Subgroups — C₃₁×#62090 #21518849

Order 7936.

1778 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×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3398	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3323	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×#3276	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3223	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3046	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	complemented
22	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#135	C₂²	1	2	yes	—
24	C₃₁×#563	—	2	1	no	—
25	C₃₁×#562	—	2	1	no	—
26	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#553	—	2	1	no	—
31	C₃₁×#552	—	2	2	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	C₂²	1	2	yes	—
34	C₃₁×#551	—	2	2	no	—
35	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
36	C₃₁×#548	C₂²	1	2	yes	—
37	C₃₁×#547	C₂²	1	2	yes	—
38	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#546	C₂²	1	2	yes	—
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	—	2	2	no	—
42	C₃₁×#542	C₂²	1	2	yes	—
43	C₃₁×#541	C₂²	1	2	yes	complemented
44	C₃₁×#539	—	2	2	no	—
45	C₃₁×#538	—	2	1	no	—
46	C₃₁×#536	C₂²	1	2	yes	—
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#529	—	2	1	no	—
50	C₃₁×#529	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×#125	—	2	1	no	—
52	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
53	C₃₁×#520	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	—
57	C₃₁×#494	C₂²	1	2	yes	complemented
58	C₃₁×#491	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#488	C₂²	1	2	yes	—
61	C₃₁×#485	C₂²	1	2	yes	—
62	C₃₁×#483	C₂²	1	2	yes	complemented
63	C₃₁×#481	C₂²	1	2	yes	—
64	C₃₁×#479	C₂²	1	2	yes	complemented
65	C₃₁×#478	C₂²	1	2	yes	—
66	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#476	C₂²	1	1	yes	characteristic, 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×#468	C₂²	1	2	yes	—
74	C₃₁×#467	C₂²	1	2	yes	complemented
75	C₃₁×#465	C₂²	1	2	yes	—
76	C₃₁×#464	C₂²	1	2	yes	—
77	C₃₁×#464	C₂²	1	2	yes	—
78	C₃₁×#464	C₂²	1	2	yes	—
79	C₃₁×#464	C₂²	1	2	yes	—
80	C₃₁×#464	C₂²	1	2	yes	—
81	C₃₁×#463	C₂²	1	2	yes	—
82	C₃₁×#463	C₂²	1	2	yes	—
83	C₃₁×#463	C₂²	1	2	yes	—
84	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#462	C₂²	1	2	yes	complemented
86	C₃₁×#462	C₂²	1	2	yes	complemented
87	C₃₁×#462	C₂²	1	2	yes	complemented
88	C₃₁×#462	C₂²	1	2	yes	complemented
89	C₃₁×#461	C₂²	1	2	yes	—
90	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#461	C₂²	1	2	yes	complemented
92	C₃₁×#452	C₂²	1	2	yes	—
93	C₃₁×#452	C₂²	1	2	yes	—
94	C₃₁×#452	C₂²	1	2	yes	—
95	C₃₁×#452	C₂²	1	2	yes	complemented
96	C₃₁×#451	C₂²	1	2	yes	—
97	C₃₁×#451	C₂²	1	2	yes	complemented
98	C₃₁×#451	C₂²	1	2	yes	complemented
99	C₃₁×#450	C₂²	1	2	yes	—
100	C₃₁×#449	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#442	C₂²	1	2	yes	—
103	C₃₁×#441	C₂²	1	2	yes	complemented
104	C₃₁×#441	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
107	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
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×#418	C₂²	1	1	yes	characteristic
117	C₃₁×#417	C₂²	1	2	yes	—
118	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
119	C₂×#41×C₃₁	C₂³	1	2	yes	—
120	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₃₁×#137	—	4	2	no	—
126	C₃₁×#137	—	4	4	no	—
127	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
128	C₃₁×#135	—	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	2	yes	—
142	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
145	C₃₁×C₄⋊Q₈	—	2	2	no	—
146	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
147	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
148	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
150	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₃₁×#126	—	2	2	no	—
153	C₃₁×#126	—	2	2	no	—
154	C₃₁×#126	—	2	2	no	—
155	C₃₁×#126	—	2	2	no	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	D₄	1	2	yes	—
159	C₃₁×#125	—	2	2	no	—
160	C₃₁×#125	—	2	2	no	—
161	C₃₁×#125	—	2	1	no	—
162	C₃₁×#125	—	2	1	no	—
163	C₃₁×#125	—	2	2	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	1	no	—
166	C₃₁×#125	—	2	1	no	—
167	C₃₁×#125	D₄	1	1	yes	characteristic
168	C₃₁×#125	C₂³	1	2	yes	—
169	C₃₁×#124	—	2	2	no	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	1	no	—
172	C₃₁×#124	—	2	1	no	—
173	C₃₁×#124	D₄	1	1	yes	characteristic
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#124	C₂³	1	2	yes	—
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	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	D₄	1	2	yes	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	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×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	D₄	1	1	yes	characteristic
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#120	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₃₁	—	2	1	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₃₁	C₂³	1	2	yes	—
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₃₁×#117	—	2	1	no	—
235	C₃₁×#117	—	2	1	no	—
236	C₃₁×#117	—	2	2	no	—
237	C₃₁×#117	—	2	2	no	—
238	C₃₁×#117	—	2	2	no	—
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	C₂³	1	1	yes	characteristic
241	C₃₁×#117	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
243	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
244	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
245	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₂×C₄⋊C₄×C₃₁	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	4	no	—
286	#41×C₃₁	—	2	2	no	—
287	#41×C₃₁	—	4	1	no	—
288	#41×C₃₁	—	4	2	no	—
289	#41×C₃₁	—	4	2	no	—
290	#41×C₃₁	—	4	2	no	—
291	C₂×Q₈×C₃₁	—	2	1	no	—
292	C₂×Q₈×C₃₁	—	2	1	no	—
293	C₂×Q₈×C₃₁	—	2	2	no	—
294	C₂×Q₈×C₃₁	—	2	1	no	—
295	C₂×Q₈×C₃₁	—	4	2	no	—
296	C₂×Q₈×C₃₁	—	4	1	no	—
297	C₂×Q₈×C₃₁	—	4	1	no	—
298	C₂×Q₈×C₃₁	—	4	2	no	—
299	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
301	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
302	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
304	C₂×D₄×C₃₁	—	2	1	no	—
305	C₂×D₄×C₃₁	—	2	2	no	—
306	C₂×D₄×C₃₁	—	2	2	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	1	no	—
309	C₂×D₄×C₃₁	—	4	1	no	—
310	C₂×D₄×C₃₁	—	4	1	no	—
311	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
312	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
313	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
314	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₃₁	—	2	1	no	—
316	C₂²×C₄×C₃₁	—	2	2	no	—
317	C₂²×C₄×C₃₁	—	2	2	no	—
318	C₂²×C₄×C₃₁	—	2	1	no	—
319	C₂²×C₄×C₃₁	—	2	1	no	—
320	C₂²×C₄×C₃₁	—	2	2	no	—
321	C₂²×C₄×C₃₁	—	2	1	no	—
322	C₂²×C₄×C₃₁	—	2	2	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	—	4	2	no	—
330	Q₁₆×C₃₁	—	4	2	no	—
331	Q₁₆×C₃₁	—	4	2	no	—
332	Q₁₆×C₃₁	—	4	2	no	—
333	Q₁₆×C₃₁	—	4	2	no	—
334	Q₁₆×C₃₁	—	4	2	no	—
335	SD₁₆×C₃₁	—	2	4	no	—
336	SD₁₆×C₃₁	—	2	4	no	—
337	SD₁₆×C₃₁	—	4	2	no	—
338	SD₁₆×C₃₁	—	4	2	no	—
339	SD₁₆×C₃₁	—	4	2	no	—
340	D₈×C₃₁	—	2	4	no	—
341	M₁₆×C₃₁	—	4	1	no	—
342	M₁₆×C₃₁	—	4	2	no	—
343	M₁₆×C₃₁	—	4	1	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	2	no	—
350	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	1	no	—
360	C₄⋊C₄×C₃₁	—	2	1	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	1	no	—
363	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
381	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	1	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	1	no	—
396	C₂²⋊C₄×C₃₁	—	2	1	no	—
397	C₂²⋊C₄×C₃₁	—	2	2	no	—
398	C₂²⋊C₄×C₃₁	—	2	2	no	—
399	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄²×C₃₁	—	2	1	no	—
406	C₄²×C₃₁	—	2	1	no	—
407	C₄²×C₃₁	—	2	1	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	#62090	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	2	no	—
426	Q₈×C₃₁	—	2	2	no	—
427	Q₈×C₃₁	—	2	1	no	—
428	Q₈×C₃₁	—	2	2	no	—
429	Q₈×C₃₁	—	2	2	no	—
430	Q₈×C₃₁	—	2	1	no	—
431	Q₈×C₃₁	—	2	2	no	—
432	Q₈×C₃₁	—	2	2	no	—
433	Q₈×C₃₁	—	4	1	no	—
434	Q₈×C₃₁	—	8	1	no	—
435	Q₈×C₃₁	—	8	1	no	—
436	Q₈×C₃₁	—	8	2	no	—
437	Q₈×C₃₁	—	8	1	no	—
438	D₄×C₃₁	—	2	2	no	—
439	D₄×C₃₁	—	2	1	no	—
440	D₄×C₃₁	—	2	2	no	—
441	D₄×C₃₁	—	4	1	no	—
442	D₄×C₃₁	—	4	2	no	—
443	D₄×C₃₁	—	4	4	no	—
444	D₄×C₃₁	—	4	2	no	—
445	D₄×C₃₁	—	8	1	no	—
446	D₄×C₃₁	—	8	2	no	—
447	D₄×C₃₁	—	8	2	no	—
448	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	1	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	2	no	—
461	C₂×C₄×C₃₁	—	4	1	no	—
462	C₂×C₄×C₃₁	—	4	1	no	—
463	C₂×C₄×C₃₁	—	4	4	no	—
464	C₂×C₄×C₃₁	—	4	2	no	—
465	C₂×C₄×C₃₁	—	4	2	no	—
466	C₂×C₄×C₃₁	—	8	1	no	—
467	C₂×C₄×C₃₁	—	8	2	no	—
468	C₂×C₄×C₃₁	—	8	2	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	1	yes	characteristic
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	2	yes	—
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	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3398	C₂×C₃₁	1	2	yes	complemented
489	#3376	C₂×C₃₁	1	2	yes	complemented
490	#3323	C₂×C₃₁	1	2	yes	complemented
491	#3316	C₂×C₃₁	1	2	yes	complemented
492	#3312	C₂×C₃₁	1	2	yes	complemented
493	#3276	C₂×C₃₁	1	2	yes	complemented
494	#3269	C₂×C₃₁	1	2	yes	complemented
495	#3267	C₂×C₃₁	1	2	yes	complemented
496	#3258	C₂×C₃₁	1	2	yes	complemented
497	#3255	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3223	C₂×C₃₁	1	2	yes	complemented
499	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3125	C₂×C₃₁	1	2	yes	complemented
501	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#3046	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	—	2	2	no	—
512	C₂²×C₃₁	—	4	1	no	—
513	C₂²×C₃₁	—	4	1	no	—
514	C₂²×C₃₁	—	4	2	no	—
515	C₂²×C₃₁	—	4	2	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	2	no	—
526	C₄×C₃₁	—	2	1	no	—
527	C₄×C₃₁	—	4	1	no	—
528	C₄×C₃₁	—	4	1	no	—
529	C₄×C₃₁	—	4	2	no	—
530	C₄×C₃₁	—	4	2	no	—
531	C₄×C₃₁	—	4	1	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	complemented
539	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
540	C₂×#135	C₂²×C₃₁	1	2	yes	—
541	#563	—	2	1	no	—
542	#562	—	2	1	no	—
543	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
544	#556	C₂²×C₃₁	1	2	yes	—
545	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
546	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
547	#553	—	2	1	no	—
548	#552	—	2	2	no	—
549	#552	—	2	1	no	—
550	#552	C₂²×C₃₁	1	2	yes	—
551	#551	—	2	2	no	—
552	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
553	#548	C₂²×C₃₁	1	2	yes	—
554	#547	C₂²×C₃₁	1	2	yes	—
555	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
556	#546	C₂²×C₃₁	1	2	yes	—
557	#543	—	2	1	no	—
558	#542	—	2	2	no	—
559	#542	C₂²×C₃₁	1	2	yes	—
560	#541	C₂²×C₃₁	1	2	yes	complemented
561	#539	—	2	2	no	—
562	#538	—	2	1	no	—
563	#536	C₂²×C₃₁	1	2	yes	—
564	#533	C₂²×C₃₁	1	1	yes	characteristic
565	#533	C₂²×C₃₁	1	1	yes	characteristic
566	#529	—	2	1	no	—
567	#529	C₂²×C₃₁	1	1	yes	characteristic
568	C₂×#125	—	2	1	no	—
569	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
570	#520	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	—
574	#494	C₂²×C₃₁	1	2	yes	complemented
575	#491	C₂²×C₃₁	1	2	yes	complemented
576	#489	C₂²×C₃₁	1	2	yes	—
577	#488	C₂²×C₃₁	1	2	yes	—
578	#485	C₂²×C₃₁	1	2	yes	—
579	#483	C₂²×C₃₁	1	2	yes	complemented
580	#481	C₂²×C₃₁	1	2	yes	—
581	#479	C₂²×C₃₁	1	2	yes	complemented
582	#478	C₂²×C₃₁	1	2	yes	—
583	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	#476	C₂²×C₃₁	1	1	yes	characteristic, 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	#468	C₂²×C₃₁	1	2	yes	—
591	#467	C₂²×C₃₁	1	2	yes	complemented
592	#465	C₂²×C₃₁	1	2	yes	—
593	#464	C₂²×C₃₁	1	2	yes	—
594	#464	C₂²×C₃₁	1	2	yes	—
595	#464	C₂²×C₃₁	1	2	yes	—
596	#464	C₂²×C₃₁	1	2	yes	—
597	#464	C₂²×C₃₁	1	2	yes	—
598	#463	C₂²×C₃₁	1	2	yes	—
599	#463	C₂²×C₃₁	1	2	yes	—
600	#463	C₂²×C₃₁	1	2	yes	—
601	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#462	C₂²×C₃₁	1	2	yes	complemented
603	#462	C₂²×C₃₁	1	2	yes	complemented
604	#462	C₂²×C₃₁	1	2	yes	complemented
605	#462	C₂²×C₃₁	1	2	yes	complemented
606	#461	C₂²×C₃₁	1	2	yes	—
607	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	#461	C₂²×C₃₁	1	2	yes	complemented
609	#452	C₂²×C₃₁	1	2	yes	—
610	#452	C₂²×C₃₁	1	2	yes	—
611	#452	C₂²×C₃₁	1	2	yes	—
612	#452	C₂²×C₃₁	1	2	yes	complemented
613	#451	C₂²×C₃₁	1	2	yes	—
614	#451	C₂²×C₃₁	1	2	yes	complemented
615	#451	C₂²×C₃₁	1	2	yes	complemented
616	#450	C₂²×C₃₁	1	2	yes	—
617	#449	C₂²×C₃₁	1	2	yes	—
618	#446	C₂²×C₃₁	1	2	yes	complemented
619	#442	C₂²×C₃₁	1	2	yes	—
620	#441	C₂²×C₃₁	1	2	yes	complemented
621	#441	C₂²×C₃₁	1	2	yes	complemented
622	#440	C₂²×C₃₁	1	2	yes	complemented
623	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
624	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
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	#418	C₂²×C₃₁	1	1	yes	characteristic
634	#417	C₂²×C₃₁	1	2	yes	—
635	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
636	C₂×C₃₁	—	4	2	no	—
637	C₂×C₃₁	—	4	1	no	—
638	C₂×C₃₁	—	4	2	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	C₂×#41	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	2	no	—
650	#137	—	4	4	no	—
651	AGL(1,ℤ/8)	—	4	2	no	—
652	#135	—	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	2	no	—
670	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
671	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
672	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
673	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
674	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
675	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
676	#126	—	2	2	no	—
677	#126	—	2	2	no	—
678	#126	—	2	2	no	—
679	#126	—	2	2	no	—
680	#126	—	2	2	no	—
681	#126	—	2	2	no	—
682	#126	D₄×C₃₁	1	2	yes	—
683	#125	—	2	2	no	—
684	#125	—	2	2	no	—
685	#125	—	2	1	no	—
686	#125	—	2	1	no	—
687	#125	—	2	2	no	—
688	#125	—	2	2	no	—
689	#125	—	2	1	no	—
690	#125	—	2	1	no	—
691	#125	D₄×C₃₁	1	1	yes	characteristic
692	#125	C₂³×C₃₁	1	2	yes	—
693	#124	—	2	2	no	—
694	#124	—	2	2	no	—
695	#124	—	2	1	no	—
696	#124	—	2	1	no	—
697	#124	D₄×C₃₁	1	1	yes	characteristic
698	#124	C₂³×C₃₁	1	2	yes	—
699	#124	C₂³×C₃₁	1	2	yes	—
700	#124	C₂³×C₃₁	1	2	yes	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
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	—	2	2	no	—
709	#123	D₄×C₃₁	1	2	yes	—
710	C₂²⋊Q₈	—	2	1	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	1	no	—
713	C₂²⋊Q₈	—	2	1	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	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
728	#121	—	2	1	no	—
729	#121	—	2	2	no	—
730	#121	—	2	2	no	—
731	#121	—	2	2	no	—
732	#121	D₄×C₃₁	1	1	yes	characteristic
733	#121	C₂³×C₃₁	1	2	yes	—
734	#120	—	2	2	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
741	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
742	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
743	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
744	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
745	C₄×D₄	—	2	1	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	1	no	—
748	C₄×D₄	—	2	1	no	—
749	C₄×D₄	—	2	2	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
753	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
754	C₄×D₄	C₂³×C₃₁	1	2	yes	—
755	C₄×D₄	C₂³×C₃₁	1	2	yes	—
756	C₄×D₄	C₂³×C₃₁	1	2	yes	—
757	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
758	#117	—	2	1	no	—
759	#117	—	2	1	no	—
760	#117	—	2	2	no	—
761	#117	—	2	2	no	—
762	#117	—	2	2	no	—
763	#117	—	2	1	no	—
764	#117	C₂³×C₃₁	1	1	yes	characteristic
765	#117	C₂³×C₃₁	1	2	yes	—
766	C₂×C₄⋊C₄	—	2	2	no	—
767	C₂×C₄⋊C₄	—	2	2	no	—
768	C₂×C₄⋊C₄	—	2	1	no	—
769	C₂×C₄⋊C₄	—	2	1	no	—
770	C₂×C₄⋊C₄	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	#62090	1	1	yes	characteristic, direct product factor, Sylow
809	C₂⁴	—	2	1	no	—
810	#41	—	2	4	no	—
811	#41	—	2	2	no	—
812	#41	—	4	1	no	—
813	#41	—	4	2	no	—
814	#41	—	4	2	no	—
815	#41	—	4	2	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	2	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	4	2	no	—
821	C₂×Q₈	—	4	1	no	—
822	C₂×Q₈	—	4	1	no	—
823	C₂×Q₈	—	4	2	no	—
824	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
825	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
826	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
827	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	4	1	no	—
835	C₂×D₄	—	4	1	no	—
836	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
837	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
838	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
839	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	2	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	—	4	2	no	—
855	Q₁₆	—	4	2	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	—	2	4	no	—
862	SD₁₆	—	4	2	no	—
863	SD₁₆	—	4	2	no	—
864	SD₁₆	—	4	2	no	—
865	D₈	—	2	4	no	—
866	M₁₆	—	4	1	no	—
867	M₁₆	—	4	2	no	—
868	M₁₆	—	4	1	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	2	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	2	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	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	2	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	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
899	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
900	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
901	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
902	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
903	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
904	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
906	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	1	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	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	1	no	—
921	C₂²⋊C₄	—	2	1	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
930	C₄²	—	2	1	no	—
931	C₄²	—	2	1	no	—
932	C₄²	—	2	1	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	2	no	—
950	Q₈	—	2	2	no	—
951	Q₈	—	2	1	no	—
952	Q₈	—	2	2	no	—
953	Q₈	—	2	2	no	—
954	Q₈	—	2	1	no	—
955	Q₈	—	2	2	no	—
956	Q₈	—	2	2	no	—
957	Q₈	—	4	1	no	—
958	Q₈	—	8	1	no	—
959	Q₈	—	8	1	no	—
960	Q₈	—	8	2	no	—
961	Q₈	—	8	1	no	—
962	D₄	—	2	2	no	—
963	D₄	—	2	1	no	—
964	D₄	—	2	2	no	—
965	D₄	—	4	1	no	—
966	D₄	—	4	2	no	—
967	D₄	—	4	4	no	—
968	D₄	—	4	2	no	—
969	D₄	—	8	1	no	—
970	D₄	—	8	2	no	—
971	D₄	—	8	2	no	—
972	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	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	2	no	—
985	C₂×C₄	—	4	1	no	—
986	C₂×C₄	—	4	1	no	—
987	C₂×C₄	—	4	4	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	2	no	—
990	C₂×C₄	—	8	1	no	—
991	C₂×C₄	—	8	2	no	—
992	C₂×C₄	—	8	2	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	1	yes	characteristic
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	2	yes	—
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	2	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	2	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	2	no	—
1025	C₄	—	2	1	no	—
1026	C₄	—	2	1	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	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	—	4	2	no	—
1045	C₂	—	8	2	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×#3515	C₂	semidirect
3. C₃₁×#3398	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3323	C₂	semidirect
6. C₃₁×#3316	C₂	semidirect
7. C₃₁×#3312	C₂	semidirect
8. C₃₁×#3276	C₂	semidirect
9. C₃₁×#3269	C₂	semidirect
10. C₃₁×#3267	C₂	semidirect
11. C₃₁×#3258	C₂	semidirect
12. C₃₁×#3255	C₂	semidirect
13. C₃₁×#3223	C₂	semidirect
14. C₃₁×#3215	C₂	semidirect
15. C₃₁×#3125	C₂	semidirect
16. C₃₁×#3116	C₂	semidirect
17. C₃₁×#3046	C₂	semidirect
18. C₃₁×#3040	C₂	semidirect
19. C₃₁×#2995	C₂	semidirect
21. C₂×C₃₁×#137	C₂²	semidirect
26. C₃₁×#557	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
43. C₃₁×#541	C₂²	semidirect
53. C₃₁×#520	C₂²	semidirect
57. C₃₁×#494	C₂²	semidirect
58. C₃₁×#491	C₂²	semidirect
62. C₃₁×#483	C₂²	semidirect
64. C₃₁×#479	C₂²	semidirect
66. C₃₁×#477	C₂²	semidirect
67. C₃₁×#476	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
69. C₃₁×#475	C₂²	semidirect
72. C₃₁×#470	C₂²	semidirect
74. C₃₁×#467	C₂²	semidirect
84. C₃₁×#462	C₂²	semidirect
85. C₃₁×#462	C₂²	semidirect
86. C₃₁×#462	C₂²	semidirect
87. C₃₁×#462	C₂²	semidirect
88. C₃₁×#462	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
91. C₃₁×#461	C₂²	semidirect
95. C₃₁×#452	C₂²	semidirect
97. C₃₁×#451	C₂²	semidirect
98. C₃₁×#451	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
103. C₃₁×#441	C₂²	semidirect
104. C₃₁×#441	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
107. C₄×SD₁₆×C₃₁	C₂²	semidirect
110. C₃₁×#435	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
118. C₂×C₃₁×#103	C₂²	semidirect
417. #62090	C₃₁	direct (N × H)
486. #3561	C₂×C₃₁	semidirect
487. #3515	C₂×C₃₁	semidirect
488. #3398	C₂×C₃₁	semidirect
489. #3376	C₂×C₃₁	semidirect
490. #3323	C₂×C₃₁	semidirect
491. #3316	C₂×C₃₁	semidirect
492. #3312	C₂×C₃₁	semidirect
493. #3276	C₂×C₃₁	semidirect
494. #3269	C₂×C₃₁	semidirect
495. #3267	C₂×C₃₁	semidirect
496. #3258	C₂×C₃₁	semidirect
497. #3255	C₂×C₃₁	semidirect
498. #3223	C₂×C₃₁	semidirect
499. #3215	C₂×C₃₁	semidirect
500. #3125	C₂×C₃₁	semidirect
501. #3116	C₂×C₃₁	semidirect
502. #3046	C₂×C₃₁	semidirect
503. #3040	C₂×C₃₁	semidirect
504. #2995	C₂×C₃₁	semidirect
538. C₂×#137	C₂²×C₃₁	semidirect
543. #557	C₂²×C₃₁	semidirect
545. #554	C₂²×C₃₁	semidirect
546. #554	C₂²×C₃₁	semidirect
555. #547	C₂²×C₃₁	semidirect
560. #541	C₂²×C₃₁	semidirect
570. #520	C₂²×C₃₁	semidirect
574. #494	C₂²×C₃₁	semidirect
575. #491	C₂²×C₃₁	semidirect
579. #483	C₂²×C₃₁	semidirect
581. #479	C₂²×C₃₁	semidirect
583. #477	C₂²×C₃₁	semidirect
584. #476	C₂²×C₃₁	semidirect
585. #475	C₂²×C₃₁	semidirect
586. #475	C₂²×C₃₁	semidirect
589. #470	C₂²×C₃₁	semidirect
591. #467	C₂²×C₃₁	semidirect
601. #462	C₂²×C₃₁	semidirect
602. #462	C₂²×C₃₁	semidirect
603. #462	C₂²×C₃₁	semidirect
604. #462	C₂²×C₃₁	semidirect
605. #462	C₂²×C₃₁	semidirect
607. #461	C₂²×C₃₁	semidirect
608. #461	C₂²×C₃₁	semidirect
612. #452	C₂²×C₃₁	semidirect
614. #451	C₂²×C₃₁	semidirect
615. #451	C₂²×C₃₁	semidirect
618. #446	C₂²×C₃₁	semidirect
620. #441	C₂²×C₃₁	semidirect
621. #441	C₂²×C₃₁	semidirect
622. #440	C₂²×C₃₁	semidirect
624. C₄×SD₁₆	C₂²×C₃₁	semidirect
627. #435	C₂²×C₃₁	semidirect
628. #433	C₂²×C₃₁	semidirect
630. #424	C₂²×C₃₁	semidirect
635. C₂×#103	C₂²×C₃₁	semidirect
808. C₃₁	#62090	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×#3515	2
C₃₁×#3398	2
C₃₁×#3376	2
C₃₁×#3323	2
C₃₁×#3316	2
C₃₁×#3312	2
C₃₁×#3276	2
C₃₁×#3269	2
C₃₁×#3267	2
C₃₁×#3258	2
C₃₁×#3255	2
C₃₁×#3223	2
C₃₁×#3215	2
C₃₁×#3125	2
C₃₁×#3116	2
C₃₁×#3046	2
C₃₁×#3040	2
C₃₁×#2995	2
#62090	31

Subgroups — C31×#62090 #21518849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62090 #21518849