Subgroups — C₃₁×#61995 #21518754

Order 7936.

1978 conjugacy classes of subgroups.

The subgroup lattice has 928 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×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3396	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3333	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3322	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3274	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3273	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3100	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3036	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#559	C₂²	1	2	yes	complemented
22	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#553	—	2	1	no	—
26	C₃₁×#553	C₂²	1	2	yes	—
27	C₃₁×#551	—	2	2	no	—
28	C₃₁×#550	—	2	1	no	—
29	C₃₁×#550	C₂²	1	2	yes	—
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	—	2	2	no	—
32	C₃₁×#546	C₂²	1	2	yes	—
33	C₃₁×#546	C₂²	1	4	yes	complemented
34	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#540	—	2	2	no	—
36	C₃₁×#535	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	2	yes	complemented
40	C₃₁×#532	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#529	—	2	1	no	—
43	C₃₁×#529	C₂²	1	2	yes	complemented
44	C₃₁×#525	—	2	2	no	—
45	C₃₁×#518	—	2	1	no	—
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₃₁	—	2	1	no	—
49	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
50	C₃₁×#495	C₂²	1	4	yes	complemented
51	C₃₁×#493	C₂²	1	2	yes	—
52	C₃₁×#488	C₂²	1	4	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	complemented
54	C₃₁×#485	C₂²	1	2	yes	complemented
55	C₃₁×#480	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#477	C₂²	1	2	yes	complemented
58	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#474	C₂²	1	2	yes	complemented
61	C₃₁×#469	C₂²	1	4	yes	complemented
62	C₃₁×#468	C₂²	1	4	yes	complemented
63	C₃₁×#468	C₂²	1	4	yes	complemented
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#463	C₂²	1	4	yes	complemented
66	C₃₁×#463	C₂²	1	4	yes	complemented
67	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#461	C₂²	1	2	yes	complemented
70	C₃₁×#460	C₂²	1	2	yes	complemented
71	C₃₁×#460	C₂²	1	2	yes	complemented
72	C₃₁×#460	C₂²	1	2	yes	complemented
73	C₃₁×#459	C₂²	1	2	yes	—
74	C₃₁×#459	C₂²	1	2	yes	—
75	C₃₁×#459	C₂²	1	2	yes	complemented
76	C₃₁×#459	C₂²	1	2	yes	complemented
77	C₃₁×#452	C₂²	1	2	yes	—
78	C₃₁×#452	C₂²	1	4	yes	complemented
79	C₃₁×#449	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	4	yes	complemented
81	C₃₁×#447	C₂²	1	4	yes	complemented
82	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
86	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
87	C₃₁×#436	C₂²	1	2	yes	complemented
88	C₃₁×#436	C₂²	1	4	yes	complemented
89	C₃₁×#431	C₂²	1	2	yes	complemented
90	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#423	C₂²	1	2	yes	complemented
92	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#418	C₂²	1	2	yes	complemented
94	C₃₁×#417	C₂²	1	4	yes	complemented
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₃₁	C₂³	1	4	yes	—
100	C₂²×D₄×C₃₁	—	2	1	no	—
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	—	2	1	no	—
103	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
104	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
105	C₂³×C₄×C₃₁	—	2	2	no	—
106	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
107	C₃₁×AGL(1,ℤ/8)	—	4	8	no	—
108	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×D₈×C₃₁	C₂³	1	4	yes	—
113	C₂×D₈×C₃₁	C₂³	1	4	yes	—
114	C₂×D₈×C₃₁	C₂³	1	4	yes	—
115	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
116	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
117	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×#127	—	2	2	no	—
121	C₃₁×#127	—	2	1	no	—
122	C₃₁×#127	—	2	1	no	—
123	C₃₁×#127	C₂³	1	2	yes	—
124	C₃₁×#127	C₂³	1	2	yes	—
125	C₃₁×#127	C₂³	1	1	yes	characteristic
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#125	—	2	1	no	—
129	C₃₁×#125	—	2	1	no	—
130	C₃₁×#125	C₂³	1	2	yes	—
131	C₃₁×#124	—	2	1	no	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#124	—	2	1	no	—
134	C₃₁×#124	—	2	2	no	—
135	C₃₁×#124	C₂³	1	4	yes	—
136	C₃₁×#124	C₂³	1	2	yes	—
137	C₃₁×#123	—	2	2	no	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	2	2	no	—
140	C₃₁×#123	—	2	4	no	—
141	C₃₁×#123	—	2	4	no	—
142	C₃₁×#123	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	—	2	1	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	1	no	—
151	C₃₁×#121	—	2	2	no	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	1	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	4	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	C₂³	1	2	yes	—
159	C₃₁×#121	C₂³	1	4	yes	—
160	C₃₁×#121	C₂³	1	2	yes	—
161	C₃₁×#120	—	2	2	no	—
162	C₃₁×#120	—	2	4	no	—
163	C₃₁×#120	—	2	2	no	—
164	C₄×Q₈×C₃₁	—	2	1	no	—
165	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	—	2	1	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
185	C₄×D₄×C₃₁	D₄	1	2	yes	—
186	C₄×D₄×C₃₁	C₂³	1	2	yes	—
187	C₄×D₄×C₃₁	C₂³	1	2	yes	—
188	C₄×D₄×C₃₁	C₂³	1	4	yes	—
189	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₃₁	C₂³	1	2	yes	—
192	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₃₁	C₂³	1	2	yes	—
194	C₃₁×#117	—	2	1	no	—
195	C₃₁×#117	—	2	1	no	—
196	C₃₁×#117	—	2	2	no	—
197	C₃₁×#117	D₄	1	1	yes	characteristic
198	C₃₁×#117	D₄	1	2	yes	—
199	C₃₁×#117	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
205	C₂×C₄²×C₃₁	—	2	1	no	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#107	C₂³	1	4	yes	—
210	C₃₁×#106	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×#103	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	2	yes	—
219	C₃₁×#103	C₂³	1	2	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₄×C₈×C₃₁	C₂³	1	4	yes	—
229	C₄×C₈×C₃₁	C₂³	1	2	yes	—
230	C₂⁴×C₃₁	—	2	2	no	—
231	C₂⁴×C₃₁	—	2	2	no	—
232	#41×C₃₁	—	2	2	no	—
233	#41×C₃₁	—	4	2	no	—
234	#41×C₃₁	—	4	1	no	—
235	#41×C₃₁	—	4	4	no	—
236	#41×C₃₁	—	4	4	no	—
237	#41×C₃₁	—	8	2	no	—
238	#41×C₃₁	—	8	4	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	1	no	—
241	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	2	1	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	4	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	4	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	1	no	—
256	C₂×D₄×C₃₁	—	2	2	no	—
257	C₂×D₄×C₃₁	—	2	2	no	—
258	C₂×D₄×C₃₁	—	4	2	no	—
259	C₂×D₄×C₃₁	—	4	2	no	—
260	C₂×D₄×C₃₁	—	4	2	no	—
261	C₂×D₄×C₃₁	—	4	4	no	—
262	C₂×D₄×C₃₁	—	4	4	no	—
263	C₂×D₄×C₃₁	—	8	2	no	—
264	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
267	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
268	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	—	2	2	no	—
270	C₂²×C₄×C₃₁	—	2	1	no	—
271	C₂²×C₄×C₃₁	—	2	1	no	—
272	C₂²×C₄×C₃₁	—	2	1	no	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	2	2	no	—
275	C₂²×C₄×C₃₁	—	2	4	no	—
276	C₂²×C₄×C₃₁	—	2	4	no	—
277	C₂²×C₄×C₃₁	—	2	2	no	—
278	C₂²×C₄×C₃₁	—	8	4	no	—
279	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
285	Q₁₆×C₃₁	—	4	2	no	—
286	SD₁₆×C₃₁	—	2	4	no	—
287	SD₁₆×C₃₁	—	4	4	no	—
288	SD₁₆×C₃₁	—	4	4	no	—
289	D₈×C₃₁	—	2	8	no	—
290	D₈×C₃₁	—	4	4	no	—
291	D₈×C₃₁	—	4	4	no	—
292	M₁₆×C₃₁	—	4	2	no	—
293	M₁₆×C₃₁	—	4	4	no	—
294	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
295	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
296	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₃₁	—	2	1	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	1	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	1	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	2	no	—
306	C₄⋊C₄×C₃₁	—	2	1	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	1	no	—
320	C₂²⋊C₄×C₃₁	—	2	1	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	2	no	—
327	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	4	no	—
332	C₂²⋊C₄×C₃₁	—	2	4	no	—
333	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₄²×C₃₁	—	2	1	no	—
337	C₄²×C₃₁	—	2	1	no	—
338	C₄²×C₃₁	—	2	1	no	—
339	C₄²×C₃₁	—	2	2	no	—
340	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₃₁	C₂×D₄	1	2	yes	—
343	C₄²×C₃₁	C₂×D₄	1	2	yes	—
344	C₄²×C₃₁	C₂⁴	1	2	yes	—
345	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
347	#61995	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂³×C₃₁	—	2	1	no	—
349	C₂³×C₃₁	—	2	2	no	—
350	C₂³×C₃₁	—	2	4	no	—
351	C₂³×C₃₁	—	4	4	no	—
352	C₂³×C₃₁	—	4	4	no	—
353	C₂³×C₃₁	—	4	4	no	—
354	C₂³×C₃₁	—	8	2	no	—
355	C₂³×C₃₁	—	8	2	no	—
356	C₂³×C₃₁	—	8	2	no	—
357	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
358	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
359	Q₈×C₃₁	—	2	2	no	—
360	Q₈×C₃₁	—	2	2	no	—
361	Q₈×C₃₁	—	2	1	no	—
362	Q₈×C₃₁	—	2	1	no	—
363	Q₈×C₃₁	—	2	2	no	—
364	Q₈×C₃₁	—	4	2	no	—
365	Q₈×C₃₁	—	8	1	no	—
366	D₄×C₃₁	—	2	2	no	—
367	D₄×C₃₁	—	2	4	no	—
368	D₄×C₃₁	—	2	2	no	—
369	D₄×C₃₁	—	2	1	no	—
370	D₄×C₃₁	—	2	2	no	—
371	D₄×C₃₁	—	2	4	no	—
372	D₄×C₃₁	—	4	2	no	—
373	D₄×C₃₁	—	4	4	no	—
374	D₄×C₃₁	—	4	4	no	—
375	D₄×C₃₁	—	4	2	no	—
376	D₄×C₃₁	—	4	4	no	—
377	D₄×C₃₁	—	4	2	no	—
378	D₄×C₃₁	—	4	4	no	—
379	D₄×C₃₁	—	4	4	no	—
380	D₄×C₃₁	—	8	2	no	—
381	D₄×C₃₁	—	8	2	no	—
382	D₄×C₃₁	—	8	1	no	—
383	D₄×C₃₁	—	8	4	no	—
384	D₄×C₃₁	—	8	2	no	—
385	D₄×C₃₁	—	8	4	no	—
386	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	4	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	1	no	—
392	C₂×C₄×C₃₁	—	2	1	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	1	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	4	2	no	—
401	C₂×C₄×C₃₁	—	4	2	no	—
402	C₂×C₄×C₃₁	—	4	2	no	—
403	C₂×C₄×C₃₁	—	4	2	no	—
404	C₂×C₄×C₃₁	—	4	4	no	—
405	C₂×C₄×C₃₁	—	8	2	no	—
406	C₂×C₄×C₃₁	—	8	2	no	—
407	C₂×C₄×C₃₁	—	8	4	no	—
408	C₂×C₄×C₃₁	—	8	4	no	—
409	C₂×C₄×C₃₁	—	8	2	no	—
410	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
419	C₈×C₃₁	—	2	4	no	—
420	C₈×C₃₁	—	2	2	no	—
421	C₈×C₃₁	—	2	2	no	—
422	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
423	#3481	C₂×C₃₁	1	1	yes	characteristic, complemented
424	#3396	C₂×C₃₁	1	2	yes	complemented
425	#3361	C₂×C₃₁	1	2	yes	complemented
426	#3333	C₂×C₃₁	1	2	yes	complemented
427	#3322	C₂×C₃₁	1	4	yes	complemented
428	#3274	C₂×C₃₁	1	2	yes	complemented
429	#3273	C₂×C₃₁	1	4	yes	complemented
430	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
431	#3251	C₂×C₃₁	1	2	yes	complemented
432	#3212	C₂×C₃₁	1	2	yes	complemented
433	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
435	#3100	C₂×C₃₁	1	2	yes	complemented
436	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
437	#3036	C₂×C₃₁	1	2	yes	complemented
438	#2991	C₂×C₃₁	1	1	yes	characteristic, complemented
439	C₂²×C₃₁	—	2	1	no	—
440	C₂²×C₃₁	—	2	2	no	—
441	C₂²×C₃₁	—	2	2	no	—
442	C₂²×C₃₁	—	2	1	no	—
443	C₂²×C₃₁	—	2	2	no	—
444	C₂²×C₃₁	—	2	2	no	—
445	C₂²×C₃₁	—	2	1	no	—
446	C₂²×C₃₁	—	4	1	no	—
447	C₂²×C₃₁	—	4	1	no	—
448	C₂²×C₃₁	—	4	4	no	—
449	C₂²×C₃₁	—	4	2	no	—
450	C₂²×C₃₁	—	4	2	no	—
451	C₂²×C₃₁	—	4	4	no	—
452	C₂²×C₃₁	—	4	2	no	—
453	C₂²×C₃₁	—	4	4	no	—
454	C₂²×C₃₁	—	8	8	no	—
455	C₂²×C₃₁	—	16	4	no	—
456	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
457	C₄×C₃₁	—	2	1	no	—
458	C₄×C₃₁	—	2	2	no	—
459	C₄×C₃₁	—	2	1	no	—
460	C₄×C₃₁	—	2	2	no	—
461	C₄×C₃₁	—	2	2	no	—
462	C₄×C₃₁	—	2	1	no	—
463	C₄×C₃₁	—	4	1	no	—
464	C₄×C₃₁	—	4	2	no	—
465	C₄×C₃₁	—	4	1	no	—
466	C₄×C₃₁	—	4	1	no	—
467	C₄×C₃₁	—	4	2	no	—
468	C₄×C₃₁	—	4	2	no	—
469	C₄×C₃₁	#575	1	2	yes	—
470	C₄×C₃₁	#576	1	2	yes	—
471	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₄×C₃₁	#585	1	1	yes	characteristic
473	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
474	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
475	#559	—	2	1	no	—
476	#559	C₂²×C₃₁	1	2	yes	complemented
477	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
478	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
479	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
480	#553	—	2	1	no	—
481	#553	C₂²×C₃₁	1	2	yes	—
482	#551	—	2	2	no	—
483	#550	—	2	1	no	—
484	#550	C₂²×C₃₁	1	2	yes	—
485	#546	—	2	1	no	—
486	#546	—	2	2	no	—
487	#546	C₂²×C₃₁	1	2	yes	—
488	#546	C₂²×C₃₁	1	4	yes	complemented
489	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
490	#540	—	2	2	no	—
491	#535	—	2	1	no	—
492	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
493	#532	C₂²×C₃₁	1	1	yes	characteristic
494	#532	C₂²×C₃₁	1	2	yes	complemented
495	#532	C₂²×C₃₁	1	2	yes	complemented
496	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
497	#529	—	2	1	no	—
498	#529	C₂²×C₃₁	1	2	yes	complemented
499	#525	—	2	2	no	—
500	#518	—	2	1	no	—
501	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
502	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
503	C₂×C₄×D₄	—	2	1	no	—
504	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
505	#495	C₂²×C₃₁	1	4	yes	complemented
506	#493	C₂²×C₃₁	1	2	yes	—
507	#488	C₂²×C₃₁	1	4	yes	complemented
508	#486	C₂²×C₃₁	1	2	yes	complemented
509	#485	C₂²×C₃₁	1	2	yes	complemented
510	#480	C₂²×C₃₁	1	4	yes	complemented
511	#478	C₂²×C₃₁	1	4	yes	complemented
512	#477	C₂²×C₃₁	1	2	yes	complemented
513	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
515	#474	C₂²×C₃₁	1	2	yes	complemented
516	#469	C₂²×C₃₁	1	4	yes	complemented
517	#468	C₂²×C₃₁	1	4	yes	complemented
518	#468	C₂²×C₃₁	1	4	yes	complemented
519	#463	C₂²×C₃₁	1	4	yes	complemented
520	#463	C₂²×C₃₁	1	4	yes	complemented
521	#463	C₂²×C₃₁	1	4	yes	complemented
522	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
523	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
524	#461	C₂²×C₃₁	1	2	yes	complemented
525	#460	C₂²×C₃₁	1	2	yes	complemented
526	#460	C₂²×C₃₁	1	2	yes	complemented
527	#460	C₂²×C₃₁	1	2	yes	complemented
528	#459	C₂²×C₃₁	1	2	yes	—
529	#459	C₂²×C₃₁	1	2	yes	—
530	#459	C₂²×C₃₁	1	2	yes	complemented
531	#459	C₂²×C₃₁	1	2	yes	complemented
532	#452	C₂²×C₃₁	1	2	yes	—
533	#452	C₂²×C₃₁	1	4	yes	complemented
534	#449	C₂²×C₃₁	1	4	yes	complemented
535	#447	C₂²×C₃₁	1	4	yes	complemented
536	#447	C₂²×C₃₁	1	4	yes	complemented
537	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
538	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
539	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
540	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
541	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
542	#436	C₂²×C₃₁	1	2	yes	complemented
543	#436	C₂²×C₃₁	1	4	yes	complemented
544	#431	C₂²×C₃₁	1	2	yes	complemented
545	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
546	#423	C₂²×C₃₁	1	2	yes	complemented
547	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#418	C₂²×C₃₁	1	2	yes	complemented
549	#417	C₂²×C₃₁	1	4	yes	complemented
550	C₂×C₃₁	—	4	2	no	—
551	C₂×C₃₁	—	4	1	no	—
552	C₂×C₃₁	—	4	2	no	—
553	C₂×C₃₁	—	8	2	no	—
554	C₂×C₃₁	—	8	4	no	—
555	C₂×C₃₁	#3488	1	1	yes	characteristic
556	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
557	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
558	C₂×#41	—	2	1	no	—
559	C₂×#41	—	2	2	no	—
560	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
561	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
562	C₂×#41	C₂³×C₃₁	1	4	yes	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
567	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
568	C₂³×C₄	—	2	2	no	—
569	AGL(1,ℤ/8)	—	4	4	no	—
570	AGL(1,ℤ/8)	—	4	8	no	—
571	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
572	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
573	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
574	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
575	C₂×D₈	C₂³×C₃₁	1	4	yes	—
576	C₂×D₈	C₂³×C₃₁	1	4	yes	—
577	C₂×D₈	C₂³×C₃₁	1	4	yes	—
578	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
579	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
580	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
581	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
583	#127	—	2	2	no	—
584	#127	—	2	1	no	—
585	#127	—	2	1	no	—
586	#127	C₂³×C₃₁	1	2	yes	—
587	#127	C₂³×C₃₁	1	2	yes	—
588	#127	C₂³×C₃₁	1	1	yes	characteristic
589	#126	—	2	2	no	—
590	#126	—	2	2	no	—
591	#125	—	2	1	no	—
592	#125	—	2	1	no	—
593	#125	C₂³×C₃₁	1	2	yes	—
594	#124	—	2	1	no	—
595	#124	—	2	2	no	—
596	#124	—	2	1	no	—
597	#124	—	2	2	no	—
598	#124	C₂³×C₃₁	1	2	yes	—
599	#124	C₂³×C₃₁	1	4	yes	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	4	no	—
604	#123	—	2	4	no	—
605	#123	—	2	2	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
611	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
612	#121	—	2	2	no	—
613	#121	—	2	1	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	—	2	2	no	—
617	#121	—	2	1	no	—
618	#121	—	2	2	no	—
619	#121	—	2	4	no	—
620	#121	—	2	4	no	—
621	#121	C₂³×C₃₁	1	2	yes	—
622	#121	C₂³×C₃₁	1	2	yes	—
623	#121	C₂³×C₃₁	1	4	yes	—
624	#120	—	2	2	no	—
625	#120	—	2	4	no	—
626	#120	—	2	2	no	—
627	C₄×Q₈	—	2	1	no	—
628	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
629	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
630	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
631	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
632	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	1	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
648	C₄×D₄	D₄×C₃₁	1	2	yes	—
649	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₃₁	1	2	yes	—
651	C₄×D₄	C₂³×C₃₁	1	2	yes	—
652	C₄×D₄	C₂³×C₃₁	1	2	yes	—
653	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₃₁	1	4	yes	—
655	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
656	C₄×D₄	C₂³×C₃₁	1	2	yes	—
657	#117	—	2	1	no	—
658	#117	—	2	1	no	—
659	#117	—	2	2	no	—
660	#117	D₄×C₃₁	1	1	yes	characteristic
661	#117	D₄×C₃₁	1	2	yes	—
662	#117	C₂³×C₃₁	1	1	yes	characteristic
663	C₂×C₄⋊C₄	—	2	1	no	—
664	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₂²⋊C₄	—	2	4	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
670	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
671	#107	C₂³×C₃₁	1	2	yes	—
672	#107	C₂³×C₃₁	1	4	yes	—
673	#106	C₂³×C₃₁	1	2	yes	—
674	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
675	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
676	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
677	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
678	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
679	#103	C₂³×C₃₁	1	2	yes	—
680	#103	C₂³×C₃₁	1	4	yes	—
681	#103	C₂³×C₃₁	1	2	yes	—
682	#103	C₂³×C₃₁	1	2	yes	—
683	#102	C₂³×C₃₁	1	4	yes	—
684	#102	C₂³×C₃₁	1	4	yes	—
685	#102	C₂³×C₃₁	1	4	yes	—
686	#102	C₂³×C₃₁	1	2	yes	—
687	#102	C₂³×C₃₁	1	4	yes	—
688	#102	C₂³×C₃₁	1	4	yes	—
689	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
690	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
691	C₄×C₈	C₂³×C₃₁	1	4	yes	—
692	C₄×C₈	C₂³×C₃₁	1	2	yes	—
693	C₃₁	#61995	1	1	yes	characteristic, direct product factor, Sylow
694	C₂⁴	—	2	2	no	—
695	C₂⁴	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	4	2	no	—
698	#41	—	4	1	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	8	2	no	—
702	#41	—	8	4	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	2	1	no	—
705	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
706	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
707	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	4	4	no	—
727	C₂×D₄	—	8	2	no	—
728	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
729	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
730	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
731	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
732	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	8	4	no	—
743	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
745	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
749	Q₁₆	—	4	2	no	—
750	SD₁₆	—	2	4	no	—
751	SD₁₆	—	4	4	no	—
752	SD₁₆	—	4	4	no	—
753	D₈	—	2	8	no	—
754	D₈	—	4	4	no	—
755	D₈	—	4	4	no	—
756	M₁₆	—	4	2	no	—
757	M₁₆	—	4	4	no	—
758	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
759	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
760	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
774	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
775	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
776	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
780	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	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	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
798	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
799	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
800	C₄²	—	2	1	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	1	no	—
803	C₄²	—	2	2	no	—
804	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
805	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
806	C₄²	C₂×D₄×C₃₁	1	2	yes	—
807	C₄²	C₂×D₄×C₃₁	1	2	yes	—
808	C₄²	C₂⁴×C₃₁	1	2	yes	—
809	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
810	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
811	C₂³	—	2	1	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	4	no	—
817	C₂³	—	8	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
821	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	2	1	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	8	1	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	4	no	—
831	D₄	—	2	2	no	—
832	D₄	—	2	1	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	4	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	2	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	1	no	—
846	D₄	—	8	4	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	4	no	—
849	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
880	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
881	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	4	no	—
900	C₂²	—	8	8	no	—
901	C₂²	—	16	4	no	—
902	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
903	C₄	—	2	1	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	C₃₁×#575	1	2	yes	—
916	C₄	C₃₁×#576	1	2	yes	—
917	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
918	C₄	C₃₁×#585	1	1	yes	characteristic
919	C₂	—	4	2	no	—
920	C₂	—	4	1	no	—
921	C₂	—	4	2	no	—
922	C₂	—	8	2	no	—
923	C₂	—	8	4	no	—
924	C₂	C₃₁×#3488	1	1	yes	characteristic
925	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
926	C₂	C₂×C₃₁×#576	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3481	C₂	semidirect
3. C₃₁×#3396	C₂	semidirect
4. C₃₁×#3361	C₂	semidirect
5. C₃₁×#3333	C₂	semidirect
6. C₃₁×#3322	C₂	semidirect
7. C₃₁×#3274	C₂	semidirect
8. C₃₁×#3273	C₂	semidirect
9. C₃₁×#3254	C₂	semidirect
10. C₃₁×#3251	C₂	semidirect
11. C₃₁×#3212	C₂	semidirect
12. C₃₁×#3205	C₂	semidirect
13. C₃₁×#3107	C₂	semidirect
14. C₃₁×#3100	C₂	semidirect
15. C₃₁×#3038	C₂	semidirect
16. C₃₁×#3036	C₂	semidirect
17. C₃₁×#2991	C₂	semidirect
19. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
21. C₃₁×#559	C₂²	semidirect
22. C₃₁×#559	C₂²	semidirect
23. C₃₁×#554	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
33. C₃₁×#546	C₂²	semidirect
34. D₄²×C₃₁	C₂²	semidirect
37. C₃₁×#533	C₂²	semidirect
39. C₃₁×#532	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
41. C₂×C₃₁×#127	C₂²	semidirect
43. C₃₁×#529	C₂²	semidirect
49. C₂×C₄×D₄×C₃₁	C₂²	semidirect
50. C₃₁×#495	C₂²	semidirect
52. C₃₁×#488	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
54. C₃₁×#485	C₂²	semidirect
55. C₃₁×#480	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
58. C₃₁×#475	C₂²	semidirect
59. C₃₁×#474	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
61. C₃₁×#469	C₂²	semidirect
62. C₃₁×#468	C₂²	semidirect
63. C₃₁×#468	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
65. C₃₁×#463	C₂²	semidirect
66. C₃₁×#463	C₂²	semidirect
67. C₃₁×#462	C₂²	semidirect
68. C₃₁×#461	C₂²	semidirect
69. C₃₁×#461	C₂²	semidirect
70. C₃₁×#460	C₂²	semidirect
71. C₃₁×#460	C₂²	semidirect
72. C₃₁×#460	C₂²	semidirect
75. C₃₁×#459	C₂²	semidirect
76. C₃₁×#459	C₂²	semidirect
78. C₃₁×#452	C₂²	semidirect
79. C₃₁×#449	C₂²	semidirect
80. C₃₁×#447	C₂²	semidirect
81. C₃₁×#447	C₂²	semidirect
82. C₈×Q₈×C₃₁	C₂²	semidirect
83. C₄×Q₁₆×C₃₁	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₄×D₈×C₃₁	C₂²	semidirect
86. C₄×D₈×C₃₁	C₂²	semidirect
87. C₃₁×#436	C₂²	semidirect
88. C₃₁×#436	C₂²	semidirect
89. C₃₁×#431	C₂²	semidirect
90. C₃₁×#431	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₃₁×#423	C₂²	semidirect
93. C₃₁×#418	C₂²	semidirect
94. C₃₁×#417	C₂²	semidirect
347. #61995	C₃₁	direct (N × H)
422. #3508	C₂×C₃₁	semidirect
423. #3481	C₂×C₃₁	semidirect
424. #3396	C₂×C₃₁	semidirect
425. #3361	C₂×C₃₁	semidirect
426. #3333	C₂×C₃₁	semidirect
427. #3322	C₂×C₃₁	semidirect
428. #3274	C₂×C₃₁	semidirect
429. #3273	C₂×C₃₁	semidirect
430. #3254	C₂×C₃₁	semidirect
431. #3251	C₂×C₃₁	semidirect
432. #3212	C₂×C₃₁	semidirect
433. #3205	C₂×C₃₁	semidirect
434. #3107	C₂×C₃₁	semidirect
435. #3100	C₂×C₃₁	semidirect
436. #3038	C₂×C₃₁	semidirect
437. #3036	C₂×C₃₁	semidirect
438. #2991	C₂×C₃₁	semidirect
474. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
476. #559	C₂²×C₃₁	semidirect
477. #559	C₂²×C₃₁	semidirect
478. #554	C₂²×C₃₁	semidirect
479. #554	C₂²×C₃₁	semidirect
488. #546	C₂²×C₃₁	semidirect
489. D₄²	C₂²×C₃₁	semidirect
492. #533	C₂²×C₃₁	semidirect
494. #532	C₂²×C₃₁	semidirect
495. #532	C₂²×C₃₁	semidirect
496. C₂×#127	C₂²×C₃₁	semidirect
498. #529	C₂²×C₃₁	semidirect
504. C₂×C₄×D₄	C₂²×C₃₁	semidirect
505. #495	C₂²×C₃₁	semidirect
507. #488	C₂²×C₃₁	semidirect
508. #486	C₂²×C₃₁	semidirect
509. #485	C₂²×C₃₁	semidirect
510. #480	C₂²×C₃₁	semidirect
511. #478	C₂²×C₃₁	semidirect
512. #477	C₂²×C₃₁	semidirect
513. #475	C₂²×C₃₁	semidirect
514. #474	C₂²×C₃₁	semidirect
515. #474	C₂²×C₃₁	semidirect
516. #469	C₂²×C₃₁	semidirect
517. #468	C₂²×C₃₁	semidirect
518. #468	C₂²×C₃₁	semidirect
519. #463	C₂²×C₃₁	semidirect
520. #463	C₂²×C₃₁	semidirect
521. #463	C₂²×C₃₁	semidirect
522. #462	C₂²×C₃₁	semidirect
523. #461	C₂²×C₃₁	semidirect
524. #461	C₂²×C₃₁	semidirect
525. #460	C₂²×C₃₁	semidirect
526. #460	C₂²×C₃₁	semidirect
527. #460	C₂²×C₃₁	semidirect
530. #459	C₂²×C₃₁	semidirect
531. #459	C₂²×C₃₁	semidirect
533. #452	C₂²×C₃₁	semidirect
534. #449	C₂²×C₃₁	semidirect
535. #447	C₂²×C₃₁	semidirect
536. #447	C₂²×C₃₁	semidirect
537. C₈×Q₈	C₂²×C₃₁	semidirect
538. C₄×Q₁₆	C₂²×C₃₁	semidirect
539. C₄×SD₁₆	C₂²×C₃₁	semidirect
540. C₄×D₈	C₂²×C₃₁	semidirect
541. C₄×D₈	C₂²×C₃₁	semidirect
542. #436	C₂²×C₃₁	semidirect
543. #436	C₂²×C₃₁	semidirect
544. #431	C₂²×C₃₁	semidirect
545. #431	C₂²×C₃₁	semidirect
546. #423	C₂²×C₃₁	semidirect
547. #423	C₂²×C₃₁	semidirect
548. #418	C₂²×C₃₁	semidirect
549. #417	C₂²×C₃₁	semidirect
693. C₃₁	#61995	direct (N × H)

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×#3481	2
C₃₁×#3396	2
C₃₁×#3361	2
C₃₁×#3333	2
C₃₁×#3322	2
C₃₁×#3274	2
C₃₁×#3273	2
C₃₁×#3254	2
C₃₁×#3251	2
C₃₁×#3212	2
C₃₁×#3205	2
C₃₁×#3107	2
C₃₁×#3100	2
C₃₁×#3038	2
C₃₁×#3036	2
C₃₁×#2991	2
#61995	31

Subgroups — C31×#61995 #21518754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61995 #21518754