Subgroups — C₃₁×#62593 #21519352

Order 7936.

1734 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3327	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3324	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3323	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3215	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3172	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3172	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3140	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#559	C₂²	1	1	yes	characteristic
19	C₃₁×#557	—	2	1	no	—
20	C₃₁×#557	C₂²	1	2	yes	complemented
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#556	C₂²	1	1	yes	characteristic
23	C₃₁×#556	C₂²	1	2	yes	—
24	C₃₁×#555	—	2	1	no	—
25	C₃₁×#552	—	2	2	no	—
26	C₃₁×#552	C₂²	1	4	yes	complemented
27	C₃₁×#551	—	2	2	no	—
28	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#548	C₂²	1	2	yes	—
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	C₂²	1	2	yes	—
32	D₄²×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#542	—	2	1	no	—
34	C₃₁×#541	—	2	2	no	—
35	C₃₁×#538	—	2	2	no	—
36	C₃₁×#536	—	2	1	no	—
37	C₃₁×#533	C₂²	1	2	yes	complemented
38	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#533	C₂²	1	2	yes	complemented
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#529	C₂²	1	1	yes	characteristic
43	C₃₁×#529	C₂²	1	2	yes	—
44	C₂×C₃₁×#124	C₂²	1	2	yes	—
45	C₃₁×#519	—	2	1	no	—
46	C₃₁×#518	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	2	yes	complemented
49	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#497	C₂²	1	1	yes	characteristic
51	C₃₁×#497	C₂²	1	2	yes	complemented
52	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#489	C₂²	1	1	yes	characteristic
54	C₃₁×#489	C₂²	1	2	yes	—
55	C₃₁×#489	C₂²	1	2	yes	complemented
56	C₃₁×#489	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	complemented
58	C₃₁×#488	C₂²	1	4	yes	—
59	C₃₁×#488	C₂²	1	4	yes	complemented
60	C₃₁×#487	C₂²	1	2	yes	complemented
61	C₃₁×#486	C₂²	1	2	yes	—
62	C₃₁×#485	C₂²	1	4	yes	complemented
63	C₃₁×#484	C₂²	1	2	yes	complemented
64	C₃₁×#482	C₂²	1	4	yes	—
65	C₃₁×#481	C₂²	1	2	yes	—
66	C₃₁×#479	C₂²	1	4	yes	complemented
67	C₃₁×#478	C₂²	1	4	yes	complemented
68	C₃₁×#475	C₂²	1	2	yes	complemented
69	C₃₁×#474	C₂²	1	2	yes	—
70	C₃₁×#470	C₂²	1	4	yes	complemented
71	C₃₁×#470	C₂²	1	2	yes	complemented
72	C₃₁×#468	C₂²	1	2	yes	—
73	C₃₁×#468	C₂²	1	4	yes	—
74	C₃₁×#464	C₂²	1	4	yes	—
75	C₃₁×#464	C₂²	1	4	yes	complemented
76	C₃₁×#462	C₂²	1	2	yes	complemented
77	C₃₁×#460	C₂²	1	2	yes	—
78	C₃₁×#452	C₂²	1	4	yes	complemented
79	C₃₁×#451	C₂²	1	4	yes	complemented
80	C₃₁×#450	C₂²	1	4	yes	—
81	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
82	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
83	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
86	C₃₁×#436	C₂²	1	2	yes	—
87	C₃₁×#436	C₂²	1	4	yes	complemented
88	C₃₁×#432	C₂²	1	2	yes	complemented
89	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#419	C₂²	1	4	yes	complemented
91	C₃₁×#418	C₂²	1	4	yes	—
92	C₃₁×#417	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
94	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
95	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
96	C₂×#41×C₃₁	C₂³	1	2	yes	—
97	C₂²×Q₈×C₃₁	—	2	1	no	—
98	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
99	C₂²×D₄×C₃₁	—	2	1	no	—
100	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
106	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	—	2	1	no	—
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃₁×#127	C₂³	1	1	yes	characteristic
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#126	—	2	2	no	—
121	C₃₁×#126	—	2	1	no	—
122	C₃₁×#125	—	2	4	no	—
123	C₃₁×#125	—	2	4	no	—
124	C₃₁×#125	—	2	1	no	—
125	C₃₁×#125	—	2	2	no	—
126	C₃₁×#125	C₂³	1	4	yes	—
127	C₃₁×#125	C₂³	1	1	yes	characteristic
128	C₃₁×#124	—	2	1	no	—
129	C₃₁×#124	—	2	2	no	—
130	C₃₁×#124	—	2	2	no	—
131	C₃₁×#124	—	2	2	no	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#124	C₂³	1	2	yes	—
134	C₃₁×#124	C₂³	1	2	yes	—
135	C₃₁×#124	C₂³	1	1	yes	characteristic
136	C₃₁×#124	C₂³	1	2	yes	—
137	C₃₁×#123	—	2	4	no	—
138	C₃₁×#123	—	2	1	no	—
139	C₃₁×#123	—	2	2	no	—
140	C₃₁×#123	—	2	2	no	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×C₂²⋊Q₈	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	—	2	1	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	2	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
152	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	1	no	—
155	C₃₁×#121	—	2	1	no	—
156	C₃₁×#121	—	2	1	no	—
157	C₃₁×#121	—	2	2	no	—
158	C₃₁×#121	C₂³	1	1	yes	characteristic
159	C₃₁×#121	C₂³	1	2	yes	—
160	C₃₁×#120	—	2	2	no	—
161	C₃₁×#120	—	2	2	no	—
162	C₄×Q₈×C₃₁	—	2	2	no	—
163	C₄×Q₈×C₃₁	—	2	2	no	—
164	C₄×Q₈×C₃₁	—	2	2	no	—
165	C₄×Q₈×C₃₁	—	2	2	no	—
166	C₄×Q₈×C₃₁	—	2	2	no	—
167	C₄×Q₈×C₃₁	—	2	1	no	—
168	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
169	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
170	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
171	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
173	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₃₁	—	2	1	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	—	2	1	no	—
181	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
182	C₄×D₄×C₃₁	D₄	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₃₁	C₂³	1	2	yes	—
187	C₃₁×#117	—	2	1	no	—
188	C₃₁×#117	—	2	2	no	—
189	C₃₁×#117	—	2	1	no	—
190	C₃₁×#117	—	2	4	no	—
191	C₃₁×#117	—	2	1	no	—
192	C₃₁×#117	—	2	2	no	—
193	C₃₁×#117	D₄	1	1	yes	characteristic
194	C₃₁×#117	D₄	1	2	yes	—
195	C₃₁×#117	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	2	yes	—
205	C₃₁×#106	C₂³	1	2	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
209	C₃₁×#103	C₂³	1	4	yes	—
210	C₃₁×#103	C₂³	1	4	yes	—
211	C₃₁×#103	C₂³	1	2	yes	—
212	C₃₁×#103	C₂³	1	4	yes	—
213	C₃₁×#103	C₂³	1	4	yes	—
214	C₃₁×#103	C₂³	1	2	yes	—
215	C₃₁×#103	C₂³	1	2	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	2	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
222	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₃₁×#97	C₂³	1	1	yes	characteristic
224	C₃₁×#97	C₂³	1	2	yes	—
225	C₃₁×#97	C₂³	1	1	yes	characteristic
226	C₄×C₈×C₃₁	C₂³	1	2	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	C₂⁴×C₃₁	—	2	2	no	—
229	#41×C₃₁	—	4	2	no	—
230	#41×C₃₁	—	4	4	no	—
231	C₂×Q₈×C₃₁	—	2	1	no	—
232	C₂×Q₈×C₃₁	—	2	2	no	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	4	4	no	—
236	C₂×Q₈×C₃₁	—	4	4	no	—
237	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
240	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×D₄×C₃₁	—	2	2	no	—
242	C₂×D₄×C₃₁	—	2	1	no	—
243	C₂×D₄×C₃₁	—	2	2	no	—
244	C₂×D₄×C₃₁	—	2	1	no	—
245	C₂×D₄×C₃₁	—	2	1	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	4	4	no	—
248	C₂×D₄×C₃₁	—	4	4	no	—
249	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	1	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	Q₁₆×C₃₁	—	4	2	no	—
265	Q₁₆×C₃₁	—	4	4	no	—
266	SD₁₆×C₃₁	—	4	2	no	—
267	SD₁₆×C₃₁	—	4	4	no	—
268	M₁₆×C₃₁	—	4	4	no	—
269	M₁₆×C₃₁	—	4	2	no	—
270	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
271	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
272	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₄⋊C₄×C₃₁	—	2	1	no	—
278	C₄⋊C₄×C₃₁	—	2	1	no	—
279	C₄⋊C₄×C₃₁	—	2	1	no	—
280	C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₄⋊C₄×C₃₁	—	2	1	no	—
282	C₄⋊C₄×C₃₁	—	2	1	no	—
283	C₄⋊C₄×C₃₁	—	2	4	no	—
284	C₄⋊C₄×C₃₁	—	2	4	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₄⋊C₄×C₃₁	—	2	4	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	4	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂²⋊C₄×C₃₁	—	2	2	no	—
302	C₂²⋊C₄×C₃₁	—	2	2	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₃₁	—	2	1	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	1	no	—
308	C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂²⋊C₄×C₃₁	—	2	1	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	1	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
321	C₄²×C₃₁	—	2	2	no	—
322	C₄²×C₃₁	—	2	4	no	—
323	C₄²×C₃₁	—	2	4	no	—
324	C₄²×C₃₁	—	2	1	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	C₂×D₄	1	2	yes	—
327	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₃₁	C₂×D₄	1	2	yes	—
330	C₄²×C₃₁	C₂⁴	1	2	yes	—
331	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
333	#62593	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₃₁	—	2	1	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	4	4	no	—
337	C₂³×C₃₁	—	8	2	no	—
338	C₂³×C₃₁	—	8	2	no	—
339	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
340	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₃₁	—	2	2	no	—
342	Q₈×C₃₁	—	2	2	no	—
343	Q₈×C₃₁	—	2	2	no	—
344	Q₈×C₃₁	—	2	2	no	—
345	Q₈×C₃₁	—	2	4	no	—
346	Q₈×C₃₁	—	4	2	no	—
347	Q₈×C₃₁	—	4	4	no	—
348	Q₈×C₃₁	—	4	4	no	—
349	Q₈×C₃₁	—	8	2	no	—
350	D₄×C₃₁	—	2	2	no	—
351	D₄×C₃₁	—	2	2	no	—
352	D₄×C₃₁	—	2	4	no	—
353	D₄×C₃₁	—	4	2	no	—
354	D₄×C₃₁	—	4	4	no	—
355	D₄×C₃₁	—	4	2	no	—
356	D₄×C₃₁	—	8	1	no	—
357	D₄×C₃₁	—	8	2	no	—
358	D₄×C₃₁	—	8	1	no	—
359	D₄×C₃₁	—	8	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	4	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	1	no	—
366	C₂×C₄×C₃₁	—	2	4	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	1	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	4	2	no	—
371	C₂×C₄×C₃₁	—	4	1	no	—
372	C₂×C₄×C₃₁	—	4	2	no	—
373	C₂×C₄×C₃₁	—	4	4	no	—
374	C₂×C₄×C₃₁	—	4	2	no	—
375	C₂×C₄×C₃₁	—	8	2	no	—
376	C₂×C₄×C₃₁	—	8	2	no	—
377	C₂×C₄×C₃₁	—	8	2	no	—
378	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
387	C₈×C₃₁	—	2	2	no	—
388	C₈×C₃₁	—	2	2	no	—
389	C₈×C₃₁	—	2	4	no	—
390	#3514	C₂×C₃₁	1	1	yes	characteristic
391	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
392	#3365	C₂×C₃₁	1	2	yes	complemented
393	#3364	C₂×C₃₁	1	2	yes	complemented
394	#3328	C₂×C₃₁	1	2	yes	complemented
395	#3327	C₂×C₃₁	1	4	yes	complemented
396	#3324	C₂×C₃₁	1	2	yes	complemented
397	#3323	C₂×C₃₁	1	4	yes	complemented
398	#3240	C₂×C₃₁	1	2	yes	complemented
399	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
400	#3216	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#3215	C₂×C₃₁	1	2	yes	complemented
402	#3172	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#3172	C₂×C₃₁	1	2	yes	complemented
404	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
405	#3140	C₂×C₃₁	1	2	yes	complemented
406	#2971	C₂×C₃₁	1	1	yes	characteristic, complemented
407	C₂²×C₃₁	—	2	1	no	—
408	C₂²×C₃₁	—	2	2	no	—
409	C₂²×C₃₁	—	2	2	no	—
410	C₂²×C₃₁	—	2	1	no	—
411	C₂²×C₃₁	—	2	1	no	—
412	C₂²×C₃₁	—	2	2	no	—
413	C₂²×C₃₁	—	4	2	no	—
414	C₂²×C₃₁	—	4	1	no	—
415	C₂²×C₃₁	—	4	2	no	—
416	C₂²×C₃₁	—	4	1	no	—
417	C₂²×C₃₁	—	4	1	no	—
418	C₂²×C₃₁	—	4	2	no	—
419	C₂²×C₃₁	—	16	4	no	—
420	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₃₁	—	2	1	no	—
422	C₄×C₃₁	—	2	2	no	—
423	C₄×C₃₁	—	2	1	no	—
424	C₄×C₃₁	—	2	1	no	—
425	C₄×C₃₁	—	2	2	no	—
426	C₄×C₃₁	—	2	1	no	—
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	4	1	no	—
429	C₄×C₃₁	—	4	2	no	—
430	C₄×C₃₁	—	4	2	no	—
431	C₄×C₃₁	—	4	1	no	—
432	C₄×C₃₁	—	4	2	no	—
433	C₄×C₃₁	—	4	1	no	—
434	C₄×C₃₁	—	4	4	no	—
435	C₄×C₃₁	#575	1	2	yes	—
436	C₄×C₃₁	#585	1	2	yes	—
437	#559	C₂²×C₃₁	1	1	yes	characteristic
438	#557	—	2	1	no	—
439	#557	C₂²×C₃₁	1	2	yes	complemented
440	#556	—	2	1	no	—
441	#556	C₂²×C₃₁	1	1	yes	characteristic
442	#556	C₂²×C₃₁	1	2	yes	—
443	#555	—	2	1	no	—
444	#552	—	2	2	no	—
445	#552	C₂²×C₃₁	1	4	yes	complemented
446	#551	—	2	2	no	—
447	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
448	#548	C₂²×C₃₁	1	2	yes	—
449	#546	—	2	1	no	—
450	#546	C₂²×C₃₁	1	2	yes	—
451	D₄²	C₂²×C₃₁	1	1	yes	characteristic
452	#542	—	2	1	no	—
453	#541	—	2	2	no	—
454	#538	—	2	2	no	—
455	#536	—	2	1	no	—
456	#533	C₂²×C₃₁	1	2	yes	complemented
457	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
458	#533	C₂²×C₃₁	1	2	yes	complemented
459	#532	C₂²×C₃₁	1	1	yes	characteristic
460	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
461	#529	C₂²×C₃₁	1	1	yes	characteristic
462	#529	C₂²×C₃₁	1	2	yes	—
463	C₂×#124	C₂²×C₃₁	1	2	yes	—
464	#519	—	2	1	no	—
465	#518	—	2	1	no	—
466	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
467	#501	C₂²×C₃₁	1	2	yes	complemented
468	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
469	#497	C₂²×C₃₁	1	1	yes	characteristic
470	#497	C₂²×C₃₁	1	2	yes	complemented
471	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
472	#489	C₂²×C₃₁	1	1	yes	characteristic
473	#489	C₂²×C₃₁	1	2	yes	—
474	#489	C₂²×C₃₁	1	2	yes	complemented
475	#489	C₂²×C₃₁	1	2	yes	complemented
476	#489	C₂²×C₃₁	1	2	yes	complemented
477	#488	C₂²×C₃₁	1	4	yes	—
478	#488	C₂²×C₃₁	1	4	yes	complemented
479	#487	C₂²×C₃₁	1	2	yes	complemented
480	#486	C₂²×C₃₁	1	2	yes	—
481	#485	C₂²×C₃₁	1	4	yes	complemented
482	#484	C₂²×C₃₁	1	2	yes	complemented
483	#482	C₂²×C₃₁	1	4	yes	—
484	#481	C₂²×C₃₁	1	2	yes	—
485	#479	C₂²×C₃₁	1	4	yes	complemented
486	#478	C₂²×C₃₁	1	4	yes	complemented
487	#475	C₂²×C₃₁	1	2	yes	complemented
488	#474	C₂²×C₃₁	1	2	yes	—
489	#470	C₂²×C₃₁	1	4	yes	complemented
490	#470	C₂²×C₃₁	1	2	yes	complemented
491	#468	C₂²×C₃₁	1	2	yes	—
492	#468	C₂²×C₃₁	1	4	yes	—
493	#464	C₂²×C₃₁	1	4	yes	—
494	#464	C₂²×C₃₁	1	4	yes	complemented
495	#462	C₂²×C₃₁	1	2	yes	complemented
496	#460	C₂²×C₃₁	1	2	yes	—
497	#452	C₂²×C₃₁	1	4	yes	complemented
498	#451	C₂²×C₃₁	1	4	yes	complemented
499	#450	C₂²×C₃₁	1	4	yes	—
500	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
501	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
502	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
503	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
504	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
505	#436	C₂²×C₃₁	1	2	yes	—
506	#436	C₂²×C₃₁	1	4	yes	complemented
507	#432	C₂²×C₃₁	1	2	yes	complemented
508	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
509	#419	C₂²×C₃₁	1	4	yes	complemented
510	#418	C₂²×C₃₁	1	4	yes	—
511	#417	C₂²×C₃₁	1	4	yes	complemented
512	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
513	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	C₂×C₃₁	—	4	1	no	—
515	C₂×C₃₁	—	4	2	no	—
516	C₂×C₃₁	—	8	2	no	—
517	C₂×C₃₁	—	8	1	no	—
518	C₂×C₃₁	#3500	1	1	yes	characteristic
519	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
520	C₂×C₃₁	#3586	1	1	yes	characteristic
521	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
522	C₂×#41	C₂³×C₃₁	1	2	yes	—
523	C₂²×Q₈	—	2	1	no	—
524	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
527	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
528	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
529	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
530	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
531	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
532	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
533	C₄⋊Q₈	—	2	2	no	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
540	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
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	4	no	—
545	#126	—	2	4	no	—
546	#126	—	2	2	no	—
547	#126	—	2	1	no	—
548	#125	—	2	4	no	—
549	#125	—	2	4	no	—
550	#125	—	2	1	no	—
551	#125	—	2	2	no	—
552	#125	C₂³×C₃₁	1	1	yes	characteristic
553	#125	C₂³×C₃₁	1	4	yes	—
554	#124	—	2	1	no	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	2	no	—
559	#124	C₂³×C₃₁	1	1	yes	characteristic
560	#124	C₂³×C₃₁	1	2	yes	—
561	#124	C₂³×C₃₁	1	2	yes	—
562	#124	C₂³×C₃₁	1	2	yes	—
563	#123	—	2	4	no	—
564	#123	—	2	1	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
576	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
577	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
578	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
579	#121	—	2	2	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	—	2	1	no	—
583	#121	—	2	2	no	—
584	#121	C₂³×C₃₁	1	2	yes	—
585	#121	C₂³×C₃₁	1	1	yes	characteristic
586	#120	—	2	2	no	—
587	#120	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
595	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
596	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
598	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
599	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
608	C₄×D₄	D₄×C₃₁	1	2	yes	—
609	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₄×D₄	C₂³×C₃₁	1	2	yes	—
611	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₃₁	1	2	yes	—
613	#117	—	2	1	no	—
614	#117	—	2	2	no	—
615	#117	—	2	1	no	—
616	#117	—	2	4	no	—
617	#117	—	2	1	no	—
618	#117	—	2	2	no	—
619	#117	D₄×C₃₁	1	1	yes	characteristic
620	#117	D₄×C₃₁	1	2	yes	—
621	#117	C₂³×C₃₁	1	4	yes	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
624	C₂×C₂²⋊C₄	—	2	2	no	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₂²⋊C₄	—	2	2	no	—
627	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
628	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
629	#107	C₂³×C₃₁	1	4	yes	—
630	#107	C₂³×C₃₁	1	2	yes	—
631	#106	C₂³×C₃₁	1	2	yes	—
632	#106	C₂³×C₃₁	1	4	yes	—
633	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
634	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
635	#103	C₂³×C₃₁	1	4	yes	—
636	#103	C₂³×C₃₁	1	4	yes	—
637	#103	C₂³×C₃₁	1	2	yes	—
638	#103	C₂³×C₃₁	1	4	yes	—
639	#103	C₂³×C₃₁	1	4	yes	—
640	#103	C₂³×C₃₁	1	2	yes	—
641	#103	C₂³×C₃₁	1	2	yes	—
642	#102	C₂³×C₃₁	1	4	yes	—
643	#102	C₂³×C₃₁	1	4	yes	—
644	#102	C₂³×C₃₁	1	2	yes	—
645	#102	C₂³×C₃₁	1	4	yes	—
646	#102	C₂³×C₃₁	1	4	yes	—
647	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
648	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
649	#97	C₂³×C₃₁	1	1	yes	characteristic
650	#97	C₂³×C₃₁	1	2	yes	—
651	#97	C₂³×C₃₁	1	1	yes	characteristic
652	C₄×C₈	C₂³×C₃₁	1	2	yes	—
653	C₄×C₈	C₂³×C₃₁	1	4	yes	—
654	C₃₁	#62593	1	1	yes	characteristic, direct product factor, Sylow
655	C₂⁴	—	2	2	no	—
656	#41	—	4	2	no	—
657	#41	—	4	4	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	—	4	4	no	—
664	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
665	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
666	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	—	4	4	no	—
676	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
677	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
678	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
687	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
688	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
691	Q₁₆	—	4	2	no	—
692	Q₁₆	—	4	4	no	—
693	SD₁₆	—	4	2	no	—
694	SD₁₆	—	4	4	no	—
695	M₁₆	—	4	4	no	—
696	M₁₆	—	4	2	no	—
697	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
698	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
699	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
721	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
723	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
725	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	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	—	2	1	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
746	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
747	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	4	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	1	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	C₂×D₄×C₃₁	1	2	yes	—
757	C₄²	C₂⁴×C₃₁	1	2	yes	—
758	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
759	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
760	C₂³	—	2	1	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	8	2	no	—
764	C₂³	—	8	2	no	—
765	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
766	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	4	no	—
772	Q₈	—	4	2	no	—
773	Q₈	—	4	4	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	8	2	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	4	2	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	2	no	—
782	D₄	—	8	1	no	—
783	D₄	—	8	2	no	—
784	D₄	—	8	1	no	—
785	D₄	—	8	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	—	8	2	no	—
803	C₂×C₄	—	8	2	no	—
804	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
810	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
812	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
813	C₈	—	2	2	no	—
814	C₈	—	2	2	no	—
815	C₈	—	2	4	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	16	4	no	—
829	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
830	C₄	—	2	1	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	4	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	2	no	—
844	C₄	C₃₁×#575	1	2	yes	—
845	C₄	C₃₁×#585	1	2	yes	—
846	C₂	—	4	2	no	—
847	C₂	—	4	1	no	—
848	C₂	—	8	1	no	—
849	C₂	—	8	2	no	—
850	C₂	C₃₁×#3500	1	1	yes	characteristic
851	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
852	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3509	C₂	semidirect
3. C₃₁×#3365	C₂	semidirect
4. C₃₁×#3364	C₂	semidirect
5. C₃₁×#3328	C₂	semidirect
6. C₃₁×#3327	C₂	semidirect
7. C₃₁×#3324	C₂	semidirect
8. C₃₁×#3323	C₂	semidirect
9. C₃₁×#3240	C₂	semidirect
10. C₃₁×#3239	C₂	semidirect
11. C₃₁×#3216	C₂	semidirect
12. C₃₁×#3215	C₂	semidirect
13. C₃₁×#3172	C₂	semidirect
14. C₃₁×#3172	C₂	semidirect
15. C₃₁×#3141	C₂	semidirect
16. C₃₁×#3140	C₂	semidirect
17. C₃₁×#2971	C₂	semidirect
20. C₃₁×#557	C₂²	semidirect
26. C₃₁×#552	C₂²	semidirect
37. C₃₁×#533	C₂²	semidirect
38. C₃₁×#533	C₂²	semidirect
39. C₃₁×#533	C₂²	semidirect
41. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
51. C₃₁×#497	C₂²	semidirect
52. C₃₁×#491	C₂²	semidirect
55. C₃₁×#489	C₂²	semidirect
56. C₃₁×#489	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
59. C₃₁×#488	C₂²	semidirect
60. C₃₁×#487	C₂²	semidirect
62. C₃₁×#485	C₂²	semidirect
63. C₃₁×#484	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#478	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
70. C₃₁×#470	C₂²	semidirect
71. C₃₁×#470	C₂²	semidirect
75. C₃₁×#464	C₂²	semidirect
76. C₃₁×#462	C₂²	semidirect
78. C₃₁×#452	C₂²	semidirect
79. C₃₁×#451	C₂²	semidirect
81. C₈×Q₈×C₃₁	C₂²	semidirect
82. C₄×Q₁₆×C₃₁	C₂²	semidirect
83. C₄×Q₁₆×C₃₁	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
87. C₃₁×#436	C₂²	semidirect
88. C₃₁×#432	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
90. C₃₁×#419	C₂²	semidirect
92. C₃₁×#417	C₂²	semidirect
93. C₄×M₁₆×C₃₁	C₂²	semidirect
94. C₄×M₁₆×C₃₁	C₂²	semidirect
333. #62593	C₃₁	direct (N × H)
391. #3509	C₂×C₃₁	semidirect
392. #3365	C₂×C₃₁	semidirect
393. #3364	C₂×C₃₁	semidirect
394. #3328	C₂×C₃₁	semidirect
395. #3327	C₂×C₃₁	semidirect
396. #3324	C₂×C₃₁	semidirect
397. #3323	C₂×C₃₁	semidirect
398. #3240	C₂×C₃₁	semidirect
399. #3239	C₂×C₃₁	semidirect
400. #3216	C₂×C₃₁	semidirect
401. #3215	C₂×C₃₁	semidirect
402. #3172	C₂×C₃₁	semidirect
403. #3172	C₂×C₃₁	semidirect
404. #3141	C₂×C₃₁	semidirect
405. #3140	C₂×C₃₁	semidirect
406. #2971	C₂×C₃₁	semidirect
439. #557	C₂²×C₃₁	semidirect
445. #552	C₂²×C₃₁	semidirect
456. #533	C₂²×C₃₁	semidirect
457. #533	C₂²×C₃₁	semidirect
458. #533	C₂²×C₃₁	semidirect
460. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
467. #501	C₂²×C₃₁	semidirect
468. #501	C₂²×C₃₁	semidirect
470. #497	C₂²×C₃₁	semidirect
471. #491	C₂²×C₃₁	semidirect
474. #489	C₂²×C₃₁	semidirect
475. #489	C₂²×C₃₁	semidirect
476. #489	C₂²×C₃₁	semidirect
478. #488	C₂²×C₃₁	semidirect
479. #487	C₂²×C₃₁	semidirect
481. #485	C₂²×C₃₁	semidirect
482. #484	C₂²×C₃₁	semidirect
485. #479	C₂²×C₃₁	semidirect
486. #478	C₂²×C₃₁	semidirect
487. #475	C₂²×C₃₁	semidirect
489. #470	C₂²×C₃₁	semidirect
490. #470	C₂²×C₃₁	semidirect
494. #464	C₂²×C₃₁	semidirect
495. #462	C₂²×C₃₁	semidirect
497. #452	C₂²×C₃₁	semidirect
498. #451	C₂²×C₃₁	semidirect
500. C₈×Q₈	C₂²×C₃₁	semidirect
501. C₄×Q₁₆	C₂²×C₃₁	semidirect
502. C₄×Q₁₆	C₂²×C₃₁	semidirect
504. C₄×SD₁₆	C₂²×C₃₁	semidirect
506. #436	C₂²×C₃₁	semidirect
507. #432	C₂²×C₃₁	semidirect
508. #432	C₂²×C₃₁	semidirect
509. #419	C₂²×C₃₁	semidirect
511. #417	C₂²×C₃₁	semidirect
512. C₄×M₁₆	C₂²×C₃₁	semidirect
513. C₄×M₁₆	C₂²×C₃₁	semidirect
654. C₃₁	#62593	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×#3514	2
C₃₁×#3509	2
C₃₁×#3365	2
C₃₁×#3364	2
C₃₁×#3328	2
C₃₁×#3327	2
C₃₁×#3324	2
C₃₁×#3323	2
C₃₁×#3240	2
C₃₁×#3239	2
C₃₁×#3216	2
C₃₁×#3215	2
C₃₁×#3172	2
C₃₁×#3141	2
C₃₁×#3140	2
C₃₁×#2971	2
#62593	31

Subgroups — C31×#62593 #21519352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62593 #21519352