Subgroups — C₃₁×#61258 #21518017

Order 7936.

1866 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3492	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3346	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3343	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3338	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3336	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3334	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3092	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₃₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#554	—	2	2	no	—
22	C₃₁×#554	C₂²	1	4	yes	—
23	C₃₁×#553	—	2	2	no	—
24	C₃₁×#553	C₂²	1	4	yes	—
25	C₃₁×#552	—	2	2	no	—
26	C₃₁×#552	C₂²	1	4	yes	—
27	C₃₁×#547	—	2	2	no	—
28	C₃₁×#547	C₂²	1	4	yes	—
29	C₃₁×#544	C₂²	1	2	yes	—
30	C₃₁×#539	—	2	4	no	—
31	C₃₁×#537	C₂²	1	2	yes	—
32	C₃₁×#525	—	2	4	no	—
33	C₃₁×#525	C₂²	1	2	yes	—
34	C₃₁×#525	C₂²	1	1	yes	characteristic
35	C₃₁×#520	C₂²	1	2	yes	—
36	C₃₁×#520	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
38	C₃₁×#501	C₂²	1	4	yes	complemented
39	C₃₁×#500	C₂²	1	2	yes	complemented
40	C₃₁×#499	C₂²	1	2	yes	complemented
41	C₃₁×#485	C₂²	1	4	yes	complemented
42	C₃₁×#484	C₂²	1	4	yes	—
43	C₃₁×#484	C₂²	1	4	yes	complemented
44	C₃₁×#483	C₂²	1	4	yes	—
45	C₃₁×#482	C₂²	1	4	yes	complemented
46	C₃₁×#481	C₂²	1	4	yes	—
47	C₃₁×#480	C₂²	1	4	yes	—
48	C₃₁×#480	C₂²	1	4	yes	complemented
49	C₃₁×#479	C₂²	1	4	yes	complemented
50	C₃₁×#478	C₂²	1	4	yes	complemented
51	C₃₁×#477	C₂²	1	4	yes	complemented
52	C₃₁×#474	C₂²	1	4	yes	complemented
53	C₃₁×#468	C₂²	1	4	yes	complemented
54	C₃₁×#467	C₂²	1	1	yes	characteristic
55	C₃₁×#467	C₂²	1	1	yes	characteristic
56	C₃₁×#467	C₂²	1	2	yes	complemented
57	C₃₁×#466	C₂²	1	1	yes	characteristic
58	C₃₁×#466	C₂²	1	1	yes	characteristic
59	C₃₁×#466	C₂²	1	2	yes	complemented
60	C₃₁×#465	C₂²	1	2	yes	—
61	C₃₁×#465	C₂²	1	2	yes	—
62	C₃₁×#440	C₂²	1	4	yes	complemented
63	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
64	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
65	C₃₁×#435	C₂²	1	2	yes	—
66	C₃₁×#435	C₂²	1	2	yes	—
67	C₈×D₄×C₃₁	C₂²	1	2	yes	—
68	C₈×D₄×C₃₁	C₂²	1	2	yes	—
69	C₃₁×#428	C₂²	1	2	yes	—
70	C₃₁×#428	C₂²	1	2	yes	—
71	C₃₁×#428	C₂²	1	4	yes	complemented
72	C₃₁×#427	C₂²	1	1	yes	characteristic
73	C₃₁×#427	C₂²	1	2	yes	complemented
74	C₂×C₃₁×#107	C₂²	1	2	yes	—
75	C₂×C₃₁×#107	C₂²	1	2	yes	—
76	C₂×C₃₁×#107	C₂²	1	2	yes	—
77	C₂×C₃₁×#107	C₂²	1	2	yes	—
78	C₂×C₃₁×#107	C₂²	1	2	yes	—
79	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
80	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
81	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
82	C₃₁×#424	C₂²	1	1	yes	characteristic
83	C₃₁×#417	C₂²	1	2	yes	—
84	C₃₁×#417	C₂²	1	2	yes	—
85	C₃₁×#416	C₂²	1	2	yes	—
86	C₃₁×#408	C₂²	1	1	yes	characteristic
87	C₃₁×#407	C₂²	1	1	yes	characteristic
88	C₃₁×#405	C₂²	1	1	yes	characteristic
89	C₂×#41×C₃₁	—	2	4	no	—
90	C₂×#41×C₃₁	C₂³	1	2	yes	—
91	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	—	2	2	no	—
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₃₁×#135	—	2	4	no	—
95	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
96	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
97	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
98	C₃₁×#131	—	2	4	no	—
99	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂²×C₈×C₃₁	—	2	4	no	—
103	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
109	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	—	2	2	no	—
111	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
112	C₃₁×#126	—	2	4	no	—
113	C₃₁×#126	—	2	4	no	—
114	C₃₁×#125	—	2	4	no	—
115	C₃₁×#125	—	2	4	no	—
116	C₃₁×#125	—	2	2	no	—
117	C₃₁×#125	C₂³	1	4	yes	—
118	C₃₁×#123	—	2	4	no	—
119	C₃₁×#123	—	2	2	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	D₄	1	2	yes	—
124	C₃₁×C₂²⋊Q₈	—	2	2	no	—
125	C₃₁×C₂²⋊Q₈	—	2	4	no	—
126	C₃₁×C₂²⋊Q₈	—	2	4	no	—
127	C₃₁×C₂²⋊Q₈	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	4	no	—
129	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
130	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
131	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₃₁×#121	—	2	4	no	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	D₄	1	1	yes	characteristic
138	C₃₁×#121	D₄	1	1	yes	characteristic
139	C₃₁×#121	C₂³	1	2	yes	—
140	C₃₁×#121	C₂³	1	2	yes	—
141	C₃₁×#121	C₂³	1	4	yes	—
142	C₃₁×#120	—	2	2	no	—
143	C₃₁×#120	D₄	1	2	yes	—
144	C₄×Q₈×C₃₁	—	2	2	no	—
145	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
146	C₄×D₄×C₃₁	—	2	4	no	—
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	—	2	4	no	—
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	4	no	—
153	C₄×D₄×C₃₁	C₂³	1	4	yes	—
154	C₄×D₄×C₃₁	C₂³	1	2	yes	—
155	C₄×D₄×C₃₁	C₂³	1	2	yes	—
156	C₃₁×#117	—	2	2	no	—
157	C₃₁×#117	—	2	4	no	—
158	C₃₁×#117	C₂³	1	2	yes	—
159	C₃₁×#117	C₂³	1	4	yes	—
160	C₃₁×#117	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
163	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
164	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	2	yes	—
172	C₃₁×#107	C₂³	1	2	yes	—
173	C₃₁×#107	C₂³	1	2	yes	—
174	C₃₁×#107	C₂³	1	4	yes	—
175	C₃₁×#107	C₂³	1	4	yes	—
176	C₃₁×#107	C₂³	1	1	yes	characteristic
177	C₃₁×#107	C₂³	1	4	yes	—
178	C₃₁×#107	C₂³	1	1	yes	characteristic
179	C₃₁×#107	C₂³	1	4	yes	—
180	C₃₁×#106	C₂³	1	2	yes	—
181	C₃₁×#106	C₂³	1	4	yes	—
182	C₃₁×#106	C₂³	1	4	yes	—
183	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
184	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
185	C₃₁×#103	C₂³	1	2	yes	—
186	C₃₁×#103	C₂³	1	2	yes	—
187	C₃₁×#103	C₂³	1	4	yes	—
188	C₃₁×#103	C₂³	1	4	yes	—
189	C₃₁×#102	C₂³	1	2	yes	—
190	C₃₁×#102	C₂³	1	2	yes	—
191	C₃₁×#102	C₂³	1	4	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₃₁×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₃₁	C₂³	1	2	yes	—
199	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
200	#41×C₃₁	—	2	2	no	—
201	#41×C₃₁	—	2	2	no	—
202	#41×C₃₁	—	2	4	no	—
203	#41×C₃₁	—	2	4	no	—
204	#41×C₃₁	—	8	8	no	—
205	C₂×Q₈×C₃₁	—	2	4	no	—
206	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
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	2	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	4	no	—
220	C₂²×C₄×C₃₁	—	2	2	no	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	4	no	—
224	C₂²×C₄×C₃₁	—	2	2	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	8	4	no	—
227	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
234	Q₁₆×C₃₁	—	2	2	no	—
235	SD₁₆×C₃₁	—	2	4	no	—
236	D₈×C₃₁	—	2	2	no	—
237	M₁₆×C₃₁	—	2	2	no	—
238	M₁₆×C₃₁	—	2	2	no	—
239	M₁₆×C₃₁	—	2	4	no	—
240	C₂×C₈×C₃₁	—	2	2	no	—
241	C₂×C₈×C₃₁	—	2	2	no	—
242	C₂×C₈×C₃₁	—	2	2	no	—
243	C₂×C₈×C₃₁	—	2	2	no	—
244	C₂×C₈×C₃₁	—	2	2	no	—
245	C₂×C₈×C₃₁	—	2	4	no	—
246	C₂×C₈×C₃₁	#41	1	4	yes	complemented
247	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
248	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
249	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	2	4	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	2	no	—
265	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
268	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
271	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
273	C₂²⋊C₄×C₃₁	—	2	2	no	—
274	C₂²⋊C₄×C₃₁	—	2	2	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₂²⋊C₄×C₃₁	—	2	2	no	—
277	C₂²⋊C₄×C₃₁	—	2	4	no	—
278	C₂²⋊C₄×C₃₁	—	2	4	no	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	2	2	no	—
281	C₂²⋊C₄×C₃₁	—	2	2	no	—
282	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
285	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
286	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
287	C₄²×C₃₁	—	2	4	no	—
288	C₄²×C₃₁	—	2	4	no	—
289	C₄²×C₃₁	—	2	2	no	—
290	C₄²×C₃₁	C₂⁴	1	2	yes	—
291	#61258	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂³×C₃₁	—	2	2	no	—
293	C₂³×C₃₁	—	2	2	no	—
294	C₂³×C₃₁	—	2	2	no	—
295	C₂³×C₃₁	—	2	2	no	—
296	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
297	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
299	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₃₁	—	2	2	no	—
301	Q₈×C₃₁	—	2	2	no	—
302	Q₈×C₃₁	—	2	2	no	—
303	Q₈×C₃₁	—	8	4	no	—
304	D₄×C₃₁	—	2	4	no	—
305	D₄×C₃₁	—	2	4	no	—
306	D₄×C₃₁	—	2	4	no	—
307	D₄×C₃₁	—	2	2	no	—
308	D₄×C₃₁	—	2	2	no	—
309	D₄×C₃₁	—	2	2	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	4	4	no	—
312	D₄×C₃₁	—	4	4	no	—
313	D₄×C₃₁	—	8	4	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	1	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	1	no	—
321	C₂×C₄×C₃₁	—	2	1	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	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	4	no	—
328	C₂×C₄×C₃₁	—	4	8	no	—
329	C₂×C₄×C₃₁	—	4	4	no	—
330	C₂×C₄×C₃₁	—	8	4	no	—
331	C₂×C₄×C₃₁	—	8	2	no	—
332	C₂×C₄×C₃₁	—	8	4	no	—
333	C₂×C₄×C₃₁	—	8	2	no	—
334	C₂×C₄×C₃₁	—	8	4	no	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
342	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
343	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
344	C₈×C₃₁	—	2	1	no	—
345	C₈×C₃₁	—	2	1	no	—
346	C₈×C₃₁	—	2	2	no	—
347	C₈×C₃₁	—	2	2	no	—
348	C₈×C₃₁	C₂×#41	1	2	yes	—
349	C₈×C₃₁	C₂×#41	1	2	yes	—
350	#3492	C₂×C₃₁	1	2	yes	complemented
351	#3346	C₂×C₃₁	1	4	yes	complemented
352	#3343	C₂×C₃₁	1	4	yes	complemented
353	#3339	C₂×C₃₁	1	2	yes	complemented
354	#3338	C₂×C₃₁	1	2	yes	complemented
355	#3336	C₂×C₃₁	1	2	yes	complemented
356	#3334	C₂×C₃₁	1	2	yes	complemented
357	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#3098	C₂×C₃₁	1	2	yes	complemented
359	#3092	C₂×C₃₁	1	2	yes	complemented
360	#3083	C₂×C₃₁	1	2	yes	complemented
361	#3061	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#2929	C₂×C₃₁	1	1	yes	characteristic, complemented
365	#2913	C₂×C₃₁	1	1	yes	characteristic, complemented
366	C₂²×#107	C₂×C₃₁	1	1	yes	characteristic, complemented
367	C₂²×C₃₁	—	2	8	no	—
368	C₂²×C₃₁	—	2	1	no	—
369	C₂²×C₃₁	—	2	1	no	—
370	C₂²×C₃₁	—	2	1	no	—
371	C₂²×C₃₁	—	2	1	no	—
372	C₂²×C₃₁	—	2	1	no	—
373	C₂²×C₃₁	—	2	1	no	—
374	C₂²×C₃₁	—	2	2	no	—
375	C₂²×C₃₁	—	2	2	no	—
376	C₂²×C₃₁	—	2	2	no	—
377	C₂²×C₃₁	—	4	2	no	—
378	C₂²×C₃₁	—	4	2	no	—
379	C₂²×C₃₁	—	4	2	no	—
380	C₂²×C₃₁	#547	1	2	yes	—
381	C₂²×C₃₁	#576	1	2	yes	—
382	C₂²×C₃₁	#578	1	2	yes	—
383	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	2	1	no	—
386	C₄×C₃₁	—	2	2	no	—
387	C₄×C₃₁	—	2	2	no	—
388	C₄×C₃₁	—	2	2	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	—	4	4	no	—
391	C₄×C₃₁	—	4	4	no	—
392	C₄×C₃₁	—	4	2	no	—
393	C₄×C₃₁	—	4	2	no	—
394	C₄×C₃₁	#547	1	2	yes	—
395	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
396	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
397	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
398	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
399	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
400	#554	—	2	2	no	—
401	#554	C₂²×C₃₁	1	4	yes	—
402	#553	—	2	2	no	—
403	#553	C₂²×C₃₁	1	4	yes	—
404	#552	—	2	2	no	—
405	#552	C₂²×C₃₁	1	4	yes	—
406	#547	—	2	2	no	—
407	#547	C₂²×C₃₁	1	4	yes	—
408	#544	C₂²×C₃₁	1	2	yes	—
409	#539	—	2	4	no	—
410	#537	C₂²×C₃₁	1	2	yes	—
411	#525	—	2	4	no	—
412	#525	C₂²×C₃₁	1	2	yes	—
413	#525	C₂²×C₃₁	1	1	yes	characteristic
414	#520	C₂²×C₃₁	1	2	yes	—
415	#520	C₂²×C₃₁	1	2	yes	—
416	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
417	#501	C₂²×C₃₁	1	4	yes	complemented
418	#500	C₂²×C₃₁	1	2	yes	complemented
419	#499	C₂²×C₃₁	1	2	yes	complemented
420	#485	C₂²×C₃₁	1	4	yes	complemented
421	#484	C₂²×C₃₁	1	4	yes	—
422	#484	C₂²×C₃₁	1	4	yes	complemented
423	#483	C₂²×C₃₁	1	4	yes	—
424	#482	C₂²×C₃₁	1	4	yes	complemented
425	#481	C₂²×C₃₁	1	4	yes	—
426	#480	C₂²×C₃₁	1	4	yes	—
427	#480	C₂²×C₃₁	1	4	yes	complemented
428	#479	C₂²×C₃₁	1	4	yes	complemented
429	#478	C₂²×C₃₁	1	4	yes	complemented
430	#477	C₂²×C₃₁	1	4	yes	complemented
431	#474	C₂²×C₃₁	1	4	yes	complemented
432	#468	C₂²×C₃₁	1	4	yes	complemented
433	#467	C₂²×C₃₁	1	1	yes	characteristic
434	#467	C₂²×C₃₁	1	1	yes	characteristic
435	#467	C₂²×C₃₁	1	2	yes	complemented
436	#466	C₂²×C₃₁	1	1	yes	characteristic
437	#466	C₂²×C₃₁	1	1	yes	characteristic
438	#466	C₂²×C₃₁	1	2	yes	complemented
439	#465	C₂²×C₃₁	1	2	yes	—
440	#465	C₂²×C₃₁	1	2	yes	—
441	#440	C₂²×C₃₁	1	4	yes	complemented
442	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
443	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
444	#435	C₂²×C₃₁	1	2	yes	—
445	#435	C₂²×C₃₁	1	2	yes	—
446	C₈×D₄	C₂²×C₃₁	1	2	yes	—
447	C₈×D₄	C₂²×C₃₁	1	2	yes	—
448	#428	C₂²×C₃₁	1	2	yes	—
449	#428	C₂²×C₃₁	1	2	yes	—
450	#428	C₂²×C₃₁	1	4	yes	complemented
451	#427	C₂²×C₃₁	1	1	yes	characteristic
452	#427	C₂²×C₃₁	1	2	yes	complemented
453	C₂×#107	C₂²×C₃₁	1	2	yes	—
454	C₂×#107	C₂²×C₃₁	1	2	yes	—
455	C₂×#107	C₂²×C₃₁	1	2	yes	—
456	C₂×#107	C₂²×C₃₁	1	2	yes	—
457	C₂×#107	C₂²×C₃₁	1	2	yes	—
458	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
459	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
460	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
461	#424	C₂²×C₃₁	1	1	yes	characteristic
462	#417	C₂²×C₃₁	1	2	yes	—
463	#417	C₂²×C₃₁	1	2	yes	—
464	#416	C₂²×C₃₁	1	2	yes	—
465	#408	C₂²×C₃₁	1	1	yes	characteristic
466	#407	C₂²×C₃₁	1	1	yes	characteristic
467	#405	C₂²×C₃₁	1	1	yes	characteristic
468	C₂×C₃₁	—	2	2	no	—
469	C₂×C₃₁	—	2	2	no	—
470	C₂×C₃₁	—	2	2	no	—
471	C₂×C₃₁	—	4	2	no	—
472	C₂×C₃₁	—	8	2	no	—
473	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
474	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
475	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
476	C₂×#41	—	2	4	no	—
477	C₂×#41	C₂³×C₃₁	1	2	yes	—
478	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
479	C₂³×C₄	—	2	2	no	—
480	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
481	#135	—	2	4	no	—
482	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
483	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
484	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
485	#131	—	2	4	no	—
486	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
488	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
489	C₂²×C₈	—	2	4	no	—
490	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
496	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
499	#126	—	2	4	no	—
500	#126	—	2	4	no	—
501	#125	—	2	4	no	—
502	#125	—	2	4	no	—
503	#125	—	2	2	no	—
504	#125	C₂³×C₃₁	1	4	yes	—
505	#123	—	2	4	no	—
506	#123	—	2	2	no	—
507	#123	—	2	4	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	#123	D₄×C₃₁	1	2	yes	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
517	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
518	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
519	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
520	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
521	#121	—	2	4	no	—
522	#121	—	2	4	no	—
523	#121	—	2	2	no	—
524	#121	D₄×C₃₁	1	1	yes	characteristic
525	#121	D₄×C₃₁	1	1	yes	characteristic
526	#121	C₂³×C₃₁	1	2	yes	—
527	#121	C₂³×C₃₁	1	2	yes	—
528	#121	C₂³×C₃₁	1	4	yes	—
529	#120	—	2	2	no	—
530	#120	D₄×C₃₁	1	2	yes	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	4	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	C₂³×C₃₁	1	4	yes	—
541	C₄×D₄	C₂³×C₃₁	1	2	yes	—
542	C₄×D₄	C₂³×C₃₁	1	2	yes	—
543	#117	—	2	2	no	—
544	#117	—	2	4	no	—
545	#117	C₂³×C₃₁	1	2	yes	—
546	#117	C₂³×C₃₁	1	4	yes	—
547	#117	C₂³×C₃₁	1	1	yes	characteristic
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	—	2	2	no	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
557	#107	C₂³×C₃₁	1	2	yes	—
558	#107	C₂³×C₃₁	1	2	yes	—
559	#107	C₂³×C₃₁	1	2	yes	—
560	#107	C₂³×C₃₁	1	2	yes	—
561	#107	C₂³×C₃₁	1	4	yes	—
562	#107	C₂³×C₃₁	1	4	yes	—
563	#107	C₂³×C₃₁	1	1	yes	characteristic
564	#107	C₂³×C₃₁	1	4	yes	—
565	#107	C₂³×C₃₁	1	1	yes	characteristic
566	#107	C₂³×C₃₁	1	4	yes	—
567	#106	C₂³×C₃₁	1	2	yes	—
568	#106	C₂³×C₃₁	1	4	yes	—
569	#106	C₂³×C₃₁	1	4	yes	—
570	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
571	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
572	#103	C₂³×C₃₁	1	2	yes	—
573	#103	C₂³×C₃₁	1	2	yes	—
574	#103	C₂³×C₃₁	1	4	yes	—
575	#103	C₂³×C₃₁	1	4	yes	—
576	#102	C₂³×C₃₁	1	2	yes	—
577	#102	C₂³×C₃₁	1	2	yes	—
578	#102	C₂³×C₃₁	1	4	yes	—
579	#102	C₂³×C₃₁	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
581	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
582	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
584	#97	C₂³×C₃₁	1	2	yes	—
585	C₄×C₈	C₂³×C₃₁	1	2	yes	—
586	C₃₁	#61258	1	1	yes	characteristic, direct product factor, Sylow
587	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
588	#41	—	2	2	no	—
589	#41	—	2	2	no	—
590	#41	—	2	4	no	—
591	#41	—	2	4	no	—
592	#41	—	8	8	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
601	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
602	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
603	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
604	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	8	4	no	—
615	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
622	Q₁₆	—	2	2	no	—
623	SD₁₆	—	2	4	no	—
624	D₈	—	2	2	no	—
625	M₁₆	—	2	2	no	—
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	4	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	4	no	—
634	C₂×C₈	#41×C₃₁	1	4	yes	complemented
635	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
636	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
637	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
638	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
654	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
655	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
656	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
658	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
659	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
660	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
673	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
674	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	2	no	—
678	C₄²	C₂⁴×C₃₁	1	2	yes	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
684	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
685	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
686	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
687	Q₈	—	2	2	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	8	4	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	8	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	8	4	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
723	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
728	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
729	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
730	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
731	C₈	—	2	1	no	—
732	C₈	—	2	1	no	—
733	C₈	—	2	2	no	—
734	C₈	—	2	2	no	—
735	C₈	C₂×#41×C₃₁	1	2	yes	—
736	C₈	C₂×#41×C₃₁	1	2	yes	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	C₃₁×#547	1	2	yes	—
751	C₂²	C₃₁×#576	1	2	yes	—
752	C₂²	C₃₁×#578	1	2	yes	—
753	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	4	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₃₁×#547	1	2	yes	—
765	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
766	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
767	C₂	—	2	2	no	—
768	C₂	—	2	2	no	—
769	C₂	—	2	2	no	—
770	C₂	—	4	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
773	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
774	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 ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3492	C₂	semidirect
2. C₃₁×#3346	C₂	semidirect
3. C₃₁×#3343	C₂	semidirect
4. C₃₁×#3339	C₂	semidirect
5. C₃₁×#3338	C₂	semidirect
6. C₃₁×#3336	C₂	semidirect
7. C₃₁×#3334	C₂	semidirect
8. C₃₁×#3164	C₂	semidirect
9. C₃₁×#3098	C₂	semidirect
10. C₃₁×#3092	C₂	semidirect
11. C₃₁×#3083	C₂	semidirect
12. C₃₁×#3061	C₂	semidirect
13. C₃₁×#3050	C₂	semidirect
14. C₃₁×#2951	C₂	semidirect
15. C₃₁×#2929	C₂	semidirect
16. C₃₁×#2913	C₂	semidirect
17. C₂²×C₃₁×#107	C₂	semidirect
38. C₃₁×#501	C₂²	semidirect
39. C₃₁×#500	C₂²	semidirect
40. C₃₁×#499	C₂²	semidirect
41. C₃₁×#485	C₂²	semidirect
43. C₃₁×#484	C₂²	semidirect
45. C₃₁×#482	C₂²	semidirect
48. C₃₁×#480	C₂²	semidirect
49. C₃₁×#479	C₂²	semidirect
50. C₃₁×#478	C₂²	semidirect
51. C₃₁×#477	C₂²	semidirect
52. C₃₁×#474	C₂²	semidirect
53. C₃₁×#468	C₂²	semidirect
56. C₃₁×#467	C₂²	semidirect
59. C₃₁×#466	C₂²	semidirect
62. C₃₁×#440	C₂²	semidirect
63. C₄×Q₁₆×C₃₁	C₂²	semidirect
64. C₄×D₈×C₃₁	C₂²	semidirect
71. C₃₁×#428	C₂²	semidirect
73. C₃₁×#427	C₂²	semidirect
81. C₂×C₃₁×#107	C₂²	semidirect
246. C₂×C₈×C₃₁	#41	semidirect
291. #61258	C₃₁	direct (N × H)
350. #3492	C₂×C₃₁	semidirect
351. #3346	C₂×C₃₁	semidirect
352. #3343	C₂×C₃₁	semidirect
353. #3339	C₂×C₃₁	semidirect
354. #3338	C₂×C₃₁	semidirect
355. #3336	C₂×C₃₁	semidirect
356. #3334	C₂×C₃₁	semidirect
357. #3164	C₂×C₃₁	semidirect
358. #3098	C₂×C₃₁	semidirect
359. #3092	C₂×C₃₁	semidirect
360. #3083	C₂×C₃₁	semidirect
361. #3061	C₂×C₃₁	semidirect
362. #3050	C₂×C₃₁	semidirect
363. #2951	C₂×C₃₁	semidirect
364. #2929	C₂×C₃₁	semidirect
365. #2913	C₂×C₃₁	semidirect
366. C₂²×#107	C₂×C₃₁	semidirect
417. #501	C₂²×C₃₁	semidirect
418. #500	C₂²×C₃₁	semidirect
419. #499	C₂²×C₃₁	semidirect
420. #485	C₂²×C₃₁	semidirect
422. #484	C₂²×C₃₁	semidirect
424. #482	C₂²×C₃₁	semidirect
427. #480	C₂²×C₃₁	semidirect
428. #479	C₂²×C₃₁	semidirect
429. #478	C₂²×C₃₁	semidirect
430. #477	C₂²×C₃₁	semidirect
431. #474	C₂²×C₃₁	semidirect
432. #468	C₂²×C₃₁	semidirect
435. #467	C₂²×C₃₁	semidirect
438. #466	C₂²×C₃₁	semidirect
441. #440	C₂²×C₃₁	semidirect
442. C₄×Q₁₆	C₂²×C₃₁	semidirect
443. C₄×D₈	C₂²×C₃₁	semidirect
450. #428	C₂²×C₃₁	semidirect
452. #427	C₂²×C₃₁	semidirect
460. C₂×#107	C₂²×C₃₁	semidirect
586. C₃₁	#61258	direct (N × H)
634. 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×#3492	2
C₃₁×#3346	2
C₃₁×#3343	2
C₃₁×#3339	2
C₃₁×#3338	2
C₃₁×#3336	2
C₃₁×#3334	2
C₃₁×#3164	2
C₃₁×#3098	2
C₃₁×#3092	2
C₃₁×#3083	2
C₃₁×#3061	2
C₃₁×#3050	2
C₃₁×#2951	2
C₃₁×#2929	2
C₃₁×#2913	2
C₂²×C₃₁×#107	2
#61258	31

Subgroups — C31×#61258 #21518017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61258 #21518017