Subgroups — C₃₁×#61481 #21518240

Order 7936.

1880 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×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
13	D₄×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3174	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3126	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2949	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#557	—	2	1	no	—
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#556	—	2	1	no	—
30	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#555	C₂²	1	1	yes	characteristic
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#553	C₂²	1	2	yes	—
35	C₃₁×#552	—	2	2	no	—
36	C₃₁×#552	C₂²	1	2	yes	complemented
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	—	2	2	no	—
42	D₄²×C₃₁	C₂²	1	2	yes	—
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#541	—	2	2	no	—
45	C₃₁×#541	C₂²	1	2	yes	complemented
46	C₃₁×#540	C₂²	1	2	yes	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#533	—	2	1	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×#121	—	2	1	no	—
55	C₃₁×#519	C₂²	1	2	yes	complemented
56	C₃₁×#518	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
59	C₃₁×#499	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#492	C₂²	1	2	yes	complemented
63	C₃₁×#491	C₂²	1	2	yes	complemented
64	C₃₁×#490	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#484	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#474	C₂²	1	1	yes	characteristic
80	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#468	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#465	C₂²	1	2	yes	complemented
84	C₃₁×#465	C₂²	1	2	yes	complemented
85	C₃₁×#465	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	complemented
87	C₃₁×#461	C₂²	1	1	yes	characteristic
88	C₃₁×#461	C₂²	1	2	yes	—
89	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#461	C₂²	1	2	yes	complemented
91	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#460	C₂²	1	2	yes	complemented
94	C₃₁×#460	C₂²	1	2	yes	complemented
95	C₃₁×#450	C₂²	1	2	yes	—
96	C₃₁×#450	C₂²	1	2	yes	—
97	C₃₁×#450	C₂²	1	2	yes	—
98	C₃₁×#448	C₂²	1	2	yes	complemented
99	C₃₁×#448	C₂²	1	2	yes	complemented
100	C₃₁×#448	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#440	C₂²	1	2	yes	—
104	C₃₁×#440	C₂²	1	2	yes	—
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₃₁×#440	C₂²	1	2	yes	complemented
107	C₃₁×#440	C₂²	1	2	yes	complemented
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#427	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#419	C₂²	1	2	yes	complemented
130	C₃₁×#418	C₂²	1	2	yes	—
131	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	2	no	—
141	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₃₁	—	2	1	no	—
144	C₂×SD₁₆×C₃₁	—	2	4	no	—
145	C₂×SD₁₆×C₃₁	—	2	8	no	—
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	—	2	1	no	—
162	C₃₁×C₄⋊Q₈	—	2	2	no	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	2	yes	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	D₄	1	2	yes	—
175	C₃₁×#125	—	2	1	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	1	no	—
182	C₃₁×#125	D₄	1	1	yes	characteristic
183	C₃₁×#125	C₂³	1	2	yes	—
184	C₃₁×#125	C₂³	1	2	yes	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	D₄	1	1	yes	characteristic
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	D₄	1	2	yes	—
194	C₃₁×C₂²⋊Q₈	—	2	1	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	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	D₄	1	1	yes	characteristic
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#120	—	2	2	no	—
218	C₃₁×#120	—	2	2	no	—
219	C₃₁×#120	—	2	2	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	—	2	2	no	—
222	C₄×Q₈×C₃₁	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	—	2	2	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	2	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₃₁×#117	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₂⁴×C₃₁	—	2	1	no	—
315	C₂⁴×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	4	no	—
324	C₂×Q₈×C₃₁	—	4	1	no	—
325	C₂×Q₈×C₃₁	—	4	2	no	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	4	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	2	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	1	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	4	1	no	—
342	C₂×D₄×C₃₁	—	4	2	no	—
343	C₂×D₄×C₃₁	—	8	2	no	—
344	C₂×D₄×C₃₁	—	8	4	no	—
345	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	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	1	no	—
361	C₂²×C₄×C₃₁	—	8	2	no	—
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
366	SD₁₆×C₃₁	—	2	2	no	—
367	SD₁₆×C₃₁	—	2	4	no	—
368	SD₁₆×C₃₁	—	2	2	no	—
369	SD₁₆×C₃₁	—	2	4	no	—
370	SD₁₆×C₃₁	—	2	2	no	—
371	SD₁₆×C₃₁	—	2	4	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	SD₁₆×C₃₁	—	4	2	no	—
374	SD₁₆×C₃₁	—	4	2	no	—
375	SD₁₆×C₃₁	#41	1	4	yes	complemented
376	M₁₆×C₃₁	—	4	2	no	—
377	C₂×C₈×C₃₁	—	2	2	no	—
378	C₂×C₈×C₃₁	—	2	4	no	—
379	C₂×C₈×C₃₁	—	4	1	no	—
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
384	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
385	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
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	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	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	1	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	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	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	—	2	2	no	—
448	C₄²×C₃₁	—	2	2	no	—
449	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₃₁	C₂⁴	1	2	yes	—
454	#61481	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	2	1	no	—
457	C₂³×C₃₁	—	2	2	no	—
458	C₂³×C₃₁	—	4	2	no	—
459	C₂³×C₃₁	—	4	4	no	—
460	C₂³×C₃₁	—	4	2	no	—
461	C₂³×C₃₁	—	8	1	no	—
462	C₂³×C₃₁	—	8	2	no	—
463	C₂³×C₃₁	—	8	2	no	—
464	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
465	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₃₁	—	2	2	no	—
467	Q₈×C₃₁	—	2	1	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	—	4	2	no	—
473	Q₈×C₃₁	—	4	4	no	—
474	Q₈×C₃₁	—	4	2	no	—
475	Q₈×C₃₁	—	8	1	no	—
476	Q₈×C₃₁	C₂×#41	1	2	yes	—
477	D₄×C₃₁	—	2	4	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	2	1	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	2	1	no	—
482	D₄×C₃₁	—	2	1	no	—
483	D₄×C₃₁	—	2	2	no	—
484	D₄×C₃₁	—	4	2	no	—
485	D₄×C₃₁	—	4	4	no	—
486	D₄×C₃₁	—	4	4	no	—
487	D₄×C₃₁	—	4	2	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	1	no	—
490	D₄×C₃₁	—	8	2	no	—
491	D₄×C₃₁	—	8	2	no	—
492	D₄×C₃₁	—	8	2	no	—
493	D₄×C₃₁	C₂×#41	1	2	yes	—
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	2	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	2	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	4	2	no	—
510	C₂×C₄×C₃₁	—	4	4	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	1	no	—
516	C₂×C₄×C₃₁	—	8	2	no	—
517	C₂×C₄×C₃₁	—	8	2	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	—	8	1	no	—
520	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
524	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
529	C₈×C₃₁	—	2	1	no	—
530	C₈×C₃₁	—	2	2	no	—
531	C₈×C₃₁	—	2	1	no	—
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	2	no	—
534	C₈×C₃₁	C₂×#41	1	2	yes	—
535	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3519	C₂×C₃₁	1	1	yes	characteristic
537	#3392	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3337	C₂×C₃₁	1	2	yes	complemented
543	#3329	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3320	C₂×C₃₁	1	2	yes	complemented
546	#3310	C₂×C₃₁	1	2	yes	complemented
547	D₄×SD₁₆	C₂×C₃₁	1	2	yes	complemented
548	D₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3174	C₂×C₃₁	1	2	yes	complemented
550	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3126	C₂×C₃₁	1	2	yes	complemented
552	#3123	C₂×C₃₁	1	2	yes	complemented
553	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#2949	C₂×C₃₁	1	2	yes	complemented
557	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
558	C₂²×C₃₁	—	2	1	no	—
559	C₂²×C₃₁	—	2	1	no	—
560	C₂²×C₃₁	—	2	2	no	—
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	2	no	—
568	C₂²×C₃₁	—	4	1	no	—
569	C₂²×C₃₁	—	4	2	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	8	4	no	—
573	C₂²×C₃₁	—	16	4	no	—
574	C₂²×C₃₁	#577	1	2	yes	—
575	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	2	no	—
578	C₄×C₃₁	—	2	2	no	—
579	C₄×C₃₁	—	2	1	no	—
580	C₄×C₃₁	—	2	1	no	—
581	C₄×C₃₁	—	2	1	no	—
582	C₄×C₃₁	—	2	2	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	2	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	2	no	—
591	C₄×C₃₁	—	4	2	no	—
592	C₄×C₃₁	#577	1	2	yes	—
593	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
594	C₄×C₃₁	#585	1	1	yes	characteristic
595	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
596	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
597	#557	—	2	1	no	—
598	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#556	—	2	1	no	—
601	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#555	C₂²×C₃₁	1	1	yes	characteristic
603	#554	C₂²×C₃₁	1	1	yes	characteristic
604	#553	—	2	1	no	—
605	#553	C₂²×C₃₁	1	2	yes	—
606	#552	—	2	2	no	—
607	#552	C₂²×C₃₁	1	2	yes	complemented
608	#550	C₂²×C₃₁	1	1	yes	characteristic
609	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
611	#546	—	2	1	no	—
612	#546	—	2	2	no	—
613	D₄²	C₂²×C₃₁	1	2	yes	—
614	D₄²	C₂²×C₃₁	1	1	yes	characteristic
615	#541	—	2	2	no	—
616	#541	C₂²×C₃₁	1	2	yes	complemented
617	#540	C₂²×C₃₁	1	2	yes	—
618	#538	—	2	2	no	—
619	#533	—	2	1	no	—
620	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#532	C₂²×C₃₁	1	1	yes	characteristic
622	#529	—	2	1	no	—
623	#529	C₂²×C₃₁	1	1	yes	characteristic
624	#525	—	2	1	no	—
625	C₂×#121	—	2	1	no	—
626	#519	C₂²×C₃₁	1	2	yes	complemented
627	#518	C₂²×C₃₁	1	2	yes	—
628	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
630	#499	C₂²×C₃₁	1	2	yes	complemented
631	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#492	C₂²×C₃₁	1	2	yes	complemented
634	#491	C₂²×C₃₁	1	2	yes	complemented
635	#490	C₂²×C₃₁	1	2	yes	complemented
636	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#485	C₂²×C₃₁	1	2	yes	complemented
639	#485	C₂²×C₃₁	1	2	yes	complemented
640	#484	C₂²×C₃₁	1	2	yes	complemented
641	#482	C₂²×C₃₁	1	2	yes	complemented
642	#482	C₂²×C₃₁	1	2	yes	complemented
643	#480	C₂²×C₃₁	1	2	yes	complemented
644	#479	C₂²×C₃₁	1	2	yes	complemented
645	#479	C₂²×C₃₁	1	2	yes	complemented
646	#478	C₂²×C₃₁	1	2	yes	—
647	#478	C₂²×C₃₁	1	2	yes	complemented
648	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#474	C₂²×C₃₁	1	1	yes	characteristic
651	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#468	C₂²×C₃₁	1	2	yes	complemented
653	#468	C₂²×C₃₁	1	2	yes	complemented
654	#465	C₂²×C₃₁	1	2	yes	complemented
655	#465	C₂²×C₃₁	1	2	yes	complemented
656	#465	C₂²×C₃₁	1	2	yes	complemented
657	#465	C₂²×C₃₁	1	2	yes	complemented
658	#461	C₂²×C₃₁	1	1	yes	characteristic
659	#461	C₂²×C₃₁	1	2	yes	—
660	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#461	C₂²×C₃₁	1	2	yes	complemented
662	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	#460	C₂²×C₃₁	1	2	yes	complemented
665	#460	C₂²×C₃₁	1	2	yes	complemented
666	#450	C₂²×C₃₁	1	2	yes	—
667	#450	C₂²×C₃₁	1	2	yes	—
668	#450	C₂²×C₃₁	1	2	yes	—
669	#448	C₂²×C₃₁	1	2	yes	complemented
670	#448	C₂²×C₃₁	1	2	yes	complemented
671	#448	C₂²×C₃₁	1	2	yes	complemented
672	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	#440	C₂²×C₃₁	1	2	yes	—
675	#440	C₂²×C₃₁	1	2	yes	—
676	#440	C₂²×C₃₁	1	2	yes	complemented
677	#440	C₂²×C₃₁	1	2	yes	complemented
678	#440	C₂²×C₃₁	1	2	yes	complemented
679	#440	C₂²×C₃₁	1	2	yes	complemented
680	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
684	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
687	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
689	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#435	C₂²×C₃₁	1	2	yes	complemented
694	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
695	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
696	#433	C₂²×C₃₁	1	2	yes	complemented
697	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#427	C₂²×C₃₁	1	2	yes	complemented
699	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	#419	C₂²×C₃₁	1	2	yes	complemented
701	#418	C₂²×C₃₁	1	2	yes	—
702	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
704	#405	C₂²×C₃₁	1	2	yes	complemented
705	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	C₂×C₃₁	—	2	2	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	D₄×#41	1	1	yes	characteristic
712	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
713	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	1	no	—
716	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
718	C₂²×D₄	—	2	1	no	—
719	C₂²×D₄	—	2	2	no	—
720	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
721	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
722	C₂³×C₄	—	2	1	no	—
723	C₂×SD₁₆	—	2	4	no	—
724	C₂×SD₁₆	—	2	8	no	—
725	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
735	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
738	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄⋊Q₈	—	2	1	no	—
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	—	2	2	no	—
742	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
744	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
746	#127	C₂³×C₃₁	1	1	yes	characteristic
747	#127	C₂³×C₃₁	1	2	yes	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	D₄×C₃₁	1	2	yes	—
754	#125	—	2	1	no	—
755	#125	—	2	2	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	2	no	—
759	#125	—	2	2	no	—
760	#125	—	2	1	no	—
761	#125	D₄×C₃₁	1	1	yes	characteristic
762	#125	C₂³×C₃₁	1	2	yes	—
763	#125	C₂³×C₃₁	1	2	yes	—
764	#124	—	2	1	no	—
765	#124	—	2	2	no	—
766	#124	—	2	1	no	—
767	#124	D₄×C₃₁	1	1	yes	characteristic
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	D₄×C₃₁	1	2	yes	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
780	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
782	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	1	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	D₄×C₃₁	1	1	yes	characteristic
793	#121	C₂³×C₃₁	1	2	yes	—
794	#121	C₂³×C₃₁	1	2	yes	—
795	#121	C₂³×C₃₁	1	2	yes	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	2	no	—
801	C₄×Q₈	—	2	2	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
812	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
813	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
814	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₃₁	1	2	yes	—
828	C₄×D₄	C₂³×C₃₁	1	2	yes	—
829	C₄×D₄	C₂³×C₃₁	1	2	yes	—
830	C₄×D₄	C₂³×C₃₁	1	2	yes	—
831	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
832	#117	—	2	1	no	—
833	#117	—	2	1	no	—
834	#117	—	2	2	no	—
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	C₂³×C₃₁	1	2	yes	—
838	#117	C₂³×C₃₁	1	2	yes	—
839	#117	C₂³×C₃₁	1	2	yes	—
840	C₂×C₄⋊C₄	—	2	1	no	—
841	C₂×C₄⋊C₄	—	2	1	no	—
842	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	—	2	1	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₄²	—	2	1	no	—
848	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
853	#106	C₂³×C₃₁	1	1	yes	characteristic
854	#106	C₂³×C₃₁	1	1	yes	characteristic
855	#106	C₂³×C₃₁	1	1	yes	characteristic
856	#106	C₂³×C₃₁	1	1	yes	characteristic
857	#106	C₂³×C₃₁	1	2	yes	—
858	#106	C₂³×C₃₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
863	#103	C₂³×C₃₁	1	1	yes	characteristic
864	#103	C₂³×C₃₁	1	1	yes	characteristic
865	#103	C₂³×C₃₁	1	1	yes	characteristic
866	#103	C₂³×C₃₁	1	1	yes	characteristic
867	#103	C₂³×C₃₁	1	2	yes	—
868	#103	C₂³×C₃₁	1	2	yes	—
869	#103	C₂³×C₃₁	1	2	yes	—
870	#103	C₂³×C₃₁	1	2	yes	—
871	#103	C₂³×C₃₁	1	2	yes	—
872	#103	C₂³×C₃₁	1	2	yes	—
873	#102	C₂³×C₃₁	1	1	yes	characteristic
874	#102	C₂³×C₃₁	1	1	yes	characteristic
875	#102	C₂³×C₃₁	1	1	yes	characteristic
876	#102	C₂³×C₃₁	1	1	yes	characteristic
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
886	#97	C₂³×C₃₁	1	2	yes	—
887	#97	C₂³×C₃₁	1	2	yes	—
888	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₃₁	1	2	yes	—
893	C₃₁	#61481	1	1	yes	characteristic, direct product factor, Sylow
894	C₂⁴	—	2	1	no	—
895	C₂⁴	—	2	2	no	—
896	#41	—	8	2	no	—
897	#41	—	8	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	4	no	—
904	C₂×Q₈	—	4	1	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
909	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	4	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	4	1	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	8	2	no	—
924	C₂×D₄	—	8	4	no	—
925	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
926	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
929	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	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	1	no	—
941	C₂²×C₄	—	8	2	no	—
942	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	2	2	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	2	4	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	#41×C₃₁	1	4	yes	complemented
956	M₁₆	—	4	2	no	—
957	C₂×C₈	—	2	2	no	—
958	C₂×C₈	—	2	4	no	—
959	C₂×C₈	—	4	1	no	—
960	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
964	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
965	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
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	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	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	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
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	C₂⁴×C₃₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1030	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₃₁	1	2	yes	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	4	2	no	—
1038	C₂³	—	4	4	no	—
1039	C₂³	—	4	2	no	—
1040	C₂³	—	8	1	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1044	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	4	4	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	8	1	no	—
1055	Q₈	C₂×#41×C₃₁	1	2	yes	—
1056	D₄	—	2	4	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	C₂×#41×C₃₁	1	2	yes	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	4	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	1	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	1	no	—
1099	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
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	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1107	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1108	C₈	—	2	1	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	2	no	—
1113	C₈	C₂×#41×C₃₁	1	2	yes	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	8	4	no	—
1129	C₂²	—	16	4	no	—
1130	C₂²	C₃₁×#577	1	2	yes	—
1131	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	2	no	—
1148	C₄	C₃₁×#577	1	2	yes	—
1149	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1150	C₄	C₃₁×#585	1	1	yes	characteristic
1151	C₂	—	2	2	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	1	no	—
1155	C₂	—	8	2	no	—
1156	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1157	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1158	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3519	C₂
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×#3523	C₂	semidirect
3. C₃₁×#3392	C₂	semidirect
4. C₃₁×#3381	C₂	semidirect
5. C₃₁×#3372	C₂	semidirect
6. C₃₁×#3368	C₂	semidirect
7. C₃₁×#3340	C₂	semidirect
8. C₃₁×#3337	C₂	semidirect
9. C₃₁×#3329	C₂	semidirect
10. C₃₁×#3324	C₂	semidirect
11. C₃₁×#3320	C₂	semidirect
12. C₃₁×#3310	C₂	semidirect
13. D₄×SD₁₆×C₃₁	C₂	semidirect
14. D₄×SD₁₆×C₃₁	C₂	semidirect
15. C₃₁×#3174	C₂	semidirect
16. C₃₁×#3167	C₂	semidirect
17. C₃₁×#3126	C₂	semidirect
18. C₃₁×#3123	C₂	semidirect
19. C₃₁×#3112	C₂	semidirect
20. C₃₁×#3110	C₂	semidirect
21. C₃₁×#2966	C₂	semidirect
22. C₃₁×#2949	C₂	semidirect
23. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
27. C₃₁×#557	C₂²	semidirect
28. C₃₁×#557	C₂²	semidirect
30. C₃₁×#556	C₂²	semidirect
36. C₃₁×#552	C₂²	semidirect
38. D₄×Q₈×C₃₁	C₂²	semidirect
39. D₄×Q₈×C₃₁	C₂²	semidirect
45. C₃₁×#541	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
55. C₃₁×#519	C₂²	semidirect
57. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
59. C₃₁×#499	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#492	C₂²	semidirect
62. C₃₁×#492	C₂²	semidirect
63. C₃₁×#491	C₂²	semidirect
64. C₃₁×#490	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#484	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
78. C₃₁×#477	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#468	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#465	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
85. C₃₁×#465	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
89. C₃₁×#461	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
91. C₃₁×#460	C₂²	semidirect
92. C₃₁×#460	C₂²	semidirect
93. C₃₁×#460	C₂²	semidirect
94. C₃₁×#460	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
99. C₃₁×#448	C₂²	semidirect
100. C₃₁×#448	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₃₁×#440	C₂²	semidirect
107. C₃₁×#440	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
114. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#427	C₂²	semidirect
128. C₂×C₃₁×#106	C₂²	semidirect
129. C₃₁×#419	C₂²	semidirect
131. C₂×C₃₁×#103	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
375. SD₁₆×C₃₁	#41	semidirect
454. #61481	C₃₁	direct (N × H)
535. #3523	C₂×C₃₁	semidirect
537. #3392	C₂×C₃₁	semidirect
538. #3381	C₂×C₃₁	semidirect
539. #3372	C₂×C₃₁	semidirect
540. #3368	C₂×C₃₁	semidirect
541. #3340	C₂×C₃₁	semidirect
542. #3337	C₂×C₃₁	semidirect
543. #3329	C₂×C₃₁	semidirect
544. #3324	C₂×C₃₁	semidirect
545. #3320	C₂×C₃₁	semidirect
546. #3310	C₂×C₃₁	semidirect
547. D₄×SD₁₆	C₂×C₃₁	semidirect
548. D₄×SD₁₆	C₂×C₃₁	semidirect
549. #3174	C₂×C₃₁	semidirect
550. #3167	C₂×C₃₁	semidirect
551. #3126	C₂×C₃₁	semidirect
552. #3123	C₂×C₃₁	semidirect
553. #3112	C₂×C₃₁	semidirect
554. #3110	C₂×C₃₁	semidirect
555. #2966	C₂×C₃₁	semidirect
556. #2949	C₂×C₃₁	semidirect
557. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
598. #557	C₂²×C₃₁	semidirect
599. #557	C₂²×C₃₁	semidirect
601. #556	C₂²×C₃₁	semidirect
607. #552	C₂²×C₃₁	semidirect
609. D₄×Q₈	C₂²×C₃₁	semidirect
610. D₄×Q₈	C₂²×C₃₁	semidirect
616. #541	C₂²×C₃₁	semidirect
620. #533	C₂²×C₃₁	semidirect
626. #519	C₂²×C₃₁	semidirect
628. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
630. #499	C₂²×C₃₁	semidirect
631. #498	C₂²×C₃₁	semidirect
632. #492	C₂²×C₃₁	semidirect
633. #492	C₂²×C₃₁	semidirect
634. #491	C₂²×C₃₁	semidirect
635. #490	C₂²×C₃₁	semidirect
636. #487	C₂²×C₃₁	semidirect
637. #486	C₂²×C₃₁	semidirect
638. #485	C₂²×C₃₁	semidirect
639. #485	C₂²×C₃₁	semidirect
640. #484	C₂²×C₃₁	semidirect
641. #482	C₂²×C₃₁	semidirect
642. #482	C₂²×C₃₁	semidirect
643. #480	C₂²×C₃₁	semidirect
644. #479	C₂²×C₃₁	semidirect
645. #479	C₂²×C₃₁	semidirect
647. #478	C₂²×C₃₁	semidirect
648. #477	C₂²×C₃₁	semidirect
649. #477	C₂²×C₃₁	semidirect
651. #474	C₂²×C₃₁	semidirect
652. #468	C₂²×C₃₁	semidirect
653. #468	C₂²×C₃₁	semidirect
654. #465	C₂²×C₃₁	semidirect
655. #465	C₂²×C₃₁	semidirect
656. #465	C₂²×C₃₁	semidirect
657. #465	C₂²×C₃₁	semidirect
660. #461	C₂²×C₃₁	semidirect
661. #461	C₂²×C₃₁	semidirect
662. #460	C₂²×C₃₁	semidirect
663. #460	C₂²×C₃₁	semidirect
664. #460	C₂²×C₃₁	semidirect
665. #460	C₂²×C₃₁	semidirect
669. #448	C₂²×C₃₁	semidirect
670. #448	C₂²×C₃₁	semidirect
671. #448	C₂²×C₃₁	semidirect
672. #446	C₂²×C₃₁	semidirect
673. C₈×Q₈	C₂²×C₃₁	semidirect
676. #440	C₂²×C₃₁	semidirect
677. #440	C₂²×C₃₁	semidirect
678. #440	C₂²×C₃₁	semidirect
679. #440	C₂²×C₃₁	semidirect
685. C₄×SD₁₆	C₂²×C₃₁	semidirect
686. C₄×SD₁₆	C₂²×C₃₁	semidirect
687. C₄×SD₁₆	C₂²×C₃₁	semidirect
688. C₄×SD₁₆	C₂²×C₃₁	semidirect
689. C₄×SD₁₆	C₂²×C₃₁	semidirect
690. C₄×SD₁₆	C₂²×C₃₁	semidirect
691. C₄×SD₁₆	C₂²×C₃₁	semidirect
692. #436	C₂²×C₃₁	semidirect
693. #435	C₂²×C₃₁	semidirect
694. C₈×D₄	C₂²×C₃₁	semidirect
695. C₈×D₄	C₂²×C₃₁	semidirect
696. #433	C₂²×C₃₁	semidirect
697. #432	C₂²×C₃₁	semidirect
698. #427	C₂²×C₃₁	semidirect
699. C₂×#106	C₂²×C₃₁	semidirect
700. #419	C₂²×C₃₁	semidirect
702. C₂×#103	C₂²×C₃₁	semidirect
704. #405	C₂²×C₃₁	semidirect
705. C₂×C₄×C₈	C₂²×C₃₁	semidirect
893. C₃₁	#61481	direct (N × H)
955. SD₁₆	#41×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3523	2
C₃₁×#3519	2
C₃₁×#3392	2
C₃₁×#3381	2
C₃₁×#3372	2
C₃₁×#3368	2
C₃₁×#3340	2
C₃₁×#3337	2
C₃₁×#3329	2
C₃₁×#3324	2
C₃₁×#3320	2
C₃₁×#3310	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3174	2
C₃₁×#3167	2
C₃₁×#3126	2
C₃₁×#3123	2
C₃₁×#3112	2
C₃₁×#3110	2
C₃₁×#2966	2
C₃₁×#2949	2
C₂×C₄×SD₁₆×C₃₁	2
#61481	31

Subgroups — C31×#61481 #21518240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61481 #21518240