Subgroups — C₃₁×#61160 #21517919

Order 7936.

2172 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3333	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3332	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3317	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3309	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3304	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3094	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3005	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₃₁	C₂²	1	2	yes	—
19	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
22	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#553	C₂²	1	2	yes	complemented
26	C₃₁×#552	—	2	1	no	—
27	C₃₁×#552	C₂²	1	2	yes	complemented
28	C₃₁×#551	—	2	2	no	—
29	C₃₁×#550	—	2	1	no	—
30	C₃₁×#550	—	2	1	no	—
31	C₃₁×#550	—	2	2	no	—
32	C₃₁×#550	C₂²	1	2	yes	—
33	C₃₁×#550	C₂²	1	2	yes	—
34	C₃₁×#550	C₂²	1	4	yes	—
35	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#546	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#127	—	2	1	no	—
39	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
40	C₃₁×#529	—	2	2	no	—
41	C₃₁×#529	—	2	1	no	—
42	C₃₁×#525	C₂²	1	2	yes	—
43	C₂×C₃₁×#121	—	2	2	no	—
44	C₂×C₃₁×#121	C₂²	1	2	yes	—
45	C₄×#41×C₃₁	—	2	1	no	—
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₃₁	—	2	1	no	—
49	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#117	C₂²	1	2	yes	—
51	C₃₁×#490	C₂²	1	4	yes	complemented
52	C₃₁×#486	C₂²	1	2	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	complemented
54	C₃₁×#482	C₂²	1	4	yes	complemented
55	C₃₁×#482	C₂²	1	4	yes	complemented
56	C₃₁×#481	C₂²	1	4	yes	complemented
57	C₃₁×#480	C₂²	1	4	yes	complemented
58	C₃₁×#479	C₂²	1	4	yes	complemented
59	C₃₁×#477	C₂²	1	2	yes	complemented
60	C₃₁×#475	C₂²	1	2	yes	complemented
61	C₃₁×#469	C₂²	1	4	yes	complemented
62	C₃₁×#468	C₂²	1	4	yes	complemented
63	C₃₁×#466	C₂²	1	4	yes	complemented
64	C₃₁×#465	C₂²	1	4	yes	complemented
65	C₃₁×#460	C₂²	1	2	yes	complemented
66	C₃₁×#460	C₂²	1	2	yes	complemented
67	C₃₁×#459	C₂²	1	2	yes	complemented
68	C₃₁×#459	C₂²	1	2	yes	complemented
69	C₃₁×#452	C₂²	1	4	yes	complemented
70	C₃₁×#452	C₂²	1	4	yes	complemented
71	C₃₁×#449	C₂²	1	4	yes	complemented
72	C₃₁×#449	C₂²	1	4	yes	complemented
73	C₃₁×#441	C₂²	1	2	yes	complemented
74	C₃₁×#440	C₂²	1	2	yes	complemented
75	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
77	C₃₁×#436	C₂²	1	2	yes	complemented
78	C₃₁×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
80	C₃₁×#428	C₂²	1	2	yes	—
81	C₃₁×#428	C₂²	1	1	yes	characteristic
82	C₃₁×#423	C₂²	1	1	yes	characteristic
83	C₃₁×#419	C₂²	1	2	yes	—
84	C₃₁×#419	C₂²	1	1	yes	characteristic
85	C₃₁×#418	C₂²	1	2	yes	—
86	C₃₁×#418	C₂²	1	2	yes	—
87	C₃₁×#418	C₂²	1	2	yes	—
88	C₃₁×#417	C₂²	1	1	yes	characteristic
89	C₃₁×#417	C₂²	1	4	yes	complemented
90	C₃₁×#417	C₂²	1	4	yes	complemented
91	C₃₁×#416	C₂²	1	4	yes	complemented
92	C₃₁×#416	C₂²	1	4	yes	complemented
93	C₃₁×#407	C₂²	1	2	yes	—
94	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂×#41×C₃₁	—	2	8	no	—
99	C₂×#41×C₃₁	—	4	4	no	—
100	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
101	C₂×#41×C₃₁	C₂³	1	4	yes	—
102	C₂×#41×C₃₁	C₂³	1	4	yes	—
103	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₃₁	—	2	2	no	—
105	C₂²×D₄×C₃₁	—	2	2	no	—
106	C₂²×D₄×C₃₁	—	2	1	no	—
107	C₂²×D₄×C₃₁	—	2	1	no	—
108	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
110	C₂³×C₄×C₃₁	—	2	2	no	—
111	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
112	C₃₁×#137	—	2	4	no	—
113	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
114	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
117	C₂×D₈×C₃₁	C₂³	1	4	yes	—
118	C₂×M₁₆×C₃₁	—	4	4	no	—
119	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
122	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
123	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
124	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₃₁×#127	—	2	2	no	—
127	C₃₁×#127	—	2	2	no	—
128	C₃₁×#127	—	2	4	no	—
129	C₃₁×#127	—	2	1	no	—
130	C₃₁×#127	—	2	1	no	—
131	C₃₁×#127	C₂³	1	2	yes	—
132	C₃₁×#127	C₂³	1	2	yes	—
133	C₃₁×#126	—	2	2	no	—
134	C₃₁×#126	—	2	2	no	—
135	C₃₁×#126	—	2	2	no	—
136	C₃₁×#125	—	2	2	no	—
137	C₃₁×#125	—	2	1	no	—
138	C₃₁×#125	C₂³	1	2	yes	—
139	C₃₁×#124	—	2	1	no	—
140	C₃₁×#124	—	2	2	no	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×#123	—	2	2	no	—
143	C₃₁×#123	—	2	2	no	—
144	C₃₁×#123	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	—	2	1	no	—
146	C₃₁×C₂²⋊Q₈	—	2	1	no	—
147	C₃₁×C₂²⋊Q₈	—	2	1	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×#121	—	2	2	no	—
152	C₃₁×#121	—	2	1	no	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	4	no	—
156	C₃₁×#121	—	2	4	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#121	C₂³	1	2	yes	—
160	C₃₁×#121	C₂³	1	2	yes	—
161	C₃₁×#121	C₂³	1	4	yes	—
162	C₃₁×#121	C₂³	1	4	yes	—
163	C₃₁×#120	—	2	2	no	—
164	C₄×Q₈×C₃₁	—	2	1	no	—
165	C₄×Q₈×C₃₁	—	2	1	no	—
166	C₄×Q₈×C₃₁	—	2	1	no	—
167	C₄×Q₈×C₃₁	—	2	1	no	—
168	C₄×Q₈×C₃₁	—	2	1	no	—
169	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	4	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
183	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
184	C₄×D₄×C₃₁	D₄	1	2	yes	—
185	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₃₁	C₂³	1	2	yes	—
189	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₃₁×#117	—	2	2	no	—
191	C₃₁×#117	—	2	2	no	—
192	C₃₁×#117	—	2	1	no	—
193	C₃₁×#117	—	2	2	no	—
194	C₃₁×#117	—	2	1	no	—
195	C₃₁×#117	C₂³	1	2	yes	—
196	C₃₁×#117	C₂³	1	2	yes	—
197	C₃₁×#117	C₂³	1	1	yes	characteristic
198	C₃₁×#117	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
207	C₂×C₄²×C₃₁	—	2	2	no	—
208	C₂×C₄²×C₃₁	—	2	1	no	—
209	C₂×C₄²×C₃₁	—	2	1	no	—
210	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
211	C₃₁×#107	C₂³	1	2	yes	—
212	C₃₁×#107	C₂³	1	4	yes	—
213	C₃₁×#106	C₂³	1	2	yes	—
214	C₃₁×#106	C₂³	1	4	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
216	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	2	yes	—
218	C₃₁×#103	C₂³	1	2	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#103	C₂³	1	4	yes	—
221	C₃₁×#103	C₂³	1	2	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×#102	C₂³	1	2	yes	—
227	C₃₁×#102	C₂³	1	4	yes	—
228	C₃₁×#102	C₂³	1	4	yes	—
229	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₃₁×#97	C₂³	1	2	yes	—
232	C₄×C₈×C₃₁	C₂³	1	2	yes	—
233	C₂⁴×C₃₁	—	2	2	no	—
234	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
235	#41×C₃₁	—	2	8	no	—
236	#41×C₃₁	—	2	8	no	—
237	#41×C₃₁	—	2	2	no	—
238	#41×C₃₁	—	2	2	no	—
239	#41×C₃₁	—	4	4	no	—
240	#41×C₃₁	—	4	4	no	—
241	#41×C₃₁	—	4	8	no	—
242	#41×C₃₁	—	4	8	no	—
243	#41×C₃₁	—	4	4	no	—
244	C₂×Q₈×C₃₁	—	2	1	no	—
245	C₂×Q₈×C₃₁	—	2	1	no	—
246	C₂×Q₈×C₃₁	—	2	1	no	—
247	C₂×Q₈×C₃₁	—	2	2	no	—
248	C₂×Q₈×C₃₁	#41	1	4	yes	complemented
249	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	4	no	—
254	C₂×D₄×C₃₁	—	2	4	no	—
255	C₂×D₄×C₃₁	—	2	2	no	—
256	C₂×D₄×C₃₁	—	2	4	no	—
257	C₂×D₄×C₃₁	—	2	4	no	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	2	2	no	—
261	C₂×D₄×C₃₁	—	2	2	no	—
262	C₂×D₄×C₃₁	—	2	2	no	—
263	C₂×D₄×C₃₁	—	2	4	no	—
264	C₂×D₄×C₃₁	—	2	4	no	—
265	C₂×D₄×C₃₁	—	4	2	no	—
266	C₂×D₄×C₃₁	—	4	8	no	—
267	C₂×D₄×C₃₁	—	4	4	no	—
268	C₂×D₄×C₃₁	—	8	2	no	—
269	C₂×D₄×C₃₁	—	8	4	no	—
270	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
271	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
274	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	—	2	1	no	—
276	C₂²×C₄×C₃₁	—	2	4	no	—
277	C₂²×C₄×C₃₁	—	2	4	no	—
278	C₂²×C₄×C₃₁	—	2	1	no	—
279	C₂²×C₄×C₃₁	—	2	2	no	—
280	C₂²×C₄×C₃₁	—	2	2	no	—
281	C₂²×C₄×C₃₁	—	2	1	no	—
282	C₂²×C₄×C₃₁	—	2	1	no	—
283	C₂²×C₄×C₃₁	—	2	4	no	—
284	C₂²×C₄×C₃₁	—	2	4	no	—
285	C₂²×C₄×C₃₁	—	2	1	no	—
286	C₂²×C₄×C₃₁	—	4	8	no	—
287	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	Q₁₆×C₃₁	—	2	4	no	—
296	SD₁₆×C₃₁	—	2	4	no	—
297	SD₁₆×C₃₁	—	4	4	no	—
298	D₈×C₃₁	—	4	4	no	—
299	M₁₆×C₃₁	—	2	2	no	—
300	M₁₆×C₃₁	—	2	2	no	—
301	M₁₆×C₃₁	—	2	4	no	—
302	M₁₆×C₃₁	—	4	4	no	—
303	C₂×C₈×C₃₁	—	4	4	no	—
304	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
305	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
306	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₄⋊C₄×C₃₁	—	2	2	no	—
311	C₄⋊C₄×C₃₁	—	2	1	no	—
312	C₄⋊C₄×C₃₁	—	2	1	no	—
313	C₄⋊C₄×C₃₁	—	2	2	no	—
314	C₄⋊C₄×C₃₁	—	2	2	no	—
315	C₄⋊C₄×C₃₁	—	2	1	no	—
316	C₄⋊C₄×C₃₁	—	2	1	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	2	no	—
319	C₄⋊C₄×C₃₁	—	2	1	no	—
320	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
323	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
325	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
327	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
328	C₂²⋊C₄×C₃₁	—	2	1	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	4	no	—
335	C₂²⋊C₄×C₃₁	—	2	4	no	—
336	C₂²⋊C₄×C₃₁	—	2	2	no	—
337	C₂²⋊C₄×C₃₁	—	2	1	no	—
338	C₂²⋊C₄×C₃₁	—	2	1	no	—
339	C₂²⋊C₄×C₃₁	—	2	2	no	—
340	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₄²×C₃₁	—	2	1	no	—
345	C₄²×C₃₁	—	2	2	no	—
346	C₄²×C₃₁	—	2	1	no	—
347	C₄²×C₃₁	—	2	2	no	—
348	C₄²×C₃₁	—	2	2	no	—
349	C₄²×C₃₁	—	2	1	no	—
350	C₄²×C₃₁	—	2	2	no	—
351	C₄²×C₃₁	—	2	2	no	—
352	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
356	#61160	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
357	C₂³×C₃₁	—	2	4	no	—
358	C₂³×C₃₁	—	2	1	no	—
359	C₂³×C₃₁	—	2	4	no	—
360	C₂³×C₃₁	—	4	2	no	—
361	C₂³×C₃₁	—	4	2	no	—
362	C₂³×C₃₁	—	4	4	no	—
363	C₂³×C₃₁	—	4	4	no	—
364	C₂³×C₃₁	—	4	4	no	—
365	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
366	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
367	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
368	Q₈×C₃₁	—	2	4	no	—
369	Q₈×C₃₁	—	2	2	no	—
370	Q₈×C₃₁	—	2	1	no	—
371	Q₈×C₃₁	—	2	1	no	—
372	Q₈×C₃₁	—	4	2	no	—
373	Q₈×C₃₁	—	8	1	no	—
374	Q₈×C₃₁	C₂×#41	1	4	yes	—
375	D₄×C₃₁	—	2	2	no	—
376	D₄×C₃₁	—	2	2	no	—
377	D₄×C₃₁	—	2	1	no	—
378	D₄×C₃₁	—	2	4	no	—
379	D₄×C₃₁	—	2	1	no	—
380	D₄×C₃₁	—	2	4	no	—
381	D₄×C₃₁	—	4	2	no	—
382	D₄×C₃₁	—	4	8	no	—
383	D₄×C₃₁	—	4	8	no	—
384	D₄×C₃₁	—	4	4	no	—
385	D₄×C₃₁	—	4	4	no	—
386	D₄×C₃₁	—	4	2	no	—
387	D₄×C₃₁	—	4	4	no	—
388	D₄×C₃₁	—	4	4	no	—
389	D₄×C₃₁	—	8	2	no	—
390	D₄×C₃₁	—	8	2	no	—
391	D₄×C₃₁	—	8	2	no	—
392	D₄×C₃₁	—	8	4	no	—
393	D₄×C₃₁	—	8	4	no	—
394	C₂×C₄×C₃₁	—	2	4	no	—
395	C₂×C₄×C₃₁	—	2	4	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	4	no	—
398	C₂×C₄×C₃₁	—	2	4	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	1	no	—
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	4	1	no	—
411	C₂×C₄×C₃₁	—	4	8	no	—
412	C₂×C₄×C₃₁	—	4	8	no	—
413	C₂×C₄×C₃₁	—	4	2	no	—
414	C₂×C₄×C₃₁	—	4	4	no	—
415	C₂×C₄×C₃₁	—	4	2	no	—
416	C₂×C₄×C₃₁	—	4	2	no	—
417	C₂×C₄×C₃₁	—	8	1	no	—
418	C₂×C₄×C₃₁	—	8	2	no	—
419	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
427	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
428	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
429	C₈×C₃₁	—	2	2	no	—
430	C₈×C₃₁	—	2	2	no	—
431	C₈×C₃₁	—	2	4	no	—
432	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
433	C₂×#550	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#3333	C₂×C₃₁	1	2	yes	complemented
435	#3332	C₂×C₃₁	1	2	yes	complemented
436	#3317	C₂×C₃₁	1	4	yes	complemented
437	#3309	C₂×C₃₁	1	4	yes	complemented
438	#3305	C₂×C₃₁	1	2	yes	complemented
439	#3304	C₂×C₃₁	1	2	yes	complemented
440	#3138	C₂×C₃₁	1	1	yes	characteristic, complemented
441	#3094	C₂×C₃₁	1	2	yes	complemented
442	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
443	#3055	C₂×C₃₁	1	2	yes	complemented
444	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#3005	C₂×C₃₁	1	2	yes	complemented
446	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
447	D₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#2896	C₂×C₃₁	1	2	yes	complemented
449	C₂²×C₃₁	—	2	1	no	—
450	C₂²×C₃₁	—	2	1	no	—
451	C₂²×C₃₁	—	2	2	no	—
452	C₂²×C₃₁	—	2	2	no	—
453	C₂²×C₃₁	—	2	2	no	—
454	C₂²×C₃₁	—	2	2	no	—
455	C₂²×C₃₁	—	2	2	no	—
456	C₂²×C₃₁	—	2	2	no	—
457	C₂²×C₃₁	—	4	1	no	—
458	C₂²×C₃₁	—	4	4	no	—
459	C₂²×C₃₁	—	4	4	no	—
460	C₂²×C₃₁	—	4	1	no	—
461	C₂²×C₃₁	—	4	1	no	—
462	C₂²×C₃₁	—	4	4	no	—
463	C₂²×C₃₁	—	8	4	no	—
464	C₂²×C₃₁	—	8	8	no	—
465	C₂²×C₃₁	#546	1	2	yes	—
466	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
467	C₄×C₃₁	—	2	1	no	—
468	C₄×C₃₁	—	2	1	no	—
469	C₄×C₃₁	—	2	2	no	—
470	C₄×C₃₁	—	2	2	no	—
471	C₄×C₃₁	—	2	4	no	—
472	C₄×C₃₁	—	2	1	no	—
473	C₄×C₃₁	—	4	2	no	—
474	C₄×C₃₁	—	4	1	no	—
475	C₄×C₃₁	—	4	2	no	—
476	C₄×C₃₁	—	4	1	no	—
477	C₄×C₃₁	—	4	1	no	—
478	C₄×C₃₁	—	4	2	no	—
479	C₄×C₃₁	#546	1	2	yes	—
480	C₄×C₃₁	#575	1	2	yes	—
481	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
482	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂²×#41	C₂²×C₃₁	1	2	yes	—
484	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
485	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
486	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
487	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
488	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
489	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
490	#553	C₂²×C₃₁	1	2	yes	complemented
491	#552	—	2	1	no	—
492	#552	C₂²×C₃₁	1	2	yes	complemented
493	#551	—	2	2	no	—
494	#550	—	2	1	no	—
495	#550	—	2	1	no	—
496	#550	—	2	2	no	—
497	#550	C₂²×C₃₁	1	2	yes	—
498	#550	C₂²×C₃₁	1	2	yes	—
499	#550	C₂²×C₃₁	1	4	yes	—
500	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
501	#546	—	2	1	no	—
502	#533	C₂²×C₃₁	1	1	yes	characteristic
503	C₂×#127	—	2	1	no	—
504	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
505	#529	—	2	2	no	—
506	#529	—	2	1	no	—
507	#525	C₂²×C₃₁	1	2	yes	—
508	C₂×#121	—	2	2	no	—
509	C₂×#121	C₂²×C₃₁	1	2	yes	—
510	C₄×#41	—	2	1	no	—
511	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
512	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
513	C₂×C₄×D₄	—	2	1	no	—
514	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
515	C₂×#117	C₂²×C₃₁	1	2	yes	—
516	#490	C₂²×C₃₁	1	4	yes	complemented
517	#486	C₂²×C₃₁	1	2	yes	complemented
518	#486	C₂²×C₃₁	1	2	yes	complemented
519	#482	C₂²×C₃₁	1	4	yes	complemented
520	#482	C₂²×C₃₁	1	4	yes	complemented
521	#481	C₂²×C₃₁	1	4	yes	complemented
522	#480	C₂²×C₃₁	1	4	yes	complemented
523	#479	C₂²×C₃₁	1	4	yes	complemented
524	#477	C₂²×C₃₁	1	2	yes	complemented
525	#475	C₂²×C₃₁	1	2	yes	complemented
526	#469	C₂²×C₃₁	1	4	yes	complemented
527	#468	C₂²×C₃₁	1	4	yes	complemented
528	#466	C₂²×C₃₁	1	4	yes	complemented
529	#465	C₂²×C₃₁	1	4	yes	complemented
530	#460	C₂²×C₃₁	1	2	yes	complemented
531	#460	C₂²×C₃₁	1	2	yes	complemented
532	#459	C₂²×C₃₁	1	2	yes	complemented
533	#459	C₂²×C₃₁	1	2	yes	complemented
534	#452	C₂²×C₃₁	1	4	yes	complemented
535	#452	C₂²×C₃₁	1	4	yes	complemented
536	#449	C₂²×C₃₁	1	4	yes	complemented
537	#449	C₂²×C₃₁	1	4	yes	complemented
538	#441	C₂²×C₃₁	1	2	yes	complemented
539	#440	C₂²×C₃₁	1	2	yes	complemented
540	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
541	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
542	#436	C₂²×C₃₁	1	2	yes	complemented
543	#435	C₂²×C₃₁	1	4	yes	complemented
544	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
545	#428	C₂²×C₃₁	1	2	yes	—
546	#428	C₂²×C₃₁	1	1	yes	characteristic
547	#423	C₂²×C₃₁	1	1	yes	characteristic
548	#419	C₂²×C₃₁	1	2	yes	—
549	#419	C₂²×C₃₁	1	1	yes	characteristic
550	#418	C₂²×C₃₁	1	2	yes	—
551	#418	C₂²×C₃₁	1	2	yes	—
552	#418	C₂²×C₃₁	1	2	yes	—
553	#417	C₂²×C₃₁	1	1	yes	characteristic
554	#417	C₂²×C₃₁	1	4	yes	complemented
555	#417	C₂²×C₃₁	1	4	yes	complemented
556	#416	C₂²×C₃₁	1	4	yes	complemented
557	#416	C₂²×C₃₁	1	4	yes	complemented
558	#407	C₂²×C₃₁	1	2	yes	—
559	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
560	C₂×C₃₁	—	2	2	no	—
561	C₂×C₃₁	—	4	2	no	—
562	C₂×C₃₁	—	4	2	no	—
563	C₂×C₃₁	—	8	1	no	—
564	C₂×C₃₁	—	8	4	no	—
565	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
566	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
567	C₂×C₃₁	#3585	1	1	yes	characteristic
568	C₂×#41	—	2	1	no	—
569	C₂×#41	—	2	2	no	—
570	C₂×#41	—	2	2	no	—
571	C₂×#41	—	2	8	no	—
572	C₂×#41	—	4	4	no	—
573	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
574	C₂×#41	C₂³×C₃₁	1	4	yes	—
575	C₂×#41	C₂³×C₃₁	1	4	yes	—
576	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
577	C₂²×D₄	—	2	2	no	—
578	C₂²×D₄	—	2	2	no	—
579	C₂²×D₄	—	2	1	no	—
580	C₂²×D₄	—	2	1	no	—
581	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
582	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
583	C₂³×C₄	—	2	2	no	—
584	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
585	#137	—	2	4	no	—
586	AGL(1,ℤ/8)	—	4	4	no	—
587	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
588	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
589	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
590	C₂×D₈	C₂³×C₃₁	1	4	yes	—
591	C₂×M₁₆	—	4	4	no	—
592	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
593	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
594	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
595	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
596	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
597	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
598	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
599	#127	—	2	2	no	—
600	#127	—	2	2	no	—
601	#127	—	2	4	no	—
602	#127	—	2	1	no	—
603	#127	—	2	1	no	—
604	#127	C₂³×C₃₁	1	2	yes	—
605	#127	C₂³×C₃₁	1	2	yes	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#125	—	2	2	no	—
610	#125	—	2	1	no	—
611	#125	C₂³×C₃₁	1	2	yes	—
612	#124	—	2	1	no	—
613	#124	—	2	2	no	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	1	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
623	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
624	#121	—	2	2	no	—
625	#121	—	2	1	no	—
626	#121	—	2	2	no	—
627	#121	—	2	2	no	—
628	#121	—	2	4	no	—
629	#121	—	2	4	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	#121	C₂³×C₃₁	1	4	yes	—
633	#121	C₂³×C₃₁	1	4	yes	—
634	#121	C₂³×C₃₁	1	2	yes	—
635	#121	C₂³×C₃₁	1	2	yes	—
636	#120	—	2	2	no	—
637	C₄×Q₈	—	2	1	no	—
638	C₄×Q₈	—	2	1	no	—
639	C₄×Q₈	—	2	1	no	—
640	C₄×Q₈	—	2	1	no	—
641	C₄×Q₈	—	2	1	no	—
642	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
643	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
644	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
645	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
656	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
657	C₄×D₄	D₄×C₃₁	1	2	yes	—
658	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
659	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
660	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
661	C₄×D₄	C₂³×C₃₁	1	2	yes	—
662	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
663	#117	—	2	2	no	—
664	#117	—	2	2	no	—
665	#117	—	2	1	no	—
666	#117	—	2	2	no	—
667	#117	—	2	1	no	—
668	#117	C₂³×C₃₁	1	1	yes	characteristic
669	#117	C₂³×C₃₁	1	2	yes	—
670	#117	C₂³×C₃₁	1	2	yes	—
671	#117	C₂³×C₃₁	1	2	yes	—
672	C₂×C₄⋊C₄	—	2	1	no	—
673	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	—	2	2	no	—
678	C₂×C₂²⋊C₄	—	2	2	no	—
679	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
680	C₂×C₄²	—	2	2	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	—	2	1	no	—
683	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
684	#107	C₂³×C₃₁	1	2	yes	—
685	#107	C₂³×C₃₁	1	4	yes	—
686	#106	C₂³×C₃₁	1	2	yes	—
687	#106	C₂³×C₃₁	1	4	yes	—
688	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
689	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
690	#103	C₂³×C₃₁	1	2	yes	—
691	#103	C₂³×C₃₁	1	2	yes	—
692	#103	C₂³×C₃₁	1	4	yes	—
693	#103	C₂³×C₃₁	1	4	yes	—
694	#103	C₂³×C₃₁	1	2	yes	—
695	#102	C₂³×C₃₁	1	4	yes	—
696	#102	C₂³×C₃₁	1	4	yes	—
697	#102	C₂³×C₃₁	1	4	yes	—
698	#102	C₂³×C₃₁	1	4	yes	—
699	#102	C₂³×C₃₁	1	2	yes	—
700	#102	C₂³×C₃₁	1	4	yes	—
701	#102	C₂³×C₃₁	1	4	yes	—
702	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
703	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
704	#97	C₂³×C₃₁	1	2	yes	—
705	C₄×C₈	C₂³×C₃₁	1	2	yes	—
706	C₃₁	#61160	1	1	yes	characteristic, direct product factor, Sylow
707	C₂⁴	—	2	2	no	—
708	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
709	#41	—	2	8	no	—
710	#41	—	2	8	no	—
711	#41	—	2	2	no	—
712	#41	—	2	2	no	—
713	#41	—	4	4	no	—
714	#41	—	4	4	no	—
715	#41	—	4	8	no	—
716	#41	—	4	8	no	—
717	#41	—	4	4	no	—
718	C₂×Q₈	—	2	1	no	—
719	C₂×Q₈	—	2	1	no	—
720	C₂×Q₈	—	2	1	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	#41×C₃₁	1	4	yes	complemented
723	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
724	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	8	no	—
741	C₂×D₄	—	4	4	no	—
742	C₂×D₄	—	8	2	no	—
743	C₂×D₄	—	8	4	no	—
744	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
745	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
746	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
747	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
748	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	4	8	no	—
761	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
763	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
764	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
765	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
769	Q₁₆	—	2	4	no	—
770	SD₁₆	—	2	4	no	—
771	SD₁₆	—	4	4	no	—
772	D₈	—	4	4	no	—
773	M₁₆	—	2	2	no	—
774	M₁₆	—	2	2	no	—
775	M₁₆	—	2	4	no	—
776	M₁₆	—	4	4	no	—
777	C₂×C₈	—	4	4	no	—
778	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
779	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
780	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
795	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
796	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
797	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
798	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
799	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
800	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
802	C₂²⋊C₄	—	2	1	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	1	no	—
812	C₂²⋊C₄	—	2	1	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
816	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
817	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
818	C₄²	—	2	1	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	1	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	1	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
827	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
828	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
829	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
830	C₂³	—	2	4	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	4	no	—
833	C₂³	—	4	2	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	4	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
839	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
840	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
841	Q₈	—	2	4	no	—
842	Q₈	—	2	2	no	—
843	Q₈	—	2	1	no	—
844	Q₈	—	2	1	no	—
845	Q₈	—	4	2	no	—
846	Q₈	—	8	1	no	—
847	Q₈	C₂×#41×C₃₁	1	4	yes	—
848	D₄	—	2	2	no	—
849	D₄	—	2	2	no	—
850	D₄	—	2	1	no	—
851	D₄	—	2	4	no	—
852	D₄	—	2	1	no	—
853	D₄	—	2	4	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	8	no	—
857	D₄	—	4	4	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	4	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	4	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	2	4	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	4	no	—
871	C₂×C₄	—	2	4	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	8	no	—
885	C₂×C₄	—	4	8	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	4	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	8	1	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
893	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
897	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
898	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
899	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
900	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
901	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	4	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	4	4	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	4	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	4	no	—
919	C₂²	—	8	4	no	—
920	C₂²	—	8	8	no	—
921	C₂²	C₃₁×#546	1	2	yes	—
922	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	4	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	1	no	—
934	C₄	—	4	2	no	—
935	C₄	C₃₁×#546	1	2	yes	—
936	C₄	C₃₁×#575	1	2	yes	—
937	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
938	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
939	C₂	—	2	2	no	—
940	C₂	—	4	2	no	—
941	C₂	—	4	2	no	—
942	C₂	—	8	4	no	—
943	C₂	—	8	1	no	—
944	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
945	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
946	C₂	C₃₁×#3585	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×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3475	C₂	semidirect
2. C₂×C₃₁×#550	C₂	semidirect
3. C₃₁×#3333	C₂	semidirect
4. C₃₁×#3332	C₂	semidirect
5. C₃₁×#3317	C₂	semidirect
6. C₃₁×#3309	C₂	semidirect
7. C₃₁×#3305	C₂	semidirect
8. C₃₁×#3304	C₂	semidirect
9. C₃₁×#3138	C₂	semidirect
10. C₃₁×#3094	C₂	semidirect
11. C₃₁×#3078	C₂	semidirect
12. C₃₁×#3055	C₂	semidirect
13. C₃₁×#3038	C₂	semidirect
14. C₃₁×#3005	C₂	semidirect
15. C₄×C₃₁×#137	C₂	semidirect
16. D₄×M₁₆×C₃₁	C₂	semidirect
17. C₃₁×#2896	C₂	semidirect
22. C₃₁×#556	C₂²	semidirect
23. C₃₁×#555	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
25. C₃₁×#553	C₂²	semidirect
27. C₃₁×#552	C₂²	semidirect
35. C₃₁×#547	C₂²	semidirect
51. C₃₁×#490	C₂²	semidirect
52. C₃₁×#486	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
54. C₃₁×#482	C₂²	semidirect
55. C₃₁×#482	C₂²	semidirect
56. C₃₁×#481	C₂²	semidirect
57. C₃₁×#480	C₂²	semidirect
58. C₃₁×#479	C₂²	semidirect
59. C₃₁×#477	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#469	C₂²	semidirect
62. C₃₁×#468	C₂²	semidirect
63. C₃₁×#466	C₂²	semidirect
64. C₃₁×#465	C₂²	semidirect
65. C₃₁×#460	C₂²	semidirect
66. C₃₁×#460	C₂²	semidirect
67. C₃₁×#459	C₂²	semidirect
68. C₃₁×#459	C₂²	semidirect
69. C₃₁×#452	C₂²	semidirect
70. C₃₁×#452	C₂²	semidirect
71. C₃₁×#449	C₂²	semidirect
72. C₃₁×#449	C₂²	semidirect
73. C₃₁×#441	C₂²	semidirect
74. C₃₁×#440	C₂²	semidirect
75. C₄×Q₁₆×C₃₁	C₂²	semidirect
76. C₄×SD₁₆×C₃₁	C₂²	semidirect
77. C₃₁×#436	C₂²	semidirect
78. C₃₁×#435	C₂²	semidirect
79. C₈×D₄×C₃₁	C₂²	semidirect
89. C₃₁×#417	C₂²	semidirect
90. C₃₁×#417	C₂²	semidirect
91. C₃₁×#416	C₂²	semidirect
92. C₃₁×#416	C₂²	semidirect
248. C₂×Q₈×C₃₁	#41	semidirect
356. #61160	C₃₁	direct (N × H)
432. #3475	C₂×C₃₁	semidirect
433. C₂×#550	C₂×C₃₁	semidirect
434. #3333	C₂×C₃₁	semidirect
435. #3332	C₂×C₃₁	semidirect
436. #3317	C₂×C₃₁	semidirect
437. #3309	C₂×C₃₁	semidirect
438. #3305	C₂×C₃₁	semidirect
439. #3304	C₂×C₃₁	semidirect
440. #3138	C₂×C₃₁	semidirect
441. #3094	C₂×C₃₁	semidirect
442. #3078	C₂×C₃₁	semidirect
443. #3055	C₂×C₃₁	semidirect
444. #3038	C₂×C₃₁	semidirect
445. #3005	C₂×C₃₁	semidirect
446. C₄×#137	C₂×C₃₁	semidirect
447. D₄×M₁₆	C₂×C₃₁	semidirect
448. #2896	C₂×C₃₁	semidirect
487. #556	C₂²×C₃₁	semidirect
488. #555	C₂²×C₃₁	semidirect
489. #554	C₂²×C₃₁	semidirect
490. #553	C₂²×C₃₁	semidirect
492. #552	C₂²×C₃₁	semidirect
500. #547	C₂²×C₃₁	semidirect
516. #490	C₂²×C₃₁	semidirect
517. #486	C₂²×C₃₁	semidirect
518. #486	C₂²×C₃₁	semidirect
519. #482	C₂²×C₃₁	semidirect
520. #482	C₂²×C₃₁	semidirect
521. #481	C₂²×C₃₁	semidirect
522. #480	C₂²×C₃₁	semidirect
523. #479	C₂²×C₃₁	semidirect
524. #477	C₂²×C₃₁	semidirect
525. #475	C₂²×C₃₁	semidirect
526. #469	C₂²×C₃₁	semidirect
527. #468	C₂²×C₃₁	semidirect
528. #466	C₂²×C₃₁	semidirect
529. #465	C₂²×C₃₁	semidirect
530. #460	C₂²×C₃₁	semidirect
531. #460	C₂²×C₃₁	semidirect
532. #459	C₂²×C₃₁	semidirect
533. #459	C₂²×C₃₁	semidirect
534. #452	C₂²×C₃₁	semidirect
535. #452	C₂²×C₃₁	semidirect
536. #449	C₂²×C₃₁	semidirect
537. #449	C₂²×C₃₁	semidirect
538. #441	C₂²×C₃₁	semidirect
539. #440	C₂²×C₃₁	semidirect
540. C₄×Q₁₆	C₂²×C₃₁	semidirect
541. C₄×SD₁₆	C₂²×C₃₁	semidirect
542. #436	C₂²×C₃₁	semidirect
543. #435	C₂²×C₃₁	semidirect
544. C₈×D₄	C₂²×C₃₁	semidirect
554. #417	C₂²×C₃₁	semidirect
555. #417	C₂²×C₃₁	semidirect
556. #416	C₂²×C₃₁	semidirect
557. #416	C₂²×C₃₁	semidirect
706. C₃₁	#61160	direct (N × H)
722. C₂×Q₈	#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×#3475	2
C₂×C₃₁×#550	2
C₃₁×#3333	2
C₃₁×#3332	2
C₃₁×#3317	2
C₃₁×#3309	2
C₃₁×#3305	2
C₃₁×#3304	2
C₃₁×#3138	2
C₃₁×#3094	2
C₃₁×#3078	2
C₃₁×#3055	2
C₃₁×#3038	2
C₃₁×#3005	2
C₄×C₃₁×#137	2
D₄×M₁₆×C₃₁	2
C₃₁×#2896	2
#61160	31

Subgroups — C31×#61160 #21517919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61160 #21517919