Subgroups — C₃₁×#62563 #21519322

Order 7936.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3546	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3304	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#560	—	2	2	no	—
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#557	—	2	1	no	—
28	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#556	—	2	1	no	—
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	1	yes	characteristic
32	C₃₁×#556	C₂²	1	2	yes	complemented
33	C₃₁×#554	C₂²	1	1	yes	characteristic
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#552	C₂²	1	2	yes	complemented
36	C₃₁×#550	C₂²	1	2	yes	—
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	C₃₁×#547	C₂²	1	1	yes	characteristic
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	C₂²	1	2	yes	—
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	2	yes	complemented
43	C₃₁×#542	—	2	1	no	—
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#541	—	2	2	no	—
46	C₃₁×#541	—	2	1	no	—
47	C₃₁×#541	C₂²	1	2	yes	complemented
48	C₃₁×#538	—	2	2	no	—
49	C₃₁×#537	—	2	1	no	—
50	C₃₁×#535	—	2	1	no	—
51	C₃₁×#535	C₂²	1	2	yes	—
52	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#532	C₂²	1	1	yes	characteristic
55	C₃₁×#532	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#497	C₂²	1	2	yes	complemented
60	C₃₁×#492	C₂²	1	1	yes	characteristic
61	C₃₁×#490	C₂²	1	2	yes	—
62	C₃₁×#490	C₂²	1	2	yes	complemented
63	C₃₁×#489	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#488	C₂²	1	2	yes	—
66	C₃₁×#488	C₂²	1	2	yes	complemented
67	C₃₁×#488	C₂²	1	2	yes	complemented
68	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#486	C₂²	1	1	yes	characteristic
72	C₃₁×#486	C₂²	1	1	yes	characteristic
73	C₃₁×#486	C₂²	1	1	yes	characteristic
74	C₃₁×#486	C₂²	1	2	yes	complemented
75	C₃₁×#485	C₂²	1	2	yes	complemented
76	C₃₁×#483	C₂²	1	2	yes	complemented
77	C₃₁×#482	C₂²	1	2	yes	—
78	C₃₁×#482	C₂²	1	2	yes	—
79	C₃₁×#482	C₂²	1	2	yes	complemented
80	C₃₁×#481	C₂²	1	2	yes	—
81	C₃₁×#479	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	2	yes	complemented
83	C₃₁×#476	C₂²	1	1	yes	characteristic
84	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#476	C₂²	1	2	yes	complemented
86	C₃₁×#475	C₂²	1	2	yes	complemented
87	C₃₁×#474	C₂²	1	1	yes	characteristic
88	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#470	C₂²	1	2	yes	complemented
90	C₃₁×#468	C₂²	1	2	yes	—
91	C₃₁×#467	C₂²	1	2	yes	complemented
92	C₃₁×#465	C₂²	1	1	yes	characteristic
93	C₃₁×#465	C₂²	1	1	yes	characteristic
94	C₃₁×#465	C₂²	1	2	yes	—
95	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#464	C₂²	1	2	yes	—
98	C₃₁×#464	C₂²	1	2	yes	—
99	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#460	C₂²	1	1	yes	characteristic
102	C₃₁×#460	C₂²	1	1	yes	characteristic
103	C₃₁×#460	C₂²	1	2	yes	complemented
104	C₃₁×#460	C₂²	1	2	yes	complemented
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#452	C₂²	1	2	yes	complemented
108	C₃₁×#452	C₂²	1	2	yes	complemented
109	C₃₁×#450	C₂²	1	2	yes	—
110	C₃₁×#450	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#441	C₂²	1	2	yes	complemented
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×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×#418	C₂²	1	2	yes	—
128	C₃₁×#417	C₂²	1	2	yes	complemented
129	C₃₁×#416	C₂²	1	2	yes	complemented
130	C₃₁×#416	C₂²	1	2	yes	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	C₂³	1	2	yes	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	—	2	2	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	—	2	2	no	—
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×#127	—	2	2	no	—
165	C₃₁×#127	C₂³	1	1	yes	characteristic
166	C₃₁×#127	C₂³	1	2	yes	—
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	D₄	1	2	yes	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	1	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	2	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	D₄	1	1	yes	characteristic
185	C₃₁×#125	C₂³	1	2	yes	—
186	C₃₁×#125	C₂³	1	2	yes	—
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	—	2	2	no	—
189	C₃₁×#124	—	2	2	no	—
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	D₄	1	1	yes	characteristic
192	C₃₁×#124	C₂³	1	2	yes	—
193	C₃₁×#124	C₂³	1	2	yes	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	D₄	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	no	—
202	C₃₁×C₂²⋊Q₈	—	2	1	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	1	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	D₄	1	1	yes	characteristic
226	C₃₁×#121	C₂³	1	1	yes	characteristic
227	C₃₁×#121	C₂³	1	2	yes	—
228	C₃₁×#121	C₂³	1	1	yes	characteristic
229	C₃₁×#120	—	2	2	no	—
230	C₃₁×#120	—	2	2	no	—
231	C₃₁×#120	—	2	2	no	—
232	C₃₁×#120	—	2	2	no	—
233	C₄×Q₈×C₃₁	—	2	1	no	—
234	C₄×Q₈×C₃₁	—	2	1	no	—
235	C₄×Q₈×C₃₁	—	2	2	no	—
236	C₄×Q₈×C₃₁	—	2	1	no	—
237	C₄×Q₈×C₃₁	—	2	1	no	—
238	C₄×Q₈×C₃₁	—	2	1	no	—
239	C₄×Q₈×C₃₁	—	2	1	no	—
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
243	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
244	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
245	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	2	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	—	2	1	no	—
250	C₄×D₄×C₃₁	—	2	1	no	—
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	1	no	—
258	C₃₁×#117	—	2	2	no	—
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₃₁×#117	C₂³	1	2	yes	—
261	C₃₁×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#106	C₂³	1	1	yes	characteristic
269	C₃₁×#106	C₂³	1	1	yes	characteristic
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×#103	C₂³	1	2	yes	—
279	C₃₁×#103	C₂³	1	2	yes	—
280	C₃₁×#103	C₂³	1	2	yes	—
281	C₃₁×#103	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	2	yes	—
283	C₃₁×#103	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×#102	C₂³	1	1	yes	characteristic
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	1	yes	characteristic
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	#41×C₃₁	—	8	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	4	2	no	—
341	C₂×D₄×C₃₁	—	4	2	no	—
342	C₂×D₄×C₃₁	—	8	2	no	—
343	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
347	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	1	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	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
358	Q₁₆×C₃₁	—	4	2	no	—
359	Q₁₆×C₃₁	—	4	2	no	—
360	SD₁₆×C₃₁	—	4	1	no	—
361	SD₁₆×C₃₁	—	4	1	no	—
362	SD₁₆×C₃₁	—	4	1	no	—
363	SD₁₆×C₃₁	—	4	1	no	—
364	SD₁₆×C₃₁	—	4	2	no	—
365	SD₁₆×C₃₁	—	4	2	no	—
366	M₁₆×C₃₁	—	4	2	no	—
367	C₂×C₈×C₃₁	—	4	1	no	—
368	C₂×C₈×C₃₁	—	4	2	no	—
369	C₂×C₈×C₃₁	—	4	1	no	—
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	2	yes	—
446	#62563	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	2	2	no	—
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	—	8	2	no	—
451	C₂³×C₃₁	—	8	2	no	—
452	C₂³×C₃₁	—	8	2	no	—
453	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	1	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	2	2	no	—
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	4	2	no	—
463	Q₈×C₃₁	—	8	1	no	—
464	Q₈×C₃₁	—	8	1	no	—
465	Q₈×C₃₁	—	8	2	no	—
466	Q₈×C₃₁	—	8	1	no	—
467	D₄×C₃₁	—	2	2	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	2	no	—
471	D₄×C₃₁	—	2	2	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	4	2	no	—
476	D₄×C₃₁	—	8	1	no	—
477	D₄×C₃₁	—	8	1	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	8	1	no	—
481	D₄×C₃₁	—	8	2	no	—
482	D₄×C₃₁	—	8	2	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	—	8	1	no	—
486	D₄×C₃₁	—	8	1	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	1	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	—	4	1	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	8	2	no	—
505	C₂×C₄×C₃₁	—	8	2	no	—
506	C₂×C₄×C₃₁	—	8	2	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
517	C₈×C₃₁	—	2	1	no	—
518	C₈×C₃₁	—	2	1	no	—
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	1	no	—
521	C₈×C₃₁	—	2	2	no	—
522	C₈×C₃₁	—	2	2	no	—
523	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3546	C₂×C₃₁	1	1	yes	characteristic
525	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3362	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3317	C₂×C₃₁	1	2	yes	complemented
532	#3311	C₂×C₃₁	1	2	yes	complemented
533	#3304	C₂×C₃₁	1	2	yes	complemented
534	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3296	C₂×C₃₁	1	2	yes	complemented
536	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3244	C₂×C₃₁	1	2	yes	complemented
538	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3222	C₂×C₃₁	1	2	yes	complemented
540	#3216	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3178	C₂×C₃₁	1	2	yes	complemented
542	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3136	C₂×C₃₁	1	2	yes	complemented
544	#3131	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	2	2	no	—
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	2	no	—
550	C₂²×C₃₁	—	2	1	no	—
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	2	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	2	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	2	no	—
561	C₂²×C₃₁	—	16	4	no	—
562	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
563	C₄×C₃₁	—	2	1	no	—
564	C₄×C₃₁	—	2	1	no	—
565	C₄×C₃₁	—	2	2	no	—
566	C₄×C₃₁	—	2	1	no	—
567	C₄×C₃₁	—	2	2	no	—
568	C₄×C₃₁	—	2	1	no	—
569	C₄×C₃₁	—	2	2	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	2	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	1	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	1	no	—
578	C₄×C₃₁	—	4	2	no	—
579	C₄×C₃₁	#577	1	2	yes	—
580	C₄×C₃₁	#585	1	1	yes	characteristic
581	C₄×C₃₁	#585	1	1	yes	characteristic
582	#563	—	2	2	no	—
583	#560	—	2	2	no	—
584	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
585	#557	—	2	1	no	—
586	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#556	—	2	1	no	—
588	#556	C₂²×C₃₁	1	1	yes	characteristic
589	#556	C₂²×C₃₁	1	1	yes	characteristic
590	#556	C₂²×C₃₁	1	2	yes	complemented
591	#554	C₂²×C₃₁	1	1	yes	characteristic
592	#553	—	2	1	no	—
593	#552	C₂²×C₃₁	1	2	yes	complemented
594	#550	C₂²×C₃₁	1	2	yes	—
595	#550	C₂²×C₃₁	1	1	yes	characteristic
596	#547	C₂²×C₃₁	1	1	yes	characteristic
597	#546	—	2	1	no	—
598	#546	C₂²×C₃₁	1	2	yes	—
599	D₄²	C₂²×C₃₁	1	1	yes	characteristic
600	#544	C₂²×C₃₁	1	2	yes	complemented
601	#542	—	2	1	no	—
602	#542	C₂²×C₃₁	1	2	yes	—
603	#541	—	2	2	no	—
604	#541	—	2	1	no	—
605	#541	C₂²×C₃₁	1	2	yes	complemented
606	#538	—	2	2	no	—
607	#537	—	2	1	no	—
608	#535	—	2	1	no	—
609	#535	C₂²×C₃₁	1	2	yes	—
610	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#532	C₂²×C₃₁	1	1	yes	characteristic
613	#532	C₂²×C₃₁	1	1	yes	characteristic
614	#529	C₂²×C₃₁	1	1	yes	characteristic
615	#501	C₂²×C₃₁	1	2	yes	complemented
616	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#497	C₂²×C₃₁	1	2	yes	complemented
618	#492	C₂²×C₃₁	1	1	yes	characteristic
619	#490	C₂²×C₃₁	1	2	yes	—
620	#490	C₂²×C₃₁	1	2	yes	complemented
621	#489	C₂²×C₃₁	1	2	yes	—
622	#489	C₂²×C₃₁	1	2	yes	complemented
623	#488	C₂²×C₃₁	1	2	yes	—
624	#488	C₂²×C₃₁	1	2	yes	complemented
625	#488	C₂²×C₃₁	1	2	yes	complemented
626	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#486	C₂²×C₃₁	1	1	yes	characteristic
630	#486	C₂²×C₃₁	1	1	yes	characteristic
631	#486	C₂²×C₃₁	1	1	yes	characteristic
632	#486	C₂²×C₃₁	1	2	yes	complemented
633	#485	C₂²×C₃₁	1	2	yes	complemented
634	#483	C₂²×C₃₁	1	2	yes	complemented
635	#482	C₂²×C₃₁	1	2	yes	—
636	#482	C₂²×C₃₁	1	2	yes	—
637	#482	C₂²×C₃₁	1	2	yes	complemented
638	#481	C₂²×C₃₁	1	2	yes	—
639	#479	C₂²×C₃₁	1	2	yes	complemented
640	#478	C₂²×C₃₁	1	2	yes	complemented
641	#476	C₂²×C₃₁	1	1	yes	characteristic
642	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#476	C₂²×C₃₁	1	2	yes	complemented
644	#475	C₂²×C₃₁	1	2	yes	complemented
645	#474	C₂²×C₃₁	1	1	yes	characteristic
646	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#470	C₂²×C₃₁	1	2	yes	complemented
648	#468	C₂²×C₃₁	1	2	yes	—
649	#467	C₂²×C₃₁	1	2	yes	complemented
650	#465	C₂²×C₃₁	1	1	yes	characteristic
651	#465	C₂²×C₃₁	1	1	yes	characteristic
652	#465	C₂²×C₃₁	1	2	yes	—
653	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#464	C₂²×C₃₁	1	2	yes	—
656	#464	C₂²×C₃₁	1	2	yes	—
657	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#460	C₂²×C₃₁	1	1	yes	characteristic
660	#460	C₂²×C₃₁	1	1	yes	characteristic
661	#460	C₂²×C₃₁	1	2	yes	complemented
662	#460	C₂²×C₃₁	1	2	yes	complemented
663	#452	C₂²×C₃₁	1	2	yes	complemented
664	#452	C₂²×C₃₁	1	2	yes	complemented
665	#452	C₂²×C₃₁	1	2	yes	complemented
666	#452	C₂²×C₃₁	1	2	yes	complemented
667	#450	C₂²×C₃₁	1	2	yes	—
668	#450	C₂²×C₃₁	1	2	yes	—
669	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#441	C₂²×C₃₁	1	2	yes	complemented
672	#440	C₂²×C₃₁	1	2	yes	complemented
673	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
674	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
676	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
679	#436	C₂²×C₃₁	1	1	yes	characteristic
680	#435	C₂²×C₃₁	1	2	yes	complemented
681	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
682	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
683	#433	C₂²×C₃₁	1	2	yes	complemented
684	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	#418	C₂²×C₃₁	1	2	yes	—
686	#417	C₂²×C₃₁	1	2	yes	complemented
687	#416	C₂²×C₃₁	1	2	yes	complemented
688	#416	C₂²×C₃₁	1	2	yes	complemented
689	#416	C₂²×C₃₁	1	2	yes	complemented
690	C₂×#102	C₂²×C₃₁	1	2	yes	—
691	#405	C₂²×C₃₁	1	2	yes	complemented
692	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	C₂×C₃₁	—	4	1	no	—
694	C₂×C₃₁	—	4	2	no	—
695	C₂×C₃₁	—	8	1	no	—
696	C₂×C₃₁	—	8	2	no	—
697	C₂×C₃₁	—	8	1	no	—
698	C₂×C₃₁	#3500	1	1	yes	characteristic
699	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
700	C₂×C₃₁	#3584	1	1	yes	characteristic
701	C₂×#41	—	2	1	no	—
702	C₂×#41	—	2	1	no	—
703	C₂×#41	C₂³×C₃₁	1	2	yes	—
704	C₂×#41	C₂³×C₃₁	1	2	yes	—
705	C₂²×D₄	—	2	1	no	—
706	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
708	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
710	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
716	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	—	2	2	no	—
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	—	2	2	no	—
723	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
730	#127	—	2	2	no	—
731	#127	C₂³×C₃₁	1	1	yes	characteristic
732	#127	C₂³×C₃₁	1	1	yes	characteristic
733	#127	C₂³×C₃₁	1	2	yes	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	D₄×C₃₁	1	2	yes	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	D₄×C₃₁	1	1	yes	characteristic
751	#125	C₂³×C₃₁	1	2	yes	—
752	#125	C₂³×C₃₁	1	2	yes	—
753	#124	—	2	1	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	1	no	—
757	#124	D₄×C₃₁	1	1	yes	characteristic
758	#124	C₂³×C₃₁	1	2	yes	—
759	#124	C₂³×C₃₁	1	2	yes	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	D₄×C₃₁	1	2	yes	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	D₄×C₃₁	1	1	yes	characteristic
792	#121	C₂³×C₃₁	1	1	yes	characteristic
793	#121	C₂³×C₃₁	1	1	yes	characteristic
794	#121	C₂³×C₃₁	1	2	yes	—
795	#120	—	2	2	no	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	2	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
810	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
811	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₃₁	1	2	yes	—
820	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₃₁	1	2	yes	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	C₂³×C₃₁	1	2	yes	—
826	#117	C₂³×C₃₁	1	2	yes	—
827	#117	C₂³×C₃₁	1	2	yes	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
830	C₂×C₂²⋊C₄	—	2	2	no	—
831	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
832	#107	C₂³×C₃₁	1	2	yes	—
833	#107	C₂³×C₃₁	1	2	yes	—
834	#106	C₂³×C₃₁	1	1	yes	characteristic
835	#106	C₂³×C₃₁	1	1	yes	characteristic
836	#106	C₂³×C₃₁	1	1	yes	characteristic
837	#106	C₂³×C₃₁	1	1	yes	characteristic
838	#106	C₂³×C₃₁	1	2	yes	—
839	#106	C₂³×C₃₁	1	2	yes	—
840	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
843	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	2	yes	—
846	#103	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	2	yes	—
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	1	yes	characteristic
853	#103	C₂³×C₃₁	1	1	yes	characteristic
854	#102	C₂³×C₃₁	1	1	yes	characteristic
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	2	yes	—
857	#102	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	2	yes	—
861	#102	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	2	yes	—
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	1	yes	characteristic
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
871	#97	C₂³×C₃₁	1	2	yes	—
872	#97	C₂³×C₃₁	1	2	yes	—
873	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₃₁	1	2	yes	—
878	C₃₁	#62563	1	1	yes	characteristic, direct product factor, Sylow
879	C₂⁴	—	2	2	no	—
880	#41	—	4	2	no	—
881	#41	—	4	2	no	—
882	#41	—	4	2	no	—
883	#41	—	4	2	no	—
884	#41	—	8	2	no	—
885	#41	—	8	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	2	no	—
909	C₂×D₄	—	8	2	no	—
910	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
911	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
912	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
914	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
922	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
925	Q₁₆	—	4	2	no	—
926	Q₁₆	—	4	2	no	—
927	SD₁₆	—	4	1	no	—
928	SD₁₆	—	4	1	no	—
929	SD₁₆	—	4	1	no	—
930	SD₁₆	—	4	1	no	—
931	SD₁₆	—	4	2	no	—
932	SD₁₆	—	4	2	no	—
933	M₁₆	—	4	2	no	—
934	C₂×C₈	—	4	1	no	—
935	C₂×C₈	—	4	2	no	—
936	C₂×C₈	—	4	1	no	—
937	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
942	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
970	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1009	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1011	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1012	C₄²	C₂⁴×C₃₁	1	2	yes	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	8	2	no	—
1017	C₂³	—	8	2	no	—
1018	C₂³	—	8	2	no	—
1019	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1020	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1021	Q₈	—	2	2	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	8	1	no	—
1030	Q₈	—	8	1	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	1	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	8	1	no	—
1043	D₄	—	8	1	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	4	1	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	8	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1077	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1079	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1082	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	2	no	—
1088	C₈	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	16	4	no	—
1105	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	1	no	—
1122	C₄	C₃₁×#577	1	2	yes	—
1123	C₄	C₃₁×#585	1	1	yes	characteristic
1124	C₄	C₃₁×#585	1	1	yes	characteristic
1125	C₂	—	4	2	no	—
1126	C₂	—	4	1	no	—
1127	C₂	—	8	1	no	—
1128	C₂	—	8	2	no	—
1129	C₂	—	8	1	no	—
1130	C₂	C₃₁×#3500	1	1	yes	characteristic
1131	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1132	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3555	C₂	semidirect
3. C₃₁×#3369	C₂	semidirect
4. C₃₁×#3368	C₂	semidirect
5. C₃₁×#3364	C₂	semidirect
6. C₃₁×#3362	C₂	semidirect
7. C₃₁×#3331	C₂	semidirect
8. C₃₁×#3324	C₂	semidirect
9. C₃₁×#3317	C₂	semidirect
10. C₃₁×#3311	C₂	semidirect
11. C₃₁×#3304	C₂	semidirect
12. C₃₁×#3302	C₂	semidirect
13. C₃₁×#3296	C₂	semidirect
14. C₃₁×#3295	C₂	semidirect
15. C₃₁×#3244	C₂	semidirect
16. C₃₁×#3235	C₂	semidirect
17. C₃₁×#3222	C₂	semidirect
18. C₃₁×#3216	C₂	semidirect
19. C₃₁×#3178	C₂	semidirect
20. C₃₁×#3167	C₂	semidirect
21. C₃₁×#3136	C₂	semidirect
22. C₃₁×#3131	C₂	semidirect
23. C₃₁×#2966	C₂	semidirect
26. Q₈²×C₃₁	C₂²	semidirect
28. C₃₁×#557	C₂²	semidirect
32. C₃₁×#556	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
47. C₃₁×#541	C₂²	semidirect
52. C₃₁×#533	C₂²	semidirect
53. C₃₁×#533	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#498	C₂²	semidirect
59. C₃₁×#497	C₂²	semidirect
62. C₃₁×#490	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
66. C₃₁×#488	C₂²	semidirect
67. C₃₁×#488	C₂²	semidirect
68. C₃₁×#487	C₂²	semidirect
69. C₃₁×#487	C₂²	semidirect
70. C₃₁×#487	C₂²	semidirect
74. C₃₁×#486	C₂²	semidirect
75. C₃₁×#485	C₂²	semidirect
76. C₃₁×#483	C₂²	semidirect
79. C₃₁×#482	C₂²	semidirect
81. C₃₁×#479	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
84. C₃₁×#476	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#475	C₂²	semidirect
88. C₃₁×#474	C₂²	semidirect
89. C₃₁×#470	C₂²	semidirect
91. C₃₁×#467	C₂²	semidirect
95. C₃₁×#465	C₂²	semidirect
96. C₃₁×#465	C₂²	semidirect
99. C₃₁×#462	C₂²	semidirect
100. C₃₁×#462	C₂²	semidirect
103. C₃₁×#460	C₂²	semidirect
104. C₃₁×#460	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
107. C₃₁×#452	C₂²	semidirect
108. C₃₁×#452	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
113. C₃₁×#441	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₄×Q₁₆×C₃₁	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
128. C₃₁×#417	C₂²	semidirect
129. C₃₁×#416	C₂²	semidirect
130. C₃₁×#416	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
446. #62563	C₃₁	direct (N × H)
523. #3555	C₂×C₃₁	semidirect
525. #3369	C₂×C₃₁	semidirect
526. #3368	C₂×C₃₁	semidirect
527. #3364	C₂×C₃₁	semidirect
528. #3362	C₂×C₃₁	semidirect
529. #3331	C₂×C₃₁	semidirect
530. #3324	C₂×C₃₁	semidirect
531. #3317	C₂×C₃₁	semidirect
532. #3311	C₂×C₃₁	semidirect
533. #3304	C₂×C₃₁	semidirect
534. #3302	C₂×C₃₁	semidirect
535. #3296	C₂×C₃₁	semidirect
536. #3295	C₂×C₃₁	semidirect
537. #3244	C₂×C₃₁	semidirect
538. #3235	C₂×C₃₁	semidirect
539. #3222	C₂×C₃₁	semidirect
540. #3216	C₂×C₃₁	semidirect
541. #3178	C₂×C₃₁	semidirect
542. #3167	C₂×C₃₁	semidirect
543. #3136	C₂×C₃₁	semidirect
544. #3131	C₂×C₃₁	semidirect
545. #2966	C₂×C₃₁	semidirect
584. Q₈²	C₂²×C₃₁	semidirect
586. #557	C₂²×C₃₁	semidirect
590. #556	C₂²×C₃₁	semidirect
593. #552	C₂²×C₃₁	semidirect
600. #544	C₂²×C₃₁	semidirect
605. #541	C₂²×C₃₁	semidirect
610. #533	C₂²×C₃₁	semidirect
611. #533	C₂²×C₃₁	semidirect
615. #501	C₂²×C₃₁	semidirect
616. #498	C₂²×C₃₁	semidirect
617. #497	C₂²×C₃₁	semidirect
620. #490	C₂²×C₃₁	semidirect
622. #489	C₂²×C₃₁	semidirect
624. #488	C₂²×C₃₁	semidirect
625. #488	C₂²×C₃₁	semidirect
626. #487	C₂²×C₃₁	semidirect
627. #487	C₂²×C₃₁	semidirect
628. #487	C₂²×C₃₁	semidirect
632. #486	C₂²×C₃₁	semidirect
633. #485	C₂²×C₃₁	semidirect
634. #483	C₂²×C₃₁	semidirect
637. #482	C₂²×C₃₁	semidirect
639. #479	C₂²×C₃₁	semidirect
640. #478	C₂²×C₃₁	semidirect
642. #476	C₂²×C₃₁	semidirect
643. #476	C₂²×C₃₁	semidirect
644. #475	C₂²×C₃₁	semidirect
646. #474	C₂²×C₃₁	semidirect
647. #470	C₂²×C₃₁	semidirect
649. #467	C₂²×C₃₁	semidirect
653. #465	C₂²×C₃₁	semidirect
654. #465	C₂²×C₃₁	semidirect
657. #462	C₂²×C₃₁	semidirect
658. #462	C₂²×C₃₁	semidirect
661. #460	C₂²×C₃₁	semidirect
662. #460	C₂²×C₃₁	semidirect
663. #452	C₂²×C₃₁	semidirect
664. #452	C₂²×C₃₁	semidirect
665. #452	C₂²×C₃₁	semidirect
666. #452	C₂²×C₃₁	semidirect
669. #446	C₂²×C₃₁	semidirect
670. C₈×Q₈	C₂²×C₃₁	semidirect
671. #441	C₂²×C₃₁	semidirect
672. #440	C₂²×C₃₁	semidirect
673. C₄×Q₁₆	C₂²×C₃₁	semidirect
676. C₄×SD₁₆	C₂²×C₃₁	semidirect
677. C₄×SD₁₆	C₂²×C₃₁	semidirect
678. C₄×SD₁₆	C₂²×C₃₁	semidirect
680. #435	C₂²×C₃₁	semidirect
682. C₈×D₄	C₂²×C₃₁	semidirect
683. #433	C₂²×C₃₁	semidirect
684. #432	C₂²×C₃₁	semidirect
686. #417	C₂²×C₃₁	semidirect
687. #416	C₂²×C₃₁	semidirect
688. #416	C₂²×C₃₁	semidirect
689. #416	C₂²×C₃₁	semidirect
691. #405	C₂²×C₃₁	semidirect
692. C₂×C₄×C₈	C₂²×C₃₁	semidirect
878. C₃₁	#62563	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×#3555	2
C₃₁×#3546	2
C₃₁×#3369	2
C₃₁×#3368	2
C₃₁×#3364	2
C₃₁×#3362	2
C₃₁×#3331	2
C₃₁×#3324	2
C₃₁×#3317	2
C₃₁×#3311	2
C₃₁×#3304	2
C₃₁×#3302	2
C₃₁×#3296	2
C₃₁×#3295	2
C₃₁×#3244	2
C₃₁×#3235	2
C₃₁×#3222	2
C₃₁×#3216	2
C₃₁×#3178	2
C₃₁×#3167	2
C₃₁×#3136	2
C₃₁×#3131	2
C₃₁×#2966	2
#62563	31

Subgroups — C31×#62563 #21519322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62563 #21519322