Subgroups — C₃₁×#62559 #21519318

Order 7936.

1666 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3561	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3236	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×#3178	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#488	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#564	—	2	1	no	—
21	C₃₁×#563	—	2	1	no	—
22	C₃₁×#563	—	2	1	no	—
23	C₃₁×#562	—	2	1	no	—
24	C₃₁×#557	C₂²	1	2	yes	complemented
25	C₃₁×#556	C₂²	1	2	yes	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	C₃₁×#552	—	2	2	no	—
28	C₃₁×#552	C₂²	1	2	yes	—
29	C₃₁×#552	C₂²	1	2	yes	complemented
30	C₃₁×#551	—	2	2	no	—
31	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
32	C₃₁×#548	C₂²	1	2	yes	—
33	C₃₁×#546	C₂²	1	2	yes	—
34	C₃₁×#544	—	2	1	no	—
35	C₃₁×#544	C₂²	1	2	yes	complemented
36	C₃₁×#543	—	2	1	no	—
37	C₃₁×#542	—	2	2	no	—
38	C₃₁×#542	C₂²	1	2	yes	—
39	C₃₁×#541	—	2	2	no	—
40	C₃₁×#541	C₂²	1	2	yes	complemented
41	C₃₁×#539	—	2	1	no	—
42	C₃₁×#538	—	2	1	no	—
43	C₃₁×#536	C₂²	1	2	yes	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#529	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
49	C₃₁×#501	C₂²	1	2	yes	complemented
50	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#497	C₂²	1	2	yes	—
52	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#491	C₂²	1	2	yes	complemented
54	C₃₁×#491	C₂²	1	2	yes	complemented
55	C₃₁×#489	C₂²	1	2	yes	—
56	C₃₁×#489	C₂²	1	2	yes	—
57	C₃₁×#488	C₂²	1	2	yes	—
58	C₃₁×#488	C₂²	1	2	yes	—
59	C₃₁×#488	C₂²	1	2	yes	—
60	C₃₁×#488	C₂²	1	2	yes	—
61	C₃₁×#488	C₂²	1	2	yes	—
62	C₃₁×#487	C₂²	1	2	yes	complemented
63	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#484	C₂²	1	2	yes	—
67	C₃₁×#484	C₂²	1	2	yes	complemented
68	C₃₁×#483	C₂²	1	2	yes	—
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#480	C₂²	1	2	yes	—
71	C₃₁×#479	C₂²	1	2	yes	complemented
72	C₃₁×#479	C₂²	1	2	yes	complemented
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×#474	C₂²	1	2	yes	—
77	C₃₁×#470	C₂²	1	2	yes	complemented
78	C₃₁×#468	C₂²	1	2	yes	—
79	C₃₁×#467	C₂²	1	2	yes	—
80	C₃₁×#467	C₂²	1	2	yes	—
81	C₃₁×#467	C₂²	1	2	yes	complemented
82	C₃₁×#465	C₂²	1	2	yes	—
83	C₃₁×#464	C₂²	1	2	yes	—
84	C₃₁×#464	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	2	yes	—
86	C₃₁×#464	C₂²	1	2	yes	—
87	C₃₁×#462	C₂²	1	2	yes	complemented
88	C₃₁×#462	C₂²	1	2	yes	complemented
89	C₃₁×#452	C₂²	1	2	yes	—
90	C₃₁×#452	C₂²	1	2	yes	—
91	C₃₁×#451	C₂²	1	2	yes	—
92	C₃₁×#451	C₂²	1	2	yes	complemented
93	C₃₁×#451	C₂²	1	2	yes	complemented
94	C₃₁×#450	C₂²	1	2	yes	—
95	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
96	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#441	C₂²	1	2	yes	complemented
98	C₃₁×#440	C₂²	1	2	yes	—
99	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
103	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#435	C₂²	1	2	yes	—
105	C₈×D₄×C₃₁	C₂²	1	2	yes	—
106	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#433	C₂²	1	2	yes	complemented
108	C₃₁×#432	C₂²	1	1	yes	characteristic
109	C₃₁×#419	C₂²	1	2	yes	complemented
110	C₃₁×#417	C₂²	1	2	yes	—
111	C₃₁×#416	C₂²	1	2	yes	—
112	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
113	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
114	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
115	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
116	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
117	C₃₁×#405	C₂²	1	2	yes	complemented
118	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	C₂³	1	2	yes	—
120	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
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	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
133	C₃₁×C₄⋊Q₈	—	2	2	no	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
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	D₄	1	2	yes	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	—	2	2	no	—
154	C₃₁×#125	—	2	2	no	—
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	1	no	—
160	C₃₁×#125	—	2	1	no	—
161	C₃₁×#125	—	2	1	no	—
162	C₃₁×#125	D₄	1	1	yes	characteristic
163	C₃₁×#125	C₂³	1	2	yes	—
164	C₃₁×#125	C₂³	1	2	yes	—
165	C₃₁×#125	C₂³	1	2	yes	—
166	C₃₁×#124	—	2	2	no	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	1	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	D₄	1	1	yes	characteristic
171	C₃₁×#124	C₂³	1	2	yes	—
172	C₃₁×#124	C₂³	1	2	yes	—
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	2	no	—
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	D₄	1	2	yes	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	1	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	D₄	1	1	yes	characteristic
203	C₃₁×#121	C₂³	1	2	yes	—
204	C₃₁×#120	—	2	2	no	—
205	C₄×Q₈×C₃₁	—	2	2	no	—
206	C₄×Q₈×C₃₁	—	2	1	no	—
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	—	2	2	no	—
217	C₄×D₄×C₃₁	C₂³	1	2	yes	—
218	C₄×D₄×C₃₁	C₂³	1	2	yes	—
219	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
220	C₃₁×#117	—	2	1	no	—
221	C₃₁×#117	—	2	1	no	—
222	C₃₁×#117	—	2	2	no	—
223	C₃₁×#117	—	2	2	no	—
224	C₃₁×#117	—	2	2	no	—
225	C₃₁×#117	C₂³	1	2	yes	—
226	C₃₁×#117	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
228	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
233	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
234	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
235	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
236	C₃₁×#107	C₂³	1	2	yes	—
237	C₃₁×#107	C₂³	1	2	yes	—
238	C₃₁×#107	C₂³	1	2	yes	—
239	C₃₁×#107	C₂³	1	2	yes	—
240	C₃₁×#106	C₂³	1	2	yes	—
241	C₃₁×#106	C₂³	1	2	yes	—
242	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
243	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
244	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
245	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#103	C₂³	1	2	yes	—
249	C₃₁×#103	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×#102	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×#102	C₂³	1	2	yes	—
263	C₃₁×#102	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
269	C₃₁×#97	C₂³	1	2	yes	—
270	C₃₁×#97	C₂³	1	2	yes	—
271	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
272	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
273	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
274	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
275	C₄×C₈×C₃₁	C₂³	1	2	yes	—
276	C₂⁴×C₃₁	—	2	1	no	—
277	#41×C₃₁	—	4	2	no	—
278	#41×C₃₁	—	4	2	no	—
279	C₂×Q₈×C₃₁	—	2	1	no	—
280	C₂×Q₈×C₃₁	—	2	1	no	—
281	C₂×Q₈×C₃₁	—	2	2	no	—
282	C₂×Q₈×C₃₁	—	2	2	no	—
283	C₂×Q₈×C₃₁	—	2	1	no	—
284	C₂×Q₈×C₃₁	—	4	1	no	—
285	C₂×Q₈×C₃₁	—	4	1	no	—
286	C₂×Q₈×C₃₁	—	4	2	no	—
287	C₂×Q₈×C₃₁	—	4	2	no	—
288	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
289	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
290	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
291	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
292	C₂×D₄×C₃₁	—	2	2	no	—
293	C₂×D₄×C₃₁	—	2	2	no	—
294	C₂×D₄×C₃₁	—	2	1	no	—
295	C₂×D₄×C₃₁	—	4	1	no	—
296	C₂×D₄×C₃₁	—	4	1	no	—
297	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₃₁	—	2	1	no	—
301	C₂²×C₄×C₃₁	—	2	1	no	—
302	C₂²×C₄×C₃₁	—	2	1	no	—
303	C₂²×C₄×C₃₁	—	2	2	no	—
304	C₂²×C₄×C₃₁	—	2	2	no	—
305	C₂²×C₄×C₃₁	—	2	2	no	—
306	C₂²×C₄×C₃₁	—	2	2	no	—
307	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
311	Q₁₆×C₃₁	—	4	2	no	—
312	Q₁₆×C₃₁	—	4	2	no	—
313	Q₁₆×C₃₁	—	4	2	no	—
314	Q₁₆×C₃₁	—	4	2	no	—
315	SD₁₆×C₃₁	—	4	2	no	—
316	SD₁₆×C₃₁	—	4	2	no	—
317	M₁₆×C₃₁	—	4	2	no	—
318	C₂×C₈×C₃₁	—	4	2	no	—
319	C₂×C₈×C₃₁	—	4	1	no	—
320	C₂×C₈×C₃₁	—	4	1	no	—
321	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
335	C₄⋊C₄×C₃₁	—	2	1	no	—
336	C₄⋊C₄×C₃₁	—	2	1	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	1	no	—
341	C₄⋊C₄×C₃₁	—	2	1	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	2	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	1	no	—
350	C₄⋊C₄×C₃₁	—	2	2	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	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	2	yes	—
362	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₂²⋊C₄×C₃₁	—	2	2	no	—
366	C₂²⋊C₄×C₃₁	—	2	2	no	—
367	C₂²⋊C₄×C₃₁	—	2	2	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	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	C₂×D₄	1	2	yes	—
380	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
384	C₄²×C₃₁	—	2	2	no	—
385	C₄²×C₃₁	—	2	2	no	—
386	C₄²×C₃₁	—	2	2	no	—
387	C₄²×C₃₁	—	2	2	no	—
388	C₄²×C₃₁	—	2	2	no	—
389	C₄²×C₃₁	—	2	2	no	—
390	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₄²×C₃₁	C₂⁴	1	2	yes	—
395	#62559	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂³×C₃₁	—	2	2	no	—
397	C₂³×C₃₁	—	4	2	no	—
398	C₂³×C₃₁	—	8	1	no	—
399	C₂³×C₃₁	—	8	1	no	—
400	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
401	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	Q₈×C₃₁	—	2	2	no	—
403	Q₈×C₃₁	—	2	2	no	—
404	Q₈×C₃₁	—	2	2	no	—
405	Q₈×C₃₁	—	2	2	no	—
406	Q₈×C₃₁	—	2	2	no	—
407	Q₈×C₃₁	—	2	2	no	—
408	Q₈×C₃₁	—	4	1	no	—
409	Q₈×C₃₁	—	8	1	no	—
410	Q₈×C₃₁	—	8	1	no	—
411	Q₈×C₃₁	—	8	2	no	—
412	Q₈×C₃₁	—	8	2	no	—
413	Q₈×C₃₁	—	8	1	no	—
414	D₄×C₃₁	—	2	4	no	—
415	D₄×C₃₁	—	2	2	no	—
416	D₄×C₃₁	—	2	2	no	—
417	D₄×C₃₁	—	4	1	no	—
418	D₄×C₃₁	—	8	1	no	—
419	D₄×C₃₁	—	8	2	no	—
420	D₄×C₃₁	—	8	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	1	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	2	no	—
427	C₂×C₄×C₃₁	—	2	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	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	4	1	no	—
434	C₂×C₄×C₃₁	—	4	2	no	—
435	C₂×C₄×C₃₁	—	8	2	no	—
436	C₂×C₄×C₃₁	—	8	2	no	—
437	C₂×C₄×C₃₁	—	8	1	no	—
438	C₂×C₄×C₃₁	—	8	2	no	—
439	C₂×C₄×C₃₁	—	8	2	no	—
440	C₂×C₄×C₃₁	—	8	1	no	—
441	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
450	C₈×C₃₁	—	2	1	no	—
451	C₈×C₃₁	—	2	1	no	—
452	C₈×C₃₁	—	2	2	no	—
453	C₈×C₃₁	—	2	1	no	—
454	C₈×C₃₁	—	2	1	no	—
455	C₈×C₃₁	—	2	2	no	—
456	#3563	C₂×C₃₁	1	1	yes	characteristic, complemented
457	#3561	C₂×C₃₁	1	1	yes	characteristic
458	#3377	C₂×C₃₁	1	2	yes	complemented
459	#3364	C₂×C₃₁	1	2	yes	complemented
460	#3327	C₂×C₃₁	1	2	yes	complemented
461	#3314	C₂×C₃₁	1	2	yes	complemented
462	#3312	C₂×C₃₁	1	2	yes	complemented
463	#3300	C₂×C₃₁	1	2	yes	complemented
464	#3299	C₂×C₃₁	1	2	yes	complemented
465	#3296	C₂×C₃₁	1	2	yes	complemented
466	#3243	C₂×C₃₁	1	2	yes	complemented
467	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#3223	C₂×C₃₁	1	2	yes	complemented
469	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
470	#3178	C₂×C₃₁	1	2	yes	complemented
471	#3170	C₂×C₃₁	1	1	yes	characteristic, complemented
472	#3137	C₂×C₃₁	1	2	yes	complemented
473	C₂×#488	C₂×C₃₁	1	1	yes	characteristic, complemented
474	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
475	C₂²×C₃₁	—	2	1	no	—
476	C₂²×C₃₁	—	2	1	no	—
477	C₂²×C₃₁	—	2	2	no	—
478	C₂²×C₃₁	—	2	2	no	—
479	C₂²×C₃₁	—	2	2	no	—
480	C₂²×C₃₁	—	4	2	no	—
481	C₂²×C₃₁	—	4	2	no	—
482	C₂²×C₃₁	—	4	2	no	—
483	C₂²×C₃₁	—	16	2	no	—
484	C₂²×C₃₁	#578	1	2	yes	—
485	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
486	C₄×C₃₁	—	2	1	no	—
487	C₄×C₃₁	—	2	1	no	—
488	C₄×C₃₁	—	2	2	no	—
489	C₄×C₃₁	—	2	2	no	—
490	C₄×C₃₁	—	2	1	no	—
491	C₄×C₃₁	—	2	1	no	—
492	C₄×C₃₁	—	2	1	no	—
493	C₄×C₃₁	—	2	2	no	—
494	C₄×C₃₁	—	4	2	no	—
495	C₄×C₃₁	—	4	2	no	—
496	C₄×C₃₁	—	4	2	no	—
497	C₄×C₃₁	—	4	2	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	#585	1	1	yes	characteristic
502	C₄×C₃₁	#585	1	1	yes	characteristic
503	#564	—	2	1	no	—
504	#563	—	2	1	no	—
505	#563	—	2	1	no	—
506	#562	—	2	1	no	—
507	#557	C₂²×C₃₁	1	2	yes	complemented
508	#556	C₂²×C₃₁	1	2	yes	—
509	#554	C₂²×C₃₁	1	2	yes	—
510	#552	—	2	2	no	—
511	#552	C₂²×C₃₁	1	2	yes	—
512	#552	C₂²×C₃₁	1	2	yes	complemented
513	#551	—	2	2	no	—
514	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
515	#548	C₂²×C₃₁	1	2	yes	—
516	#546	C₂²×C₃₁	1	2	yes	—
517	#544	—	2	1	no	—
518	#544	C₂²×C₃₁	1	2	yes	complemented
519	#543	—	2	1	no	—
520	#542	—	2	2	no	—
521	#542	C₂²×C₃₁	1	2	yes	—
522	#541	—	2	2	no	—
523	#541	C₂²×C₃₁	1	2	yes	complemented
524	#539	—	2	1	no	—
525	#538	—	2	1	no	—
526	#536	C₂²×C₃₁	1	2	yes	—
527	#533	C₂²×C₃₁	1	1	yes	characteristic
528	#533	C₂²×C₃₁	1	1	yes	characteristic
529	#529	C₂²×C₃₁	1	1	yes	characteristic
530	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
531	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
532	#501	C₂²×C₃₁	1	2	yes	complemented
533	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
534	#497	C₂²×C₃₁	1	2	yes	—
535	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
536	#491	C₂²×C₃₁	1	2	yes	complemented
537	#491	C₂²×C₃₁	1	2	yes	complemented
538	#489	C₂²×C₃₁	1	2	yes	—
539	#489	C₂²×C₃₁	1	2	yes	—
540	#488	C₂²×C₃₁	1	2	yes	—
541	#488	C₂²×C₃₁	1	2	yes	—
542	#488	C₂²×C₃₁	1	2	yes	—
543	#488	C₂²×C₃₁	1	2	yes	—
544	#488	C₂²×C₃₁	1	2	yes	—
545	#487	C₂²×C₃₁	1	2	yes	complemented
546	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
547	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#485	C₂²×C₃₁	1	2	yes	complemented
549	#484	C₂²×C₃₁	1	2	yes	—
550	#484	C₂²×C₃₁	1	2	yes	complemented
551	#483	C₂²×C₃₁	1	2	yes	—
552	#482	C₂²×C₃₁	1	2	yes	—
553	#480	C₂²×C₃₁	1	2	yes	—
554	#479	C₂²×C₃₁	1	2	yes	complemented
555	#479	C₂²×C₃₁	1	2	yes	complemented
556	#479	C₂²×C₃₁	1	2	yes	complemented
557	#478	C₂²×C₃₁	1	2	yes	—
558	#477	C₂²×C₃₁	1	2	yes	complemented
559	#474	C₂²×C₃₁	1	2	yes	—
560	#470	C₂²×C₃₁	1	2	yes	complemented
561	#468	C₂²×C₃₁	1	2	yes	—
562	#467	C₂²×C₃₁	1	2	yes	—
563	#467	C₂²×C₃₁	1	2	yes	—
564	#467	C₂²×C₃₁	1	2	yes	complemented
565	#465	C₂²×C₃₁	1	2	yes	—
566	#464	C₂²×C₃₁	1	2	yes	—
567	#464	C₂²×C₃₁	1	2	yes	—
568	#464	C₂²×C₃₁	1	2	yes	—
569	#464	C₂²×C₃₁	1	2	yes	—
570	#462	C₂²×C₃₁	1	2	yes	complemented
571	#462	C₂²×C₃₁	1	2	yes	complemented
572	#452	C₂²×C₃₁	1	2	yes	—
573	#452	C₂²×C₃₁	1	2	yes	—
574	#451	C₂²×C₃₁	1	2	yes	—
575	#451	C₂²×C₃₁	1	2	yes	complemented
576	#451	C₂²×C₃₁	1	2	yes	complemented
577	#450	C₂²×C₃₁	1	2	yes	—
578	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
579	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
580	#441	C₂²×C₃₁	1	2	yes	complemented
581	#440	C₂²×C₃₁	1	2	yes	—
582	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
583	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
584	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
585	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
586	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#435	C₂²×C₃₁	1	2	yes	—
588	C₈×D₄	C₂²×C₃₁	1	2	yes	—
589	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
590	#433	C₂²×C₃₁	1	2	yes	complemented
591	#432	C₂²×C₃₁	1	1	yes	characteristic
592	#419	C₂²×C₃₁	1	2	yes	complemented
593	#417	C₂²×C₃₁	1	2	yes	—
594	#416	C₂²×C₃₁	1	2	yes	—
595	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
596	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
597	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
598	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
599	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
600	#405	C₂²×C₃₁	1	2	yes	complemented
601	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
602	C₂×C₃₁	—	2	2	no	—
603	C₂×C₃₁	—	4	2	no	—
604	C₂×C₃₁	—	8	2	no	—
605	C₂×C₃₁	#3500	1	1	yes	characteristic
606	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
607	C₂×C₃₁	#3584	1	1	yes	characteristic
608	C₂×#41	C₂³×C₃₁	1	2	yes	—
609	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
610	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
611	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
612	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
613	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
614	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
615	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
616	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
617	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
618	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
619	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
620	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
621	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
622	C₄⋊Q₈	—	2	2	no	—
623	C₄⋊Q₈	—	2	2	no	—
624	C₄⋊Q₈	—	2	2	no	—
625	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
626	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
627	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
628	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
629	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
630	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	D₄×C₃₁	1	2	yes	—
639	#125	—	2	2	no	—
640	#125	—	2	2	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	1	no	—
648	#125	—	2	1	no	—
649	#125	—	2	1	no	—
650	#125	—	2	1	no	—
651	#125	D₄×C₃₁	1	1	yes	characteristic
652	#125	C₂³×C₃₁	1	2	yes	—
653	#125	C₂³×C₃₁	1	2	yes	—
654	#125	C₂³×C₃₁	1	2	yes	—
655	#124	—	2	2	no	—
656	#124	—	2	2	no	—
657	#124	—	2	1	no	—
658	#124	—	2	1	no	—
659	#124	D₄×C₃₁	1	1	yes	characteristic
660	#124	C₂³×C₃₁	1	2	yes	—
661	#124	C₂³×C₃₁	1	2	yes	—
662	#124	C₂³×C₃₁	1	2	yes	—
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	D₄×C₃₁	1	2	yes	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	1	no	—
672	C₂²⋊Q₈	—	2	1	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
684	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
685	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
688	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
689	#121	—	2	2	no	—
690	#121	—	2	2	no	—
691	#121	D₄×C₃₁	1	1	yes	characteristic
692	#121	C₂³×C₃₁	1	2	yes	—
693	#120	—	2	2	no	—
694	C₄×Q₈	—	2	2	no	—
695	C₄×Q₈	—	2	1	no	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
698	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
699	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
700	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
701	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
702	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
703	C₄×D₄	—	2	2	no	—
704	C₄×D₄	—	2	2	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	C₂³×C₃₁	1	2	yes	—
707	C₄×D₄	C₂³×C₃₁	1	2	yes	—
708	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
709	#117	—	2	1	no	—
710	#117	—	2	1	no	—
711	#117	—	2	2	no	—
712	#117	—	2	2	no	—
713	#117	—	2	2	no	—
714	#117	C₂³×C₃₁	1	2	yes	—
715	#117	C₂³×C₃₁	1	2	yes	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	—	2	1	no	—
718	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
721	C₂×C₂²⋊C₄	—	2	1	no	—
722	C₂×C₂²⋊C₄	—	2	1	no	—
723	C₂×C₂²⋊C₄	—	2	2	no	—
724	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
725	#107	C₂³×C₃₁	1	2	yes	—
726	#107	C₂³×C₃₁	1	2	yes	—
727	#107	C₂³×C₃₁	1	2	yes	—
728	#107	C₂³×C₃₁	1	2	yes	—
729	#106	C₂³×C₃₁	1	2	yes	—
730	#106	C₂³×C₃₁	1	2	yes	—
731	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
732	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
733	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
734	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
735	#103	C₂³×C₃₁	1	2	yes	—
736	#103	C₂³×C₃₁	1	2	yes	—
737	#103	C₂³×C₃₁	1	2	yes	—
738	#103	C₂³×C₃₁	1	2	yes	—
739	#103	C₂³×C₃₁	1	2	yes	—
740	#103	C₂³×C₃₁	1	2	yes	—
741	#103	C₂³×C₃₁	1	2	yes	—
742	#103	C₂³×C₃₁	1	2	yes	—
743	#103	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	#102	C₂³×C₃₁	1	2	yes	—
750	#102	C₂³×C₃₁	1	2	yes	—
751	#102	C₂³×C₃₁	1	2	yes	—
752	#102	C₂³×C₃₁	1	2	yes	—
753	#102	C₂³×C₃₁	1	2	yes	—
754	#102	C₂³×C₃₁	1	2	yes	—
755	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
756	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
757	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
758	#97	C₂³×C₃₁	1	2	yes	—
759	#97	C₂³×C₃₁	1	2	yes	—
760	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
761	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
762	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
764	C₄×C₈	C₂³×C₃₁	1	2	yes	—
765	C₃₁	#62559	1	1	yes	characteristic, direct product factor, Sylow
766	C₂⁴	—	2	1	no	—
767	#41	—	4	2	no	—
768	#41	—	4	2	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	4	1	no	—
775	C₂×Q₈	—	4	1	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	—	4	2	no	—
778	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
779	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
780	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	1	no	—
787	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
788	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
789	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
801	Q₁₆	—	4	2	no	—
802	Q₁₆	—	4	2	no	—
803	Q₁₆	—	4	2	no	—
804	Q₁₆	—	4	2	no	—
805	SD₁₆	—	4	2	no	—
806	SD₁₆	—	4	2	no	—
807	M₁₆	—	4	2	no	—
808	C₂×C₈	—	4	2	no	—
809	C₂×C₈	—	4	1	no	—
810	C₂×C₈	—	4	1	no	—
811	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
812	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
813	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
814	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
815	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
816	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
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	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
846	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
847	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
848	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
849	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
850	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
851	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₃₁	1	2	yes	—
870	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
871	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
872	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
873	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
881	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
882	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
884	C₄²	C₂⁴×C₃₁	1	2	yes	—
885	C₂³	—	2	2	no	—
886	C₂³	—	4	2	no	—
887	C₂³	—	8	1	no	—
888	C₂³	—	8	1	no	—
889	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
890	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
891	Q₈	—	2	2	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	2	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	2	2	no	—
896	Q₈	—	2	2	no	—
897	Q₈	—	4	1	no	—
898	Q₈	—	8	1	no	—
899	Q₈	—	8	1	no	—
900	Q₈	—	8	2	no	—
901	Q₈	—	8	2	no	—
902	Q₈	—	8	1	no	—
903	D₄	—	2	4	no	—
904	D₄	—	2	2	no	—
905	D₄	—	2	2	no	—
906	D₄	—	4	1	no	—
907	D₄	—	8	1	no	—
908	D₄	—	8	2	no	—
909	D₄	—	8	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	8	2	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	1	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	1	no	—
930	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
933	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
934	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
938	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
939	C₈	—	2	1	no	—
940	C₈	—	2	1	no	—
941	C₈	—	2	2	no	—
942	C₈	—	2	1	no	—
943	C₈	—	2	1	no	—
944	C₈	—	2	2	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	16	2	no	—
954	C₂²	C₃₁×#578	1	2	yes	—
955	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
956	C₄	—	2	2	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	C₃₁×#585	1	1	yes	characteristic
972	C₄	C₃₁×#585	1	1	yes	characteristic
973	C₂	—	2	2	no	—
974	C₂	—	4	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₃₁×#3500	1	1	yes	characteristic
977	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
978	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×#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
1. C₃₁×#3563	C₂	semidirect
3. C₃₁×#3377	C₂	semidirect
4. C₃₁×#3364	C₂	semidirect
5. C₃₁×#3327	C₂	semidirect
6. C₃₁×#3314	C₂	semidirect
7. C₃₁×#3312	C₂	semidirect
8. C₃₁×#3300	C₂	semidirect
9. C₃₁×#3299	C₂	semidirect
10. C₃₁×#3296	C₂	semidirect
11. C₃₁×#3243	C₂	semidirect
12. C₃₁×#3236	C₂	semidirect
13. C₃₁×#3223	C₂	semidirect
14. C₃₁×#3215	C₂	semidirect
15. C₃₁×#3178	C₂	semidirect
16. C₃₁×#3170	C₂	semidirect
17. C₃₁×#3137	C₂	semidirect
18. C₂×C₃₁×#488	C₂	semidirect
19. C₃₁×#2966	C₂	semidirect
24. C₃₁×#557	C₂²	semidirect
29. C₃₁×#552	C₂²	semidirect
35. C₃₁×#544	C₂²	semidirect
40. C₃₁×#541	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
50. C₃₁×#500	C₂²	semidirect
52. C₃₁×#494	C₂²	semidirect
53. C₃₁×#491	C₂²	semidirect
54. C₃₁×#491	C₂²	semidirect
62. C₃₁×#487	C₂²	semidirect
63. C₃₁×#487	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
67. C₃₁×#484	C₂²	semidirect
71. C₃₁×#479	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
77. C₃₁×#470	C₂²	semidirect
81. C₃₁×#467	C₂²	semidirect
87. C₃₁×#462	C₂²	semidirect
88. C₃₁×#462	C₂²	semidirect
92. C₃₁×#451	C₂²	semidirect
93. C₃₁×#451	C₂²	semidirect
95. C₃₁×#446	C₂²	semidirect
96. C₈×Q₈×C₃₁	C₂²	semidirect
97. C₃₁×#441	C₂²	semidirect
99. C₄×Q₁₆×C₃₁	C₂²	semidirect
100. C₄×Q₁₆×C₃₁	C₂²	semidirect
101. C₄×Q₁₆×C₃₁	C₂²	semidirect
103. C₃₁×#436	C₂²	semidirect
106. C₈×D₄×C₃₁	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
109. C₃₁×#419	C₂²	semidirect
114. C₂×C₃₁×#103	C₂²	semidirect
117. C₃₁×#405	C₂²	semidirect
395. #62559	C₃₁	direct (N × H)
456. #3563	C₂×C₃₁	semidirect
458. #3377	C₂×C₃₁	semidirect
459. #3364	C₂×C₃₁	semidirect
460. #3327	C₂×C₃₁	semidirect
461. #3314	C₂×C₃₁	semidirect
462. #3312	C₂×C₃₁	semidirect
463. #3300	C₂×C₃₁	semidirect
464. #3299	C₂×C₃₁	semidirect
465. #3296	C₂×C₃₁	semidirect
466. #3243	C₂×C₃₁	semidirect
467. #3236	C₂×C₃₁	semidirect
468. #3223	C₂×C₃₁	semidirect
469. #3215	C₂×C₃₁	semidirect
470. #3178	C₂×C₃₁	semidirect
471. #3170	C₂×C₃₁	semidirect
472. #3137	C₂×C₃₁	semidirect
473. C₂×#488	C₂×C₃₁	semidirect
474. #2966	C₂×C₃₁	semidirect
507. #557	C₂²×C₃₁	semidirect
512. #552	C₂²×C₃₁	semidirect
518. #544	C₂²×C₃₁	semidirect
523. #541	C₂²×C₃₁	semidirect
532. #501	C₂²×C₃₁	semidirect
533. #500	C₂²×C₃₁	semidirect
535. #494	C₂²×C₃₁	semidirect
536. #491	C₂²×C₃₁	semidirect
537. #491	C₂²×C₃₁	semidirect
545. #487	C₂²×C₃₁	semidirect
546. #487	C₂²×C₃₁	semidirect
547. #487	C₂²×C₃₁	semidirect
548. #485	C₂²×C₃₁	semidirect
550. #484	C₂²×C₃₁	semidirect
554. #479	C₂²×C₃₁	semidirect
555. #479	C₂²×C₃₁	semidirect
556. #479	C₂²×C₃₁	semidirect
558. #477	C₂²×C₃₁	semidirect
560. #470	C₂²×C₃₁	semidirect
564. #467	C₂²×C₃₁	semidirect
570. #462	C₂²×C₃₁	semidirect
571. #462	C₂²×C₃₁	semidirect
575. #451	C₂²×C₃₁	semidirect
576. #451	C₂²×C₃₁	semidirect
578. #446	C₂²×C₃₁	semidirect
579. C₈×Q₈	C₂²×C₃₁	semidirect
580. #441	C₂²×C₃₁	semidirect
582. C₄×Q₁₆	C₂²×C₃₁	semidirect
583. C₄×Q₁₆	C₂²×C₃₁	semidirect
584. C₄×Q₁₆	C₂²×C₃₁	semidirect
586. #436	C₂²×C₃₁	semidirect
589. C₈×D₄	C₂²×C₃₁	semidirect
590. #433	C₂²×C₃₁	semidirect
592. #419	C₂²×C₃₁	semidirect
597. C₂×#103	C₂²×C₃₁	semidirect
600. #405	C₂²×C₃₁	semidirect
765. C₃₁	#62559	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×#3563	2
C₃₁×#3561	2
C₃₁×#3377	2
C₃₁×#3364	2
C₃₁×#3327	2
C₃₁×#3314	2
C₃₁×#3312	2
C₃₁×#3300	2
C₃₁×#3299	2
C₃₁×#3296	2
C₃₁×#3243	2
C₃₁×#3236	2
C₃₁×#3223	2
C₃₁×#3215	2
C₃₁×#3178	2
C₃₁×#3170	2
C₃₁×#3137	2
C₂×C₃₁×#488	2
C₃₁×#2966	2
#62559	31

Subgroups — C31×#62559 #21519318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62559 #21519318