Subgroups — C₃₁×#60584 #21517343

Order 7936.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 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	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3124	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3119	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3112	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3108	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3100	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3092	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3045	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3002	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2951	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₃₁×#135	C₂²	1	2	yes	—
21	C₃₁×#555	—	2	1	no	—
22	C₃₁×#553	—	2	1	no	—
23	C₃₁×#553	—	2	1	no	—
24	C₃₁×#551	—	2	2	no	—
25	C₃₁×#547	—	2	1	no	—
26	C₃₁×#546	—	2	2	no	—
27	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#542	C₂²	1	2	yes	complemented
29	C₃₁×#540	C₂²	1	2	yes	complemented
30	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#532	C₂²	1	2	yes	—
32	C₃₁×#529	C₂²	1	2	yes	—
33	C₃₁×#525	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
35	C₃₁×#520	—	2	1	no	—
36	C₃₁×#520	—	2	1	no	—
37	C₃₁×#520	—	2	2	no	—
38	C₃₁×#520	C₂²	1	2	yes	—
39	C₃₁×#520	C₂²	1	2	yes	—
40	C₃₁×#520	C₂²	1	4	yes	complemented
41	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#518	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₃₁	—	2	2	no	—
45	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
46	C₂×C₃₁×#117	—	2	1	no	—
47	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
49	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
50	C₃₁×#484	C₂²	1	2	yes	complemented
51	C₃₁×#483	C₂²	1	2	yes	complemented
52	C₃₁×#481	C₂²	1	2	yes	complemented
53	C₃₁×#480	C₂²	1	2	yes	—
54	C₃₁×#480	C₂²	1	2	yes	—
55	C₃₁×#480	C₂²	1	4	yes	complemented
56	C₃₁×#480	C₂²	1	2	yes	complemented
57	C₃₁×#479	C₂²	1	4	yes	complemented
58	C₃₁×#478	C₂²	1	4	yes	complemented
59	C₃₁×#477	C₂²	1	4	yes	complemented
60	C₃₁×#474	C₂²	1	4	yes	complemented
61	C₃₁×#464	C₂²	1	4	yes	complemented
62	C₃₁×#463	C₂²	1	4	yes	complemented
63	C₃₁×#460	C₂²	1	4	yes	complemented
64	C₃₁×#459	C₂²	1	4	yes	complemented
65	C₃₁×#452	C₂²	1	2	yes	complemented
66	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#449	C₂²	1	4	yes	—
69	C₃₁×#449	C₂²	1	2	yes	complemented
70	C₃₁×#448	C₂²	1	2	yes	—
71	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#447	C₂²	1	2	yes	—
73	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#442	C₂²	1	4	yes	complemented
75	C₃₁×#440	C₂²	1	4	yes	complemented
76	C₃₁×#440	C₂²	1	4	yes	complemented
77	C₃₁×#440	C₂²	1	4	yes	complemented
78	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
80	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
81	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
82	C₃₁×#433	C₂²	1	4	yes	complemented
83	C₃₁×#432	C₂²	1	2	yes	complemented
84	C₃₁×#431	C₂²	1	2	yes	complemented
85	C₃₁×#428	C₂²	1	2	yes	complemented
86	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
87	C₃₁×#424	C₂²	1	2	yes	complemented
88	C₃₁×#417	C₂²	1	2	yes	—
89	C₃₁×#417	C₂²	1	2	yes	complemented
90	C₃₁×#416	C₂²	1	2	yes	—
91	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
92	C₃₁×#407	C₂²	1	1	yes	characteristic
93	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₃₁×#405	C₂²	1	2	yes	complemented
95	C₂×#41×C₃₁	—	2	8	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	—	2	1	no	—
98	C₂×#41×C₃₁	—	2	2	no	—
99	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
100	C₂×#41×C₃₁	C₂³	1	2	yes	—
101	C₂×#41×C₃₁	C₂³	1	2	yes	—
102	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₃₁	—	2	1	no	—
104	C₂²×D₄×C₃₁	—	2	1	no	—
105	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₃₁	—	2	1	no	—
108	C₂³×C₄×C₃₁	—	2	1	no	—
109	C₂³×C₄×C₃₁	—	2	2	no	—
110	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
112	C₃₁×#135	—	2	8	no	—
113	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
117	C₂×D₈×C₃₁	C₂³	1	2	yes	—
118	C₂×D₈×C₃₁	C₂³	1	4	yes	—
119	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
120	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
121	C₃₁×C₄⋊Q₈	—	2	1	no	—
122	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₃₁×#127	C₂³	1	2	yes	—
124	C₃₁×#126	—	2	2	no	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#125	—	2	1	no	—
127	C₃₁×#125	C₂³	1	2	yes	—
128	C₃₁×#124	—	2	2	no	—
129	C₃₁×#124	—	2	2	no	—
130	C₃₁×#124	C₂³	1	2	yes	—
131	C₃₁×#123	—	2	1	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×#123	—	2	2	no	—
134	C₃₁×#123	—	2	2	no	—
135	C₃₁×#123	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×#121	—	2	1	no	—
141	C₃₁×#121	—	2	1	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	—	2	1	no	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	C₂³	1	2	yes	—
148	C₃₁×#121	C₂³	1	1	yes	characteristic
149	C₃₁×#121	C₂³	1	2	yes	—
150	C₃₁×#121	C₂³	1	1	yes	characteristic
151	C₃₁×#120	—	2	1	no	—
152	C₃₁×#120	—	2	2	no	—
153	C₄×Q₈×C₃₁	—	2	2	no	—
154	C₄×Q₈×C₃₁	—	2	2	no	—
155	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
158	C₄×D₄×C₃₁	—	2	1	no	—
159	C₄×D₄×C₃₁	—	2	1	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	1	no	—
162	C₄×D₄×C₃₁	—	2	1	no	—
163	C₄×D₄×C₃₁	—	2	4	no	—
164	C₄×D₄×C₃₁	—	2	4	no	—
165	C₄×D₄×C₃₁	—	2	4	no	—
166	C₄×D₄×C₃₁	—	2	4	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	2	no	—
169	C₄×D₄×C₃₁	—	2	2	no	—
170	C₄×D₄×C₃₁	—	2	2	no	—
171	C₄×D₄×C₃₁	C₂³	1	2	yes	—
172	C₄×D₄×C₃₁	C₂³	1	2	yes	—
173	C₄×D₄×C₃₁	C₂³	1	4	yes	—
174	C₄×D₄×C₃₁	C₂³	1	2	yes	—
175	C₄×D₄×C₃₁	C₂³	1	4	yes	—
176	C₃₁×#117	—	2	2	no	—
177	C₃₁×#117	—	2	2	no	—
178	C₃₁×#117	—	2	4	no	—
179	C₃₁×#117	—	2	1	no	—
180	C₃₁×#117	—	2	2	no	—
181	C₃₁×#117	D₄	1	2	yes	—
182	C₃₁×#117	D₄	1	1	yes	characteristic
183	C₃₁×#117	D₄	1	1	yes	characteristic
184	C₃₁×#117	C₂³	1	1	yes	characteristic
185	C₃₁×#117	C₂³	1	1	yes	characteristic
186	C₃₁×#117	C₂³	1	1	yes	characteristic
187	C₃₁×#117	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
189	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
190	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
192	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
193	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
194	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
195	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
196	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
204	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
206	C₂×C₄²×C₃₁	—	2	2	no	—
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#107	C₂³	1	4	yes	—
209	C₃₁×#107	C₂³	1	4	yes	—
210	C₃₁×#107	C₂³	1	4	yes	—
211	C₃₁×#106	C₂³	1	4	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
214	C₃₁×#103	C₂³	1	2	yes	—
215	C₃₁×#103	C₂³	1	2	yes	—
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
226	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
229	C₃₁×#97	C₂³	1	4	yes	—
230	C₄×C₈×C₃₁	C₂³	1	4	yes	—
231	C₂⁴×C₃₁	—	2	1	no	—
232	C₂⁴×C₃₁	—	2	1	no	—
233	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
234	#41×C₃₁	—	2	8	no	—
235	#41×C₃₁	—	2	8	no	—
236	#41×C₃₁	—	2	4	no	—
237	#41×C₃₁	—	2	4	no	—
238	#41×C₃₁	—	2	4	no	—
239	#41×C₃₁	—	2	4	no	—
240	#41×C₃₁	—	8	4	no	—
241	#41×C₃₁	#41	1	8	yes	complemented
242	C₂×Q₈×C₃₁	—	2	4	no	—
243	C₂×Q₈×C₃₁	—	2	1	no	—
244	C₂×Q₈×C₃₁	—	2	2	no	—
245	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×D₄×C₃₁	—	2	8	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	1	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	1	no	—
255	C₂×D₄×C₃₁	—	2	2	no	—
256	C₂×D₄×C₃₁	—	2	1	no	—
257	C₂×D₄×C₃₁	—	2	1	no	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	2	4	no	—
261	C₂×D₄×C₃₁	—	8	2	no	—
262	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₃₁	—	2	8	no	—
266	C₂²×C₄×C₃₁	—	2	1	no	—
267	C₂²×C₄×C₃₁	—	2	2	no	—
268	C₂²×C₄×C₃₁	—	2	2	no	—
269	C₂²×C₄×C₃₁	—	2	4	no	—
270	C₂²×C₄×C₃₁	—	2	2	no	—
271	C₂²×C₄×C₃₁	—	2	1	no	—
272	C₂²×C₄×C₃₁	—	2	2	no	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	2	1	no	—
275	C₂²×C₄×C₃₁	—	2	2	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	2	no	—
280	C₂²×C₄×C₃₁	—	8	4	no	—
281	C₂²×C₄×C₃₁	—	8	2	no	—
282	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	Q₁₆×C₃₁	—	2	4	no	—
291	SD₁₆×C₃₁	—	2	4	no	—
292	SD₁₆×C₃₁	—	2	8	no	—
293	SD₁₆×C₃₁	—	2	4	no	—
294	D₈×C₃₁	—	2	4	no	—
295	D₈×C₃₁	—	2	8	no	—
296	M₁₆×C₃₁	—	2	4	no	—
297	C₂×C₈×C₃₁	—	2	4	no	—
298	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
299	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
300	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	—	2	4	no	—
304	C₄⋊C₄×C₃₁	—	2	4	no	—
305	C₄⋊C₄×C₃₁	—	2	2	no	—
306	C₄⋊C₄×C₃₁	—	2	1	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	1	no	—
309	C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₄⋊C₄×C₃₁	—	2	2	no	—
311	C₄⋊C₄×C₃₁	—	2	2	no	—
312	C₄⋊C₄×C₃₁	—	2	1	no	—
313	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
314	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
315	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
319	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
320	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
322	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂²⋊C₄×C₃₁	—	2	1	no	—
324	C₂²⋊C₄×C₃₁	—	2	1	no	—
325	C₂²⋊C₄×C₃₁	—	2	1	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	2	2	no	—
329	C₂²⋊C₄×C₃₁	—	2	2	no	—
330	C₂²⋊C₄×C₃₁	—	2	2	no	—
331	C₂²⋊C₄×C₃₁	—	2	2	no	—
332	C₂²⋊C₄×C₃₁	—	2	2	no	—
333	C₂²⋊C₄×C₃₁	—	2	2	no	—
334	C₂²⋊C₄×C₃₁	—	2	1	no	—
335	C₂²⋊C₄×C₃₁	—	2	2	no	—
336	C₂²⋊C₄×C₃₁	—	2	1	no	—
337	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₄²×C₃₁	—	2	4	no	—
342	C₄²×C₃₁	—	2	4	no	—
343	C₄²×C₃₁	—	2	2	no	—
344	C₄²×C₃₁	—	2	1	no	—
345	C₄²×C₃₁	C₂×D₄	1	2	yes	—
346	C₄²×C₃₁	C₂×D₄	1	2	yes	—
347	C₄²×C₃₁	C₂⁴	1	2	yes	—
348	C₄²×C₃₁	C₂⁴	1	2	yes	—
349	#60584	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₂³×C₃₁	—	2	4	no	—
351	C₂³×C₃₁	—	2	2	no	—
352	C₂³×C₃₁	—	2	2	no	—
353	C₂³×C₃₁	—	2	2	no	—
354	C₂³×C₃₁	—	2	2	no	—
355	C₂³×C₃₁	—	2	1	no	—
356	C₂³×C₃₁	—	4	1	no	—
357	C₂³×C₃₁	—	4	2	no	—
358	C₂³×C₃₁	—	4	2	no	—
359	C₂³×C₃₁	—	4	2	no	—
360	C₂³×C₃₁	—	8	1	no	—
361	C₂³×C₃₁	—	8	1	no	—
362	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
363	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
364	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
365	Q₈×C₃₁	—	2	4	no	—
366	Q₈×C₃₁	—	2	2	no	—
367	Q₈×C₃₁	—	2	2	no	—
368	Q₈×C₃₁	—	8	2	no	—
369	Q₈×C₃₁	C₂×#41	1	4	yes	—
370	D₄×C₃₁	—	2	8	no	—
371	D₄×C₃₁	—	2	4	no	—
372	D₄×C₃₁	—	2	8	no	—
373	D₄×C₃₁	—	2	2	no	—
374	D₄×C₃₁	—	2	4	no	—
375	D₄×C₃₁	—	2	2	no	—
376	D₄×C₃₁	—	4	2	no	—
377	D₄×C₃₁	—	4	4	no	—
378	D₄×C₃₁	—	4	2	no	—
379	D₄×C₃₁	—	4	2	no	—
380	D₄×C₃₁	—	8	2	no	—
381	D₄×C₃₁	—	8	2	no	—
382	D₄×C₃₁	—	8	1	no	—
383	D₄×C₃₁	—	8	2	no	—
384	D₄×C₃₁	C₂×#41	1	4	yes	—
385	C₂×C₄×C₃₁	—	2	4	no	—
386	C₂×C₄×C₃₁	—	2	8	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	4	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	8	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	2	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	4	no	—
397	C₂×C₄×C₃₁	—	2	1	no	—
398	C₂×C₄×C₃₁	—	2	1	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	4	2	no	—
401	C₂×C₄×C₃₁	—	4	4	no	—
402	C₂×C₄×C₃₁	—	4	2	no	—
403	C₂×C₄×C₃₁	—	8	2	no	—
404	C₂×C₄×C₃₁	—	8	4	no	—
405	C₂×C₄×C₃₁	—	8	4	no	—
406	C₂×C₄×C₃₁	—	8	2	no	—
407	C₂×C₄×C₃₁	—	8	2	no	—
408	C₂×C₄×C₃₁	—	8	2	no	—
409	C₂×C₄×C₃₁	—	8	2	no	—
410	C₂×C₄×C₃₁	—	8	1	no	—
411	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
419	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
420	C₈×C₃₁	—	2	2	no	—
421	C₈×C₃₁	—	2	2	no	—
422	C₈×C₃₁	—	2	4	no	—
423	#3494	C₂×C₃₁	1	1	yes	characteristic, complemented
424	C₂×#520	C₂×C₃₁	1	1	yes	characteristic, complemented
425	#3124	C₂×C₃₁	1	4	yes	complemented
426	#3119	C₂×C₃₁	1	4	yes	complemented
427	#3114	C₂×C₃₁	1	2	yes	complemented
428	#3112	C₂×C₃₁	1	2	yes	complemented
429	#3108	C₂×C₃₁	1	2	yes	complemented
430	#3100	C₂×C₃₁	1	2	yes	complemented
431	#3092	C₂×C₃₁	1	1	yes	characteristic, complemented
432	C₂×#480	C₂×C₃₁	1	1	yes	characteristic, complemented
433	#3083	C₂×C₃₁	1	2	yes	complemented
434	#3045	C₂×C₃₁	1	2	yes	complemented
435	#3006	C₂×C₃₁	1	1	yes	characteristic, complemented
436	#3002	C₂×C₃₁	1	1	yes	characteristic, complemented
437	#2951	C₂×C₃₁	1	2	yes	complemented
438	#2946	C₂×C₃₁	1	2	yes	complemented
439	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
440	C₂²×C₃₁	—	2	1	no	—
441	C₂²×C₃₁	—	2	1	no	—
442	C₂²×C₃₁	—	2	1	no	—
443	C₂²×C₃₁	—	2	1	no	—
444	C₂²×C₃₁	—	2	1	no	—
445	C₂²×C₃₁	—	2	1	no	—
446	C₂²×C₃₁	—	2	4	no	—
447	C₂²×C₃₁	—	2	1	no	—
448	C₂²×C₃₁	—	4	4	no	—
449	C₂²×C₃₁	—	4	8	no	—
450	C₂²×C₃₁	—	4	2	no	—
451	C₂²×C₃₁	—	4	2	no	—
452	C₂²×C₃₁	—	4	2	no	—
453	C₂²×C₃₁	—	4	1	no	—
454	C₂²×C₃₁	—	4	1	no	—
455	C₂²×C₃₁	—	4	2	no	—
456	C₂²×C₃₁	—	4	1	no	—
457	C₂²×C₃₁	—	4	2	no	—
458	C₂²×C₃₁	—	16	2	no	—
459	C₂²×C₃₁	#525	1	2	yes	—
460	C₂²×C₃₁	#576	1	2	yes	—
461	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
462	C₄×C₃₁	—	2	2	no	—
463	C₄×C₃₁	—	2	2	no	—
464	C₄×C₃₁	—	2	1	no	—
465	C₄×C₃₁	—	2	4	no	—
466	C₄×C₃₁	—	2	1	no	—
467	C₄×C₃₁	—	2	2	no	—
468	C₄×C₃₁	—	2	2	no	—
469	C₄×C₃₁	—	4	1	no	—
470	C₄×C₃₁	—	4	1	no	—
471	C₄×C₃₁	—	4	4	no	—
472	C₄×C₃₁	—	4	2	no	—
473	C₄×C₃₁	—	4	1	no	—
474	C₄×C₃₁	#525	1	2	yes	—
475	C₄×C₃₁	C₂²×#41	1	2	yes	—
476	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
477	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
478	C₂×#135	C₂²×C₃₁	1	2	yes	—
479	#555	—	2	1	no	—
480	#553	—	2	1	no	—
481	#553	—	2	1	no	—
482	#551	—	2	2	no	—
483	#547	—	2	1	no	—
484	#546	—	2	2	no	—
485	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
486	#542	C₂²×C₃₁	1	2	yes	complemented
487	#540	C₂²×C₃₁	1	2	yes	complemented
488	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
489	#532	C₂²×C₃₁	1	2	yes	—
490	#529	C₂²×C₃₁	1	2	yes	—
491	#525	C₂²×C₃₁	1	1	yes	characteristic
492	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
493	#520	—	2	1	no	—
494	#520	—	2	1	no	—
495	#520	—	2	2	no	—
496	#520	C₂²×C₃₁	1	2	yes	—
497	#520	C₂²×C₃₁	1	2	yes	—
498	#520	C₂²×C₃₁	1	4	yes	complemented
499	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
500	#518	C₂²×C₃₁	1	1	yes	characteristic, complemented
501	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
502	C₂×C₄×D₄	—	2	2	no	—
503	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
504	C₂×#117	—	2	1	no	—
505	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
506	C₂²×C₄⋊C₄	—	2	1	no	—
507	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
508	#484	C₂²×C₃₁	1	2	yes	complemented
509	#483	C₂²×C₃₁	1	2	yes	complemented
510	#481	C₂²×C₃₁	1	2	yes	complemented
511	#480	C₂²×C₃₁	1	2	yes	—
512	#480	C₂²×C₃₁	1	2	yes	—
513	#480	C₂²×C₃₁	1	4	yes	complemented
514	#480	C₂²×C₃₁	1	2	yes	complemented
515	#479	C₂²×C₃₁	1	4	yes	complemented
516	#478	C₂²×C₃₁	1	4	yes	complemented
517	#477	C₂²×C₃₁	1	4	yes	complemented
518	#474	C₂²×C₃₁	1	4	yes	complemented
519	#464	C₂²×C₃₁	1	4	yes	complemented
520	#463	C₂²×C₃₁	1	4	yes	complemented
521	#460	C₂²×C₃₁	1	4	yes	complemented
522	#459	C₂²×C₃₁	1	4	yes	complemented
523	#452	C₂²×C₃₁	1	2	yes	complemented
524	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
525	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
526	#449	C₂²×C₃₁	1	4	yes	—
527	#449	C₂²×C₃₁	1	2	yes	complemented
528	#448	C₂²×C₃₁	1	2	yes	—
529	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
530	#447	C₂²×C₃₁	1	2	yes	—
531	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#442	C₂²×C₃₁	1	4	yes	complemented
533	#440	C₂²×C₃₁	1	4	yes	complemented
534	#440	C₂²×C₃₁	1	4	yes	complemented
535	#440	C₂²×C₃₁	1	4	yes	complemented
536	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
537	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
538	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
539	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
540	#433	C₂²×C₃₁	1	4	yes	complemented
541	#432	C₂²×C₃₁	1	2	yes	complemented
542	#431	C₂²×C₃₁	1	2	yes	complemented
543	#428	C₂²×C₃₁	1	2	yes	complemented
544	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
545	#424	C₂²×C₃₁	1	2	yes	complemented
546	#417	C₂²×C₃₁	1	2	yes	—
547	#417	C₂²×C₃₁	1	2	yes	complemented
548	#416	C₂²×C₃₁	1	2	yes	—
549	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
550	#407	C₂²×C₃₁	1	1	yes	characteristic
551	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
552	#405	C₂²×C₃₁	1	2	yes	complemented
553	C₂×C₃₁	—	2	2	no	—
554	C₂×C₃₁	—	2	2	no	—
555	C₂×C₃₁	—	4	1	no	—
556	C₂×C₃₁	—	4	4	no	—
557	C₂×C₃₁	—	8	1	no	—
558	C₂×C₃₁	—	8	2	no	—
559	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
560	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
561	C₂×C₃₁	#3586	1	1	yes	characteristic
562	C₂×#41	—	2	8	no	—
563	C₂×#41	—	2	1	no	—
564	C₂×#41	—	2	1	no	—
565	C₂×#41	—	2	2	no	—
566	C₂×#41	C₂³×C₃₁	1	2	yes	—
567	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
568	C₂×#41	C₂³×C₃₁	1	2	yes	—
569	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
570	C₂²×D₄	—	2	1	no	—
571	C₂²×D₄	—	2	1	no	—
572	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
573	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
574	C₂³×C₄	—	2	1	no	—
575	C₂³×C₄	—	2	1	no	—
576	C₂³×C₄	—	2	2	no	—
577	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
578	AGL(1,ℤ/8)	—	2	8	no	—
579	#135	—	2	8	no	—
580	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
584	C₂×D₈	C₂³×C₃₁	1	2	yes	—
585	C₂×D₈	C₂³×C₃₁	1	4	yes	—
586	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
587	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
588	C₄⋊Q₈	—	2	1	no	—
589	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
590	#127	C₂³×C₃₁	1	2	yes	—
591	#126	—	2	2	no	—
592	#126	—	2	2	no	—
593	#125	—	2	1	no	—
594	#125	C₂³×C₃₁	1	2	yes	—
595	#124	—	2	2	no	—
596	#124	—	2	2	no	—
597	#124	C₂³×C₃₁	1	2	yes	—
598	#123	—	2	1	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
606	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
607	#121	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	—	2	1	no	—
611	#121	—	2	1	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	C₂³×C₃₁	1	2	yes	—
615	#121	C₂³×C₃₁	1	2	yes	—
616	#121	C₂³×C₃₁	1	1	yes	characteristic
617	#121	C₂³×C₃₁	1	1	yes	characteristic
618	#120	—	2	1	no	—
619	#120	—	2	2	no	—
620	C₄×Q₈	—	2	2	no	—
621	C₄×Q₈	—	2	2	no	—
622	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
623	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
624	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	4	no	—
631	C₄×D₄	—	2	4	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	C₂³×C₃₁	1	4	yes	—
639	C₄×D₄	C₂³×C₃₁	1	4	yes	—
640	C₄×D₄	C₂³×C₃₁	1	2	yes	—
641	C₄×D₄	C₂³×C₃₁	1	2	yes	—
642	C₄×D₄	C₂³×C₃₁	1	2	yes	—
643	#117	—	2	2	no	—
644	#117	—	2	2	no	—
645	#117	—	2	4	no	—
646	#117	—	2	1	no	—
647	#117	—	2	2	no	—
648	#117	D₄×C₃₁	1	2	yes	—
649	#117	D₄×C₃₁	1	1	yes	characteristic
650	#117	D₄×C₃₁	1	1	yes	characteristic
651	#117	C₂³×C₃₁	1	1	yes	characteristic
652	#117	C₂³×C₃₁	1	1	yes	characteristic
653	#117	C₂³×C₃₁	1	1	yes	characteristic
654	#117	C₂³×C₃₁	1	2	yes	—
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	2	no	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	—	2	2	no	—
660	C₂×C₄⋊C₄	—	2	2	no	—
661	C₂×C₄⋊C₄	—	2	4	no	—
662	C₂×C₄⋊C₄	—	2	1	no	—
663	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
664	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	—	2	2	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	2	no	—
672	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
673	C₂×C₄²	—	2	2	no	—
674	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
675	#107	C₂³×C₃₁	1	4	yes	—
676	#107	C₂³×C₃₁	1	4	yes	—
677	#107	C₂³×C₃₁	1	4	yes	—
678	#106	C₂³×C₃₁	1	4	yes	—
679	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
680	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
681	#103	C₂³×C₃₁	1	2	yes	—
682	#103	C₂³×C₃₁	1	2	yes	—
683	#103	C₂³×C₃₁	1	4	yes	—
684	#103	C₂³×C₃₁	1	4	yes	—
685	#102	C₂³×C₃₁	1	4	yes	—
686	#102	C₂³×C₃₁	1	4	yes	—
687	#102	C₂³×C₃₁	1	2	yes	—
688	#102	C₂³×C₃₁	1	2	yes	—
689	#102	C₂³×C₃₁	1	4	yes	—
690	#102	C₂³×C₃₁	1	4	yes	—
691	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
693	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
694	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
695	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
696	#97	C₂³×C₃₁	1	4	yes	—
697	C₄×C₈	C₂³×C₃₁	1	4	yes	—
698	C₃₁	#60584	1	1	yes	characteristic, direct product factor, Sylow
699	C₂⁴	—	2	1	no	—
700	C₂⁴	—	2	1	no	—
701	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
702	#41	—	2	8	no	—
703	#41	—	2	8	no	—
704	#41	—	2	4	no	—
705	#41	—	2	4	no	—
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	8	4	no	—
709	#41	#41×C₃₁	1	8	yes	complemented
710	C₂×Q₈	—	2	4	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
714	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	8	2	no	—
730	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
731	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
732	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
733	C₂²×C₄	—	2	8	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	8	4	no	—
749	C₂²×C₄	—	8	2	no	—
750	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
751	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
752	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
753	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
754	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
758	Q₁₆	—	2	4	no	—
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	2	8	no	—
761	SD₁₆	—	2	4	no	—
762	D₈	—	2	4	no	—
763	D₈	—	2	8	no	—
764	M₁₆	—	2	4	no	—
765	C₂×C₈	—	2	4	no	—
766	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
767	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
768	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
782	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
783	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
784	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
785	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
786	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
787	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
788	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
789	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
790	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	1	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	1	no	—
805	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
807	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
808	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
809	C₄²	—	2	4	no	—
810	C₄²	—	2	4	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	1	no	—
813	C₄²	C₂×D₄×C₃₁	1	2	yes	—
814	C₄²	C₂×D₄×C₃₁	1	2	yes	—
815	C₄²	C₂⁴×C₃₁	1	2	yes	—
816	C₄²	C₂⁴×C₃₁	1	2	yes	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	2	no	—
825	C₂³	—	4	2	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	8	1	no	—
828	C₂³	—	8	1	no	—
829	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
830	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
831	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
832	Q₈	—	2	4	no	—
833	Q₈	—	2	2	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	8	2	no	—
836	Q₈	C₂×#41×C₃₁	1	4	yes	—
837	D₄	—	2	8	no	—
838	D₄	—	2	4	no	—
839	D₄	—	2	8	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	4	no	—
842	D₄	—	2	2	no	—
843	D₄	—	4	2	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	2	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	1	no	—
850	D₄	—	8	2	no	—
851	D₄	C₂×#41×C₃₁	1	4	yes	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	8	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	—	8	4	no	—
873	C₂×C₄	—	8	2	no	—
874	C₂×C₄	—	8	2	no	—
875	C₂×C₄	—	8	2	no	—
876	C₂×C₄	—	8	2	no	—
877	C₂×C₄	—	8	1	no	—
878	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
879	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
880	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
881	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
882	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
883	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
885	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
886	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
887	C₈	—	2	2	no	—
888	C₈	—	2	2	no	—
889	C₈	—	2	4	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	4	8	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	16	2	no	—
909	C₂²	C₃₁×#525	1	2	yes	—
910	C₂²	C₃₁×#576	1	2	yes	—
911	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
912	C₄	—	2	1	no	—
913	C₄	—	2	4	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	4	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	1	no	—
924	C₄	C₃₁×#525	1	2	yes	—
925	C₄	C₂²×#41×C₃₁	1	2	yes	—
926	C₂	—	2	2	no	—
927	C₂	—	2	2	no	—
928	C₂	—	4	1	no	—
929	C₂	—	4	4	no	—
930	C₂	—	8	2	no	—
931	C₂	—	8	1	no	—
932	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
933	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
934	C₂	C₃₁×#3586	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. C₂×C₃₁×#520	C₂	semidirect
3. C₃₁×#3124	C₂	semidirect
4. C₃₁×#3119	C₂	semidirect
5. C₃₁×#3114	C₂	semidirect
6. C₃₁×#3112	C₂	semidirect
7. C₃₁×#3108	C₂	semidirect
8. C₃₁×#3100	C₂	semidirect
9. C₃₁×#3092	C₂	semidirect
10. C₂×C₃₁×#480	C₂	semidirect
11. C₃₁×#3083	C₂	semidirect
12. C₃₁×#3045	C₂	semidirect
13. C₃₁×#3006	C₂	semidirect
14. C₃₁×#3002	C₂	semidirect
15. C₃₁×#2951	C₂	semidirect
16. C₃₁×#2946	C₂	semidirect
17. C₃₁×#2924	C₂	semidirect
27. C₃₁×#544	C₂²	semidirect
28. C₃₁×#542	C₂²	semidirect
29. C₃₁×#540	C₂²	semidirect
30. C₃₁×#535	C₂²	semidirect
40. C₃₁×#520	C₂²	semidirect
41. C₃₁×#520	C₂²	semidirect
42. C₃₁×#518	C₂²	semidirect
43. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
45. C₂×C₄×D₄×C₃₁	C₂²	semidirect
50. C₃₁×#484	C₂²	semidirect
51. C₃₁×#483	C₂²	semidirect
52. C₃₁×#481	C₂²	semidirect
55. C₃₁×#480	C₂²	semidirect
56. C₃₁×#480	C₂²	semidirect
57. C₃₁×#479	C₂²	semidirect
58. C₃₁×#478	C₂²	semidirect
59. C₃₁×#477	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
61. C₃₁×#464	C₂²	semidirect
62. C₃₁×#463	C₂²	semidirect
63. C₃₁×#460	C₂²	semidirect
64. C₃₁×#459	C₂²	semidirect
65. C₃₁×#452	C₂²	semidirect
66. C₃₁×#451	C₂²	semidirect
67. C₃₁×#450	C₂²	semidirect
69. C₃₁×#449	C₂²	semidirect
71. C₃₁×#448	C₂²	semidirect
73. C₃₁×#447	C₂²	semidirect
74. C₃₁×#442	C₂²	semidirect
75. C₃₁×#440	C₂²	semidirect
76. C₃₁×#440	C₂²	semidirect
77. C₃₁×#440	C₂²	semidirect
78. C₄×Q₁₆×C₃₁	C₂²	semidirect
79. C₄×SD₁₆×C₃₁	C₂²	semidirect
80. C₄×D₈×C₃₁	C₂²	semidirect
81. C₄×D₈×C₃₁	C₂²	semidirect
82. C₃₁×#433	C₂²	semidirect
83. C₃₁×#432	C₂²	semidirect
84. C₃₁×#431	C₂²	semidirect
85. C₃₁×#428	C₂²	semidirect
86. C₂×C₃₁×#107	C₂²	semidirect
87. C₃₁×#424	C₂²	semidirect
89. C₃₁×#417	C₂²	semidirect
91. C₂×C₃₁×#102	C₂²	semidirect
94. C₃₁×#405	C₂²	semidirect
241. #41×C₃₁	#41	semidirect
349. #60584	C₃₁	direct (N × H)
423. #3494	C₂×C₃₁	semidirect
424. C₂×#520	C₂×C₃₁	semidirect
425. #3124	C₂×C₃₁	semidirect
426. #3119	C₂×C₃₁	semidirect
427. #3114	C₂×C₃₁	semidirect
428. #3112	C₂×C₃₁	semidirect
429. #3108	C₂×C₃₁	semidirect
430. #3100	C₂×C₃₁	semidirect
431. #3092	C₂×C₃₁	semidirect
432. C₂×#480	C₂×C₃₁	semidirect
433. #3083	C₂×C₃₁	semidirect
434. #3045	C₂×C₃₁	semidirect
435. #3006	C₂×C₃₁	semidirect
436. #3002	C₂×C₃₁	semidirect
437. #2951	C₂×C₃₁	semidirect
438. #2946	C₂×C₃₁	semidirect
439. #2924	C₂×C₃₁	semidirect
485. #544	C₂²×C₃₁	semidirect
486. #542	C₂²×C₃₁	semidirect
487. #540	C₂²×C₃₁	semidirect
488. #535	C₂²×C₃₁	semidirect
498. #520	C₂²×C₃₁	semidirect
499. #520	C₂²×C₃₁	semidirect
500. #518	C₂²×C₃₁	semidirect
501. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
503. C₂×C₄×D₄	C₂²×C₃₁	semidirect
508. #484	C₂²×C₃₁	semidirect
509. #483	C₂²×C₃₁	semidirect
510. #481	C₂²×C₃₁	semidirect
513. #480	C₂²×C₃₁	semidirect
514. #480	C₂²×C₃₁	semidirect
515. #479	C₂²×C₃₁	semidirect
516. #478	C₂²×C₃₁	semidirect
517. #477	C₂²×C₃₁	semidirect
518. #474	C₂²×C₃₁	semidirect
519. #464	C₂²×C₃₁	semidirect
520. #463	C₂²×C₃₁	semidirect
521. #460	C₂²×C₃₁	semidirect
522. #459	C₂²×C₃₁	semidirect
523. #452	C₂²×C₃₁	semidirect
524. #451	C₂²×C₃₁	semidirect
525. #450	C₂²×C₃₁	semidirect
527. #449	C₂²×C₃₁	semidirect
529. #448	C₂²×C₃₁	semidirect
531. #447	C₂²×C₃₁	semidirect
532. #442	C₂²×C₃₁	semidirect
533. #440	C₂²×C₃₁	semidirect
534. #440	C₂²×C₃₁	semidirect
535. #440	C₂²×C₃₁	semidirect
536. C₄×Q₁₆	C₂²×C₃₁	semidirect
537. C₄×SD₁₆	C₂²×C₃₁	semidirect
538. C₄×D₈	C₂²×C₃₁	semidirect
539. C₄×D₈	C₂²×C₃₁	semidirect
540. #433	C₂²×C₃₁	semidirect
541. #432	C₂²×C₃₁	semidirect
542. #431	C₂²×C₃₁	semidirect
543. #428	C₂²×C₃₁	semidirect
544. C₂×#107	C₂²×C₃₁	semidirect
545. #424	C₂²×C₃₁	semidirect
547. #417	C₂²×C₃₁	semidirect
549. C₂×#102	C₂²×C₃₁	semidirect
552. #405	C₂²×C₃₁	semidirect
698. C₃₁	#60584	direct (N × H)
709. #41	#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
C₂×C₃₁×#520	2
C₃₁×#3124	2
C₃₁×#3119	2
C₃₁×#3114	2
C₃₁×#3112	2
C₃₁×#3108	2
C₃₁×#3100	2
C₃₁×#3092	2
C₂×C₃₁×#480	2
C₃₁×#3083	2
C₃₁×#3045	2
C₃₁×#3006	2
C₃₁×#3002	2
C₃₁×#2951	2
C₃₁×#2946	2
C₃₁×#2924	2
#60584	31

Subgroups — C31×#60584 #21517343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60584 #21517343