Subgroups — C₃₁×#60946 #21517705

Order 7936.

2104 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3247	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3228	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3207	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3188	C₂	1	4	yes	maximal, complemented
11	C₃₁×#3169	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3167	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3106	C₂	1	4	yes	maximal, complemented
14	C₃₁×#3105	C₂	1	4	yes	maximal, complemented
15	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₁	—	2	1	no	—
17	C₃₁×#533	C₂²	1	1	yes	characteristic
18	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
19	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
20	C₃₁×#532	—	2	1	no	—
21	C₃₁×#532	—	2	1	no	—
22	C₃₁×#532	—	2	1	no	—
23	C₃₁×#532	—	2	1	no	—
24	C₃₁×#532	C₂²	1	2	yes	—
25	C₃₁×#532	C₂²	1	2	yes	—
26	C₃₁×#532	C₂²	1	2	yes	—
27	C₃₁×#532	C₂²	1	2	yes	—
28	C₃₁×#532	C₂²	1	1	yes	characteristic
29	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
33	C₃₁×#529	—	2	1	no	—
34	C₃₁×#529	—	2	1	no	—
35	C₃₁×#529	—	2	1	no	—
36	C₃₁×#529	—	2	1	no	—
37	C₃₁×#529	C₂²	1	2	yes	—
38	C₃₁×#529	C₂²	1	2	yes	complemented
39	C₂×C₃₁×#124	—	2	1	no	—
40	C₃₁×#525	—	2	1	no	—
41	C₃₁×#525	—	2	1	no	—
42	C₃₁×#525	C₂²	1	2	yes	—
43	C₂×C₃₁×#121	—	2	1	no	—
44	C₂×C₃₁×#121	C₂²	1	2	yes	—
45	C₄×#41×C₃₁	—	2	1	no	—
46	C₄×#41×C₃₁	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₃₁	—	2	1	no	—
49	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
50	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#500	C₂²	1	2	yes	complemented
52	C₃₁×#498	C₂²	1	2	yes	complemented
53	C₃₁×#493	C₂²	1	2	yes	complemented
54	C₃₁×#492	C₂²	1	2	yes	complemented
55	C₃₁×#487	C₂²	1	2	yes	complemented
56	C₃₁×#486	C₂²	1	2	yes	complemented
57	C₃₁×#486	C₂²	1	2	yes	complemented
58	C₃₁×#486	C₂²	1	2	yes	complemented
59	C₃₁×#484	C₂²	1	4	yes	—
60	C₃₁×#482	C₂²	1	8	yes	complemented
61	C₃₁×#481	C₂²	1	4	yes	—
62	C₃₁×#478	C₂²	1	8	yes	complemented
63	C₃₁×#477	C₂²	1	4	yes	complemented
64	C₃₁×#476	C₂²	1	4	yes	complemented
65	C₃₁×#466	C₂²	1	8	yes	complemented
66	C₃₁×#465	C₂²	1	8	yes	complemented
67	C₃₁×#463	C₂²	1	8	yes	complemented
68	C₃₁×#460	C₂²	1	4	yes	complemented
69	C₃₁×#459	C₂²	1	4	yes	complemented
70	C₃₁×#450	C₂²	1	4	yes	—
71	C₃₁×#449	C₂²	1	8	yes	complemented
72	C₃₁×#447	C₂²	1	4	yes	—
73	C₄×SD₁₆×C₃₁	C₂²	1	8	yes	complemented
74	C₄×D₈×C₃₁	C₂²	1	8	yes	complemented
75	C₃₁×#431	C₂²	1	2	yes	—
76	C₃₁×#431	C₂²	1	1	yes	characteristic
77	C₃₁×#431	C₂²	1	1	yes	characteristic
78	C₃₁×#431	C₂²	1	2	yes	complemented
79	C₃₁×#431	C₂²	1	2	yes	complemented
80	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
81	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
82	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	complemented
83	C₂×#41×C₃₁	—	2	1	no	—
84	C₂×#41×C₃₁	—	2	1	no	—
85	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	—	2	2	no	—
87	C₂×#41×C₃₁	—	2	2	no	—
88	C₂×#41×C₃₁	—	2	2	no	—
89	C₂×#41×C₃₁	—	4	8	no	—
90	C₂×#41×C₃₁	C₂³	1	2	yes	—
91	C₂²×Q₈×C₃₁	—	2	1	no	—
92	C₂²×D₄×C₃₁	—	2	2	no	—
93	C₂²×D₄×C₃₁	—	2	1	no	—
94	C₂²×D₄×C₃₁	—	2	1	no	—
95	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₃₁	—	2	2	no	—
97	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
101	C₂×D₈×C₃₁	C₂³	1	8	yes	—
102	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
103	C₃₁×C₄⋊Q₈	—	2	1	no	—
104	C₃₁×C₄⋊Q₈	—	2	1	no	—
105	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₃₁×#127	—	2	1	no	—
111	C₃₁×#127	—	2	1	no	—
112	C₃₁×#127	C₂³	1	2	yes	—
113	C₃₁×#127	C₂³	1	2	yes	—
114	C₃₁×#127	C₂³	1	1	yes	characteristic
115	C₃₁×#126	—	2	2	no	—
116	C₃₁×#126	—	2	2	no	—
117	C₃₁×#125	—	2	1	no	—
118	C₃₁×#125	—	2	1	no	—
119	C₃₁×#125	C₂³	1	2	yes	—
120	C₃₁×#124	—	2	2	no	—
121	C₃₁×#124	—	2	2	no	—
122	C₃₁×#124	—	2	2	no	—
123	C₃₁×#124	—	2	2	no	—
124	C₃₁×#124	—	2	1	no	—
125	C₃₁×#124	—	2	1	no	—
126	C₃₁×#124	C₂³	1	2	yes	—
127	C₃₁×#123	—	2	2	no	—
128	C₃₁×#123	—	2	2	no	—
129	C₃₁×#123	—	2	2	no	—
130	C₃₁×C₂²⋊Q₈	—	2	1	no	—
131	C₃₁×C₂²⋊Q₈	—	2	1	no	—
132	C₃₁×C₂²⋊Q₈	—	2	1	no	—
133	C₃₁×C₂²⋊Q₈	—	2	1	no	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	2	no	—
138	C₃₁×#121	—	2	2	no	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	1	no	—
143	C₃₁×#121	—	2	1	no	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	—	2	1	no	—
146	C₃₁×#121	C₂³	1	2	yes	—
147	C₃₁×#121	C₂³	1	4	yes	—
148	C₃₁×#121	C₂³	1	4	yes	—
149	C₃₁×#121	C₂³	1	2	yes	—
150	C₃₁×#120	—	2	2	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×D₄×C₃₁	—	2	2	no	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	2	no	—
165	C₄×D₄×C₃₁	—	2	2	no	—
166	C₄×D₄×C₃₁	—	2	2	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	2	no	—
169	C₄×D₄×C₃₁	—	2	1	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	1	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	C₂³	1	2	yes	—
174	C₄×D₄×C₃₁	C₂³	1	4	yes	—
175	C₄×D₄×C₃₁	C₂³	1	2	yes	—
176	C₄×D₄×C₃₁	C₂³	1	4	yes	—
177	C₃₁×#117	—	2	1	no	—
178	C₃₁×#117	—	2	1	no	—
179	C₃₁×#117	—	2	2	no	—
180	C₃₁×#117	—	2	2	no	—
181	C₃₁×#117	—	2	2	no	—
182	C₃₁×#117	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
186	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
187	C₂×C₄²×C₃₁	—	2	2	no	—
188	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₃₁×#107	C₂³	1	8	yes	—
201	C₃₁×#106	C₂³	1	8	yes	—
202	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
203	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
204	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
205	C₃₁×#103	C₂³	1	8	yes	—
206	C₃₁×#102	C₂³	1	8	yes	—
207	C₃₁×#102	C₂³	1	8	yes	—
208	C₃₁×#102	C₂³	1	8	yes	—
209	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₄×C₈×C₃₁	C₂³	1	4	yes	—
213	C₄×C₈×C₃₁	C₂³	1	2	yes	—
214	C₄×C₈×C₃₁	C₂³	1	2	yes	—
215	C₂⁴×C₃₁	—	2	2	no	—
216	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
217	#41×C₃₁	—	4	4	no	—
218	#41×C₃₁	—	4	8	no	—
219	#41×C₃₁	—	4	8	no	—
220	#41×C₃₁	—	4	8	no	—
221	#41×C₃₁	—	4	4	no	—
222	#41×C₃₁	—	4	4	no	—
223	#41×C₃₁	—	4	8	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	—	2	2	no	—
228	C₂×Q₈×C₃₁	—	4	4	no	—
229	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
230	C₂×D₄×C₃₁	—	2	2	no	—
231	C₂×D₄×C₃₁	—	2	2	no	—
232	C₂×D₄×C₃₁	—	2	2	no	—
233	C₂×D₄×C₃₁	—	2	4	no	—
234	C₂×D₄×C₃₁	—	2	4	no	—
235	C₂×D₄×C₃₁	—	2	1	no	—
236	C₂×D₄×C₃₁	—	2	1	no	—
237	C₂×D₄×C₃₁	—	2	2	no	—
238	C₂×D₄×C₃₁	—	2	2	no	—
239	C₂×D₄×C₃₁	—	2	2	no	—
240	C₂×D₄×C₃₁	—	2	2	no	—
241	C₂×D₄×C₃₁	—	2	2	no	—
242	C₂×D₄×C₃₁	—	4	4	no	—
243	C₂×D₄×C₃₁	—	4	4	no	—
244	C₂×D₄×C₃₁	—	4	8	no	—
245	C₂×D₄×C₃₁	—	4	4	no	—
246	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₃₁	—	2	4	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	4	no	—
256	C₂²×C₄×C₃₁	—	4	2	no	—
257	C₂²×C₄×C₃₁	—	4	8	no	—
258	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	SD₁₆×C₃₁	—	4	8	no	—
277	D₈×C₃₁	—	4	8	no	—
278	C₂×C₈×C₃₁	—	4	4	no	—
279	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
280	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
295	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂²⋊C₄×C₃₁	—	2	2	no	—
300	C₂²⋊C₄×C₃₁	—	2	4	no	—
301	C₂²⋊C₄×C₃₁	—	2	4	no	—
302	C₂²⋊C₄×C₃₁	—	2	4	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	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	C₄²×C₃₁	—	2	2	no	—
311	C₄²×C₃₁	—	2	2	no	—
312	C₄²×C₃₁	—	2	2	no	—
313	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
329	#60946	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂³×C₃₁	—	2	2	no	—
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	—	2	2	no	—
333	C₂³×C₃₁	—	2	4	no	—
334	C₂³×C₃₁	—	4	1	no	—
335	C₂³×C₃₁	—	4	4	no	—
336	C₂³×C₃₁	—	4	4	no	—
337	C₂³×C₃₁	—	4	4	no	—
338	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
339	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₃₁	—	2	4	no	—
342	Q₈×C₃₁	—	4	4	no	—
343	Q₈×C₃₁	—	4	2	no	—
344	Q₈×C₃₁	—	4	4	no	—
345	Q₈×C₃₁	—	4	2	no	—
346	D₄×C₃₁	—	2	4	no	—
347	D₄×C₃₁	—	2	8	no	—
348	D₄×C₃₁	—	4	4	no	—
349	D₄×C₃₁	—	4	4	no	—
350	D₄×C₃₁	—	4	8	no	—
351	D₄×C₃₁	—	4	4	no	—
352	D₄×C₃₁	—	4	4	no	—
353	D₄×C₃₁	—	4	8	no	—
354	D₄×C₃₁	—	4	4	no	—
355	D₄×C₃₁	—	4	4	no	—
356	D₄×C₃₁	—	4	4	no	—
357	D₄×C₃₁	—	4	2	no	—
358	D₄×C₃₁	—	4	4	no	—
359	D₄×C₃₁	—	4	2	no	—
360	C₂×C₄×C₃₁	—	2	2	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	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	4	no	—
377	C₂×C₄×C₃₁	—	4	1	no	—
378	C₂×C₄×C₃₁	—	4	1	no	—
379	C₂×C₄×C₃₁	—	4	1	no	—
380	C₂×C₄×C₃₁	—	4	8	no	—
381	C₂×C₄×C₃₁	—	4	4	no	—
382	C₂×C₄×C₃₁	—	4	4	no	—
383	C₂×C₄×C₃₁	—	4	4	no	—
384	C₂×C₄×C₃₁	—	4	8	no	—
385	C₂×C₄×C₃₁	—	4	4	no	—
386	C₂×C₄×C₃₁	#135	1	4	yes	—
387	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
400	C₈×C₃₁	—	2	4	no	—
401	C₈×C₃₁	—	2	4	no	—
402	#3444	C₂×C₃₁	1	1	yes	characteristic, complemented
403	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
404	#3247	C₂×C₃₁	1	4	yes	complemented
405	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#3228	C₂×C₃₁	1	2	yes	complemented
407	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
409	#3207	C₂×C₃₁	1	2	yes	complemented
410	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#3188	C₂×C₃₁	1	4	yes	complemented
412	#3169	C₂×C₃₁	1	2	yes	complemented
413	#3167	C₂×C₃₁	1	2	yes	complemented
414	#3106	C₂×C₃₁	1	4	yes	complemented
415	#3105	C₂×C₃₁	1	4	yes	complemented
416	C₂×#431	C₂×C₃₁	1	1	yes	characteristic, complemented
417	C₂²×C₃₁	—	2	1	no	—
418	C₂²×C₃₁	—	2	1	no	—
419	C₂²×C₃₁	—	2	1	no	—
420	C₂²×C₃₁	—	2	1	no	—
421	C₂²×C₃₁	—	2	1	no	—
422	C₂²×C₃₁	—	2	1	no	—
423	C₂²×C₃₁	—	2	1	no	—
424	C₂²×C₃₁	—	4	4	no	—
425	C₂²×C₃₁	—	4	2	no	—
426	C₂²×C₃₁	—	4	4	no	—
427	C₂²×C₃₁	—	4	2	no	—
428	C₂²×C₃₁	—	4	4	no	—
429	C₂²×C₃₁	—	4	4	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	8	8	no	—
432	C₂²×C₃₁	C₂×#135	1	2	yes	—
433	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
434	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
435	C₄×C₃₁	—	2	1	no	—
436	C₄×C₃₁	—	2	1	no	—
437	C₄×C₃₁	—	2	1	no	—
438	C₄×C₃₁	—	2	1	no	—
439	C₄×C₃₁	—	2	1	no	—
440	C₄×C₃₁	—	2	1	no	—
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	4	2	no	—
443	C₄×C₃₁	—	4	2	no	—
444	C₄×C₃₁	—	4	4	no	—
445	C₄×C₃₁	—	4	2	no	—
446	C₄×C₃₁	C₂×#135	1	2	yes	—
447	C₄×C₃₁	C₂×#135	1	2	yes	—
448	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
449	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
450	C₄×C₃₁	#585	1	2	yes	—
451	C₂²×#41	—	2	1	no	—
452	#533	C₂²×C₃₁	1	1	yes	characteristic
453	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
455	#532	—	2	1	no	—
456	#532	—	2	1	no	—
457	#532	—	2	1	no	—
458	#532	—	2	1	no	—
459	#532	C₂²×C₃₁	1	2	yes	—
460	#532	C₂²×C₃₁	1	2	yes	—
461	#532	C₂²×C₃₁	1	2	yes	—
462	#532	C₂²×C₃₁	1	2	yes	—
463	#532	C₂²×C₃₁	1	1	yes	characteristic
464	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
465	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
466	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
467	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
468	#529	—	2	1	no	—
469	#529	—	2	1	no	—
470	#529	—	2	1	no	—
471	#529	—	2	1	no	—
472	#529	C₂²×C₃₁	1	2	yes	—
473	#529	C₂²×C₃₁	1	2	yes	complemented
474	C₂×#124	—	2	1	no	—
475	#525	—	2	1	no	—
476	#525	—	2	1	no	—
477	#525	C₂²×C₃₁	1	2	yes	—
478	C₂×#121	—	2	1	no	—
479	C₂×#121	C₂²×C₃₁	1	2	yes	—
480	C₄×#41	—	2	1	no	—
481	C₄×#41	—	2	1	no	—
482	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
483	C₂×C₄×D₄	—	2	1	no	—
484	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
485	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
486	#500	C₂²×C₃₁	1	2	yes	complemented
487	#498	C₂²×C₃₁	1	2	yes	complemented
488	#493	C₂²×C₃₁	1	2	yes	complemented
489	#492	C₂²×C₃₁	1	2	yes	complemented
490	#487	C₂²×C₃₁	1	2	yes	complemented
491	#486	C₂²×C₃₁	1	2	yes	complemented
492	#486	C₂²×C₃₁	1	2	yes	complemented
493	#486	C₂²×C₃₁	1	2	yes	complemented
494	#484	C₂²×C₃₁	1	4	yes	—
495	#482	C₂²×C₃₁	1	8	yes	complemented
496	#481	C₂²×C₃₁	1	4	yes	—
497	#478	C₂²×C₃₁	1	8	yes	complemented
498	#477	C₂²×C₃₁	1	4	yes	complemented
499	#476	C₂²×C₃₁	1	4	yes	complemented
500	#466	C₂²×C₃₁	1	8	yes	complemented
501	#465	C₂²×C₃₁	1	8	yes	complemented
502	#463	C₂²×C₃₁	1	8	yes	complemented
503	#460	C₂²×C₃₁	1	4	yes	complemented
504	#459	C₂²×C₃₁	1	4	yes	complemented
505	#450	C₂²×C₃₁	1	4	yes	—
506	#449	C₂²×C₃₁	1	8	yes	complemented
507	#447	C₂²×C₃₁	1	4	yes	—
508	C₄×SD₁₆	C₂²×C₃₁	1	8	yes	complemented
509	C₄×D₈	C₂²×C₃₁	1	8	yes	complemented
510	#431	C₂²×C₃₁	1	2	yes	—
511	#431	C₂²×C₃₁	1	1	yes	characteristic
512	#431	C₂²×C₃₁	1	1	yes	characteristic
513	#431	C₂²×C₃₁	1	2	yes	complemented
514	#431	C₂²×C₃₁	1	2	yes	complemented
515	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
516	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
517	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	complemented
518	C₂×C₃₁	—	2	2	no	—
519	C₂×C₃₁	—	2	2	no	—
520	C₂×C₃₁	—	4	1	no	—
521	C₂×C₃₁	—	8	2	no	—
522	C₂×C₃₁	—	8	4	no	—
523	C₂×C₃₁	#3449	1	1	yes	characteristic
524	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
525	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
526	C₂×#41	—	2	1	no	—
527	C₂×#41	—	2	1	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	—	2	2	no	—
530	C₂×#41	—	2	2	no	—
531	C₂×#41	—	2	2	no	—
532	C₂×#41	—	4	8	no	—
533	C₂×#41	C₂³×C₃₁	1	2	yes	—
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×D₄	—	2	2	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
539	C₂³×C₄	—	2	2	no	—
540	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
541	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
544	C₂×D₈	C₂³×C₃₁	1	8	yes	—
545	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
552	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
553	#127	—	2	1	no	—
554	#127	—	2	1	no	—
555	#127	C₂³×C₃₁	1	2	yes	—
556	#127	C₂³×C₃₁	1	2	yes	—
557	#127	C₂³×C₃₁	1	1	yes	characteristic
558	#126	—	2	2	no	—
559	#126	—	2	2	no	—
560	#125	—	2	1	no	—
561	#125	—	2	1	no	—
562	#125	C₂³×C₃₁	1	2	yes	—
563	#124	—	2	2	no	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	—	2	2	no	—
567	#124	—	2	1	no	—
568	#124	—	2	1	no	—
569	#124	C₂³×C₃₁	1	2	yes	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
578	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	2	no	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	1	no	—
586	#121	—	2	1	no	—
587	#121	—	2	1	no	—
588	#121	—	2	1	no	—
589	#121	C₂³×C₃₁	1	4	yes	—
590	#121	C₂³×C₃₁	1	4	yes	—
591	#121	C₂³×C₃₁	1	2	yes	—
592	#121	C₂³×C₃₁	1	2	yes	—
593	#120	—	2	2	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
599	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	C₂³×C₃₁	1	4	yes	—
617	C₄×D₄	C₂³×C₃₁	1	4	yes	—
618	C₄×D₄	C₂³×C₃₁	1	2	yes	—
619	C₄×D₄	C₂³×C₃₁	1	2	yes	—
620	#117	—	2	1	no	—
621	#117	—	2	1	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	—	2	2	no	—
625	#117	C₂³×C₃₁	1	2	yes	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₄²	—	2	2	no	—
631	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
632	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
633	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
634	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
635	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
636	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
643	#107	C₂³×C₃₁	1	8	yes	—
644	#106	C₂³×C₃₁	1	8	yes	—
645	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
646	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
647	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
648	#103	C₂³×C₃₁	1	8	yes	—
649	#102	C₂³×C₃₁	1	8	yes	—
650	#102	C₂³×C₃₁	1	8	yes	—
651	#102	C₂³×C₃₁	1	8	yes	—
652	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
654	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
655	C₄×C₈	C₂³×C₃₁	1	4	yes	—
656	C₄×C₈	C₂³×C₃₁	1	2	yes	—
657	C₄×C₈	C₂³×C₃₁	1	2	yes	—
658	C₃₁	#60946	1	1	yes	characteristic, direct product factor, Sylow
659	C₂⁴	—	2	2	no	—
660	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
661	#41	—	4	4	no	—
662	#41	—	4	8	no	—
663	#41	—	4	8	no	—
664	#41	—	4	8	no	—
665	#41	—	4	4	no	—
666	#41	—	4	4	no	—
667	#41	—	4	8	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	4	4	no	—
673	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	—	4	8	no	—
689	C₂×D₄	—	4	4	no	—
690	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
691	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	8	no	—
702	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
720	SD₁₆	—	4	8	no	—
721	D₈	—	4	8	no	—
722	C₂×C₈	—	4	4	no	—
723	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
724	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
758	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
759	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
760	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
769	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
770	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
771	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	4	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	4	4	no	—
781	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
782	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
783	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
784	Q₈	—	2	4	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	2	no	—
787	Q₈	—	4	4	no	—
788	Q₈	—	4	2	no	—
789	D₄	—	2	4	no	—
790	D₄	—	2	8	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	8	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	8	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	8	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	8	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	C₃₁×#135	1	4	yes	—
830	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
831	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
842	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
843	C₈	—	2	4	no	—
844	C₈	—	2	4	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	4	4	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	4	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	4	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	8	8	no	—
860	C₂²	C₂×C₃₁×#135	1	2	yes	—
861	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
862	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	1	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	4	no	—
873	C₄	—	4	2	no	—
874	C₄	C₂×C₃₁×#135	1	2	yes	—
875	C₄	C₂×C₃₁×#135	1	2	yes	—
876	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
877	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
878	C₄	C₃₁×#585	1	2	yes	—
879	C₂	—	2	2	no	—
880	C₂	—	2	2	no	—
881	C₂	—	4	1	no	—
882	C₂	—	8	4	no	—
883	C₂	—	8	2	no	—
884	C₂	C₃₁×#3449	1	1	yes	characteristic
885	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
886	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
socle	C₂²×C₃₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3444	C₂	semidirect
2. C₂×C₃₁×#532	C₂	semidirect
3. C₃₁×#3247	C₂	semidirect
4. C₃₁×#3230	C₂	semidirect
5. C₃₁×#3228	C₂	semidirect
6. C₃₁×#3227	C₂	semidirect
7. C₃₁×#3208	C₂	semidirect
8. C₃₁×#3207	C₂	semidirect
9. C₃₁×#3205	C₂	semidirect
10. C₃₁×#3188	C₂	semidirect
11. C₃₁×#3169	C₂	semidirect
12. C₃₁×#3167	C₂	semidirect
13. C₃₁×#3106	C₂	semidirect
14. C₃₁×#3105	C₂	semidirect
15. C₂×C₃₁×#431	C₂	semidirect
18. C₃₁×#533	C₂²	semidirect
19. C₃₁×#533	C₂²	semidirect
29. C₃₁×#532	C₂²	semidirect
30. C₃₁×#532	C₂²	semidirect
38. C₃₁×#529	C₂²	semidirect
47. C₄×#41×C₃₁	C₂²	semidirect
51. C₃₁×#500	C₂²	semidirect
52. C₃₁×#498	C₂²	semidirect
53. C₃₁×#493	C₂²	semidirect
54. C₃₁×#492	C₂²	semidirect
55. C₃₁×#487	C₂²	semidirect
56. C₃₁×#486	C₂²	semidirect
57. C₃₁×#486	C₂²	semidirect
58. C₃₁×#486	C₂²	semidirect
60. C₃₁×#482	C₂²	semidirect
62. C₃₁×#478	C₂²	semidirect
63. C₃₁×#477	C₂²	semidirect
64. C₃₁×#476	C₂²	semidirect
65. C₃₁×#466	C₂²	semidirect
66. C₃₁×#465	C₂²	semidirect
67. C₃₁×#463	C₂²	semidirect
68. C₃₁×#460	C₂²	semidirect
69. C₃₁×#459	C₂²	semidirect
71. C₃₁×#449	C₂²	semidirect
73. C₄×SD₁₆×C₃₁	C₂²	semidirect
74. C₄×D₈×C₃₁	C₂²	semidirect
78. C₃₁×#431	C₂²	semidirect
79. C₃₁×#431	C₂²	semidirect
80. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
82. C₂×C₄×C₈×C₃₁	C₂²	semidirect
329. #60946	C₃₁	direct (N × H)
402. #3444	C₂×C₃₁	semidirect
403. C₂×#532	C₂×C₃₁	semidirect
404. #3247	C₂×C₃₁	semidirect
405. #3230	C₂×C₃₁	semidirect
406. #3228	C₂×C₃₁	semidirect
407. #3227	C₂×C₃₁	semidirect
408. #3208	C₂×C₃₁	semidirect
409. #3207	C₂×C₃₁	semidirect
410. #3205	C₂×C₃₁	semidirect
411. #3188	C₂×C₃₁	semidirect
412. #3169	C₂×C₃₁	semidirect
413. #3167	C₂×C₃₁	semidirect
414. #3106	C₂×C₃₁	semidirect
415. #3105	C₂×C₃₁	semidirect
416. C₂×#431	C₂×C₃₁	semidirect
453. #533	C₂²×C₃₁	semidirect
454. #533	C₂²×C₃₁	semidirect
464. #532	C₂²×C₃₁	semidirect
465. #532	C₂²×C₃₁	semidirect
473. #529	C₂²×C₃₁	semidirect
482. C₄×#41	C₂²×C₃₁	semidirect
486. #500	C₂²×C₃₁	semidirect
487. #498	C₂²×C₃₁	semidirect
488. #493	C₂²×C₃₁	semidirect
489. #492	C₂²×C₃₁	semidirect
490. #487	C₂²×C₃₁	semidirect
491. #486	C₂²×C₃₁	semidirect
492. #486	C₂²×C₃₁	semidirect
493. #486	C₂²×C₃₁	semidirect
495. #482	C₂²×C₃₁	semidirect
497. #478	C₂²×C₃₁	semidirect
498. #477	C₂²×C₃₁	semidirect
499. #476	C₂²×C₃₁	semidirect
500. #466	C₂²×C₃₁	semidirect
501. #465	C₂²×C₃₁	semidirect
502. #463	C₂²×C₃₁	semidirect
503. #460	C₂²×C₃₁	semidirect
504. #459	C₂²×C₃₁	semidirect
506. #449	C₂²×C₃₁	semidirect
508. C₄×SD₁₆	C₂²×C₃₁	semidirect
509. C₄×D₈	C₂²×C₃₁	semidirect
513. #431	C₂²×C₃₁	semidirect
514. #431	C₂²×C₃₁	semidirect
515. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
517. C₂×C₄×C₈	C₂²×C₃₁	semidirect
658. C₃₁	#60946	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×#3444	2
C₂×C₃₁×#532	2
C₃₁×#3247	2
C₃₁×#3230	2
C₃₁×#3228	2
C₃₁×#3227	2
C₃₁×#3208	2
C₃₁×#3207	2
C₃₁×#3205	2
C₃₁×#3188	2
C₃₁×#3169	2
C₃₁×#3167	2
C₃₁×#3106	2
C₃₁×#3105	2
C₂×C₃₁×#431	2
#60946	31

Subgroups — C31×#60946 #21517705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60946 #21517705