Subgroups — C₃₁×#61384 #21518143

Order 7936.

1726 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3390	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3387	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3386	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3385	C₂	1	2	yes	maximal, complemented
7	Q₈×Q₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3381	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3164	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3083	C₂	1	2	yes	maximal
12	C₃₁×#3082	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic
14	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2947	C₂	1	2	yes	maximal
17	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic
18	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
19	Q₈²×C₃₁	—	2	1	no	—
20	Q₈²×C₃₁	C₂²	1	2	yes	—
21	Q₈²×C₃₁	C₂²	1	2	yes	—
22	C₃₁×#557	—	2	1	no	—
23	C₃₁×#557	—	2	2	no	—
24	C₃₁×#557	C₂²	1	2	yes	—
25	C₃₁×#557	C₂²	1	4	yes	—
26	C₃₁×#557	C₂²	1	2	yes	—
27	C₃₁×#554	—	2	2	no	—
28	C₃₁×#554	C₂²	1	2	yes	—
29	D₄×Q₈×C₃₁	—	2	2	no	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
31	C₃₁×#544	—	2	2	no	—
32	C₃₁×#544	—	2	2	no	—
33	C₃₁×#544	C₂²	1	2	yes	—
34	C₃₁×#544	C₂²	1	2	yes	—
35	C₃₁×#533	—	2	1	no	—
36	C₃₁×#533	—	2	2	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₃₁×#520	C₂²	1	2	yes	—
42	C₃₁×#519	C₂²	1	2	yes	—
43	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#501	C₂²	1	4	yes	—
46	C₃₁×#501	C₂²	1	4	yes	—
47	C₃₁×#501	C₂²	1	4	yes	—
48	C₃₁×#500	C₂²	1	2	yes	—
49	C₃₁×#500	C₂²	1	4	yes	—
50	C₃₁×#499	C₂²	1	4	yes	—
51	C₃₁×#498	C₂²	1	2	yes	—
52	C₃₁×#479	C₂²	1	2	yes	—
53	C₃₁×#479	C₂²	1	4	yes	—
54	C₃₁×#479	C₂²	1	4	yes	—
55	C₃₁×#479	C₂²	1	4	yes	—
56	C₃₁×#478	C₂²	1	2	yes	—
57	C₃₁×#478	C₂²	1	4	yes	—
58	C₃₁×#477	C₂²	1	1	yes	characteristic
59	C₃₁×#477	C₂²	1	4	yes	—
60	C₃₁×#477	C₂²	1	4	yes	—
61	C₃₁×#477	C₂²	1	2	yes	—
62	C₃₁×#477	C₂²	1	2	yes	—
63	C₃₁×#477	C₂²	1	4	yes	—
64	C₃₁×#476	C₂²	1	1	yes	characteristic
65	C₃₁×#475	C₂²	1	1	yes	characteristic
66	C₃₁×#475	C₂²	1	4	yes	—
67	C₃₁×#474	C₂²	1	1	yes	characteristic
68	C₃₁×#474	C₂²	1	4	yes	—
69	C₃₁×#446	C₂²	1	2	yes	—
70	C₃₁×#446	C₂²	1	4	yes	—
71	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
72	C₃₁×#441	C₂²	1	4	yes	—
73	C₃₁×#441	C₂²	1	2	yes	—
74	C₃₁×#440	C₂²	1	4	yes	—
75	C₃₁×#440	C₂²	1	2	yes	—
76	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
77	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
78	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
80	C₃₁×#428	C₂²	1	2	yes	—
81	C₃₁×#428	C₂²	1	1	yes	characteristic
82	C₃₁×#428	C₂²	1	2	yes	—
83	C₃₁×#427	C₂²	1	2	yes	—
84	C₂×C₃₁×#107	C₂²	1	2	yes	—
85	C₃₁×#424	C₂²	1	2	yes	—
86	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₃₁×#419	C₂²	1	1	yes	characteristic
88	C₃₁×#417	C₂²	1	1	yes	characteristic
89	C₃₁×#416	C₂²	1	2	yes	—
90	C₂×C₃₁×#103	C₂²	1	2	yes	—
91	C₃₁×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₃₁	—	2	2	no	—
95	C₂²×Q₈×C₃₁	—	2	1	no	—
96	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
97	C₃₁×#137	Q₈	1	8	yes	complemented
98	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
103	C₃₁×C₄⋊Q₈	—	2	2	no	—
104	C₃₁×C₄⋊Q₈	—	2	2	no	—
105	C₃₁×C₄⋊Q₈	—	2	4	no	—
106	C₃₁×C₄⋊Q₈	—	2	2	no	—
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	—	2	2	no	—
109	C₃₁×C₄⋊Q₈	—	2	4	no	—
110	C₃₁×C₄⋊Q₈	—	2	4	no	—
111	C₃₁×C₄⋊Q₈	—	2	2	no	—
112	C₃₁×C₄⋊Q₈	—	2	1	no	—
113	C₃₁×C₄⋊Q₈	—	2	1	no	—
114	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
115	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
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×#125	—	2	2	no	—
123	C₃₁×#125	—	2	4	no	—
124	C₃₁×#125	—	2	4	no	—
125	C₃₁×#125	—	2	4	no	—
126	C₃₁×#125	—	2	4	no	—
127	C₃₁×#125	—	2	2	no	—
128	C₃₁×#125	D₄	1	2	yes	—
129	C₃₁×#125	C₂³	1	4	yes	—
130	C₃₁×#125	C₂³	1	2	yes	—
131	C₃₁×#125	C₂³	1	4	yes	—
132	C₃₁×C₂²⋊Q₈	—	2	2	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	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	4	no	—
139	C₃₁×C₂²⋊Q₈	—	2	4	no	—
140	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₄×Q₈×C₃₁	—	2	2	no	—
143	C₄×Q₈×C₃₁	—	2	2	no	—
144	C₄×Q₈×C₃₁	—	2	2	no	—
145	C₄×Q₈×C₃₁	—	2	2	no	—
146	C₄×Q₈×C₃₁	—	2	2	no	—
147	C₄×Q₈×C₃₁	—	2	4	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	C₂³	1	2	yes	—
154	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
158	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
161	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
162	C₄×D₄×C₃₁	—	2	1	no	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	—	2	4	no	—
165	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₃₁	C₂³	1	4	yes	—
167	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₃₁×#117	—	2	2	no	—
169	C₃₁×#117	—	2	4	no	—
170	C₃₁×#117	—	2	1	no	—
171	C₃₁×#117	C₂³	1	2	yes	—
172	C₃₁×#117	C₂³	1	1	yes	characteristic
173	C₃₁×#117	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
175	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
176	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
177	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄²×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	4	yes	—
184	C₃₁×#107	C₂³	1	4	yes	—
185	C₃₁×#107	C₂³	1	2	yes	—
186	C₃₁×#107	C₂³	1	2	yes	—
187	C₃₁×#107	C₂³	1	2	yes	—
188	C₃₁×#107	C₂³	1	4	yes	—
189	C₃₁×#107	C₂³	1	4	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	2	yes	—
194	C₃₁×#106	C₂³	1	4	yes	—
195	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
196	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
197	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
198	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
199	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
200	C₃₁×#103	C₂³	1	4	yes	—
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#103	C₂³	1	2	yes	—
203	C₃₁×#103	C₂³	1	2	yes	—
204	C₃₁×#103	C₂³	1	2	yes	—
205	C₃₁×#103	C₂³	1	2	yes	—
206	C₃₁×#103	C₂³	1	2	yes	—
207	C₃₁×#102	C₂³	1	2	yes	—
208	C₃₁×#102	C₂³	1	2	yes	—
209	C₃₁×#102	C₂³	1	2	yes	—
210	C₃₁×#97	C₂³	1	2	yes	—
211	C₃₁×#97	C₂³	1	4	yes	—
212	C₄×C₈×C₃₁	C₂³	1	2	yes	—
213	C₄×C₈×C₃₁	C₂³	1	4	yes	—
214	#41×C₃₁	—	2	2	no	—
215	#41×C₃₁	C₂×Q₈	1	4	yes	—
216	C₂×Q₈×C₃₁	—	2	1	no	—
217	C₂×Q₈×C₃₁	—	2	1	no	—
218	C₂×Q₈×C₃₁	—	2	2	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	4	no	—
221	C₂×Q₈×C₃₁	—	2	4	no	—
222	C₂×Q₈×C₃₁	—	2	2	no	—
223	C₂×Q₈×C₃₁	—	2	2	no	—
224	C₂×Q₈×C₃₁	—	8	2	no	—
225	C₂×Q₈×C₃₁	—	8	4	no	—
226	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₃₁	C₂×Q₈	1	4	yes	complemented
229	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
230	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂×D₄×C₃₁	—	2	1	no	—
232	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	—	2	1	no	—
234	C₂²×C₄×C₃₁	—	2	1	no	—
235	C₂²×C₄×C₃₁	—	2	1	no	—
236	C₂²×C₄×C₃₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
243	Q₁₆×C₃₁	C₂×Q₈	1	8	yes	complemented
244	SD₁₆×C₃₁	C₂×Q₈	1	8	yes	complemented
245	M₁₆×C₃₁	—	2	2	no	—
246	M₁₆×C₃₁	C₂×Q₈	1	4	yes	complemented
247	C₂×C₈×C₃₁	—	2	4	no	—
248	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
249	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
250	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
251	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₄⋊C₄×C₃₁	—	2	1	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	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	4	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₄⋊C₄×C₃₁	—	2	4	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	4	no	—
273	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂×D₄	1	4	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	1	yes	characteristic
283	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₂²⋊C₄×C₃₁	—	2	2	no	—
286	C₂²⋊C₄×C₃₁	—	2	1	no	—
287	C₂²⋊C₄×C₃₁	—	2	1	no	—
288	C₂²⋊C₄×C₃₁	—	2	1	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
291	C₄²×C₃₁	—	2	1	no	—
292	C₄²×C₃₁	—	2	1	no	—
293	C₄²×C₃₁	—	2	1	no	—
294	C₄²×C₃₁	—	2	2	no	—
295	C₄²×C₃₁	—	2	2	no	—
296	C₄²×C₃₁	—	2	4	no	—
297	C₄²×C₃₁	—	2	4	no	—
298	C₄²×C₃₁	—	2	4	no	—
299	C₄²×C₃₁	—	2	2	no	—
300	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₄²×C₃₁	C₂⁴	1	4	yes	—
304	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
305	#61384	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂³×C₃₁	—	2	1	no	—
307	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
308	Q₈×C₃₁	—	2	4	no	—
309	Q₈×C₃₁	—	2	4	no	—
310	Q₈×C₃₁	—	2	2	no	—
311	Q₈×C₃₁	—	2	1	no	—
312	Q₈×C₃₁	—	4	2	no	—
313	Q₈×C₃₁	—	4	4	no	—
314	Q₈×C₃₁	—	4	2	no	—
315	Q₈×C₃₁	—	8	1	no	—
316	Q₈×C₃₁	—	8	4	no	—
317	Q₈×C₃₁	—	8	2	no	—
318	Q₈×C₃₁	—	8	4	no	—
319	Q₈×C₃₁	C₂²×Q₈	1	4	yes	—
320	Q₈×C₃₁	C₂²×Q₈	1	2	yes	—
321	D₄×C₃₁	—	2	4	no	—
322	D₄×C₃₁	—	2	1	no	—
323	D₄×C₃₁	C₂²×Q₈	1	2	yes	—
324	C₂×C₄×C₃₁	—	2	4	no	—
325	C₂×C₄×C₃₁	—	2	1	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	4	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	1	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	4	no	—
335	C₂×C₄×C₃₁	—	4	1	no	—
336	C₂×C₄×C₃₁	—	4	2	no	—
337	C₂×C₄×C₃₁	—	4	2	no	—
338	C₂×C₄×C₃₁	—	8	4	no	—
339	C₂×C₄×C₃₁	—	8	1	no	—
340	C₂×C₄×C₃₁	—	8	2	no	—
341	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
343	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
349	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
350	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
351	C₈×C₃₁	—	2	2	no	—
352	C₈×C₃₁	—	2	2	no	—
353	C₈×C₃₁	—	2	2	no	—
354	C₈×C₃₁	C₂²×Q₈	1	4	yes	—
355	#3503	C₂×C₃₁	1	1	yes	characteristic
356	#3502	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#3390	C₂×C₃₁	1	4	yes	complemented
358	#3387	C₂×C₃₁	1	2	yes	complemented
359	#3386	C₂×C₃₁	1	4	yes	complemented
360	#3385	C₂×C₃₁	1	2	yes	complemented
361	Q₈×Q₁₆	C₂×C₃₁	1	2	yes	complemented
362	#3381	C₂×C₃₁	1	2	yes	complemented
363	#3165	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#3164	C₂×C₃₁	1	2	yes	complemented
365	#3083	C₂×C₃₁	1	2	yes	—
366	#3082	C₂×C₃₁	1	2	yes	complemented
367	#3076	C₂×C₃₁	1	1	yes	characteristic
368	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
369	#2962	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#2947	C₂×C₃₁	1	2	yes	—
371	C₄×#137	C₂×C₃₁	1	1	yes	characteristic
372	C₂²×C₃₁	—	2	1	no	—
373	C₂²×C₃₁	—	2	1	no	—
374	C₂²×C₃₁	—	2	2	no	—
375	C₂²×C₃₁	—	4	1	no	—
376	C₂²×C₃₁	—	4	1	no	—
377	C₂²×C₃₁	D₄×Q₈	1	2	yes	—
378	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₃₁	—	2	1	no	—
380	C₄×C₃₁	—	2	1	no	—
381	C₄×C₃₁	—	2	4	no	—
382	C₄×C₃₁	—	2	2	no	—
383	C₄×C₃₁	—	2	4	no	—
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	2	4	no	—
386	C₄×C₃₁	—	4	1	no	—
387	C₄×C₃₁	—	4	4	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	—	4	1	no	—
391	C₄×C₃₁	—	4	2	no	—
392	C₄×C₃₁	D₄×Q₈	1	2	yes	—
393	C₄×C₃₁	#578	1	2	yes	—
394	C₄×C₃₁	C₂³×Q₈	1	1	yes	characteristic
395	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
396	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
397	Q₈²	—	2	1	no	—
398	Q₈²	C₂²×C₃₁	1	2	yes	—
399	Q₈²	C₂²×C₃₁	1	2	yes	—
400	#557	—	2	1	no	—
401	#557	—	2	2	no	—
402	#557	C₂²×C₃₁	1	2	yes	—
403	#557	C₂²×C₃₁	1	4	yes	—
404	#557	C₂²×C₃₁	1	2	yes	—
405	#554	—	2	2	no	—
406	#554	C₂²×C₃₁	1	2	yes	—
407	D₄×Q₈	—	2	2	no	—
408	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
409	#544	—	2	2	no	—
410	#544	—	2	2	no	—
411	#544	C₂²×C₃₁	1	2	yes	—
412	#544	C₂²×C₃₁	1	2	yes	—
413	#533	—	2	1	no	—
414	#533	—	2	2	no	—
415	#533	C₂²×C₃₁	1	1	yes	characteristic
416	#533	C₂²×C₃₁	1	1	yes	characteristic
417	C₂×C₄⋊Q₈	—	2	1	no	—
418	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
419	#520	C₂²×C₃₁	1	2	yes	—
420	#519	C₂²×C₃₁	1	2	yes	—
421	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
422	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
423	#501	C₂²×C₃₁	1	4	yes	—
424	#501	C₂²×C₃₁	1	4	yes	—
425	#501	C₂²×C₃₁	1	4	yes	—
426	#500	C₂²×C₃₁	1	2	yes	—
427	#500	C₂²×C₃₁	1	4	yes	—
428	#499	C₂²×C₃₁	1	4	yes	—
429	#498	C₂²×C₃₁	1	2	yes	—
430	#479	C₂²×C₃₁	1	2	yes	—
431	#479	C₂²×C₃₁	1	4	yes	—
432	#479	C₂²×C₃₁	1	4	yes	—
433	#479	C₂²×C₃₁	1	4	yes	—
434	#478	C₂²×C₃₁	1	2	yes	—
435	#478	C₂²×C₃₁	1	4	yes	—
436	#477	C₂²×C₃₁	1	2	yes	—
437	#477	C₂²×C₃₁	1	2	yes	—
438	#477	C₂²×C₃₁	1	4	yes	—
439	#477	C₂²×C₃₁	1	1	yes	characteristic
440	#477	C₂²×C₃₁	1	4	yes	—
441	#477	C₂²×C₃₁	1	4	yes	—
442	#476	C₂²×C₃₁	1	1	yes	characteristic
443	#475	C₂²×C₃₁	1	1	yes	characteristic
444	#475	C₂²×C₃₁	1	4	yes	—
445	#474	C₂²×C₃₁	1	1	yes	characteristic
446	#474	C₂²×C₃₁	1	4	yes	—
447	#446	C₂²×C₃₁	1	2	yes	—
448	#446	C₂²×C₃₁	1	4	yes	—
449	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
450	#441	C₂²×C₃₁	1	4	yes	—
451	#441	C₂²×C₃₁	1	2	yes	—
452	#440	C₂²×C₃₁	1	4	yes	—
453	#440	C₂²×C₃₁	1	2	yes	—
454	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
455	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
456	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
457	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
458	#428	C₂²×C₃₁	1	2	yes	—
459	#428	C₂²×C₃₁	1	1	yes	characteristic
460	#428	C₂²×C₃₁	1	2	yes	—
461	#427	C₂²×C₃₁	1	2	yes	—
462	C₂×#107	C₂²×C₃₁	1	2	yes	—
463	#424	C₂²×C₃₁	1	2	yes	—
464	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
465	#419	C₂²×C₃₁	1	1	yes	characteristic
466	#417	C₂²×C₃₁	1	1	yes	characteristic
467	#416	C₂²×C₃₁	1	2	yes	—
468	C₂×#103	C₂²×C₃₁	1	2	yes	—
469	#405	C₂²×C₃₁	1	2	yes	—
470	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
471	C₂×C₃₁	—	2	2	no	—
472	C₂×C₃₁	—	4	2	no	—
473	C₂×C₃₁	C₂×D₄×Q₈	1	1	yes	characteristic
474	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
475	C₂×C₃₁	#3585	1	1	yes	characteristic
476	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
477	C₂²×Q₈	—	2	2	no	—
478	C₂²×Q₈	—	2	1	no	—
479	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
480	#137	Q₈×C₃₁	1	8	yes	complemented
481	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
482	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
483	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
484	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	—	2	4	no	—
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	—	2	2	no	—
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	—	2	4	no	—
493	C₄⋊Q₈	—	2	4	no	—
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	—	2	1	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
498	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
500	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
501	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
504	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
505	#125	—	2	2	no	—
506	#125	—	2	4	no	—
507	#125	—	2	4	no	—
508	#125	—	2	4	no	—
509	#125	—	2	4	no	—
510	#125	—	2	2	no	—
511	#125	D₄×C₃₁	1	2	yes	—
512	#125	C₂³×C₃₁	1	2	yes	—
513	#125	C₂³×C₃₁	1	4	yes	—
514	#125	C₂³×C₃₁	1	4	yes	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	1	no	—
517	C₂²⋊Q₈	—	2	1	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
524	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	4	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	1	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
537	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
538	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
539	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
540	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
541	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
542	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
543	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
544	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
545	C₄×D₄	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	—	2	4	no	—
548	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
549	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
550	C₄×D₄	C₂³×C₃₁	1	4	yes	—
551	#117	—	2	2	no	—
552	#117	—	2	4	no	—
553	#117	—	2	1	no	—
554	#117	C₂³×C₃₁	1	1	yes	characteristic
555	#117	C₂³×C₃₁	1	2	yes	—
556	#117	C₂³×C₃₁	1	2	yes	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	2	no	—
560	C₂×C₄⋊C₄	—	2	2	no	—
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
563	C₂×C₄²	—	2	1	no	—
564	C₂×C₄²	—	2	1	no	—
565	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
566	#107	C₂³×C₃₁	1	4	yes	—
567	#107	C₂³×C₃₁	1	4	yes	—
568	#107	C₂³×C₃₁	1	2	yes	—
569	#107	C₂³×C₃₁	1	2	yes	—
570	#107	C₂³×C₃₁	1	2	yes	—
571	#107	C₂³×C₃₁	1	4	yes	—
572	#107	C₂³×C₃₁	1	4	yes	—
573	#106	C₂³×C₃₁	1	2	yes	—
574	#106	C₂³×C₃₁	1	2	yes	—
575	#106	C₂³×C₃₁	1	4	yes	—
576	#106	C₂³×C₃₁	1	2	yes	—
577	#106	C₂³×C₃₁	1	4	yes	—
578	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
579	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
580	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
581	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
582	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
583	#103	C₂³×C₃₁	1	4	yes	—
584	#103	C₂³×C₃₁	1	4	yes	—
585	#103	C₂³×C₃₁	1	2	yes	—
586	#103	C₂³×C₃₁	1	2	yes	—
587	#103	C₂³×C₃₁	1	2	yes	—
588	#103	C₂³×C₃₁	1	2	yes	—
589	#103	C₂³×C₃₁	1	2	yes	—
590	#102	C₂³×C₃₁	1	2	yes	—
591	#102	C₂³×C₃₁	1	2	yes	—
592	#102	C₂³×C₃₁	1	2	yes	—
593	#97	C₂³×C₃₁	1	2	yes	—
594	#97	C₂³×C₃₁	1	4	yes	—
595	C₄×C₈	C₂³×C₃₁	1	2	yes	—
596	C₄×C₈	C₂³×C₃₁	1	4	yes	—
597	C₃₁	#61384	1	1	yes	characteristic, direct product factor, Sylow
598	#41	—	2	2	no	—
599	#41	C₂×Q₈×C₃₁	1	4	yes	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	4	no	—
605	C₂×Q₈	—	2	4	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	8	2	no	—
609	C₂×Q₈	—	8	4	no	—
610	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
611	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
612	C₂×Q₈	C₂×Q₈×C₃₁	1	4	yes	complemented
613	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
614	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
627	Q₁₆	C₂×Q₈×C₃₁	1	8	yes	complemented
628	SD₁₆	C₂×Q₈×C₃₁	1	8	yes	complemented
629	M₁₆	—	2	2	no	—
630	M₁₆	C₂×Q₈×C₃₁	1	4	yes	complemented
631	C₂×C₈	—	2	4	no	—
632	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
633	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
634	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
635	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
658	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
659	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
660	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
661	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
663	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
667	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
668	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
675	C₄²	—	2	1	no	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	2	no	—
684	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
685	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
686	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
687	C₄²	C₂⁴×C₃₁	1	4	yes	—
688	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
689	C₂³	—	2	1	no	—
690	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
691	Q₈	—	2	4	no	—
692	Q₈	—	2	4	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	2	1	no	—
695	Q₈	—	4	2	no	—
696	Q₈	—	4	4	no	—
697	Q₈	—	4	2	no	—
698	Q₈	—	8	1	no	—
699	Q₈	—	8	4	no	—
700	Q₈	—	8	2	no	—
701	Q₈	—	8	4	no	—
702	Q₈	C₂²×Q₈×C₃₁	1	4	yes	—
703	Q₈	C₂²×Q₈×C₃₁	1	2	yes	—
704	D₄	—	2	4	no	—
705	D₄	—	2	1	no	—
706	D₄	C₂²×Q₈×C₃₁	1	2	yes	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	1	no	—
723	C₂×C₄	—	8	2	no	—
724	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
726	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
728	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
731	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
732	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
733	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
734	C₈	—	2	2	no	—
735	C₈	—	2	2	no	—
736	C₈	—	2	2	no	—
737	C₈	C₂²×Q₈×C₃₁	1	4	yes	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	D₄×Q₈×C₃₁	1	2	yes	—
744	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	2	4	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	4	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	D₄×Q₈×C₃₁	1	2	yes	—
759	C₄	C₃₁×#578	1	2	yes	—
760	C₄	C₂³×Q₈×C₃₁	1	1	yes	characteristic
761	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
762	C₂	—	2	2	no	—
763	C₂	—	4	2	no	—
764	C₂	C₂×D₄×Q₈×C₃₁	1	1	yes	characteristic
765	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
766	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×#41×C₃₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3502	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3387	C₂	semidirect
5. C₃₁×#3386	C₂	semidirect
6. C₃₁×#3385	C₂	semidirect
7. Q₈×Q₁₆×C₃₁	C₂	semidirect
8. C₃₁×#3381	C₂	semidirect
9. C₃₁×#3165	C₂	semidirect
10. C₃₁×#3164	C₂	semidirect
12. C₃₁×#3082	C₂	semidirect
14. C₂×C₃₁×#477	C₂	semidirect
15. C₃₁×#2962	C₂	semidirect
97. C₃₁×#137	Q₈	semidirect
228. C₂×Q₈×C₃₁	C₂×Q₈	semidirect
243. Q₁₆×C₃₁	C₂×Q₈	semidirect
244. SD₁₆×C₃₁	C₂×Q₈	semidirect
246. M₁₆×C₃₁	C₂×Q₈	semidirect
305. #61384	C₃₁	direct (N × H)
356. #3502	C₂×C₃₁	semidirect
357. #3390	C₂×C₃₁	semidirect
358. #3387	C₂×C₃₁	semidirect
359. #3386	C₂×C₃₁	semidirect
360. #3385	C₂×C₃₁	semidirect
361. Q₈×Q₁₆	C₂×C₃₁	semidirect
362. #3381	C₂×C₃₁	semidirect
363. #3165	C₂×C₃₁	semidirect
364. #3164	C₂×C₃₁	semidirect
366. #3082	C₂×C₃₁	semidirect
368. C₂×#477	C₂×C₃₁	semidirect
369. #2962	C₂×C₃₁	semidirect
480. #137	Q₈×C₃₁	semidirect
597. C₃₁	#61384	direct (N × H)
612. C₂×Q₈	C₂×Q₈×C₃₁	semidirect
627. Q₁₆	C₂×Q₈×C₃₁	semidirect
628. SD₁₆	C₂×Q₈×C₃₁	semidirect
630. M₁₆	C₂×Q₈×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3503	2
C₃₁×#3502	2
C₃₁×#3390	2
C₃₁×#3387	2
C₃₁×#3386	2
C₃₁×#3385	2
Q₈×Q₁₆×C₃₁	2
C₃₁×#3381	2
C₃₁×#3165	2
C₃₁×#3164	2
C₃₁×#3083	2
C₃₁×#3082	2
C₃₁×#3076	2
C₂×C₃₁×#477	2
C₃₁×#2962	2
C₃₁×#2947	2
C₄×C₃₁×#137	2
#61384	31

Subgroups — C31×#61384 #21518143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61384 #21518143