Subgroups — C₃₁×#61468 #21518227

Order 7936.

1908 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3355	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3326	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3275	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3183	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₃₁×#2971	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₃₁×#559	—	2	1	no	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic
28	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#556	—	2	1	no	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#554	C₂²	1	1	yes	characteristic
34	C₃₁×#553	—	2	2	no	—
35	C₃₁×#553	—	2	1	no	—
36	C₃₁×#553	C₂²	1	2	yes	—
37	C₃₁×#553	C₂²	1	2	yes	complemented
38	C₃₁×#551	—	2	2	no	—
39	C₃₁×#550	C₂²	1	1	yes	characteristic
40	C₃₁×#548	C₂²	1	2	yes	complemented
41	C₃₁×#546	—	2	1	no	—
42	C₃₁×#546	C₂²	1	2	yes	—
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#532	—	2	1	no	—
45	C₃₁×#532	C₂²	1	1	yes	characteristic
46	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#529	—	2	1	no	—
48	C₃₁×#529	—	2	2	no	—
49	C₃₁×#529	C₂²	1	2	yes	—
50	C₃₁×#529	C₂²	1	2	yes	complemented
51	C₃₁×#525	—	2	2	no	—
52	C₄×#41×C₃₁	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₃₁	—	2	1	no	—
58	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
59	C₃₁×#499	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#495	C₂²	1	2	yes	complemented
62	C₃₁×#493	C₂²	1	1	yes	characteristic
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#488	C₂²	1	2	yes	complemented
65	C₃₁×#486	C₂²	1	1	yes	characteristic
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#483	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#480	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#474	C₂²	1	1	yes	characteristic
81	C₃₁×#470	C₂²	1	2	yes	complemented
82	C₃₁×#469	C₂²	1	2	yes	—
83	C₃₁×#469	C₂²	1	2	yes	complemented
84	C₃₁×#469	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	—
86	C₃₁×#468	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#463	C₂²	1	2	yes	complemented
91	C₃₁×#460	C₂²	1	1	yes	characteristic
92	C₃₁×#460	C₂²	1	1	yes	characteristic
93	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#459	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	complemented
96	C₃₁×#450	C₂²	1	2	yes	—
97	C₃₁×#449	C₂²	1	2	yes	—
98	C₃₁×#449	C₂²	1	2	yes	—
99	C₃₁×#448	C₂²	1	2	yes	complemented
100	C₃₁×#447	C₂²	1	2	yes	—
101	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	complemented
105	C₃₁×#442	C₂²	1	2	yes	complemented
106	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#440	C₂²	1	1	yes	characteristic
109	C₃₁×#440	C₂²	1	1	yes	characteristic
110	C₃₁×#440	C₂²	1	2	yes	complemented
111	C₃₁×#440	C₂²	1	2	yes	complemented
112	C₃₁×#440	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₃₁	C₂²	1	2	yes	—
120	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	1	yes	characteristic
123	C₃₁×#436	C₂²	1	2	yes	complemented
124	C₃₁×#436	C₂²	1	2	yes	complemented
125	C₃₁×#432	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#428	C₂²	1	2	yes	complemented
129	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#418	C₂²	1	2	yes	—
131	C₃₁×#417	C₂²	1	1	yes	characteristic
132	C₃₁×#417	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₃₁	—	2	2	no	—
144	C₃₁×#137	—	2	4	no	—
145	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#127	—	2	1	no	—
164	C₃₁×#127	C₂³	1	1	yes	characteristic
165	C₃₁×#127	C₂³	1	1	yes	characteristic
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#125	—	2	1	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	C₂³	1	2	yes	—
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#124	—	2	1	no	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	C₂³	1	2	yes	—
182	C₃₁×#124	C₂³	1	2	yes	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#120	—	2	2	no	—
209	C₃₁×#120	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
241	C₄×D₄×C₃₁	D₄	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	—	2	2	no	—
254	C₃₁×#117	—	2	2	no	—
255	C₃₁×#117	D₄	1	1	yes	characteristic
256	C₃₁×#117	D₄	1	2	yes	—
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₃₁×#117	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	—	2	1	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	1	yes	characteristic
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	1	yes	characteristic
308	C₃₁×#97	C₂³	1	1	yes	characteristic
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	2	yes	—
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₂⁴×C₃₁	—	2	2	no	—
315	#41×C₃₁	—	2	4	no	—
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	1	no	—
320	#41×C₃₁	—	4	4	no	—
321	#41×C₃₁	—	8	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	—	2	2	no	—
326	C₂×Q₈×C₃₁	—	4	1	no	—
327	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₃₁	—	2	4	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	4	2	no	—
344	C₂×D₄×C₃₁	—	4	4	no	—
345	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
348	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	1	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	—	8	4	no	—
363	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
369	Q₁₆×C₃₁	—	2	2	no	—
370	Q₁₆×C₃₁	—	2	2	no	—
371	SD₁₆×C₃₁	—	2	4	no	—
372	SD₁₆×C₃₁	—	2	2	no	—
373	SD₁₆×C₃₁	—	4	2	no	—
374	SD₁₆×C₃₁	—	4	2	no	—
375	SD₁₆×C₃₁	#41	1	4	yes	complemented
376	D₈×C₃₁	—	2	4	no	—
377	D₈×C₃₁	—	2	4	no	—
378	D₈×C₃₁	—	4	2	no	—
379	M₁₆×C₃₁	—	2	4	no	—
380	M₁₆×C₃₁	—	2	2	no	—
381	M₁₆×C₃₁	—	4	1	no	—
382	M₁₆×C₃₁	—	4	2	no	—
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	1	no	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	—	2	1	no	—
447	C₄²×C₃₁	C₂×D₄	1	2	yes	—
448	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₃₁	C₂×D₄	1	2	yes	—
450	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₃₁	C₂⁴	1	2	yes	—
452	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
454	#61468	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	2	2	no	—
457	C₂³×C₃₁	—	2	2	no	—
458	C₂³×C₃₁	—	4	4	no	—
459	C₂³×C₃₁	—	4	4	no	—
460	C₂³×C₃₁	—	8	2	no	—
461	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
462	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	2	1	no	—
468	Q₈×C₃₁	—	2	1	no	—
469	Q₈×C₃₁	—	4	2	no	—
470	Q₈×C₃₁	—	4	2	no	—
471	Q₈×C₃₁	—	8	1	no	—
472	Q₈×C₃₁	C₂×#41	1	2	yes	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	2	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	2	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	4	4	no	—
481	D₄×C₃₁	—	4	4	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	4	4	no	—
484	D₄×C₃₁	—	4	4	no	—
485	D₄×C₃₁	—	4	2	no	—
486	D₄×C₃₁	—	4	2	no	—
487	D₄×C₃₁	—	8	1	no	—
488	D₄×C₃₁	—	8	1	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	2	no	—
491	D₄×C₃₁	C₂×#41	1	2	yes	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	2	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	4	1	no	—
509	C₂×C₄×C₃₁	—	4	4	no	—
510	C₂×C₄×C₃₁	—	4	2	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	4	4	no	—
514	C₂×C₄×C₃₁	—	4	4	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	8	2	no	—
517	C₂×C₄×C₃₁	—	8	2	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	—	8	1	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
530	C₈×C₃₁	—	2	2	no	—
531	C₈×C₃₁	—	2	1	no	—
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	2	no	—
535	C₈×C₃₁	C₂×#41	1	2	yes	—
536	#3481	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3396	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3355	C₂×C₃₁	1	2	yes	complemented
544	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3326	C₂×C₃₁	1	2	yes	complemented
546	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3322	C₂×C₃₁	1	2	yes	complemented
548	#3275	C₂×C₃₁	1	2	yes	complemented
549	#3274	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3184	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3183	C₂×C₃₁	1	2	yes	complemented
552	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3114	C₂×C₃₁	1	2	yes	complemented
554	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3111	C₂×C₃₁	1	2	yes	complemented
556	#2971	C₂×C₃₁	1	1	yes	characteristic, complemented
557	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
558	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	2	yes	complemented
559	C₂²×C₃₁	—	2	1	no	—
560	C₂²×C₃₁	—	2	2	no	—
561	C₂²×C₃₁	—	2	1	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	2	1	no	—
565	C₂²×C₃₁	—	2	2	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	2	no	—
569	C₂²×C₃₁	—	4	2	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	2	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	8	8	no	—
575	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	2	no	—
578	C₄×C₃₁	—	2	1	no	—
579	C₄×C₃₁	—	2	2	no	—
580	C₄×C₃₁	—	2	1	no	—
581	C₄×C₃₁	—	2	2	no	—
582	C₄×C₃₁	—	2	1	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	2	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	1	no	—
591	C₄×C₃₁	—	4	2	no	—
592	C₄×C₃₁	#575	1	2	yes	—
593	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
594	C₄×C₃₁	#585	1	1	yes	characteristic
595	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
596	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
597	#559	—	2	1	no	—
598	#559	C₂²×C₃₁	1	1	yes	characteristic
599	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	#556	—	2	1	no	—
602	#556	C₂²×C₃₁	1	1	yes	characteristic
603	#554	C₂²×C₃₁	1	1	yes	characteristic
604	#554	C₂²×C₃₁	1	1	yes	characteristic
605	#553	—	2	2	no	—
606	#553	—	2	1	no	—
607	#553	C₂²×C₃₁	1	2	yes	—
608	#553	C₂²×C₃₁	1	2	yes	complemented
609	#551	—	2	2	no	—
610	#550	C₂²×C₃₁	1	1	yes	characteristic
611	#548	C₂²×C₃₁	1	2	yes	complemented
612	#546	—	2	1	no	—
613	#546	C₂²×C₃₁	1	2	yes	—
614	D₄²	C₂²×C₃₁	1	1	yes	characteristic
615	#532	—	2	1	no	—
616	#532	C₂²×C₃₁	1	1	yes	characteristic
617	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#529	—	2	1	no	—
619	#529	—	2	2	no	—
620	#529	C₂²×C₃₁	1	2	yes	—
621	#529	C₂²×C₃₁	1	2	yes	complemented
622	#525	—	2	2	no	—
623	C₄×#41	—	2	1	no	—
624	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
625	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
626	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
627	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	C₂×C₄×D₄	—	2	1	no	—
629	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
630	#499	C₂²×C₃₁	1	2	yes	complemented
631	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#495	C₂²×C₃₁	1	2	yes	complemented
633	#493	C₂²×C₃₁	1	1	yes	characteristic
634	#488	C₂²×C₃₁	1	2	yes	complemented
635	#488	C₂²×C₃₁	1	2	yes	complemented
636	#486	C₂²×C₃₁	1	1	yes	characteristic
637	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#485	C₂²×C₃₁	1	2	yes	complemented
639	#483	C₂²×C₃₁	1	2	yes	complemented
640	#482	C₂²×C₃₁	1	2	yes	—
641	#482	C₂²×C₃₁	1	2	yes	complemented
642	#480	C₂²×C₃₁	1	2	yes	complemented
643	#480	C₂²×C₃₁	1	2	yes	complemented
644	#479	C₂²×C₃₁	1	2	yes	complemented
645	#478	C₂²×C₃₁	1	2	yes	—
646	#478	C₂²×C₃₁	1	2	yes	complemented
647	#478	C₂²×C₃₁	1	2	yes	complemented
648	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#474	C₂²×C₃₁	1	1	yes	characteristic
652	#470	C₂²×C₃₁	1	2	yes	complemented
653	#469	C₂²×C₃₁	1	2	yes	—
654	#469	C₂²×C₃₁	1	2	yes	complemented
655	#469	C₂²×C₃₁	1	2	yes	complemented
656	#468	C₂²×C₃₁	1	2	yes	—
657	#468	C₂²×C₃₁	1	2	yes	complemented
658	#464	C₂²×C₃₁	1	2	yes	complemented
659	#463	C₂²×C₃₁	1	2	yes	—
660	#463	C₂²×C₃₁	1	2	yes	complemented
661	#463	C₂²×C₃₁	1	2	yes	complemented
662	#460	C₂²×C₃₁	1	1	yes	characteristic
663	#460	C₂²×C₃₁	1	1	yes	characteristic
664	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#459	C₂²×C₃₁	1	1	yes	characteristic
666	#452	C₂²×C₃₁	1	2	yes	complemented
667	#450	C₂²×C₃₁	1	2	yes	—
668	#449	C₂²×C₃₁	1	2	yes	—
669	#449	C₂²×C₃₁	1	2	yes	—
670	#448	C₂²×C₃₁	1	2	yes	complemented
671	#447	C₂²×C₃₁	1	2	yes	—
672	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	#442	C₂²×C₃₁	1	2	yes	—
675	#442	C₂²×C₃₁	1	2	yes	complemented
676	#442	C₂²×C₃₁	1	2	yes	complemented
677	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#440	C₂²×C₃₁	1	1	yes	characteristic
680	#440	C₂²×C₃₁	1	1	yes	characteristic
681	#440	C₂²×C₃₁	1	2	yes	complemented
682	#440	C₂²×C₃₁	1	2	yes	complemented
683	#440	C₂²×C₃₁	1	2	yes	complemented
684	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
687	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
688	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
689	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
690	C₄×D₈	C₂²×C₃₁	1	2	yes	—
691	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
692	#436	C₂²×C₃₁	1	1	yes	characteristic
693	#436	C₂²×C₃₁	1	1	yes	characteristic
694	#436	C₂²×C₃₁	1	2	yes	complemented
695	#436	C₂²×C₃₁	1	2	yes	complemented
696	#432	C₂²×C₃₁	1	2	yes	complemented
697	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#428	C₂²×C₃₁	1	2	yes	complemented
700	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#418	C₂²×C₃₁	1	2	yes	—
702	#417	C₂²×C₃₁	1	1	yes	characteristic
703	#417	C₂²×C₃₁	1	2	yes	complemented
704	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
705	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	C₂×C₃₁	—	4	1	no	—
707	C₂×C₃₁	—	4	2	no	—
708	C₂×C₃₁	—	4	2	no	—
709	C₂×C₃₁	—	8	2	no	—
710	C₂×C₃₁	—	8	2	no	—
711	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
712	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
713	C₂×C₃₁	#3585	1	1	yes	characteristic
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
717	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×#41	C₂³×C₃₁	1	2	yes	—
719	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₂²×D₄	—	2	1	no	—
721	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
722	C₂³×C₄	—	2	2	no	—
723	#137	—	2	4	no	—
724	AGL(1,ℤ/8)	—	2	8	no	—
725	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×D₈	C₂³×C₃₁	1	2	yes	—
733	C₂×D₈	C₂³×C₃₁	1	2	yes	—
734	C₂×D₈	C₂³×C₃₁	1	2	yes	—
735	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
739	C₄⋊Q₈	—	2	1	no	—
740	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
742	#127	—	2	1	no	—
743	#127	C₂³×C₃₁	1	1	yes	characteristic
744	#127	C₂³×C₃₁	1	1	yes	characteristic
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#125	—	2	1	no	—
751	#125	—	2	2	no	—
752	#125	C₂³×C₃₁	1	2	yes	—
753	#125	C₂³×C₃₁	1	2	yes	—
754	#124	—	2	1	no	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	2	2	no	—
758	#124	—	2	1	no	—
759	#124	—	2	1	no	—
760	#124	C₂³×C₃₁	1	2	yes	—
761	#124	C₂³×C₃₁	1	2	yes	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	C₂³×C₃₁	1	2	yes	—
784	#121	C₂³×C₃₁	1	2	yes	—
785	#121	C₂³×C₃₁	1	2	yes	—
786	#121	C₂³×C₃₁	1	2	yes	—
787	#120	—	2	2	no	—
788	#120	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
801	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
820	C₄×D₄	D₄×C₃₁	1	2	yes	—
821	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₃₁	1	2	yes	—
823	C₄×D₄	C₂³×C₃₁	1	2	yes	—
824	C₄×D₄	C₂³×C₃₁	1	2	yes	—
825	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₃₁	1	2	yes	—
827	C₄×D₄	C₂³×C₃₁	1	2	yes	—
828	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₃₁	1	2	yes	—
830	#117	—	2	2	no	—
831	#117	—	2	1	no	—
832	#117	—	2	2	no	—
833	#117	—	2	2	no	—
834	#117	D₄×C₃₁	1	1	yes	characteristic
835	#117	D₄×C₃₁	1	2	yes	—
836	#117	C₂³×C₃₁	1	1	yes	characteristic
837	#117	C₂³×C₃₁	1	2	yes	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
841	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₄²	—	2	1	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	—	2	2	no	—
847	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
848	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
849	#107	C₂³×C₃₁	1	1	yes	characteristic
850	#107	C₂³×C₃₁	1	2	yes	—
851	#107	C₂³×C₃₁	1	1	yes	characteristic
852	#107	C₂³×C₃₁	1	2	yes	—
853	#107	C₂³×C₃₁	1	2	yes	—
854	#106	C₂³×C₃₁	1	1	yes	characteristic
855	#106	C₂³×C₃₁	1	1	yes	characteristic
856	#106	C₂³×C₃₁	1	2	yes	—
857	#106	C₂³×C₃₁	1	2	yes	—
858	#106	C₂³×C₃₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
863	#103	C₂³×C₃₁	1	1	yes	characteristic
864	#103	C₂³×C₃₁	1	1	yes	characteristic
865	#103	C₂³×C₃₁	1	1	yes	characteristic
866	#103	C₂³×C₃₁	1	2	yes	—
867	#103	C₂³×C₃₁	1	1	yes	characteristic
868	#103	C₂³×C₃₁	1	1	yes	characteristic
869	#103	C₂³×C₃₁	1	1	yes	characteristic
870	#103	C₂³×C₃₁	1	2	yes	—
871	#103	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	1	yes	characteristic
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
886	#97	C₂³×C₃₁	1	1	yes	characteristic
887	#97	C₂³×C₃₁	1	1	yes	characteristic
888	#97	C₂³×C₃₁	1	2	yes	—
889	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₃₁	1	2	yes	—
892	C₄×C₈	C₂³×C₃₁	1	2	yes	—
893	C₃₁	#61468	1	1	yes	characteristic, direct product factor, Sylow
894	C₂⁴	—	2	2	no	—
895	#41	—	2	4	no	—
896	#41	—	2	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	1	no	—
900	#41	—	4	4	no	—
901	#41	—	8	2	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	4	1	no	—
907	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×D₄	—	2	4	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	4	no	—
925	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
926	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
927	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
928	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
929	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	8	4	no	—
943	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
945	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
949	Q₁₆	—	2	2	no	—
950	Q₁₆	—	2	2	no	—
951	SD₁₆	—	2	4	no	—
952	SD₁₆	—	2	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	#41×C₃₁	1	4	yes	complemented
956	D₈	—	2	4	no	—
957	D₈	—	2	4	no	—
958	D₈	—	4	2	no	—
959	M₁₆	—	2	4	no	—
960	M₁₆	—	2	2	no	—
961	M₁₆	—	4	1	no	—
962	M₁₆	—	4	2	no	—
963	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
966	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
967	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
987	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1028	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1030	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₃₁	1	2	yes	—
1032	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	4	4	no	—
1038	C₂³	—	4	4	no	—
1039	C₂³	—	8	2	no	—
1040	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1041	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	4	2	no	—
1050	Q₈	—	8	1	no	—
1051	Q₈	C₂×#41×C₃₁	1	2	yes	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	8	1	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	C₂×#41×C₃₁	1	2	yes	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	1	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	2	no	—
1114	C₈	C₂×#41×C₃₁	1	2	yes	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	8	8	no	—
1131	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1132	C₄	—	2	2	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	C₃₁×#575	1	2	yes	—
1149	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1150	C₄	C₃₁×#585	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	2	no	—
1156	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1157	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1158	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3481	C₂	semidirect
2. C₃₁×#3480	C₂	semidirect
3. C₃₁×#3396	C₂	semidirect
4. C₃₁×#3381	C₂	semidirect
5. C₃₁×#3365	C₂	semidirect
6. C₃₁×#3361	C₂	semidirect
7. C₃₁×#3356	C₂	semidirect
8. C₃₁×#3355	C₂	semidirect
9. C₃₁×#3333	C₂	semidirect
10. C₃₁×#3326	C₂	semidirect
11. C₃₁×#3324	C₂	semidirect
12. C₃₁×#3322	C₂	semidirect
13. C₃₁×#3275	C₂	semidirect
14. C₃₁×#3274	C₂	semidirect
15. C₃₁×#3184	C₂	semidirect
16. C₃₁×#3183	C₂	semidirect
17. C₃₁×#3115	C₂	semidirect
18. C₃₁×#3114	C₂	semidirect
19. C₃₁×#3112	C₂	semidirect
20. C₃₁×#3111	C₂	semidirect
21. C₃₁×#2971	C₂	semidirect
22. C₄×C₃₁×#137	C₂	semidirect
23. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
28. C₃₁×#559	C₂²	semidirect
29. C₃₁×#557	C₂²	semidirect
37. C₃₁×#553	C₂²	semidirect
40. C₃₁×#548	C₂²	semidirect
46. C₃₁×#532	C₂²	semidirect
50. C₃₁×#529	C₂²	semidirect
55. C₄×#41×C₃₁	C₂²	semidirect
56. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
59. C₃₁×#499	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#495	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#488	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#480	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
78. C₃₁×#477	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
83. C₃₁×#469	C₂²	semidirect
84. C₃₁×#469	C₂²	semidirect
86. C₃₁×#468	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#463	C₂²	semidirect
93. C₃₁×#460	C₂²	semidirect
95. C₃₁×#452	C₂²	semidirect
99. C₃₁×#448	C₂²	semidirect
101. C₈×Q₈×C₃₁	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
104. C₃₁×#442	C₂²	semidirect
105. C₃₁×#442	C₂²	semidirect
106. C₃₁×#441	C₂²	semidirect
107. C₃₁×#441	C₂²	semidirect
110. C₃₁×#440	C₂²	semidirect
111. C₃₁×#440	C₂²	semidirect
112. C₃₁×#440	C₂²	semidirect
113. C₄×Q₁₆×C₃₁	C₂²	semidirect
114. C₄×Q₁₆×C₃₁	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
123. C₃₁×#436	C₂²	semidirect
124. C₃₁×#436	C₂²	semidirect
125. C₃₁×#432	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₃₁×#428	C₂²	semidirect
129. C₃₁×#419	C₂²	semidirect
132. C₃₁×#417	C₂²	semidirect
133. C₄×M₁₆×C₃₁	C₂²	semidirect
134. C₄×M₁₆×C₃₁	C₂²	semidirect
375. SD₁₆×C₃₁	#41	semidirect
454. #61468	C₃₁	direct (N × H)
536. #3481	C₂×C₃₁	semidirect
537. #3480	C₂×C₃₁	semidirect
538. #3396	C₂×C₃₁	semidirect
539. #3381	C₂×C₃₁	semidirect
540. #3365	C₂×C₃₁	semidirect
541. #3361	C₂×C₃₁	semidirect
542. #3356	C₂×C₃₁	semidirect
543. #3355	C₂×C₃₁	semidirect
544. #3333	C₂×C₃₁	semidirect
545. #3326	C₂×C₃₁	semidirect
546. #3324	C₂×C₃₁	semidirect
547. #3322	C₂×C₃₁	semidirect
548. #3275	C₂×C₃₁	semidirect
549. #3274	C₂×C₃₁	semidirect
550. #3184	C₂×C₃₁	semidirect
551. #3183	C₂×C₃₁	semidirect
552. #3115	C₂×C₃₁	semidirect
553. #3114	C₂×C₃₁	semidirect
554. #3112	C₂×C₃₁	semidirect
555. #3111	C₂×C₃₁	semidirect
556. #2971	C₂×C₃₁	semidirect
557. C₄×#137	C₂×C₃₁	semidirect
558. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
599. #559	C₂²×C₃₁	semidirect
600. #557	C₂²×C₃₁	semidirect
608. #553	C₂²×C₃₁	semidirect
611. #548	C₂²×C₃₁	semidirect
617. #532	C₂²×C₃₁	semidirect
621. #529	C₂²×C₃₁	semidirect
626. C₄×#41	C₂²×C₃₁	semidirect
627. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
630. #499	C₂²×C₃₁	semidirect
631. #498	C₂²×C₃₁	semidirect
632. #495	C₂²×C₃₁	semidirect
634. #488	C₂²×C₃₁	semidirect
635. #488	C₂²×C₃₁	semidirect
637. #486	C₂²×C₃₁	semidirect
638. #485	C₂²×C₃₁	semidirect
639. #483	C₂²×C₃₁	semidirect
641. #482	C₂²×C₃₁	semidirect
642. #480	C₂²×C₃₁	semidirect
643. #480	C₂²×C₃₁	semidirect
644. #479	C₂²×C₃₁	semidirect
646. #478	C₂²×C₃₁	semidirect
647. #478	C₂²×C₃₁	semidirect
648. #477	C₂²×C₃₁	semidirect
649. #477	C₂²×C₃₁	semidirect
650. #475	C₂²×C₃₁	semidirect
652. #470	C₂²×C₃₁	semidirect
654. #469	C₂²×C₃₁	semidirect
655. #469	C₂²×C₃₁	semidirect
657. #468	C₂²×C₃₁	semidirect
658. #464	C₂²×C₃₁	semidirect
660. #463	C₂²×C₃₁	semidirect
661. #463	C₂²×C₃₁	semidirect
664. #460	C₂²×C₃₁	semidirect
666. #452	C₂²×C₃₁	semidirect
670. #448	C₂²×C₃₁	semidirect
672. C₈×Q₈	C₂²×C₃₁	semidirect
673. C₈×Q₈	C₂²×C₃₁	semidirect
675. #442	C₂²×C₃₁	semidirect
676. #442	C₂²×C₃₁	semidirect
677. #441	C₂²×C₃₁	semidirect
678. #441	C₂²×C₃₁	semidirect
681. #440	C₂²×C₃₁	semidirect
682. #440	C₂²×C₃₁	semidirect
683. #440	C₂²×C₃₁	semidirect
684. C₄×Q₁₆	C₂²×C₃₁	semidirect
685. C₄×Q₁₆	C₂²×C₃₁	semidirect
689. C₄×SD₁₆	C₂²×C₃₁	semidirect
691. C₄×D₈	C₂²×C₃₁	semidirect
694. #436	C₂²×C₃₁	semidirect
695. #436	C₂²×C₃₁	semidirect
696. #432	C₂²×C₃₁	semidirect
697. #432	C₂²×C₃₁	semidirect
698. #428	C₂²×C₃₁	semidirect
699. #428	C₂²×C₃₁	semidirect
700. #419	C₂²×C₃₁	semidirect
703. #417	C₂²×C₃₁	semidirect
704. C₄×M₁₆	C₂²×C₃₁	semidirect
705. C₄×M₁₆	C₂²×C₃₁	semidirect
893. C₃₁	#61468	direct (N × H)
955. SD₁₆	#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×#3481	2
C₃₁×#3480	2
C₃₁×#3396	2
C₃₁×#3381	2
C₃₁×#3365	2
C₃₁×#3361	2
C₃₁×#3356	2
C₃₁×#3355	2
C₃₁×#3333	2
C₃₁×#3326	2
C₃₁×#3324	2
C₃₁×#3322	2
C₃₁×#3275	2
C₃₁×#3274	2
C₃₁×#3184	2
C₃₁×#3183	2
C₃₁×#3115	2
C₃₁×#3114	2
C₃₁×#3112	2
C₃₁×#3111	2
C₃₁×#2971	2
C₄×C₃₁×#137	2
C₄×C₃₁×AGL(1,ℤ/8)	2
#61468	31

Subgroups — C31×#61468 #21518227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61468 #21518227