Subgroups — C₃₁×#61489 #21518248

Order 7936.

1910 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3513	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3403	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3355	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3273	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#559	C₂²	1	2	yes	complemented
23	C₃₁×#554	C₂²	1	2	yes	complemented
24	C₃₁×#553	—	2	2	no	—
25	C₃₁×#553	C₂²	1	2	yes	complemented
26	C₃₁×#552	C₂²	1	2	yes	complemented
27	C₃₁×#551	—	2	2	no	—
28	C₃₁×#551	—	2	2	no	—
29	C₃₁×#547	C₂²	1	2	yes	—
30	C₃₁×#546	—	2	2	no	—
31	C₃₁×#546	C₂²	1	2	yes	—
32	C₃₁×#546	C₂²	1	2	yes	complemented
33	D₄²×C₃₁	C₂²	1	2	yes	complemented
34	C₃₁×#542	C₂²	1	2	yes	complemented
35	C₃₁×#540	C₂²	1	2	yes	complemented
36	C₃₁×#539	—	2	2	no	—
37	C₃₁×#538	—	2	2	no	—
38	C₃₁×#529	C₂²	1	1	yes	characteristic
39	C₃₁×#529	C₂²	1	2	yes	complemented
40	C₃₁×#525	—	2	2	no	—
41	C₂×C₃₁×#123	—	2	2	no	—
42	C₃₁×#520	C₂²	1	2	yes	complemented
43	C₃₁×#518	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
45	C₃₁×#501	C₂²	1	2	yes	complemented
46	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#496	C₂²	1	2	yes	complemented
48	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#488	C₂²	1	2	yes	complemented
50	C₃₁×#488	C₂²	1	2	yes	complemented
51	C₃₁×#486	C₂²	1	2	yes	complemented
52	C₃₁×#484	C₂²	1	2	yes	complemented
53	C₃₁×#483	C₂²	1	2	yes	complemented
54	C₃₁×#482	C₂²	1	2	yes	complemented
55	C₃₁×#482	C₂²	1	2	yes	complemented
56	C₃₁×#480	C₂²	1	2	yes	complemented
57	C₃₁×#480	C₂²	1	2	yes	complemented
58	C₃₁×#478	C₂²	1	2	yes	complemented
59	C₃₁×#478	C₂²	1	2	yes	complemented
60	C₃₁×#478	C₂²	1	2	yes	complemented
61	C₃₁×#478	C₂²	1	2	yes	complemented
62	C₃₁×#477	C₂²	1	2	yes	complemented
63	C₃₁×#474	C₂²	1	2	yes	complemented
64	C₃₁×#469	C₂²	1	2	yes	complemented
65	C₃₁×#468	C₂²	1	2	yes	complemented
66	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#466	C₂²	1	1	yes	characteristic
68	C₃₁×#466	C₂²	1	2	yes	complemented
69	C₃₁×#465	C₂²	1	2	yes	complemented
70	C₃₁×#465	C₂²	1	2	yes	complemented
71	C₃₁×#464	C₂²	1	2	yes	complemented
72	C₃₁×#463	C₂²	1	2	yes	complemented
73	C₃₁×#463	C₂²	1	2	yes	complemented
74	C₃₁×#463	C₂²	1	2	yes	complemented
75	C₃₁×#459	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	2	yes	complemented
77	C₃₁×#452	C₂²	1	2	yes	complemented
78	C₃₁×#450	C₂²	1	2	yes	complemented
79	C₃₁×#449	C₂²	1	2	yes	—
80	C₃₁×#447	C₂²	1	2	yes	—
81	C₃₁×#447	C₂²	1	2	yes	complemented
82	C₃₁×#447	C₂²	1	2	yes	complemented
83	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
84	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#442	C₂²	1	2	yes	—
86	C₃₁×#442	C₂²	1	2	yes	complemented
87	C₃₁×#442	C₂²	1	2	yes	complemented
88	C₃₁×#440	C₂²	1	2	yes	complemented
89	C₃₁×#440	C₂²	1	2	yes	complemented
90	C₃₁×#440	C₂²	1	2	yes	complemented
91	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
92	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
93	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
94	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
95	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
96	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
98	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
99	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
100	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
101	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
105	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#433	C₂²	1	2	yes	complemented
107	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#428	C₂²	1	2	yes	complemented
109	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#416	C₂²	1	2	yes	complemented
111	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
112	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
113	C₃₁×#405	C₂²	1	2	yes	complemented
114	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₃₁	—	2	2	no	—
116	C₂×#41×C₃₁	C₂³	1	2	yes	—
117	C₂²×D₄×C₃₁	—	2	2	no	—
118	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
119	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
120	C₂³×C₄×C₃₁	—	2	2	no	—
121	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
122	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
123	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×D₈×C₃₁	—	2	4	no	—
127	C₂×D₈×C₃₁	C₂³	1	2	yes	—
128	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×D₈×C₃₁	C₂³	1	2	yes	—
132	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×#127	C₂³	1	2	yes	—
139	C₃₁×#126	—	2	2	no	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	D₄	1	2	yes	—
144	C₃₁×#125	—	2	2	no	—
145	C₃₁×#125	D₄	1	1	yes	characteristic
146	C₃₁×#125	C₂³	1	2	yes	—
147	C₃₁×#125	C₂³	1	2	yes	—
148	C₃₁×#124	—	2	2	no	—
149	C₃₁×#124	—	2	2	no	—
150	C₃₁×#124	D₄	1	1	yes	characteristic
151	C₃₁×#124	C₂³	1	2	yes	—
152	C₃₁×#124	C₂³	1	2	yes	—
153	C₃₁×#123	—	2	2	no	—
154	C₃₁×#123	—	2	2	no	—
155	C₃₁×#123	—	2	2	no	—
156	C₃₁×#123	—	2	2	no	—
157	C₃₁×#123	—	2	2	no	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×#123	D₄	1	2	yes	—
166	C₃₁×C₂²⋊Q₈	—	2	2	no	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	—	2	2	no	—
169	C₃₁×C₂²⋊Q₈	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
172	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₃₁×#121	—	2	2	no	—
175	C₃₁×#121	—	2	2	no	—
176	C₃₁×#121	—	2	2	no	—
177	C₃₁×#121	—	2	2	no	—
178	C₃₁×#121	—	2	2	no	—
179	C₃₁×#121	—	2	2	no	—
180	C₃₁×#121	D₄	1	1	yes	characteristic
181	C₃₁×#121	C₂³	1	2	yes	—
182	C₃₁×#121	C₂³	1	2	yes	—
183	C₃₁×#121	C₂³	1	2	yes	—
184	C₃₁×#121	C₂³	1	2	yes	—
185	C₃₁×#120	—	2	2	no	—
186	C₃₁×#120	—	2	2	no	—
187	C₃₁×#120	—	2	2	no	—
188	C₃₁×#120	—	2	2	no	—
189	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
190	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
191	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₃₁	—	2	2	no	—
193	C₄×D₄×C₃₁	—	2	2	no	—
194	C₄×D₄×C₃₁	—	2	2	no	—
195	C₄×D₄×C₃₁	—	2	2	no	—
196	C₄×D₄×C₃₁	—	2	2	no	—
197	C₄×D₄×C₃₁	—	2	2	no	—
198	C₄×D₄×C₃₁	—	2	2	no	—
199	C₄×D₄×C₃₁	—	2	2	no	—
200	C₄×D₄×C₃₁	—	2	2	no	—
201	C₄×D₄×C₃₁	C₂³	1	2	yes	—
202	C₄×D₄×C₃₁	C₂³	1	2	yes	—
203	C₄×D₄×C₃₁	C₂³	1	2	yes	—
204	C₄×D₄×C₃₁	C₂³	1	2	yes	—
205	C₄×D₄×C₃₁	C₂³	1	2	yes	—
206	C₄×D₄×C₃₁	C₂³	1	2	yes	—
207	C₄×D₄×C₃₁	C₂³	1	2	yes	—
208	C₄×D₄×C₃₁	C₂³	1	2	yes	—
209	C₄×D₄×C₃₁	C₂³	1	2	yes	—
210	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
211	C₃₁×#117	—	2	2	no	—
212	C₃₁×#117	—	2	2	no	—
213	C₃₁×#117	—	2	2	no	—
214	C₃₁×#117	C₂³	1	2	yes	—
215	C₃₁×#117	C₂³	1	2	yes	—
216	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
217	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
218	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
219	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
221	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
222	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
223	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
224	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
225	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
226	C₃₁×#107	C₂³	1	1	yes	characteristic
227	C₃₁×#107	C₂³	1	1	yes	characteristic
228	C₃₁×#107	C₂³	1	2	yes	—
229	C₃₁×#107	C₂³	1	2	yes	—
230	C₃₁×#107	C₂³	1	1	yes	characteristic
231	C₃₁×#107	C₂³	1	1	yes	characteristic
232	C₃₁×#107	C₂³	1	2	yes	—
233	C₃₁×#106	C₂³	1	2	yes	—
234	C₃₁×#106	C₂³	1	2	yes	—
235	C₃₁×#106	C₂³	1	2	yes	—
236	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
237	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
239	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
240	C₃₁×#103	C₂³	1	2	yes	—
241	C₃₁×#103	C₂³	1	2	yes	—
242	C₃₁×#103	C₂³	1	2	yes	—
243	C₃₁×#103	C₂³	1	2	yes	—
244	C₃₁×#102	C₂³	1	2	yes	—
245	C₃₁×#102	C₂³	1	2	yes	—
246	C₃₁×#102	C₂³	1	2	yes	—
247	C₃₁×#102	C₂³	1	2	yes	—
248	C₃₁×#102	C₂³	1	2	yes	—
249	C₃₁×#102	C₂³	1	2	yes	—
250	C₃₁×#102	C₂³	1	2	yes	—
251	C₃₁×#102	C₂³	1	2	yes	—
252	C₃₁×#102	C₂³	1	2	yes	—
253	C₃₁×#102	C₂³	1	2	yes	—
254	C₃₁×#102	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₃₁×#97	C₂³	1	2	yes	—
260	C₃₁×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₃₁	C₂³	1	2	yes	—
266	C₂⁴×C₃₁	—	2	2	no	—
267	C₂⁴×C₃₁	—	2	2	no	—
268	#41×C₃₁	—	2	4	no	—
269	#41×C₃₁	—	4	2	no	—
270	#41×C₃₁	—	8	4	no	—
271	C₂×Q₈×C₃₁	—	2	2	no	—
272	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
274	C₂×D₄×C₃₁	—	2	4	no	—
275	C₂×D₄×C₃₁	—	2	4	no	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	2	2	no	—
279	C₂×D₄×C₃₁	—	2	2	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	2	2	no	—
282	C₂×D₄×C₃₁	—	2	2	no	—
283	C₂×D₄×C₃₁	—	2	2	no	—
284	C₂×D₄×C₃₁	—	2	2	no	—
285	C₂×D₄×C₃₁	—	4	2	no	—
286	C₂×D₄×C₃₁	—	4	2	no	—
287	C₂×D₄×C₃₁	—	8	4	no	—
288	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
291	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
292	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₃₁	—	2	2	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	—	2	2	no	—
296	C₂²×C₄×C₃₁	—	2	2	no	—
297	C₂²×C₄×C₃₁	—	2	2	no	—
298	C₂²×C₄×C₃₁	—	2	2	no	—
299	C₂²×C₄×C₃₁	—	2	2	no	—
300	C₂²×C₄×C₃₁	—	2	2	no	—
301	C₂²×C₄×C₃₁	—	2	2	no	—
302	C₂²×C₄×C₃₁	—	2	2	no	—
303	C₂²×C₄×C₃₁	—	2	2	no	—
304	C₂²×C₄×C₃₁	—	8	4	no	—
305	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
309	Q₁₆×C₃₁	—	4	1	no	—
310	SD₁₆×C₃₁	—	2	4	no	—
311	SD₁₆×C₃₁	—	2	4	no	—
312	SD₁₆×C₃₁	—	4	2	no	—
313	D₈×C₃₁	—	2	4	no	—
314	D₈×C₃₁	—	2	4	no	—
315	D₈×C₃₁	—	2	2	no	—
316	D₈×C₃₁	—	4	2	no	—
317	D₈×C₃₁	—	4	1	no	—
318	D₈×C₃₁	#41	1	4	yes	complemented
319	M₁₆×C₃₁	—	2	4	no	—
320	C₂×C₈×C₃₁	—	2	2	no	—
321	C₂×C₈×C₃₁	—	4	2	no	—
322	C₂×C₈×C₃₁	—	4	1	no	—
323	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
345	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
349	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	—	2	2	no	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₃₁	—	2	2	no	—
365	C₂²⋊C₄×C₃₁	—	2	2	no	—
366	C₂²⋊C₄×C₃₁	—	2	2	no	—
367	C₂²⋊C₄×C₃₁	—	2	2	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
370	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
371	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
372	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
373	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₄²×C₃₁	—	2	2	no	—
375	C₄²×C₃₁	—	2	2	no	—
376	C₄²×C₃₁	—	2	2	no	—
377	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₄²×C₃₁	C₂⁴	1	2	yes	—
382	#61489	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂³×C₃₁	—	2	2	no	—
384	C₂³×C₃₁	—	2	2	no	—
385	C₂³×C₃₁	—	2	2	no	—
386	C₂³×C₃₁	—	4	4	no	—
387	C₂³×C₃₁	—	4	4	no	—
388	C₂³×C₃₁	—	4	4	no	—
389	C₂³×C₃₁	—	8	2	no	—
390	C₂³×C₃₁	—	8	2	no	—
391	C₂³×C₃₁	—	8	2	no	—
392	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
393	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	Q₈×C₃₁	—	2	2	no	—
395	Q₈×C₃₁	—	2	2	no	—
396	Q₈×C₃₁	—	4	1	no	—
397	Q₈×C₃₁	—	8	2	no	—
398	D₄×C₃₁	—	2	4	no	—
399	D₄×C₃₁	—	2	2	no	—
400	D₄×C₃₁	—	2	2	no	—
401	D₄×C₃₁	—	2	2	no	—
402	D₄×C₃₁	—	2	2	no	—
403	D₄×C₃₁	—	2	2	no	—
404	D₄×C₃₁	—	4	1	no	—
405	D₄×C₃₁	—	4	4	no	—
406	D₄×C₃₁	—	4	4	no	—
407	D₄×C₃₁	—	4	4	no	—
408	D₄×C₃₁	—	4	4	no	—
409	D₄×C₃₁	—	8	2	no	—
410	D₄×C₃₁	—	8	2	no	—
411	D₄×C₃₁	—	8	2	no	—
412	D₄×C₃₁	—	8	2	no	—
413	D₄×C₃₁	—	8	2	no	—
414	D₄×C₃₁	C₂×#41	1	4	yes	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	4	1	no	—
426	C₂×C₄×C₃₁	—	4	4	no	—
427	C₂×C₄×C₃₁	—	4	4	no	—
428	C₂×C₄×C₃₁	—	8	2	no	—
429	C₂×C₄×C₃₁	—	8	2	no	—
430	C₂×C₄×C₃₁	—	8	2	no	—
431	C₂×C₄×C₃₁	—	8	2	no	—
432	C₂×C₄×C₃₁	—	8	2	no	—
433	C₂×C₄×C₃₁	—	8	2	no	—
434	C₂×C₄×C₃₁	—	8	2	no	—
435	C₂×C₄×C₃₁	—	8	2	no	—
436	C₂×C₄×C₃₁	—	8	2	no	—
437	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
446	C₈×C₃₁	—	2	1	no	—
447	C₈×C₃₁	—	2	2	no	—
448	C₈×C₃₁	—	2	1	no	—
449	C₈×C₃₁	—	2	2	no	—
450	C₈×C₃₁	—	2	1	no	—
451	C₈×C₃₁	C₂×#41	1	2	yes	—
452	#3513	C₂×C₃₁	1	2	yes	complemented
453	#3403	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#3389	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#3361	C₂×C₃₁	1	2	yes	complemented
456	#3355	C₂×C₃₁	1	1	yes	characteristic, complemented
457	#3343	C₂×C₃₁	1	2	yes	complemented
458	#3297	C₂×C₃₁	1	2	yes	complemented
459	#3296	C₂×C₃₁	1	2	yes	complemented
460	#3294	C₂×C₃₁	1	2	yes	complemented
461	#3273	C₂×C₃₁	1	1	yes	characteristic, complemented
462	#3264	C₂×C₃₁	1	2	yes	complemented
463	#3179	C₂×C₃₁	1	2	yes	complemented
464	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
465	#3124	C₂×C₃₁	1	2	yes	complemented
466	#3122	C₂×C₃₁	1	2	yes	complemented
467	#3114	C₂×C₃₁	1	2	yes	complemented
468	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
469	#2946	C₂×C₃₁	1	2	yes	complemented
470	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
471	C₂²×C₃₁	—	2	1	no	—
472	C₂²×C₃₁	—	2	1	no	—
473	C₂²×C₃₁	—	2	2	no	—
474	C₂²×C₃₁	—	2	2	no	—
475	C₂²×C₃₁	—	2	4	no	—
476	C₂²×C₃₁	—	2	2	no	—
477	C₂²×C₃₁	—	4	2	no	—
478	C₂²×C₃₁	—	4	2	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	—	4	2	no	—
481	C₂²×C₃₁	—	4	2	no	—
482	C₂²×C₃₁	—	4	2	no	—
483	C₂²×C₃₁	—	4	2	no	—
484	C₂²×C₃₁	—	4	2	no	—
485	C₂²×C₃₁	—	8	8	no	—
486	C₂²×C₃₁	—	16	4	no	—
487	C₂²×C₃₁	#576	1	2	yes	—
488	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
489	C₄×C₃₁	—	2	1	no	—
490	C₄×C₃₁	—	2	1	no	—
491	C₄×C₃₁	—	2	2	no	—
492	C₄×C₃₁	—	2	2	no	—
493	C₄×C₃₁	—	2	1	no	—
494	C₄×C₃₁	—	2	1	no	—
495	C₄×C₃₁	—	2	1	no	—
496	C₄×C₃₁	—	2	2	no	—
497	C₄×C₃₁	—	4	2	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	2	no	—
502	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
503	C₄×C₃₁	#585	1	1	yes	characteristic
504	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
505	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
506	#559	C₂²×C₃₁	1	2	yes	complemented
507	#554	C₂²×C₃₁	1	2	yes	complemented
508	#553	—	2	2	no	—
509	#553	C₂²×C₃₁	1	2	yes	complemented
510	#552	C₂²×C₃₁	1	2	yes	complemented
511	#551	—	2	2	no	—
512	#551	—	2	2	no	—
513	#547	C₂²×C₃₁	1	2	yes	—
514	#546	—	2	2	no	—
515	#546	C₂²×C₃₁	1	2	yes	—
516	#546	C₂²×C₃₁	1	2	yes	complemented
517	D₄²	C₂²×C₃₁	1	2	yes	complemented
518	#542	C₂²×C₃₁	1	2	yes	complemented
519	#540	C₂²×C₃₁	1	2	yes	complemented
520	#539	—	2	2	no	—
521	#538	—	2	2	no	—
522	#529	C₂²×C₃₁	1	1	yes	characteristic
523	#529	C₂²×C₃₁	1	2	yes	complemented
524	#525	—	2	2	no	—
525	C₂×#123	—	2	2	no	—
526	#520	C₂²×C₃₁	1	2	yes	complemented
527	#518	C₂²×C₃₁	1	2	yes	complemented
528	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
529	#501	C₂²×C₃₁	1	2	yes	complemented
530	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
531	#496	C₂²×C₃₁	1	2	yes	complemented
532	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
533	#488	C₂²×C₃₁	1	2	yes	complemented
534	#488	C₂²×C₃₁	1	2	yes	complemented
535	#486	C₂²×C₃₁	1	2	yes	complemented
536	#484	C₂²×C₃₁	1	2	yes	complemented
537	#483	C₂²×C₃₁	1	2	yes	complemented
538	#482	C₂²×C₃₁	1	2	yes	complemented
539	#482	C₂²×C₃₁	1	2	yes	complemented
540	#480	C₂²×C₃₁	1	2	yes	complemented
541	#480	C₂²×C₃₁	1	2	yes	complemented
542	#478	C₂²×C₃₁	1	2	yes	complemented
543	#478	C₂²×C₃₁	1	2	yes	complemented
544	#478	C₂²×C₃₁	1	2	yes	complemented
545	#478	C₂²×C₃₁	1	2	yes	complemented
546	#477	C₂²×C₃₁	1	2	yes	complemented
547	#474	C₂²×C₃₁	1	2	yes	complemented
548	#469	C₂²×C₃₁	1	2	yes	complemented
549	#468	C₂²×C₃₁	1	2	yes	complemented
550	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
551	#466	C₂²×C₃₁	1	1	yes	characteristic
552	#466	C₂²×C₃₁	1	2	yes	complemented
553	#465	C₂²×C₃₁	1	2	yes	complemented
554	#465	C₂²×C₃₁	1	2	yes	complemented
555	#464	C₂²×C₃₁	1	2	yes	complemented
556	#463	C₂²×C₃₁	1	2	yes	complemented
557	#463	C₂²×C₃₁	1	2	yes	complemented
558	#463	C₂²×C₃₁	1	2	yes	complemented
559	#459	C₂²×C₃₁	1	2	yes	—
560	#459	C₂²×C₃₁	1	2	yes	complemented
561	#452	C₂²×C₃₁	1	2	yes	complemented
562	#450	C₂²×C₃₁	1	2	yes	complemented
563	#449	C₂²×C₃₁	1	2	yes	—
564	#447	C₂²×C₃₁	1	2	yes	—
565	#447	C₂²×C₃₁	1	2	yes	complemented
566	#447	C₂²×C₃₁	1	2	yes	complemented
567	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
569	#442	C₂²×C₃₁	1	2	yes	—
570	#442	C₂²×C₃₁	1	2	yes	complemented
571	#442	C₂²×C₃₁	1	2	yes	complemented
572	#440	C₂²×C₃₁	1	2	yes	complemented
573	#440	C₂²×C₃₁	1	2	yes	complemented
574	#440	C₂²×C₃₁	1	2	yes	complemented
575	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
576	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
577	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
578	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
579	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
580	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
581	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
582	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
583	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
585	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#435	C₂²×C₃₁	1	2	yes	complemented
588	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
589	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
590	#433	C₂²×C₃₁	1	2	yes	complemented
591	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
592	#428	C₂²×C₃₁	1	2	yes	complemented
593	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
594	#416	C₂²×C₃₁	1	2	yes	complemented
595	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
596	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
597	#405	C₂²×C₃₁	1	2	yes	complemented
598	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	C₂×C₃₁	—	2	2	no	—
600	C₂×C₃₁	—	4	2	no	—
601	C₂×C₃₁	—	4	4	no	—
602	C₂×C₃₁	—	8	2	no	—
603	C₂×C₃₁	—	8	2	no	—
604	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
605	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
606	C₂×C₃₁	#3584	1	1	yes	characteristic
607	C₂×#41	—	2	2	no	—
608	C₂×#41	C₂³×C₃₁	1	2	yes	—
609	C₂²×D₄	—	2	2	no	—
610	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
611	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
612	C₂³×C₄	—	2	2	no	—
613	AGL(1,ℤ/8)	—	2	8	no	—
614	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
615	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
616	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
617	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
618	C₂×D₈	—	2	4	no	—
619	C₂×D₈	C₂³×C₃₁	1	2	yes	—
620	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
621	C₂×D₈	C₂³×C₃₁	1	2	yes	—
622	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
623	C₂×D₈	C₂³×C₃₁	1	2	yes	—
624	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
626	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
627	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
628	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
629	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
630	#127	C₂³×C₃₁	1	2	yes	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#126	D₄×C₃₁	1	2	yes	—
636	#125	—	2	2	no	—
637	#125	D₄×C₃₁	1	1	yes	characteristic
638	#125	C₂³×C₃₁	1	2	yes	—
639	#125	C₂³×C₃₁	1	2	yes	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	D₄×C₃₁	1	1	yes	characteristic
643	#124	C₂³×C₃₁	1	2	yes	—
644	#124	C₂³×C₃₁	1	2	yes	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	#123	—	2	2	no	—
654	#123	—	2	2	no	—
655	#123	—	2	2	no	—
656	#123	—	2	2	no	—
657	#123	D₄×C₃₁	1	2	yes	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
664	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
665	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	—	2	2	no	—
672	#121	D₄×C₃₁	1	1	yes	characteristic
673	#121	C₂³×C₃₁	1	2	yes	—
674	#121	C₂³×C₃₁	1	2	yes	—
675	#121	C₂³×C₃₁	1	2	yes	—
676	#121	C₂³×C₃₁	1	2	yes	—
677	#120	—	2	2	no	—
678	#120	—	2	2	no	—
679	#120	—	2	2	no	—
680	#120	—	2	2	no	—
681	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
682	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
683	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	C₂³×C₃₁	1	2	yes	—
694	C₄×D₄	C₂³×C₃₁	1	2	yes	—
695	C₄×D₄	C₂³×C₃₁	1	2	yes	—
696	C₄×D₄	C₂³×C₃₁	1	2	yes	—
697	C₄×D₄	C₂³×C₃₁	1	2	yes	—
698	C₄×D₄	C₂³×C₃₁	1	2	yes	—
699	C₄×D₄	C₂³×C₃₁	1	2	yes	—
700	C₄×D₄	C₂³×C₃₁	1	2	yes	—
701	C₄×D₄	C₂³×C₃₁	1	2	yes	—
702	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
703	#117	—	2	2	no	—
704	#117	—	2	2	no	—
705	#117	—	2	2	no	—
706	#117	C₂³×C₃₁	1	2	yes	—
707	#117	C₂³×C₃₁	1	2	yes	—
708	C₂×C₄⋊C₄	—	2	2	no	—
709	C₂×C₄⋊C₄	—	2	2	no	—
710	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
712	C₂×C₂²⋊C₄	—	2	2	no	—
713	C₂×C₂²⋊C₄	—	2	2	no	—
714	C₂×C₂²⋊C₄	—	2	2	no	—
715	C₂×C₂²⋊C₄	—	2	2	no	—
716	C₂×C₂²⋊C₄	—	2	2	no	—
717	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
718	#107	C₂³×C₃₁	1	1	yes	characteristic
719	#107	C₂³×C₃₁	1	1	yes	characteristic
720	#107	C₂³×C₃₁	1	2	yes	—
721	#107	C₂³×C₃₁	1	2	yes	—
722	#107	C₂³×C₃₁	1	1	yes	characteristic
723	#107	C₂³×C₃₁	1	1	yes	characteristic
724	#107	C₂³×C₃₁	1	2	yes	—
725	#106	C₂³×C₃₁	1	2	yes	—
726	#106	C₂³×C₃₁	1	2	yes	—
727	#106	C₂³×C₃₁	1	2	yes	—
728	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
730	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
731	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
732	#103	C₂³×C₃₁	1	2	yes	—
733	#103	C₂³×C₃₁	1	2	yes	—
734	#103	C₂³×C₃₁	1	2	yes	—
735	#103	C₂³×C₃₁	1	2	yes	—
736	#102	C₂³×C₃₁	1	2	yes	—
737	#102	C₂³×C₃₁	1	2	yes	—
738	#102	C₂³×C₃₁	1	2	yes	—
739	#102	C₂³×C₃₁	1	2	yes	—
740	#102	C₂³×C₃₁	1	2	yes	—
741	#102	C₂³×C₃₁	1	2	yes	—
742	#102	C₂³×C₃₁	1	2	yes	—
743	#102	C₂³×C₃₁	1	2	yes	—
744	#102	C₂³×C₃₁	1	2	yes	—
745	#102	C₂³×C₃₁	1	2	yes	—
746	#102	C₂³×C₃₁	1	2	yes	—
747	#102	C₂³×C₃₁	1	2	yes	—
748	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
749	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
750	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
751	#97	C₂³×C₃₁	1	2	yes	—
752	#97	C₂³×C₃₁	1	2	yes	—
753	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
754	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
756	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
757	C₄×C₈	C₂³×C₃₁	1	2	yes	—
758	C₃₁	#61489	1	1	yes	characteristic, direct product factor, Sylow
759	C₂⁴	—	2	2	no	—
760	C₂⁴	—	2	2	no	—
761	#41	—	2	4	no	—
762	#41	—	4	2	no	—
763	#41	—	8	4	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
766	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
767	C₂×D₄	—	2	4	no	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	8	4	no	—
781	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
782	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
783	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
784	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
785	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	8	4	no	—
798	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
802	Q₁₆	—	4	1	no	—
803	SD₁₆	—	2	4	no	—
804	SD₁₆	—	2	4	no	—
805	SD₁₆	—	4	2	no	—
806	D₈	—	2	4	no	—
807	D₈	—	2	4	no	—
808	D₈	—	2	2	no	—
809	D₈	—	4	2	no	—
810	D₈	—	4	1	no	—
811	D₈	#41×C₃₁	1	4	yes	complemented
812	M₁₆	—	2	4	no	—
813	C₂×C₈	—	2	2	no	—
814	C₂×C₈	—	4	2	no	—
815	C₂×C₈	—	4	1	no	—
816	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
817	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
818	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
819	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
820	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
821	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
834	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
835	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
836	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
837	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
838	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
839	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
840	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
841	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
863	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
864	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
865	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
866	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
871	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
872	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
873	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
874	C₄²	C₂⁴×C₃₁	1	2	yes	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	4	4	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	4	4	no	—
881	C₂³	—	8	2	no	—
882	C₂³	—	8	2	no	—
883	C₂³	—	8	2	no	—
884	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
885	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
886	Q₈	—	2	2	no	—
887	Q₈	—	2	2	no	—
888	Q₈	—	4	1	no	—
889	Q₈	—	8	2	no	—
890	D₄	—	2	4	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	2	2	no	—
895	D₄	—	2	2	no	—
896	D₄	—	4	1	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	4	4	no	—
900	D₄	—	4	4	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	D₄	—	8	2	no	—
904	D₄	—	8	2	no	—
905	D₄	—	8	2	no	—
906	D₄	C₂×#41×C₃₁	1	4	yes	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	—	8	2	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	2	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
931	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
937	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
938	C₈	—	2	1	no	—
939	C₈	—	2	2	no	—
940	C₈	—	2	1	no	—
941	C₈	—	2	2	no	—
942	C₈	—	2	1	no	—
943	C₈	C₂×#41×C₃₁	1	2	yes	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	4	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	8	8	no	—
959	C₂²	—	16	4	no	—
960	C₂²	C₃₁×#576	1	2	yes	—
961	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
962	C₄	—	2	2	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	2	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
976	C₄	C₃₁×#585	1	1	yes	characteristic
977	C₂	—	2	2	no	—
978	C₂	—	4	2	no	—
979	C₂	—	4	4	no	—
980	C₂	—	8	2	no	—
981	C₂	—	8	2	no	—
982	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
983	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
984	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3513	C₂	semidirect
2. C₃₁×#3403	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3361	C₂	semidirect
5. C₃₁×#3355	C₂	semidirect
6. C₃₁×#3343	C₂	semidirect
7. C₃₁×#3297	C₂	semidirect
8. C₃₁×#3296	C₂	semidirect
9. C₃₁×#3294	C₂	semidirect
10. C₃₁×#3273	C₂	semidirect
11. C₃₁×#3264	C₂	semidirect
12. C₃₁×#3179	C₂	semidirect
13. C₃₁×#3168	C₂	semidirect
14. C₃₁×#3124	C₂	semidirect
15. C₃₁×#3122	C₂	semidirect
16. C₃₁×#3114	C₂	semidirect
17. C₃₁×#2966	C₂	semidirect
18. C₃₁×#2946	C₂	semidirect
19. C₂×C₄×D₈×C₃₁	C₂	semidirect
22. C₃₁×#559	C₂²	semidirect
23. C₃₁×#554	C₂²	semidirect
25. C₃₁×#553	C₂²	semidirect
26. C₃₁×#552	C₂²	semidirect
32. C₃₁×#546	C₂²	semidirect
33. D₄²×C₃₁	C₂²	semidirect
34. C₃₁×#542	C₂²	semidirect
35. C₃₁×#540	C₂²	semidirect
39. C₃₁×#529	C₂²	semidirect
42. C₃₁×#520	C₂²	semidirect
43. C₃₁×#518	C₂²	semidirect
44. C₂×C₄×D₄×C₃₁	C₂²	semidirect
45. C₃₁×#501	C₂²	semidirect
46. C₃₁×#499	C₂²	semidirect
47. C₃₁×#496	C₂²	semidirect
48. C₃₁×#495	C₂²	semidirect
49. C₃₁×#488	C₂²	semidirect
50. C₃₁×#488	C₂²	semidirect
51. C₃₁×#486	C₂²	semidirect
52. C₃₁×#484	C₂²	semidirect
53. C₃₁×#483	C₂²	semidirect
54. C₃₁×#482	C₂²	semidirect
55. C₃₁×#482	C₂²	semidirect
56. C₃₁×#480	C₂²	semidirect
57. C₃₁×#480	C₂²	semidirect
58. C₃₁×#478	C₂²	semidirect
59. C₃₁×#478	C₂²	semidirect
60. C₃₁×#478	C₂²	semidirect
61. C₃₁×#478	C₂²	semidirect
62. C₃₁×#477	C₂²	semidirect
63. C₃₁×#474	C₂²	semidirect
64. C₃₁×#469	C₂²	semidirect
65. C₃₁×#468	C₂²	semidirect
66. C₃₁×#467	C₂²	semidirect
68. C₃₁×#466	C₂²	semidirect
69. C₃₁×#465	C₂²	semidirect
70. C₃₁×#465	C₂²	semidirect
71. C₃₁×#464	C₂²	semidirect
72. C₃₁×#463	C₂²	semidirect
73. C₃₁×#463	C₂²	semidirect
74. C₃₁×#463	C₂²	semidirect
76. C₃₁×#459	C₂²	semidirect
77. C₃₁×#452	C₂²	semidirect
78. C₃₁×#450	C₂²	semidirect
81. C₃₁×#447	C₂²	semidirect
82. C₃₁×#447	C₂²	semidirect
83. C₃₁×#446	C₂²	semidirect
84. C₈×Q₈×C₃₁	C₂²	semidirect
86. C₃₁×#442	C₂²	semidirect
87. C₃₁×#442	C₂²	semidirect
88. C₃₁×#440	C₂²	semidirect
89. C₃₁×#440	C₂²	semidirect
90. C₃₁×#440	C₂²	semidirect
91. C₄×Q₁₆×C₃₁	C₂²	semidirect
92. C₄×SD₁₆×C₃₁	C₂²	semidirect
93. C₄×SD₁₆×C₃₁	C₂²	semidirect
96. C₄×D₈×C₃₁	C₂²	semidirect
97. C₄×D₈×C₃₁	C₂²	semidirect
98. C₄×D₈×C₃₁	C₂²	semidirect
99. C₄×D₈×C₃₁	C₂²	semidirect
100. C₄×D₈×C₃₁	C₂²	semidirect
101. C₄×D₈×C₃₁	C₂²	semidirect
102. C₃₁×#436	C₂²	semidirect
103. C₃₁×#435	C₂²	semidirect
104. C₈×D₄×C₃₁	C₂²	semidirect
105. C₈×D₄×C₃₁	C₂²	semidirect
106. C₃₁×#433	C₂²	semidirect
107. C₃₁×#432	C₂²	semidirect
108. C₃₁×#428	C₂²	semidirect
109. C₂×C₃₁×#107	C₂²	semidirect
110. C₃₁×#416	C₂²	semidirect
111. C₂×C₃₁×#102	C₂²	semidirect
112. C₂×C₃₁×#102	C₂²	semidirect
113. C₃₁×#405	C₂²	semidirect
114. C₂×C₄×C₈×C₃₁	C₂²	semidirect
318. D₈×C₃₁	#41	semidirect
382. #61489	C₃₁	direct (N × H)
452. #3513	C₂×C₃₁	semidirect
453. #3403	C₂×C₃₁	semidirect
454. #3389	C₂×C₃₁	semidirect
455. #3361	C₂×C₃₁	semidirect
456. #3355	C₂×C₃₁	semidirect
457. #3343	C₂×C₃₁	semidirect
458. #3297	C₂×C₃₁	semidirect
459. #3296	C₂×C₃₁	semidirect
460. #3294	C₂×C₃₁	semidirect
461. #3273	C₂×C₃₁	semidirect
462. #3264	C₂×C₃₁	semidirect
463. #3179	C₂×C₃₁	semidirect
464. #3168	C₂×C₃₁	semidirect
465. #3124	C₂×C₃₁	semidirect
466. #3122	C₂×C₃₁	semidirect
467. #3114	C₂×C₃₁	semidirect
468. #2966	C₂×C₃₁	semidirect
469. #2946	C₂×C₃₁	semidirect
470. C₂×C₄×D₈	C₂×C₃₁	semidirect
506. #559	C₂²×C₃₁	semidirect
507. #554	C₂²×C₃₁	semidirect
509. #553	C₂²×C₃₁	semidirect
510. #552	C₂²×C₃₁	semidirect
516. #546	C₂²×C₃₁	semidirect
517. D₄²	C₂²×C₃₁	semidirect
518. #542	C₂²×C₃₁	semidirect
519. #540	C₂²×C₃₁	semidirect
523. #529	C₂²×C₃₁	semidirect
526. #520	C₂²×C₃₁	semidirect
527. #518	C₂²×C₃₁	semidirect
528. C₂×C₄×D₄	C₂²×C₃₁	semidirect
529. #501	C₂²×C₃₁	semidirect
530. #499	C₂²×C₃₁	semidirect
531. #496	C₂²×C₃₁	semidirect
532. #495	C₂²×C₃₁	semidirect
533. #488	C₂²×C₃₁	semidirect
534. #488	C₂²×C₃₁	semidirect
535. #486	C₂²×C₃₁	semidirect
536. #484	C₂²×C₃₁	semidirect
537. #483	C₂²×C₃₁	semidirect
538. #482	C₂²×C₃₁	semidirect
539. #482	C₂²×C₃₁	semidirect
540. #480	C₂²×C₃₁	semidirect
541. #480	C₂²×C₃₁	semidirect
542. #478	C₂²×C₃₁	semidirect
543. #478	C₂²×C₃₁	semidirect
544. #478	C₂²×C₃₁	semidirect
545. #478	C₂²×C₃₁	semidirect
546. #477	C₂²×C₃₁	semidirect
547. #474	C₂²×C₃₁	semidirect
548. #469	C₂²×C₃₁	semidirect
549. #468	C₂²×C₃₁	semidirect
550. #467	C₂²×C₃₁	semidirect
552. #466	C₂²×C₃₁	semidirect
553. #465	C₂²×C₃₁	semidirect
554. #465	C₂²×C₃₁	semidirect
555. #464	C₂²×C₃₁	semidirect
556. #463	C₂²×C₃₁	semidirect
557. #463	C₂²×C₃₁	semidirect
558. #463	C₂²×C₃₁	semidirect
560. #459	C₂²×C₃₁	semidirect
561. #452	C₂²×C₃₁	semidirect
562. #450	C₂²×C₃₁	semidirect
565. #447	C₂²×C₃₁	semidirect
566. #447	C₂²×C₃₁	semidirect
567. #446	C₂²×C₃₁	semidirect
568. C₈×Q₈	C₂²×C₃₁	semidirect
570. #442	C₂²×C₃₁	semidirect
571. #442	C₂²×C₃₁	semidirect
572. #440	C₂²×C₃₁	semidirect
573. #440	C₂²×C₃₁	semidirect
574. #440	C₂²×C₃₁	semidirect
575. C₄×Q₁₆	C₂²×C₃₁	semidirect
576. C₄×SD₁₆	C₂²×C₃₁	semidirect
577. C₄×SD₁₆	C₂²×C₃₁	semidirect
580. C₄×D₈	C₂²×C₃₁	semidirect
581. C₄×D₈	C₂²×C₃₁	semidirect
582. C₄×D₈	C₂²×C₃₁	semidirect
583. C₄×D₈	C₂²×C₃₁	semidirect
584. C₄×D₈	C₂²×C₃₁	semidirect
585. C₄×D₈	C₂²×C₃₁	semidirect
586. #436	C₂²×C₃₁	semidirect
587. #435	C₂²×C₃₁	semidirect
588. C₈×D₄	C₂²×C₃₁	semidirect
589. C₈×D₄	C₂²×C₃₁	semidirect
590. #433	C₂²×C₃₁	semidirect
591. #432	C₂²×C₃₁	semidirect
592. #428	C₂²×C₃₁	semidirect
593. C₂×#107	C₂²×C₃₁	semidirect
594. #416	C₂²×C₃₁	semidirect
595. C₂×#102	C₂²×C₃₁	semidirect
596. C₂×#102	C₂²×C₃₁	semidirect
597. #405	C₂²×C₃₁	semidirect
598. C₂×C₄×C₈	C₂²×C₃₁	semidirect
758. C₃₁	#61489	direct (N × H)
811. D₈	#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×#3513	2
C₃₁×#3403	2
C₃₁×#3389	2
C₃₁×#3361	2
C₃₁×#3355	2
C₃₁×#3343	2
C₃₁×#3297	2
C₃₁×#3296	2
C₃₁×#3294	2
C₃₁×#3273	2
C₃₁×#3264	2
C₃₁×#3179	2
C₃₁×#3168	2
C₃₁×#3124	2
C₃₁×#3122	2
C₃₁×#3114	2
C₃₁×#2966	2
C₃₁×#2946	2
C₂×C₄×D₈×C₃₁	2
#61489	31

Subgroups — C31×#61489 #21518248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61489 #21518248