Subgroups — C₃₁×#62137 #21518896

Order 7936.

1990 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3234	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#478	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	—	2	1	no	—
25	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#553	C₂²	1	2	yes	complemented
29	C₃₁×#552	—	2	2	no	—
30	C₃₁×#552	—	2	1	no	—
31	C₃₁×#552	C₂²	1	2	yes	complemented
32	C₃₁×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#547	—	2	1	no	—
36	C₃₁×#547	C₂²	1	1	yes	characteristic
37	C₃₁×#547	C₂²	1	2	yes	—
38	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	—	2	2	no	—
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic
42	D₄²×C₃₁	C₂²	1	2	yes	—
43	C₃₁×#541	—	2	1	no	—
44	C₃₁×#539	—	2	2	no	—
45	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#532	C₂²	1	1	yes	characteristic
47	C₃₁×#532	C₂²	1	2	yes	—
48	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#529	C₂²	1	2	yes	complemented
50	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
51	C₃₁×#525	—	2	1	no	—
52	C₃₁×#525	—	2	2	no	—
53	C₃₁×#520	—	2	1	no	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#501	C₂²	1	2	yes	complemented
59	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#490	C₂²	1	2	yes	complemented
62	C₃₁×#490	C₂²	1	2	yes	complemented
63	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#483	C₂²	1	2	yes	complemented
67	C₃₁×#482	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#481	C₂²	1	2	yes	complemented
70	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#481	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	2	yes	complemented
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	1	yes	characteristic
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#478	C₂²	1	2	yes	complemented
81	C₃₁×#478	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#478	C₂²	1	2	yes	complemented
84	C₃₁×#478	C₂²	1	2	yes	complemented
85	C₃₁×#478	C₂²	1	2	yes	complemented
86	C₃₁×#477	C₂²	1	2	yes	complemented
87	C₃₁×#476	C₂²	1	1	yes	characteristic
88	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#476	C₂²	1	2	yes	complemented
90	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#474	C₂²	1	1	yes	characteristic
92	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#469	C₂²	1	2	yes	complemented
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#466	C₂²	1	2	yes	complemented
97	C₃₁×#466	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#463	C₂²	1	1	yes	characteristic
101	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#463	C₂²	1	2	yes	complemented
103	C₃₁×#460	C₂²	1	2	yes	complemented
104	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#459	C₂²	1	2	yes	complemented
106	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#450	C₂²	1	1	yes	characteristic
108	C₃₁×#450	C₂²	1	2	yes	—
109	C₃₁×#447	C₂²	1	1	yes	characteristic
110	C₃₁×#447	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#442	C₂²	1	2	yes	—
114	C₃₁×#442	C₂²	1	2	yes	complemented
115	C₃₁×#440	C₂²	1	2	yes	—
116	C₃₁×#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#435	C₂²	1	2	yes	complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#432	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
129	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
130	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
132	C₃₁×#418	C₂²	1	2	yes	—
133	C₂×C₃₁×#102	C₂²	1	2	yes	—
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	—	2	2	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	4	8	no	—
142	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
143	C₂²×Q₈×C₃₁	—	2	1	no	—
144	C₂²×D₄×C₃₁	—	2	2	no	—
145	C₂²×D₄×C₃₁	—	2	1	no	—
146	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
147	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₃₁	—	2	2	no	—
149	C₂³×C₄×C₃₁	—	2	1	no	—
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×#127	C₂³	1	1	yes	characteristic
165	C₃₁×#127	C₂³	1	2	yes	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	1	no	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	1	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	C₂³	1	1	yes	characteristic
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#125	C₂³	1	2	yes	—
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	C₂³	1	1	yes	characteristic
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	1	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	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#121	C₂³	1	1	yes	characteristic
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#121	C₂³	1	2	yes	—
213	C₃₁×#121	C₂³	1	2	yes	—
214	C₃₁×#120	—	2	2	no	—
215	C₃₁×#120	—	2	2	no	—
216	C₃₁×#120	—	2	2	no	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	2	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	1	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
235	C₄×D₄×C₃₁	D₄	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₃₁×#117	—	2	2	no	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	D₄	1	1	yes	characteristic
251	C₃₁×#117	D₄	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
263	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	1	yes	characteristic
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×C₄⋊C₈	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×#102	C₂³	1	1	yes	characteristic
289	C₃₁×#102	C₂³	1	1	yes	characteristic
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₂⁴×C₃₁	—	2	1	no	—
314	C₂⁴×C₃₁	—	2	2	no	—
315	#41×C₃₁	—	2	4	no	—
316	#41×C₃₁	—	4	8	no	—
317	#41×C₃₁	—	4	4	no	—
318	#41×C₃₁	—	4	8	no	—
319	#41×C₃₁	—	4	4	no	—
320	#41×C₃₁	—	4	4	no	—
321	#41×C₃₁	—	4	4	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	—	2	1	no	—
326	C₂×Q₈×C₃₁	—	4	4	no	—
327	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₃₁	—	2	4	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	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	2	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	4	2	no	—
343	C₂×D₄×C₃₁	—	4	1	no	—
344	C₂×D₄×C₃₁	—	4	8	no	—
345	C₂×D₄×C₃₁	—	4	4	no	—
346	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	2	no	—
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	2	no	—
365	C₂²×C₄×C₃₁	—	4	8	no	—
366	C₂²×C₄×C₃₁	—	4	4	no	—
367	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	SD₁₆×C₃₁	—	2	2	no	—
374	SD₁₆×C₃₁	—	4	1	no	—
375	SD₁₆×C₃₁	—	4	2	no	—
376	D₈×C₃₁	—	2	2	no	—
377	D₈×C₃₁	—	4	1	no	—
378	D₈×C₃₁	—	4	2	no	—
379	M₁₆×C₃₁	—	4	2	no	—
380	C₂×C₈×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	1	yes	characteristic
386	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	C₂×D₄	1	2	yes	—
445	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂×D₄	1	2	yes	—
448	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	2	yes	—
450	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
451	#62137	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂³×C₃₁	—	2	1	no	—
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	2	no	—
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	4	4	no	—
457	C₂³×C₃₁	—	4	2	no	—
458	C₂³×C₃₁	—	4	2	no	—
459	C₂³×C₃₁	—	4	4	no	—
460	C₂³×C₃₁	—	8	2	no	—
461	C₂³×C₃₁	—	8	1	no	—
462	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
463	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
464	Q₈×C₃₁	—	2	2	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	4	4	no	—
468	Q₈×C₃₁	—	4	2	no	—
469	Q₈×C₃₁	—	4	2	no	—
470	Q₈×C₃₁	—	8	1	no	—
471	D₄×C₃₁	—	2	4	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	4	4	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	4	4	no	—
482	D₄×C₃₁	—	4	4	no	—
483	D₄×C₃₁	—	4	4	no	—
484	D₄×C₃₁	—	4	4	no	—
485	D₄×C₃₁	—	4	4	no	—
486	D₄×C₃₁	—	4	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	1	no	—
489	D₄×C₃₁	—	8	1	no	—
490	D₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
491	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
492	C₂×C₄×C₃₁	—	2	4	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	2	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	2	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	4	1	no	—
508	C₂×C₄×C₃₁	—	4	2	no	—
509	C₂×C₄×C₃₁	—	4	4	no	—
510	C₂×C₄×C₃₁	—	4	4	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	4	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	4	no	—
515	C₂×C₄×C₃₁	—	4	4	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
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	1	no	—
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	2	no	—
535	C₈×C₃₁	—	2	2	no	—
536	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
537	D₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3345	C₂×C₃₁	1	2	yes	complemented
543	#3343	C₂×C₃₁	1	2	yes	complemented
544	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3318	C₂×C₃₁	1	2	yes	complemented
547	#3310	C₂×C₃₁	1	2	yes	complemented
548	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3247	C₂×C₃₁	1	2	yes	complemented
552	#3234	C₂×C₃₁	1	2	yes	complemented
553	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3114	C₂×C₃₁	1	2	yes	complemented
555	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
557	C₂×#478	C₂×C₃₁	1	2	yes	complemented
558	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
559	C₂²×C₃₁	—	2	2	no	—
560	C₂²×C₃₁	—	2	2	no	—
561	C₂²×C₃₁	—	2	1	no	—
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	2	1	no	—
565	C₂²×C₃₁	—	4	1	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	2	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	4	1	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	8	8	no	—
577	C₂²×C₃₁	—	8	4	no	—
578	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
579	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
585	C₄×C₃₁	—	2	1	no	—
586	C₄×C₃₁	—	2	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	1	no	—
592	C₄×C₃₁	—	4	2	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	2	no	—
595	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
596	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
597	C₄×C₃₁	#585	1	1	yes	characteristic
598	C₂²×#41	—	2	1	no	—
599	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#553	C₂²×C₃₁	1	2	yes	complemented
603	#552	—	2	2	no	—
604	#552	—	2	1	no	—
605	#552	C₂²×C₃₁	1	2	yes	complemented
606	#550	C₂²×C₃₁	1	1	yes	characteristic
607	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
608	#548	—	2	1	no	—
609	#547	—	2	1	no	—
610	#547	C₂²×C₃₁	1	1	yes	characteristic
611	#547	C₂²×C₃₁	1	2	yes	—
612	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#546	—	2	1	no	—
614	#546	—	2	2	no	—
615	D₄²	C₂²×C₃₁	1	1	yes	characteristic
616	D₄²	C₂²×C₃₁	1	2	yes	—
617	#541	—	2	1	no	—
618	#539	—	2	2	no	—
619	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#532	C₂²×C₃₁	1	1	yes	characteristic
621	#532	C₂²×C₃₁	1	2	yes	—
622	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#529	C₂²×C₃₁	1	2	yes	complemented
624	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
625	#525	—	2	1	no	—
626	#525	—	2	2	no	—
627	#520	—	2	1	no	—
628	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
629	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
630	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
631	#501	C₂²×C₃₁	1	2	yes	complemented
632	#501	C₂²×C₃₁	1	2	yes	complemented
633	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#490	C₂²×C₃₁	1	2	yes	complemented
636	#490	C₂²×C₃₁	1	2	yes	complemented
637	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#483	C₂²×C₃₁	1	2	yes	complemented
641	#482	C₂²×C₃₁	1	2	yes	complemented
642	#482	C₂²×C₃₁	1	2	yes	complemented
643	#481	C₂²×C₃₁	1	2	yes	complemented
644	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#481	C₂²×C₃₁	1	2	yes	complemented
646	#480	C₂²×C₃₁	1	2	yes	complemented
647	#480	C₂²×C₃₁	1	2	yes	complemented
648	#480	C₂²×C₃₁	1	2	yes	complemented
649	#478	C₂²×C₃₁	1	1	yes	characteristic
650	#478	C₂²×C₃₁	1	2	yes	—
651	#478	C₂²×C₃₁	1	2	yes	—
652	#478	C₂²×C₃₁	1	2	yes	—
653	#478	C₂²×C₃₁	1	2	yes	complemented
654	#478	C₂²×C₃₁	1	2	yes	complemented
655	#478	C₂²×C₃₁	1	2	yes	complemented
656	#478	C₂²×C₃₁	1	2	yes	complemented
657	#478	C₂²×C₃₁	1	2	yes	complemented
658	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#478	C₂²×C₃₁	1	2	yes	complemented
660	#477	C₂²×C₃₁	1	2	yes	complemented
661	#476	C₂²×C₃₁	1	1	yes	characteristic
662	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#476	C₂²×C₃₁	1	2	yes	complemented
664	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#474	C₂²×C₃₁	1	1	yes	characteristic
666	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#469	C₂²×C₃₁	1	2	yes	complemented
669	#468	C₂²×C₃₁	1	2	yes	complemented
670	#466	C₂²×C₃₁	1	2	yes	complemented
671	#466	C₂²×C₃₁	1	2	yes	complemented
672	#465	C₂²×C₃₁	1	2	yes	complemented
673	#465	C₂²×C₃₁	1	2	yes	complemented
674	#463	C₂²×C₃₁	1	1	yes	characteristic
675	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#463	C₂²×C₃₁	1	2	yes	complemented
677	#460	C₂²×C₃₁	1	2	yes	complemented
678	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#459	C₂²×C₃₁	1	2	yes	complemented
680	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#450	C₂²×C₃₁	1	1	yes	characteristic
682	#450	C₂²×C₃₁	1	2	yes	—
683	#447	C₂²×C₃₁	1	1	yes	characteristic
684	#447	C₂²×C₃₁	1	2	yes	—
685	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#442	C₂²×C₃₁	1	2	yes	—
688	#442	C₂²×C₃₁	1	2	yes	complemented
689	#440	C₂²×C₃₁	1	2	yes	—
690	#440	C₂²×C₃₁	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
692	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
694	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#435	C₂²×C₃₁	1	2	yes	complemented
696	#435	C₂²×C₃₁	1	2	yes	complemented
697	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#432	C₂²×C₃₁	1	2	yes	complemented
700	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#428	C₂²×C₃₁	1	2	yes	complemented
702	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
703	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
704	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
706	#418	C₂²×C₃₁	1	2	yes	—
707	C₂×#102	C₂²×C₃₁	1	2	yes	—
708	C₂×#102	C₂²×C₃₁	1	2	yes	—
709	C₂×C₃₁	—	2	4	no	—
710	C₂×C₃₁	—	4	1	no	—
711	C₂×C₃₁	—	4	2	no	—
712	C₂×C₃₁	—	8	1	no	—
713	C₂×C₃₁	—	8	2	no	—
714	C₂×C₃₁	—	8	1	no	—
715	C₂×C₃₁	#3489	1	1	yes	characteristic
716	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
717	C₂×C₃₁	#3584	1	1	yes	characteristic
718	C₂×#41	—	2	1	no	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	2	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	2	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	4	8	no	—
725	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
726	C₂²×Q₈	—	2	1	no	—
727	C₂²×D₄	—	2	2	no	—
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
730	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂³×C₄	—	2	2	no	—
732	C₂³×C₄	—	2	1	no	—
733	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
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	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
741	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
745	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
747	#127	C₂³×C₃₁	1	1	yes	characteristic
748	#127	C₂³×C₃₁	1	2	yes	—
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	1	no	—
753	#125	—	2	2	no	—
754	#125	—	2	2	no	—
755	#125	—	2	1	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	C₂³×C₃₁	1	1	yes	characteristic
759	#125	C₂³×C₃₁	1	2	yes	—
760	#125	C₂³×C₃₁	1	2	yes	—
761	#125	C₂³×C₃₁	1	2	yes	—
762	#124	—	2	1	no	—
763	#124	—	2	2	no	—
764	#124	C₂³×C₃₁	1	1	yes	characteristic
765	#123	—	2	2	no	—
766	#123	—	2	1	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	1	no	—
791	#121	—	2	2	no	—
792	#121	C₂³×C₃₁	1	2	yes	—
793	#121	C₂³×C₃₁	1	1	yes	characteristic
794	#121	C₂³×C₃₁	1	2	yes	—
795	#121	C₂³×C₃₁	1	2	yes	—
796	#121	C₂³×C₃₁	1	2	yes	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
805	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
818	C₄×D₄	D₄×C₃₁	1	2	yes	—
819	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₃₁	1	2	yes	—
821	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₃₁	1	2	yes	—
824	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₃₁	1	2	yes	—
826	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
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	D₄×C₃₁	1	1	yes	characteristic
834	#117	D₄×C₃₁	1	2	yes	—
835	#117	C₂³×C₃₁	1	2	yes	—
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
840	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
842	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₂²⋊C₄	—	2	1	no	—
845	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
846	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
847	#107	C₂³×C₃₁	1	1	yes	characteristic
848	#107	C₂³×C₃₁	1	2	yes	—
849	#107	C₂³×C₃₁	1	2	yes	—
850	#107	C₂³×C₃₁	1	2	yes	—
851	#107	C₂³×C₃₁	1	2	yes	—
852	#107	C₂³×C₃₁	1	1	yes	characteristic
853	#107	C₂³×C₃₁	1	2	yes	—
854	#106	C₂³×C₃₁	1	1	yes	characteristic
855	#106	C₂³×C₃₁	1	2	yes	—
856	#106	C₂³×C₃₁	1	2	yes	—
857	#106	C₂³×C₃₁	1	2	yes	—
858	#106	C₂³×C₃₁	1	2	yes	—
859	#106	C₂³×C₃₁	1	1	yes	characteristic
860	#106	C₂³×C₃₁	1	2	yes	—
861	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
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	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₄⋊C₈	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	#102	C₂³×C₃₁	1	1	yes	characteristic
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	1	yes	characteristic
884	#102	C₂³×C₃₁	1	1	yes	characteristic
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
892	#97	C₂³×C₃₁	1	2	yes	—
893	#97	C₂³×C₃₁	1	2	yes	—
894	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
896	C₃₁	#62137	1	1	yes	characteristic, direct product factor, Sylow
897	C₂⁴	—	2	1	no	—
898	C₂⁴	—	2	2	no	—
899	#41	—	2	4	no	—
900	#41	—	4	8	no	—
901	#41	—	4	4	no	—
902	#41	—	4	8	no	—
903	#41	—	4	4	no	—
904	#41	—	4	4	no	—
905	#41	—	4	4	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	4	4	no	—
911	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂×D₄	—	2	4	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	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	1	no	—
928	C₂×D₄	—	4	8	no	—
929	C₂×D₄	—	4	4	no	—
930	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
931	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
933	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	4	8	no	—
950	C₂²×C₄	—	4	4	no	—
951	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
952	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
954	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
957	SD₁₆	—	2	2	no	—
958	SD₁₆	—	4	1	no	—
959	SD₁₆	—	4	2	no	—
960	D₈	—	2	2	no	—
961	D₈	—	4	1	no	—
962	D₈	—	4	2	no	—
963	M₁₆	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	—	4	2	no	—
966	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
971	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
972	C₄⋊C₄	—	2	2	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	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	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	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	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1029	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1030	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1031	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1032	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₃₁	1	2	yes	—
1034	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	4	4	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	—	4	4	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	—	8	1	no	—
1045	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1046	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	4	4	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	4	2	no	—
1053	Q₈	—	8	1	no	—
1054	D₄	—	2	4	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	4	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	1	no	—
1073	D₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
1074	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1075	C₂×C₄	—	2	4	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	1	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	—	4	4	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	4	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	C₂²×D₄×C₃₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1112	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	8	8	no	—
1137	C₂²	—	8	4	no	—
1138	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
1139	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	2	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	2	no	—
1155	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
1156	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1157	C₄	C₃₁×#585	1	1	yes	characteristic
1158	C₂	—	2	4	no	—
1159	C₂	—	4	1	no	—
1160	C₂	—	4	2	no	—
1161	C₂	—	8	2	no	—
1162	C₂	—	8	1	no	—
1163	C₂	—	8	1	no	—
1164	C₂	C₃₁×#3489	1	1	yes	characteristic
1165	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
1166	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×#3515	C₂	semidirect
2. D₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#3386	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. C₃₁×#3368	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3345	C₂	semidirect
8. C₃₁×#3343	C₂	semidirect
9. C₃₁×#3335	C₂	semidirect
10. C₃₁×#3334	C₂	semidirect
11. C₃₁×#3318	C₂	semidirect
12. C₃₁×#3310	C₂	semidirect
13. C₃₁×#3295	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3251	C₂	semidirect
16. C₃₁×#3247	C₂	semidirect
17. C₃₁×#3234	C₂	semidirect
18. C₃₁×#3228	C₂	semidirect
19. C₃₁×#3114	C₂	semidirect
20. C₃₁×#3105	C₂	semidirect
21. C₃₁×#3077	C₂	semidirect
22. C₂×C₃₁×#478	C₂	semidirect
23. C₃₁×#2990	C₂	semidirect
25. C₃₁×#557	C₂²	semidirect
26. C₃₁×#554	C₂²	semidirect
27. C₃₁×#554	C₂²	semidirect
28. C₃₁×#553	C₂²	semidirect
31. C₃₁×#552	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
45. C₃₁×#533	C₂²	semidirect
48. C₃₁×#529	C₂²	semidirect
49. C₃₁×#529	C₂²	semidirect
50. C₂×C₃₁×#125	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#501	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#490	C₂²	semidirect
62. C₃₁×#490	C₂²	semidirect
63. C₃₁×#486	C₂²	semidirect
64. C₃₁×#486	C₂²	semidirect
65. C₃₁×#484	C₂²	semidirect
66. C₃₁×#483	C₂²	semidirect
67. C₃₁×#482	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#481	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#480	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#478	C₂²	semidirect
81. C₃₁×#478	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
83. C₃₁×#478	C₂²	semidirect
84. C₃₁×#478	C₂²	semidirect
85. C₃₁×#478	C₂²	semidirect
86. C₃₁×#477	C₂²	semidirect
88. C₃₁×#476	C₂²	semidirect
89. C₃₁×#476	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
94. C₃₁×#469	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
96. C₃₁×#466	C₂²	semidirect
97. C₃₁×#466	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
101. C₃₁×#463	C₂²	semidirect
102. C₃₁×#463	C₂²	semidirect
103. C₃₁×#460	C₂²	semidirect
104. C₃₁×#460	C₂²	semidirect
105. C₃₁×#459	C₂²	semidirect
106. C₃₁×#459	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₃₁×#446	C₂²	semidirect
114. C₃₁×#442	C₂²	semidirect
116. C₃₁×#440	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
121. C₃₁×#435	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#432	C₂²	semidirect
126. C₃₁×#431	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₂×C₃₁×#107	C₂²	semidirect
129. C₂×C₃₁×#106	C₂²	semidirect
130. C₃₁×#423	C₂²	semidirect
131. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
451. #62137	C₃₁	direct (N × H)
536. #3515	C₂×C₃₁	semidirect
537. D₄×#41	C₂×C₃₁	semidirect
538. #3386	C₂×C₃₁	semidirect
539. #3384	C₂×C₃₁	semidirect
540. #3368	C₂×C₃₁	semidirect
541. #3366	C₂×C₃₁	semidirect
542. #3345	C₂×C₃₁	semidirect
543. #3343	C₂×C₃₁	semidirect
544. #3335	C₂×C₃₁	semidirect
545. #3334	C₂×C₃₁	semidirect
546. #3318	C₂×C₃₁	semidirect
547. #3310	C₂×C₃₁	semidirect
548. #3295	C₂×C₃₁	semidirect
549. #3294	C₂×C₃₁	semidirect
550. #3251	C₂×C₃₁	semidirect
551. #3247	C₂×C₃₁	semidirect
552. #3234	C₂×C₃₁	semidirect
553. #3228	C₂×C₃₁	semidirect
554. #3114	C₂×C₃₁	semidirect
555. #3105	C₂×C₃₁	semidirect
556. #3077	C₂×C₃₁	semidirect
557. C₂×#478	C₂×C₃₁	semidirect
558. #2990	C₂×C₃₁	semidirect
599. #557	C₂²×C₃₁	semidirect
600. #554	C₂²×C₃₁	semidirect
601. #554	C₂²×C₃₁	semidirect
602. #553	C₂²×C₃₁	semidirect
605. #552	C₂²×C₃₁	semidirect
612. #547	C₂²×C₃₁	semidirect
619. #533	C₂²×C₃₁	semidirect
622. #529	C₂²×C₃₁	semidirect
623. #529	C₂²×C₃₁	semidirect
624. C₂×#125	C₂²×C₃₁	semidirect
631. #501	C₂²×C₃₁	semidirect
632. #501	C₂²×C₃₁	semidirect
633. #500	C₂²×C₃₁	semidirect
634. #498	C₂²×C₃₁	semidirect
635. #490	C₂²×C₃₁	semidirect
636. #490	C₂²×C₃₁	semidirect
637. #486	C₂²×C₃₁	semidirect
638. #486	C₂²×C₃₁	semidirect
639. #484	C₂²×C₃₁	semidirect
640. #483	C₂²×C₃₁	semidirect
641. #482	C₂²×C₃₁	semidirect
642. #482	C₂²×C₃₁	semidirect
643. #481	C₂²×C₃₁	semidirect
644. #481	C₂²×C₃₁	semidirect
645. #481	C₂²×C₃₁	semidirect
646. #480	C₂²×C₃₁	semidirect
647. #480	C₂²×C₃₁	semidirect
648. #480	C₂²×C₃₁	semidirect
653. #478	C₂²×C₃₁	semidirect
654. #478	C₂²×C₃₁	semidirect
655. #478	C₂²×C₃₁	semidirect
656. #478	C₂²×C₃₁	semidirect
657. #478	C₂²×C₃₁	semidirect
658. #478	C₂²×C₃₁	semidirect
659. #478	C₂²×C₃₁	semidirect
660. #477	C₂²×C₃₁	semidirect
662. #476	C₂²×C₃₁	semidirect
663. #476	C₂²×C₃₁	semidirect
664. #475	C₂²×C₃₁	semidirect
666. #474	C₂²×C₃₁	semidirect
667. #474	C₂²×C₃₁	semidirect
668. #469	C₂²×C₃₁	semidirect
669. #468	C₂²×C₃₁	semidirect
670. #466	C₂²×C₃₁	semidirect
671. #466	C₂²×C₃₁	semidirect
672. #465	C₂²×C₃₁	semidirect
673. #465	C₂²×C₃₁	semidirect
675. #463	C₂²×C₃₁	semidirect
676. #463	C₂²×C₃₁	semidirect
677. #460	C₂²×C₃₁	semidirect
678. #460	C₂²×C₃₁	semidirect
679. #459	C₂²×C₃₁	semidirect
680. #459	C₂²×C₃₁	semidirect
685. #446	C₂²×C₃₁	semidirect
686. #446	C₂²×C₃₁	semidirect
688. #442	C₂²×C₃₁	semidirect
690. #440	C₂²×C₃₁	semidirect
692. C₄×SD₁₆	C₂²×C₃₁	semidirect
694. C₄×D₈	C₂²×C₃₁	semidirect
695. #435	C₂²×C₃₁	semidirect
696. #435	C₂²×C₃₁	semidirect
697. C₈×D₄	C₂²×C₃₁	semidirect
698. C₈×D₄	C₂²×C₃₁	semidirect
699. #432	C₂²×C₃₁	semidirect
700. #431	C₂²×C₃₁	semidirect
701. #428	C₂²×C₃₁	semidirect
702. C₂×#107	C₂²×C₃₁	semidirect
703. C₂×#106	C₂²×C₃₁	semidirect
704. #423	C₂²×C₃₁	semidirect
705. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
896. C₃₁	#62137	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×#3515	2
D₄×#41×C₃₁	2
C₃₁×#3386	2
C₃₁×#3384	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3345	2
C₃₁×#3343	2
C₃₁×#3335	2
C₃₁×#3334	2
C₃₁×#3318	2
C₃₁×#3310	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3251	2
C₃₁×#3247	2
C₃₁×#3234	2
C₃₁×#3228	2
C₃₁×#3114	2
C₃₁×#3105	2
C₃₁×#3077	2
C₂×C₃₁×#478	2
C₃₁×#2990	2
#62137	31

Subgroups — C31×#62137 #21518896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62137 #21518896