Subgroups — C₃₁×#62603 #21519362

Order 7936.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1010 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, complemented
2	C₃₁×#3544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3369	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3211	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3181	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3173	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#489	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	2	no	—
21	C₃₁×#563	—	2	1	no	—
22	C₃₁×#562	—	2	1	no	—
23	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#556	C₂²	1	2	yes	—
25	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#552	—	2	1	no	—
29	C₃₁×#552	C₂²	1	2	yes	—
30	C₃₁×#551	—	2	2	no	—
31	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
32	C₃₁×#548	C₂²	1	2	yes	—
33	C₃₁×#547	—	2	1	no	—
34	C₃₁×#547	C₂²	1	2	yes	—
35	C₃₁×#546	C₂²	1	2	yes	—
36	C₃₁×#544	—	2	1	no	—
37	C₃₁×#544	C₂²	1	2	yes	complemented
38	C₃₁×#543	—	2	1	no	—
39	C₃₁×#542	—	2	2	no	—
40	C₃₁×#542	—	2	1	no	—
41	C₃₁×#542	C₂²	1	2	yes	—
42	C₃₁×#542	C₂²	1	2	yes	complemented
43	C₃₁×#538	—	2	1	no	—
44	C₃₁×#536	—	2	2	no	—
45	C₃₁×#536	C₂²	1	2	yes	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
48	C₃₁×#529	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#498	C₂²	1	2	yes	complemented
53	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#495	C₂²	1	2	yes	—
55	C₃₁×#491	C₂²	1	2	yes	complemented
56	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#489	C₂²	1	2	yes	—
58	C₃₁×#489	C₂²	1	2	yes	—
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#489	C₂²	1	2	yes	—
61	C₃₁×#489	C₂²	1	2	yes	—
62	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#488	C₂²	1	2	yes	—
64	C₃₁×#488	C₂²	1	2	yes	—
65	C₃₁×#487	C₂²	1	2	yes	complemented
66	C₃₁×#487	C₂²	1	2	yes	complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#483	C₂²	1	2	yes	—
69	C₃₁×#483	C₂²	1	2	yes	—
70	C₃₁×#483	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#476	C₂²	1	2	yes	—
76	C₃₁×#475	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	2	yes	complemented
78	C₃₁×#475	C₂²	1	2	yes	complemented
79	C₃₁×#470	C₂²	1	2	yes	complemented
80	C₃₁×#469	C₂²	1	2	yes	—
81	C₃₁×#467	C₂²	1	2	yes	—
82	C₃₁×#465	C₂²	1	2	yes	—
83	C₃₁×#465	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	complemented
85	C₃₁×#464	C₂²	1	2	yes	—
86	C₃₁×#464	C₂²	1	2	yes	—
87	C₃₁×#463	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#462	C₂²	1	2	yes	complemented
90	C₃₁×#461	C₂²	1	2	yes	complemented
91	C₃₁×#452	C₂²	1	2	yes	—
92	C₃₁×#451	C₂²	1	1	yes	characteristic
93	C₃₁×#451	C₂²	1	2	yes	complemented
94	C₃₁×#450	C₂²	1	1	yes	characteristic
95	C₃₁×#449	C₂²	1	2	yes	—
96	C₃₁×#448	C₂²	1	1	yes	characteristic
97	C₃₁×#448	C₂²	1	2	yes	complemented
98	C₃₁×#447	C₂²	1	1	yes	characteristic
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#442	C₂²	1	2	yes	—
101	C₃₁×#441	C₂²	1	2	yes	complemented
102	C₃₁×#441	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
105	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₃₁×#435	C₂²	1	2	yes	—
107	C₃₁×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₃₁	C₂²	1	2	yes	—
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#431	C₂²	1	1	yes	characteristic
111	C₃₁×#419	C₂²	1	2	yes	complemented
112	C₃₁×#417	C₂²	1	2	yes	—
113	C₃₁×#416	C₂²	1	2	yes	—
114	C₂×C₃₁×#103	C₂²	1	2	yes	—
115	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
116	C₂×C₃₁×#102	C₂²	1	2	yes	—
117	C₃₁×#405	C₂²	1	2	yes	complemented
118	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂²×Q₈×C₃₁	—	2	1	no	—
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	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×SD₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×D₈×C₃₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
133	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	—	2	2	no	—
137	C₃₁×C₄⋊Q₈	—	2	1	no	—
138	C₃₁×C₄⋊Q₈	—	2	1	no	—
139	C₃₁×C₄⋊Q₈	—	2	1	no	—
140	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
145	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
146	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
147	C₃₁×#126	—	2	2	no	—
148	C₃₁×#126	—	2	2	no	—
149	C₃₁×#126	—	2	2	no	—
150	C₃₁×#126	—	2	2	no	—
151	C₃₁×#126	—	2	2	no	—
152	C₃₁×#126	—	2	1	no	—
153	C₃₁×#126	D₄	1	2	yes	—
154	C₃₁×#125	—	2	1	no	—
155	C₃₁×#125	—	2	2	no	—
156	C₃₁×#125	—	2	2	no	—
157	C₃₁×#125	—	2	1	no	—
158	C₃₁×#125	D₄	1	1	yes	characteristic
159	C₃₁×#125	C₂³	1	2	yes	—
160	C₃₁×#125	C₂³	1	1	yes	characteristic
161	C₃₁×#124	—	2	2	no	—
162	C₃₁×#124	—	2	2	no	—
163	C₃₁×#124	—	2	2	no	—
164	C₃₁×#124	—	2	2	no	—
165	C₃₁×#124	—	2	1	no	—
166	C₃₁×#124	—	2	1	no	—
167	C₃₁×#124	D₄	1	1	yes	characteristic
168	C₃₁×#124	C₂³	1	2	yes	—
169	C₃₁×#124	C₂³	1	2	yes	—
170	C₃₁×#124	C₂³	1	2	yes	—
171	C₃₁×#124	C₂³	1	1	yes	characteristic
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	—	2	1	no	—
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	—	2	2	no	—
181	C₃₁×#123	D₄	1	2	yes	—
182	C₃₁×C₂²⋊Q₈	—	2	1	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
198	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	D₄	1	1	yes	characteristic
206	C₃₁×#121	C₂³	1	1	yes	characteristic
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#120	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	1	no	—
219	C₄×D₄×C₃₁	—	2	1	no	—
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	C₂³	1	2	yes	—
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₃₁	C₂³	1	2	yes	—
225	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
226	C₃₁×#117	—	2	1	no	—
227	C₃₁×#117	—	2	2	no	—
228	C₃₁×#117	—	2	1	no	—
229	C₃₁×#117	—	2	2	no	—
230	C₃₁×#117	—	2	1	no	—
231	C₃₁×#117	C₂³	1	2	yes	—
232	C₃₁×#117	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
234	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
240	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#106	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#102	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	1	yes	characteristic
275	C₃₁×#97	C₂³	1	1	yes	characteristic
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₃₁	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	8	4	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	2	no	—
286	C₂×Q₈×C₃₁	—	2	1	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	2	2	no	—
289	C₂×Q₈×C₃₁	—	2	2	no	—
290	C₂×Q₈×C₃₁	—	2	1	no	—
291	C₂×Q₈×C₃₁	—	4	2	no	—
292	C₂×Q₈×C₃₁	—	4	2	no	—
293	C₂×Q₈×C₃₁	—	4	2	no	—
294	C₂×Q₈×C₃₁	—	8	2	no	—
295	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
297	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₂×D₄×C₃₁	—	2	1	no	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	2	2	no	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	—	2	1	no	—
304	C₂×D₄×C₃₁	—	4	2	no	—
305	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
306	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
308	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	—	2	1	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	—	2	2	no	—
313	C₂²×C₄×C₃₁	—	2	1	no	—
314	C₂²×C₄×C₃₁	—	2	2	no	—
315	C₂²×C₄×C₃₁	—	2	2	no	—
316	C₂²×C₄×C₃₁	—	2	2	no	—
317	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
321	Q₁₆×C₃₁	—	4	2	no	—
322	Q₁₆×C₃₁	—	4	2	no	—
323	SD₁₆×C₃₁	—	4	2	no	—
324	SD₁₆×C₃₁	—	4	2	no	—
325	SD₁₆×C₃₁	—	4	2	no	—
326	D₈×C₃₁	—	4	2	no	—
327	M₁₆×C₃₁	—	4	2	no	—
328	C₂×C₈×C₃₁	—	4	2	no	—
329	C₂×C₈×C₃₁	—	4	2	no	—
330	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
331	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
333	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₃₁	—	2	1	no	—
335	C₄⋊C₄×C₃₁	—	2	1	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	2	no	—
343	C₄⋊C₄×C₃₁	—	2	1	no	—
344	C₄⋊C₄×C₃₁	—	2	1	no	—
345	C₄⋊C₄×C₃₁	—	2	1	no	—
346	C₄⋊C₄×C₃₁	—	2	1	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	1	no	—
352	C₄⋊C₄×C₃₁	—	2	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	2	no	—
357	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
361	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	1	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	2	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	1	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	1	no	—
383	C₂²⋊C₄×C₃₁	—	2	1	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	1	no	—
387	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₄²×C₃₁	—	2	2	no	—
393	C₄²×C₃₁	—	2	2	no	—
394	C₄²×C₃₁	—	2	1	no	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	—	2	2	no	—
397	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄²×C₃₁	C₂⁴	1	2	yes	—
401	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
402	#62603	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂³×C₃₁	—	2	1	no	—
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	—	4	2	no	—
406	C₂³×C₃₁	—	8	1	no	—
407	C₂³×C₃₁	—	8	1	no	—
408	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
409	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₃₁	—	2	2	no	—
411	Q₈×C₃₁	—	2	2	no	—
412	Q₈×C₃₁	—	2	2	no	—
413	Q₈×C₃₁	—	2	2	no	—
414	Q₈×C₃₁	—	2	2	no	—
415	Q₈×C₃₁	—	4	1	no	—
416	Q₈×C₃₁	—	8	1	no	—
417	Q₈×C₃₁	—	8	2	no	—
418	Q₈×C₃₁	—	8	1	no	—
419	Q₈×C₃₁	—	8	1	no	—
420	Q₈×C₃₁	—	8	2	no	—
421	Q₈×C₃₁	—	8	1	no	—
422	Q₈×C₃₁	—	8	2	no	—
423	D₄×C₃₁	—	2	4	no	—
424	D₄×C₃₁	—	2	2	no	—
425	D₄×C₃₁	—	2	2	no	—
426	D₄×C₃₁	—	2	2	no	—
427	D₄×C₃₁	—	4	1	no	—
428	D₄×C₃₁	—	4	2	no	—
429	D₄×C₃₁	—	8	1	no	—
430	D₄×C₃₁	—	8	2	no	—
431	D₄×C₃₁	—	8	2	no	—
432	D₄×C₃₁	—	8	2	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	1	no	—
438	C₂×C₄×C₃₁	—	2	1	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	2	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	2	no	—
443	C₂×C₄×C₃₁	—	2	1	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	4	1	no	—
446	C₂×C₄×C₃₁	—	4	2	no	—
447	C₂×C₄×C₃₁	—	4	4	no	—
448	C₂×C₄×C₃₁	—	8	2	no	—
449	C₂×C₄×C₃₁	—	8	2	no	—
450	C₂×C₄×C₃₁	—	8	2	no	—
451	C₂×C₄×C₃₁	—	8	2	no	—
452	C₂×C₄×C₃₁	—	8	1	no	—
453	C₂×C₄×C₃₁	—	8	2	no	—
454	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
463	C₈×C₃₁	—	2	2	no	—
464	C₈×C₃₁	—	2	2	no	—
465	C₈×C₃₁	—	2	2	no	—
466	C₈×C₃₁	—	2	2	no	—
467	#3561	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#3544	C₂×C₃₁	1	1	yes	characteristic, complemented
469	#3376	C₂×C₃₁	1	2	yes	complemented
470	#3369	C₂×C₃₁	1	2	yes	complemented
471	#3321	C₂×C₃₁	1	2	yes	complemented
472	#3316	C₂×C₃₁	1	2	yes	complemented
473	#3312	C₂×C₃₁	1	2	yes	complemented
474	#3306	C₂×C₃₁	1	2	yes	complemented
475	#3298	C₂×C₃₁	1	2	yes	complemented
476	#3296	C₂×C₃₁	1	2	yes	complemented
477	#3244	C₂×C₃₁	1	2	yes	complemented
478	#3229	C₂×C₃₁	1	1	yes	characteristic, complemented
479	#3225	C₂×C₃₁	1	2	yes	complemented
480	#3211	C₂×C₃₁	1	1	yes	characteristic, complemented
481	#3181	C₂×C₃₁	1	1	yes	characteristic, complemented
482	#3173	C₂×C₃₁	1	2	yes	complemented
483	#3137	C₂×C₃₁	1	2	yes	complemented
484	C₂×#489	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#2968	C₂×C₃₁	1	1	yes	characteristic, complemented
486	C₂²×C₃₁	—	2	1	no	—
487	C₂²×C₃₁	—	2	1	no	—
488	C₂²×C₃₁	—	2	2	no	—
489	C₂²×C₃₁	—	2	2	no	—
490	C₂²×C₃₁	—	2	2	no	—
491	C₂²×C₃₁	—	4	1	no	—
492	C₂²×C₃₁	—	4	2	no	—
493	C₂²×C₃₁	—	4	2	no	—
494	C₂²×C₃₁	—	4	1	no	—
495	C₂²×C₃₁	—	4	1	no	—
496	C₂²×C₃₁	—	4	2	no	—
497	C₂²×C₃₁	—	16	2	no	—
498	C₂²×C₃₁	#577	1	2	yes	—
499	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
500	C₄×C₃₁	—	2	1	no	—
501	C₄×C₃₁	—	2	1	no	—
502	C₄×C₃₁	—	2	2	no	—
503	C₄×C₃₁	—	2	2	no	—
504	C₄×C₃₁	—	2	1	no	—
505	C₄×C₃₁	—	2	1	no	—
506	C₄×C₃₁	—	2	1	no	—
507	C₄×C₃₁	—	2	2	no	—
508	C₄×C₃₁	—	4	1	no	—
509	C₄×C₃₁	—	4	2	no	—
510	C₄×C₃₁	—	4	2	no	—
511	C₄×C₃₁	—	4	2	no	—
512	C₄×C₃₁	—	4	1	no	—
513	C₄×C₃₁	—	4	2	no	—
514	C₄×C₃₁	—	4	2	no	—
515	C₄×C₃₁	—	4	1	no	—
516	C₄×C₃₁	#585	1	2	yes	—
517	#563	—	2	2	no	—
518	#563	—	2	1	no	—
519	#562	—	2	1	no	—
520	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
521	#556	C₂²×C₃₁	1	2	yes	—
522	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
523	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
524	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
525	#552	—	2	1	no	—
526	#552	C₂²×C₃₁	1	2	yes	—
527	#551	—	2	2	no	—
528	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
529	#548	C₂²×C₃₁	1	2	yes	—
530	#547	—	2	1	no	—
531	#547	C₂²×C₃₁	1	2	yes	—
532	#546	C₂²×C₃₁	1	2	yes	—
533	#544	—	2	1	no	—
534	#544	C₂²×C₃₁	1	2	yes	complemented
535	#543	—	2	1	no	—
536	#542	—	2	2	no	—
537	#542	—	2	1	no	—
538	#542	C₂²×C₃₁	1	2	yes	—
539	#542	C₂²×C₃₁	1	2	yes	complemented
540	#538	—	2	1	no	—
541	#536	—	2	2	no	—
542	#536	C₂²×C₃₁	1	2	yes	—
543	#533	C₂²×C₃₁	1	1	yes	characteristic
544	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
545	#529	C₂²×C₃₁	1	1	yes	characteristic
546	#529	C₂²×C₃₁	1	1	yes	characteristic
547	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
548	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
549	#498	C₂²×C₃₁	1	2	yes	complemented
550	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
551	#495	C₂²×C₃₁	1	2	yes	—
552	#491	C₂²×C₃₁	1	2	yes	complemented
553	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#489	C₂²×C₃₁	1	2	yes	—
555	#489	C₂²×C₃₁	1	2	yes	—
556	#489	C₂²×C₃₁	1	2	yes	—
557	#489	C₂²×C₃₁	1	2	yes	—
558	#489	C₂²×C₃₁	1	2	yes	—
559	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	#488	C₂²×C₃₁	1	2	yes	—
561	#488	C₂²×C₃₁	1	2	yes	—
562	#487	C₂²×C₃₁	1	2	yes	complemented
563	#487	C₂²×C₃₁	1	2	yes	complemented
564	#485	C₂²×C₃₁	1	2	yes	complemented
565	#483	C₂²×C₃₁	1	2	yes	—
566	#483	C₂²×C₃₁	1	2	yes	—
567	#483	C₂²×C₃₁	1	2	yes	complemented
568	#482	C₂²×C₃₁	1	2	yes	—
569	#481	C₂²×C₃₁	1	2	yes	—
570	#479	C₂²×C₃₁	1	2	yes	complemented
571	#478	C₂²×C₃₁	1	2	yes	—
572	#476	C₂²×C₃₁	1	2	yes	—
573	#475	C₂²×C₃₁	1	2	yes	complemented
574	#475	C₂²×C₃₁	1	2	yes	complemented
575	#475	C₂²×C₃₁	1	2	yes	complemented
576	#470	C₂²×C₃₁	1	2	yes	complemented
577	#469	C₂²×C₃₁	1	2	yes	—
578	#467	C₂²×C₃₁	1	2	yes	—
579	#465	C₂²×C₃₁	1	2	yes	—
580	#465	C₂²×C₃₁	1	2	yes	—
581	#465	C₂²×C₃₁	1	2	yes	complemented
582	#464	C₂²×C₃₁	1	2	yes	—
583	#464	C₂²×C₃₁	1	2	yes	—
584	#463	C₂²×C₃₁	1	2	yes	—
585	#463	C₂²×C₃₁	1	2	yes	—
586	#462	C₂²×C₃₁	1	2	yes	complemented
587	#461	C₂²×C₃₁	1	2	yes	complemented
588	#452	C₂²×C₃₁	1	2	yes	—
589	#451	C₂²×C₃₁	1	1	yes	characteristic
590	#451	C₂²×C₃₁	1	2	yes	complemented
591	#450	C₂²×C₃₁	1	1	yes	characteristic
592	#449	C₂²×C₃₁	1	2	yes	—
593	#448	C₂²×C₃₁	1	1	yes	characteristic
594	#448	C₂²×C₃₁	1	2	yes	complemented
595	#447	C₂²×C₃₁	1	1	yes	characteristic
596	#446	C₂²×C₃₁	1	2	yes	complemented
597	#442	C₂²×C₃₁	1	2	yes	—
598	#441	C₂²×C₃₁	1	2	yes	complemented
599	#441	C₂²×C₃₁	1	2	yes	complemented
600	#440	C₂²×C₃₁	1	2	yes	complemented
601	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
602	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
603	#435	C₂²×C₃₁	1	2	yes	—
604	#435	C₂²×C₃₁	1	2	yes	complemented
605	C₈×D₄	C₂²×C₃₁	1	2	yes	—
606	#433	C₂²×C₃₁	1	2	yes	complemented
607	#431	C₂²×C₃₁	1	1	yes	characteristic
608	#419	C₂²×C₃₁	1	2	yes	complemented
609	#417	C₂²×C₃₁	1	2	yes	—
610	#416	C₂²×C₃₁	1	2	yes	—
611	C₂×#103	C₂²×C₃₁	1	2	yes	—
612	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
613	C₂×#102	C₂²×C₃₁	1	2	yes	—
614	#405	C₂²×C₃₁	1	2	yes	complemented
615	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
616	C₂×C₃₁	—	2	2	no	—
617	C₂×C₃₁	—	4	2	no	—
618	C₂×C₃₁	—	8	1	no	—
619	C₂×C₃₁	—	8	2	no	—
620	C₂×C₃₁	#3500	1	1	yes	characteristic
621	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
622	C₂×C₃₁	#3586	1	1	yes	characteristic
623	C₂×#41	—	2	2	no	—
624	C₂×#41	C₂³×C₃₁	1	2	yes	—
625	C₂²×Q₈	—	2	1	no	—
626	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
627	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
628	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
629	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
630	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
634	C₂×D₈	C₂³×C₃₁	1	2	yes	—
635	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
636	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
637	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
638	C₄⋊Q₈	—	2	2	no	—
639	C₄⋊Q₈	—	2	2	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	1	no	—
642	C₄⋊Q₈	—	2	1	no	—
643	C₄⋊Q₈	—	2	1	no	—
644	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
646	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
647	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
648	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	1	no	—
657	#126	D₄×C₃₁	1	2	yes	—
658	#125	—	2	1	no	—
659	#125	—	2	2	no	—
660	#125	—	2	2	no	—
661	#125	—	2	1	no	—
662	#125	D₄×C₃₁	1	1	yes	characteristic
663	#125	C₂³×C₃₁	1	1	yes	characteristic
664	#125	C₂³×C₃₁	1	2	yes	—
665	#124	—	2	2	no	—
666	#124	—	2	2	no	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	1	no	—
670	#124	—	2	1	no	—
671	#124	D₄×C₃₁	1	1	yes	characteristic
672	#124	C₂³×C₃₁	1	2	yes	—
673	#124	C₂³×C₃₁	1	2	yes	—
674	#124	C₂³×C₃₁	1	1	yes	characteristic
675	#124	C₂³×C₃₁	1	2	yes	—
676	#123	—	2	2	no	—
677	#123	—	2	1	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	D₄×C₃₁	1	2	yes	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
702	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
703	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
704	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
705	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
706	#121	—	2	2	no	—
707	#121	—	2	1	no	—
708	#121	—	2	2	no	—
709	#121	D₄×C₃₁	1	1	yes	characteristic
710	#121	C₂³×C₃₁	1	1	yes	characteristic
711	#121	C₂³×C₃₁	1	2	yes	—
712	#121	C₂³×C₃₁	1	2	yes	—
713	#120	—	2	2	no	—
714	C₄×Q₈	—	2	1	no	—
715	C₄×Q₈	—	2	1	no	—
716	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
718	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
719	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
720	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	1	no	—
723	C₄×D₄	—	2	1	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
726	C₄×D₄	C₂³×C₃₁	1	2	yes	—
727	C₄×D₄	C₂³×C₃₁	1	2	yes	—
728	C₄×D₄	C₂³×C₃₁	1	2	yes	—
729	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
730	#117	—	2	1	no	—
731	#117	—	2	2	no	—
732	#117	—	2	1	no	—
733	#117	—	2	2	no	—
734	#117	—	2	1	no	—
735	#117	C₂³×C₃₁	1	2	yes	—
736	#117	C₂³×C₃₁	1	2	yes	—
737	C₂×C₄⋊C₄	—	2	1	no	—
738	C₂×C₄⋊C₄	—	2	1	no	—
739	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
741	C₂×C₂²⋊C₄	—	2	1	no	—
742	C₂×C₂²⋊C₄	—	2	1	no	—
743	C₂×C₂²⋊C₄	—	2	2	no	—
744	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
745	#107	C₂³×C₃₁	1	2	yes	—
746	#106	C₂³×C₃₁	1	2	yes	—
747	#106	C₂³×C₃₁	1	2	yes	—
748	#106	C₂³×C₃₁	1	2	yes	—
749	#106	C₂³×C₃₁	1	2	yes	—
750	#106	C₂³×C₃₁	1	2	yes	—
751	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
752	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
753	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
754	#103	C₂³×C₃₁	1	2	yes	—
755	#103	C₂³×C₃₁	1	2	yes	—
756	#103	C₂³×C₃₁	1	2	yes	—
757	#103	C₂³×C₃₁	1	2	yes	—
758	#103	C₂³×C₃₁	1	2	yes	—
759	#103	C₂³×C₃₁	1	2	yes	—
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	#102	C₂³×C₃₁	1	2	yes	—
768	#102	C₂³×C₃₁	1	2	yes	—
769	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
775	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
778	#97	C₂³×C₃₁	1	1	yes	characteristic
779	#97	C₂³×C₃₁	1	1	yes	characteristic
780	#97	C₂³×C₃₁	1	2	yes	—
781	#97	C₂³×C₃₁	1	2	yes	—
782	C₄×C₈	C₂³×C₃₁	1	2	yes	—
783	C₄×C₈	C₂³×C₃₁	1	2	yes	—
784	C₃₁	#62603	1	1	yes	characteristic, direct product factor, Sylow
785	C₂⁴	—	2	1	no	—
786	#41	—	4	2	no	—
787	#41	—	4	2	no	—
788	#41	—	8	4	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	4	2	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	—	4	2	no	—
799	C₂×Q₈	—	8	2	no	—
800	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
801	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
802	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
803	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	4	2	no	—
810	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
811	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
812	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
813	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
823	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
826	Q₁₆	—	4	2	no	—
827	Q₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	SD₁₆	—	4	2	no	—
830	SD₁₆	—	4	2	no	—
831	D₈	—	4	2	no	—
832	M₁₆	—	4	2	no	—
833	C₂×C₈	—	4	2	no	—
834	C₂×C₈	—	4	2	no	—
835	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
836	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
837	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
838	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	1	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	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
863	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
864	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
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	1	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	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	1	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	1	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
893	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
894	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	1	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
903	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
904	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₄²	C₂⁴×C₃₁	1	2	yes	—
906	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₂³	—	2	1	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	4	2	no	—
910	C₂³	—	8	1	no	—
911	C₂³	—	8	1	no	—
912	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
913	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
914	Q₈	—	2	2	no	—
915	Q₈	—	2	2	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	2	2	no	—
919	Q₈	—	4	1	no	—
920	Q₈	—	8	1	no	—
921	Q₈	—	8	2	no	—
922	Q₈	—	8	1	no	—
923	Q₈	—	8	1	no	—
924	Q₈	—	8	2	no	—
925	Q₈	—	8	1	no	—
926	Q₈	—	8	2	no	—
927	D₄	—	2	4	no	—
928	D₄	—	2	2	no	—
929	D₄	—	2	2	no	—
930	D₄	—	2	2	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	2	no	—
933	D₄	—	8	1	no	—
934	D₄	—	8	2	no	—
935	D₄	—	8	2	no	—
936	D₄	—	8	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	4	1	no	—
950	C₂×C₄	—	4	2	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	—	8	2	no	—
955	C₂×C₄	—	8	2	no	—
956	C₂×C₄	—	8	1	no	—
957	C₂×C₄	—	8	2	no	—
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	2	yes	—
961	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
962	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
963	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
966	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
967	C₈	—	2	2	no	—
968	C₈	—	2	2	no	—
969	C₈	—	2	2	no	—
970	C₈	—	2	2	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	16	2	no	—
983	C₂²	C₃₁×#577	1	2	yes	—
984	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
985	C₄	—	2	2	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	2	no	—
1001	C₄	C₃₁×#585	1	2	yes	—
1002	C₂	—	2	2	no	—
1003	C₂	—	4	2	no	—
1004	C₂	—	8	2	no	—
1005	C₂	—	8	1	no	—
1006	C₂	C₃₁×#3500	1	1	yes	characteristic
1007	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1008	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
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×#3561	C₂	semidirect
2. C₃₁×#3544	C₂	semidirect
3. C₃₁×#3376	C₂	semidirect
4. C₃₁×#3369	C₂	semidirect
5. C₃₁×#3321	C₂	semidirect
6. C₃₁×#3316	C₂	semidirect
7. C₃₁×#3312	C₂	semidirect
8. C₃₁×#3306	C₂	semidirect
9. C₃₁×#3298	C₂	semidirect
10. C₃₁×#3296	C₂	semidirect
11. C₃₁×#3244	C₂	semidirect
12. C₃₁×#3229	C₂	semidirect
13. C₃₁×#3225	C₂	semidirect
14. C₃₁×#3211	C₂	semidirect
15. C₃₁×#3181	C₂	semidirect
16. C₃₁×#3173	C₂	semidirect
17. C₃₁×#3137	C₂	semidirect
18. C₂×C₃₁×#489	C₂	semidirect
19. C₃₁×#2968	C₂	semidirect
23. Q₈²×C₃₁	C₂²	semidirect
25. C₃₁×#555	C₂²	semidirect
26. C₃₁×#554	C₂²	semidirect
27. C₃₁×#554	C₂²	semidirect
37. C₃₁×#544	C₂²	semidirect
42. C₃₁×#542	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#498	C₂²	semidirect
53. C₃₁×#497	C₂²	semidirect
55. C₃₁×#491	C₂²	semidirect
56. C₃₁×#491	C₂²	semidirect
62. C₃₁×#489	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
70. C₃₁×#483	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
76. C₃₁×#475	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
78. C₃₁×#475	C₂²	semidirect
79. C₃₁×#470	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
93. C₃₁×#451	C₂²	semidirect
97. C₃₁×#448	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
101. C₃₁×#441	C₂²	semidirect
102. C₃₁×#441	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
105. C₄×SD₁₆×C₃₁	C₂²	semidirect
107. C₃₁×#435	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
111. C₃₁×#419	C₂²	semidirect
115. C₂×C₃₁×#103	C₂²	semidirect
117. C₃₁×#405	C₂²	semidirect
402. #62603	C₃₁	direct (N × H)
467. #3561	C₂×C₃₁	semidirect
468. #3544	C₂×C₃₁	semidirect
469. #3376	C₂×C₃₁	semidirect
470. #3369	C₂×C₃₁	semidirect
471. #3321	C₂×C₃₁	semidirect
472. #3316	C₂×C₃₁	semidirect
473. #3312	C₂×C₃₁	semidirect
474. #3306	C₂×C₃₁	semidirect
475. #3298	C₂×C₃₁	semidirect
476. #3296	C₂×C₃₁	semidirect
477. #3244	C₂×C₃₁	semidirect
478. #3229	C₂×C₃₁	semidirect
479. #3225	C₂×C₃₁	semidirect
480. #3211	C₂×C₃₁	semidirect
481. #3181	C₂×C₃₁	semidirect
482. #3173	C₂×C₃₁	semidirect
483. #3137	C₂×C₃₁	semidirect
484. C₂×#489	C₂×C₃₁	semidirect
485. #2968	C₂×C₃₁	semidirect
520. Q₈²	C₂²×C₃₁	semidirect
522. #555	C₂²×C₃₁	semidirect
523. #554	C₂²×C₃₁	semidirect
524. #554	C₂²×C₃₁	semidirect
534. #544	C₂²×C₃₁	semidirect
539. #542	C₂²×C₃₁	semidirect
548. #501	C₂²×C₃₁	semidirect
549. #498	C₂²×C₃₁	semidirect
550. #497	C₂²×C₃₁	semidirect
552. #491	C₂²×C₃₁	semidirect
553. #491	C₂²×C₃₁	semidirect
559. #489	C₂²×C₃₁	semidirect
562. #487	C₂²×C₃₁	semidirect
563. #487	C₂²×C₃₁	semidirect
564. #485	C₂²×C₃₁	semidirect
567. #483	C₂²×C₃₁	semidirect
570. #479	C₂²×C₃₁	semidirect
573. #475	C₂²×C₃₁	semidirect
574. #475	C₂²×C₃₁	semidirect
575. #475	C₂²×C₃₁	semidirect
576. #470	C₂²×C₃₁	semidirect
581. #465	C₂²×C₃₁	semidirect
586. #462	C₂²×C₃₁	semidirect
587. #461	C₂²×C₃₁	semidirect
590. #451	C₂²×C₃₁	semidirect
594. #448	C₂²×C₃₁	semidirect
596. #446	C₂²×C₃₁	semidirect
598. #441	C₂²×C₃₁	semidirect
599. #441	C₂²×C₃₁	semidirect
600. #440	C₂²×C₃₁	semidirect
602. C₄×SD₁₆	C₂²×C₃₁	semidirect
604. #435	C₂²×C₃₁	semidirect
606. #433	C₂²×C₃₁	semidirect
608. #419	C₂²×C₃₁	semidirect
612. C₂×#103	C₂²×C₃₁	semidirect
614. #405	C₂²×C₃₁	semidirect
784. C₃₁	#62603	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×#3544	2
C₃₁×#3376	2
C₃₁×#3369	2
C₃₁×#3321	2
C₃₁×#3316	2
C₃₁×#3312	2
C₃₁×#3306	2
C₃₁×#3298	2
C₃₁×#3296	2
C₃₁×#3244	2
C₃₁×#3229	2
C₃₁×#3225	2
C₃₁×#3211	2
C₃₁×#3181	2
C₃₁×#3173	2
C₃₁×#3137	2
C₂×C₃₁×#489	2
C₃₁×#2968	2
#62603	31

Subgroups — C31×#62603 #21519362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62603 #21519362