Subgroups — C₃₁×#62006 #21518765

Order 7936.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3514	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×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3326	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3277	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×#3256	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3211	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3040	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
25	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
27	C₃₁×#559	—	2	1	no	—
28	C₃₁×#559	C₂²	1	1	yes	characteristic
29	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#556	—	2	1	no	—
32	C₃₁×#556	C₂²	1	1	yes	characteristic
33	C₃₁×#556	C₂²	1	1	yes	characteristic
34	C₃₁×#555	—	2	1	no	—
35	C₃₁×#553	—	2	2	no	—
36	C₃₁×#553	C₂²	1	2	yes	complemented
37	C₃₁×#551	—	2	2	no	—
38	C₃₁×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#548	C₂²	1	2	yes	—
41	C₃₁×#548	C₂²	1	2	yes	complemented
42	C₃₁×#546	—	2	1	no	—
43	C₃₁×#546	C₂²	1	2	yes	—
44	D₄²×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#542	—	2	1	no	—
46	C₃₁×#538	—	2	2	no	—
47	C₃₁×#532	—	2	1	no	—
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#529	—	2	2	no	—
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#529	C₂²	1	2	yes	complemented
54	C₂×C₃₁×#124	C₂²	1	2	yes	—
55	C₃₁×#518	—	2	1	no	—
56	C₄×#41×C₃₁	—	2	1	no	—
57	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
58	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#495	C₂²	1	2	yes	—
61	C₃₁×#495	C₂²	1	2	yes	complemented
62	C₃₁×#493	C₂²	1	1	yes	characteristic
63	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#488	C₂²	1	2	yes	—
65	C₃₁×#488	C₂²	1	2	yes	complemented
66	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#486	C₂²	1	1	yes	characteristic
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#482	C₂²	1	2	yes	—
71	C₃₁×#480	C₂²	1	1	yes	characteristic
72	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#474	C₂²	1	1	yes	characteristic
79	C₃₁×#470	C₂²	1	2	yes	complemented
80	C₃₁×#469	C₂²	1	2	yes	—
81	C₃₁×#469	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	—
83	C₃₁×#468	C₂²	1	2	yes	complemented
84	C₃₁×#468	C₂²	1	2	yes	complemented
85	C₃₁×#464	C₂²	1	1	yes	characteristic
86	C₃₁×#464	C₂²	1	1	yes	characteristic
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	complemented
89	C₃₁×#464	C₂²	1	2	yes	complemented
90	C₃₁×#464	C₂²	1	2	yes	complemented
91	C₃₁×#464	C₂²	1	2	yes	complemented
92	C₃₁×#463	C₂²	1	2	yes	—
93	C₃₁×#463	C₂²	1	2	yes	—
94	C₃₁×#463	C₂²	1	2	yes	complemented
95	C₃₁×#463	C₂²	1	2	yes	complemented
96	C₃₁×#463	C₂²	1	2	yes	complemented
97	C₃₁×#463	C₂²	1	2	yes	complemented
98	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#460	C₂²	1	1	yes	characteristic
101	C₃₁×#460	C₂²	1	1	yes	characteristic
102	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#452	C₂²	1	2	yes	complemented
105	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#451	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	2	yes	complemented
110	C₃₁×#449	C₂²	1	2	yes	complemented
111	C₃₁×#448	C₂²	1	1	yes	characteristic
112	C₃₁×#448	C₂²	1	2	yes	complemented
113	C₃₁×#447	C₂²	1	2	yes	—
114	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
123	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
124	C₃₁×#436	C₂²	1	1	yes	characteristic
125	C₃₁×#436	C₂²	1	1	yes	characteristic
126	C₃₁×#436	C₂²	1	2	yes	complemented
127	C₃₁×#436	C₂²	1	2	yes	complemented
128	C₃₁×#431	C₂²	1	2	yes	complemented
129	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#423	C₂²	1	2	yes	complemented
132	C₃₁×#419	C₂²	1	2	yes	complemented
133	C₃₁×#418	C₂²	1	2	yes	—
134	C₃₁×#417	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₃₁×#137	—	4	4	no	—
144	C₃₁×#137	—	4	4	no	—
145	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	2	yes	—
159	C₂×D₈×C₃₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
162	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	—	2	1	no	—
164	C₃₁×C₄⋊Q₈	—	2	1	no	—
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#127	—	2	1	no	—
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	C₂³	1	1	yes	characteristic
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	1	no	—
187	C₃₁×#124	C₂³	1	1	yes	characteristic
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#124	C₂³	1	2	yes	—
191	C₃₁×#124	C₂³	1	2	yes	—
192	C₃₁×#123	—	2	1	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	1	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#120	—	2	2	no	—
220	C₃₁×#120	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	2	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	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	2	no	—
245	C₄×D₄×C₃₁	—	2	2	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
250	C₄×D₄×C₃₁	D₄	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₃₁	C₂³	1	2	yes	—
257	C₃₁×#117	—	2	1	no	—
258	C₃₁×#117	—	2	2	no	—
259	C₃₁×#117	—	2	2	no	—
260	C₃₁×#117	—	2	1	no	—
261	C₃₁×#117	—	2	2	no	—
262	C₃₁×#117	D₄	1	1	yes	characteristic
263	C₃₁×#117	D₄	1	2	yes	—
264	C₃₁×#117	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂×C₄²×C₃₁	—	2	1	no	—
271	C₂×C₄²×C₃₁	—	2	2	no	—
272	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₄×C₈×C₃₁	C₂³	1	2	yes	—
315	C₂⁴×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	4	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	4	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	4	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	2	2	no	—
326	C₂×Q₈×C₃₁	—	4	1	no	—
327	C₂×Q₈×C₃₁	—	4	2	no	—
328	C₂×Q₈×C₃₁	—	4	2	no	—
329	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	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	—	2	1	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	4	2	no	—
346	C₂×D₄×C₃₁	—	4	2	no	—
347	C₂×D₄×C₃₁	—	4	4	no	—
348	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
358	C₂²×C₄×C₃₁	—	2	1	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	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
368	Q₁₆×C₃₁	—	2	2	no	—
369	Q₁₆×C₃₁	—	2	4	no	—
370	Q₁₆×C₃₁	—	4	1	no	—
371	Q₁₆×C₃₁	—	4	2	no	—
372	SD₁₆×C₃₁	—	2	2	no	—
373	SD₁₆×C₃₁	—	2	4	no	—
374	SD₁₆×C₃₁	—	4	2	no	—
375	SD₁₆×C₃₁	—	4	1	no	—
376	SD₁₆×C₃₁	—	4	2	no	—
377	SD₁₆×C₃₁	—	4	2	no	—
378	SD₁₆×C₃₁	—	4	2	no	—
379	D₈×C₃₁	—	4	2	no	—
380	D₈×C₃₁	—	4	2	no	—
381	D₈×C₃₁	—	4	2	no	—
382	M₁₆×C₃₁	—	4	2	no	—
383	M₁₆×C₃₁	—	4	2	no	—
384	M₁₆×C₃₁	—	4	2	no	—
385	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	1	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	—	2	1	no	—
448	C₄²×C₃₁	—	2	1	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	—	2	1	no	—
451	C₄²×C₃₁	C₂×D₄	1	2	yes	—
452	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₃₁	C₂×D₄	1	2	yes	—
454	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₃₁	C₂⁴	1	2	yes	—
456	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
457	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
458	#62006	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂³×C₃₁	—	2	1	no	—
460	C₂³×C₃₁	—	2	2	no	—
461	C₂³×C₃₁	—	2	2	no	—
462	C₂³×C₃₁	—	4	4	no	—
463	C₂³×C₃₁	—	8	2	no	—
464	C₂³×C₃₁	—	8	2	no	—
465	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
466	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₃₁	—	2	2	no	—
468	Q₈×C₃₁	—	2	1	no	—
469	Q₈×C₃₁	—	2	1	no	—
470	Q₈×C₃₁	—	2	1	no	—
471	Q₈×C₃₁	—	2	2	no	—
472	Q₈×C₃₁	—	2	1	no	—
473	Q₈×C₃₁	—	2	2	no	—
474	Q₈×C₃₁	—	2	1	no	—
475	Q₈×C₃₁	—	4	2	no	—
476	Q₈×C₃₁	—	4	2	no	—
477	Q₈×C₃₁	—	8	2	no	—
478	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
479	D₄×C₃₁	—	2	2	no	—
480	D₄×C₃₁	—	2	1	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	2	no	—
483	D₄×C₃₁	—	2	2	no	—
484	D₄×C₃₁	—	2	2	no	—
485	D₄×C₃₁	—	2	1	no	—
486	D₄×C₃₁	—	4	2	no	—
487	D₄×C₃₁	—	4	4	no	—
488	D₄×C₃₁	—	4	4	no	—
489	D₄×C₃₁	—	4	4	no	—
490	D₄×C₃₁	—	4	2	no	—
491	D₄×C₃₁	—	4	2	no	—
492	D₄×C₃₁	—	8	1	no	—
493	D₄×C₃₁	—	8	1	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	1	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	2	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	1	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
507	C₂×C₄×C₃₁	—	2	2	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	2	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	4	1	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	4	4	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	4	4	no	—
518	C₂×C₄×C₃₁	—	4	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	—	8	2	no	—
522	C₂×C₄×C₃₁	—	8	1	no	—
523	C₂×C₄×C₃₁	—	8	2	no	—
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	2	no	—
535	C₈×C₃₁	—	2	1	no	—
536	C₈×C₃₁	—	2	2	no	—
537	C₈×C₃₁	—	2	1	no	—
538	C₈×C₃₁	—	2	1	no	—
539	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3396	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3394	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3328	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3326	C₂×C₃₁	1	2	yes	complemented
547	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3322	C₂×C₃₁	1	2	yes	complemented
549	#3278	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3277	C₂×C₃₁	1	2	yes	complemented
551	#3275	C₂×C₃₁	1	2	yes	complemented
552	#3274	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3256	C₂×C₃₁	1	2	yes	complemented
554	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3211	C₂×C₃₁	1	2	yes	complemented
556	#3207	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3102	C₂×C₃₁	1	2	yes	complemented
559	#3040	C₂×C₃₁	1	2	yes	complemented
560	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#2991	C₂×C₃₁	1	1	yes	characteristic, complemented
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	2	1	no	—
565	C₂²×C₃₁	—	2	2	no	—
566	C₂²×C₃₁	—	2	1	no	—
567	C₂²×C₃₁	—	2	2	no	—
568	C₂²×C₃₁	—	4	2	no	—
569	C₂²×C₃₁	—	4	2	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	2	no	—
573	C₂²×C₃₁	—	4	1	no	—
574	C₂²×C₃₁	—	4	2	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	4	2	no	—
577	C₂²×C₃₁	—	16	4	no	—
578	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
579	C₄×C₃₁	—	2	1	no	—
580	C₄×C₃₁	—	2	2	no	—
581	C₄×C₃₁	—	2	1	no	—
582	C₄×C₃₁	—	2	2	no	—
583	C₄×C₃₁	—	2	1	no	—
584	C₄×C₃₁	—	2	2	no	—
585	C₄×C₃₁	—	2	1	no	—
586	C₄×C₃₁	—	2	2	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	—	4	1	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	2	no	—
595	C₄×C₃₁	#575	1	2	yes	—
596	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₄×C₃₁	#585	1	1	yes	characteristic
598	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
599	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
600	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
601	#559	—	2	1	no	—
602	#559	C₂²×C₃₁	1	1	yes	characteristic
603	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	#556	—	2	1	no	—
606	#556	C₂²×C₃₁	1	1	yes	characteristic
607	#556	C₂²×C₃₁	1	1	yes	characteristic
608	#555	—	2	1	no	—
609	#553	—	2	2	no	—
610	#553	C₂²×C₃₁	1	2	yes	complemented
611	#551	—	2	2	no	—
612	#550	C₂²×C₃₁	1	1	yes	characteristic
613	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
614	#548	C₂²×C₃₁	1	2	yes	—
615	#548	C₂²×C₃₁	1	2	yes	complemented
616	#546	—	2	1	no	—
617	#546	C₂²×C₃₁	1	2	yes	—
618	D₄²	C₂²×C₃₁	1	1	yes	characteristic
619	#542	—	2	1	no	—
620	#538	—	2	2	no	—
621	#532	—	2	1	no	—
622	#532	C₂²×C₃₁	1	1	yes	characteristic
623	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#529	—	2	2	no	—
625	#529	C₂²×C₃₁	1	2	yes	—
626	#529	C₂²×C₃₁	1	1	yes	characteristic
627	#529	C₂²×C₃₁	1	2	yes	complemented
628	C₂×#124	C₂²×C₃₁	1	2	yes	—
629	#518	—	2	1	no	—
630	C₄×#41	—	2	1	no	—
631	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
632	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
633	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#495	C₂²×C₃₁	1	2	yes	—
635	#495	C₂²×C₃₁	1	2	yes	complemented
636	#493	C₂²×C₃₁	1	1	yes	characteristic
637	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#488	C₂²×C₃₁	1	2	yes	—
639	#488	C₂²×C₃₁	1	2	yes	complemented
640	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#486	C₂²×C₃₁	1	1	yes	characteristic
642	#485	C₂²×C₃₁	1	2	yes	complemented
643	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#482	C₂²×C₃₁	1	2	yes	—
645	#480	C₂²×C₃₁	1	1	yes	characteristic
646	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#479	C₂²×C₃₁	1	2	yes	complemented
649	#478	C₂²×C₃₁	1	2	yes	complemented
650	#478	C₂²×C₃₁	1	2	yes	complemented
651	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#474	C₂²×C₃₁	1	1	yes	characteristic
653	#470	C₂²×C₃₁	1	2	yes	complemented
654	#469	C₂²×C₃₁	1	2	yes	—
655	#469	C₂²×C₃₁	1	2	yes	—
656	#468	C₂²×C₃₁	1	2	yes	—
657	#468	C₂²×C₃₁	1	2	yes	complemented
658	#468	C₂²×C₃₁	1	2	yes	complemented
659	#464	C₂²×C₃₁	1	1	yes	characteristic
660	#464	C₂²×C₃₁	1	1	yes	characteristic
661	#464	C₂²×C₃₁	1	2	yes	—
662	#464	C₂²×C₃₁	1	2	yes	complemented
663	#464	C₂²×C₃₁	1	2	yes	complemented
664	#464	C₂²×C₃₁	1	2	yes	complemented
665	#464	C₂²×C₃₁	1	2	yes	complemented
666	#463	C₂²×C₃₁	1	2	yes	—
667	#463	C₂²×C₃₁	1	2	yes	—
668	#463	C₂²×C₃₁	1	2	yes	complemented
669	#463	C₂²×C₃₁	1	2	yes	complemented
670	#463	C₂²×C₃₁	1	2	yes	complemented
671	#463	C₂²×C₃₁	1	2	yes	complemented
672	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	#460	C₂²×C₃₁	1	1	yes	characteristic
675	#460	C₂²×C₃₁	1	1	yes	characteristic
676	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#459	C₂²×C₃₁	1	1	yes	characteristic
678	#452	C₂²×C₃₁	1	2	yes	complemented
679	#451	C₂²×C₃₁	1	2	yes	complemented
680	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#450	C₂²×C₃₁	1	2	yes	—
682	#449	C₂²×C₃₁	1	2	yes	—
683	#449	C₂²×C₃₁	1	2	yes	complemented
684	#449	C₂²×C₃₁	1	2	yes	complemented
685	#448	C₂²×C₃₁	1	1	yes	characteristic
686	#448	C₂²×C₃₁	1	2	yes	complemented
687	#447	C₂²×C₃₁	1	2	yes	—
688	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
692	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
694	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
695	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
696	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
697	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
698	#436	C₂²×C₃₁	1	1	yes	characteristic
699	#436	C₂²×C₃₁	1	1	yes	characteristic
700	#436	C₂²×C₃₁	1	2	yes	complemented
701	#436	C₂²×C₃₁	1	2	yes	complemented
702	#431	C₂²×C₃₁	1	2	yes	complemented
703	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	#423	C₂²×C₃₁	1	2	yes	complemented
706	#419	C₂²×C₃₁	1	2	yes	complemented
707	#418	C₂²×C₃₁	1	2	yes	—
708	#417	C₂²×C₃₁	1	2	yes	complemented
709	C₂×C₃₁	—	4	1	no	—
710	C₂×C₃₁	—	4	2	no	—
711	C₂×C₃₁	—	8	2	no	—
712	C₂×C₃₁	—	8	2	no	—
713	C₂×C₃₁	—	8	1	no	—
714	C₂×C₃₁	#3488	1	1	yes	characteristic
715	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
716	C₂×C₃₁	#3584	1	1	yes	characteristic
717	C₂×#41	—	2	1	no	—
718	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
719	C₂×#41	C₂³×C₃₁	1	2	yes	—
720	C₂×#41	C₂³×C₃₁	1	2	yes	—
721	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
723	C₂²×D₄	—	2	1	no	—
724	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
725	#137	—	4	4	no	—
726	#137	—	4	4	no	—
727	AGL(1,ℤ/8)	—	4	4	no	—
728	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
731	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
739	C₂×D₈	C₂³×C₃₁	1	2	yes	—
740	C₂×D₈	C₂³×C₃₁	1	2	yes	—
741	C₂×D₈	C₂³×C₃₁	1	2	yes	—
742	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
743	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
744	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
749	#127	—	2	1	no	—
750	#127	C₂³×C₃₁	1	1	yes	characteristic
751	#127	C₂³×C₃₁	1	1	yes	characteristic
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	1	no	—
757	#126	—	2	2	no	—
758	#125	—	2	2	no	—
759	#125	C₂³×C₃₁	1	1	yes	characteristic
760	#125	C₂³×C₃₁	1	2	yes	—
761	#124	—	2	1	no	—
762	#124	—	2	1	no	—
763	#124	—	2	1	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	1	no	—
769	#124	C₂³×C₃₁	1	1	yes	characteristic
770	#124	C₂³×C₃₁	1	2	yes	—
771	#124	C₂³×C₃₁	1	2	yes	—
772	#124	C₂³×C₃₁	1	2	yes	—
773	#124	C₂³×C₃₁	1	2	yes	—
774	#123	—	2	1	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	C₂³×C₃₁	1	2	yes	—
798	#121	C₂³×C₃₁	1	1	yes	characteristic
799	#121	C₂³×C₃₁	1	2	yes	—
800	#121	C₂³×C₃₁	1	2	yes	—
801	#120	—	2	2	no	—
802	#120	—	2	2	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
813	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
814	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
832	C₄×D₄	D₄×C₃₁	1	2	yes	—
833	C₄×D₄	C₂³×C₃₁	1	2	yes	—
834	C₄×D₄	C₂³×C₃₁	1	2	yes	—
835	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₃₁	1	2	yes	—
837	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₃₁	1	2	yes	—
839	#117	—	2	1	no	—
840	#117	—	2	2	no	—
841	#117	—	2	2	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	D₄×C₃₁	1	1	yes	characteristic
845	#117	D₄×C₃₁	1	2	yes	—
846	#117	C₂³×C₃₁	1	2	yes	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₄²	—	2	1	no	—
853	C₂×C₄²	—	2	2	no	—
854	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
855	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
856	#107	C₂³×C₃₁	1	1	yes	characteristic
857	#107	C₂³×C₃₁	1	2	yes	—
858	#107	C₂³×C₃₁	1	1	yes	characteristic
859	#106	C₂³×C₃₁	1	1	yes	characteristic
860	#106	C₂³×C₃₁	1	1	yes	characteristic
861	#106	C₂³×C₃₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
867	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
869	#103	C₂³×C₃₁	1	2	yes	—
870	#103	C₂³×C₃₁	1	2	yes	—
871	#103	C₂³×C₃₁	1	1	yes	characteristic
872	#103	C₂³×C₃₁	1	2	yes	—
873	#103	C₂³×C₃₁	1	2	yes	—
874	#103	C₂³×C₃₁	1	1	yes	characteristic
875	#103	C₂³×C₃₁	1	1	yes	characteristic
876	#103	C₂³×C₃₁	1	1	yes	characteristic
877	#103	C₂³×C₃₁	1	1	yes	characteristic
878	#103	C₂³×C₃₁	1	1	yes	characteristic
879	#103	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	2	yes	—
884	#102	C₂³×C₃₁	1	2	yes	—
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	1	yes	characteristic
887	#102	C₂³×C₃₁	1	2	yes	—
888	#102	C₂³×C₃₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
892	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₃₁	1	2	yes	—
896	C₄×C₈	C₂³×C₃₁	1	2	yes	—
897	C₃₁	#62006	1	1	yes	characteristic, direct product factor, Sylow
898	C₂⁴	—	2	2	no	—
899	#41	—	2	4	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	4	4	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	—	4	2	no	—
912	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	4	no	—
931	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
933	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
936	C₂²×C₄	—	2	1	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	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
947	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
948	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
951	Q₁₆	—	2	2	no	—
952	Q₁₆	—	2	4	no	—
953	Q₁₆	—	4	1	no	—
954	Q₁₆	—	4	2	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	2	4	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	1	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	D₈	—	4	2	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	4	2	no	—
966	M₁₆	—	4	2	no	—
967	M₁₆	—	4	2	no	—
968	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
972	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
973	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1035	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1037	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₃₁	1	2	yes	—
1039	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1048	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	4	2	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1114	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	16	4	no	—
1137	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	2	no	—
1145	C₄	—	2	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	C₃₁×#575	1	2	yes	—
1155	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1156	C₄	C₃₁×#585	1	1	yes	characteristic
1157	C₂	—	4	2	no	—
1158	C₂	—	4	1	no	—
1159	C₂	—	8	1	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	8	2	no	—
1162	C₂	C₃₁×#3488	1	1	yes	characteristic
1163	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1164	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3514	C₂	semidirect
2. C₃₁×#3480	C₂	semidirect
3. C₃₁×#3396	C₂	semidirect
4. C₃₁×#3394	C₂	semidirect
5. C₃₁×#3365	C₂	semidirect
6. C₃₁×#3364	C₂	semidirect
7. C₃₁×#3328	C₂	semidirect
8. C₃₁×#3326	C₂	semidirect
9. C₃₁×#3324	C₂	semidirect
10. C₃₁×#3322	C₂	semidirect
11. C₃₁×#3278	C₂	semidirect
12. C₃₁×#3277	C₂	semidirect
13. C₃₁×#3275	C₂	semidirect
14. C₃₁×#3274	C₂	semidirect
15. C₃₁×#3256	C₂	semidirect
16. C₃₁×#3251	C₂	semidirect
17. C₃₁×#3211	C₂	semidirect
18. C₃₁×#3207	C₂	semidirect
19. C₃₁×#3108	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3040	C₂	semidirect
22. C₃₁×#3037	C₂	semidirect
23. C₃₁×#2991	C₂	semidirect
24. C₂×C₃₁×#137	C₂²	semidirect
25. C₂×C₃₁×#137	C₂²	semidirect
29. C₃₁×#559	C₂²	semidirect
30. C₃₁×#557	C₂²	semidirect
36. C₃₁×#553	C₂²	semidirect
41. C₃₁×#548	C₂²	semidirect
49. C₃₁×#532	C₂²	semidirect
53. C₃₁×#529	C₂²	semidirect
58. C₄×#41×C₃₁	C₂²	semidirect
59. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
61. C₃₁×#495	C₂²	semidirect
63. C₃₁×#492	C₂²	semidirect
65. C₃₁×#488	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
79. C₃₁×#470	C₂²	semidirect
83. C₃₁×#468	C₂²	semidirect
84. C₃₁×#468	C₂²	semidirect
88. C₃₁×#464	C₂²	semidirect
89. C₃₁×#464	C₂²	semidirect
90. C₃₁×#464	C₂²	semidirect
91. C₃₁×#464	C₂²	semidirect
94. C₃₁×#463	C₂²	semidirect
95. C₃₁×#463	C₂²	semidirect
96. C₃₁×#463	C₂²	semidirect
97. C₃₁×#463	C₂²	semidirect
98. C₃₁×#462	C₂²	semidirect
99. C₃₁×#462	C₂²	semidirect
102. C₃₁×#460	C₂²	semidirect
104. C₃₁×#452	C₂²	semidirect
105. C₃₁×#451	C₂²	semidirect
106. C₃₁×#451	C₂²	semidirect
109. C₃₁×#449	C₂²	semidirect
110. C₃₁×#449	C₂²	semidirect
112. C₃₁×#448	C₂²	semidirect
114. C₈×Q₈×C₃₁	C₂²	semidirect
115. C₈×Q₈×C₃₁	C₂²	semidirect
116. C₄×Q₁₆×C₃₁	C₂²	semidirect
117. C₄×Q₁₆×C₃₁	C₂²	semidirect
118. C₄×Q₁₆×C₃₁	C₂²	semidirect
121. C₄×SD₁₆×C₃₁	C₂²	semidirect
122. C₄×SD₁₆×C₃₁	C₂²	semidirect
123. C₄×D₈×C₃₁	C₂²	semidirect
126. C₃₁×#436	C₂²	semidirect
127. C₃₁×#436	C₂²	semidirect
128. C₃₁×#431	C₂²	semidirect
129. C₃₁×#431	C₂²	semidirect
130. C₃₁×#423	C₂²	semidirect
131. C₃₁×#423	C₂²	semidirect
132. C₃₁×#419	C₂²	semidirect
134. C₃₁×#417	C₂²	semidirect
458. #62006	C₃₁	direct (N × H)
539. #3514	C₂×C₃₁	semidirect
540. #3480	C₂×C₃₁	semidirect
541. #3396	C₂×C₃₁	semidirect
542. #3394	C₂×C₃₁	semidirect
543. #3365	C₂×C₃₁	semidirect
544. #3364	C₂×C₃₁	semidirect
545. #3328	C₂×C₃₁	semidirect
546. #3326	C₂×C₃₁	semidirect
547. #3324	C₂×C₃₁	semidirect
548. #3322	C₂×C₃₁	semidirect
549. #3278	C₂×C₃₁	semidirect
550. #3277	C₂×C₃₁	semidirect
551. #3275	C₂×C₃₁	semidirect
552. #3274	C₂×C₃₁	semidirect
553. #3256	C₂×C₃₁	semidirect
554. #3251	C₂×C₃₁	semidirect
555. #3211	C₂×C₃₁	semidirect
556. #3207	C₂×C₃₁	semidirect
557. #3108	C₂×C₃₁	semidirect
558. #3102	C₂×C₃₁	semidirect
559. #3040	C₂×C₃₁	semidirect
560. #3037	C₂×C₃₁	semidirect
561. #2991	C₂×C₃₁	semidirect
598. C₂×#137	C₂²×C₃₁	semidirect
599. C₂×#137	C₂²×C₃₁	semidirect
603. #559	C₂²×C₃₁	semidirect
604. #557	C₂²×C₃₁	semidirect
610. #553	C₂²×C₃₁	semidirect
615. #548	C₂²×C₃₁	semidirect
623. #532	C₂²×C₃₁	semidirect
627. #529	C₂²×C₃₁	semidirect
632. C₄×#41	C₂²×C₃₁	semidirect
633. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
635. #495	C₂²×C₃₁	semidirect
637. #492	C₂²×C₃₁	semidirect
639. #488	C₂²×C₃₁	semidirect
640. #487	C₂²×C₃₁	semidirect
642. #485	C₂²×C₃₁	semidirect
643. #483	C₂²×C₃₁	semidirect
646. #479	C₂²×C₃₁	semidirect
647. #479	C₂²×C₃₁	semidirect
648. #479	C₂²×C₃₁	semidirect
649. #478	C₂²×C₃₁	semidirect
650. #478	C₂²×C₃₁	semidirect
651. #475	C₂²×C₃₁	semidirect
653. #470	C₂²×C₃₁	semidirect
657. #468	C₂²×C₃₁	semidirect
658. #468	C₂²×C₃₁	semidirect
662. #464	C₂²×C₃₁	semidirect
663. #464	C₂²×C₃₁	semidirect
664. #464	C₂²×C₃₁	semidirect
665. #464	C₂²×C₃₁	semidirect
668. #463	C₂²×C₃₁	semidirect
669. #463	C₂²×C₃₁	semidirect
670. #463	C₂²×C₃₁	semidirect
671. #463	C₂²×C₃₁	semidirect
672. #462	C₂²×C₃₁	semidirect
673. #462	C₂²×C₃₁	semidirect
676. #460	C₂²×C₃₁	semidirect
678. #452	C₂²×C₃₁	semidirect
679. #451	C₂²×C₃₁	semidirect
680. #451	C₂²×C₃₁	semidirect
683. #449	C₂²×C₃₁	semidirect
684. #449	C₂²×C₃₁	semidirect
686. #448	C₂²×C₃₁	semidirect
688. C₈×Q₈	C₂²×C₃₁	semidirect
689. C₈×Q₈	C₂²×C₃₁	semidirect
690. C₄×Q₁₆	C₂²×C₃₁	semidirect
691. C₄×Q₁₆	C₂²×C₃₁	semidirect
692. C₄×Q₁₆	C₂²×C₃₁	semidirect
695. C₄×SD₁₆	C₂²×C₃₁	semidirect
696. C₄×SD₁₆	C₂²×C₃₁	semidirect
697. C₄×D₈	C₂²×C₃₁	semidirect
700. #436	C₂²×C₃₁	semidirect
701. #436	C₂²×C₃₁	semidirect
702. #431	C₂²×C₃₁	semidirect
703. #431	C₂²×C₃₁	semidirect
704. #423	C₂²×C₃₁	semidirect
705. #423	C₂²×C₃₁	semidirect
706. #419	C₂²×C₃₁	semidirect
708. #417	C₂²×C₃₁	semidirect
897. C₃₁	#62006	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×#3514	2
C₃₁×#3480	2
C₃₁×#3396	2
C₃₁×#3394	2
C₃₁×#3365	2
C₃₁×#3364	2
C₃₁×#3328	2
C₃₁×#3326	2
C₃₁×#3324	2
C₃₁×#3322	2
C₃₁×#3278	2
C₃₁×#3277	2
C₃₁×#3275	2
C₃₁×#3274	2
C₃₁×#3256	2
C₃₁×#3251	2
C₃₁×#3211	2
C₃₁×#3207	2
C₃₁×#3108	2
C₃₁×#3102	2
C₃₁×#3040	2
C₃₁×#3037	2
C₃₁×#2991	2
#62006	31

Subgroups — C31×#62006 #21518765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62006 #21518765