Subgroups — C₃₁×#61339 #21518098

Order 7936.

1912 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3370	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3366	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3358	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3041	C₂	1	2	yes	maximal, complemented
14	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2948	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#559	C₂²	1	2	yes	complemented
21	C₃₁×#559	C₂²	1	2	yes	complemented
22	C₃₁×#554	—	2	1	no	—
23	C₃₁×#554	—	2	2	no	—
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#554	C₂²	1	4	yes	complemented
26	C₃₁×#550	C₂²	1	2	yes	complemented
27	C₃₁×#550	C₂²	1	2	yes	complemented
28	D₄×Q₈×C₃₁	—	2	1	no	—
29	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
30	C₃₁×#546	—	2	2	no	—
31	C₃₁×#546	—	2	2	no	—
32	C₃₁×#544	C₂²	1	2	yes	—
33	C₃₁×#543	—	2	2	no	—
34	C₃₁×#540	—	2	2	no	—
35	C₃₁×#535	C₂²	1	2	yes	—
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	—	2	1	no	—
39	C₃₁×#532	—	2	1	no	—
40	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
42	C₃₁×#518	C₂²	1	2	yes	—
43	C₃₁×#518	C₂²	1	2	yes	—
44	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₃₁×#490	C₂²	1	4	yes	complemented
47	C₃₁×#490	C₂²	1	4	yes	complemented
48	C₃₁×#489	C₂²	1	4	yes	complemented
49	C₃₁×#488	C₂²	1	4	yes	complemented
50	C₃₁×#486	C₂²	1	4	yes	complemented
51	C₃₁×#486	C₂²	1	2	yes	complemented
52	C₃₁×#486	C₂²	1	2	yes	complemented
53	C₃₁×#479	C₂²	1	2	yes	complemented
54	C₃₁×#478	C₂²	1	2	yes	complemented
55	C₃₁×#478	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#476	C₂²	1	4	yes	complemented
60	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#474	C₂²	1	4	yes	complemented
63	C₃₁×#463	C₂²	1	4	yes	complemented
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#459	C₂²	1	2	yes	—
66	C₃₁×#459	C₂²	1	4	yes	—
67	C₃₁×#459	C₂²	1	2	yes	—
68	C₃₁×#459	C₂²	1	4	yes	complemented
69	C₃₁×#459	C₂²	1	4	yes	complemented
70	C₃₁×#446	C₂²	1	4	yes	complemented
71	C₃₁×#446	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
73	C₃₁×#442	C₂²	1	2	yes	complemented
74	C₃₁×#442	C₂²	1	4	yes	complemented
75	C₃₁×#442	C₂²	1	4	yes	complemented
76	C₃₁×#440	C₂²	1	2	yes	complemented
77	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
78	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
79	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
80	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
81	C₃₁×#428	C₂²	1	1	yes	characteristic
82	C₃₁×#427	C₂²	1	2	yes	—
83	C₃₁×#424	C₂²	1	2	yes	—
84	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₃₁×#418	C₂²	1	2	yes	—
86	C₃₁×#418	C₂²	1	2	yes	—
87	C₃₁×#418	C₂²	1	1	yes	characteristic
88	C₃₁×#417	C₂²	1	1	yes	characteristic
89	C₃₁×#416	C₂²	1	2	yes	—
90	C₂×C₃₁×#102	C₂²	1	2	yes	—
91	C₃₁×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	—	2	2	no	—
94	C₂×#41×C₃₁	—	2	2	no	—
95	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₃₁	—	2	2	no	—
97	C₂²×D₄×C₃₁	—	2	1	no	—
98	C₂²×D₄×C₃₁	—	2	1	no	—
99	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
100	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₃₁	—	2	1	no	—
102	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×D₈×C₃₁	—	2	8	no	—
105	C₂×D₈×C₃₁	C₂³	1	4	yes	—
106	C₂×D₈×C₃₁	C₂³	1	2	yes	—
107	C₂×D₈×C₃₁	C₂³	1	4	yes	—
108	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
111	C₃₁×C₄⋊Q₈	—	2	2	no	—
112	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃₁×#127	—	2	1	no	—
118	C₃₁×#127	—	2	1	no	—
119	C₃₁×#127	C₂³	1	2	yes	—
120	C₃₁×#127	C₂³	1	2	yes	—
121	C₃₁×#127	C₂³	1	4	yes	—
122	C₃₁×#125	—	2	2	no	—
123	C₃₁×#125	D₄	1	2	yes	—
124	C₃₁×#125	C₂³	1	4	yes	—
125	C₃₁×#125	C₂³	1	2	yes	—
126	C₃₁×#124	—	2	2	no	—
127	C₃₁×#124	—	2	2	no	—
128	C₃₁×#124	C₂³	1	4	yes	—
129	C₃₁×#123	—	2	4	no	—
130	C₃₁×#123	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	—	2	1	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	4	no	—
139	C₃₁×C₂²⋊Q₈	—	2	4	no	—
140	C₃₁×C₂²⋊Q₈	—	2	4	no	—
141	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
143	C₃₁×#121	—	2	2	no	—
144	C₃₁×#121	—	2	2	no	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	—	2	4	no	—
148	C₃₁×#121	—	2	4	no	—
149	C₃₁×#120	—	2	4	no	—
150	C₄×Q₈×C₃₁	—	2	1	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
156	C₄×D₄×C₃₁	—	2	1	no	—
157	C₄×D₄×C₃₁	—	2	1	no	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₃₁	C₂³	1	2	yes	—
168	C₄×D₄×C₃₁	C₂³	1	4	yes	—
169	C₄×D₄×C₃₁	C₂³	1	4	yes	—
170	C₄×D₄×C₃₁	C₂³	1	4	yes	—
171	C₄×D₄×C₃₁	C₂³	1	4	yes	—
172	C₄×D₄×C₃₁	C₂³	1	2	yes	—
173	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₃₁×#117	—	2	1	no	—
175	C₃₁×#117	C₂³	1	2	yes	—
176	C₃₁×#117	C₂³	1	1	yes	characteristic
177	C₃₁×#117	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
179	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
183	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
184	C₂×C₄²×C₃₁	—	2	1	no	—
185	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
186	C₃₁×#107	C₂³	1	2	yes	—
187	C₃₁×#107	C₂³	1	2	yes	—
188	C₃₁×#107	C₂³	1	2	yes	—
189	C₃₁×#106	C₂³	1	2	yes	—
190	C₃₁×#106	C₂³	1	2	yes	—
191	C₃₁×#106	C₂³	1	2	yes	—
192	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
195	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
196	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
197	C₃₁×#103	C₂³	1	2	yes	—
198	C₃₁×#103	C₂³	1	2	yes	—
199	C₃₁×#103	C₂³	1	2	yes	—
200	C₃₁×#102	C₂³	1	4	yes	—
201	C₃₁×#102	C₂³	1	4	yes	—
202	C₃₁×#102	C₂³	1	2	yes	—
203	C₃₁×#102	C₂³	1	2	yes	—
204	C₃₁×#102	C₂³	1	2	yes	—
205	C₃₁×#102	C₂³	1	2	yes	—
206	C₃₁×#102	C₂³	1	2	yes	—
207	C₃₁×#102	C₂³	1	4	yes	—
208	C₃₁×#102	C₂³	1	4	yes	—
209	C₃₁×#102	C₂³	1	4	yes	—
210	C₃₁×#102	C₂³	1	4	yes	—
211	C₃₁×#97	C₂³	1	2	yes	—
212	C₃₁×#97	C₂³	1	4	yes	—
213	C₄×C₈×C₃₁	C₂³	1	2	yes	—
214	C₄×C₈×C₃₁	C₂³	1	4	yes	—
215	C₂⁴×C₃₁	—	2	1	no	—
216	C₂⁴×C₃₁	—	2	2	no	—
217	#41×C₃₁	—	2	2	no	—
218	#41×C₃₁	—	2	2	no	—
219	#41×C₃₁	—	8	4	no	—
220	#41×C₃₁	—	8	4	no	—
221	C₂×Q₈×C₃₁	—	2	1	no	—
222	C₂×Q₈×C₃₁	—	2	1	no	—
223	C₂×Q₈×C₃₁	—	2	4	no	—
224	C₂×Q₈×C₃₁	—	8	4	no	—
225	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
228	C₂×D₄×C₃₁	—	2	1	no	—
229	C₂×D₄×C₃₁	—	2	1	no	—
230	C₂×D₄×C₃₁	—	2	2	no	—
231	C₂×D₄×C₃₁	—	2	2	no	—
232	C₂×D₄×C₃₁	—	2	2	no	—
233	C₂×D₄×C₃₁	—	2	4	no	—
234	C₂×D₄×C₃₁	—	2	4	no	—
235	C₂×D₄×C₃₁	—	2	2	no	—
236	C₂×D₄×C₃₁	—	2	2	no	—
237	C₂×D₄×C₃₁	—	2	4	no	—
238	C₂×D₄×C₃₁	—	2	2	no	—
239	C₂×D₄×C₃₁	—	2	4	no	—
240	C₂×D₄×C₃₁	—	8	2	no	—
241	C₂×D₄×C₃₁	—	8	2	no	—
242	C₂×D₄×C₃₁	#41	1	4	yes	complemented
243	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
244	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₃₁	—	2	1	no	—
247	C₂²×C₄×C₃₁	—	2	1	no	—
248	C₂²×C₄×C₃₁	—	2	1	no	—
249	C₂²×C₄×C₃₁	—	2	1	no	—
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	4	no	—
252	C₂²×C₄×C₃₁	—	2	4	no	—
253	C₂²×C₄×C₃₁	—	2	4	no	—
254	C₂²×C₄×C₃₁	—	2	4	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	8	2	no	—
257	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	SD₁₆×C₃₁	—	2	4	no	—
261	D₈×C₃₁	—	2	8	no	—
262	D₈×C₃₁	—	2	8	no	—
263	D₈×C₃₁	—	2	4	no	—
264	M₁₆×C₃₁	—	2	2	no	—
265	M₁₆×C₃₁	—	2	2	no	—
266	C₂×C₈×C₃₁	—	2	4	no	—
267	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
268	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
269	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
270	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	4	no	—
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	—	2	4	no	—
276	C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₄⋊C₄×C₃₁	—	2	1	no	—
278	C₄⋊C₄×C₃₁	—	2	1	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
287	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂²⋊C₄×C₃₁	—	2	1	no	—
293	C₂²⋊C₄×C₃₁	—	2	2	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	4	no	—
297	C₂²⋊C₄×C₃₁	—	2	4	no	—
298	C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂²⋊C₄×C₃₁	—	2	2	no	—
300	C₂²⋊C₄×C₃₁	—	2	1	no	—
301	C₂²⋊C₄×C₃₁	—	2	1	no	—
302	C₂²⋊C₄×C₃₁	—	2	4	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
305	C₄²×C₃₁	—	2	1	no	—
306	C₄²×C₃₁	—	2	1	no	—
307	C₄²×C₃₁	—	2	1	no	—
308	C₄²×C₃₁	—	2	2	no	—
309	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₄²×C₃₁	C₂⁴	1	4	yes	—
313	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
314	#61339	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂³×C₃₁	—	2	2	no	—
316	C₂³×C₃₁	—	2	4	no	—
317	C₂³×C₃₁	—	2	4	no	—
318	C₂³×C₃₁	—	2	1	no	—
319	C₂³×C₃₁	—	4	4	no	—
320	C₂³×C₃₁	—	8	1	no	—
321	C₂³×C₃₁	—	8	1	no	—
322	C₂³×C₃₁	—	8	2	no	—
323	C₂³×C₃₁	—	8	2	no	—
324	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₃₁	—	2	4	no	—
326	Q₈×C₃₁	—	2	1	no	—
327	Q₈×C₃₁	—	2	1	no	—
328	Q₈×C₃₁	—	4	2	no	—
329	Q₈×C₃₁	—	4	2	no	—
330	Q₈×C₃₁	—	8	1	no	—
331	Q₈×C₃₁	—	8	4	no	—
332	D₄×C₃₁	—	2	4	no	—
333	D₄×C₃₁	—	2	4	no	—
334	D₄×C₃₁	—	2	1	no	—
335	D₄×C₃₁	—	2	2	no	—
336	D₄×C₃₁	—	2	4	no	—
337	D₄×C₃₁	—	2	1	no	—
338	D₄×C₃₁	—	4	4	no	—
339	D₄×C₃₁	—	4	2	no	—
340	D₄×C₃₁	—	4	4	no	—
341	D₄×C₃₁	—	4	4	no	—
342	D₄×C₃₁	—	8	2	no	—
343	D₄×C₃₁	—	8	2	no	—
344	D₄×C₃₁	—	8	4	no	—
345	D₄×C₃₁	—	8	4	no	—
346	D₄×C₃₁	C₂×#41	1	4	yes	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	1	no	—
349	C₂×C₄×C₃₁	—	2	1	no	—
350	C₂×C₄×C₃₁	—	2	1	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	4	1	no	—
355	C₂×C₄×C₃₁	—	4	2	no	—
356	C₂×C₄×C₃₁	—	4	2	no	—
357	C₂×C₄×C₃₁	—	4	4	no	—
358	C₂×C₄×C₃₁	—	4	2	no	—
359	C₂×C₄×C₃₁	—	8	4	no	—
360	C₂×C₄×C₃₁	—	8	2	no	—
361	C₂×C₄×C₃₁	—	8	4	no	—
362	C₂×C₄×C₃₁	—	8	4	no	—
363	C₂×C₄×C₃₁	—	8	4	no	—
364	C₂×C₄×C₃₁	—	8	1	no	—
365	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
369	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
373	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
374	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
375	C₈×C₃₁	—	2	2	no	—
376	C₈×C₃₁	—	2	2	no	—
377	C₈×C₃₁	—	2	2	no	—
378	C₈×C₃₁	—	2	2	no	—
379	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
380	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#3373	C₂×C₃₁	1	2	yes	complemented
382	#3370	C₂×C₃₁	1	4	yes	complemented
383	#3366	C₂×C₃₁	1	2	yes	complemented
384	#3366	C₂×C₃₁	1	4	yes	complemented
385	#3361	C₂×C₃₁	1	2	yes	complemented
386	#3358	C₂×C₃₁	1	2	yes	complemented
387	#3138	C₂×C₃₁	1	1	yes	characteristic, complemented
388	#3136	C₂×C₃₁	1	2	yes	complemented
389	#3081	C₂×C₃₁	1	2	yes	complemented
390	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
391	#3041	C₂×C₃₁	1	2	yes	complemented
392	C₂×#459	C₂×C₃₁	1	1	yes	characteristic, complemented
393	#2962	C₂×C₃₁	1	1	yes	characteristic, complemented
394	#2948	C₂×C₃₁	1	2	yes	complemented
395	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
396	C₂²×C₃₁	—	2	1	no	—
397	C₂²×C₃₁	—	2	1	no	—
398	C₂²×C₃₁	—	2	4	no	—
399	C₂²×C₃₁	—	4	2	no	—
400	C₂²×C₃₁	—	4	2	no	—
401	C₂²×C₃₁	—	4	1	no	—
402	C₂²×C₃₁	—	4	4	no	—
403	C₂²×C₃₁	—	4	1	no	—
404	C₂²×C₃₁	—	4	4	no	—
405	C₂²×C₃₁	—	4	1	no	—
406	C₂²×C₃₁	—	4	4	no	—
407	C₂²×C₃₁	—	8	4	no	—
408	C₂²×C₃₁	—	16	4	no	—
409	C₂²×C₃₁	#548	1	2	yes	—
410	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
411	C₄×C₃₁	—	2	1	no	—
412	C₄×C₃₁	—	2	1	no	—
413	C₄×C₃₁	—	2	4	no	—
414	C₄×C₃₁	—	2	1	no	—
415	C₄×C₃₁	—	2	4	no	—
416	C₄×C₃₁	—	4	1	no	—
417	C₄×C₃₁	—	4	2	no	—
418	C₄×C₃₁	—	4	1	no	—
419	C₄×C₃₁	—	4	1	no	—
420	C₄×C₃₁	—	4	2	no	—
421	C₄×C₃₁	—	4	2	no	—
422	C₄×C₃₁	#548	1	2	yes	—
423	C₄×C₃₁	#576	1	2	yes	—
424	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
425	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
426	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
427	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
428	#559	C₂²×C₃₁	1	2	yes	complemented
429	#559	C₂²×C₃₁	1	2	yes	complemented
430	#554	—	2	1	no	—
431	#554	—	2	2	no	—
432	#554	C₂²×C₃₁	1	2	yes	complemented
433	#554	C₂²×C₃₁	1	4	yes	complemented
434	#550	C₂²×C₃₁	1	2	yes	complemented
435	#550	C₂²×C₃₁	1	2	yes	complemented
436	D₄×Q₈	—	2	1	no	—
437	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
438	#546	—	2	2	no	—
439	#546	—	2	2	no	—
440	#544	C₂²×C₃₁	1	2	yes	—
441	#543	—	2	2	no	—
442	#540	—	2	2	no	—
443	#535	C₂²×C₃₁	1	2	yes	—
444	#533	C₂²×C₃₁	1	1	yes	characteristic
445	#533	C₂²×C₃₁	1	1	yes	characteristic
446	#532	—	2	1	no	—
447	#532	—	2	1	no	—
448	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×C₂²⋊Q₈	—	2	2	no	—
450	#518	C₂²×C₃₁	1	2	yes	—
451	#518	C₂²×C₃₁	1	2	yes	—
452	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
454	#490	C₂²×C₃₁	1	4	yes	complemented
455	#490	C₂²×C₃₁	1	4	yes	complemented
456	#489	C₂²×C₃₁	1	4	yes	complemented
457	#488	C₂²×C₃₁	1	4	yes	complemented
458	#486	C₂²×C₃₁	1	4	yes	complemented
459	#486	C₂²×C₃₁	1	2	yes	complemented
460	#486	C₂²×C₃₁	1	2	yes	complemented
461	#479	C₂²×C₃₁	1	2	yes	complemented
462	#478	C₂²×C₃₁	1	2	yes	complemented
463	#478	C₂²×C₃₁	1	4	yes	complemented
464	#478	C₂²×C₃₁	1	4	yes	complemented
465	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
466	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
467	#476	C₂²×C₃₁	1	4	yes	complemented
468	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
469	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
470	#474	C₂²×C₃₁	1	4	yes	complemented
471	#463	C₂²×C₃₁	1	4	yes	complemented
472	#463	C₂²×C₃₁	1	4	yes	complemented
473	#459	C₂²×C₃₁	1	2	yes	—
474	#459	C₂²×C₃₁	1	4	yes	—
475	#459	C₂²×C₃₁	1	2	yes	—
476	#459	C₂²×C₃₁	1	4	yes	complemented
477	#459	C₂²×C₃₁	1	4	yes	complemented
478	#446	C₂²×C₃₁	1	4	yes	complemented
479	#446	C₂²×C₃₁	1	2	yes	complemented
480	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
481	#442	C₂²×C₃₁	1	2	yes	complemented
482	#442	C₂²×C₃₁	1	4	yes	complemented
483	#442	C₂²×C₃₁	1	4	yes	complemented
484	#440	C₂²×C₃₁	1	2	yes	complemented
485	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
486	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
487	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
488	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
489	#428	C₂²×C₃₁	1	1	yes	characteristic
490	#427	C₂²×C₃₁	1	2	yes	—
491	#424	C₂²×C₃₁	1	2	yes	—
492	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
493	#418	C₂²×C₃₁	1	2	yes	—
494	#418	C₂²×C₃₁	1	2	yes	—
495	#418	C₂²×C₃₁	1	1	yes	characteristic
496	#417	C₂²×C₃₁	1	1	yes	characteristic
497	#416	C₂²×C₃₁	1	2	yes	—
498	C₂×#102	C₂²×C₃₁	1	2	yes	—
499	#405	C₂²×C₃₁	1	2	yes	—
500	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
501	C₂×C₃₁	—	2	2	no	—
502	C₂×C₃₁	—	4	4	no	—
503	C₂×C₃₁	—	8	1	no	—
504	C₂×C₃₁	—	8	4	no	—
505	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
506	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
507	C₂×C₃₁	#3585	1	1	yes	characteristic
508	C₂×#41	—	2	2	no	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
511	C₂²×Q₈	—	2	2	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
515	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
516	C₂³×C₄	—	2	1	no	—
517	AGL(1,ℤ/8)	—	2	4	no	—
518	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
519	C₂×D₈	—	2	8	no	—
520	C₂×D₈	C₂³×C₃₁	1	4	yes	—
521	C₂×D₈	C₂³×C₃₁	1	4	yes	—
522	C₂×D₈	C₂³×C₃₁	1	2	yes	—
523	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
524	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
525	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
528	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
532	#127	—	2	1	no	—
533	#127	—	2	1	no	—
534	#127	C₂³×C₃₁	1	2	yes	—
535	#127	C₂³×C₃₁	1	2	yes	—
536	#127	C₂³×C₃₁	1	4	yes	—
537	#125	—	2	2	no	—
538	#125	D₄×C₃₁	1	2	yes	—
539	#125	C₂³×C₃₁	1	2	yes	—
540	#125	C₂³×C₃₁	1	4	yes	—
541	#124	—	2	2	no	—
542	#124	—	2	2	no	—
543	#124	C₂³×C₃₁	1	4	yes	—
544	#123	—	2	4	no	—
545	#123	—	2	4	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	4	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	4	no	—
552	C₂²⋊Q₈	—	2	4	no	—
553	C₂²⋊Q₈	—	2	4	no	—
554	C₂²⋊Q₈	—	2	4	no	—
555	C₂²⋊Q₈	—	2	4	no	—
556	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
557	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
558	#121	—	2	2	no	—
559	#121	—	2	2	no	—
560	#121	—	2	2	no	—
561	#121	—	2	2	no	—
562	#121	—	2	4	no	—
563	#121	—	2	4	no	—
564	#120	—	2	4	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
568	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
569	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
570	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	C₂³×C₃₁	1	2	yes	—
582	C₄×D₄	C₂³×C₃₁	1	2	yes	—
583	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
584	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
585	C₄×D₄	C₂³×C₃₁	1	4	yes	—
586	C₄×D₄	C₂³×C₃₁	1	4	yes	—
587	C₄×D₄	C₂³×C₃₁	1	4	yes	—
588	C₄×D₄	C₂³×C₃₁	1	4	yes	—
589	#117	—	2	1	no	—
590	#117	C₂³×C₃₁	1	1	yes	characteristic
591	#117	C₂³×C₃₁	1	2	yes	—
592	#117	C₂³×C₃₁	1	2	yes	—
593	C₂×C₄⋊C₄	—	2	4	no	—
594	C₂×C₄⋊C₄	—	2	2	no	—
595	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	4	no	—
598	C₂×C₂²⋊C₄	—	2	4	no	—
599	C₂×C₄²	—	2	1	no	—
600	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
601	#107	C₂³×C₃₁	1	2	yes	—
602	#107	C₂³×C₃₁	1	2	yes	—
603	#107	C₂³×C₃₁	1	2	yes	—
604	#106	C₂³×C₃₁	1	2	yes	—
605	#106	C₂³×C₃₁	1	2	yes	—
606	#106	C₂³×C₃₁	1	2	yes	—
607	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
608	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
609	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
610	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
611	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
612	#103	C₂³×C₃₁	1	2	yes	—
613	#103	C₂³×C₃₁	1	2	yes	—
614	#103	C₂³×C₃₁	1	2	yes	—
615	#102	C₂³×C₃₁	1	4	yes	—
616	#102	C₂³×C₃₁	1	4	yes	—
617	#102	C₂³×C₃₁	1	2	yes	—
618	#102	C₂³×C₃₁	1	2	yes	—
619	#102	C₂³×C₃₁	1	2	yes	—
620	#102	C₂³×C₃₁	1	2	yes	—
621	#102	C₂³×C₃₁	1	2	yes	—
622	#102	C₂³×C₃₁	1	4	yes	—
623	#102	C₂³×C₃₁	1	4	yes	—
624	#102	C₂³×C₃₁	1	4	yes	—
625	#102	C₂³×C₃₁	1	4	yes	—
626	#97	C₂³×C₃₁	1	2	yes	—
627	#97	C₂³×C₃₁	1	4	yes	—
628	C₄×C₈	C₂³×C₃₁	1	2	yes	—
629	C₄×C₈	C₂³×C₃₁	1	4	yes	—
630	C₃₁	#61339	1	1	yes	characteristic, direct product factor, Sylow
631	C₂⁴	—	2	1	no	—
632	C₂⁴	—	2	2	no	—
633	#41	—	2	2	no	—
634	#41	—	2	2	no	—
635	#41	—	8	4	no	—
636	#41	—	8	4	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	4	no	—
640	C₂×Q₈	—	8	4	no	—
641	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
642	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
643	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	8	2	no	—
657	C₂×D₄	—	8	2	no	—
658	C₂×D₄	#41×C₃₁	1	4	yes	complemented
659	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
660	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
661	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	8	2	no	—
673	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
676	SD₁₆	—	2	4	no	—
677	D₈	—	2	8	no	—
678	D₈	—	2	8	no	—
679	D₈	—	2	4	no	—
680	M₁₆	—	2	2	no	—
681	M₁₆	—	2	2	no	—
682	C₂×C₈	—	2	4	no	—
683	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
684	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
685	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
686	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
698	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
699	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
700	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
702	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
703	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
705	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
707	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	2	1	no	—
724	C₄²	—	2	2	no	—
725	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
726	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
727	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₄²	C₂⁴×C₃₁	1	4	yes	—
729	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
730	C₂³	—	2	2	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	4	4	no	—
735	C₂³	—	8	1	no	—
736	C₂³	—	8	1	no	—
737	C₂³	—	8	2	no	—
738	C₂³	—	8	2	no	—
739	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
740	Q₈	—	2	4	no	—
741	Q₈	—	2	1	no	—
742	Q₈	—	2	1	no	—
743	Q₈	—	4	2	no	—
744	Q₈	—	4	2	no	—
745	Q₈	—	8	1	no	—
746	Q₈	—	8	4	no	—
747	D₄	—	2	4	no	—
748	D₄	—	2	4	no	—
749	D₄	—	2	1	no	—
750	D₄	—	2	2	no	—
751	D₄	—	2	4	no	—
752	D₄	—	2	1	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	4	no	—
756	D₄	—	4	4	no	—
757	D₄	—	8	2	no	—
758	D₄	—	8	2	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	C₂×#41×C₃₁	1	4	yes	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	8	4	no	—
775	C₂×C₄	—	8	2	no	—
776	C₂×C₄	—	8	4	no	—
777	C₂×C₄	—	8	4	no	—
778	C₂×C₄	—	8	4	no	—
779	C₂×C₄	—	8	1	no	—
780	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
784	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
785	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
787	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
788	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
789	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₈	—	2	2	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	4	no	—
805	C₂²	—	8	4	no	—
806	C₂²	—	16	4	no	—
807	C₂²	C₃₁×#548	1	2	yes	—
808	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
809	C₄	—	2	1	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	4	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	2	no	—
820	C₄	C₃₁×#548	1	2	yes	—
821	C₄	C₃₁×#576	1	2	yes	—
822	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
823	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
824	C₂	—	2	2	no	—
825	C₂	—	4	4	no	—
826	C₂	—	8	4	no	—
827	C₂	—	8	1	no	—
828	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
829	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
830	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 ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3501	C₂	semidirect
3. C₃₁×#3373	C₂	semidirect
4. C₃₁×#3370	C₂	semidirect
5. C₃₁×#3366	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3361	C₂	semidirect
8. C₃₁×#3358	C₂	semidirect
9. C₃₁×#3138	C₂	semidirect
10. C₃₁×#3136	C₂	semidirect
11. C₃₁×#3081	C₂	semidirect
12. C₃₁×#3076	C₂	semidirect
13. C₃₁×#3041	C₂	semidirect
14. C₂×C₃₁×#459	C₂	semidirect
15. C₃₁×#2962	C₂	semidirect
16. C₃₁×#2948	C₂	semidirect
17. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
20. C₃₁×#559	C₂²	semidirect
21. C₃₁×#559	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
25. C₃₁×#554	C₂²	semidirect
26. C₃₁×#550	C₂²	semidirect
27. C₃₁×#550	C₂²	semidirect
29. D₄×Q₈×C₃₁	C₂²	semidirect
46. C₃₁×#490	C₂²	semidirect
47. C₃₁×#490	C₂²	semidirect
48. C₃₁×#489	C₂²	semidirect
49. C₃₁×#488	C₂²	semidirect
50. C₃₁×#486	C₂²	semidirect
51. C₃₁×#486	C₂²	semidirect
52. C₃₁×#486	C₂²	semidirect
53. C₃₁×#479	C₂²	semidirect
54. C₃₁×#478	C₂²	semidirect
55. C₃₁×#478	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
58. C₃₁×#476	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#474	C₂²	semidirect
62. C₃₁×#474	C₂²	semidirect
63. C₃₁×#463	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
68. C₃₁×#459	C₂²	semidirect
69. C₃₁×#459	C₂²	semidirect
70. C₃₁×#446	C₂²	semidirect
71. C₃₁×#446	C₂²	semidirect
72. C₈×Q₈×C₃₁	C₂²	semidirect
73. C₃₁×#442	C₂²	semidirect
74. C₃₁×#442	C₂²	semidirect
75. C₃₁×#442	C₂²	semidirect
76. C₃₁×#440	C₂²	semidirect
77. C₄×SD₁₆×C₃₁	C₂²	semidirect
78. C₄×D₈×C₃₁	C₂²	semidirect
79. C₄×D₈×C₃₁	C₂²	semidirect
80. C₄×D₈×C₃₁	C₂²	semidirect
242. C₂×D₄×C₃₁	#41	semidirect
314. #61339	C₃₁	direct (N × H)
379. #3508	C₂×C₃₁	semidirect
380. #3501	C₂×C₃₁	semidirect
381. #3373	C₂×C₃₁	semidirect
382. #3370	C₂×C₃₁	semidirect
383. #3366	C₂×C₃₁	semidirect
384. #3366	C₂×C₃₁	semidirect
385. #3361	C₂×C₃₁	semidirect
386. #3358	C₂×C₃₁	semidirect
387. #3138	C₂×C₃₁	semidirect
388. #3136	C₂×C₃₁	semidirect
389. #3081	C₂×C₃₁	semidirect
390. #3076	C₂×C₃₁	semidirect
391. #3041	C₂×C₃₁	semidirect
392. C₂×#459	C₂×C₃₁	semidirect
393. #2962	C₂×C₃₁	semidirect
394. #2948	C₂×C₃₁	semidirect
395. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
428. #559	C₂²×C₃₁	semidirect
429. #559	C₂²×C₃₁	semidirect
432. #554	C₂²×C₃₁	semidirect
433. #554	C₂²×C₃₁	semidirect
434. #550	C₂²×C₃₁	semidirect
435. #550	C₂²×C₃₁	semidirect
437. D₄×Q₈	C₂²×C₃₁	semidirect
454. #490	C₂²×C₃₁	semidirect
455. #490	C₂²×C₃₁	semidirect
456. #489	C₂²×C₃₁	semidirect
457. #488	C₂²×C₃₁	semidirect
458. #486	C₂²×C₃₁	semidirect
459. #486	C₂²×C₃₁	semidirect
460. #486	C₂²×C₃₁	semidirect
461. #479	C₂²×C₃₁	semidirect
462. #478	C₂²×C₃₁	semidirect
463. #478	C₂²×C₃₁	semidirect
464. #478	C₂²×C₃₁	semidirect
465. #477	C₂²×C₃₁	semidirect
466. #476	C₂²×C₃₁	semidirect
467. #476	C₂²×C₃₁	semidirect
468. #475	C₂²×C₃₁	semidirect
469. #474	C₂²×C₃₁	semidirect
470. #474	C₂²×C₃₁	semidirect
471. #463	C₂²×C₃₁	semidirect
472. #463	C₂²×C₃₁	semidirect
476. #459	C₂²×C₃₁	semidirect
477. #459	C₂²×C₃₁	semidirect
478. #446	C₂²×C₃₁	semidirect
479. #446	C₂²×C₃₁	semidirect
480. C₈×Q₈	C₂²×C₃₁	semidirect
481. #442	C₂²×C₃₁	semidirect
482. #442	C₂²×C₃₁	semidirect
483. #442	C₂²×C₃₁	semidirect
484. #440	C₂²×C₃₁	semidirect
485. C₄×SD₁₆	C₂²×C₃₁	semidirect
486. C₄×D₈	C₂²×C₃₁	semidirect
487. C₄×D₈	C₂²×C₃₁	semidirect
488. C₄×D₈	C₂²×C₃₁	semidirect
630. C₃₁	#61339	direct (N × H)
658. C₂×D₄	#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×#3508	2
C₃₁×#3501	2
C₃₁×#3373	2
C₃₁×#3370	2
C₃₁×#3366	2
C₃₁×#3361	2
C₃₁×#3358	2
C₃₁×#3138	2
C₃₁×#3136	2
C₃₁×#3081	2
C₃₁×#3076	2
C₃₁×#3041	2
C₂×C₃₁×#459	2
C₃₁×#2962	2
C₃₁×#2948	2
C₄×C₃₁×AGL(1,ℤ/8)	2
#61339	31

Subgroups — C31×#61339 #21518098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61339 #21518098