Subgroups — C₃₁×#61974 #21518733

Order 7936.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3256	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3036	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂×C₃₁×#135	C₂²	1	2	yes	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic
28	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#554	C₂²	1	1	yes	characteristic
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#553	—	2	1	no	—
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#553	—	2	2	no	—
34	C₃₁×#553	C₂²	1	2	yes	—
35	C₃₁×#551	—	2	2	no	—
36	C₃₁×#550	—	2	1	no	—
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	C₃₁×#550	C₂²	1	2	yes	complemented
39	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#547	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×#540	—	2	1	no	—
46	C₃₁×#540	—	2	2	no	—
47	C₃₁×#532	C₂²	1	1	yes	characteristic
48	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#532	C₂²	1	2	yes	complemented
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#529	C₂²	1	2	yes	complemented
54	C₃₁×#525	—	2	2	no	—
55	C₃₁×#520	—	2	1	no	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₃₁	—	2	1	no	—
59	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
60	C₃₁×#497	C₂²	1	2	yes	complemented
61	C₃₁×#496	C₂²	1	2	yes	complemented
62	C₃₁×#493	C₂²	1	1	yes	characteristic
63	C₃₁×#492	C₂²	1	1	yes	characteristic
64	C₃₁×#491	C₂²	1	2	yes	complemented
65	C₃₁×#490	C₂²	1	2	yes	complemented
66	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#483	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#480	C₂²	1	2	yes	complemented
72	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	1	yes	characteristic
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#470	C₂²	1	2	yes	complemented
80	C₃₁×#469	C₂²	1	2	yes	—
81	C₃₁×#468	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	2	yes	complemented
84	C₃₁×#465	C₂²	1	2	yes	complemented
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×#463	C₂²	1	2	yes	complemented
93	C₃₁×#463	C₂²	1	2	yes	complemented
94	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#461	C₂²	1	2	yes	—
96	C₃₁×#461	C₂²	1	1	yes	characteristic
97	C₃₁×#461	C₂²	1	2	yes	complemented
98	C₃₁×#460	C₂²	1	1	yes	characteristic
99	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#459	C₂²	1	2	yes	—
101	C₃₁×#459	C₂²	1	1	yes	characteristic
102	C₃₁×#459	C₂²	1	1	yes	characteristic
103	C₃₁×#459	C₂²	1	2	yes	complemented
104	C₃₁×#452	C₂²	1	1	yes	characteristic
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#449	C₂²	1	2	yes	—
111	C₃₁×#449	C₂²	1	2	yes	complemented
112	C₃₁×#449	C₂²	1	2	yes	complemented
113	C₃₁×#447	C₂²	1	2	yes	—
114	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#442	C₂²	1	2	yes	—
117	C₃₁×#442	C₂²	1	2	yes	complemented
118	C₃₁×#440	C₂²	1	2	yes	—
119	C₃₁×#440	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
124	C₃₁×#436	C₂²	1	1	yes	characteristic
125	C₃₁×#436	C₂²	1	1	yes	characteristic
126	C₃₁×#435	C₂²	1	2	yes	complemented
127	C₃₁×#435	C₂²	1	2	yes	complemented
128	C₃₁×#432	C₂²	1	2	yes	complemented
129	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#423	C₂²	1	2	yes	complemented
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#417	C₂²	1	2	yes	complemented
133	C₃₁×#417	C₂²	1	2	yes	complemented
134	C₃₁×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂×#41×C₃₁	C₂³	1	2	yes	—
142	C₂²×D₄×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₃₁	—	2	2	no	—
145	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
146	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
147	C₃₁×#135	—	4	4	no	—
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	1	yes	characteristic
158	C₂×D₈×C₃₁	C₂³	1	2	yes	—
159	C₂×D₈×C₃₁	C₂³	1	2	yes	—
160	C₂×D₈×C₃₁	C₂³	1	2	yes	—
161	C₂×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
163	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
164	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×#127	—	2	1	no	—
169	C₃₁×#127	—	2	2	no	—
170	C₃₁×#127	C₂³	1	2	yes	—
171	C₃₁×#127	C₂³	1	1	yes	characteristic
172	C₃₁×#127	C₂³	1	1	yes	characteristic
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	C₂³	1	1	yes	characteristic
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	C₂³	1	1	yes	characteristic
185	C₃₁×#124	C₂³	1	2	yes	—
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	1	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	1	yes	characteristic
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#120	—	2	2	no	—
222	C₃₁×#120	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	2	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	2	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	2	no	—
247	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
248	C₄×D₄×C₃₁	D₄	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₄×D₄×C₃₁	C₂³	1	2	yes	—
257	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₃₁×#117	—	2	1	no	—
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	2	no	—
261	C₃₁×#117	—	2	2	no	—
262	C₃₁×#117	D₄	1	2	yes	—
263	C₃₁×#117	D₄	1	1	yes	characteristic
264	C₃₁×#117	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂×C₄²×C₃₁	—	2	1	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	1	yes	characteristic
276	C₃₁×#107	C₂³	1	2	yes	—
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	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	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	2	yes	—
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	C₃₁×#97	C₂³	1	2	yes	—
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
315	C₂⁴×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	1	no	—
319	#41×C₃₁	—	4	2	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	4	2	no	—
322	#41×C₃₁	—	4	2	no	—
323	#41×C₃₁	—	4	2	no	—
324	#41×C₃₁	—	4	2	no	—
325	#41×C₃₁	—	4	4	no	—
326	#41×C₃₁	—	8	2	no	—
327	C₂×Q₈×C₃₁	—	2	1	no	—
328	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₃₁	—	2	4	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	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	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	2	no	—
344	C₂×D₄×C₃₁	—	2	1	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	1	no	—
347	C₂×D₄×C₃₁	—	2	1	no	—
348	C₂×D₄×C₃₁	—	4	2	no	—
349	C₂×D₄×C₃₁	—	4	4	no	—
350	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	1	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	2	no	—
364	C₂²×C₄×C₃₁	—	2	2	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	2	no	—
367	C₂²×C₄×C₃₁	—	2	2	no	—
368	C₂²×C₄×C₃₁	—	8	4	no	—
369	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
371	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
372	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
375	Q₁₆×C₃₁	—	4	1	no	—
376	Q₁₆×C₃₁	—	4	2	no	—
377	SD₁₆×C₃₁	—	2	4	no	—
378	SD₁₆×C₃₁	—	2	2	no	—
379	SD₁₆×C₃₁	—	4	1	no	—
380	SD₁₆×C₃₁	—	4	2	no	—
381	SD₁₆×C₃₁	—	4	2	no	—
382	SD₁₆×C₃₁	—	4	2	no	—
383	SD₁₆×C₃₁	—	4	2	no	—
384	D₈×C₃₁	—	2	4	no	—
385	D₈×C₃₁	—	2	2	no	—
386	D₈×C₃₁	—	4	2	no	—
387	D₈×C₃₁	—	4	2	no	—
388	D₈×C₃₁	—	4	2	no	—
389	M₁₆×C₃₁	—	4	2	no	—
390	M₁₆×C₃₁	—	4	2	no	—
391	C₂×C₈×C₃₁	—	4	2	no	—
392	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
397	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	1	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	1	no	—
411	C₄⋊C₄×C₃₁	—	2	2	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	1	no	—
442	C₂²⋊C₄×C₃₁	—	2	2	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	1	no	—
445	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
448	C₄²×C₃₁	—	2	1	no	—
449	C₄²×C₃₁	—	2	1	no	—
450	C₄²×C₃₁	—	2	1	no	—
451	C₄²×C₃₁	—	2	2	no	—
452	C₄²×C₃₁	—	2	1	no	—
453	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₃₁	C₂×D₄	1	2	yes	—
455	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₃₁	C₂×D₄	1	2	yes	—
457	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
458	C₄²×C₃₁	C₂⁴	1	2	yes	—
459	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
460	#61974	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂³×C₃₁	—	2	1	no	—
462	C₂³×C₃₁	—	2	2	no	—
463	C₂³×C₃₁	—	2	1	no	—
464	C₂³×C₃₁	—	2	2	no	—
465	C₂³×C₃₁	—	4	4	no	—
466	C₂³×C₃₁	—	4	4	no	—
467	C₂³×C₃₁	—	8	2	no	—
468	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
469	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
470	Q₈×C₃₁	—	2	2	no	—
471	Q₈×C₃₁	—	2	1	no	—
472	Q₈×C₃₁	—	2	2	no	—
473	Q₈×C₃₁	—	2	1	no	—
474	Q₈×C₃₁	—	2	1	no	—
475	Q₈×C₃₁	—	2	2	no	—
476	Q₈×C₃₁	—	2	1	no	—
477	Q₈×C₃₁	—	8	1	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	2	1	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	1	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	2	no	—
490	D₄×C₃₁	—	4	4	no	—
491	D₄×C₃₁	—	4	2	no	—
492	D₄×C₃₁	—	4	2	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	—	8	1	no	—
495	D₄×C₃₁	—	8	1	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	—	8	1	no	—
498	D₄×C₃₁	—	8	2	no	—
499	D₄×C₃₁	—	8	2	no	—
500	D₄×C₃₁	—	8	2	no	—
501	D₄×C₃₁	—	8	2	no	—
502	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
503	C₂×C₄×C₃₁	—	2	2	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	2	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	1	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	1	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	2	no	—
514	C₂×C₄×C₃₁	—	2	1	no	—
515	C₂×C₄×C₃₁	—	2	2	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	4	2	no	—
518	C₂×C₄×C₃₁	—	4	1	no	—
519	C₂×C₄×C₃₁	—	4	2	no	—
520	C₂×C₄×C₃₁	—	4	2	no	—
521	C₂×C₄×C₃₁	—	4	4	no	—
522	C₂×C₄×C₃₁	—	4	4	no	—
523	C₂×C₄×C₃₁	—	4	2	no	—
524	C₂×C₄×C₃₁	—	4	2	no	—
525	C₂×C₄×C₃₁	—	8	2	no	—
526	C₂×C₄×C₃₁	—	8	2	no	—
527	C₂×C₄×C₃₁	—	8	2	no	—
528	C₂×C₄×C₃₁	—	8	2	no	—
529	C₂×C₄×C₃₁	—	8	2	no	—
530	C₂×C₄×C₃₁	—	8	2	no	—
531	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
540	C₈×C₃₁	—	2	2	no	—
541	C₈×C₃₁	—	2	2	no	—
542	C₈×C₃₁	—	2	1	no	—
543	C₈×C₃₁	—	2	1	no	—
544	C₈×C₃₁	—	2	1	no	—
545	C₈×C₃₁	—	2	1	no	—
546	#3517	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3481	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3309	C₂×C₃₁	1	2	yes	complemented
555	#3307	C₂×C₃₁	1	2	yes	complemented
556	#3274	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3272	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3268	C₂×C₃₁	1	2	yes	complemented
559	#3267	C₂×C₃₁	1	2	yes	complemented
560	#3256	C₂×C₃₁	1	2	yes	complemented
561	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3219	C₂×C₃₁	1	2	yes	complemented
563	#3207	C₂×C₃₁	1	1	yes	characteristic, complemented
564	#3114	C₂×C₃₁	1	2	yes	complemented
565	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
566	#3036	C₂×C₃₁	1	2	yes	complemented
567	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
569	C₂²×C₃₁	—	2	2	no	—
570	C₂²×C₃₁	—	2	1	no	—
571	C₂²×C₃₁	—	2	1	no	—
572	C₂²×C₃₁	—	2	2	no	—
573	C₂²×C₃₁	—	2	2	no	—
574	C₂²×C₃₁	—	2	1	no	—
575	C₂²×C₃₁	—	2	2	no	—
576	C₂²×C₃₁	—	4	1	no	—
577	C₂²×C₃₁	—	4	1	no	—
578	C₂²×C₃₁	—	4	2	no	—
579	C₂²×C₃₁	—	4	1	no	—
580	C₂²×C₃₁	—	4	2	no	—
581	C₂²×C₃₁	—	4	1	no	—
582	C₂²×C₃₁	—	4	2	no	—
583	C₂²×C₃₁	—	4	2	no	—
584	C₂²×C₃₁	—	4	2	no	—
585	C₂²×C₃₁	—	4	1	no	—
586	C₂²×C₃₁	—	4	2	no	—
587	C₂²×C₃₁	—	8	8	no	—
588	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
589	C₄×C₃₁	—	2	1	no	—
590	C₄×C₃₁	—	2	2	no	—
591	C₄×C₃₁	—	2	1	no	—
592	C₄×C₃₁	—	2	1	no	—
593	C₄×C₃₁	—	2	2	no	—
594	C₄×C₃₁	—	2	1	no	—
595	C₄×C₃₁	—	2	2	no	—
596	C₄×C₃₁	—	4	1	no	—
597	C₄×C₃₁	—	4	2	no	—
598	C₄×C₃₁	—	4	1	no	—
599	C₄×C₃₁	—	4	1	no	—
600	C₄×C₃₁	—	4	1	no	—
601	C₄×C₃₁	—	4	2	no	—
602	C₄×C₃₁	—	4	1	no	—
603	C₄×C₃₁	—	4	1	no	—
604	C₄×C₃₁	#575	1	2	yes	—
605	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
606	C₄×C₃₁	#585	1	1	yes	characteristic
607	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
608	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
609	C₂×#135	C₂²×C₃₁	1	2	yes	—
610	#559	C₂²×C₃₁	1	1	yes	characteristic
611	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#554	C₂²×C₃₁	1	1	yes	characteristic
613	#554	C₂²×C₃₁	1	1	yes	characteristic
614	#553	—	2	1	no	—
615	#553	—	2	1	no	—
616	#553	—	2	2	no	—
617	#553	C₂²×C₃₁	1	2	yes	—
618	#551	—	2	2	no	—
619	#550	—	2	1	no	—
620	#550	C₂²×C₃₁	1	1	yes	characteristic
621	#550	C₂²×C₃₁	1	2	yes	complemented
622	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#547	C₂²×C₃₁	1	1	yes	characteristic
624	#547	C₂²×C₃₁	1	2	yes	complemented
625	#546	—	2	1	no	—
626	#546	C₂²×C₃₁	1	2	yes	—
627	D₄²	C₂²×C₃₁	1	1	yes	characteristic
628	#540	—	2	1	no	—
629	#540	—	2	2	no	—
630	#532	C₂²×C₃₁	1	1	yes	characteristic
631	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#532	C₂²×C₃₁	1	2	yes	complemented
633	#529	—	2	1	no	—
634	#529	C₂²×C₃₁	1	2	yes	—
635	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#529	C₂²×C₃₁	1	2	yes	complemented
637	#525	—	2	2	no	—
638	#520	—	2	1	no	—
639	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
640	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
641	C₂×C₄×D₄	—	2	1	no	—
642	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
643	#497	C₂²×C₃₁	1	2	yes	complemented
644	#496	C₂²×C₃₁	1	2	yes	complemented
645	#493	C₂²×C₃₁	1	1	yes	characteristic
646	#492	C₂²×C₃₁	1	1	yes	characteristic
647	#491	C₂²×C₃₁	1	2	yes	complemented
648	#490	C₂²×C₃₁	1	2	yes	complemented
649	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#483	C₂²×C₃₁	1	2	yes	complemented
653	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#480	C₂²×C₃₁	1	2	yes	complemented
655	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#479	C₂²×C₃₁	1	2	yes	complemented
657	#478	C₂²×C₃₁	1	1	yes	characteristic
658	#478	C₂²×C₃₁	1	2	yes	complemented
659	#478	C₂²×C₃₁	1	2	yes	complemented
660	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#470	C₂²×C₃₁	1	2	yes	complemented
663	#469	C₂²×C₃₁	1	2	yes	—
664	#468	C₂²×C₃₁	1	2	yes	—
665	#468	C₂²×C₃₁	1	2	yes	complemented
666	#466	C₂²×C₃₁	1	2	yes	complemented
667	#465	C₂²×C₃₁	1	2	yes	complemented
668	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#464	C₂²×C₃₁	1	2	yes	complemented
670	#464	C₂²×C₃₁	1	2	yes	complemented
671	#463	C₂²×C₃₁	1	1	yes	characteristic
672	#463	C₂²×C₃₁	1	2	yes	—
673	#463	C₂²×C₃₁	1	2	yes	complemented
674	#463	C₂²×C₃₁	1	2	yes	complemented
675	#463	C₂²×C₃₁	1	2	yes	complemented
676	#463	C₂²×C₃₁	1	2	yes	complemented
677	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#461	C₂²×C₃₁	1	2	yes	—
679	#461	C₂²×C₃₁	1	1	yes	characteristic
680	#461	C₂²×C₃₁	1	2	yes	complemented
681	#460	C₂²×C₃₁	1	1	yes	characteristic
682	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#459	C₂²×C₃₁	1	2	yes	—
684	#459	C₂²×C₃₁	1	1	yes	characteristic
685	#459	C₂²×C₃₁	1	1	yes	characteristic
686	#459	C₂²×C₃₁	1	2	yes	complemented
687	#452	C₂²×C₃₁	1	1	yes	characteristic
688	#452	C₂²×C₃₁	1	2	yes	complemented
689	#452	C₂²×C₃₁	1	2	yes	complemented
690	#450	C₂²×C₃₁	1	2	yes	—
691	#449	C₂²×C₃₁	1	1	yes	characteristic
692	#449	C₂²×C₃₁	1	2	yes	—
693	#449	C₂²×C₃₁	1	2	yes	—
694	#449	C₂²×C₃₁	1	2	yes	complemented
695	#449	C₂²×C₃₁	1	2	yes	complemented
696	#447	C₂²×C₃₁	1	2	yes	—
697	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#442	C₂²×C₃₁	1	2	yes	—
700	#442	C₂²×C₃₁	1	2	yes	complemented
701	#440	C₂²×C₃₁	1	2	yes	—
702	#440	C₂²×C₃₁	1	2	yes	complemented
703	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
705	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
707	#436	C₂²×C₃₁	1	1	yes	characteristic
708	#436	C₂²×C₃₁	1	1	yes	characteristic
709	#435	C₂²×C₃₁	1	2	yes	complemented
710	#435	C₂²×C₃₁	1	2	yes	complemented
711	#432	C₂²×C₃₁	1	2	yes	complemented
712	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	#423	C₂²×C₃₁	1	2	yes	complemented
714	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	#417	C₂²×C₃₁	1	2	yes	complemented
716	#417	C₂²×C₃₁	1	2	yes	complemented
717	#416	C₂²×C₃₁	1	2	yes	complemented
718	C₂×C₃₁	—	4	1	no	—
719	C₂×C₃₁	—	4	2	no	—
720	C₂×C₃₁	—	4	2	no	—
721	C₂×C₃₁	—	8	1	no	—
722	C₂×C₃₁	—	8	2	no	—
723	C₂×C₃₁	—	8	2	no	—
724	C₂×C₃₁	#3488	1	1	yes	characteristic
725	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
726	C₂×C₃₁	#3585	1	1	yes	characteristic
727	C₂×#41	—	2	1	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
730	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×#41	C₂³×C₃₁	1	2	yes	—
732	C₂×#41	C₂³×C₃₁	1	2	yes	—
733	C₂×#41	C₂³×C₃₁	1	2	yes	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
736	C₂³×C₄	—	2	2	no	—
737	AGL(1,ℤ/8)	—	4	4	no	—
738	AGL(1,ℤ/8)	—	4	4	no	—
739	#135	—	4	4	no	—
740	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
741	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
748	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
749	C₂×D₈	C₂³×C₃₁	1	2	yes	—
750	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
751	C₂×D₈	C₂³×C₃₁	1	2	yes	—
752	C₂×D₈	C₂³×C₃₁	1	2	yes	—
753	C₂×D₈	C₂³×C₃₁	1	2	yes	—
754	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
755	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
756	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
757	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
758	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
759	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
760	#127	—	2	1	no	—
761	#127	—	2	2	no	—
762	#127	C₂³×C₃₁	1	1	yes	characteristic
763	#127	C₂³×C₃₁	1	1	yes	characteristic
764	#127	C₂³×C₃₁	1	2	yes	—
765	#126	—	2	2	no	—
766	#126	—	2	2	no	—
767	#126	—	2	1	no	—
768	#126	—	2	2	no	—
769	#125	—	2	1	no	—
770	#125	—	2	1	no	—
771	#125	—	2	2	no	—
772	#125	C₂³×C₃₁	1	2	yes	—
773	#125	C₂³×C₃₁	1	1	yes	characteristic
774	#124	—	2	1	no	—
775	#124	—	2	1	no	—
776	#124	C₂³×C₃₁	1	2	yes	—
777	#124	C₂³×C₃₁	1	1	yes	characteristic
778	#124	C₂³×C₃₁	1	2	yes	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	1	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	#121	—	2	2	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	C₂³×C₃₁	1	2	yes	—
810	#121	C₂³×C₃₁	1	2	yes	—
811	#121	C₂³×C₃₁	1	1	yes	characteristic
812	#121	C₂³×C₃₁	1	2	yes	—
813	#120	—	2	2	no	—
814	#120	—	2	2	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
821	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
840	C₄×D₄	D₄×C₃₁	1	2	yes	—
841	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₃₁	1	2	yes	—
843	C₄×D₄	C₂³×C₃₁	1	2	yes	—
844	C₄×D₄	C₂³×C₃₁	1	2	yes	—
845	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₃₁	1	2	yes	—
848	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
849	C₄×D₄	C₂³×C₃₁	1	2	yes	—
850	#117	—	2	1	no	—
851	#117	—	2	1	no	—
852	#117	—	2	2	no	—
853	#117	—	2	2	no	—
854	#117	D₄×C₃₁	1	2	yes	—
855	#117	D₄×C₃₁	1	1	yes	characteristic
856	#117	C₂³×C₃₁	1	1	yes	characteristic
857	C₂×C₄⋊C₄	—	2	1	no	—
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	—	2	2	no	—
860	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
861	C₂×C₂²⋊C₄	—	2	2	no	—
862	C₂×C₂²⋊C₄	—	2	2	no	—
863	C₂×C₄²	—	2	1	no	—
864	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
865	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
866	#107	C₂³×C₃₁	1	1	yes	characteristic
867	#107	C₂³×C₃₁	1	1	yes	characteristic
868	#107	C₂³×C₃₁	1	2	yes	—
869	#106	C₂³×C₃₁	1	1	yes	characteristic
870	#106	C₂³×C₃₁	1	1	yes	characteristic
871	#106	C₂³×C₃₁	1	2	yes	—
872	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
873	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
877	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
878	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
879	#103	C₂³×C₃₁	1	2	yes	—
880	#103	C₂³×C₃₁	1	2	yes	—
881	#103	C₂³×C₃₁	1	1	yes	characteristic
882	#103	C₂³×C₃₁	1	2	yes	—
883	#103	C₂³×C₃₁	1	2	yes	—
884	#103	C₂³×C₃₁	1	1	yes	characteristic
885	#103	C₂³×C₃₁	1	1	yes	characteristic
886	#103	C₂³×C₃₁	1	1	yes	characteristic
887	#103	C₂³×C₃₁	1	2	yes	—
888	#102	C₂³×C₃₁	1	2	yes	—
889	#102	C₂³×C₃₁	1	2	yes	—
890	#102	C₂³×C₃₁	1	1	yes	characteristic
891	#102	C₂³×C₃₁	1	2	yes	—
892	#102	C₂³×C₃₁	1	2	yes	—
893	#102	C₂³×C₃₁	1	1	yes	characteristic
894	#102	C₂³×C₃₁	1	1	yes	characteristic
895	#102	C₂³×C₃₁	1	1	yes	characteristic
896	#102	C₂³×C₃₁	1	2	yes	—
897	#102	C₂³×C₃₁	1	2	yes	—
898	#102	C₂³×C₃₁	1	2	yes	—
899	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
900	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
903	#97	C₂³×C₃₁	1	2	yes	—
904	#97	C₂³×C₃₁	1	2	yes	—
905	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
906	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
907	C₃₁	#61974	1	1	yes	characteristic, direct product factor, Sylow
908	C₂⁴	—	2	2	no	—
909	#41	—	2	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	1	no	—
912	#41	—	4	2	no	—
913	#41	—	4	2	no	—
914	#41	—	4	2	no	—
915	#41	—	4	2	no	—
916	#41	—	4	2	no	—
917	#41	—	4	2	no	—
918	#41	—	4	4	no	—
919	#41	—	8	2	no	—
920	C₂×Q₈	—	2	1	no	—
921	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
924	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
925	C₂×D₄	—	2	4	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	4	no	—
943	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
945	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
947	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
948	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	8	4	no	—
962	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
964	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
967	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	Q₁₆	—	4	1	no	—
969	Q₁₆	—	4	2	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	2	no	—
972	SD₁₆	—	4	1	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	SD₁₆	—	4	2	no	—
977	D₈	—	2	4	no	—
978	D₈	—	2	2	no	—
979	D₈	—	4	2	no	—
980	D₈	—	4	2	no	—
981	D₈	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	M₁₆	—	4	2	no	—
984	C₂×C₈	—	4	2	no	—
985	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
990	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1011	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1039	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1047	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1048	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1049	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1050	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₃₁	1	2	yes	—
1052	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	4	4	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1061	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	2	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	8	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	4	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	1	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	4	4	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1130	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1131	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1132	C₈	—	2	2	no	—
1133	C₈	—	2	2	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	8	8	no	—
1157	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	C₃₁×#575	1	2	yes	—
1174	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1175	C₄	C₃₁×#585	1	1	yes	characteristic
1176	C₂	—	4	2	no	—
1177	C₂	—	4	1	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	2	no	—
1180	C₂	—	8	1	no	—
1181	C₂	—	8	2	no	—
1182	C₂	C₃₁×#3488	1	1	yes	characteristic
1183	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1184	C₂	C₃₁×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3517	C₂	semidirect
2. C₃₁×#3481	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3399	C₂	semidirect
5. C₃₁×#3372	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3333	C₂	semidirect
8. C₃₁×#3331	C₂	semidirect
9. C₃₁×#3309	C₂	semidirect
10. C₃₁×#3307	C₂	semidirect
11. C₃₁×#3274	C₂	semidirect
12. C₃₁×#3272	C₂	semidirect
13. C₃₁×#3268	C₂	semidirect
14. C₃₁×#3267	C₂	semidirect
15. C₃₁×#3256	C₂	semidirect
16. C₃₁×#3247	C₂	semidirect
17. C₃₁×#3219	C₂	semidirect
18. C₃₁×#3207	C₂	semidirect
19. C₃₁×#3114	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3036	C₂	semidirect
22. C₃₁×#3035	C₂	semidirect
23. C₃₁×#2989	C₂	semidirect
28. C₃₁×#557	C₂²	semidirect
38. C₃₁×#550	C₂²	semidirect
39. C₃₁×#550	C₂²	semidirect
41. C₃₁×#547	C₂²	semidirect
48. C₃₁×#532	C₂²	semidirect
49. C₃₁×#532	C₂²	semidirect
52. C₃₁×#529	C₂²	semidirect
53. C₃₁×#529	C₂²	semidirect
60. C₃₁×#497	C₂²	semidirect
61. C₃₁×#496	C₂²	semidirect
64. C₃₁×#491	C₂²	semidirect
65. C₃₁×#490	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
67. C₃₁×#486	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#480	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
79. C₃₁×#470	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#466	C₂²	semidirect
84. C₃₁×#465	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×#463	C₂²	semidirect
93. C₃₁×#463	C₂²	semidirect
94. C₃₁×#462	C₂²	semidirect
97. C₃₁×#461	C₂²	semidirect
99. C₃₁×#460	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
111. C₃₁×#449	C₂²	semidirect
112. C₃₁×#449	C₂²	semidirect
114. C₃₁×#446	C₂²	semidirect
115. C₃₁×#446	C₂²	semidirect
117. C₃₁×#442	C₂²	semidirect
119. C₃₁×#440	C₂²	semidirect
120. C₄×Q₁₆×C₃₁	C₂²	semidirect
122. C₄×SD₁₆×C₃₁	C₂²	semidirect
126. C₃₁×#435	C₂²	semidirect
127. C₃₁×#435	C₂²	semidirect
128. C₃₁×#432	C₂²	semidirect
129. C₃₁×#431	C₂²	semidirect
130. C₃₁×#423	C₂²	semidirect
131. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
132. C₃₁×#417	C₂²	semidirect
133. C₃₁×#417	C₂²	semidirect
134. C₃₁×#416	C₂²	semidirect
460. #61974	C₃₁	direct (N × H)
546. #3517	C₂×C₃₁	semidirect
547. #3481	C₂×C₃₁	semidirect
548. #3400	C₂×C₃₁	semidirect
549. #3399	C₂×C₃₁	semidirect
550. #3372	C₂×C₃₁	semidirect
551. #3366	C₂×C₃₁	semidirect
552. #3333	C₂×C₃₁	semidirect
553. #3331	C₂×C₃₁	semidirect
554. #3309	C₂×C₃₁	semidirect
555. #3307	C₂×C₃₁	semidirect
556. #3274	C₂×C₃₁	semidirect
557. #3272	C₂×C₃₁	semidirect
558. #3268	C₂×C₃₁	semidirect
559. #3267	C₂×C₃₁	semidirect
560. #3256	C₂×C₃₁	semidirect
561. #3247	C₂×C₃₁	semidirect
562. #3219	C₂×C₃₁	semidirect
563. #3207	C₂×C₃₁	semidirect
564. #3114	C₂×C₃₁	semidirect
565. #3102	C₂×C₃₁	semidirect
566. #3036	C₂×C₃₁	semidirect
567. #3035	C₂×C₃₁	semidirect
568. #2989	C₂×C₃₁	semidirect
611. #557	C₂²×C₃₁	semidirect
621. #550	C₂²×C₃₁	semidirect
622. #550	C₂²×C₃₁	semidirect
624. #547	C₂²×C₃₁	semidirect
631. #532	C₂²×C₃₁	semidirect
632. #532	C₂²×C₃₁	semidirect
635. #529	C₂²×C₃₁	semidirect
636. #529	C₂²×C₃₁	semidirect
643. #497	C₂²×C₃₁	semidirect
644. #496	C₂²×C₃₁	semidirect
647. #491	C₂²×C₃₁	semidirect
648. #490	C₂²×C₃₁	semidirect
649. #487	C₂²×C₃₁	semidirect
650. #486	C₂²×C₃₁	semidirect
651. #485	C₂²×C₃₁	semidirect
652. #483	C₂²×C₃₁	semidirect
653. #482	C₂²×C₃₁	semidirect
654. #480	C₂²×C₃₁	semidirect
655. #479	C₂²×C₃₁	semidirect
656. #479	C₂²×C₃₁	semidirect
658. #478	C₂²×C₃₁	semidirect
659. #478	C₂²×C₃₁	semidirect
660. #477	C₂²×C₃₁	semidirect
661. #476	C₂²×C₃₁	semidirect
662. #470	C₂²×C₃₁	semidirect
665. #468	C₂²×C₃₁	semidirect
666. #466	C₂²×C₃₁	semidirect
667. #465	C₂²×C₃₁	semidirect
668. #464	C₂²×C₃₁	semidirect
669. #464	C₂²×C₃₁	semidirect
670. #464	C₂²×C₃₁	semidirect
673. #463	C₂²×C₃₁	semidirect
674. #463	C₂²×C₃₁	semidirect
675. #463	C₂²×C₃₁	semidirect
676. #463	C₂²×C₃₁	semidirect
677. #462	C₂²×C₃₁	semidirect
680. #461	C₂²×C₃₁	semidirect
682. #460	C₂²×C₃₁	semidirect
686. #459	C₂²×C₃₁	semidirect
688. #452	C₂²×C₃₁	semidirect
689. #452	C₂²×C₃₁	semidirect
694. #449	C₂²×C₃₁	semidirect
695. #449	C₂²×C₃₁	semidirect
697. #446	C₂²×C₃₁	semidirect
698. #446	C₂²×C₃₁	semidirect
700. #442	C₂²×C₃₁	semidirect
702. #440	C₂²×C₃₁	semidirect
703. C₄×Q₁₆	C₂²×C₃₁	semidirect
705. C₄×SD₁₆	C₂²×C₃₁	semidirect
709. #435	C₂²×C₃₁	semidirect
710. #435	C₂²×C₃₁	semidirect
711. #432	C₂²×C₃₁	semidirect
712. #431	C₂²×C₃₁	semidirect
713. #423	C₂²×C₃₁	semidirect
714. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
715. #417	C₂²×C₃₁	semidirect
716. #417	C₂²×C₃₁	semidirect
717. #416	C₂²×C₃₁	semidirect
907. C₃₁	#61974	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×#3517	2
C₃₁×#3481	2
C₃₁×#3400	2
C₃₁×#3399	2
C₃₁×#3372	2
C₃₁×#3366	2
C₃₁×#3333	2
C₃₁×#3331	2
C₃₁×#3309	2
C₃₁×#3307	2
C₃₁×#3274	2
C₃₁×#3272	2
C₃₁×#3268	2
C₃₁×#3267	2
C₃₁×#3256	2
C₃₁×#3247	2
C₃₁×#3219	2
C₃₁×#3207	2
C₃₁×#3114	2
C₃₁×#3102	2
C₃₁×#3036	2
C₃₁×#3035	2
C₃₁×#2989	2
#61974	31

Subgroups — C31×#61974 #21518733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61974 #21518733