Subgroups — C₃₁×#60707 #21517466

Order 7936.

1980 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3494	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3180	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3179	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3176	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3175	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3169	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3168	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
17	C₂×C₃₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#555	—	2	2	no	—
24	C₃₁×#553	—	2	2	no	—
25	C₃₁×#553	—	2	2	no	—
26	C₃₁×#551	—	2	4	no	—
27	C₃₁×#547	—	2	2	no	—
28	C₃₁×#546	—	2	4	no	—
29	C₃₁×#544	C₂²	1	2	yes	—
30	C₃₁×#542	C₂²	1	4	yes	complemented
31	C₃₁×#540	C₂²	1	4	yes	complemented
32	C₃₁×#535	C₂²	1	2	yes	—
33	C₃₁×#532	C₂²	1	4	yes	complemented
34	C₃₁×#529	C₂²	1	4	yes	complemented
35	C₃₁×#525	C₂²	1	2	yes	—
36	C₂×C₃₁×#121	C₂²	1	2	yes	—
37	C₃₁×#520	C₂²	1	2	yes	—
38	C₃₁×#518	C₂²	1	2	yes	—
39	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
40	C₃₁×#501	C₂²	1	4	yes	complemented
41	C₃₁×#500	C₂²	1	2	yes	complemented
42	C₃₁×#499	C₂²	1	2	yes	complemented
43	C₃₁×#496	C₂²	1	4	yes	complemented
44	C₃₁×#495	C₂²	1	2	yes	complemented
45	C₃₁×#493	C₂²	1	2	yes	complemented
46	C₃₁×#490	C₂²	1	4	yes	complemented
47	C₃₁×#489	C₂²	1	4	yes	complemented
48	C₃₁×#488	C₂²	1	4	yes	complemented
49	C₃₁×#486	C₂²	1	4	yes	complemented
50	C₃₁×#469	C₂²	1	4	yes	complemented
51	C₃₁×#468	C₂²	1	4	yes	complemented
52	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#466	C₂²	1	2	yes	—
55	C₃₁×#466	C₂²	1	2	yes	—
56	C₃₁×#466	C₂²	1	2	yes	—
57	C₃₁×#466	C₂²	1	2	yes	—
58	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#466	C₂²	1	4	yes	complemented
60	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#465	C₂²	1	4	yes	complemented
62	C₃₁×#465	C₂²	1	2	yes	complemented
63	C₃₁×#465	C₂²	1	2	yes	complemented
64	C₃₁×#442	C₂²	1	4	yes	complemented
65	C₃₁×#442	C₂²	1	4	yes	complemented
66	C₃₁×#440	C₂²	1	4	yes	complemented
67	C₃₁×#440	C₂²	1	4	yes	complemented
68	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
69	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
70	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
71	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
72	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
73	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
74	C₃₁×#428	C₂²	1	2	yes	—
75	C₃₁×#427	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
77	C₃₁×#418	C₂²	1	2	yes	—
78	C₃₁×#417	C₂²	1	2	yes	—
79	C₃₁×#416	C₂²	1	2	yes	—
80	C₂×C₃₁×#102	C₂²	1	2	yes	—
81	C₃₁×#405	C₂²	1	1	yes	characteristic
82	C₃₁×#405	C₂²	1	1	yes	characteristic
83	C₃₁×#405	C₂²	1	1	yes	characteristic
84	C₃₁×#405	C₂²	1	1	yes	characteristic
85	C₃₁×#405	C₂²	1	2	yes	complemented
86	C₃₁×#405	C₂²	1	2	yes	complemented
87	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	complemented
89	C₂×#41×C₃₁	—	2	4	no	—
90	C₂×#41×C₃₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₃₁	—	2	2	no	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
95	C₃₁×#135	—	2	4	no	—
96	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
99	C₂×D₈×C₃₁	—	2	4	no	—
100	C₂×D₈×C₃₁	C₂³	1	2	yes	—
101	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂×D₈×C₃₁	C₂³	1	4	yes	—
103	C₂×D₈×C₃₁	C₂³	1	2	yes	—
104	C₂×M₁₆×C₃₁	—	2	4	no	—
105	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₃₁	—	2	4	no	—
109	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
111	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	—	2	2	no	—
117	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₃₁×#127	C₂³	1	4	yes	—
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#126	—	2	4	no	—
121	C₃₁×#125	—	2	2	no	—
122	C₃₁×#125	C₂³	1	4	yes	—
123	C₃₁×#124	—	2	4	no	—
124	C₃₁×#124	—	2	4	no	—
125	C₃₁×#124	C₂³	1	4	yes	—
126	C₃₁×#123	—	2	2	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×#123	—	2	4	no	—
129	C₃₁×#123	—	2	4	no	—
130	C₃₁×#123	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	—	2	2	no	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	4	no	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	C₂³	1	4	yes	—
143	C₃₁×#121	C₂³	1	2	yes	—
144	C₃₁×#121	C₂³	1	2	yes	—
145	C₃₁×#121	C₂³	1	4	yes	—
146	C₃₁×#120	—	2	2	no	—
147	C₃₁×#120	—	2	4	no	—
148	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	—	2	4	no	—
152	C₄×D₄×C₃₁	—	2	2	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	4	no	—
155	C₄×D₄×C₃₁	—	2	4	no	—
156	C₄×D₄×C₃₁	C₂³	1	4	yes	—
157	C₄×D₄×C₃₁	C₂³	1	4	yes	—
158	C₄×D₄×C₃₁	C₂³	1	4	yes	—
159	C₃₁×#117	—	2	2	no	—
160	C₃₁×#117	—	2	4	no	—
161	C₃₁×#117	D₄	1	2	yes	—
162	C₃₁×#117	D₄	1	1	yes	characteristic
163	C₃₁×#117	D₄	1	1	yes	characteristic
164	C₃₁×#117	C₂³	1	2	yes	—
165	C₃₁×#117	C₂³	1	1	yes	characteristic
166	C₃₁×#117	C₂³	1	1	yes	characteristic
167	C₃₁×#117	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
169	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
173	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
174	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
175	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
176	C₃₁×#107	C₂³	1	2	yes	—
177	C₃₁×#107	C₂³	1	2	yes	—
178	C₃₁×#107	C₂³	1	1	yes	characteristic
179	C₃₁×#107	C₂³	1	1	yes	characteristic
180	C₃₁×#107	C₂³	1	4	yes	—
181	C₃₁×#106	C₂³	1	2	yes	—
182	C₃₁×#106	C₂³	1	4	yes	—
183	C₃₁×#103	C₂³	1	2	yes	—
184	C₃₁×#103	C₂³	1	2	yes	—
185	C₃₁×#103	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×#102	C₂³	1	2	yes	—
189	C₃₁×#102	C₂³	1	2	yes	—
190	C₃₁×#102	C₂³	1	4	yes	—
191	C₃₁×#102	C₂³	1	4	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×#97	C₂³	1	2	yes	—
194	C₃₁×#97	C₂³	1	2	yes	—
195	C₃₁×#97	C₂³	1	2	yes	—
196	C₃₁×#97	C₂³	1	2	yes	—
197	C₄×C₈×C₃₁	C₂³	1	2	yes	—
198	C₄×C₈×C₃₁	C₂³	1	2	yes	—
199	C₄×C₈×C₃₁	C₂³	1	2	yes	—
200	C₄×C₈×C₃₁	C₂³	1	2	yes	—
201	C₂⁴×C₃₁	—	2	2	no	—
202	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
203	#41×C₃₁	—	2	4	no	—
204	#41×C₃₁	—	2	4	no	—
205	#41×C₃₁	—	8	8	no	—
206	C₂×Q₈×C₃₁	—	2	4	no	—
207	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	4	no	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	—	2	4	no	—
215	C₂×D₄×C₃₁	—	2	4	no	—
216	C₂×D₄×C₃₁	—	2	4	no	—
217	C₂×D₄×C₃₁	—	2	4	no	—
218	C₂×D₄×C₃₁	—	8	4	no	—
219	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
220	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	2	2	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	4	no	—
227	C₂²×C₄×C₃₁	—	2	4	no	—
228	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₃₁	—	2	2	no	—
237	SD₁₆×C₃₁	—	2	4	no	—
238	SD₁₆×C₃₁	—	2	8	no	—
239	D₈×C₃₁	—	2	4	no	—
240	D₈×C₃₁	—	2	4	no	—
241	D₈×C₃₁	—	2	2	no	—
242	D₈×C₃₁	—	2	8	no	—
243	M₁₆×C₃₁	—	2	2	no	—
244	M₁₆×C₃₁	—	2	4	no	—
245	M₁₆×C₃₁	#41	1	4	yes	complemented
246	C₂×C₈×C₃₁	—	2	2	no	—
247	C₂×C₈×C₃₁	—	2	2	no	—
248	C₂×C₈×C₃₁	—	2	2	no	—
249	C₂×C₈×C₃₁	—	2	2	no	—
250	C₂×C₈×C₃₁	—	2	2	no	—
251	C₂×C₈×C₃₁	—	2	4	no	—
252	C₂×C₈×C₃₁	#41	1	4	yes	complemented
253	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
255	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
258	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	4	no	—
261	C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₄⋊C₄×C₃₁	—	2	4	no	—
263	C₄⋊C₄×C₃₁	—	2	4	no	—
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
269	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
274	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²⋊C₄×C₃₁	—	2	2	no	—
276	C₂²⋊C₄×C₃₁	—	2	2	no	—
277	C₂²⋊C₄×C₃₁	—	2	2	no	—
278	C₂²⋊C₄×C₃₁	—	2	4	no	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	2	4	no	—
281	C₂²⋊C₄×C₃₁	—	2	4	no	—
282	C₂²⋊C₄×C₃₁	—	2	4	no	—
283	C₂²⋊C₄×C₃₁	—	2	4	no	—
284	C₂²⋊C₄×C₃₁	—	2	2	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	2	2	no	—
287	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
288	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
289	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
290	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
291	C₄²×C₃₁	—	2	4	no	—
292	C₄²×C₃₁	—	2	2	no	—
293	C₄²×C₃₁	C₂×D₄	1	2	yes	—
294	C₄²×C₃₁	C₂×D₄	1	2	yes	—
295	C₄²×C₃₁	C₂⁴	1	2	yes	—
296	C₄²×C₃₁	C₂⁴	1	2	yes	—
297	#60707	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂³×C₃₁	—	2	2	no	—
299	C₂³×C₃₁	—	2	2	no	—
300	C₂³×C₃₁	—	2	4	no	—
301	C₂³×C₃₁	—	2	2	no	—
302	C₂³×C₃₁	—	4	1	no	—
303	C₂³×C₃₁	—	4	4	no	—
304	C₂³×C₃₁	—	8	2	no	—
305	C₂³×C₃₁	—	8	2	no	—
306	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
307	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
308	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₃₁	—	2	2	no	—
310	Q₈×C₃₁	—	2	2	no	—
311	Q₈×C₃₁	—	8	4	no	—
312	D₄×C₃₁	—	2	4	no	—
313	D₄×C₃₁	—	2	2	no	—
314	D₄×C₃₁	—	2	4	no	—
315	D₄×C₃₁	—	2	2	no	—
316	D₄×C₃₁	—	4	4	no	—
317	D₄×C₃₁	—	4	8	no	—
318	D₄×C₃₁	—	4	4	no	—
319	D₄×C₃₁	—	4	4	no	—
320	D₄×C₃₁	—	8	4	no	—
321	D₄×C₃₁	—	8	4	no	—
322	D₄×C₃₁	—	8	2	no	—
323	D₄×C₃₁	—	8	4	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	4	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	1	no	—
329	C₂×C₄×C₃₁	—	2	1	no	—
330	C₂×C₄×C₃₁	—	2	1	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	4	no	—
336	C₂×C₄×C₃₁	—	4	2	no	—
337	C₂×C₄×C₃₁	—	4	4	no	—
338	C₂×C₄×C₃₁	—	8	4	no	—
339	C₂×C₄×C₃₁	—	8	4	no	—
340	C₂×C₄×C₃₁	—	8	4	no	—
341	C₂×C₄×C₃₁	—	8	2	no	—
342	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
350	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
351	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
352	C₈×C₃₁	—	2	1	no	—
353	C₈×C₃₁	—	2	1	no	—
354	C₈×C₃₁	—	2	2	no	—
355	C₈×C₃₁	C₂×#41	1	2	yes	—
356	C₈×C₃₁	C₂×#41	1	2	yes	—
357	C₈×C₃₁	C₂×#41	1	4	yes	—
358	#3494	C₂×C₃₁	1	2	yes	complemented
359	#3180	C₂×C₃₁	1	4	yes	complemented
360	#3179	C₂×C₃₁	1	4	yes	complemented
361	#3176	C₂×C₃₁	1	2	yes	complemented
362	#3175	C₂×C₃₁	1	2	yes	complemented
363	#3169	C₂×C₃₁	1	2	yes	complemented
364	#3168	C₂×C₃₁	1	2	yes	complemented
365	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
366	#3155	C₂×C₃₁	1	1	yes	characteristic, complemented
367	#3136	C₂×C₃₁	1	2	yes	complemented
368	#3055	C₂×C₃₁	1	2	yes	complemented
369	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
370	C₂×#466	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#2948	C₂×C₃₁	1	1	yes	characteristic, complemented
373	#2946	C₂×C₃₁	1	2	yes	complemented
374	C₂×#405	C₂×C₃₁	1	1	yes	characteristic, complemented
375	C₂²×C₃₁	—	2	1	no	—
376	C₂²×C₃₁	—	2	1	no	—
377	C₂²×C₃₁	—	2	1	no	—
378	C₂²×C₃₁	—	2	1	no	—
379	C₂²×C₃₁	—	2	1	no	—
380	C₂²×C₃₁	—	2	1	no	—
381	C₂²×C₃₁	—	2	1	no	—
382	C₂²×C₃₁	—	4	4	no	—
383	C₂²×C₃₁	—	4	4	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	—	4	2	no	—
386	C₂²×C₃₁	—	4	4	no	—
387	C₂²×C₃₁	—	4	2	no	—
388	C₂²×C₃₁	—	4	4	no	—
389	C₂²×C₃₁	—	16	4	no	—
390	C₂²×C₃₁	#532	1	2	yes	—
391	C₂²×C₃₁	#576	1	2	yes	—
392	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₃₁	—	2	2	no	—
394	C₄×C₃₁	—	2	2	no	—
395	C₄×C₃₁	—	2	1	no	—
396	C₄×C₃₁	—	2	1	no	—
397	C₄×C₃₁	—	2	2	no	—
398	C₄×C₃₁	—	2	2	no	—
399	C₄×C₃₁	—	4	2	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	—	4	4	no	—
402	C₄×C₃₁	—	4	2	no	—
403	C₄×C₃₁	#532	1	2	yes	—
404	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
405	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
406	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
407	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
408	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
409	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
410	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
411	#555	—	2	2	no	—
412	#553	—	2	2	no	—
413	#553	—	2	2	no	—
414	#551	—	2	4	no	—
415	#547	—	2	2	no	—
416	#546	—	2	4	no	—
417	#544	C₂²×C₃₁	1	2	yes	—
418	#542	C₂²×C₃₁	1	4	yes	complemented
419	#540	C₂²×C₃₁	1	4	yes	complemented
420	#535	C₂²×C₃₁	1	2	yes	—
421	#532	C₂²×C₃₁	1	4	yes	complemented
422	#529	C₂²×C₃₁	1	4	yes	complemented
423	#525	C₂²×C₃₁	1	2	yes	—
424	C₂×#121	C₂²×C₃₁	1	2	yes	—
425	#520	C₂²×C₃₁	1	2	yes	—
426	#518	C₂²×C₃₁	1	2	yes	—
427	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
428	#501	C₂²×C₃₁	1	4	yes	complemented
429	#500	C₂²×C₃₁	1	2	yes	complemented
430	#499	C₂²×C₃₁	1	2	yes	complemented
431	#496	C₂²×C₃₁	1	4	yes	complemented
432	#495	C₂²×C₃₁	1	2	yes	complemented
433	#493	C₂²×C₃₁	1	2	yes	complemented
434	#490	C₂²×C₃₁	1	4	yes	complemented
435	#489	C₂²×C₃₁	1	4	yes	complemented
436	#488	C₂²×C₃₁	1	4	yes	complemented
437	#486	C₂²×C₃₁	1	4	yes	complemented
438	#469	C₂²×C₃₁	1	4	yes	complemented
439	#468	C₂²×C₃₁	1	4	yes	complemented
440	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
441	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
442	#466	C₂²×C₃₁	1	2	yes	—
443	#466	C₂²×C₃₁	1	2	yes	—
444	#466	C₂²×C₃₁	1	2	yes	—
445	#466	C₂²×C₃₁	1	2	yes	—
446	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
447	#466	C₂²×C₃₁	1	4	yes	complemented
448	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
449	#465	C₂²×C₃₁	1	4	yes	complemented
450	#465	C₂²×C₃₁	1	2	yes	complemented
451	#465	C₂²×C₃₁	1	2	yes	complemented
452	#442	C₂²×C₃₁	1	4	yes	complemented
453	#442	C₂²×C₃₁	1	4	yes	complemented
454	#440	C₂²×C₃₁	1	4	yes	complemented
455	#440	C₂²×C₃₁	1	4	yes	complemented
456	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
457	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
458	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
459	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
460	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
461	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
462	#428	C₂²×C₃₁	1	2	yes	—
463	#427	C₂²×C₃₁	1	1	yes	characteristic
464	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
465	#418	C₂²×C₃₁	1	2	yes	—
466	#417	C₂²×C₃₁	1	2	yes	—
467	#416	C₂²×C₃₁	1	2	yes	—
468	C₂×#102	C₂²×C₃₁	1	2	yes	—
469	#405	C₂²×C₃₁	1	1	yes	characteristic
470	#405	C₂²×C₃₁	1	1	yes	characteristic
471	#405	C₂²×C₃₁	1	1	yes	characteristic
472	#405	C₂²×C₃₁	1	1	yes	characteristic
473	#405	C₂²×C₃₁	1	2	yes	complemented
474	#405	C₂²×C₃₁	1	2	yes	complemented
475	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
476	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	complemented
477	C₂×C₃₁	—	2	2	no	—
478	C₂×C₃₁	—	2	2	no	—
479	C₂×C₃₁	—	4	1	no	—
480	C₂×C₃₁	—	8	2	no	—
481	C₂×C₃₁	—	8	4	no	—
482	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
483	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
484	C₂×C₃₁	#3584	1	1	yes	characteristic
485	C₂×#41	—	2	4	no	—
486	C₂×#41	C₂³×C₃₁	1	2	yes	—
487	C₂²×D₄	—	2	2	no	—
488	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
489	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
490	AGL(1,ℤ/8)	—	2	8	no	—
491	#135	—	2	4	no	—
492	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
493	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
494	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
495	C₂×D₈	—	2	4	no	—
496	C₂×D₈	C₂³×C₃₁	1	2	yes	—
497	C₂×D₈	C₂³×C₃₁	1	2	yes	—
498	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
499	C₂×D₈	C₂³×C₃₁	1	4	yes	—
500	C₂×M₁₆	—	2	4	no	—
501	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
502	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
503	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
504	C₂²×C₈	—	2	4	no	—
505	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
511	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
514	#127	C₂³×C₃₁	1	4	yes	—
515	#126	—	2	4	no	—
516	#126	—	2	4	no	—
517	#125	—	2	2	no	—
518	#125	C₂³×C₃₁	1	4	yes	—
519	#124	—	2	4	no	—
520	#124	—	2	4	no	—
521	#124	C₂³×C₃₁	1	4	yes	—
522	#123	—	2	2	no	—
523	#123	—	2	4	no	—
524	#123	—	2	4	no	—
525	#123	—	2	4	no	—
526	#123	—	2	4	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
530	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	2	4	no	—
534	#121	—	2	2	no	—
535	#121	—	2	2	no	—
536	#121	—	2	4	no	—
537	#121	—	2	4	no	—
538	#121	C₂³×C₃₁	1	4	yes	—
539	#121	C₂³×C₃₁	1	4	yes	—
540	#121	C₂³×C₃₁	1	2	yes	—
541	#121	C₂³×C₃₁	1	2	yes	—
542	#120	—	2	2	no	—
543	#120	—	2	4	no	—
544	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	4	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	C₂³×C₃₁	1	4	yes	—
553	C₄×D₄	C₂³×C₃₁	1	4	yes	—
554	C₄×D₄	C₂³×C₃₁	1	4	yes	—
555	#117	—	2	2	no	—
556	#117	—	2	4	no	—
557	#117	D₄×C₃₁	1	2	yes	—
558	#117	D₄×C₃₁	1	1	yes	characteristic
559	#117	D₄×C₃₁	1	1	yes	characteristic
560	#117	C₂³×C₃₁	1	2	yes	—
561	#117	C₂³×C₃₁	1	1	yes	characteristic
562	#117	C₂³×C₃₁	1	1	yes	characteristic
563	#117	C₂³×C₃₁	1	2	yes	—
564	C₂×C₄⋊C₄	—	2	2	no	—
565	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
566	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂×C₂²⋊C₄	—	2	2	no	—
569	C₂×C₂²⋊C₄	—	2	4	no	—
570	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
571	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
572	#107	C₂³×C₃₁	1	2	yes	—
573	#107	C₂³×C₃₁	1	2	yes	—
574	#107	C₂³×C₃₁	1	1	yes	characteristic
575	#107	C₂³×C₃₁	1	1	yes	characteristic
576	#107	C₂³×C₃₁	1	4	yes	—
577	#106	C₂³×C₃₁	1	2	yes	—
578	#106	C₂³×C₃₁	1	4	yes	—
579	#103	C₂³×C₃₁	1	2	yes	—
580	#103	C₂³×C₃₁	1	2	yes	—
581	#103	C₂³×C₃₁	1	4	yes	—
582	#102	C₂³×C₃₁	1	4	yes	—
583	#102	C₂³×C₃₁	1	4	yes	—
584	#102	C₂³×C₃₁	1	2	yes	—
585	#102	C₂³×C₃₁	1	2	yes	—
586	#102	C₂³×C₃₁	1	4	yes	—
587	#102	C₂³×C₃₁	1	4	yes	—
588	#102	C₂³×C₃₁	1	4	yes	—
589	#97	C₂³×C₃₁	1	2	yes	—
590	#97	C₂³×C₃₁	1	2	yes	—
591	#97	C₂³×C₃₁	1	2	yes	—
592	#97	C₂³×C₃₁	1	2	yes	—
593	C₄×C₈	C₂³×C₃₁	1	2	yes	—
594	C₄×C₈	C₂³×C₃₁	1	2	yes	—
595	C₄×C₈	C₂³×C₃₁	1	2	yes	—
596	C₄×C₈	C₂³×C₃₁	1	2	yes	—
597	C₃₁	#60707	1	1	yes	characteristic, direct product factor, Sylow
598	C₂⁴	—	2	2	no	—
599	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
600	#41	—	2	4	no	—
601	#41	—	2	4	no	—
602	#41	—	8	8	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	8	4	no	—
616	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
617	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
626	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
628	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
633	Q₁₆	—	2	2	no	—
634	SD₁₆	—	2	4	no	—
635	SD₁₆	—	2	8	no	—
636	D₈	—	2	4	no	—
637	D₈	—	2	4	no	—
638	D₈	—	2	2	no	—
639	D₈	—	2	8	no	—
640	M₁₆	—	2	2	no	—
641	M₁₆	—	2	4	no	—
642	M₁₆	#41×C₃₁	1	4	yes	complemented
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	2	2	no	—
648	C₂×C₈	—	2	4	no	—
649	C₂×C₈	#41×C₃₁	1	4	yes	complemented
650	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
652	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
654	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
655	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
664	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
665	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
666	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
667	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
668	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
671	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
685	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
686	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
687	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₄²	C₂×D₄×C₃₁	1	2	yes	—
691	C₄²	C₂×D₄×C₃₁	1	2	yes	—
692	C₄²	C₂⁴×C₃₁	1	2	yes	—
693	C₄²	C₂⁴×C₃₁	1	2	yes	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	4	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	8	2	no	—
701	C₂³	—	8	2	no	—
702	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
703	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
704	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	8	4	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	2	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	4	no	—
716	D₄	—	8	4	no	—
717	D₄	—	8	4	no	—
718	D₄	—	8	2	no	—
719	D₄	—	8	4	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	4	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	—	8	2	no	—
738	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
740	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
742	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
743	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
745	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
746	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
747	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
748	C₈	—	2	1	no	—
749	C₈	—	2	1	no	—
750	C₈	—	2	2	no	—
751	C₈	C₂×#41×C₃₁	1	2	yes	—
752	C₈	C₂×#41×C₃₁	1	2	yes	—
753	C₈	C₂×#41×C₃₁	1	4	yes	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	4	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	4	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	16	4	no	—
769	C₂²	C₃₁×#532	1	2	yes	—
770	C₂²	C₃₁×#576	1	2	yes	—
771	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	4	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	C₃₁×#532	1	2	yes	—
783	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
784	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	2	2	no	—
787	C₂	—	4	1	no	—
788	C₂	—	8	4	no	—
789	C₂	—	8	2	no	—
790	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
791	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
792	C₂	C₃₁×#3584	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 ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3494	C₂	semidirect
2. C₃₁×#3180	C₂	semidirect
3. C₃₁×#3179	C₂	semidirect
4. C₃₁×#3176	C₂	semidirect
5. C₃₁×#3175	C₂	semidirect
6. C₃₁×#3169	C₂	semidirect
7. C₃₁×#3168	C₂	semidirect
8. C₃₁×#3164	C₂	semidirect
9. C₃₁×#3155	C₂	semidirect
10. C₃₁×#3136	C₂	semidirect
11. C₃₁×#3055	C₂	semidirect
12. C₃₁×#3050	C₂	semidirect
13. C₂×C₃₁×#466	C₂	semidirect
14. C₃₁×#2951	C₂	semidirect
15. C₃₁×#2948	C₂	semidirect
16. C₃₁×#2946	C₂	semidirect
17. C₂×C₃₁×#405	C₂	semidirect
30. C₃₁×#542	C₂²	semidirect
31. C₃₁×#540	C₂²	semidirect
33. C₃₁×#532	C₂²	semidirect
34. C₃₁×#529	C₂²	semidirect
40. C₃₁×#501	C₂²	semidirect
41. C₃₁×#500	C₂²	semidirect
42. C₃₁×#499	C₂²	semidirect
43. C₃₁×#496	C₂²	semidirect
44. C₃₁×#495	C₂²	semidirect
45. C₃₁×#493	C₂²	semidirect
46. C₃₁×#490	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
48. C₃₁×#488	C₂²	semidirect
49. C₃₁×#486	C₂²	semidirect
50. C₃₁×#469	C₂²	semidirect
51. C₃₁×#468	C₂²	semidirect
52. C₃₁×#467	C₂²	semidirect
53. C₃₁×#467	C₂²	semidirect
58. C₃₁×#466	C₂²	semidirect
59. C₃₁×#466	C₂²	semidirect
60. C₃₁×#466	C₂²	semidirect
61. C₃₁×#465	C₂²	semidirect
62. C₃₁×#465	C₂²	semidirect
63. C₃₁×#465	C₂²	semidirect
64. C₃₁×#442	C₂²	semidirect
65. C₃₁×#442	C₂²	semidirect
66. C₃₁×#440	C₂²	semidirect
67. C₃₁×#440	C₂²	semidirect
68. C₄×Q₁₆×C₃₁	C₂²	semidirect
69. C₄×SD₁₆×C₃₁	C₂²	semidirect
70. C₄×D₈×C₃₁	C₂²	semidirect
71. C₄×D₈×C₃₁	C₂²	semidirect
72. C₄×D₈×C₃₁	C₂²	semidirect
73. C₄×D₈×C₃₁	C₂²	semidirect
85. C₃₁×#405	C₂²	semidirect
86. C₃₁×#405	C₂²	semidirect
87. C₂×C₃₁×#97	C₂²	semidirect
88. C₂×C₄×C₈×C₃₁	C₂²	semidirect
245. M₁₆×C₃₁	#41	semidirect
252. C₂×C₈×C₃₁	#41	semidirect
297. #60707	C₃₁	direct (N × H)
358. #3494	C₂×C₃₁	semidirect
359. #3180	C₂×C₃₁	semidirect
360. #3179	C₂×C₃₁	semidirect
361. #3176	C₂×C₃₁	semidirect
362. #3175	C₂×C₃₁	semidirect
363. #3169	C₂×C₃₁	semidirect
364. #3168	C₂×C₃₁	semidirect
365. #3164	C₂×C₃₁	semidirect
366. #3155	C₂×C₃₁	semidirect
367. #3136	C₂×C₃₁	semidirect
368. #3055	C₂×C₃₁	semidirect
369. #3050	C₂×C₃₁	semidirect
370. C₂×#466	C₂×C₃₁	semidirect
371. #2951	C₂×C₃₁	semidirect
372. #2948	C₂×C₃₁	semidirect
373. #2946	C₂×C₃₁	semidirect
374. C₂×#405	C₂×C₃₁	semidirect
418. #542	C₂²×C₃₁	semidirect
419. #540	C₂²×C₃₁	semidirect
421. #532	C₂²×C₃₁	semidirect
422. #529	C₂²×C₃₁	semidirect
428. #501	C₂²×C₃₁	semidirect
429. #500	C₂²×C₃₁	semidirect
430. #499	C₂²×C₃₁	semidirect
431. #496	C₂²×C₃₁	semidirect
432. #495	C₂²×C₃₁	semidirect
433. #493	C₂²×C₃₁	semidirect
434. #490	C₂²×C₃₁	semidirect
435. #489	C₂²×C₃₁	semidirect
436. #488	C₂²×C₃₁	semidirect
437. #486	C₂²×C₃₁	semidirect
438. #469	C₂²×C₃₁	semidirect
439. #468	C₂²×C₃₁	semidirect
440. #467	C₂²×C₃₁	semidirect
441. #467	C₂²×C₃₁	semidirect
446. #466	C₂²×C₃₁	semidirect
447. #466	C₂²×C₃₁	semidirect
448. #466	C₂²×C₃₁	semidirect
449. #465	C₂²×C₃₁	semidirect
450. #465	C₂²×C₃₁	semidirect
451. #465	C₂²×C₃₁	semidirect
452. #442	C₂²×C₃₁	semidirect
453. #442	C₂²×C₃₁	semidirect
454. #440	C₂²×C₃₁	semidirect
455. #440	C₂²×C₃₁	semidirect
456. C₄×Q₁₆	C₂²×C₃₁	semidirect
457. C₄×SD₁₆	C₂²×C₃₁	semidirect
458. C₄×D₈	C₂²×C₃₁	semidirect
459. C₄×D₈	C₂²×C₃₁	semidirect
460. C₄×D₈	C₂²×C₃₁	semidirect
461. C₄×D₈	C₂²×C₃₁	semidirect
473. #405	C₂²×C₃₁	semidirect
474. #405	C₂²×C₃₁	semidirect
475. C₂×#97	C₂²×C₃₁	semidirect
476. C₂×C₄×C₈	C₂²×C₃₁	semidirect
597. C₃₁	#60707	direct (N × H)
642. M₁₆	#41×C₃₁	semidirect
649. C₂×C₈	#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×#3494	2
C₃₁×#3180	2
C₃₁×#3179	2
C₃₁×#3176	2
C₃₁×#3175	2
C₃₁×#3169	2
C₃₁×#3168	2
C₃₁×#3164	2
C₃₁×#3155	2
C₃₁×#3136	2
C₃₁×#3055	2
C₃₁×#3050	2
C₂×C₃₁×#466	2
C₃₁×#2951	2
C₃₁×#2948	2
C₃₁×#2946	2
C₂×C₃₁×#405	2
#60707	31

Subgroups — C31×#60707 #21517466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60707 #21517466