Subgroups — C₃₁×#62020 #21518779

Order 7936.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1038 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×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3398	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
8	D₄×Q₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3266	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3249	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×#3121	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3044	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#137	C₂²	1	2	yes	—
21	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
23	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#563	—	2	1	no	—
25	C₃₁×#562	—	2	1	no	—
26	C₃₁×#557	—	2	1	no	—
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#556	—	2	1	no	—
30	C₃₁×#556	C₂²	1	2	yes	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#552	—	2	2	no	—
33	C₃₁×#552	C₂²	1	2	yes	—
34	C₃₁×#551	—	2	2	no	—
35	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
36	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#548	C₂²	1	2	yes	—
39	C₃₁×#546	C₂²	1	2	yes	—
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	—	2	2	no	—
42	C₃₁×#542	C₂²	1	2	yes	—
43	C₃₁×#541	—	2	2	no	—
44	C₃₁×#541	C₂²	1	2	yes	complemented
45	C₃₁×#538	—	2	1	no	—
46	C₃₁×#536	C₂²	1	2	yes	—
47	C₃₁×#533	—	2	1	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
53	C₃₁×#519	C₂²	1	2	yes	complemented
54	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
55	C₃₁×#497	C₂²	1	2	yes	—
56	C₃₁×#497	C₂²	1	2	yes	—
57	C₃₁×#494	C₂²	1	2	yes	complemented
58	C₃₁×#491	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#488	C₂²	1	2	yes	—
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#483	C₂²	1	2	yes	—
63	C₃₁×#482	C₂²	1	2	yes	—
64	C₃₁×#479	C₂²	1	2	yes	complemented
65	C₃₁×#478	C₂²	1	2	yes	—
66	C₃₁×#477	C₂²	1	2	yes	complemented
67	C₃₁×#477	C₂²	1	2	yes	complemented
68	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#470	C₂²	1	2	yes	complemented
71	C₃₁×#468	C₂²	1	2	yes	—
72	C₃₁×#467	C₂²	1	2	yes	—
73	C₃₁×#467	C₂²	1	2	yes	—
74	C₃₁×#467	C₂²	1	2	yes	complemented
75	C₃₁×#465	C₂²	1	2	yes	—
76	C₃₁×#464	C₂²	1	2	yes	—
77	C₃₁×#464	C₂²	1	2	yes	—
78	C₃₁×#464	C₂²	1	2	yes	—
79	C₃₁×#464	C₂²	1	2	yes	—
80	C₃₁×#464	C₂²	1	2	yes	—
81	C₃₁×#464	C₂²	1	2	yes	—
82	C₃₁×#464	C₂²	1	2	yes	—
83	C₃₁×#464	C₂²	1	2	yes	—
84	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#462	C₂²	1	2	yes	complemented
87	C₃₁×#462	C₂²	1	2	yes	complemented
88	C₃₁×#462	C₂²	1	2	yes	complemented
89	C₃₁×#462	C₂²	1	2	yes	complemented
90	C₃₁×#462	C₂²	1	2	yes	complemented
91	C₃₁×#461	C₂²	1	2	yes	—
92	C₃₁×#452	C₂²	1	2	yes	—
93	C₃₁×#452	C₂²	1	2	yes	—
94	C₃₁×#451	C₂²	1	2	yes	—
95	C₃₁×#451	C₂²	1	2	yes	—
96	C₃₁×#451	C₂²	1	2	yes	complemented
97	C₃₁×#451	C₂²	1	2	yes	complemented
98	C₃₁×#451	C₂²	1	2	yes	complemented
99	C₃₁×#450	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#441	C₂²	1	2	yes	complemented
103	C₃₁×#441	C₂²	1	2	yes	complemented
104	C₃₁×#441	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	—
106	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
108	C₃₁×#435	C₂²	1	2	yes	—
109	C₃₁×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₃₁	C₂²	1	2	yes	—
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#432	C₂²	1	1	yes	characteristic
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₃₁×#419	C₂²	1	2	yes	complemented
116	C₃₁×#416	C₂²	1	2	yes	—
117	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#102	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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
124	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₃₁×#137	—	4	4	no	—
126	C₂×Q₁₆×C₃₁	—	4	2	no	—
127	C₂×Q₁₆×C₃₁	—	4	4	no	—
128	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
135	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₃₁	—	4	2	no	—
137	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
145	C₃₁×C₄⋊Q₈	—	2	1	no	—
146	C₃₁×C₄⋊Q₈	—	2	1	no	—
147	C₃₁×C₄⋊Q₈	—	2	2	no	—
148	C₃₁×C₄⋊Q₈	—	2	2	no	—
149	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
150	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×#126	—	2	2	no	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	D₄	1	2	yes	—
163	C₃₁×#125	—	2	1	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	D₄	1	1	yes	characteristic
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#124	—	2	1	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	D₄	1	1	yes	characteristic
179	C₃₁×#124	C₂³	1	2	yes	—
180	C₃₁×#124	C₂³	1	2	yes	—
181	C₃₁×#124	C₂³	1	2	yes	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	D₄	1	2	yes	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	D₄	1	1	yes	characteristic
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#120	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	C₂³	1	2	yes	—
235	C₄×D₄×C₃₁	C₂³	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₃₁×#117	—	2	1	no	—
238	C₃₁×#117	—	2	1	no	—
239	C₃₁×#117	—	2	2	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	—	2	2	no	—
242	C₃₁×#117	—	2	2	no	—
243	C₃₁×#117	C₂³	1	2	yes	—
244	C₃₁×#117	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂×C₄²×C₃₁	—	2	1	no	—
251	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#107	C₂³	1	2	yes	—
253	C₃₁×#107	C₂³	1	2	yes	—
254	C₃₁×#106	C₂³	1	2	yes	—
255	C₃₁×#106	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
261	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#103	C₂³	1	2	yes	—
271	C₃₁×#103	C₂³	1	2	yes	—
272	C₃₁×#103	C₂³	1	2	yes	—
273	C₃₁×#103	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₃₁×#97	C₂³	1	2	yes	—
282	C₃₁×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₃₁	C₂³	1	2	yes	—
284	C₂⁴×C₃₁	—	2	1	no	—
285	#41×C₃₁	—	4	2	no	—
286	#41×C₃₁	—	4	2	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	2	2	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	2	1	no	—
291	C₂×Q₈×C₃₁	—	2	2	no	—
292	C₂×Q₈×C₃₁	—	2	1	no	—
293	C₂×Q₈×C₃₁	—	2	2	no	—
294	C₂×Q₈×C₃₁	—	2	4	no	—
295	C₂×Q₈×C₃₁	—	4	1	no	—
296	C₂×Q₈×C₃₁	—	4	2	no	—
297	C₂×Q₈×C₃₁	—	4	1	no	—
298	C₂×Q₈×C₃₁	—	4	2	no	—
299	C₂×Q₈×C₃₁	—	4	1	no	—
300	C₂×Q₈×C₃₁	—	4	2	no	—
301	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
306	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	1	no	—
310	C₂×D₄×C₃₁	—	4	1	no	—
311	C₂×D₄×C₃₁	—	4	1	no	—
312	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
313	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
314	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₃₁	—	2	1	no	—
316	C₂²×C₄×C₃₁	—	2	1	no	—
317	C₂²×C₄×C₃₁	—	2	2	no	—
318	C₂²×C₄×C₃₁	—	2	1	no	—
319	C₂²×C₄×C₃₁	—	2	2	no	—
320	C₂²×C₄×C₃₁	—	2	2	no	—
321	C₂²×C₄×C₃₁	—	2	2	no	—
322	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
326	Q₁₆×C₃₁	—	2	4	no	—
327	Q₁₆×C₃₁	—	2	4	no	—
328	Q₁₆×C₃₁	—	4	2	no	—
329	Q₁₆×C₃₁	—	4	2	no	—
330	Q₁₆×C₃₁	—	4	2	no	—
331	Q₁₆×C₃₁	—	4	2	no	—
332	Q₁₆×C₃₁	—	4	2	no	—
333	Q₁₆×C₃₁	—	4	2	no	—
334	SD₁₆×C₃₁	—	2	4	no	—
335	SD₁₆×C₃₁	—	4	2	no	—
336	SD₁₆×C₃₁	—	4	2	no	—
337	SD₁₆×C₃₁	—	4	2	no	—
338	M₁₆×C₃₁	—	4	2	no	—
339	C₂×C₈×C₃₁	—	4	1	no	—
340	C₂×C₈×C₃₁	—	4	1	no	—
341	C₂×C₈×C₃₁	—	4	2	no	—
342	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
343	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
344	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
345	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₃₁	—	2	1	no	—
347	C₄⋊C₄×C₃₁	—	2	1	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	1	no	—
350	C₄⋊C₄×C₃₁	—	2	1	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	1	no	—
356	C₄⋊C₄×C₃₁	—	2	1	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	1	no	—
359	C₄⋊C₄×C₃₁	—	2	1	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	1	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	1	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
382	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	—	2	2	no	—
397	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄²×C₃₁	—	2	1	no	—
403	C₄²×C₃₁	—	2	1	no	—
404	C₄²×C₃₁	—	2	1	no	—
405	C₄²×C₃₁	—	2	1	no	—
406	C₄²×C₃₁	—	2	2	no	—
407	C₄²×C₃₁	—	2	2	no	—
408	C₄²×C₃₁	—	2	2	no	—
409	C₄²×C₃₁	—	2	2	no	—
410	C₄²×C₃₁	—	2	2	no	—
411	C₄²×C₃₁	—	2	2	no	—
412	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
413	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₃₁	C₂⁴	1	2	yes	—
415	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
417	#62020	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
418	C₂³×C₃₁	—	2	2	no	—
419	C₂³×C₃₁	—	4	2	no	—
420	C₂³×C₃₁	—	8	1	no	—
421	C₂³×C₃₁	—	8	1	no	—
422	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
423	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
424	Q₈×C₃₁	—	2	1	no	—
425	Q₈×C₃₁	—	2	1	no	—
426	Q₈×C₃₁	—	2	2	no	—
427	Q₈×C₃₁	—	2	2	no	—
428	Q₈×C₃₁	—	2	2	no	—
429	Q₈×C₃₁	—	2	2	no	—
430	Q₈×C₃₁	—	2	1	no	—
431	Q₈×C₃₁	—	2	2	no	—
432	Q₈×C₃₁	—	2	2	no	—
433	Q₈×C₃₁	—	4	1	no	—
434	Q₈×C₃₁	—	4	4	no	—
435	Q₈×C₃₁	—	4	2	no	—
436	Q₈×C₃₁	—	4	2	no	—
437	Q₈×C₃₁	—	8	1	no	—
438	Q₈×C₃₁	—	8	2	no	—
439	Q₈×C₃₁	—	8	1	no	—
440	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
441	D₄×C₃₁	—	2	4	no	—
442	D₄×C₃₁	—	2	2	no	—
443	D₄×C₃₁	—	2	2	no	—
444	D₄×C₃₁	—	4	1	no	—
445	D₄×C₃₁	—	8	1	no	—
446	D₄×C₃₁	—	8	2	no	—
447	D₄×C₃₁	—	8	2	no	—
448	C₂×C₄×C₃₁	—	2	2	no	—
449	C₂×C₄×C₃₁	—	2	1	no	—
450	C₂×C₄×C₃₁	—	2	1	no	—
451	C₂×C₄×C₃₁	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	1	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	1	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	1	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	4	1	no	—
463	C₂×C₄×C₃₁	—	4	2	no	—
464	C₂×C₄×C₃₁	—	4	4	no	—
465	C₂×C₄×C₃₁	—	4	2	no	—
466	C₂×C₄×C₃₁	—	8	2	no	—
467	C₂×C₄×C₃₁	—	8	2	no	—
468	C₂×C₄×C₃₁	—	8	2	no	—
469	C₂×C₄×C₃₁	—	8	1	no	—
470	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
479	C₈×C₃₁	—	2	2	no	—
480	C₈×C₃₁	—	2	2	no	—
481	C₈×C₃₁	—	2	2	no	—
482	C₈×C₃₁	—	2	2	no	—
483	#3561	C₂×C₃₁	1	1	yes	characteristic
484	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#3398	C₂×C₃₁	1	2	yes	complemented
486	#3377	C₂×C₃₁	1	2	yes	complemented
487	#3313	C₂×C₃₁	1	2	yes	complemented
488	#3312	C₂×C₃₁	1	2	yes	complemented
489	#3296	C₂×C₃₁	1	2	yes	complemented
490	D₄×Q₁₆	C₂×C₃₁	1	2	yes	complemented
491	#3270	C₂×C₃₁	1	2	yes	complemented
492	#3266	C₂×C₃₁	1	2	yes	complemented
493	#3258	C₂×C₃₁	1	2	yes	complemented
494	#3249	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#3223	C₂×C₃₁	1	2	yes	complemented
496	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
497	#3121	C₂×C₃₁	1	2	yes	complemented
498	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#3044	C₂×C₃₁	1	2	yes	complemented
500	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
501	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
502	C₂²×C₃₁	—	2	1	no	—
503	C₂²×C₃₁	—	2	1	no	—
504	C₂²×C₃₁	—	2	2	no	—
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	2	2	no	—
507	C₂²×C₃₁	—	4	2	no	—
508	C₂²×C₃₁	—	4	2	no	—
509	C₂²×C₃₁	—	4	2	no	—
510	C₂²×C₃₁	—	16	2	no	—
511	C₂²×C₃₁	#578	1	2	yes	—
512	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₃₁	—	2	1	no	—
514	C₄×C₃₁	—	2	1	no	—
515	C₄×C₃₁	—	2	2	no	—
516	C₄×C₃₁	—	2	2	no	—
517	C₄×C₃₁	—	2	1	no	—
518	C₄×C₃₁	—	2	2	no	—
519	C₄×C₃₁	—	2	1	no	—
520	C₄×C₃₁	—	2	1	no	—
521	C₄×C₃₁	—	2	2	no	—
522	C₄×C₃₁	—	4	2	no	—
523	C₄×C₃₁	—	4	2	no	—
524	C₄×C₃₁	—	4	1	no	—
525	C₄×C₃₁	—	4	2	no	—
526	C₄×C₃₁	—	4	2	no	—
527	C₄×C₃₁	—	4	2	no	—
528	C₄×C₃₁	—	4	1	no	—
529	C₄×C₃₁	—	4	1	no	—
530	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₄×C₃₁	#585	1	1	yes	characteristic
532	C₂×#137	C₂²×C₃₁	1	2	yes	—
533	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
534	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
535	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
536	#563	—	2	1	no	—
537	#562	—	2	1	no	—
538	#557	—	2	1	no	—
539	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
540	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
541	#556	—	2	1	no	—
542	#556	C₂²×C₃₁	1	2	yes	—
543	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
544	#552	—	2	2	no	—
545	#552	C₂²×C₃₁	1	2	yes	—
546	#551	—	2	2	no	—
547	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
548	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
549	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
550	#548	C₂²×C₃₁	1	2	yes	—
551	#546	C₂²×C₃₁	1	2	yes	—
552	#543	—	2	1	no	—
553	#542	—	2	2	no	—
554	#542	C₂²×C₃₁	1	2	yes	—
555	#541	—	2	2	no	—
556	#541	C₂²×C₃₁	1	2	yes	complemented
557	#538	—	2	1	no	—
558	#536	C₂²×C₃₁	1	2	yes	—
559	#533	—	2	1	no	—
560	#533	C₂²×C₃₁	1	1	yes	characteristic
561	#533	C₂²×C₃₁	1	1	yes	characteristic
562	#529	—	2	1	no	—
563	#529	C₂²×C₃₁	1	1	yes	characteristic
564	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
565	#519	C₂²×C₃₁	1	2	yes	complemented
566	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
567	#497	C₂²×C₃₁	1	2	yes	—
568	#497	C₂²×C₃₁	1	2	yes	—
569	#494	C₂²×C₃₁	1	2	yes	complemented
570	#491	C₂²×C₃₁	1	2	yes	complemented
571	#489	C₂²×C₃₁	1	2	yes	—
572	#488	C₂²×C₃₁	1	2	yes	—
573	#485	C₂²×C₃₁	1	2	yes	complemented
574	#483	C₂²×C₃₁	1	2	yes	—
575	#482	C₂²×C₃₁	1	2	yes	—
576	#479	C₂²×C₃₁	1	2	yes	complemented
577	#478	C₂²×C₃₁	1	2	yes	—
578	#477	C₂²×C₃₁	1	2	yes	complemented
579	#477	C₂²×C₃₁	1	2	yes	complemented
580	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
581	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	#470	C₂²×C₃₁	1	2	yes	complemented
583	#468	C₂²×C₃₁	1	2	yes	—
584	#467	C₂²×C₃₁	1	2	yes	—
585	#467	C₂²×C₃₁	1	2	yes	—
586	#467	C₂²×C₃₁	1	2	yes	complemented
587	#465	C₂²×C₃₁	1	2	yes	—
588	#464	C₂²×C₃₁	1	2	yes	—
589	#464	C₂²×C₃₁	1	2	yes	—
590	#464	C₂²×C₃₁	1	2	yes	—
591	#464	C₂²×C₃₁	1	2	yes	—
592	#464	C₂²×C₃₁	1	2	yes	—
593	#464	C₂²×C₃₁	1	2	yes	—
594	#464	C₂²×C₃₁	1	2	yes	—
595	#464	C₂²×C₃₁	1	2	yes	—
596	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
597	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#462	C₂²×C₃₁	1	2	yes	complemented
599	#462	C₂²×C₃₁	1	2	yes	complemented
600	#462	C₂²×C₃₁	1	2	yes	complemented
601	#462	C₂²×C₃₁	1	2	yes	complemented
602	#462	C₂²×C₃₁	1	2	yes	complemented
603	#461	C₂²×C₃₁	1	2	yes	—
604	#452	C₂²×C₃₁	1	2	yes	—
605	#452	C₂²×C₃₁	1	2	yes	—
606	#451	C₂²×C₃₁	1	2	yes	—
607	#451	C₂²×C₃₁	1	2	yes	—
608	#451	C₂²×C₃₁	1	2	yes	complemented
609	#451	C₂²×C₃₁	1	2	yes	complemented
610	#451	C₂²×C₃₁	1	2	yes	complemented
611	#450	C₂²×C₃₁	1	2	yes	—
612	#448	C₂²×C₃₁	1	2	yes	—
613	#446	C₂²×C₃₁	1	2	yes	complemented
614	#441	C₂²×C₃₁	1	2	yes	complemented
615	#441	C₂²×C₃₁	1	2	yes	complemented
616	#441	C₂²×C₃₁	1	2	yes	complemented
617	#440	C₂²×C₃₁	1	2	yes	—
618	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
619	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
620	#435	C₂²×C₃₁	1	2	yes	—
621	#435	C₂²×C₃₁	1	2	yes	complemented
622	C₈×D₄	C₂²×C₃₁	1	2	yes	—
623	#433	C₂²×C₃₁	1	2	yes	complemented
624	#432	C₂²×C₃₁	1	1	yes	characteristic
625	#424	C₂²×C₃₁	1	2	yes	complemented
626	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
627	#419	C₂²×C₃₁	1	2	yes	complemented
628	#416	C₂²×C₃₁	1	2	yes	—
629	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
630	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
631	C₂×C₃₁	—	2	2	no	—
632	C₂×C₃₁	—	4	2	no	—
633	C₂×C₃₁	—	8	2	no	—
634	C₂×C₃₁	#3488	1	1	yes	characteristic
635	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
636	C₂×C₃₁	#3586	1	1	yes	characteristic
637	C₂×#41	C₂³×C₃₁	1	2	yes	—
638	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
639	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
640	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
641	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
642	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
643	#137	—	4	4	no	—
644	C₂×Q₁₆	—	4	2	no	—
645	C₂×Q₁₆	—	4	4	no	—
646	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
647	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
648	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
649	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
650	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
651	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
652	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
653	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
654	C₂×SD₁₆	—	4	2	no	—
655	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
656	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
657	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
658	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
659	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
660	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
661	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
662	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
663	C₄⋊Q₈	—	2	1	no	—
664	C₄⋊Q₈	—	2	1	no	—
665	C₄⋊Q₈	—	2	2	no	—
666	C₄⋊Q₈	—	2	2	no	—
667	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
668	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
669	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
670	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
671	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
672	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
673	#126	—	2	2	no	—
674	#126	—	2	2	no	—
675	#126	—	2	2	no	—
676	#126	—	2	2	no	—
677	#126	—	2	2	no	—
678	#126	—	2	2	no	—
679	#126	—	2	2	no	—
680	#126	D₄×C₃₁	1	2	yes	—
681	#125	—	2	1	no	—
682	#125	—	2	2	no	—
683	#125	—	2	2	no	—
684	#125	—	2	2	no	—
685	#125	—	2	2	no	—
686	#125	—	2	2	no	—
687	#125	—	2	1	no	—
688	#125	—	2	1	no	—
689	#125	D₄×C₃₁	1	1	yes	characteristic
690	#125	C₂³×C₃₁	1	2	yes	—
691	#124	—	2	1	no	—
692	#124	—	2	2	no	—
693	#124	—	2	2	no	—
694	#124	—	2	1	no	—
695	#124	—	2	1	no	—
696	#124	D₄×C₃₁	1	1	yes	characteristic
697	#124	C₂³×C₃₁	1	2	yes	—
698	#124	C₂³×C₃₁	1	2	yes	—
699	#124	C₂³×C₃₁	1	2	yes	—
700	#123	—	2	2	no	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	D₄×C₃₁	1	2	yes	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	—	2	1	no	—
708	C₂²⋊Q₈	—	2	1	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
719	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
720	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
721	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
722	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
723	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	D₄×C₃₁	1	1	yes	characteristic
727	#121	C₂³×C₃₁	1	2	yes	—
728	#120	—	2	2	no	—
729	C₄×Q₈	—	2	1	no	—
730	C₄×Q₈	—	2	2	no	—
731	C₄×Q₈	—	2	2	no	—
732	C₄×Q₈	—	2	1	no	—
733	C₄×Q₈	—	2	1	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
742	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
743	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
744	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
745	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
746	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
747	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
748	C₄×D₄	—	2	2	no	—
749	C₄×D₄	—	2	1	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	C₂³×C₃₁	1	2	yes	—
753	C₄×D₄	C₂³×C₃₁	1	2	yes	—
754	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
755	#117	—	2	1	no	—
756	#117	—	2	1	no	—
757	#117	—	2	2	no	—
758	#117	—	2	2	no	—
759	#117	—	2	2	no	—
760	#117	—	2	2	no	—
761	#117	C₂³×C₃₁	1	2	yes	—
762	#117	C₂³×C₃₁	1	2	yes	—
763	C₂×C₄⋊C₄	—	2	1	no	—
764	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	—	2	1	no	—
766	C₂×C₂²⋊C₄	—	2	1	no	—
767	C₂×C₂²⋊C₄	—	2	2	no	—
768	C₂×C₄²	—	2	1	no	—
769	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
770	#107	C₂³×C₃₁	1	2	yes	—
771	#107	C₂³×C₃₁	1	2	yes	—
772	#106	C₂³×C₃₁	1	2	yes	—
773	#106	C₂³×C₃₁	1	2	yes	—
774	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
775	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
776	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
778	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
779	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
780	#103	C₂³×C₃₁	1	2	yes	—
781	#103	C₂³×C₃₁	1	2	yes	—
782	#103	C₂³×C₃₁	1	2	yes	—
783	#103	C₂³×C₃₁	1	2	yes	—
784	#103	C₂³×C₃₁	1	2	yes	—
785	#103	C₂³×C₃₁	1	2	yes	—
786	#103	C₂³×C₃₁	1	2	yes	—
787	#103	C₂³×C₃₁	1	2	yes	—
788	#103	C₂³×C₃₁	1	2	yes	—
789	#103	C₂³×C₃₁	1	2	yes	—
790	#103	C₂³×C₃₁	1	2	yes	—
791	#103	C₂³×C₃₁	1	2	yes	—
792	#102	C₂³×C₃₁	1	2	yes	—
793	#102	C₂³×C₃₁	1	2	yes	—
794	#102	C₂³×C₃₁	1	2	yes	—
795	#102	C₂³×C₃₁	1	2	yes	—
796	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
797	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
798	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
799	#97	C₂³×C₃₁	1	2	yes	—
800	#97	C₂³×C₃₁	1	2	yes	—
801	C₄×C₈	C₂³×C₃₁	1	2	yes	—
802	C₃₁	#62020	1	1	yes	characteristic, direct product factor, Sylow
803	C₂⁴	—	2	1	no	—
804	#41	—	4	2	no	—
805	#41	—	4	2	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	2	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	2	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	2	no	—
813	C₂×Q₈	—	2	4	no	—
814	C₂×Q₈	—	4	1	no	—
815	C₂×Q₈	—	4	2	no	—
816	C₂×Q₈	—	4	1	no	—
817	C₂×Q₈	—	4	2	no	—
818	C₂×Q₈	—	4	1	no	—
819	C₂×Q₈	—	4	2	no	—
820	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
821	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
822	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
823	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
824	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
825	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	4	1	no	—
830	C₂×D₄	—	4	1	no	—
831	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
832	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
833	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
842	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
845	Q₁₆	—	2	4	no	—
846	Q₁₆	—	2	4	no	—
847	Q₁₆	—	4	2	no	—
848	Q₁₆	—	4	2	no	—
849	Q₁₆	—	4	2	no	—
850	Q₁₆	—	4	2	no	—
851	Q₁₆	—	4	2	no	—
852	Q₁₆	—	4	2	no	—
853	SD₁₆	—	2	4	no	—
854	SD₁₆	—	4	2	no	—
855	SD₁₆	—	4	2	no	—
856	SD₁₆	—	4	2	no	—
857	M₁₆	—	4	2	no	—
858	C₂×C₈	—	4	1	no	—
859	C₂×C₈	—	4	1	no	—
860	C₂×C₈	—	4	2	no	—
861	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
862	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
863	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
864	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
893	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
894	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
895	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
896	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
898	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
900	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
901	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
917	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
918	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
919	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
920	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
921	C₄²	—	2	1	no	—
922	C₄²	—	2	1	no	—
923	C₄²	—	2	1	no	—
924	C₄²	—	2	1	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	2	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	2	2	no	—
931	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
933	C₄²	C₂⁴×C₃₁	1	2	yes	—
934	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂³	—	2	2	no	—
937	C₂³	—	4	2	no	—
938	C₂³	—	8	1	no	—
939	C₂³	—	8	1	no	—
940	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
941	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
942	Q₈	—	2	1	no	—
943	Q₈	—	2	1	no	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	2	2	no	—
948	Q₈	—	2	1	no	—
949	Q₈	—	2	2	no	—
950	Q₈	—	2	2	no	—
951	Q₈	—	4	1	no	—
952	Q₈	—	4	4	no	—
953	Q₈	—	4	2	no	—
954	Q₈	—	4	2	no	—
955	Q₈	—	8	1	no	—
956	Q₈	—	8	2	no	—
957	Q₈	—	8	1	no	—
958	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
959	D₄	—	2	4	no	—
960	D₄	—	2	2	no	—
961	D₄	—	2	2	no	—
962	D₄	—	4	1	no	—
963	D₄	—	8	1	no	—
964	D₄	—	8	2	no	—
965	D₄	—	8	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	2	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	2	no	—
984	C₂×C₄	—	8	2	no	—
985	C₂×C₄	—	8	2	no	—
986	C₂×C₄	—	8	2	no	—
987	C₂×C₄	—	8	1	no	—
988	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
989	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
991	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
992	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
993	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
994	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
995	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
996	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
997	C₈	—	2	2	no	—
998	C₈	—	2	2	no	—
999	C₈	—	2	2	no	—
1000	C₈	—	2	2	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	16	2	no	—
1010	C₂²	C₃₁×#578	1	2	yes	—
1011	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1012	C₄	—	2	2	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1030	C₄	C₃₁×#585	1	1	yes	characteristic
1031	C₂	—	2	2	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	8	2	no	—
1034	C₂	C₃₁×#3488	1	1	yes	characteristic
1035	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1036	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×#3523	C₂	semidirect
3. C₃₁×#3398	C₂	semidirect
4. C₃₁×#3377	C₂	semidirect
5. C₃₁×#3313	C₂	semidirect
6. C₃₁×#3312	C₂	semidirect
7. C₃₁×#3296	C₂	semidirect
8. D₄×Q₁₆×C₃₁	C₂	semidirect
9. C₃₁×#3270	C₂	semidirect
10. C₃₁×#3266	C₂	semidirect
11. C₃₁×#3258	C₂	semidirect
12. C₃₁×#3249	C₂	semidirect
13. C₃₁×#3223	C₂	semidirect
14. C₃₁×#3215	C₂	semidirect
15. C₃₁×#3121	C₂	semidirect
16. C₃₁×#3113	C₂	semidirect
17. C₃₁×#3044	C₂	semidirect
18. C₂×C₃₁×#464	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
22. C₂²×Q₁₆×C₃₁	C₂²	semidirect
27. C₃₁×#557	C₂²	semidirect
28. C₃₁×#557	C₂²	semidirect
31. C₃₁×#556	C₂²	semidirect
37. D₄×Q₈×C₃₁	C₂²	semidirect
44. C₃₁×#541	C₂²	semidirect
53. C₃₁×#519	C₂²	semidirect
57. C₃₁×#494	C₂²	semidirect
58. C₃₁×#491	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
64. C₃₁×#479	C₂²	semidirect
66. C₃₁×#477	C₂²	semidirect
67. C₃₁×#477	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
69. C₃₁×#475	C₂²	semidirect
70. C₃₁×#470	C₂²	semidirect
74. C₃₁×#467	C₂²	semidirect
84. C₃₁×#462	C₂²	semidirect
85. C₃₁×#462	C₂²	semidirect
86. C₃₁×#462	C₂²	semidirect
87. C₃₁×#462	C₂²	semidirect
88. C₃₁×#462	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
96. C₃₁×#451	C₂²	semidirect
97. C₃₁×#451	C₂²	semidirect
98. C₃₁×#451	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#441	C₂²	semidirect
103. C₃₁×#441	C₂²	semidirect
104. C₃₁×#441	C₂²	semidirect
106. C₄×Q₁₆×C₃₁	C₂²	semidirect
109. C₃₁×#435	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
115. C₃₁×#419	C₂²	semidirect
417. #62020	C₃₁	direct (N × H)
484. #3523	C₂×C₃₁	semidirect
485. #3398	C₂×C₃₁	semidirect
486. #3377	C₂×C₃₁	semidirect
487. #3313	C₂×C₃₁	semidirect
488. #3312	C₂×C₃₁	semidirect
489. #3296	C₂×C₃₁	semidirect
490. D₄×Q₁₆	C₂×C₃₁	semidirect
491. #3270	C₂×C₃₁	semidirect
492. #3266	C₂×C₃₁	semidirect
493. #3258	C₂×C₃₁	semidirect
494. #3249	C₂×C₃₁	semidirect
495. #3223	C₂×C₃₁	semidirect
496. #3215	C₂×C₃₁	semidirect
497. #3121	C₂×C₃₁	semidirect
498. #3113	C₂×C₃₁	semidirect
499. #3044	C₂×C₃₁	semidirect
500. C₂×#464	C₂×C₃₁	semidirect
501. #2992	C₂×C₃₁	semidirect
534. C₂²×Q₁₆	C₂²×C₃₁	semidirect
539. #557	C₂²×C₃₁	semidirect
540. #557	C₂²×C₃₁	semidirect
543. #556	C₂²×C₃₁	semidirect
549. D₄×Q₈	C₂²×C₃₁	semidirect
556. #541	C₂²×C₃₁	semidirect
565. #519	C₂²×C₃₁	semidirect
569. #494	C₂²×C₃₁	semidirect
570. #491	C₂²×C₃₁	semidirect
573. #485	C₂²×C₃₁	semidirect
576. #479	C₂²×C₃₁	semidirect
578. #477	C₂²×C₃₁	semidirect
579. #477	C₂²×C₃₁	semidirect
580. #475	C₂²×C₃₁	semidirect
581. #475	C₂²×C₃₁	semidirect
582. #470	C₂²×C₃₁	semidirect
586. #467	C₂²×C₃₁	semidirect
596. #462	C₂²×C₃₁	semidirect
597. #462	C₂²×C₃₁	semidirect
598. #462	C₂²×C₃₁	semidirect
599. #462	C₂²×C₃₁	semidirect
600. #462	C₂²×C₃₁	semidirect
601. #462	C₂²×C₃₁	semidirect
602. #462	C₂²×C₃₁	semidirect
608. #451	C₂²×C₃₁	semidirect
609. #451	C₂²×C₃₁	semidirect
610. #451	C₂²×C₃₁	semidirect
613. #446	C₂²×C₃₁	semidirect
614. #441	C₂²×C₃₁	semidirect
615. #441	C₂²×C₃₁	semidirect
616. #441	C₂²×C₃₁	semidirect
618. C₄×Q₁₆	C₂²×C₃₁	semidirect
621. #435	C₂²×C₃₁	semidirect
623. #433	C₂²×C₃₁	semidirect
625. #424	C₂²×C₃₁	semidirect
627. #419	C₂²×C₃₁	semidirect
802. C₃₁	#62020	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×#3523	2
C₃₁×#3398	2
C₃₁×#3377	2
C₃₁×#3313	2
C₃₁×#3312	2
C₃₁×#3296	2
D₄×Q₁₆×C₃₁	2
C₃₁×#3270	2
C₃₁×#3266	2
C₃₁×#3258	2
C₃₁×#3249	2
C₃₁×#3223	2
C₃₁×#3215	2
C₃₁×#3121	2
C₃₁×#3113	2
C₃₁×#3044	2
C₂×C₃₁×#464	2
C₃₁×#2992	2
#62020	31

Subgroups — C31×#62020 #21518779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62020 #21518779