Subgroups — C₃₁×#60860 #21517619

Order 7936.

2006 conjugacy classes of subgroups.

The subgroup lattice has 778 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
2	C₂²×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3239	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3238	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3230	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3229	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3227	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3226	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3165	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3141	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3092	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3079	C₂	1	4	yes	maximal, complemented
13	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×Q₈×C₃₁	—	2	1	no	—
15	C₃₁×#533	C₂²	1	1	yes	characteristic
16	C₃₁×#533	C₂²	1	1	yes	characteristic
17	C₃₁×#533	C₂²	1	1	yes	characteristic
18	C₃₁×#532	C₂²	1	1	yes	characteristic
19	C₃₁×#532	C₂²	1	1	yes	characteristic
20	C₃₁×#532	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
23	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
24	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
25	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
26	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
27	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
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	—
39	C₃₁×#525	—	2	1	no	—
40	C₃₁×#525	—	2	1	no	—
41	C₃₁×#525	C₂²	1	2	yes	—
42	C₄×#41×C₃₁	—	2	1	no	—
43	C₄×#41×C₃₁	—	2	1	no	—
44	C₄×#41×C₃₁	C₂²	1	2	yes	—
45	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
46	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
47	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	8	yes	complemented
49	C₃₁×#500	C₂²	1	4	yes	complemented
50	C₃₁×#498	C₂²	1	4	yes	complemented
51	C₃₁×#489	C₂²	1	8	yes	complemented
52	C₃₁×#487	C₂²	1	4	yes	complemented
53	C₃₁×#486	C₂²	1	4	yes	complemented
54	C₃₁×#484	C₂²	1	8	yes	—
55	C₃₁×#483	C₂²	1	8	yes	—
56	C₃₁×#481	C₂²	1	8	yes	—
57	C₃₁×#480	C₂²	1	8	yes	—
58	C₃₁×#477	C₂²	1	8	yes	complemented
59	C₃₁×#476	C₂²	1	8	yes	complemented
60	C₃₁×#475	C₂²	1	8	yes	complemented
61	C₃₁×#474	C₂²	1	8	yes	complemented
62	C₃₁×#432	C₂²	1	2	yes	—
63	C₃₁×#432	C₂²	1	2	yes	—
64	C₃₁×#431	C₂²	1	2	yes	—
65	C₃₁×#431	C₂²	1	2	yes	—
66	C₃₁×#428	C₂²	1	8	yes	—
67	C₃₁×#423	C₂²	1	2	yes	—
68	C₃₁×#417	C₂²	1	8	yes	—
69	C₃₁×#407	C₂²	1	2	yes	—
70	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
71	C₂×#41×C₃₁	—	2	1	no	—
72	C₂×#41×C₃₁	—	2	1	no	—
73	C₂×#41×C₃₁	C₂³	1	2	yes	—
74	C₂²×Q₈×C₃₁	—	2	2	no	—
75	C₂²×Q₈×C₃₁	—	2	2	no	—
76	C₂²×Q₈×C₃₁	—	2	2	no	—
77	C₂²×Q₈×C₃₁	—	2	2	no	—
78	C₂²×Q₈×C₃₁	—	2	2	no	—
79	C₂²×Q₈×C₃₁	—	2	2	no	—
80	C₂²×Q₈×C₃₁	—	4	8	no	—
81	C₂³×C₄×C₃₁	—	2	2	no	—
82	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
86	C₃₁×C₄⋊Q₈	—	2	2	no	—
87	C₃₁×C₄⋊Q₈	—	2	2	no	—
88	C₃₁×C₄⋊Q₈	—	2	2	no	—
89	C₃₁×C₄⋊Q₈	—	2	2	no	—
90	C₃₁×C₄⋊Q₈	—	2	2	no	—
91	C₃₁×C₄⋊Q₈	—	2	2	no	—
92	C₃₁×C₄⋊Q₈	—	2	2	no	—
93	C₃₁×C₄⋊Q₈	—	2	2	no	—
94	C₃₁×C₄⋊Q₈	—	2	2	no	—
95	C₃₁×C₄⋊Q₈	—	2	2	no	—
96	C₃₁×C₄⋊Q₈	—	2	2	no	—
97	C₃₁×C₄⋊Q₈	—	2	2	no	—
98	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
103	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃₁×#127	C₂³	1	1	yes	characteristic
106	C₃₁×#126	—	2	2	no	—
107	C₃₁×#126	—	2	2	no	—
108	C₃₁×#125	—	2	1	no	—
109	C₃₁×#125	—	2	1	no	—
110	C₃₁×#125	C₂³	1	2	yes	—
111	C₃₁×#124	—	2	1	no	—
112	C₃₁×#124	—	2	1	no	—
113	C₃₁×#124	C₂³	1	2	yes	—
114	C₃₁×#123	—	2	2	no	—
115	C₃₁×#123	—	2	2	no	—
116	C₃₁×#123	—	2	2	no	—
117	C₃₁×C₂²⋊Q₈	—	2	1	no	—
118	C₃₁×C₂²⋊Q₈	—	2	1	no	—
119	C₃₁×C₂²⋊Q₈	—	2	1	no	—
120	C₃₁×C₂²⋊Q₈	—	2	1	no	—
121	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
122	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
123	C₃₁×#121	—	2	1	no	—
124	C₃₁×#121	—	2	1	no	—
125	C₃₁×#121	—	2	1	no	—
126	C₃₁×#121	—	2	1	no	—
127	C₃₁×#121	C₂³	1	2	yes	—
128	C₃₁×#121	C₂³	1	2	yes	—
129	C₃₁×#120	—	2	2	no	—
130	C₄×Q₈×C₃₁	—	2	1	no	—
131	C₄×Q₈×C₃₁	—	2	1	no	—
132	C₄×Q₈×C₃₁	—	2	1	no	—
133	C₄×Q₈×C₃₁	—	2	1	no	—
134	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
135	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
136	C₄×D₄×C₃₁	—	2	2	no	—
137	C₄×D₄×C₃₁	—	2	2	no	—
138	C₄×D₄×C₃₁	—	2	2	no	—
139	C₄×D₄×C₃₁	—	2	2	no	—
140	C₄×D₄×C₃₁	—	2	2	no	—
141	C₄×D₄×C₃₁	—	2	2	no	—
142	C₄×D₄×C₃₁	—	2	1	no	—
143	C₄×D₄×C₃₁	—	2	1	no	—
144	C₄×D₄×C₃₁	—	2	1	no	—
145	C₄×D₄×C₃₁	—	2	1	no	—
146	C₄×D₄×C₃₁	C₂³	1	2	yes	—
147	C₄×D₄×C₃₁	C₂³	1	2	yes	—
148	C₃₁×#117	—	2	1	no	—
149	C₃₁×#117	—	2	1	no	—
150	C₃₁×#117	—	2	2	no	—
151	C₃₁×#117	—	2	2	no	—
152	C₃₁×#117	—	2	2	no	—
153	C₃₁×#117	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
155	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
156	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
157	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
158	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
159	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
160	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
161	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
166	C₂×C₄²×C₃₁	—	2	2	no	—
167	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
168	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
169	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
170	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
171	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
172	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
173	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₃₁×#107	C₂³	1	16	yes	—
180	C₃₁×#106	C₂³	1	16	yes	—
181	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
182	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
183	C₃₁×#103	C₂³	1	16	yes	—
184	C₃₁×#102	C₂³	1	16	yes	—
185	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₃₁×#97	C₂³	1	4	yes	—
188	C₄×C₈×C₃₁	C₂³	1	4	yes	—
189	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
190	#41×C₃₁	—	2	8	no	—
191	#41×C₃₁	—	4	4	no	—
192	#41×C₃₁	—	4	4	no	—
193	C₂×Q₈×C₃₁	—	2	1	no	—
194	C₂×Q₈×C₃₁	—	2	1	no	—
195	C₂×Q₈×C₃₁	—	2	4	no	—
196	C₂×Q₈×C₃₁	—	2	4	no	—
197	C₂×Q₈×C₃₁	—	2	4	no	—
198	C₂×Q₈×C₃₁	—	2	4	no	—
199	C₂×Q₈×C₃₁	—	4	8	no	—
200	C₂×Q₈×C₃₁	—	4	8	no	—
201	C₂×Q₈×C₃₁	—	4	8	no	—
202	C₂×Q₈×C₃₁	—	4	8	no	—
203	C₂×Q₈×C₃₁	—	4	8	no	—
204	C₂×Q₈×C₃₁	—	4	8	no	—
205	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	1	no	—
210	C₂×D₄×C₃₁	—	2	1	no	—
211	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₃₁	—	2	4	no	—
213	C₂²×C₄×C₃₁	—	2	4	no	—
214	C₂²×C₄×C₃₁	—	2	4	no	—
215	C₂²×C₄×C₃₁	—	2	4	no	—
216	C₂²×C₄×C₃₁	—	2	4	no	—
217	C₂²×C₄×C₃₁	—	2	4	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	2	no	—
221	C₂²×C₄×C₃₁	—	4	8	no	—
222	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	M₁₆×C₃₁	—	2	8	no	—
241	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
242	C₄⋊C₄×C₃₁	—	2	4	no	—
243	C₄⋊C₄×C₃₁	—	2	4	no	—
244	C₄⋊C₄×C₃₁	—	2	4	no	—
245	C₄⋊C₄×C₃₁	—	2	4	no	—
246	C₄⋊C₄×C₃₁	—	2	4	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	1	no	—
250	C₄⋊C₄×C₃₁	—	2	1	no	—
251	C₄⋊C₄×C₃₁	—	2	1	no	—
252	C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₄²×C₃₁	—	2	2	no	—
272	C₄²×C₃₁	—	2	2	no	—
273	C₄²×C₃₁	—	2	2	no	—
274	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
290	#60860	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	2	2	no	—
293	C₂³×C₃₁	—	2	2	no	—
294	C₂³×C₃₁	—	2	2	no	—
295	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
296	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
297	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₃₁	—	2	4	no	—
299	Q₈×C₃₁	—	4	8	no	—
300	Q₈×C₃₁	—	4	8	no	—
301	Q₈×C₃₁	—	4	8	no	—
302	Q₈×C₃₁	—	4	8	no	—
303	Q₈×C₃₁	—	4	2	no	—
304	Q₈×C₃₁	—	4	2	no	—
305	D₄×C₃₁	—	2	4	no	—
306	D₄×C₃₁	—	4	4	no	—
307	D₄×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	4	4	no	—
309	D₄×C₃₁	—	4	2	no	—
310	D₄×C₃₁	—	4	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	8	no	—
330	C₂×C₄×C₃₁	—	4	8	no	—
331	C₂×C₄×C₃₁	—	4	8	no	—
332	C₂×C₄×C₃₁	—	4	8	no	—
333	C₂×C₄×C₃₁	—	4	4	no	—
334	C₂×C₄×C₃₁	—	4	4	no	—
335	C₂×C₄×C₃₁	—	4	4	no	—
336	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
337	C₂×C₄×C₃₁	#137	1	4	yes	—
338	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
350	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
351	C₈×C₃₁	—	2	8	no	—
352	#3444	C₂×C₃₁	1	1	yes	characteristic
353	C₂²×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3239	C₂×C₃₁	1	4	yes	complemented
355	#3238	C₂×C₃₁	1	4	yes	complemented
356	#3230	C₂×C₃₁	1	2	yes	complemented
357	#3229	C₂×C₃₁	1	2	yes	complemented
358	#3227	C₂×C₃₁	1	2	yes	complemented
359	#3226	C₂×C₃₁	1	2	yes	complemented
360	#3165	C₂×C₃₁	1	2	yes	complemented
361	#3141	C₂×C₃₁	1	2	yes	complemented
362	#3092	C₂×C₃₁	1	4	yes	complemented
363	#3079	C₂×C₃₁	1	4	yes	complemented
364	#2920	C₂×C₃₁	1	1	yes	characteristic, complemented
365	C₂²×C₃₁	—	2	8	no	—
366	C₂²×C₃₁	—	2	1	no	—
367	C₂²×C₃₁	—	2	1	no	—
368	C₂²×C₃₁	—	2	1	no	—
369	C₂²×C₃₁	—	2	1	no	—
370	C₂²×C₃₁	—	2	1	no	—
371	C₂²×C₃₁	—	2	1	no	—
372	C₂²×C₃₁	—	4	2	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	2	no	—
375	C₂²×C₃₁	#536	1	2	yes	—
376	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
377	C₂²×C₃₁	C₂×#137	1	2	yes	—
378	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₃₁	—	2	1	no	—
380	C₄×C₃₁	—	2	1	no	—
381	C₄×C₃₁	—	2	1	no	—
382	C₄×C₃₁	—	2	1	no	—
383	C₄×C₃₁	—	2	1	no	—
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	4	2	no	—
386	C₄×C₃₁	—	4	8	no	—
387	C₄×C₃₁	—	4	2	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	#536	1	2	yes	—
390	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
391	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
392	C₄×C₃₁	C₂×#137	1	2	yes	—
393	C₄×C₃₁	C₂×#137	1	2	yes	—
394	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
395	C₂³×Q₈	—	2	1	no	—
396	#533	C₂²×C₃₁	1	1	yes	characteristic
397	#533	C₂²×C₃₁	1	1	yes	characteristic
398	#533	C₂²×C₃₁	1	1	yes	characteristic
399	#532	C₂²×C₃₁	1	1	yes	characteristic
400	#532	C₂²×C₃₁	1	1	yes	characteristic
401	#532	C₂²×C₃₁	1	1	yes	characteristic
402	C₂×C₄⋊Q₈	—	2	1	no	—
403	C₂×C₄⋊Q₈	—	2	1	no	—
404	C₂×C₄⋊Q₈	—	2	1	no	—
405	C₂×C₄⋊Q₈	—	2	1	no	—
406	C₂×C₄⋊Q₈	—	2	1	no	—
407	C₂×C₄⋊Q₈	—	2	1	no	—
408	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
409	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
410	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
411	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
412	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
413	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
414	#529	—	2	1	no	—
415	#529	—	2	1	no	—
416	#529	—	2	1	no	—
417	#529	—	2	1	no	—
418	#529	C₂²×C₃₁	1	2	yes	—
419	#529	C₂²×C₃₁	1	2	yes	—
420	#525	—	2	1	no	—
421	#525	—	2	1	no	—
422	#525	C₂²×C₃₁	1	2	yes	—
423	C₄×#41	—	2	1	no	—
424	C₄×#41	—	2	1	no	—
425	C₄×#41	C₂²×C₃₁	1	2	yes	—
426	C₂²×C₄⋊C₄	—	2	1	no	—
427	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
428	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
429	#501	C₂²×C₃₁	1	8	yes	complemented
430	#500	C₂²×C₃₁	1	4	yes	complemented
431	#498	C₂²×C₃₁	1	4	yes	complemented
432	#489	C₂²×C₃₁	1	8	yes	complemented
433	#487	C₂²×C₃₁	1	4	yes	complemented
434	#486	C₂²×C₃₁	1	4	yes	complemented
435	#484	C₂²×C₃₁	1	8	yes	—
436	#483	C₂²×C₃₁	1	8	yes	—
437	#481	C₂²×C₃₁	1	8	yes	—
438	#480	C₂²×C₃₁	1	8	yes	—
439	#477	C₂²×C₃₁	1	8	yes	complemented
440	#476	C₂²×C₃₁	1	8	yes	complemented
441	#475	C₂²×C₃₁	1	8	yes	complemented
442	#474	C₂²×C₃₁	1	8	yes	complemented
443	#432	C₂²×C₃₁	1	2	yes	—
444	#432	C₂²×C₃₁	1	2	yes	—
445	#431	C₂²×C₃₁	1	2	yes	—
446	#431	C₂²×C₃₁	1	2	yes	—
447	#428	C₂²×C₃₁	1	8	yes	—
448	#423	C₂²×C₃₁	1	2	yes	—
449	#417	C₂²×C₃₁	1	8	yes	—
450	#407	C₂²×C₃₁	1	2	yes	—
451	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
452	C₂×C₃₁	—	2	2	no	—
453	C₂×C₃₁	—	2	2	no	—
454	C₂×C₃₁	—	2	2	no	—
455	C₂×C₃₁	—	8	2	no	—
456	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
457	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
458	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	C₂³×C₃₁	1	2	yes	—
462	C₂²×Q₈	—	2	2	no	—
463	C₂²×Q₈	—	2	2	no	—
464	C₂²×Q₈	—	2	2	no	—
465	C₂²×Q₈	—	2	2	no	—
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×Q₈	—	4	8	no	—
469	C₂³×C₄	—	2	2	no	—
470	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
471	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	—	2	2	no	—
478	C₄⋊Q₈	—	2	2	no	—
479	C₄⋊Q₈	—	2	2	no	—
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	—	2	2	no	—
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	—	2	2	no	—
485	C₄⋊Q₈	—	2	2	no	—
486	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
487	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
488	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
489	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
490	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
491	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
492	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
493	#127	C₂³×C₃₁	1	1	yes	characteristic
494	#126	—	2	2	no	—
495	#126	—	2	2	no	—
496	#125	—	2	1	no	—
497	#125	—	2	1	no	—
498	#125	C₂³×C₃₁	1	2	yes	—
499	#124	—	2	1	no	—
500	#124	—	2	1	no	—
501	#124	C₂³×C₃₁	1	2	yes	—
502	#123	—	2	2	no	—
503	#123	—	2	2	no	—
504	#123	—	2	2	no	—
505	C₂²⋊Q₈	—	2	1	no	—
506	C₂²⋊Q₈	—	2	1	no	—
507	C₂²⋊Q₈	—	2	1	no	—
508	C₂²⋊Q₈	—	2	1	no	—
509	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
510	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
511	#121	—	2	1	no	—
512	#121	—	2	1	no	—
513	#121	—	2	1	no	—
514	#121	—	2	1	no	—
515	#121	C₂³×C₃₁	1	2	yes	—
516	#121	C₂³×C₃₁	1	2	yes	—
517	#120	—	2	2	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	—	2	1	no	—
522	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
523	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	C₂³×C₃₁	1	2	yes	—
535	C₄×D₄	C₂³×C₃₁	1	2	yes	—
536	#117	—	2	1	no	—
537	#117	—	2	1	no	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	#117	—	2	2	no	—
541	#117	C₂³×C₃₁	1	2	yes	—
542	C₂×C₄⋊C₄	—	2	2	no	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	—	2	2	no	—
546	C₂×C₄⋊C₄	—	2	2	no	—
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	—	2	2	no	—
551	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
554	C₂×C₄²	—	2	2	no	—
555	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
556	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
557	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
558	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
559	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
560	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
567	#107	C₂³×C₃₁	1	16	yes	—
568	#106	C₂³×C₃₁	1	16	yes	—
569	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
570	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
571	#103	C₂³×C₃₁	1	16	yes	—
572	#102	C₂³×C₃₁	1	16	yes	—
573	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
574	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
575	#97	C₂³×C₃₁	1	4	yes	—
576	C₄×C₈	C₂³×C₃₁	1	4	yes	—
577	C₃₁	#60860	1	1	yes	characteristic, direct product factor, Sylow
578	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
579	#41	—	2	8	no	—
580	#41	—	4	4	no	—
581	#41	—	4	4	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	4	no	—
585	C₂×Q₈	—	2	4	no	—
586	C₂×Q₈	—	2	4	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	8	no	—
589	C₂×Q₈	—	4	8	no	—
590	C₂×Q₈	—	4	8	no	—
591	C₂×Q₈	—	4	8	no	—
592	C₂×Q₈	—	4	8	no	—
593	C₂×Q₈	—	4	8	no	—
594	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	4	8	no	—
611	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
629	M₁₆	—	2	8	no	—
630	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
649	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
650	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	2	no	—
663	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
664	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
665	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
666	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
667	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
668	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
669	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
670	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
671	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
672	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
673	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
674	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
675	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
676	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
684	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
685	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
686	Q₈	—	2	4	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	4	8	no	—
689	Q₈	—	4	8	no	—
690	Q₈	—	4	8	no	—
691	Q₈	—	4	2	no	—
692	Q₈	—	4	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	4	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	—	4	8	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	4	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
725	C₂×C₄	C₃₁×#137	1	4	yes	—
726	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
737	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
738	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
739	C₈	—	2	8	no	—
740	C₂²	—	2	8	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	C₃₁×#536	1	2	yes	—
751	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
752	C₂²	C₂×C₃₁×#137	1	2	yes	—
753	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	8	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₃₁×#536	1	2	yes	—
765	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
766	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
767	C₄	C₂×C₃₁×#137	1	2	yes	—
768	C₄	C₂×C₃₁×#137	1	2	yes	—
769	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
770	C₂	—	2	2	no	—
771	C₂	—	2	2	no	—
772	C₂	—	2	2	no	—
773	C₂	—	8	2	no	—
774	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
775	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
776	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃₁×C₄⋊Q₈	C₂	semidirect
3. C₃₁×#3239	C₂	semidirect
4. C₃₁×#3238	C₂	semidirect
5. C₃₁×#3230	C₂	semidirect
6. C₃₁×#3229	C₂	semidirect
7. C₃₁×#3227	C₂	semidirect
8. C₃₁×#3226	C₂	semidirect
9. C₃₁×#3165	C₂	semidirect
10. C₃₁×#3141	C₂	semidirect
11. C₃₁×#3092	C₂	semidirect
12. C₃₁×#3079	C₂	semidirect
13. C₃₁×#2920	C₂	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#500	C₂²	semidirect
50. C₃₁×#498	C₂²	semidirect
51. C₃₁×#489	C₂²	semidirect
52. C₃₁×#487	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#474	C₂²	semidirect
290. #60860	C₃₁	direct (N × H)
353. C₂²×C₄⋊Q₈	C₂×C₃₁	semidirect
354. #3239	C₂×C₃₁	semidirect
355. #3238	C₂×C₃₁	semidirect
356. #3230	C₂×C₃₁	semidirect
357. #3229	C₂×C₃₁	semidirect
358. #3227	C₂×C₃₁	semidirect
359. #3226	C₂×C₃₁	semidirect
360. #3165	C₂×C₃₁	semidirect
361. #3141	C₂×C₃₁	semidirect
362. #3092	C₂×C₃₁	semidirect
363. #3079	C₂×C₃₁	semidirect
364. #2920	C₂×C₃₁	semidirect
429. #501	C₂²×C₃₁	semidirect
430. #500	C₂²×C₃₁	semidirect
431. #498	C₂²×C₃₁	semidirect
432. #489	C₂²×C₃₁	semidirect
433. #487	C₂²×C₃₁	semidirect
434. #486	C₂²×C₃₁	semidirect
439. #477	C₂²×C₃₁	semidirect
440. #476	C₂²×C₃₁	semidirect
441. #475	C₂²×C₃₁	semidirect
442. #474	C₂²×C₃₁	semidirect
577. C₃₁	#60860	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
C₂²×C₃₁×C₄⋊Q₈	2
C₃₁×#3239	2
C₃₁×#3238	2
C₃₁×#3230	2
C₃₁×#3229	2
C₃₁×#3227	2
C₃₁×#3226	2
C₃₁×#3165	2
C₃₁×#3141	2
C₃₁×#3092	2
C₃₁×#3079	2
C₃₁×#2920	2
#60860	31

Subgroups — C31×#60860 #21517619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60860 #21517619