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
418	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
419	C₂×#477	C₂×C₃₁	1	2	yes	complemented
420	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
421	C₂²×C₃₁	—	2	2	no	—
422	C₂²×C₃₁	—	2	2	no	—
423	C₂²×C₃₁	—	2	1	no	—
424	C₂²×C₃₁	—	2	1	no	—
425	C₂²×C₃₁	—	2	1	no	—
426	C₂²×C₃₁	—	4	1	no	—
427	C₂²×C₃₁	—	4	2	no	—
428	C₂²×C₃₁	—	4	2	no	—
429	C₂²×C₃₁	—	4	1	no	—
430	C₂²×C₃₁	—	4	1	no	—
431	C₂²×C₃₁	—	4	2	no	—
432	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
433	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₃₁	—	2	1	no	—
435	C₄×C₃₁	—	2	2	no	—
436	C₄×C₃₁	—	2	2	no	—
437	C₄×C₃₁	—	2	1	no	—
438	C₄×C₃₁	—	2	2	no	—
439	C₄×C₃₁	—	2	2	no	—
440	C₄×C₃₁	—	2	1	no	—
441	C₄×C₃₁	—	4	2	no	—
442	C₄×C₃₁	—	4	1	no	—
443	C₄×C₃₁	—	4	4	no	—
444	C₄×C₃₁	—	4	2	no	—
445	C₄×C₃₁	—	4	2	no	—
446	C₄×C₃₁	—	4	1	no	—
447	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
448	C₄×C₃₁	#578	1	2	yes	—
449	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
450	C₄×C₃₁	#585	1	1	yes	characteristic
451	C₂×2₋¹⁺⁴	—	2	1	no	—
452	#557	C₂²×C₃₁	1	1	yes	characteristic
453	#556	—	2	1	no	—
454	#556	C₂²×C₃₁	1	1	yes	characteristic
455	#552	—	2	2	no	—
456	#552	C₂²×C₃₁	1	2	yes	—
457	D₄×Q₈	—	2	1	no	—
458	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
459	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
460	#548	C₂²×C₃₁	1	2	yes	—
461	#547	—	2	1	no	—
462	#547	—	2	1	no	—
463	#547	—	2	2	no	—
464	#547	C₂²×C₃₁	1	1	yes	characteristic
465	#547	C₂²×C₃₁	1	2	yes	—
466	#547	C₂²×C₃₁	1	4	yes	—
467	#536	—	2	2	no	—
468	#536	—	2	1	no	—
469	#533	—	2	1	no	—
470	#533	C₂²×C₃₁	1	1	yes	characteristic
471	#532	C₂²×C₃₁	1	1	yes	characteristic
472	#532	C₂²×C₃₁	1	2	yes	—
473	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
474	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
475	#529	—	2	2	no	—
476	#529	C₂²×C₃₁	1	2	yes	—
477	C₄×#41	—	2	1	no	—
478	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
479	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
481	#501	C₂²×C₃₁	1	4	yes	—
482	#500	C₂²×C₃₁	1	2	yes	—
483	#489	C₂²×C₃₁	1	4	yes	—
484	#487	C₂²×C₃₁	1	2	yes	—
485	#484	C₂²×C₃₁	1	4	yes	—
486	#483	C₂²×C₃₁	1	4	yes	—
487	#482	C₂²×C₃₁	1	2	yes	—
488	#480	C₂²×C₃₁	1	4	yes	—
489	#480	C₂²×C₃₁	1	4	yes	—
490	#478	C₂²×C₃₁	1	4	yes	—
491	#477	C₂²×C₃₁	1	1	yes	characteristic
492	#477	C₂²×C₃₁	1	2	yes	—
493	#477	C₂²×C₃₁	1	4	yes	—
494	#477	C₂²×C₃₁	1	4	yes	—
495	#477	C₂²×C₃₁	1	2	yes	—
496	#477	C₂²×C₃₁	1	2	yes	—
497	#477	C₂²×C₃₁	1	2	yes	—
498	#476	C₂²×C₃₁	1	2	yes	—
499	#476	C₂²×C₃₁	1	1	yes	characteristic
500	#475	C₂²×C₃₁	1	2	yes	—
501	#474	C₂²×C₃₁	1	2	yes	—
502	#474	C₂²×C₃₁	1	2	yes	—
503	#468	C₂²×C₃₁	1	4	yes	—
504	#466	C₂²×C₃₁	1	4	yes	—
505	#465	C₂²×C₃₁	1	4	yes	—
506	#463	C₂²×C₃₁	1	4	yes	—
507	#461	C₂²×C₃₁	1	2	yes	—
508	#460	C₂²×C₃₁	1	1	yes	characteristic
509	#460	C₂²×C₃₁	1	2	yes	—
510	#459	C₂²×C₃₁	1	1	yes	characteristic
511	#449	C₂²×C₃₁	1	2	yes	—
512	#448	C₂²×C₃₁	1	4	yes	—
513	#446	C₂²×C₃₁	1	2	yes	—
514	#440	C₂²×C₃₁	1	4	yes	—
515	#440	C₂²×C₃₁	1	4	yes	—
516	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
517	C₄×D₈	C₂²×C₃₁	1	2	yes	—
518	#435	C₂²×C₃₁	1	4	yes	—
519	C₈×D₄	C₂²×C₃₁	1	2	yes	—
520	#432	C₂²×C₃₁	1	2	yes	—
521	#431	C₂²×C₃₁	1	1	yes	characteristic
522	#428	C₂²×C₃₁	1	2	yes	—
523	C₂×#107	C₂²×C₃₁	1	4	yes	—
524	#423	C₂²×C₃₁	1	1	yes	characteristic
525	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
526	#417	C₂²×C₃₁	1	2	yes	—
527	C₂×#103	C₂²×C₃₁	1	4	yes	—
528	C₂×C₃₁	—	2	4	no	—
529	C₂×C₃₁	—	4	1	no	—
530	C₂×C₃₁	—	8	1	no	—
531	C₂×C₃₁	—	8	2	no	—
532	C₂×C₃₁	#3489	1	1	yes	characteristic
533	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
534	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
535	2₋¹⁺⁴	—	4	8	no	—
536	C₂×#41	—	2	1	no	—
537	C₂×#41	—	2	4	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	—	2	2	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
542	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
543	C₂²×Q₈	—	2	2	no	—
544	C₂²×Q₈	—	2	2	no	—
545	C₂²×Q₈	—	2	1	no	—
546	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
547	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
548	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
549	C₂×D₈	C₂³×C₃₁	1	2	yes	—
550	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
551	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
552	C₄⋊Q₈	—	2	1	no	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	—	2	2	no	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	2	no	—
558	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
560	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
563	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
564	#127	C₂³×C₃₁	1	1	yes	characteristic
565	#126	—	2	2	no	—
566	#126	—	2	2	no	—
567	#126	—	2	2	no	—
568	#125	—	2	2	no	—
569	#125	—	2	2	no	—
570	#125	—	2	1	no	—
571	#125	C₂³×C₃₁	1	2	yes	—
572	#124	—	2	2	no	—
573	#124	—	2	1	no	—
574	#124	—	2	2	no	—
575	#124	C₂³×C₃₁	1	2	yes	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	4	no	—
580	#123	—	2	4	no	—
581	#123	—	2	4	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
592	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	1	no	—
596	#121	C₂³×C₃₁	1	2	yes	—
597	#121	C₂³×C₃₁	1	4	yes	—
598	#121	C₂³×C₃₁	1	2	yes	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
606	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
607	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
608	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
618	C₄×D₄	D₄×C₃₁	1	2	yes	—
619	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₃₁	1	2	yes	—
622	C₄×D₄	C₂³×C₃₁	1	4	yes	—
623	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₃₁	1	2	yes	—
625	#117	—	2	1	no	—
626	#117	—	2	1	no	—
627	#117	—	2	2	no	—
628	#117	—	2	1	no	—
629	#117	—	2	2	no	—
630	#117	D₄×C₃₁	1	2	yes	—
631	#117	D₄×C₃₁	1	1	yes	characteristic
632	#117	C₂³×C₃₁	1	1	yes	characteristic
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
639	C₂×C₄²	—	2	2	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
642	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
643	#107	C₂³×C₃₁	1	2	yes	—
644	#107	C₂³×C₃₁	1	4	yes	—
645	#107	C₂³×C₃₁	1	4	yes	—
646	#107	C₂³×C₃₁	1	4	yes	—
647	#107	C₂³×C₃₁	1	4	yes	—
648	#106	C₂³×C₃₁	1	4	yes	—
649	#106	C₂³×C₃₁	1	2	yes	—
650	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
651	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
652	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
653	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
654	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
655	#103	C₂³×C₃₁	1	2	yes	—
656	#103	C₂³×C₃₁	1	4	yes	—
657	#103	C₂³×C₃₁	1	4	yes	—
658	#103	C₂³×C₃₁	1	4	yes	—
659	#103	C₂³×C₃₁	1	4	yes	—
660	#102	C₂³×C₃₁	1	4	yes	—
661	#102	C₂³×C₃₁	1	2	yes	—
662	#102	C₂³×C₃₁	1	2	yes	—
663	#102	C₂³×C₃₁	1	2	yes	—
664	#102	C₂³×C₃₁	1	4	yes	—
665	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
666	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
667	#97	C₂³×C₃₁	1	4	yes	—
668	C₄×C₈	C₂³×C₃₁	1	2	yes	—
669	C₃₁	#62132	1	1	yes	characteristic, direct product factor, Sylow
670	#41	—	2	4	no	—
671	#41	—	2	2	no	—
672	#41	—	4	1	no	—
673	#41	—	4	8	no	—
674	#41	—	4	4	no	—
675	#41	—	4	16	no	—
676	#41	—	4	4	no	—
677	#41	—	4	8	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	1	no	—
680	C₂×Q₈	—	2	4	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	4	2	no	—
686	C₂×Q₈	—	4	8	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	—	4	8	no	—
689	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
690	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
691	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
700	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
712	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
714	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
717	SD₁₆	—	2	4	no	—
718	SD₁₆	—	4	4	no	—
719	D₈	—	4	2	no	—
720	M₁₆	—	4	2	no	—
721	C₂×C₈	—	4	4	no	—
722	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
723	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
724	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
745	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
746	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
747	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
748	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
749	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
750	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
766	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
767	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
768	C₄²	—	2	1	no	—
769	C₄²	—	2	1	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	2	no	—
774	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₃₁	1	2	yes	—
777	C₄²	C₂×D₄×C₃₁	1	2	yes	—
778	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
779	C₄²	C₂⁴×C₃₁	1	2	yes	—
780	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
784	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	4	4	no	—
790	Q₈	—	4	4	no	—
791	Q₈	—	4	2	no	—
792	Q₈	—	4	8	no	—
793	Q₈	—	4	4	no	—
794	Q₈	—	4	2	no	—
795	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	complemented
796	D₄	—	2	4	no	—
797	D₄	—	2	2	no	—
798	D₄	—	2	1	no	—
799	D₄	—	2	1	no	—
800	D₄	—	2	2	no	—
801	D₄	—	4	2	no	—
802	D₄	—	4	2	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	8	no	—
806	D₄	—	4	2	no	—
807	D₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	4	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	4	8	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	8	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
840	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₈	—	2	4	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	1	no	—
854	C₂²	—	4	2	no	—
855	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
856	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
857	C₄	—	2	1	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	1	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	4	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
871	C₄	C₃₁×#578	1	2	yes	—
872	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
873	C₄	C₃₁×#585	1	1	yes	characteristic
874	C₂	—	2	4	no	—
875	C₂	—	4	1	no	—
876	C₂	—	8	1	no	—
877	C₂	—	8	2	no	—
878	C₂	C₃₁×#3489	1	1	yes	characteristic
879	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
880	C₂	C₂×C₃₁×#578	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×#3499	C₂	semidirect
2. C₃₁×#3482	C₂	semidirect
3. C₃₁×#3386	C₂	semidirect
4. C₃₁×#3367	C₂	semidirect
5. C₃₁×#3343	C₂	semidirect
6. C₃₁×#3334	C₂	semidirect
7. C₃₁×#3308	C₂	semidirect
8. C₃₁×#3298	C₂	semidirect
9. C₃₁×#3254	C₂	semidirect
10. C₃₁×#3247	C₂	semidirect
11. C₃₁×#3238	C₂	semidirect
12. C₃₁×#3230	C₂	semidirect
13. C₃₁×#3112	C₂	semidirect
14. C₃₁×#3106	C₂	semidirect
15. C₃₁×#3079	C₂	semidirect
16. C₂×C₃₁×#477	C₂	semidirect
17. C₃₁×#2990	C₂	semidirect
340. #62132	C₃₁	direct (N × H)
355. Q₈×C₃₁	2₋¹⁺⁴	semidirect
404. #3499	C₂×C₃₁	semidirect
405. #3482	C₂×C₃₁	semidirect
406. #3386	C₂×C₃₁	semidirect
407. #3367	C₂×C₃₁	semidirect
408. #3343	C₂×C₃₁	semidirect
409. #3334	C₂×C₃₁	semidirect
410. #3308	C₂×C₃₁	semidirect
411. #3298	C₂×C₃₁	semidirect
412. #3254	C₂×C₃₁	semidirect
413. #3247	C₂×C₃₁	semidirect
414. #3238	C₂×C₃₁	semidirect
415. #3230	C₂×C₃₁	semidirect
416. #3112	C₂×C₃₁	semidirect
417. #3106	C₂×C₃₁	semidirect
418. #3079	C₂×C₃₁	semidirect
419. C₂×#477	C₂×C₃₁	semidirect
420. #2990	C₂×C₃₁	semidirect
669. C₃₁	#62132	direct (N × H)
795. Q₈	C₃₁×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3499	2
C₃₁×#3482	2
C₃₁×#3386	2
C₃₁×#3367	2
C₃₁×#3343	2
C₃₁×#3334	2
C₃₁×#3308	2
C₃₁×#3298	2
C₃₁×#3254	2
C₃₁×#3247	2
C₃₁×#3238	2
C₃₁×#3230	2
C₃₁×#3112	2
C₃₁×#3106	2
C₃₁×#3079	2
C₂×C₃₁×#477	2
C₃₁×#2990	2
#62132	31

Subgroups — C31×#62132 #21518891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62132 #21518891