Subgroups — C₃₁×#60587 #21517346

Order 7936.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3126	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3115	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3106	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3006	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3002	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2946	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×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
29	C₃₁×#555	—	2	1	no	—
30	C₃₁×#553	—	2	1	no	—
31	C₃₁×#553	—	2	1	no	—
32	C₃₁×#551	—	2	2	no	—
33	C₃₁×#547	—	2	1	no	—
34	C₃₁×#546	—	2	2	no	—
35	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#542	C₂²	1	2	yes	—
37	C₃₁×#540	C₂²	1	2	yes	—
38	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#532	C₂²	1	2	yes	complemented
40	C₃₁×#529	C₂²	1	2	yes	complemented
41	C₃₁×#525	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
43	C₃₁×#520	—	2	1	no	—
44	C₃₁×#520	—	2	1	no	—
45	C₃₁×#520	C₂²	1	1	yes	characteristic
46	C₃₁×#520	C₂²	1	1	yes	characteristic
47	C₃₁×#520	C₂²	1	1	yes	characteristic
48	C₃₁×#520	C₂²	1	1	yes	characteristic
49	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#519	C₂²	1	2	yes	complemented
51	C₃₁×#518	—	2	2	no	—
52	C₃₁×#518	C₂²	1	2	yes	complemented
53	C₃₁×#518	C₂²	1	1	yes	characteristic, complemented
54	C₄×#41×C₃₁	—	2	2	no	—
55	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
56	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
57	C₂×C₃₁×#117	—	2	1	no	—
58	C₂×C₃₁×#117	—	2	1	no	—
59	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#485	C₂²	1	2	yes	complemented
63	C₃₁×#482	C₂²	1	2	yes	—
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#482	C₂²	1	2	yes	complemented
66	C₃₁×#482	C₂²	1	2	yes	complemented
67	C₃₁×#482	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#479	C₂²	1	2	yes	complemented
70	C₃₁×#479	C₂²	1	2	yes	complemented
71	C₃₁×#478	C₂²	1	2	yes	complemented
72	C₃₁×#478	C₂²	1	2	yes	complemented
73	C₃₁×#477	C₂²	1	2	yes	complemented
74	C₃₁×#476	C₂²	1	2	yes	complemented
75	C₃₁×#475	C₂²	1	2	yes	complemented
76	C₃₁×#474	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#464	C₂²	1	2	yes	complemented
79	C₃₁×#463	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#460	C₂²	1	2	yes	complemented
82	C₃₁×#460	C₂²	1	2	yes	complemented
83	C₃₁×#459	C₂²	1	2	yes	complemented
84	C₃₁×#459	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#449	C₂²	1	2	yes	—
90	C₃₁×#449	C₂²	1	2	yes	—
91	C₃₁×#449	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#449	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#448	C₂²	1	2	yes	—
94	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#447	C₂²	1	2	yes	—
96	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#442	C₂²	1	2	yes	complemented
98	C₃₁×#442	C₂²	1	2	yes	complemented
99	C₃₁×#442	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×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×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×D₈×C₃₁	C₂²	1	2	yes	complemented
111	C₄×D₈×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, complemented
118	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#417	C₂²	1	1	yes	characteristic
124	C₃₁×#417	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
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, complemented
134	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
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	—	2	2	no	—
140	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₃₁	—	2	1	no	—
147	C₂²×D₄×C₃₁	—	2	1	no	—
148	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₃₁	—	2	1	no	—
151	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
153	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
154	C₃₁×#135	—	2	4	no	—
155	C₃₁×#135	—	2	4	no	—
156	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×D₈×C₃₁	C₂³	1	2	yes	—
166	C₂×D₈×C₃₁	C₂³	1	2	yes	—
167	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
170	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₃₁×C₄⋊Q₈	—	2	1	no	—
173	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₃₁×#127	C₂³	1	2	yes	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	C₂³	1	2	yes	—
182	C₃₁×#123	—	2	1	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
190	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
191	C₃₁×#121	—	2	1	no	—
192	C₃₁×#121	—	2	1	no	—
193	C₃₁×#121	—	2	2	no	—
194	C₃₁×#121	—	2	1	no	—
195	C₃₁×#121	—	2	1	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	C₂³	1	2	yes	—
199	C₃₁×#121	C₂³	1	1	yes	characteristic
200	C₃₁×#121	C₂³	1	2	yes	—
201	C₃₁×#121	C₂³	1	1	yes	characteristic
202	C₃₁×#120	—	2	1	no	—
203	C₃₁×#120	—	2	2	no	—
204	C₄×Q₈×C₃₁	—	2	2	no	—
205	C₄×Q₈×C₃₁	—	2	2	no	—
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×Q₈×C₃₁	C₂³	1	2	yes	—
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	2	no	—
215	C₄×D₄×C₃₁	—	2	1	no	—
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	1	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	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
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	C₄×D₄×C₃₁	C₂³	1	2	yes	—
232	C₄×D₄×C₃₁	C₂³	1	2	yes	—
233	C₄×D₄×C₃₁	C₂³	1	2	yes	—
234	C₄×D₄×C₃₁	C₂³	1	2	yes	—
235	C₃₁×#117	—	2	1	no	—
236	C₃₁×#117	—	2	1	no	—
237	C₃₁×#117	—	2	1	no	—
238	C₃₁×#117	—	2	1	no	—
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	1	no	—
241	C₃₁×#117	—	2	1	no	—
242	C₃₁×#117	—	2	2	no	—
243	C₃₁×#117	—	2	2	no	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	D₄	1	1	yes	characteristic
248	C₃₁×#117	D₄	1	1	yes	characteristic
249	C₃₁×#117	D₄	1	2	yes	—
250	C₃₁×#117	C₂³	1	1	yes	characteristic
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	1	yes	characteristic
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
268	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
272	C₂×C₄²×C₃₁	—	2	1	no	—
273	C₂×C₄²×C₃₁	—	2	2	no	—
274	C₂×C₄²×C₃₁	—	2	2	no	—
275	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#107	C₂³	1	2	yes	—
278	C₃₁×#107	C₂³	1	2	yes	—
279	C₃₁×#107	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	2	yes	—
281	C₃₁×#106	C₂³	1	2	yes	—
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	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
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×#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	—	2	1	no	—
320	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
321	#41×C₃₁	—	2	8	no	—
322	#41×C₃₁	—	2	8	no	—
323	#41×C₃₁	—	2	2	no	—
324	#41×C₃₁	—	2	2	no	—
325	#41×C₃₁	—	2	2	no	—
326	#41×C₃₁	—	2	2	no	—
327	#41×C₃₁	—	2	2	no	—
328	#41×C₃₁	—	2	2	no	—
329	#41×C₃₁	—	2	2	no	—
330	#41×C₃₁	—	2	2	no	—
331	#41×C₃₁	—	8	4	no	—
332	#41×C₃₁	#41	1	4	yes	complemented
333	#41×C₃₁	#41	1	4	yes	complemented
334	C₂×Q₈×C₃₁	—	2	2	no	—
335	C₂×Q₈×C₃₁	—	2	2	no	—
336	C₂×Q₈×C₃₁	—	2	1	no	—
337	C₂×Q₈×C₃₁	—	2	2	no	—
338	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₃₁	—	2	8	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	1	no	—
346	C₂×D₄×C₃₁	—	2	2	no	—
347	C₂×D₄×C₃₁	—	2	2	no	—
348	C₂×D₄×C₃₁	—	2	1	no	—
349	C₂×D₄×C₃₁	—	2	1	no	—
350	C₂×D₄×C₃₁	—	2	2	no	—
351	C₂×D₄×C₃₁	—	2	1	no	—
352	C₂×D₄×C₃₁	—	2	2	no	—
353	C₂×D₄×C₃₁	—	2	1	no	—
354	C₂×D₄×C₃₁	—	2	1	no	—
355	C₂×D₄×C₃₁	—	2	2	no	—
356	C₂×D₄×C₃₁	—	2	2	no	—
357	C₂×D₄×C₃₁	—	2	2	no	—
358	C₂×D₄×C₃₁	—	2	2	no	—
359	C₂×D₄×C₃₁	—	8	2	no	—
360	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
361	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	—	2	8	no	—
365	C₂²×C₄×C₃₁	—	2	1	no	—
366	C₂²×C₄×C₃₁	—	2	1	no	—
367	C₂²×C₄×C₃₁	—	2	1	no	—
368	C₂²×C₄×C₃₁	—	2	1	no	—
369	C₂²×C₄×C₃₁	—	2	1	no	—
370	C₂²×C₄×C₃₁	—	2	2	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	2	1	no	—
373	C₂²×C₄×C₃₁	—	2	1	no	—
374	C₂²×C₄×C₃₁	—	2	1	no	—
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	2	no	—
377	C₂²×C₄×C₃₁	—	2	2	no	—
378	C₂²×C₄×C₃₁	—	2	2	no	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	—	2	2	no	—
381	C₂²×C₄×C₃₁	—	2	2	no	—
382	C₂²×C₄×C₃₁	—	2	2	no	—
383	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
387	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
391	Q₁₆×C₃₁	—	2	2	no	—
392	Q₁₆×C₃₁	—	2	2	no	—
393	SD₁₆×C₃₁	—	2	2	no	—
394	SD₁₆×C₃₁	—	2	2	no	—
395	SD₁₆×C₃₁	—	2	4	no	—
396	SD₁₆×C₃₁	—	2	4	no	—
397	SD₁₆×C₃₁	—	2	2	no	—
398	SD₁₆×C₃₁	—	2	2	no	—
399	D₈×C₃₁	—	2	2	no	—
400	D₈×C₃₁	—	2	2	no	—
401	D₈×C₃₁	—	2	4	no	—
402	D₈×C₃₁	—	2	4	no	—
403	M₁₆×C₃₁	—	2	2	no	—
404	M₁₆×C₃₁	—	2	2	no	—
405	C₂×C₈×C₃₁	—	2	2	no	—
406	C₂×C₈×C₃₁	—	2	2	no	—
407	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
410	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
411	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	—	2	2	no	—
420	C₄⋊C₄×C₃₁	—	2	2	no	—
421	C₄⋊C₄×C₃₁	—	2	1	no	—
422	C₄⋊C₄×C₃₁	—	2	2	no	—
423	C₄⋊C₄×C₃₁	—	2	2	no	—
424	C₄⋊C₄×C₃₁	—	2	2	no	—
425	C₄⋊C₄×C₃₁	—	2	1	no	—
426	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
427	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
428	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
429	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
430	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
433	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
434	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
435	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	1	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	1	no	—
441	C₂²⋊C₄×C₃₁	—	2	1	no	—
442	C₂²⋊C₄×C₃₁	—	2	2	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	2	no	—
445	C₂²⋊C₄×C₃₁	—	2	2	no	—
446	C₂²⋊C₄×C₃₁	—	2	2	no	—
447	C₂²⋊C₄×C₃₁	—	2	2	no	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	—	2	2	no	—
450	C₂²⋊C₄×C₃₁	—	2	2	no	—
451	C₂²⋊C₄×C₃₁	—	2	2	no	—
452	C₂²⋊C₄×C₃₁	—	2	1	no	—
453	C₂²⋊C₄×C₃₁	—	2	2	no	—
454	C₂²⋊C₄×C₃₁	—	2	1	no	—
455	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
456	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
459	C₄²×C₃₁	—	2	2	no	—
460	C₄²×C₃₁	—	2	2	no	—
461	C₄²×C₃₁	—	2	2	no	—
462	C₄²×C₃₁	—	2	2	no	—
463	C₄²×C₃₁	—	2	2	no	—
464	C₄²×C₃₁	—	2	2	no	—
465	C₄²×C₃₁	—	2	2	no	—
466	C₄²×C₃₁	—	2	1	no	—
467	C₄²×C₃₁	C₂×D₄	1	2	yes	—
468	C₄²×C₃₁	C₂×D₄	1	2	yes	—
469	C₄²×C₃₁	C₂⁴	1	2	yes	—
470	C₄²×C₃₁	C₂⁴	1	2	yes	—
471	#60587	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₂³×C₃₁	—	2	4	no	—
473	C₂³×C₃₁	—	2	1	no	—
474	C₂³×C₃₁	—	2	1	no	—
475	C₂³×C₃₁	—	2	2	no	—
476	C₂³×C₃₁	—	2	2	no	—
477	C₂³×C₃₁	—	2	1	no	—
478	C₂³×C₃₁	—	4	1	no	—
479	C₂³×C₃₁	—	4	1	no	—
480	C₂³×C₃₁	—	4	2	no	—
481	C₂³×C₃₁	—	8	1	no	—
482	C₂³×C₃₁	—	8	1	no	—
483	C₂³×C₃₁	—	8	1	no	—
484	C₂³×C₃₁	—	8	1	no	—
485	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
487	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
488	Q₈×C₃₁	—	2	4	no	—
489	Q₈×C₃₁	—	2	1	no	—
490	Q₈×C₃₁	—	2	1	no	—
491	Q₈×C₃₁	—	2	1	no	—
492	Q₈×C₃₁	—	2	1	no	—
493	Q₈×C₃₁	—	8	2	no	—
494	Q₈×C₃₁	C₂×#41	1	2	yes	—
495	Q₈×C₃₁	C₂×#41	1	2	yes	—
496	D₄×C₃₁	—	2	4	no	—
497	D₄×C₃₁	—	2	4	no	—
498	D₄×C₃₁	—	2	4	no	—
499	D₄×C₃₁	—	2	4	no	—
500	D₄×C₃₁	—	2	4	no	—
501	D₄×C₃₁	—	2	1	no	—
502	D₄×C₃₁	—	2	1	no	—
503	D₄×C₃₁	—	2	2	no	—
504	D₄×C₃₁	—	2	2	no	—
505	D₄×C₃₁	—	2	1	no	—
506	D₄×C₃₁	—	2	1	no	—
507	D₄×C₃₁	—	4	4	no	—
508	D₄×C₃₁	—	4	2	no	—
509	D₄×C₃₁	—	4	2	no	—
510	D₄×C₃₁	—	4	2	no	—
511	D₄×C₃₁	—	8	2	no	—
512	D₄×C₃₁	—	8	2	no	—
513	D₄×C₃₁	—	8	1	no	—
514	D₄×C₃₁	—	8	2	no	—
515	D₄×C₃₁	C₂×#41	1	2	yes	—
516	D₄×C₃₁	C₂×#41	1	2	yes	—
517	C₂×C₄×C₃₁	—	2	4	no	—
518	C₂×C₄×C₃₁	—	2	4	no	—
519	C₂×C₄×C₃₁	—	2	4	no	—
520	C₂×C₄×C₃₁	—	2	2	no	—
521	C₂×C₄×C₃₁	—	2	1	no	—
522	C₂×C₄×C₃₁	—	2	1	no	—
523	C₂×C₄×C₃₁	—	2	2	no	—
524	C₂×C₄×C₃₁	—	2	4	no	—
525	C₂×C₄×C₃₁	—	2	4	no	—
526	C₂×C₄×C₃₁	—	2	2	no	—
527	C₂×C₄×C₃₁	—	2	1	no	—
528	C₂×C₄×C₃₁	—	2	1	no	—
529	C₂×C₄×C₃₁	—	2	1	no	—
530	C₂×C₄×C₃₁	—	2	1	no	—
531	C₂×C₄×C₃₁	—	2	2	no	—
532	C₂×C₄×C₃₁	—	2	2	no	—
533	C₂×C₄×C₃₁	—	2	1	no	—
534	C₂×C₄×C₃₁	—	2	1	no	—
535	C₂×C₄×C₃₁	—	2	1	no	—
536	C₂×C₄×C₃₁	—	2	2	no	—
537	C₂×C₄×C₃₁	—	4	2	no	—
538	C₂×C₄×C₃₁	—	4	2	no	—
539	C₂×C₄×C₃₁	—	4	2	no	—
540	C₂×C₄×C₃₁	—	8	2	no	—
541	C₂×C₄×C₃₁	—	8	2	no	—
542	C₂×C₄×C₃₁	—	8	2	no	—
543	C₂×C₄×C₃₁	—	8	2	no	—
544	C₂×C₄×C₃₁	—	8	2	no	—
545	C₂×C₄×C₃₁	—	8	2	no	—
546	C₂×C₄×C₃₁	—	8	2	no	—
547	C₂×C₄×C₃₁	—	8	1	no	—
548	C₂×C₄×C₃₁	—	8	1	no	—
549	C₂×C₄×C₃₁	—	8	1	no	—
550	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
558	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
559	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
560	C₈×C₃₁	—	2	1	no	—
561	C₈×C₃₁	—	2	1	no	—
562	C₈×C₃₁	—	2	1	no	—
563	C₈×C₃₁	—	2	1	no	—
564	C₈×C₃₁	—	2	2	no	—
565	C₈×C₃₁	—	2	2	no	—
566	#3494	C₂×C₃₁	1	1	yes	characteristic, complemented
567	#3428	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3126	C₂×C₃₁	1	2	yes	complemented
569	#3122	C₂×C₃₁	1	2	yes	complemented
570	#3121	C₂×C₃₁	1	2	yes	complemented
571	#3118	C₂×C₃₁	1	2	yes	complemented
572	#3115	C₂×C₃₁	1	2	yes	complemented
573	#3111	C₂×C₃₁	1	2	yes	complemented
574	#3106	C₂×C₃₁	1	2	yes	complemented
575	#3102	C₂×C₃₁	1	2	yes	complemented
576	#3093	C₂×C₃₁	1	1	yes	characteristic, complemented
577	C₂×#482	C₂×C₃₁	1	1	yes	characteristic, complemented
578	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
579	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
580	#3045	C₂×C₃₁	1	1	yes	characteristic, complemented
581	#3045	C₂×C₃₁	1	1	yes	characteristic, complemented
582	#3006	C₂×C₃₁	1	1	yes	characteristic, complemented
583	#3002	C₂×C₃₁	1	1	yes	characteristic, complemented
584	#2952	C₂×C₃₁	1	1	yes	characteristic, complemented
585	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
586	#2946	C₂×C₃₁	1	1	yes	characteristic, complemented
587	#2946	C₂×C₃₁	1	1	yes	characteristic, complemented
588	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
589	C₂²×C₃₁	—	2	1	no	—
590	C₂²×C₃₁	—	2	1	no	—
591	C₂²×C₃₁	—	2	1	no	—
592	C₂²×C₃₁	—	2	1	no	—
593	C₂²×C₃₁	—	2	1	no	—
594	C₂²×C₃₁	—	2	1	no	—
595	C₂²×C₃₁	—	2	1	no	—
596	C₂²×C₃₁	—	2	1	no	—
597	C₂²×C₃₁	—	2	2	no	—
598	C₂²×C₃₁	—	2	2	no	—
599	C₂²×C₃₁	—	4	1	no	—
600	C₂²×C₃₁	—	4	1	no	—
601	C₂²×C₃₁	—	4	1	no	—
602	C₂²×C₃₁	—	4	1	no	—
603	C₂²×C₃₁	—	4	2	no	—
604	C₂²×C₃₁	—	4	1	no	—
605	C₂²×C₃₁	—	4	1	no	—
606	C₂²×C₃₁	—	4	2	no	—
607	C₂²×C₃₁	—	4	1	no	—
608	C₂²×C₃₁	—	4	2	no	—
609	C₂²×C₃₁	—	8	2	no	—
610	C₂²×C₃₁	—	8	4	no	—
611	C₂²×C₃₁	—	16	2	no	—
612	C₂²×C₃₁	#525	1	2	yes	—
613	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
614	C₄×C₃₁	—	2	2	no	—
615	C₄×C₃₁	—	2	2	no	—
616	C₄×C₃₁	—	2	2	no	—
617	C₄×C₃₁	—	2	2	no	—
618	C₄×C₃₁	—	2	1	no	—
619	C₄×C₃₁	—	2	2	no	—
620	C₄×C₃₁	—	2	2	no	—
621	C₄×C₃₁	—	2	1	no	—
622	C₄×C₃₁	—	4	2	no	—
623	C₄×C₃₁	—	4	1	no	—
624	C₄×C₃₁	—	4	2	no	—
625	C₄×C₃₁	—	4	2	no	—
626	C₄×C₃₁	—	4	1	no	—
627	C₄×C₃₁	—	4	1	no	—
628	C₄×C₃₁	#525	1	2	yes	—
629	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
630	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
631	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
632	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
633	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
634	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
635	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
636	#555	—	2	1	no	—
637	#553	—	2	1	no	—
638	#553	—	2	1	no	—
639	#551	—	2	2	no	—
640	#547	—	2	1	no	—
641	#546	—	2	2	no	—
642	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#542	C₂²×C₃₁	1	2	yes	—
644	#540	C₂²×C₃₁	1	2	yes	—
645	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#532	C₂²×C₃₁	1	2	yes	complemented
647	#529	C₂²×C₃₁	1	2	yes	complemented
648	#525	C₂²×C₃₁	1	1	yes	characteristic
649	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
650	#520	—	2	1	no	—
651	#520	—	2	1	no	—
652	#520	C₂²×C₃₁	1	1	yes	characteristic
653	#520	C₂²×C₃₁	1	1	yes	characteristic
654	#520	C₂²×C₃₁	1	1	yes	characteristic
655	#520	C₂²×C₃₁	1	1	yes	characteristic
656	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#519	C₂²×C₃₁	1	2	yes	complemented
658	#518	—	2	2	no	—
659	#518	C₂²×C₃₁	1	2	yes	complemented
660	#518	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	C₄×#41	—	2	2	no	—
662	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
663	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
664	C₂×#117	—	2	1	no	—
665	C₂×#117	—	2	1	no	—
666	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
667	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
668	#485	C₂²×C₃₁	1	2	yes	complemented
669	#485	C₂²×C₃₁	1	2	yes	complemented
670	#482	C₂²×C₃₁	1	2	yes	—
671	#482	C₂²×C₃₁	1	2	yes	—
672	#482	C₂²×C₃₁	1	2	yes	complemented
673	#482	C₂²×C₃₁	1	2	yes	complemented
674	#482	C₂²×C₃₁	1	2	yes	complemented
675	#482	C₂²×C₃₁	1	2	yes	complemented
676	#479	C₂²×C₃₁	1	2	yes	complemented
677	#479	C₂²×C₃₁	1	2	yes	complemented
678	#478	C₂²×C₃₁	1	2	yes	complemented
679	#478	C₂²×C₃₁	1	2	yes	complemented
680	#477	C₂²×C₃₁	1	2	yes	complemented
681	#476	C₂²×C₃₁	1	2	yes	complemented
682	#475	C₂²×C₃₁	1	2	yes	complemented
683	#474	C₂²×C₃₁	1	2	yes	complemented
684	#464	C₂²×C₃₁	1	2	yes	complemented
685	#464	C₂²×C₃₁	1	2	yes	complemented
686	#463	C₂²×C₃₁	1	2	yes	complemented
687	#463	C₂²×C₃₁	1	2	yes	complemented
688	#460	C₂²×C₃₁	1	2	yes	complemented
689	#460	C₂²×C₃₁	1	2	yes	complemented
690	#459	C₂²×C₃₁	1	2	yes	complemented
691	#459	C₂²×C₃₁	1	2	yes	complemented
692	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
696	#449	C₂²×C₃₁	1	2	yes	—
697	#449	C₂²×C₃₁	1	2	yes	—
698	#449	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#449	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	#448	C₂²×C₃₁	1	2	yes	—
701	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#447	C₂²×C₃₁	1	2	yes	—
703	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	#442	C₂²×C₃₁	1	2	yes	complemented
705	#442	C₂²×C₃₁	1	2	yes	complemented
706	#442	C₂²×C₃₁	1	2	yes	complemented
707	#441	C₂²×C₃₁	1	2	yes	complemented
708	#440	C₂²×C₃₁	1	2	yes	complemented
709	#440	C₂²×C₃₁	1	2	yes	complemented
710	#440	C₂²×C₃₁	1	2	yes	complemented
711	#440	C₂²×C₃₁	1	2	yes	complemented
712	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
713	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
714	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
715	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
716	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
717	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
718	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
719	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
720	#433	C₂²×C₃₁	1	2	yes	complemented
721	#433	C₂²×C₃₁	1	2	yes	complemented
722	#432	C₂²×C₃₁	1	2	yes	complemented
723	#431	C₂²×C₃₁	1	2	yes	complemented
724	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
725	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
729	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
730	#417	C₂²×C₃₁	1	1	yes	characteristic
731	#417	C₂²×C₃₁	1	1	yes	characteristic
732	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
733	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
734	#416	C₂²×C₃₁	1	1	yes	characteristic
735	#416	C₂²×C₃₁	1	1	yes	characteristic
736	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
737	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
738	#407	C₂²×C₃₁	1	1	yes	characteristic
739	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
740	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
741	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
742	C₂×C₃₁	—	2	2	no	—
743	C₂×C₃₁	—	4	1	no	—
744	C₂×C₃₁	—	4	1	no	—
745	C₂×C₃₁	—	4	2	no	—
746	C₂×C₃₁	—	4	2	no	—
747	C₂×C₃₁	—	8	1	no	—
748	C₂×C₃₁	—	8	2	no	—
749	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
750	C₂×C₃₁	#3584	1	1	yes	characteristic
751	C₂×C₃₁	#3585	1	1	yes	characteristic
752	C₂×#41	—	2	4	no	—
753	C₂×#41	—	2	4	no	—
754	C₂×#41	—	2	1	no	—
755	C₂×#41	—	2	1	no	—
756	C₂×#41	—	2	2	no	—
757	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
758	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
759	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
760	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
761	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
762	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
766	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
767	C₂³×C₄	—	2	1	no	—
768	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
769	AGL(1,ℤ/8)	—	2	4	no	—
770	AGL(1,ℤ/8)	—	2	4	no	—
771	#135	—	2	4	no	—
772	#135	—	2	4	no	—
773	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
774	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
775	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
778	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
779	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
781	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₂×D₈	C₂³×C₃₁	1	2	yes	—
784	C₂×D₈	C₂³×C₃₁	1	2	yes	—
785	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
786	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
787	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
788	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
791	#127	C₂³×C₃₁	1	2	yes	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#125	—	2	1	no	—
795	#125	C₂³×C₃₁	1	2	yes	—
796	#124	—	2	2	no	—
797	#124	—	2	2	no	—
798	#124	C₂³×C₃₁	1	2	yes	—
799	#123	—	2	1	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
807	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	2	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	C₂³×C₃₁	1	2	yes	—
816	#121	C₂³×C₃₁	1	2	yes	—
817	#121	C₂³×C₃₁	1	1	yes	characteristic
818	#121	C₂³×C₃₁	1	1	yes	characteristic
819	#120	—	2	1	no	—
820	#120	—	2	2	no	—
821	C₄×Q₈	—	2	2	no	—
822	C₄×Q₈	—	2	2	no	—
823	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
824	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
825	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
826	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
827	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	—	2	2	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	C₂³×C₃₁	1	2	yes	—
846	C₄×D₄	C₂³×C₃₁	1	2	yes	—
847	C₄×D₄	C₂³×C₃₁	1	2	yes	—
848	C₄×D₄	C₂³×C₃₁	1	2	yes	—
849	C₄×D₄	C₂³×C₃₁	1	2	yes	—
850	C₄×D₄	C₂³×C₃₁	1	2	yes	—
851	C₄×D₄	C₂³×C₃₁	1	2	yes	—
852	#117	—	2	1	no	—
853	#117	—	2	1	no	—
854	#117	—	2	1	no	—
855	#117	—	2	1	no	—
856	#117	—	2	1	no	—
857	#117	—	2	1	no	—
858	#117	—	2	1	no	—
859	#117	—	2	2	no	—
860	#117	—	2	2	no	—
861	#117	—	2	2	no	—
862	#117	—	2	2	no	—
863	#117	—	2	2	no	—
864	#117	D₄×C₃₁	1	1	yes	characteristic
865	#117	D₄×C₃₁	1	1	yes	characteristic
866	#117	D₄×C₃₁	1	2	yes	—
867	#117	C₂³×C₃₁	1	2	yes	—
868	#117	C₂³×C₃₁	1	2	yes	—
869	#117	C₂³×C₃₁	1	1	yes	characteristic
870	#117	C₂³×C₃₁	1	2	yes	—
871	#117	C₂³×C₃₁	1	1	yes	characteristic
872	#117	C₂³×C₃₁	1	1	yes	characteristic
873	C₂×C₄⋊C₄	—	2	1	no	—
874	C₂×C₄⋊C₄	—	2	1	no	—
875	C₂×C₄⋊C₄	—	2	1	no	—
876	C₂×C₄⋊C₄	—	2	1	no	—
877	C₂×C₄⋊C₄	—	2	1	no	—
878	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
879	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
883	C₂×C₂²⋊C₄	—	2	1	no	—
884	C₂×C₂²⋊C₄	—	2	1	no	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₂²⋊C₄	—	2	2	no	—
888	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
889	C₂×C₄²	—	2	1	no	—
890	C₂×C₄²	—	2	2	no	—
891	C₂×C₄²	—	2	2	no	—
892	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
893	#107	C₂³×C₃₁	1	2	yes	—
894	#107	C₂³×C₃₁	1	2	yes	—
895	#107	C₂³×C₃₁	1	2	yes	—
896	#107	C₂³×C₃₁	1	2	yes	—
897	#106	C₂³×C₃₁	1	2	yes	—
898	#106	C₂³×C₃₁	1	2	yes	—
899	#106	C₂³×C₃₁	1	2	yes	—
900	#106	C₂³×C₃₁	1	2	yes	—
901	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
902	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
903	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
904	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
905	#103	C₂³×C₃₁	1	1	yes	characteristic
906	#103	C₂³×C₃₁	1	1	yes	characteristic
907	#103	C₂³×C₃₁	1	1	yes	characteristic
908	#103	C₂³×C₃₁	1	1	yes	characteristic
909	#103	C₂³×C₃₁	1	2	yes	—
910	#103	C₂³×C₃₁	1	2	yes	—
911	#103	C₂³×C₃₁	1	2	yes	—
912	#103	C₂³×C₃₁	1	2	yes	—
913	#102	C₂³×C₃₁	1	2	yes	—
914	#102	C₂³×C₃₁	1	2	yes	—
915	#102	C₂³×C₃₁	1	2	yes	—
916	#102	C₂³×C₃₁	1	2	yes	—
917	#102	C₂³×C₃₁	1	1	yes	characteristic
918	#102	C₂³×C₃₁	1	1	yes	characteristic
919	#102	C₂³×C₃₁	1	1	yes	characteristic
920	#102	C₂³×C₃₁	1	1	yes	characteristic
921	#102	C₂³×C₃₁	1	2	yes	—
922	#102	C₂³×C₃₁	1	2	yes	—
923	#102	C₂³×C₃₁	1	2	yes	—
924	#102	C₂³×C₃₁	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
926	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
927	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
931	#97	C₂³×C₃₁	1	2	yes	—
932	#97	C₂³×C₃₁	1	2	yes	—
933	C₄×C₈	C₂³×C₃₁	1	2	yes	—
934	C₄×C₈	C₂³×C₃₁	1	2	yes	—
935	C₃₁	#60587	1	1	yes	characteristic, direct product factor, Sylow
936	C₂⁴	—	2	1	no	—
937	C₂⁴	—	2	1	no	—
938	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
939	#41	—	2	8	no	—
940	#41	—	2	8	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	2	no	—
949	#41	—	8	4	no	—
950	#41	#41×C₃₁	1	4	yes	complemented
951	#41	#41×C₃₁	1	4	yes	complemented
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	1	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
958	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂×D₄	—	2	8	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	8	2	no	—
978	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
979	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
980	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
981	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₂²×C₄	—	2	8	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1002	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1003	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1004	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1005	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1009	Q₁₆	—	2	2	no	—
1010	Q₁₆	—	2	2	no	—
1011	SD₁₆	—	2	2	no	—
1012	SD₁₆	—	2	2	no	—
1013	SD₁₆	—	2	4	no	—
1014	SD₁₆	—	2	4	no	—
1015	SD₁₆	—	2	2	no	—
1016	SD₁₆	—	2	2	no	—
1017	D₈	—	2	2	no	—
1018	D₈	—	2	2	no	—
1019	D₈	—	2	4	no	—
1020	D₈	—	2	4	no	—
1021	M₁₆	—	2	2	no	—
1022	M₁₆	—	2	2	no	—
1023	C₂×C₈	—	2	2	no	—
1024	C₂×C₈	—	2	2	no	—
1025	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1029	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1045	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1046	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1047	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1048	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1049	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1050	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1053	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1077	C₄²	—	2	2	no	—
1078	C₄²	—	2	2	no	—
1079	C₄²	—	2	2	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	—	2	2	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1086	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1087	C₄²	C₂⁴×C₃₁	1	2	yes	—
1088	C₄²	C₂⁴×C₃₁	1	2	yes	—
1089	C₂³	—	2	4	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	2	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	4	1	no	—
1096	C₂³	—	4	1	no	—
1097	C₂³	—	4	2	no	—
1098	C₂³	—	8	1	no	—
1099	C₂³	—	8	1	no	—
1100	C₂³	—	8	1	no	—
1101	C₂³	—	8	1	no	—
1102	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1103	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1104	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1105	Q₈	—	2	4	no	—
1106	Q₈	—	2	1	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	2	1	no	—
1110	Q₈	—	8	2	no	—
1111	Q₈	C₂×#41×C₃₁	1	2	yes	—
1112	Q₈	C₂×#41×C₃₁	1	2	yes	—
1113	D₄	—	2	4	no	—
1114	D₄	—	2	4	no	—
1115	D₄	—	2	4	no	—
1116	D₄	—	2	4	no	—
1117	D₄	—	2	4	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	2	no	—
1121	D₄	—	2	2	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	1	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	8	2	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	1	no	—
1131	D₄	—	8	2	no	—
1132	D₄	C₂×#41×C₃₁	1	2	yes	—
1133	D₄	C₂×#41×C₃₁	1	2	yes	—
1134	C₂×C₄	—	2	4	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	2	4	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	4	no	—
1142	C₂×C₄	—	2	4	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	—	8	2	no	—
1163	C₂×C₄	—	8	2	no	—
1164	C₂×C₄	—	8	1	no	—
1165	C₂×C₄	—	8	1	no	—
1166	C₂×C₄	—	8	1	no	—
1167	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1169	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1170	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1171	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1172	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1173	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1174	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1175	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1176	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1177	C₈	—	2	1	no	—
1178	C₈	—	2	1	no	—
1179	C₈	—	2	1	no	—
1180	C₈	—	2	1	no	—
1181	C₈	—	2	2	no	—
1182	C₈	—	2	2	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	2	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	8	2	no	—
1204	C₂²	—	8	4	no	—
1205	C₂²	—	16	2	no	—
1206	C₂²	C₃₁×#525	1	2	yes	—
1207	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1208	C₄	—	2	1	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	2	2	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	2	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	2	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	2	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	1	no	—
1222	C₄	C₃₁×#525	1	2	yes	—
1223	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1224	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1225	C₂	—	2	2	no	—
1226	C₂	—	4	1	no	—
1227	C₂	—	4	1	no	—
1228	C₂	—	4	2	no	—
1229	C₂	—	4	2	no	—
1230	C₂	—	8	2	no	—
1231	C₂	—	8	1	no	—
1232	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
1233	C₂	C₃₁×#3584	1	1	yes	characteristic
1234	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 ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3494	C₂	semidirect
2. C₃₁×#3428	C₂	semidirect
3. C₃₁×#3126	C₂	semidirect
4. C₃₁×#3122	C₂	semidirect
5. C₃₁×#3121	C₂	semidirect
6. C₃₁×#3118	C₂	semidirect
7. C₃₁×#3115	C₂	semidirect
8. C₃₁×#3111	C₂	semidirect
9. C₃₁×#3106	C₂	semidirect
10. C₃₁×#3102	C₂	semidirect
11. C₃₁×#3093	C₂	semidirect
12. C₂×C₃₁×#482	C₂	semidirect
13. C₃₁×#3084	C₂	semidirect
14. C₃₁×#3083	C₂	semidirect
15. C₃₁×#3045	C₂	semidirect
16. C₃₁×#3045	C₂	semidirect
17. C₃₁×#3006	C₂	semidirect
18. C₃₁×#3002	C₂	semidirect
19. C₃₁×#2952	C₂	semidirect
20. C₃₁×#2951	C₂	semidirect
21. C₃₁×#2946	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₃₁×#2924	C₂	semidirect
35. C₃₁×#544	C₂²	semidirect
38. C₃₁×#535	C₂²	semidirect
39. C₃₁×#532	C₂²	semidirect
40. C₃₁×#529	C₂²	semidirect
49. C₃₁×#520	C₂²	semidirect
50. C₃₁×#519	C₂²	semidirect
52. C₃₁×#518	C₂²	semidirect
53. C₃₁×#518	C₂²	semidirect
55. C₄×#41×C₃₁	C₂²	semidirect
56. C₄×#41×C₃₁	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#485	C₂²	semidirect
65. C₃₁×#482	C₂²	semidirect
66. C₃₁×#482	C₂²	semidirect
67. C₃₁×#482	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#479	C₂²	semidirect
70. C₃₁×#479	C₂²	semidirect
71. C₃₁×#478	C₂²	semidirect
72. C₃₁×#478	C₂²	semidirect
73. C₃₁×#477	C₂²	semidirect
74. C₃₁×#476	C₂²	semidirect
75. C₃₁×#475	C₂²	semidirect
76. C₃₁×#474	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#463	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#460	C₂²	semidirect
82. C₃₁×#460	C₂²	semidirect
83. C₃₁×#459	C₂²	semidirect
84. C₃₁×#459	C₂²	semidirect
85. C₃₁×#452	C₂²	semidirect
86. C₃₁×#452	C₂²	semidirect
87. C₃₁×#451	C₂²	semidirect
88. C₃₁×#450	C₂²	semidirect
91. C₃₁×#449	C₂²	semidirect
92. C₃₁×#449	C₂²	semidirect
94. C₃₁×#448	C₂²	semidirect
96. C₃₁×#447	C₂²	semidirect
97. C₃₁×#442	C₂²	semidirect
98. C₃₁×#442	C₂²	semidirect
99. C₃₁×#442	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×SD₁₆×C₃₁	C₂²	semidirect
107. C₄×SD₁₆×C₃₁	C₂²	semidirect
108. C₄×SD₁₆×C₃₁	C₂²	semidirect
109. C₄×SD₁₆×C₃₁	C₂²	semidirect
110. C₄×D₈×C₃₁	C₂²	semidirect
111. C₄×D₈×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
117. C₃₁×#428	C₂²	semidirect
118. C₃₁×#428	C₂²	semidirect
119. C₂×C₃₁×#107	C₂²	semidirect
120. C₂×C₃₁×#106	C₂²	semidirect
121. C₃₁×#424	C₂²	semidirect
122. C₃₁×#424	C₂²	semidirect
125. C₃₁×#417	C₂²	semidirect
126. C₃₁×#417	C₂²	semidirect
129. C₂×C₃₁×#102	C₂²	semidirect
130. C₂×C₃₁×#102	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₃₁×#405	C₂²	semidirect
332. #41×C₃₁	#41	semidirect
333. #41×C₃₁	#41	semidirect
471. #60587	C₃₁	direct (N × H)
566. #3494	C₂×C₃₁	semidirect
567. #3428	C₂×C₃₁	semidirect
568. #3126	C₂×C₃₁	semidirect
569. #3122	C₂×C₃₁	semidirect
570. #3121	C₂×C₃₁	semidirect
571. #3118	C₂×C₃₁	semidirect
572. #3115	C₂×C₃₁	semidirect
573. #3111	C₂×C₃₁	semidirect
574. #3106	C₂×C₃₁	semidirect
575. #3102	C₂×C₃₁	semidirect
576. #3093	C₂×C₃₁	semidirect
577. C₂×#482	C₂×C₃₁	semidirect
578. #3084	C₂×C₃₁	semidirect
579. #3083	C₂×C₃₁	semidirect
580. #3045	C₂×C₃₁	semidirect
581. #3045	C₂×C₃₁	semidirect
582. #3006	C₂×C₃₁	semidirect
583. #3002	C₂×C₃₁	semidirect
584. #2952	C₂×C₃₁	semidirect
585. #2951	C₂×C₃₁	semidirect
586. #2946	C₂×C₃₁	semidirect
587. #2946	C₂×C₃₁	semidirect
588. #2924	C₂×C₃₁	semidirect
642. #544	C₂²×C₃₁	semidirect
645. #535	C₂²×C₃₁	semidirect
646. #532	C₂²×C₃₁	semidirect
647. #529	C₂²×C₃₁	semidirect
656. #520	C₂²×C₃₁	semidirect
657. #519	C₂²×C₃₁	semidirect
659. #518	C₂²×C₃₁	semidirect
660. #518	C₂²×C₃₁	semidirect
662. C₄×#41	C₂²×C₃₁	semidirect
663. C₄×#41	C₂²×C₃₁	semidirect
668. #485	C₂²×C₃₁	semidirect
669. #485	C₂²×C₃₁	semidirect
672. #482	C₂²×C₃₁	semidirect
673. #482	C₂²×C₃₁	semidirect
674. #482	C₂²×C₃₁	semidirect
675. #482	C₂²×C₃₁	semidirect
676. #479	C₂²×C₃₁	semidirect
677. #479	C₂²×C₃₁	semidirect
678. #478	C₂²×C₃₁	semidirect
679. #478	C₂²×C₃₁	semidirect
680. #477	C₂²×C₃₁	semidirect
681. #476	C₂²×C₃₁	semidirect
682. #475	C₂²×C₃₁	semidirect
683. #474	C₂²×C₃₁	semidirect
684. #464	C₂²×C₃₁	semidirect
685. #464	C₂²×C₃₁	semidirect
686. #463	C₂²×C₃₁	semidirect
687. #463	C₂²×C₃₁	semidirect
688. #460	C₂²×C₃₁	semidirect
689. #460	C₂²×C₃₁	semidirect
690. #459	C₂²×C₃₁	semidirect
691. #459	C₂²×C₃₁	semidirect
692. #452	C₂²×C₃₁	semidirect
693. #452	C₂²×C₃₁	semidirect
694. #451	C₂²×C₃₁	semidirect
695. #450	C₂²×C₃₁	semidirect
698. #449	C₂²×C₃₁	semidirect
699. #449	C₂²×C₃₁	semidirect
701. #448	C₂²×C₃₁	semidirect
703. #447	C₂²×C₃₁	semidirect
704. #442	C₂²×C₃₁	semidirect
705. #442	C₂²×C₃₁	semidirect
706. #442	C₂²×C₃₁	semidirect
707. #441	C₂²×C₃₁	semidirect
708. #440	C₂²×C₃₁	semidirect
709. #440	C₂²×C₃₁	semidirect
710. #440	C₂²×C₃₁	semidirect
711. #440	C₂²×C₃₁	semidirect
712. C₄×Q₁₆	C₂²×C₃₁	semidirect
713. C₄×SD₁₆	C₂²×C₃₁	semidirect
714. C₄×SD₁₆	C₂²×C₃₁	semidirect
715. C₄×SD₁₆	C₂²×C₃₁	semidirect
716. C₄×SD₁₆	C₂²×C₃₁	semidirect
717. C₄×D₈	C₂²×C₃₁	semidirect
718. C₄×D₈	C₂²×C₃₁	semidirect
719. C₄×D₈	C₂²×C₃₁	semidirect
720. #433	C₂²×C₃₁	semidirect
721. #433	C₂²×C₃₁	semidirect
722. #432	C₂²×C₃₁	semidirect
723. #431	C₂²×C₃₁	semidirect
724. #428	C₂²×C₃₁	semidirect
725. #428	C₂²×C₃₁	semidirect
726. C₂×#107	C₂²×C₃₁	semidirect
727. C₂×#106	C₂²×C₃₁	semidirect
728. #424	C₂²×C₃₁	semidirect
729. #424	C₂²×C₃₁	semidirect
732. #417	C₂²×C₃₁	semidirect
733. #417	C₂²×C₃₁	semidirect
736. C₂×#102	C₂²×C₃₁	semidirect
737. C₂×#102	C₂²×C₃₁	semidirect
740. #405	C₂²×C₃₁	semidirect
741. #405	C₂²×C₃₁	semidirect
935. C₃₁	#60587	direct (N × H)
950. #41	#41×C₃₁	semidirect
951. #41	#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×#3494	2
C₃₁×#3428	2
C₃₁×#3126	2
C₃₁×#3122	2
C₃₁×#3121	2
C₃₁×#3118	2
C₃₁×#3115	2
C₃₁×#3111	2
C₃₁×#3106	2
C₃₁×#3102	2
C₃₁×#3093	2
C₂×C₃₁×#482	2
C₃₁×#3084	2
C₃₁×#3083	2
C₃₁×#3045	2
C₃₁×#3006	2
C₃₁×#3002	2
C₃₁×#2952	2
C₃₁×#2951	2
C₃₁×#2946	2
C₃₁×#2924	2
#60587	31

Subgroups — C31×#60587 #21517346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60587 #21517346