Subgroups — C₃₁×#62091 #21518850

Order 7936.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1050 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×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3369	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3275	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3263	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3044	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#137	C₂²	1	2	yes	—
22	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
24	C₃₁×#563	—	2	1	no	—
25	C₃₁×#562	—	2	1	no	—
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	—	2	2	no	—
28	C₃₁×#556	—	2	1	no	—
29	C₃₁×#556	C₂²	1	2	yes	—
30	C₃₁×#556	C₂²	1	2	yes	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#555	—	2	1	no	—
33	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#551	—	2	2	no	—
35	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#548	C₂²	1	2	yes	—
38	C₃₁×#548	C₂²	1	2	yes	—
39	C₃₁×#546	C₂²	1	2	yes	—
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	—	2	2	no	—
42	C₃₁×#542	—	2	2	no	—
43	C₃₁×#542	C₂²	1	2	yes	—
44	C₃₁×#542	C₂²	1	2	yes	complemented
45	C₃₁×#538	—	2	1	no	—
46	C₃₁×#536	C₂²	1	2	yes	—
47	C₃₁×#533	—	2	1	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
53	C₃₁×#519	C₂²	1	2	yes	complemented
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₃₁×#497	C₂²	1	2	yes	—
56	C₃₁×#497	C₂²	1	2	yes	complemented
57	C₃₁×#495	C₂²	1	2	yes	—
58	C₃₁×#489	C₂²	1	2	yes	—
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#487	C₂²	1	2	yes	complemented
61	C₃₁×#485	C₂²	1	2	yes	—
62	C₃₁×#485	C₂²	1	2	yes	complemented
63	C₃₁×#482	C₂²	1	2	yes	—
64	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#476	C₂²	1	2	yes	—
66	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#475	C₂²	1	2	yes	complemented
68	C₃₁×#475	C₂²	1	2	yes	complemented
69	C₃₁×#475	C₂²	1	2	yes	complemented
70	C₃₁×#470	C₂²	1	2	yes	—
71	C₃₁×#470	C₂²	1	2	yes	—
72	C₃₁×#470	C₂²	1	2	yes	complemented
73	C₃₁×#469	C₂²	1	2	yes	—
74	C₃₁×#465	C₂²	1	2	yes	—
75	C₃₁×#465	C₂²	1	2	yes	complemented
76	C₃₁×#464	C₂²	1	2	yes	—
77	C₃₁×#464	C₂²	1	2	yes	—
78	C₃₁×#464	C₂²	1	2	yes	—
79	C₃₁×#464	C₂²	1	2	yes	—
80	C₃₁×#464	C₂²	1	2	yes	—
81	C₃₁×#464	C₂²	1	2	yes	—
82	C₃₁×#464	C₂²	1	2	yes	complemented
83	C₃₁×#463	C₂²	1	2	yes	—
84	C₃₁×#463	C₂²	1	2	yes	—
85	C₃₁×#463	C₂²	1	2	yes	—
86	C₃₁×#462	C₂²	1	2	yes	complemented
87	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#462	C₂²	1	2	yes	complemented
89	C₃₁×#462	C₂²	1	2	yes	complemented
90	C₃₁×#462	C₂²	1	2	yes	complemented
91	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#452	C₂²	1	2	yes	—
93	C₃₁×#452	C₂²	1	2	yes	—
94	C₃₁×#451	C₂²	1	2	yes	—
95	C₃₁×#451	C₂²	1	2	yes	complemented
96	C₃₁×#451	C₂²	1	2	yes	complemented
97	C₃₁×#450	C₂²	1	2	yes	—
98	C₃₁×#449	C₂²	1	2	yes	—
99	C₃₁×#448	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#441	C₂²	1	2	yes	complemented
103	C₃₁×#441	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	—
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
108	C₃₁×#436	C₂²	1	2	yes	—
109	C₃₁×#435	C₂²	1	2	yes	—
110	C₃₁×#435	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#432	C₂²	1	1	yes	characteristic
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₃₁×#423	C₂²	1	1	yes	characteristic
115	C₃₁×#419	C₂²	1	1	yes	characteristic
116	C₃₁×#419	C₂²	1	2	yes	complemented
117	C₃₁×#418	C₂²	1	1	yes	characteristic
118	C₃₁×#416	C₂²	1	2	yes	—
119	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
124	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₃₁×#137	—	4	4	no	—
126	C₃₁×#137	—	4	2	no	—
127	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
128	C₂×Q₁₆×C₃₁	—	4	4	no	—
129	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×D₈×C₃₁	C₂³	1	2	yes	—
141	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
145	C₃₁×C₄⋊Q₈	—	2	1	no	—
146	C₃₁×C₄⋊Q₈	—	2	1	no	—
147	C₃₁×C₄⋊Q₈	—	2	2	no	—
148	C₃₁×C₄⋊Q₈	—	2	2	no	—
149	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
150	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×#126	—	2	2	no	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	D₄	1	2	yes	—
163	C₃₁×#125	—	2	1	no	—
164	C₃₁×#125	—	2	1	no	—
165	C₃₁×#125	D₄	1	1	yes	characteristic
166	C₃₁×#124	—	2	2	no	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	2	no	—
169	C₃₁×#124	—	2	2	no	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	1	no	—
173	C₃₁×#124	—	2	1	no	—
174	C₃₁×#124	D₄	1	1	yes	characteristic
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#124	C₂³	1	2	yes	—
177	C₃₁×#124	C₂³	1	2	yes	—
178	C₃₁×#124	C₂³	1	2	yes	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	D₄	1	2	yes	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	D₄	1	1	yes	characteristic
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#120	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	2	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	C₂³	1	2	yes	—
232	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	2	yes	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₃₁×#117	—	2	1	no	—
237	C₃₁×#117	—	2	1	no	—
238	C₃₁×#117	—	2	1	no	—
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	—	2	2	no	—
242	C₃₁×#117	—	2	2	no	—
243	C₃₁×#117	—	2	1	no	—
244	C₃₁×#117	C₂³	1	2	yes	—
245	C₃₁×#117	C₂³	1	1	yes	characteristic
246	C₃₁×#117	C₂³	1	2	yes	—
247	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂×C₄²×C₃₁	—	2	1	no	—
251	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#107	C₂³	1	2	yes	—
253	C₃₁×#106	C₂³	1	2	yes	—
254	C₃₁×#106	C₂³	1	2	yes	—
255	C₃₁×#106	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
261	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#103	C₂³	1	2	yes	—
271	C₃₁×#103	C₂³	1	2	yes	—
272	C₃₁×#103	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₃₁×#97	C₂³	1	2	yes	—
282	C₃₁×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₃₁	C₂³	1	2	yes	—
284	C₂⁴×C₃₁	—	2	1	no	—
285	#41×C₃₁	—	2	2	no	—
286	#41×C₃₁	—	4	1	no	—
287	#41×C₃₁	—	4	2	no	—
288	#41×C₃₁	—	4	2	no	—
289	C₂×Q₈×C₃₁	—	2	2	no	—
290	C₂×Q₈×C₃₁	—	2	1	no	—
291	C₂×Q₈×C₃₁	—	2	1	no	—
292	C₂×Q₈×C₃₁	—	2	2	no	—
293	C₂×Q₈×C₃₁	—	2	2	no	—
294	C₂×Q₈×C₃₁	—	2	1	no	—
295	C₂×Q₈×C₃₁	—	2	4	no	—
296	C₂×Q₈×C₃₁	—	4	2	no	—
297	C₂×Q₈×C₃₁	—	4	2	no	—
298	C₂×Q₈×C₃₁	—	4	1	no	—
299	C₂×Q₈×C₃₁	—	4	1	no	—
300	C₂×Q₈×C₃₁	—	4	2	no	—
301	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₃₁	—	2	1	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	1	no	—
311	C₂×D₄×C₃₁	—	4	1	no	—
312	C₂×D₄×C₃₁	—	4	1	no	—
313	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
316	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₃₁	—	2	2	no	—
318	C₂²×C₄×C₃₁	—	2	1	no	—
319	C₂²×C₄×C₃₁	—	2	2	no	—
320	C₂²×C₄×C₃₁	—	2	1	no	—
321	C₂²×C₄×C₃₁	—	2	1	no	—
322	C₂²×C₄×C₃₁	—	2	1	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	2	no	—
325	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
329	Q₁₆×C₃₁	—	2	4	no	—
330	Q₁₆×C₃₁	—	2	4	no	—
331	Q₁₆×C₃₁	—	4	2	no	—
332	Q₁₆×C₃₁	—	4	2	no	—
333	Q₁₆×C₃₁	—	4	2	no	—
334	Q₁₆×C₃₁	—	4	2	no	—
335	SD₁₆×C₃₁	—	2	4	no	—
336	SD₁₆×C₃₁	—	4	2	no	—
337	SD₁₆×C₃₁	—	4	2	no	—
338	SD₁₆×C₃₁	—	4	2	no	—
339	SD₁₆×C₃₁	—	4	2	no	—
340	D₈×C₃₁	—	4	2	no	—
341	M₁₆×C₃₁	—	4	1	no	—
342	M₁₆×C₃₁	—	4	1	no	—
343	M₁₆×C₃₁	—	4	2	no	—
344	C₂×C₈×C₃₁	—	4	2	no	—
345	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
346	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
347	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
348	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
349	C₄⋊C₄×C₃₁	—	2	1	no	—
350	C₄⋊C₄×C₃₁	—	2	1	no	—
351	C₄⋊C₄×C₃₁	—	2	1	no	—
352	C₄⋊C₄×C₃₁	—	2	1	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	1	no	—
358	C₄⋊C₄×C₃₁	—	2	1	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	1	no	—
364	C₄⋊C₄×C₃₁	—	2	1	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
372	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
373	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	1	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	1	no	—
392	C₂²⋊C₄×C₃₁	—	2	1	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	—	2	2	no	—
397	C₂²⋊C₄×C₃₁	—	2	2	no	—
398	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄²×C₃₁	—	2	1	no	—
404	C₄²×C₃₁	—	2	1	no	—
405	C₄²×C₃₁	—	2	1	no	—
406	C₄²×C₃₁	—	2	2	no	—
407	C₄²×C₃₁	—	2	2	no	—
408	C₄²×C₃₁	—	2	2	no	—
409	C₄²×C₃₁	—	2	2	no	—
410	C₄²×C₃₁	—	2	2	no	—
411	C₄²×C₃₁	—	2	2	no	—
412	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
413	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₃₁	C₂⁴	1	2	yes	—
415	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
417	#62091	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
418	C₂³×C₃₁	—	2	1	no	—
419	C₂³×C₃₁	—	2	2	no	—
420	C₂³×C₃₁	—	4	2	no	—
421	C₂³×C₃₁	—	8	1	no	—
422	C₂³×C₃₁	—	8	1	no	—
423	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
424	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
425	Q₈×C₃₁	—	2	1	no	—
426	Q₈×C₃₁	—	2	2	no	—
427	Q₈×C₃₁	—	2	2	no	—
428	Q₈×C₃₁	—	2	2	no	—
429	Q₈×C₃₁	—	2	2	no	—
430	Q₈×C₃₁	—	2	2	no	—
431	Q₈×C₃₁	—	2	2	no	—
432	Q₈×C₃₁	—	4	1	no	—
433	Q₈×C₃₁	—	4	4	no	—
434	Q₈×C₃₁	—	8	1	no	—
435	Q₈×C₃₁	—	8	1	no	—
436	Q₈×C₃₁	—	8	2	no	—
437	Q₈×C₃₁	—	8	1	no	—
438	Q₈×C₃₁	—	8	2	no	—
439	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
440	D₄×C₃₁	—	2	1	no	—
441	D₄×C₃₁	—	2	2	no	—
442	D₄×C₃₁	—	2	1	no	—
443	D₄×C₃₁	—	2	2	no	—
444	D₄×C₃₁	—	4	1	no	—
445	D₄×C₃₁	—	4	2	no	—
446	D₄×C₃₁	—	4	2	no	—
447	D₄×C₃₁	—	8	1	no	—
448	D₄×C₃₁	—	8	2	no	—
449	D₄×C₃₁	—	8	2	no	—
450	D₄×C₃₁	—	8	2	no	—
451	C₂×C₄×C₃₁	—	2	1	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	1	no	—
454	C₂×C₄×C₃₁	—	2	1	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	1	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	2	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	1	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	2	no	—
463	C₂×C₄×C₃₁	—	4	1	no	—
464	C₂×C₄×C₃₁	—	4	1	no	—
465	C₂×C₄×C₃₁	—	4	2	no	—
466	C₂×C₄×C₃₁	—	4	4	no	—
467	C₂×C₄×C₃₁	—	4	2	no	—
468	C₂×C₄×C₃₁	—	8	1	no	—
469	C₂×C₄×C₃₁	—	8	2	no	—
470	C₂×C₄×C₃₁	—	8	2	no	—
471	C₂×C₄×C₃₁	—	8	2	no	—
472	C₂×C₄×C₃₁	—	8	1	no	—
473	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
482	C₈×C₃₁	—	2	2	no	—
483	C₈×C₃₁	—	2	2	no	—
484	C₈×C₃₁	—	2	2	no	—
485	C₈×C₃₁	—	2	2	no	—
486	#3561	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3518	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3402	C₂×C₃₁	1	2	yes	complemented
489	#3369	C₂×C₃₁	1	2	yes	complemented
490	#3328	C₂×C₃₁	1	2	yes	complemented
491	#3321	C₂×C₃₁	1	2	yes	complemented
492	#3311	C₂×C₃₁	1	2	yes	complemented
493	#3275	C₂×C₃₁	1	2	yes	complemented
494	#3270	C₂×C₃₁	1	2	yes	complemented
495	#3270	C₂×C₃₁	1	2	yes	complemented
496	#3263	C₂×C₃₁	1	2	yes	complemented
497	#3255	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3225	C₂×C₃₁	1	2	yes	complemented
499	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3121	C₂×C₃₁	1	2	yes	complemented
501	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#3044	C₂×C₃₁	1	2	yes	complemented
503	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#2995	C₂×C₃₁	1	1	yes	characteristic, complemented
505	C₂²×C₃₁	—	2	1	no	—
506	C₂²×C₃₁	—	2	1	no	—
507	C₂²×C₃₁	—	2	2	no	—
508	C₂²×C₃₁	—	2	2	no	—
509	C₂²×C₃₁	—	2	2	no	—
510	C₂²×C₃₁	—	2	1	no	—
511	C₂²×C₃₁	—	4	1	no	—
512	C₂²×C₃₁	—	4	1	no	—
513	C₂²×C₃₁	—	4	2	no	—
514	C₂²×C₃₁	—	4	2	no	—
515	C₂²×C₃₁	—	4	1	no	—
516	C₂²×C₃₁	—	4	2	no	—
517	C₂²×C₃₁	—	16	2	no	—
518	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₃₁	—	2	1	no	—
520	C₄×C₃₁	—	2	1	no	—
521	C₄×C₃₁	—	2	1	no	—
522	C₄×C₃₁	—	2	1	no	—
523	C₄×C₃₁	—	2	2	no	—
524	C₄×C₃₁	—	2	2	no	—
525	C₄×C₃₁	—	2	1	no	—
526	C₄×C₃₁	—	2	2	no	—
527	C₄×C₃₁	—	2	2	no	—
528	C₄×C₃₁	—	4	1	no	—
529	C₄×C₃₁	—	4	2	no	—
530	C₄×C₃₁	—	4	1	no	—
531	C₄×C₃₁	—	4	2	no	—
532	C₄×C₃₁	—	4	2	no	—
533	C₄×C₃₁	—	4	2	no	—
534	C₄×C₃₁	—	4	2	no	—
535	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
536	C₄×C₃₁	#585	1	1	yes	characteristic
537	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
538	C₂×#137	C₂²×C₃₁	1	2	yes	—
539	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
540	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
541	#563	—	2	1	no	—
542	#562	—	2	1	no	—
543	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
544	#556	—	2	2	no	—
545	#556	—	2	1	no	—
546	#556	C₂²×C₃₁	1	2	yes	—
547	#556	C₂²×C₃₁	1	2	yes	—
548	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
549	#555	—	2	1	no	—
550	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
551	#551	—	2	2	no	—
552	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
553	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#548	C₂²×C₃₁	1	2	yes	—
555	#548	C₂²×C₃₁	1	2	yes	—
556	#546	C₂²×C₃₁	1	2	yes	—
557	#543	—	2	1	no	—
558	#542	—	2	2	no	—
559	#542	—	2	2	no	—
560	#542	C₂²×C₃₁	1	2	yes	—
561	#542	C₂²×C₃₁	1	2	yes	complemented
562	#538	—	2	1	no	—
563	#536	C₂²×C₃₁	1	2	yes	—
564	#533	—	2	1	no	—
565	#533	C₂²×C₃₁	1	1	yes	characteristic
566	#533	C₂²×C₃₁	1	1	yes	characteristic
567	#529	—	2	1	no	—
568	#529	C₂²×C₃₁	1	1	yes	characteristic
569	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
570	#519	C₂²×C₃₁	1	2	yes	complemented
571	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
572	#497	C₂²×C₃₁	1	2	yes	—
573	#497	C₂²×C₃₁	1	2	yes	complemented
574	#495	C₂²×C₃₁	1	2	yes	—
575	#489	C₂²×C₃₁	1	2	yes	—
576	#489	C₂²×C₃₁	1	2	yes	—
577	#487	C₂²×C₃₁	1	2	yes	complemented
578	#485	C₂²×C₃₁	1	2	yes	—
579	#485	C₂²×C₃₁	1	2	yes	complemented
580	#482	C₂²×C₃₁	1	2	yes	—
581	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	#476	C₂²×C₃₁	1	2	yes	—
583	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	#475	C₂²×C₃₁	1	2	yes	complemented
585	#475	C₂²×C₃₁	1	2	yes	complemented
586	#475	C₂²×C₃₁	1	2	yes	complemented
587	#470	C₂²×C₃₁	1	2	yes	—
588	#470	C₂²×C₃₁	1	2	yes	—
589	#470	C₂²×C₃₁	1	2	yes	complemented
590	#469	C₂²×C₃₁	1	2	yes	—
591	#465	C₂²×C₃₁	1	2	yes	—
592	#465	C₂²×C₃₁	1	2	yes	complemented
593	#464	C₂²×C₃₁	1	2	yes	—
594	#464	C₂²×C₃₁	1	2	yes	—
595	#464	C₂²×C₃₁	1	2	yes	—
596	#464	C₂²×C₃₁	1	2	yes	—
597	#464	C₂²×C₃₁	1	2	yes	—
598	#464	C₂²×C₃₁	1	2	yes	—
599	#464	C₂²×C₃₁	1	2	yes	complemented
600	#463	C₂²×C₃₁	1	2	yes	—
601	#463	C₂²×C₃₁	1	2	yes	—
602	#463	C₂²×C₃₁	1	2	yes	—
603	#462	C₂²×C₃₁	1	2	yes	complemented
604	#462	C₂²×C₃₁	1	2	yes	complemented
605	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	#462	C₂²×C₃₁	1	2	yes	complemented
607	#462	C₂²×C₃₁	1	2	yes	complemented
608	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#452	C₂²×C₃₁	1	2	yes	—
610	#452	C₂²×C₃₁	1	2	yes	—
611	#451	C₂²×C₃₁	1	2	yes	—
612	#451	C₂²×C₃₁	1	2	yes	complemented
613	#451	C₂²×C₃₁	1	2	yes	complemented
614	#450	C₂²×C₃₁	1	2	yes	—
615	#449	C₂²×C₃₁	1	2	yes	—
616	#448	C₂²×C₃₁	1	2	yes	—
617	#448	C₂²×C₃₁	1	2	yes	complemented
618	#446	C₂²×C₃₁	1	2	yes	complemented
619	#441	C₂²×C₃₁	1	2	yes	complemented
620	#441	C₂²×C₃₁	1	2	yes	complemented
621	#440	C₂²×C₃₁	1	2	yes	—
622	#440	C₂²×C₃₁	1	2	yes	complemented
623	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
624	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
625	#436	C₂²×C₃₁	1	2	yes	—
626	#435	C₂²×C₃₁	1	2	yes	—
627	#435	C₂²×C₃₁	1	2	yes	complemented
628	#433	C₂²×C₃₁	1	2	yes	complemented
629	#432	C₂²×C₃₁	1	1	yes	characteristic
630	#424	C₂²×C₃₁	1	2	yes	complemented
631	#423	C₂²×C₃₁	1	1	yes	characteristic
632	#419	C₂²×C₃₁	1	1	yes	characteristic
633	#419	C₂²×C₃₁	1	2	yes	complemented
634	#418	C₂²×C₃₁	1	1	yes	characteristic
635	#416	C₂²×C₃₁	1	2	yes	—
636	C₂×C₃₁	—	4	2	no	—
637	C₂×C₃₁	—	4	1	no	—
638	C₂×C₃₁	—	8	1	no	—
639	C₂×C₃₁	—	8	2	no	—
640	C₂×C₃₁	#3488	1	1	yes	characteristic
641	C₂×C₃₁	#3586	1	1	yes	characteristic
642	C₂×C₃₁	#3586	1	1	yes	characteristic
643	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×#41	C₂³×C₃₁	1	2	yes	—
645	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
646	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
647	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
648	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
649	#137	—	4	4	no	—
650	#137	—	4	2	no	—
651	AGL(1,ℤ/8)	—	4	2	no	—
652	C₂×Q₁₆	—	4	4	no	—
653	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
654	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
655	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
656	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
657	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
658	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
659	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
660	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
661	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
662	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
663	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
664	C₂×D₈	C₂³×C₃₁	1	2	yes	—
665	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
666	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
667	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
668	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
669	C₄⋊Q₈	—	2	1	no	—
670	C₄⋊Q₈	—	2	1	no	—
671	C₄⋊Q₈	—	2	2	no	—
672	C₄⋊Q₈	—	2	2	no	—
673	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
674	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
675	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
676	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
677	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
678	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
679	#126	—	2	2	no	—
680	#126	—	2	2	no	—
681	#126	—	2	2	no	—
682	#126	—	2	2	no	—
683	#126	—	2	2	no	—
684	#126	—	2	2	no	—
685	#126	—	2	2	no	—
686	#126	D₄×C₃₁	1	2	yes	—
687	#125	—	2	1	no	—
688	#125	—	2	1	no	—
689	#125	D₄×C₃₁	1	1	yes	characteristic
690	#124	—	2	2	no	—
691	#124	—	2	2	no	—
692	#124	—	2	2	no	—
693	#124	—	2	2	no	—
694	#124	—	2	2	no	—
695	#124	—	2	2	no	—
696	#124	—	2	1	no	—
697	#124	—	2	1	no	—
698	#124	D₄×C₃₁	1	1	yes	characteristic
699	#124	C₂³×C₃₁	1	2	yes	—
700	#124	C₂³×C₃₁	1	2	yes	—
701	#124	C₂³×C₃₁	1	2	yes	—
702	#124	C₂³×C₃₁	1	2	yes	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	—	2	2	no	—
706	#123	—	2	2	no	—
707	#123	—	2	2	no	—
708	#123	D₄×C₃₁	1	2	yes	—
709	C₂²⋊Q₈	—	2	1	no	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	1	no	—
712	C₂²⋊Q₈	—	2	1	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
723	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
724	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
725	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
726	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
727	#121	—	2	1	no	—
728	#121	—	2	2	no	—
729	#121	—	2	2	no	—
730	#121	—	2	2	no	—
731	#121	D₄×C₃₁	1	1	yes	characteristic
732	#121	C₂³×C₃₁	1	2	yes	—
733	#121	C₂³×C₃₁	1	2	yes	—
734	#120	—	2	2	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	2	no	—
737	C₄×Q₈	—	2	2	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
742	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
743	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
744	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
745	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
746	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
747	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
748	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
749	C₄×D₄	—	2	1	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	1	no	—
752	C₄×D₄	—	2	1	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
756	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
757	C₄×D₄	C₂³×C₃₁	1	2	yes	—
758	C₄×D₄	C₂³×C₃₁	1	2	yes	—
759	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
760	#117	—	2	1	no	—
761	#117	—	2	1	no	—
762	#117	—	2	1	no	—
763	#117	—	2	1	no	—
764	#117	—	2	2	no	—
765	#117	—	2	2	no	—
766	#117	—	2	2	no	—
767	#117	—	2	1	no	—
768	#117	C₂³×C₃₁	1	1	yes	characteristic
769	#117	C₂³×C₃₁	1	2	yes	—
770	#117	C₂³×C₃₁	1	2	yes	—
771	C₂×C₂²⋊C₄	—	2	1	no	—
772	C₂×C₂²⋊C₄	—	2	1	no	—
773	C₂×C₂²⋊C₄	—	2	2	no	—
774	C₂×C₄²	—	2	1	no	—
775	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
776	#107	C₂³×C₃₁	1	2	yes	—
777	#106	C₂³×C₃₁	1	2	yes	—
778	#106	C₂³×C₃₁	1	2	yes	—
779	#106	C₂³×C₃₁	1	2	yes	—
780	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
781	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
782	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
784	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
785	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
786	#103	C₂³×C₃₁	1	2	yes	—
787	#103	C₂³×C₃₁	1	2	yes	—
788	#103	C₂³×C₃₁	1	2	yes	—
789	#103	C₂³×C₃₁	1	2	yes	—
790	#103	C₂³×C₃₁	1	2	yes	—
791	#103	C₂³×C₃₁	1	2	yes	—
792	#103	C₂³×C₃₁	1	2	yes	—
793	#103	C₂³×C₃₁	1	2	yes	—
794	#103	C₂³×C₃₁	1	2	yes	—
795	#103	C₂³×C₃₁	1	2	yes	—
796	#103	C₂³×C₃₁	1	2	yes	—
797	#102	C₂³×C₃₁	1	2	yes	—
798	#102	C₂³×C₃₁	1	2	yes	—
799	#102	C₂³×C₃₁	1	2	yes	—
800	#102	C₂³×C₃₁	1	2	yes	—
801	#102	C₂³×C₃₁	1	2	yes	—
802	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
803	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
804	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
805	#97	C₂³×C₃₁	1	2	yes	—
806	#97	C₂³×C₃₁	1	2	yes	—
807	C₄×C₈	C₂³×C₃₁	1	2	yes	—
808	C₃₁	#62091	1	1	yes	characteristic, direct product factor, Sylow
809	C₂⁴	—	2	1	no	—
810	#41	—	2	2	no	—
811	#41	—	4	1	no	—
812	#41	—	4	2	no	—
813	#41	—	4	2	no	—
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	2	no	—
818	C₂×Q₈	—	2	2	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	4	no	—
821	C₂×Q₈	—	4	2	no	—
822	C₂×Q₈	—	4	2	no	—
823	C₂×Q₈	—	4	1	no	—
824	C₂×Q₈	—	4	1	no	—
825	C₂×Q₈	—	4	2	no	—
826	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
827	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
828	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
829	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
830	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	4	1	no	—
837	C₂×D₄	—	4	1	no	—
838	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
839	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
840	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
841	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
851	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
854	Q₁₆	—	2	4	no	—
855	Q₁₆	—	2	4	no	—
856	Q₁₆	—	4	2	no	—
857	Q₁₆	—	4	2	no	—
858	Q₁₆	—	4	2	no	—
859	Q₁₆	—	4	2	no	—
860	SD₁₆	—	2	4	no	—
861	SD₁₆	—	4	2	no	—
862	SD₁₆	—	4	2	no	—
863	SD₁₆	—	4	2	no	—
864	SD₁₆	—	4	2	no	—
865	D₈	—	4	2	no	—
866	M₁₆	—	4	1	no	—
867	M₁₆	—	4	1	no	—
868	M₁₆	—	4	2	no	—
869	C₂×C₈	—	4	2	no	—
870	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
871	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
872	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
873	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
895	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
896	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
898	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
899	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
900	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	1	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	1	no	—
917	C₂²⋊C₄	—	2	1	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
925	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
926	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
927	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
928	C₄²	—	2	1	no	—
929	C₄²	—	2	1	no	—
930	C₄²	—	2	1	no	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	2	no	—
933	C₄²	—	2	2	no	—
934	C₄²	—	2	2	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
938	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
939	C₄²	C₂⁴×C₃₁	1	2	yes	—
940	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
942	C₂³	—	2	1	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	4	2	no	—
945	C₂³	—	8	1	no	—
946	C₂³	—	8	1	no	—
947	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
948	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
949	Q₈	—	2	1	no	—
950	Q₈	—	2	2	no	—
951	Q₈	—	2	2	no	—
952	Q₈	—	2	2	no	—
953	Q₈	—	2	2	no	—
954	Q₈	—	2	2	no	—
955	Q₈	—	2	2	no	—
956	Q₈	—	4	1	no	—
957	Q₈	—	4	4	no	—
958	Q₈	—	8	1	no	—
959	Q₈	—	8	1	no	—
960	Q₈	—	8	2	no	—
961	Q₈	—	8	1	no	—
962	Q₈	—	8	2	no	—
963	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
964	D₄	—	2	1	no	—
965	D₄	—	2	2	no	—
966	D₄	—	2	1	no	—
967	D₄	—	2	2	no	—
968	D₄	—	4	1	no	—
969	D₄	—	4	2	no	—
970	D₄	—	4	2	no	—
971	D₄	—	8	1	no	—
972	D₄	—	8	2	no	—
973	D₄	—	8	2	no	—
974	D₄	—	8	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	1	no	—
989	C₂×C₄	—	4	2	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	2	no	—
992	C₂×C₄	—	8	1	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	2	no	—
996	C₂×C₄	—	8	1	no	—
997	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
998	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
999	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1001	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1004	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1005	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₈	—	2	2	no	—
1009	C₈	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	16	2	no	—
1023	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1024	C₄	—	2	1	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	1	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	2	no	—
1040	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1041	C₄	C₃₁×#585	1	1	yes	characteristic
1042	C₂	—	4	1	no	—
1043	C₂	—	4	2	no	—
1044	C₂	—	8	2	no	—
1045	C₂	—	8	1	no	—
1046	C₂	C₃₁×#3488	1	1	yes	characteristic
1047	C₂	C₃₁×#3586	1	1	yes	characteristic
1048	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×#3518	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3369	C₂	semidirect
5. C₃₁×#3328	C₂	semidirect
6. C₃₁×#3321	C₂	semidirect
7. C₃₁×#3311	C₂	semidirect
8. C₃₁×#3275	C₂	semidirect
9. C₃₁×#3270	C₂	semidirect
10. C₃₁×#3270	C₂	semidirect
11. C₃₁×#3263	C₂	semidirect
12. C₃₁×#3255	C₂	semidirect
13. C₃₁×#3225	C₂	semidirect
14. C₃₁×#3215	C₂	semidirect
15. C₃₁×#3121	C₂	semidirect
16. C₃₁×#3116	C₂	semidirect
17. C₃₁×#3044	C₂	semidirect
18. C₃₁×#3040	C₂	semidirect
19. C₃₁×#2995	C₂	semidirect
23. C₂²×Q₁₆×C₃₁	C₂²	semidirect
26. Q₈²×C₃₁	C₂²	semidirect
31. C₃₁×#556	C₂²	semidirect
33. C₃₁×#555	C₂²	semidirect
36. D₄×Q₈×C₃₁	C₂²	semidirect
44. C₃₁×#542	C₂²	semidirect
53. C₃₁×#519	C₂²	semidirect
56. C₃₁×#497	C₂²	semidirect
60. C₃₁×#487	C₂²	semidirect
62. C₃₁×#485	C₂²	semidirect
64. C₃₁×#477	C₂²	semidirect
66. C₃₁×#476	C₂²	semidirect
67. C₃₁×#475	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
69. C₃₁×#475	C₂²	semidirect
72. C₃₁×#470	C₂²	semidirect
75. C₃₁×#465	C₂²	semidirect
82. C₃₁×#464	C₂²	semidirect
86. C₃₁×#462	C₂²	semidirect
87. C₃₁×#462	C₂²	semidirect
88. C₃₁×#462	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
91. C₃₁×#461	C₂²	semidirect
95. C₃₁×#451	C₂²	semidirect
96. C₃₁×#451	C₂²	semidirect
100. C₃₁×#448	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#441	C₂²	semidirect
103. C₃₁×#441	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₄×Q₁₆×C₃₁	C₂²	semidirect
110. C₃₁×#435	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
116. C₃₁×#419	C₂²	semidirect
417. #62091	C₃₁	direct (N × H)
486. #3561	C₂×C₃₁	semidirect
487. #3518	C₂×C₃₁	semidirect
488. #3402	C₂×C₃₁	semidirect
489. #3369	C₂×C₃₁	semidirect
490. #3328	C₂×C₃₁	semidirect
491. #3321	C₂×C₃₁	semidirect
492. #3311	C₂×C₃₁	semidirect
493. #3275	C₂×C₃₁	semidirect
494. #3270	C₂×C₃₁	semidirect
495. #3270	C₂×C₃₁	semidirect
496. #3263	C₂×C₃₁	semidirect
497. #3255	C₂×C₃₁	semidirect
498. #3225	C₂×C₃₁	semidirect
499. #3215	C₂×C₃₁	semidirect
500. #3121	C₂×C₃₁	semidirect
501. #3116	C₂×C₃₁	semidirect
502. #3044	C₂×C₃₁	semidirect
503. #3040	C₂×C₃₁	semidirect
504. #2995	C₂×C₃₁	semidirect
540. C₂²×Q₁₆	C₂²×C₃₁	semidirect
543. Q₈²	C₂²×C₃₁	semidirect
548. #556	C₂²×C₃₁	semidirect
550. #555	C₂²×C₃₁	semidirect
553. D₄×Q₈	C₂²×C₃₁	semidirect
561. #542	C₂²×C₃₁	semidirect
570. #519	C₂²×C₃₁	semidirect
573. #497	C₂²×C₃₁	semidirect
577. #487	C₂²×C₃₁	semidirect
579. #485	C₂²×C₃₁	semidirect
581. #477	C₂²×C₃₁	semidirect
583. #476	C₂²×C₃₁	semidirect
584. #475	C₂²×C₃₁	semidirect
585. #475	C₂²×C₃₁	semidirect
586. #475	C₂²×C₃₁	semidirect
589. #470	C₂²×C₃₁	semidirect
592. #465	C₂²×C₃₁	semidirect
599. #464	C₂²×C₃₁	semidirect
603. #462	C₂²×C₃₁	semidirect
604. #462	C₂²×C₃₁	semidirect
605. #462	C₂²×C₃₁	semidirect
606. #462	C₂²×C₃₁	semidirect
607. #462	C₂²×C₃₁	semidirect
608. #461	C₂²×C₃₁	semidirect
612. #451	C₂²×C₃₁	semidirect
613. #451	C₂²×C₃₁	semidirect
617. #448	C₂²×C₃₁	semidirect
618. #446	C₂²×C₃₁	semidirect
619. #441	C₂²×C₃₁	semidirect
620. #441	C₂²×C₃₁	semidirect
622. #440	C₂²×C₃₁	semidirect
623. C₄×Q₁₆	C₂²×C₃₁	semidirect
627. #435	C₂²×C₃₁	semidirect
628. #433	C₂²×C₃₁	semidirect
630. #424	C₂²×C₃₁	semidirect
633. #419	C₂²×C₃₁	semidirect
808. C₃₁	#62091	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×#3518	2
C₃₁×#3402	2
C₃₁×#3369	2
C₃₁×#3328	2
C₃₁×#3321	2
C₃₁×#3311	2
C₃₁×#3275	2
C₃₁×#3270	2
C₃₁×#3263	2
C₃₁×#3255	2
C₃₁×#3225	2
C₃₁×#3215	2
C₃₁×#3121	2
C₃₁×#3116	2
C₃₁×#3044	2
C₃₁×#3040	2
C₃₁×#2995	2
#62091	31

Subgroups — C31×#62091 #21518850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62091 #21518850