Subgroups — C₃₁×#60565 #21517324

Order 7936.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3125	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3124	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3120	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3119	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3092	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3005	C₂	1	2	yes	maximal, complemented
13	C₄×C₃₁×#137	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2921	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#137	C₂²	1	2	yes	—
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₃₁×#542	C₂²	1	2	yes	complemented
20	C₃₁×#542	C₂²	1	2	yes	complemented
21	C₃₁×#541	C₂²	1	2	yes	complemented
22	C₃₁×#540	C₂²	1	2	yes	complemented
23	C₃₁×#539	—	2	1	no	—
24	C₃₁×#539	—	2	1	no	—
25	C₃₁×#538	—	2	1	no	—
26	C₃₁×#538	—	2	1	no	—
27	C₃₁×#533	C₂²	1	1	yes	characteristic
28	C₃₁×#532	C₂²	1	1	yes	characteristic
29	C₃₁×#529	—	2	2	no	—
30	C₃₁×#529	—	2	2	no	—
31	C₃₁×#525	C₂²	1	2	yes	—
32	C₃₁×#520	—	2	2	no	—
33	C₃₁×#520	—	2	2	no	—
34	C₃₁×#520	C₂²	1	4	yes	—
35	C₃₁×#520	C₂²	1	4	yes	—
36	C₄×#41×C₃₁	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	—	2	1	no	—
40	C₂×C₄×D₄×C₃₁	—	2	1	no	—
41	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#117	—	2	1	no	—
44	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
46	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#484	C₂²	1	4	yes	complemented
48	C₃₁×#483	C₂²	1	4	yes	complemented
49	C₃₁×#481	C₂²	1	4	yes	complemented
50	C₃₁×#480	C₂²	1	4	yes	complemented
51	C₃₁×#479	C₂²	1	4	yes	complemented
52	C₃₁×#478	C₂²	1	4	yes	complemented
53	C₃₁×#477	C₂²	1	2	yes	complemented
54	C₃₁×#476	C₂²	1	2	yes	complemented
55	C₃₁×#475	C₂²	1	2	yes	complemented
56	C₃₁×#474	C₂²	1	2	yes	complemented
57	C₃₁×#464	C₂²	1	4	yes	complemented
58	C₃₁×#463	C₂²	1	4	yes	complemented
59	C₃₁×#462	C₂²	1	2	yes	complemented
60	C₃₁×#461	C₂²	1	2	yes	complemented
61	C₃₁×#460	C₂²	1	2	yes	complemented
62	C₃₁×#459	C₂²	1	2	yes	complemented
63	C₃₁×#452	C₂²	1	4	yes	—
64	C₃₁×#452	C₂²	1	4	yes	—
65	C₃₁×#449	C₂²	1	4	yes	—
66	C₃₁×#449	C₂²	1	4	yes	—
67	C₃₁×#442	C₂²	1	4	yes	complemented
68	C₃₁×#441	C₂²	1	4	yes	complemented
69	C₃₁×#440	C₂²	1	4	yes	complemented
70	C₃₁×#440	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
74	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
75	C₃₁×#433	C₂²	1	4	yes	complemented
76	C₃₁×#433	C₂²	1	4	yes	complemented
77	C₃₁×#428	C₂²	1	2	yes	—
78	C₃₁×#428	C₂²	1	2	yes	—
79	C₃₁×#423	C₂²	1	1	yes	characteristic
80	C₃₁×#423	C₂²	1	1	yes	characteristic
81	C₃₁×#419	C₂²	1	2	yes	—
82	C₃₁×#418	C₂²	1	2	yes	—
83	C₃₁×#417	C₂²	1	2	yes	—
84	C₃₁×#417	C₂²	1	2	yes	—
85	C₃₁×#407	C₂²	1	2	yes	—
86	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
87	C₂×#41×C₃₁	—	2	4	no	—
88	C₂×#41×C₃₁	—	2	4	no	—
89	C₂×#41×C₃₁	—	2	2	no	—
90	C₂×#41×C₃₁	C₂³	1	2	yes	—
91	C₂×#41×C₃₁	C₂³	1	4	yes	—
92	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₃₁	—	2	1	no	—
94	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₃₁	—	2	1	no	—
96	C₂³×C₄×C₃₁	—	2	1	no	—
97	C₂³×C₄×C₃₁	—	2	1	no	—
98	C₂³×C₄×C₃₁	—	2	1	no	—
99	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₃₁×#137	—	2	8	no	—
101	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
102	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×D₈×C₃₁	C₂³	1	4	yes	—
106	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
108	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×#127	C₂³	1	1	yes	characteristic
112	C₃₁×#126	—	2	2	no	—
113	C₃₁×#126	—	2	2	no	—
114	C₃₁×#126	—	2	2	no	—
115	C₃₁×#126	—	2	2	no	—
116	C₃₁×#125	—	2	2	no	—
117	C₃₁×#125	—	2	2	no	—
118	C₃₁×#125	C₂³	1	2	yes	—
119	C₃₁×#124	—	2	2	no	—
120	C₃₁×#124	—	2	2	no	—
121	C₃₁×#124	C₂³	1	2	yes	—
122	C₃₁×#123	—	2	2	no	—
123	C₃₁×#123	—	2	2	no	—
124	C₃₁×#123	—	2	2	no	—
125	C₃₁×#123	—	2	2	no	—
126	C₃₁×#123	—	2	2	no	—
127	C₃₁×C₂²⋊Q₈	—	2	1	no	—
128	C₃₁×C₂²⋊Q₈	—	2	1	no	—
129	C₃₁×C₂²⋊Q₈	—	2	2	no	—
130	C₃₁×C₂²⋊Q₈	—	2	2	no	—
131	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₃₁×#121	—	2	1	no	—
134	C₃₁×#121	—	2	1	no	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	C₂³	1	2	yes	—
138	C₃₁×#121	C₂³	1	2	yes	—
139	C₃₁×#120	—	2	2	no	—
140	C₄×Q₈×C₃₁	—	2	2	no	—
141	C₄×Q₈×C₃₁	—	2	1	no	—
142	C₄×Q₈×C₃₁	—	2	1	no	—
143	C₄×Q₈×C₃₁	—	2	1	no	—
144	C₄×Q₈×C₃₁	—	2	1	no	—
145	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
146	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
147	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	—	2	2	no	—
152	C₄×D₄×C₃₁	—	2	2	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	4	no	—
155	C₄×D₄×C₃₁	—	2	4	no	—
156	C₄×D₄×C₃₁	—	2	4	no	—
157	C₄×D₄×C₃₁	—	2	4	no	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	1	no	—
160	C₄×D₄×C₃₁	—	2	1	no	—
161	C₄×D₄×C₃₁	—	2	1	no	—
162	C₄×D₄×C₃₁	—	2	1	no	—
163	C₄×D₄×C₃₁	C₂³	1	2	yes	—
164	C₄×D₄×C₃₁	C₂³	1	4	yes	—
165	C₄×D₄×C₃₁	C₂³	1	2	yes	—
166	C₄×D₄×C₃₁	C₂³	1	2	yes	—
167	C₄×D₄×C₃₁	C₂³	1	2	yes	—
168	C₃₁×#117	—	2	4	no	—
169	C₃₁×#117	—	2	4	no	—
170	C₃₁×#117	—	2	2	no	—
171	C₃₁×#117	D₄	1	2	yes	—
172	C₃₁×#117	D₄	1	2	yes	—
173	C₃₁×#117	C₂³	1	2	yes	—
174	C₃₁×#117	C₂³	1	2	yes	—
175	C₃₁×#117	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
178	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
180	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
181	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
182	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
187	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	—	2	1	no	—
192	C₂×C₄²×C₃₁	—	2	1	no	—
193	C₂×C₄²×C₃₁	—	2	2	no	—
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₃₁×#107	C₂³	1	4	yes	—
197	C₃₁×#107	C₂³	1	4	yes	—
198	C₃₁×#106	C₂³	1	4	yes	—
199	C₃₁×#106	C₂³	1	4	yes	—
200	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
201	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
202	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
203	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
204	C₃₁×#103	C₂³	1	4	yes	—
205	C₃₁×#103	C₂³	1	4	yes	—
206	C₃₁×#103	C₂³	1	4	yes	—
207	C₃₁×#103	C₂³	1	4	yes	—
208	C₃₁×#102	C₂³	1	4	yes	—
209	C₃₁×#102	C₂³	1	4	yes	—
210	C₃₁×#102	C₂³	1	4	yes	—
211	C₃₁×#102	C₂³	1	4	yes	—
212	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
214	C₃₁×#97	C₂³	1	4	yes	—
215	C₄×C₈×C₃₁	C₂³	1	4	yes	—
216	C₂⁴×C₃₁	—	2	1	no	—
217	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
218	#41×C₃₁	—	2	16	no	—
219	#41×C₃₁	—	2	8	no	—
220	#41×C₃₁	—	2	8	no	—
221	#41×C₃₁	—	2	4	no	—
222	#41×C₃₁	—	2	4	no	—
223	C₂×Q₈×C₃₁	—	2	1	no	—
224	C₂×Q₈×C₃₁	—	2	1	no	—
225	C₂×Q₈×C₃₁	—	2	1	no	—
226	C₂×Q₈×C₃₁	—	2	2	no	—
227	C₂×Q₈×C₃₁	#41	1	4	yes	—
228	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
230	C₂×D₄×C₃₁	—	2	8	no	—
231	C₂×D₄×C₃₁	—	2	4	no	—
232	C₂×D₄×C₃₁	—	2	2	no	—
233	C₂×D₄×C₃₁	—	2	2	no	—
234	C₂×D₄×C₃₁	—	2	2	no	—
235	C₂×D₄×C₃₁	—	2	1	no	—
236	C₂×D₄×C₃₁	—	2	1	no	—
237	C₂×D₄×C₃₁	—	2	1	no	—
238	C₂×D₄×C₃₁	—	2	2	no	—
239	C₂×D₄×C₃₁	#41	1	4	yes	—
240	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₃₁	—	2	8	no	—
243	C₂²×C₄×C₃₁	—	2	1	no	—
244	C₂²×C₄×C₃₁	—	2	4	no	—
245	C₂²×C₄×C₃₁	—	2	2	no	—
246	C₂²×C₄×C₃₁	—	2	2	no	—
247	C₂²×C₄×C₃₁	—	2	1	no	—
248	C₂²×C₄×C₃₁	—	2	1	no	—
249	C₂²×C₄×C₃₁	—	2	4	no	—
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
253	C₂²×C₄×C₃₁	—	2	4	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	8	2	no	—
257	C₂²×C₄×C₃₁	—	8	2	no	—
258	C₂²×C₄×C₃₁	—	8	2	no	—
259	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
267	Q₁₆×C₃₁	—	2	8	no	—
268	SD₁₆×C₃₁	—	2	8	no	—
269	SD₁₆×C₃₁	—	2	8	no	—
270	D₈×C₃₁	—	2	8	no	—
271	M₁₆×C₃₁	—	2	4	no	—
272	M₁₆×C₃₁	—	2	4	no	—
273	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
274	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
275	C₄⋊C₄×C₃₁	—	2	4	no	—
276	C₄⋊C₄×C₃₁	—	2	4	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	1	no	—
280	C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	1	no	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
292	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₂²⋊C₄×C₃₁	—	2	2	no	—
300	C₂²⋊C₄×C₃₁	—	2	2	no	—
301	C₂²⋊C₄×C₃₁	—	2	2	no	—
302	C₂²⋊C₄×C₃₁	—	2	4	no	—
303	C₂²⋊C₄×C₃₁	—	2	2	no	—
304	C₂²⋊C₄×C₃₁	—	2	2	no	—
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	2	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
312	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
313	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
314	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
315	C₄²×C₃₁	—	2	4	no	—
316	C₄²×C₃₁	—	2	2	no	—
317	C₄²×C₃₁	—	2	2	no	—
318	C₄²×C₃₁	—	2	2	no	—
319	C₄²×C₃₁	—	2	2	no	—
320	C₄²×C₃₁	—	2	2	no	—
321	C₄²×C₃₁	C₂×D₄	1	2	yes	—
322	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₃₁	C₂⁴	1	2	yes	—
325	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
327	#60565	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
328	C₂³×C₃₁	—	2	2	no	—
329	C₂³×C₃₁	—	2	4	no	—
330	C₂³×C₃₁	—	2	2	no	—
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	—	4	1	no	—
333	C₂³×C₃₁	—	4	1	no	—
334	C₂³×C₃₁	—	4	2	no	—
335	C₂³×C₃₁	—	4	2	no	—
336	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
337	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
338	Q₈×C₃₁	—	2	4	no	—
339	Q₈×C₃₁	—	2	2	no	—
340	Q₈×C₃₁	—	2	2	no	—
341	Q₈×C₃₁	—	2	2	no	—
342	Q₈×C₃₁	—	8	1	no	—
343	Q₈×C₃₁	—	8	1	no	—
344	Q₈×C₃₁	C₂×#41	1	4	yes	—
345	D₄×C₃₁	—	2	16	no	—
346	D₄×C₃₁	—	2	4	no	—
347	D₄×C₃₁	—	2	2	no	—
348	D₄×C₃₁	—	2	2	no	—
349	D₄×C₃₁	—	2	2	no	—
350	D₄×C₃₁	—	4	4	no	—
351	D₄×C₃₁	—	8	1	no	—
352	D₄×C₃₁	—	8	1	no	—
353	D₄×C₃₁	—	8	2	no	—
354	D₄×C₃₁	—	8	2	no	—
355	D₄×C₃₁	C₂×#41	1	4	yes	—
356	C₂×C₄×C₃₁	—	2	16	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	4	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	4	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	4	1	no	—
369	C₂×C₄×C₃₁	—	4	1	no	—
370	C₂×C₄×C₃₁	—	4	1	no	—
371	C₂×C₄×C₃₁	—	4	1	no	—
372	C₂×C₄×C₃₁	—	4	2	no	—
373	C₂×C₄×C₃₁	—	4	2	no	—
374	C₂×C₄×C₃₁	—	4	4	no	—
375	C₂×C₄×C₃₁	—	8	2	no	—
376	C₂×C₄×C₃₁	—	8	2	no	—
377	C₂×C₄×C₃₁	—	8	4	no	—
378	C₂×C₄×C₃₁	—	8	2	no	—
379	C₂×C₄×C₃₁	—	8	2	no	—
380	C₂×C₄×C₃₁	—	8	4	no	—
381	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
390	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
391	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
392	C₈×C₃₁	—	2	4	no	—
393	C₈×C₃₁	—	2	4	no	—
394	#3455	C₂×C₃₁	1	1	yes	characteristic, complemented
395	C₂×#520	C₂×C₃₁	1	1	yes	characteristic, complemented
396	#3125	C₂×C₃₁	1	4	yes	complemented
397	#3124	C₂×C₃₁	1	4	yes	complemented
398	#3120	C₂×C₃₁	1	4	yes	complemented
399	#3119	C₂×C₃₁	1	4	yes	complemented
400	#3092	C₂×C₃₁	1	2	yes	complemented
401	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
402	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
404	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
405	#3005	C₂×C₃₁	1	2	yes	complemented
406	C₄×#137	C₂×C₃₁	1	2	yes	complemented
407	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	2	yes	complemented
408	#2921	C₂×C₃₁	1	1	yes	characteristic, complemented
409	C₂²×C₃₁	—	2	1	no	—
410	C₂²×C₃₁	—	2	1	no	—
411	C₂²×C₃₁	—	2	2	no	—
412	C₂²×C₃₁	—	2	2	no	—
413	C₂²×C₃₁	—	2	2	no	—
414	C₂²×C₃₁	—	2	4	no	—
415	C₂²×C₃₁	—	4	4	no	—
416	C₂²×C₃₁	—	4	8	no	—
417	C₂²×C₃₁	—	4	2	no	—
418	C₂²×C₃₁	—	4	2	no	—
419	C₂²×C₃₁	—	4	2	no	—
420	C₂²×C₃₁	—	4	2	no	—
421	C₂²×C₃₁	—	4	2	no	—
422	C₂²×C₃₁	#525	1	2	yes	—
423	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
424	C₄×C₃₁	—	2	2	no	—
425	C₄×C₃₁	—	2	1	no	—
426	C₄×C₃₁	—	2	1	no	—
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	2	1	no	—
429	C₄×C₃₁	—	2	1	no	—
430	C₄×C₃₁	—	2	2	no	—
431	C₄×C₃₁	—	2	4	no	—
432	C₄×C₃₁	—	4	2	no	—
433	C₄×C₃₁	—	4	2	no	—
434	C₄×C₃₁	—	4	2	no	—
435	C₄×C₃₁	—	4	2	no	—
436	C₄×C₃₁	—	4	2	no	—
437	C₄×C₃₁	#525	1	2	yes	—
438	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
439	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
440	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
441	C₂×#137	C₂²×C₃₁	1	2	yes	—
442	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
443	#542	C₂²×C₃₁	1	2	yes	complemented
444	#542	C₂²×C₃₁	1	2	yes	complemented
445	#541	C₂²×C₃₁	1	2	yes	complemented
446	#540	C₂²×C₃₁	1	2	yes	complemented
447	#539	—	2	1	no	—
448	#539	—	2	1	no	—
449	#538	—	2	1	no	—
450	#538	—	2	1	no	—
451	#533	C₂²×C₃₁	1	1	yes	characteristic
452	#532	C₂²×C₃₁	1	1	yes	characteristic
453	#529	—	2	2	no	—
454	#529	—	2	2	no	—
455	#525	C₂²×C₃₁	1	2	yes	—
456	#520	—	2	2	no	—
457	#520	—	2	2	no	—
458	#520	C₂²×C₃₁	1	4	yes	—
459	#520	C₂²×C₃₁	1	4	yes	—
460	C₄×#41	C₂²×C₃₁	1	2	yes	—
461	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
462	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
463	C₂×C₄×D₄	—	2	1	no	—
464	C₂×C₄×D₄	—	2	1	no	—
465	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
467	C₂×#117	—	2	1	no	—
468	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
469	C₂²×C₄⋊C₄	—	2	1	no	—
470	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
471	#484	C₂²×C₃₁	1	4	yes	complemented
472	#483	C₂²×C₃₁	1	4	yes	complemented
473	#481	C₂²×C₃₁	1	4	yes	complemented
474	#480	C₂²×C₃₁	1	4	yes	complemented
475	#479	C₂²×C₃₁	1	4	yes	complemented
476	#478	C₂²×C₃₁	1	4	yes	complemented
477	#477	C₂²×C₃₁	1	2	yes	complemented
478	#476	C₂²×C₃₁	1	2	yes	complemented
479	#475	C₂²×C₃₁	1	2	yes	complemented
480	#474	C₂²×C₃₁	1	2	yes	complemented
481	#464	C₂²×C₃₁	1	4	yes	complemented
482	#463	C₂²×C₃₁	1	4	yes	complemented
483	#462	C₂²×C₃₁	1	2	yes	complemented
484	#461	C₂²×C₃₁	1	2	yes	complemented
485	#460	C₂²×C₃₁	1	2	yes	complemented
486	#459	C₂²×C₃₁	1	2	yes	complemented
487	#452	C₂²×C₃₁	1	4	yes	—
488	#452	C₂²×C₃₁	1	4	yes	—
489	#449	C₂²×C₃₁	1	4	yes	—
490	#449	C₂²×C₃₁	1	4	yes	—
491	#442	C₂²×C₃₁	1	4	yes	complemented
492	#441	C₂²×C₃₁	1	4	yes	complemented
493	#440	C₂²×C₃₁	1	4	yes	complemented
494	#440	C₂²×C₃₁	1	4	yes	complemented
495	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
496	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
497	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
498	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
499	#433	C₂²×C₃₁	1	4	yes	complemented
500	#433	C₂²×C₃₁	1	4	yes	complemented
501	#428	C₂²×C₃₁	1	2	yes	—
502	#428	C₂²×C₃₁	1	2	yes	—
503	#423	C₂²×C₃₁	1	1	yes	characteristic
504	#423	C₂²×C₃₁	1	1	yes	characteristic
505	#419	C₂²×C₃₁	1	2	yes	—
506	#418	C₂²×C₃₁	1	2	yes	—
507	#417	C₂²×C₃₁	1	2	yes	—
508	#417	C₂²×C₃₁	1	2	yes	—
509	#407	C₂²×C₃₁	1	2	yes	—
510	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
511	C₂×C₃₁	—	2	2	no	—
512	C₂×C₃₁	—	4	2	no	—
513	C₂×C₃₁	—	4	4	no	—
514	C₂×C₃₁	—	8	2	no	—
515	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
516	C₂×C₃₁	#3585	1	1	yes	characteristic
517	C₂×C₃₁	#3586	1	1	yes	characteristic
518	C₂×#41	—	2	4	no	—
519	C₂×#41	—	2	4	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	C₂³×C₃₁	1	2	yes	—
522	C₂×#41	C₂³×C₃₁	1	4	yes	—
523	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
526	C₂³×C₄	—	2	1	no	—
527	C₂³×C₄	—	2	1	no	—
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	—	2	1	no	—
530	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
531	#137	—	2	8	no	—
532	AGL(1,ℤ/8)	—	2	8	no	—
533	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
534	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
535	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
536	C₂×D₈	C₂³×C₃₁	1	4	yes	—
537	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
538	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
539	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
542	#127	C₂³×C₃₁	1	1	yes	characteristic
543	#126	—	2	2	no	—
544	#126	—	2	2	no	—
545	#126	—	2	2	no	—
546	#126	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	2	2	no	—
549	#125	C₂³×C₃₁	1	2	yes	—
550	#124	—	2	2	no	—
551	#124	—	2	2	no	—
552	#124	C₂³×C₃₁	1	2	yes	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
563	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
564	#121	—	2	1	no	—
565	#121	—	2	1	no	—
566	#121	—	2	2	no	—
567	#121	—	2	2	no	—
568	#121	C₂³×C₃₁	1	2	yes	—
569	#121	C₂³×C₃₁	1	2	yes	—
570	#120	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	1	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
577	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
578	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
579	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
580	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	4	no	—
586	C₄×D₄	—	2	4	no	—
587	C₄×D₄	—	2	4	no	—
588	C₄×D₄	—	2	4	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	C₂³×C₃₁	1	4	yes	—
595	C₄×D₄	C₂³×C₃₁	1	2	yes	—
596	C₄×D₄	C₂³×C₃₁	1	2	yes	—
597	C₄×D₄	C₂³×C₃₁	1	2	yes	—
598	C₄×D₄	C₂³×C₃₁	1	2	yes	—
599	#117	—	2	4	no	—
600	#117	—	2	4	no	—
601	#117	—	2	2	no	—
602	#117	D₄×C₃₁	1	2	yes	—
603	#117	D₄×C₃₁	1	2	yes	—
604	#117	C₂³×C₃₁	1	2	yes	—
605	#117	C₂³×C₃₁	1	2	yes	—
606	#117	C₂³×C₃₁	1	2	yes	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	2	no	—
611	C₂×C₄⋊C₄	—	2	4	no	—
612	C₂×C₄⋊C₄	—	2	4	no	—
613	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
614	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
622	C₂×C₄²	—	2	1	no	—
623	C₂×C₄²	—	2	1	no	—
624	C₂×C₄²	—	2	2	no	—
625	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
627	#107	C₂³×C₃₁	1	4	yes	—
628	#107	C₂³×C₃₁	1	4	yes	—
629	#106	C₂³×C₃₁	1	4	yes	—
630	#106	C₂³×C₃₁	1	4	yes	—
631	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
632	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
633	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
634	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
635	#103	C₂³×C₃₁	1	4	yes	—
636	#103	C₂³×C₃₁	1	4	yes	—
637	#103	C₂³×C₃₁	1	4	yes	—
638	#103	C₂³×C₃₁	1	4	yes	—
639	#102	C₂³×C₃₁	1	4	yes	—
640	#102	C₂³×C₃₁	1	4	yes	—
641	#102	C₂³×C₃₁	1	4	yes	—
642	#102	C₂³×C₃₁	1	4	yes	—
643	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
644	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
645	#97	C₂³×C₃₁	1	4	yes	—
646	C₄×C₈	C₂³×C₃₁	1	4	yes	—
647	C₃₁	#60565	1	1	yes	characteristic, direct product factor, Sylow
648	C₂⁴	—	2	1	no	—
649	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
650	#41	—	2	16	no	—
651	#41	—	2	8	no	—
652	#41	—	2	8	no	—
653	#41	—	2	4	no	—
654	#41	—	2	4	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	#41×C₃₁	1	4	yes	—
660	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
661	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
662	C₂×D₄	—	2	8	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	#41×C₃₁	1	4	yes	—
672	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
673	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
674	C₂²×C₄	—	2	8	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	8	2	no	—
689	C₂²×C₄	—	8	2	no	—
690	C₂²×C₄	—	8	2	no	—
691	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
693	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
699	Q₁₆	—	2	8	no	—
700	SD₁₆	—	2	8	no	—
701	SD₁₆	—	2	8	no	—
702	D₈	—	2	8	no	—
703	M₁₆	—	2	4	no	—
704	M₁₆	—	2	4	no	—
705	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
706	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
724	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
726	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
744	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
745	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
746	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₄²	C₂×D₄×C₃₁	1	2	yes	—
754	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
756	C₄²	C₂⁴×C₃₁	1	2	yes	—
757	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
758	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
759	C₂³	—	2	2	no	—
760	C₂³	—	2	4	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	4	1	no	—
764	C₂³	—	4	1	no	—
765	C₂³	—	4	2	no	—
766	C₂³	—	4	2	no	—
767	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
768	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
769	Q₈	—	2	4	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	8	1	no	—
774	Q₈	—	8	1	no	—
775	Q₈	C₂×#41×C₃₁	1	4	yes	—
776	D₄	—	2	16	no	—
777	D₄	—	2	4	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	4	4	no	—
782	D₄	—	8	1	no	—
783	D₄	—	8	1	no	—
784	D₄	—	8	2	no	—
785	D₄	—	8	2	no	—
786	D₄	C₂×#41×C₃₁	1	4	yes	—
787	C₂×C₄	—	2	16	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
813	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
820	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
821	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
822	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
823	C₈	—	2	4	no	—
824	C₈	—	2	4	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	8	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	C₃₁×#525	1	2	yes	—
839	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	4	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	C₃₁×#525	1	2	yes	—
854	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
855	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
856	C₂	—	2	2	no	—
857	C₂	—	4	2	no	—
858	C₂	—	4	4	no	—
859	C₂	—	8	2	no	—
860	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
861	C₂	C₃₁×#3585	1	1	yes	characteristic
862	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 ◁ C₂×C₃₁×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₁×#3455	C₂	semidirect
2. C₂×C₃₁×#520	C₂	semidirect
3. C₃₁×#3125	C₂	semidirect
4. C₃₁×#3124	C₂	semidirect
5. C₃₁×#3120	C₂	semidirect
6. C₃₁×#3119	C₂	semidirect
7. C₃₁×#3092	C₂	semidirect
8. C₃₁×#3078	C₂	semidirect
9. C₃₁×#3077	C₂	semidirect
10. C₃₁×#3037	C₂	semidirect
11. C₃₁×#3036	C₂	semidirect
12. C₃₁×#3005	C₂	semidirect
13. C₄×C₃₁×#137	C₂	semidirect
14. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
15. C₃₁×#2921	C₂	semidirect
19. C₃₁×#542	C₂²	semidirect
20. C₃₁×#542	C₂²	semidirect
21. C₃₁×#541	C₂²	semidirect
22. C₃₁×#540	C₂²	semidirect
47. C₃₁×#484	C₂²	semidirect
48. C₃₁×#483	C₂²	semidirect
49. C₃₁×#481	C₂²	semidirect
50. C₃₁×#480	C₂²	semidirect
51. C₃₁×#479	C₂²	semidirect
52. C₃₁×#478	C₂²	semidirect
53. C₃₁×#477	C₂²	semidirect
54. C₃₁×#476	C₂²	semidirect
55. C₃₁×#475	C₂²	semidirect
56. C₃₁×#474	C₂²	semidirect
57. C₃₁×#464	C₂²	semidirect
58. C₃₁×#463	C₂²	semidirect
59. C₃₁×#462	C₂²	semidirect
60. C₃₁×#461	C₂²	semidirect
61. C₃₁×#460	C₂²	semidirect
62. C₃₁×#459	C₂²	semidirect
67. C₃₁×#442	C₂²	semidirect
68. C₃₁×#441	C₂²	semidirect
69. C₃₁×#440	C₂²	semidirect
70. C₃₁×#440	C₂²	semidirect
71. C₄×Q₁₆×C₃₁	C₂²	semidirect
72. C₄×SD₁₆×C₃₁	C₂²	semidirect
73. C₄×SD₁₆×C₃₁	C₂²	semidirect
74. C₄×D₈×C₃₁	C₂²	semidirect
75. C₃₁×#433	C₂²	semidirect
76. C₃₁×#433	C₂²	semidirect
327. #60565	C₃₁	direct (N × H)
394. #3455	C₂×C₃₁	semidirect
395. C₂×#520	C₂×C₃₁	semidirect
396. #3125	C₂×C₃₁	semidirect
397. #3124	C₂×C₃₁	semidirect
398. #3120	C₂×C₃₁	semidirect
399. #3119	C₂×C₃₁	semidirect
400. #3092	C₂×C₃₁	semidirect
401. #3078	C₂×C₃₁	semidirect
402. #3077	C₂×C₃₁	semidirect
403. #3037	C₂×C₃₁	semidirect
404. #3036	C₂×C₃₁	semidirect
405. #3005	C₂×C₃₁	semidirect
406. C₄×#137	C₂×C₃₁	semidirect
407. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
408. #2921	C₂×C₃₁	semidirect
443. #542	C₂²×C₃₁	semidirect
444. #542	C₂²×C₃₁	semidirect
445. #541	C₂²×C₃₁	semidirect
446. #540	C₂²×C₃₁	semidirect
471. #484	C₂²×C₃₁	semidirect
472. #483	C₂²×C₃₁	semidirect
473. #481	C₂²×C₃₁	semidirect
474. #480	C₂²×C₃₁	semidirect
475. #479	C₂²×C₃₁	semidirect
476. #478	C₂²×C₃₁	semidirect
477. #477	C₂²×C₃₁	semidirect
478. #476	C₂²×C₃₁	semidirect
479. #475	C₂²×C₃₁	semidirect
480. #474	C₂²×C₃₁	semidirect
481. #464	C₂²×C₃₁	semidirect
482. #463	C₂²×C₃₁	semidirect
483. #462	C₂²×C₃₁	semidirect
484. #461	C₂²×C₃₁	semidirect
485. #460	C₂²×C₃₁	semidirect
486. #459	C₂²×C₃₁	semidirect
491. #442	C₂²×C₃₁	semidirect
492. #441	C₂²×C₃₁	semidirect
493. #440	C₂²×C₃₁	semidirect
494. #440	C₂²×C₃₁	semidirect
495. C₄×Q₁₆	C₂²×C₃₁	semidirect
496. C₄×SD₁₆	C₂²×C₃₁	semidirect
497. C₄×SD₁₆	C₂²×C₃₁	semidirect
498. C₄×D₈	C₂²×C₃₁	semidirect
499. #433	C₂²×C₃₁	semidirect
500. #433	C₂²×C₃₁	semidirect
647. C₃₁	#60565	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×#3455	2
C₂×C₃₁×#520	2
C₃₁×#3125	2
C₃₁×#3124	2
C₃₁×#3120	2
C₃₁×#3119	2
C₃₁×#3092	2
C₃₁×#3078	2
C₃₁×#3077	2
C₃₁×#3037	2
C₃₁×#3036	2
C₃₁×#3005	2
C₄×C₃₁×#137	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₃₁×#2921	2
#60565	31

Subgroups — C31×#60565 #21517324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60565 #21517324