Subgroups — C₃₁×#62165 #21518924

Order 7936.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1006 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×#3520	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3386	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3344	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3338	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3315	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3296	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×#3243	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#564	—	2	1	no	—
21	C₃₁×#563	—	2	1	no	—
22	C₃₁×#557	C₂²	1	2	yes	complemented
23	C₃₁×#556	C₂²	1	1	yes	characteristic
24	C₃₁×#554	C₂²	1	2	yes	—
25	C₃₁×#554	C₂²	1	2	yes	—
26	C₃₁×#552	—	2	1	no	—
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	1	yes	characteristic
32	C₃₁×#548	—	2	1	no	—
33	C₃₁×#547	C₂²	1	1	yes	characteristic
34	C₃₁×#547	C₂²	1	1	yes	characteristic
35	C₃₁×#546	C₂²	1	2	yes	—
36	C₃₁×#544	—	2	1	no	—
37	C₃₁×#544	C₂²	1	2	yes	complemented
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	2	no	—
42	C₃₁×#539	—	2	1	no	—
43	C₃₁×#533	C₂²	1	1	yes	characteristic
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#529	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
47	C₃₁×#525	—	2	1	no	—
48	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
49	C₃₁×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#501	C₂²	1	2	yes	complemented
53	C₃₁×#500	C₂²	1	2	yes	complemented
54	C₃₁×#491	C₂²	1	2	yes	complemented
55	C₃₁×#489	C₂²	1	2	yes	—
56	C₃₁×#488	C₂²	1	2	yes	—
57	C₃₁×#485	C₂²	1	2	yes	complemented
58	C₃₁×#484	C₂²	1	2	yes	—
59	C₃₁×#484	C₂²	1	2	yes	—
60	C₃₁×#484	C₂²	1	2	yes	complemented
61	C₃₁×#484	C₂²	1	2	yes	complemented
62	C₃₁×#483	C₂²	1	2	yes	—
63	C₃₁×#483	C₂²	1	2	yes	complemented
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#480	C₂²	1	2	yes	—
66	C₃₁×#479	C₂²	1	2	yes	complemented
67	C₃₁×#479	C₂²	1	2	yes	complemented
68	C₃₁×#479	C₂²	1	2	yes	complemented
69	C₃₁×#478	C₂²	1	2	yes	—
70	C₃₁×#478	C₂²	1	2	yes	—
71	C₃₁×#478	C₂²	1	2	yes	—
72	C₃₁×#478	C₂²	1	2	yes	—
73	C₃₁×#478	C₂²	1	2	yes	—
74	C₃₁×#477	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#477	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	2	yes	complemented
78	C₃₁×#475	C₂²	1	2	yes	complemented
79	C₃₁×#474	C₂²	1	1	yes	characteristic
80	C₃₁×#474	C₂²	1	2	yes	—
81	C₃₁×#474	C₂²	1	1	yes	characteristic
82	C₃₁×#470	C₂²	1	2	yes	complemented
83	C₃₁×#468	C₂²	1	2	yes	—
84	C₃₁×#467	C₂²	1	2	yes	—
85	C₃₁×#467	C₂²	1	2	yes	—
86	C₃₁×#467	C₂²	1	2	yes	complemented
87	C₃₁×#465	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#464	C₂²	1	2	yes	—
90	C₃₁×#462	C₂²	1	2	yes	complemented
91	C₃₁×#462	C₂²	1	2	yes	complemented
92	C₃₁×#461	C₂²	1	1	yes	characteristic
93	C₃₁×#461	C₂²	1	1	yes	characteristic
94	C₃₁×#452	C₂²	1	2	yes	—
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#450	C₂²	1	2	yes	—
97	C₃₁×#446	C₂²	1	2	yes	complemented
98	C₃₁×#441	C₂²	1	2	yes	complemented
99	C₃₁×#440	C₂²	1	2	yes	—
100	C₃₁×#440	C₂²	1	2	yes	—
101	C₃₁×#440	C₂²	1	2	yes	—
102	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
104	C₃₁×#435	C₂²	1	2	yes	—
105	C₃₁×#435	C₂²	1	2	yes	complemented
106	C₈×D₄×C₃₁	C₂²	1	2	yes	—
107	C₃₁×#433	C₂²	1	2	yes	complemented
108	C₃₁×#432	C₂²	1	1	yes	characteristic
109	C₃₁×#428	C₂²	1	2	yes	complemented
110	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
111	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
112	C₂×C₃₁×#106	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×#417	C₂²	1	2	yes	—
116	C₃₁×#416	C₂²	1	2	yes	—
117	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂²×Q₈×C₃₁	—	2	1	no	—
122	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₃₁	—	2	1	no	—
124	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
132	C₃₁×C₄⋊Q₈	—	2	2	no	—
133	C₃₁×C₄⋊Q₈	—	2	2	no	—
134	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
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	D₄	1	2	yes	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	2	no	—
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	1	no	—
157	C₃₁×#125	—	2	1	no	—
158	C₃₁×#125	—	2	1	no	—
159	C₃₁×#125	—	2	1	no	—
160	C₃₁×#125	D₄	1	1	yes	characteristic
161	C₃₁×#125	C₂³	1	2	yes	—
162	C₃₁×#125	C₂³	1	2	yes	—
163	C₃₁×#125	C₂³	1	2	yes	—
164	C₃₁×#124	—	2	2	no	—
165	C₃₁×#124	D₄	1	1	yes	characteristic
166	C₃₁×#124	C₂³	1	2	yes	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	D₄	1	2	yes	—
174	C₃₁×C₂²⋊Q₈	—	2	1	no	—
175	C₃₁×C₂²⋊Q₈	—	2	1	no	—
176	C₃₁×C₂²⋊Q₈	—	2	1	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	1	no	—
179	C₃₁×C₂²⋊Q₈	—	2	1	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
188	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×#121	—	2	1	no	—
194	C₃₁×#121	—	2	2	no	—
195	C₃₁×#121	D₄	1	1	yes	characteristic
196	C₃₁×#121	C₂³	1	2	yes	—
197	C₃₁×#120	—	2	2	no	—
198	C₄×Q₈×C₃₁	—	2	2	no	—
199	C₄×Q₈×C₃₁	—	2	1	no	—
200	C₄×Q₈×C₃₁	—	2	1	no	—
201	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
202	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
203	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
205	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
206	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	2	no	—
209	C₄×D₄×C₃₁	—	2	2	no	—
210	C₄×D₄×C₃₁	—	2	2	no	—
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	—	2	1	no	—
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
215	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	no	—
224	C₃₁×#117	—	2	2	no	—
225	C₃₁×#117	—	2	2	no	—
226	C₃₁×#117	C₂³	1	2	yes	—
227	C₃₁×#117	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
230	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
231	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
239	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#107	C₂³	1	2	yes	—
245	C₃₁×#107	C₂³	1	2	yes	—
246	C₃₁×#107	C₂³	1	2	yes	—
247	C₃₁×#107	C₂³	1	2	yes	—
248	C₃₁×#106	C₂³	1	2	yes	—
249	C₃₁×#106	C₂³	1	2	yes	—
250	C₃₁×#106	C₂³	1	2	yes	—
251	C₃₁×#106	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#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×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₃₁×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	#41×C₃₁	—	2	4	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	8	2	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	1	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	8	2	no	—
289	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
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	2	no	—
295	C₂×D₄×C₃₁	—	2	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	1	yes	characteristic
300	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	—	2	1	no	—
302	C₂²×C₄×C₃₁	—	2	1	no	—
303	C₂²×C₄×C₃₁	—	2	1	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	—	2	1	no	—
308	C₂²×C₄×C₃₁	—	2	1	no	—
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	—	2	1	no	—
311	C₂²×C₄×C₃₁	—	2	1	no	—
312	C₂²×C₄×C₃₁	—	8	2	no	—
313	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
317	Q₁₆×C₃₁	—	4	2	no	—
318	Q₁₆×C₃₁	—	4	2	no	—
319	SD₁₆×C₃₁	—	2	4	no	—
320	SD₁₆×C₃₁	—	4	2	no	—
321	M₁₆×C₃₁	—	4	2	no	—
322	C₂×C₈×C₃₁	—	4	1	no	—
323	C₂×C₈×C₃₁	—	4	2	no	—
324	C₂×C₈×C₃₁	—	4	1	no	—
325	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
326	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	1	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	1	no	—
342	C₄⋊C₄×C₃₁	—	2	1	no	—
343	C₄⋊C₄×C₃₁	—	2	1	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	1	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
377	C₂²⋊C₄×C₃₁	—	2	1	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₄²×C₃₁	—	2	2	no	—
390	C₄²×C₃₁	—	2	2	no	—
391	C₄²×C₃₁	—	2	2	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	2	yes	—
398	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
400	#62165	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂³×C₃₁	—	2	1	no	—
402	C₂³×C₃₁	—	2	1	no	—
403	C₂³×C₃₁	—	4	2	no	—
404	C₂³×C₃₁	—	4	2	no	—
405	C₂³×C₃₁	—	8	1	no	—
406	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
407	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	—	4	1	no	—
413	Q₈×C₃₁	—	4	2	no	—
414	Q₈×C₃₁	—	8	1	no	—
415	Q₈×C₃₁	—	8	2	no	—
416	Q₈×C₃₁	—	8	2	no	—
417	D₄×C₃₁	—	2	4	no	—
418	D₄×C₃₁	—	2	1	no	—
419	D₄×C₃₁	—	2	1	no	—
420	D₄×C₃₁	—	2	1	no	—
421	D₄×C₃₁	—	4	1	no	—
422	D₄×C₃₁	—	4	2	no	—
423	D₄×C₃₁	—	4	4	no	—
424	D₄×C₃₁	—	8	2	no	—
425	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
426	C₂×C₄×C₃₁	—	2	2	no	—
427	C₂×C₄×C₃₁	—	2	1	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	1	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	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	1	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	1	no	—
439	C₂×C₄×C₃₁	—	4	1	no	—
440	C₂×C₄×C₃₁	—	4	4	no	—
441	C₂×C₄×C₃₁	—	4	2	no	—
442	C₂×C₄×C₃₁	—	4	2	no	—
443	C₂×C₄×C₃₁	—	4	2	no	—
444	C₂×C₄×C₃₁	—	8	1	no	—
445	C₂×C₄×C₃₁	—	8	1	no	—
446	C₂×C₄×C₃₁	—	8	2	no	—
447	C₂×C₄×C₃₁	—	8	1	no	—
448	C₂×C₄×C₃₁	—	8	2	no	—
449	C₂×C₄×C₃₁	—	8	1	no	—
450	C₂×C₄×C₃₁	—	8	2	no	—
451	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
460	C₈×C₃₁	—	2	2	no	—
461	C₈×C₃₁	—	2	2	no	—
462	C₈×C₃₁	—	2	2	no	—
463	C₈×C₃₁	—	2	2	no	—
464	#3563	C₂×C₃₁	1	1	yes	characteristic, complemented
465	#3520	C₂×C₃₁	1	1	yes	characteristic
466	#3386	C₂×C₃₁	1	2	yes	complemented
467	#3377	C₂×C₃₁	1	2	yes	complemented
468	#3344	C₂×C₃₁	1	2	yes	complemented
469	#3343	C₂×C₃₁	1	2	yes	complemented
470	#3338	C₂×C₃₁	1	2	yes	complemented
471	#3315	C₂×C₃₁	1	2	yes	complemented
472	#3314	C₂×C₃₁	1	2	yes	complemented
473	#3296	C₂×C₃₁	1	2	yes	complemented
474	#3258	C₂×C₃₁	1	2	yes	complemented
475	#3249	C₂×C₃₁	1	1	yes	characteristic, complemented
476	#3243	C₂×C₃₁	1	2	yes	complemented
477	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
478	#3120	C₂×C₃₁	1	2	yes	complemented
479	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
480	#3083	C₂×C₃₁	1	2	yes	complemented
481	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
482	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
483	C₂²×C₃₁	—	2	1	no	—
484	C₂²×C₃₁	—	2	1	no	—
485	C₂²×C₃₁	—	2	2	no	—
486	C₂²×C₃₁	—	2	2	no	—
487	C₂²×C₃₁	—	2	2	no	—
488	C₂²×C₃₁	—	2	2	no	—
489	C₂²×C₃₁	—	4	1	no	—
490	C₂²×C₃₁	—	4	1	no	—
491	C₂²×C₃₁	—	4	1	no	—
492	C₂²×C₃₁	—	4	1	no	—
493	C₂²×C₃₁	—	4	1	no	—
494	C₂²×C₃₁	—	8	4	no	—
495	C₂²×C₃₁	#578	1	2	yes	—
496	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₃₁	—	2	1	no	—
498	C₄×C₃₁	—	2	1	no	—
499	C₄×C₃₁	—	2	2	no	—
500	C₄×C₃₁	—	2	2	no	—
501	C₄×C₃₁	—	2	1	no	—
502	C₄×C₃₁	—	2	1	no	—
503	C₄×C₃₁	—	2	1	no	—
504	C₄×C₃₁	—	2	2	no	—
505	C₄×C₃₁	—	4	1	no	—
506	C₄×C₃₁	—	4	1	no	—
507	C₄×C₃₁	—	4	2	no	—
508	C₄×C₃₁	—	4	2	no	—
509	C₄×C₃₁	—	4	2	no	—
510	C₄×C₃₁	—	4	2	no	—
511	C₄×C₃₁	—	4	2	no	—
512	C₄×C₃₁	—	4	2	no	—
513	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
514	C₄×C₃₁	#585	1	1	yes	characteristic
515	#564	—	2	1	no	—
516	#563	—	2	1	no	—
517	#557	C₂²×C₃₁	1	2	yes	complemented
518	#556	C₂²×C₃₁	1	1	yes	characteristic
519	#554	C₂²×C₃₁	1	2	yes	—
520	#554	C₂²×C₃₁	1	2	yes	—
521	#552	—	2	1	no	—
522	#552	—	2	2	no	—
523	#552	C₂²×C₃₁	1	2	yes	—
524	#552	C₂²×C₃₁	1	2	yes	complemented
525	#551	—	2	2	no	—
526	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
527	#548	—	2	1	no	—
528	#547	C₂²×C₃₁	1	1	yes	characteristic
529	#547	C₂²×C₃₁	1	1	yes	characteristic
530	#546	C₂²×C₃₁	1	2	yes	—
531	#544	—	2	1	no	—
532	#544	C₂²×C₃₁	1	2	yes	complemented
533	#542	C₂²×C₃₁	1	2	yes	—
534	#541	—	2	2	no	—
535	#541	C₂²×C₃₁	1	2	yes	complemented
536	#539	—	2	2	no	—
537	#539	—	2	1	no	—
538	#533	C₂²×C₃₁	1	1	yes	characteristic
539	#533	C₂²×C₃₁	1	1	yes	characteristic
540	#529	C₂²×C₃₁	1	1	yes	characteristic
541	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
542	#525	—	2	1	no	—
543	C₂×C₂²⋊Q₈	—	2	1	no	—
544	#520	C₂²×C₃₁	1	2	yes	—
545	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
546	#501	C₂²×C₃₁	1	2	yes	complemented
547	#501	C₂²×C₃₁	1	2	yes	complemented
548	#500	C₂²×C₃₁	1	2	yes	complemented
549	#491	C₂²×C₃₁	1	2	yes	complemented
550	#489	C₂²×C₃₁	1	2	yes	—
551	#488	C₂²×C₃₁	1	2	yes	—
552	#485	C₂²×C₃₁	1	2	yes	complemented
553	#484	C₂²×C₃₁	1	2	yes	—
554	#484	C₂²×C₃₁	1	2	yes	—
555	#484	C₂²×C₃₁	1	2	yes	complemented
556	#484	C₂²×C₃₁	1	2	yes	complemented
557	#483	C₂²×C₃₁	1	2	yes	—
558	#483	C₂²×C₃₁	1	2	yes	complemented
559	#482	C₂²×C₃₁	1	2	yes	—
560	#480	C₂²×C₃₁	1	2	yes	—
561	#479	C₂²×C₃₁	1	2	yes	complemented
562	#479	C₂²×C₃₁	1	2	yes	complemented
563	#479	C₂²×C₃₁	1	2	yes	complemented
564	#478	C₂²×C₃₁	1	2	yes	—
565	#478	C₂²×C₃₁	1	2	yes	—
566	#478	C₂²×C₃₁	1	2	yes	—
567	#478	C₂²×C₃₁	1	2	yes	—
568	#478	C₂²×C₃₁	1	2	yes	—
569	#477	C₂²×C₃₁	1	2	yes	complemented
570	#477	C₂²×C₃₁	1	2	yes	complemented
571	#477	C₂²×C₃₁	1	2	yes	complemented
572	#477	C₂²×C₃₁	1	2	yes	complemented
573	#475	C₂²×C₃₁	1	2	yes	complemented
574	#474	C₂²×C₃₁	1	1	yes	characteristic
575	#474	C₂²×C₃₁	1	2	yes	—
576	#474	C₂²×C₃₁	1	1	yes	characteristic
577	#470	C₂²×C₃₁	1	2	yes	complemented
578	#468	C₂²×C₃₁	1	2	yes	—
579	#467	C₂²×C₃₁	1	2	yes	—
580	#467	C₂²×C₃₁	1	2	yes	—
581	#467	C₂²×C₃₁	1	2	yes	complemented
582	#465	C₂²×C₃₁	1	2	yes	—
583	#464	C₂²×C₃₁	1	2	yes	—
584	#464	C₂²×C₃₁	1	2	yes	—
585	#462	C₂²×C₃₁	1	2	yes	complemented
586	#462	C₂²×C₃₁	1	2	yes	complemented
587	#461	C₂²×C₃₁	1	1	yes	characteristic
588	#461	C₂²×C₃₁	1	1	yes	characteristic
589	#452	C₂²×C₃₁	1	2	yes	—
590	#452	C₂²×C₃₁	1	2	yes	—
591	#450	C₂²×C₃₁	1	2	yes	—
592	#446	C₂²×C₃₁	1	2	yes	complemented
593	#441	C₂²×C₃₁	1	2	yes	complemented
594	#440	C₂²×C₃₁	1	2	yes	—
595	#440	C₂²×C₃₁	1	2	yes	—
596	#440	C₂²×C₃₁	1	2	yes	—
597	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
598	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
599	#435	C₂²×C₃₁	1	2	yes	—
600	#435	C₂²×C₃₁	1	2	yes	complemented
601	C₈×D₄	C₂²×C₃₁	1	2	yes	—
602	#433	C₂²×C₃₁	1	2	yes	complemented
603	#432	C₂²×C₃₁	1	1	yes	characteristic
604	#428	C₂²×C₃₁	1	2	yes	complemented
605	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
606	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
607	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
608	#424	C₂²×C₃₁	1	2	yes	complemented
609	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
610	#417	C₂²×C₃₁	1	2	yes	—
611	#416	C₂²×C₃₁	1	2	yes	—
612	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
613	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
614	C₂×C₃₁	—	2	2	no	—
615	C₂×C₃₁	—	4	2	no	—
616	C₂×C₃₁	—	4	2	no	—
617	C₂×C₃₁	—	8	1	no	—
618	C₂×C₃₁	#3489	1	1	yes	characteristic
619	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
620	C₂×C₃₁	#3585	1	1	yes	characteristic
621	C₂×#41	—	2	1	no	—
622	C₂×#41	C₂³×C₃₁	1	2	yes	—
623	C₂²×Q₈	—	2	1	no	—
624	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂³×C₄	—	2	1	no	—
626	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
627	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
628	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
629	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
630	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
631	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
632	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
633	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
634	C₄⋊Q₈	—	2	2	no	—
635	C₄⋊Q₈	—	2	2	no	—
636	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
637	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
638	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
639	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
640	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
641	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
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	2	no	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	2	no	—
658	#125	—	2	1	no	—
659	#125	—	2	1	no	—
660	#125	—	2	1	no	—
661	#125	—	2	1	no	—
662	#125	D₄×C₃₁	1	1	yes	characteristic
663	#125	C₂³×C₃₁	1	2	yes	—
664	#125	C₂³×C₃₁	1	2	yes	—
665	#125	C₂³×C₃₁	1	2	yes	—
666	#124	—	2	2	no	—
667	#124	D₄×C₃₁	1	1	yes	characteristic
668	#124	C₂³×C₃₁	1	2	yes	—
669	#123	—	2	2	no	—
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	1	no	—
677	C₂²⋊Q₈	—	2	1	no	—
678	C₂²⋊Q₈	—	2	1	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	1	no	—
681	C₂²⋊Q₈	—	2	1	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	D₄×C₃₁	1	1	yes	characteristic
690	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
691	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
692	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
695	#121	—	2	1	no	—
696	#121	—	2	2	no	—
697	#121	D₄×C₃₁	1	1	yes	characteristic
698	#121	C₂³×C₃₁	1	2	yes	—
699	#120	—	2	2	no	—
700	C₄×Q₈	—	2	2	no	—
701	C₄×Q₈	—	2	1	no	—
702	C₄×Q₈	—	2	1	no	—
703	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
704	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
705	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
706	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
707	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
708	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₄×D₄	—	2	2	no	—
710	C₄×D₄	—	2	2	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	1	no	—
714	C₄×D₄	—	2	1	no	—
715	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
716	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
717	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
718	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
719	C₄×D₄	C₂³×C₃₁	1	2	yes	—
720	C₄×D₄	C₂³×C₃₁	1	2	yes	—
721	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
722	#117	—	2	1	no	—
723	#117	—	2	1	no	—
724	#117	—	2	2	no	—
725	#117	—	2	1	no	—
726	#117	—	2	2	no	—
727	#117	—	2	2	no	—
728	#117	C₂³×C₃₁	1	2	yes	—
729	#117	C₂³×C₃₁	1	2	yes	—
730	C₂×C₄⋊C₄	—	2	1	no	—
731	C₂×C₄⋊C₄	—	2	1	no	—
732	C₂×C₄⋊C₄	—	2	2	no	—
733	C₂×C₄⋊C₄	—	2	1	no	—
734	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
739	C₂×C₂²⋊C₄	—	2	1	no	—
740	C₂×C₂²⋊C₄	—	2	2	no	—
741	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
742	#107	C₂³×C₃₁	1	2	yes	—
743	#107	C₂³×C₃₁	1	2	yes	—
744	#107	C₂³×C₃₁	1	2	yes	—
745	#107	C₂³×C₃₁	1	2	yes	—
746	#107	C₂³×C₃₁	1	2	yes	—
747	#107	C₂³×C₃₁	1	2	yes	—
748	#107	C₂³×C₃₁	1	2	yes	—
749	#107	C₂³×C₃₁	1	2	yes	—
750	#106	C₂³×C₃₁	1	2	yes	—
751	#106	C₂³×C₃₁	1	2	yes	—
752	#106	C₂³×C₃₁	1	2	yes	—
753	#106	C₂³×C₃₁	1	2	yes	—
754	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
755	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
756	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
757	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
758	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
759	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
760	#103	C₂³×C₃₁	1	2	yes	—
761	#103	C₂³×C₃₁	1	2	yes	—
762	#103	C₂³×C₃₁	1	2	yes	—
763	#103	C₂³×C₃₁	1	2	yes	—
764	#103	C₂³×C₃₁	1	2	yes	—
765	#103	C₂³×C₃₁	1	2	yes	—
766	#103	C₂³×C₃₁	1	2	yes	—
767	#103	C₂³×C₃₁	1	2	yes	—
768	#103	C₂³×C₃₁	1	2	yes	—
769	#103	C₂³×C₃₁	1	2	yes	—
770	#102	C₂³×C₃₁	1	2	yes	—
771	#102	C₂³×C₃₁	1	2	yes	—
772	#102	C₂³×C₃₁	1	2	yes	—
773	#102	C₂³×C₃₁	1	2	yes	—
774	#102	C₂³×C₃₁	1	2	yes	—
775	#102	C₂³×C₃₁	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
779	#97	C₂³×C₃₁	1	2	yes	—
780	#97	C₂³×C₃₁	1	2	yes	—
781	C₄×C₈	C₂³×C₃₁	1	2	yes	—
782	C₃₁	#62165	1	1	yes	characteristic, direct product factor, Sylow
783	C₂⁴	—	2	1	no	—
784	#41	—	2	4	no	—
785	#41	—	4	2	no	—
786	#41	—	8	2	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	8	2	no	—
792	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
793	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
794	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	4	1	no	—
800	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
801	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
802	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
803	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	8	2	no	—
816	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
817	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
820	Q₁₆	—	4	2	no	—
821	Q₁₆	—	4	2	no	—
822	SD₁₆	—	2	4	no	—
823	SD₁₆	—	4	2	no	—
824	M₁₆	—	4	2	no	—
825	C₂×C₈	—	4	1	no	—
826	C₂×C₈	—	4	2	no	—
827	C₂×C₈	—	4	1	no	—
828	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
829	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
830	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
831	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	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	2	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
862	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
863	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
864	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
865	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
870	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
872	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
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	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	1	no	—
881	C₂²⋊C₄	—	2	1	no	—
882	C₂²⋊C₄	—	2	1	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
888	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
889	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
890	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
891	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
899	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
900	C₄²	C₂⁴×C₃₁	1	2	yes	—
901	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	4	2	no	—
906	C₂³	—	4	2	no	—
907	C₂³	—	8	1	no	—
908	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
909	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
910	Q₈	—	2	2	no	—
911	Q₈	—	2	2	no	—
912	Q₈	—	2	2	no	—
913	Q₈	—	2	2	no	—
914	Q₈	—	4	1	no	—
915	Q₈	—	4	2	no	—
916	Q₈	—	8	1	no	—
917	Q₈	—	8	2	no	—
918	Q₈	—	8	2	no	—
919	D₄	—	2	4	no	—
920	D₄	—	2	1	no	—
921	D₄	—	2	1	no	—
922	D₄	—	2	1	no	—
923	D₄	—	4	1	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	4	no	—
926	D₄	—	8	2	no	—
927	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	4	1	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	4	2	no	—
944	C₂×C₄	—	4	2	no	—
945	C₂×C₄	—	4	2	no	—
946	C₂×C₄	—	8	1	no	—
947	C₂×C₄	—	8	1	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	1	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	1	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
955	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
956	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
958	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
961	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
962	C₈	—	2	2	no	—
963	C₈	—	2	2	no	—
964	C₈	—	2	2	no	—
965	C₈	—	2	2	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	8	4	no	—
978	C₂²	C₃₁×#578	1	2	yes	—
979	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
980	C₄	—	2	2	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
997	C₄	C₃₁×#585	1	1	yes	characteristic
998	C₂	—	2	2	no	—
999	C₂	—	4	2	no	—
1000	C₂	—	4	2	no	—
1001	C₂	—	8	1	no	—
1002	C₂	C₃₁×#3489	1	1	yes	characteristic
1003	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1004	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3520	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×#3386	C₂	semidirect
4. C₃₁×#3377	C₂	semidirect
5. C₃₁×#3344	C₂	semidirect
6. C₃₁×#3343	C₂	semidirect
7. C₃₁×#3338	C₂	semidirect
8. C₃₁×#3315	C₂	semidirect
9. C₃₁×#3314	C₂	semidirect
10. C₃₁×#3296	C₂	semidirect
11. C₃₁×#3258	C₂	semidirect
12. C₃₁×#3249	C₂	semidirect
13. C₃₁×#3243	C₂	semidirect
14. C₃₁×#3236	C₂	semidirect
15. C₃₁×#3120	C₂	semidirect
16. C₃₁×#3110	C₂	semidirect
17. C₃₁×#3083	C₂	semidirect
18. C₂×C₃₁×#478	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
22. C₃₁×#557	C₂²	semidirect
29. C₃₁×#552	C₂²	semidirect
37. C₃₁×#544	C₂²	semidirect
40. C₃₁×#541	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#501	C₂²	semidirect
53. C₃₁×#500	C₂²	semidirect
54. C₃₁×#491	C₂²	semidirect
57. C₃₁×#485	C₂²	semidirect
60. C₃₁×#484	C₂²	semidirect
61. C₃₁×#484	C₂²	semidirect
63. C₃₁×#483	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#479	C₂²	semidirect
68. C₃₁×#479	C₂²	semidirect
74. C₃₁×#477	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#477	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
78. C₃₁×#475	C₂²	semidirect
82. C₃₁×#470	C₂²	semidirect
86. C₃₁×#467	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
91. C₃₁×#462	C₂²	semidirect
97. C₃₁×#446	C₂²	semidirect
98. C₃₁×#441	C₂²	semidirect
102. C₄×Q₁₆×C₃₁	C₂²	semidirect
105. C₃₁×#435	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
109. C₃₁×#428	C₂²	semidirect
111. C₂×C₃₁×#107	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
400. #62165	C₃₁	direct (N × H)
464. #3563	C₂×C₃₁	semidirect
466. #3386	C₂×C₃₁	semidirect
467. #3377	C₂×C₃₁	semidirect
468. #3344	C₂×C₃₁	semidirect
469. #3343	C₂×C₃₁	semidirect
470. #3338	C₂×C₃₁	semidirect
471. #3315	C₂×C₃₁	semidirect
472. #3314	C₂×C₃₁	semidirect
473. #3296	C₂×C₃₁	semidirect
474. #3258	C₂×C₃₁	semidirect
475. #3249	C₂×C₃₁	semidirect
476. #3243	C₂×C₃₁	semidirect
477. #3236	C₂×C₃₁	semidirect
478. #3120	C₂×C₃₁	semidirect
479. #3110	C₂×C₃₁	semidirect
480. #3083	C₂×C₃₁	semidirect
481. C₂×#478	C₂×C₃₁	semidirect
482. #2992	C₂×C₃₁	semidirect
517. #557	C₂²×C₃₁	semidirect
524. #552	C₂²×C₃₁	semidirect
532. #544	C₂²×C₃₁	semidirect
535. #541	C₂²×C₃₁	semidirect
546. #501	C₂²×C₃₁	semidirect
547. #501	C₂²×C₃₁	semidirect
548. #500	C₂²×C₃₁	semidirect
549. #491	C₂²×C₃₁	semidirect
552. #485	C₂²×C₃₁	semidirect
555. #484	C₂²×C₃₁	semidirect
556. #484	C₂²×C₃₁	semidirect
558. #483	C₂²×C₃₁	semidirect
561. #479	C₂²×C₃₁	semidirect
562. #479	C₂²×C₃₁	semidirect
563. #479	C₂²×C₃₁	semidirect
569. #477	C₂²×C₃₁	semidirect
570. #477	C₂²×C₃₁	semidirect
571. #477	C₂²×C₃₁	semidirect
572. #477	C₂²×C₃₁	semidirect
573. #475	C₂²×C₃₁	semidirect
577. #470	C₂²×C₃₁	semidirect
581. #467	C₂²×C₃₁	semidirect
585. #462	C₂²×C₃₁	semidirect
586. #462	C₂²×C₃₁	semidirect
592. #446	C₂²×C₃₁	semidirect
593. #441	C₂²×C₃₁	semidirect
597. C₄×Q₁₆	C₂²×C₃₁	semidirect
600. #435	C₂²×C₃₁	semidirect
602. #433	C₂²×C₃₁	semidirect
604. #428	C₂²×C₃₁	semidirect
606. C₂×#107	C₂²×C₃₁	semidirect
608. #424	C₂²×C₃₁	semidirect
782. C₃₁	#62165	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×#3520	2
C₃₁×#3386	2
C₃₁×#3377	2
C₃₁×#3344	2
C₃₁×#3343	2
C₃₁×#3338	2
C₃₁×#3315	2
C₃₁×#3314	2
C₃₁×#3296	2
C₃₁×#3258	2
C₃₁×#3249	2
C₃₁×#3243	2
C₃₁×#3236	2
C₃₁×#3120	2
C₃₁×#3110	2
C₃₁×#3083	2
C₂×C₃₁×#478	2
C₃₁×#2992	2
#62165	31

Subgroups — C31×#62165 #21518924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62165 #21518924