Subgroups — C₃₁×#60581 #21517340

Order 7936.

2024 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3116	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3107	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3042	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3005	C₂	1	1	yes	maximal, characteristic
18	C₂×C₃₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#556	—	2	1	no	—
30	C₃₁×#554	—	2	1	no	—
31	C₃₁×#552	—	2	2	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#551	—	2	2	no	—
35	C₃₁×#544	C₂²	1	1	yes	characteristic
36	C₃₁×#542	C₂²	1	2	yes	complemented
37	C₃₁×#541	C₂²	1	2	yes	complemented
38	C₃₁×#536	C₂²	1	1	yes	characteristic
39	C₃₁×#533	C₂²	1	2	yes	complemented
40	C₃₁×#529	C₂²	1	2	yes	complemented
41	C₃₁×#525	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃₁×#520	—	2	1	no	—
44	C₃₁×#520	—	2	1	no	—
45	C₃₁×#520	C₂²	1	2	yes	—
46	C₃₁×#520	C₂²	1	2	yes	—
47	C₃₁×#520	C₂²	1	1	yes	characteristic
48	C₃₁×#519	C₂²	1	1	yes	characteristic
49	C₃₁×#519	C₂²	1	1	yes	characteristic
50	C₃₁×#519	C₂²	1	1	yes	characteristic
51	C₃₁×#518	—	2	2	no	—
52	C₃₁×#518	C₂²	1	1	yes	characteristic
53	C₃₁×#518	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	—	2	1	no	—
55	C₄×#41×C₃₁	—	2	1	no	—
56	C₄×#41×C₃₁	C₂²	1	2	yes	—
57	C₄×#41×C₃₁	C₂²	1	2	yes	—
58	C₂×C₃₁×#117	—	2	2	no	—
59	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
61	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#485	C₂²	1	2	yes	complemented
64	C₃₁×#485	C₂²	1	2	yes	complemented
65	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#484	C₂²	1	2	yes	complemented
67	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#483	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	2	yes	complemented
78	C₃₁×#476	C₂²	1	2	yes	complemented
79	C₃₁×#475	C₂²	1	2	yes	complemented
80	C₃₁×#474	C₂²	1	2	yes	complemented
81	C₃₁×#464	C₂²	1	2	yes	complemented
82	C₃₁×#464	C₂²	1	2	yes	complemented
83	C₃₁×#463	C₂²	1	2	yes	complemented
84	C₃₁×#463	C₂²	1	2	yes	complemented
85	C₃₁×#462	C₂²	1	2	yes	complemented
86	C₃₁×#462	C₂²	1	2	yes	complemented
87	C₃₁×#461	C₂²	1	2	yes	complemented
88	C₃₁×#461	C₂²	1	2	yes	complemented
89	C₃₁×#452	C₂²	1	2	yes	—
90	C₃₁×#452	C₂²	1	2	yes	—
91	C₃₁×#452	C₂²	1	2	yes	—
92	C₃₁×#452	C₂²	1	2	yes	—
93	C₃₁×#452	C₂²	1	2	yes	—
94	C₃₁×#452	C₂²	1	2	yes	—
95	C₃₁×#449	C₂²	1	2	yes	—
96	C₃₁×#449	C₂²	1	2	yes	—
97	C₃₁×#442	C₂²	1	2	yes	complemented
98	C₃₁×#441	C₂²	1	2	yes	complemented
99	C₃₁×#441	C₂²	1	2	yes	complemented
100	C₃₁×#441	C₂²	1	2	yes	complemented
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
112	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
113	C₃₁×#433	C₂²	1	2	yes	complemented
114	C₃₁×#433	C₂²	1	2	yes	complemented
115	C₃₁×#432	C₂²	1	2	yes	complemented
116	C₃₁×#431	C₂²	1	2	yes	complemented
117	C₃₁×#428	C₂²	1	1	yes	characteristic
118	C₃₁×#428	C₂²	1	1	yes	characteristic
119	C₃₁×#427	C₂²	1	1	yes	characteristic
120	C₃₁×#427	C₂²	1	1	yes	characteristic
121	C₃₁×#424	C₂²	1	1	yes	characteristic
122	C₃₁×#424	C₂²	1	1	yes	characteristic
123	C₃₁×#419	C₂²	1	1	yes	characteristic
124	C₃₁×#419	C₂²	1	1	yes	characteristic
125	C₃₁×#419	C₂²	1	1	yes	characteristic
126	C₃₁×#418	C₂²	1	1	yes	characteristic
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
131	C₃₁×#407	C₂²	1	1	yes	characteristic
132	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic
134	C₃₁×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	4	no	—
136	C₂×#41×C₃₁	—	2	4	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂×#41×C₃₁	C₂³	1	2	yes	—
142	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₃₁	—	2	1	no	—
145	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₃₁	—	2	1	no	—
147	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₃₁×#137	—	2	4	no	—
149	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
150	C₂×Q₁₆×C₃₁	—	2	4	no	—
151	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	—	2	4	no	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×D₈×C₃₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	—	2	1	no	—
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	C₂³	1	2	yes	—
178	C₃₁×#123	—	2	1	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	1	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
191	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
193	C₃₁×#121	C₂³	1	1	yes	characteristic
194	C₃₁×#121	C₂³	1	1	yes	characteristic
195	C₃₁×#120	—	2	1	no	—
196	C₄×Q₈×C₃₁	—	2	1	no	—
197	C₄×Q₈×C₃₁	—	2	1	no	—
198	C₄×Q₈×C₃₁	—	2	1	no	—
199	C₄×Q₈×C₃₁	—	2	1	no	—
200	C₄×Q₈×C₃₁	—	2	1	no	—
201	C₄×Q₈×C₃₁	—	2	1	no	—
202	C₄×Q₈×C₃₁	—	2	2	no	—
203	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
205	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
206	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
210	C₄×D₄×C₃₁	—	2	2	no	—
211	C₄×D₄×C₃₁	—	2	2	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	2	no	—
214	C₄×D₄×C₃₁	—	2	1	no	—
215	C₄×D₄×C₃₁	—	2	1	no	—
216	C₄×D₄×C₃₁	—	2	2	no	—
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	—	2	1	no	—
219	C₄×D₄×C₃₁	—	2	1	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	C₂³	1	2	yes	—
227	C₄×D₄×C₃₁	C₂³	1	2	yes	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₃₁×#117	—	2	1	no	—
232	C₃₁×#117	—	2	1	no	—
233	C₃₁×#117	—	2	2	no	—
234	C₃₁×#117	—	2	2	no	—
235	C₃₁×#117	—	2	2	no	—
236	C₃₁×#117	—	2	1	no	—
237	C₃₁×#117	—	2	2	no	—
238	C₃₁×#117	—	2	2	no	—
239	C₃₁×#117	—	2	2	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	—	2	2	no	—
242	C₃₁×#117	—	2	2	no	—
243	C₃₁×#117	D₄	1	2	yes	—
244	C₃₁×#117	D₄	1	1	yes	characteristic
245	C₃₁×#117	D₄	1	1	yes	characteristic
246	C₃₁×#117	C₂³	1	1	yes	characteristic
247	C₃₁×#117	C₂³	1	1	yes	characteristic
248	C₃₁×#117	C₂³	1	1	yes	characteristic
249	C₃₁×#117	C₂³	1	1	yes	characteristic
250	C₃₁×#117	C₂³	1	1	yes	characteristic
251	C₃₁×#117	C₂³	1	1	yes	characteristic
252	C₃₁×#117	C₂³	1	1	yes	characteristic
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	—	2	2	no	—
270	C₂×C₄²×C₃₁	—	2	2	no	—
271	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	1	yes	characteristic
273	C₃₁×#107	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#107	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	1	yes	characteristic
280	C₃₁×#106	C₂³	1	1	yes	characteristic
281	C₃₁×#106	C₂³	1	1	yes	characteristic
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×#106	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
287	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	2	yes	—
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
312	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₃₁×#97	C₂³	1	2	yes	—
315	C₃₁×#97	C₂³	1	2	yes	—
316	C₄×C₈×C₃₁	C₂³	1	2	yes	—
317	C₄×C₈×C₃₁	C₂³	1	2	yes	—
318	C₂⁴×C₃₁	—	2	1	no	—
319	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
320	#41×C₃₁	—	2	8	no	—
321	#41×C₃₁	—	2	8	no	—
322	#41×C₃₁	—	2	4	no	—
323	#41×C₃₁	—	2	4	no	—
324	#41×C₃₁	—	2	4	no	—
325	#41×C₃₁	—	2	4	no	—
326	#41×C₃₁	—	2	2	no	—
327	#41×C₃₁	—	2	2	no	—
328	C₂×Q₈×C₃₁	—	2	1	no	—
329	C₂×Q₈×C₃₁	—	2	1	no	—
330	C₂×Q₈×C₃₁	—	2	2	no	—
331	C₂×Q₈×C₃₁	—	2	2	no	—
332	C₂×Q₈×C₃₁	—	2	2	no	—
333	C₂×Q₈×C₃₁	—	2	2	no	—
334	C₂×Q₈×C₃₁	#41	1	4	yes	—
335	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
336	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
338	C₂×D₄×C₃₁	—	2	8	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	1	no	—
344	C₂×D₄×C₃₁	—	2	1	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	#41	1	4	yes	—
347	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₃₁	—	2	8	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	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	2	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	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
369	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	Q₁₆×C₃₁	—	2	4	no	—
374	Q₁₆×C₃₁	—	2	4	no	—
375	Q₁₆×C₃₁	—	2	4	no	—
376	SD₁₆×C₃₁	—	2	4	no	—
377	SD₁₆×C₃₁	—	2	4	no	—
378	SD₁₆×C₃₁	—	2	4	no	—
379	SD₁₆×C₃₁	—	2	4	no	—
380	D₈×C₃₁	—	2	4	no	—
381	M₁₆×C₃₁	—	2	2	no	—
382	M₁₆×C₃₁	—	2	2	no	—
383	C₂×C₈×C₃₁	—	2	2	no	—
384	C₂×C₈×C₃₁	—	2	2	no	—
385	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
388	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	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	2	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	1	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
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	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂×D₄	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	1	yes	characteristic
420	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	1	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	—	2	1	no	—
447	C₄²×C₃₁	—	2	2	no	—
448	C₄²×C₃₁	—	2	2	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	—	2	2	no	—
451	C₄²×C₃₁	—	2	1	no	—
452	C₄²×C₃₁	—	2	1	no	—
453	C₄²×C₃₁	—	2	2	no	—
454	C₄²×C₃₁	—	2	2	no	—
455	C₄²×C₃₁	—	2	2	no	—
456	C₄²×C₃₁	—	2	1	no	—
457	C₄²×C₃₁	C₂×D₄	1	2	yes	—
458	C₄²×C₃₁	C₂×D₄	1	2	yes	—
459	C₄²×C₃₁	C₂⁴	1	2	yes	—
460	C₄²×C₃₁	C₂⁴	1	2	yes	—
461	#60581	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
462	C₂³×C₃₁	—	2	2	no	—
463	C₂³×C₃₁	—	2	2	no	—
464	C₂³×C₃₁	—	2	4	no	—
465	C₂³×C₃₁	—	2	1	no	—
466	C₂³×C₃₁	—	4	1	no	—
467	C₂³×C₃₁	—	4	1	no	—
468	C₂³×C₃₁	—	8	1	no	—
469	C₂³×C₃₁	—	8	1	no	—
470	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
471	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
472	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
473	Q₈×C₃₁	—	2	4	no	—
474	Q₈×C₃₁	—	2	2	no	—
475	Q₈×C₃₁	—	2	2	no	—
476	Q₈×C₃₁	—	2	1	no	—
477	Q₈×C₃₁	—	2	2	no	—
478	Q₈×C₃₁	—	2	1	no	—
479	Q₈×C₃₁	—	4	2	no	—
480	Q₈×C₃₁	—	8	2	no	—
481	Q₈×C₃₁	C₂×#41	1	4	yes	—
482	D₄×C₃₁	—	2	8	no	—
483	D₄×C₃₁	—	2	8	no	—
484	D₄×C₃₁	—	2	4	no	—
485	D₄×C₃₁	—	2	2	no	—
486	D₄×C₃₁	—	2	1	no	—
487	D₄×C₃₁	—	2	1	no	—
488	D₄×C₃₁	—	4	2	no	—
489	D₄×C₃₁	—	4	2	no	—
490	D₄×C₃₁	—	8	1	no	—
491	D₄×C₃₁	C₂×#41	1	4	yes	—
492	C₂×C₄×C₃₁	—	2	8	no	—
493	C₂×C₄×C₃₁	—	2	8	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	4	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	2	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	8	2	no	—
517	C₂×C₄×C₃₁	—	8	2	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	—	8	1	no	—
522	C₂×C₄×C₃₁	—	8	1	no	—
523	C₂×C₄×C₃₁	—	8	1	no	—
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	2	yes	—
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
532	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
533	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
534	C₈×C₃₁	—	2	1	no	—
535	C₈×C₃₁	—	2	1	no	—
536	C₈×C₃₁	—	2	1	no	—
537	C₈×C₃₁	—	2	1	no	—
538	C₈×C₃₁	—	2	2	no	—
539	C₈×C₃₁	—	2	2	no	—
540	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3428	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3125	C₂×C₃₁	1	2	yes	complemented
543	#3124	C₂×C₃₁	1	2	yes	complemented
544	#3120	C₂×C₃₁	1	2	yes	complemented
545	#3120	C₂×C₃₁	1	2	yes	complemented
546	#3116	C₂×C₃₁	1	2	yes	complemented
547	#3111	C₂×C₃₁	1	2	yes	complemented
548	#3107	C₂×C₃₁	1	2	yes	complemented
549	#3102	C₂×C₃₁	1	2	yes	complemented
550	#3095	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3091	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3044	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3042	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3005	C₂×C₃₁	1	1	yes	characteristic
557	C₂×#452	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#2950	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#2949	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#2947	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#2946	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
563	C₂²×C₃₁	—	2	1	no	—
564	C₂²×C₃₁	—	2	1	no	—
565	C₂²×C₃₁	—	2	1	no	—
566	C₂²×C₃₁	—	2	1	no	—
567	C₂²×C₃₁	—	2	1	no	—
568	C₂²×C₃₁	—	2	1	no	—
569	C₂²×C₃₁	—	2	1	no	—
570	C₂²×C₃₁	—	2	1	no	—
571	C₂²×C₃₁	—	2	4	no	—
572	C₂²×C₃₁	—	4	2	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	4	1	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	4	1	no	—
577	C₂²×C₃₁	—	8	2	no	—
578	C₂²×C₃₁	—	8	4	no	—
579	C₂²×C₃₁	#525	1	2	yes	—
580	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
581	C₄×C₃₁	—	2	2	no	—
582	C₄×C₃₁	—	2	2	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	2	2	no	—
585	C₄×C₃₁	—	2	1	no	—
586	C₄×C₃₁	—	2	1	no	—
587	C₄×C₃₁	—	2	4	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	2	no	—
591	C₄×C₃₁	—	4	1	no	—
592	C₄×C₃₁	—	4	1	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	1	no	—
595	C₄×C₃₁	—	4	1	no	—
596	C₄×C₃₁	—	4	2	no	—
597	C₄×C₃₁	#525	1	2	yes	—
598	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
599	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
600	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
601	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
602	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
603	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
604	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
605	#556	—	2	1	no	—
606	#554	—	2	1	no	—
607	#552	—	2	2	no	—
608	#552	—	2	1	no	—
609	#552	—	2	1	no	—
610	#551	—	2	2	no	—
611	#544	C₂²×C₃₁	1	1	yes	characteristic
612	#542	C₂²×C₃₁	1	2	yes	complemented
613	#541	C₂²×C₃₁	1	2	yes	complemented
614	#536	C₂²×C₃₁	1	1	yes	characteristic
615	#533	C₂²×C₃₁	1	2	yes	complemented
616	#529	C₂²×C₃₁	1	2	yes	complemented
617	#525	C₂²×C₃₁	1	1	yes	characteristic
618	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
619	#520	—	2	1	no	—
620	#520	—	2	1	no	—
621	#520	C₂²×C₃₁	1	2	yes	—
622	#520	C₂²×C₃₁	1	2	yes	—
623	#520	C₂²×C₃₁	1	1	yes	characteristic
624	#519	C₂²×C₃₁	1	1	yes	characteristic
625	#519	C₂²×C₃₁	1	1	yes	characteristic
626	#519	C₂²×C₃₁	1	1	yes	characteristic
627	#518	—	2	2	no	—
628	#518	C₂²×C₃₁	1	1	yes	characteristic
629	#518	C₂²×C₃₁	1	1	yes	characteristic
630	C₄×#41	—	2	1	no	—
631	C₄×#41	—	2	1	no	—
632	C₄×#41	C₂²×C₃₁	1	2	yes	—
633	C₄×#41	C₂²×C₃₁	1	2	yes	—
634	C₂×#117	—	2	2	no	—
635	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
636	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
637	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#485	C₂²×C₃₁	1	2	yes	complemented
640	#485	C₂²×C₃₁	1	2	yes	complemented
641	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#484	C₂²×C₃₁	1	2	yes	complemented
643	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#483	C₂²×C₃₁	1	2	yes	complemented
645	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#479	C₂²×C₃₁	1	2	yes	complemented
650	#479	C₂²×C₃₁	1	2	yes	complemented
651	#478	C₂²×C₃₁	1	2	yes	complemented
652	#478	C₂²×C₃₁	1	2	yes	complemented
653	#477	C₂²×C₃₁	1	2	yes	complemented
654	#476	C₂²×C₃₁	1	2	yes	complemented
655	#475	C₂²×C₃₁	1	2	yes	complemented
656	#474	C₂²×C₃₁	1	2	yes	complemented
657	#464	C₂²×C₃₁	1	2	yes	complemented
658	#464	C₂²×C₃₁	1	2	yes	complemented
659	#463	C₂²×C₃₁	1	2	yes	complemented
660	#463	C₂²×C₃₁	1	2	yes	complemented
661	#462	C₂²×C₃₁	1	2	yes	complemented
662	#462	C₂²×C₃₁	1	2	yes	complemented
663	#461	C₂²×C₃₁	1	2	yes	complemented
664	#461	C₂²×C₃₁	1	2	yes	complemented
665	#452	C₂²×C₃₁	1	2	yes	—
666	#452	C₂²×C₃₁	1	2	yes	—
667	#452	C₂²×C₃₁	1	2	yes	—
668	#452	C₂²×C₃₁	1	2	yes	—
669	#452	C₂²×C₃₁	1	2	yes	—
670	#452	C₂²×C₃₁	1	2	yes	—
671	#449	C₂²×C₃₁	1	2	yes	—
672	#449	C₂²×C₃₁	1	2	yes	—
673	#442	C₂²×C₃₁	1	2	yes	complemented
674	#441	C₂²×C₃₁	1	2	yes	complemented
675	#441	C₂²×C₃₁	1	2	yes	complemented
676	#441	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	#440	C₂²×C₃₁	1	2	yes	complemented
681	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
682	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
683	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
684	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
685	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
686	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
687	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
688	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
689	#433	C₂²×C₃₁	1	2	yes	complemented
690	#433	C₂²×C₃₁	1	2	yes	complemented
691	#432	C₂²×C₃₁	1	2	yes	complemented
692	#431	C₂²×C₃₁	1	2	yes	complemented
693	#428	C₂²×C₃₁	1	1	yes	characteristic
694	#428	C₂²×C₃₁	1	1	yes	characteristic
695	#427	C₂²×C₃₁	1	1	yes	characteristic
696	#427	C₂²×C₃₁	1	1	yes	characteristic
697	#424	C₂²×C₃₁	1	1	yes	characteristic
698	#424	C₂²×C₃₁	1	1	yes	characteristic
699	#419	C₂²×C₃₁	1	1	yes	characteristic
700	#419	C₂²×C₃₁	1	1	yes	characteristic
701	#419	C₂²×C₃₁	1	1	yes	characteristic
702	#418	C₂²×C₃₁	1	1	yes	characteristic
703	#416	C₂²×C₃₁	1	1	yes	characteristic
704	#416	C₂²×C₃₁	1	1	yes	characteristic
705	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
706	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
707	#407	C₂²×C₃₁	1	1	yes	characteristic
708	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
709	#405	C₂²×C₃₁	1	1	yes	characteristic
710	#405	C₂²×C₃₁	1	1	yes	characteristic
711	C₂×C₃₁	—	2	2	no	—
712	C₂×C₃₁	—	4	1	no	—
713	C₂×C₃₁	—	4	1	no	—
714	C₂×C₃₁	—	4	4	no	—
715	C₂×C₃₁	—	8	1	no	—
716	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
717	C₂×C₃₁	#3584	1	1	yes	characteristic
718	C₂×C₃₁	#3586	1	1	yes	characteristic
719	C₂×#41	—	2	4	no	—
720	C₂×#41	—	2	4	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	C₂³×C₃₁	1	2	yes	—
724	C₂×#41	C₂³×C₃₁	1	2	yes	—
725	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
726	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
730	C₂³×C₄	—	2	1	no	—
731	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
732	#137	—	2	4	no	—
733	AGL(1,ℤ/8)	—	2	4	no	—
734	C₂×Q₁₆	—	2	4	no	—
735	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
737	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
738	C₂×SD₁₆	—	2	4	no	—
739	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
743	C₂×D₈	C₂³×C₃₁	1	2	yes	—
744	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
745	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
746	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
748	C₄⋊Q₈	—	2	1	no	—
749	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#125	—	2	2	no	—
756	#125	—	2	2	no	—
757	#125	—	2	1	no	—
758	#125	—	2	2	no	—
759	#125	C₂³×C₃₁	1	2	yes	—
760	#124	—	2	2	no	—
761	#124	C₂³×C₃₁	1	2	yes	—
762	#123	—	2	1	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	#121	C₂³×C₃₁	1	1	yes	characteristic
778	#121	C₂³×C₃₁	1	1	yes	characteristic
779	#120	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	2	no	—
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
789	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
790	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
791	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
792	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
793	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	C₂³×C₃₁	1	2	yes	—
811	C₄×D₄	C₂³×C₃₁	1	2	yes	—
812	C₄×D₄	C₂³×C₃₁	1	2	yes	—
813	C₄×D₄	C₂³×C₃₁	1	2	yes	—
814	C₄×D₄	C₂³×C₃₁	1	2	yes	—
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	—	2	2	no	—
818	#117	—	2	2	no	—
819	#117	—	2	2	no	—
820	#117	—	2	1	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	—	2	2	no	—
827	#117	D₄×C₃₁	1	2	yes	—
828	#117	D₄×C₃₁	1	1	yes	characteristic
829	#117	D₄×C₃₁	1	1	yes	characteristic
830	#117	C₂³×C₃₁	1	1	yes	characteristic
831	#117	C₂³×C₃₁	1	1	yes	characteristic
832	#117	C₂³×C₃₁	1	1	yes	characteristic
833	#117	C₂³×C₃₁	1	1	yes	characteristic
834	#117	C₂³×C₃₁	1	1	yes	characteristic
835	#117	C₂³×C₃₁	1	1	yes	characteristic
836	#117	C₂³×C₃₁	1	1	yes	characteristic
837	#117	C₂³×C₃₁	1	2	yes	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	—	2	2	no	—
840	C₂×C₄⋊C₄	—	2	2	no	—
841	C₂×C₄⋊C₄	—	2	1	no	—
842	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
843	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
845	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
846	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	—	2	1	no	—
848	C₂×C₂²⋊C₄	—	2	1	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
852	C₂×C₄²	—	2	1	no	—
853	C₂×C₄²	—	2	2	no	—
854	C₂×C₄²	—	2	2	no	—
855	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
856	#107	C₂³×C₃₁	1	1	yes	characteristic
857	#107	C₂³×C₃₁	1	1	yes	characteristic
858	#107	C₂³×C₃₁	1	1	yes	characteristic
859	#107	C₂³×C₃₁	1	1	yes	characteristic
860	#107	C₂³×C₃₁	1	2	yes	—
861	#107	C₂³×C₃₁	1	2	yes	—
862	#106	C₂³×C₃₁	1	1	yes	characteristic
863	#106	C₂³×C₃₁	1	1	yes	characteristic
864	#106	C₂³×C₃₁	1	1	yes	characteristic
865	#106	C₂³×C₃₁	1	1	yes	characteristic
866	#106	C₂³×C₃₁	1	2	yes	—
867	#106	C₂³×C₃₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
869	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
870	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
871	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
872	#103	C₂³×C₃₁	1	2	yes	—
873	#103	C₂³×C₃₁	1	2	yes	—
874	#103	C₂³×C₃₁	1	1	yes	characteristic
875	#103	C₂³×C₃₁	1	1	yes	characteristic
876	#103	C₂³×C₃₁	1	1	yes	characteristic
877	#103	C₂³×C₃₁	1	1	yes	characteristic
878	#103	C₂³×C₃₁	1	2	yes	—
879	#103	C₂³×C₃₁	1	2	yes	—
880	#103	C₂³×C₃₁	1	2	yes	—
881	#103	C₂³×C₃₁	1	2	yes	—
882	#103	C₂³×C₃₁	1	2	yes	—
883	#103	C₂³×C₃₁	1	2	yes	—
884	#102	C₂³×C₃₁	1	2	yes	—
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	1	yes	characteristic
887	#102	C₂³×C₃₁	1	1	yes	characteristic
888	#102	C₂³×C₃₁	1	1	yes	characteristic
889	#102	C₂³×C₃₁	1	1	yes	characteristic
890	#102	C₂³×C₃₁	1	2	yes	—
891	#102	C₂³×C₃₁	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
893	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
894	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
895	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
898	#97	C₂³×C₃₁	1	2	yes	—
899	#97	C₂³×C₃₁	1	2	yes	—
900	C₄×C₈	C₂³×C₃₁	1	2	yes	—
901	C₄×C₈	C₂³×C₃₁	1	2	yes	—
902	C₃₁	#60581	1	1	yes	characteristic, direct product factor, Sylow
903	C₂⁴	—	2	1	no	—
904	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
905	#41	—	2	8	no	—
906	#41	—	2	8	no	—
907	#41	—	2	4	no	—
908	#41	—	2	4	no	—
909	#41	—	2	4	no	—
910	#41	—	2	4	no	—
911	#41	—	2	2	no	—
912	#41	—	2	2	no	—
913	C₂×Q₈	—	2	1	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	—	2	2	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	2	2	no	—
919	C₂×Q₈	#41×C₃₁	1	4	yes	—
920	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
921	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
923	C₂×D₄	—	2	8	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	#41×C₃₁	1	4	yes	—
932	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
934	C₂²×C₄	—	2	8	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	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	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
951	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	2	yes	—
955	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
958	Q₁₆	—	2	4	no	—
959	Q₁₆	—	2	4	no	—
960	Q₁₆	—	2	4	no	—
961	SD₁₆	—	2	4	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	2	4	no	—
964	SD₁₆	—	2	4	no	—
965	D₈	—	2	4	no	—
966	M₁₆	—	2	2	no	—
967	M₁₆	—	2	2	no	—
968	C₂×C₈	—	2	2	no	—
969	C₂×C₈	—	2	2	no	—
970	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
973	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
974	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	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	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
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	C₂×D₄×C₃₁	1	2	yes	—
996	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1043	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1044	C₄²	C₂⁴×C₃₁	1	2	yes	—
1045	C₄²	C₂⁴×C₃₁	1	2	yes	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	4	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	—	8	1	no	—
1054	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1055	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1056	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1057	Q₈	—	2	4	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	1	no	—
1063	Q₈	—	4	2	no	—
1064	Q₈	—	8	2	no	—
1065	Q₈	C₂×#41×C₃₁	1	4	yes	—
1066	D₄	—	2	8	no	—
1067	D₄	—	2	8	no	—
1068	D₄	—	2	4	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	C₂×#41×C₃₁	1	4	yes	—
1076	C₂×C₄	—	2	8	no	—
1077	C₂×C₄	—	2	8	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	4	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	1	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	1	no	—
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	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1115	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1116	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1117	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	2	1	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	2	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	4	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	8	2	no	—
1139	C₂²	—	8	4	no	—
1140	C₂²	C₃₁×#525	1	2	yes	—
1141	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1142	C₄	—	2	1	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	4	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	2	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	C₃₁×#525	1	2	yes	—
1159	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1160	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1161	C₂	—	2	2	no	—
1162	C₂	—	4	1	no	—
1163	C₂	—	4	1	no	—
1164	C₂	—	4	4	no	—
1165	C₂	—	8	1	no	—
1166	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
1167	C₂	C₃₁×#3584	1	1	yes	characteristic
1168	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3005	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3495	C₂	semidirect
2. C₃₁×#3428	C₂	semidirect
3. C₃₁×#3125	C₂	semidirect
4. C₃₁×#3124	C₂	semidirect
5. C₃₁×#3120	C₂	semidirect
6. C₃₁×#3120	C₂	semidirect
7. C₃₁×#3116	C₂	semidirect
8. C₃₁×#3111	C₂	semidirect
9. C₃₁×#3107	C₂	semidirect
10. C₃₁×#3102	C₂	semidirect
11. C₃₁×#3095	C₂	semidirect
12. C₃₁×#3091	C₂	semidirect
13. C₃₁×#3082	C₂	semidirect
14. C₃₁×#3081	C₂	semidirect
15. C₃₁×#3044	C₂	semidirect
16. C₃₁×#3042	C₂	semidirect
18. C₂×C₃₁×#452	C₂	semidirect
19. C₃₁×#2950	C₂	semidirect
20. C₃₁×#2949	C₂	semidirect
21. C₃₁×#2947	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₃₁×#2924	C₂	semidirect
36. C₃₁×#542	C₂²	semidirect
37. C₃₁×#541	C₂²	semidirect
39. C₃₁×#533	C₂²	semidirect
40. C₃₁×#529	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#485	C₂²	semidirect
63. C₃₁×#485	C₂²	semidirect
64. C₃₁×#485	C₂²	semidirect
65. C₃₁×#484	C₂²	semidirect
66. C₃₁×#484	C₂²	semidirect
67. C₃₁×#483	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. 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×#475	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#464	C₂²	semidirect
82. C₃₁×#464	C₂²	semidirect
83. C₃₁×#463	C₂²	semidirect
84. C₃₁×#463	C₂²	semidirect
85. C₃₁×#462	C₂²	semidirect
86. C₃₁×#462	C₂²	semidirect
87. C₃₁×#461	C₂²	semidirect
88. C₃₁×#461	C₂²	semidirect
97. C₃₁×#442	C₂²	semidirect
98. C₃₁×#441	C₂²	semidirect
99. C₃₁×#441	C₂²	semidirect
100. C₃₁×#441	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₄×Q₁₆×C₃₁	C₂²	semidirect
106. C₄×Q₁₆×C₃₁	C₂²	semidirect
107. C₄×Q₁₆×C₃₁	C₂²	semidirect
108. C₄×SD₁₆×C₃₁	C₂²	semidirect
109. C₄×SD₁₆×C₃₁	C₂²	semidirect
110. C₄×SD₁₆×C₃₁	C₂²	semidirect
111. C₄×SD₁₆×C₃₁	C₂²	semidirect
112. C₄×D₈×C₃₁	C₂²	semidirect
113. C₃₁×#433	C₂²	semidirect
114. C₃₁×#433	C₂²	semidirect
115. C₃₁×#432	C₂²	semidirect
116. C₃₁×#431	C₂²	semidirect
461. #60581	C₃₁	direct (N × H)
540. #3495	C₂×C₃₁	semidirect
541. #3428	C₂×C₃₁	semidirect
542. #3125	C₂×C₃₁	semidirect
543. #3124	C₂×C₃₁	semidirect
544. #3120	C₂×C₃₁	semidirect
545. #3120	C₂×C₃₁	semidirect
546. #3116	C₂×C₃₁	semidirect
547. #3111	C₂×C₃₁	semidirect
548. #3107	C₂×C₃₁	semidirect
549. #3102	C₂×C₃₁	semidirect
550. #3095	C₂×C₃₁	semidirect
551. #3091	C₂×C₃₁	semidirect
552. #3082	C₂×C₃₁	semidirect
553. #3081	C₂×C₃₁	semidirect
554. #3044	C₂×C₃₁	semidirect
555. #3042	C₂×C₃₁	semidirect
557. C₂×#452	C₂×C₃₁	semidirect
558. #2950	C₂×C₃₁	semidirect
559. #2949	C₂×C₃₁	semidirect
560. #2947	C₂×C₃₁	semidirect
561. #2946	C₂×C₃₁	semidirect
562. #2924	C₂×C₃₁	semidirect
612. #542	C₂²×C₃₁	semidirect
613. #541	C₂²×C₃₁	semidirect
615. #533	C₂²×C₃₁	semidirect
616. #529	C₂²×C₃₁	semidirect
637. #485	C₂²×C₃₁	semidirect
638. #485	C₂²×C₃₁	semidirect
639. #485	C₂²×C₃₁	semidirect
640. #485	C₂²×C₃₁	semidirect
641. #484	C₂²×C₃₁	semidirect
642. #484	C₂²×C₃₁	semidirect
643. #483	C₂²×C₃₁	semidirect
644. #483	C₂²×C₃₁	semidirect
645. #482	C₂²×C₃₁	semidirect
646. #482	C₂²×C₃₁	semidirect
647. #481	C₂²×C₃₁	semidirect
648. #480	C₂²×C₃₁	semidirect
649. #479	C₂²×C₃₁	semidirect
650. #479	C₂²×C₃₁	semidirect
651. #478	C₂²×C₃₁	semidirect
652. #478	C₂²×C₃₁	semidirect
653. #477	C₂²×C₃₁	semidirect
654. #476	C₂²×C₃₁	semidirect
655. #475	C₂²×C₃₁	semidirect
656. #474	C₂²×C₃₁	semidirect
657. #464	C₂²×C₃₁	semidirect
658. #464	C₂²×C₃₁	semidirect
659. #463	C₂²×C₃₁	semidirect
660. #463	C₂²×C₃₁	semidirect
661. #462	C₂²×C₃₁	semidirect
662. #462	C₂²×C₃₁	semidirect
663. #461	C₂²×C₃₁	semidirect
664. #461	C₂²×C₃₁	semidirect
673. #442	C₂²×C₃₁	semidirect
674. #441	C₂²×C₃₁	semidirect
675. #441	C₂²×C₃₁	semidirect
676. #441	C₂²×C₃₁	semidirect
677. #440	C₂²×C₃₁	semidirect
678. #440	C₂²×C₃₁	semidirect
679. #440	C₂²×C₃₁	semidirect
680. #440	C₂²×C₃₁	semidirect
681. C₄×Q₁₆	C₂²×C₃₁	semidirect
682. C₄×Q₁₆	C₂²×C₃₁	semidirect
683. C₄×Q₁₆	C₂²×C₃₁	semidirect
684. C₄×SD₁₆	C₂²×C₃₁	semidirect
685. C₄×SD₁₆	C₂²×C₃₁	semidirect
686. C₄×SD₁₆	C₂²×C₃₁	semidirect
687. C₄×SD₁₆	C₂²×C₃₁	semidirect
688. C₄×D₈	C₂²×C₃₁	semidirect
689. #433	C₂²×C₃₁	semidirect
690. #433	C₂²×C₃₁	semidirect
691. #432	C₂²×C₃₁	semidirect
692. #431	C₂²×C₃₁	semidirect
902. C₃₁	#60581	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×#3495	2
C₃₁×#3428	2
C₃₁×#3125	2
C₃₁×#3124	2
C₃₁×#3120	2
C₃₁×#3116	2
C₃₁×#3111	2
C₃₁×#3107	2
C₃₁×#3102	2
C₃₁×#3095	2
C₃₁×#3091	2
C₃₁×#3082	2
C₃₁×#3081	2
C₃₁×#3044	2
C₃₁×#3042	2
C₃₁×#3005	2
C₂×C₃₁×#452	2
C₃₁×#2950	2
C₃₁×#2949	2
C₃₁×#2947	2
C₃₁×#2946	2
C₃₁×#2924	2
#60581	31

Subgroups — C31×#60581 #21517340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60581 #21517340