Subgroups — C₃₁×#62571 #21519330

Order 7936.

1656 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3561	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3369	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3223	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#563	—	2	2	no	—
22	C₃₁×#562	—	2	1	no	—
23	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#557	—	2	1	no	—
25	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#556	C₂²	1	2	yes	—
29	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#552	C₂²	1	2	yes	—
32	C₃₁×#551	—	2	2	no	—
33	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
34	C₃₁×#548	C₂²	1	2	yes	—
35	C₃₁×#546	C₂²	1	2	yes	—
36	C₃₁×#544	C₂²	1	2	yes	complemented
37	C₃₁×#543	—	2	1	no	—
38	C₃₁×#542	—	2	2	no	—
39	C₃₁×#542	—	2	1	no	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#541	—	2	2	no	—
42	C₃₁×#541	—	2	1	no	—
43	C₃₁×#541	C₂²	1	2	yes	complemented
44	C₃₁×#538	—	2	1	no	—
45	C₃₁×#536	C₂²	1	2	yes	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#497	C₂²	1	2	yes	—
54	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#491	C₂²	1	2	yes	complemented
56	C₃₁×#491	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	—
58	C₃₁×#489	C₂²	1	2	yes	—
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#489	C₂²	1	2	yes	—
61	C₃₁×#488	C₂²	1	2	yes	—
62	C₃₁×#488	C₂²	1	2	yes	—
63	C₃₁×#488	C₂²	1	2	yes	—
64	C₃₁×#487	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#485	C₂²	1	2	yes	complemented
70	C₃₁×#483	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#476	C₂²	1	2	yes	—
77	C₃₁×#475	C₂²	1	2	yes	complemented
78	C₃₁×#475	C₂²	1	2	yes	complemented
79	C₃₁×#470	C₂²	1	2	yes	—
80	C₃₁×#470	C₂²	1	2	yes	—
81	C₃₁×#470	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	—
83	C₃₁×#467	C₂²	1	2	yes	complemented
84	C₃₁×#465	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	2	yes	—
86	C₃₁×#464	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#462	C₂²	1	2	yes	complemented
90	C₃₁×#462	C₂²	1	2	yes	complemented
91	C₃₁×#452	C₂²	1	2	yes	—
92	C₃₁×#452	C₂²	1	2	yes	—
93	C₃₁×#451	C₂²	1	1	yes	characteristic
94	C₃₁×#451	C₂²	1	1	yes	characteristic
95	C₃₁×#451	C₂²	1	2	yes	complemented
96	C₃₁×#451	C₂²	1	2	yes	complemented
97	C₃₁×#450	C₂²	1	1	yes	characteristic
98	C₃₁×#450	C₂²	1	1	yes	characteristic
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#441	C₂²	1	2	yes	complemented
101	C₃₁×#441	C₂²	1	2	yes	complemented
102	C₃₁×#441	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	—
104	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
106	C₃₁×#436	C₂²	1	2	yes	—
107	C₃₁×#435	C₂²	1	2	yes	—
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#432	C₂²	1	1	yes	characteristic
111	C₃₁×#419	C₂²	1	2	yes	—
112	C₃₁×#419	C₂²	1	2	yes	complemented
113	C₃₁×#418	C₂²	1	2	yes	—
114	C₃₁×#417	C₂²	1	2	yes	—
115	C₃₁×#416	C₂²	1	2	yes	—
116	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
117	C₃₁×#405	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	C₂³	1	2	yes	—
120	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
121	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
123	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
132	C₃₁×C₄⋊Q₈	—	2	1	no	—
133	C₃₁×C₄⋊Q₈	—	2	2	no	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	—	2	1	no	—
136	C₃₁×C₄⋊Q₈	—	2	2	no	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#126	—	2	2	no	—
148	C₃₁×#126	—	2	2	no	—
149	C₃₁×#126	—	2	2	no	—
150	C₃₁×#126	—	2	2	no	—
151	C₃₁×#126	—	2	2	no	—
152	C₃₁×#126	—	2	2	no	—
153	C₃₁×#126	—	2	2	no	—
154	C₃₁×#126	D₄	1	2	yes	—
155	C₃₁×#125	—	2	2	no	—
156	C₃₁×#125	—	2	2	no	—
157	C₃₁×#125	—	2	2	no	—
158	C₃₁×#125	—	2	1	no	—
159	C₃₁×#125	—	2	2	no	—
160	C₃₁×#125	—	2	2	no	—
161	C₃₁×#125	—	2	1	no	—
162	C₃₁×#125	—	2	1	no	—
163	C₃₁×#125	D₄	1	1	yes	characteristic
164	C₃₁×#125	C₂³	1	2	yes	—
165	C₃₁×#125	C₂³	1	2	yes	—
166	C₃₁×#124	—	2	1	no	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	2	no	—
169	C₃₁×#124	—	2	2	no	—
170	C₃₁×#124	—	2	1	no	—
171	C₃₁×#124	—	2	1	no	—
172	C₃₁×#124	D₄	1	1	yes	characteristic
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	D₄	1	2	yes	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
197	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
198	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	D₄	1	1	yes	characteristic
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#120	—	2	2	no	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	C₂³	1	2	yes	—
227	C₄×D₄×C₃₁	C₂³	1	2	yes	—
228	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
229	C₃₁×#117	—	2	1	no	—
230	C₃₁×#117	—	2	1	no	—
231	C₃₁×#117	—	2	2	no	—
232	C₃₁×#117	—	2	2	no	—
233	C₃₁×#117	C₂³	1	2	yes	—
234	C₃₁×#117	C₂³	1	2	yes	—
235	C₃₁×#117	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
240	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	2	yes	—
275	C₃₁×#97	C₂³	1	2	yes	—
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	C₂×Q₈×C₃₁	—	2	1	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	1	no	—
286	C₂×Q₈×C₃₁	—	2	1	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	2	2	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	4	2	no	—
291	C₂×Q₈×C₃₁	—	4	2	no	—
292	C₂×Q₈×C₃₁	—	4	2	no	—
293	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
295	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
296	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂×D₄×C₃₁	—	2	2	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	1	no	—
301	C₂×D₄×C₃₁	—	4	2	no	—
302	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
303	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₃₁	—	2	1	no	—
306	C₂²×C₄×C₃₁	—	2	2	no	—
307	C₂²×C₄×C₃₁	—	2	2	no	—
308	C₂²×C₄×C₃₁	—	2	2	no	—
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
314	Q₁₆×C₃₁	—	4	2	no	—
315	Q₁₆×C₃₁	—	4	2	no	—
316	Q₁₆×C₃₁	—	4	2	no	—
317	Q₁₆×C₃₁	—	4	2	no	—
318	SD₁₆×C₃₁	—	4	2	no	—
319	SD₁₆×C₃₁	—	4	2	no	—
320	M₁₆×C₃₁	—	4	2	no	—
321	M₁₆×C₃₁	—	4	2	no	—
322	C₂×C₈×C₃₁	—	4	2	no	—
323	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
324	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
325	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
326	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	1	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	1	no	—
331	C₄⋊C₄×C₃₁	—	2	1	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	1	no	—
334	C₄⋊C₄×C₃₁	—	2	1	no	—
335	C₄⋊C₄×C₃₁	—	2	1	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	1	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	1	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	2	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	1	no	—
346	C₄⋊C₄×C₃₁	—	2	1	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	2	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	1	no	—
352	C₄⋊C₄×C₃₁	—	2	1	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₂²⋊C₄×C₃₁	—	2	2	no	—
367	C₂²⋊C₄×C₃₁	—	2	1	no	—
368	C₂²⋊C₄×C₃₁	—	2	1	no	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
387	C₄²×C₃₁	—	2	2	no	—
388	C₄²×C₃₁	—	2	2	no	—
389	C₄²×C₃₁	—	2	1	no	—
390	C₄²×C₃₁	—	2	2	no	—
391	C₄²×C₃₁	—	2	1	no	—
392	C₄²×C₃₁	—	2	2	no	—
393	C₄²×C₃₁	—	2	2	no	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₄²×C₃₁	C₂⁴	1	2	yes	—
399	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
400	#62571	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂³×C₃₁	—	2	2	no	—
402	C₂³×C₃₁	—	4	2	no	—
403	C₂³×C₃₁	—	8	1	no	—
404	C₂³×C₃₁	—	8	1	no	—
405	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
406	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
407	Q₈×C₃₁	—	2	2	no	—
408	Q₈×C₃₁	—	2	2	no	—
409	Q₈×C₃₁	—	2	2	no	—
410	Q₈×C₃₁	—	2	2	no	—
411	Q₈×C₃₁	—	2	2	no	—
412	Q₈×C₃₁	—	2	2	no	—
413	Q₈×C₃₁	—	4	1	no	—
414	Q₈×C₃₁	—	4	2	no	—
415	Q₈×C₃₁	—	8	1	no	—
416	Q₈×C₃₁	—	8	1	no	—
417	Q₈×C₃₁	—	8	1	no	—
418	Q₈×C₃₁	—	8	2	no	—
419	Q₈×C₃₁	—	8	2	no	—
420	Q₈×C₃₁	—	8	1	no	—
421	D₄×C₃₁	—	2	2	no	—
422	D₄×C₃₁	—	2	2	no	—
423	D₄×C₃₁	—	4	1	no	—
424	D₄×C₃₁	—	4	2	no	—
425	D₄×C₃₁	—	8	1	no	—
426	D₄×C₃₁	—	8	2	no	—
427	D₄×C₃₁	—	8	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	1	no	—
432	C₂×C₄×C₃₁	—	2	1	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	1	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	1	no	—
440	C₂×C₄×C₃₁	—	4	1	no	—
441	C₂×C₄×C₃₁	—	4	1	no	—
442	C₂×C₄×C₃₁	—	8	2	no	—
443	C₂×C₄×C₃₁	—	8	2	no	—
444	C₂×C₄×C₃₁	—	8	2	no	—
445	C₂×C₄×C₃₁	—	8	2	no	—
446	C₂×C₄×C₃₁	—	8	1	no	—
447	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
456	C₈×C₃₁	—	2	2	no	—
457	C₈×C₃₁	—	2	2	no	—
458	C₈×C₃₁	—	2	2	no	—
459	C₈×C₃₁	—	2	2	no	—
460	#3561	C₂×C₃₁	1	1	yes	characteristic
461	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
462	#3377	C₂×C₃₁	1	2	yes	complemented
463	#3369	C₂×C₃₁	1	2	yes	complemented
464	#3328	C₂×C₃₁	1	2	yes	complemented
465	#3323	C₂×C₃₁	1	2	yes	complemented
466	#3316	C₂×C₃₁	1	2	yes	complemented
467	#3313	C₂×C₃₁	1	2	yes	complemented
468	#3312	C₂×C₃₁	1	2	yes	complemented
469	#3311	C₂×C₃₁	1	2	yes	complemented
470	#3244	C₂×C₃₁	1	2	yes	complemented
471	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
472	#3223	C₂×C₃₁	1	2	yes	complemented
473	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
474	#3185	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#3178	C₂×C₃₁	1	2	yes	complemented
476	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
477	#3137	C₂×C₃₁	1	2	yes	complemented
478	#2967	C₂×C₃₁	1	1	yes	characteristic, complemented
479	C₂²×C₃₁	—	2	1	no	—
480	C₂²×C₃₁	—	2	1	no	—
481	C₂²×C₃₁	—	2	2	no	—
482	C₂²×C₃₁	—	2	2	no	—
483	C₂²×C₃₁	—	2	2	no	—
484	C₂²×C₃₁	—	2	1	no	—
485	C₂²×C₃₁	—	4	2	no	—
486	C₂²×C₃₁	—	4	2	no	—
487	C₂²×C₃₁	—	4	2	no	—
488	C₂²×C₃₁	—	16	2	no	—
489	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
490	C₄×C₃₁	—	2	1	no	—
491	C₄×C₃₁	—	2	1	no	—
492	C₄×C₃₁	—	2	1	no	—
493	C₄×C₃₁	—	2	1	no	—
494	C₄×C₃₁	—	2	2	no	—
495	C₄×C₃₁	—	2	2	no	—
496	C₄×C₃₁	—	2	2	no	—
497	C₄×C₃₁	—	2	1	no	—
498	C₄×C₃₁	—	4	1	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	2	no	—
502	C₄×C₃₁	—	4	1	no	—
503	C₄×C₃₁	—	4	2	no	—
504	C₄×C₃₁	—	4	2	no	—
505	C₄×C₃₁	—	4	1	no	—
506	C₄×C₃₁	—	4	1	no	—
507	C₄×C₃₁	#585	1	2	yes	—
508	#563	—	2	1	no	—
509	#563	—	2	2	no	—
510	#562	—	2	1	no	—
511	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
512	#557	—	2	1	no	—
513	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	#556	—	2	1	no	—
515	#556	C₂²×C₃₁	1	2	yes	—
516	#556	C₂²×C₃₁	1	2	yes	—
517	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
518	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
519	#552	C₂²×C₃₁	1	2	yes	—
520	#551	—	2	2	no	—
521	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
522	#548	C₂²×C₃₁	1	2	yes	—
523	#546	C₂²×C₃₁	1	2	yes	—
524	#544	C₂²×C₃₁	1	2	yes	complemented
525	#543	—	2	1	no	—
526	#542	—	2	2	no	—
527	#542	—	2	1	no	—
528	#542	C₂²×C₃₁	1	2	yes	—
529	#541	—	2	2	no	—
530	#541	—	2	1	no	—
531	#541	C₂²×C₃₁	1	2	yes	complemented
532	#538	—	2	1	no	—
533	#536	C₂²×C₃₁	1	2	yes	—
534	#533	C₂²×C₃₁	1	1	yes	characteristic
535	#533	C₂²×C₃₁	1	1	yes	characteristic
536	#533	C₂²×C₃₁	1	1	yes	characteristic
537	#529	C₂²×C₃₁	1	1	yes	characteristic
538	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
539	#501	C₂²×C₃₁	1	2	yes	complemented
540	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
541	#497	C₂²×C₃₁	1	2	yes	—
542	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
543	#491	C₂²×C₃₁	1	2	yes	complemented
544	#491	C₂²×C₃₁	1	2	yes	complemented
545	#489	C₂²×C₃₁	1	2	yes	—
546	#489	C₂²×C₃₁	1	2	yes	—
547	#489	C₂²×C₃₁	1	2	yes	—
548	#489	C₂²×C₃₁	1	2	yes	—
549	#488	C₂²×C₃₁	1	2	yes	—
550	#488	C₂²×C₃₁	1	2	yes	—
551	#488	C₂²×C₃₁	1	2	yes	—
552	#487	C₂²×C₃₁	1	2	yes	complemented
553	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
555	#485	C₂²×C₃₁	1	2	yes	—
556	#485	C₂²×C₃₁	1	2	yes	—
557	#485	C₂²×C₃₁	1	2	yes	complemented
558	#483	C₂²×C₃₁	1	2	yes	complemented
559	#482	C₂²×C₃₁	1	2	yes	—
560	#481	C₂²×C₃₁	1	2	yes	—
561	#479	C₂²×C₃₁	1	2	yes	complemented
562	#478	C₂²×C₃₁	1	2	yes	—
563	#477	C₂²×C₃₁	1	2	yes	complemented
564	#476	C₂²×C₃₁	1	2	yes	—
565	#475	C₂²×C₃₁	1	2	yes	complemented
566	#475	C₂²×C₃₁	1	2	yes	complemented
567	#470	C₂²×C₃₁	1	2	yes	—
568	#470	C₂²×C₃₁	1	2	yes	—
569	#470	C₂²×C₃₁	1	2	yes	complemented
570	#468	C₂²×C₃₁	1	2	yes	—
571	#467	C₂²×C₃₁	1	2	yes	complemented
572	#465	C₂²×C₃₁	1	2	yes	—
573	#464	C₂²×C₃₁	1	2	yes	—
574	#464	C₂²×C₃₁	1	2	yes	—
575	#464	C₂²×C₃₁	1	2	yes	—
576	#464	C₂²×C₃₁	1	2	yes	—
577	#462	C₂²×C₃₁	1	2	yes	complemented
578	#462	C₂²×C₃₁	1	2	yes	complemented
579	#452	C₂²×C₃₁	1	2	yes	—
580	#452	C₂²×C₃₁	1	2	yes	—
581	#451	C₂²×C₃₁	1	1	yes	characteristic
582	#451	C₂²×C₃₁	1	1	yes	characteristic
583	#451	C₂²×C₃₁	1	2	yes	complemented
584	#451	C₂²×C₃₁	1	2	yes	complemented
585	#450	C₂²×C₃₁	1	1	yes	characteristic
586	#450	C₂²×C₃₁	1	1	yes	characteristic
587	#446	C₂²×C₃₁	1	2	yes	complemented
588	#441	C₂²×C₃₁	1	2	yes	complemented
589	#441	C₂²×C₃₁	1	2	yes	complemented
590	#441	C₂²×C₃₁	1	2	yes	complemented
591	#440	C₂²×C₃₁	1	2	yes	—
592	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
593	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
594	#436	C₂²×C₃₁	1	2	yes	—
595	#435	C₂²×C₃₁	1	2	yes	—
596	#435	C₂²×C₃₁	1	2	yes	complemented
597	#433	C₂²×C₃₁	1	2	yes	complemented
598	#432	C₂²×C₃₁	1	1	yes	characteristic
599	#419	C₂²×C₃₁	1	2	yes	—
600	#419	C₂²×C₃₁	1	2	yes	complemented
601	#418	C₂²×C₃₁	1	2	yes	—
602	#417	C₂²×C₃₁	1	2	yes	—
603	#416	C₂²×C₃₁	1	2	yes	—
604	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
605	#405	C₂²×C₃₁	1	2	yes	complemented
606	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
607	C₂×C₃₁	—	4	2	no	—
608	C₂×C₃₁	—	4	1	no	—
609	C₂×C₃₁	—	8	2	no	—
610	C₂×C₃₁	#3500	1	1	yes	characteristic
611	C₂×C₃₁	#3586	1	1	yes	characteristic
612	C₂×C₃₁	#3586	1	1	yes	characteristic
613	C₂×#41	C₂³×C₃₁	1	2	yes	—
614	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
615	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
616	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
618	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
619	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
620	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
622	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
623	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
624	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
625	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
626	C₄⋊Q₈	—	2	1	no	—
627	C₄⋊Q₈	—	2	2	no	—
628	C₄⋊Q₈	—	2	2	no	—
629	C₄⋊Q₈	—	2	1	no	—
630	C₄⋊Q₈	—	2	2	no	—
631	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
633	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
634	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
635	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
636	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
637	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
638	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#126	—	2	2	no	—
643	#126	—	2	2	no	—
644	#126	—	2	2	no	—
645	#126	—	2	2	no	—
646	#126	—	2	2	no	—
647	#126	—	2	2	no	—
648	#126	D₄×C₃₁	1	2	yes	—
649	#125	—	2	2	no	—
650	#125	—	2	2	no	—
651	#125	—	2	2	no	—
652	#125	—	2	1	no	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	—	2	1	no	—
656	#125	—	2	1	no	—
657	#125	D₄×C₃₁	1	1	yes	characteristic
658	#125	C₂³×C₃₁	1	2	yes	—
659	#125	C₂³×C₃₁	1	2	yes	—
660	#124	—	2	1	no	—
661	#124	—	2	2	no	—
662	#124	—	2	2	no	—
663	#124	—	2	2	no	—
664	#124	—	2	1	no	—
665	#124	—	2	1	no	—
666	#124	D₄×C₃₁	1	1	yes	characteristic
667	#124	C₂³×C₃₁	1	2	yes	—
668	#124	C₂³×C₃₁	1	2	yes	—
669	#124	C₂³×C₃₁	1	2	yes	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	D₄×C₃₁	1	2	yes	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	1	no	—
678	C₂²⋊Q₈	—	2	1	no	—
679	C₂²⋊Q₈	—	2	1	no	—
680	C₂²⋊Q₈	—	2	1	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
691	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
692	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
693	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
694	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
696	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
697	#121	—	2	2	no	—
698	#121	—	2	2	no	—
699	#121	D₄×C₃₁	1	1	yes	characteristic
700	#121	C₂³×C₃₁	1	2	yes	—
701	#120	—	2	2	no	—
702	C₄×Q₈	—	2	1	no	—
703	C₄×Q₈	—	2	2	no	—
704	C₄×Q₈	—	2	1	no	—
705	C₄×Q₈	—	2	1	no	—
706	C₄×Q₈	—	2	1	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	—	2	1	no	—
710	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
711	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
712	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
714	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
715	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
716	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	C₂³×C₃₁	1	2	yes	—
721	C₄×D₄	C₂³×C₃₁	1	2	yes	—
722	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
723	#117	—	2	1	no	—
724	#117	—	2	1	no	—
725	#117	—	2	2	no	—
726	#117	—	2	2	no	—
727	#117	C₂³×C₃₁	1	2	yes	—
728	#117	C₂³×C₃₁	1	2	yes	—
729	#117	C₂³×C₃₁	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
731	C₂×C₂²⋊C₄	—	2	1	no	—
732	C₂×C₂²⋊C₄	—	2	1	no	—
733	C₂×C₂²⋊C₄	—	2	2	no	—
734	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
735	#107	C₂³×C₃₁	1	2	yes	—
736	#107	C₂³×C₃₁	1	2	yes	—
737	#106	C₂³×C₃₁	1	2	yes	—
738	#106	C₂³×C₃₁	1	2	yes	—
739	#106	C₂³×C₃₁	1	2	yes	—
740	#106	C₂³×C₃₁	1	2	yes	—
741	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
742	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
743	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
744	#103	C₂³×C₃₁	1	2	yes	—
745	#103	C₂³×C₃₁	1	2	yes	—
746	#103	C₂³×C₃₁	1	2	yes	—
747	#103	C₂³×C₃₁	1	2	yes	—
748	#103	C₂³×C₃₁	1	2	yes	—
749	#103	C₂³×C₃₁	1	2	yes	—
750	#103	C₂³×C₃₁	1	2	yes	—
751	#103	C₂³×C₃₁	1	2	yes	—
752	#103	C₂³×C₃₁	1	2	yes	—
753	#103	C₂³×C₃₁	1	2	yes	—
754	#103	C₂³×C₃₁	1	2	yes	—
755	#103	C₂³×C₃₁	1	2	yes	—
756	#103	C₂³×C₃₁	1	2	yes	—
757	#103	C₂³×C₃₁	1	2	yes	—
758	#102	C₂³×C₃₁	1	2	yes	—
759	#102	C₂³×C₃₁	1	2	yes	—
760	#102	C₂³×C₃₁	1	2	yes	—
761	#102	C₂³×C₃₁	1	2	yes	—
762	#102	C₂³×C₃₁	1	2	yes	—
763	#102	C₂³×C₃₁	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
766	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
768	#97	C₂³×C₃₁	1	2	yes	—
769	#97	C₂³×C₃₁	1	2	yes	—
770	#97	C₂³×C₃₁	1	2	yes	—
771	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
772	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
773	C₄×C₈	C₂³×C₃₁	1	2	yes	—
774	C₃₁	#62571	1	1	yes	characteristic, direct product factor, Sylow
775	C₂⁴	—	2	1	no	—
776	#41	—	4	2	no	—
777	#41	—	4	2	no	—
778	C₂×Q₈	—	2	1	no	—
779	C₂×Q₈	—	2	1	no	—
780	C₂×Q₈	—	2	1	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	2	2	no	—
783	C₂×Q₈	—	2	2	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	4	2	no	—
786	C₂×Q₈	—	4	2	no	—
787	C₂×Q₈	—	4	2	no	—
788	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
789	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
790	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
791	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	4	2	no	—
797	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
798	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
799	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
806	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
809	Q₁₆	—	4	2	no	—
810	Q₁₆	—	4	2	no	—
811	Q₁₆	—	4	2	no	—
812	Q₁₆	—	4	2	no	—
813	SD₁₆	—	4	2	no	—
814	SD₁₆	—	4	2	no	—
815	M₁₆	—	4	2	no	—
816	M₁₆	—	4	2	no	—
817	C₂×C₈	—	4	2	no	—
818	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
819	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
820	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
821	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
851	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
852	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
853	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
854	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
855	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
856	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
857	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
858	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
859	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
860	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	1	no	—
863	C₂²⋊C₄	—	2	1	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
878	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
879	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
880	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
881	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	1	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	1	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
891	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
892	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₄²	C₂⁴×C₃₁	1	2	yes	—
894	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂³	—	2	2	no	—
896	C₂³	—	4	2	no	—
897	C₂³	—	8	1	no	—
898	C₂³	—	8	1	no	—
899	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
900	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
901	Q₈	—	2	2	no	—
902	Q₈	—	2	2	no	—
903	Q₈	—	2	2	no	—
904	Q₈	—	2	2	no	—
905	Q₈	—	2	2	no	—
906	Q₈	—	2	2	no	—
907	Q₈	—	4	1	no	—
908	Q₈	—	4	2	no	—
909	Q₈	—	8	1	no	—
910	Q₈	—	8	1	no	—
911	Q₈	—	8	1	no	—
912	Q₈	—	8	2	no	—
913	Q₈	—	8	2	no	—
914	Q₈	—	8	1	no	—
915	D₄	—	2	2	no	—
916	D₄	—	2	2	no	—
917	D₄	—	4	1	no	—
918	D₄	—	4	2	no	—
919	D₄	—	8	1	no	—
920	D₄	—	8	2	no	—
921	D₄	—	8	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	8	2	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	—	8	2	no	—
940	C₂×C₄	—	8	1	no	—
941	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
942	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
943	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
944	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
945	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
946	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
947	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
949	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
950	C₈	—	2	2	no	—
951	C₈	—	2	2	no	—
952	C₈	—	2	2	no	—
953	C₈	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	16	2	no	—
964	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
965	C₄	—	2	2	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	1	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	1	no	—
982	C₄	C₃₁×#585	1	2	yes	—
983	C₂	—	4	1	no	—
984	C₂	—	4	2	no	—
985	C₂	—	8	2	no	—
986	C₂	C₃₁×#3500	1	1	yes	characteristic
987	C₂	C₃₁×#3586	1	1	yes	characteristic
988	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3561	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
2. C₃₁×#3555	C₂	semidirect
3. C₃₁×#3377	C₂	semidirect
4. C₃₁×#3369	C₂	semidirect
5. C₃₁×#3328	C₂	semidirect
6. C₃₁×#3323	C₂	semidirect
7. C₃₁×#3316	C₂	semidirect
8. C₃₁×#3313	C₂	semidirect
9. C₃₁×#3312	C₂	semidirect
10. C₃₁×#3311	C₂	semidirect
11. C₃₁×#3244	C₂	semidirect
12. C₃₁×#3237	C₂	semidirect
13. C₃₁×#3223	C₂	semidirect
14. C₃₁×#3215	C₂	semidirect
15. C₃₁×#3185	C₂	semidirect
16. C₃₁×#3178	C₂	semidirect
17. C₃₁×#3140	C₂	semidirect
18. C₃₁×#3137	C₂	semidirect
19. C₃₁×#2967	C₂	semidirect
23. Q₈²×C₃₁	C₂²	semidirect
25. C₃₁×#557	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
36. C₃₁×#544	C₂²	semidirect
43. C₃₁×#541	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#498	C₂²	semidirect
54. C₃₁×#494	C₂²	semidirect
55. C₃₁×#491	C₂²	semidirect
56. C₃₁×#491	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
69. C₃₁×#485	C₂²	semidirect
70. C₃₁×#483	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
78. C₃₁×#475	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
83. C₃₁×#467	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
95. C₃₁×#451	C₂²	semidirect
96. C₃₁×#451	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
100. C₃₁×#441	C₂²	semidirect
101. C₃₁×#441	C₂²	semidirect
102. C₃₁×#441	C₂²	semidirect
104. C₄×Q₁₆×C₃₁	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
112. C₃₁×#419	C₂²	semidirect
116. C₂×C₃₁×#103	C₂²	semidirect
117. C₃₁×#405	C₂²	semidirect
400. #62571	C₃₁	direct (N × H)
461. #3555	C₂×C₃₁	semidirect
462. #3377	C₂×C₃₁	semidirect
463. #3369	C₂×C₃₁	semidirect
464. #3328	C₂×C₃₁	semidirect
465. #3323	C₂×C₃₁	semidirect
466. #3316	C₂×C₃₁	semidirect
467. #3313	C₂×C₃₁	semidirect
468. #3312	C₂×C₃₁	semidirect
469. #3311	C₂×C₃₁	semidirect
470. #3244	C₂×C₃₁	semidirect
471. #3237	C₂×C₃₁	semidirect
472. #3223	C₂×C₃₁	semidirect
473. #3215	C₂×C₃₁	semidirect
474. #3185	C₂×C₃₁	semidirect
475. #3178	C₂×C₃₁	semidirect
476. #3140	C₂×C₃₁	semidirect
477. #3137	C₂×C₃₁	semidirect
478. #2967	C₂×C₃₁	semidirect
511. Q₈²	C₂²×C₃₁	semidirect
513. #557	C₂²×C₃₁	semidirect
517. #556	C₂²×C₃₁	semidirect
518. #554	C₂²×C₃₁	semidirect
524. #544	C₂²×C₃₁	semidirect
531. #541	C₂²×C₃₁	semidirect
539. #501	C₂²×C₃₁	semidirect
540. #498	C₂²×C₃₁	semidirect
542. #494	C₂²×C₃₁	semidirect
543. #491	C₂²×C₃₁	semidirect
544. #491	C₂²×C₃₁	semidirect
552. #487	C₂²×C₃₁	semidirect
553. #487	C₂²×C₃₁	semidirect
554. #487	C₂²×C₃₁	semidirect
557. #485	C₂²×C₃₁	semidirect
558. #483	C₂²×C₃₁	semidirect
561. #479	C₂²×C₃₁	semidirect
563. #477	C₂²×C₃₁	semidirect
565. #475	C₂²×C₃₁	semidirect
566. #475	C₂²×C₃₁	semidirect
569. #470	C₂²×C₃₁	semidirect
571. #467	C₂²×C₃₁	semidirect
577. #462	C₂²×C₃₁	semidirect
578. #462	C₂²×C₃₁	semidirect
583. #451	C₂²×C₃₁	semidirect
584. #451	C₂²×C₃₁	semidirect
587. #446	C₂²×C₃₁	semidirect
588. #441	C₂²×C₃₁	semidirect
589. #441	C₂²×C₃₁	semidirect
590. #441	C₂²×C₃₁	semidirect
592. C₄×Q₁₆	C₂²×C₃₁	semidirect
596. #435	C₂²×C₃₁	semidirect
597. #433	C₂²×C₃₁	semidirect
600. #419	C₂²×C₃₁	semidirect
604. C₂×#103	C₂²×C₃₁	semidirect
605. #405	C₂²×C₃₁	semidirect
774. C₃₁	#62571	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×#3561	2
C₃₁×#3555	2
C₃₁×#3377	2
C₃₁×#3369	2
C₃₁×#3328	2
C₃₁×#3323	2
C₃₁×#3316	2
C₃₁×#3313	2
C₃₁×#3312	2
C₃₁×#3311	2
C₃₁×#3244	2
C₃₁×#3237	2
C₃₁×#3223	2
C₃₁×#3215	2
C₃₁×#3185	2
C₃₁×#3178	2
C₃₁×#3140	2
C₃₁×#3137	2
C₃₁×#2967	2
#62571	31

Subgroups — C31×#62571 #21519330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62571 #21519330