Subgroups — C₃₁×#61494 #21518253

Order 7936.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
23	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
26	C₃₁×#559	C₂²	1	1	yes	characteristic
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#556	C₂²	1	1	yes	characteristic
29	C₃₁×#555	C₂²	1	2	yes	—
30	C₃₁×#553	—	2	2	no	—
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#551	—	2	2	no	—
33	C₃₁×#550	—	2	1	no	—
34	C₃₁×#550	C₂²	1	1	yes	characteristic
35	C₃₁×#550	C₂²	1	2	yes	complemented
36	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#548	—	2	1	no	—
39	C₃₁×#547	—	2	1	no	—
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#546	—	2	1	no	—
42	C₃₁×#546	C₂²	1	2	yes	—
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#540	—	2	2	no	—
46	C₃₁×#540	C₂²	1	2	yes	complemented
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#532	—	2	1	no	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	—	2	1	no	—
53	C₃₁×#529	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×#124	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	complemented
56	C₃₁×#518	C₂²	1	2	yes	—
57	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
58	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#496	C₂²	1	2	yes	complemented
62	C₃₁×#493	C₂²	1	1	yes	characteristic
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#486	C₂²	1	1	yes	characteristic
65	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	2	yes	complemented
67	C₃₁×#484	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#482	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	—
73	C₃₁×#478	C₂²	1	2	yes	—
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#474	C₂²	1	1	yes	characteristic
79	C₃₁×#474	C₂²	1	2	yes	complemented
80	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#469	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	2	yes	—
84	C₃₁×#466	C₂²	1	2	yes	complemented
85	C₃₁×#466	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#460	C₂²	1	1	yes	characteristic
90	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#459	C₂²	1	1	yes	characteristic
92	C₃₁×#459	C₂²	1	2	yes	—
93	C₃₁×#459	C₂²	1	1	yes	characteristic
94	C₃₁×#459	C₂²	1	2	yes	complemented
95	C₃₁×#452	C₂²	1	2	yes	complemented
96	C₃₁×#449	C₂²	1	2	yes	—
97	C₃₁×#449	C₂²	1	2	yes	—
98	C₃₁×#449	C₂²	1	2	yes	complemented
99	C₃₁×#447	C₂²	1	2	yes	—
100	C₃₁×#447	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	complemented
105	C₃₁×#442	C₂²	1	2	yes	complemented
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	complemented
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
110	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₃₁	C₂²	1	2	yes	—
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
120	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#416	C₂²	1	1	yes	characteristic
130	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#416	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	—
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	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	1	yes	characteristic
142	C₂²×Q₈×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	—	2	1	no	—
144	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
145	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
146	C₃₁×#135	—	2	4	no	—
147	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	—	2	1	no	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×#127	—	2	1	no	—
166	C₃₁×#127	—	2	2	no	—
167	C₃₁×#127	C₂³	1	2	yes	—
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	D₄	1	2	yes	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	D₄	1	1	yes	characteristic
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	D₄	1	1	yes	characteristic
185	C₃₁×#124	C₂³	1	2	yes	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#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	D₄	1	1	yes	characteristic
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	2	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×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#120	—	2	2	no	—
220	C₃₁×#120	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	2	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	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₃₁×#117	—	2	2	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	1	no	—
258	C₃₁×#117	C₂³	1	1	yes	characteristic
259	C₃₁×#117	C₂³	1	1	yes	characteristic
260	C₃₁×#117	C₂³	1	2	yes	—
261	C₃₁×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#107	C₂³	1	2	yes	—
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×#102	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
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	2	no	—
315	#41×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	4	no	—
317	#41×C₃₁	—	2	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	1	no	—
320	#41×C₃₁	—	4	1	no	—
321	#41×C₃₁	—	8	2	no	—
322	#41×C₃₁	—	8	2	no	—
323	#41×C₃₁	—	8	2	no	—
324	#41×C₃₁	—	8	2	no	—
325	C₂×Q₈×C₃₁	—	2	1	no	—
326	C₂×Q₈×C₃₁	—	2	1	no	—
327	C₂×Q₈×C₃₁	—	2	2	no	—
328	C₂×Q₈×C₃₁	—	8	2	no	—
329	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₃₁	—	2	4	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	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	—	4	2	no	—
349	C₂×D₄×C₃₁	—	8	2	no	—
350	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	2	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	2	no	—
367	C₂²×C₄×C₃₁	—	2	2	no	—
368	C₂²×C₄×C₃₁	—	2	2	no	—
369	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
373	Q₁₆×C₃₁	—	2	2	no	—
374	SD₁₆×C₃₁	—	2	4	no	—
375	SD₁₆×C₃₁	—	2	2	no	—
376	SD₁₆×C₃₁	—	4	2	no	—
377	SD₁₆×C₃₁	#41	1	4	yes	complemented
378	D₈×C₃₁	—	2	2	no	—
379	D₈×C₃₁	—	2	4	no	—
380	D₈×C₃₁	—	2	4	no	—
381	D₈×C₃₁	—	4	2	no	—
382	D₈×C₃₁	—	4	2	no	—
383	M₁₆×C₃₁	—	2	4	no	—
384	C₂×C₈×C₃₁	—	2	2	no	—
385	C₂×C₈×C₃₁	—	4	1	no	—
386	C₂×C₈×C₃₁	—	4	2	no	—
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
391	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
392	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	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	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	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	2	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	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	—	2	1	no	—
447	C₄²×C₃₁	—	2	1	no	—
448	C₄²×C₃₁	—	2	2	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
454	C₄²×C₃₁	C₂⁴	1	2	yes	—
455	#61494	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₂³×C₃₁	—	2	1	no	—
457	C₂³×C₃₁	—	2	2	no	—
458	C₂³×C₃₁	—	2	1	no	—
459	C₂³×C₃₁	—	2	2	no	—
460	C₂³×C₃₁	—	4	4	no	—
461	C₂³×C₃₁	—	8	2	no	—
462	C₂³×C₃₁	—	8	2	no	—
463	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
464	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
465	Q₈×C₃₁	—	2	2	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	2	1	no	—
468	Q₈×C₃₁	—	2	1	no	—
469	Q₈×C₃₁	—	4	2	no	—
470	Q₈×C₃₁	—	4	2	no	—
471	Q₈×C₃₁	—	8	2	no	—
472	Q₈×C₃₁	C₂×#41	1	2	yes	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	2	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	2	1	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	4	4	no	—
483	D₄×C₃₁	—	4	2	no	—
484	D₄×C₃₁	—	4	4	no	—
485	D₄×C₃₁	—	4	2	no	—
486	D₄×C₃₁	—	4	2	no	—
487	D₄×C₃₁	—	4	2	no	—
488	D₄×C₃₁	—	8	1	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	—	8	2	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	2	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	C₂×#41	1	2	yes	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	2	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	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	2	no	—
511	C₂×C₄×C₃₁	—	4	1	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	4	4	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	8	1	no	—
518	C₂×C₄×C₃₁	—	8	1	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	—	8	2	no	—
522	C₂×C₄×C₃₁	—	8	2	no	—
523	C₂×C₄×C₃₁	—	8	2	no	—
524	C₂×C₄×C₃₁	—	8	2	no	—
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	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	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
534	C₈×C₃₁	—	2	1	no	—
535	C₈×C₃₁	—	2	2	no	—
536	C₈×C₃₁	—	2	1	no	—
537	C₈×C₃₁	—	2	1	no	—
538	C₈×C₃₁	—	2	2	no	—
539	C₈×C₃₁	C₂×#41	1	2	yes	—
540	#3517	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3347	C₂×C₃₁	1	2	yes	complemented
548	#3305	C₂×C₃₁	1	2	yes	complemented
549	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3297	C₂×C₃₁	1	2	yes	complemented
551	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3274	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3268	C₂×C₃₁	1	2	yes	complemented
554	#3179	C₂×C₃₁	1	2	yes	complemented
555	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3124	C₂×C₃₁	1	2	yes	complemented
557	#3122	C₂×C₃₁	1	2	yes	complemented
558	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#2946	C₂×C₃₁	1	2	yes	complemented
562	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
563	C₂²×C₃₁	—	2	1	no	—
564	C₂²×C₃₁	—	2	2	no	—
565	C₂²×C₃₁	—	2	1	no	—
566	C₂²×C₃₁	—	2	2	no	—
567	C₂²×C₃₁	—	2	2	no	—
568	C₂²×C₃₁	—	2	1	no	—
569	C₂²×C₃₁	—	2	2	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	4	2	no	—
575	C₂²×C₃₁	—	4	2	no	—
576	C₂²×C₃₁	—	4	1	no	—
577	C₂²×C₃₁	—	4	2	no	—
578	C₂²×C₃₁	—	4	1	no	—
579	C₂²×C₃₁	—	4	2	no	—
580	C₂²×C₃₁	—	4	2	no	—
581	C₂²×C₃₁	—	16	4	no	—
582	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
583	C₄×C₃₁	—	2	1	no	—
584	C₄×C₃₁	—	2	1	no	—
585	C₄×C₃₁	—	2	2	no	—
586	C₄×C₃₁	—	2	1	no	—
587	C₄×C₃₁	—	2	2	no	—
588	C₄×C₃₁	—	2	2	no	—
589	C₄×C₃₁	—	2	1	no	—
590	C₄×C₃₁	—	2	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	—	4	2	no	—
598	C₄×C₃₁	#576	1	2	yes	—
599	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
600	C₄×C₃₁	#585	1	1	yes	characteristic
601	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
602	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
603	#559	C₂²×C₃₁	1	1	yes	characteristic
604	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	#556	C₂²×C₃₁	1	1	yes	characteristic
606	#555	C₂²×C₃₁	1	2	yes	—
607	#553	—	2	2	no	—
608	#553	C₂²×C₃₁	1	2	yes	complemented
609	#551	—	2	2	no	—
610	#550	—	2	1	no	—
611	#550	C₂²×C₃₁	1	1	yes	characteristic
612	#550	C₂²×C₃₁	1	2	yes	complemented
613	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
615	#548	—	2	1	no	—
616	#547	—	2	1	no	—
617	#547	C₂²×C₃₁	1	1	yes	characteristic
618	#546	—	2	1	no	—
619	#546	C₂²×C₃₁	1	2	yes	—
620	D₄²	C₂²×C₃₁	1	1	yes	characteristic
621	#542	C₂²×C₃₁	1	2	yes	—
622	#540	—	2	2	no	—
623	#540	C₂²×C₃₁	1	2	yes	complemented
624	#538	—	2	2	no	—
625	#532	—	2	1	no	—
626	#532	C₂²×C₃₁	1	1	yes	characteristic
627	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	#529	—	2	1	no	—
629	#529	—	2	1	no	—
630	#529	C₂²×C₃₁	1	1	yes	characteristic
631	C₂×#124	—	2	1	no	—
632	#520	C₂²×C₃₁	1	2	yes	complemented
633	#518	C₂²×C₃₁	1	2	yes	—
634	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
635	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#501	C₂²×C₃₁	1	2	yes	complemented
637	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#496	C₂²×C₃₁	1	2	yes	complemented
639	#493	C₂²×C₃₁	1	1	yes	characteristic
640	#488	C₂²×C₃₁	1	2	yes	complemented
641	#486	C₂²×C₃₁	1	1	yes	characteristic
642	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#486	C₂²×C₃₁	1	2	yes	complemented
644	#484	C₂²×C₃₁	1	2	yes	complemented
645	#482	C₂²×C₃₁	1	2	yes	complemented
646	#482	C₂²×C₃₁	1	2	yes	complemented
647	#482	C₂²×C₃₁	1	2	yes	complemented
648	#482	C₂²×C₃₁	1	2	yes	complemented
649	#480	C₂²×C₃₁	1	2	yes	—
650	#478	C₂²×C₃₁	1	2	yes	—
651	#478	C₂²×C₃₁	1	2	yes	complemented
652	#477	C₂²×C₃₁	1	2	yes	complemented
653	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#474	C₂²×C₃₁	1	1	yes	characteristic
656	#474	C₂²×C₃₁	1	2	yes	complemented
657	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#469	C₂²×C₃₁	1	2	yes	—
659	#468	C₂²×C₃₁	1	2	yes	complemented
660	#466	C₂²×C₃₁	1	2	yes	—
661	#466	C₂²×C₃₁	1	2	yes	complemented
662	#466	C₂²×C₃₁	1	2	yes	complemented
663	#465	C₂²×C₃₁	1	2	yes	complemented
664	#464	C₂²×C₃₁	1	2	yes	complemented
665	#463	C₂²×C₃₁	1	2	yes	complemented
666	#460	C₂²×C₃₁	1	1	yes	characteristic
667	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#459	C₂²×C₃₁	1	1	yes	characteristic
669	#459	C₂²×C₃₁	1	2	yes	—
670	#459	C₂²×C₃₁	1	1	yes	characteristic
671	#459	C₂²×C₃₁	1	2	yes	complemented
672	#452	C₂²×C₃₁	1	2	yes	complemented
673	#449	C₂²×C₃₁	1	2	yes	—
674	#449	C₂²×C₃₁	1	2	yes	—
675	#449	C₂²×C₃₁	1	2	yes	complemented
676	#447	C₂²×C₃₁	1	2	yes	—
677	#447	C₂²×C₃₁	1	2	yes	—
678	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#442	C₂²×C₃₁	1	2	yes	—
681	#442	C₂²×C₃₁	1	2	yes	complemented
682	#442	C₂²×C₃₁	1	2	yes	complemented
683	#440	C₂²×C₃₁	1	2	yes	—
684	#440	C₂²×C₃₁	1	2	yes	complemented
685	#440	C₂²×C₃₁	1	2	yes	complemented
686	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
689	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
694	C₄×D₈	C₂²×C₃₁	1	2	yes	—
695	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
696	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
697	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
698	#436	C₂²×C₃₁	1	1	yes	characteristic
699	#435	C₂²×C₃₁	1	2	yes	complemented
700	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
701	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
702	#433	C₂²×C₃₁	1	2	yes	complemented
703	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	#428	C₂²×C₃₁	1	2	yes	complemented
705	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#416	C₂²×C₃₁	1	1	yes	characteristic
707	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
708	#416	C₂²×C₃₁	1	2	yes	complemented
709	C₂×#102	C₂²×C₃₁	1	2	yes	—
710	#405	C₂²×C₃₁	1	2	yes	complemented
711	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	C₂×C₃₁	—	4	1	no	—
713	C₂×C₃₁	—	4	2	no	—
714	C₂×C₃₁	—	4	2	no	—
715	C₂×C₃₁	—	8	1	no	—
716	C₂×C₃₁	—	8	2	no	—
717	C₂×C₃₁	—	8	2	no	—
718	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
719	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
720	C₂×C₃₁	#3584	1	1	yes	characteristic
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×#41	C₂³×C₃₁	1	2	yes	—
728	C₂²×Q₈	—	2	1	no	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
731	AGL(1,ℤ/8)	—	2	8	no	—
732	#135	—	2	4	no	—
733	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₃₁	1	2	yes	—
740	C₂×D₈	C₂³×C₃₁	1	2	yes	—
741	C₂×D₈	C₂³×C₃₁	1	2	yes	—
742	C₂×D₈	C₂³×C₃₁	1	2	yes	—
743	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
744	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
745	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
751	#127	—	2	1	no	—
752	#127	—	2	2	no	—
753	#127	C₂³×C₃₁	1	1	yes	characteristic
754	#127	C₂³×C₃₁	1	1	yes	characteristic
755	#127	C₂³×C₃₁	1	2	yes	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	D₄×C₃₁	1	2	yes	—
760	#125	—	2	2	no	—
761	#125	D₄×C₃₁	1	1	yes	characteristic
762	#125	C₂³×C₃₁	1	2	yes	—
763	#124	—	2	1	no	—
764	#124	—	2	1	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	1	no	—
769	#124	—	2	1	no	—
770	#124	D₄×C₃₁	1	1	yes	characteristic
771	#124	C₂³×C₃₁	1	2	yes	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	D₄×C₃₁	1	2	yes	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	D₄×C₃₁	1	1	yes	characteristic
800	#121	C₂³×C₃₁	1	2	yes	—
801	#121	C₂³×C₃₁	1	2	yes	—
802	#121	C₂³×C₃₁	1	2	yes	—
803	#121	C₂³×C₃₁	1	2	yes	—
804	#121	C₂³×C₃₁	1	2	yes	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
814	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₃₁	1	2	yes	—
834	C₄×D₄	C₂³×C₃₁	1	2	yes	—
835	C₄×D₄	C₂³×C₃₁	1	2	yes	—
836	C₄×D₄	C₂³×C₃₁	1	2	yes	—
837	C₄×D₄	C₂³×C₃₁	1	2	yes	—
838	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₃₁	1	2	yes	—
840	#117	—	2	2	no	—
841	#117	—	2	2	no	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	C₂³×C₃₁	1	1	yes	characteristic
845	#117	C₂³×C₃₁	1	1	yes	characteristic
846	#117	C₂³×C₃₁	1	2	yes	—
847	#117	C₂³×C₃₁	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	2	no	—
849	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₄²	—	2	1	no	—
854	C₂×C₄²	—	2	1	no	—
855	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
856	#107	C₂³×C₃₁	1	1	yes	characteristic
857	#107	C₂³×C₃₁	1	1	yes	characteristic
858	#107	C₂³×C₃₁	1	2	yes	—
859	#107	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
865	#106	C₂³×C₃₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
869	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
870	#103	C₂³×C₃₁	1	1	yes	characteristic
871	#103	C₂³×C₃₁	1	1	yes	characteristic
872	#103	C₂³×C₃₁	1	1	yes	characteristic
873	#103	C₂³×C₃₁	1	1	yes	characteristic
874	#103	C₂³×C₃₁	1	2	yes	—
875	#103	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
881	#102	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	1	yes	characteristic
884	#102	C₂³×C₃₁	1	2	yes	—
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	2	yes	—
888	#102	C₂³×C₃₁	1	2	yes	—
889	#102	C₂³×C₃₁	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
893	#97	C₂³×C₃₁	1	2	yes	—
894	#97	C₂³×C₃₁	1	2	yes	—
895	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
899	C₄×C₈	C₂³×C₃₁	1	2	yes	—
900	C₃₁	#61494	1	1	yes	characteristic, direct product factor, Sylow
901	C₂⁴	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	—	2	4	no	—
904	#41	—	2	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	1	no	—
907	#41	—	4	1	no	—
908	#41	—	8	2	no	—
909	#41	—	8	2	no	—
910	#41	—	8	2	no	—
911	#41	—	8	2	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	1	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	—	8	2	no	—
916	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
919	C₂×D₄	—	2	4	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	4	2	no	—
936	C₂×D₄	—	8	2	no	—
937	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
938	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
939	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
940	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
941	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
957	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
960	Q₁₆	—	2	2	no	—
961	SD₁₆	—	2	4	no	—
962	SD₁₆	—	2	2	no	—
963	SD₁₆	—	4	2	no	—
964	SD₁₆	#41×C₃₁	1	4	yes	complemented
965	D₈	—	2	2	no	—
966	D₈	—	2	4	no	—
967	D₈	—	2	4	no	—
968	D₈	—	4	2	no	—
969	D₈	—	4	2	no	—
970	M₁₆	—	2	4	no	—
971	C₂×C₈	—	2	2	no	—
972	C₂×C₈	—	4	1	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
978	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
979	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
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	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1038	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₃₁	1	2	yes	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	4	4	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1050	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	8	2	no	—
1058	Q₈	C₂×#41×C₃₁	1	2	yes	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	4	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	C₂×#41×C₃₁	1	2	yes	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	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	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	8	1	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	2	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1119	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	1	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	C₂×#41×C₃₁	1	2	yes	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	16	4	no	—
1145	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1146	C₄	—	2	1	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	2	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	C₃₁×#576	1	2	yes	—
1162	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1163	C₄	C₃₁×#585	1	1	yes	characteristic
1164	C₂	—	4	2	no	—
1165	C₂	—	4	1	no	—
1166	C₂	—	4	2	no	—
1167	C₂	—	8	2	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	2	no	—
1170	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1171	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1172	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3517	C₂	semidirect
2. C₃₁×#3514	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3386	C₂	semidirect
5. C₃₁×#3365	C₂	semidirect
6. C₃₁×#3358	C₂	semidirect
7. C₃₁×#3353	C₂	semidirect
8. C₃₁×#3347	C₂	semidirect
9. C₃₁×#3305	C₂	semidirect
10. C₃₁×#3304	C₂	semidirect
11. C₃₁×#3297	C₂	semidirect
12. C₃₁×#3294	C₂	semidirect
13. C₃₁×#3274	C₂	semidirect
14. C₃₁×#3268	C₂	semidirect
15. C₃₁×#3179	C₂	semidirect
16. C₃₁×#3169	C₂	semidirect
17. C₃₁×#3124	C₂	semidirect
18. C₃₁×#3122	C₂	semidirect
19. C₃₁×#3115	C₂	semidirect
20. C₃₁×#3115	C₂	semidirect
21. C₃₁×#2966	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₄×C₃₁×#135	C₂	semidirect
27. C₃₁×#557	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
35. C₃₁×#550	C₂²	semidirect
36. C₃₁×#550	C₂²	semidirect
46. C₃₁×#540	C₂²	semidirect
50. C₃₁×#532	C₂²	semidirect
55. C₃₁×#520	C₂²	semidirect
58. C₄×#41×C₃₁	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#500	C₂²	semidirect
61. C₃₁×#496	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
65. C₃₁×#486	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#484	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#475	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
79. C₃₁×#474	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
84. C₃₁×#466	C₂²	semidirect
85. C₃₁×#466	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
90. C₃₁×#460	C₂²	semidirect
94. C₃₁×#459	C₂²	semidirect
95. C₃₁×#452	C₂²	semidirect
98. C₃₁×#449	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
104. C₃₁×#442	C₂²	semidirect
105. C₃₁×#442	C₂²	semidirect
107. C₃₁×#440	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₄×Q₁₆×C₃₁	C₂²	semidirect
110. C₄×Q₁₆×C₃₁	C₂²	semidirect
113. C₄×SD₁₆×C₃₁	C₂²	semidirect
114. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×D₈×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₃₁×#427	C₂²	semidirect
130. C₃₁×#416	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
377. SD₁₆×C₃₁	#41	semidirect
455. #61494	C₃₁	direct (N × H)
540. #3517	C₂×C₃₁	semidirect
541. #3514	C₂×C₃₁	semidirect
542. #3399	C₂×C₃₁	semidirect
543. #3386	C₂×C₃₁	semidirect
544. #3365	C₂×C₃₁	semidirect
545. #3358	C₂×C₃₁	semidirect
546. #3353	C₂×C₃₁	semidirect
547. #3347	C₂×C₃₁	semidirect
548. #3305	C₂×C₃₁	semidirect
549. #3304	C₂×C₃₁	semidirect
550. #3297	C₂×C₃₁	semidirect
551. #3294	C₂×C₃₁	semidirect
552. #3274	C₂×C₃₁	semidirect
553. #3268	C₂×C₃₁	semidirect
554. #3179	C₂×C₃₁	semidirect
555. #3169	C₂×C₃₁	semidirect
556. #3124	C₂×C₃₁	semidirect
557. #3122	C₂×C₃₁	semidirect
558. #3115	C₂×C₃₁	semidirect
559. #3115	C₂×C₃₁	semidirect
560. #2966	C₂×C₃₁	semidirect
561. #2946	C₂×C₃₁	semidirect
562. C₄×#135	C₂×C₃₁	semidirect
604. #557	C₂²×C₃₁	semidirect
608. #553	C₂²×C₃₁	semidirect
612. #550	C₂²×C₃₁	semidirect
613. #550	C₂²×C₃₁	semidirect
623. #540	C₂²×C₃₁	semidirect
627. #532	C₂²×C₃₁	semidirect
632. #520	C₂²×C₃₁	semidirect
635. C₄×#41	C₂²×C₃₁	semidirect
636. #501	C₂²×C₃₁	semidirect
637. #500	C₂²×C₃₁	semidirect
638. #496	C₂²×C₃₁	semidirect
640. #488	C₂²×C₃₁	semidirect
642. #486	C₂²×C₃₁	semidirect
643. #486	C₂²×C₃₁	semidirect
644. #484	C₂²×C₃₁	semidirect
645. #482	C₂²×C₃₁	semidirect
646. #482	C₂²×C₃₁	semidirect
647. #482	C₂²×C₃₁	semidirect
648. #482	C₂²×C₃₁	semidirect
651. #478	C₂²×C₃₁	semidirect
652. #477	C₂²×C₃₁	semidirect
653. #475	C₂²×C₃₁	semidirect
654. #475	C₂²×C₃₁	semidirect
656. #474	C₂²×C₃₁	semidirect
657. #474	C₂²×C₃₁	semidirect
659. #468	C₂²×C₃₁	semidirect
661. #466	C₂²×C₃₁	semidirect
662. #466	C₂²×C₃₁	semidirect
663. #465	C₂²×C₃₁	semidirect
664. #464	C₂²×C₃₁	semidirect
665. #463	C₂²×C₃₁	semidirect
667. #460	C₂²×C₃₁	semidirect
671. #459	C₂²×C₃₁	semidirect
672. #452	C₂²×C₃₁	semidirect
675. #449	C₂²×C₃₁	semidirect
678. #446	C₂²×C₃₁	semidirect
679. C₈×Q₈	C₂²×C₃₁	semidirect
681. #442	C₂²×C₃₁	semidirect
682. #442	C₂²×C₃₁	semidirect
684. #440	C₂²×C₃₁	semidirect
685. #440	C₂²×C₃₁	semidirect
686. C₄×Q₁₆	C₂²×C₃₁	semidirect
687. C₄×Q₁₆	C₂²×C₃₁	semidirect
690. C₄×SD₁₆	C₂²×C₃₁	semidirect
691. C₄×SD₁₆	C₂²×C₃₁	semidirect
692. C₄×SD₁₆	C₂²×C₃₁	semidirect
696. C₄×D₈	C₂²×C₃₁	semidirect
697. C₄×D₈	C₂²×C₃₁	semidirect
699. #435	C₂²×C₃₁	semidirect
701. C₈×D₄	C₂²×C₃₁	semidirect
702. #433	C₂²×C₃₁	semidirect
703. #432	C₂²×C₃₁	semidirect
704. #428	C₂²×C₃₁	semidirect
705. #427	C₂²×C₃₁	semidirect
707. #416	C₂²×C₃₁	semidirect
708. #416	C₂²×C₃₁	semidirect
710. #405	C₂²×C₃₁	semidirect
711. C₂×C₄×C₈	C₂²×C₃₁	semidirect
900. C₃₁	#61494	direct (N × H)
964. 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×#3517	2
C₃₁×#3514	2
C₃₁×#3399	2
C₃₁×#3386	2
C₃₁×#3365	2
C₃₁×#3358	2
C₃₁×#3353	2
C₃₁×#3347	2
C₃₁×#3305	2
C₃₁×#3304	2
C₃₁×#3297	2
C₃₁×#3294	2
C₃₁×#3274	2
C₃₁×#3268	2
C₃₁×#3179	2
C₃₁×#3169	2
C₃₁×#3124	2
C₃₁×#3122	2
C₃₁×#3115	2
C₃₁×#2966	2
C₃₁×#2946	2
C₄×C₃₁×#135	2
#61494	31

Subgroups — C31×#61494 #21518253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61494 #21518253