Subgroups — C₃₁×#61285 #21518044

Order 7936.

1818 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3353	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3351	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3337	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3335	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3096	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3057	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2912	C₂	1	2	yes	maximal, complemented
18	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#131	C₂²	1	2	yes	—
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#559	—	2	2	no	—
22	C₃₁×#557	—	2	1	no	—
23	C₃₁×#556	—	2	1	no	—
24	C₃₁×#556	—	2	2	no	—
25	C₃₁×#556	C₂²	1	2	yes	complemented
26	C₃₁×#555	C₂²	1	2	yes	—
27	C₃₁×#554	C₂²	1	2	yes	complemented
28	C₃₁×#553	C₂²	1	4	yes	—
29	C₃₁×#552	C₂²	1	4	yes	complemented
30	C₃₁×#550	—	2	1	no	—
31	C₃₁×#547	C₂²	1	2	yes	—
32	C₃₁×#539	—	2	2	no	—
33	C₃₁×#538	—	2	2	no	—
34	C₃₁×#536	C₂²	1	2	yes	—
35	C₃₁×#535	C₂²	1	2	yes	—
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#529	—	2	2	no	—
40	C₃₁×#525	—	2	2	no	—
41	C₃₁×#520	C₂²	1	2	yes	—
42	C₃₁×#520	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#499	C₂²	1	2	yes	complemented
48	C₃₁×#499	C₂²	1	2	yes	complemented
49	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#485	C₂²	1	4	yes	complemented
52	C₃₁×#485	C₂²	1	4	yes	complemented
53	C₃₁×#484	C₂²	1	4	yes	complemented
54	C₃₁×#483	C₂²	1	4	yes	complemented
55	C₃₁×#482	C₂²	1	4	yes	—
56	C₃₁×#482	C₂²	1	4	yes	—
57	C₃₁×#481	C₂²	1	4	yes	—
58	C₃₁×#480	C₂²	1	4	yes	—
59	C₃₁×#479	C₂²	1	4	yes	complemented
60	C₃₁×#478	C₂²	1	4	yes	—
61	C₃₁×#477	C₂²	1	2	yes	complemented
62	C₃₁×#476	C₂²	1	2	yes	—
63	C₃₁×#475	C₂²	1	2	yes	complemented
64	C₃₁×#474	C₂²	1	2	yes	—
65	C₃₁×#468	C₂²	1	4	yes	—
66	C₃₁×#468	C₂²	1	4	yes	—
67	C₃₁×#465	C₂²	1	4	yes	—
68	C₃₁×#465	C₂²	1	4	yes	—
69	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
70	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
71	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
72	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
73	C₃₁×#436	C₂²	1	2	yes	complemented
74	C₃₁×#436	C₂²	1	2	yes	complemented
75	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
76	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
77	C₃₁×#428	C₂²	1	2	yes	—
78	C₃₁×#428	C₂²	1	2	yes	—
79	C₃₁×#428	C₂²	1	4	yes	complemented
80	C₃₁×#428	C₂²	1	4	yes	complemented
81	C₃₁×#427	C₂²	1	2	yes	—
82	C₃₁×#427	C₂²	1	2	yes	—
83	C₃₁×#427	C₂²	1	4	yes	complemented
84	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
85	C₂×C₃₁×#106	C₂²	1	4	yes	complemented
86	C₃₁×#423	C₂²	1	1	yes	characteristic
87	C₃₁×#419	C₂²	1	2	yes	—
88	C₃₁×#418	C₂²	1	2	yes	—
89	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
90	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
91	C₃₁×#408	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	—	2	2	no	—
94	C₂×#41×C₃₁	C₂³	1	2	yes	—
95	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	—	2	1	no	—
98	C₂×SD₁₆×C₃₁	—	2	4	no	—
99	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
101	C₃₁×#131	—	2	8	no	—
102	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
109	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×#127	—	2	2	no	—
114	C₃₁×#127	D₄	1	1	yes	characteristic
115	C₃₁×#126	—	2	4	no	—
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#125	—	2	2	no	—
119	C₃₁×#125	—	2	4	no	—
120	C₃₁×#125	C₂³	1	2	yes	—
121	C₃₁×#125	C₂³	1	2	yes	—
122	C₃₁×#124	—	2	2	no	—
123	C₃₁×#124	—	2	2	no	—
124	C₃₁×#124	—	2	2	no	—
125	C₃₁×#124	—	2	4	no	—
126	C₃₁×#124	D₄	1	2	yes	—
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	1	no	—
132	C₃₁×C₂²⋊Q₈	—	2	1	no	—
133	C₃₁×C₂²⋊Q₈	—	2	1	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	4	no	—
141	C₃₁×#121	D₄	1	2	yes	—
142	C₃₁×#121	D₄	1	2	yes	—
143	C₃₁×#121	C₂³	1	4	yes	—
144	C₃₁×#121	C₂³	1	4	yes	—
145	C₃₁×#120	—	2	4	no	—
146	C₄×Q₈×C₃₁	—	2	2	no	—
147	C₄×Q₈×C₃₁	—	2	2	no	—
148	C₄×Q₈×C₃₁	—	2	2	no	—
149	C₄×Q₈×C₃₁	—	2	1	no	—
150	C₄×Q₈×C₃₁	—	2	1	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×D₄×C₃₁	—	2	4	no	—
158	C₄×D₄×C₃₁	—	2	4	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	4	no	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	C₂³	1	2	yes	—
166	C₄×D₄×C₃₁	C₂³	1	2	yes	—
167	C₄×D₄×C₃₁	C₂³	1	2	yes	—
168	C₄×D₄×C₃₁	C₂³	1	2	yes	—
169	C₃₁×#117	—	2	2	no	—
170	C₃₁×#117	—	2	4	no	—
171	C₃₁×#117	C₂³	1	2	yes	—
172	C₃₁×#117	C₂³	1	2	yes	—
173	C₃₁×#117	C₂³	1	4	yes	—
174	C₃₁×#117	C₂³	1	4	yes	—
175	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
180	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
181	C₂×C₄²×C₃₁	—	2	1	no	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₃₁×#107	C₂³	1	2	yes	—
184	C₃₁×#107	C₂³	1	2	yes	—
185	C₃₁×#107	C₂³	1	2	yes	—
186	C₃₁×#107	C₂³	1	2	yes	—
187	C₃₁×#107	C₂³	1	4	yes	—
188	C₃₁×#107	C₂³	1	4	yes	—
189	C₃₁×#106	C₂³	1	2	yes	—
190	C₃₁×#106	C₂³	1	2	yes	—
191	C₃₁×#106	C₂³	1	2	yes	—
192	C₃₁×#106	C₂³	1	4	yes	—
193	C₃₁×#106	C₂³	1	4	yes	—
194	C₃₁×#106	C₂³	1	2	yes	—
195	C₃₁×#106	C₂³	1	2	yes	—
196	C₃₁×#106	C₂³	1	2	yes	—
197	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
198	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
199	C₃₁×#103	C₂³	1	2	yes	—
200	C₃₁×#103	C₂³	1	2	yes	—
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#103	C₂³	1	4	yes	—
203	C₃₁×#102	C₂³	1	2	yes	—
204	C₃₁×#102	C₂³	1	2	yes	—
205	C₃₁×#102	C₂³	1	4	yes	—
206	C₃₁×#102	C₂³	1	4	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
213	C₂⁴×C₃₁	—	2	1	no	—
214	#41×C₃₁	—	2	4	no	—
215	#41×C₃₁	—	2	4	no	—
216	#41×C₃₁	—	8	4	no	—
217	C₂×Q₈×C₃₁	—	2	1	no	—
218	C₂×Q₈×C₃₁	—	2	1	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	1	no	—
221	C₂×Q₈×C₃₁	—	2	1	no	—
222	C₂×Q₈×C₃₁	—	2	2	no	—
223	C₂×Q₈×C₃₁	—	2	2	no	—
224	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
226	C₂×D₄×C₃₁	—	2	4	no	—
227	C₂×D₄×C₃₁	—	2	4	no	—
228	C₂×D₄×C₃₁	—	2	1	no	—
229	C₂×D₄×C₃₁	—	2	2	no	—
230	C₂×D₄×C₃₁	—	2	2	no	—
231	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₃₁	—	2	1	no	—
237	C₂²×C₄×C₃₁	—	2	1	no	—
238	C₂²×C₄×C₃₁	—	2	1	no	—
239	C₂²×C₄×C₃₁	—	2	4	no	—
240	C₂²×C₄×C₃₁	—	2	4	no	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	2	2	no	—
243	C₂²×C₄×C₃₁	—	8	2	no	—
244	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	SD₁₆×C₃₁	—	2	4	no	—
249	SD₁₆×C₃₁	—	2	4	no	—
250	M₁₆×C₃₁	—	2	4	no	—
251	M₁₆×C₃₁	—	2	8	no	—
252	C₂×C₈×C₃₁	—	2	2	no	—
253	C₂×C₈×C₃₁	—	2	8	no	—
254	C₂×C₈×C₃₁	#41	1	4	yes	complemented
255	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
258	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	2	4	no	—
266	C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	1	no	—
275	C₄⋊C₄×C₃₁	—	2	4	no	—
276	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	2	no	—
286	C₂²⋊C₄×C₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₃₁	—	2	2	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	—	2	2	no	—
291	C₂²⋊C₄×C₃₁	—	2	2	no	—
292	C₂²⋊C₄×C₃₁	—	2	4	no	—
293	C₂²⋊C₄×C₃₁	—	2	4	no	—
294	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
295	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
296	C₄²×C₃₁	—	2	2	no	—
297	C₄²×C₃₁	—	2	2	no	—
298	C₄²×C₃₁	—	2	4	no	—
299	C₄²×C₃₁	—	2	4	no	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	—	2	2	no	—
302	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
306	#61285	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂³×C₃₁	—	2	2	no	—
308	C₂³×C₃₁	—	4	2	no	—
309	C₂³×C₃₁	—	8	1	no	—
310	C₂³×C₃₁	—	8	1	no	—
311	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
312	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₃₁	—	2	4	no	—
314	Q₈×C₃₁	—	2	2	no	—
315	Q₈×C₃₁	—	2	2	no	—
316	Q₈×C₃₁	—	4	2	no	—
317	Q₈×C₃₁	—	4	2	no	—
318	Q₈×C₃₁	—	4	2	no	—
319	Q₈×C₃₁	—	8	1	no	—
320	Q₈×C₃₁	—	8	1	no	—
321	D₄×C₃₁	—	2	8	no	—
322	D₄×C₃₁	—	2	4	no	—
323	D₄×C₃₁	—	2	4	no	—
324	D₄×C₃₁	—	2	2	no	—
325	D₄×C₃₁	—	2	2	no	—
326	D₄×C₃₁	—	4	2	no	—
327	D₄×C₃₁	—	4	2	no	—
328	D₄×C₃₁	—	8	4	no	—
329	D₄×C₃₁	—	8	4	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	4	no	—
332	C₂×C₄×C₃₁	—	2	4	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	4	1	no	—
341	C₂×C₄×C₃₁	—	4	2	no	—
342	C₂×C₄×C₃₁	—	4	4	no	—
343	C₂×C₄×C₃₁	—	8	2	no	—
344	C₂×C₄×C₃₁	—	8	1	no	—
345	C₂×C₄×C₃₁	—	8	4	no	—
346	C₂×C₄×C₃₁	—	8	1	no	—
347	C₂×C₄×C₃₁	—	8	4	no	—
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
355	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
356	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
357	C₈×C₃₁	—	2	4	no	—
358	C₈×C₃₁	—	2	1	no	—
359	C₈×C₃₁	—	2	1	no	—
360	C₈×C₃₁	C₂×#41	1	2	yes	—
361	C₈×C₃₁	C₂×#41	1	2	yes	—
362	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#3506	C₂×C₃₁	1	1	yes	characteristic
364	#3357	C₂×C₃₁	1	2	yes	complemented
365	#3353	C₂×C₃₁	1	2	yes	complemented
366	#3351	C₂×C₃₁	1	4	yes	complemented
367	#3340	C₂×C₃₁	1	2	yes	complemented
368	#3337	C₂×C₃₁	1	4	yes	complemented
369	#3335	C₂×C₃₁	1	2	yes	complemented
370	#3160	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#3097	C₂×C₃₁	1	2	yes	complemented
372	#3096	C₂×C₃₁	1	2	yes	complemented
373	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
374	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
375	#3057	C₂×C₃₁	1	2	yes	complemented
376	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
377	#2931	C₂×C₃₁	1	1	yes	characteristic, complemented
378	#2912	C₂×C₃₁	1	2	yes	complemented
379	C₂²×C₃₁	—	2	1	no	—
380	C₂²×C₃₁	—	2	1	no	—
381	C₂²×C₃₁	—	2	4	no	—
382	C₂²×C₃₁	—	2	4	no	—
383	C₂²×C₃₁	—	2	4	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	—	4	2	no	—
386	C₂²×C₃₁	—	4	2	no	—
387	C₂²×C₃₁	—	8	4	no	—
388	C₂²×C₃₁	#547	1	2	yes	—
389	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
390	C₄×C₃₁	—	2	1	no	—
391	C₄×C₃₁	—	2	1	no	—
392	C₄×C₃₁	—	2	4	no	—
393	C₄×C₃₁	—	2	1	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	—	4	2	no	—
396	C₄×C₃₁	—	4	2	no	—
397	C₄×C₃₁	—	4	2	no	—
398	C₄×C₃₁	—	4	2	no	—
399	C₄×C₃₁	—	4	2	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	#547	1	2	yes	—
402	C₄×C₃₁	#577	1	2	yes	—
403	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
404	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
405	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
406	C₂×#131	C₂²×C₃₁	1	2	yes	—
407	#559	—	2	1	no	—
408	#559	—	2	2	no	—
409	#557	—	2	1	no	—
410	#556	—	2	1	no	—
411	#556	—	2	2	no	—
412	#556	C₂²×C₃₁	1	2	yes	complemented
413	#555	C₂²×C₃₁	1	2	yes	—
414	#554	C₂²×C₃₁	1	2	yes	complemented
415	#553	C₂²×C₃₁	1	4	yes	—
416	#552	C₂²×C₃₁	1	4	yes	complemented
417	#550	—	2	1	no	—
418	#547	C₂²×C₃₁	1	2	yes	—
419	#539	—	2	2	no	—
420	#538	—	2	2	no	—
421	#536	C₂²×C₃₁	1	2	yes	—
422	#535	C₂²×C₃₁	1	2	yes	—
423	#533	C₂²×C₃₁	1	1	yes	characteristic
424	#533	C₂²×C₃₁	1	1	yes	characteristic
425	#532	C₂²×C₃₁	1	1	yes	characteristic
426	#529	—	2	2	no	—
427	#525	—	2	2	no	—
428	#520	C₂²×C₃₁	1	2	yes	—
429	#520	C₂²×C₃₁	1	2	yes	—
430	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
432	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
433	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
434	#499	C₂²×C₃₁	1	2	yes	complemented
435	#499	C₂²×C₃₁	1	2	yes	complemented
436	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
437	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
438	#485	C₂²×C₃₁	1	4	yes	complemented
439	#485	C₂²×C₃₁	1	4	yes	complemented
440	#484	C₂²×C₃₁	1	4	yes	complemented
441	#483	C₂²×C₃₁	1	4	yes	complemented
442	#482	C₂²×C₃₁	1	4	yes	—
443	#482	C₂²×C₃₁	1	4	yes	—
444	#481	C₂²×C₃₁	1	4	yes	—
445	#480	C₂²×C₃₁	1	4	yes	—
446	#479	C₂²×C₃₁	1	4	yes	complemented
447	#478	C₂²×C₃₁	1	4	yes	—
448	#477	C₂²×C₃₁	1	2	yes	complemented
449	#476	C₂²×C₃₁	1	2	yes	—
450	#475	C₂²×C₃₁	1	2	yes	complemented
451	#474	C₂²×C₃₁	1	2	yes	—
452	#468	C₂²×C₃₁	1	4	yes	—
453	#468	C₂²×C₃₁	1	4	yes	—
454	#465	C₂²×C₃₁	1	4	yes	—
455	#465	C₂²×C₃₁	1	4	yes	—
456	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
457	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
458	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
459	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
460	#436	C₂²×C₃₁	1	2	yes	complemented
461	#436	C₂²×C₃₁	1	2	yes	complemented
462	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
463	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
464	#428	C₂²×C₃₁	1	2	yes	—
465	#428	C₂²×C₃₁	1	2	yes	—
466	#428	C₂²×C₃₁	1	4	yes	complemented
467	#428	C₂²×C₃₁	1	4	yes	complemented
468	#427	C₂²×C₃₁	1	2	yes	—
469	#427	C₂²×C₃₁	1	2	yes	—
470	#427	C₂²×C₃₁	1	4	yes	complemented
471	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
472	C₂×#106	C₂²×C₃₁	1	4	yes	complemented
473	#423	C₂²×C₃₁	1	1	yes	characteristic
474	#419	C₂²×C₃₁	1	2	yes	—
475	#418	C₂²×C₃₁	1	2	yes	—
476	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
477	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
478	#408	C₂²×C₃₁	1	2	yes	—
479	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×C₃₁	—	2	2	no	—
481	C₂×C₃₁	—	4	4	no	—
482	C₂×C₃₁	—	8	2	no	—
483	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
484	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
485	C₂×C₃₁	#3584	1	1	yes	characteristic
486	C₂×#41	—	2	2	no	—
487	C₂×#41	C₂³×C₃₁	1	2	yes	—
488	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
490	C₂³×C₄	—	2	1	no	—
491	C₂×SD₁₆	—	2	4	no	—
492	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
493	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
494	#131	—	2	8	no	—
495	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
496	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
497	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
498	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
500	C₄⋊Q₈	—	2	2	no	—
501	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
506	#127	—	2	2	no	—
507	#127	D₄×C₃₁	1	1	yes	characteristic
508	#126	—	2	4	no	—
509	#126	—	2	4	no	—
510	#126	—	2	4	no	—
511	#125	—	2	2	no	—
512	#125	—	2	4	no	—
513	#125	C₂³×C₃₁	1	2	yes	—
514	#125	C₂³×C₃₁	1	2	yes	—
515	#124	—	2	2	no	—
516	#124	—	2	2	no	—
517	#124	—	2	2	no	—
518	#124	—	2	4	no	—
519	#124	D₄×C₃₁	1	2	yes	—
520	#123	—	2	4	no	—
521	#123	—	2	4	no	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	—	2	1	no	—
526	C₂²⋊Q₈	—	2	1	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
531	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
532	#121	—	2	2	no	—
533	#121	—	2	4	no	—
534	#121	D₄×C₃₁	1	2	yes	—
535	#121	D₄×C₃₁	1	2	yes	—
536	#121	C₂³×C₃₁	1	4	yes	—
537	#121	C₂³×C₃₁	1	4	yes	—
538	#120	—	2	4	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	2	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
549	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	4	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	C₂³×C₃₁	1	2	yes	—
559	C₄×D₄	C₂³×C₃₁	1	2	yes	—
560	C₄×D₄	C₂³×C₃₁	1	2	yes	—
561	C₄×D₄	C₂³×C₃₁	1	2	yes	—
562	#117	—	2	2	no	—
563	#117	—	2	4	no	—
564	#117	C₂³×C₃₁	1	2	yes	—
565	#117	C₂³×C₃₁	1	2	yes	—
566	#117	C₂³×C₃₁	1	4	yes	—
567	#117	C₂³×C₃₁	1	4	yes	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₄²	—	2	1	no	—
575	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
576	#107	C₂³×C₃₁	1	2	yes	—
577	#107	C₂³×C₃₁	1	2	yes	—
578	#107	C₂³×C₃₁	1	2	yes	—
579	#107	C₂³×C₃₁	1	2	yes	—
580	#107	C₂³×C₃₁	1	4	yes	—
581	#107	C₂³×C₃₁	1	4	yes	—
582	#106	C₂³×C₃₁	1	2	yes	—
583	#106	C₂³×C₃₁	1	2	yes	—
584	#106	C₂³×C₃₁	1	2	yes	—
585	#106	C₂³×C₃₁	1	4	yes	—
586	#106	C₂³×C₃₁	1	4	yes	—
587	#106	C₂³×C₃₁	1	2	yes	—
588	#106	C₂³×C₃₁	1	2	yes	—
589	#106	C₂³×C₃₁	1	2	yes	—
590	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
591	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
592	#103	C₂³×C₃₁	1	2	yes	—
593	#103	C₂³×C₃₁	1	2	yes	—
594	#103	C₂³×C₃₁	1	4	yes	—
595	#103	C₂³×C₃₁	1	4	yes	—
596	#102	C₂³×C₃₁	1	2	yes	—
597	#102	C₂³×C₃₁	1	2	yes	—
598	#102	C₂³×C₃₁	1	4	yes	—
599	#102	C₂³×C₃₁	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
602	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
603	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
604	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
605	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
606	C₃₁	#61285	1	1	yes	characteristic, direct product factor, Sylow
607	C₂⁴	—	2	1	no	—
608	#41	—	2	4	no	—
609	#41	—	2	4	no	—
610	#41	—	8	4	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
626	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
627	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
628	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
629	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	8	2	no	—
638	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
641	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
642	SD₁₆	—	2	4	no	—
643	SD₁₆	—	2	4	no	—
644	M₁₆	—	2	4	no	—
645	M₁₆	—	2	8	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	2	8	no	—
648	C₂×C₈	#41×C₃₁	1	4	yes	complemented
649	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
650	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
652	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
689	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
697	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
698	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
699	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₂³	—	2	2	no	—
701	C₂³	—	4	2	no	—
702	C₂³	—	8	1	no	—
703	C₂³	—	8	1	no	—
704	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
705	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
706	Q₈	—	2	4	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	4	2	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	8	1	no	—
713	Q₈	—	8	1	no	—
714	D₄	—	2	8	no	—
715	D₄	—	2	4	no	—
716	D₄	—	2	4	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	4	2	no	—
720	D₄	—	4	2	no	—
721	D₄	—	8	4	no	—
722	D₄	—	8	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	8	2	no	—
737	C₂×C₄	—	8	1	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	1	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
743	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
747	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
748	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
749	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
750	C₈	—	2	4	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	C₂×#41×C₃₁	1	2	yes	—
754	C₈	C₂×#41×C₃₁	1	2	yes	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	8	4	no	—
764	C₂²	C₃₁×#547	1	2	yes	—
765	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
766	C₄	—	2	4	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	1	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	C₃₁×#547	1	2	yes	—
778	C₄	C₃₁×#577	1	2	yes	—
779	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
780	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
781	C₂	—	2	2	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
785	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
786	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3507	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3353	C₂	semidirect
5. C₃₁×#3351	C₂	semidirect
6. C₃₁×#3340	C₂	semidirect
7. C₃₁×#3337	C₂	semidirect
8. C₃₁×#3335	C₂	semidirect
9. C₃₁×#3160	C₂	semidirect
10. C₃₁×#3097	C₂	semidirect
11. C₃₁×#3096	C₂	semidirect
12. C₃₁×#3078	C₂	semidirect
13. C₃₁×#3077	C₂	semidirect
14. C₃₁×#3057	C₂	semidirect
15. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
16. C₃₁×#2931	C₂	semidirect
17. C₃₁×#2912	C₂	semidirect
25. C₃₁×#556	C₂²	semidirect
27. C₃₁×#554	C₂²	semidirect
29. C₃₁×#552	C₂²	semidirect
45. C₃₁×#500	C₂²	semidirect
46. C₃₁×#500	C₂²	semidirect
47. C₃₁×#499	C₂²	semidirect
48. C₃₁×#499	C₂²	semidirect
49. C₃₁×#498	C₂²	semidirect
50. C₃₁×#498	C₂²	semidirect
51. C₃₁×#485	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
53. C₃₁×#484	C₂²	semidirect
54. C₃₁×#483	C₂²	semidirect
59. C₃₁×#479	C₂²	semidirect
61. C₃₁×#477	C₂²	semidirect
63. C₃₁×#475	C₂²	semidirect
73. C₃₁×#436	C₂²	semidirect
74. C₃₁×#436	C₂²	semidirect
75. C₈×D₄×C₃₁	C₂²	semidirect
76. C₈×D₄×C₃₁	C₂²	semidirect
79. C₃₁×#428	C₂²	semidirect
80. C₃₁×#428	C₂²	semidirect
83. C₃₁×#427	C₂²	semidirect
85. C₂×C₃₁×#106	C₂²	semidirect
254. C₂×C₈×C₃₁	#41	semidirect
306. #61285	C₃₁	direct (N × H)
362. #3507	C₂×C₃₁	semidirect
364. #3357	C₂×C₃₁	semidirect
365. #3353	C₂×C₃₁	semidirect
366. #3351	C₂×C₃₁	semidirect
367. #3340	C₂×C₃₁	semidirect
368. #3337	C₂×C₃₁	semidirect
369. #3335	C₂×C₃₁	semidirect
370. #3160	C₂×C₃₁	semidirect
371. #3097	C₂×C₃₁	semidirect
372. #3096	C₂×C₃₁	semidirect
373. #3078	C₂×C₃₁	semidirect
374. #3077	C₂×C₃₁	semidirect
375. #3057	C₂×C₃₁	semidirect
376. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
377. #2931	C₂×C₃₁	semidirect
378. #2912	C₂×C₃₁	semidirect
412. #556	C₂²×C₃₁	semidirect
414. #554	C₂²×C₃₁	semidirect
416. #552	C₂²×C₃₁	semidirect
432. #500	C₂²×C₃₁	semidirect
433. #500	C₂²×C₃₁	semidirect
434. #499	C₂²×C₃₁	semidirect
435. #499	C₂²×C₃₁	semidirect
436. #498	C₂²×C₃₁	semidirect
437. #498	C₂²×C₃₁	semidirect
438. #485	C₂²×C₃₁	semidirect
439. #485	C₂²×C₃₁	semidirect
440. #484	C₂²×C₃₁	semidirect
441. #483	C₂²×C₃₁	semidirect
446. #479	C₂²×C₃₁	semidirect
448. #477	C₂²×C₃₁	semidirect
450. #475	C₂²×C₃₁	semidirect
460. #436	C₂²×C₃₁	semidirect
461. #436	C₂²×C₃₁	semidirect
462. C₈×D₄	C₂²×C₃₁	semidirect
463. C₈×D₄	C₂²×C₃₁	semidirect
466. #428	C₂²×C₃₁	semidirect
467. #428	C₂²×C₃₁	semidirect
470. #427	C₂²×C₃₁	semidirect
472. C₂×#106	C₂²×C₃₁	semidirect
606. C₃₁	#61285	direct (N × H)
648. 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×#3507	2
C₃₁×#3506	2
C₃₁×#3357	2
C₃₁×#3353	2
C₃₁×#3351	2
C₃₁×#3340	2
C₃₁×#3337	2
C₃₁×#3335	2
C₃₁×#3160	2
C₃₁×#3097	2
C₃₁×#3096	2
C₃₁×#3078	2
C₃₁×#3077	2
C₃₁×#3057	2
C₂×C₄×SD₁₆×C₃₁	2
C₃₁×#2931	2
C₃₁×#2912	2
#61285	31

Subgroups — C31×#61285 #21518044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61285 #21518044