Subgroups — C₃₁×#62032 #21518791

Order 7936.

1832 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×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3329	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3275	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3266	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3042	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	—
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#563	—	2	2	no	—
28	C₃₁×#559	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#555	C₂²	1	2	yes	—
33	C₃₁×#554	—	2	1	no	—
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#551	—	2	2	no	—
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
39	C₃₁×#548	—	2	1	no	—
40	C₃₁×#548	C₂²	1	2	yes	complemented
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#546	—	2	1	no	—
43	C₃₁×#546	C₂²	1	2	yes	—
44	D₄²×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#544	—	2	1	no	—
46	C₃₁×#542	—	2	1	no	—
47	C₃₁×#542	C₂²	1	2	yes	—
48	C₃₁×#541	C₂²	1	2	yes	complemented
49	C₃₁×#539	—	2	2	no	—
50	C₃₁×#538	—	2	2	no	—
51	C₃₁×#536	C₂²	1	2	yes	complemented
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#529	—	2	1	no	—
55	C₃₁×#529	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃₁×#124	—	2	1	no	—
58	C₃₁×#518	C₂²	1	2	yes	—
59	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
60	C₃₁×#497	C₂²	1	2	yes	complemented
61	C₃₁×#495	C₂²	1	2	yes	complemented
62	C₃₁×#492	C₂²	1	1	yes	characteristic
63	C₃₁×#492	C₂²	1	1	yes	characteristic
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#487	C₂²	1	2	yes	complemented
67	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#485	C₂²	1	2	yes	complemented
70	C₃₁×#485	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#478	C₂²	1	1	yes	characteristic
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#475	C₂²	1	2	yes	complemented
78	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#470	C₂²	1	2	yes	complemented
80	C₃₁×#469	C₂²	1	2	yes	complemented
81	C₃₁×#468	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#467	C₂²	1	2	yes	complemented
84	C₃₁×#465	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#464	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	1	yes	characteristic
89	C₃₁×#463	C₂²	1	2	yes	—
90	C₃₁×#463	C₂²	1	2	yes	complemented
91	C₃₁×#463	C₂²	1	2	yes	complemented
92	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#462	C₂²	1	2	yes	complemented
95	C₃₁×#461	C₂²	1	2	yes	—
96	C₃₁×#461	C₂²	1	1	yes	characteristic
97	C₃₁×#461	C₂²	1	1	yes	characteristic
98	C₃₁×#461	C₂²	1	2	yes	—
99	C₃₁×#461	C₂²	1	2	yes	complemented
100	C₃₁×#461	C₂²	1	2	yes	complemented
101	C₃₁×#461	C₂²	1	2	yes	complemented
102	C₃₁×#460	C₂²	1	1	yes	characteristic
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#452	C₂²	1	1	yes	characteristic
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#451	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	2	yes	—
108	C₃₁×#450	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	1	yes	characteristic
110	C₃₁×#449	C₂²	1	2	yes	—
111	C₃₁×#448	C₂²	1	2	yes	—
112	C₃₁×#448	C₂²	1	2	yes	complemented
113	C₃₁×#448	C₂²	1	2	yes	complemented
114	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#440	C₂²	1	2	yes	—
117	C₃₁×#440	C₂²	1	2	yes	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	2	yes	—
121	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
123	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
124	C₃₁×#436	C₂²	1	1	yes	characteristic
125	C₃₁×#436	C₂²	1	2	yes	complemented
126	C₃₁×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
128	C₃₁×#433	C₂²	1	2	yes	complemented
129	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#419	C₂²	1	2	yes	complemented
133	C₃₁×#419	C₂²	1	2	yes	complemented
134	C₃₁×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
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×AGL(1,ℤ/8)	—	4	4	no	—
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	—	4	4	no	—
149	C₂×SD₁₆×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	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	—	2	1	no	—
164	C₃₁×C₄⋊Q₈	—	2	2	no	—
165	C₃₁×C₄⋊Q₈	—	2	1	no	—
166	C₃₁×C₄⋊Q₈	—	2	1	no	—
167	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×#127	C₂³	1	1	yes	characteristic
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#126	—	2	2	no	—
179	C₃₁×#126	—	2	1	no	—
180	C₃₁×#126	D₄	1	2	yes	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	2	no	—
183	C₃₁×#125	—	2	2	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	D₄	1	1	yes	characteristic
186	C₃₁×#125	C₂³	1	1	yes	characteristic
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	—	2	1	no	—
189	C₃₁×#124	—	2	2	no	—
190	C₃₁×#124	—	2	2	no	—
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	—	2	2	no	—
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	D₄	1	1	yes	characteristic
195	C₃₁×#124	C₂³	1	1	yes	characteristic
196	C₃₁×#124	C₂³	1	2	yes	—
197	C₃₁×#124	C₂³	1	2	yes	—
198	C₃₁×#123	—	2	1	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	—	2	2	no	—
205	C₃₁×#123	D₄	1	2	yes	—
206	C₃₁×C₂²⋊Q₈	—	2	1	no	—
207	C₃₁×C₂²⋊Q₈	—	2	1	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	—	2	2	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	2	no	—
213	C₃₁×C₂²⋊Q₈	—	2	2	no	—
214	C₃₁×C₂²⋊Q₈	—	2	2	no	—
215	C₃₁×C₂²⋊Q₈	—	2	2	no	—
216	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
217	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	1	no	—
224	C₃₁×#121	—	2	1	no	—
225	C₃₁×#121	—	2	1	no	—
226	C₃₁×#121	—	2	2	no	—
227	C₃₁×#121	D₄	1	1	yes	characteristic
228	C₃₁×#121	C₂³	1	2	yes	—
229	C₃₁×#121	C₂³	1	2	yes	—
230	C₃₁×#121	C₂³	1	1	yes	characteristic
231	C₃₁×#120	—	2	2	no	—
232	C₃₁×#120	—	2	2	no	—
233	C₄×Q₈×C₃₁	—	2	1	no	—
234	C₄×Q₈×C₃₁	—	2	1	no	—
235	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
237	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	2	no	—
247	C₄×D₄×C₃₁	—	2	2	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	—	2	2	no	—
250	C₄×D₄×C₃₁	—	2	1	no	—
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₃₁	C₂³	1	2	yes	—
259	C₃₁×#117	—	2	2	no	—
260	C₃₁×#117	—	2	1	no	—
261	C₃₁×#117	—	2	1	no	—
262	C₃₁×#117	—	2	1	no	—
263	C₃₁×#117	C₂³	1	2	yes	—
264	C₃₁×#117	C₂³	1	1	yes	characteristic
265	C₃₁×#117	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂×C₄²×C₃₁	—	2	1	no	—
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	1	yes	characteristic
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
308	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	2	yes	—
315	C₂⁴×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	4	1	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	2	no	—
320	#41×C₃₁	—	8	2	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	4	2	no	—
326	C₂×Q₈×C₃₁	—	4	2	no	—
327	C₂×Q₈×C₃₁	—	4	2	no	—
328	C₂×Q₈×C₃₁	—	4	2	no	—
329	C₂×Q₈×C₃₁	—	8	2	no	—
330	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₃₁	—	2	4	no	—
336	C₂×D₄×C₃₁	—	2	1	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	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	1	no	—
344	C₂×D₄×C₃₁	—	4	2	no	—
345	C₂×D₄×C₃₁	—	8	2	no	—
346	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
350	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₃₁	—	2	2	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	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
365	Q₁₆×C₃₁	—	4	1	no	—
366	Q₁₆×C₃₁	—	4	2	no	—
367	Q₁₆×C₃₁	—	4	2	no	—
368	SD₁₆×C₃₁	—	2	2	no	—
369	SD₁₆×C₃₁	—	2	4	no	—
370	SD₁₆×C₃₁	—	2	4	no	—
371	SD₁₆×C₃₁	—	4	2	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	SD₁₆×C₃₁	—	4	2	no	—
374	SD₁₆×C₃₁	—	4	1	no	—
375	SD₁₆×C₃₁	—	4	2	no	—
376	SD₁₆×C₃₁	—	4	2	no	—
377	D₈×C₃₁	—	2	2	no	—
378	D₈×C₃₁	—	4	2	no	—
379	M₁₆×C₃₁	—	4	2	no	—
380	M₁₆×C₃₁	—	4	2	no	—
381	C₂×C₈×C₃₁	—	4	2	no	—
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
387	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
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	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	no	—
436	C₂²⋊C₄×C₃₁	—	2	1	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	—	2	1	no	—
441	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
446	C₄²×C₃₁	—	2	1	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	—	2	2	no	—
452	C₄²×C₃₁	—	2	2	no	—
453	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₃₁	C₂⁴	1	2	yes	—
457	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
458	#62032	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂³×C₃₁	—	2	1	no	—
460	C₂³×C₃₁	—	2	1	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	2	no	—
470	Q₈×C₃₁	—	2	2	no	—
471	Q₈×C₃₁	—	2	1	no	—
472	Q₈×C₃₁	—	2	1	no	—
473	Q₈×C₃₁	—	2	2	no	—
474	Q₈×C₃₁	—	2	2	no	—
475	Q₈×C₃₁	—	2	1	no	—
476	Q₈×C₃₁	—	4	2	no	—
477	Q₈×C₃₁	—	8	2	no	—
478	Q₈×C₃₁	—	8	2	no	—
479	Q₈×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	2	1	no	—
482	D₄×C₃₁	—	2	2	no	—
483	D₄×C₃₁	—	2	1	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	2	no	—
489	D₄×C₃₁	—	4	2	no	—
490	D₄×C₃₁	—	4	2	no	—
491	D₄×C₃₁	—	8	1	no	—
492	D₄×C₃₁	—	8	2	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	1	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	2	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	2	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	4	1	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	8	1	no	—
515	C₂×C₄×C₃₁	—	8	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	2	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	2	yes	—
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	1	yes	characteristic
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	1	no	—
531	C₈×C₃₁	—	2	2	no	—
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	2	no	—
534	C₈×C₃₁	—	2	1	no	—
535	C₈×C₃₁	—	2	1	no	—
536	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3394	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3359	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3329	C₂×C₃₁	1	2	yes	complemented
543	#3328	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3321	C₂×C₃₁	1	2	yes	complemented
545	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
546	D₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3275	C₂×C₃₁	1	2	yes	complemented
548	#3272	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3266	C₂×C₃₁	1	2	yes	complemented
550	#3258	C₂×C₃₁	1	2	yes	complemented
551	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3225	C₂×C₃₁	1	2	yes	complemented
553	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3123	C₂×C₃₁	1	2	yes	complemented
555	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3042	C₂×C₃₁	1	2	yes	complemented
557	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#2993	C₂×C₃₁	1	1	yes	characteristic, 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	1	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	16	4	no	—
575	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	1	no	—
578	C₄×C₃₁	—	2	2	no	—
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	—	4	1	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	2	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	2	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	1	no	—
591	C₄×C₃₁	—	4	2	no	—
592	C₄×C₃₁	#577	1	2	yes	—
593	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
594	C₄×C₃₁	#585	1	1	yes	characteristic
595	C₂×#137	C₂²×C₃₁	1	2	yes	—
596	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
597	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
598	#563	—	2	2	no	—
599	#559	C₂²×C₃₁	1	1	yes	characteristic
600	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	#556	C₂²×C₃₁	1	1	yes	characteristic
602	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#555	C₂²×C₃₁	1	2	yes	—
604	#554	—	2	1	no	—
605	#553	—	2	1	no	—
606	#551	—	2	2	no	—
607	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
608	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
609	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
610	#548	—	2	1	no	—
611	#548	C₂²×C₃₁	1	2	yes	complemented
612	#547	C₂²×C₃₁	1	1	yes	characteristic
613	#546	—	2	1	no	—
614	#546	C₂²×C₃₁	1	2	yes	—
615	D₄²	C₂²×C₃₁	1	1	yes	characteristic
616	#544	—	2	1	no	—
617	#542	—	2	1	no	—
618	#542	C₂²×C₃₁	1	2	yes	—
619	#541	C₂²×C₃₁	1	2	yes	complemented
620	#539	—	2	2	no	—
621	#538	—	2	2	no	—
622	#536	C₂²×C₃₁	1	2	yes	complemented
623	#532	C₂²×C₃₁	1	1	yes	characteristic
624	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#529	—	2	1	no	—
626	#529	C₂²×C₃₁	1	1	yes	characteristic
627	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	C₂×#124	—	2	1	no	—
629	#518	C₂²×C₃₁	1	2	yes	—
630	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
631	#497	C₂²×C₃₁	1	2	yes	complemented
632	#495	C₂²×C₃₁	1	2	yes	complemented
633	#492	C₂²×C₃₁	1	1	yes	characteristic
634	#492	C₂²×C₃₁	1	1	yes	characteristic
635	#489	C₂²×C₃₁	1	2	yes	complemented
636	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#487	C₂²×C₃₁	1	2	yes	complemented
638	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#485	C₂²×C₃₁	1	2	yes	complemented
640	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#485	C₂²×C₃₁	1	2	yes	complemented
642	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#478	C₂²×C₃₁	1	1	yes	characteristic
645	#478	C₂²×C₃₁	1	2	yes	complemented
646	#477	C₂²×C₃₁	1	2	yes	complemented
647	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#475	C₂²×C₃₁	1	2	yes	complemented
649	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#470	C₂²×C₃₁	1	2	yes	complemented
651	#469	C₂²×C₃₁	1	2	yes	complemented
652	#468	C₂²×C₃₁	1	2	yes	—
653	#468	C₂²×C₃₁	1	2	yes	complemented
654	#467	C₂²×C₃₁	1	2	yes	complemented
655	#465	C₂²×C₃₁	1	2	yes	—
656	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#464	C₂²×C₃₁	1	2	yes	complemented
658	#464	C₂²×C₃₁	1	2	yes	complemented
659	#463	C₂²×C₃₁	1	1	yes	characteristic
660	#463	C₂²×C₃₁	1	2	yes	—
661	#463	C₂²×C₃₁	1	2	yes	complemented
662	#463	C₂²×C₃₁	1	2	yes	complemented
663	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#462	C₂²×C₃₁	1	2	yes	complemented
666	#461	C₂²×C₃₁	1	2	yes	—
667	#461	C₂²×C₃₁	1	1	yes	characteristic
668	#461	C₂²×C₃₁	1	1	yes	characteristic
669	#461	C₂²×C₃₁	1	2	yes	—
670	#461	C₂²×C₃₁	1	2	yes	complemented
671	#461	C₂²×C₃₁	1	2	yes	complemented
672	#461	C₂²×C₃₁	1	2	yes	complemented
673	#460	C₂²×C₃₁	1	1	yes	characteristic
674	#459	C₂²×C₃₁	1	1	yes	characteristic
675	#452	C₂²×C₃₁	1	1	yes	characteristic
676	#452	C₂²×C₃₁	1	2	yes	complemented
677	#451	C₂²×C₃₁	1	2	yes	complemented
678	#450	C₂²×C₃₁	1	2	yes	—
679	#450	C₂²×C₃₁	1	2	yes	—
680	#449	C₂²×C₃₁	1	1	yes	characteristic
681	#449	C₂²×C₃₁	1	2	yes	—
682	#448	C₂²×C₃₁	1	2	yes	—
683	#448	C₂²×C₃₁	1	2	yes	complemented
684	#448	C₂²×C₃₁	1	2	yes	complemented
685	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#440	C₂²×C₃₁	1	2	yes	—
688	#440	C₂²×C₃₁	1	2	yes	complemented
689	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
691	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
692	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
695	#436	C₂²×C₃₁	1	1	yes	characteristic
696	#436	C₂²×C₃₁	1	2	yes	complemented
697	#435	C₂²×C₃₁	1	2	yes	complemented
698	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
699	#433	C₂²×C₃₁	1	2	yes	complemented
700	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#424	C₂²×C₃₁	1	2	yes	complemented
702	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	#419	C₂²×C₃₁	1	2	yes	complemented
704	#419	C₂²×C₃₁	1	2	yes	complemented
705	#416	C₂²×C₃₁	1	2	yes	complemented
706	C₂×C₃₁	—	4	1	no	—
707	C₂×C₃₁	—	4	2	no	—
708	C₂×C₃₁	—	4	2	no	—
709	C₂×C₃₁	—	8	1	no	—
710	C₂×C₃₁	—	8	2	no	—
711	C₂×C₃₁	#3488	1	1	yes	characteristic
712	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
713	C₂×C₃₁	#3586	1	1	yes	characteristic
714	C₂×#41	—	2	1	no	—
715	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×#41	C₂³×C₃₁	1	2	yes	—
717	C₂²×Q₈	—	2	1	no	—
718	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
719	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
720	C₂²×D₄	—	2	1	no	—
721	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
722	#137	—	4	4	no	—
723	AGL(1,ℤ/8)	—	4	4	no	—
724	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
725	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
726	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×SD₁₆	—	4	4	no	—
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	2	yes	—
732	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
736	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
737	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₃₁	1	2	yes	—
739	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
740	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
741	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	—	2	2	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
747	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
752	#127	C₂³×C₃₁	1	1	yes	characteristic
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	1	no	—
759	#126	D₄×C₃₁	1	2	yes	—
760	#125	—	2	2	no	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	1	no	—
764	#125	D₄×C₃₁	1	1	yes	characteristic
765	#125	C₂³×C₃₁	1	1	yes	characteristic
766	#124	—	2	1	no	—
767	#124	—	2	1	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	—	2	1	no	—
773	#124	D₄×C₃₁	1	1	yes	characteristic
774	#124	C₂³×C₃₁	1	1	yes	characteristic
775	#124	C₂³×C₃₁	1	2	yes	—
776	#124	C₂³×C₃₁	1	2	yes	—
777	#123	—	2	1	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	D₄×C₃₁	1	2	yes	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
796	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
798	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	D₄×C₃₁	1	1	yes	characteristic
807	#121	C₂³×C₃₁	1	1	yes	characteristic
808	#121	C₂³×C₃₁	1	2	yes	—
809	#121	C₂³×C₃₁	1	2	yes	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
818	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
819	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×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	1	yes	characteristic
837	C₄×D₄	C₂³×C₃₁	1	2	yes	—
838	#117	—	2	2	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	C₂³×C₃₁	1	1	yes	characteristic
843	#117	C₂³×C₃₁	1	2	yes	—
844	#117	C₂³×C₃₁	1	2	yes	—
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₄²	—	2	1	no	—
852	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
853	#107	C₂³×C₃₁	1	1	yes	characteristic
854	#107	C₂³×C₃₁	1	1	yes	characteristic
855	#107	C₂³×C₃₁	1	2	yes	—
856	#106	C₂³×C₃₁	1	1	yes	characteristic
857	#106	C₂³×C₃₁	1	2	yes	—
858	#106	C₂³×C₃₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
860	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	#103	C₂³×C₃₁	1	2	yes	—
867	#103	C₂³×C₃₁	1	2	yes	—
868	#103	C₂³×C₃₁	1	2	yes	—
869	#103	C₂³×C₃₁	1	1	yes	characteristic
870	#103	C₂³×C₃₁	1	2	yes	—
871	#103	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
876	#103	C₂³×C₃₁	1	1	yes	characteristic
877	#103	C₂³×C₃₁	1	1	yes	characteristic
878	#103	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	1	yes	characteristic
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	1	yes	characteristic
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	1	yes	characteristic
884	#102	C₂³×C₃₁	1	2	yes	—
885	#102	C₂³×C₃₁	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
890	#97	C₂³×C₃₁	1	2	yes	—
891	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₃₁	1	2	yes	—
894	C₃₁	#62032	1	1	yes	characteristic, direct product factor, Sylow
895	C₂⁴	—	2	2	no	—
896	#41	—	2	2	no	—
897	#41	—	4	1	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	8	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	2	no	—
909	C₂×Q₈	—	8	2	no	—
910	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂×D₄	—	2	4	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	4	2	no	—
925	C₂×D₄	—	8	2	no	—
926	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
927	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
928	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
929	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
930	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
942	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
945	Q₁₆	—	4	1	no	—
946	Q₁₆	—	4	2	no	—
947	Q₁₆	—	4	2	no	—
948	SD₁₆	—	2	2	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	2	4	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	1	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	D₈	—	2	2	no	—
958	D₈	—	4	2	no	—
959	M₁₆	—	4	2	no	—
960	M₁₆	—	4	2	no	—
961	C₂×C₈	—	4	2	no	—
962	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	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	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
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	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1034	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₃₁	1	2	yes	—
1037	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1045	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	—	8	2	no	—
1058	Q₈	—	8	2	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	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	2	yes	—
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	1	yes	characteristic
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	1	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	2	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
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	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	C₃₁×#577	1	2	yes	—
1149	C₄	C₂×C₃₁×H(5,𝔽₂)	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	1	no	—
1156	C₂	C₃₁×#3488	1	1	yes	characteristic
1157	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1158	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3552	C₂	semidirect
2. C₃₁×#3514	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3394	C₂	semidirect
5. C₃₁×#3367	C₂	semidirect
6. C₃₁×#3359	C₂	semidirect
7. C₃₁×#3329	C₂	semidirect
8. C₃₁×#3328	C₂	semidirect
9. C₃₁×#3321	C₂	semidirect
10. C₃₁×#3302	C₂	semidirect
11. D₄×SD₁₆×C₃₁	C₂	semidirect
12. C₃₁×#3275	C₂	semidirect
13. C₃₁×#3272	C₂	semidirect
14. C₃₁×#3266	C₂	semidirect
15. C₃₁×#3258	C₂	semidirect
16. C₃₁×#3251	C₂	semidirect
17. C₃₁×#3225	C₂	semidirect
18. C₃₁×#3206	C₂	semidirect
19. C₃₁×#3123	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3042	C₂	semidirect
22. C₃₁×#3039	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
29. C₃₁×#557	C₂²	semidirect
31. C₃₁×#556	C₂²	semidirect
38. D₄×Q₈×C₃₁	C₂²	semidirect
40. C₃₁×#548	C₂²	semidirect
48. C₃₁×#541	C₂²	semidirect
51. C₃₁×#536	C₂²	semidirect
53. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
56. C₃₁×#529	C₂²	semidirect
60. C₃₁×#497	C₂²	semidirect
61. C₃₁×#495	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
67. C₃₁×#487	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#485	C₂²	semidirect
70. C₃₁×#485	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#475	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
78. C₃₁×#474	C₂²	semidirect
79. C₃₁×#470	C₂²	semidirect
80. C₃₁×#469	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#467	C₂²	semidirect
85. C₃₁×#464	C₂²	semidirect
86. C₃₁×#464	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
90. C₃₁×#463	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#462	C₂²	semidirect
93. C₃₁×#462	C₂²	semidirect
94. C₃₁×#462	C₂²	semidirect
99. C₃₁×#461	C₂²	semidirect
100. C₃₁×#461	C₂²	semidirect
101. C₃₁×#461	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#451	C₂²	semidirect
112. C₃₁×#448	C₂²	semidirect
113. C₃₁×#448	C₂²	semidirect
114. C₃₁×#446	C₂²	semidirect
115. C₈×Q₈×C₃₁	C₂²	semidirect
117. C₃₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₃₁	C₂²	semidirect
121. C₄×SD₁₆×C₃₁	C₂²	semidirect
122. C₄×SD₁₆×C₃₁	C₂²	semidirect
125. C₃₁×#436	C₂²	semidirect
126. C₃₁×#435	C₂²	semidirect
128. C₃₁×#433	C₂²	semidirect
129. C₃₁×#431	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
131. C₃₁×#423	C₂²	semidirect
132. C₃₁×#419	C₂²	semidirect
133. C₃₁×#419	C₂²	semidirect
134. C₃₁×#416	C₂²	semidirect
458. #62032	C₃₁	direct (N × H)
536. #3552	C₂×C₃₁	semidirect
537. #3514	C₂×C₃₁	semidirect
538. #3400	C₂×C₃₁	semidirect
539. #3394	C₂×C₃₁	semidirect
540. #3367	C₂×C₃₁	semidirect
541. #3359	C₂×C₃₁	semidirect
542. #3329	C₂×C₃₁	semidirect
543. #3328	C₂×C₃₁	semidirect
544. #3321	C₂×C₃₁	semidirect
545. #3302	C₂×C₃₁	semidirect
546. D₄×SD₁₆	C₂×C₃₁	semidirect
547. #3275	C₂×C₃₁	semidirect
548. #3272	C₂×C₃₁	semidirect
549. #3266	C₂×C₃₁	semidirect
550. #3258	C₂×C₃₁	semidirect
551. #3251	C₂×C₃₁	semidirect
552. #3225	C₂×C₃₁	semidirect
553. #3206	C₂×C₃₁	semidirect
554. #3123	C₂×C₃₁	semidirect
555. #3102	C₂×C₃₁	semidirect
556. #3042	C₂×C₃₁	semidirect
557. #3039	C₂×C₃₁	semidirect
558. #2993	C₂×C₃₁	semidirect
600. #557	C₂²×C₃₁	semidirect
602. #556	C₂²×C₃₁	semidirect
609. D₄×Q₈	C₂²×C₃₁	semidirect
611. #548	C₂²×C₃₁	semidirect
619. #541	C₂²×C₃₁	semidirect
622. #536	C₂²×C₃₁	semidirect
624. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
627. #529	C₂²×C₃₁	semidirect
631. #497	C₂²×C₃₁	semidirect
632. #495	C₂²×C₃₁	semidirect
635. #489	C₂²×C₃₁	semidirect
636. #487	C₂²×C₃₁	semidirect
637. #487	C₂²×C₃₁	semidirect
638. #487	C₂²×C₃₁	semidirect
639. #485	C₂²×C₃₁	semidirect
640. #485	C₂²×C₃₁	semidirect
641. #485	C₂²×C₃₁	semidirect
642. #482	C₂²×C₃₁	semidirect
643. #479	C₂²×C₃₁	semidirect
645. #478	C₂²×C₃₁	semidirect
646. #477	C₂²×C₃₁	semidirect
647. #475	C₂²×C₃₁	semidirect
648. #475	C₂²×C₃₁	semidirect
649. #474	C₂²×C₃₁	semidirect
650. #470	C₂²×C₃₁	semidirect
651. #469	C₂²×C₃₁	semidirect
653. #468	C₂²×C₃₁	semidirect
654. #467	C₂²×C₃₁	semidirect
656. #464	C₂²×C₃₁	semidirect
657. #464	C₂²×C₃₁	semidirect
658. #464	C₂²×C₃₁	semidirect
661. #463	C₂²×C₃₁	semidirect
662. #463	C₂²×C₃₁	semidirect
663. #462	C₂²×C₃₁	semidirect
664. #462	C₂²×C₃₁	semidirect
665. #462	C₂²×C₃₁	semidirect
670. #461	C₂²×C₃₁	semidirect
671. #461	C₂²×C₃₁	semidirect
672. #461	C₂²×C₃₁	semidirect
676. #452	C₂²×C₃₁	semidirect
677. #451	C₂²×C₃₁	semidirect
683. #448	C₂²×C₃₁	semidirect
684. #448	C₂²×C₃₁	semidirect
685. #446	C₂²×C₃₁	semidirect
686. C₈×Q₈	C₂²×C₃₁	semidirect
688. #440	C₂²×C₃₁	semidirect
689. C₄×Q₁₆	C₂²×C₃₁	semidirect
692. C₄×SD₁₆	C₂²×C₃₁	semidirect
693. C₄×SD₁₆	C₂²×C₃₁	semidirect
696. #436	C₂²×C₃₁	semidirect
697. #435	C₂²×C₃₁	semidirect
699. #433	C₂²×C₃₁	semidirect
700. #431	C₂²×C₃₁	semidirect
701. #424	C₂²×C₃₁	semidirect
702. #423	C₂²×C₃₁	semidirect
703. #419	C₂²×C₃₁	semidirect
704. #419	C₂²×C₃₁	semidirect
705. #416	C₂²×C₃₁	semidirect
894. C₃₁	#62032	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×#3552	2
C₃₁×#3514	2
C₃₁×#3400	2
C₃₁×#3394	2
C₃₁×#3367	2
C₃₁×#3359	2
C₃₁×#3329	2
C₃₁×#3328	2
C₃₁×#3321	2
C₃₁×#3302	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3275	2
C₃₁×#3272	2
C₃₁×#3266	2
C₃₁×#3258	2
C₃₁×#3251	2
C₃₁×#3225	2
C₃₁×#3206	2
C₃₁×#3123	2
C₃₁×#3102	2
C₃₁×#3042	2
C₃₁×#3039	2
C₃₁×#2993	2
#62032	31

Subgroups — C31×#62032 #21518791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62032 #21518791